de

f, Sw

Statistical modelComparison

WE)kmsicahe oridapsnce

with a mean difference in the total volumes between the two statistical models of 8%, and betweenthe physical model and the statistical ones of 3% to 10%.

glacieand rein thenaturautes to

the interface between snow and ground (see e.g. [22,67]). Snow

(e.g. [1]).SWE is fundamental to quantify the availability of water re-

sources, to study the spacetime distribution of snow (see e.g.[8,12,61,64]) and to evaluate the snowmelt and its impact onspring and summer ows in snow inuenced watersheds (seee.g. [47,57,63]). SWE modeling is also of great importance tounderstand the distribution and dynamics of water resources in

resolution or larger areas at very coarse spatial resolution.tion of SWE byr a givential interp

by the snow covered area provided by remote s([7,18,34,41,42,50,53,58]). The interpolation has been carrby kriging, or altitude-detrended kriging, [14,15], bydistance weighting [24,43], by regression-like models, includingbinary tree regression [3,23], hypsometric-detrending [17],multivariate [25], and generalized additive models [43]. Statisticalmodels are usually employed to calculate the spatial distribution ofSWE at the end of the accumulation season to estimate the totalsnow water availability (see e.g. [7,8,15,23]). As rule of thumb,the end of the accumulation season is often assumed to occur atthe beginning of April. For example, for the Italian Alps, April 1st

Corresponding author. Tel.: +39 02 23996233; fax: +39 02 23996207.

Advances in Water Resources 63 (2014) 167178

Contents lists availab

a

lseE-mail address: carlo.demichele@polimi.it (C. De Michele).cover patterns show a great variability in space and time [11,68],both at macro [20] and micro [44] scales is very important tounderstand the processes behind the snow distribution patterns

Statistical models provide a spatial distribuspatially interpolating local SWE values ove(e.g. [2,15,19,23,65]) or conditioning the spa0309-1708/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.advwatres.2013.11.011areaolationensingied outinverseing season. The snow water equivalent is the water height thatwould result from the instantaneous melting of the entire snowpack. The dynamics of SWE are governed by snow accumulation[40,52], ablation [48] and redistribution [51]. These in turn aregoverned by precipitation, energy transfer and several forces, suchas gravity and wind, at the interface between snow and air and at

ing energy and mass balance equations for the snowpack over agrid. The application of physically-based models often requires alarger meteorological data set and larger computational efforts[26,39,40,46] in order to provide higher quality results. Thus phys-ically-based models are suitable for areas discretized into a rela-tively small number of pixels, i.e. small areas at high spatial1. Introduction

Melt water from snowpacks andsource for agriculture, hydropower,cold, mountain environment, anddeposited on the ground works as athe accumulation season and contrib 2013 Elsevier Ltd. All rights reserved.

rs is a fundamental re-creational use both inlower valleys. Snow

l water storage duringrivers during the melt-

mountainous areas, in present and future climate conditions[4,5,9,33,45,56].

In the Literature, the spatial distribution of SWE over a certainarea has been calculated using either physically-based models(e.g. CROCUS [35], GEOTOP [69], ALPINE3D [29,39] or statisticalmodels (e.g. [16,32,42,43,49,60]). Physically-based models attemptto describe the dynamics of SWE accumulation and ablation solv-Snow water equivalentPhysical model tribution of SWE. The comparison shows a general good agreement of the results of the three models,A comparison between two statistical anin snow water equivalent mapping

D. Bavera a,b, M. Bavay b, T. Jonas b, M. Lehning b, C. DaDICA, Politecnico di Milano, P.zza L. da Vinci 32, I-20133 Milano, ItalybWSL Institute for Snow and Avalanche Research SLF, Flelastr. 11, CH-7260 Davos Dor

a r t i c l e i n f o

Article history:Received 13 January 2010Received in revised form 26 November 2013Accepted 27 November 2013Available online 4 December 2013

Keywords:

a b s t r a c t

Snow water equivalent (S20022006 period in a 200model, ALPINE3D, is a phymass balance equations. Tpolating snow data on a ginterpolated snow depth mcuss similarities and differe

Advances in W

journal homepage: www.ea physically-based model

Michele a,

itzerland

estimates at the end of the winter season have been compared for the2 mountainous area in Switzerland, using three different models. The rstlly based process-oriented model, which solves the snowpack energy andther two models, SWE-SEM and HS-SWE, are statistical algorithms inter-. While SWE-SEM interpolates local estimates of SWE, HS-SWE convertsinto maps of SWE using a regionally-calibrated conversion model. We dis-s among the models results, both in terms of total volume, and spatial dis-

le at ScienceDirect

ter Resources

vier .com/ locate/advwatres

bution of SWE over a certain area. Physically-based models

ded snow depth distribution maps. These maps thus only reect

temperature) are not explicitly considered here.

