Upward Transport of Westerly Momentum due to Disturbances of the. Equatorial Lower Stratosphere in the Period Range of about 2 Days

Transcription

1 June 1994 T. Maruyama 423 Upward Transport of Westerly Momentum due to Disturbances of the Equatorial Lower Stratosphere in the Period Range of about 2 Days -A Singapore Data Analysis for By Taketo Maruyama Meteorological Research Institute Tsukuba 305, Japan (Manuscript received 30 November 1993, in revised form 21 February 1994) Abstract Twice-daily time series upper-air data at Singapore (1.4N, 104.0E) during the years are analyzed to examine disturbances in the period range of about 2 days. The covariance between the zonal wind component and the temperature change per day is found to be prevailingly negative in the hPa layer. This indicates upward transport of the westerly momentum. The fluxes are shown to be related strongly with the QBO cycle and the largest flux occurs in the region where the westerly regime is descending. The fluxes caused by the disturbances in the period range of about 2 days are as large as those by Kelvin waves in the period range of days. The disturbances behave like Kelvin waves to the extent that the disturbances are associated with the zonal wind component and temperature but no corresponding meridional component. 1. Introduction Two types of large-scale equatorial waves have been observed in the lower stratosphere: One is Kelvin waves with a period of about 15 days (Wallace and Kousky, 1968), and the other is mixed Rossbygravity waves with a period of about 4-5 days (Yanai and Maruyama, 1966; Maruyama, 1967). These waves appear to drive the quasi-biennial oscillation (QBO) as the Kelvin waves accelerate the westerly wind and the mixed Rossby-gravity waves accelerates the easterly wind (Lindzen and Holton, 1968; Lindzen, 1970). Hirota (1978), by using rocketsonde data at Ascension Island (8S, 14W), showed that some Kelvin waves with a period of about 10 days attained the upper stratosphere and lower mesosphere and suggested that the waves drove the semi-annual oscillation there. Furthermore, Hirota (1979), by using the satellite sounding data from Nimbus 5 SCR, confirmed the existence of eastward-moving waves with a period of 4-9 days. Salby et al (1984), by using the data from Nimbus-7 LIMS, showed evidence of Kelvin waves with periods of 7 days and 4 days. Basically, the mechanism of the QBO has been explained as Lindzen and Holton (1968) proposed, but amounts of momentum fluxes due to these waves estimated by previous studies (Maruyama, 1969; (C)1994, Meteorological Society of Japan Lindzen and Tsay, 1974; Maruyama, 1991; etc.) are, however, insufficient to drive the QBO, and further possibilities have been studied. One possibility is the existence of meridional circulation non-linearly induced by eddies. It is difficult to estimate the mean circulation directly from observations because it is generally very small. As a mechanism to accelerate the mean zonal flow, the mean meridional circulation has been studied by the use of numerical models (Plumb and Bell, 1982; Hamilton, 1984; Dunkerton, 1985;1991). Takahashi and Boville (1992) successfully obtained a simulation of the equatorial QBO by using a three-dimensional mechanical model. They noted that the model wave forcing required was considerably larger than the observed wave activity by including the effect of the wave-induced meridional flow. Additional momentum sources are thus required according to the results of numerical simulations. Another possibility for zonal wind acceleration is sought through the activity of other kinds of disturbances such as gravity waves and Rossby waves which have not yet been fully analyzed and which have been considered to be in shorter period ranges with thinner vertical wavelengths. The model by Lindzen and Holton (1968) could include various wave modes to contribute to the vertical momentum flux. Lindzen and Matsuno (1968) pointed the possibility of waves with very short wavelength. Observational studies based on the data with finer resolution in time and

