Snow Distribution and Melt Modeling for Mittivakkat Glacier, Ammassalik Island, Southeast Greenland

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1 808 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 7 Snow Distribution and Melt Modeling for Mittivakkat Glacier, Ammassalik Island, Southeast Greenland SEBASTIAN H. MERNILD Institute of Geography, University of Copenhagen, Copenhagen, Denmark GLEN E. LISTON Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado BENT HASHOLT Institute of Geography, University of Copenhagen, Copenhagen, Denmark NIELS T. KNUDSEN Department of Earth Science, University of Aarhus, Aarhus, Denmark (Manuscript submitted 23 May 2005, in final form 1 December 2005) ABSTRACT A physically based snow-evolution modeling system (SnowModel) that includes four submodels the Micrometeorological Model (MicroMet), EnBal, SnowPack, and SnowTran-3D was used to simulate five full-year evolutions of snow accumulation, distribution, sublimation, and surface melt on the Mittivakkat Glacier, in southeast Greenland. Model modifications were implemented and used 1) to adjust underestimated observed meteorological station solid precipitation until the model matched the observed Mittivakkat Glacier winter mass balance, and 2) to simulate glacier-ice melt after the winter snow accumulation had ablated. Meteorological observations from two meteorological stations were used as model inputs, and glaciological mass balance observations were used for model calibration and testing of solid precipitation observations. The modeled end-of-winter snow-water equivalent (w.eq.) accumulation increased with elevation from 200 to 700 m above sea level (ASL) in response to both elevation and topographic influences, and the simulated end-of-summer location of the glacier equilibrium line altitude was confirmed by glaciological observations and digital images. The modeled test-period-averaged annual mass balance was 150 mm w.eq. yr 1,or 15%, less than the observed. Approximately 12% of the precipitation was returned to the atmosphere by sublimation. Glacier-averaged mean annual modeled surface melt ranged from 1272 to 2221 mm w.eq. yr 1, of which snowmelt contributed from 610 to 1040 mm w.eq. yr 1. The surface-melt period started between mid-may and the beginning of June, and lasted until mid-september; there were as many as 120 melt days at the glacier terminus. The model simulated a Mittivakkat Glacier recession averaging 616 mm w.eq. yr 1, almost equal to the observed 600 mm w.eq. yr Introduction Corresponding author address: Sebastian H. Mernild, Institute of Geography, University of Copenhagen, Øster Voldgade 10, DK-1350 Copenhagen K, Denmark. sm@geogr.ku.dk Throughout the Arctic, much of the winter precipitation falls as a solid under windy conditions (Ohmura and Reeh 1991; Liston and Sturm 2002). As winter progresses, the solid precipitation accumulates on the ground and is frequently redistributed during blowingsnow events. A further consequence of this blowing snow is that significant portions (10% 50%) of snow cover can be returned to the atmosphere by sublimation of windborne snow particles (Liston and Sturm 1998, 2002; Essery et al. 1999; Pomeroy and Essery 1999; Hasholt et al. 2003). As spring and summer progress, the variation, duration, and intensity of snow and glacier melt increases in response to variations in weather and climate (e.g., insolation, temperature in American Meteorological Society

2 AUGUST 2006 M E R N I L D E T A L. 809 versions, and wind speed) and surface characteristics (e.g., albedo, roughness). The moisture in this system also changes phase (solid, liquid, and vapor) throughout the year as part of various physical processes and in response to the available surface energy fluxes. All of these seasonally changing processes directly impact the high-latitude hydrological cycle s seasonal evolution (e.g., Kane 1997; Liston and Sturm 2002). Across the Arctic, precipitation gauges significantly underestimate solid precipitation (e.g., Woo et al. 1982; Yang et al. 1998; Allerup et al. 1998, 2000a,b; Liston and Sturm 2002, 2004) because of aerodynamic errors at the precipitation gauging station (Hasholt et al. 2003). In addition, due to the generally rough terrain, harsh climatic conditions, and remote locations of arctic glaciers, extensive snow-distribution, snowmelt, and glacier-melt measurements have typically not been possible. Furthermore, logistical constraints make it difficult to monitor arctic glaciers at the beginning of the melt period and during the freeze-up period, resulting, for example, in a lack of discharge measurements during these periods and thus causing uncertainty in yearly water balance calculations. The use of gauging stations that underestimate the true amount of solid precipitation, limited numbers of arctic meteorological stations, and limited winter and summer glacier mass-balance measurements, lead us to conclude that we have few quality observations related to the spatial and temporal distribution of snow precipitation, snow sublimation, and surface melt across much of the glaciated Arctic. The limited measurement of such key climate-system components is a serious impediment to hydrological research efforts (Liston and Sturm 2004). Thus, there is a clear need to explore issues associated with data sparseness and modeling capabilities. The goal of this study is to apply and test a snowevolution modeling system (SnowModel; Liston and Elder 2006a) over the Mittivakkat Glacier catchment in southeast Greenland. We performed the model simulations with the following objectives: 1) to simulate winter processes related to snow accumulation, snow redistribution by wind, and snow sublimation on the Mittivakkat Glacier; 2) to simulate summer snowmelt and glacier-ice melt on the Mittivakkat Glacier; 3) to define the location of the Mittivakkat Glacier equilibrium line altitude (ELA); 4) to generate area-distributed melt fluxes from the seasonal snowpack and the exposed glacier surface to be used as meltwater inputs to hydrological models; 5) to model the winter mass balance, summer mass balance, and annual mass balance of the Mittivakkat Glacier; and 6) to compare these modeled outputs with available observational datasets. 2. Study area a. Physical settings The Mittivakkat Glacier (65 42 N latitude; W longitude) is situated on Ammassalik Island approximately 15 km northwest of the town Tasiilaq (Ammassalik) and 50 km east of the eastern margin of the Greenland Ice Sheet, separated from the mainland by the km-wide Sermilik Fjord. The entire Mittivakkat Glacier complex has several outlets and covers 31 km 2 (Fig. 1). Since the first observation in 1933, there has been an almost continuous recession of the Mittivakkat Glacier (Knudsen and Hasholt 2004). The observed average winter mass balance, summer mass balance, and net mass balance for 1999 through 2004 are, respectively, 1270, 1730, and 600 mm water equivalent (w.eq.) (Table 1), showing a negative net mass balance for this time period. The observed net mass balance from 1999 to 2002, based on 100-m-altitude interval observations, indicates that the ELA (where annual ablation equals annual accumulation) was 800 m above seal level (ASL) for 2000/01 (Table 2). The model simulation domain (Fig. 1a) includes a subarea (Fig. 1b, the investigated area) where snow and glacier observations are available from previous studies (Knudsen and Hasholt 1999, 2004; Hasholt and Mernild 2004). This subarea covers approximately 17.6 km 2 of the Mittivakkat Glacier (in the following discussion the investigated glacier area is referred to as the Mittivakkat Glacier ). Strong alpine relief characterizes the simulation domain, with elevations ranging from 200 to above 1000 m ASL at the highest peaks (Fig. 1); avalanches are rare near the glacier. Proglacier valleys west of the glacier generally run in a westerly direction toward Sermilik Fjord, whereas east of the glacier, valleys run in a southerly direction toward Tasiilaq Fjord. The land cover within the simulation domain is dominated by bare bedrock in the upper parts, and loose talus and debris-flow deposits in the lower parts of the slopes. Proglacier valley bottoms contain both morainic deposits and fluvial sediments. b. Meteorological stations and climate There are two primary meteorological stations within the simulation domain: Station Nunatak (515 m ASL; representative of the glacier) and Station Coast (25 m ASL; representative of the coastal and valley area) (Fig. 1a). Station Nunatak is located at the highest peak on a small nunatak ( 5 m from the glacier in the dominant wind directions) close to the ELA on the Mittivakkat Glacier. Station Coast includes a site located on a rock hill close to the coast and a proglacier

