Impact of Earth's curvature on coastal sea level altimetry with ground-based GNSS Reflectometry

Global mean sea level is rising at an increasing rate. It is expected to cause more frequent extreme events on coastal sites. The main sea level monitoring systems are conventional tide gauges and satellite altimeters. However, tide gauges are few and satellite altimeters do not work well near the coasts. Ground-based GNSS Reflectometry (GNSS-R) is a promising alternative for coastal sea level measurements. GNSS-R works as a bistatic radar, based on the use of radio waves continuously emitted by GNSS satellites, such as GPS and Galileo, that are reflected on the Earth’s surface. The delay between reflected and direct signals, known as interferometric delay, can be used to retrieve geophysical parameters, such as sea level. One advantage of ground-based GNSS-R is the slant sensing direction, which implies the reflection points can occur at long distances from the receiving antenna. The higher is the receiving antenna and the lower is the satellite elevation angle, the longer will be the distance to the reflection point. The geometrical modeling of interferometric delay, in general, adopts a planar and horizontal model to represent the reflector surface. This assumption may be not valid for far away reflection points due to Earth’s curvature. It must be emphasized that ground-based GNSS-R sensors can be located at high altitudes, such in lighthouses and cliffs, and GNSS satellites are often tracked near grazing incidence and even at negative elevation angles. Eventually, Earth’s curvature would have a significant impact on altimetry retrievals. The osculating spherical model is more adequate to represent the Earth’s surface since its mathematical complexity is in between a plane and an ellipsoid. The present work aims to quantify the effect of Earth’s curvature on ground-based GNSS-R altimetry. Firstly, we modeled the interferometric delay for each plane and sphere and we calculated the differences across the two surface models, for varying satellite elevation and antenna altitude. Then, we developed an altimetry correction in terms of half of the rate of change of the delay correction with respect to the sine of elevation. We simulated observation scenarios with satellite elevation angles from zenith down to the minimum observable elevation on the spherical horizon (negative) and antenna altitudes from 10 m to 500 m. We noted that due to Earth’s curvature, the reflection point is displaced, brought closer in the x-axis and bent downward in the y-axis. The displacement of the reflection point increases the interferometric delay. Near the planar horizon, at zero elevation, the difference increases quickly and so does the altimetry correction. Finally, considering a 1-cm altimetry precision threshold to sea-level measurements, we observed that the altimetry correction for Earth’s curvature is needed at 10°, 20°, and 30° satellite elevation, for an antenna altitude of 60 m, 120 m, and 160 m, respectively.