Post-midnight irregularities in the equatorial regions of topside ionosphere obtained by the CSES satellite

Post-midnight irregularities in the equatorial regions of topside ionosphere obtained by the CSES satellite | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Post-midnight irregularities in the equatorial regions of topside ionosphere obtained by the CSES satellite Xiuying Wang, Wanli Cheng, Xueqing Zhang, Guocun Zhao, Qiao Wang, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2722826/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The equatorial post-midnight irregularities, which has been less studied, are investigated using the in situ electron density (Ne) measurements from 2019 to 2021 obtained by the China Seismo-Electromagnetic Satellite (CSES) orbiting in the topside ionosphere. Some results are obtained as following. (1) The equatorial post-midnight irregularities are distributed along the dip equator with a longitude variation pattern of wavenumber 4 and seasonal variation pattern of summer-winter peaks during low solar activity (LSA) period in the topside ionosphere. (2) The longitude variation pattern of post-midnight irregularities is consistent with that of the background Ne with the irregularities concentrated on the peaks of background Ne. (3) The occurrence rate of post-midnight irregularities increases rapidly with increasing solar flux, which can be attributed to the rapid increase in the background Ne during LSA period; moreover, growth rate of occurrence rate is different across different longitudes, with the Pacific and the Atlantic longitudes being the most outstanding regions. (4) The similar characteristics for both post-midnight and post-sunset irregularities suggests they may have similar generation mechanisms, which are supported by the fact that conditions favorable to post-sunset irregularity generation can appear at midnight hours during LSA period. Since there have been far fewer post-midnight irregularity studies compared to post-sunset irregularity studies, much more work is still required to understand its generation mechanisms. The large number of post-midnight Ne measurements from the CSES satellite provides a good opportunity for this study, which can help to understand the post-midnight ionospheric dynamical processes and their variations with solar activity, as well as to develop a more comprehensive irregularity forecast model. the CSES satellite in situ electron density measurements post-midnight irregularity topside ionosphere generation mechanism Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction Ionospheric scintillations are fluctuations of radio wave signals caused by the scattering of irregularities in the ionosphere when radio waves traverse the ionosphere (Aarons, 1982 ; Kil and Heelis, 1998 ; Huang et al., 2001 ; Basu et al., 2002 ). Severe scintillation can prevent a GPS receiver from locking on to the signal and less severe scintillations can reduce the accuracy and the confidence of positioning results (Whalen, 1997 ; Kintner et al., 2007 ; Tsai et al., 2017 ). In addition, ionospheric scintillation can significantly degrade both the performance and availability of space-based communication and navigation systems (Groves et al., 1997 ; Basu et al. 2002 ; Gentile et al., 2006 ; Kintner et al., 2007 ). For these reasons, ionospheric scintillation has long been one of the focuses on ionosphere research. According to Burke ( 1979 ), equatorial scintillation is called equatorial spread F (ESF) at lower altitude, and it is called plasma depletion or plasma bubble at higher altitudes (Singh et al., 1997 ; Kil and Heelis, 1998 ; Burke et al., 2004 ; Gentile et al., 2006 ). From the morphology of the ionospheric variations, this phenomenon is also called irregularities (Fejer and Kelley, 1980 ). All the above mentioned terms indicate the same phenomenon unless otherwise specified in this paper. Though ionospheric scintillation has been studied extensively so far, it remains a difficult phenomenon to predict due to its complex variation with local time, season, geomagnetic activity, and solar cycle (Aarons, 1982 , 1993 ; Whalen, 1997 ; Huang et al., 2002 ; Burke et al., 2004 ; Hei et al., 2005 ; Su et al., 2006 , 2008 ; Gentile et al., 2006 ; Tsai et al. 2017 ; Beshir et al., 2020 ; Jin et al. 2020 ; Wang et al., 2022 ). Previous studies show that ionospheric scintillations are mainly concentrated at three regions: the geomagnetic equator, the auroral ovals, and inside the polar caps (Aarons, 1982 ; Basu et al., 1988 , 2002 ; Tsunoda, 1988 ; Jin et al., 2020 ). As scintillation is so severe in the Equator and its vicinity, it is the region most vulnerable to scintillation-induced communication problems. Therefore, many studies on scintillation have focused on this region (Abdu et al., 1985 ; Aarons, 1993 ; Kil and Heelis, 1998 ; Huang et al., 2001 , 2002 ; Burke et al., 2004 ; Gentile et al., 2006 ; Heelis et al., 2010 ; Dao et al., 2011 ; Ajith et al., 2016 ; Jin et al. 2020 ). We will also follow this convention, focusing on the scintillations in equatorial and its vicinity region in this paper. Previous studies on scintillation normally conduct the work using different observations, such as ground-based measurements (Aarons et al., 1982; Abdu et al., 1985 ; Basu et al., 1988 ; Whalen, 1997 ), satellite sounding measurements (Maruyama and Matsuura, 1984), radio occultation technique (Dymond, 2012 ; Carter et al., 2013 ; Tsai et al., 2017 ;), and satellite in situ measurements (Singh et al., 1997 ; McClure et al., 1998 ; Kil and Heelis, 1998 ; Huang et al. 2001 , 2002 ; Burke et al. 2004 ; Gentile et al. 2006 ; Dao et al., 2011 ; Jin et al., 2020 ). As the ground-based measurements are limited in spatial coverage, it is difficult to get global images of scintillation with this kind of observations. In situ ionospheric measurements on LEO satellites provides the chances to study the global spatiotemporal features of this phenomenon (Burke et al., 2004 ; Su et al., 2006 ; Dao et al. 2011 ; Wang et al., 2022 ). For satellite in situ measurements, most of the studies on ionospheric scintillation focus on the time period from sunset to pre-midnight hours as most scintillations are clustered around this time period (Huang et al., 2001 , 2002 ; Burke et al., 2004 ; Gentile et al., 2006 ; Su et al., 2006 ), or on all the local times (LTs) as the LTs of the satellite in situ measurements are not fixed (Jin et al., 2020 ). Whereas global ionospheric scintillation studies on post-midnight are relatively few, especially during low solar activity (LSA) period, although there are some of the studies using the C/NOFS measurements (Dao et al. 2011 ; Yizengaw et al., 2013 ). According to the studies by Wang et al. ( 2021a , b ; 2022 ) using the in situ electron density (Ne) measurements from the China Seismo-electromagnetic Satellite (CSES), the topside ionosphere after midnight exhibits some special space climatology features during LSA period, such as the nighttime winter anomaly (NWA) phenomenon (i.e. nighttime Ne is smaller in summer than in winter) and the frequently occurred post-midnight irregularity phenomenon, etc. So far, relatively fewer studies have been conducted on post-midnight scintillation in the topside ionosphere, and its generation mechanism remains unclear and under extensively debated (Yizengaw et al., 2013 ). The CSES satellite, performing nighttime measurements at about 02:00 LT with a sun synchronous orbit at the altitude of 507km (Wang et al., 2019a ), has been accumulating a large amount of in situ Ne measurements since its launch in February 2018, which provides a good opportunity to study the climatology and detailed features of post-midnight irregularities in topside ionosphere. In this paper, the equatorial irregularities, detected using the nighttime in situ Ne measurements from the CSES satellite, are studied to analyze the spatiotemporal distribution features of the topside ionospheric irregularities after midnight and their variation with solar activity. The longitudinal distributions for post-midnight irregularities and background Ne are also compared to reveal their relations; and finally, the generation mechanisms are discussed for the post-midnight irregularities in topside ionosphere. The study of post-midnight irregularities in topside ionosphere during LSA can help to understand scintillation from a different perspective and to further understand the dynamical processes of the ionosphere, which will promote the work of building a more practically integrated prediction model for trans-ionospheric communication systems. 2. Data And Methods The in situ Ne measurements from the CSES (China Seismo-Electromagnetic Satellite, also called Zhangheng-1 or ZH-1 for short) satellite are used in this paper to carry out the analysis work. The CSES satellite, launched on February 2nd, 2018, is orbiting in a sun synchronous mode with an angle of 97.8°at the altitude of 507 km. The observation range is 65°of northern and southern geographical latitude and the observation local times (LT) for descending (daytime) and ascending (nighttime) orbits are about 14:00LT and 02:00LT, respectively. The solar activity has been very low since the launch of this satellite, which leads to the relatively lower altitude of the F2 layer. Therefore, the altitude of the satellite is much higher than the peak height region of F2 layer (hmF2) during this period, which means the observation altitude is at the topside ionosphere. The in situ Ne measurements obtained under this altitude and this nighttime LT provide us a good opportunity to study the fine features of the post-midnight irregularities in the topside ionosphere. The Ne disturbances along the satellite track are the one-dimensional mapping of the irregularities in the topside ionosphere, and relative fluctuation of the disturbance amplitude can indicate the intensity of the irregularities. Therefore, detecting disturbances or irregularities events along the satellite orbit is the first step in this study. To detect irregularity events, a simplified method is used, which is an improvement on the method used in our previous work (Wang et al., 2022 ). The outline of the method is as following. Standardize the in situ Ne measurements along the orbit so that a unified criterion on determining irregularity event can be applied to all the orbit measurements. Calculate the first-order differentiation on the normalized measurements in step (1) to remove trends existed in the orbit measurements over a large latitude range. Calculate the standard error (SE) of a slipping window using the first-order differentiation series in step (2) and determine irregularity event with a given SE threshold criterion. An irregularity event is determined for continual SEs greater than the threshold value (TV). The location of the event is decided using the average latitude and longitude of the SEs > = TV; and the intensity of this irregularity event is decided using the average SEs. Therefore, SE with a bigger value indicates irregularity with relative large amplitude variation, namely large SE means strong irregularity intensity. This detecting method is generally similar to the method by Beshir et al. ( 2020 ), the only difference is that the normalization process in this study is performed on the original track measurements, while in the paper by Beshir et al. ( 2020 ) the normalization process is performed on the deviation. In essence, the final results are similar for the two methods. An explanation is given here that how to select the threshold value depends on the objective of the work. If a smaller threshold is adopted, more irregularity events will be detected; in contrast, with a relative larger threshold value, less irregularity events can be identified. Different threshold values are examined in this study and also in another study (Wang et al., 2022 ), and all the results show similar statistical features, indicating that the number of detected irregularities does not change the spatiotemporal statistical properties. Following the detection method described above, the nighttime in situ Ne measurements obtained by the CSES satellite from 2019 to 2021 are used to identify the irregularity events along the orbit track in the equatorial regions to analyze the spatial distribution, seasonal variations, and variation with solar activity for the post-midnight irregularities in topside ionosphere during LSA year. The numbers of total orbit tracks in the three years are 5249, 5374, and 5406, respectively. Based on the Ne measurements from these orbit tracks, the monthly background Ne is also calculated to compare with the irregularity distributions. The monthly background Ne is obtained by averaging the Ne measurements in a month in a latitude and longitude grid of 2°×5°. When calculating averaging Ne, the Ne measurements lower than 1/4 quantile and higher than 3/4 quantile are removed to reduce the influence of data fluctuations. For detailed calculation process, please refer to Wang et al. ( 2021a ). The solar activity index F10.7 and geomagnetic activity index Dst during 2019 to2021 are given in Fig. 1 . It can be seen clearly from Fig. 1 a that the solar activity level is extremely low in 2019, and begins to increase from about October 2020. In addition, there are only a few very small geomagnetic activity events (Dst<-30nT) during the study period as shown in Fig. 1 b except the relatively bigger one (Dst<-70nT) in November 2021. As geomagnetic activities generally inhibit irregularity generation (Aaron et al., 1982; Singh et al., 1997 ), we therefore use all the observations without excluding the data obtained during geomagnetic activities. 3. Results 3.1 Spatiotemporal distribution According to Fig. 1 , the overall solar activity level in 2019 is generally consistent, with a very low F10.7 index. Therefore, in situ Ne measurements in 2019 are used in this section to demonstrate the spatiotemporal distribution and seasonal variation to avoid biases caused by different solar radiation and to perform statistics under similar conditions. Spatiotemporal distribution of the irregularity events in 2019, detected using the method described in Section 2 with a threshold value of 0.15, is given in Fig. 2 , which covers the ± 30° geographical latitude near the Equator. The region between ± 20° geomagnetic latitude (shown as red dashed line) is chosen as the near equatorial region following the conventional approach adopted by previous studies. It should be noted that geomagnetic coordinates here are from the geomagnetic dipole coordinate system and are provided in the in situ Ne measurements dataset. The geomagnetic coordinates are different from those of the IGRF model, such as the geomagnetic equator (black dashed line) and the dip equator (black solid line) shown in Fig. 2 . As the geomagnetic coordinates are provided in the dataset, we use them when calculating parameters related to the geomagnetic coordinate. In Fig. 2 , also given are the histograms of these irregularity events, representing density variations of the irregularities along with geographical longitude and geomagnetic latitude, which are placed above and to the right of the spatiotemporal distribution plot, respectively. The histograms are drawn using the events within ± 20° geomagnetic latitude, i.e. the irregularity events within the two red dashed lines in Fig. 2 . (In Fig. 2 , each irregularity event is represented by a dot. SS indicates irregularity intensity, represented by the dot size, and Month indicates the occurrence month, represented by dot colors. The dotted line is the Equator, and the black solid line is the dip equator obtained from the IGRF12. The dashed lines are geomagnetic latitudes from the dipole field geomagnetic coordinate provided by the original dataset; the black dashed line is the geomagnetic equator, the red lines ± 20°geomagnetic latitude, and the purples lines ± 35° geomagnetic latitude. ) In Fig. 2 , each dot represents an irregularity event with the color indicating the occurrence month and the size its intensity; the larger the dot, the stronger the intensity of the irregularity event. The solid black line is the dip equator obtained from the 12th IGRF model at the CSES orbiting altitude, and the black dotted line is the Equator. The dashed lines are geomagnetic latitudes given by the original dataset, with the black dashed line representing the dipole field geomagnetic equator, the red dashed lines the ± 20°dipole field geomagnetic latitude, and the purple dashed lines the ± 35° dipole field geomagnetic latitude. It can be seen clearly from Fig. 2 that, besides the equatorial regions between the two red dashed lines, the irregularities are also concentrated in two regions beyond the equatorial region, which are in the longitude sectors where the geomagnetic poles are located, and on the hemisphere close to the geomagnetic pole. In fact, the post-midnight irregularities can be found throughout the satellite spatial coverage according to Wang et al. ( 2022 ), indicating that post-midnight irregularities are frequently occurred phenomenon during LSA period. As the equatorial irregularities are the focus of this paper, we will concentrate on the data between the two red dashed lines in Fig. 2 . As shown in Fig. 2 , the equatorial irregularities are distributed well along the dip equator, i.e., the solid black line in Fig. 2 . An obvious wavenumber pattern is shown along geographical longitude in the spatial distribution and in the histogram above it, with the African, Asian, Central Pacific, and West American longitude sectors being the peak and the Indian, West Pacific, East Pacific, and Atlantic longitude sectors being the valley of the wave structure. It should be noted that the Atlantic longitude sector is a valley of the wave structure with only a few irregularity events. The low number of irregularities in the Atlantic longitude sector is quite different from previous findings that the Atlantic sector is a region of concentrated post-sunset irregularities (Maruyama and Matuura, 1984 ; Kil and Heelis, 1998 ; Huang et al., 2001 , 2002 ; Burke et al., 2004 ; Su et al., 2006 ;), which will be discussed in Section 4 . Latitude distribution of the equatorial irregularities is basically symmetrical about the geomagnetic equator, as shown in the histogram to the right of the spatial distribution plot. Among the four irregularity peaks, three are generally symmetrically distributed on the two sides of the dip equator, including the peaks in the Central Pacific, West American, and African longitude sectors, where the geomagnetic declination is eastward or close to zero. The one exception is the distribution peak in Asian longitude sector, where the detected irregularities are located in the northern hemisphere. In contrast, the irregularities in the West Pacific longitude sector, which connect with the Central Pacific peak, are mostly located in the southern hemisphere, closer to the southern 20° geomagnetic latitude. In addition, the occurrence seasons are contrary for the Asian