3 810 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 7 FIG. 1. Mittivakkat Glacier simulation domain (a) topography (gray shades, 100-m contour interval) and the entire glacier complex outlined by the black line, (b) the investigated area (the main Mittivakkat Glacier), and (c) surface characteristics. Also shown in (a) are the two meteorological tower stations: Station Nunatak (515 m ASL and shown within glacier outline) and Station Coast (25 m ASL). The inset figure in (a) indicates the general location of the Mittivakkat Glacier in eastern Greenland. The domain coordinates can be converted to UTM by adding 548 km to the west east origin (easting) and 7281 km to the south north origin (northing) and converting to meters. valley site approximately 200 m southeast of Station Coast (Fig. 1a). The Mittivakkat Glacier area climate is an ET, tundra climate, according to the Köppen classification system. Based on data from these stations, the mean annual air temperature (MAAT) ( ) is 2.1, 1.1, and 1.6 C for Station Nunatak, Station Coast, and for the area [derived from Micrometeorological Model (MicroMet) air temperature forcing fields], respectively. The maximum monthly average area air TABLE 1. Winter, summer, and net mass balance for the Mittivakkat Glacier based on observations ( ). Winter mass balance observations are carried out in late May and early June and summer mass balance observations in late August (Knudsen and Hasholt 2004). The assumed accuracy of the observed winter and summer mass balance are within 15%; however, large errors might occur especially in areas with many crevasses. Year Observed winter mass balance Observed summer mass balance Observed net mass balance 1999/ / / / /04 No data No data 1060 Average temperature is 4.9 C in July and the minimum is 7.6 C in February, and mean annual area relative humidity is 88% ( ) (derived from MicroMet). The total annual precipitation (TAP) at Station Nunatak is 1629 mm w.eq. [after applying a wind speed correction, due to the exposed station location at the nunatak (Hasholt and Mernild 2004)] and 1143 mm w.eq. at Station Coast ( ) (no wind speed correction was needed or applied at Station Coast), indicating a positive orographic effect between the stations. Approximately 65% 85% of TAP falls as snow from ap- TABLE 2. Observed net mass balance from Mittivakkat Glacier ( ) based on 100-m-altitude-interval data (N. T. Knudsen 2006, unpublished manuscript). Altitude (m ASL) Observed net mass balance, 1999/2000 Observed net mass balance, 2000/01 Observed net mass balance, 2001/

4 AUGUST 2006 M E R N I L D E T A L. 811 proximately mid-september to late May. The mean annual wind speed is 3.9 and 4.2 m s 1 for Station Nunatak and Station Coast, respectively, mainly dominated by N and E winds during autumn, winter, and spring, and SW, S, and E winds during summer (Fig. 2). Strong winds (neqqajaaq, similar to a foehn wind) occur during winter on the Mittivakkat Glacier, mainly coming from the E and NE, and often followed by katabatic winds (piteraq) from the Greenland Ice Sheet and channeled through the Sermilik Fjord in a northerly direction. Wind velocities during a piteraq can gust to 85 m s 1, causing severe blowing and drifting snow. Together, the factors of topography, precipitation, and wind result in significant winter snow redistribution (Hasholt et al. 2003). 3. SnowModel a. SnowModel description SnowModel (Liston and Elder 2006a) is a spatially distributed snowpack evolution modeling system specifically designed to be applicable over the wide range of snow landscapes, climates, and conditions found around the world. It is made up of four submodels: MicroMet defines the meteorological forcing conditions (Liston and Elder 2006b), EnBal calculates the surface energy exchanges, including melt (Liston 1995; Liston et al. 1999), SnowPack simulates snow depth and water-equivalent evolution (Liston and Hall 1995), and SnowTran-3D is a blowing-snow model accounting for snow redistribution by wind (Liston and Sturm 1998, 2002). While other distributed-snow models exist (e.g., Tarboton et al. 1995; Marks et al. 1999), SnowModel includes a blowing-snow submodel that allows application in arctic, alpine (above treeline), and prairie environments: environments that comprise 68% of seasonally snow-covered Northern Hemisphere land (Liston 2004): Winstral and Marks (2002) also include a blowing-snow model. SnowModel simulates snow-related physical processes occurring at spatial scales of 5mto global and temporal scales of 10 min to seasonal. These include 1) accumulation and loss from snow precipitation, blowing-snow redistribution, and sublimation; 2) loading, unloading, and sublimation within forest canopies; 3) snow-density evolution; and 4) snowpack ripening and melt. 1) MICROMET MicroMet is a quasi physically-based meteorological distribution model (Liston and Elder 2006b) designed specifically to produce the high-resolution meteorologi- FIG. 2. Daily atmospheric forcing values used as input for the model: (top to bottom) air temperature, relative humidity, wind speed, and wind direction for Stations Nunatak and Coast, and adjusted SWE precipitation from Station Nunatak and original precipitation from Station Coast ( ).

