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Prediction of spatio-temporal chaotic systems is important in various fields,such as Numerical Weather Prediction (NWP). While data assimilation methodshave been applied in NWP, machine learning techniques, such as ReservoirComputing (RC), are recently recognized as promising tools to predictspatio-temporal chaotic systems. However, the sensitivity of the skill of themachine learning based prediction to the imperfectness of observations isunclear. In this study, we evaluate the skill of RC with noisy and sparselydistributed observations. We intensively compare the performances of RC andLocal Ensemble Transform Kalman Filter (LETKF) by applying them to theprediction of the Lorenz 96 system. Although RC can successfully predict theLorenz 96 system if the system is perfectly observed, we find that RC isvulnerable to observation sparsity compared with LETKF. To overcome thislimitation 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 estimatedby LETKF. Our proposed method can successfully predict the Lorenz 96 systemusing noisy and sparsely distributed observations. Most importantly, our methodcan predict better than LETKF when the process-based model is imperfect.

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