Pergamon Journal o/Armosphmc and Solar-Terrestrial Physics, Vol. 60, No. I, pp. 63-69. 1998

8 1998 Elsevm Saence Ltd

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A special oscillation of zoral mean temperatures of the middle atmosphere

Ma Ruiping, Zhang Feng, Mu Xiangming

Center for Space Science & Applied Research, Academia Sinica, 100080, Beijing, China (Ma Ruiping e-mail : tmi@center.cssar.ac.cn)

(Receiwd 2 April 1997, in revisedform 28 August 1997, and accepted 5 September 1997)

Abstract-Through an analysis of SAMS temperature data of the Nimbus 7 satellite, an oscillation of the zonal mean temperature superimposed on the seasonal trend is discovered. Its character is to oscillate synchronously on the constant pressure surface and to form standing waves in the vertical direction. It is proposed that this oscillation may be a characteristic mode of the atmosphere, and the zonal wavenumber 111 = 0, meridional wavenumber n = 0, and the geopotential eigenfunction is fi, which indicates a simple vertical motion of the atmosphere. The existence of reflection levels in the vertical direction may be the causes for the formation of these standing waves and the harmonic oscillations, whose fundamental period is _ 16 days. 0 1998 Elsevier Science Ltd. All rights reserved

1. INTRODUCTION

In the atmosphere there exist long period oscillation phenomena such as the annual oscillations of the zonal mean temperature, pressure and wind, and the semi-annual oscillations as well as the quasibiennial oscillations (Andrews et al., 1987). Short-period oscil- lations with periods from days to weeks have also been studied extensively. For example, Madden (1975) has found that there exist short period zonal mean temperature oscillations in the lower stratosphere ; the repeated occurrences of warmings in the stratosphere every winter are examples of such oscillations. Using numerical simulations, it has been shown by Holton and Mass (1976) that the phenomenon of quasi- periodic oscillations can be formed in the stratosphere through wave-flow interactions in response to plan- etary scale disturbances of the lower boundary (the tropopause). Chao (1985) and Yoden (1987) pointed out that the zonal mean oscillation is in a state of bifurcation according to the theory of bifurcation. Lindzen et al. (1982) proposed that the reciprocal interference of the waves can also give rise to zonal mean oscillations which usually occur in the middle- high latitude in the winter hemisphere and lower stratosphere. This has been confirmed by radiosonde data.

There has been comparatively little research on whether the zonal mean temperature oscillation also exists in the upper stratosphere or in the mesosphere. Such research requires a continuous synchronous

observation along a certain latitude and on a global scale. This is rather difficult to organize considering the required cooperation among radar, rocket and other observation systems. Satellites of the middle atmosphere, however, provide new opportunities for the study of such zonal mean temperature oscillations.

The purpose of this paper is to analyse the oscil- lating characters of the zonal mean temperature in the middle atmosphere at low to middle latitudes and to discuss the mechanism of its formulation using retrieved SAMS temperature data from the Nimbus- 7 satellite.

2. DATA

The data used here are the SAMS temperature grid of the Nimbus-7 satellite provided by the World Data Center A (WDC-A) and are retrieved from the infra- red radiation data. The horizontal range is from 50”s to 67.5’N (the interval is 2.5”), and from 18O”W to 170”E (the interval is 10”). The vertical range is from about 10 km (In PO/P = 1.4, where P is the atmo- spheric pressure and PO = 1013 hPa) to about 96 km (In PO/P = 13.6) with the interval of 0.2 scale height. Using the limb scanning method, SAMS sounded the atmospheric thermal and resonance radiation, and retrieved the vertical profile of atmospheric tempera- ture. Drummond et al. (1980) and Rodgers et al. (1984) described the instrument and the retrieval method. Barnett and Corney (1984) discussed the pre-

