A surface mass balance model for the Greenland Ice Sheet

Marion Bougamont and Jonathan L. BamberSchool of Geographical Sciences, University of Bristol, Bristol, UK

Wouter GreuellInstitute for Marine and Atmospheric Research Utrecht (IMAU), Utrecht University, Utrecht, Netherlands

Received 6 June 2005; revised 6 September 2005; accepted 20 September 2005; published 7 December 2005.

[1] A surface mass balance model aimed at being coupled to a Global Circulation Model(GCM) for future climate prediction is described and tested for the Greenland Ice Sheet.The model builds on previous modeling designed to be forced by automatic weatherstation data, and includes surface energy balance as well as processes occurring near thesurface such as water percolation and refreezing. Surface albedo is calculated with anew scheme that differentiates the timescale for aging of wet and dry snow andincorporates the effect of a thin layer of water and/or fresh snow at the surface. The modelwas driven with automatic weather station data from two sites located in the ablation zonein the Kangerlussuaq area (West Greenland), and calculated reasonable annual massbalance values (within 10% in seven out of eight cases) for four individual andconsecutive years (1998–2001), using both measured and calculated albedo. This impliesthat the albedo parameterization is adequate and climate feedbacks affecting the massbalance are well captured. The model was then applied to a distributed 20-km-resolutiongrid covering the whole ice sheet, and forced with 10 years of the European Centrefor Medium-range Weather Forecast (ECMWF) reanalysis (ERA-40) data. With the aim ofcoupling the model to a GCM, this study focuses on the ability to model the interannualvariability in mass balance rather than to assess the present state of balance of theice sheet. Modeled spatial and temporal wet zone extent compares well with informationderived from passive microwave satellite data.

Citation: Bougamont, M., J. L. Bamber, and W. Greuell (2005), A surface mass balance model for the Greenland Ice Sheet,

J. Geophys. Res., 110, F04018, doi:10.1029/2005JF000348.

1. Introduction

[2] The Arctic climate is currently warming at a faster ratethan observed elsewhere on the planet [Church et al., 2001]. Ifit were to melt completely the Greenland Ice Sheet (GrIS)would raise sea level by 7 m [Warrick and Oerlemans, 1990].Currently the best estimate of the ice sheet’s mass balance isaround �80 km3 yr�1[Krabill et al., 2004], and the GrIS isexpected to increase its contribution to sea level rise throughenhanced surface melt by 20–50% per degree of warming[Braithwaite and Olesen, 1993; Ohmura et al., 1996; van deWal, 1996; Janssens and Huybrechts, 2000]. In addition,recent observations suggest that increased surface meltingcould increase the ice velocities [Zwally et al., 2002; Krabillet al., 2004], making it more vulnerable to atmosphericwarming than previously believed. Moreover, it is nowwidely accepted that rapid (approximately a few decades)climate change has occurred in the Northern Hemisphereduring the last glacial period [Ganopolski and Rahmstorf,2001; Alley et al., 2003], possibly triggered by a shutdown ofthe thermohaline circulation (THC) in the North Atlantic[Stocker, 2000; Ganopolski and Rahmstorf, 2001]. The GrIS

lies close to two key regions of ocean convection in theLabrador and Irminger Seas (Figure 1). Therefore, in additionto changing sea level, the ice sheet could also play a role inmodulating the THC of the North Atlantic [Rahmstorf, 1995;Fichefet et al., 2003].[3] Global Circulation Models (GCMs) are powerful

tools for analyzing and quantifying feedback mechanisms,and in particular for elucidating the role of the cryosphere inclimate change [Thompson and Pollard, 1997; Glover,1999; Church et al., 2001; Murphy et al., 2002; Wild etal., 2003]. However, the window of uncertainty remainslarge, as model results differ greatly under different resolu-tion and model physics [Stainforth et al., 2005]. Whileassessing accurately the mass balance of the GrIS isimportant, the lack of resolution often prevents correctrepresentation of the narrow ablation zone of the ice sheet.Another problem is that few studies using GCMs incorpo-rate detailed snow/firn processes specific to an ice sheetmass balance [Bugnion and Stone, 2002; Huybrechts et al.,2002] or couple interactively an ice sheet model with anatmosphere-ocean-GCM (AOGCM) [Huybrechts et al.,2002; Fichefet et al., 2003].[4] The goal of this paper is to validate a detailed, high-

resolution surface mass balance model (SMBM) of the GrISaimed at being interactively coupled with an AOGCM

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, F04018, doi:10.1029/2005JF000348, 2005

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(based on the Hadley Centre Climate Model version 3,HadCM3) in order to not only assess the contribution of theGrIS to sea level variations in the next few centuries, butalso to evaluate the response of the oceanic circulation tofreshening from the increased freshwater flux from the icesheet. The SMBM has been set up to run at 20 kmresolution and is a modified version of SOMARS(Simulation Of glacier surface Mass balance And RelatedSub-surface processes, http://www.phys.uu.nl/�greuell/massbalmodel.html). SOMARS has been tested at theETH-Camp (West Greenland, 1155m a.s.l.) on data collectedduring summer 1990 [Greuell and Konzelmann, 1994].Located near the equilibrium line, this site was ideal fortesting the subsurface component of the model, and thegood agreement between model results and observationssuggests that SOMARS is suitable for the study presentedhere. In SOMARS and in this study, refreezing, meltwaterpercolation and runoff are modeled within the first 40 m offirn with a detailed near-surface model. The surface ablation

