modeling energy and mass balance of shallap …...1788 w. gurgiser et al.: modeling energy and mass...

The Cryosphere 7 1787ndash1802 2013wwwthe-cryospherenet717872013doi105194tc-7-1787-2013copy Author(s) 2013 CC Attribution 30 License

The Cryosphere

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Modeling energy and mass balance of Shallap Glacier Peru

W Gurgiser B Marzeion L Nicholson M Ortner and G Kaser

Center for Climate and Cryosphere University of Innsbruck Innsbruck Austria

Correspondence toW Gurgiser (wolfganggurgiseruibkacat)

Received 6 July 2013 ndash Published in The Cryosphere Discuss 9 August 2013Revised 8 October 2013 ndash Accepted 24 October 2013 ndash Published 22 November 2013

Abstract We calculated the distributed surface mass andenergy balance of Shallap Glacier Cordillera Blanca Peru(9 S 77 W 4700ndash5700 m aslsim 7 km2) on hourly timesteps for two years (September 2006ndashAugust 2008) usinga process-based model and meteorological measurementsas input Model parameter combinations were optimizedagainst 21 temporal readings of 20 stakes in the ablation zoneof the glacier Uncertainty caused by model input parametersand parameterization schemes was estimated using a leave-one out cross-validation scheme which yields values of rootmean square deviation (RMSD) of surface height changelt 1 m (lt 10 of the measured amplitude) for all stakesWith the best parameter combination (smallest RMSD) ap-plied the modeled annual surface mass balance of the glacierwas minus032plusmn 04 m we (water equivalent) for September2006ndashAugust 2007 and 051plusmn 056 m we for September2007ndashAugust 2008 While the mass balance above 5000 mwas similar in both years (1033plusmn 068 m we) due to sim-ilar annual sums of solid precipitation a difference of197plusmn 068 m we was calculated for the lower parts of theglacier This difference is associated with more frequent oc-currence of higher snow line altitudes during the first yearwhich was mainly caused by a higher fraction of liquid pre-cipitation due to higher mean air temperatures As the netshortwave budget was found to be the main source for ab-lation throughout the year at Shallap Glacier lower sur-face albedo especially caused by lower solid precipitationamounts explains most of the difference in modeled ablationand mass balance between the two years

1 Introduction

In the semi-arid outer-tropical climate of the CordilleraBlanca range of the Peruvian Andes glacier meltwater is cru-

cial to sustaining regional runoff during the dry season fromMay to September (Juen et al 2007 Kaser et al 2010)Andean glaciers and the hydrological stores they representhave been shrinking substantially over recent decades (Raba-tel et al 2013 Vuille et al 2008 Mark and Seltzer 2003Kaser and Georges 1999 Ames 1998) Investigations basedon measured hydrographs (Baraer et al 2012) and semi-empirical models (Juen et al 2007) suggest glacier retreatis changing the future runoff regime resulting in seasonaldecreases of river discharge of up to 30 if the glaciers arelost entirely Concurrently growth in population as well ashydropower agriculture and tourism activities increases thehydrological demand and vulnerability of local communitiesto changes in year-round water availability (Bury et al 2010Mark and Seltzer 2003) Therefore there is a critical needto develop reliable projections of the glacier contribution torunoff in the Cordillera Blanca in order to inform regionalplanning of hydrological resource usage

A crucial first step in determining glacier runoff underchanging climatic conditions is to investigate glacier massbalance and the processes through which climate conditionsdrive glacier response Where sufficiently high quality in-put data are available this is best done through applicationof process-based surface energy and mass balance modelswith high temporal and spatial resolution (eg Moumllg et al2008 2009a 2012 MacDougall et al 2011 Machguth et al2009 Hock 2005 Klok and Oerlemans 2002) which pro-vide crucial additional information to empirical temperatureindex (eg Carenzo et al 2009) or semi-empirical energybalance models (eg Kaser 2001 Juen et al 2007)

Mass and energy balance studies in the tropical Andeshave been carried out within the inner tropics at AntisanaGlacier Ecuador (028prime S) and in the outer tropics at ZongoGlacier Bolivia (16 S) At Antisana Glacier point energybalance studies in the ablation zone show that net shortwave

Published by Copernicus Publications on behalf of the European Geosciences Union

1788 W Gurgiser et al Modeling energy and mass balance of Shallap Glacier

radiation is closely coupled to surface ablation throughoutthe year (Favier et al 2004a) and variations in glacier-wideablation are controlled by surface albedo and the positionof the snow line which are both governed by the occur-rence and spatial distribution of solid precipitation (Fran-cou et al 2004) As air temperature controls the phase ofprecipitation the sensitivity of the annual mass balance toboth precipitation amount and temperature is high Seasonalvariations in energy fluxes are small and related to a slightseasonality in wind speeds In the outer tropics at ZongoGlacier there is a clear seasonality in meteorological con-ditions dominated by changes in atmospheric humidity andresultant cloud cover conditions and atmospheric long waveemissions While the surface energy balance is still domi-nated by the net shortwave radiation low atmospheric hu-midity and atmospheric long wave emissions during the dryseason result in high energy losses via the net long waveflux which reduces the energy available for melting theglacier and consequently restricts ablation to sublimation(eg Wagnon et al 1999 Favier et al 2004a Moumllg andHardy 2004 Nicholson et al 2012) In contrast to AntisanaGlacier the sensitivity of Zongo Glacier mass balance to airtemperature was found to be low because air temperatures atthis site are sufficiently low that precipitation over the wholeglacier area was solid (Favier et al 2004a) Instead glaciermass balance here is most strongly controlled by atmospherichumidity cloudiness and precipitation especially at the on-set of the humid season (Sicart et al 2011) Kaser (2001)generally suggests that the mass balance in the inner tropicsis most sensitive to variations in air temperature whereas inthe outer tropics sensitivity to atmospheric moisture is high-est due to its multiple impacts on mass balance

The Cordillera Blanca of Peru lies between the latitudesof Ecuador (inner Tropics) and Bolivia (outer Tropics) Asno high spatial and temporal resolution mass and energy bal-ance investigations have been carried out in this region sofar it is not clear how the seasonal and annual characteris-tics of glacier mass and energy balance relate to those iden-tified in Ecuador and Bolivia Furthermore the atmosphericvariables that exert the strongest control on glacier mass bal-ance which is crucial information for estimating the possibleimpact of climate change on the glaciers of the CordilleraBlanca remain unknown Thus the aims of this study areto (1) use a process-based model to compute and comparethe characteristics of glacier mass balance of Shallap Glacier(9 S) Cordillera Blanca Peru for two hydrological yearsand (2) investigate the energetic drivers of the surface massbalance

2 Study area measurements and methods

Shallap Glacier (920prime Sminus7720prime W) lies west of the divideof the Cordillera Blanca range of the Peruvian Andes (Fig 1)The outer tropical climate is characterized by relatively con-

stant annual temperature and a distinct variation in precip-itation (eg Juen et al 2007 Favier et al 2004b Kaser2001) with a wet season from October to April and a dryseason from May to September (see Supplement Fig S1)On the basis of satellite data (SPOT XS Sensor) obtainedin 2002 (Georges 2004) the glacier at that time spanned4700 to 5740 masl with more than half of the 7035 km2

glacier surface area below 5200 m In the absence of more re-cent information the 50 m resolution digital elevation model(DEM) derived from these satellite images was used as theglacier surface for our mass balance modeling

21 Measurements

211 Automatic weather stations

In 2002 an automatic weather station was installed onthe southern glacier moraine (4950 masl) approximately150 m above the glacier surface (hereafter AWSM) (Fig 1)Continuous hourly data of temperature humidity windspeed global radiation and precipitation are available fromJanuary 2006 to November 2009 and from July 2011 toMarch 2012 Data from AWSM were used as input for thesurface energy and mass balance model applied in this study(Sect 22) From July 2010 to September 2012 a secondweather station (hereafter AWSG) was operated in the abla-tion zone of the glacier (4796 masl) recording hourly tem-perature humidity wind direction and speed and net radia-tion at 2 m above the glacier surface No data are availablefrom February 2012 to April 2012 due to a defect in powersupply Data from AWSG were used to improve the surfacealbedo module of the mass balance model (Sect 22) andto develop a function for transferring temperature from themoraine to the glacier surface The temperature transfer func-tion is based on a multiple regression considering tempera-ture relative humidity and wind speed measured at AWSM(Gurgiser et al 2013) Figure S2 (Supplement) showingmeasured and transferred temperature and information onthe meteorological sensors used at both AWS are included inthe supplement

212 Stake measurements

Stake measurements (between 4758 and 4824 m asl) inthe ablation zone of Shallap Glacier were conducted bythe Unidad de Glaciologia y Recursos Hidricos (UGRH) ofthe Peruvian Autoridad Nacional de Agua (ANA) from Au-gust 2005 to August 2008 At 20 stake locations (Fig 1)relative surface height change was measured over 21 inter-vals spanning 14 to 64 days (dates are shown in Fig 4) Asneither snow depth nor snow density were recorded regu-larly measurements cannot be readily transferred into massunits but as the stake measurement area was snow free on 29August 2006 21 August 2007 and 27 August 2008 annualmass balances can be derived between these dates assuming

