Topographic controls on the surface energy balance of a high Arctic valley glacier

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2005jf000426, 2006 Topographic controls on the surface energy balance of a high Arctic valley glacier Neil S. Arnold, 1 W. Gareth Rees, 1 Andrew J. Hodson, 2 and Jack Kohler 3 Received 18 October 2005; revised 12 January 2006; accepted 17 February 2006; published 27 May [1] This paper presents the results of a distributed, two-dimensional surface energy balance model used to investigate the spatial and temporal variations in the surface energy balance of Midre Lovénbreen, a small valley glacier in northwest Spitsbergen, Svalbard, over the summer of We utilize high-resolution airborne lidar data to derive a digital elevation model of the glacier and surrounding topography, on which a surface energy balance is computed, driven by meteorological data obtained from a meteorological station located on the glacier and a synoptic station maintained at the nearby Ny-Ålesund research base. Given the high-resolution topographic data, we focus particularly on whether the long duration of sunshine at high latitudes compensates for the higher solar zenith angles on the season-long energy balance and whether shading by the surrounding topography plus glacier surface slope and aspect play an increased role in the patterns of solar radiation receipt (and hence melt) over the glacier surface. The model results are validated using a combination of mass balance data from the glacier, measured surface lowering at the glacier meteorological station, and by comparing a derived energy balance component from the model with a measured energy flux. Overall, the model performance is very good. Glacier topography is found to play a fundamental role in determining the surface energy balance; topographic shading, slope, and aspect and correction of the surface albedo for high solar zenith angles are found to play a crucial role in determining spatial patterns of surface energy balance and therefore melt. Citation: Arnold, N. S., W. G. Rees, A. J. Hodson, and J. Kohler (2006), Topographic controls on the surface energy balance of a high Arctic valley glacier, J. Geophys. Res., 111,, doi: /2005jf Introduction [2] Together with winter snow accumulation, the overall determinant of the mass balance of a glacier or ice sheet at middle and high latitudes is the surface energy balance, especially in the summer months. If the surface energy balance is positive, the surface will warm, and if it reaches 0 C, any excess energy will result in melting. Although a wide variation in the types of models used to understand glacier melt rates exist, ranging from very simple empirical relationships between meteorological variables and melt [e.g., Willis et al., 1993] through degree day approaches [e.g., Laumann and Reeh, 1993; Braithwaite and Zhang, 2000] and zero- or one-dimensional (centerline) energy balance studies [e.g., Braithwaite and Olesen, 1990; Munro, 1990; Oerlemans, 1993], it is generally acknowledged that only fully two-dimensional approaches can capture the complexity in spatial (and temporal) patterns of the surface energy balance, and therefore in melt rates and ultimately 1 Scott Polar Research Institute, University of Cambridge, Cambridge, UK. 2 Department of Geography, University of Sheffield, Sheffield, UK. 3 Norwegian Polar Institute, Polar Environmental Centre, Tromsø, Norway. Copyright 2006 by the American Geophysical Union /06/2005JF mass balance [e.g., Munro and Young, 1982; Arnold et al., 1996; Hock and Noetzli, 1997; Brock et al., 2000a; Klok and Oerlemans, 2002]. Distributed energy balance models of both mid and high-latitude glaciers have generally found that net shortwave radiation is the dominant component in the summer surface energy balance, accounting for up to 99% of the energy available at the surface [Arendt, 1999], although figures of around 75% are perhaps more typical [e.g., Greuell and Smeets, 2001; Oerlemans and Klok, 2002]. Incoming solar radiation is strongly affected by both the topography of the glacier surface itself, through the interactions between solar geometry and the surface slope and aspect, which determine the incident angle of direct solar radiation, and by any surrounding higher terrain, which will control shading patterns over the glacier (affecting direct solar radiation), and which will also affect the proportion of the sky hemisphere visible from any point on the glacier, which will affect the amount of diffuse ( sky ) radiation received. These effects are likely to be larger in the high Arctic compared with lower latitudes, due to the relatively high solar zenith angles which could increase shading of a glacier surface by the surrounding terrain; slope and aspect may also play a more important relative role in determining the incident angle of solar radiation to the glacier surface, although this effect may be tempered by the long period of 24 hour daylight at very high latitudes. 1of15

2 [3] All distributed energy balance models, by their nature, have the potential to evaluate the importance of topography on the patterns of solar energy receipt. However, the digital elevation models (DEMs) used by such studies are typically based on interpolated map, ground survey or air photography data, and so are inherently smoothed by the interpolation process; small-scale (perhaps under 100 m horizontal scale) topographic features will typically be absent from such DEMs. In this study, however, we use a DEM derived from high-resolution airborne lidar data, which does not need interpolation (except for a very small area of the upper basin affected by cloud, see below), and which therefore preserves such small scale features, and their impact on the subtle local variations in slope and aspect over the glacier surface. In this study we investigate in particular whether the long duration of sunshine compensates for the higher solar zenith angles on the overall surface energy balance; and whether shading by the surrounding topography plus slope and aspect play an increased role in the patterns of solar radiation receipt over the glacier surface. 