discharge.

ateraltitude gradients and spatial patterns resolved by the snow sta-tion network. The software used for interpolation is WinMet,which is part of the hydrological modeling system PREVAH (Vivir-oli et al., [66]). Then the snow depth distribution maps were con-verted into SWE distribution maps using an empirical conversionmodel based on historical data of HS and SWE as described in detailin Jonas et al. [31]. Since SWE Hsqs=qw, SWE can be calculatedfrom HS if the local snow bulk density qS is known, where qw isthe water density. qw is assumed to be 1000 kg/m3. qs is typicallyin the range of 100600 kg/m3. In the conversion model, qS isexpressed as a function of snow depth, date, altitude, and snow re-gion evaluated from biweekly measurements over ve decades at37 sites throughout the Swiss Alps (for details, see [31]. Thisparameterization allowed a season- and location-specic conver-sion of HS into SWE, which nally enabled to calculate maps ofSWE from HS maps.

2.2. SWE-SEM

SWE-SEM is a statistical model to estimate SWE distributionmaps using snow depth and density data at ground level and EOimages of snow covered area (SCA). For details see, Bavera andDe Michele [7]. SWE-SEM is a two-step procedure: (1) local SWEestimates are obtained at snow-gauged sites coupling snow depth(HS) measurements and snow density (qS) estimates, (2) the spatialattempt to provide an accurate description of the settled snow-pack. On the other hand, statistical models are quite simple andeasy to apply thus appealing from the practical point of view. Herewe compare the results of two statistical models vs. a physically-based model, to reveal if statistical models provide SWE estimatesclose to the ones provided by the physically-based models.

The spatial distribution of snow water equivalent at the end ofthe accumulation season over a Swiss mountain area is assessedexploiting three different models: (1) HS-SWE: a spatial interpola-tion method only based on ground data [31], (2) SWE-SEM: a sta-tistical regressive approach based on ground and earth observation(EO) data [7], and (3) ALPINE3D: a physically-based model [39].Section 2 outlines the models considered, Section 3 describes thecase study and hydro-meteorological data available, Section 4shows the models results, Section 5 discusses the comparison ofthe models results.

2. Models for the calculation of SWE

2.1. Hs-swe

HS-SWE calculates the spatial distribution of SWE from mea-surements of snow depth, HS, typically available from a set of snowgauges. For this work, snow depth data from 30 stations within orsurrounding the study area were interpolated over a grid. A simplesegmental linear detrending scheme was applied in combinationwith a local inverse distance weighting correction to generate grid-is used as a reference date (see e.g. [13,57]). Of course this date isvariable from site to site, particularly depending on altitude.Statistical models can be applied over both small and large areas,without restrictions on the spatial extent and resolution. Theuser-friendly application of statistical models makes them widelyapplied, especially in operational applications.

In the literature, no studies are available on the comparison be-tween statistical and physically-based models for the spatial distri-

168 D. Bavera et al. / Advances in Wdistribution of SWE over the basin is derived from local SWE esti-mates via an interpolation based on linear regressions of the rsttwo order moments of SWE with altitude.3. Study area

The study area, approximately 200 km2, is located in the south-eastern part of Switzerland in the canton of Grisons, on the northface of Alps, near the border with Austria (see Fig. 1). Because ofthe high elevation, all the area is snow covered in the winter.The median elevation is approximately 2452 m a.s.l. while thehighest altitude is 3200 m a.s.l. and the lowest altitude is 1500 ma.s.l. It is made of 5.9% glacier and rn, 30% Alpine grassland, and37% rock, the rest being minor contributions from forests andbushes. The discharge from the area is dominated by snowmelt2.3. ALPINE3D

ALPINE3D is a model of mountain surface processes with par-ticular attention to snow cover. It is a spatially distributed exten-sion of SNOWPACK. This model represents the snowpack as amulti-layer domain with ground, soil and vegetation processesand uses a numerical nite elements scheme. Special features ofSNOWPACK are the parameterization of thermal conductivityand viscosity as functions of (parameterized) snow microstructure[37] and a detailed treatment of surface mass- and energy ex-change [38] and Stssel et al. [62]. SNOWPACK can simulate thedeposition and re-sublimation of surface hoar layers, shortwavepenetration into the snow cover and local phase changes andgives an overall reliable representation of the local snow massbalance if accurate forcing data is available. The vertical watertransport is described by a simple bucket scheme, a good approx-imation if a ne layer resolution (a few cm per layer) is chosen inthe numerical discretization.

