Spectral Analysis of Planetary Waves in the Summer Stratosphere and Mesosphere*

Transcription

1 February 1975 Isamu Hirota 33 Spectral Analysis of Planetary Waves in the Summer Stratosphere and Mesosphere* By Isamu Hirota** Meteorological Research Institute, Tokyo (Manuscript received 5 October 1974, in revised form 14 December 1974) Abstract An analysis was made of planetary-scale variations of temperature and wind fields in the summertime stratosphere and mesosphere by the use of meteorological rocket and satellite observations. From the vertical time-section analysis of temperature and wind at Cape Kennedy (28N, 81W) and other rocket stations in subtropics of the Northern Hemisphere, it is found that the oscillation with a period of about 15 days is predominant above 30 km. To describe the nature of wind and temperature oscillation in more detail, a power spectral analysis was made of the time series rocket data during the period of three months from July to September in 1969 and The result suggests that the oscillation as revealed by the analysis for indivisual observation station is a reflection of the horizontal movement of planetary-scale wave disturbances embedded in the mesospheric easterlies. The presence of traveling planetary waves in the summertime stratosphere was confirmed by means of a zonal harmonic analysis of ITOS-D VTPR retrieval data and Nimbus-5 SCR radiance data for the Southern Hemisphere in 1972/1973 summer, and the wavenumber-frequency relation is given in a quantitative manner. 1. Introduction Observational and theoretical studies on planetary-scale waves in the upper atmosphere have been extensively made by many authors in the last decade from various points of view. Most of these studies, however, confined themselves to planetary Rossby waves embedded in the polarnight westerlies of the winter stratosphere and mesosphere, in connection with the vertical propagation of wave energy and subsequent sudden warming phenomena, and to equatorial disturbances such as Kelvin waves and mixed Rossbygravity waves, in relation to the quasi-biennial oscillation of stratospheric zonal current over the equatorial region. In contrast, there have been only a few reports on large-scale wave disturbances in the summertime stratospheric and mesospheric easterly current, * An early version of this paper was presented at the First Assembly of IAMAP/IAPSO, Melbourne, Australia, in January ** Present affiliation: Geophysical Institute, Kyoto University, Kyoto. where vertical propagation of stationary forced Rossby waves is theoreticaly prohibited. Based upon high-level balloon observations of the stratosphere in the Northern Hemisphere in July 1958, Scherhag (1960) first found a westward traveling temperature disturbance of wavenumber at the 20 mb level, and estimated 1 the wave amplitude as about 4 C and the period as about 13 days. Muench (1968) also detected a 13-day period westward traveling wave of wavenumber 1, with respect to the east-west wind component, from an analysis of rawinsonde observations in the 10 to 15 mb layer for July Recently, the global temperature distribution in the upper atmosphere has been described with the aid of carbon dioxide infra-red radiation measurements by meteorological satellites. Fritz and Soules (1972) showed a synoptic distribution of radiance from the channel 8 of SIRS on Nimbus 3, which is considered to be representative of the temperature in the middle stratosphere. Inspection of their synoptic charts reveals that planetary-scale waves of wavenumber 1 to 3 are dominant in middle latitudes of the Southern

2 34 Journal of the Meteorological Society of Japan Vol. 53, No. 1 Hemisphere for the summer season of 1969/1970. Deland (1973 a, b) made a spectral analysis of traveling planetary waves in the stratospheric temperature fields by the use of Nimbus 3 SIRS radiance data, and discussed the behavior of waves in winter and summer. These studies indicate, without doubt, the presence of planetary waves in the middle and lower stratosphere in summer. However, the (* 50 km), which are comparable to the error of meteorological rocket observations (cf. Hirota, 1968) Mean state As a background analysis of the summer stratosphere and mesosphere, Fig. 1 shows the monthly mean state of temperature and zonal wind in the meridional section for July Rocket characteristics of these waves such as a wavenumber-frequency (or phase velocity) relation and the vertical and latitudinal distribution of wave amplitude (or wave energy density) are still open to the question. Thus the main purpose of the present study is to extend the analysis of planetary-scale wave disturbances in the upper atmosphere in summertime. The first half of this paper gives a description of the nature of temperature and wind oscillations in the upper stratosphere and lower mesosphere by means of a power spectral analysis of meteorological rocket observations in the Northern Hemisphere. In the second half, to reinforce the presence of planetary waves in the summer stratosphere and to give a wavenumberfrequency relation, a zonal harmonic analysis is made of ITOS-D VTPR and Nimbus-5 SCR observations for the Southern Hemisphere. 2. Analysis of meteorological rocket data (a) 2-1. Data The data report of "High altitude meteorological data" published by World Data Center A was used in the present study. The period of analysis is three months (July-September) in two summer seasons (1969 and 1970) of the Northern Hemisphere. Since we are interested in temperature and wind variations with a time-scale longer than several days, we choose, for the time series analysis, rocket stations where observational data are available for about 30 days or more during the three months. Moreover, we use only the data of rockets launched at around the local noon, i.e., 9h `15h, to remove the effect of diurnal variations of temperature and wind in the upper atmosphere. Roughly speaking, the contribution of the diurnal variation to the observed temperature and wind oscillation may be, by this filtering, of the order of 1 C and 1 meter/sec at the stratopause level (b) Fig. 1. Monthly mean state of (a) temperature (units in C) and (b) zonal wind component (units in meter/sec) for July 1969.

