A surface mass balance model for the Greenland Ice Sheet

Abstract

[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 weather station data, and includes surface energy balance as well as processes occurring near the surface such as water percolation and refreezing. Surface albedo is calculated with a new scheme that differentiates the timescale for aging of wet and dry snow and incorporates the effect of a thin layer of water and/or fresh snow at the surface. The model was driven with automatic weather station data from two sites located in the ablation zone in the Kangerlussuaq area (West Greenland), and calculated reasonable annual mass balance values (within 10% in seven out of eight cases) for four individual and consecutive years (1998–2001), using both measured and calculated albedo. This implies that the albedo parameterization is adequate and climate feedbacks affecting the mass balance are well captured. The model was then applied to a distributed 20-km-resolution grid covering the whole ice sheet, and forced with 10 years of the European Centre for Medium-range Weather Forecast (ECMWF) reanalysis (ERA-40) data. With the aim of coupling the model to a GCM, this study focuses on the ability to model the interannual variability in mass balance rather than to assess the present state of balance of the ice sheet. Modeled spatial and temporal wet zone extent compares well with information derived from passive microwave satellite data.

1. Introduction

[2] The Arctic climate is currently warming at a faster rate than observed elsewhere on the planet [Church et al., 2001]. If it 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 is around −80 km³ yr⁻¹[Krabill et al., 2004], and the GrIS is expected to increase its contribution to sea level rise through enhanced surface melt by 20–50% per degree of warming [Braithwaite and Olesen, 1993; Ohmura et al., 1996; van de Wal, 1996; Janssens and Huybrechts, 2000]. In addition, recent observations suggest that increased surface melting could increase the ice velocities [Zwally et al., 2002; Krabill et al., 2004], making it more vulnerable to atmospheric warming than previously believed. Moreover, it is now widely accepted that rapid (approximately a few decades) climate change has occurred in the Northern Hemisphere during the last glacial period [Ganopolski and Rahmstorf, 2001; Alley et al., 2003], possibly triggered by a shutdown of the 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 the Labrador and Irminger Seas (Figure 1). Therefore, in addition to changing sea level, the ice sheet could also play a role in modulating the THC of the North Atlantic [Rahmstorf, 1995; Fichefet et al., 2003].

Figure 1

Albedo map of the western part of Greenland as derived from AVHRR data (modified from Greuell [2000]), and showing the location of the K-transect. The two AWS are 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 the Labrador Sea (LS) and Irminger Sea (IS).

[3] Global Circulation Models (GCMs) are powerful tools for analyzing and quantifying feedback mechanisms, and in particular for elucidating the role of the cryosphere in climate change [Thompson and Pollard, 1997; Glover, 1999; Church et al., 2001; Murphy et al., 2002; Wild et al., 2003]. However, the window of uncertainty remains large, as model results differ greatly under different resolution and model physics [Stainforth et al., 2005]. While assessing accurately the mass balance of the GrIS is important, the lack of resolution often prevents correct representation of the narrow ablation zone of the ice sheet. Another problem is that few studies using GCMs incorporate detailed snow/firn processes specific to an ice sheet mass balance [Bugnion and Stone, 2002; Huybrechts et al., 2002] or couple interactively an ice sheet model with an atmosphere-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 GrIS aimed at being interactively coupled with an AOGCM (based on the Hadley Centre Climate Model version 3, HadCM3) in order to not only assess the contribution of the GrIS to sea level variations in the next few centuries, but also to evaluate the response of the oceanic circulation to freshening from the increased freshwater flux from the ice sheet. The SMBM has been set up to run at 20 km resolution and is a modified version of SOMARS (Simulation Of glacier surface Mass balance And Related Sub-surface processes, http://www.phys.uu.nl/∼greuell/massbalmodel.html). SOMARS has been tested at the ETH-Camp (West Greenland, 1155m a.s.l.) on data collected during summer 1990 [Greuell and Konzelmann, 1994]. Located near the equilibrium line, this site was ideal for testing the subsurface component of the model, and the good agreement between model results and observations suggests that SOMARS is suitable for the study presented here. In SOMARS and in this study, refreezing, meltwater percolation and runoff are modeled within the first 40 m of firn with a detailed near-surface model. The surface ablation is determined using an energy balance calculation rather than applying the Positive Degree Day (PDD) technique [Reeh, 1991; Braithwaite, 1995; Jóhannesson et al., 1995; Hock, 1999; Braithwaite and Zhang, 2000]. Although computationally less expensive, the latter method can only take into account the effect of temperature change on the mass balance and not the spatial and temporal variability induced by other variables [Greuell and Genthon, 2004]. This drawback becomes particularly limiting if the model is used in climate simulation over the next few centuries, as the effect of a modified atmospheric pattern (e.g., cloud cover, turbulent fluxes and precipitation) would not be taken into account explicitly. A comparison between PDD and energy balance models suggests that the sensitivity to warmer temperatures is enhanced with a PDD compared with an energy balance model and that the latter would produce more realistic results [van de Wal, 1996].

