Identifying possible Stratification phenomenon in ionospheric F2 Layer using the data observed by the Demeter satellite: Method and Results

Abstract. Many studies have revealed the stratification phenomenon of the topside ionospheric F2 layer using ground-based or satellite-based ionograms, which can show direct signs of this phenomenon. However, it is difficult to identify this phenomenon using the satellite-based in situ electron density data. Therefore, a statistical method, using the shuffle resampling skill, is adopted in this paper. For the first time, in situ electron density data, recorded by the same Langmuir probe onboard the Demeter satellite at different altitudes, are analyzed and a possible stratification phenomenon is identified using the proposed method. Our results show that the nighttime stratification, possibly a permanent phenomenon, can cover most longitudes near the geomagnetic equator, which is not found from the daytime data. The arch-like nighttime stratification decreases slowly on the summer hemisphere and thus extends a larger latitudinal distance from the geomagnetic equator. All results, obtained by the proposed method, indicate that the stratification phenomenon is more complex than what has previously been found. The proposed method thus is an effective one, which can also be used on similar studies of comparing fluctuated data.



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Stratification of the F2 layer, an enhancement in electron density at heights above the F2 layer 25 maximum in the ionosphere at low latitudes and mid-latitudes, was first reported in the mid-26 twentieth century (Heisler, 1962;Sen, 1949;Skinner et al., 1954). Sayers et al. (1963) was then the 27 first to detect topside ledges in the equatorial ionosphere using a Langmuir probe onboard the 28 Ariel-I satellite and predicted that the topside ionograms would reveal the ledges as cusps, as later 29 proved by many studies using the topside sounding technique (Lockwood & Nelms, 1964;30 Raghavarao & Sivaraman, 1974; Sharma & Raghavarao, 1989). 31 There were few studies of the stratification phenomenon until the mid-1990s. Balan and Bailey 32 (1995) then explained the formation mechanism of the F3 layer using the SUPIM (Sheffield 33 University Plasmasphere-Ionosphere Model). They referred to the layer as G layer and was later 34 renamed as F3 layer because it has the same chemical composition as the F region (Balan et al., 35 1997). Since then, many more studies on the mechanism and spatial and temporal distributions of 36 the phenomenon have been carried out (Batista et  the occurrence of the F3 layer when the peak electron density of the F3 layer, namely NmF3, is 47 smaller than NmF2, which cannot be observed using an ionosonde on the ground. However, the 48 short-term global scale distribution of the stratification phenomenon still cannot be obtained from 49 satellite-based ionograms even though such ionograms can provide more data because the 50 obtained data are still discontinuous. 51 In addition, nearly all the above-mentioned F2 layer stratification studies were carried out using 52 indirect observation data, in which case some detailed information may be missed. A method 53 therefore is proposed in this paper, which can compare the in situ electron density data obtained 54 at different altitudes and identify their differences. Based on this method, the in situ electron 55 density data, recorded by the Demeter satellite at the topside ionosphere, is used to study the 56 stratification phenomenon, enabling us to investigate the characteristics of the global-scale 57 distribution and other information about the stratification phenomenon. 58 The result that the electron density observed at higher altitude is greater than that observed 59 at lower altitude suggests a stratification phenomenon distributed in a large area. This result was 60 obtained using in situ electron density data obtained before and after an altitude adjustment of 61 the Demeter satellite in a relatively short time, which is the first direct comparison of in situ data 62 recorded by the same instrument but at different altitudes. The results of the distribution features 63 of this phenomenon, obtained by the proposed method, are in accord with those obtained by 64 previous studies, but some features also suggest that the stratification phenomenon is more 65 complicated than previously found, thus demonstrating that the proposed method is effective. 66 index of solar activity before altitude adjustment was roughly equal to or smaller than that after 99 the adjustment. Therefore, data from January 1 to 25, 2006 will be used in this paper, because the 100 differences in geomagnetic and solar influences are negligible during this period. 101 Many studies have shown that the electron density in the F2 layer is characterized by periodic 104 changes in the diurnal, seasonal, annual and solar activity cycles and fluctuations due to other 105 random factors, such as geomagnetic storms and sunspot eruptions. Issues therefore need to be 106 addressed before carrying out this study. 107 As mentioned above, the local time that the Demeter Satellite passed over a location was 108 roughly fixed at about 10:30 in the morning and about 22:30 in the evening, which means that 109 diurnal changes in the data can be ignored when comparing the data before and after the altitude 110 adjustment at the same place because the local time is consistent. Another issue, which is the focus 111 of this study, is that when the electron density data are recorded over a relatively short time under 112 quiet observation conditions, say a few days, variations due to the long-period trend in the data 113 (e.g., seasonal and annual variations) can be ignored, that is to say, the data observed in a few days 114 is usually similar to that observed a few days ago. Against this background, the data, observed before and after the altitude adjustment of the 116 Demeter satellite in a relatively very short time, are compared and analyzed by seeking a suitable 117 mathematical method. 118