The Cryosphere 7 1787ndash1802 2013 wwwthe-cryospherenet717872013

W Gurgiser et al Modeling energy and mass balance of Shallap Glacier 1789

Fig 1Overview of Shallap Glacier located on the west side of the Peruvian Andes Study sites on Antisana and Zongo glaciers are indicatedin the inset map

a constant density of ice (900 kgmminus3) The available stakemeasurements dictated the duration of our investigation pe-riod and consequently in order to have two complete yearsof mass balance we define each mass balance year as 1Septemberndash31 August which is slightly offset from the tradi-tional hydrological year for the region defined as 1 Octoberndash30 September

All available surface height measurements at all of the 20stakes were used for model evaluation Stake elevations weremeasured by the UGRH in 2006 and 2007 The average ofthese point elevations at each stake which show a mean ab-solute difference of 10 m compared to the framing DEM gridpoints were used for model optimization and evaluation runs(Sects 222 and 223)

22 Energy and mass balance model

221 Model design

Glacier surface energy and mass balance was investigated us-ing a process-based model (Moumllg et al 2008 2009b 2012)that has been previously applied to Shallap Glacier (Gur-giser et al 2013) Here we provide only a brief overviewof the model as it is fully described in these prior publi-cations The model was run at hourly time steps from 1June 2006 to 31 August 2008 (to include three months of

spin-up which proved to be sufficient to produce reliablesnowpack patterns) using inputs of temperature humiditywind speed global radiation and all-phase precipitation mea-sured at AWSM Temperature is modified from AWSM torepresent conditions above the glacier surface using a trans-fer function (Sect 211) The reference altitude of meteoro-logical model input is 4800 m Realistic value ranges for 18free model parameters were obtained from the literature orfield measurements at Shallap Glacier and those parametersto which the model showed high sensitivity were optimizedsimultaneously (Sect 222)

Within the model the mass balance is calculated as the dif-ference between the sum of accumulation terms (solid pre-cipitation surface water deposition and refreezing of liq-uid water in the snowpack) and the sum of ablation terms(surface sublimationevaporation and surface and subsurfacemelt) Surface melt and sublimation are derived from the sur-face energy balance (all terms in W mminus2) formulated as

SWin(1minus α) + LWin + LWout+ QS+ QL + QG= F (1)

where SWin is the incoming shortwave radiationα the sur-face albedo LWin and LWout are the incoming and outgo-ing long wave radiation QS and QL are the turbulent sen-sible and latent heat fluxes and QG is energy flux into theglacier bodyF is the residual energy flux IfF is positive

wwwthe-cryospherenet717872013 The Cryosphere 7 1787ndash1802 2013


and surface temperature is 27315 K the melt energy QMequalsF OtherwiseF warms or cools a defined surfacelayer (Moumllg et al 2009a)

As described in detail in Gurgiser et al (2013) mea-sured SWin at AWSM is separated into direct and diffusecomponents following Hock and Holmgren (2005) ThenSWin(xy) is calculated as a function of topographic shad-ing slope and aspect LWin is calculated as a function of airtemperature water vapor and cloud cover following a pa-rameterization scheme developed by Sicart et al (2010) forZongo Glacier whereas the parameter values were adaptedfor the local conditions the skill of the parameterization wasdemonstrated to be similar at our site (Gurgiser et al 2013)LWout is derived from modeled surface temperature and theStefan Boltzmann law assuming emissivity to be unity Theturbulent heat fluxes QS and QL are calculated using the bulkmethod and published values of surface roughness lengthsfor snow and ice (Table A1) The effect of stable conditionson turbulent exchange is accounted for following Braithwaite(1995 Eq 11) The vertical air temperature gradient is as-sumed to beminus055 (100 m)minus1 based on measurement atthe Zongo Glacier (Sicart et al 2011) In the absence ofinformation for Shallap Glacier we again followed Sicartet al (2011) by assuming that precipitation does not varywith elevation as discussed in Sect 43 The solid fractionof measured all-phase precipitation which is derived fromlinearly interpolating between two threshold temperatures(Table A1) is converted into a snow height using an opti-mized value for fresh snow density and correcting the snowheight for the surface slope of the glacier grid point Withinthe model subsurface the thermodynamic energy equation issolved numerically on a vertical grid with 14 layers (from009 to 3 m total depth) Ice temperatures in the subsurfaceare unknown but the temperature below the lowest layer isassumed to be 273 K as measurements at AWSG suggest thatthe surface temperature is close to the melting point through-out the year and this is expected to be the best guess for mostof the glacier area because of very high SWin throughout theyear QG is the sum of QPS the fraction of net shortwaveradiation that penetrates into ice or snow and the conduc-tive heat flux at the glacier surface QC The model accountsfor compaction of snow and refreezing of liquid water asdescribed in Moumllg et al (2012) Due to its small magnitudecompared to the other energy fluxes the heat flux from pre-cipitation is not considered in the selected model setup noris mass redistribution due to wind and gravity

The surface albedo parameterization is based on Oerle-mans and Knap (1998)

α = αs+ (αi minus αs) middot exp

(minus

d

dlowast

) (2)

whereα is the surface albedo with subscripts ldquosrdquo and ldquoirdquo re-ferring to snow and ice respectivelyd is the actual snowheight anddlowast the albedo depth scale smoothing the transi-tion between snow and ice albedo whend approachesdlowast

The surface albedo of snow used within Eq (2) is calculatedas

αs = αos+ (αfs minus αos) middot exp

(minus

t

tlowast

) (3)

where subscripts ldquoosrdquo and ldquofsrdquo refer to old snow and freshsnow respectivelyt is the time elapsed since the last snowfall event andtlowast is the characteristic timescale (hereafteralbedo timescale) over which albedo transitions exponen-tially from that of fresh to old snow (Oerlemans and Knap1998) Within this scheme a snow fall event is defined aswhen snowfall accumulated over consecutive hours exceeds1 cm The findings of Gurgiser et al (2013) suggest modelskill at Shallap Glacier where frequent light snowfall onaging snowpacks are common could be improved by ac-counting for the albedo of underlying snow (Machguth et al2008) Therefore the albedo scheme was modified so that ifthe snow from a single event ablates away before reachingthe albedo of old snowαs is set back to the value precedingthe snow fall event

The albedo timescaletlowast required in the aging functionwas determined by applying a fixed value ofdlowast (1 cm) andrunning the model for the location of AWSG driven bythe data from AWSM and then comparing the model per-formance against measured surface albedo at AWSG overa 6 month period from 1 August 2012 to 31 January 2013Highest correlations and lowest root mean square errorswere found for tlowast between 1 and 4 days which reflectsthe typically fast decay of snow albedo when ablation oc-curs throughout the measurement period (Moumllg et al 2008Kaser 2001) To account for a slower decrease of snowalbedo in higher altitudes due to less surface melt we applieda vertical gradient of the albedo timescale of 1 d (100 m)minus1

(discussed in Sect 43) The skill of this albedo parameteri-zation using a mediantlowast value of 25 days (Fig 2) is compa-rable to other schemes (Brock et al 2000)

222 Values for free model parameters

The mass balance model (Sect 221) was optimized usinga Monte Carlo approach (eg Moumllg et al 2012) Firstlya single parameter sensitivity test was carried out to deter-mine to which of the 18 free model parameters modeled sur-face mass balance shows greatest sensitivity This was es-timated by computing for each of the 20 stake locationsa standard model run using median values for all parame-ters listed in Table A1 and then two further model runs us-ing the upperlower range limits (Table A1) while keepingall other parameters constant The difference of the cumula-tive mass balance at the end of two years (September 2006 toAugust 2008) between the standard run and the maxmin per-turbation runs for each point and parameter is an indicationof model sensitivity to the parameter (Fig 3) Although theinfluence of some parameters is interdependent this singleparameter sensitivity was used to identify the most crucial



Fig 2 Comparison of daily mean measured surface albedo withmodeled surface albedo computed with optimized albedo model pa-rameters RMSD is the root mean square deviationr2 the coeffi-cient of determination andn is the number of considered days Toexclude the effects of surface slope on albedo measurements onlyhourly values with solar zenith angle above 60 were considered forcalculating the daily means

free model parameters within the considered value range asthose that change the cumulative mass balance at the end ofthe time series by more thanplusmn10 (using the median ofthe values for the 20 stake locations) This procedure iden-tified 7 key parameters for subsequent optimization (Fig 3Table A1) (1) the temperature range over which precipita-tion phase changes from 100 solid precipitation to 100 liquid precipitation (2) the density of solid precipitation thataffects snow height and surface albedo in the case of verythin snow layers that are within the influence of the albedodepth scale (see Oerlemans and Knap 1998) (3) the fractionof net shortwave energy in the snow layer that influences thedistribution of energy to the surface or subsurface (4) the ice(5) old snow and (6) fresh snow albedo and (7) the albedotimescale

