Continuous Hyper-parameter OPtimization (CHOP) in an ensemble Kalman filter

TL;DR

This paper introduces a general workflow for tuning hyper-parameters in ensemble Kalman filters by framing hyper-parameter selection as a parameter estimation problem, demonstrating efficiency and robustness in experiments.

Contribution

It proposes a novel hyper-parameter estimation workflow that effectively tunes high-dimensional hyper-parameters in ensemble Kalman filters.

Findings

Workflow efficiently handles up to 1000 hyper-parameters.

Performs well across various experimental conditions.

Provides a generic approach for hyper-parameter tuning in data assimilation.

Abstract

Practical data assimilation algorithms often contain hyper-parameters, which may arise due to, for instance, the use of certain auxiliary techniques like covariance inflation and localization in an ensemble Kalman filter, the re-parameterization of certain quantities such as model and/or observation error covariance matrices, and so on. Given the richness of the established assimilation algorithms, and the abundance of the approaches through which hyper-parameters are introduced to the assimilation algorithms, one may ask whether it is possible to develop a sound and generic method to efficiently choose various types of (sometimes high-dimensional) hyper-parameters. This work aims to explore a feasible, although likely partial, answer to this question. Our main idea is built upon the notion that a data assimilation algorithm with hyper-parameters can be considered as a parametric mapping that links a set of quantities of interest (e.g., model state variables and/or parameters) to a corresponding set of predicted observations in the observation space. As such, the choice of hyper-parameters can be recast as a parameter estimation problem, in which our objective is to tune the hyper-parameters in such a way that the resulted predicted observations can match the real observations to a good extent. From this perspective, we propose a hyper-parameter estimation workflow and investigate the performance of this workflow in an ensemble Kalman filter. In a series of experiments, we observe that the proposed workflow works efficiently even in the presence of a relatively large amount (up to $10^3$) of hyper-parameters, and exhibits reasonably good and consistent performance under various conditions.