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 The global distribution of the occurrence rate for density irregularities at 600 km topside ionosphere between ±35° geographic latitudes has been studied with the ROCSAT data during moderate to high solar activity years of 1999 to 2004. The result indicates that the global occurrence distribution of the intermediate-scale (0.1 to 50 km) density irregularities can be grouped into two different populations, one in the equatorial region and the other in the middle-to-subauroral latitude region. The global seasonal/longitudinal (s/l) distribution of equatorial irregularities in the current report reproduces the result of McClure et al. (1998) obtained with the AE-E observations of the mesoscale (50 to 1000 km) plasma bubble structures during high solar activity years of 1978 to 1980, two solar cycles ago. This implies that the density irregularities of different scales from multistage cascading process of the large-scale (>1000 km) gravitational Rayleigh-Taylor instability have manifested in same global s/l distribution pattern. Furthermore, global variation in seeding mechanism and growth condition of the instability process that results in major features in global irregularity pattern seems to persist for past 25 years. In addition, the current result further indicates that an upper latitudinal limit of the equatorial irregularity distribution is located at about ±30°. A different kind of midlatitude irregularity distribution starts to fill in from this dip latitude. In other words, the equatorial density irregularity inside a depleted flux tube can only rise, on statistical average, to an apex height of ∼2000 km. Different magnetic and solar variability effects as well as the local time dependence are noted for the occurrences of density irregularities in the equatorial region versus that at midlatitudes. The occurrence frequency of equatorial density irregularities increases with solar flux intensity; whereas the midlatitude density irregularity is more likely to occur during low solar activity period. The equatorial density irregularities are more likely to occur during periods of low magnetic activity than during magnetic disturbed times. On the other hand, the occurrence of midlatitude density irregularities indicates little dependence on geomagnetic activity. The local time distribution of equatorial irregularity peaks before midnight while the midlatitude irregularity indicates a plateau of high occurrence rate after midnight. Such opposite characteristics in the occurrence pattern between these two spatially separated distributions suggest that different instability mechanisms are operated in two different latitude regions for the occurrence of intermediate-scale density irregularities.
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 One of the most spectacular phenomena in the postsunset equatorial ionosphere is the occurrence of the equatorial spread F (ESF) event in which the return echo in ionogram indicates a spread in range; and in the height-intensity plot of incoherent scatter radar echoes, spectacular echoing features of so-called “radar plumes” are observed up to a thousand kilometers in altitude or more. For the radio wave communication between space and ground, the amplitude and phase scintillations will occur; and for the spacecraft in situ observation, pronounced density depletions like bubbles are noted. The cause of an ESF event is related to density irregularity structures that have been thought to result from a multistep nonlocal plasma process initiated from the large-scale gravitational Rayleigh-Taylor instability at bottomside ionosphere after sunset when some seeding perturbations exist [see, e.g., Haerendel, 1973; Ossakow, 1981; Keskinen et al., 1980a, 1980b]. The growth rate of the gravitational Rayleigh-Taylor instability can be presented in the following form [Zalesak and Ossakow, 1980; Sultan, 1996].
where all variables in the right-hand side of the equation are flux-tube integrated quantities. and represent the F and E region Pedersen conductivities, respectively. is the vertical component of the neutral wind and νin is the effective collision frequency between ions and neutrals. , , and are the electric, magnetic and gravitational fields, respectively. R is the chemical recombination rate which is used in equation (1) to indicate decay in the growth rate. However, Huba et al.  have shown that the F region recombination is not a viable mechanism to suppress the growth. For the effect of recombination in the Rayleigh-Taylor instability, readers are referred to the paper by Huba et al.  for detailed discussion.
 The growth rate in equation (1) contains external driving forces , , , and together with background ionospheric properties , , νin, R, and ∇N/N. Equation (1) has been used to interpret many different observations of the ESF density irregularity occurrences as have been summarized, for example, in a report by Sultan . However, McClure et al.  have rejected the growth rate related to the ionospheric properties in equation (1) as the major factor that explains the global seasonal/longitudinal (s/l) distribution pattern of F region density irregularities. They concluded that the global variation of seeding mechanism that triggers the instability is the key factor in providing a satisfactory explanation to the observed global s/l distribution. The seeding mechanism may arise from the gravity waves originated in the troposphere as has been proposed by Rottger [1977, 1981]. With the aid of the annual north-south migration of the Intertropical Convergence Zone (ITCZ), they presented a good pattern match between the ITCZ variation and the s/l distribution of density irregularity pattern observed by the Atmospheric Explorer E (AE-E) satellite from 1978 to 1980.
 On the other hand, using the database constructed from many different satellite observations in the series of Defense Meteorological Satellite Programs (DMSP), Huang et al. [2001, 2002] and Burke et al. [2004a,2004b] present a series of reports indicating that the precipitation pattern of energetic particles from the inner radiation belt should complement the occurrence pattern of equatorial plasma bubbles (EPBs). The enhanced ionospheric conductivity due to precipitated particles will cause a decrease in the growth rate as seen in equation (1) that is especially noticeable in South Atlantic Anomaly region. However, no clear correlation has been established for the DMSP observed FPB distribution in the s/l variation with particle precipitation pattern. This could be due to the fact that the DMSP satellites are in sun-synchronous orbits so that it is hard to obtain a good global s/l variation pattern even though data from many different DMSP series in many years are used.
