comparison of ann and mlr models for

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Comparison of ANN and MLR models for estimating solar radiationin Turkey using NOAA/AVHRR data

Mehmet S�ahin a,⇑, Yılmaz Kaya b, Murat Uyar a

a Department of Electrical and Electronics Engineering, Siirt University, 56100 Siirt, Turkeyb Department of Computer Engineering, Siirt University, 56100 Siirt, Turkey

Received 15 September 2012; received in revised form 12 October 2012; accepted 13 October 2012Available online 22 October 2012

Abstract

In this paper, the estimation capacities of MLR and ANN are investigated to estimate monthly-average daily SR over Turkey. Thesatellite data are used for 73 different locations over Turkey. Land surface temperature, altitude, latitude, longitude and month areoffered as the input variables for modeling ANN and MLR to get SR. Estimations of SR are evaluated with the meteorological valuesby using the statistical bases. The obtained results indicated that the ANN model could achieve a satisfactory performance when com-pared to the MLR model. Moreover, it is understood that more accurate results in estimation of SR are obtained in the use of satellitedata, rather than the use of meteorological station data. Finally, the built ANN model is used to estimate the yearly average of daily SRover Turkey. As a result, satellite-based SR map for Turkey is generated.� 2012 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Solar radiation; Mapping; Land surface temperature; Artificial neural network; Multiple linear regression; NOAA/AVHRR

1. Introduction

Solar energy is one of the oldest, cleanest and the mostreliable renewable energy sources in the world. It is sup-plied from the sun in the form of solar radiation (SR).The knowledge of SR distribution at a specific geographicregion is of great importance in diverse fields such as engi-neering, agriculture, environment, hydrology, ecology, etc.(Ranzi and Rosso, 1995; Lindsey and Farnsworth, 1997;Roebeling et al., 2004; Walton et al., 2005; Benghanemand Mellit, 2010). In particular, estimation of SR is crucialfor designing solar furnaces, interior illumination of build-ings, modeling climate change, concentrating solar collec-tors, sizing photovoltaic systems and site selection ofsolar power plants (Samanta and Al-Balushi, 1998;

Ferriere and Rivoire, 2002; Kumar and Umanand, 2005;Escobedo et al., 2009; Faghih and Bahadori, 2009; Martınet al., 2010). Although SR data are known to be veryimportant, providing them is not so easy because the equip-ment needed to obtain the knowledge of SR is too expen-sive. Unfortunately, there are not always adequatefacilities to mount viable monitoring programs for thisequipment. On the other hand, the number of such meteo-rological stations is usually not sufficient to provide SRdata for the desired areas, especially in developing coun-tries. This is mainly due to the cost and the difficulty ofequipment installation, maintenance and calibration(Sozen et al., 2004; Mellit et al., 2006; Bulet and Buyukal-aca, 2007; Senkal and Kuleli, 2009). Moreover, previousstudies have reported that sometimes the measurementerror may rise up to 25% due to calibration uncertainties,especially when using of measurement equipment such aspyranometers (Justus et al., 1986; Kandırmaz et al., 2004).

Although there have been several attempts to estimateSR by using meteorological and physical parameters, thelack of the measured atmospheric variables limits the use

0273-1177/$36.00 � 2012 COSPAR. Published by Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.asr.2012.10.010

⇑ Corresponding author. Tel.: +90 484 223 12 24; fax: +90 484 223 6631.

E-mail addresses: [email protected], [email protected](M. S�ahin), [email protected] (Y. Kaya), [email protected](M. Uyar).

www.elsevier.com/locate/asr

Available online at www.sciencedirect.com

Advances in Space Research 51 (2013) 891–904


of many analytical procedures. These limitations force sci-entists and researchers to use different methods in order toprovide SR data (Bocco et al., 2010). Recently, satellitebased remote sensing (RS) is a method used increasinglyby scientists for obtaining SR data. This is mainly becauseit is quick and reliable in data processing, practical toobtain data from inaccessible or remote regions (mountain-ous and rural), easy to handle with the computer, etc.(Cano et al., 1986; Kant and Badarinath, 2000). In addi-tion, the previous studies have clearly indicated that atground level SR can be estimated within the acceptableerror limits that are better than 10%, by using satellite data(Cano et al., 1986; Diabate et al., 1989; Kandırmaz et al.,2004).

In the recent years, the soft computing approaches suchas artificial neural networks (ANNs) have been used as analternative to previous methods such as statistical, analyticand empirical methods for estimating SR. ANN provides acomputationally efficient way of determining an empirical,possibly nonlinear relationship between a number of inputsand one or more outputs. It has been applied for modeling,identification, optimization, prediction and control of com-plex systems (Li and Jiang, 2010). ANNs have been used inSR estimation studies for locations with different latitudesand climates such as Saudi Arabia (Mohandes et al., 1998),Spain (Lopez et al., 2005), Uganda (Mubiru and Banda,2007), China (Jiang, 2008) and Turkey (Koca et al.,2011). They modeled SR by using various internal topolo-gies, different input variables (geographical and climatolog-ical) and several time scales (monthly, daily and hourly). Inthese studies, the measurement of basic ground variables istypically used for estimating SR. Although the methodsused for obtaining the ground data have good performancefor estimating SR, they are incapable for mountainous ordeserts where the input variables do not exist.