is determined using an energy balance calculation ratherthan applying the Positive Degree Day (PDD) technique[Reeh, 1991; Braithwaite, 1995; Johannesson et al., 1995;Hock, 1999; Braithwaite and Zhang, 2000]. Althoughcomputationally less expensive, the latter method can onlytake into account the effect of temperature change on themass balance and not the spatial and temporal variabilityinduced by other variables [Greuell and Genthon, 2004].This drawback becomes particularly limiting if the model isused in climate simulation over the next few centuries, asthe effect of a modified atmospheric pattern (e.g., cloudcover, turbulent fluxes and precipitation) would not be takeninto account explicitly. A comparison between PDD andenergy balance models suggests that the sensitivity towarmer temperatures is enhanced with a PDD comparedwith an energy balance model and that the latter wouldproduce more realistic results [van de Wal, 1996].[5] The SMBM was first validated against observations at

two Automatic Weather Stations (AWS) along the Kanger-lussuaq transect (K-transect) (Figure 1), for four consecutiveyears (section 3.1). It was then run for the whole ice sheet,forced with 10 years of European Centre for Medium-rangeWeather Forecast (ECMWF) reanalysis (ERA-40) data(section 3.2). The re-analysis data were, however, usedsolely to assess the model skill with respect to reproducingthe observed spatial and temporal variability in melt and notthe absolute values. ERA-40 is likely to contain somesystematic biases [Hanna and Valdes, 2001; Hanna et al.,2002] which we did not attempt to correct for, and theabsolute values of ablation and accumulation are thereforeexpected to be biased. However, ERA-40 data weregenerated by assimilating available observations and thetemporal variability is therefore quite well represented[Hanna and Valdes, 2001; Hanna et al., 2002]. The abilityto capture the interannual variability is an importantfeature of a model for use with atmospheric-GCM input,which will likely contain uncertainties and biases inits forcing fields. These biases can be accounted for usingflux adjustment methods or deviations from a meanclimatology, but the ability to reproduce the spatial andtemporal variability is a function of the model physics,which cannot be tuned.

2. Model Description

[6] The model consists of two parts: the surface compo-nent (section 2.1) computes the energy available for melt-ing/freezing from energy exchange between the surface andthe atmosphere. The near-surface component (section 2.2)treats processes occurring in the subsurface, after meltwaterpercolates in the underlying layers. A nonexhaustive list ofthe input data required and of the model surface and near-surface variables is given in Table 1.

2.1. Surface Energy Model

2.1.1. Energy Balance[7] The total energy flux (Qt) from the atmosphere toward

the surface of a glacier or ice sheet equals the sum of the netradiative and the turbulent fluxes,

Qt ¼ LW# � LW"� �

þ SW# � SW"� �

þ LHF þ SHF þ Frain;

ð1Þ

Figure 1. Albedo map of the western part of Greenland asderived from AVHRR data (modified from Greuell [2000]),and showing the location of the K-transect. The two AWSare located at longitude 50.1�W (site 5) and 49.4�W (site 6).The ‘‘dark zone’’ extends from north to south around 49�W.The map in the upper right corner shows the location of theLabrador Sea (LS) and Irminger Sea (IS).

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where LW# and LW" are the downward and upwardlongwave radiations, SW# and SW" are the downward andupward shortwave radiations, LHF and SHF are respec-tively the latent heat and sensible heat fluxes, and Frain isthe energy flux supplied by rain. Details on the calculationof each component are described in the next three sections.2.1.2. Radiation[8] The downward longwave and shortwave radiation

were available either from AWS for calculations along theK-transect, or from ERA-40 for runs over the whole icesheet. Because ice and snow have both an emission coef-ficient close to one [Griggs, 1968; Warren, 1982], theupward longwave radiation can be estimated with sufficientaccuracy from the surface temperature, To,

LW" ¼ sT4o ; ð2Þ

where s = 5.67 10�8 W m�2 K�4 is the Stefan-Boltzmann constant.The upward shortwave radiation is determined by thesurface albedo, a,

SW" ¼ SW#a: ð3Þ

[9] Ice sheet albedo values can range from very high(adry = 0.82) for dendritic snow to low values when watercovers the surface (awet = 0.15, [Hummel and Reck, 1979]).Fresh snow albedo decreases with time due to metamor-phism induced by wetness of the snowpack, the temperaturegradient and pressure [Brun et al., 1992; Lefebre et al.,2003]. Other parameters decreasing the snow albedo include

grain size and shape, and the impurity content [Greuell andGenthon, 2004]. Debris and dust, bubbles and cracks, andwater content contribute to reducing the ice albedo [Greuelland Genthon, 2004]. In our model we represent snowmetamorphism by parameterizing albedo as a function ofthe age of the snow. The effect of aging and of the presenceof a thin layer of fresh snow on the albedo value can bemodeled using exponential functions to insure a smoothtransition between different states [Oerlemans and Knap,1998]. Similarly, the influence of a water layer at the surfacecan be parameterized using an exponential function [Zuoand Oerlemans, 1996]. The albedo calculation used hereand detailed next is modified from those two studies.[10] The metamorphism for dry snow differs from that of

wet snow. The latter is the fastest, as the presence of water inthe snowpack increases the effective grain size, and speedsup the rate of grain growth [Warren, 1982]. Dry snow albedodecay is much faster for air temperatures close to the meltingpoint than for lower temperatures. Below �10�C, the agingof snow is considered negligible, and the albedo remainsequal to adry [Loth et al., 1993; Reijmer et al., 2005]. Drysnow albedo decay can be modeled as a linear function ofboth the time elapsed since the last snowfall and the airtemperature [Van den Hurk and Viterbo, 2003]. Rather thanusing a linear relationship, we use an exponential decay [Zuoand Oerlemans, 1996; Oerlemans and Knap, 1998] tocombine the effect of age and snow temperature,

dadt

¼ � a� aoldð Þt*

; ð4Þ

Table 1. Symbols and Variables Used in the Model

Symbol Definition

InputLW# downward longwave radiation, W m�2

SW# downward shortwave radiation, W m�2

P surface pressure, PaPrec accumulation, m w.e.Tatm air temperature within the constant flux layer, �Cu wind speed within the constant flux layer, m s�1

