Using an Analytical Solution to Model a Season of Snowmelt
Mary R. Albert 1
There are many snowmelt models described in the literature. The detailed models use numerical
techniques to solve the governing differential equations of water flow through snow, while opera-
tional, lumped models ignore the physics of melt movement through the pack. While the detailed
models hold the potential for more realistic simulations, the matrix solutions inherent in the detailed
models consume much more computer time than the algebraic expressions used in the lumped mod-
els. In an effort to bridge the gap between the need for accurate melt assessments and the need for
computationally simple models for distributed applications, an analytical solution to the problem of
water flow through snow was presented (Albert and Krajeski 1998), and illustration of the solution
in a snowmelt model, SNAP (Snowmelt Numerical-Analytical Package), was described for several
outflow events. The purpose of this paper is to apply SNAP in simulating a full snow season, and to
compare the model results with snow depth and snowmelt lysimeter outflow measurements.
The field site for the snow measurements is the Sleepers River Research Watershed in northern
Vermont, where the seasonal winter snowpacks typically are 1 to 1.5 meters in depth, and are usually
highly layered, including ice lenses. Meteorological measurements (air temperature, relative humid-
ity, wind speed, incoming and reflected solar radiation, incoming and emitted longwave radiation,
and precipitation) are used to drive the model. Results of the model are compared to field data from
snowmelt lysimeter measurements of water flow from the base of the pack, and to ultrasonic snow
depth measurements. Snowpack stratigraphy, density, grain size, and permeability data were
obtained from snow pit measurements at various times throughout the season.
For the comparisons discussed here, model parameters were not tuned to the snow conditions; rather
all parameters were left at steady default positions throughout the course of the season in order to
identify those parts of the snowmelt season that require layering or metamorphic effects in order to
predict melt. In general, model results compare well with the field measurements. Snow depth meas-
urements over the course of the accumulationablation season agree with model results for most of
the season, with the main differences due to difficulties in ascertaining whether precipitation events
were snow or rain (model calculations assumed that precipitation for air temperature less than 0.5C
was snow). For rain on snow and for ripe snow conditions, the measurements and model compare to
within 95%. For the peak snowmelt season, model and measurements compare to within 90%, with
the main differences due to differences in predicted outflow at the start of the main melt season,
where layers are degrading and the surface albedo is changing. Future improvements and simula-
tions will focus on snow property evolution and layering/fingering effects in snowpack outflow.
1
U.S. Army Cold Regions Research and Engineering Laboratory, 72 Lyme Road, Hanover, New Hampshire
03755-1290, USA
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