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

This paper introduces a novel graph-based framework that converts heterogeneous neutron-monitor data into compact topological fingerprints, demonstrating their ability to predict geomagnetic storm severity and Forbush decrease characteristics through rigorous machine learning validation.

Original authors: Juan D. Perez-Navarro, D. Sierra-Porta

Published 2026-07-09

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CC BY 4.0

Original authors: Juan D. Perez-Navarro, D. Sierra-Porta

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Earth is surrounded by a giant, invisible force field made of magnetic lines. When the Sun sneezes a massive cloud of charged particles (a Coronal Mass Ejection), it hits this force field, causing a "Forbush Decrease." This is like a sudden, temporary dip in the cosmic rays (high-energy particles from deep space) that usually rain down on us.

For decades, scientists have watched these dips using a global network of "neutron monitors"—special detectors scattered all over the planet, from the poles to the equator. But looking at each detector's data one by one is like trying to understand a symphony by listening to just one violin. The problem is that every station hears the music differently depending on where it sits and how strong its local magnetic "shield" is.

The New Idea: A Web of Connections
In this study, the authors decided to stop listening to the violins individually and instead look at how they all play together. They treated each detector as a dot (a node) and drew lines (edges) between them based on how similar their "music" was during a storm. This created a unique "event graph" for every solar storm.

To make sure they were comparing apples to apples, they didn't just draw every possible line. Instead, they used a clever trick called a Minimum Spanning Tree (MST). Think of this as finding the absolute shortest, most efficient web of string that connects every single dot without any loops or dead ends. It's the "skeleton" of the storm's fingerprint.

The Big Discovery: The Shape Tells the Story
The researchers asked a simple question: Does the shape of this web change depending on how bad the storm is?

They found that yes, it does. The "fingerprint" of the network changes in a measurable way based on the storm's severity.

The "Low-Rigidity" Stars: Detectors near the poles (where the magnetic shield is weak) turned out to be the most important "hubs" in the web. They acted like the main connectors, bridging different parts of the network.
The "High-Rigidity" Outsiders: Detectors near the equator (where the shield is strong) were often on the edges, acting like leaves on a branch.

What They Could Predict
Using these web shapes, the team tried to predict three things about the storms:

Sorting Storms by Size (G3, G4, G5): They tried to sort storms into three buckets: Moderate (G3), Strong (G4), and Extreme (G5).
- The Result: The web shapes did a decent job, getting it right about 57.6% of the time. It wasn't perfect, and the model often confused a "Strong" storm with an "Extreme" one (or vice versa), which makes sense because storm severity is more like a sliding scale than a set of distinct boxes.
Spotting the Big Bad Ones (Binary Screening): They tried a simpler task: "Is this storm a G4 or worse, or just a G3?"
- The Result: This worked much better! The model correctly identified severe storms 87% of the time. It's like a security system that rarely misses a real intruder, even if it sometimes mistakes a friendly visitor for a threat.
Guessing the Magnitude: They tried to predict exactly how big the drop in cosmic rays would be (the "drop").
- The Result: The web shapes could predict the size better than just guessing the average. They achieved a score (R²) of 0.350, which is a real signal, though it tends to guess "medium" for the very biggest and smallest drops (a common issue called "regression to the mean").

What They Ruled Out
The authors were very careful to check if their fancy web method was actually better than just looking at simple numbers. They compared their "graph fingerprints" against standard tools like:

The minimum southward magnetic field (Bz).
The average speed of the solar wind.
The maximum drop seen at polar stations.
The Dst index (a standard storm measure).

The verdict: The simple numbers were not enough. In fact, for predicting the exact size of the drop, all the simple methods performed worse than just guessing the average (they had negative scores). The web-based method was the only one that showed real predictive skill. This proves that the pattern of how the detectors talk to each other holds secret information that a single number can't capture.

How Sure Are They?
The authors are cautious. They call their results "measurable signal" and "evidence," not a solved mystery. They worked with a small group of 33 to 34 events, so while the pattern is clear, they need more data to be 100% certain. They also note that their method is currently a "retrospective" tool—it analyzes the storm after it happens to understand its shape, rather than predicting it in real-time.

The Takeaway
This paper suggests that if you want to understand a solar storm, don't just look at the numbers; look at the shape of the connections. The way the global network of detectors links up creates a unique "morphological fingerprint" that reveals the storm's true nature in a way simple measurements cannot. It's a new, playful, and powerful way to listen to the symphony of space weather.

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

Problem Statement
Forbush decreases (FDs) are transient reductions in galactic cosmic-ray (GCR) flux driven by interplanetary disturbances, primarily Coronal Mass Ejections (CMEs) and their associated shocks. While FDs and geomagnetic storms share common drivers, their physical relationships are indirect; storm intensity depends heavily on the southward interplanetary magnetic field component ( $B_z < 0$ ), whereas FD amplitude is governed by the magnetic barrier structure of the ICME sheath and flux rope. Characterizing FDs across global neutron monitor (NMDB) networks is challenging due to heterogeneous station responses, varying geomagnetic shielding (cutoff rigidity), and data gaps. Existing methods often treat time series in isolation or rely on summary curves, lacking a unified, comparable representation that captures the multivariate nature of the network. This work addresses the need for a robust framework to compare FD event morphologies and link them to geomagnetic storm severity.