 It is further noted that McClure et al.  have not only provided a gap-free global s/l variations of F region density irregularity distribution, they also conducted a detailed comparison of their AE-E result with other satellite observations such as with ISS-b by Maruyama and Matuura [1980, 1984], with Hinotori by Watanabe and Oya , and with OGO 6 by Basu et al. . Since the AE-E result has been shown to agree with all past satellite observations that are incomplete in global s/l distribution, the AE-E result becomes a good reference for future study of equatorial F region irregularity distribution. As the AE-E data are taken during 1978 to 1980, when the yearly mean solar flux intensities F10.7 are 144, 192, and 199, respectively, one would wonder if such global s/l distribution of equatorial F region irregularity persists after two solar cycles in another solar max period when the yearly mean solar flux intensity is slightly lower.
 The scientific satellite of the Republic of China, ROCSAT-1 (now renamed as FORMOSAT-1) at 600 km circular orbit with a 35° inclined orbital plane had been observing topside ionospheric ion properties from March 1999 to June 2004. The uninterrupted data set can provide a good statistical result of equatorial F region irregularity distributions to compare with the AE-E result. Because the continuous ROCSAT observation spans in 5 years, magnetic and solar variability effects of the global s/l distribution can also be studied. In addition, the ROCSAT data further provide a new result of midlatitude density irregularity distribution in relation to the equatorial irregularity distribution. Such additional result is obtained because the 35° inclined ROCSAT orbit can reach to dip latitude of ±50° in some longitude regions because of tilt in the dipole axis with respect to the Earth rotation axis. Figure 1 shows the latitudinal extent of the ROCSAT-1 orbital coverage. Notice the two longitude regions in shades, from longitude 185° to 340° in the Northern Hemisphere and from −30° to 190° in the Southern Hemisphere, where the ROCSAT orbit reaches to dip latitudes of ±50°. Thus the current report will be for the first time that a complete global survey from in situ measurements of topside ionospheric density to study the density irregularities from equatorial to midlatitude regions.
2. ROCSAT Observations
 The 1-s averaged data of the ion density measurements taken by the Ion Trap sensor onboard ROCSAT-1 are used for the current study of density irregularity structure. An autosearch program is devised to first linearly detrend a 10-s data segment, then the density fluctuation value σ is obtained with the following equation:
where ni and noi are the measured ion density and the linearly fitted value at the ith data point, respectively. Equation (2) is the standard deviation of ion density variation in logarithmic scale divided by the mean of ion density variation in logarithmic scale for a 10-s segment of data. This criterion to identify the irregularity structure is identical to that employed by Kil and Heelis  except that they adopted an 8-s data segment with ion density in linear scale. On the other hand, it is different from what has been used by McClure et al.  where the σ value is obtained by an elaborate search scheme of examining the first 3-s data segment in an 8-s sample for eight contiguous samples. An irregularity patch of 64 s in length is defined when the σ value in any three samples is larger than 0.5%. Thus the search covers a distance of 500 km in which patches of density irregularity are counted as one occurrence. Any spacing between the irregularities in the patch has been ignored. The irregularity patch in their study belongs to the mesoscale (50 to 1000 km) plasma bubble structure. This is different from the current study where the exact length of an irregularity structure in a characteristic scale length between 7.5 km and 75 km is being counted. Spacing between two irregularity structures is excluded in the counting process. Thus our study can obtain a high spatial resolution of the irregularity structures in intermediate-scale range of 0.1 to 50 km, but will have a lower occurrence rate. The density structures in both intermediate and mesoscales have been noted to be triggered by the gravitational Rayleigh-Taylor instability [Kelley, 1989].
 The reason that we use ion density variation in logarithmic scale in equation (2) instead of linear scale is this. One count difference in raw data count in the Ion Trap sensor will result in 0.2855% variation in total ion concentration. When the σ value is calculated with equation (2), the density fluctuation is reduced by a factor 4 to 5 so that the true roughness in a density structure can be measured with a proper σ value. In Figure 2, we will notice that the value σ = 0.3% is a good threshold to identify density irregularity structures both in the equatorial region and at midlatitudes. On the other hand, if ion density in linear scale is adopted, larger threshold value such as σ ≥ 1% as has been used by Kil and Heelis  might be needed to obtain the same intermediate-scale density irregularity structure. There should be no difference in the final result.
 Since the σ value in equation (2) can reflect the roughness of a density structure, Figure 2 shows an example of the result from the autosearch program with different σ values. This example indicates that plasma bubbles with various degrees of depletion in the equatorial region as well as small density irregularities at midlatitudes can all be identified with a proper choice of σ value. We have chosen σ = 0.3% in the current study as the threshold to measure the irregularity width (and the roughness) because it can identify the density irregularity structures both in the equatorial region as well as in the midlatitude region.
 Notice in Figure 2 that the density irregularities at midlatitudes have been identified at ∼2050, ∼2215, and ∼2235 UT on 20 March 2000. The three density irregularity structures are observed at about −50°, −29°, and −53° in dip latitude, respectively. These midlatitude density irregularity structures do not have bubble-like structures of large density depletion as seen in the case of equatorial density irregularities. At a first glance, the midlatitude density irregularity might be thought as the remnant of an equatorial density structure that extends to midlatitude. This is because an equatorial plasma bubble can rise to a high apex height to extend its flux tube to midlatitude. When such high rising plasma bubble begins to decay, it will leave some fossil remnant of density irregularity as observed by ROCSAT at midlatitude. However, it will be shown later that the statistical occurrence pattern of midlatitude density irregularities indicates that this is not the case.
