1 INTRODUCTION

Making measurements of absolute neutral air temperatures near 90 km has always been considered animportant, but notoriously difficult task. The region is too high to reach for balloons; lidars and airglow canobserve temperatures, but they are limited to operation at night and only function with clear skies; Satellites canreturn atmospheric temperature, but can only observe individual locations a few times a day; rockets providethe opportunity to directly measure the atmospheric, but cost and logistics make them impractical for routineobservation(Younger, 2011). Meteor radar presented a potential for mesopause temperature detection. Atpresent the meteor radar is mainly used for the detection of upper atmospheric wind field, as a new detectionmeans of atmospheric temperature, meteor radar has been studied and applied.

When meteoroids enter the earth’s atmosphere, they drastically collide with atmospheric molecules at70~110 km altitude and start to ablate rapidly, leaving cylindrical column of plasma trails called meteor trails.Radio wave reflected by the meteor trails may be received by meteor radar on the ground. Underdense meteortrail echoes present exponential decay rate because of ambipolar diffusion, so the ambipolar diffusion coefficientcan be calculated by decay time(Chen, 2005).

Kaiser(1953)proposed the ambipolar diffusion coefficient is relative to atmospheric temperature and density. Tsutsumi et al.(1994)discussed the relation of ambipolar diffusion coefficient and temperature fluctuations.Jones et al.(1990)have predicted the theoretical formula of the ambipolar diffusion coefficient obtainedby atmospheric temperature and pressure. Based on these theories, Hocking et al.(1997)proposed a newmethod for meteor radar observations of atmospheric temperature, and utilized the CIRA(1986) atmosphericpressure model for inversion of atmospheric temperature. The method has high accuracy requirement on theatmospheric pressure, but in reality atmospheric pressure is rapidly changing with altitude, causing large errors in atmospheric temperature determination. Therefore, Hocking(1999)put forward another new method, whichuses average atmospheric temperature gradient instead of atmospheric pressure, by using least-squares fittingof a polynomial to the logarithm of the inverse decay time as a function of height, and then uses a scale heightanalysis to determine the temperature. Hocking et al.(2002)observed atmospheric temperature tides by thismethod. In order to improve the accuracy of global temperature gradient model, Hocking et al.(2004b)comparedmeteor radar temperatures with other measurement temperatures: rockets, lidars, optical instrumentsat different longitude and latitude and refined the gradient model. The accuracy of meteor radar temperatureshave been improved, in particular some results show that the meteor temperatures can be determinedwithout the need for an empirical correction term, but in some seasons and at some latitudes the errors area little larger. Holdsworth et al.(2006)observed the Antarctic atmospheric temperature near the mesopauseby pressure model(Hocking et al., 1997) and temperature gradient model(Hocking et al., 1999), comparativestudy found that temperature gradient model temperatures have good agreement with the absolute temperaturebut larger fluctuations than the pressure model temperatures, they recommend the use of the pressure modeltechnique at all sites, subject to determination of an appropriate pressure model.

Kunming Observatory Station(25.6°N, 103.8°E)of China Research Institute of Radio Wave Propagation(CRIRP)constructed an atmospheric radar system for observation of low latitude area, through the radar systemwe can obtain the atmospheric parameters of Kunming area(Zhao et al., 2011; Li et al., 2011; Zhao et al., 2011;Ding et al., 2012). The system includes an all sky meteor radar and a ST(Stratosphere Troposphere)radar, twometeor radar operate at 37.5 MHz and 53.1 MHz. In addition to the troposphere and stratosphere observationability, ST radar has an all sky meteor radar observation mode. Using two meteor radars of Kunming station, we carried out a special joint observation experiment for observation of atmospheric temperature during July9–August 8, 2011. In this paper, we utilized the meteor data and the method improved by Hocking usingdifferent temperature gradient to retrieve the atmospheric temperature at 88 km and 85 km over Kunming, and discussed the significance of temperature gradient in Hocking’s method.