Applications of ALPINE3D are given in Lehning et al. [39] andBavay et al. [5]. The same assumptions as previously describedwere used, in particular no explicit wind simulations have beenconsidered in this study (Raderschall et al., [55]) that would haveallowed running the snow transport module of ALPINE3D [40],because of the pixel size (100 m) and the length of the simulationperiod. For meaningful snow transport simulations, we should atleast work with a grid resolution of 25 m [40,51] and over ashorter time period. The spatial distribution includes shading ef-fects as well as a correction for atmospheric attenuation (com-pared to a clear sky atmosphere) from a point measurement atthe ground level, assuming that this correction coefcient re-mains constant over the whole domain, as described in Bavayet al. [5]. The model is completed by a conceptual runoff modulewhich takes the runoff from the vegetation, snow and soil col-umns through a series of linear reservoirs to produce streamowThe SWE in a point of the basin, parameterized through thevector u and for the year j, is calculated as SWEju ESWEu SWEj urSWEu, where ESWEu and rSWEuare respectively the mean and the standard deviation of SWE andSWEj u is the standardized snow water equivalent. ESWEuand rSWEu are calculated using simple linear regressionsagainst the altitude.

SWE-SEM calculates the spatial distribution of SWE consideringonly the principal factors affecting the distribution and the statusof snow: the altitude, the age of the snowpack and the local slope.Other factors like the aspect or climatic issues (i.e. mean annual

Resources 63 (2014) 167178in late springsummer.For details about the study area, and the relative APINE3D sim-

ulation see also Bavay et al. [4].

e ga

ater3.1. Snow and meteorological data

The study region features a high density of snow and weatherstations from several different monitoring networks. Stations con-sidered in this study are listed in Table 1. Two networks (IMIS,ENET) have automated measuring stations, while other two (KSand VGMS) deliver daily manual snow depth readings.

The IMIS network covers alpine sites and predominantly pro-vides the Swiss avalanche forecasting service with snow meteoro-

Fig. 1. Switzerland and in the box, the study area indicated with a square. Th

D. Bavera et al. / Advances in Wlogical data. Its snow stations are situated in mountainous sitesand measure standard parameters such as wind, air temperature,relative humidity, snow depth, surface temperature, soil tempera-ture, reected shortwave radiation and three temperatures withinthe snow cover. For more details about the IMIS network, see Leh-ning et al. [36].

ENET stations belong to networks of automated meteorologicalstations run by MeteoSwiss (MeteoSwiss web site). Measuredparameters are similar to those of the IMIS network. Most of thesestations are located outside alpine terrain, however one station(NAS) was in the vicinity of our study area.

KS and VGMS sites provide daily manual observations. KS sitesare managed by MeteoSwiss (and referred in their website as Vi-sual observations network) and give meteorological parameters,while VGMS sites predominantly provide snow cover specicinformation. For further information on the networks see http://www.meteoswiss.admin.ch/web/en/climate/observation_systems/surface.html and http://www.slf.ch/ueber/organisation/warnung_praevention/projekte/beobachter/index_DE.

3.2. HS-SWE and SWE-SEM data requirements

SWE-SEM requires both snow depth and density as input. Thisinput was available from 14 regional snow stations (IMIS). HS-SWE on the other hand can include additional data from locationsthat only provide snow depth readings. In total we selected 30 sta-tions to provide input for HS-SWE. Even if some of those were fur-ther away from the study area, they provide useful informationabout the snow depth distribution on the area and also allow cov-ering a wider range of altitude. The altitudinal distribution of snowis the key input to HS-SWE. The station selection for both models isavailable in Table 1.

The stations vary in altitude from about 500 m a.s.l. to 2700 ma.s.l. even if most of them are located in the range between 2000and 2500 m a.s.l.

The snow density is not regularly measured at all IMIS stations.Since only the snow depth is collected on a daily basis at the snow-gauging sites, an estimate of snow density is necessary to calculatethe corresponding SWE.

uging stations used in the three models are indicated with different symbols.

Resources 63 (2014) 167178 169With the HS-SWE model, SWE was calculated from HS using anexternal model which was calibrated and validated in a previouswork [31]. On the other hand, SWE-SEM includes a local/specicparameterization of the snow density for the SWE computation.Near the VGMS stations, SWE regular manual measurements areavailable, in general with biweekly frequency. In addition, otherSWE data come from manual surveys (regular and occasional pro-les obtained from snow pits). Globally, a sample of about 2900snow density measurements over a period of 40 years is available.The dataset is very well distributed in time: measurements are ta-ken from October to July, with a little reduction during the latemelting season due to the presence of snow only at the highestaltitudes. The dataset covers altitudes from 1200 to almost3000 m a.s.l., while most of the measurements are carried outaround about 2000 m a.s.l. The dataset is composed of two kindsof measurements: regular proles at manual stations (at), andoccasional proles on slopes for avalanche warning purposes. Thesnow proles collected in at areas are about 80% of the wholedataset. For this reason we have decided to not consider in the den-sity estimation equation the inuence of slope and aspect. For theformulation of snow density, we have considered as independentvariables: the altitude (z) and the number of days (D) after a refer-ence date (October 1st) for the beginning of the snowaccumulation.