2 424 Journal of the Meteorological Society of Japan Vol. 72, No. 3 altitude over the equatorial region have been very few except some special observations temporarily operated. In February-April 1967, a special observation Line Island Experiment was operated over the equatorial Pacific and upper-air soundings were made at 3-6 hour intervals with a vertical resolution of about 300m. Madden and Zipser (1970), by using the data of the experiment, described a multilayered structure of the meridional wind and showed the existence of vertically-propagating waves with a wavelength shorter than about 3km above the 14km level and below 9km. Recently, a special observation was operated over Indonesia, in February-March 1990 and Tsuda et al. (1992), by analyzing the data, showed the existence of an oscillation with a vertical wavelength of about 2-3km by examining vertical profiles of winds and temperature. These observational experiments were, however, restricted to a few months, and the long-term nature of the disturbances in the shorter period range or the relation with the QBO is still unknown. Most of observational studies of the long-term behavior of stratospheric equatorial waves have been made by a spectral analysis of once-a-day time series data at some standard pressure levels which could separate the disturbances in the period range longer than about 4 days (Maruyama, 1968; 1969; 1991; etc. ). By using twice-daily data, the period range can be extended to about a 2-days period. In the past ten years, twice-daily soundings at an equatorial station in Singapore (1.4N, 104.0E) have been attained as high as 10hPa (about 30km) more frequently. A spectral analysis was tried by using the data with same method as used by Maruyama (1991). However, no dominant spectral peaks could be separated in the shorter period range (not shown). When the amplitude and frequency of disturbances widely fluctuated, as expected in the shorter-period disturbances, the spectral analysis applied here could not fully resolve the sharpness of spectral peaks. Instead of spectral analyses, another kind of analysis should be tried to investigate the shorter-period disturbances. The purpose of this paper is to describe features of the disturbances in the period range shorter than about 4 days by the use of a covariance analysis which will be found favorable to this purpose. 2. Data and methods Upper-air data at Singapore from March 1983 to August 1993 are analyzed in this study. The observed values for each sounding are given at intervals of 0. 5 km by interpolating its significant level values. The data are compiled to twice-daily time series and missing data are covered by interpolation of the time series. At Singapore, soundings have been made at 00 UTC and 10 or 11 UTC, but it can be safely assumed that the data are given at intervals of 0.5 day (12 hours) for the present study. In the stratosphere, the fall and rise of temperature comes from upward and downward air motions, respectively, as no substantial heat sources are associated there in the period range we noted. The temperature change observed at a fixed point should be dealt with as the superposition of both the vertical motion associated with the wave propagation and the horizontal temperature advection (see the Appendix). In order to convert the temperature change into a vertical velocity, the estimation should be modified by the factor concerning the basic zonal flow z and the zonal phase speed c as given by the Eq. (3) of the Appendix: w,=-(1-u) c ae' at ae az where 0 is the potential temperature, w is the upward velocity component, t is time and z is the upward vertical coordinate, an overbar denotes the basic state and a prime any deviation from it. If the zonal basic flow u blows to the direction same as the phase propagation c and c I<uI, then the effect of u overcomes that of c. However, such a case is not considered to be observed in the present study, as discussed in Section 4. As a measure of vertical motion, a set of time series of the temperature change per a day 0 T1 is compiled by subtracting the temperature 0.5 day before a given time, Tl-1, from that 0.5 day after, T1+1: OT1=T1+1- T1-1. The time series obtained in this way enhance the oscillation with a period of about 2 days, as shown in Fig. la. The processing in this way means a kind of bandpass filtering to separate the disturbances of period around 2 days. Here, it is noteworthy that, in order to separate shorter period waves, Hirota's (1978) analysis was made by using a two-day difference of rocketsonde soundings which was usually operated on Wednesday and Friday. To separate disturbances of the zonal wind component with a period of about 2 days, a high-pass filtering is applied to the time series of the zonal wind component. The filtering is made by removing a triangular-weighted mean from the original time series as u'1=ul-(u1-3+2u1-2+3u1-1+4u1+3u1+1+2u1+2+u1+3)/16. The amplitude response is shown in Fig. 1(b). The same processing is made for the meridional wind component to obtain the filtered time series (v'1). Then, the covariance between the disturbances of zonal wind component and the temperature change per day (u's T) and the covariance between the zonal and meridional wind components (u'v') are computed at each level for each month. If an estimate u'i T is negative, the westerly momentum flux is considered to be upward. If an estimate u'v' is positive, the