5 812 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 7 cal forcing distributions (air temperature, relative humidity, wind speed, wind direction, precipitation, solar and longwave radiation, and surface pressure) required to run spatially distributed terrestrial models over a wide range of landscapes in a physically realistic manner. MicroMet uses elevation-related interpolations to modify air temperature, humidity, and precipitation following Kunkel (1989), Walcek (1994), Dodson and Marks (1997), and Liston et al. (1999). Temperature and humidity distributions are defined to be compatible with the observed lapse rates. Wind flow in complex topography is simulated following Ryan (1977) and Liston and Sturm (1998). Solar radiation variations are calculated using elevation, slope, and aspect relationships (Pielke 2002). Incoming longwave radiation is calculated while taking into account cloud cover and elevation-related variations following Iziomon et al. (2003). Precipitation is distributed following Thornton et al. (1997). In addition, any data from more than one location, at a given time, are spatially interpolated over the domain by using a Gaussian distance-dependent weighting function and interpolated to the model grid using the Barnes objective analysis scheme (Barnes 1964, 1973; Koch et al. 1983). A comparison of the various MicroMet components with observational datasets was provided by Liston and Elder (2006b). Early versions of MicroMet have been used to distribute observed and modeled meteorological variables over wide variety of landscapes in the United States (Colorado, Wyoming, Idaho, and Arctic Alaska), Norway (Svalbard and central Norway), Greenland (Ammassalik Island), and near-coastal Antarctica (e.g., Liston and Sturm 1998, 2002; Greene et al. 1999; Liston et al. 1999, 2002; Hiemstra et al. 2002; Prasad et al. 2001; Hasholt et al. 2003; Bruland et al. 2004; Liston and Winther 2005). 2) ENBAL EnBal performs standard surface energy balance calculations (Liston 1995; Liston et al. 1999). It simulates surface (skin) temperatures, and energy and moisture fluxes in response to observed and/or modeled nearsurface atmospheric conditions provided by MicroMet. Surface latent and sensible heat flux and snowmelt calculations are made using a surface energy balance model of the form 1 Q si Q li Q le Q h Q e Q c Q m, where Q si is the solar radiation reaching earth s surface, Q li is the incoming longwave radiation, Q le is the emitted longwave radiation, Q h is the turbulent exchange of sensible heat, Q e is the turbulent exchange of latent 1 heat, Q c is the conductive energy transport, Q m is the energy flux available for melt, and is the surface albedo. Details of each term in Eq. (1), and the model solution, can be found in Liston (1995) and Liston et al. (1999). In the presence of snow or glacier ice, surface temperatures greater than 0 C indicate that energy is available for melting. This energy is computed by fixing the surface temperature at 0 C and solving Eq. (1) for Q m. 3) SNOWPACK SnowPack is a single-layer, snowpack-evolution model (Liston and Hall 1995) that defines snowpack changes in response to precipitation and melt fluxes defined by MicroMet and EnBal. Its formulation closely follows Anderson (1976) to define compactionbased snow density evolution, where the density evolves over time in response to snow temperature and weight of overlying snow. A second density-modifying process results from snow melting. The melted snow reduces the snow depth and is redistributed through the snowpack until a maximum snow density, assumed to be 550 kg m 3, is reached (Liston and Hall 1995). This provides a simple method to account for heat and mass transfer processes, such as snowpack ripening, during spring melt. Any additional meltwater is assumed to reach the ground or ice at the base of the snowpack. The density of new snow (precipitation) added to the snowpack is defined following Anderson (1976). 4) SNOWTRAN-3D SnowTran-3D (Liston and Sturm 1998) is a threedimensional model that simulates snow depth evolution (deposition and erosion) resulting from windblown snow, based on a mass-balance equation that describes the temporal variation of snow depth at each grid cell within the simulation domain. SnowTran-3D s primary components are the wind-flow forcing field, the wind shear stress on the surface, the transport of snow by saltation, the transport of snow by turbulent suspension, the sublimation of saltating and suspended snow, and the accumulation and erosion of snow at the snow surface (Liston and Sturm 2002; Hasholt et al. 2003). Simulated transport and sublimation processes are influenced by the interactions among available snow, topography, and atmospheric conditions (Liston and Sturm 1998). SnowTran-3D simulates the snow depth evolution, and then uses the snow density simulated by SnowPack to convert to the more hydrologically significant snow-water equivalent (SWE) depth. Deposition and erosion, which lead to changes in snow depth [Eq. (2) below], are the result of changes in horizontal mass-