RH relative humidity within the constant flux layer, %

Surface VariablesQt total energy flux, W m�2

LW" upward longwave radiation, W m�2

SW" upward shortwave radiation, W m�2

SHF sensible heat flux, W m�2

LHF latent heat flux, W m�2

Frain heat flux supplied by rain, W m�2

z0, zT, zq roughness length for momentum, temperature, humidity respectively, mS surface slopeasurf surface albedoTo surface temperature, �CW surficial water, mdzfrsnow fresh snow thickness at the surface, mt*runoff timescale for runoff to occur, daysc1, c2, c3 runoff parameters

Englacial Variablesa albedoTsnow temperature, �Cr density, kg m�3

w water content, mm mass, m w.e.zgrid thickness of the grid box, m

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where aold is the albedo of old snow and t* is the timescalefor albedo decay, defined as follows (in days):

if the snow is wet (w > 0)

t* ¼ twet* ; ð5aÞ

if the snow is dry (w = 0) and �10�C Tsnow 0�C

t* ¼ Tsnowj j K þ tdry 0�Cð Þ* ; ð5bÞ

if the snow is dry (w = 0) and Tsnow < �10�C

t* ¼ tdry �10�Cð Þ* ; ð5cÞ

where Tsnow is the temperature of the snow/firn/ice in �C,and w is the water content of a given grid box. Thetimescale for wet snow albedo decay (t*wet), for dry snowalbedo decay at Tsnow = 0�C (t*dry(0�C)) and the constant K isset during model tuning (Table 2). Here, fresh snow albedowould decrease to the old snow albedo value in 15 days fora wet snowpack. It would take twice as long for a drysnowpack at 0�C, while over three months would benecessary at temperatures below �10�C. By calculating thetemperature (Tsnow) and water content (w) of grid boxes forthe surface and subsurface layers, the SMBM keeps track ofthe sub-surface albedo variation for each grid box.[11] The surface albedo, asurf, is the albedo of the upper

grid box, plus taking into account the effect of a thin layerof water on top of the ice (equation (6)) and/or of a thinlayer of fresh snow at the surface (equation (7)), as in thework of Zuo and Oerlemans [1996] and Oerlemans andKnap [1998], respectively,

asurf ¼ awet � awet � að Þ exp �wsurf

w*

� �ð6Þ

asurf ¼ adry � adry � a� �

exp � dzfrsnow

zsnow*

� �; ð7Þ

where wsurf is the thickness of surficial water, w* is thecharacteristic scale for surficial water, dzfrsnow is thethickness of fresh snow and z*snow is the characteristic scalefor snow depth. The albedo parameter values used here are

fixed after tuning the model for computations along theK-Transect, while ensuring that they remain within thelimits suggested by available measurements (summarizedin Table 2).2.1.3. Turbulent Heat Fluxes[12] Most details of the method used here have been

presented elsewhere [Greuell and Genthon, 2004], and onlya summary is provided in this section. The relationshipbetween the turbulent heat fluxes and the wind, temperatureand humidity profiles can be established within the Monin-Obukhov similarity theory, and read

SHF ¼ ra Cpau*Q* ð8Þ

LHF ¼ ra Ls u* q*; ð9Þ

where

u* ¼ kzFm

@u

@zð10aÞ

is the friction velocity,

Q* ¼ kzFh

@Q@z

ð10bÞ

is the temperature scale, and

q* ¼ kzFh

@q

@zð10cÞ

is the humidity scale.[13] In equations (8) and (9), ra is the air density, Cpa =

1005 J kg�1 K�1 is the specific heat capacity of the air andLs = 2.84 106 J kg�1 is the latent heat of sublimation. Inequations (10), u is the wind speed, Q is the potentialtemperature, q is the specific humidity, k = 0.4 is the vonKarman constant and fm and fh are the stability functionsfor the momentum and for the scalar quantities (temperatureand humidity). The latter have different forms for stable andunstable conditions [H}ogstr}om, 1988]. Here the turbulentheat fluxes are computed with the bulk method, whereequations (10a)–(10c) are integrated between an atmo-spheric level (2 m or 4 m for Tatm and RH, and 10 m or4 m for u, respectively, provided by ERA-40 and AWS) and

Table 2. Albedo Parameter Values Used in the Model

Parameter This Study Sources/Other Values

aice 0.52 GIMEX-91: 0.5–0.55adry 0.82 GIMEX-91: snow albedo from 0.64 up to 0.89

[van de Wal and Oerlemans, 1994]: 0.85awet 0.15 [Zuo and Oerlemans, 1996]: 0.15

[van de Wal and Oerlemans, 1994]:0.2aold 0.42 GIMEX-91: 0.27–0.53

[van de Wal and Oerlemans, 1994]: 0.65[Zuo and Oerlemans, 1996]: 0.45

t*wet 15 days [Oerlemans and Knap, 1998]: 21.9 dayst*dry(0�C) 30 days tuningK 7 tuningw* 300 mm [Zuo and Oerlemans, 1996]: 200 mm

