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Data Analysis of Upper Temperature Detected by Sounding in China

J. W. LI College of and Oceanology, People’s Liberation Army University of Science and Technology, Nanjing, China

Z. SHENG College of Meteorology and Oceanology, People’s Liberation Army University of Science and Technology, and Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing, China

Z. Q. FAN College of Meteorology and Oceanology, People’s Liberation Army University of Science and Technology, Nanjing, China

S. D. ZHOU AND W. L. SHI College of Meteorology and Oceanology, People’s Liberation Army University of Science and Technology, and Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing, China

(Manuscript received 13 May 2016, in final form 26 November 2016)

ABSTRACT

Sounding rockets launched by China have collected data on the upper atmosphere for nearly 50 years. In this work, the data accuracy and variable characteristics of upper atmosphere temperature data, gathered at heights of 20–60 km over Jiuquan, China, during 1974–2014, were analyzed. The relative accuracy of sounding temperature data was determined by comparing the data with Mass Spectrometer and Incoherent Scatter (MSIS) model data by season, and with Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) from the Thermosphere, Ionosphere, Energetics and Dynamics (TIMED) by year. The sounding rocket temperature data showed differences from MSIS in every season, with the minimum difference occurring in summer, the next smallest difference in winter, and the maximum difference occurring in autumn. The sounding rocket data showed smaller differences from the SABER data, although the deviation still fluctuated depending on the date and hour of the observations. In addition, the temperature distributions of the temperature profiles were examined at different times at the same heights. By linearly fitting the mean temperature profiles of each season, the statistical characteristics of the tem- perature changes with height were explored.

1. Introduction spacecraft orbit injection. As an important part of the fifth-dimension battlefield (land, sea, air, space, electro- The near space is the region of Earth’s atmosphere at magnetism space), near space is an important link in our heights of about 20–100 km, and it includes the strato- national security system. Emerging near-space aircraft, sphere (15–50 km), the mesosphere (50–85 km), and a such as stratospheric airships, have unique advantages small part of the thermosphere (85–100 km). The region in gathering intelligence, surveillance, scouting, com- is expected to accommodate the expansion and exten- munications relay, navigation, and electronic warfare. sion of conventional flight airspace and the channel for At present, many countries are developing military and civil applications of near space. In particular, because air- Corresponding author e-mail: Z. Sheng, [email protected] craft, airships, and aerostats are active in the stratosphere

