Statistical treatment of solar energetic particle forecasting through supervised learning approaches
S. Benella*, M. Stumpo, M. Laurenza, T. Alberti, G. Consolini and M.F. Marcucci
February 15, 2023
Solar energetic particles (SEPs) represent one of the most hazardous events in space weather. In the last decades, a great variety of techniques have been developed for the prediction of SEP occurrence, mainly based on the statistical association between the $>$10 MeV proton flux and some precursors (e.g., solar flares, coronal mass ejections, etc.). In this paper we focus on the Empirical model for Solar Proton Event Real Time Alert (ESPERTA), a model which makes a prediction for an SEP event after the occurrence of a $\geq$M2 solar flare by considering three input parameters: the flare source region longitude, the soft X-ray fluence and the radio fluence at $\sim$1 MHz. Here, we recast the ESPERTA model in the supervised learning framework and we perform the cross validation of the predictive model also applying rare event corrections (i.e., data oversampling and loss function weighting) because of the highly unbalanced nature of the SEP occurrence. The best performances are obtained by using the Synthetic Minority Oversampling Technique, leading to a probability of detection of 0.83 and a false alarm rate (FAR) of 0.39. Nevertheless, the improvement of the validation scores with respect to the unbalanced case is small. A relevant FAR on the SEP prediction comes as a natural consequence of the sample base rates. In summary we give evidence that the statistical approach to the forecasting of SEP events should take into account the following considerations: 1) the model need to be calibrated with respect to the expected occurrence of SEP events, 2) the decision threshold strongly affects model performance and 3) the features used in the model, when taken individually, are unable to fully separate the classes of events in the parameter space, thus the use of techniques for handling unbalanced problems does not guarantee a better performance.
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