Also, there are several studies using satellite data forestimating SR. These can be briefly summarized in the fol-lowing discussions. S�enkal and Kuleli estimated SR byusing ANN for analyzing satellite data. They showed thatroot mean square error (RMSE) between the estimated andground values for monthly average daily sum analyzed byANN and physical method values have been found to be3.94 MJ/m2 and 5.37 MJ/m2 for testing data, respectively(S�enkal and Kuleli, 2009). In another study, S�enkal esti-mated SR using a different architecture of ANN with theRMSE of 6.59% (S�enkal, 2010). Rahimikhoob testedANN for estimating SR as a function of air temperaturedata in a semi-arid environment. The study demonstratedthat modeling of daily SR through the use of the ANNtechnique gave better estimations than the empirical tech-niques. For the comparison between observed and esti-mated SR, RMSE and R2 for the tested data using theproposed ANN model were 2.534 MJ/m2 and 0.889,respectively (Rahimikhoob, 2010). Lu et al. (2011) used asimple algorithm with ANN modeling and proposed toexplore the non-linear physical relationship between dailyground SR measurements and Multi-Functional Transport

Satellite (MTSAT) on all-channel observations in an effortto fully exploit information contained in both data sets.The daily and monthly-average SR obtained from theANN model had an average bias of �0.33 MJ/m2

(�2.4%) and �0.41 MJ/m2 (�2.9%), an average RMSEof 2.85 MJ/m2 (20.4%) and 1.63 MJ/m2 (11.4%) and anaverage coefficient of determination of 0.85 and 0.92,respectively. Qin et al. (2011) utilized the ANN to buildthe mathematical relationship between measuredmonthly-average daily SR and several remote sensingproducts available for the public, including Moderate Res-olution Imaging Spectroradiometer (MODIS) monthlyaveraged land surface temperature (LST), the number ofdays in which the LST retrieval was performed in onemonth, MODIS enhanced vegetation index, Tropical Rain-fall Measuring Mission (TRMM) satellite monthly precip-itation. After training, validation results indicated that theANN-based method presented in the study could estimatemonthly-average daily SR at a spatial resolution of about5 km with high accuracy.

As stated previously, it is very important to estimateaccurate SR data which is used for many purposes. In lit-erature, some studies that used satellite data were studiedwith a limited amount of data from only certain locationsof the relevant region. Accordingly, solar energy potentialsof the relevant locations have been reported. Furthermore,the performances of the method proposed in these studieswere tested with these limited data. It may reduce validityand reliability of estimation results of the relevant regionof which solar energy potential was estimated. In addition,previous studies indicate that there is a limited amount ofsatellite based studies for estimating SR and there is stilla need for this kind of studies, especially in countries withhigh SR level such as Turkey.

In this paper, SR estimation is obtained for Turkey,which is located in hot climate band and which is highlyaffected from SR. Furthermore, the performance of ANNand multiple linear regression (MLR) methods, which havebeen used widespread in the recent years, are evaluatedcomparatively for estimating SR as a function of LST. Inthe study, National Oceanic and Atmospheric Administra-tion/Advanced Very High Resolution Radiometer(NOAA/AVHRR) satellite data and meteorological datafrom 2000 to 2002 at 73 locations covering approximatelythe entire areas of Turkey are used for modeling and test-ing ANN and MLR. Here, the meteorological data areused only to assess the performance of the study. Whereas,in both approaches five parameters such as satellite-esti-mated LST, altitude, latitude, longitude and months ofyear are selected as input parameters, SR is determinedas output parameter. While MLR and ANN models areformed, the dataset is divided into three parts (%60–%20–%20): 43 locations for training, 15 locations for vali-dation and the remaining 15 locations for testing. The per-formance of MLR and ANN models for both data sets areevaluated statistically in order to show the accuracy of SRestimation in these testing locations after the training. The

892 M. S�ahin et al. / Advances in Space Research 51 (2013) 891–904


obtained results indicate that this study has a potential toprovide important information about solar energy poten-tial of Turkey.

2. Study area and data sources

When a study concerning the estimation of SR potentialof a location will be carried out, using the parameters of alarger scale of the studied area is rather important in get-ting accurate estimations. In this study, the 73 locationsover Turkey are chosen as study area. Their geographicinformation such as altitude, latitude and longitude arepresented in Table 1.

This study is realized by using two separate datasets.They are NOAA/AVHRR satellite data and meteorologi-cal data. The meteorological data are used only to assessthe performance of the study. Meteorological data, a totalof 3-years (2000–2002), are obtained from Turkish StateMeteorological Service (TSMS) while satellite data areobtained from Scientific and Technological ResearchCouncil of Turkey-Bilten, simultaneously.

To build an effective estimation model, the commonpractice is to evaluate the data in three parts: the training,validation, and test dataset (Yao and Liu, 1997). Trainingset is used to find the relationship between a set of depen-dent and independent variables whereas the validation setis often used to find the optimal number of hidden unitsor determine a stopping point for ANN. In test dataset,the performance of a fully-trained model is evaluated ona set of samples which not used in training and validationstage.

In Fig. 1, the geographical locations of training, valida-tion and testing sites used in this study are illustrated. Asshown in Fig. 1, these locations, covering approximatelythe whole of Turkey are distributed to the seven geograph-ical regions. Moreover, in order to check the generalizationcapability of the constructed models, the testing locationscontain the different land cover types such as seaside,semi-desert, mountainous and forests (see Fig. 1).

To construct a better functional relationship by ANN orMLR between input variables and target variable, the effec-tive input variables must be determined. As aforemen-tioned, RS product is used in input vector to train theANN and the MLR for building their mathematical rela-

Table 1Geographic information from 73 locations over Turkey.