6 AUGUST 2006 M E R N I L D E T A L. 813 transport rates of saltation, Q salt (kg m 1 s 1 ), changes in horizontal mass-transport rates of turbulentsuspended snow, Q turb (kg m 1 s 1 ), sublimation of transported snow particles, Q (kg m 2 s 1 ), and the water-equivalent precipitation rate, P (m s 1 ). Combined, the time rate of change in snow depth, (m), is d s dt wp dqsalt dx Q, dqturb dx dqsalt dy dqturb where t (s) is time; x (m) and y (m) are the horizontal coordinates in the west east and south north directions, respectively; and s and w (kg m 3 ) are the snow and water density, respectively. At each time step, Eq. (2) is solved for each individual grid cell within the domain, and is coupled to the neighboring cells through the spatial derivatives (d/dx, d/dy). SnowTran-3D simulations have been compared against observations in glacier and glacier-free alpine, Arctic, and Antarctic landscapes (Greene et al. 1999; Liston et al. 2000; Prasad et al. 2001; Hiemstra et al. 2002; Liston and Sturm 2002; Hasholt et al. 2003; Bruland et al. 2004). 5) SNOWMODEL MODIFICATIONS FOR GLACIER SIMULATIONS The submodels that make up SnowModel were all originally developed for glacier-free landscapes. Thus, for our Mittivakkat Glacier application, two Snow- Model modifications were implemented: 1) a glacier class was added to the land-cover classification (along with the associated albedo and other land-cover characteristics, e.g., snow-holding depth, the snow depth that must be exceed before snow can be transported by wind), and 2) energy balance calculations were implemented to simulate glacier-ice melt after the winter s snow cover had melted away. b. SnowModel input and validation datasets dy 2 TABLE 3. User-defined constants used in model simulations [see Liston and Sturm (1998) for parameter definitions]. Symbol Value Parameter C Vegetation snow-holding depth (m) 0.50 Bedrock 0.01 Glacier 0.01 Lake t c 1500 Terrain curvature (m) f Snow equilibrium fetch distance (m) u *t 0.25 Threshold wind shear velocity (m s 1 ) z Snow surface roughness length (m) dt 1 Time step (day) dx dy 100 Grid cell increment (m) t fact Precipitation adjustment factor / / /02 To solve the system of equations, SnowModel requires spatially distributed fields of topography and land-cover types, and temporally varying meteorological data (air temperature, relative humidity, wind speed, wind direction, and SWE precipitation) obtained from meteorological stations located within the simulation domain (Fig. 1a). The simulations were performed on 1-day time step. Snow and ice melt and blowing snow are threshold processes and may not be accurately represented by a 1-day time step. Unfortunately, computational resources did not allow using a smaller time increment. The simulations span the 5-yr period 1 September 1999 through 31 August 2004, with 1999/2000 through 2001/02 used as a calibration period and 2002/ 03 through 2003/04 used as a test period for the winter snow simulations. The calibration and test periods were chosen arbitrarily. Summer ablation was not calibrated or tested. Topographic data were obtained from a digital elevation model (DEM) based on a 1: scale map with 25-m contour intervals (derived from 1981 aerial photos). A 100-m grid-cell increment DEM was used that covered an 11 km by 13 km simulation domain that included the Mittivakkat Glacier (Fig. 1). Each grid cell within the domain was assigned a land-cover type and classified as bedrock with a snow-holding depth of 0.50 m (Hasholt and Mernild 2004), as lake ice with a depth of 0.01 m, or as glacier with a snow-holding depth of 0.01 m (Fig. 1c; Table 3) (Liston and Sturm 2002). Each grid value of snow-holding depth was assumed to be constant throughout the winter except for lakes, which were assumed to be unable to accumulate snow until after their surface was frozen (assumed to occur in the beginning of October; Hasholt et al. 2003). Because of our lack of information regarding the timing of possible sea ice formation within the simulation domain, all fjord areas within the domain were excluded from the model simulations (Fig. 1c). Model parameter values used in the simulations are provided in Table 3 [see Liston and Sturm (1998) for parameter definitions]. Wind speed, wind direction, air temperature, and relative humidity were recorded at 2- and 4-m levels every 3 h at Station Nunatak and Station Coast (Hasholt and Mernild 2004; Hasholt et al. 2004). Figure 2 summarizes the station atmospheric forcing data used in the model simulations. Highlighted are air temperatures greater than 0 C (temperatures capable of melting) and wind speeds greater than 5 m s 1 (winds gen-