3 June 1994 T. Maruyama 425 (a) (b) Fig. 1. Amplitude responses of a time series ai. at the interval of 0.5 days by applying (a) one-day-difference processing: tai=ai+l-ai-1 and (b) a triangular-weighted mean removing: a'i=at-(ai3+2ai-z+3ai-1+4ai+3ai+1+2ai+z+ai+3)116. westerly momentum is shown to be carried northward. 3. Relation with the QBO It is interesting to compare the behavior of u'0 T and u'v' with the QBO of the zonal wind. In Fig 2, a vertical time section of the monthly mean zonal winds is shown during the years Four cycles of the QBO are found to cover the years. Measuring the period of each QBO cycle from the westerly onset at 50 hpa, we obtain 29 months (from October 1982, not shown, to March 1985), 30 months (to September 1987), 32 months (to May 1990), and 31 months (to December 1992). These four cycles tend to a rather long period stage in a history of the QBO since a long term mean is 28.3 months (17 cycles 40 years from 1953 to 1992). In Fig. 3, a vertical time section of monthly estimated covariances u'i T is shown during the years We find in the figure that the estimates are prevailingly negative throughout the layer hpa. Relatively large negative estimates (shaded in the figure) are found almost all the time in the layer hPa, and found in the shear layer where the westerly regimes are descending (Fig. 2). Positive estimates appear scattering mostly in the layer hpa. In the layer hPa, absolute values of estimates are quite small. To investigate whether the disturbances appearing in the covariance u'0 T are accompanied with the meridional component, meridional momentum fluxes are estimated. In Fig. 4, a vertical time section of monthly estimated covariances u'v' is shown during the years A definite annual cycle is observed in the layer hPa, negative in the northern winter and positive in the northern summer. Positive fluxes mean northward transport of the westerly momentum and negative southward. The covariance u'v' does not appear to have any significant correspondence with the QBO. To inspect the QBO cycles and annual cycles in u'ot and u'v' more closely, superposition is applied to their vertical time sections for four cycles of the QBO (30 months on the average) and 9 annual cycles ( ), respectively. The superposed vertical time sections in this way are given in Fig. 5. A dominant QBO cycle is observed in u'z T in the layer hpa, but no corresponding variation is found in u'v'. On the other hand, a marked annual cycle is observed in u'v'in the layer of hPa, but annual variation is not clear in u' T. This implies that no meridional component is associated with the disturbances in u't. The period of oscillation and vertical wavelength Fig. 2. Vertical time section of monthly mean zonal winds at Singapore. The contour interval is 10ms-1 and the westerly region is shaded.

4 426 Journal of the Meteorological Society of Japan Vol. 72, No. 3 Fig. 3. Vertical time section of monthly estimated covariances between u' and z T at Singapore. The contour interval is 2ms-1 K, zero contours are shown in thick lines, and negative estimates less than -1ms-1 K are shaded. Fig. 4. Vertical time section of monthly estimated covariances between u' and v' at Singapore. The contour interval is 2 (ms-1)z, zero contours are shown in thick lines, and positive estimates are shaded. (a) (b) Fig. 5. Superposed vertical time sections for the QBO synchronized cycle (left) and the annual cycle (right) of monthly estimated covariances (a) between u' and 0 T and (b) between u' and v'. Mean westerly onset months are month 16 at 20hPa, 18 at 30hPa and 21 at 50hPa. The contour intervals and shades are same as Fig. 3 for (a) and Fig. 4 for (b). can be examine by inspecting the vertical time section of disturbances. Generally speaking, downwardpropagating disturbances prevail in the layer hpa throughout all time. This shows upward energy fluxes from the troposphere. Actually, it is very difficult to identify their wave mode because the disturbances filtered out in the present analysis usually contain various components of disturbance. In Fig. 6, some examples of vertical time sections of disturbances u', v', and O T are displayed. The figure set (a) is for June 1992 when the covariance u't has a negative peak at about 15hPa and the covariance

5 June 1994 T. Maruyama 427 (a) (b) Fig. 6. Vertical time sections of OT, u' and v' for the months (a) June 1992 and (b) January Positive anomalies are shaded, and the contour intervals are 2K for T and 2ms-1 for u' and v'.

