Preliminary application of machine learning in ensemble forecasting

The optimal perturbation method is a beneficial way to generate ensemble members to be used in ensemble forecasting. With orthogonal optimal perturbation, orthogonal conditional nonlinear optimal perturbations (O-CNOPs) generating initial perturbations and orthogonal nonlinear forcing singular vectors (O-NFSVs) generating model perturbations are two kinds of skillful ensemble forecasting methods. There is main disadvantage that O-CNOPs and O-NFSVs generate optimal perturbation members may need a lot of time, but in practical weather prediction, the ensemble members usually need to be generated quickly. In order to benefit from O-CNOPs and O-NFSVs, as well as considering the cost of calculation, therefore, we present a way with the big data and machine learning thinking to simplify the process of the optimal perturbation ensemble methods. Using the historical samples and their optimal perturbations to establish a database, we look for the historical sample which is analogous to what need to be forecasted currently from the database by using the convolutional neural network (CNN). In comparison with using optimization algorithm to get O-CNOPs and O-NFSVs directly, this way gets O-CNOPs and O-NFSVs faster which still obtain acceptable prediction performance. In addition, once the CNN model is trained completely, the cost of time for prediction will be saved. We illustrate the advantage by numerical simulations of a Lorenz 96 model.

Further more, based on above study, some comparison of the ensemble forecasting skill of O-CNOPs and O-NFSVs has been done, and there are three results for the reference: (1) in the early stage (1-6 days), the O-CNOPs method perform more skillfully, and in the later stage (6-12 days), the O-NFSVs method perform more skillfully; (2) within 1-5 days, if the development of analysis error is bigger than or close to the average value of the analysis error development of historical samples, the O-CNOPs method is preferred, else the O-NFSVs method is preferred; (3) within 0-3 days, if the development of energy is bigger than or close to the average value of the energy development of the historical samples, the O-CNOPs method is preferred, else the O-NFVS method is preferred. Next, further work is required to examine and explore more and deeper research using machine learning in ensemble forecasting studies of atmosphere and other systems.