Snow is a crucial element in the Earth’s system, but snow depth and mass are very challenging to be measured globally. Here, we provide the theoretical foundation for deriving snow depth directly from space-borne lidar (ICESat-2) snow multiple scattering measurements for the first time. First, based on the Monte Carlo lidar radiative transfer simulations of ICESat-2 measurements of 532-nm laser light propagation in snow, we find that the lidar backscattering path length follows Gamma distribution. Next, we derive three simple analytical equations to compute snow depth from the average, second-, and third-order moments of the distribution. As a preliminary application, these relations are then used to retrieve snow depth over the Antarctic ice sheet and the Arctic sea ice using the ICESat-2 lidar multiple scattering measurements. The robustness of this snow depth technique is demonstrated by the agreement of snow depth computed from the three derived relations using both modeled data and ICESat-2 observations.
Snowpack is one of the most important wintertime land-surface characteristics, and it is one of the hardest features that can be accurately observed and quantified on a global scale. Seasonal snow and glaciers provide water resources for over one billion people worldwide, and it is also important for weather, climate, and ecosystem functioning through a variety of different mechanisms. While satellite passive remote sensing has successfully measured the snow cover extent , its measurements of snow water equivalent (SWE) and snow depth are much more challenging . For these reasons, the recent Earth Science Decadal Survey recommended snow mass and depth among the seven targeted observables for the NASA Earth System Explorer satellite mission competitions.
While lidar altimetry has been used in airborne measurements of snow depth as the difference between the measured snow top and snow-free ground heights , its applicability in space-borne measurements is more challenging due to stringent ground track requirements. For snow over sea ice, while space-borne lidar measurements can provide the snow top height above sea water, the broad consensus is that space-borne radar measurements are needed for the retrieval of the actual snow depth over sea ice. For these reasons, most of the explorations of space-borne measurements of SWE and snow depth have focused on radar measurements.
The scientific and technological question is as follows: can space-borne lidar measure snow depth (and SWE) over land and over sea ice? If yes, the latter measurement in combination of the measurement of snow top over sea ice would also enable the global estimate of sea ice thickness, which is of substantial importance in the Earth system and national defense.
The purpose of this study is to combine radiative transfer theory with Monte Carlo simulations to derive analytical relations of snow depth and optical properties directly from the space-borne lidar measurements of vertical backscatter profiles of snow. This would provide the theoretical foundation for space-borne lidar measurements of snow depth for the first time. We will address the robustness of our method by assessing the agreement among three derived relations and the convergence of the relations using a different approach. As a preliminary application, these relations are then used to retrieve snow depth over the Antarctic ice sheet and Arctic sea ice from ICESat-2 lidar measurements. The retrieval of SWE and comparison of SWE and snow depth with observations will be reported in separate articles.