The dataset of snow density has been divided in 9 subsets bythe month of measurement. For each month, a simple linearregression of snow density vs. altitude is calculated, see Fig. 2.The measurements of June and July are handled together becauseof their reduced number of points. From Fig. 2, one sees how inearly winter the snow density increases linearly with the altitude.

Table 1Location of the 37 stations used. The stations inside the 200 km2 study area are in italics.

Code Network Altitude X Y

m a.s.l. m m A3D SWE-SEM HS-SWE

BEV2 IMIS 2510 783,930 157,050 x xDAV2 IMIS 2560 782,100 174,760 x x xDAV3 IMIS 2450 778,300 184,580 x x xDAV4 IMIS 2330 779,125 184,125 xFLU2 IMIS 2390 791,600 180,975 x xKES2 IMIS 2725 788,350 166,300 x x xKLO2 IMIS 2140 785,500 198,200 x x xKLO3 IMIS 2310 790,100 190,800 x x xPAR2 IMIS 2290 780,430 191,680 x x xSLF2 IMIS 1560 783,800 187,400 x xWFJ2 IMIS 2540 780,850 189,260 x xZNZ2 IMIS 2680 797,300 175,080 x xSTIL 2083 785,451 183,141 x xROT2 IMIS 2700 765,050 179,550 xARO KS 1840 770,730 183,320 xCHU KS 555 759,460 193,170 xSAM KS 1705 787,150 156,040 xSCU KS 1298 817,130 186,400 x5DF VGMS 1560 783,800 187,400 x5KK VGMS 1200 787,340 192,900 x5KR VGMS 1195 786,190 193,800 x5KU VGMS 810 777,700 198,580 x5LQ VGMS 520 761,080 203,860 x5MA VGMS 1655 779,590 182,210 x5PU VGMS 940 772,770 206,100 x5SA VGMS 1510 782,250 205,320 x5VZ VGMS 1090 764,910 202,880 x5WJ VGMS 2540 780,845 189,230 x7BU VGMS 1970 816,500 170,250 x7FA VGMS 1710 813,640 186,150 x7LD VGMS 1710 810,590 170,650 x7MT VGMS 2150 816,140 188,280 x7MZ VGMS 1890 784,010 152,490 x7SC VGMS 1660 795,040 165,430 x7SD VGMS 1750 786,210 156,400 x7ZU VGMS 1710 793,350 164,590 xNAS ENET 2400 815,380 189,020 x

Fig. 2. Monthly variability of snow density with altitude. Dots indicate measurements, the lines the linear regressions. In the equations y is the snow density (kg/m3) and x isthe altitude (m).

170 D. Bavera et al. / Advances in Water Resources 63 (2014) 167178

Then in spring, the slope of this regression slowly decreases reach-ing an almost horizontal line with a very weak dependence fromaltitude during the melting season. This behavior is strongly re-lated with the beginning of the melting which depends on the alti-tude. At the lowest altitudes we observe early melting and the

snow density increases faster than at the highest altitudes. More-over at the highest altitudes and at the beginning of the accumula-tion season, there is often some old snow (sometimes left from theprevious year) and for this reason the average snow density of thewhole snowpack is higher than the snow density one can measureafter the rst snowfalls on the bare ground when there is only freshsnow.

The 9 linear regressions of snow density vs. altitude are in-cluded in the following compact form of the snow density (in kg/m3) as a function of the z (in m a.s.l.) and D (days after October1st): q^s a D b z c D d, where a = 0.00063, b = 0.10,c = 2.31, d = 61.79, having a coefcient of determination R2 ofabout 0.56. Fig. 3 shows the measured vs. calculated values of snowdensity.

We have focused our attention on the 20022006 period whenthe snow covered area (SCA) MODIS product (NASA MOD10A1) isavailable. For the SWE-SEM model we have conditioned the calcu-lation of snow water equivalent in DEM grid cells covered by snowin the snow covered area product, using a DEM with 200 m resolu-tion. A procedure to estimate the snow cover in cloud cover areashas been applied to this raw product to assess the complete snowcover [54].

3.3. ALPINE3D data requirements

ALPINE3D requires a variety of meteorological input data. It isrecommended to have at least one main meteorological stationwith air temperature TA, wind speed VW, relative humidity RH,precipitation P, incoming long and short wave radiation (respec-tively LW and SW). It is recommended to have a time resolutionof not more than three hours in the input data to reasonably

Fig. 3. Snow density: measured vs. estimated (using the equationq^s a D b z c D d, where a = 0.00063, b = 0.10, c = 2.31, d = 61.79, zis the altitude, and D is the number of days after October 1st) values.