6 428 Journal of the Meteorological Society of Japan Vol. 72, No. 3 Fig. 7. Vertical time section of monthly estimated vertical fluxes of zonal momentum in the period range about 2 days at Singapore. The contour interval is 2x10-Z(ms-1)2, zero contours are shown in thick lines, and positive estimates greater than 1x10-Z (ms1)2 are shaded. u'v' has a positive peak at about 120hPa. Especially in the latter part of the month, downward-propagating wave patterns are clearly observed for both 1 Tand u' with an inverse relationship between them. The features of this part remind one of those of Kelvin waves, though the period and vertical wavelength are quite short. Counting positive anomalies vertically in the layer hPa (17-31km) during the period from 21 to 30 June, two or three wavecrests pass through, giving a vertical wavelength of about 4-7km. Counting horizontally during the ten days, four, five or six wavecrests pass; this gives a period of oscillations of about days. The figure set (b) shows the disturbance patterns for January 1991 when the covariance u'v' has a positive peak at about 120hPa and the covariance u'0 T. is nearly zero in the layer 20-10hPa. The temperature disturbance pattern in the layer hPa shows waves with shorter vertical wavelengths and shorter periods not sufficiently resolved in the present analysis. The zonal wind disturbance pattern in the layer hPa shows rapidly descending waves with a period of about 2 days. The meridional wind disturbance pattern, different from those for the temperature and zonal wind component, displays somewhat longer-period descending waves. This pattern reminds us of mixed Rossby-gravity waves as this wave mode has the maximum amplitude of the meridional component at the equator and no corresponding zonal component and temperature there (Maruyama, 1967, etc.). In the layer hPa, disturbances of zonal and meridional winds have almost no tilting for either month. 4. Estimates of vertical momentum fluxes The vertical flux of the westerly momentum is given by Eq. (4) of the Appendix u'w'-(1 cu) (p(3)r/cp az 'OT U'LT Lt The phase speed c is generally impossible to determine based on the observation from only one station. If the disturbances are assumed to be Kelvin waves with a period of about 2 days and the vertical wavelength is about 4-7km as shown in the previous section, theoretical consideration of equatorial waves will help to determine c reasonably. An approximated relationship for a Kelvin wave is given as kv where k is the eastward angular wavenumber, A is the upward angular wavenumber, v is the wave angular frequency and N is the Brunt-Vaisala frequency (Holton, 1979). Substituting the observed values of the period and the vertical wavelength and N-'2x10-Zs-1 for the present case, then we get a zonal wavelength about 2,000-4,000km. This gives a phase speed of about 10-20ms-. By taking the monthly mean zonal wind as the basic zonal flow u, the value of u varies from-30m s-1 (easterly) to 10ms-1 (westerly) according to the QBO (see Fig. 2). Sometimes the monthly mean zonal wind takes the range -40ms-1 or 20ms-1, but such a case occurs over a very short time and its layer is very thin. Therefore such a case is not taken into consideration. In Table 1, values of the factor (1-u/c) are listed for various u and c. The factor is zero for the case of c =10ms-1 and u=10m This indicates a critical level where momentum cannot be transported through. The factor can be negative if c<iu, but such a case does not occur for stratospheric waves forced from below. Actually, the monthly mean tonal wind very seldom attained 20ms-1 (westerly). As seen in Table 1, the values of (1-u/c) has a considerable range according to the value of c, and a fixed value of c could not be determined because c estimated here was obtained under a very rough assumption for the disturbances with a period of about 2 days. Therefore, estimations of the flux are hereafter made by omitting the term

7 June 1994 T. Maruyama 429 Fig. 8. Vertical time section of monthly estimated vertical fluxes of zonal momentum in the period range of days at Singapore. The contour interval is 2x10-2 (m s-1)2, zero contours are shown in thick lines, and positive estimates greater than 1x10-2 (m s-1)2 are shaded. u/c. This gives overestimated fluxes in the westerly region and underestimated fluxes in the easterly region. The vertical time section of vertical fluxes estimated by this omission is shown in Fig. 7. The general pattern is similar to that in Fig. 3 except in the layer hPa, where the adiabatic assumption may be less adequate since heating by deep convection is active there. In the layer 50-10hPa, estimates as large as 5x10-2(ms-1) 2 are found in the westerly descending shear region. The estimates for Fig. 7 (and also Fig. 8 for comparison) are made by neglecting the term u/c. To compare the above result with the flux due to the Kelvin waves described in the previous studies (such as Maruyama, 1991), a spectrum analysis is made for the present data. In Fig. 8 a vertical time section of vertical momentum fluxes (also with the term u/c omitted; more reasonably multiplying by the values for c=30 ms-1 in Table 1) in the period range of days is shown during the years Substantial enhancement of the flux is observed in the layer hpa, corresponding with the descending westerly shear regime. The maximum flux is 8x10 (ms-1)2 for the westerly regime descent in 1987, and 2-4x10-2 (ms-1)2 for other descents. The estimates of vertical fluxes by the disturbances in the period range about 2 days are found as large as those in the period range of days. If these vertical fluxes are superposed Table 1. Values of the factor (1-u/c) to be given by the basic zonal flow u and the phase speed c. The estimates in Figs. 7 and 8 should be multiplied by this factor if u and c are determined. See the Appendix. and converged in the layer at 5km, it is possible to generate an acceleration larger than 10-5m s-2 or 30 m s-1 month-1, sufficient to drive the westerly onset in the QBO. 5. Discussion The disturbances with a period of about 2 days were separated through a covariance analysis in the present study. This does not imply the existence of disturbances with an isolated spectral peak of about a 2-day period, because the data were put through a kind of bandpass filtering before the covariance analysis. The disturbances are most likely of a Kelvin wave mode with shorter scale but also possible of higher mode gravity waves with the zonal component over the equator. Their associated meridional component is, if any, too weak to separate as the station is very close to the equator. A wider spectrum of the upward momentum flux, by Kelvin waves or eastward-moving gravity waves, is advantageous to the westerly acceleration. Numerical simulations of the QBO showed the deficiency in observed wave activities to account for the QBO, especially easterly-accelerating waves (Takahashi and Boville, 1992, etc.). On the analogy of the westerly-accelerating waves in the present study, it is interesting to investigate the existence of shorter-period disturbances accompanied with mixed Rossby-gravity waves. A variance analysis was also tried for high-pass filtering data of the meridional wind component in the shorter period range, but the analysis failed to detect disturbances accompanied with large-scale mixed Rossby gravity waves (not shown). Compared with covariance estimates between two elements (such as u' and T), variance estimates for a single element are liable to get obscured by noisy variations. Although planetary scale equatorial waves cannot entirely account for the momentum flux, this does not degrade the essential role of these large-scale waves. First, some of them may modulate convection