These 7 parameters were optimized by allowing them tovary randomly within their specified ranges over 1000 modelruns in which the other parameters were held constant at theirmedian values and the optimum parameter combination wasthat with the minimum root mean square deviation (RMSD)between measured and modeled surface height change for allstake points Parameter values of this run hereafter referredto as ldquobest parameter combinationrdquo are given in Table A1Following Machguth et al (2008) the evolution of the stan-dard deviation and the standard deviation of the standard de-viation of modeled mass balance were used to evaluate thenumber of simulations required for the optimization and asfluctuations in both variables approach zero well below 1000simulations we can assume that the upper and lower limitsof the possible solution space are reached and the sensitivitytest yields stable results

Fig 3 Sensitivity of modeled mass balance to the selected freemodel parameters set to their upperlower limit compared to the re-sults obtained with median values for all parameters at each of the20 model points framing the stake locations Points show the me-dian values the edge of the horizontal bars show the 25 and 75 percentiles the whiskers extend to the extremes not considered asoutliers and the outliers are plotted as small circles

223 Model uncertainty evaluation methods

Model parameter transferability in space and time wasestimated with a leave-one-out cross validation approach(eg Wilks 2011 Hofer et al 2010) calculated on the 1000model runs generated for the optimization procedure To in-vestigate model parameter uncertainty in space we first cal-culated the root mean square deviation (RMSD) betweenmeasured and modeled surface height change (SHC) for eachpoint as

RMSDri=

radicradicradicradicsum(SHCstakeiminusSHCmodelri

)2p=1ndash21

np[m] (4)

wherer is the number of the respective model run (1000 intotal) i is the stake location (20 in total)p is the measure-ment period (21 in total) andnp is the number of periods(21) Then we determined a RMSD for the stake locationx

by selecting the model runr that produced the smallest meanRMSD at all the other locations and calculating the RMSD ofthat run at the locationx Thus this RMSD is obtained inde-pendently from measurements at locationx and gives an esti-mate of the model error when the model using the parameter



values optimized at the stake locations is applied to a loca-tion without measurements (Supplement Fig S3a) This wasrepeated for all 20 stake locations

Even though we do not model the glacier mass balancebeyond the stake measurement period (Sect 212) we havealso evaluated model transferability in time This was donein a manner analogous to the determination of transferabilityin space described above only that measured time intervalsrather than measured locations were left out Consequentlythe error we calculated for a periody is the one that can beexpected if the model parameters optimized during the avail-ability of measurements are applied at a time when no mea-surements are available (Supplement Fig S3b)

For modeling the distributed mass balance of the wholeglacier we selected the runr where the mean RMSD of allstake locations is minimal (Sect 222) However the stakemeasurement area only covers a small part of the glacier(Fig 1) and we also apply our model outside of the eval-uation zone for calculating the spatially distributed mass bal-ance of the whole glacier Therefore we investigated whetheror not the RMSD depends on the distance between the stakelocations ie whether there is a systematic spatial patternin the error magnitudes A correlation between this distanceand the RMSD would indicate that we would have to beaware of growing model uncertainty outside of the evalua-tion zone For completeness we also investigated whether ornot there is a correlation with the temporal distance whichwould mean that our best parameter combination yields in-ferior results when applied before or after the measurementperiod

Model error for the annual specific mass balance of thewhole glacier for each year was calculated as

RMSDYear=

radicsum(CMBstakeiyearminus CMBmodeliyear

)2i=1ndash20

ni

(5)

[m we]

where CMB is the cumulated mass balance at the end of theyear which is obtained by converting measurements of an-nual surface height change into mass units (see Sect 212)and directly as an output from the mass balance model re-spectivelyni is the number of stake locations

Uncertainty in the difference in mass balance between thetwo years was calculated as

RMSDDif =(RMSDYear1+RMSDYear2)

nymiddotradic

ny [m we] (6)

whereny is the number of considered yearsThere are several other sources of uncertainty in our model

results that could arise from uncertainties in spatial gra-dients of temperature precipitation and albedo timescale(Sect 43) topographic features outside the stake area ex-tracted from the DEM or currently unconsidered processessuch as redistribution of snow and ice and modified ablationdue to debris cover Further measurements and studies will

be need to thoroughly investigate and quantify uncertaintyarising from such sources or to implement further processesin the model

3 Results

31 Model evaluation

311 Model parameter transferability in space andtime

RMSD values obtained for the spatial model parameter trans-fer (Sect 223 Supplement Fig S3a) are alllt 1 m witha mean value of 05 m This is a markedly better performancethan obtained in previous modeling (Gurgiser et al 2013)indicating that the modifications to the albedo scheme de-scribed in Sect 221 improve model performance RMSDvalues arelt 10 of the cumulated surface height changeat the end of the 2 yr at all points The time series of sur-face height change at each stake modeled using the best pa-rameter combination optimized at all other stake locationsindicates that although the modeled amplitude is generallyslightly smaller than the measured one the variability and thetotal surface height change are captured quite well (Fig 4)This is also the case for annual time steps (Fig 5) In the firstyear the model tends to slightly underestimate the surfacelowering at the lower stakes and overestimate it at the higherstakes In the second year when surface lowering was lessthis tendency is not evident but the correlation between mea-sured and modeled surface height change is slightly worse

Parameter transfer in time (Supplement Fig S3b) causesa maximum error of 13 cmdayminus1 in period 9 and a meanvalue over all periods of 06 cmdayminus1 As the distribution ofRMSD at all periods is random and does not show trendsover consecutive periods (Supplement Fig S3b) the modelperformance does not favor any particular part of the timeseries

312 Skill of best parameter combination for spatialdistributed model run

The best model parameter combination (Sect 223 and Ta-ble A1) yields mean RMSD of 06 m (or 4 of the surfaceheight change amplitude) between modeled and measuredsurface height change (calculated with Eq 4) at the 20 stakelocations for all periods The mean RMSD between mea-sured annual mass balance and that modeled with best pa-rameter combination (following Eq 5) at the 20 stake loca-tions at the end of each year is 040 mwe (water equivalent)(r = 097) for year 1 and 056 mwe (r = 081) for year 2which is small with respect to the all-stake mean of measuredamplitudes ofminus68 m we (year 1) andminus38 mwe (year 2)We found no significant correlation (p lt 005 |r| lt 013)between RMSD and location or time when the best parame-ter combination was applied therefore the computed model



Fig 4 Results of the leave-one-out-cross-validation measured(blue dots) and modeled (black solid lines) cumulative surfaceheight change for the study period at each stake Date as ddmmis shown on the upper horizontal axis Individual model parametercombinations for calculating surface height change for each pointwere derived using the best parameter combination evaluated as runwith the smallest mean RMSD considering all other points For de-tails see Sect 223

Fig 5 Results of the leave-one-out cross-validation measured vsmodeled annual surface height change for(a) year 1 (29 August2006ndash21 August 2007) and(b) year 2 (21 August 2007ndash27 Au-gust 2008) Individual model parameter combinations for calculat-ing surface height change for each point were modeled using thebest parameter combination evaluated for all other points (19) butnot the considered one (Sect 223)

uncertainty is not expected to increase when the model isemployed outside the stake area or before and after stakemeasurements

32 Characteristics of surface mass balance

The spatially distributed surface mass balance was calculatedfor all glacier grid points using the best model parametercombination for the period September 2006 to August 2008The specific mass balance was negative (minus032 mwe) in thefirst year and positive (+051 mwe) in the second year (Ta-ble 1 Fig 6a and b)

Spatially averaged values of modeled equilibrium line al-titudes (ELA) of 4985 masl and 4953 m in years 1 and 2respectively (Table 1) and accumulation area ratio (AAR)

Fig 6 Annual mass balance for(a) September 2006 to August2007 and(b) September 2007 to August 2008 showing the ELAas a black line Given uncertainty values only reflect uncertaintiesin internal model parameter values (Sect 223)(c) Difference inannual mass balance between year 2 and year 1 Differences below(in sense of altitude Fig 1) the white line are significant above the95 confidence level

of 070 and 074 in year 1 and year 2 respectively arerelatively similar in both years despite the specific massbalance being markedly different (Table 1) Specific mass



Table 1Summary of glacier mass balance characteristics for the two hydrological years and difference between year 1 and year 2 The annualmodel uncertainties are calculated with Eq (5) (yearly values) and Eq (6) (1 Y1ndashY2) as described in Sect 223 ELA means equilibriumline altitude AAR is the accumulation area ratio and MB is the mass balance

Feature Sep 2006ndashAug 2007 Sep 2007ndashAug 20081 Y1ndashY2

Specific mass balance minus032plusmn 04 mwe 051plusmn 056 mwe 083plusmn 068 mweELA 4985 m 4953 m 32 mAAR 070 074 minus004MB below ELA minus298 mwe minus101 mwe minus197 mweMB above ELA 084 mwe 117 mwe minus033 mwedMBdz below ELA 296 mwe (100 m)minus1 306 mwe (100 m)minus1

minus010 mwe (100 m)minus1

dMBdz above ELA 015 mwe (100 m)minus1 012 mwe (100 m)minus1 003 mwe (100 m)minus1

balance (Table 1 Fig 6c) above the ELA was similar forboth years (1033 mwe) coinciding with similar annualsums (10118 mwe) of precipitation (Table 2) but the dif-ferences below the ELA were large (1197 mwe) Thesepatterns are also reflected in the differences in the verticalmass balance gradients between the two years (Fig 7) Gen-erally the gradients were similar in both years (Table 1 andFig 7) and showed some deviations around the ELA re-flecting differences in the persistence of snow cover in thiszone between the two years (Fig 8a) In the first year thevertical mass balance gradient tends to zero above 5400 mwhile in the second year this occurs slightly lower at 5200 mwhich reflects the effective limit of melt over the glacier sur-face within our model The slight kink in the gradient below4800 m is a result of the model structure (Sect 221) as weset a lower limit for the albedo timescale (1 d)