City Altitude (m) Latitude (�N) Longitude (�E)

Adana 27 37.03 35.21Adıyaman 672 37.45 38.17Agrı 1632 39.43 43.03Aksaray 961 38.23 34.03Aks�ehir 1002 38.21 31.25Amasya 411 40.39 35.51Ankara 891 39.57 32.53Antakya 100 36.12 36.10Antalya 64 36.42 30.44Artvin 628 41.11 41.49Aydın 56 37.51 27.51Balıkesir-Gonen 37 40.06 27.39Batman 310 37.35 41.07Bilecik 539 40.09 29.59Bingol 1177 38.52 40.30Birecik 345 37.01 35.57Bitlis 1573 38.22 42.06Burdur 957 37.43 30.18Bursa 100 40.13 29.00Canakkale 6 40.08 26.24Corum 776 40.33 34.58Diyarbakır 674 37.54 40.12Denizli 425.29 37.47 29.05Develi 1180 38.23 35.30Dinar 864 38.04 30.10Dortyol 28 36.51 36.13Duzce 145.67 40.50 31.10Edirne 49 41.41 26.33Elazıg 989.75 38.39 39.15Ergani 1000 38.17 39.46Erzincan 1218.22 39.45 39.30Erzurum 1758.18 39.57 41.40Gaziantep 854 37.03 37.21Gumus�hane 1219 40.28 39.28Hakkari 1727.74 37.34 43.44Igdır 858 39.55 44.03Isparta 996.88 37.45 30.33_Iskenderun 3.59 36.35 36.10_Istanbul-Goztepe 32.98 40.58 29.05_Izmir 28.55 38.23 27.04Kahramanmaras� 572.13 37.36 36.56Karaman 1023.05 37.12 33.13Karatas� 22 36.34 36.23Kars 1775 40.37 43.06Kastamonu 800 41.22 33.47Kayseri 1092 38.43 35.29Kırs�ehir 1007.17 39.09 34.10Kilis 650 36.42 37.06Kocaeli-_Izmit 76 40.46 29.56Konya 1030 37.52 32.28Kutahya 969.25 39.25 29.58Kutahya-Tavs�anlı 833 39.33 29.30Malatya 947.87 38.21 38.13Marmaris 16.19 36.51 28.15Mersin 3.4 36.48 34.38Mugla 646 37.13 28.22Mus� 1322.76 38.41 41.29Nigde 1210.5 37.58 34.41Ordu 4.1 40.59 37.54Rize 8 41.02 40.30Samsun 4 41.21 36.15Siirt 895.54 37.55 41.57

Silifke 15.01 36.23 33.56Sinop 32 42.02 35.50Sivas 1285 39.45 37.01S�anlıurfa 547.18 37.09 38.47Tokat 607.9 40.18 36.34Trabzon 30 40.59 39.45Tunceli 980 39.07 39.33Van 1670.58 38.28 43.21Yalova 3.81 40.40 29.17Yozgat 1298.33 39.49 34.48Zonguldak 135.35 41.27 31.38

M. S�ahin et al. / Advances in Space Research 51 (2013) 891–904 893


tionship with measured SR. However, these RS productsmust include information that may influence SR. LST isone of the key parameter in determining the exchangeenergy and the matter between the Earth’s surface andatmosphere. At the same time, it is an important measure-ment in energy-balance applications and thus has a quitelarge influence on SR at the earth’s surface (Qin et al.,2011). In addition, it was often used as input parameterin previous studies (S�enkal, 2010; Qin et al., 2011). Thus,NOAA’s monthly averaged LSTs are selected as one partof inputs to train ANN and MLR. The entire input vectorto ANN is represented as X = [LST, Al, Lt, Ln, M]T inwhich Al (m), Lt (�), Ln (�) and M (months) denotes alti-tude, latitude, longitude and the number of months, respec-tively. The output vector Y includes monthly-average dailySR (MJ/m2).

3. Methodology

3.1. Estimation land surface temperature by using NOAA/

AVHRR

The channels 4 and 5 of Advanced Very High Resolu-tion Radiometer (AVHRR) are used widely for derivingsurface temperature (Kant and Badarinath, 2000).AVHRR is a space-borne sensor embarked on theNational Oceanic and Atmospheric Administration(NOAA) family of polar orbiting platforms. AVHRRinstruments measure the reflectance of the Earth in five rel-atively wide spectral bands. The first two are centered onthe red (0.580–0.680 lm) and near-infrared (0.725–1.100 lm) regions, the third one is located around 3.55–3.93 lm, and the last two sample the thermal radiationemitted by the planet, around 10.30–11.30 lm (channel 4)

and 11.50–12.50 lm (channel 5), respectively (Key andIntrieri, 2000).

In order to obtain the LST value, images of the channels4 and 5 of AVHRR need to be transformed. An approachbased on the differential absorption in two adjacent infra-red channels, called the “Split-Window” technique, is usedfor determining LST (Price, 1984). Lots of algorithms havebeen propounded by researchers (Price, 1984; Becker andLi, 1990; Vidal, 1991; Sobrino et al., 1994; Coll et al.,1994; Katsiabani et al., 2009; S�ahin and Kandırmaz,2010; Zaksek and Ostir, 2012). These studies indicated thatit is possible to retrieve LST at a reasonable accuracy(RMSE of 1–3 K) from current operational and researchsatellite-borne visible/infrared radiometers.

In this study, split-window technique proposed by Priceis used to get LST (Price, 1984). The technique assumesthat atmospheric attenuation (due to mostly atmosphericwater vapor) is greater in channel 5 than in channel 4and that the difference in measured radiance between thetwo channels increases with increasing water vapor (Price,1984). Firstly, raw data of NOAA 12-14-15/AVHRRwhich had no cloud, are translated into Level-1B formatby using Quorum Software and in second step, brightnesstemperature of channel-4 and channel-5 (range 10.3–11.3 lm and range 11.5–12.5 lm, respectively) are obtainedfrom Level-1B data by using Envi 4.3 image-processingprogrammer. Then, radiometric and geometric calibrationsare applied to the images to correct the deficiencies andflaws in the imaging sensors of the satellite.

