Rare Phase-Space Nucleation Events in GNSS Signals: Evidence from Windowed Circular Phase Analysis

Description

Abstract (English)

Global Navigation Satellite System (GNSS) phase data are commonly analyzed under assumptions of smooth, continuous variability driven by atmospheric, ionospheric, and instrumental effects. In this work, we adopt a complementary geometric approach by analyzing the wrapped phase variable within sliding temporal windows and characterizing its phase-space structure using circular statistics.

We introduce three window-level observables: a geometric phase-order parameter (H), an effective oscillatory activity proxy (ω), and a nucleation indicator (λₚᵢ) quantifying the fraction of phase samples near the topological boundary at φ ≈ π. Applying this framework to Antarctic GNSS data, we identify a small subset of rare events (≈0.4% of windows) exhibiting a sharp collapse of geometric order (H ≈ 0.845 versus H ≈ 0.99 background), a strong reduction in oscillatory activity (ω ≈ 6.5 versus ω ≈ 114 background), and a distinct reorganization of the phase distribution into disjoint domains dominated by boundary clustering near 0/2π with nonzero occupancy near π.

These events are spatially localized, occurring exclusively at a single station (DAV1), and persist across multiple window sizes and step configurations, demonstrating robustness against methodological choices. The results rule out purely statistical fluctuations or global instrumental effects and are consistent with a nucleation-like transition in GNSS phase space.

This study provides empirical evidence that GNSS phase dynamics can exhibit rare, localized geometric transitions, motivating the use of phase-space and extreme-event methodologies in the analysis of geophysical and space-environment signals.