# Comparison of the Heights of Sporadic E Layers and Vertical Ion Convergence Parameters
## 1 Introduction  
Sporadic E (Es) layers are thin layers of high electron density in the mesosphere and lower thermosphere. These layers have a thickness of 1-5 km and appear sporadically at an altitude range of 90-130 km [1]. Their electron densities surpass those of the background E region plasma and can even exceed the plasma density of the F layer. As a result, they can have significant impacts on high-frequency (HF) and very high-frequency (VHF) radio communications as well as navigation systems [2; 3; 4]. Researchers commonly employ tools such as the ionosonde, radio occultation (RO), incoherent scatter radar (ISR), and global navigation satellite system (GNSS) for Es layer investigations [5; 6; 7; 8]. Over the past decades, extensive research has been conducted on the morphology of Es layers. The RO observations from COSMIC-1 (FORMOsa SATellite-3/Constellation Observing System for Meteorology, Ionosphere, and Climate) indicate that Es primarily occurs at mid-latitudes and exhibits a robust seasonal variation, being most prevalent in summer and least in winter [6]. The intensity of Es was also found to have the same characteristics [9; 10]. Long-term observations from ground-based instruments, such as ionosondes and incoherent scatter radar [5; 7], have revealed that Es layers typically formaround 120 km altitude, descending to approximately 100 km with a descent rate of 0.8-1.5 km/h. Notably, the descent rate above 110 km (3.1 \(\pm\) 0.8 km/h) is faster than below 110 km (1.0 \(\pm\) 0.9 km/h). Furthermore, the descent rates of Es layers increase with latitude [11]. At the same time, the descent rate of Es layers was estimated to be between 0.9-1.6 km/h based on the occurrence rate derived from COSMIC data [12]. With the help of ionosondes and COSMIC, the signals of tide and planetary waves in the strength and height of Es were found [13; 14; 15] and were connected with the variations of atmospheric waves [16; 17]. The wind shear theory, proposed by [PERSON] in 1960 [18], is the prevailing formation mechanism of mid-latitude Es layers. According to this theory, the ions are dragged horizontally by the horizontal winds, and ions obtain vertical Lorentz forces because the magnetic field exists. So, ions move vertically due to the horizontal winds and the existence of the magnetic field. In the vertical direction, the horizontal winds are inhomogeneous (see Figure 1d). As a result, the vertical velocity of ions is also inhomogeneous (see Figure 1b). Consequently, ions may converge at specific altitudes, giving rise to the formation of Es layers. Based on the wind shear theory, the vertical velocity of metallic ions (positive for upward motion) can be estimated. Subsequently, the vertical ion convergence (VIC) is derived by taking the divergence of the ion vertical velocity and using this to quantify the strength of convergence/divergence (see Figure 1c) [19]. A positive VIC value signifies convergence, serving as a fundamental condition for Es layer formation, while a negative VIC value signifies divergence and is adverse to the formation of Es layers. This parameter has been employed to quantitatively examine the connection between Es layers and the wind shear theory. Through a combination of observations and modeling, it has been affirmed that there is a significant correlation between VIC, Es occurrence rate (EsOR), and Es intensity in their global distribution, seasonal variations, and local time variations [10; 12; 19; 20; 21]. Previous studies have employed two main parameters (i.e., the maximum positive value of vertical ion convergence (VICmax) and ion vertical velocity null (IVN)) to assess the height of Es layers [11; 12; 22; 23; 24]. The VICmax is the point that has a maximum positive  
Figure 1: An example of the sporadic E (Es) layers, ion vertical velocity, and vertical ion convergence (VIC) on 1 June 2014. **(a)** The blue curve represents the S4 profile. The black dashed curve represents the threshold (S4 > 0.3) that determines Es.