Antarctic mesospheric temperature estimation using the Davis ...

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, D05108, doi:10.1029/2005JD006589, 2006

Antarctic mesospheric temperature estimation using the Davis mesosphere-stratosphere-troposphere radar David A. Holdsworth,1,2,3 Ray J. Morris,1 Damian J. Murphy,1 Iain M. Reid,3 Gary B. Burns,1 and W. John R. French1 Received 14 August 2005; revised 17 October 2005; accepted 17 November 2005; published 15 March 2006.

[1] This paper presents the first Antarctic meteor radar temperature estimates. These

temperatures have been derived from meteor diffusion coefficients using two techniques: pressure model and temperature gradient model. The temperatures are compared with a temperature model derived using colocated OH spectrometer measurements and Northern Hemisphere rocket observations. Pressure model temperatures derived using rocketderived pressures show good agreement with the temperature model, while those derived using Mass Spectrometer and Incoherent Scatter (MSIS) and CIRA model pressures show good agreement in winter but poor agreement in summer. This confirms previous studies suggesting the unreliability of high-latitude CIRA pressures. The temperature gradient model temperatures show good agreement with the temperature model but show larger fluctuations than the pressure model temperatures. Meteor temperature estimates made during the Southern delta-Aquarids meteor shower are shown to be biased, suggesting that care should be taken in applying meteor temperature estimation during meteor showers. On the basis of our results we recommend the use of the pressure model technique at all sites, subject to determination of an appropriate pressure model. Citation: Holdsworth, D. A., R. J. Morris, D. J. Murphy, I. M. Reid, G. B. Burns, and W. J. R. French (2006), Antarctic mesospheric temperature estimation using the Davis mesosphere-stratosphere-troposphere radar, J. Geophys. Res., 111, D05108, doi:10.1029/2005JD006589.

1. Introduction [2] Radar techniques have been used for meteor observations for over 50 years. The earliest observations were predominantly for astronomical purposes, such as meteor shower studies and meteoroid velocity estimation [e.g., Elford, 2001]. Atmospheric observations were made later by measuring the radial drift velocity of the ionized trail for investigation of mesospheric and lower thermospheric dynamics [e.g., Robertson et al., 1953] and by measuring the decay times for investigation of diffusion [e.g., Greenhow and Neufeld, 1955]. The decay time t of an underdense meteor echo is typically defined as the time for the echo amplitude to decay by a factor of e
1, and is given by [e.g., McKinley, 1961] t¼

l2 ; 16p2 D

ð1Þ

where T is temperature, P is pressure, and K0 is the zero field mobility factor. In recent years, measurements of ambipolar diffusion coefficients have been used for pffiffiffi estimating T/ P [e.g., Chilson et al., 1996; Hocking et al., 1997; Cervera and Reid, 2000]. This technique has also been extended for measuring absolute temperature using a pressure model [e.g., Neilsen et al., 2001; Hall et al., 2004] and measuring pressures using a temperature model [e.g., Hocking et al., 1997]. Making little effort to estimate correct temperatures from meteor diffusion coefficients alone, Hall et al. [2004] used a pressure model to produce temperature estimates Tmet requiring recalibration using T = 1.9 Tmet – 263 to obtain agreement with colocated OH and potassium lidar temperature measurements. [3] An alternative technique for estimating absolute temperature requires use of a temperature gradient model [e.g., Hocking, 1999]. This temperature estimate is given by

where l is the radar wavelength, and D is the ambipolar diffusion coefficient. The ambipolar diffusion coefficient is given by [e.g., Cervera and Reid, 2000]
2

D ¼ 6:39  10

K0 T 2 ; P

1

ð2Þ

Australian Antarctic Division, Kingston, Tasmania, Australia. ATRAD Pty Ltd., Thebarton, South Australia, Australia. 3 Department of Physics, University of Adelaide, Adelaide, South Australia, Australia. 2

Copyright 2006 by the American Geophysical Union. 0148-0227/06/2005JD006589

T ¼S

  mg dT þ2 log10 e k dz

ð3Þ

where S is the slope estimated from the scatterplot of d = log10 D versus height, dT/dz is the temperature gradient, m is the mass of a typical atmospheric particle, g is the acceleration due to gravity, and k is Boltzmann’s constant. The initial implementation of the technique produced temperature estimates Tmet requiring recalibration using T = 0.774 Tmet + 42.8 to obtain agreement with OH spectrometer and lidar measurements made at similar latitudes, and with rocketderived climatologies. Later versions of this technique [e.g., Hocking et al., 2004; Singer et al., 2004] used a revised

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Table 1. Davis MST Radar Operating Parameters for Meteor Observations Parameter

Value

Frequency, MHz PRF, Hz Transmit pulse HPFW, km Receiver filter width, kHz Pulse type Range, km Range sampling resolution, km Coherent integrations Effective sampling time, s Number of samples Acquisition length, s

55 1960 2 20.1 Gaussian 6 – 68 1 16 0.008 6700 55

gradient model obviating the need for recalibration. The revised gradient model was determined by minimizing the temperature differences between meteor and alternative temperature measurements for several sites to derive a smoothly varying latitude-time model. [4] Although estimation of meteor temperatures using the pressure and temperature gradient model techniques is becoming more common, no comparison of these techniques or assessment of their relative strengths and weaknesses have been made in the literature to date. In this paper we apply both techniques to meteor decay times measured using the Davis (68.6S, 78.0E) mesosphere-stratospheretroposphere (MST) radar. The radar and its meteor observations are described briefly in section 2. In section 3 we determine appropriate pressure and temperature models for the application of the meteor temperature estimation techniques. Section 4 presents the results obtained using the meteor temperature estimation techniques and analyzes possible causes of discrepancies between the meteor and model temperatures. Section 5 discusses possible alternative temperature techniques. Section 6 presents a discussion of the results, and section 7 presents the summary and conclusions. In presenting these results we acknowledge there are potential biases in the estimation of meteor diffusion coefficients, such as magnetic field effects [e.g., Robson, 2001; Dyrud et al., 2001]. A number of potential limitations are currently being investigated using data from a number of

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meteor radars, including the Davis MST radar, and are the subject of a paper currently in preparation.

