Continuous mapping of distributed snow depth for mobility models using shaped solutions

High-resolution ground vehicle mobility models are used by the U.S. Army to investigate new vehicle concepts, conduct force-on-force simulations, and–in the future–support terrain analysis for battle planning. Use of these models in winter conditions requires a method to realistically represent the distribution of snow depth and density over a landscape. The objective of this work was to develop a method to use a recently identified pinched-cone-shaped solution domain to map snow properties. The method was developed with stringent computational and data storage efficiency requirements in mind and is demonstrated by mapping snow depth on the Ethan Allen Firing Range in northern Vermont, USA. The pinched-cone-shaped plots in a cylindrical coordinate system r = F(θ,z) where the no-slope snow depth is taken as the vertex (0,0), the radii (r) represent the snow depth relative to the no-slope case, and r is a function of azimuth (θ) and terrain slope (z). The pinched-cone equation uses a circular function with one or two coefficients that describe the slope-azimuth-dependent expansion of the pinched cone as snow depth differentiation increases with increased terrain slope. Equations that relate the expansion coefficients and no-slope snow depth to elevation then permit continuous mapping of snow depth with respect to terrain slope, azimuth, and elevation. The mapping is applied within five forest categories (open, sparse, deciduous, mixed, and conifer). The influence of snow depth and terrain slope on vehicle speed predictions is illustrated.