Methodology
The authors propose a graph-based event representation where each FD is mapped to an event network constructed from pairwise dissimilarities between station response time series. The methodology follows a strict, reproducible pipeline:

Data Preprocessing: Hourly neutron-monitor count rates are extracted from the NMDB. A common analysis window is defined around the disturbance. Missing data is handled via two strategies: coverage filtering (excluding stations with >50% missing data) or iterative multivariate imputation using k-nearest neighbors (k=2).
Distance Calculation: Station responses are normalized as percentage deviations from a pre-event reference level. Pairwise distances are computed using $L_p$ metrics (Manhattan $p=1$ or Euclidean $p=2$ ).
Distance-Domain Transformations: To control dynamic range and enhance comparability, distances undergo transformations: identity, logarithmic, or exponential, followed by optional normalizations (min-max, z-score, etc.).
Graph Construction: Each event is represented as a weighted, undirected graph. To ensure comparability across events with varying station counts and avoid density artifacts, a Minimum Spanning Tree (MST) is computed using Kruskal's algorithm. This yields a sparse, connected backbone with exactly $N-1$ edges, highlighting dominant inter-station couplings.
Fingerprint Extraction: A compact set of geometric and topological descriptors is computed from the MST, including:
- Global Integration: Global efficiency, Estrada index.
- Mesoscopic Structure: Modularity, assortativity.
- Centrality Aggregates: Average Katz, closeness, and betweenness centrality.
- Complexity Descriptors: Shannon entropy of edge weights, fractal dimension (via Compact-Box-Burning), and Hurst exponent (via R/S analysis).
Validation: Predictive skill is assessed using strict leave-one-event-out (LOEO) validation over a pre-defined grid of pipeline choices. Selection criteria (macro-F1 for classification, $R^2$ for regression) are fixed a priori to prevent data leakage.

Key Contributions

Reproducible Pipeline: The study introduces a controlled pipeline that maps multi-station FD time series into event graphs, explicitly managing preprocessing, missing data, and distance-domain operations.
Compact Graph Descriptors: It defines a specific set of graph fingerprints spanning integration, spectral structure, mesoscopic organization, and complexity, enabling event-level analysis in small-sample regimes.
Rigidity-Conditioned Insights: The work demonstrates that node roles in the event backbone are physically grounded in geomagnetic shielding. Low-rigidity (polar) stations consistently occupy central, bridging positions, while intermediate-rigidity stations act as spectral bridges, and high-rigidity stations remain peripheral.
Comparative Framework: The approach offers a complementary, interpretable framework for characterizing FDs that captures information not reducible to single scalar indices.

Results
The study evaluates three predictive tasks using the extracted fingerprints:

Multi-class Intensity Classification (G3/G4/G5): The model achieved moderate but consistent performance (Macro-F1 = 0.575). Errors were dominated by misclassifications between adjacent categories (e.g., G4 vs. G5), supporting the view of storm severity as a continuum. The best configuration used a log distance transform, Minkowski adjacency, and Linear Discriminant Analysis (LDA).
Binary Severity Screening (≥G4 vs. G3): Performance improved significantly (Macro-F1 = 0.741), with high sensitivity (0.87) to severe events. This suggests the fingerprints are particularly effective at distinguishing strong disturbances from moderate ones.
Drop Regression: Using Partial Least Squares (PLS) with 5 components, the model achieved an $R^2$ of 0.350, significantly outperforming a fold-wise mean baseline ( $R^2 = -0.062$ ). This indicates that global network organization encodes quantitative information about FD magnitude.
Comparison with Baselines: The graph fingerprints outperformed all scalar and vector baselines, including polar max-drop, minimum southward $B_z$ , interplanetary field magnitude, solar-wind speed, Dst index, and joint $(B_z, |B|)$ pairs. Notably, all scalar baselines yielded negative $R^2$ values in regression, whereas the graph approach yielded positive skill.

Significance and Claims
The paper claims that FD event morphology leaves reproducible network signatures that can be captured by compact graph fingerprints. These signatures provide a complementary framework for comparative FD characterization and for studying how heliospheric drivers imprint structure on global neutron-monitor responses.

The authors emphasize that the results are modest given the limited sample size ( $n \le 34$ ) and should be interpreted as evidence of a reproducible signal rather than a final operational model. The framework is currently a retrospective characterization tool; it requires the complete event window to compute fingerprints and is not yet a real-time forecasting system. However, the work establishes that topological and geometric structures in multi-station responses contain predictive information about storm severity and FD magnitude that is not captured by standard scalar indices or simple amplitude measurements. Future utility is envisioned through expanded catalogs, uncertainty-aware benchmarking, and the integration of viewing geometry and rigidity metadata.

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