Combining Ensemble Kalman Filter and Reservoir Computing to predict spatio-temporal chaotic systems from imperfect observations and models

TL;DR

This paper explores combining Ensemble Kalman Filter and Reservoir Computing to improve prediction of chaotic systems from imperfect, noisy, and sparse observations, outperforming traditional methods under model imperfections.

Contribution

It introduces a novel hybrid approach that integrates LETKF with RC, enhancing prediction accuracy in challenging observational conditions and with imperfect models.

Findings

RC performs well with perfect observations but struggles with sparse data.

Combining LETKF and RC improves prediction under noisy, sparse observations.

The hybrid method outperforms LETKF when the system model is imperfect.

Abstract

Prediction of spatio-temporal chaotic systems is important in various fields, such as Numerical Weather Prediction (NWP). While data assimilation methods have been applied in NWP, machine learning techniques, such as Reservoir Computing (RC), are recently recognized as promising tools to predict spatio-temporal chaotic systems. However, the sensitivity of the skill of the machine learning based prediction to the imperfectness of observations is unclear. In this study, we evaluate the skill of RC with noisy and sparsely distributed observations. We intensively compare the performances of RC and Local Ensemble Transform Kalman Filter (LETKF) by applying them to the prediction of the Lorenz 96 system. Although RC can successfully predict the Lorenz 96 system if the system is perfectly observed, we find that RC is vulnerable to observation sparsity compared with LETKF. To overcome this limitation of RC, we propose to combine LETKF and RC. In our proposed method, the system is predicted by RC that learned the analysis time series estimated by LETKF. Our proposed method can successfully predict the Lorenz 96 system using noisy and sparsely distributed observations. Most importantly, our method can predict better than LETKF when the process-based model is imperfect.