Research ArticleComparison of Statistical Downscaling Methods forMonthly Total Precipitation Case Study for the Paute RiverBasin in Southern Ecuador

L Campozano123 D Tenelanda1 E Sanchez12 E Samaniego12 and J Feyen1

1Departamento de Recursos Hıdricos y Ciencias Ambientales Universidad de Cuenca 10150 Cuenca Ecuador2Facultad de Ingenierıa Universidad de Cuenca Avenida 12 de Abril sn 10150 Cuenca Ecuador3Laboratory for Climatology and Remote Sensing (LCRS) Faculty of Geography University of MarburgDeutschhausstrasse 10 35032 Marburg Germany

Correspondence should be addressed to L Campozano lenincampozanoucuencaeduec

Received 27 October 2015 Accepted 27 December 2015

Academic Editor Hung Soo Kim

Copyright copy 2016 L Campozano et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Downscaling improves considerably the results of General Circulation Models (GCMs) However little information is availableon the performance of downscaling methods in the Andean mountain region The paper presents the downscaling of monthlyprecipitation estimates of the NCEPNCAR reanalysis 1 applying the statistical downscaling model (SDSM) artificial neuralnetworks (ANNs) and the least squares support vectormachines (LS-SVM) approach Downscaledmonthly precipitation estimatesafter bias and variance correction were compared to themedian and variance of the 30-year observations of 5 climate stations in thePaute River basin in southern Ecuador one of Ecuadorrsquos main river basins A preliminary comparison revealed that both artificialintelligence methods ANN and LS-SVM performed equally Results disclosed that ANN and LS-SVMmethods depict in generalbetter skills in comparison to SDSM However in somemonths SDSM estimates matched themedian and variance of the observedmonthly precipitation depths better Since synoptic variables do not always present local conditions particularly in the period goingfrom September to December it is recommended for future studies to refine estimates of downscaling for example by combiningdynamic and statistical methods or to select sets of synoptic predictors for specific months or seasons

1 Introduction

General Circulation Models (GCMs) are widely used to pre-dict the impact of climate change on for instance the regionalprecipitation trend The resolution of these models typicallyaround 2∘ times 2∘ is unsuitable for climate change impactestimations at basin scale [1 2] Additionally these modelsdo not capture well the subgrid processes which can be verycomplex in mountain regions and fail to account properlyfor the orographic features of those regions Therefore toobtain projections of the impact of climate change at basinscale particularly in a mountain region downscaling is amust In general the downscalingmethods can be subdividedinto two large groups dynamical downscaling (DD) andstatistical downscaling (SD) methods On the one hand theDDmethods integrate a regional climatemodel (RCM) in the

GCM which enables capturing the atmospheric phenomenaat a much higher resolution in the order of tenths ofkilometers The SD techniques on the other hand are basedon the determination of statistical relations between large-scale synoptic predictors and local observations from groundstations which are considered to be stationary an assumptionthat might not be true for future climate projections Thecomputational cost of thesemethods is low they are relativelyeasy to implement and they present generally higher accu-racy than dynamical models Particularly when the aim is notto understand the change in weather processes provoked byclimate change the generation of future projections at basinscale using SD methods might be convenient

Several SD techniques exist and among them the sta-tistical downscaling model (SDSM) is probably the mostwidely used [3] The SDSM approach facilitates the rapid

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2016 Article ID 6526341 13 pageshttpdxdoiorg10115520166526341

2 Advances in Meteorology

Table 1 Stations used for the present study

Code Station Regime Latitude (∘) Longitude (∘) Elevation (m asl) Annual precipitation (mm)M141 El Labrado TM minus2732 minus79073 3335 1286M139 Gualaceo BM minus2882 minus78776 2230 820M138 Paute TM minus2800 minus78763 2194 750M045 Palmas UM minus2716 minus78630 2400 1341M137 Biblian BM minus2709 minus78892 2640 1001

development of multiple low cost single-site scenarios ofdaily surface weather variables and is considered as a stochas-tic weather generator on a daily scale The limited use ofthis technique in the Andean mountain region is perhapsthe consequence of its complex topography location in thetropical zone and the influence of the warm and cold ENSOphases El Nino and LaNina respectively All these influencesadd complexity to the atmospheric processes making therepresentation by downscaling techniques more difficultArtificial neural networks (ANNs) are another SD techniquecommonly used however to a limited extent in the Andesregion As stated by [4] the success of this technique isprimarily due to its ability to map highly nonlinear relationsbetween inputs and outputs of the model Reference [5]applied ANN for downscaling monthly precipitation andtemperature in the Paute basin in the Andes of EcuadorThe application of ANN based SD was conducted in orderto evaluate the performance on seasonality representationagainst DDusing a regional climatemodelWeather Researchand Forecasting WRF model [6] With respect to rainfallrepresentation they found that although both downscalingapproaches represent qualitatively well seasonality in thishighly complex terrain ANN estimates of rainfall weremore accurate than WRF estimates This fact highlightsthe applicability of ANN when the understanding of theprocesses involved is not required Another technique withrecent application for the downscaling of GCMs is SVMsupport vector machines [7] In particular the least squaressupport vector machines LS-SVM [8] downscale GCM out-put even better mainly due to the reduction of the optimiza-tion problem to the resolution of a linear system reducingconsiderably the computational requirements Despite SDmethods presenting greater accuracy thanDDmethods froma statistical point of view they possess two handicaps biasand low variance Normally the quantile mapping (QM)technique [9] is applied to improve the representation of thedistribution of derived applications

This paper presents a comparative evaluation of down-scaled GCM estimates of monthly precipitation at the scaleof a large river basin situated in the Andean mountain regionin southern Ecuador applying SDSM and two artificial intel-ligence (AI) techniques artificial neural networks (ANNs)and the least squares support vector machines (LS-SVM)approachThe downscaled results were corrected for bias andvariance inflation applying the QM technique prior to thecomparative analysis For the evaluation historic data wasused

M141 M137 M045M138

M139

Ecuador

Paute basinStations

3∘09984000998400998400S

2∘30

9984000998400998400S

2∘09984000998400998400S

79∘09984000998400998400W 78

∘30

9984000998400998400W79

∘30

9984000998400998400W

79∘09984000998400998400W 78

∘30

9984000998400998400W79

∘30

9984000998400998400W

3∘09984000998400998400S

2∘30

9984000998400998400S

2∘09984000998400998400S

Figure 1 The study area Paute basin in the Andes of Ecuador

2 Study Area and Data

The Paute River basin tributary of the Amazon basin and6148 km2 in size was selected for the comparative evaluationof the downscaling methods a basin located between theeastern and western cordillera of the Andes in Ecuador Thebasin is characterized by a high spatial and temporal variationin precipitation that broadly can be classified into threerainfall regimes respectively subregions with a uni- bi- andthree-modal precipitation pattern [10 11] Data of 5 rainfallstations (see Table 1) were used of whom the geographicaldistribution is given in Figure 1 The measured monthlyrainfall for the 30-year period 01-1980 to 12-2009 was usedto quantify the differences in the performance of the selecteddownscaling methods The dataset was split in a first set forthe calibration of themethods encompassing 75 of the totaldataset and the remaining 25 was used for the validationThe results presented herein belong all to the validation setQuality control of the data was performed using double masscurves on the time series with gaps not exceeding 20 of theobservationsThe infilling of the datawas accomplished usingmultiple linear regression with stations with higher Pearsoncorrelation [12]

NCEPNCAR reanalysis 1 data [13] with 25∘

times 25∘

resolution was used as inputThe selected synoptic predictorsfor the SDSM and AI models are presented in Table 2

Advances in Meteorology 3

Table 2 Synoptic predictors

Synoptic predictors ANNLS-SVM SDSM(All stations) El Labrado Gualaceo Paute Palmas Biblian

1 Precipitation lowast lowast lowast lowast lowast lowast

2 Pressure (surface) lowast lowast lowast lowast

3 Relative humidity (surface) lowast lowast lowast lowast lowast

4 Specific humidity 700 hPa lowast

5 Sea level pressure lowast

6 Temperature 2m lowast lowast lowast lowast lowast

7 Potential temperature 700 hPa lowast lowast lowast lowast

8 Zonal wind (surface) lowast

9 Omega 500 hPa lowast lowast lowast

10 Geopotential height 200 hPa lowast lowast

11 Geopotential height 500 hPa lowast

12 Geopotential height 850 hPa lowast lowast

3 Methods

The methodology of the present study encompasses thefollowing steps (i) selection of the predictors (ii) calibrationand validation of the SDSM and AI models (iii) SDSM andAI ensemble generation (iv) bias correction by quantilemap-ping and (v) evaluation of results SDSM can be conceivedas a weather generator model while ANN and LS-SVM areboth transfer functions in statistical downscaling modelsGiven the analogy between ANN and LS-SVM models theresults of both formed one ensemble which were comparedto the SDSM ensemble Notwithstanding it is well known [14]that a selection of predictors for specific months or seasonsmight be a good option to improve the accuracy in climateprojections in the present study only one set of predictors forthe whole year was considered given that the main interestwas the comparison of downscaling methods rather than theanalysis of climate projectionsThe samepredictorswere usedfor the AI ensemble of ANN and LS-SVM models and oneset of predictors in each station for the SDSMmodel A moredetailed description of the tested downscalingmodels is givenin the following paragraphs

31 Downscaling Using SDSM SDSM is a hybrid betweena stochastic weather generator and a multilinear regressionmethod [14] forcing synoptic-scale weather variables to localmeteorological variables using statistical relationships Inorder to be better in agreement with the variance of theobserved time series stochastic techniques are used to arti-ficially inflate the variance of the downscaled weather timeseries The reader is referred to [3] for a detailed descriptionof the SDSM technique an approach widely used for thedownscaling of large-scale meteorological hydrological andenvironmental variables

Partial correlation at a significance level of 119901 = 005 wasused to select the predictors that capture best for each of theclimate stations the effect of global climate Precipitation datafrom the reanalysis products was evaluated as the predictorthat considerably helped improving the downscaling Forthe climate stations Biblian Paute and Gualaceo 5 predic-tors were identified of whom 4 are similar precipitation

pressure relative humidity and the temperature 2m abovethe surface For the Palmas station the only station with aunimodal regime the best results were obtained using threepredictors namely precipitation potential temperature at the700 hPa level and the geopotential height at the 850 hPa levelTable 2 provides the list of the selected predictors as a functionof the downscaling technique and station

Using the selected predictors daily precipitation wasdownscaled Given the low match with the observed timeseries of daily data monthly time series were generated Atthe monthly scale the precipitation time series in the studybasin are continuous months with zero precipitation are notpresent even during the dry months Regarding the SDSMmodel 20 versions were applied [15]Then the median of thesimulated results was calculated as the representative valuefor the ensemble of the SDSMmodel variants

32 Downscaling Using ANN An artificial neural network(ANN) is composed of several interconnected layers ofprocessing units (the neurons) that transform inputs intooutputs The inputs at the neurons are multiplied by weightsand then inserted into an activation function ANNs arecharacterized by their topology and probably themostwidelyknown neural network is the multilayer perceptron (MLP)It consists of multiple layers of adaptive weights with fullconnectivity between inputs and hidden units and betweenhidden units and outputs MLP is feed-forward artificialneural network mapping sets of input data onto a set ofappropriate outputs

The neural network toolbox of Matlab [16] was usedand optimization of the neural network was pursued usingthe Levenberg-Marquardt method minimizing the meansquare error The performance of a total of four ANNs wastested respectively a model considering either one or twointermediate neural layers and a linear or sigmoidal transferfunction in the neurons (Table 3) For the input layer allnetworks had 12 neurons (equal to the number of predictorssee Table 2) and for the network with one hidden layer8 neurons were used which was determined by trial anderror In a similar way for networks with two hidden layersrespectively 9 and 5 neurons were used

4 Advances in Meteorology

Table 3 Artificial intelligence models

Model Type Transfer function1

Ann

Linear amp 1 hidden layer2 Sigmoidal amp 1 hidden layer3 Linear amp 2 hidden layers4 Sigmoidal amp 2 hidden layers5

LS-SVMLinear

6 Polynomial7 Radial basis functions

33 Downscaling Using LS-SVM Support vector machinesSVM [7] solve nonlinear classifications and estimations offunctions and densities using quadratic programming Aleast squares support vector machine LS-SVM [8] is areformulation of a SVM replacing the solution of the convexquadratic programming problem by the solution of a set oflinear equations As explained by [8] it is possible to adoptinto LS-SVM the robustness sparseness and weightings

Due to the fact that LS-SVM has more recent applicationthan ANN and SDSM techniques for the downscaling ofGCMs we present here a succinct description of LS-SVMtheory For a more in deep description of LS-SVM see [8]

Let us consider 119909 isin R119899 and 119910 isin R the LS-SVM modelmapping the 119909 into a feature space is

119910 = 119908119879

120593 (119909) + 119887 (1)

The optimization problem can be stated as

min119908119890

Γ (119908 119890) =1

2119908119879

119908 + 1205741

2

119873

sum

119894=1

1198902

119894

(2)

where 119890 and 120574 are the error and the regularization parameterrespectively The minimization of the cost function Γ(119908 119890) issubject to the constrains

119910119894= 119908119879

120593 (119909119894) + 119887 + 119890

119894 (3)

The Lagrangian of the optimization is

L (119908 119887 119890 120572) = Γ (119908 119890) minus

119873

sum

119894=1

120572119894(119908119879

120593 (119909119894) + 119887 + 119890

119894minus 119910119894) (4)

where 120572119894are the Lagrangian multipliers

After considering the conditions for optimality

[120597L

120597119908120597L

120597119887120597L

120597119890119894

120597L

120597120572119894

]

119879

= [0 0 0 0]119879

(5)

We obtain the matrix equation

[

0 1

1 Ω minus 120574minus1

119868

] [

119887

120572

] = [

0

119910

] (6)

whereΩ119894119895= 120593(119909

119894)119879

120593(119909119895) is the Kernel function119870(119909

119894 119909119895) and

119868 is the identity matrix

Finally the LS-SVMmodel for function estimation is

119910 (119909) =

119873

sum

119894=1

120572119894119870(119909119894 119909) + 119887 (7)

A Bayesian framework with three levels of inference wasdeveloped for the optimization of parameters [8] The LS-SVMlab tool [17] developed in Matlab applying three Kerneltuning options (linear polynomial andRBF)was usedwithinthe ensemble of AI methods

34 Bias Correction Using the Quantile Mapping ApproachFirst the predictors were selected followed by the applicationof the multiple compositions of the SDSM model and the 7AI models 4 ANNs and 3 LS-SVM models (Table 3) Theoutput distributions of the ensemble of SDSM models andthe 7 AI models were grouped into two distinct populationsBoth these populations were corrected for bias and varianceinflation applying the quantile mapping technique The QMapplied to SDSM population distributions is from now oncalled the SDSM QM and the QM applied to AI the AI QM

The quantile mapping technique for bias correction andvariance inflation can be regarded as a statistical transforma-tion of the original distribution into a reference probabilitydistribution It aims to find the function that maps thedistribution of themodel variables into the distribution of theobserved variables Basically three types of approaches existto find themapping function they are adjustment (i) based ontheoretical distributions (ii) based on parametric transfor-mations and (iii) based on nonparametric transformations

After evaluation of several transformations the powerparametric transformation was applied because of its goodresults and the parsimony of the model [9] The powerparametric transformation is defined as

119875lowast

0

= 119887 (119875119898minus 1199090)119886

(8)

where 119875lowast0

and 119875119898are the corrected modeled and modeled

variables and 119886 119887 and 1199090are parameters to be determined

To find the parameters 119886 119887 and 1199090 the tool 119877 QMAP

was used [18] For SDSM QM and AI QM the parametersobtained after QM adjustment are presented in Table 4

35 Criteria for Model Evaluation For the qualitative assess-ment of the used methods of downscaling the long-termmonthly mean precipitation of both ensembles the SDSMand AI was compared with the long-term monthly meanobserved precipitation and for the quantitative evaluationstatistical metrics of the distributions of the time series ofobserved and modeled values for the validation period werecalculated In addition to the statistical metrics Box-Whiskerplots presenting both ensembles versus the observations weredrawn This type of graphical representation was selectedbecause in addition to the median the Box-Whisker plotdepicts the extreme values respectively the minimum andmaximum (the caps at the end of each box) and the outliersfalling more than 1 time of the interquartile range above thethird or below the first quartile (the points in the graph)

Advances in Meteorology 5

Table 4 Quantile mapping parameters for artificial intelligence andSDSM ensembles

Model Stations Parameters119886 119887 119909

0

AI

Biblian 003280 183727 087053El Labrado 000820 198426 minus857836Palmas 000334 221628 604480Gualaceo 031943 140124 1692140Paute 002791 194766 003257

SDSM

Biblian 000986 208840 321195El Labrado 039313 119070 minus4584738Palmas 000056 246774 minus1306023Gualaceo 000077 262716 minus114051Paute 004141 180403 391130

As statistical metrics the following were used

(1) Pearson correlation (119877) to evaluate the linear corre-lation

(2) Mean bias (MB) to evaluate the mean (the 50thpercentile) difference betweenmodeled and observeddistributions

(3) The root mean squared error (RMSE) to evaluate theerror between modeled and observed time series

(4) The interquartile relative fraction (IRF) to evaluatethe modeled variability representation relative to theobserved

IRF =119876119898

3

minus 119876119898

1

119876119900

3

minus 119876119900

1

(9)

where IRF is the interquartile relative fraction Avalue of IRF gt 1 represents overestimation of thevariability IRF = 1 is a perfect representation of thevariability and IRF lt 1 is an underestimation ofthe variability 119876119898

3

and 1198761199003

and the 75th modeled andobserved percentile119876119898

1

and1198761199001

and the 25thmodeledand observed percentile

(5) The absolute cumulative bias (ACB) to evaluate thebias of the 25th 50th and 75th percentiles or

ACB = 1003816100381610038161003816119876119898

1

minus 119876119900

1

1003816100381610038161003816 +1003816100381610038161003816119876119898

2

minus 119876119900

2

1003816100381610038161003816 +1003816100381610038161003816119876119898

3

minus 119876119900

3

1003816100381610038161003816 (10)

where ACB is the absolute cumulative bias A valueof ACB = 0 is a perfect representation of the threepercentiles (resp the 25th 50th and 75th percentile)of modeled and observed distributions while under-or overestimation indicates a divergence of ACB fromzero to positive values

