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
[email protected]

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:

• Macroscale (104-105 m) – elevation, orography, meoteorological effects, flow of wind round barriers and lake effects
• Mesoscale (102-103 m) – redistribution due to wind and avalanches, deposition and accumulation related to elevation, slope, aspect, vegetation height and density
• Microscale (10-102 m) – surface roughness and transport phenomena

Major state variable that characterises the snowpack from hydrological viewpoint is the snow water equivalent (volume of water released by melting snow). Numerous snowmelt models have been developed to describe the evolution of this variable. Generally, they can be divided into three groups – index models, energy based models and detailed models using full solutions of the energy and mass flow equations. Index models are the simplest. They are based on a relationship between the snowmelt and other easily available parameters like the air temperature. Typical example of this group of models is the degree-day model, which calculates snowmelt as:

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 (Mészároš, 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.

Catchment
The Jalovecky creek catchment (Fig. 4) is representative for the highest part of the Carpathian Mountains, the 1200 km long mountain chain situated in middle Europe. Early Quaternary glaciers intensively modeled catchment relief. Catchment area is 22.2 km2. Elevations in the catchment range from 800 to 2178 m a.s.l. (mean 1500). Mean slope is 30º. Catchment is generally south oriented – northern, north-eastern and eastern slopes represent only 15% of catchment area. Igneous (granodiorite), metamorphic (schist, gneiss, migmatite) and sedimentary (Quaternary loose sediments) build 21, 48 and 24% of the catchment, respectively. Rest 7% is made up by Mesosoic limestone and dolomite. Soils distribution is generaly characterised by vertical zonality (cambisols, podzols, ranker, lithosol). Spruce dominated forest cover 44% of catchment area. Dwarf pine covers 31% and meadows and bare rocks cover the rest 25% of catchment area.
Catchment mean precipitation (1989-2000) is 1550 mm, runoff 1015 mm, air temperature at mean elevation 3.5 ºC. Seasonal snow cover typically occurs in the catchment between November and May. First short snowmelt events usually occur in March. The snowmelt is then interrupted for about two weeks. Continual snowmelt typically begins in April and the main phase of snowmelt starts in the last decade of April.
Measurements of snow water equivalents in the last 30 years show that winter 1999/2000 was relatively cold and snow-rich (Fig. 5, Table 1). Time course of snow accumulation and melt was relatively simple without short-time melts during the accumulation period. Point UEB model provided successful simulation with different time-steps of the input data (Fig. 6).

Fig. 4 The Jalovecky creek catchment.

Fig. 5 Catchment mean snow water equivalents in two mountain catchments in the research area in winters 1968/69 – 2000/2001.

Table 1 Climatic characteristics of winters (November-March) 1995/1996 – 1999/2000 in the Jalovecky creek catchment measured at catchment mean elevation; P-precipitation, Tave-mean air temperature, Tneg-sum of negative air temperatures, SWEmax- maximum snow water equivalent

Fig. 6 Simulation of snow water equivalent at catchment mean elevation with the point version of the UEB model using different time steps of input meteorological data; 1-hourly, 2-daily, 3-input data measured at standard observation hours 7 a.m., 2 p.m. and 9 p.m.

Results
Simulations of spatial distribution of snow water equivalent were generally acceptable. Few examples from different sites are shown in Fig. 7. Good simulations were achieved for the forest sites. The simulations were slightly overestimated for forest sites at lower elevations. Snow water equivalents simulated for sites situated above forest which were not exposed to significant drift were also acceptable. Worse simulations were received for the wind exposed sites.
Spatial distributions of modelled snow water equivalents at the beginning of the winter and at the time of maximum snow accumulation are shown in Fig. 8. As can be seen that snow distribution at the beginning of winter was significantly affected by vegetation in terms of relatively small spatial differences in the forest and much larger differences above the forest. Slopes aspects played important role in the spatial distribution of snow cover at the beginning of the winter, too. At the time of maximum accumulation, elevation gradients seem to have dominant effect on spatial distribution of snow.
Another hydrologically significant output of the UEB-EHZ model is the outflow from melting snow. It may help to identify the parts of the catchment which dominate in providing meltwater for overland runoff formation. High snowmelt output areas may also contribute to acid surges at the beginning of the snowmelt thus affecting water quality and environamental hazards. Figs 9 and 10 show modelled meltwater outputs in the Jalovecky creek catchment at certain dates in snowmelt season 2000. The dates were chosen as following:

• 9 March 2000 – first melt event
• 25 March 2000 – period without snowmelt short before the beginning of continual melt period
• 15 April 2000 – beginning of the main snowmelt phase
• 22 April 2000 – maximum melt

  Spatial distribution of modelled melt outflows shown in Fig. 9 represent interesting visualization of the snowmelt process. It is clear that snowmelt during the first event around 9 March occurred only in the lower part of the catchment. On 25 March the snow melted only on the very small area at lower elevations. At the beginning of the main snowmelt phase the melt occurred almost in the whole catchment except for the highest sites. Whole catchment contributed to snowmelt on 22 April. Elevation seems to be the most important factor influencing the spatial distribution of areas with melting snow. Much higher snowmelt occurred along the forest line. All these results comply with the knowledge of snowmelt spatial distribution in mountains. Thus, the modelled results seem to be reasonable.

  Fig. 7 Comparison of measured (blue circles) and simulated (lines) snow water equivalents at sites with different characteristics.

  Fig. 8 Simulated spatial distributions of snow water equivalent [mm] at the beginning of winter (1.1.2000) and at time of maximum accumulation (7.4.2000).

  Fig 9 Spatial distribution of outflow from melting snow; white colour indicates no melt in the catchment.

  Fig. 10 Comparison of catchment integrated melt outflow (modelled) with runoff measured at catchment outlet.

  Distributed version of the energy balance UEB model provided acceptable simulations of snow water equivalent in the mountain basin of the Jalovecky creek for most sites with field observations. Interesting analyses can be made using modelled melt outflows. Due to its physical basis, the model should be applied with relatively small effort also in other mountain catchments. Proper estimation of snow redistribution by wind above the forest line is important for successful modelling of spatial variability of snow water equivalent. Further research should therefore address objective parameterisation of the drift factor. Forest line have large significant impact on the distribution of snow cover and consequently also on snowmelt. Verification of modelled results on snowmelt along the forest line with field measurements should also be performed in future research.

  References

  • Bengtsson, L., Singh, V.P., 2000: Model Sophistication in Relation to Scales in Snowmelt Runoff Modeling. Nordic Hydrology, 31 (4/5), 267-286.
  • Liston, G.E., Sturm, M., 1998: A snow transport model for complex terrain. Journal of Glaciology, vol. 44, no. 148, 498-516.
  • Mészároš, I. 1998. Modelling of incoming solar radiation in mountain basin. (in Slovak). Acta Hydrologica Slovaca 1 : 68-75.
  • McKay, G., Gray, D.M., 1981: The distribution of snowcover. In Handbook of Snow, Principles, Processes, Management&Use, edited by D.M.Gray and D.H. Male, Pergamon press, chapter 5.
  • Tarboton, D., Luce, D., 1996: Utah Energy Balance Snow Accumulation and Melt Model (UEB). Computer model technical description and users guide. Utah State University and USDA Forest Service, 39 pp.