Examining the Wind Shear Theory of Sporadic E With ICON/MIGHTI Winds and COSMIC‐2 Radio 2 Occultation Data

The wind shear theory is widely accepted as an explanation for the formation of a sporadic E (Es) layer, but the direct comparison of Es with the local wind shear has been limited due to the lack of neutral wind measurements. This study examines the role of the vertical wind shear for Es, using signal‐to‐noise ratio profiles from COSMIC‐2 radio occultation measurements and concurrent measurements of neutral wind profiles from the Ionospheric Connection Explorer. It is observed that the Es occurrence rate and average S4 index are correlated with the negative vertical shear of the eastward wind, providing observational support for the wind shear theory. Es can be observed even when the vertical wind shear is positive, which is interpreted as metallic ion layers generated at an earlier time.

where w i is the vertical ion velocity, ν i is the ion-neutral collision frequency, Ω i is the ion gyrofrequency, I is the magnetic inclination, and U m and V m are neutral wind velocities in magnetic eastward and northward directions, respectively. In (1), the relative contribution of U m and V m to w i depends on r, which decreases with height. In the height range of 90-120 km, where Es is most commonly observed, w i is dominated by the contribution of U m . Thus, the vertical convergence of the ion flux − ( ) , where N i is the ion number density, is controlled by the vertical gradient of the zonal wind. The implication is that an Es layer should preferably occur where the negative gradient of the eastward wind is large.
Es layers are composed primarily of metallic ions such as Fe + and Mg + , which have a relatively long lifetime and are abundant in the lower thermosphere due to meteor ablation (Kopp, 1997). Major ion species of the E-region ionosphere such as NO + and O + 2 make little contribution to Es layers, as they cannot maintain high concentration due to a short lifetime relative to the convergence time. Modeling studies have demonstrated that thin and intense metallic ion layers can form in the E region under the presence of proper vertical wind shear, supporting the wind shear theory (e.g., Andoh et al., 2020;Carter & Forbes, 1999;Huba et al., 2019;MacLeod et al., 1975;Resende et al., 2016).
Direct observational evidence for the wind shear theory is limited due to the lack of neutral wind measurements from the lower thermosphere. Es layers mostly occur above the height range where ground-based radars can reliably determine the wind velocity (e.g., Jacobi & Arras, 2019). Sounding rockets have sometimes provided simultaneous measurements of plasma densities and neutral winds suitable for testing the wind shear theory. Some studies found Es layers near the height of a strong negative shear of the eastward wind, supportive of the wind shear theory (e.g., Bishop et al., 2005;Larsen et al., 1998;Pfaff et al., 2020). However, Hall et al. (1971) observed an Es layer with a positive shear, contrary to the wind shear theory. Moreover, Liu et al. (2018) compared the vertical wind shear observed by the TIMED satellite and Es derived from radio occultation measurements, to find only a weak correspondence between the wind shear and Es observations. Thus, the relationship between the wind shear and Es is yet to be established by observations.
Recently, a large number of neutral wind measurements from the Ionospheric Connection Explorer (ICON) mission (Immel et al., 2018) and concurrent Es detection by the COSMIC-2 radio occultation (Yue et al., 2014) have become available, providing an opportunity for direct comparison of Es with the local wind shear. The main objective of this study is to clarify the relationship between the wind shear and Es using these data. We also use the whole atmosphere model, Ground-to-Topside Model of Atmosphere and Ionosphere for Aeronomy (GAIA) (Jin et al., 2011), to support the validation of ICON wind data. Brief descriptions of the COSMIC-2 and ICON data as well as the GAIA model are given in the following section.