4 Results and Discussion

41 Evaluation of SDSM and AI Ensembles

411 Relative Performance of ANN and LS-SVM Models Asmentioned before ANN and LS-SVM models were grouped

Table 5 Statistical metrics for ANN and LS-SVM ensembles

Station Metric ANN LS-SVM

El Labrado

Pearson correlation 049 058IRF 059 053

Mean-bias 420 616Cum bias 3163 3779RMSE 4073 3763

Gualaceo

Pearson correlation 070 071IRF 055 040

Mean-bias minus229 minus021Cum bias 3341 4170RMSE 3482 3533

Paute

Pearson correlation 055 054IRF 041 031

Mean-bias minus990 minus834Cum bias 4416 4821RMSE 3161 3104

Palmas

Pearson correlation 025 045IRF 045 053

Mean-bias minus185 787Cum bias 3699 3781RMSE 5244 4751

Biblian

Pearson correlation 067 065IRF 057 054

Mean-bias minus1839 minus705Cum bias 5234 3549RMSE 4475 4097

into one ensemble considering both models as transferfunction based models Although previous studies [19 20]demonstrated the relative superior performance of SVMbased downscalingmethods over other approaches includingANN based methods we compared for the first time in theregion to the best of our knowledge an ANN ensembleagainst a LS-SVM ensemble to evaluate their downscalingperformanceThe ensembles were not bias corrected in orderto evaluate their actual performance Table 5 presents thevalues of 119877 RMSE MB IRF and ACB comparing ANNand LS-SVM ensembles In El Labrado and Paute stationsimilar results of both ensembles are obtained Howeverboth ensembles for Gualaceo station underrepresent thevariability IRF is 055 and 040 for ANN and LS-SVMrespectivelyTherefore LS-SVMrepresents 15 less variabilitythan ANN ensemble TheMB for ANN is minus229mm whereasfor LS-SVM it is minus021mm which in monthly scale is verylow The ACB metric for ANN is 3341mm whereas for LS-SVM it is 4170mm meaning that although the MB is lowerfor LS-SVM the bias in the 25th and 75th percentiles is higherthan for the ANN ensemble In Palmas station 119877 is 025 and045 respectively for the ANN and LS-SVM ensembles IRFvalues of 045 and 053 for ANN and LS-SVM are obtainedindicating a greater representation in variability by the latterapproach However MB values of minus185 and 787 mean thatLS-SVMpresents more bias in the 50th percentile than ANNFor Biblian stationMB is minus1839mm and minus705mm andACB

6 Advances in Meteorology

Table 6 Statistical metrics for artificial intelligence and SDSM ensembles

Station Metric AI SDSM AI QM SDSM QM

El Labrado

Pearson correlation 058 037 058 038IRF 049 100 087 114

Mean-bias 437 minus4149 minus324 minus054Cum bias 3823 12689 1219 996RMSE 3770 6541 4167 5144

Gualaceo

Pearson correlation 074 053 072 050IRF 052 046 104 103

Mean-bias minus101 1028 433 185Cum bias 3402 4750 735 901RMSE 3392 3826 3287 4486

Paute

Pearson correlation 059 047 057 047IRF 036 047 080 089

Mean-bias minus1046 114 minus426 134Cum bias 4761 3173 1559 777RMSE 3060 3026 3113 3503

Palmas

Pearson correlation 044 016 044 014IRF 052 054 112 102

Mean-bias 739 1631 097 minus366Cum bias 3814 5693 877 1228RMSE 4745 5609 5573 6662

Biblian

Pearson correlation 066 046 067 045IRF 061 056 129 125

Mean-bias minus1112 minus287 minus121 166Cum bias 3501 2999 1891 1730RMSE 4173 4489 3987 5181

5234mm and 3549mm for ANN and LS-SVM ensemblesrespectively meaning a strong bias for the ANN ensemblewith respect to LS-SVM ensemble

For a qualitative evaluation of ANN and LS-SVM ensem-bles the Box-Whisker plots for the results during the valida-tion period are presented in Figure 2 For El Labrado stationboth ensembles similarly represent the median althoughthe low variance is clearly showed as measured by IRF inTable 5 For Gualaceo and Paute stations both ensemblesrepresent less variance with LS-SVM presenting lower val-ues The percentiles above 75th are strongly underestimatedin both stations making the necessity of correction on thedistribution of the ensembles evident In Palmas stationboth ensembles underrepresent the variance and the medianis rightly represented by ANN but overestimated by LS-SVM Finally for Biblian station the variance is stronglyunderestimated as well as the higher percentiles The medianis better represented by LS-SVM and underestimated byANN ensemble Bothmethods were able to perform similarlywell for the downscaling of monthly precipitation in theselected stations In addition comparison of the quantitativeanalysis based on the statistical metrics and the qualitativeanalysis based on Box-Whisker plots shed light on the relativeperformance of ANN and LS-SVMmethods

412 Comparison of SDSM and AI Ensembles Once theANN and LS-SVM ensembles were evaluated in a next step

ObservationsANNLS-SVM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

Prec

ipita

tion

(mm

)

M139 M138 M045 M137M141Paute

Figure 2 Box plots for ANN and LS-SVM ensembles evaluated instation El Labrado (M141) Gualaceo (M139) Paute (M138) Palmas(M045) and Biblian (M137)

the derived SDSM and AI ensembles were compared afterQMcorrection Table 6 depicts for the 5 climate stations in thePaute River basin of which data were used the comparisonbetween the SDSM and AI versus SDSM QM and AI QMThe evaluation between both sets is based on the statistical

Advances in Meteorology 7

ObservationsAI_QMSDSM_QM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

Prec

ipita

tion

(mm

)

M045M138 M137M141 M139Paute

Figure 3 Monthly precipitation box plots for artificial intelligenceand SDSM ensembles bias corrected Results evaluated in station ElLabrado (M141) Gualaceo (M139) Paute (M138) Palmas (M045)and Biblian (M137)

metrics R RMSE MB ACB and IRF For El Labrado stationSDSM QM presents lower correlation than AI QM with038 and 058 values Although SDSM QM presents a lowerbias than AI QM the RMSE of AI QM is a bit lower ForGualaceo station 119877 for AI QM and SDSM QM are 072 and05 RMSE as in El Labrado station is lower for AI QM thanfor SDSM QM with 3287 and 4486 respectively For Pautestation also 119877 is higher for AI QM with 057 and 047 forSDSM QM although the ACB is higher for AI QM with1559 and 777 for SDSM QM For Palmas there is a markeddifference in 119877 values with 044 for AI QM and 014 forSDSM QM depicting for the former a lower RMSE thanthe latter Similar for the Biblian station is the 119877 value forAI QM higher than for SDSM QM respectively 067 versus045 Analogous to the Palmas station a lower RMSE valuefor AI QM equal to 3987 was obtained compared to thecalculated RMSE of 5181 for SDSM QM

All other metrics in Table 6 present similar values Thestronger differences arise generally in the RMSE and 119877

statistical metrics which might be related to the fact thatQM corrects only the characteristic of the distribution ascan be seen in Figure 3 This figure presents the monthlyprecipitation Box-Whisker plots for AI and SDSM ensem-bles bias corrected for the 5 climate stations As can beobserved the distributions are fairly alike From the analysisfor all stations AI QM presented higher values of 119877 thanSDSM QM Similarly AI QMpresents better agreement withthe observed data with the exception of the Paute stationThis fact might point to a slightly better representation ofthe observed monthly precipitation distribution by AI QMensemble for this specific region

42 Evaluation of Intra-Annual Precipitation Seasonality Rep-resentation Whereas in previous section the entire distribu-tion of downscaled estimates was evaluated in the followingthe representation of seasonality is evaluated Although the

evaluation of seasonality representation might not help toquantify for example flooding events it is very importantfor issues related to water availability for hydroelectricitygeneration drinking water availability and agriculture Fur-ther the evaluation of seasonality representation is of specialimportance in the study region due to the low resolutionof GCMs unable to depict the precipitation regime due tomesoscale influences [5]

421 The Added Value of Quantile Mapping The QM cor-rection parameters for the power parametric transformationapplied to AI and SDSM ensembles are presented in Table 4The comparison of the multiyear monthly mean (mymm)precipitation of the SDSM with the SDSM QM ensembleis presented in Figures 4(a)ndash4(e) As shown in Figure 4(a)SDSM applied to the El Labrado station fails to capturethe observed seasonality However the performance biasand variance improved considerably after applying QMSeasonality applying SDSM to the Gualaceo (Figure 4(b))station is less correctly presented and fails to capture themaximum inApril and overestimates precipitation during thedry season in August Application of QM only corrects therepresentation in August but not in April The ensemble ofSDSM compositions represents well seasonality but under-estimates significantly the November precipitation depthApplication ofQM improves the representation of seasonalitybut does not improve the November estimate The SDSM inPaute station represents seasonality well but underestimatessignificantly the maximum in November QM applied toSDSM in Paute improves the performance of seasonalityyet fails to improve the representation of the Novemberprecipitation (Figure 4(c)) The SDSM approach calibratedto the observations of the Palmas station (Figure 4(d)) astation with unimodal regime (UM) depicts fairly correctseasonality notwithstanding the limited spatial extent of theUM regime and the poor representation of the mesoscaleinfluences in the synoptic predictors Application of QMnegatively affects the SDSM representation during the first 6months of the year but improves slightly the representationduring the remaining period of the year The seasonality ofthe Biblian station (Figure 4(e)) is properly represented bythe SDSM ensemble and as well as the SDSM QM Only theNovember peak in precipitation is captured by neither SDSMnor SDSM QM

The comparison of mymm of the AI with the AI QMensembles is presented in Figures 4(f)ndash4(j)TheAI emsembleunderestimates precipitation in April overestimate it in Julyand August and underestimate it in November althoughat some extent it represents seasonality QM improves theintra-annual variability but still the November maximumis not correctly estimated The AI ensemble in Gualaceo(Figure 4(g)) station captures well both peaks in Apriland November but underestimates precipitation in AugustThe estimation in August is considerably improved aftercorrection of the bias and the inflation of the variance In thePaute station (Figure 4(h)) are both the peaks respectively inApril and November and the minimum in August were wellcaptured by the AI ensemble while QM further improves thedistribution of the median of the monthly precipitation The

8 Advances in Meteorology

SDSMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(a)

Obs_GualaceoSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(b)

Obs_PauteSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(c)

Obs_PalmasSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(d)

Obs_Bibli naSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(e)

AIObs_El Labrado

AI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(f)

Figure 4 Continued

Advances in Meteorology 9

Obs_GualaceoAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(g)

Obs_PauteAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(h)

Obs_PalmasAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(i)

Obs_Bibli naAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(j)

Figure 4 Multiyear monthly mean precipitation for SDSM ensemble and SDSM ensemble bias corrected (andashe) and multiyear monthly meanprecipitation for AI and AI bias corrected (fndashj)

AI ensemble represents poorly the distribution of the Palmasstation (Figure 4(i) UM regime) even after QM applicationFor the Biblian station (Figure 4(j)) the AI QM captures theApril peak one month earlier but fails to correctly depict themagnitude of the November peak

Results clearly reveal that the application of QM tothe output of both modeling approaches SDSM and AIoverall improves the representation of seasonality as wellas the representation of rainy and dry periods Howeverboth approaches underestimate the median value of theprecipitation depth inNovemberThis fact could indicate thatthe set of synoptic predictors do not include a variable thatis related to an enhancement of precipitation in this periodFurther studies are needed to determine the variables andrelated phenomena

Table 7 Pearson correlations between observations and SDSM QMand AI QMmodels

Station AI QM SDSM QMEl Labrado 0741 0516Gualaceo 0946 0672Paute 0730 0629Palmas 0788 0593Biblian 0691 0532

422 Representation of Monthly Variability by DownscaledResults To compare the representativeness of SDSM QMand AI QM the correlation of the mymm time serieswith the observed values is shown in Table 7 For all

10 Advances in Meteorology

AI_QMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(a)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(b)

AI_QMObs_Gualaceo

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(c)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(d)

AI_QMObs_Paute

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

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embe

r

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June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(e)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(f)

Figure 5 Continued

Advances in Meteorology 11

AI_QMObs_Palmas

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(g)

ObservationsSDSM_QMAI_QM

Prec

ipita

tion

(mm

)

150

100

250

350

300

200

50

0

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(h)

AI_QMObs_Bibli na

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(i)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(j)

Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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EarthquakesJournal of

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Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

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MineralogyInternational Journal of

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MeteorologyAdvances in

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Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

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Geology Advances in

2 Advances in Meteorology

Table 1 Stations used for the present study

Code Station Regime Latitude (∘) Longitude (∘) Elevation (m asl) Annual precipitation (mm)M141 El Labrado TM minus2732 minus79073 3335 1286M139 Gualaceo BM minus2882 minus78776 2230 820M138 Paute TM minus2800 minus78763 2194 750M045 Palmas UM minus2716 minus78630 2400 1341M137 Biblian BM minus2709 minus78892 2640 1001

development of multiple low cost single-site scenarios ofdaily surface weather variables and is considered as a stochas-tic weather generator on a daily scale The limited use ofthis technique in the Andean mountain region is perhapsthe consequence of its complex topography location in thetropical zone and the influence of the warm and cold ENSOphases El Nino and LaNina respectively All these influencesadd complexity to the atmospheric processes making therepresentation by downscaling techniques more difficultArtificial neural networks (ANNs) are another SD techniquecommonly used however to a limited extent in the Andesregion As stated by [4] the success of this technique isprimarily due to its ability to map highly nonlinear relationsbetween inputs and outputs of the model Reference [5]applied ANN for downscaling monthly precipitation andtemperature in the Paute basin in the Andes of EcuadorThe application of ANN based SD was conducted in orderto evaluate the performance on seasonality representationagainst DDusing a regional climatemodelWeather Researchand Forecasting WRF model [6] With respect to rainfallrepresentation they found that although both downscalingapproaches represent qualitatively well seasonality in thishighly complex terrain ANN estimates of rainfall weremore accurate than WRF estimates This fact highlightsthe applicability of ANN when the understanding of theprocesses involved is not required Another technique withrecent application for the downscaling of GCMs is SVMsupport vector machines [7] In particular the least squaressupport vector machines LS-SVM [8] downscale GCM out-put even better mainly due to the reduction of the optimiza-tion problem to the resolution of a linear system reducingconsiderably the computational requirements Despite SDmethods presenting greater accuracy thanDDmethods froma statistical point of view they possess two handicaps biasand low variance Normally the quantile mapping (QM)technique [9] is applied to improve the representation of thedistribution of derived applications

This paper presents a comparative evaluation of down-scaled GCM estimates of monthly precipitation at the scaleof a large river basin situated in the Andean mountain regionin southern Ecuador applying SDSM and two artificial intel-ligence (AI) techniques artificial neural networks (ANNs)and the least squares support vector machines (LS-SVM)approachThe downscaled results were corrected for bias andvariance inflation applying the QM technique prior to thecomparative analysis For the evaluation historic data wasused

M141 M137 M045M138

M139

Ecuador

Paute basinStations

3∘09984000998400998400S

2∘30

9984000998400998400S

2∘09984000998400998400S

79∘09984000998400998400W 78

∘30

9984000998400998400W79

∘30

9984000998400998400W

79∘09984000998400998400W 78

∘30

9984000998400998400W79

∘30

9984000998400998400W

3∘09984000998400998400S

2∘30

9984000998400998400S

2∘09984000998400998400S

Figure 1 The study area Paute basin in the Andes of Ecuador

2 Study Area and Data

The Paute River basin tributary of the Amazon basin and6148 km2 in size was selected for the comparative evaluationof the downscaling methods a basin located between theeastern and western cordillera of the Andes in Ecuador Thebasin is characterized by a high spatial and temporal variationin precipitation that broadly can be classified into threerainfall regimes respectively subregions with a uni- bi- andthree-modal precipitation pattern [10 11] Data of 5 rainfallstations (see Table 1) were used of whom the geographicaldistribution is given in Figure 1 The measured monthlyrainfall for the 30-year period 01-1980 to 12-2009 was usedto quantify the differences in the performance of the selecteddownscaling methods The dataset was split in a first set forthe calibration of themethods encompassing 75 of the totaldataset and the remaining 25 was used for the validationThe results presented herein belong all to the validation setQuality control of the data was performed using double masscurves on the time series with gaps not exceeding 20 of theobservationsThe infilling of the datawas accomplished usingmultiple linear regression with stations with higher Pearsoncorrelation [12]

NCEPNCAR reanalysis 1 data [13] with 25∘

times 25∘

resolution was used as inputThe selected synoptic predictorsfor the SDSM and AI models are presented in Table 2

Advances in Meteorology 3

Table 2 Synoptic predictors

Synoptic predictors ANNLS-SVM SDSM(All stations) El Labrado Gualaceo Paute Palmas Biblian

1 Precipitation lowast lowast lowast lowast lowast lowast

2 Pressure (surface) lowast lowast lowast lowast

3 Relative humidity (surface) lowast lowast lowast lowast lowast

4 Specific humidity 700 hPa lowast

5 Sea level pressure lowast

6 Temperature 2m lowast lowast lowast lowast lowast

7 Potential temperature 700 hPa lowast lowast lowast lowast

8 Zonal wind (surface) lowast

9 Omega 500 hPa lowast lowast lowast

10 Geopotential height 200 hPa lowast lowast

11 Geopotential height 500 hPa lowast

12 Geopotential height 850 hPa lowast lowast

3 Methods

The methodology of the present study encompasses thefollowing steps (i) selection of the predictors (ii) calibrationand validation of the SDSM and AI models (iii) SDSM andAI ensemble generation (iv) bias correction by quantilemap-ping and (v) evaluation of results SDSM can be conceivedas a weather generator model while ANN and LS-SVM areboth transfer functions in statistical downscaling modelsGiven the analogy between ANN and LS-SVM models theresults of both formed one ensemble which were comparedto the SDSM ensemble Notwithstanding it is well known [14]that a selection of predictors for specific months or seasonsmight be a good option to improve the accuracy in climateprojections in the present study only one set of predictors forthe whole year was considered given that the main interestwas the comparison of downscaling methods rather than theanalysis of climate projectionsThe samepredictorswere usedfor the AI ensemble of ANN and LS-SVM models and oneset of predictors in each station for the SDSMmodel A moredetailed description of the tested downscalingmodels is givenin the following paragraphs

31 Downscaling Using SDSM SDSM is a hybrid betweena stochastic weather generator and a multilinear regressionmethod [14] forcing synoptic-scale weather variables to localmeteorological variables using statistical relationships Inorder to be better in agreement with the variance of theobserved time series stochastic techniques are used to arti-ficially inflate the variance of the downscaled weather timeseries The reader is referred to [3] for a detailed descriptionof the SDSM technique an approach widely used for thedownscaling of large-scale meteorological hydrological andenvironmental variables

