When travelling from the satellites to the receiving antennas located on the Earth, the radio-frequency signals emitted by Global Navigation Satellite Systems (GNSS, such as e.g. GPS, GLONASS and Galileo) traverse and interact with the Earth's atmosphere (Figure 1). The two atmospheric layers that influence the propagation of GNSS signals are :

• The Ionosphere which is a shell of electrons and electrically charged atoms and molecules that surrounds the Earth, stretching from a height of about 50 km to more than 1000 km.

• The neutral atmosphere, which ranges from 0 to 50 km and includes the troposphere.

The troposphere is the lowest region of the Earth's atmosphere, extending from the Earth's surface up to about 8 km at the poles and to about 17 km at the Equator. It contains approximately 75% of the atmospheric mass, almost all (99%) of its water vapour and aerosols and is responsible of the majority of the error due to the neutral atmosphere. This is the reason why the neutral atmosphere is usually reffered to as troposphere in the GNSS community. The troposphere is the seat of all meteorological phenomena such as clouds, fronts, and precipitation.

As an electromagnetic wave propagates from a satellite towards the Earth's surface, the wave crosses these two atmospheric layers and interacts with them. The main interaction that links the Earth's atmosphere to the electromagnetic signal propagation is the atmospheric refraction. Refraction is the phenomenon of the change of direction and speed of propagation of an electromagnetic wave as it passes from one medium to another. Both the ionosphere and the troposphere refract GNSS satellite signals and are sources of errors in GNSS applications.

The tropospheric refraction delays the GNSS signals and causes errors up to several meters in the GNSS-based position determination. To access sub-centimetre precision in GNSS positioning, the effect of the tropospheric refraction, i.e. the tropospheric delay, must be accurately corrected and/or modelled.

For that purpose, GNSS geodesists estimate the tropospheric Zenith Total path Delay (ZTD) on the received GNSS signal simultaneously with the geodetic parameters. This can be done using observations from networks of permanently observing GNSS stations and state-of-the-art GNSS data processing software. In that framework, the Royal Observatory of Belgium (ROB) started in 1998 a research program focusing on the optimal way to correct the tropospheric refraction error for precise GNSS positioning applications.

The tropospheric refraction is caused by the presence of hydrostatic gases and water vapour in the atmosphere. The part of the tropospheric delay due to the hydrostatic gases can be accurately modelled from surface observations of the total air pressure. The part due to the presence of water vapour cannot be accuratly modelled as the water vapour content varies rapidly and strongly in both space and time. The tropospheric delay must thus be precisely estimated during the GNSS data analysis.

More details on the interaction between the Earth's troposphere and the GNSS signals can be found in this tutorial. More details on the interaction between the Earth's ionosphere and the GNSS signals can be found in this tutorial.