[5] The SMBM was first validated against observations at two Automatic Weather Stations (AWS) along the Kangerlussuaq transect (K-transect) (Figure 1), for four consecutive years (section 3.1). It was then run for the whole ice sheet, forced with 10 years of European Centre for Medium-range Weather Forecast (ECMWF) reanalysis (ERA-40) data (section 3.2). The re-analysis data were, however, used solely to assess the model skill with respect to reproducing the observed spatial and temporal variability in melt and not the absolute values. ERA-40 is likely to contain some systematic biases [Hanna and Valdes, 2001; Hanna et al., 2002] which we did not attempt to correct for, and the absolute values of ablation and accumulation are therefore expected to be biased. However, ERA-40 data were generated by assimilating available observations and the temporal variability is therefore quite well represented [Hanna and Valdes, 2001; Hanna et al., 2002]. The ability to capture the interannual variability is an important feature of a model for use with atmospheric-GCM input, which will likely contain uncertainties and biases in its forcing fields. These biases can be accounted for using flux adjustment methods or deviations from a mean climatology, but the ability to reproduce the spatial and temporal variability is a function of the model physics, which cannot be tuned.

2. Model Description

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

Table 1. Symbols and Variables Used in the Model

Symbol	Definition
Input
LW↓	downward longwave radiation, W m^−2
SW↓	downward shortwave radiation, W m^−2
P	surface pressure, Pa
Prec	accumulation, m w.e.
Tatm	air temperature within the constant flux layer, °C
u	wind speed within the constant flux layer, m s^−1
RH	relative humidity within the constant flux layer, %
Surface Variables
Qt	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, m
S	surface slope
αsurf	surface albedo
To	surface temperature, °C
W	surficial water, m
dzfrsnow	fresh snow thickness at the surface, m
t*runoff	timescale for runoff to occur, days
c1, c2, c3	runoff parameters
Englacial Variables
α	albedo
Tsnow	temperature, °C
ρ	density, kg m^−3
w	water content, m
m	mass, m w.e.
zgrid	thickness of the grid box, m

2.1. Surface Energy Model

2.1.1. Energy Balance

[7] The total energy flux (Q_t) from the atmosphere toward the surface of a glacier or ice sheet equals the sum of the net radiative and the turbulent fluxes,

where LW_↓ and LW_↑ are the downward and upward longwave radiations, SW_↓ and SW_↑ are the downward and upward shortwave radiations, LHF and SHF are respectively the latent heat and sensible heat fluxes, and F_rain is the energy flux supplied by rain. Details on the calculation of 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 the K-transect, or from ERA-40 for runs over the whole ice sheet. Because ice and snow have both an emission coefficient close to one [Griggs, 1968; Warren, 1982], the upward longwave radiation can be estimated with sufficient accuracy from the surface temperature, T_o,

where σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ is the Stefan-Boltzmann constant. The upward shortwave radiation is determined by the surface albedo, α,

[9] Ice sheet albedo values can range from very high (α_dry = 0.82) for dendritic snow to low values when water covers the surface (α_wet = 0.15, [Hummel and Reck, 1979]). Fresh snow albedo decreases with time due to metamorphism induced by wetness of the snowpack, the temperature gradient 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 and Genthon, 2004]. Debris and dust, bubbles and cracks, and water content contribute to reducing the ice albedo [Greuell and Genthon, 2004]. In our model we represent snow metamorphism by parameterizing albedo as a function of the age of the snow. The effect of aging and of the presence of a thin layer of fresh snow on the albedo value can be modeled using exponential functions to insure a smooth transition between different states [Oerlemans and Knap, 1998]. Similarly, the influence of a water layer at the surface can be parameterized using an exponential function [Zuo and Oerlemans, 1996]. The albedo calculation used here and 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 in the snowpack increases the effective grain size, and speeds up the rate of grain growth [Warren, 1982]. Dry snow albedo decay is much faster for air temperatures close to the melting point than for lower temperatures. Below −10°C, the aging of snow is considered negligible, and the albedo remains equal to α_dry [Loth et al., 1993; Reijmer et al., 2005]. Dry snow albedo decay can be modeled as a linear function of both the time elapsed since the last snowfall and the air temperature [Van den Hurk and Viterbo, 2003]. Rather than using a linear relationship, we use an exponential decay [Zuo and Oerlemans, 1996; Oerlemans and Knap, 1998] to combine the effect of age and snow temperature,