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The electron density is known to dynamically change both spatially and temporally. It is 120 therefore uncertain that the difference before and after the adjustment of the orbital altitude is 121 the result of normal data fluctuation or the result of the altitude adjustment. It is necessary to 122 design a reasonable scheme with which to distinguish the cause of the difference. 123 A significance test is a statistical method of determining whether the difference between two 124 groups of data is significant. Employing this method, if the p-value, the probability that a given 125 result occurs under the null hypothesis of no difference between the two groups, is less than a 126 predefined significance level, then the null hypothesis is rejected at the chosen level of significance 127 and the alternative hypothesis of a difference between the two groups is accepted. However, if the 128 p-value is not less than the chosen significance threshold, then the evidence is insufficient to 129 support a conclusion. Significance tests can therefore be conducted to determine whether the 130 difference between before and after the adjustment of the altitude can be ascribed to the 131 randomness of the data variation. If not, it may be caused by the altitude adjustment because all 132 the other conditions are the same. 133 However, the significance test assumes data to be normally distributed, which the electron 134 density data are not. This paper thus conducts a permutation test (Hesterberg et al., 2003), a 135 distribution-independent computer simulation approach of resampling advised by Fisher and Yates 136 (Wikipedia). 137 The basic idea of the permutation test is to resample the data many times to check whether 138 the same pattern of results is observed if the observation data are randomly assigned to 139 experimental groups. If the statistics calculated from the obtained data fall outside the confidence 140 limits, say 95%, the observed difference is far out in the left or right tail, and one can conclude that 141 there is a significant difference between the groups. A permutation test is based on available data 142 rather than a set of standard assumptions about underlying populations. It is therefore distinct 143 from traditional statistics and can give accurate p-values with which to check the significance of 144 the difference between two data groups. 145 We therefore adopt the permutation test method to compare the data observed at different 146 altitudes by the Demeter satellite, and to check whether the differences between the data 147 observed at different altitudes are significant. Using this method, the general process of data 148 analysis in this study is as follows.