Precipitation was high during the wet season from Octo-ber to April in both years (Fig S1) with precipitation sumsof 140 mwe and 150 mwe in year 1 and year 2 but smallprecipitation events also occurred in the dry season from Mayto September with total precipitation sums of 017 mweand 018 mwe (Table 2) During the wet season the glacierwas regularly entirely snow covered while the snow line alti-tude generally increases progressively during the dry season(Fig 8a) Above 5000 m ablation rates were generally smallBelow 5000 m ablation occurred during both seasons withvarying magnitude and no clear seasonality Within both dryseasons individual accumulation events caused the glacierto become snow covered which coincides with dramaticallyreduced or no ablation for a time (Fig 8c)

Interannual differences in both seasons contribute to thecontrasting annual mass balances of the two years (Ta-ble 2) The first year experienced a period of intense melt(sim 50 mmwedminus1) during February of the wet season thatcoincided with a higher snow line than was experienced dur-ing the wet season in the second year and also in the dryseason of the first year the snow line rose higher than in thesecond year Similarly the frequency and duration of reducedablation were greater in the second year than in the first year

Fig 7 Mean annual mass balance vs altitude Mass balance val-ues are calculated as annual means for 10 m elevation incrementsThe grey areas indicate the estimated error ranges for each year(Sect 223)

with the contrast in ablation in the months of JanuaryndashMarchbeing particularly marked

33 Characteristics of surface energy balance

The drivers of the surface mass balance were analyzed onthe basis of the surface energy fluxes modeled with the bestparameter combination As is the case with the interannualmass balance daily means of the energy balance terms andsurface albedo averaged over 10 m elevation intervals (Fig 9)show greatest diurnal variability on the glacier tongue soenergy fluxes averaged over the glacier surface area below5000 m are examined in more detail (Fig 10 Table 2)

Extraterrestrial solar radiation is highest (SupplementFig S1) in the wet season but increased cloud cover meansthere is little difference in incoming solar radiation betweenthe two seasons The highest daily mean net shortwave flux(gt 200 Wmminus2) occurred during a clear sky interval during



Table 2 Seasonal mean values of SWin (W mminus2) the energy balance terms (all W mminus2) precipitation (mm we) temperature (C) snowline altitude SLA (m) wind speed ws (msminus1) and relative humidity RH () with differences from year to year for all area below 5000 mWS is the wet season (OctoberndashApril) and DS is the dry season (MayndashSeptember) QMS is the melt energy in the subsurfacePT is all phaseprecipitation andPL is the fraction of liquid precipitation fromPT TP is the mean temperature during precipitation

Parameter WS Year 1 WS Year 21 Y1ndashY2 DS Year 1 DS Year 2 1 Y1ndashY2

SWin 198 201 3 215 207 7

SWNet 76 59 17 125 101 14LWNet minus25 minus29 4 minus53 minus49 minus4QS 10 10 0 21 20 minus1QL minus4 minus5 1 minus28 minus25 minus3QG minus10 minus6 minus4 minus14 minus10 minus4

QM minus45 minus26 minus19 minus46 minus34 minus12QMS minus7 minus4 minus3 minus10 minus7 minus3

PT (PL ) 1395 (27) 1503 (14) minus269 (13) 173 (16) 183 (8) minus23 (8)T (TP) 16 (10) 09 (05) 07 (05) 12 (02) 08 (01) 04 (01)SLA 4768 4718 50 4885 4817 68

ws 21 21 minus 31 31 minus

RH 81 80 1 62 65 3

Fig 8Time series (September 2006ndashAugust 2008) of surface massbalance(a) with the dry and wet season duration highlighted bythe grey and blue bars and mean snow line (snow depthge 1 cm) in-dicated as black line Time series of snow accumulation and totalablation in(b) and (c) White areas in(b) correspond to no accu-mulation All values are calculated as daily means for 10 m steps inaltitude Note the different scales of the color bars

the wet season of the first year (Figs 9a and S1) but thesehigh values were restricted to a short time interval and to thelowest elevations of the glacier where albedo was also low-

est (Fig 9f) Instead net shortwave radiation in the lowerparts of the glacier is generally higher during the dry season(Table 2 Fig 10) because of a combination of lower sur-face albedo and higher SWin (Table 2 Supplement Fig S1)In general net shortwave energy decreased quickly with al-titude from the glacier terminus (Fig 11) until just abovethe mean ELA (sim 5000 m) where the glacier surface wasalways above the snow line (Fig 8a) and thus modeledalbedo (Fig 9f) was consistently high In contrast the netlong wave radiation budget varies little with altitude butshows a clear seasonality over the whole glacier surfaceMean seasonal values over the lower glacier range betweenminus25 andminus30 W mminus2 during the wet season and are aroundminus50 Wmminus2 during the dry season when maximum meandaily energy losses of up tominus100 Wmminus2 can occur on theclearest days In seasonal and spatial averages energy lossvia net long wave radiation offsets only between a third anda half of the energy gained via net shortwave radiation (Ta-ble 2)

Seasonally averaged daily means of sensible heat flux av-eraged over the lower glacier are small during the wet season(sim 10 Wmminus2) and enhanced in the dry season (sim 20 Wmminus2)during which multiple short periods of enhanced wind speedsand temperature gradients between air and the surface occurSome peaks in QS of almost 100 Wmminus2 were modeled abovethe snow line but these high values were not relevant for meltas they occur only when net shortwave radiation is low dueto the high albedo of the snow-covered surface Also latentand long wave net fluxes are strongly negative and actingto lower the surface temperature of the glacier thus increas-ing the temperature gradient between air and surface whichforces high sensible heat flux



Fig 9 Time series (September 2006ndashAugust 2008) of modeled en-ergy balance terms described in Sect 221(andashe)and of modeledsurface albedo in(f) All values are calculated as daily means for10 m steps in altitude The grey and blue bars in(a) indicate the dryand wet season Note the different value range in the color bar in(a)and(f)

Seasonally and spatially averaged latent heat flux overthe lower glacier is very small during the wet season(sim minus5 W mminus2) and increases during the dry season (sim

minus25 W mminus2) due to numerous stronger sublimation events(Figs 9 and 10) during days with low moisture and enhancedwind speeds The seasonally averaged difference in QL isdriven by seasonal differences in both wind speed and near-surface vapor pressure gradient which aresim 1 msminus1 andsim 025ndash035 hPa higher in the dry season compared to thewet season Sublimation and evaporation accounted for 4 and8 of the wet season ablation in the first and second yearsrespectively and 17 and 22 in the dry season whereas thevariation in sublimation fraction is dominated by changes inthe melting rather than the sublimation The sum of the tur-bulent fluxes is minor compared to net all-wave radiation be-cause positive QS is offset by negative QL The spatially av-eraged sum of mean turbulent fluxes is positive in the wetseason but higher sublimation rates in the dry season morethan offset the increased QS so that the summed turbulentfluxes become negative

Ground heat flux was always negative and small averagedover the whole glacier (minus3 Wmminus2) However in the low-est parts of the glacier the maximal magnitudes of groundheat flux were similar to the turbulent fluxes (Fig 9e) Asa higher fraction of the shortwave radiation absorbed at the

Fig 10 3 day running means of energy balance terms as spatialaverages over the glacier arealt 5000 m The melt energy in thesubsurface is shown as dotted line Melt energies are multiplied byminus1 to aid clarity The grey and blue bars indicate the dry and wetseason

surface penetrates into ice than snow (Table A1) QPS is mostnegative where the glacier surface is snow free Thus thehigher QG at lower elevation is driven by higher QPS wheresnow cover is less frequent and consequently lower albedo(Figs 8a and 9f) increases net shortwave flux The energylost from the surface through QG was a source for melt en-ergy in the subsurface (Figs 10 and 11)

Daily mean energy flux values averaged over the glacierarea below 5000 m highlight the high variability of net short-wave energy and its control on total melt energy over theglacier ablation zone (Fig 10) Thus high melt rates in theablation zone of Shallap Glacier can be seen to be contingenton high absorption of solar radiation

