Derivative-Aligned Anticipation of Forbush Decreases from Entropy and Fractal Markers

TL;DR

This work tackles the problem of anticipating Forbush decreases from minute-scale neutron-monitor data by framing sliding-window invariants from information theory, scaling, and geometry as temporal markers. The authors implement a derivative-aligned pipeline that computes a compact panel of markers—Shannon and sample entropy, Lempel-Ziv complexity, DFA-based Hurst, Katz fractal dimension, and related invariants—on native NMDB counts, and translate marker excursions into station-level leads via a robust pre-onset detector. Across three diverse FD events, several markers consistently precede the count-derivative minimum, with lead times ranging from tens to hundreds of minutes and strong station coverage, especially for entropy and fractal descriptors; permutation and spectral entropy show event-dependent behavior. The approach is reproducible with open code, operates without cross-station homogenization, and yields a practical nowcasting toolkit that complements amplitude thresholds for space-weather operations, providing a principled, derivative-aligned early-warning panel for multi-station FD anticipation.

Abstract

We present a feature-based framework to anticipate Forbush decreases (FDs) from one-minute neutron-monitor data by tracking sliding-window invariants from information theory, scaling, and geometry. For each station and event, we compute marker series (Shannon, spectral, permutation, sample and approximate entropy; Lempel-Ziv complexity; Hurst via DFA; correlation dimension; Higuchi, Katz, and Petrosian fractal dimensions), smooth them with an exponentially weighted moving average, and analyze within-station standardized derivatives relative to the time of the minimum of the smoothed count derivative. Leads are reported in minutes (negative = precedes) and station-level significance is defined on a pre-onset window via a robust z-score detector with bilateral threshold and persistence; no cross-correlation or hypothesis testing is required. Applied to three recent FDs (2023-04-23, 2024-03-24, 2024-05-10), a compact, robust panel-Hurst (DFA), Katz fractal dimension, Shannon and sample entropy, and Lempel-Ziv-consistently precedes the count derivative with substantial station coverage, yielding actionable lead times from tens to several hundred minutes depending on morphology. Some descriptors are event-dependent: permutation and spectral entropy are strongly anticipatory in the extreme May 2024 episode but closer to contemporaneous in the rapid March 2024 case. Heatmaps, violin plots, and station overlays corroborate these patterns. The approach is reproducible from open code, operates on native station units without cross-station homogenization, and is qualitatively stable to window, smoothing, and detector settings. These results support derivative-aligned invariant panels as practical early-warning tools that complement amplitude thresholds and enable nowcasting workflows in space-weather operations.

Figures (4)

• Figure 1: Representative minute–resolution GCR count series around the three FD events analyzed in this work. Vertical dashed lines indicate the FD onset bracket used in this study. Series are NMDB one–minute counts; axes are station–specific native units.
• Figure 2: Median lead by invariant and event (min; negative = precedes).
• Figure 3: Station-wise lag distributions by invariant for three events studied (negative = precedes).
• Figure 4: Derivative overlays for a fixed panel of markers (Katz fractal dimension, Hurst via DFA, Shannon entropy, sample entropy) against the EWM–smoothed derivative of the original count (native units). Negative excursions of marker derivatives ahead of the most negative count–derivative episode indicate anticipatory behavior.