Improved GNSS Water Vapor Tomography With Modified Mapping Functions

Abstract

The use of optimized GNSS mapping functions is here shown to lead to significant improvements in the performance of a water vapor tomographic model, totally driven by GNSS observations. The method improves a recent proposal for unconstrained tomographic inversions and is developed and validated with data from the Manaus dense GNSS network and in‐situ radiosondes, covering different seasons and synoptic conditions. The optimization uses a Monte Carlo technique to find the minimum root‐mean‐square error in a two‐dimensional parameter space. A set of fixed parameters, computed by optimizing over a small subset of cases, is found to lead to results that are overall significantly better than those produced by the three more common mapping functions used for geodesy applications. The quality of inversions is, however, found to have significant spread, an indication of the impact of varying GNSS data quality and a reminder of the need of further improvements in the method.

Optimizing Boundary Conditions in GNSS Tomography: A Continuous 7‐Month Case Study in the Amazon

“…The mean value of that scale height taken from ERA5, or the corresponding time‐varying estimate, was found to reduce the RMSE of the tomography to about 1.1 gm −3 . RMSE attained even smaller values (0.92 gm −3 ) when the scale height and the mapping coefficients are optimized with the Monte Carlo technique proposed by Miranda and Mateus (2022), but that would require a contemporaneous radiosonde. These results are close to the typical error of radiosonde observations.…”

“…The new version of the Miranda and Mateus (2021, 2022) algorithm, with local estimates of the regional scale height of water vapor, appears to be able to replicate the vertical profile of water vapor density with smaller errors than other methods (Bender & Dick, 2021; Zhang et al., 2021), even when those methods incorporate non‐GNSS data and in many cases are evaluated against indirect data such as reanalysis.…”

“…In MM22, we found that tomography could be improved by using an optimized mapping function by Chao (1972) with two free parameters ( c 1 , c 2 / c 1 ), where the best values of the parameters were obtained by a Monte Carlo technique exploring the range of parameters to minimize the Root Mean Square Error (RMSE) of the fit of the tomography to radiosonde observations. In MM22 it was found that with c 1 = 0.1 the optimal solution could be obtained by varying c 2 / c 1 . The same technique was here extended to include H v as a new free parameter.…”

“…At the times of the radiosondes, the best fit was obtained by using the Monte Carlo technique of MM22 to compute the best H v and c 2 / c 1 (Figure 2a), with c 1 = 0.1; slightly worse fits were obtained by fixing c 2 / c 1 = 220 and computing the best H v (Figure 2b), or with time‐varying H v from ERA5 (Figure 2c, where H v was computed by non‐linear least‐squares fitting of the ERA5 profiles to an exponential in the domain 250 m −10 km) or with a constant H v = 3,200 m (Figure 2d). Any of these changes reduced the root mean square error by (at least) a factor of 2 from those obtained with H v = 2,000 m, as used in MM22. The new mean tomography RMSE is approaching typical RMSE values of in situ observations and compares very well with other algorithms (cf.…”

“…Here, we apply the algorithm proposed by Miranda and Mateus (2021, 2022, hereafter MM22). This method eliminates the need for a first guess and any extra constraints on the variability of water vapor density inside the tomographic domain by the computation of virtual observations by fitting a hypersurface to the SIWV observations: $$${\overrightarrow{S}}_{A}\equiv {{\hat{S}}_{\text{IW}{\mathrm{V}}_{i,j}}=a}_{i}\mathrm{cos}\left({\alpha }_{j}\right)+{b}_{i}\,\mathrm{sin}\left({\alpha }_{j}\right)+{c}_{i}m\left({\eta }_{j}\right)+{d}_{i}(i=1,\text{\ldots }n;j=1,\text{\ldots }J)$$$ where $${\overrightarrow{S}}_{A}$$ is the fitted set of slant observations at station i within a given time window, and α j , η j ( j = 1,… J ) are prescribed co‐azimuths and elevations, and m ( η j ) is a mapping function.…”