Helsinki Mapping Functions to Compute Tropospheric Slant Delays

Accurate estimation of tropospheric slant delays is critical for reducing errors in Global Navigation Satellite System (GNSS) products during signal processing. Due to the fast variability and inhomogeneity of the atmospheric state, continuous weather data production near the receiver station is essential. While Mapping Functions (MF) have demonstrated effectiveness in computing tropospheric slant delays with a limited number of parameters, they have limitations, particularly with the variability of the azimuthal directions. Direct computation of tropospheric slant delays from a Numerical Weather Prediction (NWP) model—known as the Sky View (SV) approach—yields higher accuracy in both zenithal and azimuthal components, albeit at the expense of increased computational resources and processing time. In this study, we propose a hybrid approach that combines the benefits of both methods. Using a MF, we add an azimuthal component to generate more parameters at different azimuthal angles derived from a complete sky view at each receiver station. By increasing the number of MF-components (MFC) used per station, our goal is to reduce azimuthal errors while minimizing the number of parameters needed to represent slant delays, all without compromising the coupling between the ray tracer and the NWP model in the SV approach. For this study, atmospheric data are obtained from the Open Integrated Forecasting System (OpenIFS), a NWP model developed by the European Centre for Medium-Range Weather Forecasts (ECMWF). Tropospheric slant delays are calculated using the Least Travel Time v2 (LTTv2) ray-tracing algorithm. GNSS products are computed using the GROOPS processing toolkit. To evaluate the proposed method, we analyze the midnight discontinuities between consecutive orbits of the Global Positioning System (GPS) constellation and perform Precise Point Positioning (PPP) of a globally distributed set of receiver stations. Results from the SV approach are compared with those obtained from various configurations of the MF. The findings indicate that increasing the number of MFC per receiver station effectively reduces errors in GNSS products, with the error converging to a minimum after approximately 10 MFC.