63

64 Ma Ruiping et al.

cision of the instrument and compared the SAMS data with the sounding data of the stratospheric atmo- sphere from the Tiros N satellite as well as the rocket- sounding data. They pointed out that the discrepancy between them is limited to &2K in the stratosphere. Using the same retrieval method and instrument, the coverage of space and time and the consistency of the satellite-sounding data are better in spite of the weak resolution in the vertical direction (about 8 km). These data can be utilized rather well to analyse the atmo- spheric zonal mean state as well as the large scale variations. The paper presented here analyses the daily averaged grid temperature data of the Nimbus-7 satellite in 1980 and 1981 and we adapt linear interp- olation to process the data gaps (a default day after about three continuous sounding days).

3. OSCILLATION OF THE ZONAL MEAN

TEMPERATURE

The zonal mean temperature is obtained from the average of 36 data at one latitude which are given directly by the SAMS data. The variation of the zonal mean temperature with time at 50’S equator, and 50’N and at about 69 km height in the 1980 and 1981 is described in Fig. I. The dashed lines in Fig. 1, which show the 31 day running average of the zonal mean temperature at a latitude, represent the tendency of seasonal variations. It can be found from the figure that the variations of the zonal mean temperature are divided into two components. One is the seasonal variation and the other is the “short term oscillation” superimposed on the trend of about several days to several weeks. These short term oscillations exist dur- ing most of the year and are nearly synchronized with the oscillations at the two other latitudes, which means that the temperatures are increasing or decreasing sim- ultaneously worldwide. The amplitudes of these short term temperature oscillations at 50’N and at the equ- ator are approximately the same, but are smaller at SO S from the 90th day to the 210th day. In addition, the amplitudes of these oscillations decrease sim- ultaneously at the three latitudes in September 1980 and October 1981. For the following discussions the zonal mean temperature is processed to analyse the character of the short term oscillations. The zonal mean temperature for the 31-day moving average is subtracted from the zonal mean temperature and then the residual temperature is obtained.

Figure 2 shows the residual variation of the zonal mean temperature at heights of about 88 km, 69 km, 46 km and 35 km from 50”s to 60”N (at intervals of 10 ). The synchronization of the oscillations at the two

(h) 1981

Fig. 1. Fluctuation of zonal mean temperature at about 69 km; dashed line show 31-days running mean of zonal

mean temperature. (a) 1980. (b) 1981.

mesospheric levels is very good. There is an interesting phenomenon that the amplitudes of the oscillations at these different latitudes are almost the same, especially in the spring and autumn. This indicates the existence of a component with the meridional wavenumber II = 0. The phases of the temperature oscillations at the heights of 88 km and 69 km are opposite. The oscillations at stratospheric levels also have this synchronous character, but their amplitudes are smaller than in the mesosphere. The component with n = 0, however, can still be seen. The component of zonal asymmetry become more conspicuous due to the effect of the wave mean flow interaction.

Figure 3 describes the vertical profile of the root mean square of the zonal mean temperature residual after carrying out the 3 1 -day running average process at three latitudes (50‘S, equator and 50,N) at different heights in 1980 and in 1981. The temperature oscil-

A vertical standing wave in the middle atmosphere 65

(b) 1980 69km

Tim (days)

(c) 1980 46km

Fig. 2. Fluctuation of the zonal mean temperature residuals from the seasonal trend from 50 ‘S to 60’N in IO” intervals, (a) 88 km, (b) 69 km, (c) 46 km, (d) 35 km.

lations in these two years are very similar. They have about 69 km, and the amplitude of the oscillation in almost the same amplitude maximum and minimum the stratosphere is relatively small. The wavelength in the vertical direction. It is a typical standing wave in the mesosphere is about 25 km and that in the structure that the maximum corresponds to the wave stratosphere is about 12 km, shorter than that in the antinode and the minimum to the wave node. The mesosphere. The standing wave structure at the equ- maximum of the amplitude is located at the height of ator is presumably more pure due to the weak inter-

Ma Ruiping et al.