[Denby et al., 2002]: 600 mmz*snow 20 mm [Oerlemans and Knap, 1998]: 32 mm

[Denby et al., 2002]: 16 mm

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the roughness lengths, which are defined as the heightsabove the surface where the profiles of u, Q and q reachtheir surface values. Work by Box and Steffen [2001]suggests that the bulk method for turbulent latent heat fluxunderestimates the water vapor deposition compared to theprofile method (a difference of 57.9 1012 kg yr�1 wasfound when calculating the annual net total evaporativemass transfer using both methods). On the other hand, thebulk method appears more suitable if a wind-speed maxi-mum is present [Denby and Greuell, 2000].[14] The roughness lengths for temperature (zT) and water

vapor (zq) are computed using the equations developed byAndreas [1987], accounting for the difference in transfermechanisms for momentum from those for scalars, asdiscussed by Greuell and Genthon [2004],

lnzT

z0

� �¼ 0:317� 0:565 lnR� 0:183 lnRð Þ2 ð11aÞ

lnzq

z0

� �¼ 0:396� 0:512 lnR� 0:180 lnRð Þ2; ð11bÞ

where R is the Reynolds number (R = (u*z0)/u, with thekinematic viscosity of air u = 1.461 10�5 m2 s�1), and z0is the momentum roughness length defined as a function ofthe density of the uppermost element of the snowpack[Greuell and Konzelmann, 1994]. After model tuning, theroughness length is set to 0.12 mm for dry snow, 1.3 mm forwet snow and 3.2 mm for ice (as in the work by Greuell andKonzelmann [1994]).2.1.4. Heat Flux Supplied by Rain[15] Rain provides a small amount of energy Frain, by

falling onto a surface with a lower temperature [see e.g.,Greuell and Genthon, 2004],

Frain ¼ rwrCpw Tr � T0ð Þ; ð12Þ

Figure 2. Processes occurring in the snow/firn layer included in the model.

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where rw = 1000 kg m�3 is the density of water, r is therain-fall rate (in m s�1), Cpw = 4200 J kg�1 K�1 is thespecific heat capacity of water, Tr is the rain temperature(which can be approximated by Tatm) and T0 is the surfacetemperature.

2.2. Near-Surface Model

[16] Several studies have underscored the importance ofincluding surface water percolation, retention and refreezingwhen assessing the mass balance of the Greenland Ice Sheet[Pfeffer et al., 1991; Reeh, 1991; Braithwaite et al., 1994;Janssens and Huybrechts, 2000]. The SMBM’s near-surfacemodel (Figure 2) is similar to the one described by Greuelland Konzelmann [1994], with the exception of the effectiveconductivity parameterization, of the calculation of theirreducible water amount and of the runoff formulation.[17] Solar radiation penetrates below the surface, where it

is partly absorbed according to Beer’s law. Using a densitydependent effective conductivity [Sturm et al., 1997], thethermodynamic equation is then solved in the snow/firnlayers to determine the amount of melting and refreezing inthe firn. Positive temperatures are reset to 0�C and meltingoccurs. Water (melt + rain) can refreeze, to the degree thatwater or space is available, or that the temperature in thelayer (Tsnow) does not exceed the melting point. Theirreducible water saturation is calculated as a function ofthe firn density (r) [Coleou and Lesaffre, 1998], and thewater content of a given layer (w) exceeding the maximumretention capacity percolates downward, until an imperme-able layer is reached (i.e., with a density 910 kg m�3).Part of the free water runs off immediately inside thesnowpack, at a slower rate than at the surface. The rest fillsup all the pores to form a slush layer, which can later onrefreeze as superimposed ice. Water on top of the surfaceruns off at a timescale t*runoff that depends on the local slope[Zuo and Oerlemans, 1996],

trunoff* ¼ c1 þ c2 exp �c3Sf g; ð13Þ

where S is slope and c1 = 0.05, c2 = 15 and c3 = 142 aredetermined with model tuning. Those values are only poorlyconstrained, as no observation is available regarding thetimescale for runoff to occur [Zuo and Oerlemans, 1996].The values used in this study are such that surficial waterruns off in about 1.2 days if the slope equals one degree,while 15 days would be required on a flat surface. Note thatin the case of an infinitely steep slope, water would run offalmost immediately. Inside the snowpack, runoff is set up tooccur 10 times slower than at the surface. The distinctionbetween inside and surface runoff used here may explain thedifference with the timescales used by Zuo and Oerlemans[1996] (3.7 days with S = 1� and 26.5 days on a flatsurface), and Lefebre et al. [2003] (2.5 days with S = 1�,25.33 days on a flat surface), who both did not differentiatebetween internal and surficial runoff.[18] Precipitation falls as snow if the air temperature is

below 2�C [Oerlemans, 1993]. Snow densification due tosettling and packing is computed from empirical relations[Herron and Langway, 1980]. The mass balance isfinally computed as the sum of accumulation, precipita-tion and condensation minus evaporation/sublimation andrunoff.

