Development of High-Precision Local and Regional Ionospheric Models Based on Spherical Harmonic Expansion and Global Navigation Satellite System Data in Serbia

The relationship between ionospheric research and global navigation satellite systems (GNSS) can be analysed through two approaches. The direct approach utilises ionospheric models to mitigate its influence, while the indirect approach leverages GNSS data to model ionospheric parameters. This study presents an indirect approach in which the total electron content (TEC), a fundamental parameter for ionospheric conditions, is modelled as a harmonic function using spherical harmonic (SH) expansion. Station-specific (local) and regional ionospheric models are developed by decomposing ionospheric influence into deterministic and stochastic components. GNSS data from seven evenly distributed stations in Serbia were used to estimate TEC coefficients. Local models were provided in the ION format as SH coefficients, allowing TEC determination at any epoch, while regional models had a 0.5∘×0.5∘ spatial and 2 h temporal resolution. The TEC root mean square (RMS) values ranged from 0.2 to 0.5 TECU (total electron content unit), with a mean of 0.3 TECU. Validation against global ionospheric maps showed agreement within 5.0 TECU. The impact of the SH expansion degree and order on TEC values was also analysed. These results refine regional ionospheric modelling, improving GNSS positioning accuracy in Serbia and beyond.