“+“‘A Om Temperatue (K) Temperdue (K)

Fig. 3. Profiles of root-mean-square of zonal mean tem- perature residuals from seasonal trend, (a) 1980, (b) 1981.

action effects between the zonal mean flow and the planetary waves in the equatorial region. In order to observe the standing wave structure more distinctly, we choose several vertical profiles of the zonal mean temperature residual in the equatorial region at different times. Figure 4(a)+d) shows the profiles of 6 to 14 April 1980 ; 6 to 14 June 1980 ; 14 to 22 January 198 1 and 4 to 12 April 198 1, respectively. These seven day vertical profiles of temperature residuals clearly show standing wave structures.

To analyse the frequency spectrum of the tem- perature residuals varying with time, the Fourier Transform was carried out for the zonal mean tem- perature residual time series. Figure 5 gives the fre- quency spectra at four heights (corresponding to four wave nodes) in 1980 and in 1981, respectively. We can find two obvious characters. The first is that the frequencies which is corresponding to the major spec- tral peaks are harmonically dated. For example, the first major peak frequency in the left side in Fig. 5 is O.O6/day, the second is O.l2/day and the fourth is 0.24/day, corresponding to the periods of 16 days, 8 days and 4 days, respectively. The second is that the positions of the spectral peaks at the four heights are almost the same. This means that the oscillations are correlated at the various levels and the standing waves are from one wave system.

4. DISCUSSION

Chapman and Lindzen (1970) and Volland (1988) pointed out that both the atmospheric tide and free planetary waves have their own characteristic modes, and have discussed extensively these characteristic modes.

From the analysis of the zonal mean temperature,

we find that, all year around, there exist short-term temperature oscillations with rather large amplitudes in the middle atmosphere and which have a unique character. It is possible that the oscillation of the zonal mean temperature residuals is also a characteristic mode of the atmosphere. From the results presented above we find that oscillations are rather special, with the zonal wavenumber equal to 0 and meridional wav- enumber also equal to 0. Because the temperature that is analysed is the zonal mean temperature, the zonal wavenumber undoubtedly equals to 0. Oscillations at various latitudes are all synchronous and have approximately the same amplitude, so the meridional wavenumber equals to 0 too. According to the method used by Volland (1988), this can be expressed in the form of (0, 0, f u), where u stands for the frequency. For the situation where the geopotential disturbance is in the form of Legendre polynomial Pz, the hori- zontal winds are zero and the oscillations are purely vertical motions that can cause the temperature vari- ation under adiabatic conditions. Volland (1988) also discussed the characteristic mode (m = 0) including Rossby-Haurwitz waves, the annual waves and semi- annual waves of m = 0, but the meridional wave- numbers of these characteristic mode are not zero.

We consider how the vertical velocity can bring about the zonal mean temperature oscillations pre- sented above. If the horizontal wind is negligible, the thermodynamic equations are simplified as

where T’ is the residual of the zonal mean tempera- ture, W’ the vertical velocity, y the vertical gradient of background radiation equilibrium temperature, and yd the vertical gradient of adiabatic temperature. Assuming that the background temperature is constant, we can get a function as

yd z - lOK/km. From Fig. 1 we know that the maximum temperature difference between two days is less than 15K. For the temperature variation of lSK/day, the vertical velocity w’ w 0.017 m/s in the middle atmosphere, which is reasonable.