Partial correlation at a significance level of 119901 = 005 wasused to select the predictors that capture best for each of theclimate stations the effect of global climate Precipitation datafrom the reanalysis products was evaluated as the predictorthat considerably helped improving the downscaling Forthe climate stations Biblian Paute and Gualaceo 5 predic-tors were identified of whom 4 are similar precipitation

pressure relative humidity and the temperature 2m abovethe surface For the Palmas station the only station with aunimodal regime the best results were obtained using threepredictors namely precipitation potential temperature at the700 hPa level and the geopotential height at the 850 hPa levelTable 2 provides the list of the selected predictors as a functionof the downscaling technique and station

Using the selected predictors daily precipitation wasdownscaled Given the low match with the observed timeseries of daily data monthly time series were generated Atthe monthly scale the precipitation time series in the studybasin are continuous months with zero precipitation are notpresent even during the dry months Regarding the SDSMmodel 20 versions were applied [15]Then the median of thesimulated results was calculated as the representative valuefor the ensemble of the SDSMmodel variants

32 Downscaling Using ANN An artificial neural network(ANN) is composed of several interconnected layers ofprocessing units (the neurons) that transform inputs intooutputs The inputs at the neurons are multiplied by weightsand then inserted into an activation function ANNs arecharacterized by their topology and probably themostwidelyknown neural network is the multilayer perceptron (MLP)It consists of multiple layers of adaptive weights with fullconnectivity between inputs and hidden units and betweenhidden units and outputs MLP is feed-forward artificialneural network mapping sets of input data onto a set ofappropriate outputs

The neural network toolbox of Matlab [16] was usedand optimization of the neural network was pursued usingthe Levenberg-Marquardt method minimizing the meansquare error The performance of a total of four ANNs wastested respectively a model considering either one or twointermediate neural layers and a linear or sigmoidal transferfunction in the neurons (Table 3) For the input layer allnetworks had 12 neurons (equal to the number of predictorssee Table 2) and for the network with one hidden layer8 neurons were used which was determined by trial anderror In a similar way for networks with two hidden layersrespectively 9 and 5 neurons were used

4 Advances in Meteorology

Table 3 Artificial intelligence models

Model Type Transfer function1

Ann

Linear amp 1 hidden layer2 Sigmoidal amp 1 hidden layer3 Linear amp 2 hidden layers4 Sigmoidal amp 2 hidden layers5

LS-SVMLinear

6 Polynomial7 Radial basis functions

33 Downscaling Using LS-SVM Support vector machinesSVM [7] solve nonlinear classifications and estimations offunctions and densities using quadratic programming Aleast squares support vector machine LS-SVM [8] is areformulation of a SVM replacing the solution of the convexquadratic programming problem by the solution of a set oflinear equations As explained by [8] it is possible to adoptinto LS-SVM the robustness sparseness and weightings

Due to the fact that LS-SVM has more recent applicationthan ANN and SDSM techniques for the downscaling ofGCMs we present here a succinct description of LS-SVMtheory For a more in deep description of LS-SVM see [8]

Let us consider 119909 isin R119899 and 119910 isin R the LS-SVM modelmapping the 119909 into a feature space is

119910 = 119908119879

120593 (119909) + 119887 (1)

The optimization problem can be stated as

min119908119890

Γ (119908 119890) =1

2119908119879

119908 + 1205741

2

119873

sum

119894=1

1198902

119894

(2)

where 119890 and 120574 are the error and the regularization parameterrespectively The minimization of the cost function Γ(119908 119890) issubject to the constrains

119910119894= 119908119879

120593 (119909119894) + 119887 + 119890

119894 (3)

The Lagrangian of the optimization is

L (119908 119887 119890 120572) = Γ (119908 119890) minus

119873

sum

119894=1

120572119894(119908119879

120593 (119909119894) + 119887 + 119890

119894minus 119910119894) (4)

where 120572119894are the Lagrangian multipliers

After considering the conditions for optimality

[120597L

120597119908120597L

120597119887120597L

120597119890119894

120597L

120597120572119894

]

119879

= [0 0 0 0]119879

(5)

We obtain the matrix equation

[

0 1

1 Ω minus 120574minus1

119868

] [

119887

120572

] = [

0

119910

] (6)

whereΩ119894119895= 120593(119909

119894)119879

120593(119909119895) is the Kernel function119870(119909

119894 119909119895) and

119868 is the identity matrix

Finally the LS-SVMmodel for function estimation is

119910 (119909) =

119873

sum

119894=1

120572119894119870(119909119894 119909) + 119887 (7)

A Bayesian framework with three levels of inference wasdeveloped for the optimization of parameters [8] The LS-SVMlab tool [17] developed in Matlab applying three Kerneltuning options (linear polynomial andRBF)was usedwithinthe ensemble of AI methods

34 Bias Correction Using the Quantile Mapping ApproachFirst the predictors were selected followed by the applicationof the multiple compositions of the SDSM model and the 7AI models 4 ANNs and 3 LS-SVM models (Table 3) Theoutput distributions of the ensemble of SDSM models andthe 7 AI models were grouped into two distinct populationsBoth these populations were corrected for bias and varianceinflation applying the quantile mapping technique The QMapplied to SDSM population distributions is from now oncalled the SDSM QM and the QM applied to AI the AI QM

The quantile mapping technique for bias correction andvariance inflation can be regarded as a statistical transforma-tion of the original distribution into a reference probabilitydistribution It aims to find the function that maps thedistribution of themodel variables into the distribution of theobserved variables Basically three types of approaches existto find themapping function they are adjustment (i) based ontheoretical distributions (ii) based on parametric transfor-mations and (iii) based on nonparametric transformations

After evaluation of several transformations the powerparametric transformation was applied because of its goodresults and the parsimony of the model [9] The powerparametric transformation is defined as

119875lowast

0

= 119887 (119875119898minus 1199090)119886

(8)

where 119875lowast0

and 119875119898are the corrected modeled and modeled

variables and 119886 119887 and 1199090are parameters to be determined

To find the parameters 119886 119887 and 1199090 the tool 119877 QMAP

was used [18] For SDSM QM and AI QM the parametersobtained after QM adjustment are presented in Table 4

35 Criteria for Model Evaluation For the qualitative assess-ment of the used methods of downscaling the long-termmonthly mean precipitation of both ensembles the SDSMand AI was compared with the long-term monthly meanobserved precipitation and for the quantitative evaluationstatistical metrics of the distributions of the time series ofobserved and modeled values for the validation period werecalculated In addition to the statistical metrics Box-Whiskerplots presenting both ensembles versus the observations weredrawn This type of graphical representation was selectedbecause in addition to the median the Box-Whisker plotdepicts the extreme values respectively the minimum andmaximum (the caps at the end of each box) and the outliersfalling more than 1 time of the interquartile range above thethird or below the first quartile (the points in the graph)

Advances in Meteorology 5

Table 4 Quantile mapping parameters for artificial intelligence andSDSM ensembles

Model Stations Parameters119886 119887 119909

0

AI

Biblian 003280 183727 087053El Labrado 000820 198426 minus857836Palmas 000334 221628 604480Gualaceo 031943 140124 1692140Paute 002791 194766 003257

SDSM

Biblian 000986 208840 321195El Labrado 039313 119070 minus4584738Palmas 000056 246774 minus1306023Gualaceo 000077 262716 minus114051Paute 004141 180403 391130

As statistical metrics the following were used

(1) Pearson correlation (119877) to evaluate the linear corre-lation

(2) Mean bias (MB) to evaluate the mean (the 50thpercentile) difference betweenmodeled and observeddistributions

(3) The root mean squared error (RMSE) to evaluate theerror between modeled and observed time series

(4) The interquartile relative fraction (IRF) to evaluatethe modeled variability representation relative to theobserved

IRF =119876119898

3

minus 119876119898

1

119876119900

3

minus 119876119900

1

(9)

where IRF is the interquartile relative fraction Avalue of IRF gt 1 represents overestimation of thevariability IRF = 1 is a perfect representation of thevariability and IRF lt 1 is an underestimation ofthe variability 119876119898

3

and 1198761199003

and the 75th modeled andobserved percentile119876119898

1

and1198761199001

and the 25thmodeledand observed percentile

(5) The absolute cumulative bias (ACB) to evaluate thebias of the 25th 50th and 75th percentiles or

ACB = 1003816100381610038161003816119876119898

1

minus 119876119900

1

1003816100381610038161003816 +1003816100381610038161003816119876119898

2

minus 119876119900

2

1003816100381610038161003816 +1003816100381610038161003816119876119898

3

minus 119876119900

3

1003816100381610038161003816 (10)

where ACB is the absolute cumulative bias A valueof ACB = 0 is a perfect representation of the threepercentiles (resp the 25th 50th and 75th percentile)of modeled and observed distributions while under-or overestimation indicates a divergence of ACB fromzero to positive values

4 Results and Discussion

41 Evaluation of SDSM and AI Ensembles

411 Relative Performance of ANN and LS-SVM Models Asmentioned before ANN and LS-SVM models were grouped

Table 5 Statistical metrics for ANN and LS-SVM ensembles

Station Metric ANN LS-SVM

El Labrado

Pearson correlation 049 058IRF 059 053

Mean-bias 420 616Cum bias 3163 3779RMSE 4073 3763

Gualaceo

Pearson correlation 070 071IRF 055 040

Mean-bias minus229 minus021Cum bias 3341 4170RMSE 3482 3533

Paute

Pearson correlation 055 054IRF 041 031

Mean-bias minus990 minus834Cum bias 4416 4821RMSE 3161 3104

Palmas

Pearson correlation 025 045IRF 045 053

Mean-bias minus185 787Cum bias 3699 3781RMSE 5244 4751

Biblian

Pearson correlation 067 065IRF 057 054

Mean-bias minus1839 minus705Cum bias 5234 3549RMSE 4475 4097

into one ensemble considering both models as transferfunction based models Although previous studies [19 20]demonstrated the relative superior performance of SVMbased downscalingmethods over other approaches includingANN based methods we compared for the first time in theregion to the best of our knowledge an ANN ensembleagainst a LS-SVM ensemble to evaluate their downscalingperformanceThe ensembles were not bias corrected in orderto evaluate their actual performance Table 5 presents thevalues of 119877 RMSE MB IRF and ACB comparing ANNand LS-SVM ensembles In El Labrado and Paute stationsimilar results of both ensembles are obtained Howeverboth ensembles for Gualaceo station underrepresent thevariability IRF is 055 and 040 for ANN and LS-SVMrespectivelyTherefore LS-SVMrepresents 15 less variabilitythan ANN ensemble TheMB for ANN is minus229mm whereasfor LS-SVM it is minus021mm which in monthly scale is verylow The ACB metric for ANN is 3341mm whereas for LS-SVM it is 4170mm meaning that although the MB is lowerfor LS-SVM the bias in the 25th and 75th percentiles is higherthan for the ANN ensemble In Palmas station 119877 is 025 and045 respectively for the ANN and LS-SVM ensembles IRFvalues of 045 and 053 for ANN and LS-SVM are obtainedindicating a greater representation in variability by the latterapproach However MB values of minus185 and 787 mean thatLS-SVMpresents more bias in the 50th percentile than ANNFor Biblian stationMB is minus1839mm and minus705mm andACB

6 Advances in Meteorology

Table 6 Statistical metrics for artificial intelligence and SDSM ensembles

Station Metric AI SDSM AI QM SDSM QM

El Labrado

Pearson correlation 058 037 058 038IRF 049 100 087 114

Mean-bias 437 minus4149 minus324 minus054Cum bias 3823 12689 1219 996RMSE 3770 6541 4167 5144

Gualaceo

Pearson correlation 074 053 072 050IRF 052 046 104 103

Mean-bias minus101 1028 433 185Cum bias 3402 4750 735 901RMSE 3392 3826 3287 4486

Paute

Pearson correlation 059 047 057 047IRF 036 047 080 089

Mean-bias minus1046 114 minus426 134Cum bias 4761 3173 1559 777RMSE 3060 3026 3113 3503

Palmas

Pearson correlation 044 016 044 014IRF 052 054 112 102

Mean-bias 739 1631 097 minus366Cum bias 3814 5693 877 1228RMSE 4745 5609 5573 6662

Biblian

Pearson correlation 066 046 067 045IRF 061 056 129 125

Mean-bias minus1112 minus287 minus121 166Cum bias 3501 2999 1891 1730RMSE 4173 4489 3987 5181

5234mm and 3549mm for ANN and LS-SVM ensemblesrespectively meaning a strong bias for the ANN ensemblewith respect to LS-SVM ensemble

For a qualitative evaluation of ANN and LS-SVM ensem-bles the Box-Whisker plots for the results during the valida-tion period are presented in Figure 2 For El Labrado stationboth ensembles similarly represent the median althoughthe low variance is clearly showed as measured by IRF inTable 5 For Gualaceo and Paute stations both ensemblesrepresent less variance with LS-SVM presenting lower val-ues The percentiles above 75th are strongly underestimatedin both stations making the necessity of correction on thedistribution of the ensembles evident In Palmas stationboth ensembles underrepresent the variance and the medianis rightly represented by ANN but overestimated by LS-SVM Finally for Biblian station the variance is stronglyunderestimated as well as the higher percentiles The medianis better represented by LS-SVM and underestimated byANN ensemble Bothmethods were able to perform similarlywell for the downscaling of monthly precipitation in theselected stations In addition comparison of the quantitativeanalysis based on the statistical metrics and the qualitativeanalysis based on Box-Whisker plots shed light on the relativeperformance of ANN and LS-SVMmethods

412 Comparison of SDSM and AI Ensembles Once theANN and LS-SVM ensembles were evaluated in a next step

ObservationsANNLS-SVM

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Figure 2 Box plots for ANN and LS-SVM ensembles evaluated instation El Labrado (M141) Gualaceo (M139) Paute (M138) Palmas(M045) and Biblian (M137)

the derived SDSM and AI ensembles were compared afterQMcorrection Table 6 depicts for the 5 climate stations in thePaute River basin of which data were used the comparisonbetween the SDSM and AI versus SDSM QM and AI QMThe evaluation between both sets is based on the statistical

Advances in Meteorology 7

ObservationsAI_QMSDSM_QM

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Figure 3 Monthly precipitation box plots for artificial intelligenceand SDSM ensembles bias corrected Results evaluated in station ElLabrado (M141) Gualaceo (M139) Paute (M138) Palmas (M045)and Biblian (M137)

metrics R RMSE MB ACB and IRF For El Labrado stationSDSM QM presents lower correlation than AI QM with038 and 058 values Although SDSM QM presents a lowerbias than AI QM the RMSE of AI QM is a bit lower ForGualaceo station 119877 for AI QM and SDSM QM are 072 and05 RMSE as in El Labrado station is lower for AI QM thanfor SDSM QM with 3287 and 4486 respectively For Pautestation also 119877 is higher for AI QM with 057 and 047 forSDSM QM although the ACB is higher for AI QM with1559 and 777 for SDSM QM For Palmas there is a markeddifference in 119877 values with 044 for AI QM and 014 forSDSM QM depicting for the former a lower RMSE thanthe latter Similar for the Biblian station is the 119877 value forAI QM higher than for SDSM QM respectively 067 versus045 Analogous to the Palmas station a lower RMSE valuefor AI QM equal to 3987 was obtained compared to thecalculated RMSE of 5181 for SDSM QM

All other metrics in Table 6 present similar values Thestronger differences arise generally in the RMSE and 119877

statistical metrics which might be related to the fact thatQM corrects only the characteristic of the distribution ascan be seen in Figure 3 This figure presents the monthlyprecipitation Box-Whisker plots for AI and SDSM ensem-bles bias corrected for the 5 climate stations As can beobserved the distributions are fairly alike From the analysisfor all stations AI QM presented higher values of 119877 thanSDSM QM Similarly AI QMpresents better agreement withthe observed data with the exception of the Paute stationThis fact might point to a slightly better representation ofthe observed monthly precipitation distribution by AI QMensemble for this specific region

42 Evaluation of Intra-Annual Precipitation Seasonality Rep-resentation Whereas in previous section the entire distribu-tion of downscaled estimates was evaluated in the followingthe representation of seasonality is evaluated Although the

evaluation of seasonality representation might not help toquantify for example flooding events it is very importantfor issues related to water availability for hydroelectricitygeneration drinking water availability and agriculture Fur-ther the evaluation of seasonality representation is of specialimportance in the study region due to the low resolutionof GCMs unable to depict the precipitation regime due tomesoscale influences [5]

421 The Added Value of Quantile Mapping The QM cor-rection parameters for the power parametric transformationapplied to AI and SDSM ensembles are presented in Table 4The comparison of the multiyear monthly mean (mymm)precipitation of the SDSM with the SDSM QM ensembleis presented in Figures 4(a)ndash4(e) As shown in Figure 4(a)SDSM applied to the El Labrado station fails to capturethe observed seasonality However the performance biasand variance improved considerably after applying QMSeasonality applying SDSM to the Gualaceo (Figure 4(b))station is less correctly presented and fails to capture themaximum inApril and overestimates precipitation during thedry season in August Application of QM only corrects therepresentation in August but not in April The ensemble ofSDSM compositions represents well seasonality but under-estimates significantly the November precipitation depthApplication ofQM improves the representation of seasonalitybut does not improve the November estimate The SDSM inPaute station represents seasonality well but underestimatessignificantly the maximum in November QM applied toSDSM in Paute improves the performance of seasonalityyet fails to improve the representation of the Novemberprecipitation (Figure 4(c)) The SDSM approach calibratedto the observations of the Palmas station (Figure 4(d)) astation with unimodal regime (UM) depicts fairly correctseasonality notwithstanding the limited spatial extent of theUM regime and the poor representation of the mesoscaleinfluences in the synoptic predictors Application of QMnegatively affects the SDSM representation during the first 6months of the year but improves slightly the representationduring the remaining period of the year The seasonality ofthe Biblian station (Figure 4(e)) is properly represented bythe SDSM ensemble and as well as the SDSM QM Only theNovember peak in precipitation is captured by neither SDSMnor SDSM QM

The comparison of mymm of the AI with the AI QMensembles is presented in Figures 4(f)ndash4(j)TheAI emsembleunderestimates precipitation in April overestimate it in Julyand August and underestimate it in November althoughat some extent it represents seasonality QM improves theintra-annual variability but still the November maximumis not correctly estimated The AI ensemble in Gualaceo(Figure 4(g)) station captures well both peaks in Apriland November but underestimates precipitation in AugustThe estimation in August is considerably improved aftercorrection of the bias and the inflation of the variance In thePaute station (Figure 4(h)) are both the peaks respectively inApril and November and the minimum in August were wellcaptured by the AI ensemble while QM further improves thedistribution of the median of the monthly precipitation The