As it is known, basic split-window technique is writtenas given in Eq. (1):

T s ¼ ½T 4 þ aðT 4 � T 5Þ þ b� ð1Þwhere coefficient a and b account for atmospheric condi-tions (related to spectral radiance and transmission) and

Fig. 1. Distribution of stations used for training, validation and testing.



surface emissivity respectively. However, linear empiricalformulations do not always hold. Hence, water vapordependence is subsequently incorporated in a nonlinearquadratic equation (Coll et al., 1994; Franc�ois and Ottle,1996; Katsiabani et al., 2009; S�ahin and Kandırmaz,2010; Zaksek and Ostir, 2012). Coefficient a in Eq. (1) is gi-ven as follows:

a ¼ a5

a4

� �� 1

� ��1

ð2Þ

where a5/a4 is determined from DT5 (DT4)�1 (spatial varia-tions of brightness temperature in channels 5 and 4 ofAVHRR) for small area under study. The value of a5/a4

is calculated to be 1.30, a = 3.33 and b is linked to differ-ence of emissivity De ¼ e4 � e5, and e depends on e4 ande5 as in the formulation e ¼ e4þe5

2, where e4 and e5 are emis-

sivities of channel 4 and channel 5; T4 and T5 are brightnesstemperatures of channel 4 and channel 5 of NOAA/AVHRR, respectively (Dash et al., 2002). e4 and e5 arethe surface emission coefficients which are estimated fromatmospherically corrected and normalized difference vege-tation index (NDVI) using the equations given by Valorand Casselles for channel 4 and channel 5, respectively (Va-lor and Casselles, 1996).

e4 ¼ 0:9897þ 0:029 ln ðNDVIÞ ð3Þe4 � e5 ¼ 0:01019þ 0:01344 ln ðNDVIÞ ð4Þ

where NDVI is a simple graphical indicator that can beused to analyze RS measurements and assess whether thetarget being observed contains live green vegetation ornot. Live green plants absorb SR in the photo-syntheticallyactive radiation spectral region, on which they use as asource of energy in the process of photosynthesis. Leaf cellshave also evolved to scatter (i.e., reflect and transmit) SR inthe near-infrared spectral region (which carries approxi-mately half of the total incoming solar energy) becausethe energy level per photon in that domain (wavelengthslonger than about 700 nm) is not sufficient to be useful to

synthesize organic molecules. A strong absorption at thesewavelengths would only result in over-heating the plantand possibly damage the tissues. Hence, live green plantsappear relatively dark in the photo-synthetically activeradiation and relatively bright in the near-infrared (Gates,1980). In contrast, clouds and snow tend to be rather brightin the red (as well as other visible wavelengths) and quitedark in the near-infrared. The pigment in plant leaves,chlorophyll, strongly absorbs visible light (from 0.4 lm to0.7 lm) for use in photosynthesis. The cell structure ofthe leaves, on the other hand, strongly reflects near-infra-red light (from 0.7 lm to 1.1 lm). The more leaves a planthas, the more these wavelengths of light are affected. Sinceearly instruments of earth observation, such as NOAA’sAVHRR, acquired data in visible and near-infrared, it isnatural to exploit the strong differences in plant reflectanceto determine their spatial distribution in this satelliteimages. The NDVI is calculated from these individual mea-surements as follows:

NDVI ¼ NIR� VIS

NIRþ VISð5Þ

where VIS and NIR stand for the spectral reflectance mea-surements acquired in the visible (red) and near-infrared re-gions, respectively (Goward et al., 1991; Santos and Negri,1997). The last form of equation is as follows:

T s ¼ ½T 4 þ 3:33ðT 4 � T 5Þ�5:5� e4

4:5

� �� 0:75T 5De ð6Þ

3.2. Artificial neural network

Artificial neural network (ANN) is a mathematicalmodel that tries to simulate the structure and/or functionalaspects of biological neural networks. It consists of aninterconnected group of artificial neurons and it processesinformation using a connection to approach the computa-tion. In most cases an ANN is an adaptive system thatchanges its structure based on external or internal informa-tion that flows through the network during the learningphase. They can be used for modeling complex relation-ships between inputs and outputs or finding patterns indata. Basically, the advantages of ANNs are that theyare able to represent both linear and nonlinear relation-ships and learn these relationships directly from data(Haykin, 1999). ANNs have been trained to overcomethe limitations of the conventional approaches to solvecomplex problems (Kalogirou, 2000).

The use of the ANNs for modeling and prediction pur-poses has been increasingly becoming popular in the lastdecades. Researchers have been applying the ANN methodsuccessfully in various fields of mathematics, engineering,medicine, economics, meteorology, psychology, neurology,in electrical and thermal load predictions, in adaptive androbotic control and so on (Cam et al., 2005; S�ahin, 2012;S�ahin et al., 2012). An ANN modeling is composed of aninput layer, one or more hidden layer, and an output layer.

Fig. 2. The typical ANN architecture.



Generally, the number of neuron in the input layer is equa-ted to the input number in the problem while the number ofneuron in the output layer is equated to the desired outputnumber. The number of hidden layer and the neuron num-ber in the hidden layer are determined by trials. The cells inthe input layer are sent to the next layer without makingany changes on the input. In the hidden layer, inputs andrelevant weights are multiplied, and then the results aretransmitted to transfer function (Yongjae and Sehun,2005). The typical ANN architecture can be seen in Fig. 2.

Neurons in each of the layer and weights that connectthese to one another are shown in Fig. 2. The items shapedlike spheres represent neurons while lines that bind neuronsto one another represent for weights. One of most impor-tant issue in an ANN is the bindings that provide datatransmit between neurons. A binding that transmits datafrom a neuron to another one has also a weight value.G(x) is a summation function, and calculates the exactinput that comes to a neuron. The input, by multiplyingwith variables and weight coefficients builds up input forG(x) summation function. The basic structure of an artifi-cial neuron is shown in Fig. 3.

