Optimizing the Ensemble Kalman Filter for Novel Applications in Volcanology

Abstract:

While ensemble-based data assimilation methods, such as the Ensemble Kalman Filter (EnKF), have been widely accepted in atmospheric science and oceanography, it is only within the last decade that they have been adapted for use in volcanology. The ability to forecast volcanic eruptions based on surface observations has been a long-standing goal within the field, and initial applications of the EnKF have shown promising results when given data from recent eruptions. However, given the novelty of this method within volcanology, many questions remain about the filter’s limitations and how to optimize its ability to resolve a magma system’s true state. In particular, current implementations of the EnKF preferentially attribute observed ground uplift to changes in reservoir size rather than internal pressure. While changes in these two parameters produce similar deformation patterns, they have vastly different implications for the reservoir’s mechanical stability and the likelihood of eruption. In this study, we assimilate synthetic observations in order to test how well various implementations of the EnKF can compensate for this apparent bias and improve the filter’s overall performance. For each aspect of the EnKF workflow we varied, such as the number of ensemble members or how model parameters are scaled, we use otherwise identical formulations of the EnKF to assimilate synthetic GPS and InSAR observations from two magma reservoirs, one increasing in size and the other increasing in pressure. The best performing implementation, as determined by its ability to match both the observations and the original synthetic parameters, is then carried forward into future tests, sequentially optimizing filter performance. Ultimately, we find the best performing models use a deterministic analysis step, scale all parameters to similar orders of magnitude, and use relatively simple parameter inflation methods instead of adaptive ones. Despite the improvements in performance gained by these implementations, the filter still preferentially favors reservoir size change. However, the EnKF remains a powerful tool, accurately reproducing critical parameters such as reservoir position, overall volume change, and wall stress.