A machine learning model for the vertical correction of tropospheric zenith delays

Tropospheric delay is one of the most important error sources for space geodetic techniques, such as the Global Navigation Satellite Systems (GNSS). A priori tropospheric Zenith Hydrostatic and Wet Delays (ZHD and ZWD) should be obtained properly in advance to the GNSS data processing. Numerical Weather Model (NWM) is capable to provide accurate tropospheric zenith delays at any specific location with sophisticated calculation. As a more convenient alternative, the tropospheric zenith delays can be first modeled with NWM as a 2-D grid on the Earth surface and then corrected to the height of the specific location. In this case, accurate vertical correction algorithm is crucial. However, though empirical analytical models have been developed for the vertical correction of tropospheric zenith delays, their accuracies are limited due to the large spatiotemporal variability of the delays. In this work, we propose a Machine Learning (ML) model based on neural network for the vertical corrections of both ZHD and ZWD. The training data is obtained from the state-of-the-art NWM, the fifth-generation global reanalysis of European Centre for Medium-Range Weather Forecasts (ERA5). The proposed ML model is capable to reconstruct the tropospheric delays at any height from the Earth surface to up to 14 km. The precision of the ML model is superior to the analytical models with global average RMS values less than 2 and 3 mm for ZHD and ZWD, respectively. Therefore, it provides a convenient alternative to the sophisticated vertical integration of NWM for ordinary users with slight precision loss.