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

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 (Formula presented.) 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 (Formula presented.) M2 soft x-ray (SXR) bursts, by using as input parameters the flare heliolongitude, the SXR and the (Formula presented.) 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 (Formula presented.) M2 flares heliolongitude, the False Alarm Rate (FAR) is reduced. The cut-off is set to (Formula presented.) where the cumulative distribution of (Formula presented.) 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.