8 430 Journal of the Meteorological Society of Japan Vol. 72, No. 3 in the tropical troposphere, exciting gravity wave activity toward the stratosphere. Second, the largest-scale waves are most likely responsible for the formation of the QBO-associated shear zones. Once the shear zones are formed, gravity waves accelerate their descent. 6. Concluding remarks Twice-daily time series upper-air data at Singapore during the years are analyzed and the covariance between the tonal wind component and the temperature change per day is found to be almost always negative. This shows that upward transport of the westerly momentum is prevailing throughout the years. The fluxes are shown to be related strongly with large-scale Kelvin waves and the QBO cycle and the largest flux occurs in the shear region where the westerly regime is descending. The amount of flux caused by the disturbances in the period range about 2 days is as large as that caused by large-scale Kelvin waves in the period range of days. It is interesting to examine whether there is any gap of the momentum flux amount in the period range between the flux due to disturbances with a period of about 2 days and that due to the large-scale Kelvin waves with a period of days. The flux in the period range about 3-7 days should be analyzed, where spectral analyses have been successfully made to display the mixed Rossby-gravity waves. As for the vertical flux, however, it requires more careful treatment to fill up the period range, because the estimates for the disturbances with a period of about 2 days were obtained by a covariance analysis, while those for Kelvin waves with a period of days were found by a conventional spectral analysis. In the previous studies (Maruyama, 1968; Wallace and Kousky, 1968; etc), phase differences between disturbances at different heights have been calculated to estimate the vertical wavelength. This method, however, preferentially separates the disturbances with longer wavelengths, and thinner waves are diminished by the wide fluctuation of the period and wavelength of disturbances. By inspecting vertical time sections of the disturbances, their vertical wavelength is found to be shorter than that of large-scale Kelvin waves, but the disturbances with thinner vertical scales are still difficult to analyze in the present study. The direction of zonal propagation and phase speed of the disturbances have not yet determined by using data from several stations in the equatorial belt. At least, phase difference analyses between two equatorial stations should be required to determine the direction. Although soundings at equatorial stations have not regularly attained to higher levels, estimates of the phase differences may be obtained in some fortunate cases. Uneven distribution is more likely for small-scale disturbances than for planetary-scale waves. The longitudinal distribution of the equatorial wave activities should be examined as well as their longitudinal propagation. For such a purpose, satellite-related analyses will hopefully make an advance. Acknowledgements Members of Forecast Research Division and Climate Research Division of Meteorological Research Institute discussed and gave helpful comments on the present study. The data were compiled by the Numerical Forecast Division of Japan Meteorological Agency. The Singapore Meteorological Service kindly supplied their checked data for recovering considerable data missed during telecommunication. Computations were made at the Meteorological Research Institute. Appendix The method to estimate vertical momentum fluxes from the time change of temperature is the same as used in Maruyama (1968). If we assume that the disturbances are zonally propagating and that their meridional advection is negligible, the adiabatic equation is approximately written as (1) -+uae+w'ae-=0 at ax az where 8 is the potential temperature, u and w are eastward and upward velocity components, respectively, t is time, and x and z are eastward and upward coordinates, respectively. An overbar is the basic state and a prime is the deviation from that. The second term is, by using the eastward phase speed, c, rewritten as (2) From the Equations (3) ae'1 ae' ax c at (1) and (2), we get ae' w, --(1--) C at as az By taking monthly mean values as the basic state values and replacing the time change of potential temperature with a one-day temperature change, the vertical flux of the westerly momentum can be estimated: (4) u'w'=-(1--) yo Roc U a p u' T tt e az where p and po are the pressure and reference pres-