Data and Model
Radio occultation is a powerful remote-sensing technique for atmospheric and ionospheric soundings (e.g., Hajj et al., 2002;Wickert et al., 2009). For this study, we use radio occultation data from the COSMIC-2 satellite constellation (Anthes & Schreiner, 2019), which consists of six satellites with a 24° inclination orbit at an initial altitude of 720 km. COSMIC-2 radio occultation receivers provide up to several thousand signal-to-noise ratio (SNR) profiles per day (Schreiner et al., 2020), covering the E region at latitudes between 45°S and 45°N and up to an altitude of ∼130 km with a vertical resolution of ∼25 m. SNR is sensitive to the vertical gradient of the plasma density. The plasma density gradient due to Es is considered to be the primary source of scintillation in SNR at E-region heights. In previous studies, SNR data from various satellite missions have been used to study Es layers (Arras et al., 2008;Hocke et al., 2001;Wu et al., 2005).
For each COSMIC-2 SNR profile, the Es occurrence is evaluated and the S4 scintillation index (or simply S4 index) is derived. The method used is essentially the same as that previously described by Arras and Wickert (2018) for studying Es with radio occultation data from the COSMIC satellite constellation (Anthes et al., 2008). Briefly, the detection of Es layers is based on profiles of the standard deviation of SNR calculated using a 2.5-km sliding window. A profile is considered to contain an Es layer if the maximum standard deviation exceeds the threshold value of 0.2 and the large standard deviation ( 0.2) is confined within a layer of maximum 15-km thickness. In this way, large plasma density gradients associated with Es (irrespective of the ion composition) can be detected. The S4 index is computed using 100 SNR data points around the height of the maximum SNR fluctuation. Studies found a correlation between the S4 index derived from COSMIC SNR data and the blanketing frequency of Es layer (fbEs) observed by ionosondes (Arras & Wickert, 2018;Resende et al., 2018). fbEs corresponds to the maximum electron density of the Es layer. It is noted that there are occasionally SNR profiles that are highly disturbed at all heights, which are likely due to a technical issue. Such "bad data," accounting for ∼2%, are excluded from the analysis.
Neutral wind data are obtained from the Michelson Interferometer for Global High-Resolution Thermospheric Imaging (MIGHTI)  onboard ICON. MIGHTI measures Doppler shifts of the naturally occurring atomic oxygen airglow emissions to estimate the horizontal wind velocity. We use version 4 of the cardinal wind profiles from the green-line emission at 557.7 nm wavelength (Harding et al., 2017(Harding et al., , 2021. Wind profiles cover the latitude range between 12°S and 42°N and the height range of approximately 90-180 km, with a vertical resolution of ∼3 km. At each height, magnetic eastward (U m ) and northward (V m ) components are derived from geographic eastward (U) and northward (V) components using the magnetic declination obtained from the International Geomagnetic Reference Field (Alken et al., 2021). U m and V m are mainly used for comparisons with COSMIC-2 Es data, while U is used for comparisons with GAIA predictions. It is noted that the ICON/MIGHTI results obtained with U m and V m are generally similar to those derived with U and V. It is also noted that since the ICON/MIGHTI data are from mid and low latitudes, similar results are obtained with U m and U m cos(I). We use only the ICON/MIGHTI data with "wind quality factor" equal to one, which corresponds to the best quality data. This largely eliminates the measurements taken near the South Atlantic Anomaly, which are contaminated by radiation impacting the MIGHTI detectors.
A COSMIC-2 SNR profile and ICON/MIGHTI neutral wind profile are considered to be in "conjunction" if the spatial separation of the two is less than 2.5° in both latitude and longitude, and the temporal separation is less than 10 min in terms of the central time of the observations. Sometimes, more than one SNR profile is found for the same wind profile. In our statistical analysis, conjunctions are treated to be independent as long as the SNR profiles are different. The data during the period from June 2020 to May 2021 are used, and 10,751 conjunctions are detected.
