Combining ensemble Kalman filter and reservoir computing to predict spatiotemporal chaotic systems from imperfect observations and models

Abstract

Abstract. Prediction of spatiotemporal 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), have recently been recognized as promising tools to predict spatiotemporal 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. In order to increase the scalability to larger systems, we applied a parallelized RC framework. 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.

Lorenz’s View on the Predictability Limit of the Atmosphere

“…For example, by applying deep convolutional neural networks, CNNs), Weyn et al (2019) [77][78][79] reported lead times of 14 days (in ensemble runs or some deterministic runs). Additionally, reservoir computing has been applied for replicating chaotic solutions of Lorenz models or predicting sea surface temperature (Pathak et al, 2017 [80]; Lu et al, 2018 [81]; Tomizawa and Sawada, 2021 [82]; Walleshauser and Bollt, 2022 [83]).…”

Multi-model ensemble benchmark data for hydrological modeling in Japanese river basins

“…This method has been applied to numerical weather prediction (Arcomano et al, 2022). Tomizawa and Sawada (2021) applied sequential data assimilation to a process-based model and this output of data assimilation was learnt by reservoir computing. The skill of this reservoir computing to predict non-linear systems is much better than the purely data-driven reservoir computing even though the process-model is imperfect.…”

Machine Learning Enables Real‐Time Proactive Quality Control: A Proof‐Of‐Concept Study

“…This research was partially supported by JSPS KAKENHI (Grant JP20K14558, JP20H04196, and JP23K03502) and the Research Field of Hokkaido Weather Forecast and Technology Development (endowed by Hokkaido Weather Technology Center Co. Ltd.). TH would like to thank Prof. Y. Sawada of the University of Tokyo for sharing his experience during Tomizawa and Sawada (2021).…”

“…(2017, 2018) demonstrated that a ML method known as reservoir computing (RC, Jaeger, 2001; Jaeger & Haas, 2004; Lukoševičius & Jaeger, 2009) successfully predicts evolution of low‐dimensional dynamical systems and their chaotic behavior. Tomizawa and Sawada (2021, hereafter TS21) indicated that the forecast accuracy of RC trained by a time series of analyses can outperform that of a physics‐based model if the model is imperfect and contains a non‐negligible bias. Similarly, Arcomano et al.…”