Geophysical Research Letters

MF radar measurements of sub-scale mesospheric momentum flux

Authors


Abstract

[1] Measurements of Mesosphere and Lower Thermosphere (MLT) wind velocities and spectral widths made using the Buckland Park MF (1.98 MHz) Doppler radar, located near Adelaide, Australia (35°S, 138°E), have been analyzed to obtain the density normalized upward flux of zonal momentum for scales smaller than the radar pulse volume. The results indicate the presence of significant fluxes, with height profiles similar in magnitude and direction to those obtained for the same data for scales larger than the pulse volume.

1. Introduction

[2] Since the first Doppler radar measurements of the density normalized upward flux of horizontal momentum in the mesosphere were obtained by [Vincent and Reid, 1983], mesospheric measurements have been obtained using the same technique at Adelaide at MF [Reid and Vincent, 1987a; Fritts and Vincent, 1987], and at other sites using powerful atmospheric radars operating at VHF [e.g., Reid et al., 1989; Fritts and Yuan, 1989; Rüster and Reid, 1990; Tsuda et al., 1990]. Indirect measurements of the same parameters have been obtained using other techniques by [e.g., Thorsen et al., 1997; Tang et al., 2002; Fritts et al., 2002], but the dual beam technique still appears to be the most readily applied and least ambiguous. Furthermore, new MF/HF radars designed to utilize the Vincent and Reid technique and to investigate turbulence in the MLT region have recently been installed in northern Norway, and in Indonesia. The technique may also be applied to Doppler Lidars. It is therefore of some interest to consider another aspect of the measurement, the effect of finite pulse volumes.

[3] The density normalized upward flux of horizontal momentum is (equation image, equation image) where (u′, v′, w′) are the zonal, meridional and vertical perturbation velocities, respectively. The technique described by [Vincent and Reid, 1983] provides a direct measure of equation image or equation image from the difference between the mean square radial velocities measured in Doppler radar beams directed at equal and opposite angles to the zenith in the east-west and north-south planes, respectively. Given horizontal homogeneity of the statistics of the motions, the technique will correctly measure the contributions to the equation image and equation image terms from both gravity wave and turbulent motions. Analyzing radial velocities, however, yields values of the flux terms that refer to scales of motion larger than the radar pulse volume. In the case of the Buckland Park MF Doppler radar [Reid et al., 1995], the radar sample volume can be represented by a roughly disk shaped volume of radius ∼6 km and thickness ∼2 km at a range of 80 km. At VHF the radius would typically be ∼2 km and the thickness ∼300 m. These volumes could be expected to contain turbulence, and when compared with the scales of commonly observed high frequency mesospheric gravity waves, they are seen to be comparable in horizontal extent [e.g., Reid, 1986]. In fact, since it is the shortest horizontal scale, highest frequency gravity waves that should make the largest contribution to the flux terms [e.g., Fritts, 1984], existing measurements may underestimate the magnitude of the total flux.

[4] In this paper, we follow a suggestion by [Reid, 1987] and use the mean square spectral widths measured in beams directed at 11.6° off-zenith towards the east and west to calculate the equation image term for scales smaller than the radar pulse volume. In the interests of ease of comparison, and to reassess the impact of this term on previously presented observations, we reanalyze data used to determine the equation image term for scales larger than the pulse volume by [Reid and Vincent, 1987a].

2. Observations

[5] The Buckland Park MF Radar as utilized for the results presented here has been described by [Reid and Vincent, 1987a]. Its one way half-beam width is 4.5°. Four independent beams were utilized. These were directed vertically, and at 11.6° towards the north, east and west. A 2 km sample resolution was used, so that the 4 km radar pulse length was over-sampled. Ranges between 80 and 100 km were sampled. The radar was operated between 1122 LT on 18 May and 1040 LT on 20 May. 102.4-s of data were obtained simultaneously in each of the beams every two minutes. The beam configuration was chosen to allow estimates of the density normalized Reynolds stress tensor [see Reid and Vincent, 1987a] and gravity wave horizontal scales to be obtained [see Reid and Vincent, 1987b]. Here, we re-analyze the May data to calculate the density normalized upward flux of zonal momentum for scales smaller than the radar pulse volume.

3. Theory

[6] The general expression for the variance of the velocity measured by a Doppler radar located at the origin of a right handed co-ordinate system at an off-zenith angle of θ and an azimuth angle ϕ measured clockwise from the +y direction is

equation image

[7] The variance can be of the radial velocity, or of the spectral width. The various terms in this equation are the components of the density normalized Reynolds stress tensor, and can be retrieved through a suitable choice of beam configuration. For example, as shown by Vincent and Reid, the density normalized upward flux of zonal momentum is given by

equation image

where equation image is the variance of the velocity measured in a beam directed θEff off-zenith, the subscripts indicate east (E) and west (W), and θEff is the effective beam angle formed by the product of the angular polar diagrams of the backscatter and radar antenna. θEff is generally less than the nominal off-zenith angle, but can be calculated from the observations [e.g., Reid et al., 1988]. When equation (1) refers to the variance of the radial velocity, the results from equation (2) apply to scales larger than the radar pulse volume. When equation (1) refers to the variance of the spectral width, equation (2) refers to scales smaller than the pulse volume. A particularly useful and appealing aspect of equation (2) when applied to spectral widths is that if the wind field is horizontally homogenous, the measured value of equation image will be unaffected by effects such as beam and shear broadening, because these will be the same in each beam and thus subtract out. This will not be the case for all of the terms in equation (1), and rather more care is required in calculating them.

