Mean characteristics of the spectrum of horizontal velocity in the polar summer mesosphere and lower thermosphere observed by foil chaff

Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1831–1839

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Mean characteristics of the spectrum of horizontal velocity in the polar summer mesosphere and lower thermosphere observed by foil cha* Yong-Fu Wua , Jiyao Xua; ∗ , H.-U. Widdelb , F.-J. L4ubkenc a Laboratory

for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, P.O. Box 8701, Beijing 100080, People’s Republic of China b Max-Planck-Institut f* ur Aeronomie, D-37191 Katlenburg-Lindau, Germany c Physikalisches institut der Universit* at Bonn, Bonn, Germany Received 1 December 2000; received in revised form 12 July 2001; accepted 17 July 2001

Abstract Thirty-three foil cha* rockets were :own at high latitudes during the summers of 1987, 1988, and 1991.Vertical pro
1. Introduction It is now recognized that gravity waves play an important role in determining the mean circulation and thermal structure of the middle atmosphere. Through gravity wave saturation processes, such motions are believed to cause turbulence that acts to limit wave amplitudes, resulting in divergence of momentum :ux and the di*usion of heat and constituents in the mesosphere (Lindzen, 1981; Fritts, 1984). These processes are currently understood primarily on the basis of linear monochromatic wave theory. However, observations have provided a large body of data which ∗

Corresponding author. Fax: +86-010-62548489. E-mail address: [email protected] (J. Xu).

indicates that the atmospheric motion
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PII: S 1 3 6 4 - 6 8 2 6 ( 0 1 ) 0 0 0 6 2 - 1

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spectra of atmospheric horizontal motions obtained from aircraft data revealed a slope of −5=3 in the range 2.6 to 300 –400 km and a slope of −3 at large scales (Lilly and Petersen, 1983; Nastrom and Gage, 1983, 1985). Vertical wavenumber spectra of atmospheric horizontal motions observed by balloon, radar, and rocket techniques also have been used to assess the character, universality, and saturation of the motion
rather slowly from about 250 m=s at 103 km (1:5 m cha*) to about 20 m=s at 90 km (1:0 m cha*) and yields very detailed information on the horizontal winds. With a sampling rate of 50 Hz, this means that the spatial distance between sampling points changes from about 5.0 to 0:4 m over this height interval. We should, therefore, expect to resolve apparent spatial structure in horizontal winds of a few meters in the mesosphere and lower thermosphere. Wind data with a height resolution of 25 m were obtained using a polynomial technique. The smoothing technique is described in more detail by Wu and Widdel (1991, 1992). An example of the wind pro
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Table 1 Summary of foil cha* experiments in the polar summer mesosphere and lower thermosphere Rocket designation

Date and time (UT)

Height range measured (km)

Location

MAC=SINE campaign in 1987 S-C02 S-C04 S-C05 S-C07 S-C08 S-C09 S-C11 S-C12 S-C13 S-C14 S-C15 S-C17 S-C18 S-C19 S-C21 S-C23 S-C24 S-C25 S-C26 S-C27 S-C28

1230 1120 1153 1240 1333 1127 1244 1336 2128 2215 2334 0852 0943 1019 1203 1306 2030 2117 2201 2230 2254

22 24 24 24 24 26 26 26 01 01 01 14 14 14 14 15 15 15 15 15 15

June June June June June June June June July July July July July July July July July July July July July

82.7–74.3 92.0 –82.5 93.0 –80.1 94.6 –82.4 95.6 –83.9 93.3–81.0 94.0 –82.5 85.1–80.0 93.9 –83.0 76.8–70.5 92.8–87.3 92.8–80.0 94.4 –81.6 79.5 – 66.8 93.1–80.3 94.8–83.6 93.8–79.5 94.8–83.5 94.7–81.9 93.7–80.5 90.8–80.5

AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya

Sodium 88 campaign in 1988 M-N01 M-N02 M-N03 M-N04 M-N05 M-N06 M-N07 M-N08 M-N09 M-N10

2030 2137 2212 2224 2258 2145 2229 2221 2315 0005

24 24 24 24 24 29 04 12 12 12

June June June June June June July July July July

98.4 –86.6 94.7–88.2 97.3–88.8 96.4 –87.4 97.3–88.0 92.4 –85.0 96.2–85.0 96.5 –85.9 102.8–87.1 98.8–87.0

AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya AndIya

NLC campaign in 1991 VCH28 VCH42

0226 01 Aug. 0027 10 Aug.