Mathematical statement of an artificial neuron can bewritten as;

yi¼F ðGðxÞÞ¼FXn

i¼1

wijxj�Qi

!; xi¼ðx1;x2; . . .xnÞ ð7Þ

where x = {x1,x2,x3 . . .xn} is an input variable to be pro-cessed. On the other hand, w = {w00,w01, . . .wij} is weight,and it shows the importance of a data incoming to neuronand the impact on the neuron (Karem et al., 2008). The val-ues of the weights can change at the process of training. Qi,represents for threshold value whereas F(.) is activationfunction. An activation function takes the neuron input va-lue and produces a value which becomes the output valueof the neuron. A neuron is connected to other neuronsvia its input and output links. Each incoming neuron hasan activation value and each connection has a weight asso-ciated with it. The neuron sums the incoming weighted val-ues and this value is input to an activation function. Theoutput of the activation function is the output from theneuron. There are different activation functions such as sig-

moid, tangent sigmoid, sin, and radial basis. In ANN, all ofthe neurons may have the same or different activation func-tions. Especially, many ANN models, to be able to makethe calculations easier, require activation functions ofwhich derivatives can be taken. Type of activation functionis decided in consequence of the user trials.

There are many types of ANN architectures for variousapplications in the literature. Radial basis function net-works and multi-layer perceptron are the examples offeed-forward networks. However, MLP is the simplestand the most commonly used ANN architecture for predic-tion (Sozen and Akcayol, 2004). ANN architecture used inthis study is a multilayer feed-forward network with a sin-gle hidden layer, as shown in Fig. 4. The model composesof input layer, hidden layer and one output layer.

As aforementioned, there is no mathematical formula todetermine type of the activation function and the number ofoptimum neuron in the hidden layer of ANN. Thus, type ofactivation function and the number of neuron in the hiddenlayer must be usually decided after training of network. Inthis study, to be able to obtain the relatively optimum net-work model, the number of neuron in the hidden layer ischanged between 2 and 50 in step of 2 and the different con-figurations according to type of activation functions aretested. At the end of the 25 training runs, the best perfor-mance which is measured according to RMSE is obtainedfrom ANN configuration in Table 2. As can be seen, thelearning algorithm is the Levenberg–Marquardt. The acti-vation function of the model in the hidden layer is tansig,while the activation function in the output layer is linear.Furthermore, there are 5 neurons in the input layer ofANN, 26 in the hidden layer, and 1 in the output layer.

3.3. Multiple linear regression

The analysis of multiple linear regression (MLR) is astatistical method that examine cause-effect relationshipsbetween dependent and independent variables. In MLR,the relationship between input variable more than one (x1

,x2, . . .xn) and a dependent variable (y) is examined. Theregression function that will be used here is defined asfollow:

x1

x2

xn

xn-1

∑

w1

w2

wn-1

wn

Synaptic weightsInputs

∑ −= F(G(x)) y

y=1/[1+exp(-G(x))]

Activation function

Q

Processing element

Output

Fig. 3. The basic model of an artificial neuron.



y ¼ b0 þ b1x1 þ b2x2 þ � � � þ bnxn ð8Þ

where it is accepted that each independent variable has alinear relationship with a dependent variable (Civelekogluet al., 2008).

The functional connection between dependent and inde-pendent variable can be stated with matrix form as below.

Y ¼ Xbþ e ð9Þ

where Y is an output variable vector of size n � 1; X is aninput variable matrix of size n � (p + 1); b is a coefficientvector of size (p + 1) � 1 and e is an error vector of sizen � 1. According to Eq. (9), a variable multi-linear of p

regression can be written as below;

Y 1

Y 2

�Y n

26664

37775 ¼

1 X 11 � X 1p

1 X 21 � X 2p

� � � �1 X n1 � X np

26664

37775

b1

b2

�bn

26664

37775þ

e1

e2

�en

26664

37775 ð10Þ

b regression parameter coefficients in matrix can beshowed as below;

b ¼ ðX 0X Þ�1X 0Y ð11Þ

where b regression coefficients are obtained through leastsquare method (Apaydın et al., 1994; Ozdamar, 2004).

3.4. Performance criteria

In this study, the estimation performances of the bothmodels (ANN and MLR) are tested using the followingstatistical error criteria: root mean square error (RMSE),mean bias error (MBE), and coefficient of determination(R2). The two models are compared on the basis of statis-tical error criteria. The accuracy and the consistency ofSR estimation for the two methods are determined by usingthese criteria. They are defined by the following equations(Ma and Iqbal, 1983; Akinoglu and Ecevit, 1990; Bakirci,2009):

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

n

Xn

i¼1

ðY i � Y iÞ2s

ð12Þ

MBE ¼ 1

n

Xn

i¼1

½Y i � Y i� ð13Þ

R2 ¼Pn

i¼1ðY i � �Y iÞ2 �Pn

i¼1ðY i � Y iÞ2Pni¼1ðY i � �Y iÞ2

ð14Þ

where, Y is the actual SR value; �Y is the mean of actual SRvalue; Y is the estimated SR value and n is the total numberof observations. The MBE provides information on thelong-term performance of a model. A positive MBE repre-sents an overestimation while a negative MBE shows anunderestimation. The RMSE provides information on theshort-term performance of a model. The value of RMSEis always positive, representing zero in the ideal case (Maand Iqbal, 1983). The R2 can be used to determine the lin-ear relationship between the measured and estimated val-ues (Bakirci, 2009). For ideal data modeling, RMSE andMBE should be closer to zero, but value of R2 should ap-proach to 1 as closely as possible.

