Assessing the Representation of Wind, Terrain, and Vegetation Effects on Snow Density Distributed by Learned Regression Modeling

In snowpacks the propagation speed of electromagnetic radiation is controlled by the snow depth, density, and the amount of liquid water stored within the pore space. In the case of dry snow, if snow depth is constrained, snow density can be estimated from the travel-time of the radar wave through the snowpackbegin{equation*}{v_s} = 2frac{{{h_s}}}{tau },tag{1}end{equation*}where v_s represents the electromagnetic wavespeed, h_s is the snow depth, and τ is the two-way travel-time. The Complex Refractive Index Method [1]begin{equation*}{rho s} = {rho i}left({1 - frac{{{v_a}left({{v_i} - {v_s}}right)}}{{{v_s}left({{v_i} - {v_a}}right)}}}right),tag{2}end{equation*}where ρ represents density, v represents the propagation speed, and subscripts a,i, and s indicate air, ice or snow respectively, is one of several equations that relate electromagentic wavespeed (or permittivity) to snow density. By working equations 1 and 2 backwards, an estimate of snow density, acquired in-situ by weighing a known volume of snow, can yield snow depth provided a travel-time.Snow depth tends to vary over shorter spatial scales than snow density and can now be accurately observed over large spatial extents (~ 10-100 km²) by repeated airborne lidar surveys [2]. Because snow density is often observed infrequently, its spatial distribution is largely unknown. Snow water equivalent (SWE) is the equivalent height of water stored within a snowpack and can be calculated by the multiplication of snow depth and density. Snow density contributes a greater relative uncertainty in SWE, especially in deeper snowpacks, from either modeled or observational perspectives [3]. To improve the accuracy of SWE estimates at water shed scales, improvements are needed in the spatial observations and understanding of the drivers of spatial density patterns. In this work we present a technique for the spatial estimation and prediction of snow density within a ~ 16 km² sub-alpine study area of the western United States.We combined Ground-Penetrating Radar (GPR) surveys and airborne LiDAR snow depths from SnowEx 2020 at Grand Mesa, Colorado to constrain the radar travel-times and infer the average snow density along ~ 150 km of radar transects. Terrain and vegetation parameters derived from LiDAR acquisitions form the basis of predictive features within a supervised learning framework to extrapolate snow density estimates across the study region. Multiple Linear, Random Forest, and Artificial Neural Network Regression models of snow density were evaluated, but the choice of a best model is difficult to quantitatively assess - as outputs similarly exhibit weak correlation (average R² = 0.04) when compared to sparse validation observations, yet have low error (average RMSE = 10 %). Using Random Field Synthesis [4], a snow density model with mean and variance representative of in-situ measurements and spatial correlation comparable to that measured via variogram analysis, we generated a baseline model for evaluation against the regression model ensemble.This work implores a deepened focus on the meteorological, terrain, and ecological variables controlling the densification of snow at Grand Mesa, Colorado, with the intent of better understanding the representation of physical processes affecting snow densification in empirical models. We evaluated the characterization of wind, terrain, and vegetation interactions with snow density estimated by the distributed models using the maximum upwind slope and wind factor parameters [5]. Without informing the models with wind information, each of the regression models show greatest correlation with these wind exposure parameters in the direction of winds capable of transporting snow [6]. This finding supports that regression model ensembles contain physically meaningful and repeatable spatial structures of snow density. An improved observational comprehension of the influences of snow densification will enable snow scientists to better assess and improve physically modeled snow density.