2. Davis MST Radar [5] The Davis MST radar [e.g., Morris et al., 2004] operates at 55 MHz, with a peak power of 100 kW. The radar can be operated in two modes. In ‘‘main array’’ mode, transmission and reception is performed using a 144-element antenna array. In ‘‘meteor’’ mode, transmission is performed using a peak power of 7.2 kW feeding a pair of two-element gamma-matched crossed dipole antennas aligned along azimuths of 45 and 135. Reception is performed using five two-element linear folded dipoles aligned along an azimuth of 45, located along two perpendicular arms with spacings of 2 l and 2.5l, yielding unambiguous meteor angle of arrival (AOA) while minimizing mutual antenna coupling [e.g., Jones et al., 1998]. The radar operating parameters are shown in Table 1. Further information describing meteor observations is provided by Reid et al. [2006]. The radar has been calibrated using a delay line, and the ranges have been confirmed to be correct to within 200 m. [6] The online analysis applies criteria to determine whether the behavior of a meteor echo candidate is consistent with that expected of an underdense meteor echo [e.g., Holdsworth et al., 2004a]. The receiver time series outputs are corrected for any known phase offsets in the paths (antenna, feeder cable, and receivers) of each receiving channel [e.g., Holdsworth et al., 2004b]. The decay time, t, is determined by fitting an exponential to the combined receiver power time series from 15 ms after the meteor echo peak, to the first sample below the noise level. The fit start time avoids inclusion of any effects associated with Fresnel oscillations in the fit [e.g., Cervera and Reid, 2000]. [7] The peak height and e-1 half width of the meteor height distribution (hereafter ‘‘peak height’’ and ‘‘height width,’’ sh, respectively) for the Davis MST radar are shown in Figure 1, with the results of a harmonic fit with annual, semiannual, terannual and quadriannual components. These results reveal a significant annual variation, and significant day-to-day variation. The peak height varies

Figure 1. Annual variation of (a) peak and (b) width of the meteor height distribution for 2003 (diamonds), 2004 (crosses), and 2005 (plus signs). The grey lines indicate the values estimated using a harmonic fit with annual, semiannual, terannual, and quadriannual components. 2 of 13

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between 85 km in winter and 88 km in summer, while the height width varies from 3.5 km in summer to 5 km in winter. These observations agree qualitatively with those from a similar latitude in the Northern Hemisphere, Andenes (69.3N), Norway [e.g., Singer et al., 2004], although the peak height variation is larger than that observed by those authors (90 – 92 km). [8] In addition to the Davis MST radar, a colocated 33.2 MHz meteor radar was installed in January 2005. This radar uses the same analysis and a similar antenna configuration to the 55 MHz system. Although references to the 33.2 MHz results are made in the following sections, no results are presented. Results will be presented in subsequent publications once a more extensive data set has been collected.

3. Pressure and Temperature Models [9] Before consideration of pressure and temperature models it is appropriate to note some subtle differences between the two techniques. The temperature gradient technique provides the meteor-height-distribution-weighted temperature [e.g., Hocking et al., 2004], while the pressure model technique can theoretically determine temperatures at any height within the meteor height distribution, subject to having a suitable pressure model and sufficient meteor echoes to provide an accurate estimate of the mean diffusion coefficient at the selected height. However, height and diffusion coefficient errors, and geophysical variations in the diffusion coefficient estimates can bias the mean diffusion coefficient estimated at a particular height [e.g., Hocking et al., 1997]. This bias is minimized at the peak height. In order to best compare the techniques we calculate the pressure model temperature at the peak height. In accordance with this, we determine our pressure model assuming the peak height variation given by the harmonic fit to the peak heights illustrated in Figure 1. Likewise, we determine our temperature gradient using a weighted linear fit assuming a height distribution given by the harmonic fit to the peak heights and height widths illustrated in Figure 1. We also derive a temperature model for comparison with the resulting meteor temperatures. [10] The determination of meteor temperature estimates at the peak height is in contrast to most studies to date, which have assumed the temperatures derived from the peak height are relevant to the mean annual peak height [e.g., Hocking et al., 2004; Hall et al., 2004] and have therefore used temperature gradient and pressure models appropriate to a mean annual peak height. For temperature gradient model temperatures, this has been due to the fact that the meteor-height-distribution-weighted temperature gradients show only a small variation with height [e.g., Hocking et al., 2004]. The Davis peak heights shown in Figure 1 vary by 3 km throughout the year, which is almost equivalent to the scale height in summer. The fact that pressure can vary significantly over this height range provides further justification for the estimation of pressure model temperatures at the peak height. [11] In developing our pressure, temperature and temperature gradient models, we use colocated measurements as our first preference, and measurements from similar and

