## 4 Discussion  
The results of Section 3.1. highlighted how the application of the Lomidze correction to Swarm-measured data reduces the mismatch with IRI-modeled data but, as pointed out by Section 3.3. results and the comparison with ISRs data (Section 3.2), several differences between measured and modeled data are still present for what concerns both \(T_{\mathrm{e}}\) magnitude and the corresponding spatial, diurnal, and seasonal variations. To better highlight the relation between measured and modeled data, the conditioned probability density function between them has been calculated. Specifically, we calculated the probability density of measured \(T_{\mathrm{e}}\) values, both original and Lomidze-corrected, conditioned by IRI-modeled ones in 50 K-wide range around a given value \(T_{0}\) (ranging from 25 to 4975 K in steps of 50 K):  
\[p(T_{\mathrm{e,measured}}|T_{\mathrm{e,modeled}})|T_{\mathrm{e,modeled}}\in[T_{ 0}-25;T_{0}+25)\ \mathrm{K} \tag{6}\]  
In Equation (6), \(T_{\mathrm{e,measured}}\) is the \(T_{\mathrm{e}}\) measured by Swarm (i.e., \(T_{\mathrm{e,LP}}\)) or corrected according to [PERSON] et al. [24] (i.e., \(T_{\mathrm{e,Lom}}\)), while \(T_{\mathrm{e,modeled}}\) is the corresponding one modeled by IRI and \(p\) is the conditioned probability density. Equation (6) was calculated for each \(T_{0}\) equal to the \(T_{\mathrm{e,modeled}}\) values used to define the ranges for the conditioned probability density calculation. Conditioned probability density values are represented in Figure 9 as colored bins, while bins with \(p<10^{-6}\) are in white. For each \([T_{0}-25;T_{0}+25)\ \mathrm{K}\) range, the median is calculated and represented as a black circle, and corresponding error bars are the median absolute deviation values [46]. Median values of Figure 9 were used to perform a linear regression analysis and to obtain the corresponding slope, intercept, and Pearson correlation coefficient, namely:  
\[R\ =\ \frac{\mathrm{cov}(T_{\mathrm{e,measured}},T_{\mathrm{e,modeled}})}{ \sigma_{T_{\mathrm{e,measured}}}\sigma_{T_{\mathrm{e,modeled}}}}\in[-1,1] \tag{7}\]  
where cov is the covariance matrix and \(\sigma\) the variance. Linear regression best fit lines are represented in Figure 9 in magenta, with corresponding slope, intercept, and \(R\) values reported in each panel. The analysis was restricted to \(T_{\mathrm{e,modeled}}\leq 2200\ \mathrm{K}\) because the linear relation between measured and modeled data fully breaks above this threshold, as clearly highlighted by the median values of Figure 9.  
The results of Figure 9 confirm and complement those shown by Figures 2 and 3. Specifically, the slopes of the linear best fit, which range between 0.80 and 0.89 for the original Swarm data, after applying the Lomidze correction range between 0.97 and 1.00, while the intercept values decrease from 920-990 K to 140-320 K. This confirms the accuracy improvement provided by the Lomidze correction. Differently, the correlation coefficient (\(R\)) was slightly affected by the Lomidze correction because this correction is substantially linear, apart from the term dependent on \(N_{\mathrm{e,LP}}\) (see Equations (1)-(3)); anyway, the correlation is very high in both cases (\(R>0.94\)). However, we have to take into account that these results are valid only in the range \(T_{\mathrm{e,modeled}}\leq 2200\ \mathrm{K}\), where a linear dependence with a slope near 1 between measured and modeled data is evident. A non-linear dependence is clearly visible for \(T_{\mathrm{e,modeled}}>2200\ \mathrm{K}\) and in principle could be indifferently due to the Swarm LPs instrumentation, possible shortcomings of the Lomidze correction, and the IRI representation of the highest \(T_{\mathrm{e}}\) values. Recently, [PERSON] et al.