7 814 JOURNAL OF HYDROMETEOROLOGY VOLUME 7 TABLE 4. Monthly lapse rates based on air temperature (2 m) from Station Nunatak and Station Coast ( ). Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Ave C (100 m) erally capable of transporting snow) (Hasholt et al. 2003). There are several such transporting events throughout the winter. Also shown in Fig. 2 are the wind directions for these wind events, indicating that the majority of snow-transporting winds are from NE, E, and SE. Monthly lapse rates were also used as a model input (Table 4), with a minimum monthly lapse rate of 0.51 C (100 m) 1 for November and February, and a maximum monthly lapse rate of 0.33 C (100 m) 1 in June and July; these temperature increases with elevation are governed by summer sea breezes in daytime coming predominately from the S and SW (Mernild et al. 2005a). In addition to the meteorological observations, during each of the five study years, winter and summer mass-balance measurements were made at the end of May and the end of August, respectively. During these field campaigns, snow depth, density, and ablation from snow and glacier ice were measured using cross-glacier stake lines spaced approximately 500 m apart; the distance between the stakes in each line were m apart (Knudsen and Hasholt 2004). The assumed accuracy of the observed winter and summer mass balances are each within 15%; however, large errors might occur especially in glacier areas with many crevasses (Knudsen and Hasholt 1999). To determine the Mittivakkat Glacier ELA, daily snow-distribution variations on the upper glacier were measured using automatic digital cameras positioned at Station Nunatak. c. Precipitation datasets Liquid (rain) precipitation was measured at both stations 0.45 m above the ground and used herein without wind corrections because the orifice of the gauge was located at approximately the same height as the local roughness elements. Solid (snow) precipitation was calculated from snow depth sounder observations that are assumed to have an accuracy of within 10% 15%. The noise was removed from the sounder data and the remaining snow depth increases were adjusted using a temperature-dependent snow density (from 67.9 to kg m 3, average 85.8 kg m 3 ; Brown et al. 2003) and an hourly snowpack settling rate (Anderson 1976), to estimate the SWE precipitation. In the following discussions, the SWE precipitation from Station Nunatak is called the original SWE precipitation. Initial SnowModel simulations used the original SWE precipitation from Station Nunatak and Station Coast. When compared with the Mittivakkat Glacier winter mass-balance observations, the model underestimated end-of-winter (31 May) SWE depths by 30% (1999/2000), 38% (2000/01), 18% (2001/02), and 29% (average ) for the calibration period. As suggested by the numerous wind events above 5 m s 1 (a typical snow-transport threshold; Liston and Sturm 1998) at Station Nunatak (Fig. 2), the original SWE precipitation, P obs, was underestimated; the precipitation at the station was removed by snow drifting and did not accumulate under the snow depth sounder that was used to reconstruct the precipitation history (Hasholt and Mernild 2004). Because of these known limitations in P obs, we generated a second Station Nunatak precipitation dataset, called the adjusted SWE precipitation, P adj, by the following method [Eq. (3)]: we defined a precipitation-adjustment factor, fact, that when multiplied by the original SWE precipitation data from Station Nunatak, P obs, yielded a simulated Mittivakkat Glacier SWE depth on 31 May that was within 1% of the observed Mittivakkat Glacier winter massbalance observations. Thus, P adj fact P obs. The adjustment factor was determined by the following iterative procedure: t 1 t fact fact 3 SWE t obs SWE mod t, 4 P adj where t fact is the precipitation adjustment factor used in the current iteration, t; t t 1 is the adjustment factor to be used in the next iteration, t 1; SWE obs is the glacier-averaged observed SWE on 31 May; SWE t mod is the glacier-averaged modeled SWE on 31 May, for the current iteration; and P t adj is the glacier-averaged adjusted winter precipitation input for the current iteration (so it includes the influence of the previously defined precipitation adjustment factor). In addition to accounting for precipitation measurement errors, this method also adjusts for model deficiencies. The iterative procedure was performed for each year in the calibration period: 1999/2000, 2000/01, and 2001/ 02. Using the average annual precipitation adjustment factor ( t fact) from 1999/2000 to 2001/02 (Table 3) in linear regression together with original SWE precipitation, the adjusted SWE depth for the Mittivakkat Gla-

8 AUGUST 2006 M E R N I L D E T A L. 815 TABLE 5. Modeled SWE depth for the Mittivakkat Glacier based on original precipitation data from Station Nunatak and Station Coast, maximum annual SWE depth and date, and SWE depth on 31 May based on adjusted precipitation data from Station Nunatak together with observed winter mass balance from the Mittivakkat Glacier. Year Modeled SWE depth on 31 May for the Mittivakkat Glacier based on original precipitation data from Station Nunatak and Station Coast Modeled maximum SWE depth and date for the Mittivakkat Glacier, based on adjusted precipitation data from Station Nunatak and original precipitation data from Station Coast Modeled SWE depth on 31 May for the Mittivakkat Glacier, based on adjusted precipitation data from Station Nunatak and original precipitation data from Station Coast Observed winter mass balance carried out at the end of May to the beginning of Jun (Knudsen and Hasholt 2004) 1999/ (5 Jun) / (7 Jun) / (4 Jun) / (8 Jun) / (28 May) 1220 No data cier on 31 May was modeled for the test period 2002/03 and 2003/ Results Table 5 shows modeled SWE depth and mass-balance observations from the Mittivakkat Glacier. Defined by our precipitation adjustment scheme, the model simulation using the adjusted SWE precipitation for 1999/ 2000, 2000/01, and 2001/02 (Table 5), compared with the observed winter mass balance, indicates a SWE depth difference of less than 1%. The SWE depth for the Mittivakkat Glacier on 31 May was modeled for 2002/03 and 2003/04 and yields an SWE depth of 1240 and 1220 mm w.eq., respectively (Table 5). The adjusted precipitation data from 1999/2000 to 2003/04 yielded an orographic precipitation increase of 99 mm w.eq. 100 m 1 ( ) between the two meteorological stations. The annual (from September to August) average modeled SWE depth variation for Mittivakkat Glacier is illustrated in Fig. 3 for 1999/2000 to 2003/04, indicating an increasing average SWE depth throughout the accumulation period (September to May), a decreasing average SWE depth throughout the ablation period (June to August), and an end-of-year net accumulation in SWE depth (Fig. 3). The end-of-year net SWE depth accumulation varies from 150 mm w.eq. (2000/01) to 630 mm w.eq. (2002/03); a surplus of SWE depth is located above the ELA. In Fig. 3, the assumed end-ofwinter (31 May) is marked by an arrow illustrating that this does not necessarily correspond to the maximum simulated average SWE depth (simulated end of winter), with a maximum difference of 8 days, and a difference of average SWE depth less than 20 mm w.eq. (calculated from Table 5). Our analysis of the spatial end-of-winter distribution (31 May) between the model-adjusted SWE depth on the glacier and the observed winter mass balance from the Mittivakkat Glacier (1999/2000 to 2001/02) uses 100-m-altitude intervals (Fig. 4). Figures 4a c show an increasing SWE accumulation depth from 200 m ASL (800 mm w.eq.) to approximately 700 m ASL (1400 mm w.eq.), for both model-adjusted SWE depth and observed winter mass balance. Above 700 m ASL, the observed winter mass balance and modeled SWE depth decreases. The adjusted precipitation shown in Figs. 4a c varied for each of the 100-m intervals due to increasing altitude and changes in wind regime and topography. A significant correlation occurs between the modeled SWE depth and the observed winter mass balance expressed using the 100-m-altitude intervals: for 1999/2000, R , p 0.01 (where p is level of significance) (Fig. 4a); for 2000/01, R , p 0.01 (Fig. 4b); and for 2001/02, R , p 0.01 (Fig. 4c), even though the maximum difference in SWE depth for each interval varies by up to 120 mm w.eq. (e.g., for the interval 800 m ASL, 1999/2000). Within SnowModel, SnowTran-3D simulates spatial snow deposition patterns in response to erosion and deposition. As an example, the spatial variation in modeled SWE depth for 31 May 2000 using the adjusted precipitation is illustrated in Fig. 5a. The SWE pattern illustrates an almost identical spatial snow distribution from 1999/2000 through 2001/02, with maximum SWE deposition values between 500 and 700 m ASL on the lee side of the ridge east and south of the glacier (Fig. 5a), because the majority of snow-transporting winds are from NE, E, and SE. The end-of-summer (31 August) location of the modeled and observed ELA on Mittivakkat Glacier (1999/ 2000 to 2001/02) is a product of both snow accumula-