2. Study Site and Data Collection [4] Midre Lovénbreen is a small (6 km 2 ) valley glacier in the Kongsfjord area of northwest Spitsbergen, Svalbard (Figure 1) which flows generally northward from the interior of the southern side of Kongsfjord onto the coastal plain. The glacier tongue is predominantly north facing, with a pronounced bend at around 300 to 350 m above sea level (asl) into a predominantly east facing upper basin. The glacier is also fed by two tributary glaciers on the eastern side. The main body of the glacier has an elevation range from 50 m asl at the snout to 500 m at the headwall. Annual mass balance has been measured by the Norwegian Polar Institute (NPI) at a network of stakes (Figure 1) on the glacier surface since 1968; the glacier snout has undergone rapid retreat of over 1000 m during the 20th century, and has lost approximately 10,000,000 m 3 of ice [Hagen et al., 2003]. [5] Data requirements for the model are a DEM of the catchment; start-of-summer water equivalent snow depth, and hourly meteorological data. The model also needs empirical parameterizations or measurements for the surface roughness and surface albedo. The primary model runs were made using meteorological and snow depth data from 2000, with meteorological data from 8 May 2000 to 5 September [6] The DEM used in this study was derived from airborne lidar data obtained during the summer of The data were collected at a variable spatial resolution (depending on the elevation of the aircraft above the ground) of between 0.7 and 1.5 m; these data were converted into the 20 m spatial resolution DEM used in this study by taking the mean of all measured elevations within each 20 m grid cell as the height of that cell. A very small section of the upper glacier, close to the headwall, was obscured by cloud; these data were filled using linear interpolation from the nearest available cells with data. A more detailed discussion of the lidar imagery, and the DEM, is given by Arnold et al. [2006]; in particular, the RMS error in the lidar height measurements varies from 0.05 m on Figure 1. Location map for Midre Lovénbreen, with contours based on the 20 m spatial resolution DEM derived from airborne lidar data. Bold numbers denote NPI stake numbers. the upper glacier to 0.1 to 0.15 m on the lower glacier; the RMS error in the horizontal positions of the measurements is >0.025 m. The DEM used in this study is therefore almost completely uninterpolated; instead, it is based on accurate height measurements made in almost every DEM grid cell. Small-scale (less than 100 m) topographic features are completely preserved, and their impact on slope and aspect can be calculated. Although these data postdate the main model runs, the change in surface elevation in three years is likely to be less than 2 m, even at the snout. This is supported by surveys made using a differential GPS in July 2005 (N. Arnold and W. G. Rees, unpublished data, 2005), which showed surface elevation changes of less than 1 m across the glacier. [7] Snow depth data were measured at 29 points distributed over the glacier surface on 14 April 2000, using an avalanche probe marked indelibly at 1 cm intervals, and located by GPS (Figure 1). Given the spatial autocorrelation of snow depth over glaciated surfaces [Arnold and Rees, 2003], the depth at each of these sites was estimated by taking five measurements (arranged as the five spots on a die), separated by 50 m between the centre measurement and the four corners. The mean of the five measurements was taken as the snow depth in the area. This was then regressed against elevation, slope and aspect (calculated from the mean value for the four DEM cells nearest the centre measurement). Only slope and elevation were signif- 2of15

3 Figure 2. Meteorological parameters recorded from 8 May 2000 to 5 September (a) Air temperature, (b) precipitation, (c) global shortwave radiation, and (d) downward longwave radiation. icant at 95% confidence, yielding an empirical relationship for snow depth in m (D s ): D s ¼ 0:9436 þ 0:00166E 0:016Z 0 where E is the elevation in m above sea level of the DEM cell, and Z 0 is the DEM surface slope, in degrees from horizontal. [8] These data were then converted to water equivalent (D swe ) by multiplying by the snow density measured at 5 snow pits dug on the centerline of the glacier. These showed no consistent relationship with any terrain parameter, so the mean snow density of 331 kg m 3 was used. [9] The main source of meteorological data was an automatic weather station located on the glacier at NPI stake 2 (hereafter referred to as the GWS) at an elevation of 125 m (Figure 1). Measurements consisted of air temperature and relative humidity (made with a Campbell Scientific (CS) CS500 probe); wind speed (CS RM Young combined sensor anemometer); global radiation (CS LI200X pyranometer); and net all-wave radiation (CS Q-7.1 radiometer). A CS SR50 ultrasonic ranger was used to measure the changing elevation of the glacier surface, and an Institute of Hydrology ARG100 tipping bucket rain gauge was used to measure liquid precipitation. These data were supplemented with data collected at a synoptic weather station (SWS) maintained by the Alfred Wegener Institute at Ny-Ålesund, approximately 5 km from the glacier [Koenig- Langlo and Marx, 1997]. We use the measured downward longwave radiation, and the measured diffuse component of solar radiation from this station in the model, plus the measured direct beam solar radiation for validation. Air temperature, precipitation, and global shortwave radiation measured at the GWS, plus downward longwave radiation (measured at the SWS) are shown in Figure was an unusually cool summer; the maximum recorded temperature for 2000 during the period of the model run was C, and the mean temperature was 1.18 C, compared with the mean ð1þ for the equivalent periods from 1997 to 2003 of 2.14 C. The latter part of the summer (after around day 180, the end of June) was typically overcast, with a reduction in the global shortwave radiation compared with earlier periods, and generally higher downward longwave radiation. Significant precipitation events occurred around days 180 and 184, days , days , days , days , and days The events around day 190 and day 200 in particular seem to have been associated with the passage of midlatitude depressions; for the latter event, the warmest temperatures of the year occur at this time, plus very low solar radiation amounts but increased downward longwave radiation. The other precipitation events are associated with cold temperatures, and snowfall at higher elevations. [10] Albedo was measured using a