and West Pacific regions according to events color shown in Fig. 2 . In addition to the spatial distribution feature of wavenumber 4 pattern, seasonal variation of the equatorial irregularities are also very obvious in Fig. 2 , with most of the events occurring during the summer months of each hemisphere, i.e. for most of the irregularity events in Northern Hemisphere, the occurrence time is northern summer, and most of the events in Southern Hemisphere, the occurrence time is southern summer (northern winter), as mentioned above that events in the Asian sector is in summer and in the West Pacific peaks is in winter. To show this seasonal feature, the histogram of equatorial irregularities in each month is given in Fig. 3 . Two peaks and two valleys are shown in the monthly histogram of the equatorial irregularities in Fig. 3 , with most of those events being concentrated in the two solstice periods and less events in the two equinox periods. Another feature of the seasonal variation is that the summer peak lasts a longer time compared to the winter peak, extending from summer to the autumn season; while the winter peak is only evident at the winter solstice, with a tendency of extending towards February. To get the seasonal variation of each longitude sector, the equatorial region is divided into 12 sub-regions with a longitude interval of 30°. The monthly variation of each sub longitude regions is given in Fig. 4 . As can be seen from Fig. 4 , a generally similar pattern of seasonal variation peaking in summer, winter, or both seasons is shown in each longitude sector. Seasonal variation pattern is more obvious in longitudes of irregularity peaks in Fig. 4 , such as Region 1 and 2 (the Central Pacific longitudes), Region 4 (the West American longitudes), Region 7 (the African longitude), and Region 10 (the Asian longitudes). Region 12 indicates the irregularity concentration in the West Pacific longitudes in Southern Hemisphere, demonstrating a winter seasonal pattern. Compared to the peak longitudes, seasonal variation pattern is not so obvious for irregularity valley longitudes as there are only a few irregularity events, such as Region 3 (the east Pacific longitudes), Region 5 and 6 (the East American and Atlantic longitudes), Region 8 and 9 (the Indian longitudes). Further statistics using irregularities detected with a lower threshold of 0.1 indicates a summer or winter seasonal pattern in the irregularity valley longitude sectors. Though the general seasonal variation is summer or winter peak in each longitude sector, the time when the peaks appear and the relative amplitudes of the two peaks are varying gradually. Examples of this gradual seasonal variation with longitude are that only the summer peak appears in longitude sector of 90°to 120°(Region 10); in contrast, only the winter peak occurs in longitude sector of 150°to 180°(Region 12); and both summer and winter peaks can be seen in the longitude sector of -180°to -150°(Region 1). Summarizing the above analysis, the spatiotemporal distribution features are that the equatorial post-midnight irregularities are distributed along the dip equatorial with a wavenumber 4 pattern in the longitude direction and with a seasonal variation pattern of summer-winter peaks and spring-equinox valleys. 3.2 Comparison with background Ne distribution To compare the distribution of equatorial post-midnight irregularities with its background Ne, the seasonal background Ne distributions are plotted using the results calculated from the nighttime in situ Ne measurements in the four seasons of 2019. The background Ne calculation method is introduced in Section 2 , detailed description of the method can reference Wang et al. ( 2021a ). The four seasons are divided in the normal way, i.e. February, March, and April belong to the March Equinox, May, June, and July the June Solstice; August, September, and October the September Equinox, and November, December, and January the December Solstice. The background Ne distributions for the four seasons and their corresponding irregularity events are presented in Fig. 5 . Each event is represented by a dot with its size indicating the intensity of the irregularity, similar as that in Fig. 2 . As can be seen from Fig. 5 , a general wavenumber pattern is shown in the seasonal background Ne distributions with a typical wavenumber of 3 or 2. In addition, it is clearly shown in Fig. 5 that the peak and valley positions of the wavenumber pattern vary with seasons as well as with the wave number. Wavenumber 2 pattern is obvious for the two solstice seasons with the African and the Pacific-West American longitude sectors being the peaks for the June solstice and the Central Pacific and the American-Atlantic-African longitude sectors being the peaks for the December solstice; and wavenumber 3 pattern is obvious for the two equinox seasons with the Asian, the Central pacific, and the American-African longitude sectors being the peaks for the March Equinox and the African, the Central Pacific, and the West American longitude sectors being the peaks for the September Equinox. With the changing position of the background Ne peaks, the irregularities peaks also change their positions. The irregularities peaks generally coincide with the background Ne peaks in different seasons. As a comparison, Fig. 6 also gives the yearly distribution for background Ne and irregularity events in 2019. As mentioned above, the African, the Central Pacific, and the West American longitude sectors have been the background Ne peaks for all the seasons, as a result they are also the yearly background Ne peaks. Since the seasonal irregularity peaks coincide with the corresponding background Ne peaks, the yearly irregularity peaks are also coincide with that of the yearly background Ne peaks. Relatively higher background Ne appears in the Asian and the West Pacific longitude sectors on both side of the dip equator, where irregularities are correspondingly more concentrated. Though the Central Pacific to the West American longitude sector shows a continuous Ne peak in Summer solstice, a valley can be seen clearly in the West Pacific longitude sector for the other three seasons, as shown in Fig. 5 . Combining the background Ne of the four seasons together, a valley can be seen clearly between the Central Pacific and the West American longitude sector in the yearly background Ne distribution in Fig. 6 , which corresponds also to an irregularity valley. Both the seasonal and yearly distributions for background Ne and post-midnight irregularities show that the two (background Ne and post-midnight irregularity) have similar wavenumber distribution pattern along the longitude direction, suggesting that post-midnight irregularity distribution is closely related with the background Ne distribution. Through the comparison of the seasonal and yearly background Ne and irregularity distributions, coincidence of the two is shown in longitude distribution and peak locations. A preliminary conclusion can be drawn that the distribution of topside background Ne obviously affects the distribution of post-midnight irregularities during LSA period, that is, the background Ne distribution plays an important role in the generation of post-midnight irregularities. See Section 4 for a further discussion of this topic. 3.3 Variation with solar activity Solar activity in 2019, 2020, and 2021 belongs to low solar activity (LSA) in general. However, it can be seen clearly that the solar activity level has begun to increase since October 2020 in Fig. 1 . Therefore, irregularities detected in different month of the three year 2019, 2020, and 2021 can be compared to obtain the influence of solar activity on the generation of post-midnight irregularities in the topside ionosphere. Figure 7 gives the total irregularity numbers detected in the equatorial region in each month of the three years. As a comparison, also given in Fig. 7 is the total orbit number in each month of the three years. It is clearly shown in Fig. 7 that irregularity numbers detected in 2021 increase dramatically compared to the corresponding months in 2019 and 2020 when considering the overall similar total orbit numbers in each month of the three years. This apparent increase of irregularity number is also evident in October to December in 2020 compared to the same months in 2019. The increase of irregularity numbers coincides with the increase of solar activity when comparing Fig. 7 with Fig. 1 , and the more the solar activity increases, the more the irregularity number increases, indicating that solar activity can also affect the generation of post-midnight irregularities just as it does on post-sunset irregularities. To compare the data directly, Fig. 8 gives the monthly irregularity occurrence rates and the corresponding solar activity F10.7 index in the three years. As seen in Fig. 8 , the irregularity occurrence rate also shows increasing trend with the increasing solar activity. For the first nine months in 2019 and 2020, the solar activity levels are quite close to each other, and the corresponding irregularity occurrence rates are also close to each other with a similar variation tendency. However, with the obvious increase of solar activity in October to December in 2020 compared to that in 2019, the monthly irregularity occurrence rates increases dramatically from about 0.09, 0.13, and 0.20 in 2019 to 0.20, 0.37, and 0.28 in 2020, respectively, which correspond to 122%, 185%, and 40% increase of occurrence rates. As shown in Fig. 8 b, the solar activity in November 2020 increases the most significantly compared to 2019, and the irregularity occurrence rate also increases dramatically in this month. In addition, December 2021 is another month with significant solar activity increase compared to 2020, the corresponding irregularity occurrence rate also indicates an obvious increase, which can be seen clearly from the data shown in Table 1 . In addition to the data of monthly irregularity occurrence rates, Table 1 also gives the monthly average F10.7 index from October to December for the three years, as well as the growth rates obtained by comparing the irregularity occurrence rate and the F10.7 index for the same month in different years. Table 1 Occurrence rate, monthly average F10.7 index and their growth rates Occurrence Rate Monthly Average F10.7 month 10 11 12 10 11 12 2019 0.09 0.13 0.20 67.45 70.23 70.97 2020 0.20 0.37 0.28 71.03 89.97 71.68 2021 0.22 0.36 0.43 89.23 86.17 103.03 2019 vs 2020 122% 185% 40% 4% 28% 1% 2020 vs 2021 10% -3% 54% 26% -4% 44% The above qualitative analysis indicates that occurrence rate of post-midnight irregularity generally shows an increase trend with the increasing solar activity. Due to the very low solar activity during the study period, it is not possible to draw a definite conclusion on the variations of the post-midnight irregularity occurrence rate with solar activity as the data doesn’t even cover half of a solar cycle. However, the results in Table 1 indicate that solar activity can influence the occurrence rate of post-midnight irregularity even during LSA period. An interesting feature shown in Fig. 8 a is that the irregularity occurrence rate of summer and winter peaks are essentially the same in 2019. However, there is a significant increase in the winter peak in 2021 compared to its summer peak, though the summer-winter seasonal variation pattern is still very obvious. It is understandable that the higher amplitude of irregularity occurrence rate at the end of 2021 is caused by the obvious increase of solar activity. However, what causes the obvious increase of winter peak amplitude at the beginning of 2021 when there is not a significant increase in solar activity? This can be explained by the delayed effect of solar activity on the ionosphere and irregularities, as suggested by Wang et al. ( 2022 ), which can also explain the situations on the extension of summer peak into autumn and winter peak into spring, as shown by the seasonal variation pattern in Fig. 3 . To exam whether different longitude sectors are equally influenced by the increasing solar activity, a further comparison is conducted using the irregularity events detected in October, November, and December of the three years in different longitude sectors. Twelve longitude sectors are divided in the equatorial regions with a longitude interval of 30°as it does in Section 3.1 . The irregularity occurrence rate in each longitude sector is calculated as the ratio between the number of orbit with irregularities and the total orbit number within that longitude sector, and the results are shown in Fig. 9 . According to Fig. 9 , the comparison and calculated results show that the maximum growth of occurrence rate is in Region 5 and 6, corresponding to longitude − 60°to 0°, where is just the Atlantic longitude sector; and followed by Region 11 and 12, corresponding to longitude 120° to 180°, in the Australian and the West Pacific regions in Southern Hemisphere. The longitude variation of growth rate of irregularity occurrence rate with increasing solar activity suggests that increasing solar activity has different effects on the generation of post-midnight irregularities in different longitude sectors. If this effect continues to exert influence with the increasing solar activity, it is conceivable that the spatial distribution may change from its wavenumber 4 distribution pattern in Fig. 2 to other distribution patterns, such as changes in peak positions or in total wave numbers. For example, variation of peak position is evidently shown in Fig. 9 ; the maximum occurrence place is located at Region 12 in 2019, and it changes to Region 11 in 2020 and 2021; and moreover, the peak region seems to widen, occupying both Region 11 and 12. Clues of variation of wavenumber pattern can also be seen in Fig. 9 . Three occurrence peaks can be seen in 2019 using the detected irregularity results in October, November, and December; however, there seems only two occurrence peaks in 2021 and 2022 using the results obtained in the same three months. Due to the variation of peak position and wave number with solar activity, the Atlantic longitude sector becomes a peak in 2020 and 2021 from the valley in 2019. The above analysis suggests that even during LSA period, solar activity can obviously affect the generation of post-midnight irregularities and this influence is different in different longitude sectors, which will further affect the longitude distribution of irregularity occurrence. 4. Discussion Post-midnight irregularities during very low solar activity period are studied using the in situ Ne measurements obtained by the CSES (ZH-1) satellite orbiting at an altitude of 507km, to analyze their spatial distribution and seasonal variation features in the topside ionosphere. The results show that a general wavenumber 4 distribution pattern is shown for the post-midnight irregularities with a seasonal variation of summer-winter peaks and spring-autumn valleys. The peaks of irregularities longitude distribution in the four seasons coincide with the peaks of the corresponding background Ne distribution in that season with a general wavenumber 3 pattern for equinox seasons and wavenumber 2 pattern for solstice seasons; a wavenumber 4 longitude variation pattern is shown along the dip equator when combining the irregularities in the four seasons, which also coincides with the corresponding yearly background Ne distribution. Results, obtained by comparing the occurrence rate under different solar activities during LSA period, show that post-midnight irregularity occurrence rate increases with the increasing solar activity and different longitude sectors exhibit different growth rate of occurrence rate with the increasing solar activity; the maximum growth rate is located at the Atlantic longitude sector, followed by the Australian to West Pacific longitude sector. These features suggest that solar activity exerts influence on the generation of post-midnight irregularities although the general solar activity condition remains at LSA level. For the above results obtained in this paper, some issues need to be clarified, and the related discussions are given in the following section. 