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Next: Results Up: Modeling snow cover Previous: Snow ablation and melt

Snow cover simulation

Our model divides the height field into a grid storing the amount of snow as snow water equivalent. This is the mass of water stored as snow per m2. Snow is first deposited by elevation and then is melted in a simulation that varies temperature with height and available radiation. The available radiation is based on surface orientation and the times of day it is shadowed. The shadowing is computed at the center of each grid cell.

Ambient air temperature is a fundamental component of the calculations for snow accumulation, melt and evapotranspiration. Temperature data at specified base elevation is provided as user input and contains: (i) minimum, (ii) maximum, and (iii) average temperature. An average environmental lapse rate can also be user specified, but we adopted a rate of -0.6oC per 100m [14]. Warm air advection can make a standard lapse rate inadequate for temperature predictions in alpine environment [17]. However, over time fluctuations about the mean lapse rate will tend to even out.

Elevation is believed to be the single most important factor in snow cover distribution. Precipitation data at specified base elevation is provided as user input and contains: (i) amount of precipitation, and (ii) precipitation density (1 g/cm3 for rain). Elevation rise from the base elevation is treated very simply using an optional user specified lapse rate. As with air temperature, the simplified precipitation distribution assumptions are less likely to pose problems over long time periods.

The amount of snow accumulated depends on the balance between rain and snowfall [17]. The usual method to classify precipitation is to set a threshold ambient air temperature (Tsnow) above which all precipitation is assumed to be rain. For every simulation time step, we determine precipitation type from ambient air temperature. If precipitation is snow, the snow water equivalent is computed from snowfall and density, and accumulated. If precipitation is rain no accumulation occurs and the simulation continues to melting phase.

The major variables controlling the snow melt factor are determined using the relationship suggested by Eggleston et al. [13]:

Cm = kmkvRI(1-A)

where km is a proportionally constant, kv is a vegetation transmission coefficient for radiation, RI is a solar radiation index, and A is the snow albedo. The change in snow albedo with time t (days) is described by

A = 0.4[1+e-ket]

where ke $(\approx 0.2/day)$ is a time constant. A fall of new snow increases the albedo to 0.8 while rain reduces it to 0.4. The vegetation transmission coefficient kv is computed as

kv = e-4Cv

where Cv is the vegetation canopy density.

RI is the ratio of the radiation received by a surface with a given slope and aspect, normalized to that received by a horizontal surface at the same latitude and time of year. Note that only the ratio of energies needs to be computed. A slightly modified method of Swift [19] is used for this computation. For periods of rain the melt factor Cmis adjusted as follows:

Cm(rain) = Cm + 0.00126Prain

where Prain is amount of rainfall (mm).

Every simulation time step, if the ambient air temperature (Tair) is greater than the threshold melt temperature (Tmelt), the melt rate factor Cm is computed and the snowpack water equivalent is adjusted accordingly. When the simulation is done, grid cells with non-zero snow water equivalent are assumed to have snow cover. We do not model snow depth so we use the snow cover information only to decide where to render snow in the final image. Adding snow to regions that are uncovered in the original orthoimage is straightforward, since at a distance snow appears as a relatively diffuse reflector except for glancing illumination and viewing angles. Subtracting snow that was on the ground when the aerial image was shot is a bit more complicated. However, since almost all of the raw imagery is acquired in summer to minimize sun angle effects, we can be pretty much assured that the underlying surface cover is rock or talus.


next up previous
Next: Results Up: Modeling snow cover Previous: Snow ablation and melt
Comments: Simon PREMOZE
1999-02-05