DOI: 10.1175/JTECH-D-16-0104.1 Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 09/29/21 05:54 AM UTC 556 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 34 and the substratum of the middle atmosphere, these the temperature measurement range is 2808 to 1808C. regions are strategically important (e.g., Li et al. 2008; The precision of the temperature measurements is about Ouyang and Chen 2012; Che et al. 2010). 1.58C below 50 km and 3.08C between 50 and 60 km (e.g., Currently, research on the near-space atmosphere is Jiang et al. 2009; Liu and Jiang 2012). The temperature limited by the completeness and accuracy of atmo- profiles, which are detected by sounding rockets and spheric observations, restricting the development of have the vertical resolution of 0.5 km, are processed data near-space applications in some countries (e.g., Lu et al. from the test site. Even though there have been more 2009). Methods for detecting near-space environmental than 60 timed flights of sounding rocket in the past 50 parameters include sounding balloons, sounding rockets, years, but not all of the profiles meet the requirement of radio radar, laser radar, and satellite remote sensing. completeness across the primary altitude range of 20– However, sounding rockets are the only in situ method 60 km, because quite a few profiles have the problem of for measuring the near-space atmosphere (e.g., Jiang data missing in a certain height range. There also are et al. 2009). China launched its first sounding rocket almost some flights of sounding rocket that miss the tempera- 50 years ago, which was mainly used for meteorological ture profiles but other parameters, such density profiles sounding (Liu and Jiang 2012). In recent years, in addi- and wind profiles, are obtained. Therefore, to ensure the tion to the Meridian Space Monitoring Project, efficiency of the conclusions, we selected about 25 a sounding rocket observation system has been used to measurements for the analysis. The dates of the rocket gather general environmental data about space below a experiments we selected are presented in Table 1. height of 200 km. The temperature data gathered by sounding rockets Analyzing sounding rocket data is important for sci- over the last 50 years, which mainly consist of data col- entific investigation of the near-space atmosphere and lected over Jiuquan (41.18N, 100.28E), China, during for improving space temperature detection techniques 1974–2014, were used. Therefore, the conclusions apply (e.g., Lu and Yao 1974; Fan et al. 2013). Jiang et al. only to the middle and upper atmosphere over Jiuquan. (2011) analyzed observations of the first meteorological b. MSIS empirical prediction model temperature data rocket launched in the Meridian Space Weather Moni- toring Project. Fan et al. (2014) evaluated sounding A middle atmosphere model was developed by com- rocket data accuracy based on sounding rocket de- bining the middle atmosphere sounding data with gov- tection data from China. Their results were based on erning equations for the physical changes in the several sounding rocket experiments, and they exam- atmosphere (Shen 1990). The Mass Spectrometer and ined environmental parameters such as temperature, Incoherent Scatter (MSIS) model is an empirical model density, and pressure. Many years of sounding rocket of the upper atmosphere that provides empirical data for data should be used to analyze the general statistical atmospheric parameters, such as temperature and den- characteristics of temperature. Therefore, this paper sity, and for major atmospheric components, such as analyzes sounding rocket temperature data from China oxygen and nitrogen. MSIS-86, which is an international in terms of their temperature distributions and their reference atmosphere model, is identical to the Com- variations in the near-space atmosphere. mittee on (COSPAR) International Reference Atmosphere (CIRA) 1986 (CIRA-86) model, which provides a quantitative description of the effects of 2. Data presentation time, longitude and latitude, seasonal variation, annual variation, diurnal variation, geomagnetic disturbance, a. Near-space sounding rocket temperature data and solar activity (e.g., Batten et al. 1987; Hedin 1991; A sounding rocket for near-space atmospheric de- Picone et al. 2002). The more recent version of the MSIS tection has the unique advantage that its flying height is series is MSIS 2000 (MSIS00), which is particularly suit- between that of sounding balloons and , so it for the layer between the ground and the upper at- can provide in situ measurements of near space. The mosphere. By setting homologous parameters, such as sounding rocket launches and flies to its pathway vertex latitude, longitude, time, and geomagnetic activity index, (generally at 60 km), and then deploys its empirical temperature data were obtained from MSIS00 system, which descends gradually via a parachute. As and compared with the sounding rocket data. the radiosonde descends, a temperature sensor mea- c. TIMED/SABER satellite limb sounding sures the air temperature and transmits it to a ground temperature data radar receiver in real time, where a data processing system handles the air temperature data. The detection The Thermosphere, Ionosphere, Mesosphere Ener- height of the sounding rocket is generally 20–60 km, and getics and Dynamics (TIMED) satellite was developed