4 Discussion

The magnitudes of the calculated specific mass balance arecomparable to mass balance estimates obtained for the sameperiod from measurements available at two other glaciers inthe Cordillera Blanca (Artesonjaru Yanamarey) and withinthe range of reconstructed annual mass balances for severalcatchments in the Cordillera Blanca (Rabatel et al 2013)The modeled ELAs are close to those expected from con-ceptual approaches (Kaser and Osmaston 2002) and thehigh values of the modeled AAR compared to those typi-cal for mid-latitude glaciers (Porter 1975) are also consis-tent with values expected for tropical glaciers (eg Kaserand Georges 1997) The calculated vertical mass balancegradients (Table 1) for Shallap Glacier (Fig 7) were highin the lower parts of the glacier (sim 3 mwe (100 m)minus1) inboth years and comparable to the gradient of the lower ZongoGlacier (Sicart et al 2007) Such high vertical mass bal-ance gradients on the glacier tongue can be explained by fre-quent changes in snow cover in the ablation zone through-out the year (Sicart et al 2007 Kaser and Osmaston 2002)Above the equilibrium line the vertical mass balance gradi-ents were very small (lt 02 mwe (100 m)minus1) This form of



Fig 11 Time series of energy balance terms as mean values overthe whole study period (September 2006ndashAugust 2008) vs altitudeQMS is the melt energy in the subsurface

vertical mass balance and the occurrence of year-round abla-tion drives the high mass turnover that characterizes tropicalglaciers (Kaser 2001) Thus the modeled mass balance forShallap Glacier captures all the expected features of a tropi-cal glacier

41 Topographic signature in mass and energy balance

The similarity of the AARs between a year with negative andpositive mass balance at Shallap Glacier (Sect 32 Table 1)is strongly influenced by the local topography (Kaser andOsmaston 2002) Above 5000 m the glacier slope increases(Fig 1) and parts of the glacier above 5000 m are exposedto the southwest This combination of high slope angle andaspect result in slightly less incident solar radiation (up tominus10 W mminus2 over the whole study period) in higher altitudescompared to the flatter lower ablation zone Furthermore theslower decrease of snow albedo with altitude as set in ourmodel structure (Sects 221 and 43) reduces the amount ofshortwave energy absorbed at higher elevations

The steep surface slope abovesim 5000 m (Fig 1) and re-sultant rapid decrease in air temperature upglacier meansthat the zone of transition between areas with exclusivelysolid and areas with solid and liquid precipitation phase isvery narrow Thus the transition from ablation to accumu-lation area is abrupt at Shallap Glacier (Figs 6 and 7) Fi-nally the steep slope just above the ELA means that anyincrease in ELA will have a small impact on AAR Takentogether these factors imply that the sensitivity of the AARsto increasing temperatures is expected to be relatively low atShallap Glacier

42 Energetic drivers of ablation

At Shallap Glacier very high ablation can occur in the wetseason For example the highest modeled daily ablation(sim 50 mmwedminus1) occurred at the terminus during Febru-ary of the wet season of year 1 The high ablation rates werea result of low albedo values coinciding with very high val-

ues of incoming solar radiation due to clear skies coincid-ing with peak solar radiation (Supplement Fig S1) How-ever as both surface and subsurface melt tend to peak indry season conditions overall seasonal mean melt energywas similar or higher in the dry season than in the wet sea-son due to a more positive net radiation budget (Table 2)This is in contrast to findings at Zongo Glacier where meltrates are small or zero in the dry season due to strongly neg-ative long wave net radiation which offset shortwave energygains (Sicart et al 2011) Over the ablation zone at Shal-lap Glacier even during periods of peak net long wave en-ergy losses (sim minus90 W mminus2) and strong net turbulent energylosses (sim minus40 W mminus2) during the dry season for example atthe end of June in year 1 (Fig 10) high net shortwave radi-ation (sim 160 W mminus2) means that surplus energy for meltingremains (sim 30 W mminus2) This also holds when we considerthe whole glacier surface In general melting is mostly inhib-ited by reduced net shortwave and only rarely by strong longwave emission and sublimation which consume the avail-able energy for ablation (eg end of June in the second yearFig 10)

Comparison of the two years (Table 2 Fig 8c) shows thatmelt rates were higher in both the wet and dry seasons of year1 The largest differences from season to season and year toyear were calculated for the net shortwave budget again in-dicating that annual differences in ablation were a result ofdifferences in surface albedo and snow cover (Fig 9f) Thisis confirmed by the contrasting seasonal sums of precipita-tion and their distribution in solid and liquid phase Gener-ally precipitation was slightly lower in both seasons of thefirst year and a higher fraction fell as rain These differencesexplain why the snow line was frequently higher in the wetseason of the first year (Fig 8a Table 2) and hence surfacealbedo was lower and the resultant impact on net shortwavecaused higher ablation rates over the course of the season

The smaller snowpack developed during the wet season ofthe first year was removed more rapidly during the subse-quent dry season so that during the dry season the snow linerose to higher elevations in the first year than in the secondyear (Fig 8) causing higher mean values of melt energy (Ta-ble 2 Fig 9f) This highlights that the precipitation sums dur-ing the dry season were too small to form thick snowpacksand that precipitation and also temperature during the wetseason impact the persistence of the snowpack (and higheralbedo values) and subsequently affect the ablation rates dur-ing the dry season Therefore the temperature sensitivity ofannual mass balance and ablation are expected to be highestfor the wet season temperature

The similar evolution of the cumulative differences insnow line altitude and total melt energy in Fig 12 againconfirms that during our study period (i) the magnitudes ofthe net turbulent fluxes and net long wave radiation whichhave similar or equal energy transfer properties for snow andice were small or compensated by additional shortwave netenergy and (ii) that the seasonal and annual variability in



Fig 12 Cumulative differences in maximal snow line altitudeand total (surface+ subsurface) melt energy (QMT) between year2 (September 2007ndashAugust 2008) and year 1 (September 2006ndashAugust 2007)

melt energy was controlled by the shortwave net budget thussnow cover which was mainly a function of precipitation andtemperature So in contrast to our findings for the ELA andAAR (Sect 41) annual melt rates and the specific mass bal-ance on Shallap Glacier were sensitive to temperature espe-cially in the wet season when most of the annual precipitationoccurs

43 Uncertainties

The model uncertainty estimates presented in Sect 31 ac-count for uncertainties in model parameterization schemesparameter values and ranges (Table A1) and errors in theAWS measurements The RMSD values calculated for thespatially distributed model run (Sect 312) were within therange of previously published studies (eg MacDougall andFlowers 2011 Hock and Holmgren 2005) Higher RMSDand lower correlation in annual surface height change in year2 (Fig 5) are likely to be results of more frequent snow falland snow cover (Table 2) Observations indicate that snowcover ablates in a spatially irregular manner due to small-scale irregularities of the glacier surface which results inhigher scatter in the measured surface height change for year2 compared to year 1 (Fig 5) and as the model cannot re-solve small scale snow irregularities lower model skill

Possible errors in mass balance due to the applied verti-cal albedo timescale temperature or precipitation gradientare not captured in our evaluation as the available data ex-tend over only a small elevation range Thus we only discusspotential impacts here The dominance of melting processesfor the aging of snow surfaces and related albedo decrease(eg Gardner and Sharp 2010) requires accounting for theless frequent occurrence of melting and thus increasing aver-

age snow albedo at higher altitudes (Brock et al 2000) Wehere applied an albedo timescale gradient of 1 day (100 m)minus1

(starting at the model input reference altitude of 4800 m)which yields values between 1 d (fixed lower limit) in thelowest parts of the glacier and 103 days at the highest el-evations (5700 m) when applied to the timescale of 13 days(Table A1) As the accurate value of the gradient is uncertainwe calculated additional runs for gradient values of 05 day(100 m)minus1 and 15 day (100 m)minus1 The difference in surfacemass balance isminus028 mwe for both years (lower bound)and +019 and +011 mwe for year 1 and year 2 respec-tively (upper bound) For all of the albedo timescale gradi-ents evaluation the timescale values over the elevation rangeof the glacier are within the range of values used in formerstudies (eg Sicart et al 2011 Moumllg et al 2008 Oerlemansand Knap 1998)

Niedertscheider (1990) calculated a ldquogeneralrdquo precipita-tion gradient of 35 mm (100 m)minus1 for the Cordillera Blancabased on 21 stations between 1380 and 4550 masl whichin fact may also contain a horizontal distance effect Ourstudy site is well above the elevation range covered by thesemeasurements On Zongo glacier Bolivia no significant gra-dients in precipitation were found between 4750 and 5700 m(Sicart et al 2007 Ribstein et al 1995) which reflects thelikely profile of no or slightly negative vertical precipita-tion gradients on high tropical mountains (Weischet 1965)Therefore we accept values of our precipitation gauge lo-cated at 4950 m (Fig 1) as a best guess for the whole glacierIf precipitation does in fact increase with elevation at thissite it would yield more positive mass balance values andwe calculated that a precipitation increase of +5 (100 m)minus1

would increase mass balance by 03 mwe in both yearsMass balance is also affected by the separation of solid andliquid precipitation which was here done by linearly inter-polating between two threshold values However possibleerrors were captured within our evaluation method as mostvariability in precipitation phase occurred at the lowest partsof the glacier where the stake measurements were conducted

