Abstract. Grid-wise Vienna Mapping Functions 1 (VMF1) and Vienna Mapping Functions 3 (VMF3) tropospheric products are widely used to interpolate the a priori zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD) over GNSS (Global Navigation Satellite Systems) stations for the mitigation of tropospheric delays contained in GNSS observations. Since these two products provide ZHD and ZWD values only for the ground surface at global grid points, the ZHD and ZWD at the four grid points nearest to a GNSS site used to interpolate for the GNSS site need to be reduced to the same height of the GNSS station before a horizontal interpolation (e.g., bilinear interpolation) is implemented. However, the accuracy of the officially recommended reduction model may not be as good as desired, especially in the case that the height of the GNSS site largely differs from that of the four ground grid points. To address this, a new vertical reduction model for reducing the ZHD and ZWD at the height of grid points to a target height was developed. The sample data for the modelling were the 10-year (2010–2019) ZHD and ZWD profiles over grid points obtained from ERA5 monthly averaged reanalysis data, while the 3-year (2020–2022) radiosonde profiles and the IGS (International GNSS Service) site-wise zenith tropospheric delay (ZTD) products were used to evaluate the new model. Results demonstrated that the accuracy of ZHD, ZWD, and consequently ZTD values interpolated from VMF1/VMF3 products and the new model considerably improved compared to traditional methods, especially at the target sites that have large height differences from its closest VMF grid points. This improvement has significance for those applications that need to use tropospheric delay corrections, e.g. in GNSS positioning and GNSS meteorology for a desired accuracy.
Sun et al. (2025) studied this question.