[Paper Review] Evolving beyond collapse: An adaptive particle batch smoother for cryospheric data assimilation

Kristoffer Aalstad, Esteban Alonso-González+4 more|arXiv (Cornell University)|Jan 27, 2026

Meteorological Phenomena and Simulations0 citations

TL;DR

AdaPBS is an adaptive iterative particle smoother that combines PBS with Adaptive Multiple Importance Sampling to reduce ensemble collapse and enable early stopping, demonstrated on cryospheric snow data with open-source MuSA.

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.

Motivation & Objective

• Motivate improved data assimilation for cryospheric systems amid observational and model uncertainties.
• Develop an adaptive particle-based scheme that mitigates ensemble collapse and adjusts computational cost to problem complexity.
• Integrate Adaptive Multiple Importance Sampling with the Particle Batch Smoother to create AdaPBS.
• Benchmark AdaPBS against gold-standard MCMC and iterative ensemble Kalman methods in snow data contexts.
• Provide an open-source implementation within the MuSA toolbox for broad community use.

Proposed method

• Extend the Particle Batch Smoother (PBS) with Adaptive Multiple Importance Sampling to form AdaPBS.
• Make AdaPBS iterative and adaptive to improve resilience against ensemble collapse and enable early stopping.
• Benchmark using MCMC as a costly gold-standard in a simplified temperature index snow model.
• Evaluate AdaPBS with ES-MDA-like and ES-like ensembles on snow depth observations from ESMSnowMIP across multiple sites.
• Utilize MuSA as the open-source framework for implementation and testing.
• Compare performance to other commonly used cryospheric DA algorithms.

Figure 1: Flowchart showing the workflow in the adaptive particle batch smoother (AdaPBS) as an extension (green) of the non-iterative PBS method (yellow).

Experimental results

Research questions

• RQ1 Does AdaPBS improve robustness to ensemble collapse compared with traditional PBS?
• RQ2 How does AdaPBS perform relative to MCMC and ES-MDA benchmarks in snow data assimilation problems?
• RQ3 Can AdaPBS adapt computational cost to problem complexity, down to grid-cell and water year levels?
• RQ4 Is AdaPBS effective with dense observational datasets in cryospheric DA?
• RQ5 Can AdaPBS be implemented openly within the MuSA toolbox for broader adoption?

Key findings

• AdaPBS is a robust and reliable tool for cryospheric data assimilation.
• AdaPBS outperforms or at least matches the performance of other commonly used algorithms in tested scenarios.
• AdaPBS successfully handles complex cases with dense observational datasets.
• Experiments span multiple sites and use a more complex snow model, demonstrating broad applicability.
• All experiments are conducted within the open-source MuSA toolbox, which includes AdaPBS and MCMC among other methods.

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 corre