Comparison of Geostatistical and Binary Regression Tree Methods
in Estimating Snow Water Equivalence Distribution
in a Mountain Watershed
Benjamin Balk1, Kelly Elder1, and Jill Baron2
Understanding snow water equivalence (SWE) distribution is imperative for snowmelt models to
efficiently predict the volume and timing of runoff. Many factors contribute to the variation of SWE,
including elevation, slope, aspect, vegetation type, surface roughness, and energy exchange. Studies
of seasonal snow cover are manageable in areas with gentle terrain because the importance of factors
controlling snow distribution is greatly diminished. However, understanding the processes control-
ling the spatial distribution of snow is difficult in rugged alpine regions.
The spatial distribution of peak SWE in a mountain watershed was modeled and compared using
geostatistical and binary regression tree methods. In April 1997 and 1998, intensive snow surveys
were conducted in the Loch Vale Watershed (6.9 km2), Rocky Mountain National Park, Colorado.
This glacially scoured watershed lies in the Front Range immediately east of the Continental Divide
with elevations between 3091 and 4003 m. Sample locations of snow depth and density were chosen
to be representative of the range of elevations, slopes, and aspects of the watershed with safety
constraints. All field measurements were registered to a 10-m resolution digital elevation model.
In the geostatistical approach to modeling SWE distribution, snow depths were spatially distributed
over the watershed by kriging interpolation. The spatial variability of snow depth, in the form of a
variogram, was used to weight adjacent sampled values for interpolation. This technique, known as
kriging, has the advantage of giving an actual measure of the reliability of the estimated values
because the individual interpolation errors can be calculated. The second approach incorporates
binary regression tree methods. The independent variables of elevation, slope, net solar radiation,
and vegetation cover were used to model the dependent variable, snow depth, as they show a physi-
cally based relationship with snow distribution. These relationships are often nonlinear; however,
the binary regression tree method can describe nonlinear relationships between the independent and
dependent variables. Using regression analysis, snow densities were mapped across the watershed.
Combining the modeled depths and densities with snow-covered area produced estimates of the
spatial distribution of SWE.
Total basin SWE values were similar for both techniques; however, within basin distribution of SWE
from the two methods showed important differences. Complex energy balance, steep slopes, and
variably strong winds in the watershed contribute to a large degree of heterogeneity in snow depth.
This large heterogeneity in snow depth complicated the kriging interpolation process. Binary regres-
sion trees can more accurately handle abrupt changes in the primary variable, snow depth. Therefore,
the regression trees were able to explain more of the observed variance in the measured snow depths.
State University, Department of Earth Resources, Fort Collins, Colorado 80523, USA
State University, Natural Resource Ecology Laboratory, Fort Collins, Colorado 80523, USA