8 Advances in Meteorology

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Advances in Meteorology 9

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Figure 4 Multiyear monthly mean precipitation for SDSM ensemble and SDSM ensemble bias corrected (andashe) and multiyear monthly meanprecipitation for AI and AI bias corrected (fndashj)

AI ensemble represents poorly the distribution of the Palmasstation (Figure 4(i) UM regime) even after QM applicationFor the Biblian station (Figure 4(j)) the AI QM captures theApril peak one month earlier but fails to correctly depict themagnitude of the November peak

Results clearly reveal that the application of QM tothe output of both modeling approaches SDSM and AIoverall improves the representation of seasonality as wellas the representation of rainy and dry periods Howeverboth approaches underestimate the median value of theprecipitation depth inNovemberThis fact could indicate thatthe set of synoptic predictors do not include a variable thatis related to an enhancement of precipitation in this periodFurther studies are needed to determine the variables andrelated phenomena

Table 7 Pearson correlations between observations and SDSM QMand AI QMmodels

Station AI QM SDSM QMEl Labrado 0741 0516Gualaceo 0946 0672Paute 0730 0629Palmas 0788 0593Biblian 0691 0532

422 Representation of Monthly Variability by DownscaledResults To compare the representativeness of SDSM QMand AI QM the correlation of the mymm time serieswith the observed values is shown in Table 7 For all

10 Advances in Meteorology

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Advances in Meteorology 11

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Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 3

Table 2 Synoptic predictors

Synoptic predictors ANNLS-SVM SDSM(All stations) El Labrado Gualaceo Paute Palmas Biblian

1 Precipitation lowast lowast lowast lowast lowast lowast

2 Pressure (surface) lowast lowast lowast lowast

3 Relative humidity (surface) lowast lowast lowast lowast lowast

4 Specific humidity 700 hPa lowast

5 Sea level pressure lowast

6 Temperature 2m lowast lowast lowast lowast lowast

7 Potential temperature 700 hPa lowast lowast lowast lowast

8 Zonal wind (surface) lowast

9 Omega 500 hPa lowast lowast lowast

10 Geopotential height 200 hPa lowast lowast

11 Geopotential height 500 hPa lowast

12 Geopotential height 850 hPa lowast lowast

3 Methods

The methodology of the present study encompasses thefollowing steps (i) selection of the predictors (ii) calibrationand validation of the SDSM and AI models (iii) SDSM andAI ensemble generation (iv) bias correction by quantilemap-ping and (v) evaluation of results SDSM can be conceivedas a weather generator model while ANN and LS-SVM areboth transfer functions in statistical downscaling modelsGiven the analogy between ANN and LS-SVM models theresults of both formed one ensemble which were comparedto the SDSM ensemble Notwithstanding it is well known [14]that a selection of predictors for specific months or seasonsmight be a good option to improve the accuracy in climateprojections in the present study only one set of predictors forthe whole year was considered given that the main interestwas the comparison of downscaling methods rather than theanalysis of climate projectionsThe samepredictorswere usedfor the AI ensemble of ANN and LS-SVM models and oneset of predictors in each station for the SDSMmodel A moredetailed description of the tested downscalingmodels is givenin the following paragraphs

31 Downscaling Using SDSM SDSM is a hybrid betweena stochastic weather generator and a multilinear regressionmethod [14] forcing synoptic-scale weather variables to localmeteorological variables using statistical relationships Inorder to be better in agreement with the variance of theobserved time series stochastic techniques are used to arti-ficially inflate the variance of the downscaled weather timeseries The reader is referred to [3] for a detailed descriptionof the SDSM technique an approach widely used for thedownscaling of large-scale meteorological hydrological andenvironmental variables

Partial correlation at a significance level of 119901 = 005 wasused to select the predictors that capture best for each of theclimate stations the effect of global climate Precipitation datafrom the reanalysis products was evaluated as the predictorthat considerably helped improving the downscaling Forthe climate stations Biblian Paute and Gualaceo 5 predic-tors were identified of whom 4 are similar precipitation

pressure relative humidity and the temperature 2m abovethe surface For the Palmas station the only station with aunimodal regime the best results were obtained using threepredictors namely precipitation potential temperature at the700 hPa level and the geopotential height at the 850 hPa levelTable 2 provides the list of the selected predictors as a functionof the downscaling technique and station

Using the selected predictors daily precipitation wasdownscaled Given the low match with the observed timeseries of daily data monthly time series were generated Atthe monthly scale the precipitation time series in the studybasin are continuous months with zero precipitation are notpresent even during the dry months Regarding the SDSMmodel 20 versions were applied [15]Then the median of thesimulated results was calculated as the representative valuefor the ensemble of the SDSMmodel variants

32 Downscaling Using ANN An artificial neural network(ANN) is composed of several interconnected layers ofprocessing units (the neurons) that transform inputs intooutputs The inputs at the neurons are multiplied by weightsand then inserted into an activation function ANNs arecharacterized by their topology and probably themostwidelyknown neural network is the multilayer perceptron (MLP)It consists of multiple layers of adaptive weights with fullconnectivity between inputs and hidden units and betweenhidden units and outputs MLP is feed-forward artificialneural network mapping sets of input data onto a set ofappropriate outputs

The neural network toolbox of Matlab [16] was usedand optimization of the neural network was pursued usingthe Levenberg-Marquardt method minimizing the meansquare error The performance of a total of four ANNs wastested respectively a model considering either one or twointermediate neural layers and a linear or sigmoidal transferfunction in the neurons (Table 3) For the input layer allnetworks had 12 neurons (equal to the number of predictorssee Table 2) and for the network with one hidden layer8 neurons were used which was determined by trial anderror In a similar way for networks with two hidden layersrespectively 9 and 5 neurons were used

4 Advances in Meteorology

Table 3 Artificial intelligence models

Model Type Transfer function1

Ann

Linear amp 1 hidden layer2 Sigmoidal amp 1 hidden layer3 Linear amp 2 hidden layers4 Sigmoidal amp 2 hidden layers5

LS-SVMLinear

6 Polynomial7 Radial basis functions

33 Downscaling Using LS-SVM Support vector machinesSVM [7] solve nonlinear classifications and estimations offunctions and densities using quadratic programming Aleast squares support vector machine LS-SVM [8] is areformulation of a SVM replacing the solution of the convexquadratic programming problem by the solution of a set oflinear equations As explained by [8] it is possible to adoptinto LS-SVM the robustness sparseness and weightings

Due to the fact that LS-SVM has more recent applicationthan ANN and SDSM techniques for the downscaling ofGCMs we present here a succinct description of LS-SVMtheory For a more in deep description of LS-SVM see [8]

Let us consider 119909 isin R119899 and 119910 isin R the LS-SVM modelmapping the 119909 into a feature space is

119910 = 119908119879

120593 (119909) + 119887 (1)

The optimization problem can be stated as

min119908119890

Γ (119908 119890) =1

2119908119879

119908 + 1205741

2

119873

sum

119894=1

1198902

119894

(2)

where 119890 and 120574 are the error and the regularization parameterrespectively The minimization of the cost function Γ(119908 119890) issubject to the constrains

119910119894= 119908119879

120593 (119909119894) + 119887 + 119890

119894 (3)

The Lagrangian of the optimization is

L (119908 119887 119890 120572) = Γ (119908 119890) minus

119873

sum

119894=1

120572119894(119908119879

120593 (119909119894) + 119887 + 119890

119894minus 119910119894) (4)

where 120572119894are the Lagrangian multipliers

After considering the conditions for optimality

[120597L

120597119908120597L

120597119887120597L

120597119890119894

120597L

120597120572119894

]

119879

= [0 0 0 0]119879

(5)

We obtain the matrix equation

[

0 1

1 Ω minus 120574minus1

119868

] [

119887

120572

] = [

0

119910

] (6)

whereΩ119894119895= 120593(119909

119894)119879

120593(119909119895) is the Kernel function119870(119909

119894 119909119895) and

119868 is the identity matrix

Finally the LS-SVMmodel for function estimation is

119910 (119909) =

119873

sum

119894=1

120572119894119870(119909119894 119909) + 119887 (7)

A Bayesian framework with three levels of inference wasdeveloped for the optimization of parameters [8] The LS-SVMlab tool [17] developed in Matlab applying three Kerneltuning options (linear polynomial andRBF)was usedwithinthe ensemble of AI methods

34 Bias Correction Using the Quantile Mapping ApproachFirst the predictors were selected followed by the applicationof the multiple compositions of the SDSM model and the 7AI models 4 ANNs and 3 LS-SVM models (Table 3) Theoutput distributions of the ensemble of SDSM models andthe 7 AI models were grouped into two distinct populationsBoth these populations were corrected for bias and varianceinflation applying the quantile mapping technique The QMapplied to SDSM population distributions is from now oncalled the SDSM QM and the QM applied to AI the AI QM

The quantile mapping technique for bias correction andvariance inflation can be regarded as a statistical transforma-tion of the original distribution into a reference probabilitydistribution It aims to find the function that maps thedistribution of themodel variables into the distribution of theobserved variables Basically three types of approaches existto find themapping function they are adjustment (i) based ontheoretical distributions (ii) based on parametric transfor-mations and (iii) based on nonparametric transformations

After evaluation of several transformations the powerparametric transformation was applied because of its goodresults and the parsimony of the model [9] The powerparametric transformation is defined as

119875lowast

0

= 119887 (119875119898minus 1199090)119886

(8)

where 119875lowast0

and 119875119898are the corrected modeled and modeled

variables and 119886 119887 and 1199090are parameters to be determined

To find the parameters 119886 119887 and 1199090 the tool 119877 QMAP

was used [18] For SDSM QM and AI QM the parametersobtained after QM adjustment are presented in Table 4

35 Criteria for Model Evaluation For the qualitative assess-ment of the used methods of downscaling the long-termmonthly mean precipitation of both ensembles the SDSMand AI was compared with the long-term monthly meanobserved precipitation and for the quantitative evaluationstatistical metrics of the distributions of the time series ofobserved and modeled values for the validation period werecalculated In addition to the statistical metrics Box-Whiskerplots presenting both ensembles versus the observations weredrawn This type of graphical representation was selectedbecause in addition to the median the Box-Whisker plotdepicts the extreme values respectively the minimum andmaximum (the caps at the end of each box) and the outliersfalling more than 1 time of the interquartile range above thethird or below the first quartile (the points in the graph)

Advances in Meteorology 5

Table 4 Quantile mapping parameters for artificial intelligence andSDSM ensembles

Model Stations Parameters119886 119887 119909

0

AI

Biblian 003280 183727 087053El Labrado 000820 198426 minus857836Palmas 000334 221628 604480Gualaceo 031943 140124 1692140Paute 002791 194766 003257

SDSM

Biblian 000986 208840 321195El Labrado 039313 119070 minus4584738Palmas 000056 246774 minus1306023Gualaceo 000077 262716 minus114051Paute 004141 180403 391130

As statistical metrics the following were used

(1) Pearson correlation (119877) to evaluate the linear corre-lation

(2) Mean bias (MB) to evaluate the mean (the 50thpercentile) difference betweenmodeled and observeddistributions

(3) The root mean squared error (RMSE) to evaluate theerror between modeled and observed time series

(4) The interquartile relative fraction (IRF) to evaluatethe modeled variability representation relative to theobserved

IRF =119876119898

3

minus 119876119898

1

119876119900

3

minus 119876119900

1

(9)

where IRF is the interquartile relative fraction Avalue of IRF gt 1 represents overestimation of thevariability IRF = 1 is a perfect representation of thevariability and IRF lt 1 is an underestimation ofthe variability 119876119898

3

and 1198761199003

and the 75th modeled andobserved percentile119876119898

1

and1198761199001

and the 25thmodeledand observed percentile

(5) The absolute cumulative bias (ACB) to evaluate thebias of the 25th 50th and 75th percentiles or

ACB = 1003816100381610038161003816119876119898

1

minus 119876119900

1

1003816100381610038161003816 +1003816100381610038161003816119876119898

2

minus 119876119900

2

1003816100381610038161003816 +1003816100381610038161003816119876119898

3

minus 119876119900

3

1003816100381610038161003816 (10)

where ACB is the absolute cumulative bias A valueof ACB = 0 is a perfect representation of the threepercentiles (resp the 25th 50th and 75th percentile)of modeled and observed distributions while under-or overestimation indicates a divergence of ACB fromzero to positive values

4 Results and Discussion

41 Evaluation of SDSM and AI Ensembles

411 Relative Performance of ANN and LS-SVM Models Asmentioned before ANN and LS-SVM models were grouped

Table 5 Statistical metrics for ANN and LS-SVM ensembles

Station Metric ANN LS-SVM

El Labrado

Pearson correlation 049 058IRF 059 053

Mean-bias 420 616Cum bias 3163 3779RMSE 4073 3763

Gualaceo

Pearson correlation 070 071IRF 055 040

Mean-bias minus229 minus021Cum bias 3341 4170RMSE 3482 3533

Paute

Pearson correlation 055 054IRF 041 031

Mean-bias minus990 minus834Cum bias 4416 4821RMSE 3161 3104

Palmas

Pearson correlation 025 045IRF 045 053

Mean-bias minus185 787Cum bias 3699 3781RMSE 5244 4751

Biblian

Pearson correlation 067 065IRF 057 054

Mean-bias minus1839 minus705Cum bias 5234 3549RMSE 4475 4097

into one ensemble considering both models as transferfunction based models Although previous studies [19 20]demonstrated the relative superior performance of SVMbased downscalingmethods over other approaches includingANN based methods we compared for the first time in theregion to the best of our knowledge an ANN ensembleagainst a LS-SVM ensemble to evaluate their downscalingperformanceThe ensembles were not bias corrected in orderto evaluate their actual performance Table 5 presents thevalues of 119877 RMSE MB IRF and ACB comparing ANNand LS-SVM ensembles In El Labrado and Paute stationsimilar results of both ensembles are obtained Howeverboth ensembles for Gualaceo station underrepresent thevariability IRF is 055 and 040 for ANN and LS-SVMrespectivelyTherefore LS-SVMrepresents 15 less variabilitythan ANN ensemble TheMB for ANN is minus229mm whereasfor LS-SVM it is minus021mm which in monthly scale is verylow The ACB metric for ANN is 3341mm whereas for LS-SVM it is 4170mm meaning that although the MB is lowerfor LS-SVM the bias in the 25th and 75th percentiles is higherthan for the ANN ensemble In Palmas station 119877 is 025 and045 respectively for the ANN and LS-SVM ensembles IRFvalues of 045 and 053 for ANN and LS-SVM are obtainedindicating a greater representation in variability by the latterapproach However MB values of minus185 and 787 mean thatLS-SVMpresents more bias in the 50th percentile than ANNFor Biblian stationMB is minus1839mm and minus705mm andACB

6 Advances in Meteorology

Table 6 Statistical metrics for artificial intelligence and SDSM ensembles

Station Metric AI SDSM AI QM SDSM QM

El Labrado

Pearson correlation 058 037 058 038IRF 049 100 087 114

Mean-bias 437 minus4149 minus324 minus054Cum bias 3823 12689 1219 996RMSE 3770 6541 4167 5144

Gualaceo

Pearson correlation 074 053 072 050IRF 052 046 104 103

Mean-bias minus101 1028 433 185Cum bias 3402 4750 735 901RMSE 3392 3826 3287 4486

Paute

Pearson correlation 059 047 057 047IRF 036 047 080 089

Mean-bias minus1046 114 minus426 134Cum bias 4761 3173 1559 777RMSE 3060 3026 3113 3503

Palmas

Pearson correlation 044 016 044 014IRF 052 054 112 102

Mean-bias 739 1631 097 minus366Cum bias 3814 5693 877 1228RMSE 4745 5609 5573 6662

Biblian

Pearson correlation 066 046 067 045IRF 061 056 129 125

Mean-bias minus1112 minus287 minus121 166Cum bias 3501 2999 1891 1730RMSE 4173 4489 3987 5181

5234mm and 3549mm for ANN and LS-SVM ensemblesrespectively meaning a strong bias for the ANN ensemblewith respect to LS-SVM ensemble

For a qualitative evaluation of ANN and LS-SVM ensem-bles the Box-Whisker plots for the results during the valida-tion period are presented in Figure 2 For El Labrado stationboth ensembles similarly represent the median althoughthe low variance is clearly showed as measured by IRF inTable 5 For Gualaceo and Paute stations both ensemblesrepresent less variance with LS-SVM presenting lower val-ues The percentiles above 75th are strongly underestimatedin both stations making the necessity of correction on thedistribution of the ensembles evident In Palmas stationboth ensembles underrepresent the variance and the medianis rightly represented by ANN but overestimated by LS-SVM Finally for Biblian station the variance is stronglyunderestimated as well as the higher percentiles The medianis better represented by LS-SVM and underestimated byANN ensemble Bothmethods were able to perform similarlywell for the downscaling of monthly precipitation in theselected stations In addition comparison of the quantitativeanalysis based on the statistical metrics and the qualitativeanalysis based on Box-Whisker plots shed light on the relativeperformance of ANN and LS-SVMmethods

412 Comparison of SDSM and AI Ensembles Once theANN and LS-SVM ensembles were evaluated in a next step

ObservationsANNLS-SVM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

Prec

ipita

tion

(mm

)

M139 M138 M045 M137M141Paute

Figure 2 Box plots for ANN and LS-SVM ensembles evaluated instation El Labrado (M141) Gualaceo (M139) Paute (M138) Palmas(M045) and Biblian (M137)

the derived SDSM and AI ensembles were compared afterQMcorrection Table 6 depicts for the 5 climate stations in thePaute River basin of which data were used the comparisonbetween the SDSM and AI versus SDSM QM and AI QMThe evaluation between both sets is based on the statistical

Advances in Meteorology 7

ObservationsAI_QMSDSM_QM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

Prec

ipita

tion

(mm

)