3 (a) 35 (b) (c) Fig, 2. Vertical time-section of (a) temperature (units in C), (b) zonal wind component and (c) meridional wind component (units in meter/sec) at Cape Kennedy during the period from July to September White circles on the abscissa denote the date of rocket launchings.

4 36 Journal of the Meteorological Society of Japan Vol. 53, No. 1 stations used for the statistics are as follows; from north to south, Thule (77N, 69W), Fort Greely (64N, 146W), Fort Churchill (59N, 94W), Primrose Lake (55N, 110W), Wallops Island (38N, 75W), Point Mugu (34N, 119W), White Sands Missile Range (32N, 106W), Cape Kennedy (28N, 81W), Barking Sands (22N, 160W), Fort Sherman (9N, 80W) and Ascension Island (8S, 14W). Since the spatial variation of time-averaged components of temperature and wind with respect to longitude is, as shown later, small in the summer stratosphere, the monthly mean state shown in Fig. 1 may be considered as an approximation to the zonal mean state. The zonal mean circulation of the summer stratosphere is characterized by the poleward increase of temperature and the associated strong easterlies the core of which is located at about 30N and at the stratopause level. In the mesosphere of middle and low latitudes, the easterly zonal wind decreases with height in accordance with the equatorward increase of temperature. Similar features can be seen in the monthly mean state of July 1970, except for the zonal wind in the equatorial lower stratosphere which reflects the quasi-biennial oscillation Vertical time-sections A vertical time-section analysis was made of rocket data for July through September 1969 and 1970 at several stations in the subtropics of the Northern Hemisphere. Fig. 2 shows the time-sections of temperature, zonal wind and meridional wind at Cape Kennedy. White circles on the abscissa denote the data of rocket launchings. Most of these data are available between 25 and 60 km, and only 20% of them are missing above 55 km. One of the characteristics of temperature variation at Cape Kennedy during this season (Fig. 2a) is that the quasi-periodic oscillation with a period of about 15 days is observed above 30 km. There is also some indication that the phase of temperature change propagates downward, and the "vertical wavelength" is roughly estimated as 15 to 20 km. The quasi-periodic oscillation is found also in the time section of zonal wind and meridional wind (Fig. 2b, 2c). In addition to the 15-day period oscillation, seasonal variation of zonal wind from the summer easterlies to the autumnal westerlies is found in the mesosphere. Similar features of temperature and wind variation are observed from the vertical time-section analysis of rocket data at Barking Sands in 1970 summer as shown in Fig. 3, where the long-term (seasonal) variations are removed from the original data. (a) (b) (c) Fig. 3. Same as Fig. 2 but for Barking Sands during the period from July to September Components of seasonal variation are removed, and negative values are shaded Power spectral analysis To study the nature of quasi-periodic temperature and wind variations in a quantitative manner, an attempt is made to apply a method of power spectral analysis to these meteorological rocket data. A sub-program for power spectral analysis was supplied by Dr. T. Maruyama of

5 February 1975 Isamu Hirota 37 Meteorological Research Institute, and the procedure of computation is almost the same as that described in his paper (Maruyama, 1968). First of all, time series data are prepared in such a way that the daily values of temperature and wind are read off by a linear interpolation from the subjectively analyzed vertical time-sec tions at every 5 km level from 30 to 60 km during the period from July 1 to September 28. Thus we have a set of data (90 days, 7 levels) for each element (temperature T, zonal wind component U and meridional wind component V) at several rocket stations. Next, to remove long-term (seasonal) variations from the original data set, a high-pass filter that reserves temporal variations with periods shorter than about 40 days is applied to these data, since our attention is mainly focused on the variation range of 10 to 20 days. In practice, the response of the high-pass filter we used is shown in Table 1. The damping factor for the power density is given by R2. (a) Table 1. Response of the high-pass filter. (b) Then a power spectral analysis is made. In this computation the maximum lag number is 30, which gives 31 spectral estimates at intervals of 1/60 cycle per day in the frequency range from 0 to 0.5 cycle/day. Fig. 4 shows the frequency-height diagram of power spectral density for T,U,V at Cape Kennedy in 1969 summer. In correspond to the vertical time-section analysis mentioned above, we find in Fig. 4(a) that temperature disturbances with periods of about 12 to 20 days are predominant in the upper stratosphere and lower mesosphere. On the other hand, it seems from Fig. 4 (b) and (c) that the variation of wind fields is predominant for the period range from 10 to 15 days in the upper stratosphere. The result of power spectral analysis for other rocket stations in 1969 summer also indicates the concentration of power density to 12- to 20-day period disturbances in the upper layer. (c) Fig. 4. Frequency-height diagram of power spectral density for (a) temperature (units in deg2 Eday), (b) tonal wind and (c) meridional wind (units in (meter/sec)2 day) at Cape Kennedy for July through September 1969.

