## 3 Results and Discussion
### Comparison of Downscaled Outcome with Modeled Results in Three and Thessaly  
The methodology outlined in the previous sections has been applied in the Thrace and Thessaly Water Districts. Initially, the GPM dataset for the time period 2005-2015 was compared to measured precipitation from 4 and 6 meteorological stations operating in Thrace and Thessaly, respectively. Spatial averages for the whole study basins were estimated for each time step from point measurements using Thiessen polygons. Scatterplots of the observed (ground measured) and GPM-IMERG monthly precipitation are shown in Figure 9 for the two examined basins, indicating a satisfactory agreement of the two datasets at the monthly time step. This finding is in agreement with other evaluation studies of the GPM  
Figure 6: Downscaled GRACE-FO TWSA time series from October 2018 to March 2021 (months correspond to GRACE-FO months found in Supplementary Material of the present work). Units are in mm with reference to the 2004–2009 mean. IMERG dataset conducted previously in the study area [58] and concluded on the reliable performance of this specific dataset. Figure 8: GRACE-FO TWSA (mm), downscaled TWSA (mm) and GPM IMERG precipitation (mm) time series averaged over each of the 14 Water Districts of Greece. Figure 7: GPM-IMERG precipitation (mm) aggregated at the GRACE-FO months. To determine the time lags that could possibly contribute to the downscaling, the cross-correlation analysis presented in Section 3.1 was applied at the two study areas from 2005 to 2015 and comprised time lags up to 12 months, in order to estimate any possible contribution of precipitation up to one year before. Analogous time lags could not be covered with the GRACE-FO period until today, because it was too short to allow estimation of such time lags. Results of the cross-correlation analysis at the two test basins are shown in Figure 10 and indicate that in the Thrace area, a time lag of 1 month is high enough to support its role in the regression process. In the Thesaly basin, both time lags of 1 and 2 months demonstrate high enough values for their use in the downscaling process. The verification outcome of the downscaling approach is shown in Figures 11 and 12. In Figure 11, the computed pixel-wise intercept and slope for the Thesaly and Thrace regions using the time series from 2005 to 2015 are presented. A comparison of the modeled and downscaled TWSA is demonstrated in Figure 12. Therein, the modeled TWSA during 2005-2015 is examined against the ensemble of GRACE TWSA and downscaled GRACE TWSA (the associated datasets are provided in the Supplementary material Table S1). When it comes to the basin scale, it can be seen that the results are improved, indicating that the downscaled GRACE TWSA captures both the regional and basin-scale variability of TWS. Therefore, \(\mathbf{r}^{2}\) is considerably improved between modeled and downscaled TWSA, reaching a value of 0.85 and 0.94 in Thrace and Thessaly, respectively, whereas the \(\mathbf{r}^{2}\) between the original GRACE TWSA and the modeled TWSA is 0.42 and 0.49 for the predefined areas. An improvement is also observed comparing \(\mathbf{r}^{2}\) for the ERA5 Land TWSA and the downscaled TWSAs. In that case, the \(\mathbf{r}^{2}\) for Thrace is 0.94 and for Thessaly 0.92, while \(\mathbf{r}^{2}\) for ERA5 Land TWSAs and GRACE TWSA was found to be 0.74 and 0.79 for Thrace and Thessaly, respectively. Two other performance metrics were evaluated to measure the performance of the downscaling algorithm.