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(1) Construct data groups using the data observed before and after the altitude adjustment, 150 or data observed at same altitude. 151  Divide the area covered by the satellite orbit between latitudes of 50 south and 152 50 north into cells of 5 latitude and 10 longitude. 153  Calculate the mean electron density before and after the adjustment of altitude in 154 each cell. 155  Divide the data into different regions every 5 latitude and obtain 20 regions from 156 50 south to 50 north in the latitudinal direction. 157 (2) Compare the data groups constructed from observation at different altitudes and check 158 Ann. Geophys. Discuss., https://doi.org/10.5194/angeo-2019-55 Manuscript under review for journal Ann. Geophys. Discussion started: 29 April 2019 c Author(s) 2019. CC BY 4.0 License. the significance of their differences by employing the permutation test method. 159 (3) Compare the data groups constructed from observation at similar conditions but with 160 same altitude and check the significance of their differences as a reference. 161 (4) Draw conclusions by analyzing different results. 162 A uniform significance level of 0.05 and one-side test are adopted in this paper, and no special 163 explanation is given in the following. According to Section 2.1, the data obtained from January 1 to 25, 2016 is selected to carry out 167 the analysis. During this period, the data from January 1 to 9 was obtained before the altitude 168 adjustment, and the data from January 14 to 25 was obtained after the altitude adjustment. In 169 addition, the geomagnetic and solar activity indices were every low during this period; that is, the 170 data obtained before and after the altitude adjustment were measured under similar observation 171 conditions. 172 In order to construct the data groups for comparison, a scheme is designed to divide the data 173 into different groups. Ascending data (data recorded during the night) from January 1 to 8 and from 174 January 15 to 23, 2006, are both divided into two groups, to give a total of four groups of data with 175 each having equal observation days. Details of the grouping are given in Table 1. 176

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The four groups of data, in the region of geographical latitude −5 to 0, are compared with 185 each other as a demonstrative example of the proposed method. 186 In order to determine the differences between two groups of data are caused by random data 187 fluctuation or by altitude differences, significance tests are carried out for each pair of groups using 188 the improved Fisher-Yates permutation test method (Durstenfeld, 1964), in which the distribution 189 of the mean data difference is obtained by resampling the data 10,000 times. The actual mean data 190 differences of each pair of groups are then compared with the 5% confidence level of the 191 corresponding distribution. 192 The significance test results of each pair of groups using the data located in geographical 193 latitude (−5, 0) are shown in

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In Fig. 3, the solid lines represent mean values of data differences before and after the altitude 206 adjustment in each cell: 207 (1) 208 Here, N is total number of cells in each latitude region, B is the average value in cell i before 209 altitude adjustment, and A is the average value in the same cell after the adjustment. Equation (1)  210 shows that the mean value of data differences is equal to the data difference between average 211 values of all cells before and after the adjustment. Therefore, mean values of data differences can 212 be calculated using two average values. As shown in Fig. 3, the data differences, between the 213 average data in the two groups in random permutation tests conducted 10,000 times, follow a 214 normal distribution with a mean value of zero, and the probability of the occurrence of the original 215 data difference is zero or extremely small, which indicates that data recorded before the 216 adjustment in most cells are obviously greater than those recorded after the adjustment because 217 the mean differences are much greater than zero. 218 Figure 3 and Table 2 show that the differences between Groups 1 and 3, Groups 2 and 3, 219 Groups 1 and 4, and Groups 2 and 4, representing the differences before and after the adjustment 220 of altitude, are significant because the p-values are zero or close to zero, much less than the 221 predefined significance level of 5%. This means that the likelihood of observing the actual data 222 difference given that the two groups have no difference is unlikely. Therefore, the null hypothesis 223 of no difference can be rejected, and significant difference between the two groups is determined. same altitude before and after the adjustment respectively, are greater than the predefined 226 significance level, which means the difference between the two groups is not significant and the 227 hypothesis of no difference between the two groups cannot be rejected. 228 The permutation test results of data at different altitudes and data at similar altitudes show a 229 significant contrast, indicating that the significant differences between the data before and after 230 the adjustment are by no means accidental but due to potential causes. Moreover, an interesting 231 point is that the electron density data recorded at higher altitude is higher than that of lower 232 altitude because all differences (i.e., values before adjustment minus values after adjustment) are 233 positive, different from the normal attenuation law at the topside ionosphere, which implies the 234 possible stratification phenomenon during the selected time segment. 235