where α_old is the albedo of old snow and t* is the timescale for albedo decay, defined as follows (in days):if the snow is wet (w > 0)

if the snow is dry (w = 0) and −10°C ≤ T_snow ≤ 0°C

if the snow is dry (w = 0) and T_snow < −10°C

where T_snow is the temperature of the snow/firn/ice in °C, and w is the water content of a given grid box. The timescale for wet snow albedo decay (t*_wet), for dry snow albedo decay at T_snow = 0°C (t*_dry(0°C)) and the constant K is set during model tuning (Table 2). Here, fresh snow albedo would decrease to the old snow albedo value in 15 days for a wet snowpack. It would take twice as long for a dry snowpack at 0°C, while over three months would be necessary at temperatures below −10°C. By calculating the temperature (T_snow) and water content (w) of grid boxes for the surface and subsurface layers, the SMBM keeps track of the sub-surface albedo variation for each grid box.

Table 2. Albedo Parameter Values Used in the Model

Parameter	This Study	Sources/Other Values
αice	0.52	GIMEX-91: 0.5–0.55
αdry	0.82	GIMEX-91: snow albedo from 0.64 up to 0.89 [van de Wal and Oerlemans, 1994]: 0.85
αwet	0.15	[Zuo and Oerlemans, 1996]: 0.15 [van de Wal and Oerlemans, 1994]:0.2
αold	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 days
t*dry(0°C)	30 days	tuning
K	7	tuning
w*	300 mm	[Zuo and Oerlemans, 1996]: 200 mm [Denby et al., 2002]: 600 mm
z*snow	20 mm	[Oerlemans and Knap, 1998]: 32 mm [Denby et al., 2002]: 16 mm

[11] The surface albedo, α_surf, is the albedo of the upper grid box, plus taking into account the effect of a thin layer of water on top of the ice (equation (6)) and/or of a thin layer of fresh snow at the surface (equation (7)), as in the work of Zuo and Oerlemans [1996] and Oerlemans and Knap [1998], respectively,

where w_surf is the thickness of surficial water, w* is the characteristic scale for surficial water, dz_frsnow is the thickness of fresh snow and z*_snow is the characteristic scale for snow depth. The albedo parameter values used here are fixed after tuning the model for computations along the K-Transect, while ensuring that they remain within the limits suggested by available measurements (summarized in 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 only a summary is provided in this section. The relationship between the turbulent heat fluxes and the wind, temperature and humidity profiles can be established within the Monin-Obukhov similarity theory, and read

where

is the friction velocity,

is the temperature scale, and

is the humidity scale.

[13] In equations (8) and (9), ρ_a is the air density, C_pa = 1005 J kg⁻¹ K⁻¹ is the specific heat capacity of the air and L_s = 2.84 × 10⁶ J kg⁻¹ is the latent heat of sublimation. In -, u is the wind speed, Θ is the potential temperature, q is the specific humidity, κ = 0.4 is the von Karman constant and ϕ_m and ϕ_h are the stability functions for the momentum and for the scalar quantities (temperature and humidity). The latter have different forms for stable and unstable conditions [Hőgstrőm, 1988]. Here the turbulent heat fluxes are computed with the bulk method, where -–(10c) are integrated between an atmospheric level (2 m or 4 m for T_atm and RH, and 10 m or 4 m for u, respectively, provided by ERA-40 and AWS) and the roughness lengths, which are defined as the heights above the surface where the profiles of u, and q reach their surface values. Work by Box and Steffen [2001] suggests that the bulk method for turbulent latent heat flux underestimates the water vapor deposition compared to the profile method (a difference of 57.9 × 10¹² kg yr⁻¹ was found when calculating the annual net total evaporative mass transfer using both methods). On the other hand, the bulk method appears more suitable if a wind-speed maximum is present [Denby and Greuell, 2000].