D. Bavera et al. / Advances in Water Resources 63 (2014) 167178 171Fig. 4. Spatial distribution of SWE at the end of winter time, for each year of the 20022006 period, using HS-SWE.

resolve the diurnal cycle for the energy balance calculations. It isimportant to notice that ALPINE3D is driven by precipitation mea-sured by gauge stations and no direct observed data of snow depthor SWE are used as input.

We have selected the Versuchsfeld Weissuhjoch (WFJ) as themain AWS providing hourly data of shortwave and longwave radi-ation. The shortwave radiation is handled as described in Sec-tion 2.3, while the longwave radiation is spatially interpolatedwith a constant altitudinal gradient. We have selected 9 IMIS sta-tions, the non-IMIS Stillberg station and the ENET Davos (DAV) sta-tion for hourly values of TA, VW, RH. These stations are used toestimate altitudinal gradients and spatial interpolations of themeteorological parameters over the area.

The precipitation input is provided by two ENET stations(Weissuhjoch and Davos), and the non-IMIS Stillberg station be-cause they have a heated rain gauge. In order to compensate forthe precipitation gauge undercatch, a xed 30% correction factorhas been applied to solid precipitation, a 10% correction to mixedprecipitation and no correction to liquid precipitation [6,21]. Thesolid/mixed/liquid precipitation are distinguished through airtemperature thresholds as done by Goodison et al. [27]. The pointprecipitation measurements are spatially interpolated by apply-ing an altitudinal lapse rate recalculated for each time step fromthe data and an Inverse Distance Weighting distribution of theresiduals.

For the selected area, a grid with 100 m resolution has beenused for DEM, land-use map, and watershed denition. Snow, soiland vegetation information at the beginning of the simulation isrequired as initial condition for the model. These parameters arenot measured but constructed using an objective scheme fromthe land use map. We start the simulation with a no snow con-dition on 2000-10-01. The soil is initialized with typically 6 layersdepending on the land use map and a constant geothermal heatux is assumed, when ground temperature is not available.The canopy height, canopy leaf area index and canopy direct

Table 2Total snow water volume, and spatial mean of snow water equivalent available at theend of winter season for each year of the period 20022007, using HS-SWE, SWE-SEMand ALPINE3D.

Year

Model Water availability 2002 2003 2004 2005 2006

HS-SWE SWE volume (Mm3) 132 112 152 97 96Mean SWE (mm) 668 567 771 491 485

SWE-SEM SWE volume (Mm3) 119 102 134 97 89Mean SWE (mm) 603 517 681 493 451

ALPINE3D SWE volume (Mm3) 140 135 144 86 109Mean SWE (mm) 718 693 734 441 557

Table 3Yearly parameters of the jackknife linear regression of the mean and the standarddeviation of SWE against altitude.

Year ESWEu mmz qm rSWEu msz qsmm qm ms qs

2000 0.048 56.68 0.002 15.322001 0.049 58.64 0.005 8.642002 0.039 39.89 0.009 1.462003 0.031 17.66 0.003 14.012004 0.045 56.60 0.006 5.042005 0.029 13.16 0.003 13.392006 0.048 59.80 0.005 9.51

172 D. Bavera et al. / Advances in Water Resources 63 (2014) 167178Fig. 5. Spatial distribution of SWE, at the end of winter time, for each year of the 20022006 period, using SWE-SEM.

throughfall parameters are extracted from the land use map aswell as the initial, snow-free albedo.

4. Models results

4.1. Results of HS-SWE model

Fig. 4 gives the spatial distribution of SWE for each year of the20022006 period, using the HS-SWE method. In this study, HS-SWE constitutes the method with the lowest input data require-ments. It is only based on HS data and can thus only replicatethe spatial distribution of snow depth as resolved by the networkof snow stations. Both the detrending scheme and the spatial inter-polation method used are quite simple, such that resulting mapsonly capture rough distribution patterns. Moreover, HS-SWE doesnot assimilate measured SWE data, meaning that short-term,weather-driven variations in the relationship between HS andSWE are not picked up.

For each year of the 20022006 period, we have computed themean value of SWE conditioned to SCA > 0 and the total volume ofSWE available for the melting season, given in Table 2. Please notethat SCA is a model output and no EO data is used. The mean SWEduring these ve years is 596 mm with a standard deviation of122 mm which corresponds to a mean SWE volume of 118 Mm3

with a standard deviation of 24 Mm3.

