## 3 Results  
### Overall Statistical Comparison between Measured and Modeled Electron Temperature Values  
First of all, we aimed to investigate the effect of the application of the Lomidze correction on Swarm \(T_{\text{e}}\) measurements through a comparison with IRI-modeled values for the period 2014-2020 for all the three Swarm satellites. An overall comparison between Swarm-measured (original and Lomidze-corrected) and IRI-modeled \(T_{\text{e}}\) values is given in Figures 2 and 3 as joint histograms and distributions of residuals between measured and modeled data. From the residuals between measured and modeled values, the following statistical metrics were calculated: mean and standard deviation of the residuals, Root Mean Square Error (RMSE, Equation (4)), and Relative Root Mean Square Error (RRMSE, Equation (5)). \[\text{RMSE}\;[\text{K}]=\sqrt{\frac{\sum_{i=1}^{N}(T_{\text{e,measured},i}-T_{ \text{e,modeled},i})^{2}}{N}} \tag{4}\]  
\[\text{RRMSE}\;[\%]=\sqrt{\frac{\sum_{i=1}^{N}\left(\frac{T_{\text{e,measured },i}-T_{\text{e,modeled},i}}{T_{\text{e,modeled},i}}\cdot 100\right)^{2}}{N}} \tag{5}\]  
In Equations (4) and (5), \(T_{\text{e,measured}}\) is the \(T_{\text{e}}\) measured by Swarm (i.e., \(T_{\text{e,LP}}\)) or corrected according to [PERSON] et al. [24] (i.e., \(T_{\text{e,LO}}\)), while \(T_{\text{e,modeled}}\) is the corresponding value modeled by IRI. Temperatures are in K. \(N\) is the number of values on which the statistics are calculated. Figure 2 represents the joint histograms between \(T_{\text{e}}\) values measured by Swarm and modeled by IRI and gives information on the distribution of measured and modeled data as a function of the corresponding magnitude. Most of the values cluster in the reddish region, i.e., where more than \(10^{4}\) values are counted inside each bin (the scale is logarithmic). It is interesting to note that IRI-modeled data never go beyond about 4300 K, while Swarm data (both original and Lomidze-corrected ones) show a long tail well beyond 5000 K (not shown in the figure), even though the application of the Lomidze correction reduces their magnitude. To characterize the accordance between modeled and measured values and the global effect of the application of the Lomidze correction, corresponding residuals were studied. Figure 3 represents the statistical distributions of the residuals between values measured by Swarm and modeled by IRI. By looking at the statistical metrics reported in the upper left corner of each panel, it emerges how the application of the Lomidze correction to Swarm data improved the accuracy when compared to IRI-modeled data. In fact, the mean of the residuals decreased from about 560-650 K to about 150-250 K, with a 400 K average improvement. Conversely, the application of the Lomidze correction did not affect the precision of Swarm data, as highlighted by the standard deviation values that remained in the range 380-470 K. Nevertheless, the application of the Lomidze correction generally improved the agreement with IRI data, as demonstrated by the RMSE and RRMSE values that decreased, respectively, from about 690-780 K to about 440-530 K, and from about 27-29% to about 20-23%. To sum up, the results shown in Figure 3 demonstrate how the application of the Lomidze correction to Swarm \(T_{\mathrm{e}}\) data can improve the agreement with IRI-modeled values, without impacting the corresponding precision. However, we are aware that the comparison with a model, IRI, cannot guarantee the reliability and efficacy of the Lomidze correction; the only comparison that can truly tell whether this correction improves real \(T_{\mathrm{e}}\) observations is that with other independent measurements. This is why we performed a comparison against \(T_{\mathrm{e}}\) data observed by ISRs. Figure 2: Joint histograms between \(T_{\mathrm{e}}\) values measured by Swarm and modeled by IRI (TBT-2012+SA default option): (left panels) original Swarm-recorded values, (right panels) Swarm values corrected with [PERSON] et al. (2014).