Distribution of snow accumulation on the Svartisen ice cap, Norway, assessed by a model of orographic precipitation

Transcription

1 HYDROLOGICAL PROCESSES Hydrol. Process. 22, (28) Published online 13 June 28 in Wiley InterScience ( DOI: 1.12/hyp.773 Distribution of snow accumulation on the Svartisen ice cap, Norway, assessed by a model of orographic precipitation T. V. Schuler, 1,2 * P. Crochet, 3 R. Hock, 4,5 M. Jackson, 2 I. Barstad 6 and T. Jóhannesson 3 1 Department of Geosciences, University of Oslo, Norway 2 Norwegian Water Resources and Energy Directorate (NVE), Norway 3 Icelandic Meteorological Office, Iceland 4 Geophysical Institute, University of Alaska, Fairbanks, USA 5 Department of Earth Sciences, Uppsala University, Sweden 6 Bjerknes Centre for Climate Research, Bergen, Norway Abstract: We apply a linear model of orographic precipitation (LT model) to estimate snow accumulation on the western Svartisen ice cap (22 km 2 ) in northern Norway. This model combines 3D airflow dynamics with simple parameterizations of cloud physics. The model is forced by large-scale atmospheric input variables taken from the ECMWF Re-analysis (ERA-4) of the European Center for Medium Range Weather Forecast (ECMWF), and the model parameters are kept constant for the entire simulation period, after optimization. The domain covers a 12 ð 125 km area surrounding the ice cap. The model is run using a 1-km resolution digital elevation model, and 6-h time steps over the period from 1958 to 22. Precipitation data from surrounding meteorological stations and winter glacier mass balance measurements on several glaciers within the region are used to evaluate the model results. Precipitation obtained from the LT model agrees well with observations from precipitation gauges and there is also fair agreement between model results and specific winter mass balance observations on the ice cap if these are corrected for winter rain. The LT model reproduces well the spatial pattern of winter accumulation across the ice cap as well as the area-averaged winter mass balances of several other glaciers in the region. This indicates that it is a useful tool in providing high-resolution, deterministic estimates of precipitation in complex terrain as required for distributed hydrological and/or glacier mass balance modelling of unmeasured areas. Copyright 28 John Wiley & Sons, Ltd. KEY WORDS snow distribution; orographic precipitation; downscaling; glacier mass balance; modelling; ERA-4 Received 1 November 27; Accepted 2 April 28 INTRODUCTION The accurate assessment of precipitation is a crucial component in any attempt to model glacier mass balance and runoff from glacierized catchments. However, modelling precipitation in high mountain areas is challenging due to large spatial variability of precipitation and sparsity of data especially at higher elevations (e.g. Daly et al., 1994). In addition, the quality of precipitation-gauge observations may be affected by wind-induced undercatch, in particular when precipitation falls as snow. Low spatial coverage and a bias towards valley observations render traditional interpolation methods problematic in complex terrain, although combining these methods with regression models (e.g. Guan et al., 25) captures at least some of the effects of topography. At the other end of the spectrum in terms of complexity, high-resolution physically based numerical models, for example the MM5 model (Grell et al., 1995), provide a promising tool for spatially distributed precipitation estimates. However, the large computational requirements currently limit the scope of applications of such models. To our knowledge, high-resolution precipitation estimates * Correspondence to: T. V. Schuler, Department Geosciences, University of Oslo, Norway. t.v.schuler@geo.uio.no derived from physically based numerical models are not yet available in Norway. In glacier mass balance and runoff modelling, precipitation is often extrapolated using a linear increase of precipitation with elevation and a threshold temperature to discriminate between snow and rainfall. The gradient of precipitation with elevation, threshold temperature and under-catch correction are treated as model parameters that are tuned to fit available observations (e.g. Hock and Holmgren, 25; Schuler et al., 25; de Woul et al., 26). This simple scheme ignores all factors other than elevation that contribute to spatial variability in precipitation. Elaborating on the analyses by Taurisano et al. (27), Schuler et al. (27) modelled snow accumulation across the Austfonna ice cap in Svalbard based on multiple regression relationships that included the spatial coordinates as predictors to account for the considerable horizontal accumulation gradients observed across the ice cap. A similar approach involving vertical and horizontal gradients was used by Jóhannesson et al. (26) for modelling precipitation on the Hofsjökull ice cap and by Bergström et al. (27) on the Langjökull and Vatnajökull ice caps in Iceland. However, such empiricism restricts the transferability of these types of models to unmeasured regions due to the need for site-specific calibration based on detailed measurements. In addition, the Copyright 28 John Wiley & Sons, Ltd.