Neutral wind velocities are also obtained from GAIA, which is a physics-based model of the coupled atmosphere-ionosphere system from the surface to the upper thermosphere/ionosphere (Jin et al., 2011). The model consists of the following three parts: a whole atmosphere general circulation model (GCM) (Miyoshi & Fujiwara, 2003), an ionosphere model (Shinagawa, 2011), and an electrodynamics model (Jin et al., 2008), which are coupled to one another. The model was run for the same period as our data set, that is, from June 2020 to May 2021. The whole atmosphere GCM below the height of 40 km was constrained with meteorological reanalysis, namely, the Japanese 55-year Reanalysis (JRA55) (Kobayashi et al., 2015) using a nudging technique (e.g., Jin et al., 2012). This way, the model is able to incorporate atmospheric tides that are generated in the lower atmosphere and propagate into the upper atmosphere (e.g., Miyoshi et al., 2017). Studies have shown that these tides play an important role for the daily variation of Es (e.g., Haldoupis et al., 2006). In the upper three panels, Es layers are seen at an altitude where the magnetic eastward component of the zonal wind decreases with height (i.e., the vertical wind shear is negative). Es layers in these results conform well to expectations from the wind shear theory.

Results and Discussion
In the lower left panel of Figure 1, an Es layer is seen at a height (∼113 km) of a negative wind shear, again supporting the wind shear theory. The SNR profile also indicates the presence of another Es layer at a lower height (∼93 km), for which there is unfortunately no wind measurement. Multiple-layer Es structures have been reported in the literature (e.g., Ejiri et al., 2019;Hall et al., 1971;Raizada et al., 2020). In the lower middle panel, a negative wind shear is seen at heights of 95-105 km, but with no apparent Es layer. The absence of an Es layer might be due to the lack of metallic ions. It is also possible that an Es layer is present but SNR fluctuations are not large enough to be detected as Es. In the bottom right, an Es layer is seen at ∼112 km, but the vertical wind shear is not negative. A possible explanation is a surviving metallic ion layer generated at an earlier time. As mentioned, metallic ions have a long lifetime, and thus an Es layer would not immediately disappear when the polarity of the shear changes from a negative to a positive one.
Next, we compare daily-mean global climatologies of Es and vertical wind shear. For deriving the climatologies, not only conjunction observations, but also all other available COSMIC-2 and ICON data including all local times are used. Figure 2a shows the occurrence rate of Es over the height range 90-120 km for different periods. The following features can be noted: (1) the Es occurrence rate is higher in the summer hemisphere than in the winter hemisphere, (b) the Es occurrence rate is reduced over the magnetic equator, (c) the Es occurrence rate is also reduced in the southern mid latitudes between ±30° longitudes. These results are in good agreement with previous global observations (e.g., Arras et al., 2008). The enhanced Es occurrence rate in the summer hemisphere is due to the seasonal dependence of metallic ion densities and vertical wind shear (Chu et al., 2014;Haldoupis et al., 2007;Shinagawa et al., 2017). The reduced Es occurrence rate over the magnetic equator is thought to be due to the vertical electric field, which prevents the formation of an Es layer (e.g., Haldoupis, 2011). The reduced Es occurrence over the South Atlantic is understood in terms of relatively large magnetic inclination angle, which leads to a reduced vertical ion convergence over this region; see Equation 1.    (Arras & Wickert, 2018;Chu et al., 2014;Yu et al., 2019). The distribution of the average S4 index and its seasonal variation are similar to those of the Es occurrence rate, as pointed out by Arras and Wickert (2018). Figure 2c shows the vertical shear of the zonal wind (positive geographic eastward) at 105 km, the height around which the vertical wind shear is largest (e.g., Larsen, 2002). Mean values of the vertical wind shear are calculated using a sliding window of 5° × 10° in latitude and longitude. It is seen that there is no ICON/MIGHTI observation in the Southern Hemisphere poleward of ∼15°S. There is also no data around the South Atlantic Anomaly, as mentioned earlier. The vertical wind shear shows a consistent pattern of negative and positive wind shears poleward and equatorward of ∼20°N, respectively, in different seasons. The negative wind shear is strongest during June-August 2020, that is, local summer. This could make a contribution to the enhanced Es occurrence rate and average S4 index in local summer.
