Quantifying scale relationships in snow distributions - Deems, Jeffrey S., author; Fassnacht, Steven R., advisor; Elder, Kelly J., committee member; Liston, Glen E., committee member; Painter, Thomas H., committee member (Colorado State University. Libraries, 2007)
Spatial distributions of snow in mountain environments represent the time integration of accumulation and ablation processes, and are strongly and dynamically linked to mountain hydrologic, ecologic, and climatic systems. Accurate measurement and modeling of the spatial distribution and variability of the seasonal mountain snowpack at different scales are imperative for water supply and hydropower decision-making, for investigations of land-atmosphere interaction or biogeochemical cycling, and for accurate simulation of earth system processes and feedbacks. Assessment and prediction of snow distributions in complex terrain are heavily dependent on scale effects, as the pattern and magnitude of variability in snow distributions depends on the scale of observation. Measurement and model scales are usually different from process scales, and thereby introduce a scale bias to the estimate or prediction. To quantify this bias, or to properly design measurement schemes and model applications, the process scale must be known or estimated. Airborne Light Detection And Ranging (lidar) products provide high-resolution, broad-extent altimetry data for terrain and snowpack mapping, and allow an application of variogram fractal analysis techniques to characterize snow depth scaling properties over lag distances from 1 to 1000 meters. Snow depth patterns as measured by lidar at three Colorado mountain sites exhibit fractal (power law) scaling patterns over two distinct scale ranges, separated by a distinct break at the 15-40 m lag distance, depending on the site. Each fractal range represents a range of separation distances over which snow depth processes remain consistent. The scale break between fractal regions is a characteristic scale at which snow depth process relationships change fundamentally. Similar scale break distances in vegetation topography datasets suggest that the snow depth scale break represents a change in wind redistribution processes from wind/vegetation interactions at small lags to wind/terrain interactions at larger lags. These snow depth scale characteristics are interannually consistent, directly describe the scales of action of snow accumulation, redistribution, and ablation processes, and inform scale considerations for measurement and modeling. Snow process models are designed to represent processes acting over specific scale ranges. However, since the incorporated processes vary with scale, the model performance cannot be scale-independent. Thus, distributed snow models must represent the appropriate process interactions at each scale in order to produce reasonable simulations of snow depth or snow water equivalent (SWE) variability. By comparing fractal dimensions and scale break lengths of modeled snow depth patterns to those derived from lidar observations, the model process representations can be evaluated and subsequently refined. Snow depth simulations from the SnowModel seasonal snow process model exhibit fractal patterns, and a scale break can be produced by including a sub-model that simulates fine-scale wind drifting patterns. The fractal dimensions provide important spatial scaling information that can inform refinement of process representations. This collection of work provides a new application of methods developed in other geophysical fields for quantifying scale and variability relationships.