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

TL;DR

AdaPBS presents an adaptive, iterative particle smoothing algorithm that fuses PBS with Adaptive Multiple Importance Sampling to overcome particle degeneracy and remove a fixed-iteration constraint. It leverages a deterministic mixture proposal and data-driven adaptation to approximate challenging cryospheric posteriors in non-Gaussian, nonlinear settings, outperforming or matching common particle and ensemble Kalman methods across simple and high-dimensional tests. The approach provides automatic, site- and year-level computational scaling via an ESS-based stopping criterion, enabling efficient uncertainty quantification in distributed cryospheric data assimilation. Implemented in MuSA and validated against RAM-MCMC benchmarks, AdaPBS offers a practical, open-source route to robust, non-Gaussian data assimilation for downstream hydrology, climate reanalysis, and operational forecasting in cryospheric systems.

Abstract

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 PBS that is commonly used in cryospheric data assimilation, with the AMIS 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 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 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 MuSA toolbox, which now includes AdaPBS and MCMC among the growing list of available cryospheric data assimilation methods.

Figures (7)

• Figure 1: Flowchart showing the workflow in the adaptive particle batch smoother (AdaPBS) as an extension (green) of the non-iterative PBS method (yellow).
• Figure 2: Results from the particle batch smoother (PBS) assimilating drone-based snow depth observations in a temperature index model for a single cell at Izas in water year 2019: The model parameter space visualized as the temperature bias parameter $b$ on the $y$-axis and the precipitation correction $c$ on the $x$-axis with the prior ensemble of particles shown with red dots while green stars indicate non-negligible PBS weights and the blue-green-yellow banana-shaped distribution shows the gold-standard MCMC samples obtained via RAM (left panel); The model state space showing the trajectory of snow depth with the prior (orange) and posterior (green) mean (solid line) $\pm 1$ standard deviation (shading) with the assimilated observations (red dots).
• Figure 3: Analogous to Figure \ref{['fig:02']} but for the ensemble smoother (ES) with the prior (top left) and posterior (top right) in the model parameter space and the trajectory of snow depth (bottom) in the model state space.
• Figure 4: Analogous to Figure \ref{['fig:03']} but for an iterative ensemble smoother (IES) in the form of the ensemble smoother with multiple data assimilation (ES-MDA). The top panels show the evolution from the prior to the posterior ensemble members (red) across the MDA iterations along with the reference banana-shaped MCMC posterior samples. As before, the bottom panel shows the predicted snow depth in model state space, but with a better calibrated posterior (green).
• Figure 5: Analogous to Figure \ref{['fig:04']} but for the adaptive particle batch smoother (AdaPBS). Note that the results after the initial iteration (top left) correspond exactly (ignoring Monte Carlo variance) to those that would be obtained from the PBS in Figure \ref{['fig:02']}. The zero-based iteration counter from $0$ to $4$ corresponds to $\ell-1$ in the algorithm description, so here the AdaPBS converged (here $N_\mathrm{eff}>30$) in $\ell=5$ iterations.