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conjugate latitudes as our second preference. Colocated hydroxyl airglow rotational temperatures are available from the Davis OH spectrometer [e.g., Burns et al., 2002] between mid-February and mid-October. These temperatures have been assumed to relate to a height of 87 km [e.g., Baker and Stair, 1988]. Temperatures outside the midFebruary and mid-October period are derived from rocket based climatologies derived at conjugate latitudes in the Northern Hemisphere [e.g., Lu¨bken and von Zahn, 1991; Lu¨bken, 1999]. This climatology is used despite the availability of Southern Hemisphere rocket measurements from Rothera (68S, 68W) [e.g., Lu¨bken et al., 1999]. We use the Northern Hemisphere climatology since it agrees well with the Rothera temperatures, except in late February, where it appears that the Rothera temperatures increase more rapidly. Further, the Northern Hemisphere climatology is derived using several years of data, while the Rothera temperatures are obtained over one summer, and may not be representative of the long-term mean summer temperatures. Temperature gradients models are derived from the Northern Hemisphere rocket based climatologies, and from the Syowa lidar (69S, 39E) [e.g., Kawahara et al., 2002]. Pressures are derived from the Northern Hemisphere rocket based climatologies. For comparative purposes, model pressures are also derived using ‘‘COSPAR International Reference Atmosphere’’ (CIRA 86) [Fleming et al., 1990] and ‘‘Mass Spectrometer and Incoherent Scatter’’ (MSIS90) [Hedin, 1991] models. [12] In developing our temperature model, we have first determined a temperature model for 87 km using the 2003 Davis OH spectrometer measurements and the Northern Hemisphere rocket climatology. Figure 2a reveals a smooth extrapolation from the spectrometer measurements (plus signs) to the rocket measurements (dot-dashed line) in mid-October. This allows us to derive our model using a fourth-order polynomial fit to the spectrometer measurements from mid-March to mid-October, and the rocket climatology from mid-October to mid-January. However, extrapolation from the rocket climatology to the spectrometer measurements in mid-February is difficult because of a 15 K difference between the estimates. This is consistent with rocket observations suggesting that the temperature increase at the end of summer is more rapid in the Southern Hemisphere than the Northern Hemisphere [e.g., Lu¨bken et al., 1999]. Since the Southern Hemisphere polar mesosphere summer echo (PMSE) season ends earlier than the Northern Hemisphere [e.g., Morris et al., 2006], it is also consistent with the hypothesis that PMSEs are related to cold temperatures. However, since the earliest spectrometer measurements are made for only a few hours a day at this time of year, it is possible there is a tidal bias in the temperature measurements [e.g., Burns et al., 2002]. In formulating our model we therefore make an adjustment to the rocket temperature climatology to better fit the spectrometer measurements. However, rather than extrapolating the rocket temperatures smoothly to the spectrometer temperatures we allow for the possibility of tidal biases by applying an arbitrarily selected 4:1 weighting factor in favor of the spectrometer measurements. The uncertainty in combining the spectrometer and rocket temperatures suggests the mid-February to mid-March temperatures represents the period of least certainty in our model.

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Figure 2. (a) Estimation of temperature model: Davis OH spectrometer temperatures (plus signs), meteor-height-distribution-weighted MSIS temperatures (solid line), meteor-height-distributionweighted CIRA temperatures (diamonds), meteor-height-distribution-weighted Syowa lidar temperatures [Kawahara et al., 2002] (squares), meteor-height-distribution-weighted temperatures using Northern Hemisphere rocket climatologies of Lu¨bken and von Zahn [1991] (triangles) and Lu¨bken [1999] (dashdotted line), and the resulting temperature model (thick dashed line). (b) Estimation of temperature gradient model: meteor-height-distribution-weighted MSIS temperatures (solid line), meteor-heightdistribution-weighted Syowa lidar temperatures [e.g., Kawahara et al., 2002] (squares), meteor-heightdistribution-weighted temperatures using Northern Hemisphere rocket climatologies of Lu¨bken [1999] (dash-dotted line) and Lu¨bken and von Zahn [1991] (triangles), temperature gradient models at 90 km for 69N from Hocking [1999] (dot-dot-dot-dashed line) and Hocking et al. [2004] (long-dashed line), and the resulting model temperature estimate (thick dashed line). [13] Figure 2b illustrates the determination of the temperature gradient model. The gradients are first determined using a weighted linear fit assuming a height distribution given by the harmonic fit to the peak heights and height widths. The gradient model was then determined by applying a harmonic fit with annual, semiannual and terannual components, with the rocket climatology and Syowa lidar estimates given equal weighting. The resulting model shows a maximum in summer and a minimum in winter, with a

weak maximum at the end of August owing to the considerably larger Syowa lidar gradients in August and September. These gradients are also used to determine the temperature difference between 87 km and the fitted peak height in order to determine the temperature model at the peak height. [14] Figure 3 illustrates the determination of the pressure model from the Northern Hemisphere rocket climatology. Also shown are the CIRA and MSIS pressures estimated at

Figure 3. (a) CIRA pressures at 85 km (dotted line) and 88 km (dash-dotted line), and MSIS pressures at 85 km (long-dashed line) and 88 km (short-dashed line). (b) Estimation of pressure model at the peak height (thick solid line) using the 69 N rocket climatologies of Lu¨bken and von Zahn [1991] (squares) and Lu¨bken [1999] (diamonds). Also shown are CIRA (thin solid line) and MSIS (dot-dashed line) pressures at the peak height. 4 of 13

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Figure 4. (a) Slope and (b) correlation obtained from log diffusion coefficient versus height plots. The diamonds indicate results obtained using all zenith angles within ±5 of the value indicated by the abscissa. The squares indicate the values obtained using all zenith angles within the value indicated by the abscissa. The dashed line indicates the values obtained using all zenith angles between zero and 60 degrees. The dotted line indicates the values obtained using all zenith angles.

the peak height, and at 85 and 88 km, corresponding to the peak heights in winter and summer, respectively. The CIRA and 85 km MSIS pressures show an annual variation minimizing in winter and maximizing in summer. In contrast, the 88 km MSIS pressure reveals a semiannual variation, minimizing in winter and summer. The summer minimum is thus evident in the MSIS-derived model but not in the CIRA-derived model. The MSIS-derived model shows significantly better agreement with the rocketderived model than the CIRA-derived model.

