Research focuses on observing and predicting spatial distribution of snow depth at the kilometer scale. Observation of spatial snow depth distribution is considered by its estimation from random, sparse observations and important factors affecting this estimation. Predicting spatial distribution of both snow depth and melt rates begins from simple hypothesis wherein the spatial distribution of snow depth is structured by the spatial distribution of controlling variables. Predictions made by this structured view are evaluated in spatial modeling of peak-accumulation snow depth and applied to spatial distribution of a point-scale, temperature-index model of snowmelt runoff using minimal parameter complexity.

High-resolution light detection and ranging (LiDAR) measurements provide a rich backdrop for understanding estimation from sparse observations and developing our structured view of snow distribution. The data are used to illuminate the effects of sample size on estimation skill, the uncertainty in estimation due to random sampling, the effect of model resolution on estimation skill, and the difference between cross-validated skill and skill based on the entire distribution. None of these topics have previously been explored in the literature. The effect of predictor quality is also investigated. LiDAR derived predictors are compared to readily available predictors downloaded from the internet.

Hierarchical cluster analysis is used to decompose spatial non-stationarity of snow depth and results match qualitative understanding of the spatial distribution of physical controls. The same methodology is then used to decompose spatial non-stationarity of physical controls and infer patterns of snow depth distribution independent of observations. Even when using readily-available predictors, predicted patterns require at least 100–200 observations to be matched by standard estimation methods.

Predicted patterns are then applied to formulate a parameterized spatial distribution of a 1-dimensional, temperature-index model to account for heterogeneity of both snow accumulation and melt. Our new method introduces fewer or comparable parameters as the current subgrid distribution, the areal depletion curve. Given highly uncertain parameter selection in practical application, we demonstrate that our more physically intuitive method virtually always results in significant improvement in simulated streamflow timing when compared to the depletion curve method.