9 816 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 7 FIG. 3. Variation in average modeled SWE depth for the investigated area from 1999 to 2004: (a) 1999/2000, (b) 2000/01, (c) 2001/02, (d) 2002/03, and (e) 2003/04. The numbers by the arrows indicate the average SWE depth on 31 May (end for accumulation period) and the other numbers the average SWE depth on 31 August (end of ablation period). tion and melt processes. The observed ELA data were produced using a combination of digital camera images from Station Nunatak (Fig. 6) and glacier net massbalance measurements (Table 2). The modeled ELA locations (identical with the snow line; the boundary between bare ice and snow cover on the glacier surface) for 1999/2000 (Fig. 6a), 2000/01 (Fig. 6b), and 2001/02 (Fig. 6c) were situated between approximately 600 and 700 m ASL. These simulated ELA locations are confirmed by 1) the digital images of the glacier, indicating that ELA is located within m ASL (Figs. 6a c) and 2) the 100-m-altitude-interval data from the observed net mass balance (Table 2), which indicates a 0 mm w.eq. net mass balance at m ASL for 1999/ 2000 and between the intervals and m ASL for 2001/02, respectively. In 2000/01 the observed net mass balance is completely negative (Table 2), indicating a nonexisting ELA for the glacier that year, even though some snow patches remained on the glacier surface on 31 August (Fig. 6e). In Fig. 5b, the spatial variation in modeled SWE depth on 31 August 2000 indicates the maximum end-of-season deposition is on the lee side of the ridge on the southeastern part of the glacier. Table 6 presents the modeled winter mass balance (September May), the modeled summer mass balance (June August), and the modeled mass-balance data for the investigated area of the Mittivakkat Glacier, where the years 1999/2000 to 2001/02 are used for calibration of the winter snow simulations and 2002/03 and 2003/04 FIG. 4. A comparison between 100-m-altitude-interval end-of-winter SWE depths based on modeling with nonadjusted precipitation (dashed line), with adjusted precipitation data from Station Nunatak (dotted line), and observed winter mass balance data from the Mittivakkat Glacier (solid line) for (a) 1999/2000, (b) 2000/01, and (c) 2001/02.

10 AUGUST 2006 M E R N I L D E T A L. 817 FIG. 5. Example SnowModel-simulated SWE distribution for (a) end of winter (31 May 2000) and (b) end of summer (31 Aug 2000). The gray color in (b) indicates the glacier surface (marked Bare glacier ice ). In both (a) and (b) the contour lines indicate topography. Shown is the combination of elevation-dependent snow precipitation and topography-driven snow redistribution by wind. for model testing. For 2003/04, only annual net massbalance data were available. The modeled winter mass balance for 2002/03 was 1240 mm w.eq. (Table 6). This corresponds well with the observed winter mass balance of 1400 mm w.eq. (Table 1), or a 160 mm w.eq. (approximately 12%) difference. The modeled summer mass balance for 2002/ 03 was 1310 mm w.eq. (Table 6), corresponding to the observed summer mass balance of 1050 mm w.eq. (Table 1), a modeled loss of 260 mm w.eq., or approximately 25% higher than the observed value. For 2002/ 03 the modeled net mass balance was underestimated by 420 mm w.eq and for 2003/04 was overestimated by 120 mm w.eq. The annual difference in modeled and observed mass balance data averaged 150 mm w.eq. yr 1,or 15%, indicating a larger simulated mass loss than observed. 5. Discussion During blowing-snow events, sublimation of windtransported snow can play an important role in the high-latitude hydrological cycle. Previous Mittivakkat Glacier studies (1997/98) (Hasholt et al. 2003) showed that as much as 15% of the annual precipitation may be returned to the atmosphere by sublimation. During the investigation period , modeled annual sublimation averaged 12% of the solid precipitation inputs for the Mittivakkat Glacier. The sublimation losses are low at the Mittivakkat Glacier compared to previous studies in Arctic Canada and Greenland (e.g., Pomeroy and Gray 1995; Pomeroy et al. 1997; Liston and Sturm 1998; Essery et al. 1999; Pomeroy and Essery 1999; Hasholt et al. 2003) where approximately 5% 50% of the annual solid precipitation was returned to the atmosphere by sublimation. Blowing-snow sublimation rates are mainly dependent upon air temperature, humidity deficit, wind speed, and particle size distribution (Schmidt 1972, 1982; Tabler 1975; Pomeroy and Gray 1995; Liston and Sturm 2002; Hasholt et al. 2003). In our relatively coastal domain, high wind speeds are generally coincident with high relative humidity, and therefore, sublimation has played a lesser role in the glacier water/mass balance budget. Previous studies show significant snow redistribution; in Arctic Canada within the first 300 m of fetch, 35% 85% of annual snowfall is removed by wind erosion, and the amount increases with wind speed (Pomeroy et al. 1993). The wind redistribution processes influence snow depths over distances of tens of centimeters to hundreds of meters. On Ammassalik Island, previous blowing-snow model simulations (1997/98) (Hasholt et al. 2003) found significant snow redistribution from east-facing slopes to west-facing slopes, together with greatest drift accumulation at the head of the Mittivakkat Glacier. Figure 4 shows good agreement between modeled and observed end-of-winter SW depth in the long profile with largest SWE accumulation located between 600 and 700 m ASL, which is consistent with previous observations and simulations. Above 700 m ASL, the SWE accumulation decrease mainly results from increasing wind redistribution of snow to the lower glacier part due to wind flow pattern over and around ridges and peaks (topographic characteristics). Even reasonable agreement occurs between the modeled and observed end-of-season spatially distributed SWE depth, with maximum depths on the

