Multi-index ensemble Kalman filtering

TL;DR

This paper introduces the multi-index EnKF (MIEnKF), a novel filtering method combining multi-index Monte Carlo and ensemble Kalman filtering to improve efficiency in data assimilation tasks.

Contribution

The paper extends the multilevel EnKF to a multi-index framework, enhancing efficiency by coupling resolutions in two degrees of freedom, and provides theoretical and numerical validation.

Findings

MIEnKF outperforms EnKF and MLEnKF in efficiency under certain conditions.

Numerical tests confirm the theoretical efficiency gains.

MIEnKF is more tractable for high-resolution filtering problems.

Abstract

In this work we combine ideas from multi-index Monte Carlo and ensemble Kalman filtering (EnKF) to produce a highly efficient filtering method called multi-index EnKF (MIEnKF). MIEnKF is based on independent samples of four-coupled EnKF estimators on a multi-index hierarchy of resolution levels, and it may be viewed as an extension of the multilevel EnKF (MLEnKF) method developed by the same authors in 2020. Multi-index here refers to a two-index method, consisting of a hierarchy of EnKF estimators that are coupled in two degrees of freedom: time discretization and ensemble size. Under certain assumptions, when strong coupling between solutions on neighboring numerical resolutions is attainable, the MIEnKF method is proven to be more tractable than EnKF and MLEnKF. Said efficiency gains are also verified numerically in a series of test problems.