2 SNOW ACCUMULATION ON THE SVARTISEN ICE CAP 3999 spatial variability is described by only a few independent variables using statistical relationships rather than by physical principles. The validity of such models may also be questioned since model parameters may change due to the inter-annual variability in both precipitation patterns as well as precipitation gradients. Crochet et al. (27) applied an approach of intermediate complexity to estimate precipitation in Iceland. They dynamically down-scaled precipitation from coarse resolution European Center for Medium Range Weather Forecast (ECMWF) Re-Analysis (ERA-4) data (Kållberg et al., 24; Uppala et al., 25) over the period to a 1-km resolution grid for the whole of Iceland using the linear model of orographic precipitation (hereafter referred to as the LT model) proposed by Smith and Barstad (24). They obtained good agreement with observations from both meteorological stations and glacier mass-balance data at time scales of months to seasons, and a variable agreement on a daily time scale. The purpose of this study is to follow an approach similar to Crochet et al. (27) and estimate a time series of gridded precipitation using the LT model on the Svartisen ice cap (368 km 2 ) in northern Norway where glacier meltwater is used for hydropower (Kennett et al., 1997). We run the model at a horizontal resolution of 1 km for 1958 to 22 using atmospheric input variables from ERA-4, available at 6-h time steps. The results are compared to precipitation-gauge data for the surrounding area and glacier mass balance measurements. Finally, we produce a snow accumulation index map for the entire ice cap, which describes mean spatial variability in terms of deviation from the mean for each glacierized pixel of the 1 ð 1kmgrid. MODEL DESCRIPTION The LT model is an extension of the well-known upslope precipitation model (Smith, 1979). A detailed description is given by Smith and Barstad (24) and a description of its application by Barstad and Smith (25). The model calculates precipitation resulting from forced orographic lifting of an air mass crossing an obstacle (mountain ridge). The air mass is assumed to be saturated and to pass over the obstacle without blocking. On the windward side of the mountain, cloud water resulting from condensation is advected downstream, while changing into falling hydrometeors. On the leeward side, the condensed water and hydrometeors evaporate or precipitate, depending on conditions. According to the model formulation, the spatial pattern of precipitation is determined by the width and shape of the mountain ridge, the ambient conditions (temperature, wind speed, influx of water vapour, and stability of the air column), the airflow dynamics (variation of vertical and horizontal velocities with altitude), and the competition between the microphysical processes controlling the rate of condensation and conversion of cloud water into hydrometeors, and their fallout time to the ground. Nevertheless, the LT model represents a computationally efficient tool to estimate precipitation at fine temporal and horizontal scales, over long periods of time. However, the model is not appropriate when the atmosphere is unstable, and does not accommodate situations where the air mass is blocked by the mountain ridge. The model consists of a pair of steady-state equations describing vertically integrated advection of cloud water and hydrometeors (e.g. raindrops or snowflakes): Dq c ³ U Ðrq c D S q c / c 1 Dt Dq h ³ U Ðrq h D q c / c q h / f, 2 Dt where (q c, q h ) are vertically integrated cloud water and hydrometeor density. S is the rate of transformation to cloud water (source term; as a response to lifting over terrain) and U D Ux C Vy is the wind vector. The time required to transform cloud water into hydrometeors ( c ) and to further precipitate this to the ground ( f ) controls the amount of precipitation. The term (q h / f )represents the final sink when concatenating Equations (1) and (2) and corresponds to the precipitation rate (P). By spectral decomposition (indicated by (^)) and algebraic manipulation, the following transfer function relating the Fourier-transform of the terrain elevation (Oh) tothe precipitation field is obtained: C w is Oh(k, l) OP(k, l) D 3 [1 imh w ][1 C ist f ][1 C ist c ] Here, D Uk C Vl is the intrinsic frequency, m D [(( Nm 2 2)/ 2) ( / k 2 C l 2)] 1 2 signifies the vertical wave number, H w D R v T 2 / L is the vertical height scale of water vapour in the atmosphere, k and l are the horizontal components of the wave number and C w D v m / is a sensitivity lifting factor, equal to unity for moist neutral air. Further, v is the density of vapour at the surface, m and denote the moist adiabatic and the environmental lapse rate, respectively. R v is the gas constant for vapour, T the surface temperature, and L is the latent heat of vapourization. In contrast to the upslope model (Smith, 1979), the source term S is expanded to include airflow dynamics with flow both over and around terrain obstacles that depends among other things on the relative width of the obstacles. This new source term is equal to the numerator over the first term in brackets in the denominator in Equation (3), cf. Barstad et al. (27). The micro-physics (i.e. descriptions of conversion and fallout) are represented by the two latter brackets in the denominator. The orographic enhancement is obtained by transforming OP back to the space domain, and adding the large-scale background precipitation P 1 to yield the down-scaled precipitation field P LT x, y {( ) P LT x, y D max OP k, l e i kxcly dkdl } C P 1, 4 Copyright 28 John Wiley & Sons, Ltd. Hydrol. Process. 22, (28) DOI: 1.12/hyp

3 4 T. V. SCHULER ET AL. The background precipitation P 1 represents largescale frontal and convective precipitation, i.e. contributions other than from orographic enhancement. In order to determine Equation (3), temperature, stability of the air N m and a representative wind in the moist layer are needed. For a moist airflow with strong winds (i.e. large values of U, V), the influx of water vapour is large. An air column stable against vertical movements (i.e. small values of N m ) will produce less condensation because a smaller amount of the air column will be lifted. Slow micro-physics (i.e. long time scales c and f ) or narrow mountains will bring available condensate into the lee side where it is subjected to evaporation, reducing the amount of precipitation. Thereby, the model is capable of simulating an asymmetric precipitation pattern across a topographic obstacle with less precipitation on the lee side than on the stoss side. STUDY AREA AND OBSERVATIONS The model domain covers an area of 12 ð 125 km 2 in northern Norway (Figure 1). The area is characterized by