## 2 Data Description  
### CSES--01 Langmuir Probe Observations  
CSES--01 is a sun-synchronous LEO satellite launched on the 2 nd of February 2018 at an initial altitude of 507 km [15]. The orbit has an inclination of 97.4\({}^{\circ}\), with descending and ascending nodes at \(\sim\)14:00 Local Time (LT) and \(\sim\)02:00 LT, respectively. CSES--01 observations cover the latitudinal range between 70\({}^{\circ}\) S and 70\({}^{\circ}\) N. CSES--01 LP data are freely available at [[https://www.leos.ac.cn/](https://www.leos.ac.cn/)]([https://www.leos.ac.cn/](https://www.leos.ac.cn/)) (accessed on 7 April 2023) after registration. LPs onboard CSES--01 provide in situ \(N_{\rm e}\) observations in a range between 5\(\cdot\)10\({}^{2}\) cm\({}^{-3}\) and 1\(\cdot\)10\({}^{7}\) cm\({}^{-3}\)[28; 29]. The sampling rate of LP observations depends on the geographical location according to two operational modes: survey and burst. In burst mode, LP observations' sampling rate is 1.5 s and activates only over China and within the main seismic zones [15]. In survey mode, the sampling rate is 3 s.  
In this work, we consider CSES--01 LP \(N_{\rm e}\) observations from the 1 st of January 2019 to the 30 th of September 2021. The dataset consists of 13,957 semi-orbits in the daytime sector (\(\sim\)14:00 LT) and 13,978 in the nighttime sector (\(\sim\)02:00 LT). Both survey and burst mode data are used.  
Several studies compared and validated CSES--01 LP \(N_{\rm e}\) observations against observations made by incoherent scatter radars and similar LEO satellites, as well as against corresponding values provided by ionospheric models [30; 31; 32; 33; 34]. There is good agreement among these studies in highlighting a general underestimation of \(N_{\rm e}\) values recorded by CSES--01 when compared to different data sources. Nevertheless, CSES--01 LP \(N_{\rm e}\) observations succeed in describing both the spatial and diurnal \(N_{\rm e}\) patterns in the topside ionosphere. Since the reliability of both the magnitude and variations of \(N_{\rm e}\) values is needed for the calculation of the topside effective scale height, we applied the CSES--01 LP \(N_{\rm e}\) calibration procedure developed by the authors of [34]. This calibration is based on the comparison with Swarm B satellite LP and Face Plate (FP) \(N_{\rm e}\) observations and was validated against ISRs observations.  
Following [34], original CSES--01 \(N_{\rm e}\) measured values (in cm\({}^{-3}\)) have been calibrated by applying the following equations:  
\[\left\{\begin{array}{l}y=10^{\frac{x-q}{m}},\\ x\equiv\ \log_{10}(\text{CSES-01 LP original $N_{\rm e}$}),\\ y\equiv\ \log_{10}(\text{CSES-01 LP calibrated $N_{\rm e}$ }).\end{array}\right. \tag{1}\]where the \(m\) and \(q\) calibration coefficients were calculated for the daytime and nighttime sectors:  
\[\text{daytime}\Rightarrow\left\{\begin{array}{l}m=0.888\pm 0.013;\\ q=-0.203\pm 0.063;\\ \end{array}\right. \tag{2}\] \[\text{nighttime}\Rightarrow\left\{\begin{array}{l}m=0.938\pm 0.009; \\ q=-0.073\pm 0.038.\end{array}\right.\]  
This calibration procedure holds for the low solar activity conditions covered by the datasets used for its development. The shortness of the dataset and the FP data limitations did not allow for the investigation of the possible seasonal variations of calibration parameters [34].  
Since the CSES--01 dataset used in this paper is the same as that used in [34], the application of this calibration procedure to our dataset is straightforward. For comparison purposes, in the following, both original and calibrated CSES--01 LP \(N_{\text{e}}\) observations will be used. The authors of [34] demonstrated how this calibration procedure strongly reduces the CSES--01 \(N_{\text{e}}\) underestimation for both daytime and nighttime conditions, with calibrated values in agreement with corresponding values measured by Arecibo, Jicamarca, and Millstone Hill ISRs.