Improved height correction model for hydrostatic mapping functions in GNSS data processing

Abstract

In precise global navigation satellite system (GNSS) data processing, the mapping function is a key factor in troposphere delay modelling. Currently, site-dependent troposphere mapping functions are only provided for specific sites, while for other sites, other mapping functions, such as the gridded Vienna Mapping Function (VMF1/VMF3), are recommended, in which a height correction is always required to convert the hydrostatic mapping function from model height to site height. In this analysis, an improved height correction model is proposed based on the fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis (ERA5). Compared to the commonly used Niell model, the coefficients in the improved model are no longer constants but are provided in a global $5^\circ \times 5^\circ$ grid on a monthly basis, with the significant difference that the coefficient $a$ of the Niell model is modelled as quadratically varying with height. To evaluate its performance, we applied the improved model to VMF1 ($2^\circ \times 2.5^\circ$) and VMF3 ($5^\circ \times 5^\circ$ and $1^\circ \times 1^\circ$) gridded data for all of 2015 and then compared them with site-dependent data at 402 VMF1 sites and 505 VMF3 sites, respectively. It was shown that the improved model outperformed the Niell model at most stations, and the improvement of the slant path delay (SPD) became better with increasing height difference. The maximum improvement of the SPD at a $3^\circ$ elevation angle is 29.5 mm at SANT for the VMF1 $2^\circ \times 2.5^\circ$ grid and 18.7 mm and 16.4 mm for the VMF3 $5^\circ \times 5^\circ$ and $1^\circ \times 1^\circ$ grids, respectively, both achieved at NAMA. For all height difference intervals, the average and maximum improvements of the SPD can reach approximately 30% and 50% for both the VMF1 $2^\circ \times 2.5^\circ$ and VMF3 $1^\circ \times 1^\circ$ grids, respectively, while only approximately 14% and 30% improvements for the VMF3 $5^\circ \times 5^\circ$ grid, respectively, due to the coarse resolution of the mapping function. Therefore, we can benefit significantly from the improved model, which becomes even more important when stations with large height differences, i.e. in mountainous areas or on mid-ocean islands, are included in precise GNSS data processing.