complex topography including the western (22 km 2 ) and eastern (148 km 2 ) Svartisen ice cap, steep mountains, numerous fjords and valleys. Elevation ranges from sea level to about 16 m a.s.l. We focus on the western Svartisen ice cap since long-term records of glacier mass balance are available for this area. In the context of hydropower exploitation, the Norwegian Water Resources and Energy Directorate (NVE) conducts annual glacier mass balance measurements (e.g. Kjøllmoen et al., 26) on two outlet glaciers of western Svartisen: Engabreen (¾38 km 2, 197 present) and Storglombreen (¾62 km 2, , 2 25). Mass balance measurements have also been conducted on three smaller glaciers nearby: Høgtuvbreen (¾2Ð6 km 2, ), Svartisheibreen (¾5Ð4 km 2, ) and Trollbergdalsbreen (¾1Ð5 km 2, and ) (Figure 1). For Engabreen and Storglombreen, detailed snow depth data are available for and Each May, snow depth was measured at about 2 points along profiles on Storglombreen and Engabreen, mainly at elevations above 9 m a.s.l. These data are converted into water equivalent considering snow densities derived from several snow pits and represent specific winter mass balances. For comparison with model results, the data were resampled to the 1-km modelling grid by averaging all measurements within one grid cell for each year. In addition, we also use mean specific (i.e. area-averaged) glacier winter mass balances of all glaciers in the model domain with available mass balance measurements. These quantities are reported annually by NVE (e.g. Kjøllmoen et al., 26) and are derived from interpolating point values and integrating these over the entire glacier. (a) B6 B6 G L H S T Bodø VI Glomfjord Leiråmo Høgtuvbreen Svartisheibreen Trollbergdalsbreen (b) G L area met stations H S T Elevation (m a.s.l.) Area/number % Figure 1. (a) Model domain (12 ð 125 km) including the western and eastern Svartisen ice caps and other glaciers (black outlines). Colours denote the modelled annual precipitation (mm a 1 ) averaged over the reference period , while contour lines represent elevations with 2 m spacing. White dots mark the locations of meteorological stations. Black dots refer to the grid cells where winter snow accumulation data are available. The locations of the individual glaciers are outlined in black. The insert shows the location within Norway; (b) Hypsometric distribution (elevation-area) using 2 m elevation bands (black), and percentage of meteorological stations per elevation band (grey). Labels on the y-axis show the minimum elevation of each band. Low elevations are overrepresented by the measurements and ¾58% of the land area lies above the highest meteorological station (38 m a.s.l.) Copyright 28 John Wiley & Sons, Ltd. Hydrol. Process. 22, (28) DOI: 1.12/hyp

4 SNOW ACCUMULATION ON THE SVARTISEN ICE CAP 41 Monthly precipitation data are available from 14 weather stations operated by the Norwegian Meteorological Office (Grønligrotten, Nord-Rana, Grønfjelldal, Nord-Solvær/Sleneset, Lurøy, Myken, Glomfjord, Reipå, Sundsfjord, Beiarn-Naustvold, Leiråmo, Børnupvatn, Oldereid Kraftstasjon and Bodø VI; Figure 1). The data were extracted from but do not include corrections for gauge under-catch. However, losses are assumed to be small since the stations are generally well protected from wind effects (O.E. Tveito, Norwegian Meteorological Institute personal communication). The meteorological stations at Glomfjord (39 m a.s.l.) and Leiråmo (217 m a.s.l.) have been in operation since 1916 and 1972, respectively. They are situated along a west-east profile stretching from the coast over the mountain range, and are taken as representative for locations of orographic enhancement (long-term annual precipitation at Glomfjord: 269 mm) and for the rainshadow on the lee side (long-term annual precipitation at Leiråmo: 124 mm). These stations thus aid in a detailed assessment of model performance. To obtain more insight into the actual variation of the moist stability frequency N m during the model period, we evaluated radiosonde data from the meteorological station Bodø (11 m a.s.l.), located about 6 km north of Svartisen. Radiosondes have been launched from Bodø twice a day (h and 12h UTC) since 1957, providing information about the vertical temperature and humidity structure of the atmosphere. We used these data to roughly estimate an average moist stability frequency N m between 3 m a.s.l. according to N m 2 D g T m, 5 where and m are the environmental and the moist adiabatic lapse rates, respectively; T is an estimated average of the absolute potential temperature of the considered layer, and g is acceleration due to gravity; was directly derived from the data, and m was calculated using a standard formula (e.g. Stone and Carlson, 1979). METHODOLOGY Model input data The input data for the LT model were obtained from ERA-4 (namely, the background precipitation, nearsurface air temperature, humidity and wind vectors). ERA-4 is a global dataset for the atmosphere on a so-called Gaussian-grid, which is regular in longitude (1Ð125 ) and almost regular in latitude (¾1Ð121 ). In the vertical, the atmosphere is discretized into 6 layers called sigma-levels. These layers follow the earth s surface in the boundary layer, and become surfaces of constant pressure in the upper stratosphere. The ERA-4 period ranges from September 1957 to August 22. The dataset was produced by assimilating ground and satellite data using a numerical forecast model (e.g. Kållberg et al., 24; Uppala et al., 25). The input data to the LT model were extracted on a regular Ð5 ð Ð5 grid using a bilinear interpolation, for each 6-h time step. Since the model assumes saturated conditions, specific humidity was also extracted and used for deciding when to run the model. Orographic enhancement of precipitation depends strongly on low-level moisture and low-level wind speed (e.g. Hill et al., 1981). The wind, temperature and specific humidity were extracted from the sigma-level 53, assumed to represent low-level conditions above the terrain for the region of interest. For surface pressure of 113 hpa, the pressure at sigma-level 53 is 949 hpa. Air temperature and wind vectors were averaged over the model domain, whereas specific humidity was converted into relative humidity (RH) using standard formulae (e.g. Wallace and Hobbs, 26), and then averaged over a 1 buffer region in the respective upwind direction. Since precipitation is not among the meteorological variables reanalysed in ERA-4, we obtained 12-h precipitation directly from the forecast fields, started at : and 12 : UTC from the reanalysed state of the atmosphere. Since the forecasts are affected by spin-up effects, the initial 12-h of each run were not considered, and 12-h precipitation estimates were obtained from the second