Kipp and Zonen CM7B albedometer at the 29 snow depth measurement locations in spring 2000, at the same time as the snow depth measurements, plus at a network of 75 points between 9 and 14 July 1999, which also included snow depth measurements at the points where snow was present. The empirical relationships for ice and snow albedo derived from these measurements are given below. [11] Data for model validation were the measurements of summer mass balance made by the NPI at a network of centre line stakes on the glacier [Hagen et al., 2003], the measurements of surface height change from the ultrasonic ranger located at the GWS; and the net all-wave radiation measurements from the GWS. [12] For the mass balance data, winter balance is obtained from snow depth soundings, stake height measurements, and snow density measurements. The work is carried out at the end of the accumulation period, usually in May. Stake positions are controlled geodetically every year, when possible. The summer balance is obtained directly by comparing measurements of exposed stake heights made in spring and fall. The latter work is usually done at the end of the ablation period (typically in September). 3. Energy Balance Model [13] The model is based on that used by Arnold et al. [1996], and subsequently developed by Brock et al. [2000a, 2000b] and Arnold [2005]. The model assumes that there are four main components of the total surface energy balance (G); net shortwave (solar) radiation (Q*); net longwave (terrestrial) radiation (L*); sensible turbulent heat (S); and latent turbulent heat (T). In addition to these, the model also calculates the conductive flux from the surface into the body of the glacier. These five components are calculated for each grid cell of the DEM every hour of the melt season using the measured meteorological data and calculated solar altitude and azimuth Solar Radiation [14] Short wave radiation is generally acknowledged to be the most important of these, especially for temperate glaciers, [e.g., Munro and Young, 1982; Klok and Oerlemans, 2002], and is treated in the most detail. [15] The downward instantaneous flux of direct and diffuse solar radiation in each grid cell (Q 0 i) is calculated as follows. The model assumes that the measured global 3of15

4 incoming shortwave (Q 0 ) radiation data from the GWS is representative of the whole catchment. For each DEM grid cell, however, this initial value is then modified depending on the local circumstances at each cell. For each time step for each cell, we first determine if the cell is shaded by the surrounding topography, using the method of Arnold et al. [1996]. If a cell is in Sun, we assume that both direct and diffuse radiation reach the cell. [16] The incoming direct (i.e., in Sun) component (Q 0 idir) for each grid cell is calculated from the measured direct radiation at the GWS (Q 0 dir), which is assumed to be equal to the incoming global radiation at the GWS (Q 0 ) minus the diffuse component at the SWS (Q 0 dif). This value is then modified by the solar zenith angle and azimuth (calculated using standard astronomical theory [e.g., Walraven, 1978], and the slope and aspect of the glacier in each DEM grid cell: Q 0 idir ¼ Q0 n½ sin Z cos Z0 þ cos Z sin Z 0 cosða A 0 ÞŠ ð2þ where Q 0 n is the direct solar radiation received by a surface normal to the solar beam, given by: Q 0 n ¼ Q0 dir = sin Z; ð3þ and where Z is the angle of the Sun above the horizon, and A is the solar azimuth, defined as degrees away from due south, positive to the west of due south, and A 0 is the azimuth of the surface slope, again in degrees away from due south, positive to the west. Q 0 idir is set to zero for shaded cells. [17] This value is then supplemented by the diffuse component. Again, we assume that the measured diffuse radiation (Q 0 dif) at the SWS is representative of the whole catchment. For each cell receiving diffuse radiation, the measured value is multiplied by a sky view factor (f s )to account for the variation in the proportion of the sky visible from any given grid cell. This was calculated for each grid cell of the DEM as the finite sum: f s ¼ X360 j¼0 cos 2 q Dj 360 ; ð4þ where q is the local horizon angle at a given azimuth, j. Experimentation with Dj showed that very little change in the calculated values of f s occurred for Dj <12 ; this value was therefore adopted in all model runs. [18] This value then is supplemented by reflected radiation from the surrounding topography: Q 0 t ¼ a tð1 f s ÞQ 0 ; ð5þ where a t is the mean albedo of the surrounding visible areas (including both glaciated and ice free areas). For this study, a value of 0.25 was used; given the high values of f s over the glacier, the model is not very sensitive to the value of a t chosen. This then gives a final value for the diffuse radiation received by a given cell (Q 0 idif): Q 0 idif ¼ f s Q 0 dif þ Q 0 t : ð6þ [19] The net solar radiation flux (Q*) for each grid cell for each time step is then calculated from Q ¼ ð1 a Þ Q 0 idir þ Q0 idif ; ð7þ where a is the DEM cell albedo. A large variety of schemes to calculate the albedo of glacier surfaces are available in the literature, ranging from quite complex schemes requiring knowledge of parameters such as snow grain size, water content and the like, to simpler, more empirical schemes based on factors such as snow depth, age, or accumulated melt (see Brock et al. [2000b] for a review). For this study, measurements of albedo, snow depth and melt showed that snow depth was the only statistically significant control on the albedo of snow covered surfaces (a s ) for Midre Lovénbreen in 2000, giving a best fit exponential relationship between snow albedo and depth: a s ¼ 0:743 ð0:371 ða i 0:372ÞÞexp D swe ; ð8þ 0:4501 where a i is the albedo of the underlying ice surface, modeled with a simple empirical relationship with elevation, again based on data collected in summer 2000: E a i ¼ 0:4474 0:5878 exp : ð9þ 65:0057 If a DEM cell contains snow at a given time step, equation (8) is used; if all the snow has melted, equation 9 is used to calculate albedo. Given the high solar zenith angles typical in high Arctic regions (and the variance in incident angle of solar radiation due to the changing slope and aspect of the glacier surface), we then add an albedo correction (a c ) factor to a s or a i to give the overall surface albedo for that cell at the time period