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Obvious difference between the data groups in one latitudinal region show some information. 237 To obtain the distribution of this significant difference, permutation test results for the 20 regions 238 from 50 south to 50 north in geographical and geomagnetic latitude (where the geomagnetic 239 latitude refers to the dipole coordinates given in the Demeter satellite dataset) are obtained, and 240 the variations of p-values with latitude are presented in Fig. 4.  (1) There are significant differences in data only before and after the adjustment of altitude 249 in continuous latitudinal regions; i.e., there are significant differences in data between Groups 1 250 and 3, Groups 2 and 3, Groups 1 and 4, and Groups 2 and 4. Meanwhile, the differences between 251 observation data for the same orbital altitude, namely differences between Groups 1 and 2 and 252 Groups 3 and 4, are not obvious and no regular distribution pattern exists in the data. 253 (2) The data having a statistically significant difference are mainly distributed near the 254 geographical or geomagnetic equator regions, and are more skewed towards the Southern 255 Hemisphere, where the time of the observation data is just summer. 256 (3) Comparing the distribution of data with significant differences in Figs. 4, it is seen that the 257 distribution is 5 south in geomagnetic latitude, which indicates that this regular distribution of the 258 data with significant differences may be mainly controlled by the geomagnetic latitude, and the 259 regular distribution in terms of the geographical latitude is due to the distribution region in 260 geographical latitude overlapping with regions beside the geomagnetic equator. 261 (4) Table 3 shows that the data differences change from being positive from lower to higher 262 mid-latitudes in the Southern Hemisphere to being negative in the corresponding latitudes in the 263 Northern Hemisphere, just like an arch extending toward the higher latitudinal direction in both 264 hemispheres, as shown in Fig. 5. This regular distribution cannot be a coincidence, because 265 although most p-values in the mid-latitude regions do not reject the null hypothesis of no 266 significant difference between the data observed at different altitudes, the probability that positive 267 differences appear simultaneously in several continuously latitudinal regions (multiplication of the 268 p values in each latitudinal region) is extremely low according to the obtained p-values, which 269 indicates an underlying control factor. Regarding all differences in the Northern (winter) 270 Hemisphere being negative, this is the normal attenuation pattern of the F2 layer.   Figure 6 shows that the difference between the two groups of data before the adjustment of 284 the orbital altitude, namely Groups 1 and 2, is small while the difference between the two groups 285 after the adjustment, namely Groups 3 and 4, is also small. However, when comparing the four 286 groups together, obvious differences between the groups before and after the adjustment are seen 287 in the vicinity of a geographical latitude of −10° or a geomagnetic latitude of −15°. Moreover, 288 the difference is more pronounced in the Southern Hemisphere than in the Northern Hemisphere. 289 Although the greater data fluctuations in the summer Southern Hemisphere are a cause of this 290 phenomenon, the regular distribution cannot be explained by random fluctuation in the data. 291