89.6 –79.0 89.9 –78.3

Esrange Esrange

particularly sensitive to this problem. We checked against such distortions of our analysis in two ways. First, the original data series was prewhitened by means of a di*erentiating
(1)

where xi and yi are the data series before and after prewhitening, and is taken to be 1. As is pointed out by Blackman and Tukey (1958), the main purpose of prewhitening is to avoid diOculties with minor lobes of spectral windows. Dewan et al. (1984) and Tsuda et al. (1989) have used the prewhitening technique in their spectral analysis. Prior to the actual spectral analysis, the linear trend of each wind

pro
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Fig. 1. An example of the wind and wind error pro
to 100 m wavelengths for the two methods are listed in Table 2. The usual F test was used to
Fig. 2. Pro
the two methods mentioned above with the 90% con
We examine in this section the form and the variability of the vertical wavenumber spectra collected from 33 foil cha* measurements in the polar summer mesosphere and lower thermosphere. For this purpose, we
(2)

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Fig. 3. Comparison between power spectra obtained using di*erent boxcar functions. Right: prewhitening. Left: cosine taper window after prewhitening. The dashed lines show least-squares
Table 2 Spectral slopes derived from two methods

4.2. Average vertical wavenumber spectrum of scalar horizontal wind

Rocket designation

Prewhitening

Cosine taper after prewhitening

M-N01 M-N02 M-N03 M-N04 M-N05 M-N06 M-N07 M-N08 M-N09 M-N10

−2:73 −3:39 −3:61 −2:81 −3:67 −2:62 −2:82 −2:66 −3:98 −3:71

−2:75 −3:51 −3:79 −2:76 −3:66 −2:67 −2:85 −2:68 −3:92 −3:75

Average

−3:23 ± 0:53

−3:20 ± 0:52

Based on the N 2 structure in Fig. 2, the N 2 is taken to be 5:9 × 10−4 ; 8:5 × 10−4 , and 4:6 × 10−4 (rad=s)2 for the MAC=SINE, Sodium 88, and NLC campaigns, respectively. Calculated spectral slopes and ratios of the observed to saturated spectral amplitudes are listed in Table 3. We see from Table 3 that the values of the spectral slope and ratio of the observed to saturated spectral amplitudes vary between −2:04 and −3:92 and between 0.1 and 5.8, which clearly displays the variations in both slope and amplitude from one :ight to another. Speci
4.2.1. Average vertical wavenumber spectra of each campaign We now examine the form of the average vertical wavenumber spectra of each campaign. For this purpose, the vertical wavenumber spectra obtained from each campaign were averaged arithmetically. The resulting vertical wavenumber spectra are shown in Figs. 4, 5, and 6 for the MAC=SINE (21 horizontal wind pro
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Table 3 Spectral slopes and ratios of the observed to the model spectral amplitudes derived from 33 foil cha* rockets Rocket designation

Slopes

Ratios of the observed to model spectra

S-C02 S-C04 S-C05 S-C07 S-C08 S-C09 S-C11 S-C12 S-C13 S-C14 S-C15 S-C17 S-C18 S-C19 S-C21 S-C23 S-C24 S-C25 S-C26 S-C27 S-C28 M-N01 M-N02 M-N03 M-N04 M-N05 M-N06 M-N07 M-N08 M-N09 M-N10 VCH28 VCH42

−2:04 −2:75 −3:13 −3:47 −3:40 −3:48 −3:12 −3:25 −3:70 −2:97 −3:28 −2:75 −2:47 −2:44 −3:18 −2:68 −3:11 −2:94 −3:43 −2:89 −2:85 −2:75 −3:51 −3:79 −2:76 −3:66 −2:67 −2:85 −2:68 −3:92 −3:75 −2:76 −2:89

1.9 1.0 1.0 0.3 0.2 0.3 3.7 1.1 0.1 1.5 0.3 2.6 0.6 3.4 0.5 3.6 0.7 5.3 1.3 0.4 1.2 1.8 0.1 0.2 0.5 0.4 0.7 0.3 2.9 0.1 0.4 2.8 0.6