half of each 24-h forecast. The ERA-4 precipitation was used in the LT model as background precipitation caused by synoptic-scale lifting (Equation (4)), and is derived by adding convective and large-scale precipitation. Crochet (27) applied a cut-off precipitation threshold of Ð3 mm/12-h to ERA-4 to account for the fact that in Iceland, ERA-4 estimates light precipitation too often. This is probably caused by shortcomings of the ECMWF-model and its coarse resolution, and hence, ERA-4 overestimates the frequency of occurrence of precipitation (FOP). We evaluated the FOP of ERA-4 precipitation using observed FOPs from daily precipitation data for Glomfjord and Leiråmo. It is found that adopting the same threshold value reduced the systematic biases between modelled and observed FOPs. When this threshold is applied, the mean bias between observed FOP and ERA-4 decreases from 16Ð9% to Ð4% for Glomfjord, and from 24Ð3% to 9Ð2% for Leiråmo. Glomfjord is exposed to the main incoming weather systems while Leiråmo is located in the lee. The remaining negative bias in FOP at Leiråmo probably indicates a lack of drying in the lee of mountains in relation to the coarse resolution of the ERA-4 orography. We tested a range of different threshold values and found Ð3 mm/12-h was close to optimum. Hence, ERA-4 precipitation less than Ð3 mm/12-h was set to zero for the LT modelling. The procedure adopted to run the LT model is based on (a) the assumption of saturation, and (b) on results from Hill et al. (1981), who studied the dependence of orographic rain in Wales on meteorological conditions upwind. They observed that the enhancement depends on the existence of high RH and wind speed at low level, and on the background precipitation rate. Periods of enhanced rain over the hills were associated with the passage of pre-existing areas of precipitation, and orographic Copyright 28 John Wiley & Sons, Ltd. Hydrol. Process. 22, (28) DOI: 1.12/hyp

5 42 T. V. SCHULER ET AL. enhancement seldom occurred in the absence of background precipitation. We thus ran the LT model when the averaged upstream RH (at sigma-level 53) exceeded 9%, assuming that saturation was obtained during orographic lifting. We further assumed that orographic precipitation is formed in association with a pre-existing area of precipitation defined by ERA-4. Outside the ERA-4 precipitation field, we did not consider orographic enhancement. This implies that we did not consider orographic enhancement when RH 9% but assumed the ERA-4 background precipitation, if non-zero, without further treatment. This simple procedure was used by Crochet et al. (27), and proved satisfactory. Other diagnostic precipitation models (e.g. Sinclair, 1994; Kunz and Kottmeier, 26) have also used RH thresholds to reduce or prevent precipitation when unsaturated conditions prevailed upstream. The topography on which the ERA-4 dataset is based has coarse spatial resolution and is heavily smoothed. For instance, our study region is represented by six grid points reaching a maximum elevation of only a few hundred metres while the actual topography exceeds 16 m. Nevertheless, the ERA-4 precipitation includes some orographic enhancement based on its assumed orography. To eliminate this orographic component from the ERA-4 precipitation, we applied the LT model to the ERA-4 topography and subtracted the resulting orographic precipitation from the ERA-4 background precipitation. Negative values were set to zero. This procedure ensures a clear separation of background precipitation (provided by the corrected ERA-4 precipitation) and orographic precipitation (obtained from running the LT model). Driven by the adjusted ERA-4 precipitation, the LT model was applied on a digital elevation model of 1 km resolution which was derived from the official Norwegian 25 m digital elevation model (Statens Kartverk). This data set reproduces much of the complexity of the actual topography in the study area. Our methodology is illustrated in Figure 2. To avoid unwanted effects of the spectral decomposition at the boundaries of the domain, the 12 ð 125 km grid is wrapped into the centre of an outer domain consisting of 256 ð 256 grid cells. Model calibration and validation The LT model has three model parameters (the moist stability frequency N m, the conversion and fallout times c and f ), which were not explicitly estimated at each time step but obtained by optimization, i.e. varying their Data ERA-4 topography (.5 ) LT-Model topography DEM_1 (1km) ERA-4 data (T, U, V, RH) P ERA4 (.5 ) Preprocessing Interpolation to 1km resolution --> DEM_2 Average over domain (T, U, V) or over upwind region (RH) Interpolation to 1km resolution --> BGP Step 1 Run LTmodel on DEM_2 --> OP_1 (simulate orographic effect inherent in ERA4) BGP_adj = max(bgp OP_1,) Step 2 Run LTmodel on DEM_1 --> OP_2 P = max(bgp_adj + OP_2,) Postprocessing P-fields: monthly, seasonal, annual P-time series: for selected points Figure 2. Workflow of the applied methodology. DEM D Digital Elevation Model; T, U, V, RH D meteorological variables as defined in the text; P ERA4 D precipitation from ERA-4; BGP( adj) D adjusted background precipitation; OP D orographic precipitation Copyright 28 John Wiley & Sons, Ltd. Hydrol. Process. 22, (28) DOI: 1.12/hyp

6 SNOW ACCUMULATION ON THE SVARTISEN ICE CAP 43 values until good agreement was obtained between model results and available observations over the calibration period. The optimum values of N m, c and f,werethen kept constant throughout the entire modelling period, and additionally, we assumed c D f (Smith and Barstad, 24; Barstad and Smith, 25; Crochet et al., 27). According to Smith and Evans (27) the behaviour of the model is determined by the total time delay ( c C f ), whereas the partition between c and f is less important. The model was manually calibrated using winter totals of precipitation-gauge data from 14 stations (Figure 1) and specific winter mass balance measurements for the seven years ( and 2 22) when detailed snow depth measurements for much of the western Svartisen ice cap are available. We selected these datasets for model calibration since they provide good spatial coverage across the domain, and also over the entire elevation range. The latter is insufficiently represented by the precipitation-gauge data alone (Figure 1(b)). To obtain consistency between the two datasets, we derived an estimate of winter precipitation from the winter mass balance data because winter mass balance data are likely to underestimate winter precipitation, because they only refer to snow precipitation, not to precipitation that falls as rain and runs off directly. In addition, any snow that melts and runs off or re-freezes below the last summer surface (i.e. internal accumulation) is not included in the