4. Results [15] Before applying the techniques, it is necessary to consider how many meteors, or days of data, are required to determine a reliable temperature estimate. With this in mind, we define the ‘‘variation percentage’’ B¼

200jTiþ1
Ti j ; i ¼ 1; ::; N
1 Tiþ1 þ Ti

ð4Þ

where Ti is the ith temperature estimate, and N is the number of temperature estimates. This parameter attempts to provide an estimate of the percentage variation due solely to measurement errors. On the basis of temperature estimates made using different numbers of days of data, we found the variation percentage decreased significantly when between one and four days of data was used, before flattening off. We therefore make temperature measurements using five day data intervals. The number of meteor observations and the resulting count rates vary throughout the year [e.g., Reid et al., 2006], with between 2000 (summer) and 8000 (winter) meteors being used for each temperature estimate. 4.1. Temperature Gradient Model Temperatures [16] The temperature gradient technique requires estimation of the slope of the scatterplot of the log of the diffusion coefficient versus height (hereafter d versus h). In order to improve the accuracy of the slope estimate it is necessary to

remove unrepresentative data, such as outliers and biased values. Hocking [2004] shows that the slope is almost independent of zenith angle, while the d versus h correlation rdh decreases with increasing zenith angles. The former result is in contrast with the current observations as shown in Figure 4, derived using a linear fit with d as the independent variable. These results show that the slope decreases rapidly with increasing zenith angles above 60. We believe this is due to the use of height estimates derived using AOA estimates with large measurement errors, since the accuracy of AOA estimates reduces substantially at large zenith angles. However, it is not clear why this should affect our data set, and not that presented by Hocking [2004]. Figure 4 reveals the inclusion of echoes with zenith angles beyond 60 reduces the slope by approximately 8%, which would lead to a comparable temperature underestimate. We therefore limit our slope estimation to echoes with zenith angles below 60. This reduces the number of echoes used by about 30% but is necessary in order to improve the accuracy of our slope estimates. Additionally, we preclude any data with d <
0.5 and d > 1, and with heights above 95 km. The latter criterion is used to minimize possible biases due to magnetic field effects [e.g., Robson, 2001]. Further, we calculate the mean and standard deviation of the echo heights at intervals of d = 0.1. Any echoes whose heights lie outside the mean and 2.5 times the standard deviation at each d are precluded from the fit. These additional checks reduce the total number of echoes precluded from the fit to approximately 35% of the original number. [17] Figure 5a shows a typical d versus h scatterplot and the slopes obtained using height (Sh) and d (Sd) as independent variables. In estimating the variation of d versus height, Hocking et al. [1997] used a fifth-order polynomial fit with d as their independent variable. The resulting fit was then adjusted using pffiffiffi ‘‘bias correction,’’ as described below. They found T/ P estimates in better agreement with the literature when d was used as the independent variable. Hocking [1999] also used d as their independent variable, using a linear fit with bias correction. This technique has

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Figure 5. (a) Scatterplot of log diffusion coefficient d as a function of height for 5 April 2004 to 9 April 2004. The circles indicate the values used in the fit, while the plus signs indicate values precluded from the fit by the outlier rejection (see text for details). The lines indicate linear fits using d (dashed line) and height (long-dashed line) as the independent variables, model estimate using pressure, temperature, and temperature gradient models (dotted line), and linear fit using the statistical comparison technique (solid line). (b) Relationship between slope and errors in d (ed) and height (eh) determined using the statistical comparison technique. The dotted lines indicate the determination of the slope using (sd = 0.14). also been adopted for other studies using the temperature gradient technique [e.g., Hocking et al., 2004; Singer et al., 2003, 2004]. The justification for Hocking et al. [1997] using d as their independent variable was that the measurement errors in d are smaller than those in height. While this is true, the major source of variation in d is geophysical [e.g., Hocking, 2004], and this variation should be recognized in determining the optimal fitting procedure. Having said this, we note that temperature gradient model temperatures derived using Sd show much better agreement with our temperature model than those using Sh. [18] The need for bias correction has been justified in terms of height estimation errors, which result from range and AOA errors. The end result of applying bias correction is that meteor height estimates below (above) the peak height are corrected to lower (higher) heights. Hocking [1999] notes that applying bias corrections ‘‘steepens the slope by typically 10% to 20%.’’ However, the direction of this correction is opposite to that expected solely because of height errors. The effect of height errors is to smear the expected height distribution, such that the height estimates of echoes below (above) the peak height are biased toward lower (higher) heights. Such smearing is evident in comparisons between Davis meteor radar winds when compared with MF radar winds [e.g., Reid et al., 2006]. In this regard, any technique used to counteract height errors should result in echoes below (above) the peak height being corrected to higher (lower) heights. [19] In order to avoid the use of bias correction we use the statistical comparison technique (SCT) of Hocking et al. [2001], which incorporates d and height variations into the fit. This technique compares two normally distributed independent measurements, x and y, without a priori knowledge of the measurement errors ex and ey, other than the assumption the measurement errors are normally distributed. The technique allows for the determination of the relative magnitude (or gain) of two parameters and their measurement errors. The gain can only uniquely be deter-

