Bridging Gaussian and non-Gaussian Data Assimilation for High-Dimensional Geophysical Models

Abstract

Strongly nonlinear model dynamics and observation operators can induce bias in Gaussian-based data assimilation methods commonly used for numerical weather prediction, such as ensemble Kalman filters (EnKFs) and the 4D variational method (4DVar). This limitation is apparent for multiscale weather prediction systems that exhibit large uncertainty in smaller scales, or when observations are sensitive to cloud processes. Several methods have been proposed for improving data assimilation performance in nonlinear regimes. Examples include the adoption of an "outer loop" in variational methods, which helps reduce bias caused by linear assumptions. Likewise, numerous "iterative ensemble methods" exist, which periodically re-linearize model and measurement operators in the same manner. While the convergence properties of the latter methods are not completely known, numerical experiments performed by several previous studies suggest they can provide accurate solutions for mildly nonlinear problems. Another strategy that has gained momentum in recent years is to apply dimension-reduction procedures (namely, localization) to particle filters (PFs). PFs avoid the parametric estimation of Bayesian posterior densities, thus providing great flexibility for solving non-Gaussian data assimilation problems. However, these methods are more easily affected by sampling error than Gaussian-based methods—even when using localization.

My research introduces new approaches that bridge Gaussian and non-Gaussian data assimilation for geophysical models. To begin, the first part of this study investigates intrinsic limitations in data assimilation methods that are currently used for nonlinear applications in geoscience. We then propose novel data assimilation strategies for combining PFs with Gaussian-based methods that are more robust to sampling error. We demonstrate that the approaches have significant value within modern high-resolution regional atmospheric modeling systems, which are designed specifically for predicting tropical cyclones and severe convective storms. We further emphasize that this research has general implications for data assimilation within Earth-system models.