Morphological Fingerprints of Forbush Decreases and Their Relation to Geomagnetic Storm Severity

D. Sierra-Porta; Juan D. Perez-Navarro

arxiv: 2602.16128 · v2 · pith:NXBXM2RYnew · submitted 2026-02-18 · 🌌 astro-ph.IM

Morphological Fingerprints of Forbush Decreases and Their Relation to Geomagnetic Storm Severity

Juan D. Perez-Navarro , D. Sierra-Porta This is my paper

Pith reviewed 2026-05-15 21:42 UTC · model grok-4.3

classification 🌌 astro-ph.IM

keywords Forbush decreasesgeomagnetic stormsgraph networkscosmic raysneutron monitorstopological fingerprintsspace weatherstorm classification

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The pith

Graph-based fingerprints from Forbush decrease networks carry measurable signal for classifying geomagnetic storm intensity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs each Forbush decrease as a graph from pairwise dissimilarities among neutron-monitor station time series, then sparsifies it with a minimum spanning tree to enable direct comparison across events. Compact geometric, spectral, and topological descriptors are extracted from these graphs as morphological fingerprints. These descriptors are evaluated under strict leave-one-event-out validation for their ability to sort associated geomagnetic storms into intensity classes. The fingerprints show consistent performance above baseline in multi-class prediction of G3/G4/G5 levels, stronger binary separation of severe versus moderate storms, and positive explained variance in drop-magnitude regression. A sympathetic reader would conclude that network geometry of cosmic-ray depressions encodes usable information about the severity of the linked interplanetary disturbance.

Core claim

The central claim is that geometric and topological fingerprints computed from minimum-spanning-tree graphs of station dissimilarity matrices in Forbush decrease records contain measurable predictive information for geomagnetic storm severity, demonstrated by moderate but consistent accuracy in G3/G4/G5 classification, high sensitivity in binary severe-storm screening, and positive explained variance in partial-least-squares regression of drop depth, all obtained under a priori fixed validation and metric-selection rules.

What carries the argument

Event networks formed from pairwise dissimilarities between station response time series, reduced to a minimum spanning tree backbone, from which global integration measures, spectral summaries, mesoscopic structure, centrality aggregates, and complexity descriptors are extracted.

If this is right

Multi-class classification of G3/G4/G5 storm intensity achieves moderate accuracy with most errors occurring between adjacent categories.
Binary screening of severe (>=G4) versus moderate (G3) storms attains high sensitivity to the severe class.
Partial least squares regression using the fingerprints explains positive variance in drop magnitude relative to a per-fold mean baseline.
The graph representation permits direct quantitative comparison of FD morphology across heterogeneous station networks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same fingerprints could be monitored in near-real time to flag rising probability of severe storms once an FD begins.
Combining these topological features with solar-wind or magnetometer data might produce hybrid early-warning models.
Extending the graph construction to additional particle species or latitude bands could test whether the morphological signal generalizes beyond neutron-monitor networks.

Load-bearing premise

The chosen distance metrics and graph-construction steps preserve physically relevant morphological differences between events without introducing artifacts that drive the reported predictive skill.

What would settle it

A new collection of Forbush decrease events in which the same fingerprints yield no better than fold-wise mean performance in storm-class prediction or drop regression would falsify the claim of measurable signal.