[14] The roughness lengths for temperature (z_T) and water vapor (z_q) are computed using the equations developed by Andreas [1987], accounting for the difference in transfer mechanisms for momentum from those for scalars, as discussed by Greuell and Genthon [2004],

where R is the Reynolds number (R = (u*z₀)/υ, with the kinematic viscosity of air υ = 1.461 × 10⁻⁵ m² s⁻¹), and z₀ is the momentum roughness length defined as a function of the density of the uppermost element of the snowpack [Greuell and Konzelmann, 1994]. After model tuning, the roughness length is set to 0.12 mm for dry snow, 1.3 mm for wet snow and 3.2 mm for ice (as in the work by Greuell and Konzelmann [1994]).

2.1.4. Heat Flux Supplied by Rain

[15] Rain provides a small amount of energy F_rain, by falling onto a surface with a lower temperature [see e.g., Greuell and Genthon, 2004],

where ρ_w = 1000 kg m⁻³ is the density of water, r is the rain-fall rate (in m s⁻¹), C_pw = 4200 J kg⁻¹ K⁻¹ is the specific heat capacity of water, T_r is the rain temperature (which can be approximated by T_atm) and T₀ is the surface temperature.

2.2. Near-Surface Model

[16] Several studies have underscored the importance of including surface water percolation, retention and refreezing when 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-surface model (Figure 2) is similar to the one described by Greuell and Konzelmann [1994], with the exception of the effective conductivity parameterization, of the calculation of the irreducible water amount and of the runoff formulation.

Figure 2

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

[17] Solar radiation penetrates below the surface, where it is partly absorbed according to Beer's law. Using a density dependent effective conductivity [Sturm et al., 1997], the thermodynamic equation is then solved in the snow/firn layers to determine the amount of melting and refreezing in the firn. Positive temperatures are reset to 0°C and melting occurs. Water (melt + rain) can refreeze, to the degree that water or space is available, or that the temperature in the layer (T_snow) does not exceed the melting point. The irreducible water saturation is calculated as a function of the firn density (ρ) [Coleou and Lesaffre, 1998], and the water content of a given layer (w) exceeding the maximum retention capacity percolates downward, until an impermeable layer is reached (i.e., with a density ≥ 910 kg m⁻³). Part of the free water runs off immediately inside the snowpack, at a slower rate than at the surface. The rest fills up all the pores to form a slush layer, which can later on refreeze as superimposed ice. Water on top of the surface runs off at a timescale t*_runoff that depends on the local slope [Zuo and Oerlemans, 1996],

where S is slope and c₁ = 0.05, c₂ = 15 and c₃ = 142 are determined with model tuning. Those values are only poorly constrained, as no observation is available regarding the timescale for runoff to occur [Zuo and Oerlemans, 1996]. The values used in this study are such that surficial water runs off in about 1.2 days if the slope equals one degree, while 15 days would be required on a flat surface. Note that in the case of an infinitely steep slope, water would run off almost immediately. Inside the snowpack, runoff is set up to occur 10 times slower than at the surface. The distinction between inside and surface runoff used here may explain the difference with the timescales used by Zuo and Oerlemans [1996] (3.7 days with S = 1° and 26.5 days on a flat surface), and Lefebre et al. [2003] (2.5 days with S = 1°, 25.33 days on a flat surface), who both did not differentiate between internal and surficial runoff.

[18] Precipitation falls as snow if the air temperature is below 2°C [Oerlemans, 1993]. Snow densification due to settling and packing is computed from empirical relations [Herron and Langway, 1980]. The mass balance is finally computed as the sum of accumulation, precipitation and condensation minus evaporation/sublimation and runoff.

2.3. Numerics and Initial Conditions

[19] The near-surface processes are modeled for 40m of firn/snow/ice, composed of a maximum of 200 layers. Initially, the thickness of each individual layer (z_grid) increases linearly with depth from 0.09 m for the uppermost one to a maximum of 4 m for the lowest one. A layer thickness varies due to melting or freezing, condensation and accumulation. Layers are added/removed at the bottom to maintain a total thickness of approximately 40 m. A layer that becomes too thick is split into two new ones while one becoming too thin can be fused with the underlying one. The surface temperature is linearly extrapolated from the temperature of the two uppermost grid points [Greuell and Konzelmann, 1994].

[20] The model runs with a time step of 30 min, and the input (both from AWS and ERA-40) are interpolated accordingly. Mass and energy conservation are being checked 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 set equal to the average annual T_atm. The model is allowed to spin up for six months, and the experiment start date is 1 January, giving additional time for the model to adjust to initial conditions before the first melt season occurs. We carried out a number of experiments suggesting that the model results are not sensitive to realistic variations in initial conditions.