 In the following, the satellite transit time within a square grid of 1° in longitude and latitude during the ROCSAT mission of 5 years is recorded. The time duration when the density irregularity structure is indicated by equation (2) in a square grid is also recorded. The total time duration of the irregularity occurrence is then divided by the satellite transit time to obtain the occurrence probability in that square area. The auxiliary parameters such as local time, season, the magnetic activity with Kp index, and the daily solar flux intensity with F10.7 are also recorded for the study of density irregularity occurrence conditions. It should be kept in mind that for different auxiliary conditions, the satellite transit time used in the denominator to calculate the occurrence probability will vary according to the condition imposed. In particular, we only use the nighttime data between 1800 to 0600 LT to calculate the global s/l distribution for the occurrence of density irregularities.
3. Topside Ion Density Irregularity Distributions
3.1. Seasonal and Longitudinal Variation
 Since the statistical occurrence distribution of density irregularities has been studied for many years, it is important for the current study to offer additional information on the properties of density irregularity occurrences in addition to merely reconfirm past results. Thus we first show in Figure 3 the seasonal and longitudinal (s/l) distribution of density irregularities observed by ROCSAT in 5 years during moderate to high solar activity years of 1999 to 2004 in which the mean yearly solar flux intensity F10.7 is 154, 180, 181, 180, 129, and 107, respectively. The longitudinal distributions of the occurrence probability are separated into four panels from top to bottom to represent four different seasons, the March equinox, the June solstice, the September equinox, and the December solstice. Inside each panel of a season, the color-coded scale represents the occurrence probability of density irregularity in a square grid of 1°. There are three lines drawn across the longitudes to indicate the dip latitudes to reference the latitudinal spread of the irregularity occurrences. The dashed line is the dip equator and the dash-dotted line on each side of it indicates the dip latitude of ±15°, the approximate latitude of the equatorial ionization anomaly crest (the Appleton anomaly crest.)
 One feature that is clearly noted in Figure 3 is a good spatial resolution in the two-dimensional global density irregularity distribution pattern. An immediate impression of the s/l distribution of the equatorial density irregularity occurrence pattern is this. Almost all the equatorial density irregularities occur between ±15° in dip latitude within the Appleton crests. One high occurrence of equatorial density irregularity exists in one particular longitude region for every season. For the March and September equinoxes, and the June solstice, the density irregularity is most frequently observed in longitudes between 0° and 60° (African sector where no significant magnetic declination is noted). Region of high occurrence rate then shifts to longitudes between −60° and 0° (South American-Atlantic sector where the magnetic declination is very negative) during the December solstice. Low occurrence rate is more or less evenly distributed in other longitudes for the two equinox seasons; while much lower occurrence rate in other longitudes is noticed for two solstice seasons. As for the June solstice, a second high occurrence rate is noticed in longitudes between 150° and 210° (Pacific sector where the magnetic declination is slightly positive). Thus it seems that there are two longitudinal regions that are very prone for the occurrence of equatorial density irregularities. The first one is in the African sector during the two equinox seasons and the June solstice. The other is located in the South American-Atlantic sector during the December solstice. These two longitude regions are in fact adjacent to each other.
Figure 3 also indicates that extremely low irregularities occurrence rate exists outside the ±15° in dip latitudes except in the middle latitude regions of longitudes between 60° and 160° during the two equinoxes and the June solstice, and in the longitude region between −100° and −60° in the December solstice. We term these density irregularities as “midlatitude density irregularities” even though the occurrence locations seem a little bit higher in dip latitude to fit the usual understanding of the “midlatitude irregularities.” These midlatitude irregularities are detached from the equatorial density irregularities. Properties of these midlatitude density irregularities will become part of important findings in this report.
 In order to compare the ROCSAT observation of the irregularity occurrence pattern in s/l distribution with the AE-E result of McClure et al. , we plot the published AE-E result in Figure 4 by overlaying the ROCSAT result over it. In replotting the ROCSAT result from Figure 3 to Figure 4, a latitudinal bound of ±15° in dip latitude has been imposed. Because the irregularity occurrence probability for the ROCSAT observation is noted to be about half of that derived from the AE-E data because of different selection criteria, ROCSAT result is expanded by a factor of two to overlay over the AE-E result for better comparison. It is noted that the two s/l distribution patterns of irregularity occurrence are almost identical. Not only the trend of the longitudinal variation in the occurrence pattern is very similar in every season, many small local increases and decreases are also reproduced. However, differences are also noticed. Similarity as well as dissimilarity will be compared later in the discussion section.
3.2. Latitudinal Distribution
 Even though the longitudinal distribution of the irregularity occurrences is not uniform as noticed in Figure 3, we still sum up all irregularity occurrence rates in one dip latitude region to obtain the latitudinal distribution. The result is shown in Figure 5. It should be noted that the occurrence distributions at midlatitudes are obtained only in the shaded regions shown in Figure 1. Thus in the following presentation of the properties of midlatitude density irregularities, the ROCSAT result addresses only to these two shaded regions.
Figure 5 indicates that, for every season, the latitudinal distribution of irregularity occurrence rate is composed of two different populations. One distribution is peaked at the dip equator and tapers off to near zero around the dip latitude of ∼30° like a normal distribution. The other distribution then picks up at ∼30° and the occurrence probability increases as ROCSAT traverses into higher midlatitude regions. Although we cannot definitely ascertain that the occurrence rate will increase if the ROCSAT orbit has furthered into higher midlatitudes, the trend of latitudinal distribution in Figure 5 does indicate such possibility. Even though the trend of midlatitude irregularity distribution seems to increase toward a higher dip latitude and could belong to a population that might be better termed as “high-latitude irregularities,” we still use the term “midlatitude irregularities” because we only have these irregularity distributions within ±50° in dip latitude.