2 DATA AND METHOD 2.1 Meteor Radar Data

The two all-sky meteor radars of China Research Institute of Radio Wave Propagation are the same seriesof BPMR(Buckl and Park All-sky Interferometic Meteor Radar)(Holdsworth et al., 2004). Two meteor radarantenna arrays are 500 m apart, they can detect meteor echo in the range of 300 km and in the height of 70~110km. The antenna field consists of a pair of crossed dipoles for transmission and five pairs of crossed dipoles forreception. The main operation parameters of the two all-sky meteor radars at Kunming station are shown inTable 1. We can see from Table 1 that two meteor radars just have difference in operating frequency and peakpower.

The all-sky meteor radar can obtain approximately30000 meteor echoes per day, underdense meteorechoes which can be used for data analysis areapproximately 10000~20000. 37.5 MHz meteor radarobtains more meteor echo than 53.1 MHz meteor radar.Range and angle of arrival are used to determine theheight of meteor, these meteors are mainly distributedin the range of 70~110 km. In this paper, we use meteordata observed by two meteor radar during July9–August 8, 2011(days 190–220). Daily variation of the heights of peak meteor activity is shown in Fig. 1. 37.5MHz meteor radar observed meteor peak height changes in 89~86 km, 53.1 MHz meteor radar observed meteorpeak height changes in 83~86 km.

Figure 2 shows a histogram of the meteor height distribution obtained from 31 days meteor data. As wecan see from Fig. 2, meteor heights are detected in an approximately Gaussian distribution, the height of peakmeteor activity observed by 37.5 MHz meteor radar is 88 km, the height of peak meteor activity observed by53.1 MHz meteor radar is 85 km. This height of peak meteor activity represents the most activity height ofmeteor observed by meteor radar, also is the height we will calculate the temperature.

2.2 MLS Temperature Data

The satellite temperatures are obtained by MLS(Microwave Limb Sounder)on the Aura satellite, AuraMLS looks forward from the spacecraft and samples continuously at all latitudes 80°S~80°N, to detect theglobal atmospheric temperatures(Wang et al., 2011). The observation time of satellite temperature has beenchosen with the same days as meteor radar. The spatial criteria used to select Aura satellite observation siteswere less than 5 degrees of latitude and 10 degrees of longitude from the meteor radar site. According with therequirements, there are more than 6 observation sites data every day. In more than 2/3 of the days, satelliteobserved each site two times per day, and the time difference was 12 hours. The satellite temperatures varied with the diurnal tides, therefore, we can eliminate the tidal component to obtain the daily mean temperatures.But in the rest days, satellite sites only observed once a day, the mean temperatures have a little errors withmean absolute temperatures. The height of satellite temperature is determined by the satellite pressure, herewe can calculate the height by use of the formula of pressure and height(ITU radio communication session, 2005), in which determination of height by pressure may have some errors, but the errors are relatively small.

2.3 Method

The backscattered radio wave amplitude from an underdense trail decreases exponentially with time dueto ambipolar diffusion, it can be expressed as

where λ is the radar wavelength, t is time, D_a is the ambipolar diffusion coefficient, A₀ is the value at t = 0(thetime at which the exponential decay begins). By measuring the half-amplitude decay time τ_1/2 of the meteor signal, it is possible to estimate the parameter D_a,

ambipolar diffusion coefficient in turn depends on the atmospheric temperature and pressure, and Jones et al.(1990)have shown that D_a can be determined as