The vertical wind shear at 105 km obtained from GAIA is presented in panel (d). Mean values of the vertical wind shear are calculated from daily means at each grid point. Roughly speaking, the wind shear is positive over latitude ranges of 90°S-50°S, 20°S-20°N, and 50°N-90°N, and negative elsewhere. There is agreement between the ICON/MIGHTI results and GAIA predictions.
As a brief summary, the global patterns of the Es occurrence rate and average S4 index at 90-120 km are similar to each other, but they are only in partial agreement with the pattern of the vertical wind shear at 105 km. Since the results presented in Figure 2 contain the data from all local times, they are representative of the daily mean. Next, we address the local-time dependence of the Es occurrence rate, average S4 index, and vertical wind shear. Figure 3a shows the local-time and altitude structures of the Es occurrence rate (upper left), average S4 index (upper right), vertical wind shear from ICON/MIGHTI (lower left), and vertical wind shear from GAIA (lower right) at 20°N-40°N during June-August 2020. The Es occurrence rate undergoes a semidiurnal variation above 105 km or so, while at lower altitudes, a diurnal variation is dominant. These diurnal and semidiurnal variations of Es are known to be associated with the vertical wind shear by atmospheric tides (Arras et al., 2009;Christakis et al., 2009). Downward phase propagation, which is a fundamental feature of upward propagating tides (e.g., Forbes, 1995), can be seen in the diurnal and semidiurnal Es variations. Tidal influences are also seen in the average S4 index, but the semidiurnal variation is not as evident as in the Es occurrence rate. Comparison of the Es occurrence rate with vertical wind shears from ICON/MIGHTI and GAIA suggests that the Es occurrence rate tends to be high at local times and altitudes where the vertical shear of the zonal wind is negative, which is consistent with the wind shear theory. There is reasonable agreement between ICON/MIGHTI observations and GAIA predictions, although the magnitude of the wind shear tends to be greater in the GAIA results. Figure 3b show the same variables as panels (a) but at 10°S-10°N during September-November 2020. Compared with panel (a), both the Es occurrence rate and average S4 index are generally lower. Also, the agreement between the patterns of the Es occurrence rate and negative wind shear is not as good. For example, the Es occurrence rate is relatively high around 100-105 km at 14-18 LT, where the average vertical wind shear is positive. The results suggest that the daily variation of Es is not only due to tidal modulation of wind shear but also due to other mechanisms such as the daily variation of metallic ion density.
More direct comparisons between Es and vertical wind shear are made using only conjunction profiles of COS-MIC-2 SNR and ICON/MIGHTI winds at altitudes of 90-120 km. In the upper panels of Figure 4, the Es occurrence rate (left) and average S4 index (right) are computed for every 2.5 m/s/km in the vertical shear of the magnetic eastward wind. The black lines show the results containing all periods, latitudes, and heights of observation, with linear fits indicated by magenta lines. Both the Es occurrence rate and average S4 index correlate almost linearly with the vertical wind shear. To assess the robustness of the results, we divided the data into two parts each having approximately half of the samples, and repeated the analysis for each group of data. The results obtained for different periods (blue solid and dashed lines) and for different ranges of latitude (green solid and dashed lines) are found to be similar to the results obtained with all the available data. Meanwhile, the results obtained for different height ranges (orange solid and dashed lines) are appreciably different. That is, the dependence of the Es occurrence rate and average S4 index on the vertical wind shear is more pronounced at higher (100-120 km) than lower (90-100 km) altitudes. The difference in the slope of a linear fit (not shown here) to the higher-and lower-altitude data is significant at the 95% confidence level. Such a significant difference is not found in the results obtained for different periods or latitudes. The reduced wind-shear influence at the lower altitudes can be explained as the consequence of frequent ion-neutral collisions in the lower E region, which suppress the Es formation by the wind shear mechanism, as numerically demonstrated by Andoh et al. (2021).