M045M138 M137M141 M139Paute

Figure 3 Monthly precipitation box plots for artificial intelligenceand SDSM ensembles bias corrected Results evaluated in station ElLabrado (M141) Gualaceo (M139) Paute (M138) Palmas (M045)and Biblian (M137)

metrics R RMSE MB ACB and IRF For El Labrado stationSDSM QM presents lower correlation than AI QM with038 and 058 values Although SDSM QM presents a lowerbias than AI QM the RMSE of AI QM is a bit lower ForGualaceo station 119877 for AI QM and SDSM QM are 072 and05 RMSE as in El Labrado station is lower for AI QM thanfor SDSM QM with 3287 and 4486 respectively For Pautestation also 119877 is higher for AI QM with 057 and 047 forSDSM QM although the ACB is higher for AI QM with1559 and 777 for SDSM QM For Palmas there is a markeddifference in 119877 values with 044 for AI QM and 014 forSDSM QM depicting for the former a lower RMSE thanthe latter Similar for the Biblian station is the 119877 value forAI QM higher than for SDSM QM respectively 067 versus045 Analogous to the Palmas station a lower RMSE valuefor AI QM equal to 3987 was obtained compared to thecalculated RMSE of 5181 for SDSM QM

All other metrics in Table 6 present similar values Thestronger differences arise generally in the RMSE and 119877

statistical metrics which might be related to the fact thatQM corrects only the characteristic of the distribution ascan be seen in Figure 3 This figure presents the monthlyprecipitation Box-Whisker plots for AI and SDSM ensem-bles bias corrected for the 5 climate stations As can beobserved the distributions are fairly alike From the analysisfor all stations AI QM presented higher values of 119877 thanSDSM QM Similarly AI QMpresents better agreement withthe observed data with the exception of the Paute stationThis fact might point to a slightly better representation ofthe observed monthly precipitation distribution by AI QMensemble for this specific region

42 Evaluation of Intra-Annual Precipitation Seasonality Rep-resentation Whereas in previous section the entire distribu-tion of downscaled estimates was evaluated in the followingthe representation of seasonality is evaluated Although the

evaluation of seasonality representation might not help toquantify for example flooding events it is very importantfor issues related to water availability for hydroelectricitygeneration drinking water availability and agriculture Fur-ther the evaluation of seasonality representation is of specialimportance in the study region due to the low resolutionof GCMs unable to depict the precipitation regime due tomesoscale influences [5]

421 The Added Value of Quantile Mapping The QM cor-rection parameters for the power parametric transformationapplied to AI and SDSM ensembles are presented in Table 4The comparison of the multiyear monthly mean (mymm)precipitation of the SDSM with the SDSM QM ensembleis presented in Figures 4(a)ndash4(e) As shown in Figure 4(a)SDSM applied to the El Labrado station fails to capturethe observed seasonality However the performance biasand variance improved considerably after applying QMSeasonality applying SDSM to the Gualaceo (Figure 4(b))station is less correctly presented and fails to capture themaximum inApril and overestimates precipitation during thedry season in August Application of QM only corrects therepresentation in August but not in April The ensemble ofSDSM compositions represents well seasonality but under-estimates significantly the November precipitation depthApplication ofQM improves the representation of seasonalitybut does not improve the November estimate The SDSM inPaute station represents seasonality well but underestimatessignificantly the maximum in November QM applied toSDSM in Paute improves the performance of seasonalityyet fails to improve the representation of the Novemberprecipitation (Figure 4(c)) The SDSM approach calibratedto the observations of the Palmas station (Figure 4(d)) astation with unimodal regime (UM) depicts fairly correctseasonality notwithstanding the limited spatial extent of theUM regime and the poor representation of the mesoscaleinfluences in the synoptic predictors Application of QMnegatively affects the SDSM representation during the first 6months of the year but improves slightly the representationduring the remaining period of the year The seasonality ofthe Biblian station (Figure 4(e)) is properly represented bythe SDSM ensemble and as well as the SDSM QM Only theNovember peak in precipitation is captured by neither SDSMnor SDSM QM

The comparison of mymm of the AI with the AI QMensembles is presented in Figures 4(f)ndash4(j)TheAI emsembleunderestimates precipitation in April overestimate it in Julyand August and underestimate it in November althoughat some extent it represents seasonality QM improves theintra-annual variability but still the November maximumis not correctly estimated The AI ensemble in Gualaceo(Figure 4(g)) station captures well both peaks in Apriland November but underestimates precipitation in AugustThe estimation in August is considerably improved aftercorrection of the bias and the inflation of the variance In thePaute station (Figure 4(h)) are both the peaks respectively inApril and November and the minimum in August were wellcaptured by the AI ensemble while QM further improves thedistribution of the median of the monthly precipitation The

8 Advances in Meteorology

SDSMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(a)

Obs_GualaceoSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(b)

Obs_PauteSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(c)

Obs_PalmasSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(d)

Obs_Bibli naSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(e)

AIObs_El Labrado

AI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(f)

Figure 4 Continued

Advances in Meteorology 9

Obs_GualaceoAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(g)

Obs_PauteAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(h)

Obs_PalmasAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(i)

Obs_Bibli naAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(j)

Figure 4 Multiyear monthly mean precipitation for SDSM ensemble and SDSM ensemble bias corrected (andashe) and multiyear monthly meanprecipitation for AI and AI bias corrected (fndashj)

AI ensemble represents poorly the distribution of the Palmasstation (Figure 4(i) UM regime) even after QM applicationFor the Biblian station (Figure 4(j)) the AI QM captures theApril peak one month earlier but fails to correctly depict themagnitude of the November peak

Results clearly reveal that the application of QM tothe output of both modeling approaches SDSM and AIoverall improves the representation of seasonality as wellas the representation of rainy and dry periods Howeverboth approaches underestimate the median value of theprecipitation depth inNovemberThis fact could indicate thatthe set of synoptic predictors do not include a variable thatis related to an enhancement of precipitation in this periodFurther studies are needed to determine the variables andrelated phenomena

Table 7 Pearson correlations between observations and SDSM QMand AI QMmodels

Station AI QM SDSM QMEl Labrado 0741 0516Gualaceo 0946 0672Paute 0730 0629Palmas 0788 0593Biblian 0691 0532

422 Representation of Monthly Variability by DownscaledResults To compare the representativeness of SDSM QMand AI QM the correlation of the mymm time serieswith the observed values is shown in Table 7 For all

10 Advances in Meteorology

AI_QMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(a)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(b)

AI_QMObs_Gualaceo

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(c)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(d)

AI_QMObs_Paute

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(e)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(f)

Figure 5 Continued

Advances in Meteorology 11

AI_QMObs_Palmas

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(g)

ObservationsSDSM_QMAI_QM

Prec

ipita

tion

(mm

)

150

100

250

350

300

200

50

0

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(h)

AI_QMObs_Bibli na

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(i)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(j)

Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

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MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

4 Advances in Meteorology

Table 3 Artificial intelligence models

Model Type Transfer function1

Ann

Linear amp 1 hidden layer2 Sigmoidal amp 1 hidden layer3 Linear amp 2 hidden layers4 Sigmoidal amp 2 hidden layers5

LS-SVMLinear

6 Polynomial7 Radial basis functions

33 Downscaling Using LS-SVM Support vector machinesSVM [7] solve nonlinear classifications and estimations offunctions and densities using quadratic programming Aleast squares support vector machine LS-SVM [8] is areformulation of a SVM replacing the solution of the convexquadratic programming problem by the solution of a set oflinear equations As explained by [8] it is possible to adoptinto LS-SVM the robustness sparseness and weightings

Due to the fact that LS-SVM has more recent applicationthan ANN and SDSM techniques for the downscaling ofGCMs we present here a succinct description of LS-SVMtheory For a more in deep description of LS-SVM see [8]

Let us consider 119909 isin R119899 and 119910 isin R the LS-SVM modelmapping the 119909 into a feature space is

119910 = 119908119879

120593 (119909) + 119887 (1)

The optimization problem can be stated as

min119908119890

Γ (119908 119890) =1

2119908119879

119908 + 1205741

2

119873

sum

119894=1

1198902

119894

(2)

where 119890 and 120574 are the error and the regularization parameterrespectively The minimization of the cost function Γ(119908 119890) issubject to the constrains

119910119894= 119908119879

120593 (119909119894) + 119887 + 119890

119894 (3)

The Lagrangian of the optimization is

L (119908 119887 119890 120572) = Γ (119908 119890) minus

119873

sum

119894=1

120572119894(119908119879

120593 (119909119894) + 119887 + 119890

119894minus 119910119894) (4)

where 120572119894are the Lagrangian multipliers

After considering the conditions for optimality

[120597L

120597119908120597L

120597119887120597L

120597119890119894

120597L

120597120572119894

]

119879

= [0 0 0 0]119879

(5)

We obtain the matrix equation

[

0 1

1 Ω minus 120574minus1

119868

] [

119887

120572

] = [

0

119910

] (6)

whereΩ119894119895= 120593(119909

119894)119879

120593(119909119895) is the Kernel function119870(119909

119894 119909119895) and

119868 is the identity matrix

Finally the LS-SVMmodel for function estimation is

119910 (119909) =

119873

sum

119894=1

120572119894119870(119909119894 119909) + 119887 (7)

A Bayesian framework with three levels of inference wasdeveloped for the optimization of parameters [8] The LS-SVMlab tool [17] developed in Matlab applying three Kerneltuning options (linear polynomial andRBF)was usedwithinthe ensemble of AI methods

34 Bias Correction Using the Quantile Mapping ApproachFirst the predictors were selected followed by the applicationof the multiple compositions of the SDSM model and the 7AI models 4 ANNs and 3 LS-SVM models (Table 3) Theoutput distributions of the ensemble of SDSM models andthe 7 AI models were grouped into two distinct populationsBoth these populations were corrected for bias and varianceinflation applying the quantile mapping technique The QMapplied to SDSM population distributions is from now oncalled the SDSM QM and the QM applied to AI the AI QM

The quantile mapping technique for bias correction andvariance inflation can be regarded as a statistical transforma-tion of the original distribution into a reference probabilitydistribution It aims to find the function that maps thedistribution of themodel variables into the distribution of theobserved variables Basically three types of approaches existto find themapping function they are adjustment (i) based ontheoretical distributions (ii) based on parametric transfor-mations and (iii) based on nonparametric transformations

After evaluation of several transformations the powerparametric transformation was applied because of its goodresults and the parsimony of the model [9] The powerparametric transformation is defined as

119875lowast

0

= 119887 (119875119898minus 1199090)119886

(8)

where 119875lowast0

and 119875119898are the corrected modeled and modeled

variables and 119886 119887 and 1199090are parameters to be determined

To find the parameters 119886 119887 and 1199090 the tool 119877 QMAP

was used [18] For SDSM QM and AI QM the parametersobtained after QM adjustment are presented in Table 4

35 Criteria for Model Evaluation For the qualitative assess-ment of the used methods of downscaling the long-termmonthly mean precipitation of both ensembles the SDSMand AI was compared with the long-term monthly meanobserved precipitation and for the quantitative evaluationstatistical metrics of the distributions of the time series ofobserved and modeled values for the validation period werecalculated In addition to the statistical metrics Box-Whiskerplots presenting both ensembles versus the observations weredrawn This type of graphical representation was selectedbecause in addition to the median the Box-Whisker plotdepicts the extreme values respectively the minimum andmaximum (the caps at the end of each box) and the outliersfalling more than 1 time of the interquartile range above thethird or below the first quartile (the points in the graph)

Advances in Meteorology 5

Table 4 Quantile mapping parameters for artificial intelligence andSDSM ensembles

Model Stations Parameters119886 119887 119909

0

AI

Biblian 003280 183727 087053El Labrado 000820 198426 minus857836Palmas 000334 221628 604480Gualaceo 031943 140124 1692140Paute 002791 194766 003257

SDSM

Biblian 000986 208840 321195El Labrado 039313 119070 minus4584738Palmas 000056 246774 minus1306023Gualaceo 000077 262716 minus114051Paute 004141 180403 391130

As statistical metrics the following were used

(1) Pearson correlation (119877) to evaluate the linear corre-lation

(2) Mean bias (MB) to evaluate the mean (the 50thpercentile) difference betweenmodeled and observeddistributions

(3) The root mean squared error (RMSE) to evaluate theerror between modeled and observed time series

(4) The interquartile relative fraction (IRF) to evaluatethe modeled variability representation relative to theobserved

IRF =119876119898

3

minus 119876119898

1

119876119900

3

minus 119876119900

1

(9)

where IRF is the interquartile relative fraction Avalue of IRF gt 1 represents overestimation of thevariability IRF = 1 is a perfect representation of thevariability and IRF lt 1 is an underestimation ofthe variability 119876119898

3

and 1198761199003

and the 75th modeled andobserved percentile119876119898

1

and1198761199001

and the 25thmodeledand observed percentile

(5) The absolute cumulative bias (ACB) to evaluate thebias of the 25th 50th and 75th percentiles or

ACB = 1003816100381610038161003816119876119898

1

minus 119876119900

1

1003816100381610038161003816 +1003816100381610038161003816119876119898

2

minus 119876119900

2

1003816100381610038161003816 +1003816100381610038161003816119876119898

3

minus 119876119900

3

1003816100381610038161003816 (10)

where ACB is the absolute cumulative bias A valueof ACB = 0 is a perfect representation of the threepercentiles (resp the 25th 50th and 75th percentile)of modeled and observed distributions while under-or overestimation indicates a divergence of ACB fromzero to positive values

4 Results and Discussion

41 Evaluation of SDSM and AI Ensembles

411 Relative Performance of ANN and LS-SVM Models Asmentioned before ANN and LS-SVM models were grouped

Table 5 Statistical metrics for ANN and LS-SVM ensembles

Station Metric ANN LS-SVM

El Labrado

Pearson correlation 049 058IRF 059 053

Mean-bias 420 616Cum bias 3163 3779RMSE 4073 3763

Gualaceo

Pearson correlation 070 071IRF 055 040

Mean-bias minus229 minus021Cum bias 3341 4170RMSE 3482 3533

Paute

Pearson correlation 055 054IRF 041 031

Mean-bias minus990 minus834Cum bias 4416 4821RMSE 3161 3104

Palmas

Pearson correlation 025 045IRF 045 053

Mean-bias minus185 787Cum bias 3699 3781RMSE 5244 4751

Biblian

Pearson correlation 067 065IRF 057 054

Mean-bias minus1839 minus705Cum bias 5234 3549RMSE 4475 4097

into one ensemble considering both models as transferfunction based models Although previous studies [19 20]demonstrated the relative superior performance of SVMbased downscalingmethods over other approaches includingANN based methods we compared for the first time in theregion to the best of our knowledge an ANN ensembleagainst a LS-SVM ensemble to evaluate their downscalingperformanceThe ensembles were not bias corrected in orderto evaluate their actual performance Table 5 presents thevalues of 119877 RMSE MB IRF and ACB comparing ANNand LS-SVM ensembles In El Labrado and Paute stationsimilar results of both ensembles are obtained Howeverboth ensembles for Gualaceo station underrepresent thevariability IRF is 055 and 040 for ANN and LS-SVMrespectivelyTherefore LS-SVMrepresents 15 less variabilitythan ANN ensemble TheMB for ANN is minus229mm whereasfor LS-SVM it is minus021mm which in monthly scale is verylow The ACB metric for ANN is 3341mm whereas for LS-SVM it is 4170mm meaning that although the MB is lowerfor LS-SVM the bias in the 25th and 75th percentiles is higherthan for the ANN ensemble In Palmas station 119877 is 025 and045 respectively for the ANN and LS-SVM ensembles IRFvalues of 045 and 053 for ANN and LS-SVM are obtainedindicating a greater representation in variability by the latterapproach However MB values of minus185 and 787 mean thatLS-SVMpresents more bias in the 50th percentile than ANNFor Biblian stationMB is minus1839mm and minus705mm andACB

6 Advances in Meteorology

Table 6 Statistical metrics for artificial intelligence and SDSM ensembles

Station Metric AI SDSM AI QM SDSM QM

El Labrado

Pearson correlation 058 037 058 038IRF 049 100 087 114

Mean-bias 437 minus4149 minus324 minus054Cum bias 3823 12689 1219 996RMSE 3770 6541 4167 5144

Gualaceo

Pearson correlation 074 053 072 050IRF 052 046 104 103

Mean-bias minus101 1028 433 185Cum bias 3402 4750 735 901RMSE 3392 3826 3287 4486

Paute

Pearson correlation 059 047 057 047IRF 036 047 080 089

Mean-bias minus1046 114 minus426 134Cum bias 4761 3173 1559 777RMSE 3060 3026 3113 3503

Palmas

Pearson correlation 044 016 044 014IRF 052 054 112 102

Mean-bias 739 1631 097 minus366Cum bias 3814 5693 877 1228RMSE 4745 5609 5573 6662

Biblian

Pearson correlation 066 046 067 045IRF 061 056 129 125

Mean-bias minus1112 minus287 minus121 166Cum bias 3501 2999 1891 1730RMSE 4173 4489 3987 5181

5234mm and 3549mm for ANN and LS-SVM ensemblesrespectively meaning a strong bias for the ANN ensemblewith respect to LS-SVM ensemble

For a qualitative evaluation of ANN and LS-SVM ensem-bles the Box-Whisker plots for the results during the valida-tion period are presented in Figure 2 For El Labrado stationboth ensembles similarly represent the median althoughthe low variance is clearly showed as measured by IRF inTable 5 For Gualaceo and Paute stations both ensemblesrepresent less variance with LS-SVM presenting lower val-ues The percentiles above 75th are strongly underestimatedin both stations making the necessity of correction on thedistribution of the ensembles evident In Palmas stationboth ensembles underrepresent the variance and the medianis rightly represented by ANN but overestimated by LS-SVM Finally for Biblian station the variance is stronglyunderestimated as well as the higher percentiles The medianis better represented by LS-SVM and underestimated byANN ensemble Bothmethods were able to perform similarlywell for the downscaling of monthly precipitation in theselected stations In addition comparison of the quantitativeanalysis based on the statistical metrics and the qualitativeanalysis based on Box-Whisker plots shed light on the relativeperformance of ANN and LS-SVMmethods

412 Comparison of SDSM and AI Ensembles Once theANN and LS-SVM ensembles were evaluated in a next step

ObservationsANNLS-SVM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

Prec

ipita

tion

(mm

)

M139 M138 M045 M137M141Paute

Figure 2 Box plots for ANN and LS-SVM ensembles evaluated instation El Labrado (M141) Gualaceo (M139) Paute (M138) Palmas(M045) and Biblian (M137)

the derived SDSM and AI ensembles were compared afterQMcorrection Table 6 depicts for the 5 climate stations in thePaute River basin of which data were used the comparisonbetween the SDSM and AI versus SDSM QM and AI QMThe evaluation between both sets is based on the statistical

Advances in Meteorology 7

ObservationsAI_QMSDSM_QM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

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ipita

tion

(mm

)