4. Results and discussion

4.1. Estimation of land surface temperature

As aforementioned, LST considered as an importantinput parameter should be estimated to get SR. In thisway, the data of NOAA 12-14-15/AVHRR are initiallyconverted into Level-1B format that can be recognized byImage Processing Programs via Quorum software. Then,radiometric and geometric editing of the images in the for-mat of Level-1B is done by employing Envi 4.3 and Idrisiimage processing programs. The prime factor in determin-ing LST is the value of brightness temperature. The bright-ness temperatures of the 4th and 5th channels of the imagesare acquired once again through Envi 4.3 and Idrisi Andesimage processing programs. Another factor that is neces-sary to calculate LST is the value of NDVI. In Eq. (5),1st and 2nd channels of NOAA 12-14-15/AVHRR areemployed to get the stated values, and NDVI images areobtained. Then, the value of emissivity for the 4th and5th channels of the satellite is achieved by using NDVIimage in Eqs. (3) and (4). By adding e4 and e5 values, whichwere calculated before, to De = e4 � e5 and e ¼ e4þe5

2for-

mula, the emissivity difference and mean of emissivity ofthe 4th and 5th channels are acquired, respectively. Subse-quently, the maps of LST are obtained according to Eq.(6). LST obtained at 03.41 pm with local time on 11 August2002 through split window algorithm is shown in Fig. 5.

As can be seen in Fig. 5, most of the LST over Turkeyhas values between 302 K and 314 K. It is understood fromthe map that Central Anatolia and South Eastern Anatoliahas a very high temperature at the stated hour. Moreover,the temperature in East Black Sea region has a temperaturebetween 281 K and 296 K. Similarly, 47 monthly average

Altitude

Latitude

Longitude

Months

LST

Solar radiation

1

n

Fig. 4. ANN architecture used in this study.



LST satellite images are totally acquired providing thatleast one satellite image per month that based on split win-dow algorithm for every year from 2000 through 2002.

Over the relevant images, LST values are obtained byusing the coordinates of 73 locations stated in Table 1.By using Eqs. (12)–(14), 2628 LST values obtained viasatellite are compared to those taken from Turkish StateMeteorological Service. As a result of the comparison,R2, MBE and RMSE values are found to be 0.940,0.339 K and 2.730 K, respectively. And also, all of themare shown in Fig. 6.

In the previous studies, LST was estimated for variousregions of the world using satellite data. It is emerged thatRMSE range is between 1 K and 3 K (Price, 1984; Beckerand Li, 1990; Vidal, 1991; Sobrino et al., 1994; Collet al., 1994; Katsiabani et al., 2009; S�ahin and Kandırmaz,2010; Zaksek and Ostir, 2012). As a result, it is shown thatthe results of this study are in good agreement with the lit-erature because the value of RMSE is found to be 2.73 K.

4.2. Estimation of solar radiation

As mentioned in Section 2, this study is realized withtwo different datasets, called DS1 and DS2. WhereasLST, which used as input in DS1, is obtained throughNOAA/AVHRR satellite, LST values of the other one(DS2) are obtained through meteorological (ground) mea-surements, which are used for evaluating overall perfor-mance of the study. The rest of input variables such asaltitude, latitude, longitude and month are common vari-ables in two data sets. In other word, while LST, altitude,latitude, longitude and month are used as input, SR is

Table 2ANN architecture and training parameters.

Architecture The number of layers 3The number of neuron onthe layers

Input: 5, Hidden: 26,Output: 1

The initial weights andbiases

Random

Activation functions Hidden: tansig, Output:linear

Trainingparameters

Performance function RMSEMaximum validationfailure

5

Learning rule Levenberg–Marquardtback-propagation

Learning rate 0.5Moment constant 0.99Performance goal 1E�08

Fig. 5. LST map depending on split window algorithm.

250 260 270 280 290 300 310 320 330250

260

270

280

290

300

310

320

330

Sate

llite

valu

es (K

)

Fig. 6. The comparison of LST values obtained through split windowalgorithm with meteorological values.



obtained from the output. Firstly, DS1 dataset from 2000to 2002 at 73 locations is used for modeling and testingANN. This dataset is split into three parts (60%–20%–20%): 43 locations for training, 15 locations for validation,and the remaining 15 locations for testing. The first andsecond parts (1548 input/output pairs for training) and540 input/output pairs for validation) are used to selectthe best model whereas remaining part (540 input/outputpairs for testing) is reserved to test the estimation accuracyof methods in these unseen locations after the training.Here, the main purpose of a validation dataset is to preventoverfitting by measuring the error with respect to this inde-pendent data which is not used in training. Accordingly,when the chosen error of the validation dataset is lowerthan its value in the previous iteration, the training of thenetwork is maintained; otherwise, the training is ended.

In this way, the best ANN configuration for DS1 isobtained (see Table 2). After training process, a compari-son is performed between the estimated SR and the mea-surement ones at 15 test locations, which is considered asunseen locations. Similarly, same data set (DS1) which isused for modeling ANN is also used to build MLR model.Figs. 7 and 8 show the estimation results of the DS1 forANN and MLR. As seen in Fig. 7(c), for overall of 15 loca-tions, ANN model gives good prediction performance withthe lowest RMSE of 2.018 MJ/m2, MBE of �0.213 MJ/m2,and highest R2 of 0.913, which is better than MLR model.In addition, a comparison is performed between theestimated SR and the measured ones at the training andvalidation datasets in order to examine the training perfor-mance. Their results are also illustrated in Figs. 7(a) and (b)and 8(a) and (b). As seen, the error rates of training and

0 5 10 15 20 25 300

5

10

15

20

25

30R2= 0.913MBE = -0.213RMSE = 2.018

0 5 10 15 20 25 300

5

10

15

20

25

30

R2 = 0.901MBE = 0.282RMSE = 2.234

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

R2 = 0.946MBE = -0.167RMSE = 1.554

Estim

atio

n (M

J m

-2)

N = 540 N = 540N = 1548

a b c

Fig. 7. Comparison between ANN model estimation and (a) measurements at 43 training locations, (b) measurements at 15 validation locations and (c)measurements at the rest 15 training locations.

