Distributed modelling of snow water equivalent - coupling a snow accummulation and melt model and GIS Parajka, J., Holko, L., Kostka, Z. Institute of Hydrology, Slovak Academy of Sciences Ondrasovecka 16, 031 05 Liptovsky Mikulas, Slovakia parajka@svslm.sk Snow cover is an important hydrological phenomenon. Snowmelt is a vital source of water in many parts of the world. It may significantly contribute to river floods. At the same time the seasonal snow cover affects also biotic component and water quality in river basins. Distributed modeling of snow accumulation and melt is therefore an important issue. Recent advances in GIS technology allow powerful integration of GIS analytical and visualization tools with physically based hydrologic models. In the field of snowmelt modelling, such integration provides valuable basis for better understanding of snow accumulation and snowmelt runoff processes within the catchment, as well as for incorporating the spatial variability of hydrological and geographical variables and their impacts on catchment responses. The objective of research presented in this paper was, with the help of GIS tools, to develop the distributed version of the energy-based snow model and test it in the headwater mountain catchment of the Jalovecky creek, the Western Tatra Mountains, Slovakia. The paper also shows potential application of the spatial snowmelt modelling (meltwater outflows) in runoff generation research or studies of potential risks for the local environment or water pollution. Introduction - snow accumulation and melt modelling Physical processes within the snowpack and involved in snowmelt are very complex. They involve mass and energy balances as well as heat and mass transport. Formation of ice layers further complicates evolution of snowpack resulting in processes known from soil physics like fingering or lateral flow. 
Fig. 1 Energy fluxes involved in snowmelt (Tarboton a Luce, 1996); Qsn- net solar radiation, Qln- net longwave radiation, Qp-heat brought with precipitation,, Qh-sensible heat, Qe-latent heat of sublimation/condensation, Qg- ground heat flux, Qm-heat carried away by melt. Snowmelt is basically energy driven process. Incoming solar (shortwave) radiation, absorption and emission of longwave radiation, turbulent transfers by sensible and latent heat fluxes, and energy exchanges at snow-ground base are the main driving components (Fig. 1). Most important energy exchanges occur near the snow surface. Snowpack melts from the surface and the snowpack surface also receives any new snow or rain which can bring significant energy. Distribution of snow over the catchment is substantially affected by wind and vegetation. Wind causes redistribution of snow due to its accumulation or scouring. Vegetation influences snow distribution by interception of snowfall by canopy and affecting the wind field. McKay and Gray (1981) report on the following factors that affect the distribution of snow at different scales:
where M is snowmelt, c is the degree-day factor (volume of water released from melting snow per one degree of air temperature above the threshold), T is the air temperature, Tk is the threshold temperature above that the snowmelt starts. Energy based models use more correct physical description of basic processes affecting snow accumulation and melt, namely energy fluxes in the snowpack. Detailed models based on energy and mass flow equations are physically correct, but demand a lot of data that is not easily available or unavailable at all. Snow models are often just subroutines of rainfall-runoff models used to simulate or forecast river discharge. Bengtsson and Singh (2000) showed lately that sophistication of snowmelt model should correspond to that of runoff model. This explained why the simple degree-day models performed successfully in many applications worldwide. Methodology UEB-EHZ model working with the daily time step was used to simulate snow accumulation and melt in the catchment. The model is based on point version of an energy based UEB model (Utah Energy Balance Snow Accumulation and Melt Model, Tarboton and Luce, 1996). The UEB model uses a lumped representation of the snowpack (i.e. the snowpack is represented as one layer only) with two primary state variables, snow water equivalent and energy content. It is driven by inputs of air temperature, precipitation, wind speed, humidity and incoming solar radiation and uses physically-based parameterization of snow radiative, sensible, latent and advective heat exchanges. Because of its parsimony the model is suitable for application in distributed fashion on a grid over a catchment. GIS was used to provide the spatially distributed meteorological input data, additional spatial inputs, namely digital elevation model (DEM), slope, aspect and vegetation types maps (Fig. 2), map of incoming solar radiation and drift map describing redistribution of snow over the area. Grid size of 100 m was used in all selected raster maps. Spatial representation of incoming solar radiation was computed by the SOLEI32 algorithms (Mészáro, 1998) considering topographical shading of neighboring terrain. Field measurements showed that the incoming solar radiation in the forest should be decreased by factor 0.1 compared to computed open area radiation.  
Fig. 2 Some basic features of the Jalovecky creek catchment; circles in the DEM represent sites with snow water equivalent measurements. Spatial distribution of snow cover depends strongly on the magnitude of wind induced redistribution of snow (snow drift). Two ways of expressing the snow drift were applied in the simulations. First, simple partitioning of the catchment into forest (drift factor 0.9) and other areas (drift factor 1.2) was used to describe the tendency of the grid elements to accumulate or erode the snow cover due to wind activity. Second, the snow drift map was prepared using GIS and the interpolation of wind speed taking into account slopes and curvature of the relief using the approach of Ryan (1977, fide Liston, Strum, 1998). According to this approach the measured wind speed was first interpolated over the grid. The resulting the wind speed field was then modified according to relief using empirical coefficient W: where Ws and Wc are relief slope and curvature in the wind direction, respectively, gs and gc are constants. Comparison of corrected wind field with the snow patches pattern in the spring (Fig 3) indicate relatively good fit. Performance of the distributed UEB-EHZ model was verified against field measurements of snow water equivalent in winter 1999/2000 carried out at 13 sites in the catchment (Fig. 2). The measurements were more frequent at one site situated at catchment mean elevation (about once per week during snowmelt) and 3-4 times per winter at other sites. The UEB-EHZ model was run for the 243-day period between 1 November 1999 and 30 June 2000. Spatial representation of snow water equivalent in form of raster map was computed for each day. Snow water equivalent values were then extracted from grid cells representing measurement sites. Thus the daily values of modelled snow water equivalents for each of 13 measurement sites were obtained. 
Fig. 3 Example of correlation between spring snow patches and wind correction factors in the Jalovecky creek catchment.
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