Machine Learning Based Method of Correcting Nonlinear Local Lyapunov Vectors Ensemble Forecasting

In this study, the feasibility and effectiveness of machine learning algorithm to improve ensemble forecasts using nonlinear local Lyapunov vectors (NLLVs) are explored preliminarily based on the Lorenz96 model. The results show that the machine learning model (Ens-ML) based on the ridge regression algorithm and the results of NLLV ensemble forecasting can effectively improve the overall forecasting skill. The Ens-ML outperforms the ensemble-averaged forecasting (EnsAve) and control forecasts (Ctrl) as well as the machine learning model based on Ctrl results (Ctrl-ML). It is also found that the improvement of forecasting skill depends on the total number of ensemble members used in the Ens-ML model, i.e. the increase of the number of ensemble members is conducive to the improvement of forecasting skill and to the decrease of overfitting in the early stage. By comparing the performances among different experimental cases, we find that the experimental forecasting errors of Ens-ML, Ctrl-ML and EnsAve are gradually smaller than that of Ctrl as the forecasting time increases. The attractors forecasted by Ens-ML, Ctrl-ML and EnsAve are also analyzed. Their attractor probability distributions show a contraction of the value domain, an increase in kurtosis and a convergence to the mean, especially for Ens-ML.