[8] The relationship between the observed mean square spectral width σobs2 and the terms that contribute to it, the variance due to turbulence σturb2, wave motions σwave2, and due to beam and shear broadening σbeam+shear2 is

equation image

and the expression for the σbeam+shear2 term is

equation image

where α is the beam half-width, and uz is the vertical shear in u [Nastrom, 1997]. This term is symmetric in ϕ, and so does not contribute to the LHS of equation (4). We cannot remove the σwave2 term from the data in this study, and so have chosen to filter the time series of spectral width to remove periods longer than 8 h. The definitive study would utilize the dual beam width technique of [VanZandt et al., 2002] in both the east and west directions to calculate the σturb2 term only. We note that in addition to the Buckland Park MF radar, the Indonesian MF and SAURA HF radar in northern Norway are capable of making this measurement.

4. Results

[9] Autocorrelation functions for each 102.4-s of data were calculated and analyzed in the usual manner for these kinds of measurements [e.g., Reid and Vincent, 1987a] to obtain the corresponding returned power, radial velocity and spectral width. Signal-to-noise ratios had to exceed 5 dB before a record was accepted, and following [Doviak and Zrnic, 1993] only spectral widths lying in the range 0.02–0.2 times the Nyguist width were accepted. θEff was calculated using the procedure followed by [Reid and Vincent, 1987a]. We note that the spectral width is also affected by the aspect sensitivity [see, e.g., Hocking et al., 1986; Czechowsky et al., 1988], but the effect will be the same in the eastward and westward beams, and so not affect the final result.

[10] The flux was calculated using equation (2) for the time series filtered to remove periods longer than 8 hours. To filter the time series, a spline was applied, and the splined values used fill in missing data points. A 5th order butterworth filter with a cutoff of 8 hours was then applied to this modified time series. The variances were then calculated for the filtered time series, only using values corresponding to those times real data were obtained. Both time series were treated in the same way.

[11] The mean spectral widths measured in two westward directed Doppler beams over three days in February were used to obtain an estimate of the uncertainty in values of equation image calculated using equation (2). This assumes that the differences are typical of beams directed at equal and opposite angles to the zenith, which is reasonable. When this is done, the mean relative error in equation image and equation image for mean square spectral widths over the 10 heights is around 7%. The corresponding value for the mean square radial velocities is about 3%. We take these values to be typical of the uncertainty at each height for the May data set.

[12] Figure 1a shows the height profile of the density weighted flux values determined from the mean square spectral widths measured in the eastward and westward beams in May. The uncertainties are large, and significantly different from zero between 85 and 90 km. Figure 1b shows the results corresponding to Figure 1a for scales larger than the pulse volume. In this case, the fluxes are significantly different from zero below 90 km. Note that because equation image is a signed quantity, the addition of the sub-scale values to the values for scales larger than the pulse volume increases the total normalized flux value at some heights, but decreases it at others. It is also important to note that some scales may contribute to both sub-scale and larger scale flux values. However, it is not expected that this will be a significant source of error, and Figure 1c shows the sum of the super and sub-scale momentum fluxes shown in Figures 1a and 1b.

Figure 1.

Figure 1a (top) shows the height profile of the density weighted flux values determined from the mean square spectral widths measured in the eastward and westward beams in May 1982. Figure 1b (centre) shows the results corresponding to Figure 1a for scales larger than the pulse volume. Figure 1c (bottom) shows the sum of the density weighted fluxes shown in Figures 1a, 1b. For clarity, we have indicated 3rd order polynomial fits to these data.

[13] Clearly, some caution should be exercised in interpreting the values from above around 90 km because of the accumulated uncertainties in the sum of the density weighted flux values. We also note that we have oversampled the 4-km radar pulse width, and so some smoothing is inherent in the measurement. Nevertheless, the results suggest that the sub-scale flux could make a significant contribution to the total flux, and that it should be considered when the mean flow acceleration is calculated.

[14] Analysis of other data sets discussed by [Reid and Vincent, 1987a] indicates that the sub-scale momentum flux appears to be a significant contributor to the total flux value for measurements made at MF, and that the form is typically found to be similar between the height profiles of sub- and super-scale momentum flux.

5. Conclusions

[15] The results shown in Figure 1 suggest that there are significant fluxes associated with scales less than the pulse volume at MF. We have been unable to separate the contributions to the flux from wave and turbulence motions. However, this would be possible using the dual width experiment as described by [VanZandt et al., 2002]. The optimum technique for investigating the turbulence and wave fluxes would be a dual-width, dual-beam experiment, as this would allow the relative contributions to be separated. We note that the large Adelaide MF, Pontianak MF and SAURA HF radars are capable of this measurement.