A New Method for Probabilistic Spatiotemporal Forecasts of Solar Soft X-Ray “S-Class” (>X10) Superflares

Abstract

Solar superflares of S-class (>X10 in soft X-rays) pose extreme space weather hazards, yet their prediction remains a fundamental challenge owing to their rapid and transient natures and the limitations of conventional event-based forecasts. We introduce for the first time, a probabilistic spatiotemporal framework designed to identify extended epochs and heliographic zones with heightened superflare likelihood, rather than predicting individual events. Our methodology analyzes nearly five decades of Geostationary Operational Environmental Satellites SXR observations (1975–2025) and introduces two novel components: (a) a cross-Laplacian diagnostic, derived from the butterfly diagrams of sunspot area and SXR flare density, which identifies photosphere-corona coupling and pinpoints magnetic energy accumulation sites as preferential zones for S-flare occurrence; and (b) a temporal model based on the coupled phase states of 1.7-year and 7-year oscillations, extracted via wavelet analysis and projected forward using a Bayesian Least-Squares Support Vector Machine method. Integrating these spatial and temporal diagnostics yields a unified forecast, we identify 2025.7–2026.6 and 2027.2–2027.9 years, as the primary high-probability windows for S-class flare activity during Solar Cycle 25, corresponding preferentially to latitudinal bands in the southern ((Formula presented.) S– (Formula presented.) S) and northern ((Formula presented.) N– (Formula presented.) N) hemispheres, respectively. Subsequent windows are projected for Cycle 26. This physics-informed, probabilistic approach provides a robust strategy for anticipating periods of extreme solar activity by characterizing the inherent patterns of magnetic energy storage and release in the solar atmosphere.