Linking lidar multiple scattering profiles to snow depth and snow density: an analytical radiative transfer analysis and the implications for remote sensing of snow

Abstract

Lidar multiple scattering measurements provide the probability distribution of the distance laser light travels inside snow. Based on an analytic two-stream radiative transfer solution, the present study demonstrates why/how these lidar measurements can be used to derive snow depth and snow density. In particular, for a laser wavelength with little snow absorption, an analytical radiative transfer solution is leveraged to prove that the physical snow depth is half of the average distance photons travel inside snow and that the relationship linking lidar measurements and the extinction coefficient of the snow is valid. Theoretical formulas that link lidar measurements to the extinction coefficient and the effective grain size of snow are provided. Snow density can also be derived from the multi-wavelength lidar measurements of the snow extinction coefficient and snow effective grain size. Alternatively, lidars can provide the most direct snow density measurements and the effective discrimination between snow and trees by adding vibrational Raman scattering channels.