9 June 1994 T. Maruyama 431 sure, respectively, R and Cp are the gas constant and constant pressure specific heat of air, respectively, and Ot=1 day as the time interval for the temperature change L&T. References Dunkerton, T. J., 1985: A two dimensional model of the quasi-biennial oscillation. J. Atmos. Sci., 42, Dunkerton, T. J., 1991: Nonlinear propagation of zonal winds in an atmosphere with Newtonian cooling and equatorial wavedriving. J. Atmos. Sci., 48, Hamilton, K., 1984: Mean wind evolution through the quasi-biennial cycle in the tropical lower stratosphere. J. Atmos. Sci., 41, Hirota, I., 1978: Equatorial waves in the upper stratosphere and mesosphere in relation to the semiannual oscillation of the zonal wind. J. Atmos. Sci., 35, Hirota, I., 1979: Kelvin waves in the equatorial middle atmosphere observed by the Nimbus-5 SCR. J. Atmos. Sci., 36, Holton, J. R., 1979: An Introduction to Dynamic Meteorology. Academic Press, 391pp. Lindzen, R. S., 1970: Vertical momentum transport by large scale disturbances of the equatorial lower stratosphere. J. Meteor. Soc. Japan, 48, Lindzen, R. S., and J. R. Holton, 1968: A theory of of the quasi-biennial oscillation. J. Atmos. Sci., 25, Lindzen, R. S., and T. Matsuno, 1968: On the nature of the large scale disturbances in the equatorial lower stratosphere. J. Meteor. Soc. Japan, 46, Lindzen, R. S., and C.-Y. Tsay 1975: Wave structure of the tropical stratosphere over the Marshall Islands during 1 April-1 July J. Atmos. Sci., 32, Madden, R. A., and E. J. Zipser, 1970: Multi-layered structure of the wind over the equatorial Pacific during the Line Island Experiment. J. Atmos. Sci., 27, Maruyama, T., 1967: Large-scale disturbances in the equatorial lower stratosphere. J. Meteor. Soc. Japan, 45, Maruyama, T., 1968: Upward transport of westerly momentum due to large-scale disturbances in the lower stratosphere. J. Meteor. Soc. Japan, 46, Maruyama, T., 1969: Long term behavior of Kelvin waves and mixed Rossby-gravity waves. J. Meteor. Soc. Japan, 47, Maruyama, T., 1979: Equatorial wave intensity over the Indian Ocean during the years J. Meteor. Soc. Japan, 57, Maruyama, T., 1991: Annual and QBO-synchronized variations of lower stratospheric equatorial wave activity over Singapore during J. Meteor. Soc. Japan, 69, Plumb, R. A., and R. C. Bell, 1982: A model of the quasi-biennial oscillation in an equatorial betaplane. Quart. J. Royal Meteor. Soc., 108, Salby, M. L., D. L. Hartmann, P. L. Bailey, and G. C. Gille, 1984: Evidence for equatorial Kelvin modes in Nimbus-7 LIMS. J. Atmos. Sci., 41, Takahashi, M., and B. A. Boville 1992: A threedimensional simulation of the equatorial quasibiennial oscillation. J. Atmos. Sci., 49, Tsuda, T., Y. Murayama, H. Wiryosumarto, S. Kato, S. W. B. Harijono, M. Karmini, C. M. Mangan, S. Saraspriya and A. Suripto, 1992: A preliminary report on radiosonde observations of the equatorial atmosphere dynamics over Indonesia. J. Geomag. Geoelectr., 44, Wallace, J. M., and V. E. Kousky, 1968: Observational evidence of Kelvin waves in the tropical stratosphere. J. Atmos. Sci., 25, Yanai, M., and T. Maruyama, 1966: Stratospheric wave disturbances propagating over the equatorial Pacific. J. Meteor. Soc. Japan, 44,

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