A new tropospheric error model for ground-based GNSS interferometric reflectometry: theory and validation

We deduce a new tropospheric error model for ground-based GNSS inter-ferometric reflectometry (GNSS-IR), the NITE (New Interferometric Tropo-spheric Error) model. This model contains two parts, a straight-line geometric error and a path delay. The geometric error uses specular reflection, taking into account the atmospheric bending and the earth curvature effects. The path delay follows the definition of the mapping function. We validate the NITE model together with two previously used models, the bending correction and the mapping function path delay (MPF delay) using raytracing and radiosonde data. The raytracing results show that the newly-developed NITE model is more accurate than the previous models. Numerically, for a GNSS antenna with a 20 m height difference to the sea level, the geometric tropospheric error is < 5 % of the path delay error. We further investigate and compare six tropospheric error correction strategies for GNSS-IR sea level monitoring using two sets of experiments. With an elevation angle range test using GNSS stations with large height differences to the sea level, we show that applying no troposphere error corrections and applying the bending correction plus the MPF delay both introduce large elevation-dependent biases. Analyzing time series of differences between GNSS-IR derived sea level and corresponding results from co-located tide gauges, we show that the bending correction with the widely used Bennett equation introduces long-term (4 h to months) trends in the sea-level retrievals. This is eliminated by using the Ulich equation in the bending correction. In our experiment, the accuracy improvement due to the NITE model is not as clear as in the raytracing simulations. We identify one station where the NITE model produces better long-term (τ > 4 h) stability. In others situations, the results from the NITE model have similar levels of random error. Finally, we give a theoretical deduction showing that, except for extreme situations, both the bending correction and the MPF delay are approximations of the rigorous NITE model. Unlike what is previously regarded, the bending correction and the MPF delay are not complementary but equivalent at low elevation angles.