A Roadmap to Global High Spatial/Temporal Resolution Snow Depth Survey Through Synergistic Space Lidar and Optical Spectral Measurements

In our previous articles (Hu et al., 2022; Lu et al., 2022, Hu et al., 2023), we introduced a theoretical snow depth and snow density measurements concept using lidar measurements. The key findings of these studies are: snow depth and snow density play key roles in the probability distribution of diffused photon scattering inside snow. When absorption can be ignored, the averaged photon pathlength of laser light or sunlight traveling inside snow is proportional to snow depth. Snow density are also affect spectral absorptions and the higher order statistics of the diffused photon pathlength distribution. 

Spectral reflectance of sunlight R(k) is the Laplace transform of the diffuse photon pathlength distribution, P(L).  R(k)=∫ p(L)  e^-kL dL.  Here k is the absorption coefficient of snow at given wavelength. Thus there are information of snow depth and snow density in the spectral measurements of sunlight, of which k may change between 0.02 per meter to 100 per meter. For example, Snow depth is proportional to the first moment of the pathlength distribution, , which is simply,  -R' (k)=-dR⁄dk=∫ L p(L)  e^-kL dL. Thus, snow depth is proportional to the first order derivative of the spectral reflectance. 

Thus, snow depth and snow density can be derived from spectral reflectance of sunlight through inverse transform. Using machine learning that uses lidar measurements of snow depth and snow density to train the collocated spectral solar reflectance measurements, we can effectively perform atmospheric correction and -R’(k) at the same time This short paper describes the theory behind the measurements. We will also demonstrate the measurement concept with collocated PACE and ICESat-2 observations.