5 10 15 20 25 30

5

10

15

20

25

30 R2 = 0.798MBE= -0.509RMSE= 3.069

Estim

atio

n (M

J m

-2)

0 5 10 15 20 25 300

5

10

15

20

25

30 R2= 0.769MBE = 0.547RMSE= 3.334

0 5 10 15 20 25 300

5

10

15

20

25

30

R2 = 0.760MBE= 0.581RMSE= 3.259N = 540 N = 540N = 1548

a b c

Fig. 8. Comparison between MLR model estimation and (a) measurements at 43 training locations, (b) measurements at 15 validation locations and (c)measurements at the rest 15 testing locations.



validation dataset are very close to those from test set. Itproves that validation dataset used for early stopping canreduce the overfitting effect.

The above analysis may not guarantee that the builtmodels can be used to estimate SR on the desired area.Thus, the functional relationship between input parameters

0 5 10 15 20 25 300

5

10

15

20

25

30R2 = 0.656MBE = 0.698RMSE = 4.031N = 540

0 5 10 15 20 25 300

5

10

15

20

25

30R2 = 0.906MBE = 0.262RMSE = 2.129N = 540

Estim

atio

n (M

J m

-2)

a b

Fig. 9. The results at 15 testing locations for DS2 (a) Comparison between ANN model estimation and measurements, (b) Comparison between MLRmodel estimation and measurements.

0 5 10 15 20 25 30 350

10

20

30

40

50

SR (M

J m

-2) ANN

MLRMeasurement

0 5 10 15 20 25 30 350

10

20

30

40

50ANNMLRMeasurement

0 5 10 15 20 25 30 350

10

20

30

40

50ANNMLRMeasurement

0 5 10 15 20 25 30 350

10

20

30

40

SR (M

J m

-2)

0 5 10 15 20 25 30 350

10

20

30

40

0 5 10 15 20 25 30 350

10

20

30

40

0 5 10 15 20 25 30 350

10

20

30

40

SR (M

J m

-2)

0 5 10 15 20 25 30 350

10

20

30

40

0 5 10 15 20 25 30 350

10

20

30

40

0 5 10 15 20 25 30 350

10

20

30

40

SR (M

J m

-2)

0 5 10 15 20 25 30 350

10

20

30

40

0 5 10 15 20 25 30 350

10

20

30

40

0 5 10 15 20 25 30 350

10

20

30

40

SR (M

J m

-2)

0 5 10 15 20 25 30 350

10

20

30

40

0 5 10 15 20 25 30 350

10

20

30

40

a b c

Time period from 2000 to 2002 Time period from 2000 to 2002 Time period from 2000 to 2002

d e f

g h i

j k l

m n o

Fig. 10. Individual results at each testing locations. They are Adana, Ankara, Antalya, Balıkesir, Bitlis, Corum, Duzce, Erzincan, _Izmir, Kayseri,Malatya, Mugla, S�anlıurfa, Yalova, Rize from (a) to (o), respectively.



of DS1 and SR must be verified by comparison with thoseobtained from DS2. For this purpose, the SR estimationresults from DS1 are also compared with those obtainedfrom DS2. The estimation performances of the both mod-els (ANN and MLR) are presented in Fig. 9. As shown inFig. 9(a), RMSE, MBE and R2 values obtained from ANNmodel for DS2 are 2.129 MJ/m2, 0.262 MJ/m2 and 0.906,respectively. However, they are 4.031 MJ/m2, 0.698 MJ/m2 and 0.656 for MLR. As a result, SR estimations basedon DS1 (satellite observations) are in good agreement withSR estimations based on DS2 (ground measurements)though the results obtained from DS1 have an appreciableimprovement than those obtained from DS2. In addition,the comparison results showed that ANN model gave bet-ter results than MLR model for DS2.

Moreover, the results of this study are compared withthose of the previous SR estimation studies in the literatureso that the validity of the results and effectiveness of thestudy could be assessed. The papers of Lefevre et al.(2007), Yeom et al. (2008), S�enkal and Kuleli (2009) andLu et al. (2011) are selected for the comparison becauseof including satellite records of monthly-average SR using

ANN. In the previous studies, it is seen that the values ofRMSE which is one of the performance assessment criteriaare in the range of 1.63–3.94 MJ/m2. In this study, thevalue of RMSE is found to be 2.018 MJ/m2 when DS1 isapplied as input to ANN; whereas the same value is3.334 MJ/m2 by MLR. As can be understood from theerror statistics, this study is in good agreement with otherstudies in the literature although the built ANN modelthrough DS1 provides better results than those of Lefevreet al. (2007), Yeom et al. (2008) and Senkal and Kuleli(2009) studies, which their RMSE values are 2.16 MJ/m2,2.89 MJ/m2 and 3.94 MJ/m2, respectively.

In the above types of case studies, distribution of SRover Turkey was performed through all of test locations.In other case, the estimation accuracy of SR time seriesfor each test location is separately evaluated on basis ofstatistical error criteria by using only DS1. The acquiredresults are presented in Fig. 10 and the error statistics arealso comparatively given in Table 3. As seen in Fig. 10and Table 3, ANN method exhibits overall stronger retrie-val ability than MLR method at each testing locations. Atnine locations (Ankara, Balıkesir-Gonen, Corum, Duzce,

Table 3Estimation performance of two methods at each testing locations for DS1.

