A new flexible model to calibrate single-layer height for ionospheric modeling using a neural network model

Ionospheric effective height (IEH), a key factor affecting ionospheric modeling accuracies by dominating mapping errors, is defined as the single-layer height. From previous studies, the fixed IEH model for a global or local area is unreasonable with respect to the dynamic ionosphere. We present a flexible IEH solution based on neural network models, namely a back-propagation neural network optimized by a genetic algorithm (BP-NN-GA) and a radial basis function neural network (RBF-NN), where variables associated with spatiotemporal variations in the ionosphere are taken as inputs, and the outputs of IEHs are derived from the mapping function converting the slant total electron content (STEC) to vertical total electron content (VTEC) obtained from the International GNSS Service (IGS) final global ionospheric map (GIM). Ionospheric observables over the Hong Kong area on DOY 102, 2021, are chosen to construct and validate the flexible IEH model. First, efforts are undertaken to confirm the variability of IEH and provide support to our effort. Subsequently, the minimum root mean square (RMS) values of the VTECs from the final GIMs and ionospheric measurements are calculated based on the flexible IEH model, and the results show that the two kinds of trained NN models have slightly different performances, but most of the RMS values are below 2 TECUs, which is much smaller than those in previous studies. Finally, to validate the reliability of the flexible model, we calculate the RMS values of VTECs from the GIM and models based on the fixed and flexible IEH. Compared with approximately 2.2 TECU obtained from the fixed IEH model, the RMS values calculated based on the flexible IEH models of RBF-NN and BP-NN-GA are approximately 1.8 and 1.9 TECUs with improving accuracies of approximately 18% and 13%, respectively. The above findings verify the reliability and feasibility of the flexible IEH model constructed by a neural network model.