in question, in order to allow for the nonisotropic reflectance properties of snow and ice surfaces. This correction factor is taken from Lefebre et al. [2003]: 3 a c ¼ 0:16 1; ð1 þ 4 cos zþ ð10þ where z is the solar zenith angle at the DEM cell in question (allowing for the solar altitude and azimuth, and the slope and azimuth of the cell itself). a c is applied to the direct component only Longwave Radiation, Ice Temperature, and Heat Flux Into the Body of the Glacier [20] The net longwave radiation is the sum of the radiation emitted by the glacier surface and that received from the sky and the surrounding terrain. Unlike the previous versions of the model, which assumed a constant surface temperature of 0 C (and hence a constant outgoing longwave flux) we allow the surface temperature of the glacier to vary. We use a simple scheme, based on that of Klok and Oerlemans [2002]. This assumes a simple two-layer subsurface scheme. Energy input at the surface is the calculated total energy flux (using the surface temperature from the 4of15

5 Table 1. Model Parameter Values Parameter Symbol Value Units Specific heat capacity c 2097 J kg 1 Thermal diffusivity (ice) k m 2 s 1 Thermal diffusivity (snow) k m 2 s 1 Snow density r 331 kg m 3 Ice density r 900 kg m 3 Surface layer depth d s 0.22 m Subsurface layer depth d m Stefan-Boltzmann constant s Wm 2 K 4 Ice roughness z m Snow roughness z m previous time step). This warms the surface layer as follows: DT s Dt ð ¼ k T 2 T s Þ=Dz d s þ G crd s ; ð11þ where T s is the temperature of the surface layer, T 2 the temperature of the second layer, d s is the depth of the surface layer, k is the thermal diffusivity, c the specific heat capacity, r the density (see Table 1 for model parameter values) and G is the sum of Q*, L* (from the previous time step), S and T. The first term here represents the heat lost from the surface layer into the underlying layer, which depends on the temperature difference between the two layers; the second term is the surface heat flux. Values of k and r for ice and snow are used as appropriate (Table 1); if the snow depth is less than the depth of the surface layer, we use a weighted average between ice depth and snow depth to calculate the values, following Klok and Oerlemans [2002]. The heat loss from the surface layer forms the input to the subsurface layer, which itself loses heat into the main body of the glacier: DT 2 Dt ð ¼ k T 3 T 2 Þ=Dz ðt 2 T s Þ=Dz ; ð12þ d 2 where d 2 is the depth of the second layer, and T 3 is the temperature of the main body of the glacier. This is set to the average annual air temperature from the synoptic weather station at Ny-Ålesund, corrected for the local surface elevation using a lapse rate of 6.5 C km 1. This scheme neglects the refreezing of meltwater below the surface, but as discussed below, seems to reproduce the main features of the observed surface temperature. [21] From the calculated surface temperature, the outgoing longwave radiation flux (L out ) is calculated by: L out ¼ st 4 s ; ð13þ where s is the Stefan-Boltzmann constant. [22] Incoming longwave radiation from the portion of the sky (L insky ) visible at each DEM cell depends on a wide range of atmospheric factors, including air temperature, pressure, humidity and cloud cover. Although temperature, pressure and humidity data are available, the lack of cloud cover data in this study makes estimating L insky difficult with conventional empirical relationships. Instead, we use the measured incoming longwave radiation (L 0 d) at the synoptic weather station, corrected to allow for the changing elevation of the glacier surface, then corrected for the sky view factor for each grid cell: L insky ¼ L 0 dc f s ð14þ where L 0 dc is the elevation-corrected incoming longwave radiation. To correct for elevation, we use the Stefan- Boltzmann equation and L 0 d to calculate the effective emissive temperature of the sky; we then correct this with the standard elevation lapse rate and then recalculate L 0 d using the corrected temperature. Over the elevation range of the glacier, this leads to a maximum variation in L 0 d of W m 2. This range is consistent with the difference between the lowland and mountain sites (with a vertical separation of 1277 m) used by Iziomon et al. [2003] in a long-term study of longwave sky irradiance; they report a mean reduction in longwave radiation of 11% at the mountain site compared with the lowland site for two years of hourly data. [23] Longwave radiation from the sky is then supplemented by the longwave radiation emitted by the surrounding terrain (L interr ) visible from a grid cell: L interr¼ ð 1 fs ÞsTterr 4 ; ð15þ where T terr is the average surface temperature of the terrain visible from the grid cell. Calculation of this directly would be very difficult, and would require a separate energy balance model for the various terrain types within the catchment (such as rock or moraine), as well as the proportion of glaciated versus nonglaciated terrain visible from every grid cell. Greuell et al. [1997] estimate this proportion by eye for each of their six study sites on the Pasterze, Austria, and use their calculated glacier surface temperature for the glaciated portion. For the unglaciated proportion, they set the rock temperature to the measured air temperature at night, but allow global radiation to warm the rock during the day, with an empirical relationship between global radiation and rock temperature. This approach is not practical for this study, given its distributed nature. Instead, we adopt a simpler approach, and set T terr to the elevation-corrected air temperature in the grid cell recorded by the GWS for each time step. Although this will be affected by the local microclimate over the glaciated surface, it seems an acceptable compromise given the very small proportion of 5of15