2.3. Numerics and Initial Conditions

[19] The near-surface processes are modeled for 40m offirn/snow/ice, composed of a maximum of 200 layers.Initially, the thickness of each individual layer (zgrid)increases linearly with depth from 0.09 m for the uppermostone to a maximum of 4 m for the lowest one. A layerthickness varies due to melting or freezing, condensationand accumulation. Layers are added/removed at the bottomto maintain a total thickness of approximately 40 m. A layerthat becomes too thick is split into two new ones while onebecoming too thin can be fused with the underlying one.The surface temperature is linearly extrapolated from thetemperature of the two uppermost grid points [Greuell andKonzelmann, 1994].[20] The model runs with a time step of 30 min, and the

input (both from AWS and ERA-40) are interpolatedaccordingly. Mass and energy conservation are beingchecked throughout the model runs.[21] The initial snowpack thickness is taken from ERA-

40, downloaded for the first day of the model experiment(01 January 1991). The snowpack initial temperature is setequal to the average annual Tatm. Themodel is allowed to spinup for six months, and the experiment start date is 1 January,giving additional time for the model to adjust to initialconditions before the first melt season occurs. We carriedout a number of experiments suggesting that the modelresults are not sensitive to realistic variations in initialconditions.

3. Results and Discussion

3.1. Validation Along the K-Transect

[22] LW#, SW#, P, Tatm and u at 4 m above the surfacewere recorded hourly at two stations (S5 and S6) along theK-transect (Figure 1) between 1998 and 2001. The radiativemeasurements were made almost parallel to the surface sono correction needed to be applied. When AWS data werenot available (Prec and RH, plus any missing data recordedwith the AWS), ERA-40 climatology was downscaled fromthe global grid (2.5� 2.5� resolution) onto a 5-km-resolution grid using the center data point and a bilinearinterpolation. The orography used in the model wasobtained from a high-resolution 1-km DEM [Bamber etal., 2001] resampled to 5 km. The air temperature down-scaled from ERA-40 was corrected for surface elevationusing a constant lapse rate equal to �5�C km�1. This lapserate value has been derived for summer conditions at lowelevation in Greenland [Steffen and Box, 2001; Hanna etal., 2005] and is therefore more adapted to our study thanthe annually and spatially averaged value of ��8�C km�1.[23] S5 and S6 are located at an elevation of 475 m and

1024 m, at a distance of 6 km and 37 km from the margin,respectively. Local slopes are 1.4� and 0.6�, respectively.While both stations are in the ablation zone, it is noteworthythat S6 is located in the dark zone as described first byOerlemans and Vugts [1993]. This area is characterized by alower minimum summer albedo than observed at lower andhigher elevation, which seems to be resulting from the effectof meltwater accumulation on the gently sloping surface[Knap and Oerlemans, 1996; Greuell, 2000]. The positivefeedbacks between water accumulation and low albedostrongly affects the mass balance [Greuell, 2000], providing

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an additional challenge to modeling mass balance in thisregion. Mass balance stake measurements [Greuell et al.,2001] available along the K-transect since 1990, upwardshortwave radiation and surface height change recordedwith sonic ranger stations at S5 and S6 are used to evaluatethe modeled albedo and mass balance.[24] We now describe the three stages used to tune the

model.[25] 1. Accumulation increases the surface albedo and

therefore also affects the mass balance by reducing theabsorption of energy at the surface. Because only ERA-40accumulation was available, we first focus on summer iceablation, during periods free of accumulation. Those can bedetected by looking both at the surface height change and atthe albedo data. Early summer snow ablation periods aremore difficult to model due to inaccurate knowledge of thesnow density, and are therefore excluded from this part ofthe analysis. Using measured albedo in the simulation, thesubsurface part of the model was tuned by adjustingparameters that determine processes such as melting,refreezing, and runoff formation. In addition, the roughnesslengths affecting the atmosphere-glacier energy exchangewere tuned.

[26] 2. Albedo calculation was then included and icealbedo parameterization adjusted.[27] 3. Finally, the model was run for the whole year

(with ERA-40 accumulation), using both calculated andmeasured albedo, and the model tuned for parametersrelating to snow albedo and snowmelt. Results were com-pared with available stake measurements at S5 and S6. Thefinal set of parameters (see sections 2.1, 2.2 and Table 2) didnot differ greatly from the values adopted by Greuell andKonzelmann [1994].[28] Height change data at site S5 recorded with acoustic

sensors were available for the years 1998–2000, while atsite S6 they were available for the years 1998–1999, 2001.The difference between observed and modeled ablation(both with measured and calculated albedo) varies between1% and 13% (Figure 3 and Table 3). An overestimation of20% (25 cm w.e.) is found at site S6, and is discussed laterin this section. As expected, mean daily ablation rates(Table 3) were consistently lower at S6 than at S5. At S5,using the modeled instead of the measured albedo affectsthe calculation of ablation at the end of the accumulation-free period by an average of 2%, suggesting that the icealbedo parameterization is reasonable. At S6, using the

Figure 3. Surface elevation change (in m w.e.) during the period estimated free of accumulation, at S5and S6. Data are plotted with a solid black line. The modeled surface elevation change using themeasured albedo is shown by a solid gray line, and with calculated albedo is shown by a black dashedline.

