## 4 Summary and Conclusions  
The variability of water vapor in the troposphere presents a challenging task for weather models and observation techniques. It justifies investigating new methods to  
Figure 9: An example of a vertical cross-section of the tomographic inversion for 22 August at 00:00 UTC (**a–c**), corresponding to the beginning of the hurricane’s passage over Houston, and for 28 th at 00:00 UTC (**d–f**) during Harvey near peak intensity over Houston. The cross-section corresponds to the southeast–northwest red dashed line in Figure 1. (**a,d**) WRF; (**b,e**) ERA5; and (**c,f**) TOMO solution. estimate local water vapor. In the present study, we tested the ability of the unconstrained GNSS tomography algorithm introduced by [17] with improvements added by [18; 19] in direct estimates of the evolution of the water vapor density profile in Houston, U.S., based on GNSS observations from the Continuously Operating Reference Station (CORS) Network. Results shown here indicate that GNSS tomography outperforms ERA5 reanalysis and convection permitting simulations with WRF in the description of the temporal variability of specific PWV observations (as given by direct 30 min GNSS retrievals), in the vertical distribution of water vapor density (as given by GNSS-RO), and in the spatial distribution of PWV (as given by InSAR). Since the two latter datasets are sparsely distributed, many studies have focused on the simple comparison with the always available ERA5 data, which is not an observation. Present results do indicate that ERA5 is very good and better than WRF in the representation of the temporal evolution of PWV and in the vertical distribution of water vapor density, although it compares less favorably with observations than tomographic results. In what concerns spatial variability, WRF shows small-scale features not unlike those observed in InSAR and that are absent from low-resolution ERA5 and appear mitigated in tomography. Due to inevitable phase errors (in space and time), those features do not lead to improved point statistics for WRF and are difficult to validate with current observations. The tomographic solution was found to effectively maintain integrated water vapor values, not only at GNSS station locations but also in areas without stations, surpassing both weather models, as previously shown for the Amazon climate [19]. Remarkably, the vertical distribution of tomographic water vapor density closely aligns with GNSS-RO, exhibiting an RMSE below \(1\,\mathrm{g/m^{3}}\) across all vertical levels and a correlation exceeding 0.9. The algorithm captures the annual water vapor density cycle, exhibiting reduced noise during the wet season and agreement with a vertical density distribution simulated by the two weather models. Results also show that the system responds sensibly to the passage of an extreme weather system, such as record-breaking Hurricane Harvey. However, validation through radiosonde profiles remains necessary. Since the tested tomographic algorithm does not require any external data to constrain the system inversion, it provides an independent observation of the atmospheric state, which can be implemented operationally at high temporal resolution. The Houston GNSS network constitutes a rare example of a continuous high density GNSS network, freely available with several years of continuous data, and still operational. For the purposes of the present study, we selected the full year of 2017, because it has the advantage of containing a rare passage of a major Hurricane. The network was not designed for tomography and its horizontal distribution is very heterogeneous. That implied the choice of a relatively coarse horizontal resolution of 9 km, in a subdomain. The network is also limited to GPS in most stations, and there are no radiosonde observations in its vicinity. Present results, however, indicate the feasibility of tomographic inversions from such data and its added value against reanalysis and NWP data.