glacier observation. We considered the neglect of rain to be most significant, especially during mild winters with frequent and prolonged periods of abovefreezing air temperatures. We compute rainfall using the precipitation routine of a distributed mass balance model which has previously been calibrated and applied to Engabreen, an outlet glacier of Svartisen (Schuler et al., 25). Using the model parameters obtained in that study, we calculated the amount of rainfall in each grid cell containing winter mass balance measurements according to the distribution of precipitation and temperature by the mass balance model. Thus, obtained winter rain is added to the measured water equivalent of the snow cover to yield an estimate of winter precipitation. We did not, however, correct the winter balance for the effect of ablation during the winter season, nor subtract rain that re-freezes in the snowpack and is therefore included in the winter balance measurement. For model validation, we used data from different periods or from different locations than those used for calibration. The records of mean specific winter mass balances of Høgtuvbreen, Svartisheibreen and Trollbergdalsbreen were not used for calibrating the model and were therefore used for model validation. The long-term record of mean specific winter mass balance (197 22) for Engabreen, and the precipitation-gauge data outside the calibration period (i.e and ) were also used for model validation. Table I presents an overview of the different datasets used for calibrating and validating the model. RESULTS AND DISCUSSION Model calibration Model performance was evaluated by comparing the simulated winter precipitation with winter precipitation from precipitation-gauge data and winter precipitation derived from glacier mass balance measurements. For this purpose, model results were extracted at locations corresponding to those of the observations and integrated over a fixed period from 1 October to 31 May for the years and Instead of using a formal and automatic calibration procedure, the parameter values were changed manually until good agreement between model results and observations was evaluated by visual inspection. Good agreement was judged in terms of: (a) maximizing the quality of agreement between modelled and measured spatial patterns precipitation (correlation); (b) minimizing the bias indicative of systematic deviations; and (c) maximizing the root mean square error of the model by reducing the scatter about the observations. During calibration, N m and were changed over a range of plausible values in steps of Ð1 s 1 and 2 s, respectively. The parameter values thus obtained are N m D Ð4 s 1 and D 12 s. Crochet et al. (27) found the same values for Iceland. However, they did not account for the orographic effect inherent in the ERA-4 precipitation and hence, the parameter values are not directly comparable. Jóhannesson et al. (27) re-estimated precipitation in Iceland using the LT model and accounted for the orographic effect inherent in the ERA-4 precipitation. They report slightly different values, with N m D Ð3 s 1 and D 15 s. Figure 3 shows a scatter plot of modelled versus observed values during the calibration period using the optimized parameter set. Also presented are the corresponding values extracted directly from the ERA-4 precipitation fields to illustrate the effect achieved by the downscaling procedure. Due to the coarse resolution of the topography used in ERA-4, it considerably underestimates winter precipitation, especially at higher elevation where it deviates by up to a factor of four from the observations. Comparing the performance of ERA-4 and the LT model, we find that using the LT model not only reduces the bias (161 mm compared to 1884 mm) but also decreases the standard deviation of the residuals (47 mm versus 97 mm). The figure shows that the LT model downscales the rather featureless and underestimated ERA-4 precipitation field to produce a precipitation field with similar magnitude and range of variation as the observations. However, the scatter is large in some years, i.e. in 1986 and In Figure 4 we present mean values of the temperature and rain precipitation as derived from the mass balance model (Schuler et al., 25) for the elevation band m a.s.l., which accounts for roughly 35% of the surface area of the ice cap. This corroborates the observations that winter rainfall events even at the highest elevations of Svartisen are not uncommon. The Copyright 28 John Wiley & Sons, Ltd. Hydrol. Process. 22, (28) DOI: 1.12/hyp

7 44 T. V. SCHULER ET AL. Table I. Datasets used for model calibration and validation Calibration Validation Precipitation-gauge data Specific mass balance 14 meteorological stations, winter months (Oct May): , 2 22 Engabreen C Storglombreen 14 meteorological stations, all months , , 2 22 Mean specific mass balance Engabreen (197 22) Høgtuvbreen ( ) Svartisheibreen ( ) Trollbergdalsbreen ( , ) Modelled (mm) Observed (mm) Figure 3. Winter precipitation obtained by the LT model (1 October 31 May) versus winter precipitation derived from precipitation-gauge data (crosses) and from glacier mass balance measurements on western Svartisen ice cap (stars) for the years and 2 22 (calibration period). The dots represent the corresponding values derived from interpolating ERA-4 data. The specific mass balances are arithmetic averages of all point measurements per grid cell where measurements were made to which rain computed by a distributed glacier mass balance model was added to obtain winter precipitation amount of winter rain that was added to the observed snow water equivalent was largest for the two warmest years, 2 and 22 (Figure 4). The performance of the model is lowest for the years 1986 and Part of these deviations may be explained by the different intervals to which the measured mass balance and the modelled precipitation in the various years correspond. The mass balance measurements are based on the stratigraphic method where mass balance is measured relative to the preceding summer surface. Hence, these values refer to a budget period of unknown length. In contrast, modelled winter precipitation was integrated over a fixed period (1 October 31 May). Any differences in duration between these two measures might contribute to a mismatch between model results and observations. In fact, the field reports (e.g. Kjøllmoen et al., 26) and meteorological data indicate that in 1986 and 1987 the accumulation period started before 1 October. Therefore, the measured snow accumulation may be larger than the winter precipitation accumulated over a fixed period (1 October 31 May). Sensitivity tests confirmed that, in general, an increase in the moist stability frequency N m leadstolessorographic enhancement, and