Nonlinear dynamical structure of IRI-2020 total electron content prediction errors over the African equatorial ionosphere: recurrence quantification and Lyapunov analysis of GNSS-derived residuals during quiet and storm conditions

Recurrence quantification analysis (RQA) and the maximal Lyapunov exponent characterise the dynamical structure of ionospheric model prediction errors, but applying them to the residual between observed total electron content (TEC) and the International Reference Ionosphere (IRI) is complicated by a systematic contaminant: the plasmaspheric content above the IRI upper boundary, which any ground-based Global Navigation Satellite System (GNSS) observation integrates to the satellite shell near 20,200 km. This study develops a phase-space attribution framework and applies it to the African equatorial ionosphere, where the equatorial ionisation anomaly is intense and IRI is least constrained by the historical ground network. Slant TEC from dual-frequency GPS at six International GNSS Service stations (9.04°N–19.02°S) was bias-corrected, mapped to the vertical, and differenced against IRI-2020 for geomagnetically quiet (February 2024) and disturbed (April–May 2024, encompassing the Gannon superstorm) conditions, giving 72 residual series. Across IRI upper integration bounds of 1000–2000 km, determinism varied by at most 0.024 and the maximal Lyapunov exponent by at most 0.00097 h⁻ 1 , one to two orders of magnitude below the between-station spread, confirming that the dynamical invariants are governed by IRI prediction error while the plasmaspheric contribution, though always present in the ground-based measurement, is bounded to a small and explicitly quantified perturbation rather than eliminated. Surrogate testing against 100 amplitude-adjusted Fourier-transform realisations shows that raw determinism is misleading: expressed as an excess over the surrogate mean in standard-deviation units, it is significant at five of six stations when quiet but only two under storm forcing, and ABPO collapses from 11.4 to 0.8 standard deviations. This loss of nonlinear excess scales with distance from the dip equator (Spearman r s = −0.886, p = 0.019) but is invisible in geographic coordinates (r s = −0.143). Statistically supported predictability horizons span 36.6 to 54.2 hours and occur only in quiet conditions.