As the role of turbulent energy fluxes is minor (Sect 42)the vertical gradient of air temperature primarily impacts themass and energy balance through its effect on incoming longwave radiation and the phase of precipitation which affectsaccumulation but also ablation by impacting the position ofthe snow line Thus variable lapse rates (Petersen and Pel-licciotti 2011) could have an impact on some glaciers butfor our study site the area of the glacier that was most sensi-tive to temperature (Sect 41) was very close to the altitudewhere temperature was measured (Fig 1) If a temperaturegradient ofminus065 (100 m)minus1 (eg Kaser 2001) is applied(instead ofminus055 (100 m)minus1) mass balance would increaseby 014 m we (meters water equivalent) in year 1 and 008m we in year 2

Wind speed is kept constant in space even though it is ex-pected to vary due to topographic impacts on different scalesIn the ablation zone where ablation and mass balance would



be most sensitive to changes in available melt energy due tovariations in the turbulent fluxes our model evaluation ac-counts for possible errors in wind speed We generally ex-pect the magnitude of the wind speeds there to be very simi-lar to those used as model input (AWSM) as the wind speedsaveraged over 214 days of simultaneous records at AWSGand AWSM only varied by 01 msminus1 and the correlation forhourly values is 089 We also keep relative humidity con-stant in space as no data were available to calculate gradientsHowever the deviation between the mean values measuredat AWSG and AWSM are again low (1 ) and the correla-tion coefficient for the hourly values was high (095) whichmeans that the values should be well suitable for the mostsensitive lower parts of the glacier

For future studies additional validation data eg pro-glacier runoff data or time series of snow line altitude wouldbe desirable to provide an independent model evaluation be-yond the abilities of a cross validation approach and partic-ularly to test the robustness of the applied spatial gradients

5 Conclusions

The albedo parameterization used in the surface energy andmass balance model has been improved from an earlier study(Gurgiser et al 2013) and now better accounts for thesnowfall characteristics of tropical glacier sites with frequentsmall snowfalls coinciding with continuous ablation

Cross validation reveals that the RMSD of transferring pa-rameterizations in space islt 10 This model evaluationbenefits from the fact that the validation period included in-terannually contrasting mass balance conditions and stakedata that come from the elevation range of the glacier whichis characterized by the steepest vertical mass balance gradi-ents This means that despite the small areal coverage of val-idation data the stake locations can be expected to capturecharacteristics of the wider glacier area

Results of the cross validation and error assessment of themodel indicate that this modeling system is robust and per-forms well in comparison to previously published model re-sults (eg MacDougall and Flowers 2011 Hock and Holm-gren 2005) Furthermore as there is no evidence of positiveor negative trends between measurements and model solu-tions in space or time (Sect 312) both parameter transferand model application outside the measurement area shouldyield stable internal model uncertainty for short timescalesas long as the atmospheric conditions are comparable withthe ones captured in this study period For investigations onlonger time periods the characteristics of model input fromAWS measurements or regional climate model output shouldbe compared to the characteristics of the meteorological dataused as model input for this evaluation (Supplement Fig S1)If they are markedly different the results for the parametertransfer in space and time presented here may no longer berepresentative

Glacier-wide specific mass balance (Table 1 and Figs 6ndash8) was negative (minus032 mwe) in the first year and posi-tive (+051 mwe) in the second year with the interannualdifference in mass balance being almost exclusively pro-duced in the portion of the glacier below 5000 m (Table 1Fig 6c) The calculated ELA AAR and shape of the verti-cal mass balance profiles (Fig 7) agree with the ranges ob-tained from conceptual approaches or measurements (Sicartet al 2007 Kaser 2001) The geometry of Shallap Glacierwith steep slopes above the present day mean ELA (approx-imately 5000 m) means that the sensitivity of the AAR toincreasing temperature is low

Seasonal means of all surface energy fluxes were strongestduring the dry seasons (Table 2 and Figs 9ndash11) Averagedover the glacier arealt 5000 m net shortwave was the dom-inant energy source throughout the year and net all-waveradiation remained positive as net long wave energy lossesdid not offset net shortwave gains in either season Turbulentheat fluxes partially compensated each other and the nega-tive ground heat flux from the surface to the subsurface wasmostly balanced by subsurface melt so these fluxes did notoffset the positive radiation flux and consequently ablationrates were high in all seasons This is also the case at Anti-sana Glacier but is in contrast to Zongo Glacier where netall-wave radiation can be strongly negative in the dry seasonand melting is restricted to the humid season (Favier et al2004b Sicart et al 2011) In addition the model resultsdemonstrate that the importance of sublimation during thesetwo years is smaller than expected (eg Kaser 2001) Thisstudy cannot verify whether this reflects longer-term changesin atmospheric moisture characteristics over the CordilleraBlanca

The more negative mass balance rates for the first yearare on both annual and seasonal scales related to lower to-tal precipitation and higher fraction of liquid phase due tohigher mean temperatures especially during the wet season(Table 2) Thus variations in snow cover and the altitude ofsnow line explain most of the difference in available meltenergy in year 1 compared to year 2 (Fig 12) As meltingis the dominant ablation process throughout the year thesevariations also account for the difference in annual ablationWhereas the mass balance in the altitudes above 5000 mwhere essentially all precipitation is solid was primarily sen-sitive to annual precipitation sums the mass balance of thelower glacier area was sensitive to both precipitation andtemperature through its control on snow line altitude Thepredominant role of the snow line altitude and sensitivity ofmass balance to air temperature is a feature more similarto the mass balance regime of the inner tropical glaciers ofEcuador than the outer tropical glaciers of Bolivia (Favieret al 2004a b) Identifying this temperature and precip-itation phase sensitivity is useful for estimating likely im-pacts of a changing climate on the glaciers in the CordilleraBlanca



Appendix A

Table A1List of free model parameters for the selected model design based on Moumllg et al (2012) and Gurgiser et al (2013) The given rangeis applied in the sensitivity analysis (Sect 222) Parameters that change cumulative mass balance by more thanplusmn10 in our sensitivity test(Sect 222) are highlighted in bold The final values are the values in the best parameter combination (BPC) derived from the Monte Carloapproach (Sect 223) The precipitation gradient in the spatial distributed model run is set to zero as we have no information on precipitationabove AWSM (4950 masl) at our study site

Parameter Range Source BPC

Range for precipitation phase 10ndash25Cplusmn 05C Rohrer (1989) 11ndash26CLayer thickness for surface 05mplusmn 10 Moumllg et al (2008) 05 mtemperature schemeRoughness length ice 17mmplusmn 1mm Cullen et al (2007) 17 mm(momentum) Brock et al (2006)Roughness length ice (scalars) 17mmplusmn 1mm Cullen et al (2007) 17 mm

Brock et al (2006)Roughness length fresh snow 024mmplusmn 005mm Gromke et al (2011) 024 mmRoughness length aged snow 4mmplusmn 25mm Brock et al (2006) 4 mm(momentum)Roughness length aged snow 4mmplusmn 25mm Brock et al (2006) 4 mm(scalars)

Density of solid precipitation 250 kgmminus3plusmn 50kgmminus

3Sicart et al (2001) 203 kgmminus3

Superimposed ice constant 03plusmn 20 Moumllg et al (2009a) 03Fraction of SWnet absorbed in 08plusmn 10 Bintanja and van den Broeke (1995) 08surface layer (ice) Moumllg et al (2008)Fraction of SWnet absorbed in 09plusmn 10 Van As et al (2005) Bintanja and 089surface layer (snow) van den Broeke (1995)Extinction of penetrating 25 mminus1

plusmn 20 Bintanja and van den Broeke (1995) 25 mminus1

shortwave radiation (ice)Extinction of penetrating 17 mminus1


shortwave radiation (snow)Fixed bottom temperature 272 Kplusmn 1 K Assumed on the basis 272 K

of observationsIce albedo 02plusmn 005 Estimate from 016

measurementsFresh snow albedo 085plusmn 005 Estimate from 088

measurementsOld snow albedo 06plusmn 005 Estimate from 063

measurementsAlbedo timescale 25 dplusmn 15 d Estimate from 13 d

measurements

Supplementary material related to this article isavailable online athttpwwwthe-cryospherenet717872013tc-7-1787-2013-supplementpdf

AcknowledgementsThis work is funded by the Austrian ScienceFund (FWF projects I 900-N21 and P22106-N21) We thank An-drew MacDougall Yang Wei Marco Carenzo and one anonymousreviewer for their careful reviews They helped to substantiallyincrease the quality of the manuscript Thanks are due to JesusGomez and the Unidad de Glaciologia y Recursos Hidricos forsharing information and measurement data Irmgard Juen MarlisHofer Stephan Galos Martin Groszlighauser and Ursula Blumthalerfor sharing AWS data and Hector Oropeza and his team for theirexcellent assistance during fieldwork

Edited by V Radic

References

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Baraer M Mark B G McKenzie J M Condom T Bury JHuh K Portocarrero C and Rathay S Glacier recession andwater resources in Perursquos Cordillera Blanca J Glaciol 58 134ndash150 doi1031892012JoG11J186 2012

Bintanja R and van den Broeke M R The surface energy balanceof Antarctic snow and blue ice J Appl Meteorol 34 902ndash9261995

Braithwaite R Positive degree-day factors for ablation on theGreenland ice sheet studied by energy-balance modelling JGlaciol 41 153ndash160 1995