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TABLE 1. Dates of rocket experiments from which we selected deviation, S is the standard deviation, and r is the cor- measurements. relation coefficient: Year Date Year Date 5 2 5 ... Ei Ti T0i, i 1, 2, 3, , N. (1) 1967 30 May 1998 15 Aug 5 5 Jun 20 Aug Emax max(Ei). (2) 1979 16 Dec 1999 26 Apr 1 N 24 Dec 2000 31 Oct 5 å j 2 j E Ti T0i . (3) 1981 7 Jul 2004 8 Nov N 5 vi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 8 Jul 15 Nov u uN 10 Jul 16 Nov uå 2 2 11 Jul 17 Nov t (Ti T0i) i51 19 Nov S 5 . (4) 1985 12 Jul 2014 2 Jan N 15 Jul 3 Jan N N N å 2 å 3 å 1988 19 Dec 9 Jan N TiT0i Ti T0i 5 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii51 i51vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii51 16 Mar r u ! u ! . 7 Aug u 2 u 2 t N N t N N å 2 2 å 3 å 2 2 å N Ti Ti N T0i T0i i51 i51 i51 i51 by NASA and launched on 7 December 2001 (e.g., Russell (5) et al. 1999). Sounding of the Atmosphere using Broad- band Emission Radiometry (SABER) is a 10-channel b. Comparison of sounding rocket and MSIS infrared radiometer on the TIMED satellite for measur- temperature data ing Earth’s limb thermal radiation, and its wave band is between 1.27 and 17 mm(e.g.,Mertens et al. 2001). The Twenty-five instances of intact, effective sounding rocket temperature data from 1974 to 2014 were selected, and the SABER radiometer detects the CO2 radiation signal at a wave band of 15 mm, and temperature data at a height MSIS00 empirical prediction model temperature data with of 15–120 km can be obtained through inversion. The identical parameters, such as latitude, longitude, and time, TIMED/SABER satellite normally obtains about 1400 were obtained. Then, the temperature data were divided atmosphere profiles every day. The vertical resolution of into four groups according to season. In each season, a pair the data is about 2 km and the horizontal resolution is of intact temperature profiles was selected for comparison, 400 km, the extent of observation is 828N–548S (north- and the mean deviation and mean standard deviation were ward) or 548N–828S (southward), and the observed ori- calculated in order to compare the statistics. entations change every 60 days. The temperature accuracy 1) COMPARISON OF SPRING TEMPERATURE DATA of SABER is 2 K below 100 km, and its data product version 1.07 has high credibility (e.g., Remsberg et al. Figure 1 shows the comparison of sounding rocket and 2008; French and Mulligan 2010; Cao et al. 2012). The MSIS temperature data for spring. The two temperature SABER temperature data for the period 2004–14 for profiles show similar variations (Fig. 1a). The maximum the same latitude and longitude as the rocket data, and an deviation of the two profiles is about 216.228C at 35– altitude range of 20–60 km, were used. 50 km and 112.58C at 54–60 km (Fig. 1b). The correla- tion coefficient of the two sets of data is 0.8719, and the standard deviation is 8.738C. 3. Accuracy analysis of sounding rocket Figure 2 compares the mean deviations and the mean temperature data standard deviations for the sounding rocket and MSIS temperature data for spring. Because the sounding rocket a. Data processing method dataset is incomplete at 55–60 km, Fig. 2 shows only the The accuracy of the sounding rocket temperature data temperature profiles at 20–55 km. The mean temperature is analyzed mainly by its maximum deviation, standard deviation shows similar variations with Fig. 1b (also see deviation, and correlation coefficient compared with Fig. 2a). The mean standard deviation of the two datasets standard values. Here, T is the sounding rocket tem- is within 48C at 20–35 km, whereas at 35 km it is over 48C, 8 perature, T0 is the standard temperature (MSIS data or and the maximum of 11.8 C appears at 38–45 km (Fig. 2b). SABER data to which the sounding rocket data will 2) COMPARISON OF SUMMER TEMPERATURE DATA compare), E is the deviation, i (1, 2, 3,..., N) is the se- quence number of the data, N is the total number of Figure 3 compares the sounding rocket data and MSIS data, E̅is the mean deviation, R̅is the mean rate of summer temperature data. The two sets of temperature

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FIG. 1. Comparison of sounding rocket and MSIS spring temperature data (case on 16 Mar 2014). profiles have a higher goodness of fit than the spring similar variations (Fig. 5a). The temperature deviation temperature data (Fig. 3a). The maximum deviation is maximum of the two profiles reaches 17.58C, and the 5.88C at 35–45 km, and the temperature deviation changes deviation profile is about to be in the shape of a substantially with height, although its value is negative and ‘‘W’’ (Fig. 5b). The temperature deviation is negative at within 48C(Fig. 3b). Moreover, above 51 km, the tem- 35–52 km, whereas it is positive at 24–35 and 52–60 km. perature deviation also changes considerably, although it The correlation coefficient of the two sets of data is remains positive. The correlation coefficient of the two sets 0.8694, and the standard deviation is 7.388C. of data is 0.9902, and the standard deviation is 2.378C. Figure 6 compares the statistics for the autumn tem- Figure 4 compares the statistics for the summer datasets. perature data. The mean deviation changes substantially The maximum mean deviation of the two temperature with height above 35 km (Fig. 6a): its value is negative at datasets is 48C, and the mean deviation profile appears to 35–52 km and positive at 52–60 km. The maximum mean be in the shape of an ‘‘S’’ (Fig. 4a). The maximum mean temperature deviation is 17.58C at 44 km. The maximum standard deviation is about 5.48C at a height of 50 km mean standard deviation is 17.98Cat44km(Fig. 6b). (Fig. 4b), and the mean standard deviation changes rapidly The mean standard deviation changes with height, and with height and the variation is clear. the profile contains a peak and a trough at 35–54 km.