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modeled instead of the measured albedo leads to 1%increased ablation in 1999, while the effect is larger forthe two other years (8% in 1998 and 30% in 2001). Thisreflects perhaps the more complex state of the surface at thatsite located in the dark zone as described above, andunderscores the importance of albedo feedbacks on ablationprocesses. At the end of the estimated accumulation freeperiod, the mismatch between observed and modeled heightchange with calculated albedo varies between 1% and 13%of the observed height change in five out of six cases(Table 3). The mean difference is 7.7% for these five cases.The accuracy of the observed ablation rates is 1 cm, so thatthe uncertainty in surface height measurement is negligibleover the entire ablation season [van de Wal et al., 2005].There are several possible causes contributing to the differ-ences between modeled and observed ablation rates, whichare not related to flaws in the model itself. First, the albedoand mass balance were not measured at the exact same place(1 m to 20 m apart), so that the measured albedo used in thesimulations might not correspond exactly to the actualalbedo at the site where mass balance was measured.Second, the accuracy of the model results is dependent onthe accuracy of the input data and model parameterizations(see also results of sensitivity experiments on the modeldescribed by Greuell and Konzelmann [1994]). We per-formed sensitivity experiments to analyze the effect of inputdata accuracy (a list of instrument accuracy can be found onTable 2 of van de Wal et al. [2005] and on the website,http://www.phys.uu.nl/�wwwimau/research/ice_climate/aws/technical.html) as well as of tunable parameters defin-ing the albedo calculation. Tests were done for the annualspecific mass balance calculation, and results were averagedfor the period 1998–2001 at sites S5 and S6 (see Table 4).The experiments suggest that uncertainties in downwardlongwave radiation and relative humidity dominate. Theuncertainty in each one of these parameters represents�10% of the total ablation, and could alone explain allthe difference observed. The relative humidity was takenfrom ERA-40 and is perhaps a more likely source of error inthis study. The albedo parameterization is comparativelyless sensitive to tuning, the most sensitive parameter beingthe fresh snow albedo (see Table 4).[29] Using accumulation from ERA-40, the annual spe-

cific mass balance was calculated for individual yearsbetween 1998 and 2001, and compared with stake data(Figure 4). ERA-40 annual accumulation rates averagedalong the K-Transect were �0.32–0.41 m w.e. between1998 and 2001, while observations indicate annual rates of0.2–0.3 m w.e. [Ohmura et al., 1999]. The uncertainties in

the specific mass balance stake measurement were largercloser to the margin, and estimated to be ±0.3 m w.e. at S5and ±0.2 m w.e. at S6 [Greuell and Oerlemans, 2005].When using the measured albedo, the calculated massbalance falls each time between the uncertainties of theobserved mass balance, suggesting that the atmosphere-glacier exchanges are correctly modeled and the parametersrelated to timescale for runoff to occur are properly tuned.In simulations using calculated albedo, six out of eight casesare between measurements uncertainties, while the massbalance is overestimated by 10% at S5 in 1999, and under-estimated by 60% (discussed further in this section) at S6 in2001. In these simulations, it is likely that using ERA-40accumulation introduces errors due to the strong feedbackbetween accumulation and albedo, explaining the largerdiscrepancies found here compared with the summer abla-tion-only experiments.[30] To ensure that the mass balance calculated along the

K-transect does not match the observations only as a resultof compensating errors, we compare measured and calcu-lated albedo. Time series of weekly albedo from latesummer 1997 to summer 2001 are presented in Figure 5.Note that for our analysis, only spring and summer albedoare compared. In wintertime, the low sun angle makesmeasurements unreliable. Noise, improper offset correctionor rime formation at the sensor dome can also cause theobserved albedo to take unreasonable values. For these

Table 3. Surface Elevation Difference for Summer Ablationa

Year Site

1.ELEVobs �

ELEVmeas-alb, %

2.ELEVobs �

ELEVcalc-alb, %

3.OBS AblationRate, cm d�1

4.CALC AblationRate, cm d�1

1998 S5 +10.8 +11.7 4.31 5.02S6 �5.5 �13.32 2.28 2.37

1999 S5 +3.4 +0.8 5.31 5.33S6 �0.9 �1.7 2.97 2.87

2000 S5 +8.7 +10.8 4.85 4.332001 S6 �11.1 +20.1 2.41 2.86

aELEVobs – ELEVmeas-alb is observed minus modeled elevation obtained with measured albedo. ELEVobs – ELEVcalc-alb isobserved minus modeled elevation obtained with calculated albedo (in percent of the observed value). OBS is observed andCALC is calculated using modeled albedo.

Table 4. Results From Sensitivity Experiments on Annual

Specific Mass Balance Averaged for the Period 1998–2001 at

Sites S5 and S6a

Model Input Variation ImposedAnnual Mass BalanceVariation, m w.e.

*LW# +15 W m�2 �0.57RH +10% �0.40Prec +50% +0.16*Tatm +0.3�C �0.11*u +0.3 m s�1 �0.11*SW# +2% �0.07

Albedo parameteradry +0.05 +0.15aice +0.05 +0.08awet +0.05 +0.05aold +0.05 +0.02t*wet +5 days �0.03t*dry(0�C) +5 days �0.03K +5 �0.03w* +100 mm +0.03z*snow +5 mm �0.03aThe variation imposed on variables preceded with an asterisk equals the

magnitude of the AWS instrument accuracy.