4.1 Longitudinal/ Seasonal distribution 1. Spatiotemporal Distribution The longitudinal/seasonal variation of the post-sunset equatorial irregularities have been investigated extensively over the past decades (Maruyama and Matuura, 1984 ; Tsunoda, 1985 ; Whalen, 1997 ; McClure et al., 1998 ; Huang et al., 2001 , 2002 ; Burke et al., 2004 ; Gentile et al., 2006 ; Su et al., 2006 , 2008 ). Longitudinal variation of post-sunset irregularities is frequently mentioned in those previous studies, such as: Huang et al. ( 2001 , 2002 ) report that seasonal and longitudinal variations of post-sunset irregularities remain similar within given longitude sectors using the DMSP measurements over a full solar cycle; they suggest that the Atlantic-African sectors are the most significant occurrence longitudes and the Indian sector is the least occurrence longitudes. Burke et al. ( 2004 ) also show that the highest and lowest rates of equatorial plasma bubble (EPB) located at the Atlantic-African and Indian sectors using both the DMSP and the ROCSAT-1 measurements. Kil and Heelis ( 1998 ) suggest that scintillation is always high in the Atlantic-African longitudes and is always low in the Indian regions. All the above post-sunset longitude distribution results are in general agreement with the spatial distribution obtained in this study, with the exception of the Atlantic sector, which is a low occurrence region for the post-midnight irregularities detected in 2019. However, the subsequent results of this study further demonstrate that irregularities in the Atlantic longitude sector increase dramatically, and this region becomes the peak with the increasing solar activity as shown in Fig. 9 . In fact, the solar activity remains at low activity levels for the entire study period though it has been increasing since October 2020. Therefore, the general longitude distributions for both post-sunset and post-midnight irregularities are consistent with each other. It should be pointed out here that the low irregularity occurrence in the Atlantic longitude sector in 2019 doesn’t mean the result is not correct. In fact, this low occurrence rate of post-midnight irregularities in the Atlantic longitude sector is also noticed by Dao et al. ( 2011 ) using the C/NOFS measurements from May 2008 to March 2010, an extremely prolonged LSA period between 23/24 solar cycle. Our result is in agreement with that of Dao et al. ( 2011 ), indicating the results in this study are correct and can repeat from different dataset under similar solar activity conditions. Quite different features, namely low occurrence rate in 2019 but relatively higher occurrence rate in 2020 and 2021, are shown for the post-midnight irregularities in the Atlantic longitude sector though the general solar activity is still low over the study period in this paper, which may be closely related with the low geomagnetic field in the South Atlantic Anomaly (SAA) region. More studies are required to further analyze the mechanism behind the phenomenon. The spatiotemporal structures of post-midnight irregularities are also reported by a few studies using post-midnight measurements. For example, using the in situ measurements from ROCSAT-1 satellite obtained during moderate to high solar activity years of 1999–2004, Su et al. ( 2018 ) report that the post-midnight irregularity distribution is similar to the pre-midnight ones, with the African and Central Pacific sectors being the high occurrence places for June solstice, and the South America and the Atlantic Ocean sectors being the high occurrence place for December solstice. Dao et al. ( 2011 ) and Yizengaw et al. ( 2013 ) find the longitudinal structures using the C/NOFS in situ measurements obtained in LSA years; they also find that the maximum occurrence is located at South American and African sector sectors for summer solstice months, and significant activity occurs at Pacific and South American longitude sectors for winter solstice months. This spatiotemporal distribution is in accord with the results in this study. As shown in Fig. 4 , the South American longitude sector (-90°to -60°) and the African longitude sector ( 0°to 30°) show summer peaks, and the West Pacific longitude sector (150°to 180°) shows winter peak; while the Central Pacific longitude sector (-180°to -150°) shows both summer and winter peaks. The nighttime background Ne longitude variations obtained in this study are in agreement with the results obtained from the nightglow images (Sagawa et al., 2005 ; Immel et al., 2006 ), both presenting the large scale longitudinal variations in the Ne amplitude and separation, which are supposed to be driven by the atmospheric tide DE3 in troposphere (Hagan et al., 2002; Kil et al., 2007 ). The interesting point is that the wave-like structure of post-midnight irregularities coincides with the wave-like background Ne structure as shown in Fig. 5 and Fig. 6 in this study. According to the study by Sidorova and Filippov ( 2018 ), the wave-like structure for post-sunset irregularities is influenced by troposphere tide and associated with the troposphere DE3 tides, which affect the thermosphere parameters and ionosphere parameters through the modulation of the thermosphere winds and electric fields. Coincidence of irregularity peaks with that of background Ne peaks indicates that post-midnight irregularities are also influenced by the troposphere tides, and the background Ne controls the distribution of irregularities. Beshir et al. ( 2020 ) suggest that background plasma density is very important for post-sunset irregularities, strong plasma densities result in stronger plasmas irregularities, while relatively less dense plasma results in relatively lower plasma irregularities. The results in this paper also suggest that background Ne is very important for the post-midnight irregularities. Thus, the low occurrence in 2019 in the Atlantic longitude sector must be related to the extremely low background Ne in this region. In summary, comparisons of the longitude variation for post-midnight and post-sunset irregularities indicate they have similar wave-like structure. Moreover, the concentrated irregularities coincide with the background Ne peaks. Both these features suggest that some places provide persistent favorable conditions for the generation of equatorial irregularities, independent of the nighttime irregularity occurrence time and season. Furthermore, the background Ne plays an important role in the generation of nighttime irregularities during LSA period. 2. Seasonal Variation The general seasonal variation pattern of the post-midnight equatorial irregularities obtained in this study is summer-winter peaks with spring-autumn valleys, as shown in Fig. 3 . This seasonal variation pattern is in agreement with the results obtained by Heelis et al. ( 2010 ) using the C/NOFS in situ measurements observed under extremely LSA conditions in 2008 and 2009. Their results show that post-midnight occurrence frequency peaks during both northern winter and summer period, but is very low during equinox period. The seasonal variation pattern for post-midnight irregularities is quite different from the equinox peaks and solstice valleys pattern of post-sunset irregularities reported by many previous studies (Tsunoda, 1985 ; Huang et al., 2001 , 2002 ; Burke et al., 2004 ; Hei et al., 2005 ; Su et al., 2006 , 2008 ). Based on the long-term ground-based measurements in India, Sastri ( 1999 ) reports that post-sunset spread F occurrence peaks in equinox months during high solar activity (HSA) period; and during LSA period, post-midnight spread occurrence peaks in solstice months. Otsuka et al. (2009) also report that irregularities appear frequently at pre-midnight between March and May and at post-midnight between May and August using ground-based measurements in Indonesia in a relatively LSA period. Miller et al. ( 2010 ) find that more irregularities appear later in the winter evening during LSA period in the Pacific longitude sector. Candido et al. ( 2011 ) also find the solstice peaks seasonal variation pattern in Brazil. All these studies, using long-term ground-based measurements in different longitudes, show that the peak seasons and LTs of nighttime irregularity occurrence vary with solar activity. This result is similar to the seasonal and LT variations of nighttime irregularity obtained from the topside ionosphere measurements. Besides the results obtained in this paper, the shift of peak occurrence from post-sunset hours during HSA to post-midnight hours during LSA is noticed by the studies using the C/NOFS satellite measurements obtained during solar minimum of cycle 23/24 (Yokoyama et al. 2011 ; Yizengaw et al. 2013 ). All the studies for both the bottomside and topside ionospheric irregularity suggest that irregularity is a very common phenomenon for both the bottomside and topside ionospheres, and both the bottomside and topside ionospheres have similar irregularity seasonal and LT variation patterns with the solar activity variation. Since generation of irregularities is associated with the ionosphere dynamical processes, we believe that the variations of irregularity peak season and peak LT with solar activity can indicate the variation of ionosphere dynamical processes with solar activity. Therefore, issues related with irregularity seasonal and LT variations deserve more research work. We will carry out more studies in our subsequent work when enough measurements are accumulated. 4.2 Variation with solar activity Solar activity dependence of post-sunset irregularity occurrence has been reported by many previous studies (Abdu et al., 1985 ; Huang et al., 2002 ; Su et al., 2008 ; Nishioka et al., 2008 ). The results in this study also indicate that post-midnight irregularities are closely related to solar activity. Variation of post-midnight irregularities with solar activity shows an increasing trend with the increasing solar activity. However, this does not mean that post-midnight irregularity will always follow this trend. In fact, the general trend is that post-midnight irregularities decrease as solar activity increases, according to the study by Fejer and Scherliess (1999) based on ground-based measurements. They attribute the decrease in post-midnight irregularities to the large increase of the nighttime downward drifts with the increasing solar flux, which will be discussed further in the next section. How can we explain the result obtained in this study that post-midnight irregularities increase with increasing solar flux during the study period? Two reasons are given below. On the one hand, although solar activity has been increasing since October 2020 as shown in Fig. 1 , the overall solar activity remains very low in 2020 and 2021 with the overall monthly average F10.7 index being less than 100sfu (sfu is the solar flux unit, 1 sfu = 10 − 22 W m − 2 Hz − 1 ), which is in the range of LSA level according to the criteria used in previous studies (Huang et al., 2002 ; Nishioka et al., 2008 ). On the other hand, electron density is sensitive to solar flux, especially under LSA conditions (Liu et al., 2011 ). As in the case of 2019 shown in this study, the monthly average solar flux is around or below 70sfu, which is particularly low. Under this solar condition, increasing solar flux leads to the obvious increases of Ne, and therefore the increase of post-midnight irregularities. To demonstrate the relation between irregularities and Ne, Table 2 gives the average F10.7 index and Ne as well as irregularity occurrence rate from October to December in 2019, 2020, and 2021, using the measurements in the geographical longitude range of -50°to -20°and in the dipole geomagnetic latitude range of -10°to 10°, which belongs to the equatorial Atlantic region. Table 2 Average F10.7 index, Ne, and irregularity occurrence rate in the Atlantic region F10.7 Index(sfu) Ne (10 4 /cm 3 ) Rate (%) 2019 69 2.0 3.7 2020 83 4.0 13.8 2021 92 3.0 31.3 Ne and irregularities increase much faster than the F10.7 index, and in this case the rapid increase of irregularities is more related to Ne than to solar flux. The close relation between Ne and irregularities is also demonstrated in Fig. 5 . There are only a few irregularities during the summer and autumn seasons when the Atlantic longitude is the valley of background Ne; more irregularities appear in this region when the background Ne increases during winter and spring seasons. This suggests that background Ne plays very important role in the generation of post-midnight irregularities, which is consistent with the suggestion obtained by Basu (1988) that the drastic reduction of post-sunset scintillation occurrence from solar maximum to solar minimum indicates that the background density is the major modulating factor. It is easy to understand that large density fluctuation cannot be produced when the background density is very low; and as a result, there will be fewer irregularities (Dymond, 2012 ). When the background density condition is satisfied, irregularities increase rapidly in the longitude sectors where they are easy to generate. When it comes to the places prone to irregularities, another interesting phenomenon caused by the enhancing solar activity is that the growth rate of irregularity occurrence rate with increasing solar activity is markedly different across different longitudes, with the Atlantic and Pacific longitude sectors being the two most significant regions, where are the places both post-sunset and post-midnight irregularities frequently occur as mentioned in Section 4.1 . To demonstrate this characteristics, Fig. 10 gives the spatiotemporal distributions of irregularities detected in 2020 and 2021. As solar activity increases most significantly during the winter season, more irregularities occur at the southern hemisphere for 2020 and 2021. Due to the increasing irregularities, the wavenumber 4 pattern can be recognized in 2020, but it is not obvious in 2021 as the irregularity valley in the Atlantic longitude sector is concentrated with irregularities. It can be seen clearly that irregularities in the Atlantic and Pacific longitude sectors increase faster than it does in other longitude sectors. The imbalance increase of irregularities occurrence in different longitude sector leads to the variation of wavenumber pattern as suggested in Section 3.3 . In fact, unbalanced increases of irregularities with increasing solar activity is also noticed by Nishioka et al. ( 2008 ); they suggest that the Atlantic, African, and Asian longitudes are the regions suffered the most significant influence, which is generally consistent with our results. This result further suggests that post-midnight irregularities have similar features to those of post-sunset irregularities. As the reasons for the unbalanced increase are beyond the scope of this study, we leave this question here; more studies will be conducted on this topic in our subsequent work. Studies on post-sunset irregularities show that the Atlantic longitude sector is the region of maximum occurrence rate during winter season, which is explained by the theory that alignment of the sunset terminator with magnetic meridian as the major cause for the irregularity occurrence (Tsunoda, 1985 ). As the post-midnight irregularities have no relation with sunset, it is therefore this sunset node theory cannot explain the dramatic enhancement of irregularities with increasing solar activity in winter season in the Atlantic longitude sector during LSA period, which may suggest that this theory is not applicable for the post-midnight irregularities or this theory may not be a key factor for the generation of nighttime irregularities. 4.3 Generation mechanism The similar spatial distribution and association with background Ne as well as response to the variation of solar activity for both post-midnight and post-sunset irregularities as analyzed above suggest that the two have similar generation mechanism. This suggestion is supported by the modeling results by Yizengaw et al. ( 2013 ) that post-midnight irregularities are initiated in the same way that the post-sunset irregularities are generated. Gentile et al. ( 2011 ) also suggest that the occurrence condition of post-midnight irregularities is closely related to the upward drift velocities as it does with the post-sunset irregularities, which is also mentioned by Yizengaw et al. ( 2013 ). Using irregularities data obtained from ground-based measurements, Otsuka ( 2018 ) suggests the generation conditions for the post-midnight irregularities: (1) seeding factors from AGWs (atmospheric gravity waves) and MSTIDs (medium-scale traveling ionospheric disturbances), and (2) F region condition favorable for the Rayleigh-Taylor (R-T) instability. As the focus of this paper is irregularities in topside ionosphere, plasma upward drift is adopted as seeding factor instead of AGWs and MSTIDs because electric field reversal is found from the EFD payload measurements onboard the CSES satellite when irregularity occurs. As is well accepted, the post-sunset equatorial irregularities, known for its characteristics of fast growth after sunset during equinox seasons, result from plasma dynamic process initiated from the gravitational Rayleigh-Taylor (R-T) instability at the bottomside of ionosphere after sunset when pre-reversal enhancement (PRE) of eastward electric field occurs due to the high conductivity gradient across the day night terminator during the post-sunset hours, leading to the sudden increase of plasma upward drift (Tsunda, 1985; Farley et al., 1986 ). Upward drifts can then carry the lower density at the bottomside of ionosphere to altitudes with higher density, leading to the generation of irregularity structures in F2 layer. As the post-sunset equatorial irregularities are generated due to the PRE with an unstable conditions at the bottom of F layer. However, these favorable conditions are absent after midnight in the topside ionosphere. Therefore, two problems need to be addressed if post-midnight irregularities are assumed to have similar generation mechanism as the post-sunset irregularities. The first problem is the instability condition for the topside ionosphere. As this condition is always satisfied at the bottom side of the ionosphere F layer due to the lower plasma density compared to higher altitudes, how to satisfy this condition in the topside ionosphere? The second problem is the upward drift condition. It is well known that nighttime electric field after PRE is general westward, which causes plasma to drift downward. Reversal of electric field from westward to eastward is required to satisfy this condition. The first problem can be solved based on the results obtained in our previous studies. According to the results by Wang et al. ( 2019b ), stratification is found in the topside nighttime ionosphere near the equatorial regions during LSA period using the in situ measurements from the DEMETER satellite. Existence of stratification in topside ionosphere is further confirmed by the results from the simultaneous in situ measurements obtained by the Swarm satellites orbiting at different altitudes of the topside ionosphere during relative LSA period (Wang et al., 2020 ). Nighttime stratification, which indicates that Ne is greater in higher altitudes than in lower altitudes above hmF2 height, provides instability condition for the topside ionosphere, favoring the generation of R-T instability. Results from the two missions suggest that nighttime stratification occurs frequently in the topside ionosphere along the dip equator during LSA period. Moreover, nighttime stratification appears more frequently during solstice seasons and can keeps its status from late nighttime till post-midnight hours with or without irregularities (Wang et al., 2020 ). According to the R-T instability equation proposed by Sultan ( 1996 ), R-T instability is inversely proportional to the ion-neutral collision frequency; therefore, R-T instability will become larger at higher altitude due to the smaller ion-neutral collision frequency (Kelley, 1989). Moreover, steep vertical gradient due to the topside stratification also enhance the growth rate of R-T instability (Ajith et al., 2016 ). Under these favorable conditions, it is easy to generate R-T instability in topside ionosphere. Therefore, nighttime stratification during LSA period provides the instability condition in the topside ionosphere. For the second condition, an explanation is given as following. According to the results by Fejer et al. ( 1991 ), the downward plasma drift due to nighttime westward electric field is generally weak during the post-midnight hours of solstice seasons, particularly during LSA periods. Fejer et al. (1995) also report that average nighttime vertical drifts from the AE-E satellite are upwards during summer solstice months in 1977 of a relative LSA year and are downward in 1978 and 1979 of moderate to HSA years. In addition, simultaneous electric field and density observations from the C/NOFS satellite prove that the electric field is eastward when irregularities are observed by the in situ density measurements (de La Beaujardière et al. 2009 ), suggesting that nighttime irregularities are caused by upward plasma drifts. In addition, Gentile et al. ( 2011 ) and Yizengaw et al. ( 2013 ) prove that post-midnight occurrence condition is closely related to the upward drift velocities; Rastogi and Woodman (1978) also suggest that reversal of drift from downward to upward is the key to the generation of spread F in the ionograms. The nighttime drift reversal from downward to upward can be caused by the penetration electric field from the magnetosphere and disturbance dynamo fields originating from auroral heating (Fejer and Scherliess, 1999; Burke et al. 2009 ). As the nighttime downward drifts are very small near solar minimum, it can easily be reversed by the disturbance drifts even in the absence of large prompt penetration electric field, which provides favorable upward drifts condition for the generation of post-midnight irregularities. According Fejer and Scherliess (1999), the evening upward drifts and nighttime downward drifts increase significantly with solar activity; large nighttime downward drifts require larger upward perturbation drifts to overcome. However, disturbance dynamo fields, which lead to the reversal of nighttime drifts, do not change much with solar flux (Scherliess and Fejer, 1997 ). Thus, reversal of nighttime plasma drift from downward to upward does not occur easily during relatively HSA period, it is therefore less likely to generate post-midnight irregularities. As both the instability and nighttime upward drifts conditions can be satisfied under LSA period, it is easy to understand that post-midnight irregularities can occur frequently during solar minimum years. It should be noted here that small irregularities or irregularities with lesser intensity can occur in the topside ionosphere under the above mentioned favorable conditions. As shown in Fig. 2 , smaller irregularities account for a large proportion of the detected irregularity events. However, for some very large irregularity structures covering a latitude range of over 20°with Ne fluctuation of close to an order of magnitude, the above conditions seem to be insufficient for these large-scale irregularity structures. Since this kind of irregularities always appear in the Atlantic longitude sector, they must be related to the special geomagnetic condition there. This issue, as well as the one mention in Section 4.1 concerning the Atlantic longitude sector, requires further studies. 