mined if estimates of the measurement errors are known. The observed measurement errors contain the measurement errors specific to each measurement, and also a component related to the differences in the two measurements. For instance, for comparison of all-sky meteor and MF radar velocities the measurement error contains a component relating to the different fields of view used by two radars. The technique has been used in the current study to determine the relative magnitude (or slope of the best fit line) of d versus h, on the basis of assumed errors in d (ed) and h (eh). An example of the application of this technique is illustrated in Figure 5b. For estimation of our slopes (SSCT) we have used the values corresponding to ed = 0.14. This value was selected for several reasons. First, it was derived from the results of a simple model of height and d similar to that described by Hocking [2004]. Second, it corresponds well with the value (0.136) obtained on the basis of the estimated variations in T (D T/T = 0.08) and K0 (D K0/K0 = 0.27) derived by Hocking [2004]. Third, the resulting slope shows good agreement with the expected slope based on our temperature, temperature gradient, and revised pressure models, as illustrated in Figure 5a. Last, the resulting annual slope variation is most similar to that expected on the basis of our model temperature, and temperature gradients. Effectively, the SCT encompasses the least squares fit and ‘‘bias correction,’’ but in our opinion does so in a more rigorous manner. The mean of the ratio of SSCT and Sd is 1.36, which is significantly larger than the 10 – 20% correction to Sd resulting from bias correction reported by Hocking [1999]. Although the Davis meteor height and d distributions are normally distributed, the d distribution has a slight positive skew. Thus the assumption that the parameters used in the SCT are normally distributed is not strictly met. Despite this, the SCT appears to achieve our objectives. [20] Figure 6 illustrates the temperature estimates, revealing good agreement with the temperature model. Most temperature estimates are within 10 K of the model tem-

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Figure 6. Temperatures estimated using the temperature gradient model technique (plus signs). The solid line represents the temperature model.

perature. The most noticeable discrepancies occur in late July, where the estimated temperatures show a sudden fall of 30 K, and in late October 2004 where the meteor temperatures remain at typical winter values of around 200 K while the model temperatures have started their descent toward cooler summer temperatures. These discrepancies will be analyzed in more detail later. The correlation between the estimated and model temperatures, calibration equations and variation percentage for temperature gradient temperatures are shown in Table 2. 4.2. Pressure Model Temperatures [21] The pressure model technique requires an estimate of the mean diffusion coefficient at the peak height. Since d is almost Gaussianly distributed, we first determine the mean d and standard deviation sd. We then exclude values outside d ± 2.5sd, and repeat recalculation of d and sd and excluding values outside d ± 2.5sd until there are no further  ¼ 10d is then used as the values left to exclude. The value D estimate of the mean diffusion coefficient at the peak height, which is substituted into equation (2) with the model pressure to yield the temperature estimate. As for the temperature gradient technique, only meteor echoes with zenith angles below 60 are used. A zero field mobility factor of 2.4  10
4m2V
1s
1 is assumed in accordance with Cervera and Reid [2000]. [22] The temperatures estimated using the rocket-derived pressure model are shown in Figure 7a, revealing good agreement with the temperature model. Most temperature estimates are within 10 K of the model temperature. There is some underestimation in January, and between March and May in all years. There is some overestimation in late July, corresponding to the time of underestimation of the temperature gradient model temperatures. The temperatures estimated using MSIS and CIRA pressure models are shown in Figure 7b. The MSIS-derived temperatures show reasonable agreement with the temperature model, showing similar descent into colder summer temperatures. The

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winter (summer) temperatures are approximately 10 K smaller (larger) than the model temperature. The CIRAderived temperatures show reasonable agreement during winter but only a 20 K descent into summer. The overestimation of the CIRA-derived summer temperatures results from the summer maximum of the CIRA pressures. This is in contrast to the rocket and MSIS pressure models, which exhibit semiannual variations with minima in winter and summer. Similar semiannual variation was observed in pressures derived using meteor decay times and lidar temperature estimates at 43N [e.g., Hocking et al., 1997], indicating the CIRA pressures are unreliable at this latitude. Anomalies in high-latitude CIRA pressure values have also been noted by Hocking [1999]. The correlation between the estimated and model temperatures, calibration equations and variation percentage for the three pressure model temperature estimates are shown in Table 2. The correlation and calibration equations confirm the quality of the rocketderived measurements. The rocket- and MSIS-derived temperatures show significantly smaller calibration corrections than those required by Hall et al. [2004] to obtain agreement between pressure model meteor temperatures derived using the MSIS model and optical temperatures. 4.3. Temperature Discrepancies [23] The temperature gradient temperatures of Figure 6 show a sharp decrease in late July, while the pressure temperature estimates of Figure 7 show an small increase. This date corresponds to the activity period of the Southern delta –Aquarids meteor shower (SDA, right ascension 339, declination
16), which is active from 12 July to 19 August, peaking 28 July. Radiant mapping [e.g., Morton and Jones, 1982] reveals SDA echoes are identified in all years from 20 July to 12 August, with a maximum count rate of approximately 500 on 27 July [e.g., Reid et al., 2006]. [24] Radiant mapping has been used to separate SDA and sporadic meteors collected between 25 July and 29 July 2003 to determine the effect of SDA meteors on the temperature estimation. This was achieved by accepting any meteor producing a right ascension and declination candidate within ±1 and ±2, respectively, of the accepted value. The resulting SDA data set peaks at a larger height and have larger diffusion coefficients than the sporadic meteors. This is best summarized by Figure 8, which shows the difference in number density of meteors echoes obtained prior to (15 – 19 July 2003) and during (25 – 29 July 2003) the peak activity period of the 2003 SDA shower. Negative values indicate the d versus h values of likely SDA meteors. The lines show the linear fits to the pre-SDA and duringSDA data. The symbols indicate the mean position of positive (P+, diamond) and negative (P
, squares) differ-

Table 2. Correlation, Calibration Equations, and Variation Percentage for the Meteor Temperature Estimates Model