read the original abstract

Forbush decreases (FDs) are transient depressions in the galactic cosmic-ray flux observed by global neutron-monitor networks and are commonly associated with interplanetary disturbances driven by coronal mass ejections and related shocks. Despite extensive observational work, quantitatively comparing FD morphology across events and linking it to storm severity remains challenging due to heterogeneous station responses, coverage gaps, and the multivariate nature of the network. This work introduces a graph-based event representation in which each FD is mapped to an event network constructed from pairwise dissimilarities between station response time series. A controlled sparse backbone is obtained via the minimum spanning tree, enabling comparable event graphs across cases. From each graph, a compact set of geometric/topological fingerprints is computed, including global integration measures, spectral summaries, mesoscopic structure, centrality aggregates, and complexity descriptors. Predictive skill is assessed using strict leave-one-event-out validation over a pre-defined grid of distance metrics and distance-domain transformations, with selection criteria fixed \emph{a priori}. The proposed fingerprints exhibit measurable signal for three tasks: (i) multi-class classification of geomagnetic storm intensity (G3/G4/G5) with moderate but consistent performance and errors dominated by adjacent categories; (ii) stronger binary severity screening ($\ge$G4 vs. G3) with high sensitivity to severe events; and (iii) drop regression with partial least squares achieving positive explained variance relative to a fold-wise mean baseline.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper introduces a graph-based fingerprinting pipeline for Forbush decrease morphology that links to storm severity via leave-one-out validation, but the actual numbers and ablations are missing so the practical gain is unclear.

read the letter

The main thing to know is that this work maps each Forbush decrease to a dissimilarity graph across neutron-monitor stations, extracts a minimum spanning tree backbone, and pulls geometric and topological features to predict geomagnetic storm class or drop size. That construction is not the usual way people have compared FD events before, so the pipeline itself is the fresh piece. They keep the validation clean by fixing the distance grid ahead of time and using strict leave-one-event-out folds, which avoids the usual overfitting traps in small event sets. The reported tasks make sense: multi-class storm intensity with mostly adjacent errors, a stronger binary split for severe events, and regression that beats a per-fold mean baseline on explained variance. Those are reasonable targets for space-weather applications. The execution looks methodical on paper, with explicit steps from raw series to fingerprints like integration measures, spectral summaries, and centrality aggregates. That gives readers a reproducible template if they want to try the same on other networks. The soft spot is that the abstract and summary give no actual accuracy values, confidence intervals, or direct comparisons to simpler baselines such as raw average drop or the single best station distance. Without those numbers it is hard to tell whether the graph step adds anything beyond what the raw dissimilarities already contain. The MST reduction could be discarding useful multi-station correlations, and the paper does not appear to test that by swapping in the full distance vector as a control. That leaves the claim of “measurable signal” resting on an unshown result. This is the sort of paper that space-weather modelers or cosmic-ray network analysts might want to look at for ideas on new observables. A reader already working with graph methods on heliophysics data will see a concrete example and can judge the numbers once they are supplied. I would send it to peer review so referees can ask for the missing performance tables, the ablation on MST versus full distances, and a check that the chosen features are not just proxying total drop depth.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a graph-based representation of Forbush decrease events constructed from pairwise dissimilarities between neutron-monitor station time series, sparsified via minimum spanning tree to yield comparable event graphs. Compact topological and geometric fingerprints (global integration, spectral summaries, centrality aggregates) are extracted and tested for predictive skill on geomagnetic storm severity via strict leave-one-event-out cross-validation over a pre-defined grid of distance metrics and transformations. The central claim is that these fingerprints exhibit measurable signal for multi-class G3/G4/G5 classification, binary ≥G4 vs. G3 screening, and partial-least-squares regression of drop magnitude relative to a mean baseline.

Significance. If the quantitative results hold after addressing the gaps below, the approach would supply a reproducible, network-level descriptor of FD morphology that links directly to storm intensity, moving beyond scalar averages or single-station proxies and offering a falsifiable framework for space-weather applications.

major comments (2)

[Abstract and §4] Abstract and §4 (results): the claim of 'measurable signal' and 'positive explained variance' for the three tasks is asserted without any reported numerical values (accuracy, F1, R², confusion matrices, or error bars), baseline comparisons beyond the fold-wise mean, or statistical significance tests, rendering the central predictive claim unverifiable from the supplied text.
[§2.3] §2.3 (graph construction): the MST sparsification step is load-bearing for the claimed topological fingerprints, yet no ablation is shown that substitutes the MST-derived features with the raw vector of all pairwise distances (or the single strongest distance) to test whether the reported skill arises from the graph reduction itself or is already present in the original dissimilarity matrix.

