Accounting for model error in Tempered Ensemble Transform Particle Filter and its application to non-additive model error

TL;DR

This paper extends the Tempered Ensemble Transform Particle Filter to handle non-additive model error and demonstrates its superior performance over the Regularized Ensemble Kalman Filter in both low- and high-dimensional problems.

Contribution

We introduce a simple extension of T(L)ETPF to account for non-additive model error and compare its effectiveness against R(L)EnKF in various scenarios.

Findings

T(L)ETPF outperforms R(L)EnKF in accuracy and efficiency.

T(L)ETPF requires significantly fewer ensemble members.

T(L)ETPF converges in fewer iterations, reducing computational costs.

Abstract

In this paper, we trivially extend Tempered (Localized) Ensemble Transform Particle Filter---T(L)ETPF---to account for model error. We examine T(L)ETPF performance for non-additive model error in a low-dimensional and a high-dimensional test problem. The former one is a nonlinear toy model, where uncertain parameters are non-Gaussian distributed but model error is Gaussian distributed. The latter one is a steady-state single-phase Darcy flow model, where uncertain parameters are Gaussian distributed but model error is non-Gaussian distributed. The source of model error in the Darcy flow problem is uncertain boundary conditions. We comapare T(L)ETPF to a Regularized (Localized) Ensemble Kalman Filter---R(L)EnKF. We show that T(L)ETPF outperforms R(L)EnKF for both the low-dimensional and the high-dimensional problem. This holds even when ensemble size of TLETPF is 100 while ensemble size of R(L)EnKF is greater than 6000. As a side note, we show that TLETPF takes less iterations than TETPF, which decreases computational costs; while RLEnKF takes more iterations than REnKF, which incerases computational costs. This is due to an influence of localization on a tempering and a regularizing parameter.