Correlation

Calibration Equation

Variation Percentage, %

Temperature gradient Rocket pressure MSIS pressure CIRA pressure

0.91 0.93 0.89 0.59

0.96 Tmet + 4.21 0.94 Tmet + 13.95 1.28 Tmet
52.60 1.53 Tmet
109.7

4.60 3.38 3.20 3.20

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Figure 7. Temperatures estimated using the pressure model technique using (a) pressure model derived using the 69 N rocket climatologies of Lu¨bken and von Zahn [1991] and Lu¨bken [1999] (squares) and (b) MSIS (squares) and CIRA (plus signs) pressure models. The solid line shows the temperature model.

ences, and the mean values of d and h for the pre-SDA (Pmean, triangle) and during-SDA (cross) data. If there were no differences in the d versus h relationship of the pre-SDA and during-SDA data then P+ P
Pmean. However, P
is displaced toward a larger height and d, which we attribute to the presence of SDA meteors. Additionally, P+ is slightly displaced toward a smaller height and d, which we attribute to a reduction in atmospheric temperature. The displacement of P+ (P
) above (below) the pre-SDA linear fit would be expected to reduce the slope to the during-SDA data, and this is the case. This slope reduction causes the reduction in the temperature gradient temperatures. Further, the larger heights and diffusion coefficients result in a larger estimate of the mean diffusion coefficient at the peak height, causing an increase in the pressure temperatures. Figure 8 suggests that these effects are primarily the result of the additional SDA meteors. [25] In order to investigate this further, we have performed preliminary analysis of the diffusion coefficients and temperatures estimated using the colocated 33.2 MHz meteor radar. For the 33.2 MHz results, the d – h variation of the SDA meteors does not differ significantly from those of the sporadic meteors. Although the 33.2 MHz temperature gradient temperatures show a dip commencing at the start of July, there is no evidence of a sharp dip around the peak of the SDA shower. We therefore believe the dip in the 55 MHz temperatures is the result of a frequencydependent height ceiling effect [e.g., Steel and Elford, 1991]. At 55 MHz, SDAs echoes are observed at larger heights and with larger diffusion coefficients than sporadic meteors, leading to a reduction in the d – h slope, and a reduction in the temperature gradient temperatures. On the other hand, at 33.2 MHz, where the height ceiling is raised and echoes with larger diffusion coefficients are detected, the heights and diffusion coefficients of the SDA echoes lie within those of the sporadic meteors, and the SDA meteors do not bias the slope or temperature estimate. [26] In contrast to the July discrepancy, there appears no obvious explanation for the large October 2004 temperature gradient temperatures. Comparison of the d versus h scatterplots (not shown) suggests there is a

significant difference in the d versus h relationship, and that the temperature anomaly is not the result of a poor linear fit to the data. Figure 1 reveals a large variation in the peak heights and height widths in late October/early November 2003, which corresponds with a period of solar flare activity. It could therefore be argued that the late October/early November 2003 temperatures are actually anomalous, and that the anomaly in October 2004 is due to errors in the assumed temperature gradient. However, the temperature gradient would need to be reduced from
0.85 to
3.65 to produce agreement between the temperature model temperatures and the temperature model, and such a large negative gradient does not appear feasible, even when annual variability and the rapid

Figure 8. Number density difference of meteors obtained prior to (15 – 19 July) and during (25 –29 July) the peak activity period of the 2003 Southern delta –Aquarids meteor shower. The lines show the linear fits to the pre-SDA (solid) and during-SDA (dashed) data. The symbols indicate the mean position of positive (P+, diamond) and negative (P
, square) differences and the mean values of d and height for the pre-SDA (triangle) and during-SDA (cross) data.

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Figure 9. Correlation between temperature estimated using the temperature gradient technique and (a) d versus h correlation (rdh) and (b) height distribution width (sh). variation in temperature and temperature gradient at this time of year are considered.

5. Alternative Temperature Estimation Techniques [27] Hocking [2004] provides scatterplots of the correlation rdh derived from d versus h scatterplots versus estimated temperature, revealing excellent correlation (0.86). They therefore conclude that rdh could be used to provide an alternative temperature estimation technique. Figure 9a shows scatterplots of sh and rdh versus the temperature estimated using the temperature gradient technique, as shown in Figure 6. The rdh values (0.64 to 0.84) are higher than those of Hocking [2004] (0.45 to 0.75), which may indicate our criteria for determination of which echoes are used in the fit are more restrictive. The resulting correlation (0.74) is lower than that of Hocking [2004] (0.81), but still indicates reasonable correlation. The rdh versus temperature scatterplot reveals excellent correlation (0.89). It is important to note that since sh, rdh and temperature are determined from the same data, they are not independent measurements. It is therefore possible that this nonindependence increases the correlation. This has been investigated by correlating sh and rdh with model temperature, rather than the temperature gradient temperature estimate. This reduces the rdh correlation from 0.89 to 0.63, while the sh correlation is increased marginally from 0.89 to 0.92. [28] The high correlation between sh and temperature suggests a further alternative technique which uses only the width of the height distribution. Such a technique is obviously related to the temperature gradient technique, as the high correlation is a manifestation of the same mechanism allowing temperatures to be estimated using the slope of the d versus h scatterplot. The slope of the d versus h scatterplot can be crudely estimated by taking the ratio of the width of the height and d distributions over the entire data set. The width of the d distribution varies between 0.27 and 0.31 throughout the year, with smallest values in mid-July (midwinter) and largest values in mid-January (midsummer). This represents a variation of only ±6% throughout the year, resulting in the slope of the d

