What visibility-graph curvature measures in Forbush decreases: a calibration on the two largest events of solar cycle 25

Abstract

Discrete curvatures of visibility graphs are increasingly used as descriptors of geophysical time series, but their response to a transient has rarely been calibrated against the simplest properties of that transient. We carry out this calibration for the nodal Forman--Ricci curvature $\mathcal{F}$ of natural visibility graphs applied to neutron-monitor records of the Gannon storm (2024 May 10--11) and the 2025 June 1 Forbush decrease (FD), the two largest FDs of solar cycle 25, using 30-min NMDB data from six NM64 stations ($R_c\simeq 0$--$7$~GV), i.e.\ twelve station--event series. Curvature collapses at FD onset in every series (Cliff's $\delta =0.63$--$1.0$), but a 6-h running standard deviation separates onset from quiet time more strongly (mean $\delta =0.96$ vs $0.89$; mean block-permutation displacement $z=-27$ vs $-14$). Injecting synthetic decreases into the real pre-event records of each station shows that the curvature extreme follows $|{\mathcal{F}}_{\min }|\propto (A/\sigma {)}^{0.50}$ ($R^2=0.88$), where $A$ is the FD amplitude and $\sigma$ the station's quiet-time noise, and is independent of the duration of the main phase (exponent $0.006$ over 3--36~h). With $A$, $\sigma$ and the main-phase duration of each series as the only inputs, the calibration predicts the twelve observed extremes with standardized residuals of mean $-0.26$ and standard deviation $0.94$, and the observed extremes correlate with $A/\sigma$ at Spearman $\rho =0.95$. Within the precision allowed by these data, nodal Forman--Ricci curvature of the whole-series visibility graph carries no information about these FDs beyond their amplitude relative to station noise; in particular, it does not distinguish the single-step Gannon decrease from the two-step June 2025 decrease.

arXiv comment7 pages, 1 table, 3 figures