Because of the existence of the obvious standing wave structure, there must exist corresponding reflec- tion levels. Chen et al. (1996) also found standing wave structures in the atmospheric temperature pro- file when they analysed the temperature data of the Nimbus-7 satellite. They proposed that this situation occurred due to the interference between the incoming

A vertical standing wave in the middle atmosphere

100

Gto 14 April 1980 610 14 June 1980

80

40

20

14to22Janusry1981 4 to I2 April1981

67

0 -15 -10

Fig. 4. Profiles of zonal mean temperature residuals from seasonal trend (a) 6 to 14 April 1980, (b) 6 to 14 June 1980, (c) 14 to 22 January 1981, and (d) 4 to 12 April 1981.

and reflecting planetary waves, and proposed that the reflection level was located in the wind shear layer at the height of about 110 km. Figure 6 shows the vertical profile of buoyancy frequency N calculated from the U.S. Standard Atmosphere (1976) where N2 is the stability,

N2 =g?

eaz'

g the gravity acceleration and 8 the potential tem- perature. N reaches its maximum at the height of about 110 km where the stability is the highest, and thus the upper reflection level is most possibly formed here. The lower reflection level is either the ground, because the ground certainly confines the vertical motion of the atmosphere and causes reflection, or the tropopause where the atmospheric stability is rather high. There may be two reasons for the increase of the oscillation amplitudes in the mesosphere : one is that

the density decreases with height and thus the ampli- tudes may also increase in terms of the energy con- servation ; the other reason may be that the stability is poor in the mesosphere and the oscillations are easier to develop due to a negative background ver- tical temperature gradient. N is small in these regions. The amplitudes of the oscillations in the stratosphere are also small due to the positive temperature gradient and the good stability which suppresses the devel- opment of the oscillations.

Because of the existence of the upper and lower reflection levels, harmonic oscillations may be formed due to vertical propagating waves between the two reflection levels. Oscillations with periods of 16 days, 8 days, and 4 days discussed here may be the results of such harmonic oscillations. The difference between the vertical wavelength in the mesosphere and the stratosphere is related to the background temperature gradient. The detailed causes of these phenomena need further investigations.

Ma Ruiping et al.

2.5 I

88 km

M 69 km ---- 46 km ~ 35 km

71

Frequency (1 /day) 2.0 ,

1 (b) 1981

--- &?I km ---- 46 km - 35 km

I

0.0 , 0.0 0.1

Freqvency”J( 1 /c&) C

Fig. 5. Spectra of zonal mean temperature residuals from seasonal trend, (a) 1980, (b) 198 1.

Bittner et al. (1994) and Offermann et al. (1987) made continuous rocket explorations of the middle atmosphere in Northern Europe. They found that there existed obvious quasi-periodic variations for the atmospheric temperature with periods of from days to weeks, called ‘quiet layers’. If the special oscillation of the zonal mean temperature in the middle atmo- sphere really exists, at a single station the quasi-per- iodic variations of the temperature and the ‘quiet layers’ found by rocket exploration can also be seen. The variations of temperature with time are regarded as planetary wave activity at a single station.

4

Fig. 6. Profile of the buoyancy frequency, N, from U. S. Standard Atmosphere (1976).

5. CONCLUSIONS

Through the analyses of SAMS data of the Nimbus- 7 satellite in 1980 and 1981, we find a special charac- teristic wave mode whose zonal and meridional wav- enumbers are zero, and which can be expressed in the form of Legendre polynomial Pi which indicates a simple atmospheric vertical motion.

The vertical oscillations appear to be reflected by upper and lower reflection levels during the propa- gation processes to form standing wave structures as well as harmonic oscillation phenomena. The upper reflection level may be located at the height of about 110 km because of the highest stability (the maximum of N) there and the lower reflection level may be either the ground or the tropopause.

The amplitudes of the temperature oscillations and the vertical wavelengths in the mesosphere are appar- ently bigger than those in the stratosphere. The differ- ence in the background vertical temperature gradients may be the cause.

This newly discovered characteristic wave mode requires more sounding data to verify its existence. Further research is required to understand the under- lying physical mechanisms.

A vertical standing wave in the middle atmosphere 69

Acknowledgements-Using the SAMS data of Nimbus-7, we are grateful to members of the Nimbus-7 SAMS equipment and WDC-A. This work was supported by the National Natural Science Foundation of China, No. 49474240.

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