## 1 Introduction  
The topside ionosphere consists of the region extending from the F2-layer electron density peak to the overlying plasmasphere [1; 2; 3]. In this region, the electron density (\(N_{\mathrm{e}}\)) decreases monotonically at a vertical rate driven by the vertical scale height (VSH, [4; 5; 6]),which in turn depends on both the chemical composition of the plasma and its physical state. Since obtaining an accurate and thorough knowledge of plasma properties is difficult, an effective scale height is usually inferred from \(N_{\rm e}\) measurements and used for empirical modeling. In the topside ionosphere, the effective scale height (\(H\)) is empirically obtained by fitting measured \(N_{\rm e}\) values with different analytical functions, in order to obtain the most reliable representation of the topside vertical \(N_{\rm e}\) distribution (e.g., [7; 8; 9]). As a consequence, calculated \(H\) values depend on the topside parameterization used for their calculation and can differ from VSH values derived from the plasma ambipolar diffusion theory [6]. Many empirical ionospheric models rely on the modeling of \(H\) for an accurate description of the \(N_{\rm e}\) vertical profile. For instance, this is the approach pursued by the International Reference Ionosphere model (IRI, [10]), the NeQuick model [11], and the Empirical-Canadian High Arctic Ionospheric Model (E-CHAIM, [12]). Concerning the topside ionosphere, the modeling of \(H\) is challenging due to the reduced availability of data compared to the bottomside ionosphere, i.e., the region below the F2-layer peak. Indeed, the topside ionosphere is hidden to the widely spread ground-based ionosondes network, and \(N_{\rm e}\) observations can be obtained only through more expensive techniques such as topside sounders satellites, in situ measurements by low-Earth-orbit (LEO) satellites, radio occultation (RO) of global navigation satellite system (GNSS) signals, and incoherent scatter radars (ISRs) [13]. The challenge in modeling the topside ionosphere comes in the form of IRI difficulties in properly representing the topside variations under both quiet and disturbed conditions (e.g., [14]). As a result, the availability of new topside \(N_{\rm e}\) observations provides the opportunity to improve the description of \(H\) and, consequently, the topside \(N_{\rm e}\) modeling. This is the main motivation driving the present investigation. In this work, we characterize the global behavior of the topside effective scale height by using in situ \(N_{\rm e}\) observations by Langmuir Probes (LPs) onboard the China Seismo-Electromagnetic Satellite (CSES--01) and Swarm B LEO satellites. CSES--01 is dedicated to geophysical measurements and near-Earth environment monitoring, with a focus on the investigation of the electromagnetic perturbations possibly associated with earthquakes [15]. Swarm B is one of the three satellites of the Swarm constellation launched by the European Space Agency at the end of 2013 with the main aim of studying the geomagnetic field, the electric currents in the magnetosphere and ionosphere, and the impact of solar wind on the dynamics of the upper atmosphere [16]. In situ \(N_{\rm e}\) observations from LEO satellites alone cannot provide information on \(H\) and then on the \(N_{\rm e}\) vertical variation. They must be accompanied with \(N_{\rm e}\) observations collected at different altitudes, by different instruments, or by modeled values. For example, the authors of [7], using in situ \(N_{\rm e}\) observations made by Swarm satellites as the topside anchor point and the IRI UP data-assimilation modeled values over Europe [17] as the F2-layer peak anchor point, inferred a constant \(H\) by using different topside functions. A similar approach was also later pursued by the authors of [18] to calculate the value of the effective scale height at the F2-layer peak (\(H_{0}\)) to be used in the NeQuick topside model scale height formulation [11; 19].