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Snow, glaciers, and permafrost are essential climate variables (ECV) that regulate the global cycles of energy, carbon, and water. At the same time, these cryospheric ECVs are only partially observable by satellites due to gaps, noise, and indirect retrieval algorithms. Data assimilation (DA), namely the Bayesian fusion of uncertain models and noisy observations, presents a natural solution to the problem of partial observability. Nonetheless, unlike in numerical weather prediction, DA has received relatively little attention from the Earth observation (EO) community despite its potential as a generalized retrieval framework that adds value by filling gaps and inferring latent ECVs with uncertainty quantification. This contribution presents active research on applying ensemble-based DA techniques to carry out cryospheric reanalysis constrained by satellite data. Our future goals with these efforts are to generate consistent global high resolution reanalyses of seasonal snow mass (also known as snow water equivalent or simply SWE), glacier mass balance, and the thermal state of permafrost. In doing so, we seek to leverage a myriad of data streams including Earth observing satellites, global atmospheric reanalyses, airborne retrievals, and in-situ observations. Here we focus on seasonal snow since accurate global snow mass estimation, particularly in mountainous terrain, remains a major unsolved problem in snow hydrology. To help tackle this problem, we are developing a global scale ensemble-based snow reanalysis product by assimilating ESA Snow_cci fractional snow-covered area retrievals. Using a simple snow model we are able to devote considerable computational resources to generate a global snow reanalysis at daily temporal resolution and kilometric spatial resolution while still being able to afford using promising iterative ensemble-based DA schemes. For the latter, we explore recent developments in hybridizing iterative ensemble Kalman and particle methods to provide robust Bayesian posterior inference. In particular, we demonstrate how these schemes can be used as nested smoothers to hierarchically infer prior hyperparameters related to snow climatology. The new reanalysis approach is evaluated using independent spaceborne, airborne, and in-situ validation data by comparing its performance to state-of-the-art regional snow reanalyses and existing global snow mass products in the form of ERA5-Land reanalysis data and ESA Snow_cci SWE retrievals. Unlike existing global snow products, this new snow reanalysis product is uncertainty-aware, assimilates snow satellite data, and specifically targets a key knowledge gap concerning mountain snow mass. Concurrent efforts to adapt this DA framework towards the generation of global ensemble-based reanalyses for glaciers and permafrost will also be showcased to emphasize synergies across these terrestrial cryospheric reanalysis efforts. We highlight that, by combining EO with cryospheric models, ensemble-based DA can transform largely untapped climate data into actionable climate information on cryospheric ECVs. The baked-in uncertainty quantification in this probabilistic climate information empowers us to make decisions in response to climate change and its perilous impacts on the mountain cryosphere.