5. Conclusion The equatorial post-midnight irregularities are studied using the in situ electron density measurements from 2019 to 2021 obtained by the CSES (ZH-1) satellite orbiting at the altitude of topside ionosphere during low solar activity period. Some results are obtained. The equatorial post-midnight irregularities are distributed along the dip equator with a longitude variation pattern of wavenumber 4. The seasonal variation pattern is summer-winter peaks and spring-autumn valleys, different from the equinox peaks and solstice valleys seasonal variation pattern for post-sunset irregularities. The longitude distribution of post-midnight irregularities is similar to that of background Ne in the four seasons, with a general wave number 3 pattern for equinox seasons and wave number 2 pattern for solstice seasons. Coincidence of irregularity peaks with background Ne peaks for both seasonal and yearly distributions suggests background Ne plays very important role in post-midnight irregularity generation. Post-midnight irregularities is sensitive to solar activity under LSA conditions as occurrence rate increases rapidly with the increasing solar flux. Moreover, growth rate of irregularity occurrence rate is different across different longitudes, and the Atlantic and Pacific longitudes are the two regions with maximum irregularity growth rate. Stratification in the topside ionosphere and reversal of nighttime drifts from downward to upward at midnight hours during LSA period provide R-T instability and upward drifts conditions for the generation of post-midnight irregularities. As the generation mechanism of post-midnight irregularities is still unclear, it requires more research work. The large amount of in situ electron density measurements from the CSES (ZH-1) satellite provide us a valuable dataset to study the issues related with post-midnight irregularities, and more subsequent work will be conducted with the accumulation of measurements. Declarations Availability of data and materials The measurements of the CSES satellite can be requested and downloaded from the website: https://www.leos.ac.cn/. The Dst data used in this paper is downloaded from website http://wdc.kugi.kyoto-u.ac.jp; and the F10.7 data is downloaded from website ftp://ftp.swpc.noaa.gov/pub/indices/old_indices/ (latest access: 2022-08-18). Competing interests The authors declare that they have no conflict of interest. Funding This work is supported by the NSFC project (grant no. 42104159). 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Journal of Geophysical Research, 115(A6), A06307. doi:10.1029/2009ja014946. Nishioka M, Saito A, and Tsugawa T. 2008. Occurrence characteristics of plasma bubble derived from global ground-based GPS receiver networks. Journal of Geophysical Research: Space Physics, 113, A05301, doi:10.1029/2007JA012605. Otsuka Y. 2018. Review of the generation mechanisms of post-midnight irregularities in the equatorial and low-latitude ionosphere. Progress in Earth and Planetary Science, 5:57. doi:10.1186/s40645-018-0212-7. Otsuka Y, Ogawa T, and Effendy. 2009. VHF radar observations of nighttime F-region field-aligned irregularities over Kototabang, Indonesia. Earth, Planets and Space, 61, 431-437. Doi: 10.1186/BF03353159 Sagawa E, Immel T J, Frey H U, and Mende S B. 2005. Longitudinal structure of the equatorial anomaly in the nighttime ionosphere observed by IMAGE/FUV. J. Geophys. Res., 110, A11302, doi:10.1029/2004JA010848 Sastri J H. 1999. Post-midnight onset of spread-F at Kodaikanal during the June solstice of solar minimum. Ann. Geophys., 17, 1111–1115. DOI:10.1007/S005850050835. Scherliess L, and Fejer B G. 1997. Storm time dependence of equatorial disturbance dynamo zonal electric fields. J. Geophys. Res., 102, 24037-24046. Doi: 10.1029/97JA02165. Sidorova L N, and Filippov S V. 2018. Four-peak longitudinal distribution of the equatorial plasma bubbles observed in the topside ionosphere: Possible troposphere tide influence. Advances in Space Research, 61(6), 1412-1424. doi:10.1016/j.asr.2017.12.035. Singh S, Bamgboye D K, McClure J P, and Johnson F S. 1997. Morphology of equatorial plasma bubbles. J. Geophys. Res., 102(A9), 20 019-20 029. Doi: 10.1029/97JA01724. Su S Y, Liu C H, Ho H H, and Chao C K. 2006. Distribution characteristics of topside ionospheric density irregularities: Equatorial versus midlatitude regions. Journal of Geophysical Research, 111(A6), A06305. doi:10.1029/2005ja011330. Su S Y, Chao C K, and Liu C H. 2008. On monthly/seasonal/longitudinal variations of equatorial irregularity occurrences and their relationship with the postsunset vertical drift velocities. J. Geophys. Res., 113, A05307, doi:10.1029/2007JA012809. Su S Y, Liu C H, and Chao C K. 2018. Post-midnight equatorial irregularity distributions and vertical drift velocity variations during solstices. Advances in Space Research, 61(7), 1628-1635. doi:10.1016/j.asr.2017.07.005 Sultan P. J. 1996. Linear theory and modeling of the Rayleigh-Taylor instability leading to the occurrence of equatorial spread F. J. Geophys. Res., 101, 26 875–26 891. Doi: 10.1029/96JA00682 Tsai L C, Su S Y, and Liu C H. 2017. Global morphology of ionospheric F-layer scintillations using FS3/COSMIC GPS radio occultation data. GPS Solution, 21, 1037–1048. Doi: 10.1007/s10291-016-0591-4. Tsunoda R T. 1988. High latitude F region irregularities: a review and synthesis. Rev. Geophys., 26, 719. Tsunoda R T. 1985. Control of the seasonal and longitudinal occurrence of equatorial scintillations by the longitudinal gradient in integrated E region Pedersen conductivity. J. Geophys. Res., 90(A1), 447-456, doi:10.1029/JA090iA01p00447. Wang X Y, Cheng W L, Yang D H, and Liu D P. 2019a. Preliminary validation of in situ electron density measurements onboard CSES using observations from Swarm Satellites. Advances in Space Research, 64(4), 982-994. Doi: 10.1016/j.asr.2019.05.025. Wang X Y, Yang D H, Liu D P, and Chu W. 2019b. Identifying a possible stratification phenomenon in ionospheric F2 layer using the data observed by the DEMETER satellite: method and results. Annual Gephysicae, 37,645-655. Doi: 10.5194/angeo-37-645-2019. Wang X Y, Cheng W L, Zhou Z H, Yang D H, Cui J, and Guo F. 2020. Stratification observed by the in situ plasma density measurements from the Swarm satellites. Annual Geophysicae, 38,517-526. Doi: 10.5194/angeo-38-517-2020. Wang X Y, Yang D H, Zhou Z H, Cui J, Zhou N, and Shen X H. 2021a. Features of topside ionospheric background over China and its adjacent areas obtained by the ZH-1 satellite. Chinese Journal of Geophysics (in Chinese), 64(2): 391-409, doi:10.6038/cjg2021O0152. Wang X Y, Yang D H, He H W, Zhao G C, Guo F, Zhou N, and Jiang W L. 2021b. The nighttime winter anomaly phenomenon observed by the in situ electron density measurements from the CSES satellite. Advances in Space Research, 68(11): 4636-4645. Doi: 10.1016/j.asr.2021.09.033. Wang X Y, Yang D H, Zhang X Q, He H W, Guo F, Jiang W L, Niu C D, and Shen X H. 2022. Spatiotemporal features of topside ionospheric irregularities during low solar activity period detected by the ZH-1 Satellite. Chinese Jounral of Geophysics (in Chinese), 65(3): 862-881, doi: 10.6038/cjg2022P0327. Whalen J A. 1997. Equatorial bubbles observed at the north and south anomaly crests: Dependence on season, local time, and dip latitude. Radio Science, 32(4), 1559–1566. doi:10.1029/97rs00285. Yizengaw E, Retterer J, Pacheco E E, Roddy P, Groves K, Caton R, and Baki P. 2013. Postmidnight bubbles and scintillations in the quiet-time June solstice. Geophysical Research Letters, 40(21), 5592–5597. Doi: 10.1002/2013GL058307 Yokoyama T, Pfaff R F, Roddy P A, Yamamoto M, and Otsuka Y. 2011. On post-midnight low-latitude ionospheric irregularities during solar minimum: 2. C/NOFS observations and comparison with Equatorial Atmosphere Radar. J. Geophys. Res., 116, A11326, doi:10.1029/2011JA016798. Supplementary Files AbstractImage.pdf Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2722826","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":192026304,"identity":"7f384cc0-eda6-4d93-a06b-1d9ac0568080","order_by":0,"name":"Xiuying Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYBACfvnDhx98+GHDY9/eQKQWyRlsaYYze9JkDHgOEKnFYAaPgTQP22EbA4kEYrVINxgYzuA5zGMu+XjjDYYam2iCWsxlDiQ8+GCRzmM5O63YguFYWm4DIS2WDQkHgLZY8zDczjGTYGw4TFiLwYHEBqBfmHkYbp4hVsuNZAagFmcegxs8RGqR7DnGBgpkHskeoF8SiPELP3v/Z1BU2vOzH95440ONDWEtKI4kOmqQtJCqYxSMglEwCkYGAAAi8j++hAgW9AAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-9994-7103","institution":"National Institute of Natural Hazards, Ministry of Emergency Management of China","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Xiuying","middleName":"","lastName":"Wang","suffix":""},{"id":192026305,"identity":"d29d49aa-182b-44a9-b2a3-abf41af0aeb6","order_by":1,"name":"Wanli Cheng","email":"","orcid":"","institution":"Xinyang SeismoStation, Henan Earthquake Agency","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Wanli","middleName":"","lastName":"Cheng","suffix":""},{"id":192026306,"identity":"7c2666a4-4865-47bc-81a0-f2760b677185","order_by":2,"name":"Xueqing Zhang","email":"","orcid":"","institution":"College of Information and communication, University of national defense technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xueqing","middleName":"","lastName":"Zhang","suffix":""},{"id":192026307,"identity":"f51c0e92-5629-4d80-b8d4-75ac8683f9b7","order_by":3,"name":"Guocun Zhao","email":"","orcid":"","institution":"National Institute of Natural Hazards","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Guocun","middleName":"","lastName":"Zhao","suffix":""},{"id":192026308,"identity":"20cb4a6f-9467-437f-9cd4-db71142e3f35","order_by":4,"name":"Qiao Wang","email":"","orcid":"","institution":"National Institute of Natural Hazards","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Qiao","middleName":"","lastName":"Wang","suffix":""},{"id":192026309,"identity":"27e700fa-79cd-4261-b7c1-95f05db12db8","order_by":5,"name":"Dehe Yang","email":"","orcid":"","institution":"National Institute of Natural Hazards","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Dehe","middleName":"","lastName":"Yang","suffix":""},{"id":192026310,"identity":"2ca33445-644e-4241-b678-cf58f812955a","order_by":6,"name":"Song Xu","email":"","orcid":"","institution":"National Institute of Natural Hazards","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Song","middleName":"","lastName":"Xu","suffix":""}],"badges":[],"createdAt":"2023-03-22 11:48:44","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2722826/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2722826/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":35936704,"identity":"5254de43-e984-4c3b-84a9-e1da813b67bf","added_by":"auto","created_at":"2023-04-18 13:45:47","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":15113,"visible":true,"origin":"","legend":"\u003cp\u003eTime series of F10.7 and Dst indices from 2019 to 2021\u003c/p\u003e","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/868302d2d4517d1029c146e0.png"},{"id":35936949,"identity":"6dec1720-f3c7-4c64-998f-320224b213a7","added_by":"auto","created_at":"2023-04-18 13:53:47","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":72829,"visible":true,"origin":"","legend":"\u003cp\u003eSpatiotemporal distribution of equatorial irregularities in 2019\u003c/p\u003e","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/97ca93ed6e519c06dfcebe7c.png"},{"id":35936950,"identity":"9e08f6b3-f76f-4583-b0cd-24f5227b89d5","added_by":"auto","created_at":"2023-04-18 13:53:47","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":7360,"visible":true,"origin":"","legend":"\u003cp\u003eMonthly variation of the equatorial irregularities in 2019\u003c/p\u003e","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/7151e40208bb2cf9dbda8047.png"},{"id":35936705,"identity":"434bfb73-462d-4460-908a-360a8f4d04de","added_by":"auto","created_at":"2023-04-18 13:45:47","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":14211,"visible":true,"origin":"","legend":"\u003cp\u003eMonthly variation of equatorial irregularities in each longitude sector\u003c/p\u003e\n\u003cp\u003e(Numbers from 1 to 12 above each plot represent longitude regions from -180°to 180°with an interval of 30°.)\u003c/p\u003e","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/aee4d0e76693d91ee0815b63.png"},{"id":35936952,"identity":"c0093e3b-46b1-43e3-bc3f-0c823d961a46","added_by":"auto","created_at":"2023-04-18 13:53:48","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":94769,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of background Ne and irregularity distribution in different seasons\u003c/p\u003e","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/8479077db4445671330d2b76.png"},{"id":35936951,"identity":"cf9fe082-74a9-4e10-98c9-b117159b5339","added_by":"auto","created_at":"2023-04-18 13:53:48","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":45651,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of yearly background Ne and irregularity distributions in 2019\u003c/p\u003e","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/aa16a951551c5cc867497bd4.png"},{"id":35936708,"identity":"0b3ada97-d7f0-4532-bcb2-bb4eb4ec8dc8","added_by":"auto","created_at":"2023-04-18 13:45:47","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":16239,"visible":true,"origin":"","legend":"\u003cp\u003eEvent numbers and total orbit numbers in each month of 2019, 2020, and 2021\u003c/p\u003e","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/3a76ed01a7c06d4f0117e5a1.png"},{"id":35936713,"identity":"9e940653-819e-48cc-a38c-d01ec54102e7","added_by":"auto","created_at":"2023-04-18 13:45:48","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":23986,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of irregularity occurrence rates and solar activities in 2019, 2020, and 2021\u003c/p\u003e","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/90424d3151d762dda82c2563.png"},{"id":35936709,"identity":"3861f6e3-58b5-4f2a-b273-5572a171b7da","added_by":"auto","created_at":"2023-04-18 13:45:47","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":12249,"visible":true,"origin":"","legend":"\u003cp\u003eIrregularity occurrence rate in October, November, and December of the three years in different longitudes\u003c/p\u003e\n\u003cp\u003e(The x-axis uses numbers to indicate different longitude sectors, and the numbers represent: 1-[-180,-150); 2-[-150,-120); 3-[-120,-90); 4-[-90,-60); 5-[-60,-30); 6-[-30,0); 7-[0,30); 8-[30,60); 9-[60,90); 10-[90,120); 11-[120,150); 12[150,180). )\u003c/p\u003e","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/b9ed618fb2942694a739adbb.png"},{"id":35936953,"identity":"07e7c2da-8163-415d-bc36-e00b330e6419","added_by":"auto","created_at":"2023-04-18 13:53:48","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":151903,"visible":true,"origin":"","legend":"\u003cp\u003eSpatiotemporal distribution of equatorial irregularities in 2020 and 2021\u003c/p\u003e\n\u003cp\u003e(The symbols in Fig.10 are the same as in Fig.2. a is the data for 2020 and b for 2021.)\u003c/p\u003e","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/e408bc21a72b34e9032b7a89.png"},{"id":38362052,"identity":"dbb8bdba-a85b-4269-bfeb-4f932fea5bdc","added_by":"auto","created_at":"2023-06-11 22:44:44","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":973789,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/ebfef206-3e3d-4c83-85f1-50460b0a6d97.pdf"},{"id":35936711,"identity":"eb22b90c-ec68-4307-997e-5c745f235e92","added_by":"auto","created_at":"2023-04-18 13:45:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":153136,"visible":true,"origin":"","legend":"","description":"","filename":"AbstractImage.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2722826/v1/bd5bbb8ee92d05eb74ef88bf.pdf"}],"financialInterests":"","formattedTitle":"Post-midnight irregularities in the equatorial regions of topside ionosphere obtained by the CSES satellite","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIonospheric scintillations are fluctuations of radio wave signals caused by the scattering of irregularities in the ionosphere when radio waves traverse the ionosphere (Aarons, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1982\u003c/span\u003e; Kil and Heelis, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Basu et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Severe scintillation can prevent a GPS receiver from locking on to the signal and less severe scintillations can reduce the accuracy and the confidence of positioning results (Whalen, \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Kintner et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Tsai et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). In addition, ionospheric scintillation can significantly degrade both the performance and availability of space-based communication and navigation systems (Groves et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Basu et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Gentile et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Kintner et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). For these reasons, ionospheric scintillation has long been one of the focuses on ionosphere research. According to Burke (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1979\u003c/span\u003e), equatorial scintillation is called equatorial spread F (ESF) at lower altitude, and it is called plasma depletion or plasma bubble at higher altitudes (Singh et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Kil and Heelis, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Burke et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Gentile et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). From the morphology of the ionospheric variations, this phenomenon is also called irregularities (Fejer and Kelley, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1980\u003c/span\u003e). All the above mentioned terms indicate the same phenomenon unless otherwise specified in this paper.