Open Issues in Statistical Forecasting of Solar Proton Events: A Machine Learning Perspective. Issue 10 (5th October 2021) - Stumpo, Mirko
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 E 20 ° 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. Plain Language Summary: This paper addresses the open issues in the statistical forecasting of solar proton events by reinterpreting the ESPERTA model in a machine learning approach. Results show a good performance for central and well‐connected events and highlight the importance of validating any statistical method by preserving the base rate of the events. Key Points: We reinterpret the Empirical model for Solar Proton Events Real Time Alert (ESPERTA) model in the framework of machine learning, apply rare events corrections and perform a suitable cross validation We obtain a good performance, especially for central and well‐connected events We find that the False Alarm Rate (FAR) depends on the ratio between the Solar Proton Event (SPE) and non‐SPE flares, which has to be considered in the validation