3. Results and Discussion

3.1. Validation Along the K-Transect

[22] LW_↓, SW_↓, P, T_atm and u at 4 m above the surface were recorded hourly at two stations (S5 and S6) along the K-transect (Figure 1) between 1998 and 2001. The radiative measurements were made almost parallel to the surface so no correction needed to be applied. When AWS data were not available (Prec and RH, plus any missing data recorded with the AWS), ERA-40 climatology was downscaled from the global grid (2.5° × 2.5° resolution) onto a 5-km-resolution grid using the center data point and a bilinear interpolation. The orography used in the model was obtained from a high-resolution 1-km DEM [Bamber et al., 2001] resampled to 5 km. The air temperature downscaled from ERA-40 was corrected for surface elevation using a constant lapse rate equal to −5°C km⁻¹. This lapse rate value has been derived for summer conditions at low elevation in Greenland [Steffen and Box, 2001; Hanna et al., 2005] and is therefore more adapted to our study than the 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 noteworthy that S6 is located in the dark zone as described first by Oerlemans and Vugts [1993]. This area is characterized by a lower minimum summer albedo than observed at lower and higher elevation, which seems to be resulting from the effect of meltwater accumulation on the gently sloping surface [Knap and Oerlemans, 1996; Greuell, 2000]. The positive feedbacks between water accumulation and low albedo strongly affects the mass balance [Greuell, 2000], providing an additional challenge to modeling mass balance in this region. Mass balance stake measurements [Greuell et al., 2001] available along the K-transect since 1990, upward shortwave radiation and surface height change recorded with sonic ranger stations at S5 and S6 are used to evaluate the 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 the absorption of energy at the surface. Because only ERA-40 accumulation was available, we first focus on summer ice ablation, during periods free of accumulation. Those can be detected by looking both at the surface height change and at the albedo data. Early summer snow ablation periods are more difficult to model due to inaccurate knowledge of the snow density, and are therefore excluded from this part of the analysis. Using measured albedo in the simulation, the subsurface part of the model was tuned by adjusting parameters that determine processes such as melting, refreezing, and runoff formation. In addition, the roughness lengths affecting the atmosphere-glacier energy exchange were tuned.

[26] 2. Albedo calculation was then included and ice albedo parameterization adjusted.

[27] 3. Finally, the model was run for the whole year (with ERA-40 accumulation), using both calculated and measured albedo, and the model tuned for parameters relating to snow albedo and snowmelt. Results were compared with available stake measurements at S5 and S6. The final set of parameters (see sections 2.1, 2.2 and Table 2) did not differ greatly from the values adopted by Greuell and Konzelmann [1994].

[28] Height change data at site S5 recorded with acoustic sensors were available for the years 1998–2000, while at site S6 they were available for the years 1998–1999, 2001. The difference between observed and modeled ablation (both with measured and calculated albedo) varies between 1% and 13% (Figure 3 and Table 3). An overestimation of 20% (25 cm w.e.) is found at site S6, and is discussed later in 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 affects the calculation of ablation at the end of the accumulation-free period by an average of 2%, suggesting that the ice albedo parameterization is reasonable. At S6, using the modeled instead of the measured albedo leads to 1% increased ablation in 1999, while the effect is larger for the two other years (8% in 1998 and 30% in 2001). This reflects perhaps the more complex state of the surface at that site located in the dark zone as described above, and underscores the importance of albedo feedbacks on ablation processes. At the end of the estimated accumulation free period, the mismatch between observed and modeled height change 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 that the uncertainty in surface height measurement is negligible over the entire ablation season [van de Wal et al., 2005]. There are several possible causes contributing to the differences between modeled and observed ablation rates, which are not related to flaws in the model itself. First, the albedo and mass balance were not measured at the exact same place (1 m to 20 m apart), so that the measured albedo used in the simulations might not correspond exactly to the actual albedo at the site where mass balance was measured. Second, the accuracy of the model results is dependent on the accuracy of the input data and model parameterizations (see also results of sensitivity experiments on the model described by Greuell and Konzelmann [1994]). We performed sensitivity experiments to analyze the effect of input data accuracy (a list of instrument accuracy can be found on Table 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 defining the albedo calculation. Tests were done for the annual specific mass balance calculation, and results were averaged for the period 1998–2001 at sites S5 and S6 (see Table 4). The experiments suggest that uncertainties in downward longwave radiation and relative humidity dominate. The uncertainty in each one of these parameters represents ∼10% of the total ablation, and could alone explain all the difference observed. The relative humidity was taken from ERA-40 and is perhaps a more likely source of error in this study. The albedo parameterization is comparatively less sensitive to tuning, the most sensitive parameter being the fresh snow albedo (see Table 4).