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To further demonstrate that the phenomenon found above is caused by non-random factors, 293 several sets of data other than the above mentioned data are constructed to compare whether the 294 same regular distribution patterns can be found. 295 1. Descending data for the same period 296 The permutation test results of descending data, data recorded during the day, are calculated 297 according to the grouping information in Table 1. The results show that there are both cases of 298 significant differences and insignificant differences between the data observed at different 299 altitudes and between the data observed at same altitudes. Variations in the average electron 300 density with latitude are given in Fig. 7. The figure clearly shows that the observation data for the 301 same altitude during the day fluctuate greatly and there are no consistent regularities among 302 different data groups. Therefore, although there are cases that a higher altitude has higher electron 303 density, a definite conclusion cannot be drawn from these descending data. We conclude from the above data analysis that the phenomenon that the in situ electron 322 density observed at higher altitude is greater than that observed at lower altitude and that 323 significant differences are distributed regularly in the vicinity of the geomagnetic equator on a 324 global scale, is the stratification phenomenon of the F2 layer. Although the data were not 325 recorded at the same time, the data variation can be neglected because the time interval is short 326 and observing conditions are similar. 327 According to the data grouping and calculation method, if the phenomenon is only due to 328 random data fluctuation, the possibility that this phenomenon appears only for data recorded at 329 different altitudes and at several latitudinal regions in the vicinity of the geomagnetic equator at 330 the same time is extremely low. Moreover, the same regular distribution from data recorded at 331 other times with similar grouping conditions cannot be observed. The possibility that the regular 332 data distribution is due to random factors can therefore be excluded definitely. 333 In addition, the significant difference between two data groups before and after the altitude In fact, the stratification phenomenon has been observed at many locations using ionosonde; 343 e.g., Brazil (Balan et al., 1997(Balan et al., , 1998 Section 3 showed that the recording time of the data used in this study, namely the time of the 355 stratification, happened to coincide with the downward cycle of the 23rd solar cycle, when the 356 solar activity was relatively low. The season of stratification found in the data in this study 357 coincided with summer in the Southern Hemisphere, and the stratification was almost entirely 358 located in the Southern Hemisphere in terms of the geomagnetic latitude. These spatial and 359 temporal distribution characteristics, distinct on the summer side of low solar activity, are exactly 360 the same as those of the F2 layer stratification phenomenon obtained in many studies ( An interesting point, which has not been discussed in earlier studies, is that all differences in 386 each latitude region on the summer hemisphere are positive though some do not pass a 387 significance test. This consistent distribution cannot be obtained if data fluctuate randomly. We 388 therefore speculate that this feature may be related with the stratification phenomenon and 389 small stratification may exist in the summer hemisphere a little distance away from the 390 traditional geomagnetic equator region of stratification. 391 Summarizing the above discussions, we believe that the results obtained in this paper are the 392 stratification phenomenon in the ionospheric F2 layer, and the proposed method is effective. 393 The results of this method indicate that the stratification phenomenon may extend to a larger 394 area in the summer hemisphere, but it is difficult to detect because the differences are small. 395 The distribution features obtained by the data analytic results also indicate that the stratification 396 phenomenon is more complex than what has been found previously. 397

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To compare the in situ electron density data observed by the Demeter Satellite at different 399 altitudes, a statistical method, using the permutation resampling skill, is adopted and used to carry 400 out the data comparison and analysis work. The results of 10,000 permutation tests, using the 401 ascending data (data observed during nighttime) obtained before and after the altitude 402 adjustment, show that there are significant differences between data recorded at different 403 altitudes near the geomagnetic equator, but no significant differences can be found from the 404 multiple reference datasets. The stratification phenomenon can explain the regular distribution 405 patterns summarized from the data analytic results. In addition, the location, altitude, season and 406 local time of this phenomenon are accordance with the results of many studies on the F2 layer 407 stratification phenomenon. We therefore believe that the significant difference between the 408 observations of the Demeter satellite at different altitudes is the stratification phenomenon, and 409 the proposed method is effective and applicable to similar data analytic studies. 410 Some features of the stratification phenomenon can also be summarized from the data 411 analysis results. 412 1. The possible stratification phenomenon is found from the nighttime data but cannot be 413 obtained from the corresponding daytime data, though many studies have pointed out 414 that this phenomenon occurs mainly during the day, which implies the nighttime 415 stratification may be a permanent phenomenon. 416 2. The phenomenon can occur in most longitudinal regions, which is not in accordance with 417 the finding of studies that the phenomenon can only appear in special longitudinal 418 regions. This may be due to the peak of the stratification being less than f0F2 in most 419 longitudinal regions for most of the time. 420 3. The significance of differences decreases with latitude away from the geomagnetic 421 equator, indicating that the stratification is just as an arch along the latitude. 422 4. Data differences, all of which are positive at lower to higher mid-latitudes in the summer 423 hemisphere, indicate that the latitudinal extent of the stratification phenomenon is much 424 larger in the summer hemisphere than the winter hemisphere and small stratification 425 may exist away from the traditional stratification region. Stratification phenomenon is 426 more complex than what has previously been found. 427 Ann. Geophys. Discuss., https://doi.org/10.5194/angeo-2019-55 Manuscript under review for journal Ann. Geophys. Discussion started: 29 April 2019 c Author(s) 2019. CC BY 4.0 License.