4.2. Results of SWE-SEM model

In SWE-SEM the local SWE estimates at the snow gauges havebeen computed combining the measurements of snow depth and

snow density estimates. The jackknife linear regressions [30] ofmean and standard deviation of SWE (in cm) against altitude z(in m) have been determined. The slope of the regression of meanmm and standard deviation ms and their intercepts qm, and qs aregiven in Table 3. These estimates change from year to year becauseof the different starting date for the beginning of the melting sea-son. The standardized snow water equivalent for each year is cal-culated as the average value of the standardized snow waterequivalent estimates at the gauge stations. For the study area aDEM with square cells of 100 m has been used and the snow waterequivalent SWEj(u) has been calculated for each year j and in eachcell, parameterized by the vector u, having SCA > 0. The SCA hasbeen retrieved by MODIS EO images (MOD10A1 product). For eachyear we have selected the closest clear sky image to the date ofmaximum SWE observed at Weissuhjoch station. The selectedimages are at the following dates: 2002-05-07, 2003-04-24,2004-05-15, 2005-04-22 and 2006-05-04. For further details seeBavera [6]. Fig. 5 gives the spatial distribution of SWE for each yearof the 20022006 period using SWE-SEM.

For each year we have computed the mean SWE with SCA > 0and the total volume of SWE available for the melting season, givenin Table 2. The mean SWE during the ve years is 549 mm with astandard deviation of 92 mm, which corresponds to a mean SWEvolume of 108 Mm3 with a standard deviation of 18 Mm3. Lookingat the values given in Table 2, we found decreasing amounts ofsnow water availability during wintertime in the last years(2005, 2006), both in terms of average SWE and total volume. Thisreduction seems to be related to a decreasing amount of snow pre-cipitation, but the spatial extent of snow precipitation is only a lit-tle less than the one found in the previous years. This is probablyrelated to a little increasing of the average air temperature that

D. Bavera et al. / Advances in Water Resources 63 (2014) 167178 173Fig. 6. Spatial distribution of SWE, at the end of winter time, for each year of the 20022006 period, using ALPINE3D.

leads to a decreasing of snow precipitation in favor of liquidprecipitation. Moreover, we notice a little increase of the loweraltitude limit for snow precipitation [59].

4.3. Results of ALPINE3D/SNOWPACK model

First, the 1D module (SNOWPACK) of ALPINE3D has been run ateach IMIS station, these stations being equipped with snow gauges.The stations are the same ones used in the SWE-SEM model,excluding the Stillberg station. SNOWPACK provided a complete,1D modeled snow prole containing all the layers properties (tem-perature, water content, etc.). The goal was to simulate the bulkSWE value at the end of the accumulation season.

These simulated SWE have been compared with the 1D resultsof SWE-SEM for the same gauged stations and showed: (1) the twomodels practically simulate the same snow depth (their averagedifference is 2.5 cm, or 4.4%). Since SWE-SEM uses the mea-sured snow depth at these sites, we conclude that the SNOWPACKmodeled snow depths are in agreement with the observed data. (2)Snow density estimates obtained with SNOWPACK are in agree-ment with the ones provided by the regression equations.

Since the HS-SWE model does not provide SWE estimates forindividual points, it was not possible to compare it with the 1D re-sults of SNOWPACK. Instead, ALPINE3D has been run over thestudy area in order to provide spatialized outputs for variousparameters (albedo, surface temperature, SWE, etc.). The Fig. 6shows such a spatial distribution as computed by ALPINE3D forSWE, for each year of the period 20022006.

The best-reproduced zone is certainly the area around Davosand Weissuhjoch because of the abundance of data, as alsopointed out by Bavay et al. [4].

Table 2 shows for each year the mean and total volume of SWEat the start of the melting season. The mean SWE in the ve years is629 mm with a standard deviation of 126 mm, which correspondsto a mean SWE volume of 123 Mm3 with a standard deviation of25 Mm3.

5. Comparison of models results

Here we present a pairwise comparison of the results producedby the three models. The visual comparison of the SWE maps cal-culated by HS-SWE and SWE-SEM (Figs. 4 and 5) reveals that themethods produce similar patterns in terms of SWE spatial distribu-tion. The comparison of the total amounts of SWE, given in Table 2,indicates a mean value of the relative differences calculated asDSEM-HS = [(SWE-SEM) (HS-SWE)]/(HS-SWE) 100 of 8% inthe 20022006 period for the study area. On average HS-SWE pro-vides a little higher mean SWE value and total volume on the areathan SWE-SEM method. Both methods produce similar inter-annual patterns of total SWE. We have also made a detailedcomparison at cell size scale: for every year of the 20022006 per-iod and each cell of the domain. We have computed the relativedifference, DHS-SEM (%) of SWE estimates obtained using HS-SWEand SWE-SEM methods, see Fig. 7. From this, it is possible to notea general good agreement with |DSEM-HS| < 25% over about 70% ofthe domain. The distribution of absolute differences strongly