Figure 3

Surface elevation change (in m w.e.) during the period estimated free of accumulation, at S5 and S6. Data are plotted with a solid black line. The modeled surface elevation change using the measured albedo is shown by a solid gray line, and with calculated albedo is shown by a black dashed line.

Table 3. Surface Elevation Difference for Summer Ablation^aa ELEV_obs – ELEV_meas-alb is observed minus modeled elevation obtained with measured albedo. ELEV_obs – ELEV_calc-alb is observed minus modeled elevation obtained with calculated albedo (in percent of the observed value). OBS is observed and CALC is calculated using modeled albedo.

Year	Site	1. ELEVobs − ELEVmeas-alb, %	2. ELEVobs − ELEVcalc-alb, %	3. OBS Ablation Rate, cm d^−1	4. CALC Ablation Rate, cm d^−1
1998	S5	+10.8	+11.7	4.31	5.02
	S6	−5.5	−13.32	2.28	2.37
1999	S5	+3.4	+0.8	5.31	5.33
	S6	−0.9	−1.7	2.97	2.87
2000	S5	+8.7	+10.8	4.85	4.33
2001	S6	−11.1	+20.1	2.41	2.86

• a ELEV_obs – ELEV_meas-alb is observed minus modeled elevation obtained with measured albedo. ELEV_obs – ELEV_calc-alb is observed minus modeled elevation obtained with calculated albedo (in percent of the observed value). OBS is observed and CALC 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 S6^aa The variation imposed on variables preceded with an asterisk equals the magnitude of the AWS instrument accuracy.

Model Input	Variation Imposed	Annual Mass Balance Variation, m w.e.
*LW↓	+15 W m^−2	−0.57
RH	+10%	−0.40
Prec	+50%	+0.16
*Tatm	+0.3°C	−0.11
*u	+0.3 m s^−1	−0.11
*SW↓	+2%	−0.07
Albedo parameter
αdry	+0.05	+0.15
αice	+0.05	+0.08
αwet	+0.05	+0.05
αold	+0.05	+0.02
t*wet	+5 days	−0.03
t*dry(0°C)	+5 days	−0.03
K	+5	−0.03
w*	+100 mm	+0.03
z*snow	+5 mm	−0.03

• a The variation imposed on variables preceded with an asterisk equals the magnitude of the AWS instrument accuracy.

[29] Using accumulation from ERA-40, the annual specific mass balance was calculated for individual years between 1998 and 2001, and compared with stake data (Figure 4). ERA-40 annual accumulation rates averaged along the K-Transect were ∼0.32–0.41 m w.e. between 1998 and 2001, while observations indicate annual rates of 0.2–0.3 m w.e. [Ohmura et al., 1999]. The uncertainties in the specific mass balance stake measurement were larger closer to the margin, and estimated to be ±0.3 m w.e. at S5 and ±0.2 m w.e. at S6 [Greuell and Oerlemans, 2005]. When using the measured albedo, the calculated mass balance falls each time between the uncertainties of the observed mass balance, suggesting that the atmosphere-glacier exchanges are correctly modeled and the parameters related to timescale for runoff to occur are properly tuned. In simulations using calculated albedo, six out of eight cases are between measurements uncertainties, while the mass balance is overestimated by 10% at S5 in 1999, and underestimated by 60% (discussed further in this section) at S6 in 2001. In these simulations, it is likely that using ERA-40 accumulation introduces errors due to the strong feedback between accumulation and albedo, explaining the larger discrepancies found here compared with the summer ablation-only experiments.

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 to stake measurements (star and error bars).

