Evolving beyond collapse: an adaptive particle batch smoother for cryospheric data assimilation

We present a new adaptive particle-based data assimilation scheme for cryospheric applications that leverages promising developments in importance sampling. The proposed approach seeks to combine some of the advantages of two widely used classes of schemes: particle methods and iterative ensemble Kalman methods. Specifically, it extends the Particle Batch Smoother (PBS) that is commonly used in cryospheric data assimilation, with the Adaptive Multiple Importance Sampling algorithm. This adaptive formulation transforms the PBS into an iterative scheme with improved resilience against ensemble collapse and the ability to implement early-stopping strategies. As such, computational cost is automatically adapted to the complexity of the problem at hand, even down to the grid-cell and water year level in distributed multiyear simulations. In homage to the schemes that it builds on, we coin this new algorithm the Adaptive Particle Batch Smoother (AdaPBS) and we test it across a range of scenarios. First, we conducted an intercomparison of some of the most commonly used cryospheric data assimilation algorithms using Markov Chain Monte Carlo (MCMC) simulation as a costly gold-standard benchmark in a simplified temperature index model assimilating snow depth observations. We further evaluated AdaPBS by assimilating snow depth observations from the ESMSnowMIP project at 6 different sites spanning 3 continents, using an ensemble of simulations generated with the more complex Flexible Snow Model (FSM2). Our results demonstrate that AdaPBS is a robust and reliable tool, outperforming or at least matching the performance of other commonly used algorithms and successfully handling complex cases with dense observational datasets. All experiments were carried out using the open-source Multiple Snow Data Assimilation System (MuSA) toolbox, which now includes AdaPBS and MCMC among the growing list of available cryospheric data assimilation methods. Beyond our cryospheric focus, the scheme has the potential to be applied directly to the closely related fields of land surface and hydrological data assimilation as well as more general geoscientific Bayesian inference problems.