Snowdrift Modeling Using a Linear Particle Distribution Equation

A snowdrift is affected by numerous factors including but not limited to wind field, local turbulence, boundary layer thickness, surface roughness, particle Reynolds number, snow particle size distribution, particle shape, and density of snow particles in the air. Therefore, snow redistribution has been ignored in most practical hydrology models, and snowdrifts around well-defined snow fences have been projected mainly by empirical knowledge rather than process-based considerations. This study organized these various effects by particle motion processes rather than flow (wind) regime and particle characteristics in order to develop a predictive model for snow redistribution. The particle motion processes were characterized by three parameters: snow particle dispersion, snow drift (snow surface advection), and snow surface erosion coefficients. Among them, a linear erosion term for a fetch-eddy effect was the new addition to the existing advection dispersion equation. The newly formulated equation was named Eulerian Particle Distribution (EPD) equation, and the linear components of the EPD equation were named the Linear Particle Distribution (LPD) equation. Using analytical solutions under a few well-defined boundary conditions, possible snow particle distribution patterns were successfully mapped. The LPD equation was found to be able to describe most of the one-dimensional particle deposit patterns behind an object, including porous and solid snow fences and a tree. The snow redistribution model based on the LPD theory also reproduced snow stratigraphy observed by ground penetrating radar (GPR). Inversely, this theory may provide us an opportunity to estimate the time-averaged particle motion parameters, such as diffusion, drift, and erosion coefficients, from fieldobserved particle distributions. The model applications and numerical algorithm for snow drift patterns in irregular terrain will be presented. (KEYWORDS: snow drift, Eulerian particle distribution, particle distribution, snow redistribution, snow erosion, snow fence)