Accounting for model error due to unresolved scales within ensemble Kalman filtering

TL;DR

This paper introduces a novel method to incorporate model error due to unresolved scales into ensemble Kalman filtering, improving filter accuracy with less parameter tuning and straightforward implementation.

Contribution

The paper extends deterministic model error formulation to ensemble transform Kalman filters, proposing both time-constant and time-varying error treatments with demonstrated improvements.

Findings

Significant improvement in filter skill using the proposed methods.

Both methods require less parameter tuning than standard approaches.

The approach is simple to implement within existing ensemble schemes.

Abstract

We propose a method to account for model error due to unresolved scales in the context of the ensemble transform Kalman filter (ETKF). The approach extends to this class of algorithms the deterministic model error formulation recently explored for variational schemes and extended Kalman filter. The model error statistic required in the analysis update is estimated using historical reanalysis increments and a suitable model error evolution law. Two different versions of the method are described; a time-constant model error treatment where the same model error statistical description is time-invariant, and a time-varying treatment where the assumed model error statistics is randomly sampled at each analysis step. We compare both methods with the standard method of dealing with model error through inflation and localization, and illustrate our results with numerical simulations on a low order nonlinear system exhibiting chaotic dynamics. The results show that the filter skill is significantly improved through the proposed model error treatments, and that both methods require far less parameter tuning than the standard approach. Furthermore, the proposed approach is simple to implement within a pre-existing ensemble based scheme. The general implications for the use of the proposed approach in the framework of square-root filters such as the ETKF are also discussed.