thus, to reduced precipitation differences between the stoss and lee sides of topographic obstacles. Changes in have an effect similar to changes in N m, such that longer (or larger N m ) results in too little precipitation on the windward side and too much on the lee side. These sensitivity tests agree with the results obtained by Smith and Barstad (24) and Barstad and Smith (25). Finally, we investigated the possibility that the variation in model performance for different years is related to shortcomings in the model formulation or application. The misfit could result from significantly different weather patterns (e.g. in terms of moisture flux direction and/or magnitude) that the model is not capable of correctly handling. We found that neither direction nor magnitude of the moisture flux in 1986 and 1987 exhibit significant deviation from other years. The shortcoming of our method might also be related to the use of constant parameter values for N m and although they vary in time, and are different for different weather patterns. Although the seasonally averaged N m obtained from the radiosonde data at Bodø is observed to vary from one year to the next, there is no significant correlation between this variability and the root mean square error of the model results. This suggests that the mismatches between data Rain precipitation (mm) Figure 4. Rain precipitation (grey bars) and mean air temperature computed for the elevation interval m a.s.l. during the winter period October to May for the years and Temperature ( C) Copyright 28 John Wiley & Sons, Ltd. Hydrol. Process. 22, (28) DOI: 1.12/hyp

8 SNOW ACCUMULATION ON THE SVARTISEN ICE CAP 45 (a) Modelled (mm) r 2 =.75 (b) Elevation (m a.s.l.) Observed (mm) Deviation % Figure 5. (a) Modelled versus observed monthly precipitation sums for all 14 stations during the validation period ( , ), including all modelled data for which observations were available. The number of observations varies between stations due to different lengths in operation periods; (b) relative misfit versus elevation for each of the 14 meteorological stations. Deviation indicates the percentage the model overestimates (positive values) or underestimates (negative values) the observed precipitation over the period of operation of each station and model results are predominantly due to other factors, such as inaccuracies when correcting the glacier mass balance data for rain, melting and refreezing, or other modelrelated shortcomings. Nevertheless, the model results are sensitive to changes in N m, and it is possible that shortterm variations of N m may cancel each other out and are not apparent at a seasonal scale. The effect of including transient N m and, instead of using constant values, has not been investigated, but may be a worthwhile approach for future research. Instead of optimizing a temporally constant value, N m could be calculated for each time step, for example, by using vertical distributions of temperature and humidity from ERA-4 (following Durran and Klemp (1982)). Model validation The calibrated LT model was validated by comparing modelled monthly precipitation sums with observations from precipitation gauges of all 14 meteorological stations for all remaining years outside the calibration period. We evaluated the spatio-temporal performance of the LT model by examining modelled versus observed monthly precipitation sums for all 14 meteorological stations (Figure 5). In general, model results correlate well with observations (r 2 D Ð79 for the calibration period and r 2 D Ð75 for the validation period). However, for a few stations, the model systematically over- or underestimates precipitation (Figure 5(a)). Since these deviations do not correlate with elevation (Figure 5(b)) we rule out the possibility that the model systematically misrepresents the orographic effect. In a further test, we compared the LT model performance with the un-scaled ERA-4 performance. Results are shown in Figure 6 for the meteorological station in Glomfjord which has the longest data record of all stations. While the ERA-4 background precipitation significantly underestimates measured precipitation, the LT model reduces this bias considerably although a tendency for some overestimation is evident. The results of the LT model are clearly superior to the un-scaled ERA-4 precipitation, which cannot capture much of the topographic effects due to the coarse resolution of the underlying topography. Specific mean glacier mass balance measurements were used in testing the ability of the LT model to predict precipitation for areas and periods that have not been used for calibration. Figure 7 compares the simulated winter precipitation for the individual glaciers with the available winter mass balance data and with a time series of winter precipitation representing the ERA-4 winter precipitation averaged over the area covered by the four glaciers. ERA4 / LT model (mm) Observed (mm) Figure 6. Observed monthly precipitation (Jan Dec) at Glomfjord (39 m a.s.l.) versus precipitation obtained from the LT model (crosses) and from the ERA-4 data for the grid cell containing Glomfjord (dots) for the validation period ( , ) Copyright 28 John Wiley & Sons, Ltd. Hydrol. Process. 22, (28) DOI: 1.12/hyp

9 46 T. V. SCHULER ET AL. 6 Engabreen r 2 = Winter precip./ winter mass balance (mm) Høgtuvbreen r 2 = Svartisheibreen r 2 = Trollbergdalsbreen r 2 = ERA Calendar year Figure 7. Winter precipitation (October to May) obtained by the LT model averaged over each of the individual glaciers and observed mean specific (area-averaged) winter mass balance (bw) The circles in the top panel mark the years for which specific winter mass balance data at point locations were used to optimize model parameters. The bottom panel shows the winter precipitation directly derived from ERA-4. Note the different scaling of the y-axes In general, the LT model captures the observed temporal variation of winter mass balance at all glaciers (r 2 values >Ð6, Figure 7). The strong covariance between all time series and the ERA-4 data (r 2 D Ð88) is not surprising since the LT model was driven by input from ERA-4. However, despite the relatively good performance in reproducing temporal variations, ERA-4 considerably underestimates the amount of winter precipitation, as noted above (Section Model calibration ). Comparison of LT-modelled winter precipitation and observed winter mass balances show relatively good correspondence for Engabreen and Høgtuvbreen, both with respect to bias and correlation. For Trollbergdalsbreen and Svartisheibreen, the correlation is good but there is a negative bias (i.e. the model underestimates the observations). This may be related to the location of each of these two glaciers in topographic depressions between