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reasons, measured albedo values greater than 0.9 or lowerthan 0.15 were replaced by the model fresh snow albedovalue. Overall, the model captures generally well the firstorder evolution of the measured albedo. The modeledalbedo remains constant in winter until Tatm becomes greaterthan �10�C (equations (4) and (5)). High winter valuesrepresentative of fresh snow rapidly drop to typically lowsummer values. Site S5 is located in the bare ice zone, atlow and warmer elevation on a fairly steep slope wheremelted snow/ice runs off quickly. There the minimumcalculated summer albedo remains therefore close to aice,consistent with observations [see also Zuo and Oerlemans,1996]. The effect on the albedo of a large snowfall eventobserved during summer 1999 and 2000 is well captured bythe model, while the effect of smaller snowfalls is oftenmissed. Again, the timing and volume of snowfall events

affect the albedo value considerably (equation (7)). There-fore errors in the ERA-40 accumulation input limit thedegree of accuracy that can be reached when modelingalbedo. In addition, early spring drops in albedo values asobserved at S5 were not replicated in the results. This islikely caused by the lack of representation of blowing snowin the model, which near the margin of the ice sheet, oftenremoves freshly fallen snow. The overall impact on the massbalance is, however, limited, because in early spring solarradiation is not high enough and air temperature is too lowto cause melting even for low albedos. Located in the darkzone (see above), the presence of water (equation 6) affectsS6 more than S5. The minimum modeled weekly averagedalbedo is �0.44, which is lower than aice. The timing of thebeginning and the end of the summer ice ablation (sharpalbedo lowering/increase respectively) is fairly well caught,apart for summer 2001.[31] In Figures 3 to 5, the mass balance at site S6 in 2001

is consistently poorly reproduced when the albedo is calcu-lated. Interestingly, the albedo record for that summerdiffers in its characteristics compared with previous years(Figure 5). The transition from a high snow albedo value tothe lower ice value is slower than for other years, a featurethat the model is not able to capture. The modeled albedodrops too quickly to a bare ice surface albedo value, whichexplains why ablation is overestimated in the calculations(see Figures 3 and 4). This is confirmed by the fact thatusing measured albedo improves the results considerably.For albedo values to stay high, the presence of snow isrequired, and this is either achieved with increased precip-itation or decreased energy available for melting. Results forthis year and site are improved if the relative humidity isdecreased by 10%, or if the accumulation is increased by60%. These parameters were obtained from ERA-40 dataand are, therefore, more likely to have biases compared withthe AWS data.

Figure 5. Weekly averaged albedo at (bottom) S5 and (top) S6. The measured albedo is in black and themodeled one is in gray.

Figure 4. Specific annual mass balance at S5 and S6,between 1998 and 2001. Results using the measured albedo(square) and calculated albedo (circle) are compared tostake measurements (star and error bars).

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[32] The annual mass balance was calculated andaveraged between site 4 and site 9 (seven stations) alongthe K-transect for the period 1991–2000, and results werecompared with specific mass balance stake measurements[Greuell et al., 2001]. Because AWS data do not cover thewhole period nor all sites, here the model is forced withERA-40 data at all times, although model parameters havenot been retuned. Therefore normalized mass balance esti-mates have been compared (Figure 6). The observed andcalculated normalized mass balance are well correlated(correlation coefficient = 0.80). In addition to suggestingthat the SMBM is able to capture the interannual variability,these results also support the use of ERA-40 to further testthe model when run on a distributed grid (section 3.2).

3.2. Runs on Distributed Grid

[33] In this part, the model was run for the whole ice sheeton a distributed grid at 20-km resolution (orography aver-aged from the 5 km-DEM) forced with 10 years (1991–2000) of 6-hourly ERA-40 data. SW#, LW#, sea levelpressure, Prec, u at 10 m, Tatm and dew point temperatureat 2 m are downscaled from the global grid onto the 20-km-resolution grid, using the center data point and a bilinearinterpolation (as in section 3.1). P and RH can be calculatedrespectively from the sea level pressure and the dew pointtemperature at 2 m. We emphasize again that the focus isnow to test the model’s ability to capture interannualvariability, and not to calculate the absolute ice sheet massbalance.[34] We first check that the modeled runoff from 1991 to

1999 generated by the SMBM correlates well with estimatesover the same period by Box et al. [2004] and Hanna et al.[2005]. Box et al. [2004] have used a regional climatemodel (RCM) to calculate the ice sheet mass balancebetween 1991 and 2000. The RCM biases were analyzedand corrected using 3 years of 17 Greenland ClimateNetwork AWS data [Steffen and Box, 2001]. ECMWFoperational data were used to initialize and update theboundary conditions of the RCM. Hanna et al. [2005]estimated the runoff variability for the period 1958–2003using ECMWF (re)analysis data to drive a PDD surfacemeltwater runoff/retention model. A good correlationbetween the different model results is to be expected

because of the systematic use of ECMWF operationaldata (similar but not identical to ERA-40 data). Thecorrelation coefficients between results from those studiesare shown in Table 5.[35] The modeled wet snow zone extent was compared

with observations from passive microwave satellite data[Abdalati and Steffen, 2001] (Figure 7). The observationsdo not provide any quantitative information on how muchmelting has occurred, but simply indicate whether the snowis wet or dry. Using a model that keeps track of the watercontent in the subglacial layers could help interpretingsatellite data by comparing these to modeled melt volumedistribution. However, we do not attempt to do this in thisstudy since the model has not been tuned to ERA-40climatology, and the modeled volume of meltwater istherefore likely to contain biases. Instead, the model outputhas been saved so that the percentage of time per day whenthe firn is wet (w > 0) can be retrieved and used as a proxyfor melt intensity. The mean summer (June–July–August)averaged wet zone from 1991–1999 compares best withpassive microwave satellite data [Abdalati and Steffen,2001] when it is assumed that ‘‘wet firn’’ is captured ifwater is present �50% of the day. The mean melt extentobserved over the decade is �1.40 106 km2, while themodeled one is �1.52 106 km2 (6% larger). Thecorrelation coefficient varies between 0.90 and 0.94 if it isassumed that water must be present 25% to 75% of the day(Figure 7), indicating that the variability depends very littleon the threshold value chosen.[36] Figure 8 displays the spatial distribution of melt days

for two consecutive years experiencing very different meltconditions and illustrates the spatial resolution and fidelity

Figure 6. Normalized annual specific mass balanceaveraged along the K-transect, between 1991 and 2000.Model results (in gray) are compared with stake measure-ments (in black). The correlation coefficient between thetwo series is 0.80.