M045M138 M137M141 M139Paute

Figure 3 Monthly precipitation box plots for artificial intelligenceand SDSM ensembles bias corrected Results evaluated in station ElLabrado (M141) Gualaceo (M139) Paute (M138) Palmas (M045)and Biblian (M137)

metrics R RMSE MB ACB and IRF For El Labrado stationSDSM QM presents lower correlation than AI QM with038 and 058 values Although SDSM QM presents a lowerbias than AI QM the RMSE of AI QM is a bit lower ForGualaceo station 119877 for AI QM and SDSM QM are 072 and05 RMSE as in El Labrado station is lower for AI QM thanfor SDSM QM with 3287 and 4486 respectively For Pautestation also 119877 is higher for AI QM with 057 and 047 forSDSM QM although the ACB is higher for AI QM with1559 and 777 for SDSM QM For Palmas there is a markeddifference in 119877 values with 044 for AI QM and 014 forSDSM QM depicting for the former a lower RMSE thanthe latter Similar for the Biblian station is the 119877 value forAI QM higher than for SDSM QM respectively 067 versus045 Analogous to the Palmas station a lower RMSE valuefor AI QM equal to 3987 was obtained compared to thecalculated RMSE of 5181 for SDSM QM

All other metrics in Table 6 present similar values Thestronger differences arise generally in the RMSE and 119877

statistical metrics which might be related to the fact thatQM corrects only the characteristic of the distribution ascan be seen in Figure 3 This figure presents the monthlyprecipitation Box-Whisker plots for AI and SDSM ensem-bles bias corrected for the 5 climate stations As can beobserved the distributions are fairly alike From the analysisfor all stations AI QM presented higher values of 119877 thanSDSM QM Similarly AI QMpresents better agreement withthe observed data with the exception of the Paute stationThis fact might point to a slightly better representation ofthe observed monthly precipitation distribution by AI QMensemble for this specific region

42 Evaluation of Intra-Annual Precipitation Seasonality Rep-resentation Whereas in previous section the entire distribu-tion of downscaled estimates was evaluated in the followingthe representation of seasonality is evaluated Although the

evaluation of seasonality representation might not help toquantify for example flooding events it is very importantfor issues related to water availability for hydroelectricitygeneration drinking water availability and agriculture Fur-ther the evaluation of seasonality representation is of specialimportance in the study region due to the low resolutionof GCMs unable to depict the precipitation regime due tomesoscale influences [5]

421 The Added Value of Quantile Mapping The QM cor-rection parameters for the power parametric transformationapplied to AI and SDSM ensembles are presented in Table 4The comparison of the multiyear monthly mean (mymm)precipitation of the SDSM with the SDSM QM ensembleis presented in Figures 4(a)ndash4(e) As shown in Figure 4(a)SDSM applied to the El Labrado station fails to capturethe observed seasonality However the performance biasand variance improved considerably after applying QMSeasonality applying SDSM to the Gualaceo (Figure 4(b))station is less correctly presented and fails to capture themaximum inApril and overestimates precipitation during thedry season in August Application of QM only corrects therepresentation in August but not in April The ensemble ofSDSM compositions represents well seasonality but under-estimates significantly the November precipitation depthApplication ofQM improves the representation of seasonalitybut does not improve the November estimate The SDSM inPaute station represents seasonality well but underestimatessignificantly the maximum in November QM applied toSDSM in Paute improves the performance of seasonalityyet fails to improve the representation of the Novemberprecipitation (Figure 4(c)) The SDSM approach calibratedto the observations of the Palmas station (Figure 4(d)) astation with unimodal regime (UM) depicts fairly correctseasonality notwithstanding the limited spatial extent of theUM regime and the poor representation of the mesoscaleinfluences in the synoptic predictors Application of QMnegatively affects the SDSM representation during the first 6months of the year but improves slightly the representationduring the remaining period of the year The seasonality ofthe Biblian station (Figure 4(e)) is properly represented bythe SDSM ensemble and as well as the SDSM QM Only theNovember peak in precipitation is captured by neither SDSMnor SDSM QM

The comparison of mymm of the AI with the AI QMensembles is presented in Figures 4(f)ndash4(j)TheAI emsembleunderestimates precipitation in April overestimate it in Julyand August and underestimate it in November althoughat some extent it represents seasonality QM improves theintra-annual variability but still the November maximumis not correctly estimated The AI ensemble in Gualaceo(Figure 4(g)) station captures well both peaks in Apriland November but underestimates precipitation in AugustThe estimation in August is considerably improved aftercorrection of the bias and the inflation of the variance In thePaute station (Figure 4(h)) are both the peaks respectively inApril and November and the minimum in August were wellcaptured by the AI ensemble while QM further improves thedistribution of the median of the monthly precipitation The

8 Advances in Meteorology

SDSMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(a)

Obs_GualaceoSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

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Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(b)

Obs_PauteSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(c)

Obs_PalmasSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(d)

Obs_Bibli naSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(e)

AIObs_El Labrado

AI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(f)

Figure 4 Continued

Advances in Meteorology 9

Obs_GualaceoAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(g)

Obs_PauteAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(h)

Obs_PalmasAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(i)

Obs_Bibli naAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(j)

Figure 4 Multiyear monthly mean precipitation for SDSM ensemble and SDSM ensemble bias corrected (andashe) and multiyear monthly meanprecipitation for AI and AI bias corrected (fndashj)

AI ensemble represents poorly the distribution of the Palmasstation (Figure 4(i) UM regime) even after QM applicationFor the Biblian station (Figure 4(j)) the AI QM captures theApril peak one month earlier but fails to correctly depict themagnitude of the November peak

Results clearly reveal that the application of QM tothe output of both modeling approaches SDSM and AIoverall improves the representation of seasonality as wellas the representation of rainy and dry periods Howeverboth approaches underestimate the median value of theprecipitation depth inNovemberThis fact could indicate thatthe set of synoptic predictors do not include a variable thatis related to an enhancement of precipitation in this periodFurther studies are needed to determine the variables andrelated phenomena

Table 7 Pearson correlations between observations and SDSM QMand AI QMmodels

Station AI QM SDSM QMEl Labrado 0741 0516Gualaceo 0946 0672Paute 0730 0629Palmas 0788 0593Biblian 0691 0532

422 Representation of Monthly Variability by DownscaledResults To compare the representativeness of SDSM QMand AI QM the correlation of the mymm time serieswith the observed values is shown in Table 7 For all

10 Advances in Meteorology

AI_QMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

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June July

Febr

uary

Nov

embe

r

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Augu

st

Dec

embe

r

Janu

ary

(a)

ObservationsSDSM_QMAI_QM

0

50

100

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250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

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June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(b)

AI_QMObs_Gualaceo

SDSM_QM

0

20

40

60

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100

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140

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180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

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embe

r

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June July

Febr

uary

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embe

r

April

Augu

st

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embe

r

Janu

ary

(c)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

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embe

r

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June July

Febr

uary

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embe

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April

Augu

st

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embe

r

Janu

ary

(d)

AI_QMObs_Paute

SDSM_QM

0

20

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180

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ipita

tion

(mm

)

Oct

ober

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ch

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embe

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uary

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embe

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st

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embe

r

Janu

ary

(e)

ObservationsSDSM_QMAI_QM

0

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250

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ipita

tion

(mm

)

Oct

ober

Mar

ch

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embe

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June July

Febr

uary

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embe

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st

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embe

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Janu

ary

(f)

Figure 5 Continued

Advances in Meteorology 11

AI_QMObs_Palmas

SDSM_QM

0

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180

200Pr

ecip

itatio

n (m

m)

Oct

ober

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ch

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embe

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Febr

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embe

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st

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embe

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Janu

ary

(g)

ObservationsSDSM_QMAI_QM

Prec

ipita

tion

(mm

)

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100

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200

50

0

Oct

ober

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ch

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embe

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Febr

uary

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embe

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Augu

st

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embe

r

Janu

ary

(h)

AI_QMObs_Bibli na

SDSM_QM

0

20

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100

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140

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180

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ipita

tion

(mm

)

Oct

ober

Mar

ch

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embe

r

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June July

Febr

uary

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embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(i)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(j)

Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Geology Advances in

Advances in Meteorology 5

Table 4 Quantile mapping parameters for artificial intelligence andSDSM ensembles

Model Stations Parameters119886 119887 119909

0

AI

Biblian 003280 183727 087053El Labrado 000820 198426 minus857836Palmas 000334 221628 604480Gualaceo 031943 140124 1692140Paute 002791 194766 003257

SDSM

Biblian 000986 208840 321195El Labrado 039313 119070 minus4584738Palmas 000056 246774 minus1306023Gualaceo 000077 262716 minus114051Paute 004141 180403 391130

As statistical metrics the following were used

(1) Pearson correlation (119877) to evaluate the linear corre-lation

(2) Mean bias (MB) to evaluate the mean (the 50thpercentile) difference betweenmodeled and observeddistributions

(3) The root mean squared error (RMSE) to evaluate theerror between modeled and observed time series

(4) The interquartile relative fraction (IRF) to evaluatethe modeled variability representation relative to theobserved

IRF =119876119898

3

minus 119876119898

1

119876119900

3

minus 119876119900

1

(9)

where IRF is the interquartile relative fraction Avalue of IRF gt 1 represents overestimation of thevariability IRF = 1 is a perfect representation of thevariability and IRF lt 1 is an underestimation ofthe variability 119876119898

3

and 1198761199003

and the 75th modeled andobserved percentile119876119898

1

and1198761199001

and the 25thmodeledand observed percentile

(5) The absolute cumulative bias (ACB) to evaluate thebias of the 25th 50th and 75th percentiles or

ACB = 1003816100381610038161003816119876119898

1

minus 119876119900

1

1003816100381610038161003816 +1003816100381610038161003816119876119898

2

minus 119876119900

2

1003816100381610038161003816 +1003816100381610038161003816119876119898

3

minus 119876119900

3

1003816100381610038161003816 (10)

where ACB is the absolute cumulative bias A valueof ACB = 0 is a perfect representation of the threepercentiles (resp the 25th 50th and 75th percentile)of modeled and observed distributions while under-or overestimation indicates a divergence of ACB fromzero to positive values

4 Results and Discussion

41 Evaluation of SDSM and AI Ensembles

411 Relative Performance of ANN and LS-SVM Models Asmentioned before ANN and LS-SVM models were grouped

Table 5 Statistical metrics for ANN and LS-SVM ensembles

Station Metric ANN LS-SVM

El Labrado

Pearson correlation 049 058IRF 059 053

Mean-bias 420 616Cum bias 3163 3779RMSE 4073 3763

Gualaceo

Pearson correlation 070 071IRF 055 040

Mean-bias minus229 minus021Cum bias 3341 4170RMSE 3482 3533

Paute

Pearson correlation 055 054IRF 041 031

Mean-bias minus990 minus834Cum bias 4416 4821RMSE 3161 3104

Palmas

Pearson correlation 025 045IRF 045 053

Mean-bias minus185 787Cum bias 3699 3781RMSE 5244 4751

Biblian

Pearson correlation 067 065IRF 057 054

Mean-bias minus1839 minus705Cum bias 5234 3549RMSE 4475 4097

into one ensemble considering both models as transferfunction based models Although previous studies [19 20]demonstrated the relative superior performance of SVMbased downscalingmethods over other approaches includingANN based methods we compared for the first time in theregion to the best of our knowledge an ANN ensembleagainst a LS-SVM ensemble to evaluate their downscalingperformanceThe ensembles were not bias corrected in orderto evaluate their actual performance Table 5 presents thevalues of 119877 RMSE MB IRF and ACB comparing ANNand LS-SVM ensembles In El Labrado and Paute stationsimilar results of both ensembles are obtained Howeverboth ensembles for Gualaceo station underrepresent thevariability IRF is 055 and 040 for ANN and LS-SVMrespectivelyTherefore LS-SVMrepresents 15 less variabilitythan ANN ensemble TheMB for ANN is minus229mm whereasfor LS-SVM it is minus021mm which in monthly scale is verylow The ACB metric for ANN is 3341mm whereas for LS-SVM it is 4170mm meaning that although the MB is lowerfor LS-SVM the bias in the 25th and 75th percentiles is higherthan for the ANN ensemble In Palmas station 119877 is 025 and045 respectively for the ANN and LS-SVM ensembles IRFvalues of 045 and 053 for ANN and LS-SVM are obtainedindicating a greater representation in variability by the latterapproach However MB values of minus185 and 787 mean thatLS-SVMpresents more bias in the 50th percentile than ANNFor Biblian stationMB is minus1839mm and minus705mm andACB

6 Advances in Meteorology

Table 6 Statistical metrics for artificial intelligence and SDSM ensembles

Station Metric AI SDSM AI QM SDSM QM

El Labrado

Pearson correlation 058 037 058 038IRF 049 100 087 114

Mean-bias 437 minus4149 minus324 minus054Cum bias 3823 12689 1219 996RMSE 3770 6541 4167 5144

Gualaceo

Pearson correlation 074 053 072 050IRF 052 046 104 103

Mean-bias minus101 1028 433 185Cum bias 3402 4750 735 901RMSE 3392 3826 3287 4486

Paute

Pearson correlation 059 047 057 047IRF 036 047 080 089

Mean-bias minus1046 114 minus426 134Cum bias 4761 3173 1559 777RMSE 3060 3026 3113 3503

Palmas

Pearson correlation 044 016 044 014IRF 052 054 112 102

Mean-bias 739 1631 097 minus366Cum bias 3814 5693 877 1228RMSE 4745 5609 5573 6662

Biblian

Pearson correlation 066 046 067 045IRF 061 056 129 125

Mean-bias minus1112 minus287 minus121 166Cum bias 3501 2999 1891 1730RMSE 4173 4489 3987 5181

5234mm and 3549mm for ANN and LS-SVM ensemblesrespectively meaning a strong bias for the ANN ensemblewith respect to LS-SVM ensemble

For a qualitative evaluation of ANN and LS-SVM ensem-bles the Box-Whisker plots for the results during the valida-tion period are presented in Figure 2 For El Labrado stationboth ensembles similarly represent the median althoughthe low variance is clearly showed as measured by IRF inTable 5 For Gualaceo and Paute stations both ensemblesrepresent less variance with LS-SVM presenting lower val-ues The percentiles above 75th are strongly underestimatedin both stations making the necessity of correction on thedistribution of the ensembles evident In Palmas stationboth ensembles underrepresent the variance and the medianis rightly represented by ANN but overestimated by LS-SVM Finally for Biblian station the variance is stronglyunderestimated as well as the higher percentiles The medianis better represented by LS-SVM and underestimated byANN ensemble Bothmethods were able to perform similarlywell for the downscaling of monthly precipitation in theselected stations In addition comparison of the quantitativeanalysis based on the statistical metrics and the qualitativeanalysis based on Box-Whisker plots shed light on the relativeperformance of ANN and LS-SVMmethods

412 Comparison of SDSM and AI Ensembles Once theANN and LS-SVM ensembles were evaluated in a next step

ObservationsANNLS-SVM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

Prec

ipita

tion

(mm

)

M139 M138 M045 M137M141Paute

Figure 2 Box plots for ANN and LS-SVM ensembles evaluated instation El Labrado (M141) Gualaceo (M139) Paute (M138) Palmas(M045) and Biblian (M137)

the derived SDSM and AI ensembles were compared afterQMcorrection Table 6 depicts for the 5 climate stations in thePaute River basin of which data were used the comparisonbetween the SDSM and AI versus SDSM QM and AI QMThe evaluation between both sets is based on the statistical

Advances in Meteorology 7

ObservationsAI_QMSDSM_QM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

Prec

ipita

tion

(mm

)

M045M138 M137M141 M139Paute

Figure 3 Monthly precipitation box plots for artificial intelligenceand SDSM ensembles bias corrected Results evaluated in station ElLabrado (M141) Gualaceo (M139) Paute (M138) Palmas (M045)and Biblian (M137)

metrics R RMSE MB ACB and IRF For El Labrado stationSDSM QM presents lower correlation than AI QM with038 and 058 values Although SDSM QM presents a lowerbias than AI QM the RMSE of AI QM is a bit lower ForGualaceo station 119877 for AI QM and SDSM QM are 072 and05 RMSE as in El Labrado station is lower for AI QM thanfor SDSM QM with 3287 and 4486 respectively For Pautestation also 119877 is higher for AI QM with 057 and 047 forSDSM QM although the ACB is higher for AI QM with1559 and 777 for SDSM QM For Palmas there is a markeddifference in 119877 values with 044 for AI QM and 014 forSDSM QM depicting for the former a lower RMSE thanthe latter Similar for the Biblian station is the 119877 value forAI QM higher than for SDSM QM respectively 067 versus045 Analogous to the Palmas station a lower RMSE valuefor AI QM equal to 3987 was obtained compared to thecalculated RMSE of 5181 for SDSM QM

All other metrics in Table 6 present similar values Thestronger differences arise generally in the RMSE and 119877

statistical metrics which might be related to the fact thatQM corrects only the characteristic of the distribution ascan be seen in Figure 3 This figure presents the monthlyprecipitation Box-Whisker plots for AI and SDSM ensem-bles bias corrected for the 5 climate stations As can beobserved the distributions are fairly alike From the analysisfor all stations AI QM presented higher values of 119877 thanSDSM QM Similarly AI QMpresents better agreement withthe observed data with the exception of the Paute stationThis fact might point to a slightly better representation ofthe observed monthly precipitation distribution by AI QMensemble for this specific region

42 Evaluation of Intra-Annual Precipitation Seasonality Rep-resentation Whereas in previous section the entire distribu-tion of downscaled estimates was evaluated in the followingthe representation of seasonality is evaluated Although the

evaluation of seasonality representation might not help toquantify for example flooding events it is very importantfor issues related to water availability for hydroelectricitygeneration drinking water availability and agriculture Fur-ther the evaluation of seasonality representation is of specialimportance in the study region due to the low resolutionof GCMs unable to depict the precipitation regime due tomesoscale influences [5]