11 818 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 7 FIG. 6. Location of the modeled snow line (the difference between snow and ice) on the Mittivakkat Glacier at the end of the ablation period on (a) 31 Aug 2000, (b) 31 Aug 2001, and (c) 31 Aug 2002, and a photographic time lapse from Station Nunatak of the observed snow line on (d) 31 Aug 2000, (e) 31 Aug 2001, and (f) 31 Aug The location of the digital camera is located as indicated by the circle-cross, and the area where the snow and glacier cover was mapped is illustrated by the polygon in (a), (b), and (c).

12 AUGUST 2006 M E R N I L D E T A L. 819 TABLE 6. Modeled net winter mass balance (Sep May), modeled net summer mass balance (Jun Aug), and modeled net mass balance for the Mittivakkat Glacier (1999/2000 to 2003/04). The modeled net summer mass balance does not incorporate values for internal accumulation (superimposed layer) of meltwater. Year Modeled net winter mass balance (Sep May) Modeled net summer mass balance (Jun Aug) Modeled net mass balance (Sep Aug) 1999/ / / / / Average lee side of the ridge east and south of the glacier (Figs. 5 and 6). However, there appears to be some spatial discrepancy in the SWE depth distributions on the upper glacier and the modeled snow cover and patchy snow cover shown in the photographs (Fig. 6). This may be the result of small-scale snow depth variations ( 100 mm w.eq.) or, alternatively, local melt rate variations due to variations not captured by the 100-m DEM. The 99 mm w.eq. (100 m) 1 precipitation increase ( ) between the two meteorological stations is assumed to be closely related to the orographic influence of Ammassalik Island. Between the corrected precipitation at the Danish Meteorological station in the town of Tasiilaq and the adjusted precipitation at Station Nunatak, the orographic precipitation increase averaged 139 mm w.eq. (100 m) 1, or an increase of 12% (100 m) 1 ( ). Previous Ammassalik Island studies (1997/98) (Hasholt et al. 2003) showed orographic precipitation increases as high as 14% (100 m) 1. The difference between modeled and observed annual mass balance is mainly caused by differences in summer mass balance (Tables 1 and 6). For three out of four years, model ablation is underestimated. This variation in ablation is likely due to model limitations or the use of nonrepresentative model input data. For example, the model was not able to account for 1) the high frequency of clouds or sea fog below approximately m ASL, 2) the occurrence of a persistent temperature inversion (below approximately m ASL, based on near-surface measurements) in the western part of the Mittivakkat Glacier during summer, and 3) highly variable lapse rates in the mountains and over glaciers. Because of the adjacent rocks, air temperature data from Station Nunatak may be overestimated during times of low wind speed. Data from meteorological stations not located on the glacier surface may also be different from air temperatures over the glacier itself. Using air temperature data from Station Coast and Station Nunatak in modeling indicates positive lapse rates for the ablation period (for a temperature increase of approximately 1.5 C for the higher station). In reality, it also seems unlikely that 2-m air temperatures would increase with elevation over the glacier itself. Clearly, MicroMet/SnowModel would benefit from the ability to simulate the presence of surface temperature inversions. We expect this is particularly important in snow- and ice-covered Arctic environments, including Greenland. During summer (from June to August), the ablation processes (phase-change processes) of evaporation/ sublimation and melting dominated the watershed s snow characteristics. Previous Greenland studies (e.g., Hasholt 1997; Mernild et al. 2005b) indicated that melt season length increases at lower latitudes and decreases in the higher latitudes due to lower air temperatures and solar energy input at the northern locations. As part of the SnowModel simulations, melting from snow and glacier ice on Mittivakkat Glacier were computed. The simulations indicated the total number of annual melt days ranged from 106 (2003) to 129 (2002) during the period from mid-may/beginning of June to mid- September (Table 7). In Zackenberg (74 28 N; W), northeast Greenland, the melt season lasts approximately 90 to 105 days ( ) starting in mid-june and ending in early to mid-september (Mernild et al. 2005b); confirming an approximately 3-weekshorter melt season in Zackenberg ( 74 N) than Ammassalik Island ( 65 N). Figure 7 plots the spatial distribution of melt days on the Mittivakkat Glacier from 1999 to In some areas of the glacier (e.g., at the glacier terminus) as much as 120 melt days per year may occur. The number of melt days decreases with increasing altitude, with 40 to 50 melt days per year around highest peaks (Fig. 7), and approximately 80 melt days per year at the ELA. SnowModel outputs were also used to calculate the annual surface meltwater production over Mittivakkat Glacier. This meltwater ranged from 1272 (2002/03) to 2221 mm w.eq. yr 1 (2000/01), with a 5-yr average of 1874 mm w.eq. yr 1 (Table 7). Summer-averaged daily