mountain ridges where preferential snow accumulation by wind drift may be an important contribution to the winter mass balance. Furthermore, these glaciers are relatively small (<1 km 2 ) and represented in our model by only a few grid points. This may indicate that processes which are important at the scale of these glaciers are not resolved by our model. This interpretation is in line with the findings of Crochet et al. (27) that the performance of the LT model degrades somewhat with increasing complexity of the terrain, and that the model may not perform equally well in simulating stoss and leeside precipitation. Simulations of the long-term record of mean specific winter mass balance of Engabreen using the LT model are in good agreement with the mass balance observations, both in terms of the period mean (around 3 mm) as well as the amplitude of year-to-year variations. The high accumulation observed at Engabreen during the end of the 198s and beginning of the 199s is also well captured by the model. This increased accumulation led to an advance of Engabreen, contrary to the behaviour of most other glaciers worldwide (Meier et al., 27). Part of the discrepancy between modelled winter precipitation and winter mass balance may be related to the fact that the mass balance data are not corrected to account for the liquid precipitation on the glacier. Accumulation index map Snow accumulation on glaciers often exhibits a persistent pattern from year-to-year (e.g. Hock and Jensen, 1999; Taurisano et al., 27), and accumulation index maps have often been used to describe this pattern. Such an index map represents a mean spatial pattern of snow distribution and can be used as a distribution template Copyright 28 John Wiley & Sons, Ltd. Hydrol. Process. 22, (28) DOI: 1.12/hyp

10 SNOW ACCUMULATION ON THE SVARTISEN ICE CAP Accumulation index (%) Northing UTM33X (km) Easting UTM33X (km) 7 Figure 8. Mean spatial pattern of winter precipitation (October May) as obtained from the LT model for Values represent the ratio of local precipitation to precipitation averaged over the entire ice cap in %, and are illustrated by shades of grey and red contours (at intervals of 1%). The black contour lines illustrate the topography (at intervals of 5 m). Note that the patterns of accumulation deviate from the distribution of terrain elevation, especially on the eastern side of the ice cap for snow accumulation in distributed modelling, thereby efficiently reducing the computational effort. In doing so, the actual snow distribution for a given time step is obtained either by adding an anomaly to the prescribed mean pattern (e.g. Greve, 1997) or by distributing a point value according to a map of weighting factors (e.g. Schuler et al., 27). This approach provides a simple scheme that is particularly suitable for distributed hydrological or glaciological models that concentrate on processes other than snow distribution, but still require a reliable spatial representation of the snow cover. Accumulation index maps can be derived from densely spaced measurements (e.g. Hock and Jensen, 1999), but these are seldom available. Here, we derived an index map from high-resolution modelling using the LT model. We computed a winter (October May) precipitation index for western Svartisen defined as the percentage of the local pixel value relative to the spatial mean over the ice cap (Figure 8). Values larger than 1% indicate winter precipitation larger than the mean and vice versa. Although there is a general tendency for precipitation to increase with increasing altitude it is obvious that the spatial distribution is more complex. Figure 8 reveals that the maximum precipitation occurs several kilometres WNW from the summit of the ice cap. Also, tracing the precipitation index, for example, along the 12 m a.s.l. contour line (labelled in Figure 8), shows clearly that accumulation on the northwestern slopes of the ice cap is generally higher than on the eastern and southern slopes which are located in the rain-shadow of the mountain range. In contrast, scaling the ERA-4 precipitation directly onto the high-resolution topography using constant precipitation gradients as done in other studies (e.g. Radić and Hock, 26) would not resolve the stoss-leeside asymmetry apparent in Figure 8. CONCLUSIONS We have used a linear theory of orographic precipitation to dynamically down-scale precipitation from ERA-4 to a region surrounding the Svartisen ice cap in northern Norway, over the period The parameters of the model were calibrated such that over a seven-year period, the model performed optimally with respect to both winter precipitation from low elevation precipitation gauges and high elevation glacier mass balance measurements. Having evaluated the un-scaled ERA-4 precipitation, we observed that ERA-4 considerably underestimates winter precipitation at high elevation whereas the precipitation down-scaled using the LT model shows reasonable agreement with the observations. The numerous mass balance measurements allow a detailed assessment of model performance and it was found that the LT model captures well the asymmetric, orographically driven pattern of winter accumulation across the ice cap. The good performance illustrates the advantage of using the LT model since simple downscaling using local scaling factors would not resolve such asymmetry. The model results were validated using data from locations or periods not covered by the calibration, and we found that the model provides a useful tool for estimating the distribution of precipitation in space and time. Based on these findings, an accumulation index map was produced. This index map is useful for diagnostic mass balance modelling replacing elevation-dependent formulations, which do not accurately reproduce the spatial pattern of accumulation. The LT model also reproduced well time series of area-averaged winter mass balance of several glaciers in the region covered by the model. It should be emphasized that these data were not used to optimize the model parameters. The good agreement between modelled winter precipitation Copyright 28 John Wiley & Sons, Ltd. Hydrol. Process. 22, (28) DOI: 1.12/hyp