Brock B Willis I and Sharp M Measurement and parameteri-zation of albedo variations at Haut Glacier drsquoArolla SwitzerlandJ Glaciol 46 675ndash688 2000

Brock B W Willis I C and Sharp M J Measurement andparameterization of aerodynamic roughness length variations atHaut Glacier drsquoArolla Switzerland J Glaciol 52 281ndash297doi103189172756506781828746 2006

Bury J T Mark B G McKenzie J M French A Baraer MHuh K I Zapata Luyo M A and Goacutemez Loacutepez R J Glacierrecession and human vulnerability in the Yanamarey watershedof the Cordillera Blanca Peru Climatic Change 105 179ndash206doi101007s10584-010-9870-1 2010

Carenzo M Pellicciotti F Rimkus S and Burlando P As-sessing the transferability and robustness of an enhancedtemperature-index glacier-melt model J Glaciol 55 258ndash274doi103189002214309788608804 2009

Cullen N Molg T and Kaser G Energy-balance model valida-tion on the top of Kilimanjaro Tanzania using eddy covariancedata Ann Glaciol 46 227ndash233 2007

Favier V Wagnon P Chazarin J P Maisincho L andCoudrain A One-year measurements of surface heat budget onthe ablation zone of Antizana Glacier 15 Ecuadorian AndesJ Geophys Res 109 D18105 doi1010292003JD0043592004a

Favier V Wagnon P and Ribstein P Glaciers of the outerand inner tropics a different behaviour but a common re-sponse to climatic forcing Geophys Res Lett 31 L16403doi1010292004GL020654 2004b

Francou B Vuille M Favier V and Caceres B New evi-dence for an ENSO impact on low-latitude glaciers Antizana15 Andes of Ecuador 028prime S J Geophys Res 109 D18106doi1010292003JD004484 2004

Gardner A S and Sharp M J A review of snow and icealbedo and the development of a new physically based broad-band albedo parameterization J Geophys Res 115 F01009doi1010292009JF001444 2010

Georges C 20th-century glacier fluctuations in the tropicalCordillera Blanca Peruacute Arct Antarct Alp Res 36 100ndash107doi1016571523-0430(2004)036[0100TGFITT]20CO22004

Gromke C Manes C Walter B Lehning M and Guala MAerodynamic roughness length of fresh snow Bound-Lay Me-teorol 141 21ndash34 doi101007s10546-011-9623-3 2011

Gurgiser W Moumllg T Nicholson L and Kaser G Mass-balancemodel parameter transferability on a tropical glacier J Glaciol59 217 doi1031892013JoG12J226 2013

Hock R Glacier melt a review of processes andtheir modelling Prog Phys Geog 29 362ndash391doi1011910309133305pp453ra 2005

Hock R and Holmgren B A distributed surface energy-balancemodel for complex topography and its application to Storglacia-ren Sweden J Glaciol 51 25ndash36 2005

Hofer M Moumllg T Marzeion B and Kaser G Empiricalstatistical downscaling of reanalysis data to high resolutionair temperature and specific humidity above a glacier sur-face (Cordillera Blanca Peru) J Geophys Res 115 D12120doi1010292009JD012556 2010

Juen I Kaser G and Georges C Modelling observedand future runoff from a glacierized tropical catchment

(Cordillera Blanca Peruacute) Global Planet Change 59 37ndash48doi101016jgloplacha200611038 2007

Kaser G Glacier-climate interaction at low latitudes J Glaciol47 195ndash204 doi103189172756501781832296 2001

Kaser G and Georges C Changes of the equilibrium-line altitudein the tropical Cordillera Bianca Peru 1930ndash1950 and their spa-tial variations Ann Glaciol 24 344ndash349 1997

Kaser G and Georges C On the mass balance of low latitudeglaciers with particular consideration of the Peruvian CordilleraBlanca Ann Glaciol 24 344ndash349 1999

Kaser G and Osmaston H Tropical Glaciers Cambridge Univer-sity Press New York 2002

Kaser G Georges C Juen I and Moumllg T Low latitude glaciersunique global climate indicators and essential contributors toregional fresh water supply A conceptual approach GlobalChange and Mountain Regions 23 185ndash195 2005

Klok E J L and Oerlemans J Model study of thespatial distribution of the energy and mass balance ofMorteratschgletscher Switzerland J Glaciol 48 505ndash518doi103189172756502781831133 2002

MacDougall A H and Flowers G E Spatial and temporal trans-ferability of a distributed energy-balance glacier melt model JClimate 24 1480ndash1498 doi1011752010JCLI38211 2011

Machguth H Purves R S Oerlemans J Hoelzle M andPaul F Exploring uncertainty in glacier mass balance mod-elling with Monte Carlo simulation The Cryosphere 2 191ndash204 doi105194tc-2-191-2008 2008

Machguth H Paul F Kotlarski S and Hoelzle M Calculat-ing distributed glacier mass balance for the Swiss Alps fromregional climate model output a methodical description andinterpretation of the results J Geophys Res 114 D19106doi1010292009JD011775 2009

Mark B G and Seltzer G O Tropical glacier melt-water contribution to stream discharge a case study inthe Cordillera Blanca Peru J Glaciol 49 271ndash281doi103189172756503781830746 2003

Mark B and Seltzer G Evaluation of recent glacier recession inthe Cordillera Blanca Peru (AD 1962ndash1999) spatial distribu-tion of mass loss and climatic forcing Quaternary Sci Rev 242265ndash2280 doi101016jquascirev200501003 2005

Moumllg T and Hardy D R Ablation and associated energy balanceof a horizontal glacier surface on Kilimanjaro J Geophys Res109 D16104 doi1010292003JD004338 2004

Moumllg T Cullen N J Hardy D R Kaser G and Klok L Massbalance of a slope glacier on Kilimanjaro and its sensitivity toclimate Int J Climatol 892 881ndash892 doi101002joc15892008

Moumllg T Cullen N J Hardy D R Winkler M and Kaser GQuantifying climate change in the tropical midtroposphere overEast Africa from glacier shrinkage on Kilimanjaro J Climate22 4162ndash4181 doi1011752009JCLI29541 2009a

Moumllg T Cullen N J and Kaser G Solar radiation cloudi-ness and longwave radiation over low-latitude glaciers impli-cations for mass-balance modelling J Glaciol 55 292ndash302doi103189002214309788608822 2009b

Moumllg T Maussion F Yang W and Scherer D The footprint ofAsian monsoon dynamics in the mass and energy balance of aTibetan glacier The Cryosphere 6 1445ndash1461 doi105194tc-6-1445-2012 2012



Nicholson L I Prinz R Moumllg T and Kaser G Micrometeoro-logical conditions and surface mass and energy fluxes on LewisGlacier Mt Kenya in relation to other tropical glaciers TheCryosphere 7 1205ndash1225 doi105194tc-7-1205-2013 2013

Niedertscheider J Untersuchungen zur Hydrographie derCordillera Blanca (Peru) Master Thesis Leopold FranzensUniversity Innsbruck 1990

Oerlemans J and Knap W A 1 year record of global radiation andalbedo in the ablation zone of Morteratschgletscher SwitzerlandJ Glaciol 44 231ndash238 1998

Petersen L and Pellicciotti F Spatial and temporal variabil-ity of air temperature on a melting glacier atmospheric con-trols extrapolation methods and their effect on melt modelingJuncal Norte Glacier Chile J Geophys Res 116 D23109doi1010292011JD015842 2011

Porter C Equilibrium-Line Altitudes of Late Quaternary Glaciersin the Southern Alps New Zealand Quaternary Res 47 27ndash471975

Rabatel A Francou B Soruco A Gomez J Caacuteceres B Ce-ballos J L Basantes R Vuille M Sicart J-E Huggel CScheel M Lejeune Y Arnaud Y Collet M Condom TConsoli G Favier V Jomelli V Galarraga R Ginot PMaisincho L Mendoza J Meacuteneacutegoz M Ramirez E Rib-stein P Suarez W Villacis M and Wagnon P Current stateof glaciers in the tropical Andes a multi-century perspective onglacier evolution and climate change The Cryosphere 7 81ndash102 doi105194tc-7-81-2013 2013

Ribstein P Tiriau E Francou B and Saravia R Tropical cli-mate and glacier hydrology a case study in Bolivia J Hydrol165 221ndash234 1995

Rohrer M B Determination of the transition air tempera-ture from snow to rain and intensity of precipitation inIAHSWMOETH International Workshop on Precipitation Mea-surement St Moritz Switzerland 475ndash482 1989

Sicart J Ribstein P Francou B Pouyaud B and Condom TGlacier mass balance of tropical Zongo glacier Bolivia com-paring hydrological and glaciological methods Global PlanetChange 59 27ndash36 doi101016jgloplacha200611024 2007

Sicart J E Ribstein P Wagnon P and Brunstein D Clear-skyalbedo measurements on a sloping glacier surface a case study inthe Bolivian Andes J Geophys Res 106 31729ndash31731 2001

Sicart J E Hock R Ribstein P and Chazarin J P Sky long-wave radiation on tropical Andean glaciers parameterization andsensitivity to atmospheric variables J Glaciol 56 854ndash8602010