versus h variation (and hence temperature) being approximately proportional rdh. [29] Correlations have also been calculated between other parameters derived from the meteor observations. Of note are the high negative correlations between peak height and temperature (
0.78), and peak height and height distribution width (
0.70). These correlations can be clearly seen by comparing the peak height and height width of Figure 1 and the temperature model of Figure 2. [30] Hocking [2004] is able to reproduce his rdh versus temperature correlation reasonably well using a model assuming variations in height, temperature, and zero field mobility factor. However, at least some of the smaller correlation observed at lower temperatures probably results from the smaller height distribution width at lower temperatures. This has been verified using a simple model similar to that of Hocking [2004]. Echo heights are generated according to a normal distribution, and diffusion coefficients are determined using MSIS temperatures and pressures according to equation (2). We then calculate d, and simulate geophysical variations by adding fluctuations generated according to a Gaussian distribution. Height errors are also generated according to a Gaussian distribution. The correlations obtained for height distribution widths of 3.6 (5.2), representing those for summer (winter), are 0.41 (0.77). We note that the lowest correlations produced by the simulations of Hocking [2004] (0.52) are larger than those observed experimentally (0.4). We suggest that the difference between the lowest correlations may be due to the fact that Hocking [2004] does not appear to have simulated narrower height distribution widths in simulating low temperatures.

6. Discussion [31] The temperatures estimated using temperature gradient model and rocket-derived pressure models show good agreement with the temperature model. This is a very encouraging result. Since the difference between the meteor and model temperatures may result from imperfections in the temperature gradient and pressure models, we use the model temperatures to calculate revised pressure and tem-

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Figure 10. Estimation of revised temperature gradient model (solid line) obtained using model temperatures and slopes SSCT estimated from d versus h scatterplots. The dashed and dot-dashed lines indicate the original model and the Hocking et al. [2004] 69N model, respectively. perature gradient models. The revised pressure model is  obtained by substituting the mean diffusion coefficients D and the model temperature into equation (2), while the revised temperature gradient model is obtained by substituting SSCT and the model temperature into equation (3). [32] The revised temperature gradient model is shown in Figure 10, revealing a similar variation to the original model with an additional weak maximum in April. The largest difference between the revised and original model is
1 K/km in mid-March, the end of the period where our model temperature is probably least accurate. This maximum slope difference corresponds to a temperature adjust-

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ment of
13 K for temperatures around 200 K. The summer gradients are reduced by between 0.5 and 0.8 K/km. A reduction in the summer gradient was also required by Hocking et al. [2004], although their correction was approximately twice as large (1 to 1.5 K/km). Since the mid-March to mid-October gradients are derived using a temperature model based on colocated OH spectrometer temperatures, the revised gradients should provide an accurate estimate of the actual temperature gradient at the peak height at these times. Further supporting this, we note that the late August gradient maximum of the original model has moved closer to mid-August in the revised model, in agreement with the Syowa lidar gradients. Since there is no corresponding maximum in the Northern Hemisphere rocket climatology, we suggest this effect may be peculiar to the high-latitude Southern Hemisphere. We note, however, that there is a pressure maximum in the Northern Hemisphere rocket climatology, as shown in Figure 3. We note also that the revised model shows better agreement with the rocket climatology in October, although this is in part due to the larger temperatures observed in October 2004. [33] The revised pressure model is shown in Figure 11, revealing a semiannual oscillation similar to the rocketderived model with a more pronounced April/May maximum. Since the mid-March to mid-October revised pressures are derived using a temperature model based on colocated OH spectrometer temperatures, these pressures should provide an accurate estimate of the actual pressure variation at the peak height. The fact that there is only a small difference between the model and rocket-derived temperatures in summer also gives us confidence that the summer pressure estimates are reliable, leading us to believe we have derived an accurate pressure model for use throughout the entire year. Although the accuracy of the CIRA, and to a lesser extent, MSIS pressures have to be questioned, it is interesting to note that the different corrections required in summer and winter for the MSIS and CIRA pressures are consistent with the effects of charged

Figure 11. (a) Estimation of revised pressure model (solid line) obtained using model temperatures and meteor diffusion coefficients (plus signs). The dashed line shows the rocket-derived model. The squares and diamonds indicate the pressure model at the peak height derived from the 69N rocket climatologies of Lu¨bken and von Zahn [1991] and Lu¨bken [1999], respectively. (b) Correction factor required for conversion of rocket-derived (solid line), MSIS-derived (dotted line), and CIRA-derived (dashed line) pressure models to the revised pressure model. 10 of 13

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Figure 12. Temperature estimates made using revised pressure (squares) and temperature gradient (plus signs) models. (b) Temperature difference between model and pressure (squares) and temperature gradient (plus signs) temperatures.

dust on meteor decay times [e.g., Havnes and Sigernes, 2005]. Such charged dust particles exist in summer, and are the source of noctilucent clouds (NLC). Charged dust is expected to lead to a reduction in the decay time, leading to an increase in the diffusion coefficient, and therefore an underestimate in pressures derived using diffusion coefficients and model temperatures. [34] Figure 12 shows the temperature estimated using the revised temperature gradient and pressure models, as well as the differences between the estimated and model temperatures. The differences between the estimated and model temperatures are comparable to those measured by Hocking et al. [2004] and Singer et al. [2004]. While the pressure model temperature differences are mainly constrained to ±20, temperature gradient model temperature differences are as large as ±30. The largest differences between the model and temperature gradient model temperatures are obtained during July (all years) and October/November 2004, as discussed in section 4.3, and also around late February (all years). As discussed in section 3, the midFebruary to mid-March period represents the period of least certainty in our temperature model. Although these results may suggest the late winter temperature ascent is more rapid than that of the model, the pressure model temperatures do not support this suggestion. We note that since we have used annual, semiannual, terannual and quadriannual components in deriving our temperature gradient and pressure models, it is possible that the late February temperature gradient model temperature discrepancy could be reduced if higher-order components were used. This idea is supported by the greater seasonal variability of the temperature gradients compared to the pressure, as is illustrated in Figures 2 and 3. From the perspective of minimizing statistical fluctuations the pressure model temperatures appear to be more reliable for our data set. The correlation between the estimated and model temperatures, calibration equations and variation percentage for temperature gradient temperatures are shown in Table 3. The correlation between the temperature gradient temperature differences and the pressure gradient temperatures is poor (
0.11). This suggests that the temperature fluctuations around the model temper-