 The fact of terminating the equatorial density irregularity distribution at ≲30° in dip latitude has been noted in the AE-E data from the study of equatorial plasma bubbles (EPB) [Hanson and Sanatani, 1971; McClure et al., 1977; Singh et al., 1997; Kil and Heelis, 1998]. A normal-distribution-like distribution located at the dip equator has also been observed from the topside ionograms taken by Alouette 1 satellite from September 1962 to January 1963 from the aspect-sensitive scattering of thin field-aligned irregularity [Calvert and Schmid, 1964]. The normal-distribution-like distribution also tapers off to zero at ±30°. However, the data shown in that figure (their Figure 5) are taken between 2000 and 2100 LT and has a rather coarse latitudinal resolution with large error bars. A decreasing occurrence rate in spread F events on ionograms has also been reported by Whalen  from a chain of ground stations on both sides of the dip equator in South America. On the other hand, a skewed normal-distribution-like pattern of equatorial irregularity distribution is found with the AE-E data for altitude >350 km [Kil and Heelis, 1998]. Similar skewed distribution from the AE-E data has been reported before [Singh et al., 1997].
 The 5-year ROCSAT data in Figure 5 have provided a more definitive picture that the equatorial density irregularity is terminated at ∼30° in dip latitude and a different kind of density irregularity begins to populate beyond ∼30°. If the statistical distribution of equatorial density irregularities (including the equatorial plasma bubbles) is terminated at ∼30°, it implies the flux tube that contains the density depletion of plasma bubble in the equatorial region can only rise to an apex height of about 2000 km where the footing of the flux tube at 600 km altitude is located at ∼30° in dip latitude.
 The different kind of density irregularity that appears at midlatitudes beyond ±30° can be reconfirmed from the data of density irregularity structures seen in Figure 2. The density irregularities seen at midlatitudes are the density structures with small fluctuating amplitudes in contrast to large density depletion structures observed in the equatorial region. Large density depletion structures are seldom observed at midlatitudes except during large magnetic disturbed period when large density depletion has been observed to extend to midlatitudes. Such midlatitude large density depletions have been related to the migration of neutral N/O2 composition changes from auroral region to midlatitude during storm period (H. Kil, personal communication, 2005).
 As for the shape of latitudinal distribution seen by ROCSAT in Figure 5, a slight asymmetry in the distribution of equatorial irregularities between the two hemispheres is noted for two solstice seasons in contrast to a more symmetrical one for two equinox seasons. The summer hemisphere seems to have a slightly higher occurrence rate. On the contrary, the midlatitude irregularities indicate a much stronger asymmetrical hemispheric distribution in different seasons. Higher occurrence rate between the two observed groups of midlatitude irregularity distributions, the Northern Hemisphere versus the Southern Hemisphere, is located in the Southern Hemisphere during two equinoxes and the June solstice but shifts to the northern winter hemisphere during the December solstice. Such seasonal shift in high occurrence rate of midlatitude density irregularities is opposite to the seasonal variation of equatorial irregularity distribution in dip latitude.
3.3. Variation Due to Magnetic Conditions
 The geomagnetic effect on the occurrence rate of density irregularity is shown in Figure 6 by splitting the results of Figure 3 into two columns, one for the quiet times when Kp < 3 and the other for the disturbed periods when Kp ≥ 3. It is apparent from Figure 6 that the occurrence rate of equatorial irregularity is higher during magnetic quiet times than during the disturbed times. Furthermore, it is noticed that the latitudinal distribution of equatorial irregularity will extend slightly outside the Appleton crests during the disturbed periods. The longitudinal spread in distribution is also noticed as more irregularities are observed in other longitudinal sectors during high magnetic activity periods.
 As for the irregularities at midlatitudes, we have plotted the magnetic effect on the seasonal variation of the occurrence rate in Figure 7. The occurrence of midlatitude density irregularities apparently is not affected by the magnetic condition contrary to what is seen in Figure 6 for the equatorial density irregularities.
3.4. Effects of Solar Variability
Figure 8 shows the solar variability effect on the seasonal occurrence rate of the irregularity. We have grouped the solar flux intensity F10.7 from March 1999 to June 2004 into three different levels of solar activities: low solar activity period when 100 ≤ F10.7 < 140; medium solar activity period when 140 ≤ F10.7 < 180; and high solar activity period when 180 ≤ F10.7.
 The change in the occurrence rate due to solar variability effect is rather interesting as noted in Figure 8. For irregularities in the equatorial region, they are more likely to occur when the solar activity is high. On the contrary, the occurrence of midlatitude irregularities seems to decrease during high solar activity periods. To reassure such observation, the solar variability effect on the occurrence rate of midlatitude irregularity is expanded in Figure 9. Figure 9 now clearly shows that the occurrence rate of midlatitude irregularity in either hemisphere decreases with the solar activity. This is indeed opposite to what is revealed in Figure 8 in which the occurrence rate of equatorial irregularity increases with solar activity.
3.5. Local Time Dependence
 It is well known that when the equatorial plasma bubble occurs, it will occur shortly after sunset and the occurrence rate peaks before midnight. The equatorial plasma bubble can also be found frequently after midnight during magnetic disturbed periods. Figure 10 shows the seasonal variation in the local time distribution of equatorial density irregularity occurrence rate under two different magnetic conditions, one in the quiet times and the other in the disturbed periods. From different panels in Figure 10, we can conclude that there exist two different local time occurrence patterns. One is a skew distribution with a fast rise and slow decay with the peak located between 2100 and 2200 LT during the quiet times for all seasons and during the disturbed times for the March and September equinox seasons. The other is a slower rise with a broad plateau in late nighttime for the June and December solstice seasons under disturbed conditions.