where T is atmosphere temperature, P is pressure, and K_amb is a constant, which was determined by Chilsonet al.(1996) and Hocking et al.(1997)by experiment. As we can see from Eqs.(2) and (3), if either T orP is known, the other parameter can be deduced. Utilizing the CIRA pressure model, Hocking et al.(1997)determined atmospheric temperature. Actually, the pressure is rapidly changing with altitude, however thetemperature changing with height is relatively small, therefore the pressure must be precise enough to ensurethe accuracy of atmospheric temperature(Hocking, 1999). Hocking proposed a new temperature determinationmethod which does not need the atmospheric pressure, as the following will make a simple introduction of this method.Firstly, assuming the temperature at the height of peak meteor activity region is moderately linear withheight, with a fairly well defined temperature gradient. So we can use T = T₀(1 + αz')to simulate the temperature, where the quantity α can be expressed by α =is the mean temperature gradient.When the height of peak meteor activity is below the mesopause, is negative; but when the height ofpeak meteor activity is above the mesopause, is zero or positive. In the following, we will discuss whetherthe mesopause is above the meteor peak height in Kunming area(low latitudes of the northern hemisphere).By studying the different measurements temperature data in the past, the Eq.(4)gives a generally reasonableestimate of the gradient as a function of latitude and time at the height of peak meteor activity:

where θ is the latitude in degrees, and # is the temporal displacement in number of days from mid-June inthe northern hemisphere(or displacement in days from mid December in the southern hemisphere). As wecan know from Eq.(4), there is a mean temperature gradient of about –1.5 K/km in winter at all latitude, agradient of about –1.5 K/km in the equatorial regions in summer, a tendency to zero or positive gradients atmid-latitude in summer(low mesopause height), and a tendency to very steep negative gradients in the polarregions in summer.

Defining a vertical coordinate which is zero at the height of peak meteor activity, and the atmospherepressure:

where g is the acceleration due to gravity(9.49 m·s^-2 at 90 km altitude), m is the mass of a “typical” atmospheremolecule(28.9 at 90 km altitude), k is Boltzmann’s constant and T is the temperature, P₀ is the atmospherepressure at the height of peak meteor activity. Transforming the Eq.(3), we may write

combining the Eqs.(5) and (6)

and z' = 0, we have(Hocking, 1999)

transforming the Eq.(8), the height of peak meteor activity temperature is(Hocking et al., 2002)

where S_m =is the slope of the graph of z' versus lg(D_a), it can be obtained by least squares linear fit.

2.4 Determination of S_m

Figure 3a shows a scatterplot of height versus the logarithm of the ambipolar diffusion coefficient, thereare 16218 underdense meteors observed by 37.5 MHz meteor radar in August 5, 2011. Despite the scatter, thereis a clear b and of high density extending from the bottom left to top right of the Fig. 3a. Cervera et al.(2000)proposed the existence of some low altitude weak meteor trails, whose decay times are very short and thediffusion coefficients are very large; the ambipolar diffusion of some high altitude meteor trails is suppressedby geomagnetic field, leads to enhanced decay time and smaller diffusion coefficient. Before the meteor dataprocessing, meteor echoes whose heights are too low but the diffusion coefficients are very large(the decaytimes are very short) and the heights are too high but the diffusion coefficients are very small(decay timesare very long)will be removed. The cleaning up of the data was performed in the following manner. First, the meteors with diffusion coefficients <0.1 and >100 were rejected. The scatterplot was then divided into 200equal width vertical strips. The meteors in each strip were binned into 2 km(1.8 km is the meteor radar rangeresolution)height bins, and a Gaussian fit was performed to the resulting histogram. The upper and lower 5%of the meteors were rejected. The remaining data were then divided horizontally into 2 km wide strips, and themeteors in each strip were binned. Again, Gaussian fits to the resulting histograms were performed, and theouter 5% of meteors were rejected. The result of this procedure is shown in Fig. 3b, where only the main b and of meteors now remains.

Greenhow et al.(1955), Tsutsumi et al.(1994)showed that lg(D_a)varies roughly linearly with heightover the height range of ~ 80 ? 100 km, the slope of the least squares linear fit line is S_m = 12.216, and thecorrelation coefficient is ρ = 0.799.

