Open Issues in Statistical Forecasting of Solar Proton Events: A Machine Learning Perspective

Abstract

Abstract Several techniques have been developed in the last two decades to forecast the occurrence of Solar Proton Events (SPEs), mainly based on the statistical association between the 10 MeV proton flux and precursor parameters. The Empirical model for Solar Proton Events Real Time Alert (ESPERTA; Laurenza et al., 2009, https://doi.org/10.1029/2007sw000379 ) provides a quite good and timely prediction of SPEs after the occurrence of M2 soft x‐ray (SXR) bursts, by using as input parameters the flare heliolongitude, the SXR and the 1 MHz radio fluence. Here, we reinterpret the ESPERTA model in the framework of machine learning and perform a cross validation, leading to a comparable performance. Moreover, we find that, by applying a cut‐off on the M2 flares heliolongitude, the False Alarm Rate (FAR) is reduced. The cut‐off is set to where the cumulative distribution of M2 flares associated with SPEs shows a break which reflects the poor magnetic connection between the Earth and eastern hemisphere flares. The best performance is obtained by using the SMOTE algorithm, leading to probability of detection of 0.83 and a FAR of 0.39. Nevertheless, we demonstrate that a relevant FAR on the predictions is a natural consequence of the sample base rates. From a Bayesian point of view, we find that the FAR explicitly contains the prior knowledge about the class distributions. This is a critical issue of any statistical approach, which requires to perform the model validation by preserving the class distributions within the training and test datasets.