Sicart J E Hock R Ribstein P Litt M and Ramirez E Anal-ysis of seasonal variations in mass balance and meltwater dis-charge of the tropical Zongo Glacier by application of a dis-tributed energy balance model J Geophys Res 116 D13105doi1010292010JD015105 2011

Van As D Van Den Broeke M Reijmer C and VanDe Wal R The summer surface energy balance of thehigh Antarctic Plateau Bound-Lay Meteorol 115 289ndash317doi101007s10546-004-4631-1 2005

Vuille M Kaser G and Juen I Glacier mass balance variabilityin the Cordillera Blanca Peru and its relationship with climateand the large-scale circulation Global Planet Change 62 14ndash28 doi101016jgloplacha200711003 2008

Wagnon P Ribstein P Kaser G and Berton P Energy bal-ance and runoff seasonality of a Bolivian glacier Global PlanetChange 22 49ndash58 doi101016S0921-8181(99)00025-9 1999

Weischet W Der tropisch-konvektive und der auszligertropisch-advektive Typ der vertikalen Niederschlagsverteilung ErdkundeXIX 6ndash14 doi103112erdkunde19650102 1965

Wilks D S Statistical Methods in the Atmospheric Sciences 3rdEdn Academic Press 2011



radiation is closely coupled to surface ablation throughoutthe year (Favier et al 2004a) and variations in glacier-wideablation are controlled by surface albedo and the positionof the snow line which are both governed by the occur-rence and spatial distribution of solid precipitation (Fran-cou et al 2004) As air temperature controls the phase ofprecipitation the sensitivity of the annual mass balance toboth precipitation amount and temperature is high Seasonalvariations in energy fluxes are small and related to a slightseasonality in wind speeds In the outer tropics at ZongoGlacier there is a clear seasonality in meteorological con-ditions dominated by changes in atmospheric humidity andresultant cloud cover conditions and atmospheric long waveemissions While the surface energy balance is still domi-nated by the net shortwave radiation low atmospheric hu-midity and atmospheric long wave emissions during the dryseason result in high energy losses via the net long waveflux which reduces the energy available for melting theglacier and consequently restricts ablation to sublimation(eg Wagnon et al 1999 Favier et al 2004a Moumllg andHardy 2004 Nicholson et al 2012) In contrast to AntisanaGlacier the sensitivity of Zongo Glacier mass balance to airtemperature was found to be low because air temperatures atthis site are sufficiently low that precipitation over the wholeglacier area was solid (Favier et al 2004a) Instead glaciermass balance here is most strongly controlled by atmospherichumidity cloudiness and precipitation especially at the on-set of the humid season (Sicart et al 2011) Kaser (2001)generally suggests that the mass balance in the inner tropicsis most sensitive to variations in air temperature whereas inthe outer tropics sensitivity to atmospheric moisture is high-est due to its multiple impacts on mass balance

The Cordillera Blanca of Peru lies between the latitudesof Ecuador (inner Tropics) and Bolivia (outer Tropics) Asno high spatial and temporal resolution mass and energy bal-ance investigations have been carried out in this region sofar it is not clear how the seasonal and annual characteris-tics of glacier mass and energy balance relate to those iden-tified in Ecuador and Bolivia Furthermore the atmosphericvariables that exert the strongest control on glacier mass bal-ance which is crucial information for estimating the possibleimpact of climate change on the glaciers of the CordilleraBlanca remain unknown Thus the aims of this study areto (1) use a process-based model to compute and comparethe characteristics of glacier mass balance of Shallap Glacier(9 S) Cordillera Blanca Peru for two hydrological yearsand (2) investigate the energetic drivers of the surface massbalance

2 Study area measurements and methods

Shallap Glacier (920prime Sminus7720prime W) lies west of the divideof the Cordillera Blanca range of the Peruvian Andes (Fig 1)The outer tropical climate is characterized by relatively con-

stant annual temperature and a distinct variation in precip-itation (eg Juen et al 2007 Favier et al 2004b Kaser2001) with a wet season from October to April and a dryseason from May to September (see Supplement Fig S1)On the basis of satellite data (SPOT XS Sensor) obtainedin 2002 (Georges 2004) the glacier at that time spanned4700 to 5740 masl with more than half of the 7035 km2

glacier surface area below 5200 m In the absence of more re-cent information the 50 m resolution digital elevation model(DEM) derived from these satellite images was used as theglacier surface for our mass balance modeling

21 Measurements

211 Automatic weather stations

In 2002 an automatic weather station was installed onthe southern glacier moraine (4950 masl) approximately150 m above the glacier surface (hereafter AWSM) (Fig 1)Continuous hourly data of temperature humidity windspeed global radiation and precipitation are available fromJanuary 2006 to November 2009 and from July 2011 toMarch 2012 Data from AWSM were used as input for thesurface energy and mass balance model applied in this study(Sect 22) From July 2010 to September 2012 a secondweather station (hereafter AWSG) was operated in the abla-tion zone of the glacier (4796 masl) recording hourly tem-perature humidity wind direction and speed and net radia-tion at 2 m above the glacier surface No data are availablefrom February 2012 to April 2012 due to a defect in powersupply Data from AWSG were used to improve the surfacealbedo module of the mass balance model (Sect 22) andto develop a function for transferring temperature from themoraine to the glacier surface The temperature transfer func-tion is based on a multiple regression considering tempera-ture relative humidity and wind speed measured at AWSM(Gurgiser et al 2013) Figure S2 (Supplement) showingmeasured and transferred temperature and information onthe meteorological sensors used at both AWS are included inthe supplement

212 Stake measurements

Stake measurements (between 4758 and 4824 m asl) inthe ablation zone of Shallap Glacier were conducted bythe Unidad de Glaciologia y Recursos Hidricos (UGRH) ofthe Peruvian Autoridad Nacional de Agua (ANA) from Au-gust 2005 to August 2008 At 20 stake locations (Fig 1)relative surface height change was measured over 21 inter-vals spanning 14 to 64 days (dates are shown in Fig 4) Asneither snow depth nor snow density were recorded regu-larly measurements cannot be readily transferred into massunits but as the stake measurement area was snow free on 29August 2006 21 August 2007 and 27 August 2008 annualmass balances can be derived between these dates assuming







221 Model design












(minus

d

dlowast

) (2)




(minus

t

tlowast

) (3)














RMSDri=


)2p=1ndash21

np[m] (4)









RMSDYear=


)2i=1ndash20

ni

(5)

[m we]




nymiddotradic

ny [m we] (6)




3 Results

31 Model evaluation



































SWin 198 201 3 215 207 7





RH 81 80 1 62 65 3














4 Discussion



















43 Uncertainties













5 Conclusions









Appendix A
















measurements



Edited by V Radic

References

































































221 Model design












(minus

d

dlowast

) (2)




(minus

t

tlowast

) (3)














RMSDri=


)2p=1ndash21

np[m] (4)









RMSDYear=


)2i=1ndash20

ni

(5)

[m we]




nymiddotradic

ny [m we] (6)




3 Results

31 Model evaluation



































SWin 198 201 3 215 207 7





RH 81 80 1 62 65 3














4 Discussion



















43 Uncertainties













5 Conclusions









Appendix A
















measurements



Edited by V Radic

References

































































(minus

d

dlowast

) (2)




(minus

t

tlowast

) (3)














RMSDri=


)2p=1ndash21

np[m] (4)









RMSDYear=


)2i=1ndash20

ni

(5)

[m we]




nymiddotradic

ny [m we] (6)




3 Results

31 Model evaluation



































SWin 198 201 3 215 207 7





RH 81 80 1 62 65 3














4 Discussion



















43 Uncertainties













5 Conclusions









Appendix A
















measurements



Edited by V Radic

References



































































RMSDri=


)2p=1ndash21

np[m] (4)









RMSDYear=


)2i=1ndash20

ni

(5)

[m we]




nymiddotradic

ny [m we] (6)




3 Results

31 Model evaluation



































SWin 198 201 3 215 207 7





RH 81 80 1 62 65 3














4 Discussion



















43 Uncertainties













5 Conclusions









Appendix A
















measurements



Edited by V Radic

References

































































RMSDYear=


)2i=1ndash20

ni

(5)

[m we]




nymiddotradic

ny [m we] (6)




3 Results

31 Model evaluation



































SWin 198 201 3 215 207 7





RH 81 80 1 62 65 3














4 Discussion



















43 Uncertainties













5 Conclusions









Appendix A
















measurements



Edited by V Radic

References
























































































SWin 198 201 3 215 207 7





RH 81 80 1 62 65 3














4 Discussion



















43 Uncertainties













5 Conclusions









Appendix A
















measurements



Edited by V Radic

References




































































4 Discussion



















43 Uncertainties













5 Conclusions









Appendix A
















measurements



Edited by V Radic

References












































































43 Uncertainties













5 Conclusions









Appendix A
















measurements



Edited by V Radic

References































































5 Conclusions









Appendix A
















measurements



Edited by V Radic

References





























































Appendix A
















measurements



Edited by V Radic

References




























































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