[30] To ensure that the mass balance calculated along the K-transect does not match the observations only as a result of compensating errors, we compare measured and calculated albedo. Time series of weekly albedo from late summer 1997 to summer 2001 are presented in Figure 5. Note that for our analysis, only spring and summer albedo are compared. In wintertime, the low sun angle makes measurements unreliable. Noise, improper offset correction or rime formation at the sensor dome can also cause the observed albedo to take unreasonable values. For these reasons, measured albedo values greater than 0.9 or lower than 0.15 were replaced by the model fresh snow albedo value. Overall, the model captures generally well the first order evolution of the measured albedo. The modeled albedo remains constant in winter until T_atm becomes greater than −10°C (equations (4) and (5)). High winter values representative of fresh snow rapidly drop to typically low summer values. Site S5 is located in the bare ice zone, at low and warmer elevation on a fairly steep slope where melted snow/ice runs off quickly. There the minimum calculated summer albedo remains therefore close to α_ice, consistent with observations [see also Zuo and Oerlemans, 1996]. The effect on the albedo of a large snowfall event observed during summer 1999 and 2000 is well captured by the model, while the effect of smaller snowfalls is often missed. Again, the timing and volume of snowfall events affect the albedo value considerably (equation (7)). Therefore errors in the ERA-40 accumulation input limit the degree of accuracy that can be reached when modeling albedo. In addition, early spring drops in albedo values as observed at S5 were not replicated in the results. This is likely caused by the lack of representation of blowing snow in the model, which near the margin of the ice sheet, often removes freshly fallen snow. The overall impact on the mass balance is, however, limited, because in early spring solar radiation is not high enough and air temperature is too low to cause melting even for low albedos. Located in the dark zone (see above), the presence of water (equation 6) affects S6 more than S5. The minimum modeled weekly averaged albedo is ∼0.44, which is lower than α_ice. The timing of the beginning and the end of the summer ice ablation (sharp albedo lowering/increase respectively) is fairly well caught, apart for summer 2001.

Figure 5

Weekly averaged albedo at (bottom) S5 and (top) S6. The measured albedo is in black and the modeled one is in gray.

[31] In Figures 3 to 5, the mass balance at site S6 in 2001 is consistently poorly reproduced when the albedo is calculated. Interestingly, the albedo record for that summer differs in its characteristics compared with previous years (Figure 5). The transition from a high snow albedo value to the lower ice value is slower than for other years, a feature that the model is not able to capture. The modeled albedo drops too quickly to a bare ice surface albedo value, which explains why ablation is overestimated in the calculations (see Figures 3 and 4). This is confirmed by the fact that using measured albedo improves the results considerably. For albedo values to stay high, the presence of snow is required, and this is either achieved with increased precipitation or decreased energy available for melting. Results for this year and site are improved if the relative humidity is decreased by 10%, or if the accumulation is increased by 60%. These parameters were obtained from ERA-40 data and are, therefore, more likely to have biases compared with the AWS data.

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

Figure 6

Normalized annual specific mass balance averaged along the K-transect, between 1991 and 2000. Model results (in gray) are compared with stake measurements (in black). The correlation coefficient between the two series is 0.80.

3.2. Runs on Distributed Grid

[33] In this part, the model was run for the whole ice sheet on a distributed grid at 20-km resolution (orography averaged from the 5 km-DEM) forced with 10 years (1991–2000) of 6-hourly ERA-40 data. SW_↓, LW_↓, sea level pressure, Prec, u at 10 m, T_atm and dew point temperature at 2 m are downscaled from the global grid onto the 20-km-resolution grid, using the center data point and a bilinear interpolation (as in section 3.1). P and RH can be calculated respectively from the sea level pressure and the dew point temperature at 2 m. We emphasize again that the focus is now to test the model's ability to capture interannual variability, and not to calculate the absolute ice sheet mass balance.

[34] We first check that the modeled runoff from 1991 to 1999 generated by the SMBM correlates well with estimates over the same period by Box et al. [2004] and Hanna et al. [2005]. Box et al. [2004] have used a regional climate model (RCM) to calculate the ice sheet mass balance between 1991 and 2000. The RCM biases were analyzed and corrected using 3 years of 17 Greenland Climate Network AWS data [Steffen and Box, 2001]. ECMWF operational data were used to initialize and update the boundary conditions of the RCM. Hanna et al. [2005] estimated the runoff variability for the period 1958–2003 using ECMWF (re)analysis data to drive a PDD surface meltwater runoff/retention model. A good correlation between the different model results is to be expected because of the systematic use of ECMWF operational data (similar but not identical to ERA-40 data). The correlation coefficients between results from those studies are shown in Table 5.