Figure 11 shows the seasonal variation in the local time distribution for equatorial density irregularities from the effect of solar activity. Figure 11 again reveals two distinctive types of local time distribution. A skewed one with a fast rise that peaks at about 2100 LT for the two equinox seasons under all solar activity conditions and in two solstice seasons when solar activity is high. The other has a broader distribution with a slower rise to a plateau in late nighttime for the two solstice seasons when solar activity is lower. This is similar to the seasonal variation in the local time distribution due to magnetic effects. That is, when the occurrence rate is high during quiet magnetic conditions or in high solar activity periods, the local time distribution pattern is skewed toward premidnight with a high peak located at around 2100 LT for all seasons. When the occurrence rate decreases during the disturbed conditions or in low solar activity periods, the distribution becomes broader with a high plateau centered around midnight for the two solstice seasons.
 As for the midlatitude irregularities, the seasonal variation of the local time distribution is shown in Figure 12. The magnetic or solar variability effect is not examined in Figure 12 because of smaller data set. Contrasting to two previous figures of equatorial irregularity distribution, the midlatitude irregularities always have a broad plateau of high occurrence rate in many local hours and most often peaks after midnight. Therefore it would be interesting to compare the local time distributions of the occurrence rate between the equatorial density irregularities and the midlatitude irregularities. Figure 13 shows such a comparison. Similar to many reports in the literature, the occurrence rate of equatorial irregularities peaks at between 21 and 2200 LT as observed at 600 km topside ionosphere. On the other hand, the occurrence rate of midlatitude irregularities has a high broad plateau located between 0100 and 0400 LT. Such difference in the occurrence distribution in local time as well as the occurrence dependence on the magnetic and solar variability effects, leads us to speculate that irregularities in the equatorial region and at midlatitudes belong to two different populations of irregularities with different triggering mechanisms.
 The 5 years of ROCSAT-1 observations have resulted in an unprecedented high spatial resolution in a two-dimensional global distribution of the seasonal, longitudinal and latitudinal variations for the topside density irregularity occurrence rate shown in Figure 3. The seasonal changes in the occurrence rate due to solar variability and magnetic effects are also presented (Figures 6 and 8). Comparison of the ROCSAT result with the AE-E result of McClure et al.  is shown in Figure 4 for the reason that McClure et al. have shown that the AE-E result can reproduce all other published results from ISS-b observations [Maruyama and Matuura, 1980, 1984], Hinotori observations [Watanabe and Oya, 1986], and OGO 6 observations [Basu et al., 1976].
 Because the selection criterion adopted by McClure et al.  to study large irregularity patch in a scale size of ∼500 km is different from the selection criterion in the current report for tracing the exact spatial extent of the density irregularity structure for sizes from 7.5 to 75 km, a different occurrence rate on the density irregularity is noted in Figure 4. However, Figure 4 clearly indicates that the two global s/l distribution patterns in the occurrence rate have all the same major features. Many similar longitudinal variation of increase or decrease in occurrence rate in the two results can be identified for every season. However, there are also differences. Some noticeable differences are listed in the following. The first one is in the Pacific region during the June solstice. The peak occurrence rate from the AE-E result is located west of longitude 180°, while the peak of the ROCSAT result is located slightly east of longitude 180°. The second difference is the location of the maximum occurrence rate during the December solstice. The ROCSAT data indicate a single maximum of occurrence rate at longitude −35°, while the AE-E data indicate a dip at this location but is surrounded by two maxima at longitude −10° and at −50°. A final point of difference is the existence of finite occurrence rates in the Indian sector in comparison with other longitude locations observed by ROCSAT during the two equinox seasons. All these differences can be resolved from the fact that ROCSAT observation is composed of 5-year data set so that better statistics has been resulted. There are many small peaks and valleys in the s/l distribution of the irregularity occurrence rate in the ROCSAT yearly result. However, when the 5-year data are averaged into Figure 4, many small peaks and valleys are smoothed out. Though not shown here, we have noticed that the s/l distribution of equatorial density irregularity for the year 2000 indicates that the second peak of high occurrence in the Pacific region during the June solstice is located west of longitude of 180° similar to the AE-E result. For other years, the peak shifts to east of 180° during the June solstice. As for the case of a single peak versus double peaks in the maximum occurrence rate in the South American-Atlantic region during the December solstice, the ROCSAT data in 2003 indicate double peaks as in the AE-E result. The rest of ROCSAT data indicate a single maximum peak in the December solstice. The case of a single maximum peak at longitude –35° has also been shown by McClure et al.  in their replot of ISS-b data of Maruyama and Matuura  and in the Hinotori data of Watanabe and Oya . Thus many small differences between the ROCSAT result and the AE-E result can be resolved by the argument of statistics. The other possibility is that there are in deed some subtle differences between the existence of mesoscale density irregularity and the intermediate-scale density irregularity in the topside ionosphere, for which the cause and effect in manifesting the density irregularity should be studied in detail. However, this falls outside the scope of current report in which the emphasis is the contrasting properties of the equatorial density irregularity versus the midlatitude irregularity.
 Therefore we can conclude that the ROCSAT observation of the global s/l distribution of equatorial irregularity structure is indeed the same as what has been observed by AE-E two decades ago. On the basis of different approaches of counting the irregularity structures in two different scale sizes, one can also state that irregularity structures of different scale sizes will manifest the same global s/l distribution from the end result of multistage cascading process of the gravitational Rayleigh-Taylor instability. The height difference sampled by AE-E at 375 to 400 km and by ROCSAT-1 at 600 km as well as the choice of the σ value is irrelevant in the statistical study of the irregularity occurrence distribution. It further implies that the global variation in the seeding and growth conditions for the instability process that results in major features in global irregularity pattern seems to persist for past 25 years. There is still no consensus answer to what background condition should be.