421 The Added Value of Quantile Mapping The QM cor-rection parameters for the power parametric transformationapplied to AI and SDSM ensembles are presented in Table 4The comparison of the multiyear monthly mean (mymm)precipitation of the SDSM with the SDSM QM ensembleis presented in Figures 4(a)ndash4(e) As shown in Figure 4(a)SDSM applied to the El Labrado station fails to capturethe observed seasonality However the performance biasand variance improved considerably after applying QMSeasonality applying SDSM to the Gualaceo (Figure 4(b))station is less correctly presented and fails to capture themaximum inApril and overestimates precipitation during thedry season in August Application of QM only corrects therepresentation in August but not in April The ensemble ofSDSM compositions represents well seasonality but under-estimates significantly the November precipitation depthApplication ofQM improves the representation of seasonalitybut does not improve the November estimate The SDSM inPaute station represents seasonality well but underestimatessignificantly the maximum in November QM applied toSDSM in Paute improves the performance of seasonalityyet fails to improve the representation of the Novemberprecipitation (Figure 4(c)) The SDSM approach calibratedto the observations of the Palmas station (Figure 4(d)) astation with unimodal regime (UM) depicts fairly correctseasonality notwithstanding the limited spatial extent of theUM regime and the poor representation of the mesoscaleinfluences in the synoptic predictors Application of QMnegatively affects the SDSM representation during the first 6months of the year but improves slightly the representationduring the remaining period of the year The seasonality ofthe Biblian station (Figure 4(e)) is properly represented bythe SDSM ensemble and as well as the SDSM QM Only theNovember peak in precipitation is captured by neither SDSMnor SDSM QM

The comparison of mymm of the AI with the AI QMensembles is presented in Figures 4(f)ndash4(j)TheAI emsembleunderestimates precipitation in April overestimate it in Julyand August and underestimate it in November althoughat some extent it represents seasonality QM improves theintra-annual variability but still the November maximumis not correctly estimated The AI ensemble in Gualaceo(Figure 4(g)) station captures well both peaks in Apriland November but underestimates precipitation in AugustThe estimation in August is considerably improved aftercorrection of the bias and the inflation of the variance In thePaute station (Figure 4(h)) are both the peaks respectively inApril and November and the minimum in August were wellcaptured by the AI ensemble while QM further improves thedistribution of the median of the monthly precipitation The

8 Advances in Meteorology

SDSMObs_El Labrado

SDSM_QM

0

20

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60

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100

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180

200

Prec

ipita

tion

(mm

)

Oct

ober

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ch

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embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(a)

Obs_GualaceoSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(b)

Obs_PauteSDSMSDSM_QM

0

20

40

60

80

100

120

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160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(c)

Obs_PalmasSDSMSDSM_QM

0

20

40

60

80

100

120

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160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

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embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(d)

Obs_Bibli naSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

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June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(e)

AIObs_El Labrado

AI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(f)

Figure 4 Continued

Advances in Meteorology 9

Obs_GualaceoAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(g)

Obs_PauteAIAI_QM

0

20

40

60

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180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

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embe

r

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June July

Augu

st

April

Febr

uary

Nov

embe

r

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embe

r

Janu

ary

(h)

Obs_PalmasAIAI_QM

0

20

40

60

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200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

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embe

r

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June July

Augu

st

April

Febr

uary

Nov

embe

r

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embe

r

Janu

ary

(i)

Obs_Bibli naAIAI_QM

0

20

40

60

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180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(j)

Figure 4 Multiyear monthly mean precipitation for SDSM ensemble and SDSM ensemble bias corrected (andashe) and multiyear monthly meanprecipitation for AI and AI bias corrected (fndashj)

AI ensemble represents poorly the distribution of the Palmasstation (Figure 4(i) UM regime) even after QM applicationFor the Biblian station (Figure 4(j)) the AI QM captures theApril peak one month earlier but fails to correctly depict themagnitude of the November peak

Results clearly reveal that the application of QM tothe output of both modeling approaches SDSM and AIoverall improves the representation of seasonality as wellas the representation of rainy and dry periods Howeverboth approaches underestimate the median value of theprecipitation depth inNovemberThis fact could indicate thatthe set of synoptic predictors do not include a variable thatis related to an enhancement of precipitation in this periodFurther studies are needed to determine the variables andrelated phenomena

Table 7 Pearson correlations between observations and SDSM QMand AI QMmodels

Station AI QM SDSM QMEl Labrado 0741 0516Gualaceo 0946 0672Paute 0730 0629Palmas 0788 0593Biblian 0691 0532

422 Representation of Monthly Variability by DownscaledResults To compare the representativeness of SDSM QMand AI QM the correlation of the mymm time serieswith the observed values is shown in Table 7 For all

10 Advances in Meteorology

AI_QMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(a)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(b)

AI_QMObs_Gualaceo

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(c)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

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embe

r

April

Augu

st

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embe

r

Janu

ary

(d)

AI_QMObs_Paute

SDSM_QM

0

20

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60

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Prec

ipita

tion

(mm

)

Oct

ober

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ch

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embe

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uary

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embe

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st

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embe

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Janu

ary

(e)

ObservationsSDSM_QMAI_QM

0

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250

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ipita

tion

(mm

)

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ober

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ch

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embe

r

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June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(f)

Figure 5 Continued

Advances in Meteorology 11

AI_QMObs_Palmas

SDSM_QM

0

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ecip

itatio

n (m

m)

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ober

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ch

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embe

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embe

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ary

(g)

ObservationsSDSM_QMAI_QM

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ipita

tion

(mm

)

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50

0

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ober

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ch

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embe

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uary

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embe

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ary

(h)

AI_QMObs_Bibli na

SDSM_QM

0

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ipita

tion

(mm

)

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ober

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ch

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embe

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uary

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embe

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embe

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ary

(i)

ObservationsSDSM_QMAI_QM

0

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ecip

itatio

n (m

m)

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ober

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ch

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embe

r

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June July

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uary

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embe

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st

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embe

r

Janu

ary

(j)

Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

6 Advances in Meteorology

Table 6 Statistical metrics for artificial intelligence and SDSM ensembles

Station Metric AI SDSM AI QM SDSM QM

El Labrado

Pearson correlation 058 037 058 038IRF 049 100 087 114

Mean-bias 437 minus4149 minus324 minus054Cum bias 3823 12689 1219 996RMSE 3770 6541 4167 5144

Gualaceo

Pearson correlation 074 053 072 050IRF 052 046 104 103

Mean-bias minus101 1028 433 185Cum bias 3402 4750 735 901RMSE 3392 3826 3287 4486

Paute

Pearson correlation 059 047 057 047IRF 036 047 080 089

Mean-bias minus1046 114 minus426 134Cum bias 4761 3173 1559 777RMSE 3060 3026 3113 3503

Palmas

Pearson correlation 044 016 044 014IRF 052 054 112 102

Mean-bias 739 1631 097 minus366Cum bias 3814 5693 877 1228RMSE 4745 5609 5573 6662

Biblian

Pearson correlation 066 046 067 045IRF 061 056 129 125

Mean-bias minus1112 minus287 minus121 166Cum bias 3501 2999 1891 1730RMSE 4173 4489 3987 5181

5234mm and 3549mm for ANN and LS-SVM ensemblesrespectively meaning a strong bias for the ANN ensemblewith respect to LS-SVM ensemble

For a qualitative evaluation of ANN and LS-SVM ensem-bles the Box-Whisker plots for the results during the valida-tion period are presented in Figure 2 For El Labrado stationboth ensembles similarly represent the median althoughthe low variance is clearly showed as measured by IRF inTable 5 For Gualaceo and Paute stations both ensemblesrepresent less variance with LS-SVM presenting lower val-ues The percentiles above 75th are strongly underestimatedin both stations making the necessity of correction on thedistribution of the ensembles evident In Palmas stationboth ensembles underrepresent the variance and the medianis rightly represented by ANN but overestimated by LS-SVM Finally for Biblian station the variance is stronglyunderestimated as well as the higher percentiles The medianis better represented by LS-SVM and underestimated byANN ensemble Bothmethods were able to perform similarlywell for the downscaling of monthly precipitation in theselected stations In addition comparison of the quantitativeanalysis based on the statistical metrics and the qualitativeanalysis based on Box-Whisker plots shed light on the relativeperformance of ANN and LS-SVMmethods

412 Comparison of SDSM and AI Ensembles Once theANN and LS-SVM ensembles were evaluated in a next step

ObservationsANNLS-SVM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

Prec

ipita

tion

(mm

)

M139 M138 M045 M137M141Paute

Figure 2 Box plots for ANN and LS-SVM ensembles evaluated instation El Labrado (M141) Gualaceo (M139) Paute (M138) Palmas(M045) and Biblian (M137)

the derived SDSM and AI ensembles were compared afterQMcorrection Table 6 depicts for the 5 climate stations in thePaute River basin of which data were used the comparisonbetween the SDSM and AI versus SDSM QM and AI QMThe evaluation between both sets is based on the statistical

Advances in Meteorology 7

ObservationsAI_QMSDSM_QM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

Prec

ipita

tion

(mm

)

M045M138 M137M141 M139Paute

Figure 3 Monthly precipitation box plots for artificial intelligenceand SDSM ensembles bias corrected Results evaluated in station ElLabrado (M141) Gualaceo (M139) Paute (M138) Palmas (M045)and Biblian (M137)

metrics R RMSE MB ACB and IRF For El Labrado stationSDSM QM presents lower correlation than AI QM with038 and 058 values Although SDSM QM presents a lowerbias than AI QM the RMSE of AI QM is a bit lower ForGualaceo station 119877 for AI QM and SDSM QM are 072 and05 RMSE as in El Labrado station is lower for AI QM thanfor SDSM QM with 3287 and 4486 respectively For Pautestation also 119877 is higher for AI QM with 057 and 047 forSDSM QM although the ACB is higher for AI QM with1559 and 777 for SDSM QM For Palmas there is a markeddifference in 119877 values with 044 for AI QM and 014 forSDSM QM depicting for the former a lower RMSE thanthe latter Similar for the Biblian station is the 119877 value forAI QM higher than for SDSM QM respectively 067 versus045 Analogous to the Palmas station a lower RMSE valuefor AI QM equal to 3987 was obtained compared to thecalculated RMSE of 5181 for SDSM QM

All other metrics in Table 6 present similar values Thestronger differences arise generally in the RMSE and 119877

statistical metrics which might be related to the fact thatQM corrects only the characteristic of the distribution ascan be seen in Figure 3 This figure presents the monthlyprecipitation Box-Whisker plots for AI and SDSM ensem-bles bias corrected for the 5 climate stations As can beobserved the distributions are fairly alike From the analysisfor all stations AI QM presented higher values of 119877 thanSDSM QM Similarly AI QMpresents better agreement withthe observed data with the exception of the Paute stationThis fact might point to a slightly better representation ofthe observed monthly precipitation distribution by AI QMensemble for this specific region

42 Evaluation of Intra-Annual Precipitation Seasonality Rep-resentation Whereas in previous section the entire distribu-tion of downscaled estimates was evaluated in the followingthe representation of seasonality is evaluated Although the

evaluation of seasonality representation might not help toquantify for example flooding events it is very importantfor issues related to water availability for hydroelectricitygeneration drinking water availability and agriculture Fur-ther the evaluation of seasonality representation is of specialimportance in the study region due to the low resolutionof GCMs unable to depict the precipitation regime due tomesoscale influences [5]

421 The Added Value of Quantile Mapping The QM cor-rection parameters for the power parametric transformationapplied to AI and SDSM ensembles are presented in Table 4The comparison of the multiyear monthly mean (mymm)precipitation of the SDSM with the SDSM QM ensembleis presented in Figures 4(a)ndash4(e) As shown in Figure 4(a)SDSM applied to the El Labrado station fails to capturethe observed seasonality However the performance biasand variance improved considerably after applying QMSeasonality applying SDSM to the Gualaceo (Figure 4(b))station is less correctly presented and fails to capture themaximum inApril and overestimates precipitation during thedry season in August Application of QM only corrects therepresentation in August but not in April The ensemble ofSDSM compositions represents well seasonality but under-estimates significantly the November precipitation depthApplication ofQM improves the representation of seasonalitybut does not improve the November estimate The SDSM inPaute station represents seasonality well but underestimatessignificantly the maximum in November QM applied toSDSM in Paute improves the performance of seasonalityyet fails to improve the representation of the Novemberprecipitation (Figure 4(c)) The SDSM approach calibratedto the observations of the Palmas station (Figure 4(d)) astation with unimodal regime (UM) depicts fairly correctseasonality notwithstanding the limited spatial extent of theUM regime and the poor representation of the mesoscaleinfluences in the synoptic predictors Application of QMnegatively affects the SDSM representation during the first 6months of the year but improves slightly the representationduring the remaining period of the year The seasonality ofthe Biblian station (Figure 4(e)) is properly represented bythe SDSM ensemble and as well as the SDSM QM Only theNovember peak in precipitation is captured by neither SDSMnor SDSM QM

The comparison of mymm of the AI with the AI QMensembles is presented in Figures 4(f)ndash4(j)TheAI emsembleunderestimates precipitation in April overestimate it in Julyand August and underestimate it in November althoughat some extent it represents seasonality QM improves theintra-annual variability but still the November maximumis not correctly estimated The AI ensemble in Gualaceo(Figure 4(g)) station captures well both peaks in Apriland November but underestimates precipitation in AugustThe estimation in August is considerably improved aftercorrection of the bias and the inflation of the variance In thePaute station (Figure 4(h)) are both the peaks respectively inApril and November and the minimum in August were wellcaptured by the AI ensemble while QM further improves thedistribution of the median of the monthly precipitation The

8 Advances in Meteorology

SDSMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(a)

Obs_GualaceoSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(b)

Obs_PauteSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(c)

Obs_PalmasSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(d)

Obs_Bibli naSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(e)

AIObs_El Labrado

AI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(f)

Figure 4 Continued

Advances in Meteorology 9

Obs_GualaceoAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(g)

Obs_PauteAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(h)

Obs_PalmasAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(i)

Obs_Bibli naAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(j)

Figure 4 Multiyear monthly mean precipitation for SDSM ensemble and SDSM ensemble bias corrected (andashe) and multiyear monthly meanprecipitation for AI and AI bias corrected (fndashj)

AI ensemble represents poorly the distribution of the Palmasstation (Figure 4(i) UM regime) even after QM applicationFor the Biblian station (Figure 4(j)) the AI QM captures theApril peak one month earlier but fails to correctly depict themagnitude of the November peak

Results clearly reveal that the application of QM tothe output of both modeling approaches SDSM and AIoverall improves the representation of seasonality as wellas the representation of rainy and dry periods Howeverboth approaches underestimate the median value of theprecipitation depth inNovemberThis fact could indicate thatthe set of synoptic predictors do not include a variable thatis related to an enhancement of precipitation in this periodFurther studies are needed to determine the variables andrelated phenomena

Table 7 Pearson correlations between observations and SDSM QMand AI QMmodels

Station AI QM SDSM QMEl Labrado 0741 0516Gualaceo 0946 0672Paute 0730 0629Palmas 0788 0593Biblian 0691 0532

422 Representation of Monthly Variability by DownscaledResults To compare the representativeness of SDSM QMand AI QM the correlation of the mymm time serieswith the observed values is shown in Table 7 For all

10 Advances in Meteorology

AI_QMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(a)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(b)

AI_QMObs_Gualaceo

SDSM_QM

0

20

40

60

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100

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140

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180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

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embe

r

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June July

Febr

uary

Nov

embe

r

April

Augu

st

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embe

r

Janu

ary

(c)

ObservationsSDSM_QMAI_QM

0

50

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250Pr

ecip

itatio

n (m

m)

Oct

ober

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ch

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embe

r

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June July

Febr

uary

Nov

embe

r

April

Augu

st

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embe

r

Janu

ary

(d)

AI_QMObs_Paute

SDSM_QM

0

20

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Prec

ipita

tion

(mm

)

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ober

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ch

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embe

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uary

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embe

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st

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embe

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ary

(e)

ObservationsSDSM_QMAI_QM

0

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ipita

tion

(mm

)

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ober

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ch

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embe

r

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June July

Febr

uary

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embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(f)

Figure 5 Continued

Advances in Meteorology 11

AI_QMObs_Palmas

SDSM_QM

0

20

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ecip

itatio

n (m

m)

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ober

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ch

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embe

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embe

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ary

(g)

ObservationsSDSM_QMAI_QM

Prec

ipita

tion

(mm

)

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50

0

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ober

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embe

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st

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embe

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ary

(h)

AI_QMObs_Bibli na

SDSM_QM

0

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ipita

tion

(mm

)

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ober

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ch

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embe

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embe

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st

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embe

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ary

(i)

ObservationsSDSM_QMAI_QM

0

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250Pr

ecip

itatio

n (m

m)

Oct

ober

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ch

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embe

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June July

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uary

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embe

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st

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embe

r

Janu

ary

(j)

Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 7

ObservationsAI_QMSDSM_QM

El Labrado Gualaceo Palmas Bibli na

0

50

100

150

200

250

300

350

Prec

ipita

tion

(mm

)

M045M138 M137M141 M139Paute

Figure 3 Monthly precipitation box plots for artificial intelligenceand SDSM ensembles bias corrected Results evaluated in station ElLabrado (M141) Gualaceo (M139) Paute (M138) Palmas (M045)and Biblian (M137)

metrics R RMSE MB ACB and IRF For El Labrado stationSDSM QM presents lower correlation than AI QM with038 and 058 values Although SDSM QM presents a lowerbias than AI QM the RMSE of AI QM is a bit lower ForGualaceo station 119877 for AI QM and SDSM QM are 072 and05 RMSE as in El Labrado station is lower for AI QM thanfor SDSM QM with 3287 and 4486 respectively For Pautestation also 119877 is higher for AI QM with 057 and 047 forSDSM QM although the ACB is higher for AI QM with1559 and 777 for SDSM QM For Palmas there is a markeddifference in 119877 values with 044 for AI QM and 014 forSDSM QM depicting for the former a lower RMSE thanthe latter Similar for the Biblian station is the 119877 value forAI QM higher than for SDSM QM respectively 067 versus045 Analogous to the Palmas station a lower RMSE valuefor AI QM equal to 3987 was obtained compared to thecalculated RMSE of 5181 for SDSM QM

All other metrics in Table 6 present similar values Thestronger differences arise generally in the RMSE and 119877

statistical metrics which might be related to the fact thatQM corrects only the characteristic of the distribution ascan be seen in Figure 3 This figure presents the monthlyprecipitation Box-Whisker plots for AI and SDSM ensem-bles bias corrected for the 5 climate stations As can beobserved the distributions are fairly alike From the analysisfor all stations AI QM presented higher values of 119877 thanSDSM QM Similarly AI QMpresents better agreement withthe observed data with the exception of the Paute stationThis fact might point to a slightly better representation ofthe observed monthly precipitation distribution by AI QMensemble for this specific region

42 Evaluation of Intra-Annual Precipitation Seasonality Rep-resentation Whereas in previous section the entire distribu-tion of downscaled estimates was evaluated in the followingthe representation of seasonality is evaluated Although the

evaluation of seasonality representation might not help toquantify for example flooding events it is very importantfor issues related to water availability for hydroelectricitygeneration drinking water availability and agriculture Fur-ther the evaluation of seasonality representation is of specialimportance in the study region due to the low resolutionof GCMs unable to depict the precipitation regime due tomesoscale influences [5]

