A combined data assimilation and deep learning approach for continuous spatio-temporal SWE reconstruction from sparse ground tracks

• Lack of ground observations on snow water equivalent (SWE) in high-mountain regions • Space-based laser altimeters can provide high-resolution snow depth data with gaps • Combined data assimilation and deep learning for spatio-temporal SWE reconstruction • Tested in Dischma valley (Switzerland) • Reliable SWE estimates and uncertainty at approximately 100 m resolution Our understanding of the impact of climate change on water availability and natural hazards in high-mountain regions is limited due to the spatial and temporal scarcity of ground observations of precipitation and snow. Freely available, satellite-based information about the snowpack is currently mainly limited to indirect measurements of snow-covered area or very coarse-scale snow water equivalent (SWE), but only for flat areas in lowlands without vegetation cover. Novel space-based laser altimeters, such as ICESat-2, have the potential to provide high-resolution snow depth data in worldwide mountain regions where no ground observations exist. However, these space-based laser altimeters come with spatial gaps between ground tracks, obtained without repetition at a give location. To overcome these drawbacks, here, we present a combined probabilistic data assimilation and deep learning approach to reconstruct spatio-temporal SWE from observations of snow depth along ground tracks, imitating ICESat-2 tracks in view of a potential future global application. Our approach is based on assimilating SWE and snow cover information in a degree-day model with an iterative ensemble smoother (IES) which allows temporally reconstructing SWE along hypothetical ground tracks separated by 3 km. As input, the degree-day model uses daily precipitation and downscaled air temperature from the ERA5 reanalysis. A feedforward neural network (FNN) is then used for spatial propagation of the daily mean and standard deviation of the updated SWE ensemble members obtained from the IES. The combined IES-FNN approach provides uncertainty-aware spatio-temporally continuous estimates of SWE. We tested our approach in the alpine Dischma valley (Switzerland) using high-resolution snow depth maps obtained from photogrammetric techniques mounted on airplanes and unmanned aerial system observations. Our results show that the IES-FNN model provides reliable estimates at a resolution of approximately 100 m. Even assimilating only one SWE observation during the year (combined with satellite-based melt-out date estimates) produces satisfying results when evaluating the IES-FNN SWE reconstructions on independent dates and smaller ( < 4 km 2 ) areas: mean absolute error of 86 mm (78 mm) at Schürlialp (Latschüelfurgga) for average SWE of 180 mm (254 mm), and average spatial linear correlation with the reference SWE of 0.51 (0.48). However, the assimilated SWE observation must not be too early in the accumulation season or too late in the melt season when the snowpack is starting or ending to accumulate or melt, respectively. Smaller distances between ground tracks (1500 m and 500 m) show improved performance of the IES-FNN approach in space, with no significant improvement in terms of temporal reconstruction. Applying the IES-FNN approach to e.g., real ICESat-2 data, remains challenging due to the higher uncertainties associated with these data. However, the approach we propose remains potentially very helpful in addressing the problem of scarcity of ground observations of precipitation and snow in high-mountain regions.