 Now return to the result of Figure 3. With the impressive visual presentation for the global distribution of density irregularity pattern, one can immediately conclude that the equatorial density irregularity is evidently confined within a band between the two Appleton crests around ±15° in dip latitude. We have been using the term “equatorial density irregularities” to describe the density irregularities that are confined within ±15° in dip latitude. However, in Figure 5, we realize that the latitudinal extent of the equatorial irregularities can reach to ±30°. This is quite farther outside the Appleton crest as was initially thought.
 The s/l variations of the occurrence rate for equatorial density irregularities as well as the shifting of high occurrence rate in longitude are clearly noticed in Figure 3. The high occurrence rate in longitude is seen to move from around 0° during the March equinox to around 30° in the June solstice. It then moves back to 20° in the September equinox and settles at −30° during the December solstice. The result of high occurrence rate in longitude regions between −60° and 0° (South America and Atlantic region where the magnetic declination is highly negative) during the December solstice supports the theory that alignment of the sunset terminator with the magnetic meridian as one major cause for the irregularity occurrence [Tsunoda, 1985; Abdu et al., 1981, 1982]. Moreover, this region happens to be near the South Atlantic Anomaly region so that the enhanced vertical drift due to low magnetic field has also been thought as the cause [Huang et al., 2001]. However, neither theory can explain why the magnetic declination and strength do not play any important role in the high occurrence rates of irregularities in longitude regions between 0° and 60° in the June solstice as well as during the two equinoxes. Since the ROCSAT observation reproduces the AE-E result, control of the seasonal variation in global equatorial irregularity occurrence pattern may still be laid in the seeding perturbations of atmospheric source such as from the Intertropical Convection effect in atmosphere as was proposed by McClure et al. . We do not think we can add any further information in this report regarding to the cause of global s/l distribution of equatorial irregularities.
 The current report, however, provides new additional statistical results of the magnetic and solar variability effects on the global distribution of equatorial irregularity occurrences. In Figure 6, we noticed that the irregularities occur more frequently during the quiet time than during the disturbed time. Such outcome can be realized through the understanding of suppressing the postsunset prereversal enhancement during the disturbed period [Fejer, 1991; Fejer and Scherliess, 1997] as the growth rate of an equatorial density irregularity is related to the enhanced zonal electric field which is related to the prereversal enhancement. However, it is noted that during the disturbed periods the occurrence locations of density irregularities will spread outside the Appleton crests. In addition, more longitudinal spread in the occurrence pattern is also noted during the disturbed periods in the two solstice seasons. Thus in some local region, the irregularity occurrence does indeed seem to be increased in comparison with the quiet time observation. However, the overall global distribution of the occurrence rate is still lower during the disturbed period than in the quiet time.
 On the other hand, the probability of occurrence increases with solar activity. This can also be understood from the fact that the atmospheric driver for the zonal electric field is stronger during high solar activity period to enhance the growth in the instability process. However, there are data from the AE-E observations indicated that more cases of equatorial irregularities around the F-peak are observed during low solar activity period than during high solar activity period (B. Fejer, personal communication, 2005). Such opposite observations should be noted from the fact that the AE-E data used in the study comprise only finite numbers of observations. The long-term statistics would prove otherwise as indicated in the current report. In fact, the morphological study of gigahertz equatorial scintillation experiments carried out by Feng and Liu  has indicated that the occurrence of gigahertz scintillation decreases with magnetic activity but increases with solar activity. A high occurrence of deep scintillation within the Appleton crests during a year of high solar activity than during a year of low solar activity has also been reported by Aarons . Thus our result of solar variability effect on the occurrence of equatorial irregularities agrees with past results of scintillation experiments.
 The latitudinal variation shown in Figure 5 clearly indicates the existence of a latitudinal demarcation that separates the irregularities in the equatorial region from that at midlatitudes. Although such demarcation is inferred from the observations of midlatitude irregularities in two longitude regions only, between −30° and 190° in the Southern Hemisphere and between 185° and 340° in the Northern Hemisphere, there is no reason to believe that density irregularities at midlatitudes in other longitude regions outside the ROCSAT coverage will behave differently because the global distribution of equatorial irregularities has already tapered off significantly at dip latitudes of ±20° and terminated at about ±30°. Even with limited data in midlatitude coverage from the ROCSAT observation, we still can conclude that there exist two different distributions of intermediate-scale density irregularities, the equatorial region versus the midlatitude. The two distributions behave similarly in the seasonal variation as seen in Figure 5, but oppositely under magnetic effect as seen in Figures 6 and 7, in solar variability effect as seen in Figures 8 and 9, and in local time distribution in Figure 13. Table 1 summarizes the different characteristics of the density irregularities in the equatorial region versus at midlatitude in the current report. The result implies that the density irregularities in the equatorial region and at midlatitude belong to two different populations of intermediate-scale density irregularities at topside ionosphere.