ature are uncorrelated, and thus more likely to be statistical rather than geophysical. However, geophysical fluctuations may be more apparent if the data rates were sufficient to allow daily temperatures. [35] There are a number of different fitting techniques than can be applied to measure the slope of the d versus h scatterplot, as illustrated in Figure 5. The fitting technique used in this paper was selected after considerable experimentation, and may require adjustments for use at different sites as discussed below. In contrast, the pressure model technique only requires an estimate of the mean diffusion coefficient at the peak height. Additionally, pressure model temperatures do not show large differences from the model temperature, such as those observed during the Southern delta – Aquarids meteor shower, or during late October 2004. It may be argued that these differences could result from deficiencies in the fitting technique used to estimate the d versus h slope. Even if this is the case, it further emphasizes the difficulties in applying the temperature gradient technique. [36] The application of the temperature gradient technique described in this paper has two important advantages over previous applications [e.g., Hocking, 1999; Hocking et al., 2004; Singer et al., 2003, 2004]. First, use of the statistical comparison technique (SCT) avoids the need to apply a correction to the estimated slope, such as ‘‘bias correction.’’ Second, the adjustments to our model gradient required to produce agreement with our temperature model are significantly smaller than those required by Hocking et al. [2004], who needed to adjust their temperature gradient at a conjugate latitude by as much as
2.5 K/km, corresponding to a temperature adjustment of
32 K for Table 3. Correlation, Calibration Equations, and Variation Percentage for the Revised Meteor Temperature Estimates Parameter

Temperature Gradient

Pressure

Correlation Calibration equation Variation percentage, % RMS difference, K

0.91 0.96 Tmet + 4.21 4.74 11.0

0.97 0.93 Tmet + 12.44 3.76 7.17

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temperatures of 200 K. This is unlikely to be due to poor initial model temperature gradient estimates since they have largely relied on the rocket climatologies of Lu¨bken [1999], as used in this study. However, although the value ed = 0.14 used for the SCT was derived on the basis of theoretical considerations, we acknowledge the fact that it produced temperatures that best matched the temperature model, and this provided considerable motivation for its use. Preliminary investigations suggests ed = 0.14 appears applicable to over one year of data collected using the Buckland Park meteor radar [e.g., Holdsworth et al., 2004a], in addition to six months of data collected using the 33.2 MHz Davis meteor radar. While the use of different values at different sites is not problematic, we would prefer a technique that could be applied without site specific parameters. This is essentially achieved by Hocking et al. [2004].

7. Summary and Conclusions [37] This paper has presented meteor temperature estimates derived using two techniques: pressure model and temperature gradient model. The temperatures show good agreement with a temperature model derived using colocated OH spectrometer measurements and Northern Hemisphere rocket observations. Pressure model temperatures derived using CIRA model pressures show poor agreement in summer, confirming previous studies suggesting the unreliability of high-latitude CIRA pressures. Temperatures estimated during the Southern delta – Aquarids meteor shower are shown to be biased, suggesting that care should be taken in applying meteor temperature estimation during meteor showers. On the basis of a number of considerations (ease of implementation, minimization of statistical errors, reduced occurrence of discrepancies) we recommend the use of the pressure model technique, subject to the availability of an appropriate pressure model. In this regard, for the Davis radar we are fortuitous that we have been able to use colocated OH temperature measurements, and extensive Northern Hemisphere rocket measurements at a conjugate latitude, allowing us to estimate a suitably reliable pressure model for temperature estimation. [38] Although this paper proves the ability of the Davis MST radar to measure temperatures using meteor diffusion coefficients, work on improving the temperature estimates is continuing. In particular, an investigation of potential biases in diffusion coefficients is currently underway, and will be reported in a subsequent publication. The current work also provides the basis for temperature estimation using the new 33.2 MHz Davis meteor radar, installed in January 2005. This radar has produced daily count rates of between 9000 and 16000 since installation, which should allow temperature estimates to be made at significantly higher resolution (e.g., daily) than is possible in the current study. This can be achieved with only minor adjustments to the temperature and pressure models presented in this paper to account for the 0.5 to 1 km increase in peak height of the 33 MHz radar. [39] Acknowledgments. The authors wish to thank Graham Elford, Manuel Cervera, and Karen Berkefeld for useful discussions and to acknowledge the technical support with installation and operation of the

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meteor radar by Lloyd Symons, Richard Groncki, Damon Ward, and Peter Nink. The Davis MST radar is supported by Australian Research Council grant 20006300 and Antarctic Science Advisory Committee grants 2325 and 2529. The meteor antennas were provided by ATRAD Pty Ltd.

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G. B. Burns, W. J. R. French, R. J. Morris, and D. J. Murphy, Australian Antarctic Division, Channel Highway, Kingston, Tas 7050, Australia. D. A. Holdsworth, ATRAD Pty Ltd., 1/26 Stirling Street, Thebarton, SA 5031, Australia. ([email protected]) I. M. Reid, Department of Physics, University of Adelaide, Adelaide, SA 5005, Australia.

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