The Solar Eclipse Inverse Problem

The HamSCI Personal Space Weather Station (PSWS) is a distributed network that includes magnetometers and high frequency receivers. The Great Radio Amateur Propagation Experiment (GRAPE) is a collection of PSWS receivers that record Doppler shift from national time standard signals. The Grape project includes Grape 1 receivers recording Doppler and spectral data as well as the upgraded Grape 2 three channel receivers and the multi-channel WSPR (Weak Signal Propagation Reporter) Grapes. The network collected data during the 2023 and 2024 solar eclipses on frequencies ranging from 2.5 to 20 MHz. The recorded Doppler shift indicates a change in signal path caused when the signal passes through the ionospheric layers in the Earth’s atmosphere. Due to the scale and variability of the ionosphere, these measurements are sparse and are not accompanied by a known forward model. The reconstruction of eclipse period ionospheric behavior can therefore be viewed as a mathematical inverse problem. We explore various mathematical techniques and algorithms that could be used to solve the inverse problem and model the real time ionospheric behavior.