Source separation techniques for characterising cosmic ray transients from neutron monitor networks

The analysis of weak variations in the energetic particle flux, as detected by neutron or muon monitors, can often be considerably improved by analysing data from monitor networks and thereby exploiting the spatial coherence of the flux. We present a statistical framework for carrying out such an analysis and discuss its physical interpretation. Two other applications are also presented: filling data gaps and removing trends. This study focuses on the method and its various uses.

💡 Research Summary

The paper presents a comprehensive statistical framework for extracting weak, coherent variations in the energetic particle flux measured by global networks of neutron and muon monitors. The authors model the count rate at each detector, c(x,t), as a linear combination of a limited set of separable space‑time functions (modes) c(x,t)=∑_{i=1}^{N} A_i f_i(t) g_i(x), imposing orthonormality on the temporal and spatial basis functions. This decomposition is performed via Singular Value Decomposition (SVD), which is mathematically equivalent to Principal Component Analysis (PCA). The singular values A_i quantify how much of the total variance each mode explains.

Using one year of hourly, pressure‑corrected neutron‑monitor data from the IZMIRAN database, the authors retain 43 stations after discarding those with large gaps. The SVD of this multivariate dataset yields a steeply decreasing variance spectrum: the first four modes together account for more than 98 % of the total variance, while the remaining modes are dominated by local noise and are deemed physically uninterpretable.

Mode 1 appears as a weighted average of all stations (weights ≈ 0.94–1). Because it is essentially isotropic and almost completely free of the solar diurnal variation, it serves as a high‑fidelity proxy for the global, isotropic cosmic‑ray flux. Weak transients such as small Ground Level Enhancements (GLEs) or Forbush decreases are clearly visible in this mode without any temporal smoothing that would otherwise erase fast features.

Mode 2 captures the rigidity (or latitude) dependence of the response. Its spatial pattern is strongly anticorrelated (‑0.83) with geomagnetic cutoff rigidity, indicating that it reflects changes in the spectral hardness of the cosmic‑ray flux. During geomagnetic storms, when cutoff rigidities shift, Mode 2 records a relative increase of high‑rigidity contributions, i.e., a hardening of the spectrum.

Modes 3 and 4 are dominated by the 24‑hour solar diurnal variation. They form a quadrature pair, describing a longitudinally propagating pattern that can be interpreted as the rotating anisotropy of the incoming particles. Both modes exhibit occasional sharp transients that correspond to anisotropic events such as GLEs, providing a more detailed view of directional changes than a simple harmonic analysis.

Power‑spectral analysis of the temporal coefficients shows distinct scaling laws: Mode 1 follows a power‑law with exponent α₁ ≈ ‑2.30, characteristic of large‑scale, low‑frequency fluctuations, while Mode 2 has α₂ ≈ ‑1.30, indicating a higher proportion of short‑scale variability. This difference reinforces the physical separation between an isotropic background and rigidity‑dependent spectral changes.

Beyond scientific interpretation, the authors demonstrate two practical applications of the SVD decomposition:

1. Data Gap Filling – By reconstructing missing or corrupted samples using only the most significant M modes (typically M = 4), the method iteratively replaces flagged points with values obtained from the truncated SVD expansion. Convergence is usually achieved within 5–20 iterations, and the reconstructed series retain the statistical properties of the original data, as illustrated with a deliberately removed month of Oulu monitor data.

2. Trend Removal – For a single station, Singular Spectrum Analysis (SSA), which is essentially SVD applied to a time‑delay‑embedded vector, isolates the slowly varying background trend. Subtracting the leading SSA component yields a detrended series that preserves short‑lived transients (e.g., weak GLEs) without the subjectivity inherent in designing digital low‑pass filters.

The paper also discusses the relationship between SVD and Independent Component Analysis (ICA). While ICA can provide statistically independent sources, the authors find that for neutron‑monitor data SVD and ICA give very similar results; they therefore focus on SVD because it is less sensitive to non‑stationarity and computationally cheaper.

In summary, the study establishes that multivariate statistical techniques—particularly SVD—can exploit the spatial redundancy of global neutron‑monitor networks to (i) isolate isotropic and anisotropic components of the cosmic‑ray flux, (ii) quantify rigidity‑dependent spectral changes, (iii) fill data gaps robustly, and (iv) remove long‑term trends without distorting fast transients. These capabilities are directly relevant for space‑weather monitoring, forecasting of geomagnetic storms, and the detection of subtle cosmic‑ray events that would be invisible to any single detector.