It may be noted that the Es occurrence rate at zero shear of the zonal wind is approximately 30%. Es without vertical wind shear can be due to a metallic ion layer generated at an earlier time. Such a surviving layer would be destroyed by the divergence of vertical ion motions induced by a positive wind shear. The destruction of the layer would be more rapid for a larger positive wind shear. This explains why the Es occurrence rate and average S4 index correlate not only with the negative shear but also with the positive shear of the zonal wind.
The lower panels of Figure 4 show that the vertical shear of the magnetic northward wind has little impact on the Es occurrence rate and average S4 index at 90-120 km. This is expected from the wind shear theory, which predicts that the vertical shear of the meridional wind plays a role only above 125 km or so (e.g., Haldoupis, 2011). It is noted that the vertical shear of the meridional wind in Figure 4 is multiplied by I/|I|, considering that the contribution of the meridional wind to Es is opposite in the magnetic Northern (I > 0) and Southern (I < 0) Hemispheres; see Equation 1. Our data set is not suitable for studying the statistical relationship between Es and In the upper panels, linear fits are indicated by magenta lines. Other lines show the results obtained from a subset of the data. Blue solid and dashed lines correspond to the data from the first and last half of the period, respectively. Green solid and dashed lines correspond to the data at 15°S-15°N and 15°N-45°N, respectively. Orange solid and dashed lines correspond to the data at heights of 90-100 km and 100-120 km, respectively. vertical wind shear above 120 km, as the detection of Es at such high altitudes is rather infrequent. The validity of the wind shear theory above 120 km requires further investigation.

Conclusions
This study has examined the wind shear theory of Es, for which existing evidence is mostly based on numerical simulations and sparse observations by sounding rockets. We have investigated the relationship between Es and vertical wind shear, using vertical profiles of COSMIC-2 radio occultation signal-to-noise ratio (SNR) and ICON/MIGHTI neutral winds. Global seasonal climatologies of the Es occurrence rate and S4 scintillation index derived from COSMIC-2 SNR profiles are in good agreement with those previously reported using other data, which validates the COSMIC-2 Es data. Also, the vertical shear of the ICON/MIGHTI zonal wind at E-region heights is in reasonable agreement with GAIA model predictions. Direct comparisons are presented for COS-MIC-2 SNR and ICON/MIGHTI wind profiles for the latitude range of approximately 15°S-45°N and the altitude range of ∼90-120 km. The main results of the study may be summarized as follows: 1. Both the Es occurrence rate and average S4 index are correlated with the negative vertical shear of the eastward wind, providing observational support for the wind shear theory. The vertical shear of the meridional wind has little impact on Es for the height range of 90-120 km 2. The wind-shear effect on the Es occurrence rate and average S4 index is more pronounced above 100 km than below, consistent with the numerical work by Andoh et al. (2021). Below 100 km, frequent ion-neutral collisions suppress the formation of an Es layer by the wind shear mechanism 3. Es can be observed even in the absence of vertical wind shear. This can be due to the presence of surviving Es layers that are generated at an earlier time. The Es occurrence rate decreases with increasing magnitude of positive shear in the zonal wind, because a surviving metallic ion layer is destroyed by vertical ion flux divergence induced by the positive wind shear

Data Availability Statement
The COSMIC-2 radio occultation data (caL1Snr of level 1b, atmospheric excess phase profiles) are available from CDAAC: COSMIC Data Analysis and Archive Center: https://www.cosmic.ucar.edu/what-we-do/cosmic-2/data/. The ICON/MIGHTI Level 2.2 product Cardinal Vector Winds (Version 4) is accessible from the ICON website https://icon.ssl.berkeley.edu/Data.