Borrowing strength: a hierarchical glacier reanalysis through a robust particle filter

World-wide glacier mass loss affects global sea-level, river runoff, freshwater influx to the oceans, glacier-related hazards, and landscape changes, with implications for human livelihoods and ecosystems. Robust and high resolution glacier mass-balance estimates are hence essential to understand the past, monitor the present, and prepare effective adaptation strategies for the future. In this paper, we propose a proof of concept of a hierarchical data assimilation scheme relying on glacier-wide mass balance measurements to infer the parameters of a temperature-index glacier evolution model. We rely on a modified particle method to iteratively estimate the posterior probability distribution of the dynamical glacier state in order to successfully accommodate data gaps as well as model nonlinearity and non-Gaussianity. We further propose a hierarchical formulation of the particle filtering method, effectively imposing additional spatial constraints and regularization on the surface mass balance model parameters for individual regions and glaciers. Our method is tested on several outlet glaciers of the Jostedalsbreen ice cap in Norway. Through its spatial hierarchical formulation, the particle filter scheme is further able to borrow strength by enabling statistically consistent sharing of mass balance information between neighboring glaciers in a region, providing robust estimates of glacier mass balance and their associated uncertainties. This study underscores the value of hierarchical Bayesian data assimilation, offering a robust and computationally tractable tool for estimating past glacier changes with high spatio-temporal coverage.