Site ANN MLR

RMSE (MJ/m2) MBE (MJ/m2) R2 RMSE (MJ/m2) MBE (MJ/m2) R2

Adana 2.089 1.462 0.942 3.093 1.929 0.850Ankara 1.361 �0.544 0.966 2.482 �1.351 0.905Antalya 2.214 1.318 0.946 4.013 1.980 0.773Balıkesir-Gonen 1.459 �0.426 0.951 2.655 0.064 0.845Bitlis 2.934 �2.369 0.936 3.456 �2.533 0.885Corum 1.299 0.456 0.966 2.169 �0.037 0.884Duzce 1.633 �0.775 0.941 3.655 0.259 0.756Erzincan 1.197 0.356 0.976 2.703 �0.021 0.878_Izmir 3.155 2.579 0.982 5.511 3.852 0.763Kayseri 1.416 0.056 0.955 2.032 �0.577 0.915Malatya 1.201 0.517 0.975 2.028 0.205 0.913Mugla 1.650 �1.338 0.976 2.529 �0.809 0.847S�anlıurfa 2.261 1.304 0.964 4.096 2.541 0.818Yalova 1.749 0.204 0.971 2.544 0.062 0.876Rize 3.026 �2.327 0.911 4.726 �2.216 0.606

23

12

8

16

4

0

Fig. 11. Yearly average SR map estimated by ANN model.



Erzincan, Kayseri, Malatya, Mugla, Yalova), SR estima-tions are more accurate than the results obtained throughoverall of 15 test locations, where RMSE was found tobe 2.018 MJ/m2. However, it is found that the obtainederrors are slightly large at remaining locations (Adana,Antalya, Bitlis, _Izmir, S�anlıurfa, Rize) and biggest RMSEvalue reach 3.14 MJ/m2 at _Izmir: that is, it is still an accept-able RMSE level. It proves that ANN model can be used toestimate SR for any location within the study region.

As shown in above case study, SR may estimate by usingmeteorological station-based data with high accuracy.However, it is impossible to estimate SR on the desiredarea, where records of input variables are unavailable.The ANN model constructed by using satellite-based data(DS1) can be applied to estimate SR over the Turkey andits surroundings because the input variables can be easilyprovided by using satellite-based observations on thedesired area. In Fig. 11, the results are illustrated as mapsshowing the yearly average of daily SR over the Turkeyand its surroundings. It is observed that high SR areas pro-gressively expand from the southern coastal areas to thesoutheastern part of the country with irregular pattern.In the southern coastal areas of the country, most areasreceive SR in the range of 16–18 MJ/m2 whereas in thesouthern inner part, SR is in the range of 12–15 MJ/m2.Moreover, in some locations of this area, SR is observedslightly in the range of 18–20 MJ/m2. In the southeast,most areas receive radiation in the range of 16–21 MJ/m2

whereas in the southeastern inner part, SR is in the rangeof 12–16 MJ/m2. The low SR areas are in the northeasternpart of the country, where it is in the range of 6–12 MJ/m2.Finally, the yearly average of daily SR over country isfound to be 16.1 MJ/m2.

5. Conclusion

In this paper, the estimation capabilities of two differentapproaches are comparatively presented for estimating SRas a function of LST over Turkey. They are ANN andMLR models, which are also used commonly in differentareas. To test the effectiveness of the study, a number ofcase studies on 73 locations covering approximately thewhole of Turkey are carried out. Two different data sets(DS1, DS2) are used in the study. Whereas LST, which isused as input in the first data set (DS1), is providedthrough records of NOAA/AVHRR satellite, in the seconddata set (DS2), LST is obtained through records of meteo-rological station. Five independent variables such as satel-lite-estimated LST, altitude, latitude, longitude and monthare applied as the input to ANN and MLR models, sepa-rately. The performance of models is evaluated usingRMSE, MBE and R2. With the use of ANN for DS1, thevalues with R2 of 0.913, RMSE of 2.018 MJ/m2 andMBE of �0.213 MJ/m2 are found. With the use of MLR,the values with R2 of 0.769, RMSE of 3.334 MJ/m2 andMBE of 0.547 MJ/m2 are acquired. Similarly, for DS2 dataset, R2 value of 0.906 is found on the use of ANN. In addi-

tion, RMSE and MBE values are determined as 2.129 MJ/m2 and 0.262 MJ/m2, respectively. For MLR, the error sta-tistic values are R2 of 0.656, RMSE of 4.031 MJ/m2 andMBE of 0.698 MJ/m2. For both data sets, R2 acquired withANN is found higher than the result obtained throughMLR, and RMSE and MBE values are achieved lower.In this case, it is seen that the ANN model is more success-ful than MLR for estimating SR. Moreover, the ANNmodel is applied in order to map the SR distribution overthe Turkey. The obtained map illustrates that yearly aver-age daily SR is found to be 16.1 MJ/m2 for all areas ofTurkey.

Finally, this study has showed that the usage of satellitebased data instead of meteorological data for estimatingSR, gives more accurate results. This result is very impor-tant because the installation of meteorological stations allacross the country and achieving consistent measurementsare hard and economically burdensome. Even if they arefounded, the distribution of the stations may not be inthe desired level because of geographical conditions.Instead of meteorological stations, the meteorological sat-ellites which are capable of scanning a whole district willbe more reasonable. In addition, the usage of satellite dataand ANN can help researchers develop SR distributionmaps for cities and countries. It is expected to be a poten-tial tool for analysis and design of solar energy systems.

Acknowledgments

We would like to express our gratitude to Republic ofTurkey Ministry of Forestry and Water Affairs (TurkishState Meteorological Service) personnel, providing us everykind of facilities on getting the meteorological data and toScientific and Technological Research Council of Turkey-Bilten personnel, providing every kind of facilities on get-ting the satellite data.

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