6 the total energy balance supplied by terrain-emitted longwave radiation, given the high values of f s on Midre Lovénbreen, and as found by Greuell et al. [1997]. Although the rock surface may be warmer than the air temperature (and the glacier surface) on sunny days, the glacier surface is always limited to a maximum temperature of 0 C, so the air temperature would seem an acceptable mean value for the whole of the visible terrain from any given grid cell. During cold periods, the ice surface temperature (and presumably the temperature of the unglaciated terrain) follows the air temperature quite closely. [24] The total net longwave flux (L*) is then L* ¼ L insky þ L interr L out : ð16þ 3.3. Turbulent Heat Fluxes [25] To calculate the turbulent fluxes, the measured air temperature at the weather station is used together with an assumed lapse rate of 6.5 C km 1 to calculate the air temperature in each grid cell. This is then used to calculate the difference in temperature between the glacier surface and the air temperature in each DEM grid cell needed for the turbulent flux calculations. Relative humidity and wind speed are assumed to be constant over the catchment, and a lapse rate of 10 kpa km 1 is used to calculate air pressure over each DEM cell. From these input data, an iterative scheme is used to calculate the Obukhov length scale (following Munro [1990] and as used by Brock et al. [2000a] and Arnold [2005]), and from this the sensible and latent heat fluxes. These equations require the surface roughness length (z 0 ) scale to be known; we use the mean values for snow and ice from Arnold and Rees [2003]. All model parameter values are summarized in Table Precipitation [26] Measured precipitation at the GWS is assumed to be representative of the whole catchment, and is assumed to fall as snow in any grid cell in which the lapse rate corrected air temperature below a threshold temperature in the hour in which the precipitation was recorded. A variety of threshold temperatures for solid or liquid precipitation have been used in other studies, including 2 C [e.g., Oerlemans and Hoogendoorn, 1989; Arnold et al., 1996], 1.5 C [e.g., Hock and Noetzli, 1997], and 0 C [e.g., Greuell and Oerlemans, 1986; Greuell and Smeets, 2001]. In this study, model results were found to be not sensitive to this value over a range of 0 2 C, and we therefore adopted a value of 1 C. Snowfall is added to the snow depth (if any) in that cell; given the small size of the glacier, and low precipitation rates, liquid precipitation is assumed to run off without affecting the energy balance. [27] The four energy flux components, as calculated for each DEM cell for each hour, are added together to give the total energy flux at the surface. If this is positive, greater than the heat loss from the surface layer into the body of the glacier, and the surface temperature in the previous time step is positive, the energy input minus the energy loss is used to generate melt. If the previous temperature is below the melting point, the energy input minus energy loss is used to warm the surface layer. If more energy is available compared with that needed to bring the surface to the melting point, any excess is then used to generate melt. If the surface energy flux is negative, or smaller than the heat loss into the underlying layer, no melt occurs and the surface layer cools. [28] In order to assess the impact of topography on the surface energy balance, the standard model run includes all the topographic correction factors discussed above. In order to determine the relative importance of these factors, we also performed separate model runs without correcting for shading by the surrounding topography; without correcting for horizon obstruction (i.e., with f s of 1); without correcting for DEM cell slope and aspect; and without an albedo correction for solar zenith angle. 4. Results 4.1. Model Validation [29] The results of the model are validated using summer mass balance measurements made at a series of centerline stakes on the glacier, made by the Norwegian Polar Institute [Hagen et al., 2003] and by measurements of surface lowering on the glacier made at the GWS with the ultrasonic ranger. In addition, measurements of net allwave radiation at the GWS were available, which were not used as input for the model. We therefore also compare these data with the modeled net all-wave radiation in the DEM cell containing the GWS. Modeled net all-wave fluxes were calculated as the topographically corrected measured incoming shortwave radiation, minus the reflected shortwave radiation derived from this value and the surface albedo for the time period in question, plus the measured incoming longwave radiation, corrected for the sky view factor for the DEM cell with the GWS, minus the calculated outgoing longwave flux, based on the surface temperature in the DEM cell containing the GWS at the time period in question. This therefore tests the shortwave radiation calculations within the model, the longwave calculations, and through the influence of surface temperature on outgoing longwave radiation, the surface temperature calculations. [30] Measured summer mass balance (with estimated errors (J. Kohler, personal communication, 2005)) at the NPI stake network and the modeled melt in the equivalent DEM cell for summer 2000 are shown in Figure 3. The correlation coefficient between the modeled and measured values is (P = <0.01), although the small number of data points should be borne in mind. The highly nonlinear melt/elevation relationship in the measured data is captured well, with the exception of the values for stakes 7 and 8, at 316 m and 348 m, where the model overpredicts for stake 7, and underpredicts for stake 8. The observed melt for stake 7 in particular, however, does seem anomalous when compared with the general trend in these data for The reduction of the gradient with elevation of summer melt between 200 m and 350 m asl also occurs in the mass balance measurements for (J. Kohler, unpublished data, ), which suggests it is probably a topographic effect, rather than an effect due to the climate or winter snow-depth distribution in any given year. This will be discussed further below. 6of15