\u003c/p\u003e \u003cp\u003eThough ionospheric scintillation has been studied extensively so far, it remains a difficult phenomenon to predict due to its complex variation with local time, season, geomagnetic activity, and solar cycle (Aarons, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1982\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1993\u003c/span\u003e; Whalen, \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Burke et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Hei et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Su et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2006\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Gentile et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Tsai et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Beshir et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Jin et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Previous studies show that ionospheric scintillations are mainly concentrated at three regions: the geomagnetic equator, the auroral ovals, and inside the polar caps (Aarons, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1982\u003c/span\u003e; Basu et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1988\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Tsunoda, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Jin et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). As scintillation is so severe in the Equator and its vicinity, it is the region most vulnerable to scintillation-induced communication problems. Therefore, many studies on scintillation have focused on this region (Abdu et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1985\u003c/span\u003e; Aarons, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1993\u003c/span\u003e; Kil and Heelis, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2001\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Burke et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Gentile et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Heelis et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Dao et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Ajith et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Jin et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). We will also follow this convention, focusing on the scintillations in equatorial and its vicinity region in this paper.\u003c/p\u003e \u003cp\u003ePrevious studies on scintillation normally conduct the work using different observations, such as ground-based measurements (Aarons et al., 1982; Abdu et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1985\u003c/span\u003e; Basu et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Whalen, \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e1997\u003c/span\u003e), satellite sounding measurements (Maruyama and Matsuura, 1984), radio occultation technique (Dymond, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Carter et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Tsai et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e;), and satellite in situ measurements (Singh et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; McClure et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Kil and Heelis, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Huang et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2001\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Burke et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Gentile et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Dao et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Jin et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). As the ground-based measurements are limited in spatial coverage, it is difficult to get global images of scintillation with this kind of observations. In situ ionospheric measurements on LEO satellites provides the chances to study the global spatiotemporal features of this phenomenon (Burke et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Su et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Dao et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFor satellite in situ measurements, most of the studies on ionospheric scintillation focus on the time period from sunset to pre-midnight hours as most scintillations are clustered around this time period (Huang et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2001\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Burke et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Gentile et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Su et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), or on all the local times (LTs) as the LTs of the satellite in situ measurements are not fixed (Jin et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Whereas global ionospheric scintillation studies on post-midnight are relatively few, especially during low solar activity (LSA) period, although there are some of the studies using the C/NOFS measurements (Dao et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Yizengaw et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). According to the studies by Wang et al. (\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003eb\u003c/span\u003e; \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) using the in situ electron density (Ne) measurements from the China Seismo-electromagnetic Satellite (CSES), the topside ionosphere after midnight exhibits some special space climatology features during LSA period, such as the nighttime winter anomaly (NWA) phenomenon (i.e. nighttime Ne is smaller in summer than in winter) and the frequently occurred post-midnight irregularity phenomenon, etc. So far, relatively fewer studies have been conducted on post-midnight scintillation in the topside ionosphere, and its generation mechanism remains unclear and under extensively debated (Yizengaw et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe CSES satellite, performing nighttime measurements at about 02:00 LT with a sun synchronous orbit at the altitude of 507km (Wang et al., \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2019a\u003c/span\u003e), has been accumulating a large amount of in situ Ne measurements since its launch in February 2018, which provides a good opportunity to study the climatology and detailed features of post-midnight irregularities in topside ionosphere.\u003c/p\u003e \u003cp\u003eIn this paper, the equatorial irregularities, detected using the nighttime in situ Ne measurements from the CSES satellite, are studied to analyze the spatiotemporal distribution features of the topside ionospheric irregularities after midnight and their variation with solar activity. The longitudinal distributions for post-midnight irregularities and background Ne are also compared to reveal their relations; and finally, the generation mechanisms are discussed for the post-midnight irregularities in topside ionosphere. The study of post-midnight irregularities in topside ionosphere during LSA can help to understand scintillation from a different perspective and to further understand the dynamical processes of the ionosphere, which will promote the work of building a more practically integrated prediction model for trans-ionospheric communication systems.\u003c/p\u003e"},{"header":"2. Data And Methods","content":"\u003cp\u003eThe in situ Ne measurements from the CSES (China Seismo-Electromagnetic Satellite, also called Zhangheng-1 or ZH-1 for short) satellite are used in this paper to carry out the analysis work. The CSES satellite, launched on February 2nd, 2018, is orbiting in a sun synchronous mode with an angle of 97.8\u0026deg;at the altitude of 507 km. The observation range is 65\u0026deg;of northern and southern geographical latitude and the observation local times (LT) for descending (daytime) and ascending (nighttime) orbits are about 14:00LT and 02:00LT, respectively. The solar activity has been very low since the launch of this satellite, which leads to the relatively lower altitude of the F2 layer. Therefore, the altitude of the satellite is much higher than the peak height region of F2 layer (hmF2) during this period, which means the observation altitude is at the topside ionosphere. The in situ Ne measurements obtained under this altitude and this nighttime LT provide us a good opportunity to study the fine features of the post-midnight irregularities in the topside ionosphere.\u003c/p\u003e \u003cp\u003eThe Ne disturbances along the satellite track are the one-dimensional mapping of the irregularities in the topside ionosphere, and relative fluctuation of the disturbance amplitude can indicate the intensity of the irregularities. Therefore, detecting disturbances or irregularities events along the satellite orbit is the first step in this study. To detect irregularity events, a simplified method is used, which is an improvement on the method used in our previous work (Wang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The outline of the method is as following.\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eStandardize the in situ Ne measurements along the orbit so that a unified criterion on determining irregularity event can be applied to all the orbit measurements.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eCalculate the first-order differentiation on the normalized measurements in step (1) to remove trends existed in the orbit measurements over a large latitude range.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eCalculate the standard error (SE) of a slipping window using the first-order differentiation series in step (2) and determine irregularity event with a given SE threshold criterion.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAn irregularity event is determined for continual SEs greater than the threshold value (TV). The location of the event is decided using the average latitude and longitude of the SEs\u0026thinsp;\u0026gt;\u0026thinsp;=\u0026thinsp;TV; and the intensity of this irregularity event is decided using the average SEs. Therefore, SE with a bigger value indicates irregularity with relative large amplitude variation, namely large SE means strong irregularity intensity.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThis detecting method is generally similar to the method by Beshir et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), the only difference is that the normalization process in this study is performed on the original track measurements, while in the paper by Beshir et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) the normalization process is performed on the deviation. In essence, the final results are similar for the two methods.\u003c/p\u003e \u003cp\u003eAn explanation is given here that how to select the threshold value depends on the objective of the work. If a smaller threshold is adopted, more irregularity events will be detected; in contrast, with a relative larger threshold value, less irregularity events can be identified. Different threshold values are examined in this study and also in another study (Wang et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), and all the results show similar statistical features, indicating that the number of detected irregularities does not change the spatiotemporal statistical properties.\u003c/p\u003e \u003cp\u003eFollowing the detection method described above, the nighttime in situ Ne measurements obtained by the CSES satellite from 2019 to 2021 are used to identify the irregularity events along the orbit track in the equatorial regions to analyze the spatial distribution, seasonal variations, and variation with solar activity for the post-midnight irregularities in topside ionosphere during LSA year. The numbers of total orbit tracks in the three years are 5249, 5374, and 5406, respectively. Based on the Ne measurements from these orbit tracks, the monthly background Ne is also calculated to compare with the irregularity distributions. The monthly background Ne is obtained by averaging the Ne measurements in a month in a latitude and longitude grid of 2\u0026deg;\u0026times;5\u0026deg;. When calculating averaging Ne, the Ne measurements lower than 1/4 quantile and higher than 3/4 quantile are removed to reduce the influence of data fluctuations. For detailed calculation process, please refer to Wang et al. (\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe solar activity index F10.7 and geomagnetic activity index Dst during 2019 to2021 are given in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. It can be seen clearly from Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea that the solar activity level is extremely low in 2019, and begins to increase from about October 2020. In addition, there are only a few very small geomagnetic activity events (Dst\u0026lt;-30nT) during the study period as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb except the relatively bigger one (Dst\u0026lt;-70nT) in November 2021. As geomagnetic activities generally inhibit irregularity generation (Aaron et al., 1982; Singh et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1997\u003c/span\u003e), we therefore use all the observations without excluding the data obtained during geomagnetic activities.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Spatiotemporal distribution\u003c/h2\u003e \u003cp\u003eAccording to Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the overall solar activity level in 2019 is generally consistent, with a very low F10.7 index. Therefore, in situ Ne measurements in 2019 are used in this section to demonstrate the spatiotemporal distribution and seasonal variation to avoid biases caused by different solar radiation and to perform statistics under similar conditions.\u003c/p\u003e \u003cp\u003eSpatiotemporal distribution of the irregularity events in 2019, detected using the method described in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e with a threshold value of 0.15, is given in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, which covers the \u0026plusmn;\u0026thinsp;30\u0026deg; geographical latitude near the Equator. The region between \u0026plusmn;\u0026thinsp;20\u0026deg; geomagnetic latitude (shown as red dashed line) is chosen as the near equatorial region following the conventional approach adopted by previous studies. It should be noted that geomagnetic coordinates here are from the geomagnetic dipole coordinate system and are provided in the in situ Ne measurements dataset. The geomagnetic coordinates are different from those of the IGRF model, such as the geomagnetic equator (black dashed line) and the dip equator (black solid line) shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. As the geomagnetic coordinates are provided in the dataset, we use them when calculating parameters related to the geomagnetic coordinate.\u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, also given are the histograms of these irregularity events, representing density variations of the irregularities along with geographical longitude and geomagnetic latitude, which are placed above and to the right of the spatiotemporal distribution plot, respectively. The histograms are drawn using the events within \u0026plusmn;\u0026thinsp;20\u0026deg; geomagnetic latitude, i.e. the irregularity events within the two red dashed lines in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(In Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, each irregularity event is represented by a dot. SS indicates irregularity intensity, represented by the dot size, and Month indicates the occurrence month, represented by dot colors. The dotted line is the Equator, and the black solid line is the dip equator obtained from the IGRF12. The dashed lines are geomagnetic latitudes from the dipole field geomagnetic coordinate provided by the original dataset; the black dashed line is the geomagnetic equator, the red lines\u0026thinsp;\u0026plusmn;\u0026thinsp;20\u0026deg;geomagnetic latitude, and the purples lines\u0026thinsp;\u0026plusmn;\u0026thinsp;35\u0026deg; geomagnetic latitude. )\u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, each dot represents an irregularity event with the color indicating the occurrence month and the size its intensity; the larger the dot, the stronger the intensity of the irregularity event. The solid black line is the dip equator obtained from the 12th IGRF model at the CSES orbiting altitude, and the black dotted line is the Equator. The dashed lines are geomagnetic latitudes given by the original dataset, with the black dashed line representing the dipole field geomagnetic equator, the red dashed lines the \u0026plusmn;\u0026thinsp;20\u0026deg;dipole field geomagnetic latitude, and the purple dashed lines the \u0026plusmn;\u0026thinsp;35\u0026deg; dipole field geomagnetic latitude.