Table 1. Summary of Characteristics for Density Irregularities in the Equatorial Region and at Midlatitudes
Density Irregularities in Equatorial Region
Density Irregularities at Midlatitudes
Local time distribution
peaks before midnight at ∼2100 LT
broad peak after midnight at ∼0300 LT
slightly more during equinoxes and different longitudinal distribution
more in winter hemisphere
more occurrences during low-Kp period
Solar activity effect
high solar activity period has more
low solar activity period has more
 The cause for terminating an equatorial density irregularity at about ±30° in dip latitude is explained in the following. As the Rayleigh-Taylor instability develops in the equatorial bottomside ionosphere, the flux tube that contains low-density plasma from bottomside ionosphere begins to rise. To maintain adequate growth of the instability, the growth rate γ in equation (1) should be positive. In the study by Sultan  with modeled ionospheric and atmospheric parameters, he has shown that the height integrated density N begins to decrease above 900 km in altitude that is about ±20° in dip latitude. As the growth rate γ becomes negative above 900 km, one will see the decaying bubble only. Thus, according to the model, one should not observe a rising bubble above ±20° in dip latitude. The height below 900 km has also been quoted by Singh et al.  as the most likely regions to observe plasma bubbles. The statistical result of the ROCSAT observation indicates that the occurrence of equatorial irregularity structure decreases significantly at ±20° and terminates at about ±30° as indicated in Figure 5. This put the maximum height for the existence of an equatorial irregularity structure (that is related to an equatorial bubble) at about 2000 km. Such conclusion confirms the topside ionogram results reported from old Alouette 1 and 2 observations. Though limited with only 15-month of Alouette-1 data, Calvert and Schmid  reported that the occurrence rate of aspect-sensitive scattering events from thin field-aligned irregularity in the equatorial region terminates at about ±30° in the 2000–2100 LT sector. The Alouette 2 results reported by Muldrew  indicated that from a statistical study of the propagation of ducted echoes in the topside ionogram, plasma bubble irregularities related to the ducted echoes (due to thick field-aligned irregularities) are limited to altitudes lower than L ≲1.2 (dip latitude ≲24°). Although the current conclusion for the maximum apex height of an equatorial plasma bubble reaching to 2000 km is somewhat higher than past observations of 1100 km [Maruyama and Matuura, 1984], or 1400 km [Mendillo and Tyler, 1983], it is still lower than some other observations of 3500 km [Burke et al., 1979] or 2500 km [Sahai et al., 1994]. Nonetheless, the statistical ceiling height of an equatorial bubble seems to be set at 2000 km altitude.
 Following this argument, we draw a picture depicted in Figure 14 to show a morphological development of an equatorial plasma bubble observed by the traversing ROCSAT-1 at a constant height of 600 km from equatorial region to midlatitude. Observation of midlatitude density irregularity structures by ROCSAT is also illustrated in Figure 14. A similar graphic illustration with multiple flux tubes of filled plasma bubbles has been presented by Whalen  to indicate consecutive observations of equatorial spread F events from ground stations distributed in dip latitude. An immediate implication of Figure 14 is that the equatorial plasma bubble structures belong to a population of density irregularity that is different from the midlatitude irregularity.
 The property of equatorial density irregularity from the triggering mechanism shown in equation (1) has been well documented in the literature. For example, Sultan  has used this equation to demonstrate how the irregularities should be distributed in s/l and local time occurrence patterns. The new additional properties of the occurrence dependences on magnetic and solar variability effects could also be examined with the aid of equation (1). However, this will not be carried out here. Instead, we shall focus on the newly observed properties of midlatitude irregularities obtained by ROCSAT.
4.2. Irregularities in the Midlatitude Regions
 Midlatitude ionospheric irregularities have long been studied with echoes in ionosonde [Bowman, 1960, 1985], by propagation properties in scintillation experiments [Yeh et al., 1968; Rodger, 1976; Rodger and Aarons, 1988], or with echoes in coherent radar observation [Behnke, 1979; Fukao et al., 1991]. The first direct in situ measurement in space was made by AE-E in a report by Hanson and Johnson . The observed mesoscale (50 to 1000 km) density depletions varied in phase with the radial flow motion when AE-E was located at ∼260 km altitude in bottomside ionosphere. This observation was interpreted to be related to the Perkins instability [Perkins, 1973]. Similarly, observations of ionospheric band-like motion by Arecibo radar [Behnke, 1979] and F region field-aligned irregularities (FAI) by MU radar [Fukao et al., 1991; Kelley and Fukao, 1991] have also been interpreted with the Perkins instability. On the other hand, observations of midlatitude electric field fluctuations (MEFs) made with Dynamic Explorer 2 (DE 2) were explained with the field-aligned current flowing between the conjugate ionospheres without resorting to any instability process [Saito et al., 1995]. No clear relationship between the MEFs and the midlatitude spread F has been established in that report. The local time distribution of MEFs' occurrence pattern that is peaked after midnight is very similar to the distribution pattern of high occurrence rate from the ROCSAT observation. However, it needs to be emphasized again that the current ROCSAT observation of the midlatitude irregularities starts from the dip latitude of ±30°. This is a different distribution of the intermediate-scale density irregularity after the termination of the equatorial irregularity at ±30°. It is also different from the conventional understanding of midlatitude irregularities in which the occurrence rate peaks at ∼±30°, as in the case of MEF observation by DE 2. Therefore the difference between the property of midlatitude irregularity in this report and in some past observations should be expected.
 The statistical property of midlatitude irregularities has not been established because not many cases of midlatitude irregularities have been studied with large amount of data. From what is available in the literature (as to our best knowledge), we construct Table 2 to compare properties of midlatitude irregularities observed by different experiments. It is noted that the scale size of the observed midlatitude irregularity in the table is an important factor when comparison is made. Different triggering mechanisms could be related to different midlatitude irregularities of various scale sizes. Furthermore, we have excluded the observations of traveling ionospheric disturbances (TIDs) in Table 2 because we are only concerned about the phenomena of scale lengths in ∼50 km or less. However, it should be kept in mind that the TIDs might be the root cause of many observations in Table 2. Another important feature noted in Table 2 is the lower limit in dip latitude for observing midlatitude irregularities in different experiments. It seems that many experiments have observed the midlatitude irregularities around the dip latitude of ≳30°. This dip latitude is higher than the limiting dip latitude of ∼18° for propagating the medium-scale (50 to 1000 km) TIDs in a report by Shiokawa et al. . This lower limit in dip latitude for the MTIDs does not contradict the results in Table 2 because phenomena of different scale sizes are addressed. In fact, ROCSAT has observed many cases of mesoscale density and flow undulations as well as the plasma blob events at about 20° in dip latitude. These ROCSAT observations are not included in the current report from the autosearch result of intermediate-scale irregularities. They are presented in a separate report (S.-Y. Su et al., preprint, 2006) for the study of the mesoscale density and flow undulations in conjunction with the intermediate-scale density irregularities.
