Advancing snow data assimilation with a variable, state-dependent observation uncertainty

Seasonal snow, a critical resource for society and the climate system, provides water for billions, supports agriculture, clean energy, and tourism, and influences the global energy balance. However, accurately quantifying snow mass, particularly in mountainous regions, remains a challenge due to substantial observational and modelling limitations. As such, data assimilation (DA) offers a powerful tool for overcoming these limitations by integrating observations with physically-based models to improve estimates of thesnowpack. Previous snow DA studies have employed an Ensemble Kalman Filter (EnKF) to assimilate Sentinel-1 satellite-based snow depth retrievals, demonstrating improved accuracy in modelled snow depth, mass, and streamflow. In those studies, the observation uncertainty was assumed to be constant in space and time, which is not optimally making use of the observational information. Here, we present several advances in snow DA. Using an EnKF, we assimilate novel snow depth retrievals resulting from a machine learning product that uses Sentinel-1 backscatter observations, land cover, and topographic information over the European Alps. We also incorporate a state-dependent observation error, whereby the uncertainty of the assimilated snow depth observation varies in space and time with snow depth, better reflecting the variability of the snow depth retrieval uncertainty. The machine learning snow depth retrieval product is assimilated into the Noah-MP land surface model over the entire European Alps at 1 km for the years 2015-2023 and we evaluate modelled snow depth and snow water equivalent against independent in-situ measurements and modelled snow cover against satellite observations. This work demonstrates the benefits of machine learning based snow depth retrievals and variable observation errors in EnKF-based snow DA.