Statistical models of the variability of plasma in the topside ionosphere: 1. Development and optimisation

This work presents statistical models of the variability of plasma in the topside ionosphere based on observations made by the European Space Agency's (ESA) Swarm satellites. The models were developed in the "Swarm Variability of Ionospheric Plasma" (Swarm-VIP) project within the European Space Agency's Swarm+4D-Ionosphere framework. The configuration of the Swarm satellites, their near-polar orbits and the data products developed, enable studies of the spatial variability of the ionosphere at multiple scale sizes. The statistical modelling technique of Generalised Linear Modelling (GLM) was used to create models of both the electron density and measures of the variability of the plasma structures at horizontal spatial scales between 20 km and 100 km. Despite being developed using the Swarm data, the models provide predictions that are independent of these data. Separate models were created for low, middle, auroral and polar latitudes. The models make predictions based on heliogeophysical variables, which act as proxies for the solar and geomagnetic processes. The first and most significant term in the majority of the models was a proxy for solar activity. The most common second term varied with the latitudinal region. This was the Solar Zenith Angle (SZA) in the polar region, a measure of latitude in the auroral region, solar time in the mid-latitude region and a measure of latitude in the equatorial region. Other, less significant terms in the models covered a range of proxies for the solar wind, geomagnetic activity and location. In this paper, the formulation, optimisation and evaluation of these models are discussed. The models show very little bias, with a mean error of zero to two decimal places in 14 out of 20 cases. The models capture some, but not all, of the trends present in the data, with Pearson correlation coefficients of up to 0.75 between the observations and the model predictions. The models also capture some, but not all, of the variability of the ionospheric plasma, as indicated by the precision, which ranged between 0.20 and 0.83. The addition of the thermospheric density as an explanatory variable in the models improved the precision in the polar and auroral regions. It is suggested that, if the thermosphere could be observed at a higher spatial resolution, then even more of the variability of the plasma structures could be captured by statistical models. The formulation and optimisation of the models are presented in this paper. The capability of the model in reproducing the expected climatological features of the topside ionosphere, in supporting GNSS-based ionospheric observations and the performance of the model against the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM), are provided in a companion paper (Spogli L et al. 2024. J Space Weather Space Clim https://doi.org/10.1051/swsc/2024003).