Average

−3:07 ± 0:44

1:3 ± 1:3

Fig. 4. Average vertical wavenumber spectrum obtained from 21 cha* rockets during the MAC=SINE campaign. The long dashed straight line shows the saturated spectral amplitudes given by Eq. (2). The short dashed curve is the optimum
and that there is some evidence of aliasing e*ects at the right-hand end of the spectrum shown in Fig. 4, i.e., the spectral slope approaches zero at the right-hand end of the spectrum. Thus, the spectrum in Fig. 4 is more representative of average conditions. In Figs. 4 – 6 there are no clear breaks in the slope, which implies that a dominant vertical wavelength (if present) was longer than the ∼12:8 km height interval covered by the measurements. These observed average spectra can be
(3)

where m∗ is the characteristic vertical wavenumber. In order to obtain a reasonable estimate for m∗ , we adopt the same view as discussed in the literature (Wu and Widdel,

Fig. 5. Same as Fig. 4, but for the Sodium 88 campaign.

1992) to
∗ = 21=2 =m∗ = 10:0, 12.8, and 15:0 km, respectively. It was found that while the
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Fig. 6. Same as Fig. 4, but for the NLC 88 campaign.

Fig. 7. Same as Fig. 4, but for all 33 :ights in the polar summer.

However, it seems diOcult to exactly infer a longer characteristic vertical wavenumber from our observed spectra because of the limit of record length of data. 4.2.2. Average vertical wavenumber spectrum of 33 wind proCles We examine the form of the average vertical wavenumber spectrum of the horizontal velocity measured in the polar summer mesosphere and lower thermosphere. For this purpose, 33 vertical wavenumber spectra of the horizontal wind pro
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Fig. 7 are the saturated gravity wave spectral model given by Eq. (2) with weighted average N 2 = 6:6×10−4 (rad=s)2 and the optimum
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considerable variability. On an average, however, the average slope and ratio of the observed to saturated spectral amplitudes are −3:07 ± 0:44 and 1:3 ± 1:3, which are in excellent agreement with the saturated spectral model. Average vertical wavenumber spectra (Figs. 4 – 6) computed from each campaign are temporally less variable and exhibit approximately the same shape for wavelengths in the range from 12:8 km to 100 m. Spectral slopes and ratios of the observed to saturated spectral amplitudes are −2:92; −3:01, and −2:87 and 1:5; 0:7, and 1:7 for the MAC=SINE, Sodium 88, and NLC campaigns, respectively, suggesting that there is considerably good agreement with the saturated spectral model. This means that the saturation processes are present in the horizontal :ow during the three campaigns. Average vertical wavenumber spectrum obtained from 33 horizontal wind pro
Bendat, J.S., Piersol, A.G., 1971. Random Data: Analysis and Measurement Procedures. Wiley, New York, pp. 286 –343. Blackman, R.B., Tukey, J.W., 1958. The Measurement of Power Spectra. Dover, New York, pp. 40 – 41. Desaubies, Y.J.F., 1976. Analytical representation of internal wave spectra. Journal of Physical Oceanography 6, 976–981. Dewan, E.M., Good, R.E., 1986. Saturation and the “universal” spectrum for vertical pro
Y.-F. Wu et al. / Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1831–1839 Vincent, R.A., 1984. Gravity wave motions in the mesosphere. Journal of Atmospheric and Solar-Terrestrial Physics 46 (2), 119–128. Weinstock, J., 1990. Saturated and unsaturated spectra of gravity waves and scale-dependent di*usion. Journal of Atmospheric Science 47, 2211–2225. Widdel, H.-U., 1985. Foil clouds as a tool for measuring wind structure and irregularities in the lower thermosphere (92– 50 km). Radio Science 20, 803–812. Wu, Y.-F., Widdel, H.-U., 1989. Observational evidence of a saturated gravity wave spectrum in the mesosphere. Journal of Atmospheric Solar-Terrestrial Physics 51 (11=12), 991–996.

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Wu, Y.-F., Widdel, H.-U., 1990. Spectral analysis of atmospheric velocity :uctuations in the mesosphere. Journal of Atmospheric Solar-Terrestrial Physics 52 (1), 23–33. Wu, Y.-F., Widdel, H.-U., 1991. Further study of a saturated gravity wave spectrum in the mesosphere. Journal of Geophysical Research 96 (D5), 9263–9272. Wu, Y.-F., Widdel, H.-U., 1992. Saturated gravity wave spectrum in the polar lower thermosphere observed by foil cha* during campaign “Sodium 88”. Journal of Atmospheric Science 49 (19), 1781–1789.