\u003c/p\u003e \u003cp\u003eIt can be seen clearly from Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e that, besides the equatorial regions between the two red dashed lines, the irregularities are also concentrated in two regions beyond the equatorial region, which are in the longitude sectors where the geomagnetic poles are located, and on the hemisphere close to the geomagnetic pole. In fact, the post-midnight irregularities can be found throughout the satellite spatial coverage according to Wang et al. (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), indicating that post-midnight irregularities are frequently occurred phenomenon during LSA period. As the equatorial irregularities are the focus of this paper, we will concentrate on the data between the two red dashed lines in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the equatorial irregularities are distributed well along the dip equator, i.e., the solid black line in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. An obvious wavenumber pattern is shown along geographical longitude in the spatial distribution and in the histogram above it, with the African, Asian, Central Pacific, and West American longitude sectors being the peak and the Indian, West Pacific, East Pacific, and Atlantic longitude sectors being the valley of the wave structure. It should be noted that the Atlantic longitude sector is a valley of the wave structure with only a few irregularity events. The low number of irregularities in the Atlantic longitude sector is quite different from previous findings that the Atlantic sector is a region of concentrated post-sunset irregularities (Maruyama and Matuura, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Kil and Heelis, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2001\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Burke et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Su et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2006\u003c/span\u003e;), which will be discussed in Section \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eLatitude distribution of the equatorial irregularities is basically symmetrical about the geomagnetic equator, as shown in the histogram to the right of the spatial distribution plot. Among the four irregularity peaks, three are generally symmetrically distributed on the two sides of the dip equator, including the peaks in the Central Pacific, West American, and African longitude sectors, where the geomagnetic declination is eastward or close to zero. The one exception is the distribution peak in Asian longitude sector, where the detected irregularities are located in the northern hemisphere. In contrast, the irregularities in the West Pacific longitude sector, which connect with the Central Pacific peak, are mostly located in the southern hemisphere, closer to the southern 20\u0026deg; geomagnetic latitude. In addition, the occurrence seasons are contrary for the Asian and West Pacific regions according to events color shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eIn addition to the spatial distribution feature of wavenumber 4 pattern, seasonal variation of the equatorial irregularities are also very obvious in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, with most of the events occurring during the summer months of each hemisphere, i.e. for most of the irregularity events in Northern Hemisphere, the occurrence time is northern summer, and most of the events in Southern Hemisphere, the occurrence time is southern summer (northern winter), as mentioned above that events in the Asian sector is in summer and in the West Pacific peaks is in winter. To show this seasonal feature, the histogram of equatorial irregularities in each month is given in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTwo peaks and two valleys are shown in the monthly histogram of the equatorial irregularities in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, with most of those events being concentrated in the two solstice periods and less events in the two equinox periods. Another feature of the seasonal variation is that the summer peak lasts a longer time compared to the winter peak, extending from summer to the autumn season; while the winter peak is only evident at the winter solstice, with a tendency of extending towards February.\u003c/p\u003e \u003cp\u003eTo get the seasonal variation of each longitude sector, the equatorial region is divided into 12 sub-regions with a longitude interval of 30\u0026deg;. The monthly variation of each sub longitude regions is given in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eAs can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, a generally similar pattern of seasonal variation peaking in summer, winter, or both seasons is shown in each longitude sector. Seasonal variation pattern is more obvious in longitudes of irregularity peaks in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, such as Region 1 and 2 (the Central Pacific longitudes), Region 4 (the West American longitudes), Region 7 (the African longitude), and Region 10 (the Asian longitudes). Region 12 indicates the irregularity concentration in the West Pacific longitudes in Southern Hemisphere, demonstrating a winter seasonal pattern. Compared to the peak longitudes, seasonal variation pattern is not so obvious for irregularity valley longitudes as there are only a few irregularity events, such as Region 3 (the east Pacific longitudes), Region 5 and 6 (the East American and Atlantic longitudes), Region 8 and 9 (the Indian longitudes). Further statistics using irregularities detected with a lower threshold of 0.1 indicates a summer or winter seasonal pattern in the irregularity valley longitude sectors.\u003c/p\u003e \u003cp\u003eThough the general seasonal variation is summer or winter peak in each longitude sector, the time when the peaks appear and the relative amplitudes of the two peaks are varying gradually. Examples of this gradual seasonal variation with longitude are that only the summer peak appears in longitude sector of 90\u0026deg;to 120\u0026deg;(Region 10); in contrast, only the winter peak occurs in longitude sector of 150\u0026deg;to 180\u0026deg;(Region 12); and both summer and winter peaks can be seen in the longitude sector of -180\u0026deg;to -150\u0026deg;(Region 1).\u003c/p\u003e \u003cp\u003eSummarizing the above analysis, the spatiotemporal distribution features are that the equatorial post-midnight irregularities are distributed along the dip equatorial with a wavenumber 4 pattern in the longitude direction and with a seasonal variation pattern of summer-winter peaks and spring-equinox valleys.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Comparison with background Ne distribution\u003c/h2\u003e \u003cp\u003eTo compare the distribution of equatorial post-midnight irregularities with its background Ne, the seasonal background Ne distributions are plotted using the results calculated from the nighttime in situ Ne measurements in the four seasons of 2019. The background Ne calculation method is introduced in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, detailed description of the method can reference Wang et al. (\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e). The four seasons are divided in the normal way, i.e. February, March, and April belong to the March Equinox, May, June, and July the June Solstice; August, September, and October the September Equinox, and November, December, and January the December Solstice.\u003c/p\u003e \u003cp\u003eThe background Ne distributions for the four seasons and their corresponding irregularity events are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Each event is represented by a dot with its size indicating the intensity of the irregularity, similar as that in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, a general wavenumber pattern is shown in the seasonal background Ne distributions with a typical wavenumber of 3 or 2. In addition, it is clearly shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e that the peak and valley positions of the wavenumber pattern vary with seasons as well as with the wave number. Wavenumber 2 pattern is obvious for the two solstice seasons with the African and the Pacific-West American longitude sectors being the peaks for the June solstice and the Central Pacific and the American-Atlantic-African longitude sectors being the peaks for the December solstice; and wavenumber 3 pattern is obvious for the two equinox seasons with the Asian, the Central pacific, and the American-African longitude sectors being the peaks for the March Equinox and the African, the Central Pacific, and the West American longitude sectors being the peaks for the September Equinox. With the changing position of the background Ne peaks, the irregularities peaks also change their positions. The irregularities peaks generally coincide with the background Ne peaks in different seasons.\u003c/p\u003e \u003cp\u003eAs a comparison, Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e also gives the yearly distribution for background Ne and irregularity events in 2019. As mentioned above, the African, the Central Pacific, and the West American longitude sectors have been the background Ne peaks for all the seasons, as a result they are also the yearly background Ne peaks. Since the seasonal irregularity peaks coincide with the corresponding background Ne peaks, the yearly irregularity peaks are also coincide with that of the yearly background Ne peaks. Relatively higher background Ne appears in the Asian and the West Pacific longitude sectors on both side of the dip equator, where irregularities are correspondingly more concentrated. Though the Central Pacific to the West American longitude sector shows a continuous Ne peak in Summer solstice, a valley can be seen clearly in the West Pacific longitude sector for the other three seasons, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Combining the background Ne of the four seasons together, a valley can be seen clearly between the Central Pacific and the West American longitude sector in the yearly background Ne distribution in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, which corresponds also to an irregularity valley.\u003c/p\u003e \u003cp\u003eBoth the seasonal and yearly distributions for background Ne and post-midnight irregularities show that the two (background Ne and post-midnight irregularity) have similar wavenumber distribution pattern along the longitude direction, suggesting that post-midnight irregularity distribution is closely related with the background Ne distribution.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThrough the comparison of the seasonal and yearly background Ne and irregularity distributions, coincidence of the two is shown in longitude distribution and peak locations. A preliminary conclusion can be drawn that the distribution of topside background Ne obviously affects the distribution of post-midnight irregularities during LSA period, that is, the background Ne distribution plays an important role in the generation of post-midnight irregularities. See Section \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003e4\u003c/span\u003e for a further discussion of this topic.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Variation with solar activity\u003c/h2\u003e \u003cp\u003eSolar activity in 2019, 2020, and 2021 belongs to low solar activity (LSA) in general. However, it can be seen clearly that the solar activity level has begun to increase since October 2020 in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Therefore, irregularities detected in different month of the three year 2019, 2020, and 2021 can be compared to obtain the influence of solar activity on the generation of post-midnight irregularities in the topside ionosphere. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e gives the total irregularity numbers detected in the equatorial region in each month of the three years. As a comparison, also given in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e is the total orbit number in each month of the three years.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt is clearly shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e that irregularity numbers detected in 2021 increase dramatically compared to the corresponding months in 2019 and 2020 when considering the overall similar total orbit numbers in each month of the three years. This apparent increase of irregularity number is also evident in October to December in 2020 compared to the same months in 2019. The increase of irregularity numbers coincides with the increase of solar activity when comparing Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e with Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, and the more the solar activity increases, the more the irregularity number increases, indicating that solar activity can also affect the generation of post-midnight irregularities just as it does on post-sunset irregularities.\u003c/p\u003e \u003cp\u003eTo compare the data directly, Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e gives the monthly irregularity occurrence rates and the corresponding solar activity F10.7 index in the three years.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, the irregularity occurrence rate also shows increasing trend with the increasing solar activity. For the first nine months in 2019 and 2020, the solar activity levels are quite close to each other, and the corresponding irregularity occurrence rates are also close to each other with a similar variation tendency. However, with the obvious increase of solar activity in October to December in 2020 compared to that in 2019, the monthly irregularity occurrence rates increases dramatically from about 0.09, 0.13, and 0.20 in 2019 to 0.20, 0.37, and 0.28 in 2020, respectively, which correspond to 122%, 185%, and 40% increase of occurrence rates. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb, the solar activity in November 2020 increases the most significantly compared to 2019, and the irregularity occurrence rate also increases dramatically in this month. In addition, December 2021 is another month with significant solar activity increase compared to 2020, the corresponding irregularity occurrence rate also indicates an obvious increase, which can be seen clearly from the data shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. In addition to the data of monthly irregularity occurrence rates, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e also gives the monthly average F10.7 index from October to December for the three years, as well as the growth rates obtained by comparing the irregularity occurrence rate and the F10.7 index for the same month in different years.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOccurrence rate, monthly average F10.7 index and their growth rates\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eOccurrence Rate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003eMonthly Average F10.7\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003emonth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e67.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e70.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e70.97\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e71.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e89.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e71.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e89.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e86.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e103.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2019 vs 2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e122%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e185%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e40%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e28%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2020 vs 2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e54%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e26%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-4%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e44%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe above qualitative analysis indicates that occurrence rate of post-midnight irregularity generally shows an increase trend with the increasing solar activity. Due to the very low solar activity during the study period, it is not possible to draw a definite conclusion on the variations of the post-midnight irregularity occurrence rate with solar activity as the data doesn\u0026rsquo;t even cover half of a solar cycle. However, the results in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e indicate that solar activity can influence the occurrence rate of post-midnight irregularity even during LSA period.\u003c/p\u003e \u003cp\u003eAn interesting feature shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea is that the irregularity occurrence rate of summer and winter peaks are essentially the same in 2019. However, there is a significant increase in the winter peak in 2021 compared to its summer peak, though the summer-winter seasonal variation pattern is still very obvious. It is understandable that the higher amplitude of irregularity occurrence rate at the end of 2021 is caused by the obvious increase of solar activity. However, what causes the obvious increase of winter peak amplitude at the beginning of 2021 when there is not a significant increase in solar activity? This can be explained by the delayed effect of solar activity on the ionosphere and irregularities, as suggested by Wang et al. (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), which can also explain the situations on the extension of summer peak into autumn and winter peak into spring, as shown by the seasonal variation pattern in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eTo exam whether different longitude sectors are equally influenced by the increasing solar activity, a further comparison is conducted using the irregularity events detected in October, November, and December of the three years in different longitude sectors. Twelve longitude sectors are divided in the equatorial regions with a longitude interval of 30\u0026deg;as it does in Section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e. The irregularity occurrence rate in each longitude sector is calculated as the ratio between the number of orbit with irregularities and the total orbit number within that longitude sector, and the results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eAccording to Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, the comparison and calculated results show that the maximum growth of occurrence rate is in Region 5 and 6, corresponding to longitude \u0026minus;\u0026thinsp;60\u0026deg;to 0\u0026deg;, where is just the Atlantic longitude sector; and followed by Region 11 and 12, corresponding to longitude 120\u0026deg; to 180\u0026deg;, in the Australian and the West Pacific regions in Southern Hemisphere. The longitude variation of growth rate of irregularity occurrence rate with increasing solar activity suggests that increasing solar activity has different effects on the generation of post-midnight irregularities in different longitude sectors. If this effect continues to exert influence with the increasing solar activity, it is conceivable that the spatial distribution may change from its wavenumber 4 distribution pattern in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e to other distribution patterns, such as changes in peak positions or in total wave numbers. For example, variation of peak position is evidently shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e; the maximum occurrence place is located at Region 12 in 2019, and it changes to Region 11 in 2020 and 2021; and moreover, the peak region seems to widen, occupying both Region 11 and 12. Clues of variation of wavenumber pattern can also be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. Three occurrence peaks can be seen in 2019 using the detected irregularity results in October, November, and December; however, there seems only two occurrence peaks in 2021 and 2022 using the results obtained in the same three months. Due to the variation of peak position and wave number with solar activity, the Atlantic longitude sector becomes a peak in 2020 and 2021 from the valley in 2019.\u003c/p\u003e \u003cp\u003eThe above analysis suggests that even during LSA period, solar activity can obviously affect the generation of post-midnight irregularities and this influence is different in different longitude sectors, which will further affect the longitude distribution of irregularity occurrence.