3 RESULT 3.1 Temperatures from Global Temperature Gradient Model

In Fig. 4 the upper graph shows comparison of meteor temperatures determined using global temperaturegradient model and temperatures observed by Aura, the lower graph shows the values of the Aura temperaturesminus meteor temperatures. The 37.5 MHz and 53.1 MHz meteor radar obtain their temperatures, 37.5 MHzmeteor radar obtains the daily temperatures at height of 88 km, 53.1 MHz meteor radar obtains the dailytemperatures at the height of 85 km. The meteor temperatures are lower than Aura temperatures, the temperaturedifferences are ~ 5 ? 40 K, so Hocking(1999)proposed an empirical correction equation for calibration:T_true = 0.774T_meteor+42.8, but this calibration equation is only applicable to high latitudes and can not be usedin low latitudes. We see from the Fig. 4 that Aura temperatures at 85 km are larger than Aura temperaturesat 88 km, this illustrates that temperature decreases with height. In most days 53.1 MHz meteor temperaturesare larger than 37.5 MHz meteor temperatures, and the temperature difference curves of two heights almost coincide, this illustrates that two meteor radars observed their meteor peak height temperatures respectively. Meanwhile, there is a correlation between the meteor temperatures and the satellite temperatures. In thefollowing, the correlation of meteor temperatures and satellite temperatures surves to judge the accuracy ofmeteor radar measurements.

3.2 Temperatures from Satellite Temperature Gradient

Hocking et al.(2004b)utilized temperatures observed by multiple sites meteor radars to compare withvarious types of other temperature determinations including rockets, lidars and OH instruments, these comparisonsare used for obtaining more accurate temperature gradient model. The results show that the accuracy ofrefined temperature gradient model has been improved, but in some seasons and at some latitudes the errorsare a little larger. In this paper, meteor radar temperatures are obtained at low latitudes in summer, howeverthere is no relevant research to discuss whether the temperature gradient model is applicable in this area. Sowe utilize the satellite temperatures to obtain accurate temperature gradients directly, and then determine thetemperatures through the method in Section 2.3, and analyze the applicability of temperature gradient modelin Kunming area.

Because the Aura satellite observations of atmospheric temperature are only for particular heights, theheights which close to the height of peak meteor activity are 79 km, 85 km, 88 km, 92 km, 96 km, so we chose fourheight intervals, 79~85 km, 85~88 km, 88~92 km, and 92~96 km to calculate temperature gradients, and thesatellite temperature gradients in the four height intervals are shown in Fig. 5. Fig. 5 shows that the temperaturegradients in three intervals of 79~85 km, 85~88 km, 88~92 km are non positive, whereas in the region of 79~92km the temperature decreases with height, but the temperature gradient in 92~96 km is positive, this showsthat the mesopause may be at 92~96 km and above the meteor peak height in Kunming area. This provedthat assuming the meteor peak height region temperature varying linearly with height is suitable. We use threetemperature gradients of 79~85 km, 85~88 km, and 88~92 km to determine temperature.

Figure 6a shows the correlation between meteor temperatures determined using 79~85 km temperaturegradients and Aura temperatures is very good, the temperature difference △T is 5~40 K and variation isrelatively stable. Fig. 6b shows the correlation between meteor temperatures determined using 85~88 kmtemperature gradients and Aura temperature is poor, the temperature difference △T is 0~60 K and variationis relatively large. Fig. 6c shows the correlation between meteor temperatures determined using 88~92 kmtemperature gradients and Aura temperature is very poor, the temperature difference △T is 0~80 K and thevariation is very large. Comparative result shows that 79~85 km temperature gradients are more suitable fortemperature determination.

Figure 6a shows that two meteor radars observed their meteor peak height temperatures respectively, and in most days two meteor radar observations have height resolution obviously, but in some days observations areambiguous in height.

4 DISCUSSION

The above result is based on the method improved by Hocking using different temperature gradients for retrieval of atmospheric temperature at 88 km and 85 km over Kunming. Comparison with the Aura satellitetemperature data shows that two separate meteor radars can observe the variation of daily temperatures.

Table 2 shows the correlation analysis of temperature determination using different temperature gradients.Meteor temperatures determined using different temperature gradients are different. The correlation coefficientbetween meteor temperatures and Aura temperatures are 0.538 and 0.459 when using temperature gradientmodel, there is a certain correlation, but not very good.