3) COMPARISON OF AUTUMN TEMPERATURE 4) COMPARISON OF WINTER TEMPERATURE DATA DATA Figure 7 compares sounding rocket and MSIS winter Figure 5 compares sounding rocket and MSIS autumn temperature data. The two temperature profiles have a temperature data. The two temperature profiles show higher goodness of fit than that of spring (Fig. 7a). The

FIG. 2. Comparison of sounding rocket and MSIS temperature data statistics in spring: (a) mean deviation and (b) mean standard deviation as a function of height.

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FIG. 3. Comparison of sounding rocket and MSIS summer temperature data (12 Jul 1985). maximum temperature deviation is 8.58C at 56 km; the deviation is nearly 08C(Fig. 9a). At 35–55 km, the mean deviation is negative and within 38C at 20–25 km; and deviation profiles for each season are parabolic, and the above 45 km, the deviation increases sharply and peaks appear at 40–45 km. In summer, the mean de- reaches a peak (Fig. 7b). The correlation coefficient of viation levels off at 08C more clearly than for other the two sets of data is 0.9867, and the standard deviation seasons; it is the second smallest in winter, whereas in is 3.568C. autumn it is highest. The maximum mean deviation is Figure 8 compares the winter temperature datasets. 48C in summer, 9.88C in winter, 10.98C in spring, and Unlike the other seasons, the mean temperature de- 17.58C in autumn. In winter, the mean deviation is pos- viation in winter is mainly positive (Fig. 8a). The maxi- itive over the whole height range. In summer, the mean mum mean deviation is 9.88C around 54 km. The mean standard deviation changes slowly with height and its standard deviation fluctuates between 28 and 88C below value is small, with a maximum value of less than 58C 50 km, but it increases steadily above 50 km, reaching a (Fig. 9b). Below 55 km, the maximum mean standard maximum of about 12.58Cat59km(Fig. 8b). deviation is 10.28C in winter, 11.88C in spring, and 17.98C in autumn. In spring and autumn, the mean standard 5) COMPARISON OF TEMPERATURE DATA deviation changes substantially at 35–50 km. BETWEEN SEASONS c. Comparison of sounding rocket and SABER Figure 9 shows the mean deviation and mean standard temperature data deviation between the sounding rocket and MSIS tem- perature data as a function of height during different Two sets of temperature data from 2004 and 2014 seasons. The variation in the mean deviation in each were selected for comparison. Based on the latitude, season is slightly different, and at 20–35 km the mean longitude, and time for the data, matched temperature

FIG. 4. Comparison of sounding rocket and MSIS temperature data statistics in summer: (a) mean deviation and (b) mean standard deviation as a function of height.

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FIG. 5. Comparison of sounding rocket and MSIS autumn temperature data (19 Nov 2004). profiles were filtered from the SABER data. Because Table 2 shows a comparison of the sounding rocket the TIMED satellite cannot cover the whole Earth in a data and SABER data for five dates in November 2004. scan (e.g., Zhang et al. 2006), there are no data recorded The temperature deviation is larger between the at the same latitude and longitude as the sounding rocket sounding rocket data and satellite data than between the for certain days and times. The SABER data within an sounding rocket data and MSIS. The correlation co- error range of 658 according to the sounding rocket were efficient of the two sets of data is larger and is over 0.9 on used, and then the mean temperature profile in the error average, with a maximum of 0.9817. However, the range was taken as the standard profile for comparison maximum deviations of the five sets of data are all over with the sounding rocket data in 2004 and 2014. 108C, and the largest is 21.628C. The two datasets have the highest goodness of fit, and the other sets of data 1) TEMPERATURE COMPARISON IN 2004 have different deviations and correlation coefficients. Figure 10 compares the temperature data for 17 No- This indicates that the deviation between sounding vember 2004. The two profiles show similar variation, rocket data and SABER satellite data changes with although there are larger differences at higher altitudes date, possibly because of the variation of the upper at- (Fig. 10a). At 48–54 and 57–60 km and around 24 and mosphere and detection error. 29 km, the temperature deviation is more than 58C and 2) TEMPERATURE COMPARISON IN 2014 the maximum deviation is 10.068Cat60km(Fig. 10b). The deviation changes with height are wavelike, and the Figure 11 compares the temperature data for changes are particularly large at 45–60 km. The corre- 16 March 2014. The sounding rocket profile and the lation coefficient of the two sets of data is 0.9817, and the SABER satellite profile have similar variations, al- standard deviation is 3.548C. though the difference between them is larger at lower

