In this paper, we assess, in the framework of Global Navigation Satellite System (GNSS) meteorology, the accuracy of GNSS propagation delays corresponding to the Saastamoinen zenith hydrostatic delay (ZHD) model and the Vienna Mapping function VMF1/VMF3 (hydrostatic and wet), with reference to radiosonde ray-tracing delays over a three-year period on 28 globally distributed sites. The results show that the Saastamoinen ZHD estimates have a mean root mean square (RMS) error of 1.7 mm with respect to the radiosonde. We also detected some seasonal signatures in these Saastamoinen ZHD estimates. This indicates that the Saastamoinen model, based on the hydrostatic assumption and the ground pressure, is insufficient to capture the full variability of the ZHD estimates over time with the accuracy needed for GNSS meteorology. Furthermore, we found that VMF3 slant hydrostatic delay (SHD) estimates outperform the corresponding VMF1 SHD estimates (equivalent SHD RMS error of 4.8 mm for VMF3 versus 7.1 mm for VMF1 at 5° elevation angle), with respect to the radiosonde SHD estimates. Unexpectedly, the situation is opposite for the VMF3 slant wet delay (SWD) estimates compared to VMF1 SWD estimates (equivalent SWD RMS error of 11.4 mm for VMF3 versus 7.0 mm for VMF1 at 5° elevation angle). Our general conclusion is that the joint approach using ZHD models and mapping functions must be revisited, at least in the framework of GNSS meteorology.

We deduce a Novel Interferometric Tropospheric Error (NITE) formula for ground-based GNSS 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 the earth 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 (τ > 4 h) sea-level retrievals. Finally, we show that at low elevation angles, the bending angle correction can be reformulated as an MPF delay.

Mapping functions and gradients in GNSS and VLBI applications were introduced in the sixties and seventies to model the microwave propagation delays in the troposphere, and they were proven to be the perfect tools for these applications. In this work, we revisit the physical and mathematical basis of these tools in the context of meteorology and climate applications and propose an alternative approach for the wet delay part. This alternative approach is based on perturbation theory, where the base case is an exponential decay of the wet refractivity with altitude. The perturbation is modeled as a set of orthogonal functions in space and time, with the ability to separate eddy-scale variations of the wet refractivity.

With its high temporal resolution, unique mesoscale sampling scale and full weather capability, GNSS is now contributing as an important tool for monitoring the global atmospheric environment. The GNSS tropospheric zenith delay and the corresponding precipitable water vapor data (PW) are already widely applied in many weather models. High precision GNSS processing also estimates tropospheric delay gradients, which contain azimuthal isotropic information about the state of the atmosphere. However, the application of GNSS tropospheric delay gradients is not yet fully explored because of several obstacles. First, it suffers from the satellite constellations geometry and multipaths, and the gradients estimations are noisier than the zenithal delays. Second, the delay gradients were first developed for positioning purposes. GNSS tomography takes advantage of the delay gradients but requires a dense GNSS network. Here we introduce a new method to obtain the line-of-sight wet refractivity from a stand-alone GNSS receiver. We assume that the wet refractivity is mainly governed by a scale height (exponential law) and that the departures from the decaying exponential can be mapped as a set of low degree 3D Zernike functions and Chebyshev polynomials. We show up examples of inversion with data acquired at the IGS station in Tahiti, French Polynesia. We will also discuss the possibility of joint inversions with other measurements, using radiosonde data as an example.

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.