7 Figure 3. Modeled and observed summer mass balance for the period 8 May to 5 September 2000 at NPI stakes Error bars on the stakes are ±0.05 m, except at stakes 9 and 10, where the error bars are ±0.03 m (J. Kohler, personal communication, 2005). [31] The raw data from the ultrasonic ranger unfortunately show several problems. In particular, there are a large number of cases where the surface seems to rise rather than fall when no snowfall is reported. The possible reasons for this are discussed in more detail by Willis et al. [2002], but briefly it could be due to the thermal contraction of the mast due to cooling; errors in the estimation of distance due to air temperature variations between the instrument and the glacier surface; or refreezing of water or water vapor on the surface. Willis et al. show that the main cause of the negative surface lowering is likely to be the formation of this crust of frozen melt or vapor at the surface, and that the actual thickness of the crust is likely to be much less than the reported rise in the surface due to air pockets beneath the thin frozen crust. These problems are manifested in the raw data by large, short-term variations which appear as alternate positive/negative values in the hourly data; this gives rise to a standard deviation of the measurements of m, compared with a mean value of m. As the main aim of this paper is to discuss the season-long variations in the surface energy balance components rather than the hourly at-a-point melt variations, we therefore compare the modeled surface lowering (calculated from the modeled melt rate, corrected for the surface density (snow or ice, as appropriate)) with the observed surface lowering using a 13 point moving average to reduce these problems. Modeled versus measured surface lowering are shown in Figure 4. Noise problems in the measured data are very severe during the early part of the model run (before approximately day 173); modeled melt rates are generally zero during this time, however. For the bulk of the melt season itself, however, from approximately day 173 to day 220, when the measured time series ends, the agreement between the model and measured values is very good. For this period, r = The Nash-Sutcliffe measure of model efficiency (N) is for this period. The model captures the snowfall events on day 184 and ; the observed snowfall event on day 210, however, appears as rainfall in the model, with almost zero surface lowering due to the lack of melt (due to low temperatures and low solar radiation totals), rather than a surface lowering due to snowfall. [32] Figure 5 shows the cumulative surface lowering with the cumulative modeled surface lowering for the period between days 173 and 220, when reliable ultrasonic ranger data are available. In general, the lines run essentially parallel, although the modeled values are typically higher by 50 mm for the middle of the run. The main periods of divergence, however, are concentrated around day , and day (after the snowfall event), suggesting slight overprediction of melt during these times. The two series then reconverge after day 210, suggesting slight underprediction toward the end of the model run. [33] Finally, we compare the measured net all wave radiation with the calculated all-wave radiation. As the model assumes that measured diffuse radiation at the Figure 4. Modeled and observed surface lowering for summer 2000 at the GWS. Data are smoothed with a 13-point moving average. Figure 5. Modeled and observed cumulative surface lowering for summer 2000 at the GWS. 7of15

8 Figure 6. Modeled and observed net all-wave radiation for summer 2000 at the GWS. Note the Y axis ranges are different for Figures 6 (top) and 6 (bottom). SWS can be applied across the entire glacier, we first correlated this value plus the measured direct beam radiation (corrected for solar geometry) at the SWS, with the measured downward shortwave flux at the GWS to test this assumption. This gave an r value of (for 2948 data points), suggesting that this assumption is justified. Simple observations of typical cloudy sky conditions at Ny-Ålesund also support this assumption; the commonest thick cloud is of low-level stratus type, covering most of the sky. [34] As for the ultrasonic ranger data, some problems with the measured net radiation data occurred. Condensation was observed within the radiometer domes on occasion, and ice sometimes formed on the base of the lower dome. Both these problems would affect the measured values, and cannot be adequately corrected for, as for the bulk of the season the GWS ran unattended. Nevertheless, these data allow us to assess the overall performance of the radiative flux calculations including the impact of slope, aspect and shading, the overall albedo parameterization, and the albedo correction at high solar zenith angles on shortwave energy flux, and the surface temperature calculations, which affect the net longwave energy flux. Figure 6 shows the measured and modeled net all-wave radiation during the model run. Statistical agreement is very good; r = , N = for the whole period for which net radiation measurements at the GWS are available. An important part of the measured record which the model successfully simulates are the large negative values of net radiation around midnight, especially in the period before approximately day 180. These values were initially hard to understand, and could not be simulated; one possibility we considered, given the position of the GWS on the north facing tongue of the glacier, was that direct solar radiation at very high solar zenith angles (around midnight) was entering the downward facing sensor of the net all-wave radiometer, which would give falsely large negative values. However, the addition of the albedo correction scheme for solar zenith angles (equation (10)) allowed the model to successfully simulate these values, due to the modeled increase in albedo of the glacier surface at very high solar zenith angles which increased the upward shortwave component in the net radiation. The effect of this correction on the overall energy balance of the glacier is explored further below Impact of Topography on the Surface Energy Balance [35] Figure 7a shows the spatial distribution of the season-long melt over the whole glacier. The general trend for decreasing melt at higher elevations is very obvious, as is the reduction in the elevation gradient of melt between around 200 m to 350 m asl. Although it is hidden somewhat by the contour intervals, the roughness of the contours, particularly between 0.5 and 1 m w.e. of melt, shows that there is considerable smaller-scale complexity in the calculated melt. This is shown well in the detailed pattern in the inset area of Figure 7a, shown in Figure 7b. This reveals a high degree of spatial complexity (due largely to the preservation of small-scale topographic features in the DEM, see below), with localized high and low melt totals, especially in the central part of the inset. Here, the line of Figure 7. Summer modeled melt totals from 8 May to 5 September. (a) Whole glacier. The black rectangle denotes the area shown in Figure 7b. (b) Detail for inset area in Figure 7a. Numbers are NPI stake numbers. 8of15