174 D. Bavera et al. / Advances in Water Resources 63 (2014) 167178Fig. 7. Plot of the relative difference DSEM-HS between SWE-SEM and HS-SWE estimates of SWE, for each year of the 20022006 period and for each cell of the domain.

follows elevation bands. Most of the areas having DSEM-HS < 25%are located at the lowest altitudes (below 1800 m a.s.l.) wherethe SWE is small for both methods. These differences are easily ex-plained by the different ways of determining the SCA: SWE-SEMassimilates EO data while in HS-SEM SCA is a model output. Atthe highest altitudes (28003000 m a.s.l.) the differences have alarger impact: relative differences >25% may have signicant con-sequences on the SWE budget. Both methods have to deal with theextrapolation of SWE at higher elevations. Figs. 4 and 5 clearlyshow that HS-SWE produces higher SWE lapse rates than SWE-SEM resulting in signicant differences above 2800 m a.s.l. Sinceboth methods calculate lapse rates using a linear t of HS againstelevation, the few stations at highest elevations have a dominantrole as a consequence of the scarcity of available data. As a summary,the two statistical methods provide similar results for SWE volumeaccumulated on the ground at the end of the accumulation seasonif compared on the whole domain. However, some differences arenoticeable when comparing the resulting maps cell by cell.

Now, we compare the results of the statistical methods HS-SWEand SWE-SEM, with those of the physical model ALPINE3D. Thevisual comparison of the SWE maps calculated by HS-SWE andALPINE3D, given in Figs. 4 and 6, shows that the two methods pro-duce similar patterns but with some differences in snow distribu-tion. The same applies to the comparison of SWE maps calculatedby SWE-SEM and ALPIN3D (Figs. 5 and 6).

The mean value of the relative differences of the total SWEamounts between the physical and the statistical methods are

calculated as DHS-A3D = [(HS-SWE) (ALPINE3D)]/(ALPINE3D) 100and DSEM-A3D = [(SWE-SEM) (ALPINE3D)]/(ALPINE3D) 100, inTable 2. In the 20022006 period and for the study area we haveobtained DHS-A3D 3% and DSEM-A3D 10%.

Globally the SWE as calculated with ALPINE3D are quite similarwith those obtained with HS-SWE and SWE-SEM. In addition wehave computed for each year of the 20022006 period and eachcell of the domain, the relative differences DHS-A3D (%) and DSEM-A3D (%), given respectively in Figs. 8 and 9.

From Fig. 8, one notes that |DHS-A3D| > 25% in a portion of the do-main varying between 30% and 80% depending on the year. Inparticular areas having DHS-A3D < 25% are located at loweraltitudes, below 18002000 m a.s.l. while areas havingDHS-A3D > 25% are located at altitudes > 2000 m a.s.l. The bestagreement between these two models is at the medium altitudebelt around 2000 m a.s.l. where |DHS-A3D| is in the order of 10%. Thisis reected in the SWE distribution (see Fig. 4) with very highvalues at the highest altitudes and very low values at the lowestaltitudes.

From Fig. 9 it is possible to note that the situation is quite im-proved in respect to the previous comparison and the extent ofthe area where |DSEM-A3D| > 25% is signicantly reduced, varyingbetween 10% and 30% depending on the year. In this case too,the best agreement is mainly reached at the medium altitude lev-els (2000 m a.s.l.).

In conclusions, while the overall SWE amount calculated by thethree models is similar, the main differences relate to the vertical

D. Bavera et al. / Advances in Water Resources 63 (2014) 167178 175Fig. 8. Plot of the relative difference DHS-A3D between HS-SWE and ALPINE3D results, for each year of the 20022006 period and for each cell of the domain.

distribution of SWE. These differences may reect the way precip-itation patterns are resolved in the input data of each model, ratherthan model performance.

We emphasize the good agreement of SWE estimates obtainedby the different models also in considering the fact that the phys-ical (ALPINE3D) and the two statistical (HS-SWE and SWE-SEM)models calculate SWE in very different ways: SWE-SEM and HS-SWE are based directly on the snow measured data, they use as in-put the snow depth accumulated on the ground. ALPINE3D on thecontrary is forced by meteorological data and computes the snowdepth and the snow density simulating the accumulation, settlingand melting processes according to the meteorological conditionfollowing the respective implemented equations. More specically,ALPINE3D is forced by meteorological stations and no snow mea-sure is used as input for this model. For this reason only ALPINE3Dis affected by measurement errors at meteorological stations. It isvery difcult to quantitatively evaluate the measurement errorsat gauging stations because it is not only a problem of heatingthe gauge to convert solid in liquid precipitation but also of precip-itation undercatch for solid precipitation. Several kinds of snowprecipitation measurements have been collected and compared[21] but they are made in a very few sites with a daily frequency.Bavera [6] used direct measurements of snow water equivalentcollected at theWeissuhjoch station (WFJ). The well-known effectof reduced snow precipitation due to wind, occurring during win-ter time, is seen here and it causes an underestimation of measuredprecipitation of about 3040% [6]. Also in Egli et al. [21], the snow

gauge measurements at Weissuhjoch has been tested againstother equipment and it was found that this gauge underestimateswinter precipitation by 30%. In addition, errors at meteorologicalstations could affect the air temperature measurements [28] whichpotentially introduce a melt timing error; however these errorshave not been considered in this study.

