## 3 Results and Discussion
(**a**) Averaged WRF-, ERA5-, and TOMO-PWV; the green stars represent the PWV derived from RO. The vertical dashed lines delimit the month of August; (**b**) zoom over August. Date in month/day format. a smaller domain. Notably, this specific InSAR map exhibits the highest PWV value among all InSAR cases, reaching 69.6 kg/m\({}^{2}\), and a pronounced southeast-northwest gradient with maximum values near the ocean, which was accurately simulated by ERA5 (Figure 5c). The WRF data also show similarities with InSAR but tend to depict a drier atmosphere in the northwest at higher altitudes. This difference may be attributed to WRF's 4 km horizontal resolution, which explicitly represents deep convection processes and the heterogeneities of Earth's topography in greater detail than traditional lower-resolution climate models like ERA5 [63]. Interestingly, the water concentration variability observed in the WRF map is less evident in the InSAR map, likely due to a certain degree of smoothing introduced during the computation of the absolute interferometric phase [51]. Taking InSAR as a reference, the ERA5 (Figure 5c) exhibits the best performance metrics, with an RMSE of 3.22 kg/m\({}^{2}\), followed closely by TOMO with 3.88 kg/m\({}^{2}\), and WRF with 5.83 kg/m\({}^{2}\). The BIAS shows similar values for all cases, in the same order: 3.08, 3.29, and 5.38 kg/m\({}^{2}\). The tomographic solution achieves a spatial correlation of 0.849, close to the value achieved by ERA5 of 0.924; the WRF only achieves a correlation of 0.596. Figures 6 and 7 compare the TOMO and model data with InSAR PWV maps. A spatial bilinear interpolation was performed to match the TOMO spatial resolution across all datasets before comparison. Figure 6 provides a temporal evaluation using InSAR maps as the \"ground truth\". Averaging over all cases, the TOMO solution shows an RMSE of 1.41 kg/m\({}^{2}\) and a bias of 0.08 kg/m\({}^{2}\), representing a significant improvement compared to the WRF model, which has 3.61 and 1.35 kg/m\({}^{2}\), respectively, and ERA5, with 2.26 and \(-\)0.38 kg/m\({}^{2}\) (Figure 6a,b). The average TOMO correlation coefficient shows an improvement of about 0.4 over the WRF model. On average, the models' PWV data do not exhibit a spatial correlation with the InSAR PWV data, with correlation coefficients of approximately 0.214 and \(-\)0.029 for WRF and ERA5, respectively. In only 10 cases, the TOMO solution reveals a lower correlation (<0.2), being greater than 0.6 for 50% of all cases. Upon closer inspection, it can be observed that the higher TOMO RMSE in the southern and northern sectors of the domain (Figure 6c) can be explained by the lower number of rays in the surface voxels, which significantly impacts the accuracy of the inversion. However, this is not easy to resolve, as the number of rays in the surface voxels, unlike the higher voxels, depends on the number and location of GNSS stations, as well as the region's  
Figure 5: PWV maps for 29 August around 00:30 UTC (at the end of Hurricane Harvey’s passage over the Houston area): (**a**) estimated using the interferometric phase (ascending orbit); (**b**) simulated by WRF model; (**c**) derived from ERA5 reanalysis; and (**d**) obtained via GNSS tomography (area corresponding to the TOMO footprint, black rectangle in (**a–c**)). The dotted rectangle corresponds to the InSAR footprint in ascending orbit. topography. In this study, we adhere to the initially proposed algorithm, incorporating the abovementioned changes without any additional modifications. However, we believe there is still room for improvement. Figure 7 presents a spatial evaluation, showing similar metric values as before (Figure 7a-c), except for the correlation values, which on average exceed 0.9 in all cases, with the highest values observed for TOMO. As previously stated, considering InSAR as the \"ground truth\", we calculated the spatial skill score (SS) relative to WRF and ERA5 (Figure 7d,e).