9 Figure 8. Spatial distribution of the total modeled energy balance components for 8 May to 5 September (a) Sensible heat, (b) latent heat, (c) shortwave radiation, and (d) longwave radiation. stakes follows a distinct tongue of high melt rates, trending up glacier, with an axis somewhat to the east of the stake line. This would seem to be the cause of the flattening of the summer mass balance/elevation gradient in the stake data. There is also a distinct local minimum just to the west of stake 6 in particular, however. Figure 7 highlights the difficulty in capturing the spatial complexity of mass balance over an entire glacier with stake measurements; a change in perhaps only m in the stake position (simply due to the initial, in-the-field choice of stake location) could result in a change in the observed melt of over ±5 cm (around 10%) of the observed melt in some locations, and therefore a very different apparent mass balance profile. Averaged over several years of data, this would lead to a significant error in the estimated mass balance. Controls on this spatial complexity will be discussed further below. [36] Figure 8 shows the spatial distribution of the four main surface energy balance components. As would be expected, the primary control on the spatial variability is elevation; with the exception of the longwave radiation flux, which becomes less negative at higher elevations, the other components generally decrease at higher elevations. There is again, however, considerable spatial complexity in the flux distributions, both across glacier and with elevation. [37] In the case of the turbulent fluxes, the overall decrease with elevation is primarily due to the decrease in temperature with elevation, coupled with the lower roughness of snow as opposed to ice surfaces, which in general reduces turbulent fluxes at higher elevation. However, in the immediate vicinity of the snout, both sensible and latent heating decrease with elevation; both also display a distinct zone of reduced fluxes in the mid/upper basin (around 350 m to 400 m asl in the case of sensible heat, and 300 m to 350 m in the case of latent heat) before the fluxes rise, then fall again, at higher elevations. The negative season-long values for latent heat suggest that the glacier will also lose mass through sublimation; however, given the very small total fluxes (10 to 30 MJ), the total amount of mass loss will typically be <10 mm w.e., and so not significant for the total mass balance. For shortwave radiation, the decrease is due to the increase in albedo at higher elevations (due to the deeper and more persistent snow cover), and a decrease in available solar radiation (see below). The decrease is not uniform, however; a wide band of similar shortwave fluxes occurs between around 200 m and 350 m, with a local maximum around 300 m. [38] The increase in longwave flux at higher elevations seems to be primarily caused by the lower surface temperatures and the longer period when the surface is below 0 C at higher elevations on the glacier, reducing the upward longwave flux; this more than compensates for the reduction in incoming longwave radiation at higher elevations. [39] Figure 8 also shows the overall dominance of the radiative fluxes over the turbulent fluxes. The shortwave flux is around an order of magnitude greater than the sensible heating, and the longwave flux a factor of 5 10 larger than the latent heat flux. This would seem to indicate that in the first instance, the long hours of daylight more than compensate for the higher solar zenith angles at very high latitudes, leading to the dominance of shortwave radiation, as has been found in studies of temperate glaciers 9of15

10 Figure 9. Derived topographic factors for Midre Lovénbreen. (a) Glacier slope, in degrees. (b) Glacier aspect, degrees clockwise from due north. (c) Total hours of potential Sun between 8 May and 5 September. (d) Proportion of sky hemisphere visible from glacier surface. [e.g., Arnold et al., 1996; Klok and Oerlemans, 2002]. The low values for turbulent fluxes are due in large part to the low average summer temperatures during 2000 as discussed above. This is compounded by the generally smooth surfaces found on Midre Lovénbreen [Arnold and Rees, 2003] Derived Topographic Parameters [40] In order to understand the spatial complexity in the energy balance components, we need to understand how topography can influence the fluxes. Only the modeled radiative fluxes are affected a priori by topographic effects other than elevation. Longwave fluxes are affected by the proportion of the sky hemisphere visible from any part of the glacier (and its inverse, the proportion of the ground hemisphere visible), but shortwave radiation receipts are affected by the slope and aspect of the surface, shading by the surrounding topography, (which together with solar geometry affect the amount of direct solar radiation available over the surface), and by the proportion of the sky hemisphere visible from any given location (which affects the availability of diffuse radiation). Figure 9 shows the main topographic controls on the potential receipt of solar radiation; the slope and aspect of the glacier surface; shading by any surrounding topography (expressed as the total number of hours in which the Sun could be visible from a given grid cell, out of a total of 2948 hours for the modeled time period), and the proportion of the sky hemisphere visible from any location. [41] The bulk of the glacier shows relatively shallow slopes (4 7 ) (Figure 9a). The immediate area above the snout shows slopes of 7 15, and some slopes in the small, high elevation tributaries are also quite steep. The main area of the glacier, however, exhibits several broad areas with slopes below 4. There is a distinct ridge of higher slopes (7 9 ) running up glacier on the northern side of the main upper basin. [42] Most of the glacier is oriented just to the east of due north (Figure 9b). A few areas on the main tongue of the glacier are oriented slightly to the west of due north, with the tributary glaciers on the east facing approximately northwest, and the main upper basin facing east to northeast; the steeper ridge in this area faces east southeast. [43] Shading generally increases with elevation (Figure 9c), but there are strong shading effects toward the sidewalls of the valley. The area below around 200 m shows little shading, however; these areas are quite open due to the lower elevation of the surrounding topography, and the extension of the tongue onto the almost flat coastal plain. The main upper basin is quite shaded by the high surrounding topography; by contrast, the eastern tributaries show little shading in places, due to their higher elevation relative to the surrounding terrain. [44] The proportion of the sky visible over the surface (Figure 9d) is somewhat similar to the pattern of shading; the tongue has the highest proportion, with the proportion generally decreasing up glacier, and toward the valley sides. The impact of the valley sides is generally more symmetrical across the glacier, however, than is the case for shading. [45] Together with solar geometry and measured solar radiation, these factors then allow us to calculate the pattern 10 of 15

