Subgrid Parameterization of Snow Distribution
for an Energy and Mass Balance Snow-Cover Model
Charles H. Luce1, David G. Tarboton2, and Keith R. Cooley3
The spatial variability of snowpack accumulation and ablation processes can cause point-scale phys-
ically based snowmelt models to give poor estimates of average snowmelt over a small area or basin.
Distributed snowpack modeling is a popular tool to handle spatial variability in snowpack accumu-
lation and ablation across watersheds. Because of the high computational burden and the cost and
uncertainty of input data associated with fine grids, elements of distributed models may be made
large relative to the assumptions of uniformity of snowpack conditions within a model element.
Approaches are needed to describe a model element as a heterogeneous unit within a physically
based modeling framework.
Our approach uses a parameterization of snow-covered area as a function of area-averaged snow
water equivalence. This parameterization is linked to a physically based snowmelt model describing
the lumped energy and mass balance of the snowpack. For each time step, the energy and mass
balance are calculated for the snow-covered area. The snow-covered area is updated according to the
basin-averaged snowwater equivalence. The dimensionless relationship between snow-covered
area and averaged snowwater equivalence (area-equivalence curve) can be derived from the spatial
probability density function of snowwater equivalence at peak accumulation.
Outputs of the lumped model derived from this reasoning were compared to outputs from a dis-
tributed snowmelt model and to distributed data in the 26-ha Upper Sheep Creek sub-basin of Rey-
nolds Creek Experimental Watershed in Southwest Idaho. The snow-water equivalence observations
were taken on a 30.3-m grid with 255 cells over the basin, and the distributed model was run on the
Comparisons of the lumped model outputs to distributed model outputs show good agreement. Both
models showed reasonable agreement to the observations. Comparison of the area-equivalence
curve derived from the probability density function of snow water equivalence at peak accumulation
to one derived from a series of measurements across the basin and another based on outputs of the
distributed model also showed good agreement.
This parameterization and the method to obtain area-equivalence curves provide a practical method
for scaling-up point-scale energy and mass balance models to cover a small basin with accuracy
comparable to a distributed model. The method may be particularly useful in hydrologic models that
may use large (relative to assumptions of snowpack homogeneity) elements, such as land-surface
submodels of climate models or models of large river basins.
1 USDA Forest Service, Rocky Mountain Research Station, 316 E. Myrtle, Boise, Idaho 83702, USA
2 Civil and Environmental Engineering, Utah State University, Logan, Utah 84322, USA
3 USDA Agricultural Research Service, Northwest Watershed Research Center, 800 Park Boulevard, Plaza 4,
Suite 105, Boise, Idaho 83712-7716, USA