6 38 Journal of the Meteorological Society of Japan Vol. 53, No. 1 (a) (b) (c) Fig. 5. Same as Fig. 4 but for temperature at (a) Wallops Island, (b) Cape Kennedy and (c) Barking Sands during the period from July to September It should be noted, however, that the concentration of power density for wind fields cannot be seen so clearly as that of temperature, especially for the zonal wind component in the mesosphere, where the seasonal variation of the zonal wind is predominant. Throughout the computation of power spectral densities, a question might arise as to whether the apparent minimum for periods between 20 and 60 days is significant or not, because we applied a high-pass filter to the original data. However, in most cases, the power spectral density shows an isolated maximum between 10 to 20 days even when the high-pass filter is not applied. In some cases, the power density increases monotonically with decreasing frequency when the longterm variation is not removed, but the gradient is not so large as expected from the seasonal trend, indicating that the separation of the seasonal variation and the 10- to 20-day period oscillation is physically significant. The 12 to 20 day period oscillation of temperature can be also observed in 1970 at Wallops Island, Cape Kennedy and Barking Sands as shown in Fig. 5. It seems, in general, that the power density of temperature disturbances in this frequency range increases with height in the stratosphere and has the maximum near the stratopause. It is quite interesting to compare our result with the analysis of planetary waves in the upper atmosphere by Justus and Woodrum (1973). They showed, by the use of meteorological rocket data, that traveling planetary wave component magnitudes in mid-latitudes, which come from the period range days, have a maximum value at the 50 km altitude. Since no attempt is made to separate the planetary waves in winter and summer, however, their result would indicate the characteristics of the winter circulation where the wave amplitude is relatively large. An approximate two-week periodicity in the stratospheric circulation has been recently studied by means of spectral analysis of wind and temperature for 12 years (Angell et al., 1973) and of energy cycle for 5 years (Miller, 1974). Results of their climatological analysis strongly support the possibility of periodic variations of stratospheric circulation which is mainly contributed from the planetary wave activity in the middle latitude westerlies. In addition to their analysis, the present result indicates that the two-week

7 February 1975 Isamu Hirota 39 periodicity is predominant not only in the winter stratosphere but also in the summer stratosphere. In order to see in more detail the nature of disturbances as revealed by the power spectral analysis, we made a cross spectral analysis between two observation stations for each element at each level. If the temperature and wind oscillation at one station is due to the passage of a traveling planetary wave in the east-west direction, crossspectral estimates must show the high coherence and systematic phase differences between two stations. Results of these estimates for several pairs of rocket station are, however, not always consistent with one another, suggesting that the 12- to 20-day period oscillation is a reflection of the horizontal movement of wave disturbances with different wavenumbers and different phase velocities. If we have enough accuracy and density Fig. 6. Frequency-height diagram of co-spectral estimates between temerature and meridional wind component at Cape Kennedy for July-September 1969 and Units in deg (meter/sec). day. of rocket data, separation of traveling waves by the use of a kind of band-pass filter would give us a more detailed information. Finally, co-spectral estimates between temperature and meridional wind component at Cape Kennedy for 1969 and 1970 summers are shown in Fig. 6. The result of this computation indicates that the heat transport associated with the waves is negative (equatorward) in the frequency range under consideration. An attempt was also made to estimate the cospectrum between the zonal and the meridional wind component, but no significant result was obtained, probably due to the inaccuracy of wind observations. 3. Analysis of ITOS-VTPR data The result of time series analysis of the meteorological rocket data suggests the presence of traveling planetary waves in the summer stratosphere and mesosphere. However, because of the sparsity of the meteorological rocket network, synoptic evidence of planetary waves cannot be obtained in middle and lower latitudes. To confirm the existence of traveling planetary waves in the summertime stratosphere, an attempt is made in this section to make a zonal harmonic analysis with the use of hemispheric 10 mb level data obtained from the retrieval of infrared radiation measurements by VTPR (Vertical Temperature Profile Radiometer) on ITOS-D (NOAA- II) launched on October The period of the present analysis is one month from December 21, 1972 to January 20, 1973, which is the summer season of the Southern Hemisphere. The reason why we choose the Southern Hemisphere for the planetary wave analysis is that the 10 mb data density of VTPR retrievals in the Southern Hemisphere is larger than that in the Northern Hemisphere. First, we make daily synoptic charts of 10 mb level and read off the value of temperature and isobaric height on gridpoints at every 10 degrees in latitude from 30 S to 60 S and every 10 degrees in longitude. Then we have two sets of data for temperature and height. Next, we obtain the deviation fields of temperature and height from the one-month average at every gridpoint, to remove the effect of "standing waves" and systematic errors of VTPR observations. With the use of these data, the Fourier analysis was made of "transient waves"

