Tropospheric delays derived from ground meteorological parameters: comparison between machine learning and empirical model approaches

High spatia-temporal variability of atmospheric water vapor is directly reflected in the tropospheric pathdelays that microwave satellite signals experience. The so-called zenith total delays (ZTDs) need to be estimated in case of Global Navigation Satellite Systems (GNSS). Usually, models describe the ZTD with three meteorological parameters measured on ground: pressure, temperature and partial water vapor pressure. However, these models are determined empirically and it is especially a struggle to accurately determine the delay caused by the water vapor (wet delay) from meteorological data. In this work, we provide an alternative approach of estimating the tropospheric path delay using machine learning (ML) algorithms. During the last two decades machine learning algorithms have become widely used in many fields of science and engineering. Therefore, a large amount of time series of ZTDs and meteorological data and the successful applicability of machine learning to various applications are the main motivation behind this work. Besides, we also investigated another approach to compute ZTDs, based on the well-known Saastamoinen model [Saastamoinen, 1973], after interpolating the meteorological parameters at GNSS sites. The idea behind this work is to genarate GNSS zenith pathdelays without nrocessing any GNSS data, but only using meteorological parameters. Therefore, GNSS zenith pathdelays from 72 permanent stations in Switzerland and meteorological data from the permanent SwissMetNet network (with over 120 stations) have been used for training and validation for a period of 11 years. The distribution of the sites all over Switzerland allows the network to be trained and validated with stations at different altitudes and with various meteorological conditions. The ML approach showed an overall accuracy of 1.6 cm in terms of standard deviation, with almost no bias. Moreover, results show that stations at higher altitudes can benefit more from this approach. Compared to the Saastamoinen model, it had an overall improvement of about 20%, with a much better estimation in summer periods, when the amount of water vapor is higher. This work is a contribution to using ML algorithms to compensate for atmospheric errors in GNSS signals, and to compare its capabilities with empirically derived models.