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003ePost-midnight irregularities during very low solar activity period are studied using the in situ Ne measurements obtained by the CSES (ZH-1) satellite orbiting at an altitude of 507km, to analyze their spatial distribution and seasonal variation features in the topside ionosphere. The results show that a general wavenumber 4 distribution pattern is shown for the post-midnight irregularities with a seasonal variation of summer-winter peaks and spring-autumn valleys. The peaks of irregularities longitude distribution in the four seasons coincide with the peaks of the corresponding background Ne distribution in that season with a general wavenumber 3 pattern for equinox seasons and wavenumber 2 pattern for solstice seasons; a wavenumber 4 longitude variation pattern is shown along the dip equator when combining the irregularities in the four seasons, which also coincides with the corresponding yearly background Ne distribution. Results, obtained by comparing the occurrence rate under different solar activities during LSA period, show that post-midnight irregularity occurrence rate increases with the increasing solar activity and different longitude sectors exhibit different growth rate of occurrence rate with the increasing solar activity; the maximum growth rate is located at the Atlantic longitude sector, followed by the Australian to West Pacific longitude sector. These features suggest that solar activity exerts influence on the generation of post-midnight irregularities although the general solar activity condition remains at LSA level.\u003c/p\u003e \u003cp\u003eFor the above results obtained in this paper, some issues need to be clarified, and the related discussions are given in the following section.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Longitudinal/ Seasonal distribution\u003c/h2\u003e \u003c/div\u003e\n\u003ch3\u003e1. Spatiotemporal Distribution\u003c/h3\u003e\n\u003cp\u003eThe longitudinal/seasonal variation of the post-sunset equatorial irregularities have been investigated extensively over the past decades (Maruyama and Matuura, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Tsunoda, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e1985\u003c/span\u003e; Whalen, \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; McClure et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2001\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Burke et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Gentile et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Su et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2006\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Longitudinal variation of post-sunset irregularities is frequently mentioned in those previous studies, such as: Huang et al. (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2001\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e) report that seasonal and longitudinal variations of post-sunset irregularities remain similar within given longitude sectors using the DMSP measurements over a full solar cycle; they suggest that the Atlantic-African sectors are the most significant occurrence longitudes and the Indian sector is the least occurrence longitudes. Burke et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) also show that the highest and lowest rates of equatorial plasma bubble (EPB) located at the Atlantic-African and Indian sectors using both the DMSP and the ROCSAT-1 measurements. Kil and Heelis (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1998\u003c/span\u003e) suggest that scintillation is always high in the Atlantic-African longitudes and is always low in the Indian regions.\u003c/p\u003e \u003cp\u003eAll the above post-sunset longitude distribution results are in general agreement with the spatial distribution obtained in this study, with the exception of the Atlantic sector, which is a low occurrence region for the post-midnight irregularities detected in 2019. However, the subsequent results of this study further demonstrate that irregularities in the Atlantic longitude sector increase dramatically, and this region becomes the peak with the increasing solar activity as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. In fact, the solar activity remains at low activity levels for the entire study period though it has been increasing since October 2020. Therefore, the general longitude distributions for both post-sunset and post-midnight irregularities are consistent with each other.\u003c/p\u003e \u003cp\u003eIt should be pointed out here that the low irregularity occurrence in the Atlantic longitude sector in 2019 doesn\u0026rsquo;t mean the result is not correct. In fact, this low occurrence rate of post-midnight irregularities in the Atlantic longitude sector is also noticed by Dao et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) using the C/NOFS measurements from May 2008 to March 2010, an extremely prolonged LSA period between 23/24 solar cycle. Our result is in agreement with that of Dao et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e), indicating the results in this study are correct and can repeat from different dataset under similar solar activity conditions. Quite different features, namely low occurrence rate in 2019 but relatively higher occurrence rate in 2020 and 2021, are shown for the post-midnight irregularities in the Atlantic longitude sector though the general solar activity is still low over the study period in this paper, which may be closely related with the low geomagnetic field in the South Atlantic Anomaly (SAA) region. More studies are required to further analyze the mechanism behind the phenomenon.\u003c/p\u003e \u003cp\u003eThe spatiotemporal structures of post-midnight irregularities are also reported by a few studies using post-midnight measurements. For example, using the in situ measurements from ROCSAT-1 satellite obtained during moderate to high solar activity years of 1999\u0026ndash;2004, Su et al. (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) report that the post-midnight irregularity distribution is similar to the pre-midnight ones, with the African and Central Pacific sectors being the high occurrence places for June solstice, and the South America and the Atlantic Ocean sectors being the high occurrence place for December solstice. Dao et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) and Yizengaw et al. (\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) find the longitudinal structures using the C/NOFS in situ measurements obtained in LSA years; they also find that the maximum occurrence is located at South American and African sector sectors for summer solstice months, and significant activity occurs at Pacific and South American longitude sectors for winter solstice months. This spatiotemporal distribution is in accord with the results in this study. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the South American longitude sector (-90\u0026deg;to -60\u0026deg;) and the African longitude sector ( 0\u0026deg;to 30\u0026deg;) show summer peaks, and the West Pacific longitude sector (150\u0026deg;to 180\u0026deg;) shows winter peak; while the Central Pacific longitude sector (-180\u0026deg;to -150\u0026deg;) shows both summer and winter peaks.\u003c/p\u003e \u003cp\u003eThe nighttime background Ne longitude variations obtained in this study are in agreement with the results obtained from the nightglow images (Sagawa et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Immel et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), both presenting the large scale longitudinal variations in the Ne amplitude and separation, which are supposed to be driven by the atmospheric tide DE3 in troposphere (Hagan et al., 2002; Kil et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). The interesting point is that the wave-like structure of post-midnight irregularities coincides with the wave-like background Ne structure as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e in this study. According to the study by Sidorova and Filippov (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), the wave-like structure for post-sunset irregularities is influenced by troposphere tide and associated with the troposphere DE3 tides, which affect the thermosphere parameters and ionosphere parameters through the modulation of the thermosphere winds and electric fields. Coincidence of irregularity peaks with that of background Ne peaks indicates that post-midnight irregularities are also influenced by the troposphere tides, and the background Ne controls the distribution of irregularities. Beshir et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) suggest that background plasma density is very important for post-sunset irregularities, strong plasma densities result in stronger plasmas irregularities, while relatively less dense plasma results in relatively lower plasma irregularities. The results in this paper also suggest that background Ne is very important for the post-midnight irregularities. Thus, the low occurrence in 2019 in the Atlantic longitude sector must be related to the extremely low background Ne in this region.\u003c/p\u003e \u003cp\u003eIn summary, comparisons of the longitude variation for post-midnight and post-sunset irregularities indicate they have similar wave-like structure. Moreover, the concentrated irregularities coincide with the background Ne peaks. Both these features suggest that some places provide persistent favorable conditions for the generation of equatorial irregularities, independent of the nighttime irregularity occurrence time and season. Furthermore, the background Ne plays an important role in the generation of nighttime irregularities during LSA period.\u003c/p\u003e\n\u003ch3\u003e2. Seasonal Variation\u003c/h3\u003e\n\u003cp\u003eThe general seasonal variation pattern of the post-midnight equatorial irregularities obtained in this study is summer-winter peaks with spring-autumn valleys, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. This seasonal variation pattern is in agreement with the results obtained by Heelis et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) using the C/NOFS in situ measurements observed under extremely LSA conditions in 2008 and 2009. Their results show that post-midnight occurrence frequency peaks during both northern winter and summer period, but is very low during equinox period.\u003c/p\u003e \u003cp\u003eThe seasonal variation pattern for post-midnight irregularities is quite different from the equinox peaks and solstice valleys pattern of post-sunset irregularities reported by many previous studies (Tsunoda, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e1985\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2001\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Burke et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Hei et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Su et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2006\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Based on the long-term ground-based measurements in India, Sastri (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) reports that post-sunset spread F occurrence peaks in equinox months during high solar activity (HSA) period; and during LSA period, post-midnight spread occurrence peaks in solstice months. Otsuka et al. (2009) also report that irregularities appear frequently at pre-midnight between March and May and at post-midnight between May and August using ground-based measurements in Indonesia in a relatively LSA period. Miller et al. (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) find that more irregularities appear later in the winter evening during LSA period in the Pacific longitude sector. Candido et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) also find the solstice peaks seasonal variation pattern in Brazil. All these studies, using long-term ground-based measurements in different longitudes, show that the peak seasons and LTs of nighttime irregularity occurrence vary with solar activity. This result is similar to the seasonal and LT variations of nighttime irregularity obtained from the topside ionosphere measurements. Besides the results obtained in this paper, the shift of peak occurrence from post-sunset hours during HSA to post-midnight hours during LSA is noticed by the studies using the C/NOFS satellite measurements obtained during solar minimum of cycle 23/24 (Yokoyama et al. \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Yizengaw et al. \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). All the studies for both the bottomside and topside ionospheric irregularity suggest that irregularity is a very common phenomenon for both the bottomside and topside ionospheres, and both the bottomside and topside ionospheres have similar irregularity seasonal and LT variation patterns with the solar activity variation.\u003c/p\u003e \u003cp\u003eSince generation of irregularities is associated with the ionosphere dynamical processes, we believe that the variations of irregularity peak season and peak LT with solar activity can indicate the variation of ionosphere dynamical processes with solar activity. Therefore, issues related with irregularity seasonal and LT variations deserve more research work. We will carry out more studies in our subsequent work when enough measurements are accumulated.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Variation with solar activity\u003c/h2\u003e \u003cp\u003eSolar activity dependence of post-sunset irregularity occurrence has been reported by many previous studies (Abdu et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1985\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Su et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Nishioka et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). The results in this study also indicate that post-midnight irregularities are closely related to solar activity. Variation of post-midnight irregularities with solar activity shows an increasing trend with the increasing solar activity. However, this does not mean that post-midnight irregularity will always follow this trend. In fact, the general trend is that post-midnight irregularities decrease as solar activity increases, according to the study by Fejer and Scherliess (1999) based on ground-based measurements. They attribute the decrease in post-midnight irregularities to the large increase of the nighttime downward drifts with the increasing solar flux, which will be discussed further in the next section.\u003c/p\u003e \u003cp\u003eHow can we explain the result obtained in this study that post-midnight irregularities increase with increasing solar flux during the study period? Two reasons are given below.\u003c/p\u003e \u003cp\u003eOn the one hand, although solar activity has been increasing since October 2020 as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the overall solar activity remains very low in 2020 and 2021 with the overall monthly average F10.7 index being less than 100sfu (sfu is the solar flux unit, 1 sfu\u0026thinsp;=\u0026thinsp;10\u003csup\u003e\u0026minus;\u0026thinsp;22\u003c/sup\u003e W m\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e Hz\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), which is in the range of LSA level according to the criteria used in previous studies (Huang et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Nishioka et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOn the other hand, electron density is sensitive to solar flux, especially under LSA conditions (Liu et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). As in the case of 2019 shown in this study, the monthly average solar flux is around or below 70sfu, which is particularly low. Under this solar condition, increasing solar flux leads to the obvious increases of Ne, and therefore the increase of post-midnight irregularities. To demonstrate the relation between irregularities and Ne, Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e gives the average F10.7 index and Ne as well as irregularity occurrence rate from October to December in 2019, 2020, and 2021, using the measurements in the geographical longitude range of -50\u0026deg;to -20\u0026deg;and in the dipole geomagnetic latitude range of -10\u0026deg;to 10\u0026deg;, which belongs to the equatorial Atlantic region.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage F10.7 index, Ne, and irregularity occurrence rate in the Atlantic region\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF10.7 Index(sfu)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNe (10\u003csup\u003e4\u003c/sup\u003e/cm\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRate (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e13.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e31.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eNe and irregularities increase much faster than the F10.7 index, and in this case the rapid increase of irregularities is more related to Ne than to solar flux. The close relation between Ne and irregularities is also demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. There are only a few irregularities during the summer and autumn seasons when the Atlantic longitude is the valley of background Ne; more irregularities appear in this region when the background Ne increases during winter and spring seasons. This suggests that background Ne plays very important role in the generation of post-midnight irregularities, which is consistent with the suggestion obtained by Basu (1988) that the drastic reduction of post-sunset scintillation occurrence from solar maximum to solar minimum indicates that the background density is the major modulating factor. It is easy to understand that large density fluctuation cannot be produced when the background density is very low; and as a result, there will be fewer irregularities (Dymond, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). When the background density condition is satisfied, irregularities increase rapidly in the longitude sectors where they are easy to generate.\u003c/p\u003e \u003cp\u003eWhen it comes to the places prone to irregularities, another interesting phenomenon caused by the enhancing solar activity is that the growth rate of irregularity occurrence rate with increasing solar activity is markedly different across different longitudes, with the Atlantic and Pacific longitude sectors being the two most significant regions, where are the places both post-sunset and post-midnight irregularities frequently occur as mentioned in Section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e4.1\u003c/span\u003e. To demonstrate this characteristics, Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e gives the spatiotemporal distributions of irregularities detected in 2020 and 2021.