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

We develop a feature-based framework to anticipate Forbush decreases in one-minute neutron-monitor records by tracking sliding-window invariants from information theory, scaling, and geometry. For each station we compute marker time series, including Shannon, spectral, approximate and sample entropy; Lempel-Ziv complexity; correlation dimension; and Higuchi and Katz fractal dimensions. Markers are smoothed with an exponentially weighted moving average and analyzed through within-station standardized first differences. Timing is referenced to an operational alignment time defined as the minimum of the smoothed count first difference, and marker leads are reported in minutes (negative values indicate anticipation). Station-level detectability is evaluated on a pre-alignment window using a robust z-score detector with bilateral threshold and persistence, without cross-correlation or hypothesis testing. We apply the pipeline to two FD episodes with broad station coverage (2023-04-23 and 2024-05-10; 28 stations each). Across events, a compact CORE panel shows consistently high detection rates and predominantly anticipatory lead distributions, with typical median leads on the order of several hours depending on the invariant and event. Lead dispersion across stations is substantial, with interquartile ranges commonly spanning a few hours, highlighting the need for station-wise criteria and distributional summaries rather than single-station inference. Representative marker trajectories confirm that early flagging corresponds to sustained pre-alignment excursions in marker differences, not tabulation artifacts. The approach is reproducible from open code, operates on native station units without cross-station homogenization, and remains qualitatively stable under sensitivity sweeps of windowing, smoothing, and detector parameters.

💡 Research Summary

The paper presents a systematic, feature‑based pipeline for anticipating Forbush decreases (FDs) in one‑minute galactic cosmic‑ray (GCR) neutron‑monitor data by exploiting a suite of information‑theoretic, scaling, and geometric invariants. For each of the 28 stations examined in two distinct FD events (23 April 2023 and 10 May 2024), the authors compute sliding‑window estimates of eight markers: Shannon entropy, spectral entropy, approximate entropy, sample entropy, Lempel‑Ziv complexity, correlation dimension, and Higuchi and Katz fractal dimensions. All raw count series are first smoothed with an exponential weighted moving average (EWM) to suppress high‑frequency noise while preserving abrupt transitions.

A station‑specific alignment time t₀ is defined as the time of the minimum of the smoothed count first‑difference within a predefined search window that encompasses the main decrease. This derivative‑aligned reference allows each station’s dynamics to be synchronized without imposing a universal physical onset time. For each marker, the smoothed marker series is also differentiated, standardized, and its most negative excursion within a pre‑t₀ window of length L is located. The lead ℓ* = t_marker – t₀ (in minutes) quantifies anticipation (ℓ* < 0) or delay (ℓ* > 0).

To assess operational detectability, a robust z‑score detector is applied to the pre‑t₀ marker‑difference series. The median and median absolute deviation (MAD) of the series provide a non‑parametric baseline; a detection is flagged when the absolute z‑score exceeds a bilateral threshold Z₀ for at least d consecutive evaluation steps. This yields a binary detection indicator per station‑marker pair, and the detection coverage Detect