In this study, we present a method that combines a Long Short-Term Memory (LSTM) recurrent neural network with a Gaussian process (GP) model to provide up to 6-hr-ahead probabilistic forecasts of the Dst geomagnetic index. The proposed approach brings together the sequence modeling capabilities of a recurrent neural network with the error bars and confidence bounds provided by a GP. Our model is trained using the hourly OMNI and Global Positioning System (GPS) databases, both of which are publicly available. We first develop a LSTM network to get a single-point prediction of Dst. This model yields great accuracy in forecasting the Dst index from 1 to 6 hr ahead, with a correlation coefficient always higher than 0.873 and a root-mean-square error lower than 9.86. However, even if global metrics show excellent performance, it remains poor in predicting intense storms (Dst < À250 nT) 6 hr in advance. To improve it and to obtain probabilistic forecasts, we combine the LSTM model obtained with a GP and evaluate the hybrid predictor using the receiver operating characteristic curve and the reliability diagram. We conclude that this hybrid methodology provides improvements in the forecast of geomagnetic storms, from 1 to 6 hr ahead.

We present a methodology for generating probabilistic predictions for the Disturbance Storm Time(Dst) geomagnetic activity index. We focus on the One Step Ahead prediction task and use the OMNI hourly resolution data to build our models. Our proposed methodology is based on the technique of Gaussian Process Regression. Within this framework we develop two models; Gaussian Process Autoregressive (GP‐AR) and Gaussian Process Autoregressive with eXogenous inputs (GP‐ARX). We also propose a criterion to aid model selection with respect to the order of autoregressive inputs. Finally, we test the performance of the GP‐AR and GP‐ARX models on a set of 63 geomagnetic storms between 1998 and 2006 and illustrate sample predictions with error bars for some of these events.

We present the first study of the uncertainties associated with radiation belt simulations, performed in the standard quasi‐linear diffusion framework. In particular, we estimate how uncertainties of some input parameters propagate through the nonlinear simulation, producing a distribution of outputs that can be quite broad. Here we restrict our focus on two‐dimensional simulations (in energy and pitch angle space) of parallel‐propagating chorus waves only, and we study as stochastic input parameters the geomagnetic index Kp (that characterizes the time dependency of an idealized storm), the latitudinal extent of waves, and the average electron density. We employ a collocation method, thus performing an ensemble of simulations. The results of this work point to the necessity of shifting to a probabilistic interpretation of radiation belt simulation results and suggest that an accurate specification of a time‐dependent density model is crucial for modeling the radiation environment.

The Van Allen radiation belts in the magnetosphere have been extensively studied using models based on radial diffusion theory, which is derived from a quasi-linear approach with prescribed inner and outer boundary conditions. The 1D diffusion model requires the knowledge of a diffusion coefficient and an electron loss timescale, which is typically parameterized in terms of various quantities such as the spatial (L) coordinate or a geomagnetic index (e.g., Kp). These terms are typically empirically derived, not directly measurable, and hence are not known precisely, due to the inherent nonlinearity of the process and the variable boundary conditions. In this work, we demonstrate a probabilistic approach by inferring the values of the diffusion and loss term parameters, along with their uncertainty, in a Bayesian framework, where identification is obtained using the Van Allen Probe measurements. Our results show that the probabilistic approach statistically improves the performance of the model, compared to the empirical parameterization employed in the literature.

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