Machine Learning Methods Applied to the Global Modeling of Event-Driven Pitch Angle Diffusion Coefficients During High Speed Streams

Whistler-mode waves in the inner magnetosphere cause electron precipitation in the atmosphere through the physical process of pitch-angle diffusion. The computation of pitch-angle diffusion relies on quasi-linear theory and becomes time-consuming as soon as it is performed at high temporal resolution from satellite measurements of ambient wave and plasma properties. Such an effort is nevertheless required to capture accurately the variability and complexity of atmospheric electron precipitation, which are involved in various Earth's ionosphere-magnetosphere coupled problems. In this work, we build a global machine-learning model of event-driven pitch-angle diffusion coefficients for storm conditions based on the data of a variety of storms observed by the NASA Van Allen Probes. We first proceed step-by-step by testing 8 nonparametric machine learning methods. With them, we derive machine learning based models of event-driven diffusion coefficients for the storm of March 2013 associated with high-speed streams. We define 3 diagnostics that allow highlighting of the properties of the selected model and selection of the best method. Three methods are retained for their accuracy/efficiency: spline interpolation, the radial basis method, and neural networks (DNN), the latter being selected for the second step of the study. We then use event-driven diffusion coefficients computed from 32 high-speed stream storms in order to build for the first time a statistical event-driven diffusion coefficient that is embedded within the retained DNN model. We achieve a global mean event-driven model in which we introduce a two-parameter dependence, with both the Kp-index and time kept as in an epoch analysis following the storm evolution. The DNN model does not entail any issue to reproduce quite perfectly its target, i.e., averaged diffusion coefficients, with rare exception in the Landau resonance region. The DNN mean model is then used to analyze how mean diffusion coefficients behave compared with individual ones. We find a poor performance of any mean models compared with individual events, with mean diffusion coefficients computing the general trend at best, due to their large variability. The DNN-based model allows simple and fast data exploration of pitch-angle diffusion among its multiple variables. We finally discuss how to conduct uncertainty quantification of Fokker-Planck simulations of storm conditions for space weather nowcasting and forecasting.