13 820 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 7 TABLE 7. Number of days with meltwater at the Mittivakkat Glacier (Sep Aug), date for start and end of continuous surface melt, total amount of modeled surface melt, sum of snowmelt, and sum of glacier melt from 1999/2000 to 2003/04. Year Total days that had surface melt (Sep Aug) Start and end of period with continuous surface melt Total surface melt (Sep Aug) Total snowmelt (Sep Aug) Total glacier-ice melt (Sep Aug) 1999/ Jun to 12 Sep / May to 23 Sep / May to 15 Sep / Jun to 18 Sep /04 111* From 29 May* Average * Data are not available from 15 to 31 Aug Therefore, average melt rates from 15 to 31 Aug are used. melt values ranged from 12 to 18 mm w.eq. day 1, with maximum daily values as high as 40 mm w.eq. day 1 (Fig. 8). Daily average and maximum melt rates compare well with unpublished field observations. Figure 8 shows the daily surface meltwater variation from both snow cover and glacier ice throughout summer and winter. During winter, a few melt events occur (e.g., the end of October 1999) due to foehn conditions at the glacier. The average annual sums of snow and glacier meltwater on the Mittivakkat Glacier ( ) were 860 and 1012 mm w.eq. yr 1, respectively (Fig. 3; Table 7). Early in the melt season (June), meltwater is mainly controlled by glacier snowmelt, whereas later in the season (July and August), when the snow cover is largely gone, the melt distribution is dominated by glacier-ice melt. Throughout the year, different surface processes (snow accumulation, snow redistribution, sublimation, and surface melting) on the Mittivakkat Glacier affect the high-latitude water balance [Eq. (5)]. The yearly water balance equation for the glacier can be described by P ET R S 0, 5 FIG. 7. Total number of days from September to August on Mittivakkat Glacier that had surface melt: (a) 1999/2000, (b) 2000/01, (c) 2001/02, (d) 2002/03, and (e) 2003/04. At (e), data after 15 August were unavailable; therefore, days between 15 and 31 August were defined to be melt days based on observations from the previous years.

14 AUGUST 2006 M E R N I L D E T A L. 821 FIG. 8. Daily modeled surface melt for the Mittivakkat Glacier for (a) 1999/2000, (b) 2000/01, (c) 2001/02, (d) 2002/03, and (e) 2003/04. Data are unavailable after 15 Aug 2004.

15 822 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 7 TABLE 8. Water balance elements: adjusted precipitation (P), modeled evaporation and sublimation (ET), modeled runoff (R), observed storage ( S), and balance discrepancy (Error) ( ) for the Mittivakkat Glacier (Sep Aug) from 1999/2000 to 2003/04. Precipitation from rain and snow (P) Evaporation and sublimation (ET) Runoff (R) from snow/glacier melt and rain * Storage ( S) Balance discrepancy (Error) ( ) 1999/ / / / / Average * The runoff does not include englacial and subglacial melting. where P is the precipitation input from snow and rain (and possible condensation); ET is evaporation and sublimation; R is runoff throughout the entire period of flow; S is a change in mass balance resulting from changes in glacier storage, and snowpack storage (including local snow redistribution and snow transport from nearby catchments). Storage also includes changes in supraglacial storage (lakes, pond, channels, etc.), englacier storage (pond and water table), and subglacier storage (cavities and lakes), which we did not account for in the model simulations. Here is the water balance discrepancy (error). The error term should be 0 (or small) if the major components (P, ET, R, and S) have been determined accurately. Table 8 presents the water balance elements [Eq. (5)]: P, ET, R, S, and for the Mittivakkat Glacier (September to August) from 1999 to 2004, showing an annual average adjusted precipitation of 1491 mm w.eq. yr 1, a modeled evaporation and sublimation of 260 mm w.eq. yr 1, a modeled melt (runoff) of 1983 mm w.eq. yr 1, a modeled change in storage of 616 mm w.eq. yr 1, and a calculated water balance discrepancy ( ) of 136 mm w.eq. yr 1 as a residual term [Eq. (5)]. Previous arctic studies (Bøggild 2004; Killingtveit 2004) showed that glaciers have a dominant influence on the water balance compared to nonglaciered areas, often producing surplus of melting and runoff exceeding the precipitation. For the Mittivakkat Glacier, the negative storage indicates a glacier recession for the period, with an average glacier melt contribution of 616 mm w.eq. yr 1 ( ) and a total runoff of 1983 mm w.eq. yr Summary and conclusions A physically based snow-evolution modeling system (SnowModel) that accounts for the evolution of snow accumulation, distribution, sublimation, and melt was used to describe the variations in snow distribution and surface melt over a 17.6 km 2 arctic East Greenland glacier. This glacier area includes strong alpine topographic characteristics ranging from 200 to above 1000 m ASL at its highest peaks. During mid- September to late May, about 65% 85% of all precipitation falls as snow. The wind patterns around topography characteristics (ridge and peaks) allow significant wind redistribution of snow. High wind speeds in the area are generally coincident with high relative humidity and, therefore, snow cover returned to the atmosphere by sublimation played a relatively small role in the glacier water/mass balance budget. During approximately late May to mid-september, surface melt (snow and glacier melt) occurs, characterized by an increasing number of melt days with decreasing elevation and with quite variable daily average glacier melt rates. Our original SnowModel simulations significantly underestimated the end-of-winter SWE on the glacier compared with the observations, and we concluded that this was due to underestimated winter precipitation measured at Station Nunatak. To correct this deficiency we developed and presented a methodology that iteratively adjusts the Station Nunatak SWE precipitation observations until the simulated end-of-winter Mittivakkat Glacier SWE depth matched (within 1%) the observed winter mass balance observations. A byproduct of this approach was the SWE winter precipitation distribution on the glacier. This methodology (calibration) was done for three winter periods and tested against two others. SnowModel was modified for the glacier simulations by 1) adding a glacier class (with the associated landcover characteristics) and 2) implementing the required energy balance calculations to simulate glacier-ice melt after the winter s snow cover had melted away. By applying these adjustments and glacier features to the model, and merging the observations and model simulations, we have calculated the net winter, net summer, and net mass balances for the glacier. This research has quantified the interrelationships