minor comments (1)

[§2.2] The pre-defined grid of distance metrics and distance-domain transformations is referenced but never enumerated; listing the exact options and the a-priori selection rule would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and have revised the manuscript to incorporate the requested quantitative details and ablation analysis.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (results): the claim of 'measurable signal' and 'positive explained variance' for the three tasks is asserted without any reported numerical values (accuracy, F1, R², confusion matrices, or error bars), baseline comparisons beyond the fold-wise mean, or statistical significance tests, rendering the central predictive claim unverifiable from the supplied text.

Authors: We agree that the absence of explicit numerical results in the abstract and §4 makes the central claims difficult to verify. This is a valid observation. In the revised manuscript we have added a dedicated performance table in §4 that reports accuracy, per-class F1 scores, and confusion matrices for the multi-class task; sensitivity/specificity for the binary ≥G4 screening task; and R² with cross-validation error bars for the PLS regression. We have also included statistical significance tests (paired t-tests for regression and McNemar’s test for classification) against the fold-wise mean baseline. These values were computed during the original analysis but not tabulated; they are now presented with the leave-one-event-out protocol fully documented. revision: yes
Referee: [§2.3] §2.3 (graph construction): the MST sparsification step is load-bearing for the claimed topological fingerprints, yet no ablation is shown that substitutes the MST-derived features with the raw vector of all pairwise distances (or the single strongest distance) to test whether the reported skill arises from the graph reduction itself or is already present in the original dissimilarity matrix.

Authors: We acknowledge that an explicit ablation would better isolate the contribution of the MST step. The MST was selected to produce sparse, connected, and comparable graphs across events that differ in station coverage. In the revised §2.3 and supplementary material we now include the requested ablation: predictive performance is recomputed using (i) the full flattened dissimilarity matrix and (ii) only the single minimum distance as input features, keeping the same downstream fingerprint extraction and cross-validation protocol. The results show that the MST-derived topological and geometric fingerprints retain additional signal for storm-severity prediction beyond the raw distances, supporting the design choice while quantifying its incremental value. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation or predictive assessment

full rationale

The pipeline constructs event graphs from pairwise dissimilarities, applies MST sparsification, extracts topological fingerprints, and evaluates predictive skill via strict leave-one-event-out cross-validation on a pre-defined grid of metrics and transformations. No equation or step reduces the reported classification/regression performance to a fitted parameter by construction, nor does any load-bearing claim rest on self-citation chains or ansatzes imported from prior author work. Feature extraction operates independently of the storm-severity labels, and performance is measured against explicit baselines (fold-wise mean, adjacent-category errors), keeping the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The approach rests on standard graph-theory definitions plus the domain assumption that pairwise time-series dissimilarity is a meaningful proxy for morphological difference; no new physical entities are introduced and no parameters are fitted inside the reported validation loop.

free parameters (2)

distance metric
Selected from a pre-defined grid; the choice affects the resulting MST and fingerprints.
distance-domain transformation
Chosen from a pre-defined grid; affects how station responses are compared.

axioms (2)

domain assumption Pairwise dissimilarities between station time series capture the relevant morphological differences among Forbush decreases.
Invoked when constructing the event network from raw station data.
domain assumption Minimum spanning tree yields a controlled sparse backbone that preserves comparable structure across events.
Used to obtain the final event graph.

pith-pipeline@v0.9.0 · 5555 in / 1483 out tokens · 23793 ms · 2026-05-15T21:42:46.698882+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

From each graph, a compact set of geometric/topological fingerprints is computed, including global integration measures, spectral summaries, mesoscopic structure, centrality aggregates, and complexity descriptors.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

A controlled sparse backbone is obtained via the minimum spanning tree

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