FIG. 6. Comparison of sounding rocket and MSIS temperature data statistics in autumn: (a) mean deviation and (b) mean standard deviation as a function of height.

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FIG. 7. Comparison of sounding rocket and MSIS winter temperature data (16 Dec 1979). and higher altitudes (Fig. 11a). At 40–44, 54–60, and 4. Analysis of sounding rocket temperature data around 16 km, the absolute temperature deviation is more than 58C, and the maximum value of 10.308C oc- Historical sounding rocket data from 1974 to 2014 curs at 57.5 km (Fig. 11b). The deviation changes with were selected for horizontal and vertical comparison, height are wavelike, and the maximum negative de- and the temperature distribution at the same height and viation is 27.48C around 16 km, whereas above 39 km the temperature changes with height in different seasons the deviation is positive. The correlation coefficient of of the temperature profiles at different times were ex- the two sets of data is 0.9793, and the standard deviation amined. Temperature distributions at the same height is 4.538C. can provide a reference for the statistical trend of tem- Table 3 shows a comparison of the sounding rocket perature data. The changes in temperature with height data and SABER data for five dates in 2014. The three during different seasons can provide a reference for the sets of data for January 2014 have larger deviations in- statistical regularity of the stratopause in different sea- dividually, with a maximum deviation of 23.48C. In sons and the variation tendency of the temperature March, the sounding rocket data and SABER satellite profiles. data show the smallest deviation and a larger correlation a. Temperature distributions at the same height coefficient. The two sets of data for 7 August have the highest correlation, although their temperature de- Twenty-five intact temperature profiles were selected viation is larger. Comparing the five sets of temperature from historical sounding rocket data during 1974–2014, data shows that the deviation and correlation between and the profiles at 20–52 km were used for horizon- the sounding rocket and SABER satellite temperature tal comparison. The distributions of the 25 tempera- data show no obvious pattern. ture profiles at a certain height were not known, so a

FIG. 8. Comparison of sounding rocket and MSIS temperature data statistics in winter: (a) mean deviation and (b) mean standard deviation as a function of height.

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FIG. 9. Comparison of sounding rocket and MSIS temperature data statistics in different sea- sons: (a) mean deviation and (b) mean standard deviation as a function of height. statistical nonparametric test was used to determine the temperature eigenvalue is about 2598C. Similarly, at their population distribution. Subjecting the 25 tem- 40 km the eigenvalue is about 2428C. All the eigen- perature profiles to a one-sample Kolmogorov–Smirnov values for a certain height can be obtained, and they can test (Kar and Mohanty 2004; Hou et al. 2007) showed provide a reference for judging the validity of detection that the values obey the normal distribution at a signif- data and offer a reliable eigenvalue for estimating the icance level a of 0.05. The Kolmogorov–Smirnov test upper atmosphere temperature. results for the 25 temperature profiles at different b. Temperature changes with height in different heights showed that these temperature values were seasons normally distributed at a significance level of a 5 0.5. Furthermore, after the test, the probability density for The sounding rocket data were selected and grouped the temperature values at a certain height at set intervals by season, and then the mean temperature profiles for was calculated, and it was found that the probability each season were obtained. By developing linear re- density distribution of temperature follows the normal gression equations, the least squares method was ap- distribution. Figure 12 gives the probability density plied to fit the mean temperature profiles of each season distribution of the 25 temperature profiles at 20 linearly, and then the characteristics of the temperature and 40 km. changes with height in different seasons were analyzed. The temperature values of the profiles at different Figure 13 shows the linear fitting results of each sea- times obey the normal distribution, indicating that at a son. In each season, temperature changes with height certain height the temperature value levels off to an are roughly linear; the temperature initially increases eigenvalue. Figure 12 shows that at 20 km, the maximum linearly and then decreases linearly with height. At 20– cumulative probability occurs near 2598C, so at 20 km 60 km, there is a clear change in the profiles, although in

FIG. 10. Comparison of sounding rocket and SABER temperature data in 2004 (17 Nov 2004).

