Simultaneous evaluation of solar activity proxies during geomagnetic storms using principal component analysis: Case study of the African low and mid-latitude regions

Abstract

We simultaneously evaluate the contributions of the mostly used solar activity indices to the modelling of geomagnetic storms using principal component analysis (PCA). The selected indices are the sunspot number (SSN), solar radio flux at a wavelength of 10.7 cm ($F10.7$), 12-month running average of SSN ($R12$), 81-day running average of $F10.7$ ($F10.7_{81}$), and the modified $F10.7$ index herein referred to as $F10.7p$. The assessment of these indices was accomplished by first developing five storm-time empirical models of the ionosphere with ionospheric total electron content (TEC) as dependent variable, and each of the five solar proxies as the independent variable. As the energy from the Sun differs from one latitudinal region to another on Earth, two locations at different latitudes were considered for the analysis. Based on their long data coverage periods, Hartebeesthoek (HRAO, geographic coordinates: 25.89° S, 27.69° E; geomagnetic coordinates: 36.32° S, 94.69° E), South Africa; and Mbarara (MBAR, geographic coordinates: $0.60°$ S and $30.74°$ E, geomagnetic coordinates: $10.22°$ S and $102.36°$ E), Uganda, were chosen to represent the middle and low latitude ionospheric regions, respectively. Their data coverage periods are 27 September 1996 to 30 March 2024 (HRAO) and 17 July 2001 to 30 March 2024 (MBAR) and only storm-time TEC data within these periods selected based on the criterion $Dst⩽-50$ nT or $K_p⩾4$ were considered for the statistical analysis. Through PCA decomposition, TEC data were broken up into a matrix of principal directions of the maximum variances in the dataset (or matrix of eigenvectors of the covariance matrix) and a matrix of principal components (PCs) which represent the projection of data onto the principal directions. For each model, PCs were thereafter modelled in terms of the corresponding solar activity index and the modelled quantities were further combined with the original PC vectors to get the reconstructed TEC for the entire period of the study. With reference to the ionospheric storm-time model implemented using SSN as solar activity representation, a statistical analysis revealed that, overall, the storm-time empirical models developed using either $F10.7$, $F10.7_{81}$, $R12$, or $F10.7p$, perform about 8%, 15%, 18%, 22%, respectively, better in reconstructing actual TEC than the SSN based model for HRAO, and 11%, 23%, 19%, 24% for MBAR. Validating the models over selected four storms, results showed that running average based indices led to more accurate TEC predictions compared to the usual daily Wolf’s SSN and $F10.7$.