A Novel Tropospheric Error Formula for Ground-Based GNSS Interferometric Reflectometry

We deduce a novel interferometric tropospheric error (NITE) formula for ground-based global navigation satellite system interferometric reflectometry (GNSS-IR). This formula contains two parts: a geometric displacement error that accounts for the reflection point change due to the atmosphere and Earth's curvature, and a path delay derived following the definition of the mapping function (with the small curve path effect included). We validate the NITE formula together with two previously used approaches: the bending angle correction and the mapping function path delay (MPF delay) using raytracing and radiosonde data. The raytracing results show that the NITE formula is more accurate than the previous approaches. Numerically, the geometric displacement error is < 5% of the path delay error for a GNSS antenna located 20 m above sea level. We further evaluate six tropospheric correction strategies for GNSS-IR sea-level monitoring through two sets of experiments. With an elevation angle range test, we show that applying no tropospheric correction and applying the bending angle correction plus the MPF delay both introduce large elevation-dependent biases. Analyzing the time series of differences between GNSS-IR and tide gauges sea level, we show that the bending angle correction with the widely used Bennett equation introduces long-term (4 h to several months) trends in the sea-level retrievals. We identify one station where the NITE formula produces better long-term ( $\tau >4$ h) sea-level retrievals. Finally, we show that at low elevation angles, the bending angle correction can be reformulated as an MPF delay.