The introduction of an error correction in the precipitation data(see Section 3.3) and consequently in the ALPINE3D runs, has led toimprove the model performances. This issue highlights the impor-tance of the input data which force the model. Even if the modelwould perfectly simulate all the processes, inaccurate measure-ments would still affect the outputs. For this reason the effort incollecting and adequately preparing the input data series is of pri-mary importance as well as would be improvements to the catchefciency of the instrument collecting precipitation.

Dealing with a simulation for hydrological purposes in a moun-tain watershed where snow depth data is regularly and widelyavailable, it seems that snow depth data should also be includedin a physical model such as ALPINE3D in order to reduce the effectof precipitation measurements errors in winter time.

On the other hand, the two statistical models here consideredare not able to account for the saturation effects of snow depthand SWE with altitude as recently detected by Blanchet et al. [10].

Moreover most of the collected data in this study comes fromrelatively at areas (80% [6]) and this could lead to a non-accu-rate representativeness of the selected dataset for the whole inves-tigated area. For further analysis, a more diversied sample is

176 D. Bavera et al. / Advances in Water Resources 63 (2014) 167178Fig. 9. Plot of the relative difference DSEM-A3D between SWE-SEM and ALPINE3D results, for each year of the 20022006 period and for each cell of the domain.

aterrecommended and other parameters could be added in the estima-tion equations. Nevertheless the present structure of the statisticalmodels has the advantage of a reasonably limited amount of inputswhich are generally available, making them easy to apply.

Another aspect relative to the SWE-SEM model is the low reso-lution of the MODIS images whichmake it difcult to achieve a neestimation of the snow covered area, especially in small basins [7].The introduction of high-resolution sensors may improve the qual-ity of the model outputs.

6. Conclusions

A rst comparison between a physical (ALPINE3D) and two sta-tistical (HS-SWE and SWE-SEM) models is presented for the calcu-lation of the snow water equivalent, both in terms of spatialdistributions and total volumes. The comparison is focused onthe snow water equivalent available at the end of winter seasonfor the 20022006 years over a 200 km2 mountainous area inSwitzerland.

The results show a general good agreement among the threemodels. In particular, the comparison between the two statisticalmodels provides a mean difference in total amounts of about 8%.Similarly, the comparison of the results of the physical and thetwo statistical models shows a mean relative difference in the totalamount of about 3% (in the case HS-SWE vs. ALPINE3D), and10% (in the case SWE-SEM vs. ALPINE3D). In addition, a detailedcomparison made cell by cell and for each year, shows that theabsolute value of the relative SWE differences between the twostatistical models (HS-SWE and SWE-SEM) is on average over theve years period 625% over 70% of the domain while betweenHS-SWE and ALPINE3D it is 625% over 40% of the domain and be-tween SWE-SEM and ALPINE3D it is 625% over 80% of thedomain.

Acknowledgments

The research was partially supported by EC through AWAREproject: A tool for monitoring and forecasting Available WAter RE-source in mountain environment, contract n. SST4-CT-2004-012257 by the Swiss National Science Foundation and by the CCES(Competence Center for Environment and Sustainability) of theSwiss Federal Institute of Technology domain. The Authorsacknowledge all the Davos SLF personnel for their continuous sup-port and in particular Christoph Marty, Charles Fierz, HenningLoewe, Michel Bovey, Peter Bebi, Roland Meister for their help inthe data collection and Michael Schirmer, Christian Rixen, LucaEgli, Juliette Blanchet, Jan Magnusson, Matthias Ulmer for theirhelp in some statistical analysis and GIS analysis. We acknowledgethe staff of MeteoSwiss that provided data for the study and all theIREA-CNR personnel for the support on the satellite images and inparticular Monica Pepe and Anna Rampini.

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A comparison between two statistical and a physically-based model in snow water equivalent mapping1 Introduction2 Models for the calculation of SWE2.1 Hs-swe2.2 SWE-SEM2.3 ALPINE3D

3 Study area3.1 Snow and meteorological data3.2 HS-SWE and SWE-SEM data requirements3.3 ALPINE3D data requirements

4 Models results4.1 Results of HS-SWE model4.2 Results of SWE-SEM model4.3 Results of ALPINE3D/SNOWPACK model

5 Comparison of models results6 ConclusionsAcknowledgmentsReferences