\u003c/p\u003e \u003cp\u003eAs solar activity increases most significantly during the winter season, more irregularities occur at the southern hemisphere for 2020 and 2021. Due to the increasing irregularities, the wavenumber 4 pattern can be recognized in 2020, but it is not obvious in 2021 as the irregularity valley in the Atlantic longitude sector is concentrated with irregularities. It can be seen clearly that irregularities in the Atlantic and Pacific longitude sectors increase faster than it does in other longitude sectors. The imbalance increase of irregularities occurrence in different longitude sector leads to the variation of wavenumber pattern as suggested in Section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e3.3\u003c/span\u003e. In fact, unbalanced increases of irregularities with increasing solar activity is also noticed by Nishioka et al. (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2008\u003c/span\u003e); they suggest that the Atlantic, African, and Asian longitudes are the regions suffered the most significant influence, which is generally consistent with our results. This result further suggests that post-midnight irregularities have similar features to those of post-sunset irregularities.\u003c/p\u003e \u003cp\u003eAs the reasons for the unbalanced increase are beyond the scope of this study, we leave this question here; more studies will be conducted on this topic in our subsequent work.\u003c/p\u003e \u003cp\u003eStudies on post-sunset irregularities show that the Atlantic longitude sector is the region of maximum occurrence rate during winter season, which is explained by the theory that alignment of the sunset terminator with magnetic meridian as the major cause for the irregularity occurrence (Tsunoda, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e1985\u003c/span\u003e). As the post-midnight irregularities have no relation with sunset, it is therefore this sunset node theory cannot explain the dramatic enhancement of irregularities with increasing solar activity in winter season in the Atlantic longitude sector during LSA period, which may suggest that this theory is not applicable for the post-midnight irregularities or this theory may not be a key factor for the generation of nighttime irregularities.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Generation mechanism\u003c/h2\u003e \u003cp\u003eThe similar spatial distribution and association with background Ne as well as response to the variation of solar activity for both post-midnight and post-sunset irregularities as analyzed above suggest that the two have similar generation mechanism. This suggestion is supported by the modeling results by Yizengaw et al. (\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) that post-midnight irregularities are initiated in the same way that the post-sunset irregularities are generated. Gentile et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) also suggest that the occurrence condition of post-midnight irregularities is closely related to the upward drift velocities as it does with the post-sunset irregularities, which is also mentioned by Yizengaw et al. (\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Using irregularities data obtained from ground-based measurements, Otsuka (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) suggests the generation conditions for the post-midnight irregularities: (1) seeding factors from AGWs (atmospheric gravity waves) and MSTIDs (medium-scale traveling ionospheric disturbances), and (2) F region condition favorable for the Rayleigh-Taylor (R-T) instability. As the focus of this paper is irregularities in topside ionosphere, plasma upward drift is adopted as seeding factor instead of AGWs and MSTIDs because electric field reversal is found from the EFD payload measurements onboard the CSES satellite when irregularity occurs.\u003c/p\u003e \u003cp\u003eAs is well accepted, the post-sunset equatorial irregularities, known for its characteristics of fast growth after sunset during equinox seasons, result from plasma dynamic process initiated from the gravitational Rayleigh-Taylor (R-T) instability at the bottomside of ionosphere after sunset when pre-reversal enhancement (PRE) of eastward electric field occurs due to the high conductivity gradient across the day night terminator during the post-sunset hours, leading to the sudden increase of plasma upward drift (Tsunda, 1985; Farley et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1986\u003c/span\u003e). Upward drifts can then carry the lower density at the bottomside of ionosphere to altitudes with higher density, leading to the generation of irregularity structures in F2 layer.\u003c/p\u003e \u003cp\u003eAs the post-sunset equatorial irregularities are generated due to the PRE with an unstable conditions at the bottom of F layer. However, these favorable conditions are absent after midnight in the topside ionosphere. Therefore, two problems need to be addressed if post-midnight irregularities are assumed to have similar generation mechanism as the post-sunset irregularities. The first problem is the instability condition for the topside ionosphere. As this condition is always satisfied at the bottom side of the ionosphere F layer due to the lower plasma density compared to higher altitudes, how to satisfy this condition in the topside ionosphere? The second problem is the upward drift condition. It is well known that nighttime electric field after PRE is general westward, which causes plasma to drift downward. Reversal of electric field from westward to eastward is required to satisfy this condition.\u003c/p\u003e \u003cp\u003eThe first problem can be solved based on the results obtained in our previous studies. According to the results by Wang et al. (\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2019b\u003c/span\u003e), stratification is found in the topside nighttime ionosphere near the equatorial regions during LSA period using the in situ measurements from the DEMETER satellite. Existence of stratification in topside ionosphere is further confirmed by the results from the simultaneous in situ measurements obtained by the Swarm satellites orbiting at different altitudes of the topside ionosphere during relative LSA period (Wang et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Nighttime stratification, which indicates that Ne is greater in higher altitudes than in lower altitudes above hmF2 height, provides instability condition for the topside ionosphere, favoring the generation of R-T instability. Results from the two missions suggest that nighttime stratification occurs frequently in the topside ionosphere along the dip equator during LSA period. Moreover, nighttime stratification appears more frequently during solstice seasons and can keeps its status from late nighttime till post-midnight hours with or without irregularities (Wang et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). According to the R-T instability equation proposed by Sultan (\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e1996\u003c/span\u003e), R-T instability is inversely proportional to the ion-neutral collision frequency; therefore, R-T instability will become larger at higher altitude due to the smaller ion-neutral collision frequency (Kelley, 1989). Moreover, steep vertical gradient due to the topside stratification also enhance the growth rate of R-T instability (Ajith et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Under these favorable conditions, it is easy to generate R-T instability in topside ionosphere. Therefore, nighttime stratification during LSA period provides the instability condition in the topside ionosphere.\u003c/p\u003e \u003cp\u003eFor the second condition, an explanation is given as following. According to the results by Fejer et al. (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1991\u003c/span\u003e), the downward plasma drift due to nighttime westward electric field is generally weak during the post-midnight hours of solstice seasons, particularly during LSA periods. Fejer et al. (1995) also report that average nighttime vertical drifts from the AE-E satellite are upwards during summer solstice months in 1977 of a relative LSA year and are downward in 1978 and 1979 of moderate to HSA years. In addition, simultaneous electric field and density observations from the C/NOFS satellite prove that the electric field is eastward when irregularities are observed by the in situ density measurements (de La Beaujardi\u0026egrave;re et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), suggesting that nighttime irregularities are caused by upward plasma drifts. In addition, Gentile et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) and Yizengaw et al. (\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) prove that post-midnight occurrence condition is closely related to the upward drift velocities; Rastogi and Woodman (1978) also suggest that reversal of drift from downward to upward is the key to the generation of spread F in the ionograms. The nighttime drift reversal from downward to upward can be caused by the penetration electric field from the magnetosphere and disturbance dynamo fields originating from auroral heating (Fejer and Scherliess, 1999; Burke et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). As the nighttime downward drifts are very small near solar minimum, it can easily be reversed by the disturbance drifts even in the absence of large prompt penetration electric field, which provides favorable upward drifts condition for the generation of post-midnight irregularities.\u003c/p\u003e \u003cp\u003eAccording Fejer and Scherliess (1999), the evening upward drifts and nighttime downward drifts increase significantly with solar activity; large nighttime downward drifts require larger upward perturbation drifts to overcome. However, disturbance dynamo fields, which lead to the reversal of nighttime drifts, do not change much with solar flux (Scherliess and Fejer, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e1997\u003c/span\u003e). Thus, reversal of nighttime plasma drift from downward to upward does not occur easily during relatively HSA period, it is therefore less likely to generate post-midnight irregularities.\u003c/p\u003e \u003cp\u003eAs both the instability and nighttime upward drifts conditions can be satisfied under LSA period, it is easy to understand that post-midnight irregularities can occur frequently during solar minimum years. It should be noted here that small irregularities or irregularities with lesser intensity can occur in the topside ionosphere under the above mentioned favorable conditions. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, smaller irregularities account for a large proportion of the detected irregularity events. However, for some very large irregularity structures covering a latitude range of over 20\u0026deg;with Ne fluctuation of close to an order of magnitude, the above conditions seem to be insufficient for these large-scale irregularity structures. Since this kind of irregularities always appear in the Atlantic longitude sector, they must be related to the special geomagnetic condition there. This issue, as well as the one mention in Section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e4.1\u003c/span\u003e concerning the Atlantic longitude sector, requires further studies.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThe equatorial post-midnight irregularities are studied using the in situ electron density measurements from 2019 to 2021 obtained by the CSES (ZH-1) satellite orbiting at the altitude of topside ionosphere during low solar activity period. Some results are obtained.\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe equatorial post-midnight irregularities are distributed along the dip equator with a longitude variation pattern of wavenumber 4.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe seasonal variation pattern is summer-winter peaks and spring-autumn valleys, different from the equinox peaks and solstice valleys seasonal variation pattern for post-sunset irregularities.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe longitude distribution of post-midnight irregularities is similar to that of background Ne in the four seasons, with a general wave number 3 pattern for equinox seasons and wave number 2 pattern for solstice seasons. Coincidence of irregularity peaks with background Ne peaks for both seasonal and yearly distributions suggests background Ne plays very important role in post-midnight irregularity generation.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003ePost-midnight irregularities is sensitive to solar activity under LSA conditions as occurrence rate increases rapidly with the increasing solar flux. Moreover, growth rate of irregularity occurrence rate is different across different longitudes, and the Atlantic and Pacific longitudes are the two regions with maximum irregularity growth rate.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eStratification in the topside ionosphere and reversal of nighttime drifts from downward to upward at midnight hours during LSA period provide R-T instability and upward drifts conditions for the generation of post-midnight irregularities.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eAs the generation mechanism of post-midnight irregularities is still unclear, it requires more research work. The large amount of in situ electron density measurements from the CSES (ZH-1) satellite provide us a valuable dataset to study the issues related with post-midnight irregularities, and more subsequent work will be conducted with the accumulation of measurements.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAvailability of data and materials\u003c/h2\u003e\n\u003cp\u003eThe measurements of the CSES satellite can be requested and downloaded from the website: https://www.leos.ac.cn/. The Dst data used in this paper is downloaded from website http://wdc.kugi.kyoto-u.ac.jp; and the F10.7 data is downloaded from website ftp://ftp.swpc.noaa.gov/pub/indices/old_indices/ (latest access: 2022-08-18).\u003c/p\u003e\n\u003ch2\u003eCompeting interests\u003c/h2\u003e\n\u003cp\u003eThe authors declare that they have no conflict of interest.\u003c/p\u003e\n\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThis work is supported by the NSFC project (grant no. 42104159).\u003c/p\u003e\n\u003ch2\u003eAuthors\u0026apos; contributions\u003c/h2\u003e\n\u003cp\u003e\u0026nbsp; Xiuying Wang contributed to the conception of the study and wrote the manuscript;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; WanLi Cheng, Xueqing Zhang, and Guocun Zhao collected the dataset used in the paper;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; Qiao Wang, Dehe Yang, and Song Xu performed calculation and analysis work.\u003c/p\u003e\n\u003ch2\u003eAcknowledgement\u003c/h2\u003e\n\u003cp\u003eThis work made use of the in situ electron density measurements from the CSES (ZH-1) mission, a project funded by China National Space Administration (CNSA) and China Earthquake Administration (CEA).\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAbdu M, Sobral J, Nelson O, and Batista I. 1985. 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Chinese Jounral of Geophysics (in Chinese), 65(3): 862-881, doi: 10.6038/cjg2022P0327.\u003c/li\u003e\n\u003cli\u003eWhalen J A. 1997. Equatorial bubbles observed at the north and south anomaly crests: Dependence on season, local time, and dip latitude. Radio Science, 32(4), 1559\u0026ndash;1566. doi:10.1029/97rs00285. \u003c/li\u003e\n\u003cli\u003eYizengaw E, Retterer J, Pacheco E E, Roddy P, Groves K, Caton R, and Baki P. 2013. Postmidnight bubbles and scintillations in the quiet-time June solstice. Geophysical Research Letters, 40(21), 5592\u0026ndash;5597. Doi: 10.1002/2013GL058307\u003c/li\u003e\n\u003cli\u003eYokoyama T, Pfaff R F, Roddy P A, Yamamoto M, and Otsuka Y. 2011. On post-midnight low-latitude ionospheric irregularities during solar minimum: 2. C/NOFS observations and comparison with Equatorial Atmosphere Radar. J. Geophys. Res., 116, A11326, doi:10.1029/2011JA016798.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"the CSES satellite, in situ electron density measurements, post-midnight irregularity, topside ionosphere, generation mechanism","lastPublishedDoi":"10.21203/rs.3.rs-2722826/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2722826/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe equatorial post-midnight irregularities, which has been less studied, are investigated using the in situ electron density (Ne) measurements from 2019 to 2021 obtained by the China Seismo-Electromagnetic Satellite (CSES) orbiting in the topside ionosphere. Some results are obtained as following. (1) The equatorial post-midnight irregularities are distributed along the dip equator with a longitude variation pattern of wavenumber 4 and seasonal variation pattern of summer-winter peaks during low solar activity (LSA) period in the topside ionosphere. (2) The longitude variation pattern of post-midnight irregularities is consistent with that of the background Ne with the irregularities concentrated on the peaks of background Ne. (3) The occurrence rate of post-midnight irregularities increases rapidly with increasing solar flux, which can be attributed to the rapid increase in the background Ne during LSA period; moreover, growth rate of occurrence rate is different across different longitudes, with the Pacific and the Atlantic longitudes being the most outstanding regions. (4) The similar characteristics for both post-midnight and post-sunset irregularities suggests they may have similar generation mechanisms, which are supported by the fact that conditions favorable to post-sunset irregularity generation can appear at midnight hours during LSA period. Since there have been far fewer post-midnight irregularity studies compared to post-sunset irregularity studies, much more work is still required to understand its generation mechanisms. The large number of post-midnight Ne measurements from the CSES satellite provides a good opportunity for this study, which can help to understand the post-midnight ionospheric dynamical processes and their variations with solar activity, as well as to develop a more comprehensive irregularity forecast model.\u003c/p\u003e","manuscriptTitle":"Post-midnight irregularities in the equatorial regions of topside ionosphere obtained by the CSES satellite","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-04-18 13:45:42","doi":"10.21203/rs.3.rs-2722826/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"242a2817-aee4-4415-94a2-323524ab2dbc","owner":[],"postedDate":"April 18th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-06-11T22:44:31+00:00","versionOfRecord":[],"versionCreatedAt":"2023-04-18 13:45:42","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2722826","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2722826","identity":"rs-2722826","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}