## 2 Materials and Methods  
### ESA Swarm In-Situ Electron Temperature Data and Application of the Lomidze Correction  
The ESA Swarm mission is a constellation of three LEO satellites launched at the end of 2013, and still operating, with the aim of studying the geomagnetic field, the electric currents in the magnetosphere and ionosphere, and the impact of the solar wind on the dynamics of the upper atmosphere [25]. The three Swarm satellites are labeled A, B, and C, and share the same design and on-board instrumentation. All three satellites were put in a circular near-polar orbit. Swarm A and C have the same orbit configuration (inclination of 87.35\({}^{\circ}\), initial altitude of about 460 km, east-west separation of about 1-1.5\({}^{\circ}\) in longitude), while Swarm B has a different one (inclination of 87.75\({}^{\circ}\), initial altitude of about 510 km). As a consequence, Swarm A and C fly in tandem, while Swarm B moves away from the couple A and C by covering different local times. Each satellite takes about 130-140 days to cover all the local times. Among the instruments carried by Swarm satellites, we focused on LPs data [27]. LPs provide measurements of in-situ electron density (\(N_{\rm e}\)) and \(T_{\rm e}\) along the satellite orbit with an original sampling frequency of 2 Hz in the harmonic mode [24; 28]. Moreover, 1-Hz data are also provided by interpolation of the 2-Hz dataset; it is this dataset containing time series of in-situ \(N_{\rm e}\) and \(T_{\rm e}\) data at 1-Hz rate that is used in this work. Specifically, LP data collected by Swarm A, B, and C from 1 January 2014 to 31 December 2020 (seven full years) are taken into account. Swarm's data are freely downloadable at [[ftp://swarm-diss.eo.esa.int](ftp://swarm-diss.eo.esa.int)]([ftp://swarm-diss.eo.esa.int](ftp://swarm-diss.eo.esa.int)) (accessed on 24 September 2021). Swarm's LP data are provided with three flags [28]: _Flags_LP_ contains information on the source of LP measurements, and _Flags_Ne_ and _Flags_Te_ characterize \(N_{\rm e}\) and \(T_{\rm e}\) measurements, respectively. Detailed information about Swarm data quality is available at [[https://earth.esa.int/web/guest/swarm/data-access/quality-of-swarm-1](https://earth.esa.int/web/guest/swarm/data-access/quality-of-swarm-1) lb-2 cat2-products]([https://earth.esa.int/web/guest/swarm/data-access/quality-of-swarm-1](https://earth.esa.int/web/guest/swarm/data-access/quality-of-swarm-1) lb-2 cat2-products) (accessed on 24 September 2021). In this study, only the most reliable data were considered; specifically, those recorded by LPs in _High-Gain_ mode. LP data were then selected with the following choice of the flags: _Flags_LP_ = 1, _Flags_Ne_ \(\leq 29\), and _Flags_Te_ = 10 or 20. [PERSON] et al. [24] developed a correction of both \(N_{\rm e}\) and \(T_{\rm e}\) Swarm LP data based on the analysis of Swarm measurements matching coincident values retrieved by ISRs, COSMIC/FORMOSAT-3 GPS radio occultation, and ionosondes. For what concerns the Swarm's \(T_{\rm e}\) data correction, [PERSON] et al. [24] separately considered the measurements collected when the LPs are in _High-Gain_ mode (HG in the following) from those collected with the LPs in _Low-Gain_ mode. Since only HG data were considered in this study, we applied only the HG Lomidze correction to \(T_{\rm e}\) data. As a consequence, the Equations (4)-(6) in [PERSON] et al. [24] were applied on the Swarm A, B, and C \(T_{\rm e}\) datasets, namely:  
\[T_{\rm e,Lom} =1.2815\cdot T_{\rm e,LP}-1167+7.293\cdot N_{\rm e,LP}/10^{4} \;\rm Swarm\;A,\;HG \tag{1}\] \[T_{\rm e,Lom} =1.2248\cdot T_{\rm e,LP}-1047+8.548\cdot N_{\rm e,LP}/10^{4} \;\rm Swarm\;B,\;HG\] (2) \[T_{\rm e,Lom} =1.1334\cdot T_{\rm e,LP}-762+4.088\cdot N_{\rm e,LP}/10^{4} \;\rm Swarm\;C,\;HG \tag{3}\]  
In Equations (1)-(3) \(T_{\rm e,Lom}\) is the Lomidze-corrected \(T_{\rm e}\), \(T_{\rm e,LP}\) is the original Swarm-measured value, \(N_{\rm e,LP}\) is the corresponding \(N_{\rm e}\) value measured by Swarm LP (i.e., unadjusted).