Table 2. Occurrence Characteristics of Nighttime Midlatitude Irregularities Observed by Different Experiments
dominant when sunset terminator is aligned with magnetic meridian
more in summer season
more in winter hemisphere
more in summer hemisphere
more in summer season
Solar variability effect
more in low solar activity period
more in low solar activity period
more in low solar activity period
more during Kp ∼2 period
Local time dependence
high occurrence after midnight
high occurrence after midnight
high occurrence after midnight
high occurrence after midnight
no definitive conclusion
 Even though many midlatitude irregularities have been explained with the model of the Perkins instability, not all observations fit the theoretical prediction such as the motion of field-aligned irregularities observed by MU radar [Kelley and Fukao, 1991]. Furthermore, it has been noted by many investigators [see, e.g., Kelley and Fukao, 1991; Tsunoda et al., 2004] that the growth rate of the Perkins instability is too low to produce any significant irregularity structure to be observed in F region. On the other hand, many recent papers on the instabilities of the sporadic E layers [Cosgrove and Tsunoda, 2001, 2002, 2003; Tsunoda and Cosgrove, 2001; Haldoupis et al., 2003; Tsunoda et al., 2004] indicate that the electrodynamically coupled E and F regions will produce F region structure more rapidly than by the Perkins instability acting alone. If the current ROCSAT observation of midlatitude irregularities is related to the sporadic E layer instability, then the occurrence condition of the sporadic E layer instability can be inferred from the current report. One important feature for the occurrence of the sporadic E layer instability lies in its relationship with the wind shear condition of the neutral winds. The wind shear condition might be related to the solar variability as indicated in the report of Bowman  in which more sporadic E instability (spread Es event) occurrence is observed during the solar minimum year of 1953 than during the solar maximum year of 1949 and 1957. This would imply that the midlatitude irregularities are more likely to occur during a low solar activity period than during a high solar activity period as indicated from the ROCSAT observations.
 Finally, as the roughness of density irregularity structure at midlatitudes is concerned, we noticed with reference to Figure 2 that the spatial extent in tracing the midlatitude density irregularity decreases rapidly when the σ value increases as compared with the case of equatorial density irregularity. Thus it seems that the midlatitude irregularity is not as rough in density structure as the one in the equatorial region. From the scintillation experiments reviewed by Aarons , it is also learned that the midlatitude scintillation activity is not as intense as that encountered in the equatorial region.
 The statistical survey of the ROCSAT data taken during moderate to high solar activity years of 1999 to 2004 indicates that topside ionospheric density irregularities can be separated into two populations: the equatorial density irregularities (including equatorial plasma bubbles) versus the midlatitude density irregularities. Properties of statistical occurrence pattern for the equatorial density irregularities have been well established in the literature and the ROCSAT observations again reconfirm many past results of the global s/l distribution. From the fact that the global s/l distribution patterns of density irregularities in difference sizes are identical, it is concluded that our understanding of the basic physical processes that the multistage cascading process from the gravitational Rayleigh-Taylor instability to cause the equatorial density irregularity remains correct. Different data sets from past 25 years still result in identical global s/l distribution pattern further indicates that the global seed perturbations and growth conditions related to the instability process seem to persist and remain elusive without yielding any consensus agreements among different investigators. The current report has excluded discussion on the seeding mechanism for the occurrence of equatorial irregularities. However, the ROCSAT observations have complemented the past observations with additional information on the occurrence dependence on magnetic, solar variability, and local time conditions. Hope that these complementary results will assist theoretical investigators to better understand the background conditions that cause the equatorial irregularities.
 The ROCSAT data further discover the contrasting properties between the midlatitude density irregularities and the equatorial density irregularities. Although limited in certain longitudinal regions, the magnetic and solar variability effects as well as the local time dependence on the occurrence of midlatitude density irregularities are noticed to be opposite to that of equatorial irregularities. The midlatitude irregularities are separated from the equatorial irregularity distribution at ±30° in dip latitude. The local time variation of the midlatitude irregularities is very similar to those of the spread Es events revealed in the midlatitude ionograms. The electrodynamically coupled process between the E and F regions from the instabilities of sporadic E layers are thought to be related to the occurrences of the midlatitude topside ionosphere density irregularities observed by ROCSAT. If so, the current statistical results of the midlatitude density irregularity properties should offer valuable clues to the study of the instability conditions of sporadic E layers.
 The work is supported, in part, by NSC93-2111-M-008-023-AP5 from National Science Council of the Republic of China and, in part, by a grant from Asian Office of Aerospace Research and Development (AOARD) of U.S. Air Force Office of Scientific Research (AFOSR), AOARD-03-4010. The ROCSAT data are processed under the support of 93-NSPO(B)-IPEI-FA07-01 from National Space Organization of the Republic of China. We are grateful to many NCU ROCSAT/IPEI team members for their efforts in processing the ROCSAT/IPEI data. We have also benefited greatly from comments made by the reviewers during the revision of the paper.
 Arthur Richmond thanks J. P. McClure and Roland Tsunoda for their assistance in evaluating this paper.