Simulations of direct and reflected wave trajectories for ground-based GNSS-R experiments

Abstract. The detection of Global Navigation Satellite System (GNSS) signals that are reflected off the surface, along with the reception of direct GNSS signals, offers a unique opportunity to monitor water level variations over land and ocean. The time delay between the reception of the direct and reflected signals gives access to the altitude of the receiver over the reflecting surface. The field of view of the receiver is highly dependent on both the orbits of the GNSS satellites and the configuration of the study site geometries. A simulator has been developed to determine the location of the reflection points on the surface accurately by modeling the trajectories of GNSS electromagnetic waves that are reflected by the surface of the Earth. Only the geometric problem was considered using a specular reflection assumption. The orbit of the GNSS constellation satellites (mainly GPS, GLONASS and Galileo), and the position of a fixed receiver, are used as inputs. Four different simulation modes are proposed, depending on the choice of the Earth surface model (local plane, osculating sphere or ellipsoid) and the consideration of topography likely to cause masking effects. Angular refraction effects derived from adaptive mapping functions are also taken into account. This simulator was developed to determine where the GNSS-R receivers should be located to monitor a given study area efficiently. In this study, two test sites were considered: the first one at the top of the 65 m Cordouan lighthouse in the Gironde estuary, France, and the second one on the shore of Lake Geneva (50 m above the reflecting surface), at the border between France and Switzerland. This site is hidden by mountains in the south (orthometric altitude up to 2000 m), and overlooking the lake in the north (orthometric altitude of 370 m). For this second test site configuration, reflections occur until 560 m from the receiver. The planimetric (arc length) differences (or altimetric difference as WGS84 ellipsoid height) between the positions of the specular reflection points obtained considering the Earth's surface as an osculating sphere or as an ellipsoid were found to be on average 9 cm (or less than 1 mm) for satellite elevation angles greater than 10°, and 13.9 cm (or less than 1 mm) for satellite elevation angles between 5 and 10°. The altimetric and planimetric differences between the plane and sphere approximations are on average below 1.4 cm (or less than 1 mm) for satellite elevation angles greater than 10° and below 6.2 cm (or 2.4 mm) for satellite elevation angles between 5 and 10°. These results are the means of the differences obtained during a 24 h simulation with a complete GPS and GLONASS constellation, and thus depend on how the satellite elevation angle is sampled over the day of simulation. The simulations highlight the importance of the digital elevation model (DEM) integration: average planimetric differences (or altimetric) with and without integrating the DEM (with respect to the ellipsoid approximation) were found to be about 6.3 m (or 1.74 m), with the minimum elevation angle equal to 5°. The correction of the angular refraction due to troposphere on the signal leads to planimetric (or altimetric) differences of an approximately 18 m (or 6 cm) maximum for a 50 m receiver height above the reflecting surface, whereas the maximum is 2.9 m (or 7 mm) for a 5 m receiver height above the reflecting surface. These errors increase deeply with the receiver height above the reflecting surface. By setting it to 300 m, the planimetric errors reach 116 m, and the altimetric errors reach 32 cm for satellite elevation angles lower than 10°. The tests performed with the simulator presented in this paper highlight the importance of the choice of the Earth's representation and also the non-negligible effect of angular refraction due to the troposphere on the specular reflection point positions. Various outputs (time-varying reflection point coordinates, satellite positions and ground paths, wave trajectories, first Fresnel zones, etc.) are provided either as text or KML files for visualization with Google Earth.