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TABLE 2. Detailed comparison between sounding rocket data and TABLE 3. Detailed comparison between sounding rocket data and SABER data in November 2004. SABER data in 2014.

Date in Nov 2004 Emax (8C) E (8C) S (8C) r Date in 2014 Emax (8C) E (8C) S (8C) r 8 15.56 4.19 5.46 0.9562 2 Jan 23.40 6.46 8.31 0.9499 15 14.56 6.29 7.54 0.9064 3 Jan 21.69 5.40 7.26 0.9381 16 21.62 4.19 6.19 0.9104 9 Jan 19.78 6.23 8.37 0.9451 17 10.06 2.76 3.54 0.9817 16 Mar 10.30 3.34 4.53 0.9793 19 16.89 5.01 6.90 0.9448 7 Aug 13.48 7.72 8.26 0.9876

each season the change appears at different heights. This prediction model data and the SABER satellite sound- observation indicates that the height of the stratopause ing data, to analyze the accuracy of the sounding rocket changes with season, and in autumn the stratopause is data. The comparison with MSIS showed differences highest. The statistical properties of the mean temper- between the datasets in every season: summer showed ature profiles suggest that the stratopause height is the minimum difference, followed by winter, and au- 45.5 km in spring, 47.5 km in summer, 53.5 km in au- tumn showed the maximum difference. The SABER tumn, and 48.0 km in winter. data matched the sounding rocket data more closely, Table 4 shows fitted curve equations of the mean although the deviation still showed major differences temperature profiles in each season. Fitted curve 1 is depending on the date and time of the observations. the temperature increase curve, whereas fitted curve 2 COSMIC occultation data have better accuracy and is the temperature decrease curve. By analyzing the vertical resolution, and higher density (Guo et al. 2011; slope of the fitted curves, it was found that below the Kuo et al. 2004). In future work, a comparison of the stratopause, the rate of the temperature increase with sounding rocket temperature data with the COSMIC height in autumn is greater than that in other seasons, occultation data is planned. whereas above the stratopause the rate of tempera- Based on the historical sounding rocket data, the ture decrease with height in spring is greater. The temperature profiles were investigated at different times curve equations corresponding to fitted curves of the for temperature distributions at the same height and mean temperature profiles are empirical equations for temperature changes with height in different sea- describing temperature changes with height in each sons. Temperature data at the same height followed a season and could be used for estimating the temperature normal distribution. At 20–52 km, the temperatures at a given height. tended to an eigenvalue. However, in each season, the temperature changed almost linearly with altitude: first increasing and then decreasing. The inflexion point 5. Summary was the height eigenvalue of the stratopause that In this work, the sounding rocket temperature data corresponded to the point changes with season, and, over Jiuquan were compared with the MSIS empirical importantly, autumn showed the maximum value.

FIG. 11. Comparison of sounding rocket and SABER temperature data in 2014 (16 Mar 2014).

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FIG. 12. Temperature distribution at (left) 20 and (right) 40 km.

Empirical equations were obtained for the temperature Acknowledgments. The work was partly supported by change with altitude based on the linear fitting of the the National Natural Science Foundation of China mean temperature profiles in each season. Further- (Grant 41375028) and the National Natural Science more, below the stratopause the temperature in- Foundation of Jiangsu, China (Grant BK20151446). The creased faster in autumn than in other seasons; above SABER data used in this paper were provided by the the stratopause in spring, the temperature decreased TIMED/SABER team and the MSIS00 data were the fastest. provided by the MSIS00 model. We acknowledge the

FIG. 13. Fitting results for (upper left) spring, (upper right) summer, (lower left) autumn, and (lower right) winter.

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