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]	0.94
This study	0.91	0.80

[35] The modeled wet snow zone extent was compared with observations from passive microwave satellite data [Abdalati and Steffen, 2001] (Figure 7). The observations do not provide any quantitative information on how much melting has occurred, but simply indicate whether the snow is wet or dry. Using a model that keeps track of the water content in the subglacial layers could help interpreting satellite data by comparing these to modeled melt volume distribution. However, we do not attempt to do this in this study since the model has not been tuned to ERA-40 climatology, and the modeled volume of meltwater is therefore likely to contain biases. Instead, the model output has been saved so that the percentage of time per day when the firn is wet (w > 0) can be retrieved and used as a proxy for melt intensity. The mean summer (June–July–August) averaged wet zone from 1991–1999 compares best with passive microwave satellite data [Abdalati and Steffen, 2001] when it is assumed that “wet firn” is captured if water is present ∼50% of the day. The mean melt extent observed over the decade is ∼1.40 × 10⁶ km², while the modeled one is ∼1.52 × 10⁶ km² (6% larger). The correlation coefficient varies between 0.90 and 0.94 if it is assumed that water must be present 25% to 75% of the day (Figure 7), indicating that the variability depends very little on the threshold value chosen.

Figure 7

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

[36] Figure 8 displays the spatial distribution of melt days for two consecutive years experiencing very different melt conditions and illustrates the spatial resolution and fidelity of the model. These plots can be directly compared with the melt extent derived from the satellite microwave observations (Steffen and Huff, CIRES, http://cires.colorado.edu/steffen/melt/). The 1991 maximum melt zone extent is very large, with the whole area south of ∼78° being wet at least for a short period in summer. Accordingly, our model results indicate that the same region is wet for ∼10–15 days during summer. In contrast, the maximum melt area in 1992 is much reduced both in satellite-derived information and model results (coinciding with volcanic cooling following Pinatubo eruption), where most of the ice sheet surface does not experience more than one day of melt during that summer.

Figure 8

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

4. Conclusions

[37] A surface mass balance model of the Greenland Ice Sheet designed for interactive coupling with and AOGCM is presented and tested. Forced with AWS data along the K-transect, model results were compared with four consecutive years of observations at two sites presenting different surface properties, due to the location of site S6 in the so-called dark zone. Although the model is strictly speaking tuned to the available data rather than validated (as is commonly done [e.g., Zuo and Oerlemans, 1996; Greuell and Bőhm, 1998; Hock, 1999; Braithwaite and Zhang, 2000; Oerlemans and Reichert, 2000]), calculating and comparing mass balance for individual years (instead of averaged over a longer period) is a less common and more challenging approach in evaluating model performance [Jóhannesson et al., 1995]. When successful, such an exercise gives confidence that the model is able to capture the interannual variability induced by the climate [Greuell and Genthon, 2004]. Despite the relatively poor accuracy in annual specific mass balance estimation at site S6 in 2001, the modeled mass balance in six out of the seven other cases falls within the uncertainties of the observed annual mass balance, having a mean difference from the observations of 4.9%. The remaining case overestimates the annual mass balance by 10%. Overall, the ablation rates calculated at S6 are significantly lower than at S5, indicating that the model is also able to account for spatial variability of the mass balance.

[38] Forced with ERA-40 data, the mass balance calculation averaged for seven stations along the K-transect correlates well with measurements over a 10-year period. The model was then applied to a distributed grid for the whole of the Greenland ice sheet. Although the amount of available data covering the ice sheet limits the degree to which such an application can be tested, the interannual variability captured by the SMBM agrees well with other studies [Box et al., 2004; Hanna et al., 2005]. In addition, the model generates a mean summer melt extent whose variability correlates highly (>0.9) with passive microwave satellite data derived for the period 1991–1999 [Abdalati and Steffen, 2001]. Thus the SMBM is able to reproduce different patterns of melt extent, which are consistent with satellite-derived data.

[39] We conclude, therefore, that the SMBM presented in this study adequately calculates ablation given appropriate forcing. Its ability to capture the interannual and spatial variability induced by the climate while running on a 20-km-resolution grid and forced with low-resolution climatology makes it suitable for future climate predictions, coupled with an AOGCM.

Acknowledgments

[40] This work was funded by UK Natural Environment Research Council grant NER/T/S/2002/00462. ECMWF ERA-40 data used in this project were obtained from the ECMWF Data Server. We thank W. Abdalati and E. Hanna for the use of their data, I. Rutt for providing the code necessary to the downscaling of the ERA-40 input variables, and A. J. Payne and P. Valdes for advice on the modeling approach used. Comments from R. Anderson, G. Flowers, J. E. Box and one anonymous reviewer contributed to improving the manuscript.