421 The Added Value of Quantile Mapping The QM cor-rection parameters for the power parametric transformationapplied to AI and SDSM ensembles are presented in Table 4The comparison of the multiyear monthly mean (mymm)precipitation of the SDSM with the SDSM QM ensembleis presented in Figures 4(a)ndash4(e) As shown in Figure 4(a)SDSM applied to the El Labrado station fails to capturethe observed seasonality However the performance biasand variance improved considerably after applying QMSeasonality applying SDSM to the Gualaceo (Figure 4(b))station is less correctly presented and fails to capture themaximum inApril and overestimates precipitation during thedry season in August Application of QM only corrects therepresentation in August but not in April The ensemble ofSDSM compositions represents well seasonality but under-estimates significantly the November precipitation depthApplication ofQM improves the representation of seasonalitybut does not improve the November estimate The SDSM inPaute station represents seasonality well but underestimatessignificantly the maximum in November QM applied toSDSM in Paute improves the performance of seasonalityyet fails to improve the representation of the Novemberprecipitation (Figure 4(c)) The SDSM approach calibratedto the observations of the Palmas station (Figure 4(d)) astation with unimodal regime (UM) depicts fairly correctseasonality notwithstanding the limited spatial extent of theUM regime and the poor representation of the mesoscaleinfluences in the synoptic predictors Application of QMnegatively affects the SDSM representation during the first 6months of the year but improves slightly the representationduring the remaining period of the year The seasonality ofthe Biblian station (Figure 4(e)) is properly represented bythe SDSM ensemble and as well as the SDSM QM Only theNovember peak in precipitation is captured by neither SDSMnor SDSM QM

The comparison of mymm of the AI with the AI QMensembles is presented in Figures 4(f)ndash4(j)TheAI emsembleunderestimates precipitation in April overestimate it in Julyand August and underestimate it in November althoughat some extent it represents seasonality QM improves theintra-annual variability but still the November maximumis not correctly estimated The AI ensemble in Gualaceo(Figure 4(g)) station captures well both peaks in Apriland November but underestimates precipitation in AugustThe estimation in August is considerably improved aftercorrection of the bias and the inflation of the variance In thePaute station (Figure 4(h)) are both the peaks respectively inApril and November and the minimum in August were wellcaptured by the AI ensemble while QM further improves thedistribution of the median of the monthly precipitation The

8 Advances in Meteorology

SDSMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(a)

Obs_GualaceoSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(b)

Obs_PauteSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(c)

Obs_PalmasSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(d)

Obs_Bibli naSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(e)

AIObs_El Labrado

AI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(f)

Figure 4 Continued

Advances in Meteorology 9

Obs_GualaceoAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(g)

Obs_PauteAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(h)

Obs_PalmasAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(i)

Obs_Bibli naAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(j)

Figure 4 Multiyear monthly mean precipitation for SDSM ensemble and SDSM ensemble bias corrected (andashe) and multiyear monthly meanprecipitation for AI and AI bias corrected (fndashj)

AI ensemble represents poorly the distribution of the Palmasstation (Figure 4(i) UM regime) even after QM applicationFor the Biblian station (Figure 4(j)) the AI QM captures theApril peak one month earlier but fails to correctly depict themagnitude of the November peak

Results clearly reveal that the application of QM tothe output of both modeling approaches SDSM and AIoverall improves the representation of seasonality as wellas the representation of rainy and dry periods Howeverboth approaches underestimate the median value of theprecipitation depth inNovemberThis fact could indicate thatthe set of synoptic predictors do not include a variable thatis related to an enhancement of precipitation in this periodFurther studies are needed to determine the variables andrelated phenomena

Table 7 Pearson correlations between observations and SDSM QMand AI QMmodels

Station AI QM SDSM QMEl Labrado 0741 0516Gualaceo 0946 0672Paute 0730 0629Palmas 0788 0593Biblian 0691 0532

422 Representation of Monthly Variability by DownscaledResults To compare the representativeness of SDSM QMand AI QM the correlation of the mymm time serieswith the observed values is shown in Table 7 For all

10 Advances in Meteorology

AI_QMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(a)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(b)

AI_QMObs_Gualaceo

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(c)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(d)

AI_QMObs_Paute

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(e)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(f)

Figure 5 Continued

Advances in Meteorology 11

AI_QMObs_Palmas

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(g)

ObservationsSDSM_QMAI_QM

Prec

ipita

tion

(mm

)

150

100

250

350

300

200

50

0

Oct

ober

Mar

ch

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embe

r

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June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(h)

AI_QMObs_Bibli na

SDSM_QM

0

20

40

60

80

100

120

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Prec

ipita

tion

(mm

)

Oct

ober

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ch

Sept

embe

r

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June July

Febr

uary

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embe

r

April

Augu

st

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embe

r

Janu

ary

(i)

ObservationsSDSM_QMAI_QM

0

50

100

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200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(j)

Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

8 Advances in Meteorology

SDSMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(a)

Obs_GualaceoSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(b)

Obs_PauteSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(c)

Obs_PalmasSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(d)

Obs_Bibli naSDSMSDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(e)

AIObs_El Labrado

AI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(f)

Figure 4 Continued

Advances in Meteorology 9

Obs_GualaceoAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(g)

Obs_PauteAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(h)

Obs_PalmasAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(i)

Obs_Bibli naAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(j)

Figure 4 Multiyear monthly mean precipitation for SDSM ensemble and SDSM ensemble bias corrected (andashe) and multiyear monthly meanprecipitation for AI and AI bias corrected (fndashj)

AI ensemble represents poorly the distribution of the Palmasstation (Figure 4(i) UM regime) even after QM applicationFor the Biblian station (Figure 4(j)) the AI QM captures theApril peak one month earlier but fails to correctly depict themagnitude of the November peak

Results clearly reveal that the application of QM tothe output of both modeling approaches SDSM and AIoverall improves the representation of seasonality as wellas the representation of rainy and dry periods Howeverboth approaches underestimate the median value of theprecipitation depth inNovemberThis fact could indicate thatthe set of synoptic predictors do not include a variable thatis related to an enhancement of precipitation in this periodFurther studies are needed to determine the variables andrelated phenomena

Table 7 Pearson correlations between observations and SDSM QMand AI QMmodels

Station AI QM SDSM QMEl Labrado 0741 0516Gualaceo 0946 0672Paute 0730 0629Palmas 0788 0593Biblian 0691 0532

422 Representation of Monthly Variability by DownscaledResults To compare the representativeness of SDSM QMand AI QM the correlation of the mymm time serieswith the observed values is shown in Table 7 For all

10 Advances in Meteorology

AI_QMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(a)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(b)

AI_QMObs_Gualaceo

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(c)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(d)

AI_QMObs_Paute

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(e)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(f)

Figure 5 Continued

Advances in Meteorology 11

AI_QMObs_Palmas

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(g)

ObservationsSDSM_QMAI_QM

Prec

ipita

tion

(mm

)

150

100

250

350

300

200

50

0

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(h)

AI_QMObs_Bibli na

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(i)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(j)

Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 9

Obs_GualaceoAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(g)

Obs_PauteAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(h)

Obs_PalmasAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(i)

Obs_Bibli naAIAI_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Augu

st

April

Febr

uary

Nov

embe

r

Dec

embe

r

Janu

ary

(j)

Figure 4 Multiyear monthly mean precipitation for SDSM ensemble and SDSM ensemble bias corrected (andashe) and multiyear monthly meanprecipitation for AI and AI bias corrected (fndashj)

AI ensemble represents poorly the distribution of the Palmasstation (Figure 4(i) UM regime) even after QM applicationFor the Biblian station (Figure 4(j)) the AI QM captures theApril peak one month earlier but fails to correctly depict themagnitude of the November peak

Results clearly reveal that the application of QM tothe output of both modeling approaches SDSM and AIoverall improves the representation of seasonality as wellas the representation of rainy and dry periods Howeverboth approaches underestimate the median value of theprecipitation depth inNovemberThis fact could indicate thatthe set of synoptic predictors do not include a variable thatis related to an enhancement of precipitation in this periodFurther studies are needed to determine the variables andrelated phenomena

Table 7 Pearson correlations between observations and SDSM QMand AI QMmodels

Station AI QM SDSM QMEl Labrado 0741 0516Gualaceo 0946 0672Paute 0730 0629Palmas 0788 0593Biblian 0691 0532

422 Representation of Monthly Variability by DownscaledResults To compare the representativeness of SDSM QMand AI QM the correlation of the mymm time serieswith the observed values is shown in Table 7 For all

10 Advances in Meteorology

AI_QMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(a)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(b)

AI_QMObs_Gualaceo

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(c)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(d)

AI_QMObs_Paute

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(e)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(f)

Figure 5 Continued

Advances in Meteorology 11

AI_QMObs_Palmas

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(g)

ObservationsSDSM_QMAI_QM

Prec

ipita

tion

(mm

)

150

100

250

350

300

200

50

0

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(h)

AI_QMObs_Bibli na

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(i)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(j)

Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

10 Advances in Meteorology

AI_QMObs_El Labrado

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(a)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(b)

AI_QMObs_Gualaceo

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(c)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(d)

AI_QMObs_Paute

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(e)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(f)

Figure 5 Continued

Advances in Meteorology 11

AI_QMObs_Palmas

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(g)

ObservationsSDSM_QMAI_QM

Prec

ipita

tion

(mm

)

150

100

250

350

300

200

50

0

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(h)

AI_QMObs_Bibli na

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(i)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(j)

Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 11

AI_QMObs_Palmas

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(g)

ObservationsSDSM_QMAI_QM

Prec

ipita

tion

(mm

)

150

100

250

350

300

200

50

0

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(h)

AI_QMObs_Bibli na

SDSM_QM

0

20

40

60

80

100

120

140

160

180

200

Prec

ipita

tion

(mm

)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(i)

ObservationsSDSM_QMAI_QM

0

50

100

150

200

250Pr

ecip

itatio

n (m

m)

Oct

ober

Mar

ch

Sept

embe

r

May

June July

Febr

uary

Nov

embe

r

April

Augu

st

Dec

embe

r

Janu

ary

(j)

Figure 5 Comparison of SDSM and AI ensembles bias corrected (a c e g i) and Box-Whisker plots for SDSM and AI ensembles biascorrected from January through December (b d f h j)

stations AI QM presents greater Pearson correlation coeffi-cient than SDSM QM The multiyear median observed andestimated monthly precipitation depth using respectivelythe SDSM QM and AI QM model ensembles are presentedin Figures 5(a) 5(c) 5(e) 5(g) and 5(i) For the graphicalpresentation the Box-Whisker plot type was selected as toshow in addition to themedian the variation in estimates (seeFigures 5(b) 5(d) 5(f) 5(h) and 5(j))

For the El Labrado station (Figures 5(a) and 5(b)) theobserved interquartile range is higher for the period ofJanuary to April with lower values in August and SeptemberIt is worthwhile noticing that although AI QM capturesseasonality the intra-annual variability is not captured Evenfor some months SDSM QM captures the variability betteras is the case for MarchThis fact suggests that an assessment

for SD should be based on several models The medianand interquartile range are relatively well captured for theGualaceo station (Figures 5(c) and 5(d)) the variability ofthe months from January to September is similar for theSDSM-QM and AI QM estimates October and Novembervariability is different for the two models but the medianis well represented The variability and the median arebetter represented by AI QM and slightly overestimated bySDSM QM in the period of June to August Figures 5(e)and 5(f) depict the results for the Paute station illustratingthat both models relatively well represent the median andinterquartile ranges in the period of January to September butfail to do so for the period of October to December This facthighlights the need to further explore the relation betweenthe synoptic conditions and rainfall Neither the SDSM QM

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

12 Advances in Meteorology

nor the AI QM model estimates correctly the median ofthe Palmas station (Figures 5(g) and 5(h)) the only stationwith a unimodal regime Because both model approachesindistinctly overestimate or underestimate the median insome months it might be worthwhile to examine more indetail the representation of an ensemble of both modelsThe interquartile range of each month is relatively wellrepresented except in a distinct number of months such asJanuary April June July September and OctoberThis couldmean that in those months the influences of the mesoscalefactors are not properly represented in the synoptic variablesAn option for its remediation could be a methodology inwhich the influences of mesoscale factors are considered forexample dynamic downscaling followed by the applicationof statistical downscaling to regional predictors Howeverfurther studies are necessary to support the applicability ofsuch an approach inmountain regions For the Biblian station(Figures 5(i) and 5(j)) the two approaches overestimateprecipitation in the period of January to March AI QMcaptures adequately the median from April to Decemberwith exception of November as was the case for the otherstations Overall the AI QMdepicts fairly well the variabilityexcept for October and November whereas SDSM QMunderestimates the variability throughout the year

5 Conclusions

The evaluation of downscaling methods in mountain regionsis of major importance due to the misrepresentation of cli-mate by GCMs The low resolution of GCMs limits the accu-rate prediction of the probable impacts of climate change atbasin scale In the present work the applicability of monthlyprecipitation downscaling of global climatemodels by SDSMand methods of artificial intelligence as neural networks andleast squares support vector machines was studied Also acomparative analysis of the applied downscaling methodswas conducted Comparative analysis revealed that withrespect to the downscaling of monthly precipitation neuralnetworks and least squares support vector machine modelsperform equally Considering the statistical metrics such asPearson correlation root mean square error and percentilesbiases overall the artificial intelligence methods showedbetter skills in relation to SDSM although in some stationsand somemonths the importance of considering bothmodelapproaches was necessary in order to derive robust conclu-sions In general although the representation of precipitationfrom January to August is adequate especially in Novemberboth approaches failed to represent precipitation in somestations Further analysis of the synoptic conditions forthis period is therefore recommended and a methodologyconsidering downscaling with specific predictors by monthor season might be advisable From the analysis on Palmasstation a station with important mesoscale influences wecould derive that further evaluation of a methodology ofdownscaling using dynamic and statistical methods in cas-cade could help capture features that GCMs are not able torepresent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was funded by the Direccion de Investigacion de laUniversidad de Cuenca (DIUC) through the project ldquoAnalisisde los Efectos del Cambio Climatico en los Caudales en lasCuencas Andinas del Sur del Ecuador (Paute) Debido a losCambios en los Patrones de Iluvia y Temperaturardquo and bythe Secretaria de Educacion Superior Ciencia Tecnologıa eInnovacion (SENESCYT) through a PhD grant for the firstauthor The authors would also like to thank INAMHI forproviding the meteorological data

References

[1] W Buytaert M Vuille A Dewulf R Urrutia A Karmalkarand R Celleri ldquoUncertainties in climate change projections andregional downscaling in the tropical Andes implications forwater resources managementrdquo Hydrology and Earth SystemSciences vol 14 no 7 pp 1247ndash1258 2010

[2] D E Mora L Campozano F Cisneros G Wyseure and PWillems ldquoClimate changes of hydrometeorological and hydro-logical extremes in the Paute basin EcuadoreanAndesrdquoHydrol-ogy and Earth System Sciences vol 18 no 2 pp 631ndash648 2014

[3] R L Wilby C W Dawson and E M Barrow ldquoSDSMmdasha deci-sion support tool for the assessment of regional climate changeimpactsrdquo Environmental Modelling amp Software vol 17 no 2pp 145ndash157 2002

[4] P Coulibaly Y B Dibike and F Anctil ldquoDownscaling precipi-tation and temperature with temporal neural networksrdquo Journalof Hydrometeorology vol 6 no 4 pp 483ndash496 2005

[5] A Ochoa L Campozano E Sanchez R Gualan and ESamaniego ldquoEvaluation of downscaled estimates of monthlytemperature and precipitation for a Southern Ecuador casestudyrdquo International Journal of Climatology 2015

[6] W C Skamarock J B Klemp J Dudhia et al A Descriptionof the Advanced Research WRF Version 3 National Center forAtmospheric Research Boulder Colo USA 2008

[7] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[8] J A K Suykens T Van Gestel J De Brabanter B DeMoor andJ Vandewalle Least Squares Support Vector Machines WorldScientific Singapore 2002

[9] L Gudmundsson J B Bremnes J E Haugen and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[10] L Campozano R Celleri K Trachte J Bendix and E Sama-niego ldquoRainfall and cloud dynamics in the Andes a southernEcuador case studyrdquo Advances in Meteorology In press

[11] R Celleri P Willems W Buytaert and J Feyen ldquoSpace-time rainfall variability in the Paute basin Ecuadorian AndesrdquoHydrological Processes vol 21 no 24 pp 3316ndash3327 2007

[12] L Campozano E Sanchez A Aviles and E Samaniego ldquoEval-uation of infilling methods for time series of daily precipitationand temperature the case of the Ecuadorian AndesrdquoMaskanavol 5 no 1 pp 99ndash115 2014 httpwwwucuencaeduecojsindexphpmaskanaarticleview431

[13] E Kalnay M Kanamitsu R Kistler et al ldquoThe NCEPNCAR40-year reanalysis projectrdquo Bulletin of the AmericanMeteorolog-ical Society vol 77 no 3 pp 437ndash471 1996

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 13

[14] M S Pervez and G M Henebry ldquoProjections of the Ganges-Brahmaputra precipitation-Downscaled from GCM predic-torsrdquo Journal of Hydrology vol 517 pp 120ndash134 2014

[15] R Mahmood and M S Babel ldquoFuture changes in extremetemperature events using the statistical downscaling model(SDSM) in the trans-boundary region of the Jhelum river basinrdquoWeather and Climate Extremes vol 5-6 pp 56ndash66 2014

[16] M H Beale M T Hagan and H B Demuth ldquoNeural NetworkToolboxtrade UserrsquosGuideRrdquoMathWorksNatickMassUSA 2014

[17] K De Brabanter P Karsmakers F Ojeda et al LS-SVMlabToolbox Userrsquos Guide Version 18 2011 httpwwwesatkuleuvenbesistalssvmlabdownloadstutorialv1 8pdf

[18] A L Gudmundsson J B Bremnes J E Haugen1 and T Engen-Skaugen ldquoTechnical note downscaling RCM precipitation tothe station scale using statistical transformationsmdasha compari-son of methodsrdquo Hydrology and Earth System Sciences vol 16no 9 pp 3383ndash3390 2012

[19] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[20] S Tripathi V V Srinivas and R S Nanjundiah ldquoDownscalingof precipitation for climate change scenarios a support vectormachine approachrdquo Journal of Hydrology vol 330 no 3-4 pp621ndash640 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in