11 48 T. V. SCHULER ET AL. and measured winter mass balances demonstrates the potential of the LT model to provide high-resolution, deterministic estimates of precipitation over complex terrain where orographic enhancement is important for distributed hydrological and/or glacier mass balance modelling of unmeasured areas. ACKNOWLEDGEMENTS This project is part of the GMES-Polar View project financed by the European Space Agency (ESA) and a contribution to the CES (Climate and Energy Systems) project funded by Nordic Energy Research (NEFP). The ERA-4, radiosonde and precipitation data were provided by the Norwegian Service Centre for Climate Modelling (NoSerC), which is hosted at the Norwegian Meteorological Institute (met.no). The help of Egil Støren with extracting the ERA-4 data is highly appreciated. Further, radiosonde data was acquired through We also acknowledge Hallgeir Elvehøy for pointing out the existence of mass balance data of Høgtuvbreen, Trollbergdalsbreen and Svartisheibreen. Comments by two anonymous reviewers and the scientific editor Gwenn Flowers significantly improved the manuscript. REFERENCES Barstad I, Smith RB. 25. Evaluation of an orographic precipitation model. Journal of Hydrometeorology 6: Barstad I, Grabowski WW, Smolarkiewicz PK. 27. Characteristics of large-scale orographic precipitation. Journal of Hydrology 34: Bergström S, Jóhannesson T, Aðalgeirsdóttir G, Ahlstrøm A, Andreassen LM, Andréasson J, Beldring S, Björnsson H, Carlsson B, Crochet P, de Woul M, Einarsson B, Elvehøy H, Flowers GE, Graham P, Gröndal GO, Guðmundsson S, Hellström SS, Hock R, Holmlund P, Jónsdóttir JF, Pálsson F, Radic V, Reeh N, Roald LA, Rogozova S, Rosberg J, Sigurðsson O, Suomalainen M, Thorsteinsson Th, Vehviläinen B, Veijalainen N. 27. Impacts of climate change on river runoff, glaciers and hydropower in the Nordic area. Joint final report from the CE Hydrological Models and Snow and Ice Groups, Reykjavík, Climate and Energy, Rep. No. 6. Crochet P. 27. A study of regional precipitation trends in Iceland using a high-quality gauge network and ERA-4. Journal of Climate 2: Crochet P, Jóhannesson T, Jónsson T, Sigurðsson O, Björnsson H, Pálsson F, Barstad I. 27. Estimating the spatial distribution of precipitation in Iceland using a linear model of orographic precipitation. Journal of Hydrometeorology 8(6): Daly C, Neilson RP, Phillips DL A statistical-topographic model for mapping climatological precipitation over mountainous terrain. Journal of Applied Meteorology 33: de Woul M, Hock R, Braun M, Thorsteinsson T, Jóhannesson T, Halldórsdóttir S. 26. Firn layer impact on glacial runoff A case study at Hofsjökul, Iceland. Hydrological Processes 2: , DOI:1Ð12/hyp.621. Durran DR, Klemp JB On the effects of moisture on the Brunt-Väisälä frequency. Journal of the Atmospheric Sciences 39: Grell GA, Dudhia J, Stauffer DR A description of the Fifthgeneration Penn State-NCAR Mesoscale Model (MM5). NCAR Tech Note TN 398 CSTR, 122. Greve R Application of a polythermal three-dimensional ice sheet model to the Greenland Ice Sheet: Response to steady-state and transient climate scenarios. Journal of Climate 1(5): Guan H, Wilson JL, Makhnin O. 25. Geostatistical mapping of mountain precipitation incorporating autosearched effects of terrain and climatic characteristics. Journal of Hydrometeorology 6: Hill FF, Browning KA, Bader MJ Radar and raingauge observations of orographic rain over south Wales. Quarterly Journal of the Royal Meteorological Society 17: Hock R, Jensen H Application of Kriging interpolation for glacier mass balance computations. Geografiska Annaler 81 A(4): Hock R, Holmgren B. 25. A distributed energy balance model for complex topography and its application to Storglaciären, Sweden. Journal of Glaciology 51(172): Jóhannesson T, Sigurðsson O, Einarsson B, Thorsteinsson TH. 26. Mass balance modelling of the Hofsjökull ice cap based on data from Reykjavík, National Energy Authority, Report ISBN , OS-26/4. Jóhannesson T, Aðalgeirsdóttir G, Björnsson., Crochet P, Elíasson EB, Guðmundsson S, Jónsdóttir JF, Ólafsson H, Pálsson F, Rögnvaldsson O, Sigurðsson O, Snorrasson A, Grétar O, Sveinsson B, Thorsteinsson T. 27. Effect of climate change on hydrology and hydro-resources in Iceland, Reykjavík, National Energy Authority, Report ISBN , OS-27/11. Kållberg PW, Simmons AJ, Uppala SM, Fuentes M. 24. The ERA-4 archive. Technical Report ERA-4 Project Rep. 17, European Centre for Medium-Range Weather Forecasts: Reading, 35. Kennett M, Rolstad C, Elvehøy H, Ruud E Calculation of drainage divides beneath the Svartisen ice-cap using GIS hydrologic tool. Norsk Geografisk Tidsskrift 51: Kjøllmoen B, Andreassen LM, Engeset RV, Elvehøy H, Jackson M, Giesen RH. 26. Glaciological investigations in Norway 25, NVE Report 2 26, 91. Kunz M, Kottmeier C. 26. Orographic enhancement of precipitation over low mountain ranges. Part I: model formulation and idealized simulations. Journal of Applied Meteorology and Climatology 45: Meier MF, Dyurgerov MB, Rick UK, O Neel S, Pfeffer WT, Andersson RS, Andersson SP, Glazovsky AF. 27. Glaciers dominate eustatic sea-level rise in the 21st century. Science 317: , DOI: 1Ð1126/science Radić V, Hock R. 26. Modeling future glacier mass balance and volume changes using ERA-4 reanalysis and climate models: a sensitivity study at Storglaciären, Sweden. Journal of Geophysical Research 111: F33, DOI:1Ð129/25JF44. Schuler TV, Loe E, Taurisano A, Eiken T, Hagen JO, Kohler J. 27. Calibrating a surface mass balance model for the Austfonna ice cap, Svalbard. Annals of Glaciology 46: Schuler TV, Hock R, Jackson M, Elvehøy H, Braun M, Brown I, Hagen JO. 25. Distributed mass balance and climate sensitivity modelling of Engabreen, Norway. Annals of Glaciology 42: Sinclair MR A diagnostic model for estimating orographic precipitation. Journal of Applied Meteorology 33: Smith RB The influence of mountains on the atmosphere. Advances in Geophysics 21: Smith RB, Barstad I. 24. A linear theory of orographic precipitation. Journal of the Atmospheric Sciences 61: Smith RB, Evans JP. 27. Orographic precipitation and water vapor fractionation over the Southern Andes. Journal of Hydrometeorology 8: Stone PH, Carlson JH Atmospheric lapse rate regimes and their parameterization. Journal of Atmospheric Sciences 36: Taurisano A, Schuler TV, Hagen JO, Eiken T, Loe E, Melvold K, Kohler J. 27. The distribution of snow accumulation across the Austfonna ice cap, Svalbard: direct measurements and modelling. Polar Research 26: Uppala SM, Kallberg PW, Simmons AJ, Andrae U, Bechtold VD, Fiorino M, Gibson JK, Haseler J, Hernandez A, Kelly GA, Li X, Onogi K, Saarinen S, Sokka N, Allan RP, Andersson E, Arpe K, Balmaseda MA, Beljaars ACM, Van De Berg L, Bidlot J, Bormann N, Caires S, Chevallier F, Dethof A, Dragosavac M, Fisher M, Fuentes M, Hagemann S, Holm E, Hoskins BJ, Isaksen L, Janssen PAEM, Jenne R, McNally AP, Mahfouf JF, Morcrette JJ, Rayner NA, Saunders RW, Simon P, Sterl A, Trenberth KE, Untch A, Vasiljevic D, Viterbo P, Woollen J. 25. The ERA-4 re-analysis. Quaterly Journal of the Royal Meteorological Society 131: Wallace JM, Hobbs PV. 26. Atmospheric Science-an introductory survey, 2nd edn. Academic Press. Elsevier: Amsterdam, Boston, Heidelberg, London, New York, Oxford, Paris, San Diego, San Francisco, Singapore, Sydney, Tokyo, 483. Copyright 28 John Wiley & Sons, Ltd. Hydrol. Process. 22, (28) DOI: 1.12/hyp