11 Figure 10. Total modeled incoming solar radiation from 8 May to 5 September of total incoming solar radiation (ISR) available over the glacier surface (that is, Q 0 idir + Q 0 idif). Together with the albedo, this will be the primary control on the net shortwave energy flux (and given the dominance of this term in the overall energy balance, on the overall pattern of melt). Figure 10 shows that while ISR generally decreases with elevation, due to the general increase in shading and decrease in sky view, the ISR shows a very high degree of spatial complexity. The change in slope, aspect and sky view across the glacier snout gives rise to a distinct cross-glacier gradient in ISR below around 125 m, with the eastern snout having higher ISR than the west. Above this, a tongue of quite high radiation availability (1800 MJ m 2 ) extends up the central part of the glacier from the snout to around 375 m. There are pronounced local minima toward the valley sides at around 200 m on the eastern edge, and around 275 m on the west; there is also a local maximum extending across the glacier at around 325 m. In the upper basin, however, the area of high radiation splits, with a maximum along the southeast facing area of steeper slopes on the north side of the upper glacier, and a broader zone on the southern side Sensitivity to Topographic Controls [46] Figure 11 shows the differences between the ISR for runs with no slope and aspect (Figure 11a), no shading (Figure 11b), and no sky view variation (Figure 11c). Slope and aspect, and shading, have the largest impact, with both affecting the incoming radiation by up to 200 MJ. Sky view has a much lower effect; up to around 60 MJ. Shading and sky view both serve to reduce incoming radiation in the standard run, with generally increasing effects at higher altitudes, due to the more enclosed nature of the basin. Reductions are also observed near the valley sides. [47] Allowing for no slope or aspect can have a positive or negative impact, however, depending on how the slope and Figure 11. Difference in incoming shortwave radiation from the standard run for runs with (a) no slope or aspect, (b) no shading, and (c) no sky view factor. Positive values denote standard run is lower. (d) Values averaged by 10 m elevation band. 11 of 15

12 Figure 12. Total mass balance components for the period 8 May to 5 September 2000, averaged by 10 m elevation bands. (a) Sensible heat flux, (b) latent heat flux, (c) shortwave radiative flux, and (d) longwave radiative flux. aspect interact with solar geometry. Near the snout, for instance, incoming radiation increases on the western side but decreases on the eastern side in the run without slope and aspect. This seems to be due to the changing aspect; the eastern snout faces more eastward, orienting it toward the Sun in the early to mid morning, when incoming radiation totals are higher, due to the higher solar angles. By contrast, the western snout faces almost due north, orienting it toward the midnight Sun, when radiation totals are lower. The southeast facing areas on the upper glacier also show lower incoming radiation totals in the run with no slope or aspect for the same reason, as they are oriented toward the late morning Sun. [48] To a first approximation, then, shading plus the sky view factor are largely responsible for the variation in solar radiation with elevation; slope and aspect are largely responsible for the cross-glacier variations at any given elevation. This is summarized in Figure 11d, which shows the mean incoming radiation total, averaged over 10 m elevation bands across the glacier surface for the four runs. Removing the effect of shading leads to a more uniform receipt with elevation; removing slope and aspect increases the variation with elevation, showing that overall, slope and aspect increase radiation receipts at higher elevations, due to the more easterly orientation of the upper basin, and because cross-glacier variations are cancelled out by the averaging process. Removing the effect of the sky view factor also leads to a somewhat flatter gradient. [49] The complex patterns in the turbulent and longwave fluxes (Figure 8) suggest that topography (presumably though its impact on solar radiation) can also affect these fluxes. Figure 12 shows the impact of removing the effects of slope and aspect, shading, sky view, and the albedo correction factor, on the four energy balance components, averaged by 10 m elevation bands, and Table 2 summarizes the impact of the four factors, averaged over the whole glacier. It is immediately obvious that these derived topographic factors affect all the energy balance components, not just the radiative fluxes. Overall, the albedo correction factor has the single largest effect. Removing this factor increases the net shortwave radiative flux by 21.6%, and the overall melt by 26.6%, the equivalent of an extra 0.16 m of melt over the entire glacier surface, or m 3 of melt. Neglecting the shading correction increases Q* by 6.4%, and the overall melt by 5.3%, the equivalent of an extra 0.03 m of melt. Neglecting the sky view correction decreases Q* by 0.2%, and the total melt by 3.1%; neglecting slope and aspect Table 2. Percentage Changes in the Four Energy Balance Components Along With Percent Change in Total Melt for the Four Runs Without Topographic Correction Factors S T Q* L* Total Melt No slope/aspect No shading No sky view No albedo correction of 15