Table 5. Correlation Coefficient Between the Runoff Production

for the Period 1991–1999 Calculated in This Study and Calculated

by Box et al. [2004] and Hanna et al. [2005]

Box et al. [2004] Hanna et al. [2005]

Hanna et al. [2005] 0.94This study 0.91 0.80

Figure 7. Mean summer (June–July–August) melt extent.Satellite-derived data [Abdalati and Steffen, 2001] arecompared with modeled estimate, using three differentcriteria. The interannual variability varies little with thechoice of the latter. The correlation coefficient between thedata and the model results varies between 0.90 and 0.94,using criteria of 50%, 75%, and 25%.

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of the model. These plots can be directly compared with themelt extent derived from the satellite microwave observa-tions (Steffen and Huff, CIRES, http://cires.colorado.edu/steffen/melt/). The 1991 maximum melt zone extent is verylarge, with the whole area south of �78� being wet at leastfor a short period in summer. Accordingly, our model resultsindicate that the same region is wet for �10–15 days duringsummer. In contrast, the maximum melt area in 1992 ismuch reduced both in satellite-derived information andmodel results (coinciding with volcanic cooling followingPinatubo eruption), where most of the ice sheet surface doesnot experience more than one day of melt during thatsummer.

4. Conclusions

[37] A surface mass balance model of the Greenland IceSheet designed for interactive coupling with and AOGCMis presented and tested. Forced with AWS data along theK-transect, model results were compared with four con-secutive years of observations at two sites presentingdifferent surface properties, due to the location of site S6in the so-called dark zone. Although the model is strictlyspeaking tuned to the available data rather than validated(as is commonly done [e.g., Zuo and Oerlemans, 1996;Greuell and Bohm, 1998; Hock, 1999; Braithwaite andZhang, 2000; Oerlemans and Reichert, 2000]), calculatingand comparing mass balance for individual years (insteadof averaged over a longer period) is a less common andmore challenging approach in evaluating model perfor-mance [Johannesson et al., 1995]. When successful, such

an exercise gives confidence that the model is able tocapture the interannual variability induced by the climate[Greuell and Genthon, 2004]. Despite the relatively pooraccuracy in annual specific mass balance estimation at siteS6 in 2001, the modeled mass balance in six out of theseven other cases falls within the uncertainties of theobserved annual mass balance, having a mean differencefrom the observations of 4.9%. The remaining case over-estimates the annual mass balance by 10%. Overall, theablation rates calculated at S6 are significantly lower thanat S5, indicating that the model is also able to account forspatial variability of the mass balance.[38] Forced with ERA-40 data, the mass balance calcu-

lation averaged for seven stations along the K-transectcorrelates well with measurements over a 10-year period.The model was then applied to a distributed grid for thewhole of the Greenland ice sheet. Although the amount ofavailable data covering the ice sheet limits the degree towhich such an application can be tested, the interannualvariability captured by the SMBM agrees well with otherstudies [Box et al., 2004; Hanna et al., 2005]. In addition,the model generates a mean summer melt extent whosevariability correlates highly (>0.9) with passive microwavesatellite data derived for the period 1991–1999 [Abdalatiand Steffen, 2001]. Thus the SMBM is able to reproducedifferent patterns of melt extent, which are consistent withsatellite-derived data.[39] We conclude, therefore, that the SMBM presented in

this study adequately calculates ablation given appropriateforcing. Its ability to capture the interannual and spatialvariability induced by the climate while running on a 20-km-

Figure 8. Maps of modeled melt days during 1991 and 1992. Those maps can be compared with themaximum melt extent derived from passive microwave data by Steffen and Huff (URL: http://cires.colorado.edu/steffen/melt/gr_melt_88_02.pdf).

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resolution grid and forced with low-resolution climatologymakes it suitable for future climate predictions, coupled withan AOGCM.

[40] Acknowledgments. This work was funded by UK NaturalEnvironment Research Council grant NER/T/S/2002/00462. ECMWFERA-40 data used in this project were obtained from the ECMWF DataServer. We thank W. Abdalati and E. Hanna for the use of their data, I. Ruttfor providing the code necessary to the downscaling of the ERA-40 inputvariables, and A. J. Payne and P. Valdes for advice on the modelingapproach used. Comments from R. Anderson, G. Flowers, J. E. Box andone anonymous reviewer contributed to improving the manuscript.

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�����������������������J. L. Bamber and M. Bougamont, School of Geographical Sciences,

University of Bristol, Bristol, BS8 1SS, UK. (m.bougamont@bristol.ac.uk)W. Greuell, Institute for Marine and Atmospheric Research Utrecht

(IMAU), Utrecht University, Princetonplein 5, NL-3584 Utrecht,Netherlands.

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