Using Quantile Regression to Model Elevation/SWE Relationships in the Olympics and Central Washington Cascades

Although ordinary least squares (OLS) regression is often used to develop initial models for elevation/snow water equivalent (SWE) relationships in watersheds, such an approach cannot account for the heterogeneous variability in SWE over elevation bands common in many coastal Pacific Northwest watersheds. This is particularly problematic in attempting to model middle-elevation SWE in watersheds affected by winter rain-on-snow events. Scatterplots of this relationship often show a distinctive fan-shaped pattern that widens as elevation increases, implying that there is not a single rate of change in SWE by elevation. Thus, the use of an OLS regression in models or trend assessment could provide severely misleading estimates of SWE in middle elevation areas where no field data are collected. We compare OLS and quantile regression-based models of SWE by elevation based on four snow seasons of field assessment for the Dungeness Watershed of western Washington State, as well as for snow courses and SNOTEL sites in the Olympic Mountains and central Washington Cascades. In both cases, quantile regression better accounts for the observed data than does the typical OLS approach.