Figure 7 shows that the model temperature gradient is around –1.3 K/km at low latitude in summer, and the daily variation is very little. However the 79~85 km satellite temperature gradients change in 1~–4K/km, and daily variation is large. Because the gradient model is based in large part on the atmospheric modelpresented by Fleming et al.(1988), it is not sufficient for accurate observation of temperatures at low latitudes(Hocking et al., 2004b).

In order to obtain more accurate temperature gradients, we used the satellite temperatures directly. First, we analyzed whether the mesopause is above the height of peak meteor activity in Kunming area, as themesopause height at low latitude has not been researched. The Fleming model suggests that the mesopauseheight at Arctic latitudes in summer should be around 91~92 km altitude, but more experimental studies showa value closer to 87~88 km. Fig. 5 shows the mesopause height in Kunming area may be 92~96 km. It is veryimportant to make sure that mesopause height is above the height of peak meteor activity in Kunming area.

Then we selected different temperature gradients to determine meteor temperatures, Table 2 shows thatthe meteor radar temperatures from 79~85 km temperature gradient have very good correlation with satelliteobserved temperatures, and the correlation coefficients are 0.827 and 0.719. However using other satellitetemperature gradients, the temperature correlations are very poor. Comparison found that 79~85 km temperaturegradients are much more suitable for the meteor radar observation of temperature. It is concluded thatthe accurate temperature gradient is very important in Hocking’s method. Why only 79~85 km temperaturegradients are more suitable, we will further study this issue.

In this paper, the meteor radar temperatures are lower than satellite temperatures, the reasons may be asfollows. First, the estimated Sm value is too small, as can be seen from Eq.(9), Sm values are directly relatedwith meteor temperatures. We use Cervera’s method to reject meteor data, but the estimated slope of theleast squares linear fit line is somehow too small; second, different meteor radar observations will be different, including meteor echo decay time, ambipolar diffusion coefficient, angle of arrival, etc. Before observation oftemperatures, we did not calibrate and correct for meteor radars, this could cause the temperature smaller thanabsolute temperature. Table 3 shows the calibration equations for meteor temperatures.

It is the first time to use two different frequencie meteor radars for observation of atmospheric temperaturein the same area.

In this paper, the results show that the temperature gradient method is suitable for Kunming meteorradars, two separate meteor radars can measure correct atmospheric temperature at the height of peak meteoractivity.

In order to further improve the temperature observation, there are still some follow up works to do in thefuture. First, much more measured temperatures at low latitudes will be collected, such as lidar, SABER satelliteetc.(Li et al., 2012). These temperatures can be used to create temperature gradient for low latitudes area.Second, determination of S_m will be reconsidered to improve the accuracy of temperature observation. Hocking(2004a)analyzed the system error to improve temperature determination, Younger et al.(2008)proposed thathigh power echoes are significantly less affected by absorption from atmospheric aerosols, selection of high powerechoes will be more accurate. These studies will provide good ideas for our future meteor radar observation ofatmospheric temperature.

5 CONCLUSIONS

In this paper, using the data collected by China Research Institute of RadioWave Propagation(CRIRP)allskymeteor radar with two different operating frequencies at Kunming station(25.6°N, 103.8°E)during July 23to August 8, 2011, we determined the mesopause above the height of peak meteor activity, based on the methodimproved by Hocking with different temperature gradient retrieval of atmospheric temperatures at 88 km and 85km over Kunming. Comparison with the Aura satellite temperature data shows that two separate meteor radarscan measure correct atmospheric temperature at the height of peak meteor activity, however the correlationbetween temperature determined by meteor radar using temperature gradient model and satellite temperatureis not good. While the temperature determined by meteor radar using satellite temperature gradient have goodcorrelation with satellite temperature. It is concluded that the accurate temperature gradient is very importantin Hocking’s method.

The authors thank two anonymous reviewers for their valuable advice. This work was supported by theNational Natural Science Foundation of China(61167006).