## 4 Results and Discussion
### PlanetiQ-COSMIC Profiles Comparison
#### 4.2.2 Multi-Profile Comparison  
The spatial and temporal differences between the PlanetIQ and COSMIC observations are used to classify the data into three groups (G1, G2, and G3). G1 consists of 9 check points that represent the difference in observation time and location of 15 min and 0.25\({}^{\circ}\) in latitude and longitude, respectively. G2 is made up of 15 check points that signify a difference in observation time and location of 30 min and 0.5\({}^{\circ}\) in latitude and longitude, respectively. G3 consists of 18 check points, representing differences in observation time and location of 60 min and 1\({}^{\circ}\) in latitude and longitude, respectively. Figure 12 depicts a comprehensive view of the RMSE distributions across 12 distinct groups, each reflecting varying temporal and spatial differences between the PlanetIQ and COSMIC profiles. The groups (G1, G2, and G3) are characterized by differences in time intervals (15, 30, and 60 min) and spatial resolutions (0.25\({}^{\circ}\), 0.5\({}^{\circ}\), and 1\({}^{\circ}\) in latitude and longitude), with of 9, 15, 18 check points, respectively. G1, which has minimal spatiotemporal changes between observations, seems to have fewer medians and ranges across all variables than G2 and G3. Notably, each boxplot captures the spread of RMSE values across these categories. Key descriptive statistics, such as medians, quartiles, and whisker ranges, provide insight into the central tendency and variability of the RMSE. For instance, regarding the pressure in G1, the median RMSE is 0.29 mb with an interquartile range (IQR) of 0.07 mb, suggesting relatively low variability. In contrast, the pressure in G2 exhibits a wider IQR (0.21 mb) and five outliers, indicating higher variability and potential discrepancies in profiles with greater temporal and spatial differences. The absence of outliers in the pressure of G3 suggests robust agreement within the specified temporal and spatial bounds. Similar findings were observed in the refractivity, temperature, and WVP groups. These findings underscore the sensitivity of RMSE to temporal and spatial disparities, offering valuable insights into the reliability of altitude-pressure profiles under different observational conditions. The absence of outliers in certain groups indicates acceptable agreement, but the existence of outliers prompts consideration of data refinement for more accurate atmospheric profiling. Overall, the detailed analysis of RMSE distributions in Figure 12 provides a nuanced understanding of the reliability of PlanetIQ and COSMIC  
profiles under varying observational conditions, which will drive future data assimilation strategies and model improvements. The results depicted in Figure 13 provide a comprehensive overview of the mean difference, RMSE, and mean difference percentage profiles for all atmospheric variables. These profiles compare the G1 checkpoints profiles from PlanetQ and COSMIC. The maximum difference in pressure is approximately 0.2 mb, with a mean of 0.06 mb and a maximum RMSE of 0.4 mb. The altitude associated with the largest mean difference is 6.6 km, while the maximum RMSE occurs at 10.2 km. The mean difference percentage at the height of greatest RMSE is 0.04%. Regarding refractivity, the profiles exhibit a maximum difference of 1.71, a mean difference of 0.002%, and a maximum RMSE of 4.7. The altitude corresponding to the largest mean difference is 3.0 km, where the maximum RMSE appears at 3.5 km. The mean difference percentage at the altitude of maximum RMSE is 0.19%. Temperature profiles reveal a maximum difference of 1.52 \({}^{\circ}\)C, a mean difference of \(-0.06\) \({}^{\circ}\)C, and a maximum RMSE of 3.25 \({}^{\circ}\)C. The height associated with the largest mean difference is 27.1 km, while the maximum RMSE occurs at 38.6 km. The mean difference percentage at the altitude of maximum RMSE is 0.47%.