Calibrating tropospheric errors on ground-based GNSS reflectometry: calculation of bending and delay effects

During the last decade, GNSS interferometric reflectometry (GNSS-IR) has shown great potential for sea level monitoring. In combination with geodetic positioning, GNSS-IR provides a possibility to directly link the sea level measurements to the global terrestrial reference frame. However, many error sources can still be better modeled, and the accuracy of GNSS-IR sea level measurements can be improved. Specifically, we revise the tropospheric error model in ground-based GNSS-IR for sea level applications. Unlike GNSS positioning applications, in GNSS-IR the bending effect is as important as the delay effect. Also, usually very low elevation angle observations are used in GNSS-IR, which makes the atmospheric impact even more important. For the bending effect, we propose a new calculation which takes into account the water vapour content and utilizes the widely used mapping function approach to account for the elevation dependence. For the GNSS-IR atmospheric delay, we revise the geometry of the GNSS signal path for the case of coastal GNSS-IR where the antenna is within < 100 m from the sea surface. The atmospheric delay for the reflected signal is separately evaluated at the surface specular reflection point. The delay from the satellite to the reflection point and the direct signal can both be derived from the zenith delay and mapping function, at their respective local coordinates. The delay from the reflection point to the antenna is obtained assuming an average layer refractivity. We validated our model with ray-tracing radiosonde data. At 2° elevation angle, the new method can correct > 98 % of the atmospheric bending effect, compared to about 88 % with the previously adopted approach. With fewer approximations than the previous approach (directly using the mapping function), the new delay error model is also more accurate but with less absolute improvement of about 3 % compared to the previously existing model.