8 40 Journal of the Meteorological Society of Japan Fig. 7. Vol. 53, No. 1 Time-section of transient wave amplitude for (a) temperature (units in C) and (b) isobaric height (units in meter) at 10 mb during the period from December 21, 1972 to January 20, on the daily basis for every latitude. Results of the zonal harmonic analysis are shown in Fig. 7 and 8. Fig. 7 (a) and (b) show the time-section of planetary wave amplitude of temperature and height respectively. It is found from Fig. 7 that the transient waves of wavenumber k=1 and 3 are predominant with the maximum amplitude of the order of LO C for temperature and 100 m for height, and the wave of wavenumber 2 is rather weak compared with the other two. Waves of wavenumber 4 and more are so weak that hereafter we disregard them. Distribution of phase angle of these planetary waves during the period of analysis is shown in Fig. 8. It is quite interesting to note that the day-to-day variation of transient waves is almost systematic, indicating that the waves migrate in the east-west direction with nearly constant phase velocities. This fact strongly supports the significance of the zonal harmonic analysis, although the magnitude of computed wave amplitude itself is near the level of observational errors. Inspection of this figure reveals that the wave 1 is a westward traveling wave and the wave 2 and 3 are eastward of the marized Table traveling characteristics in Table 2. waves. of these Rough waves estimates are sum- 2. Characteristics of planetary estimated from Fig. 8. waves as "' The difference between the mean zonal velocity U at 10 mb and phase velocity is nearly constant with respect to latitude. It may be noteworthy that the wave 1, which travels westward with a period about two weeks, is very similar to those found by Scherhag (1960) and Muench (1968) in the summer stratosphere of the Northern Hemisphere. The waves of wavenumber 2 and 3 may be identified with the radiance perturbations shown by Fritz and Soules (1972) for the Southern Hemisphere in the summer season of 1969/1970 (see their Fig. 5 and 6). All of the periods of traveling planetary waves

9 February 1975 Isamu Hirota 41 (a) (b) Fig. 8. Phase angle of transient wave for (a) temperature and (b) isobaric height at 10 mb duing the period from December 21, 1972 to January 20, obtained from the zonal harmonic analysis of VTPR retrieval data fall into the period range of days. This fact reinforces the conclusion of previous section in that the quasi 15-day period oscillation of temperature and winds in the upper atmosphere as revealed by the power spectral analysis of rocket observations is due to the passage of traveling planetary waves. Further computation was made to estimate the meridional heat transport associated with the traveling planetary waves mentioned above, with the use of temperature and isobaric height of 10mb under the geostrophic assumption. The result of computation seems to indicate that the heat

10 42 Journal of the Meteorological Society of Japan Vol. 53, No. 1 transport due to the wave of wavenumber 1 is equatorward, in agreement with the estimation shown in Fig. 6. However, the direction of heat transport by wave 2 and 3 changes randomly with time, probably because the accuracy of VTPR retrievals is insufficient for second-order perturbation estimates. 4. Analysis of Nimbus 5 SCR data In order to extend the zonal harmonic analysis of planetary waves to the upper stratosphere, an attempt is made in this section to use the radiance data obtained by the Selective Chopper Radiometer (SCR) on Nimbus 5 launched on December General description of the Nimbus SCR is given by Barnett et al. (1972). The period of the present analysis is the same as that of ITOS-VTPR given in the previous section. 40 and 45 km. It is found that the radiance wave of wavenumber 1 at this level shows almost similar behavior to those at 10 mb. (Fig. 7, 8), except that the phase velocity is large to some extent. Finally, global distribution of planetary waves was analyzed with the use of radiance data from all channels of Nimbus 5 SCR. Fig. 10 shows Fig. 10. Meridional distribution of the one-month average of wavenumber 1 radiance amplitude (units are equivalent to C). See the text in detail. Fig. 9. Radiance wave amplitude (left: units are equivalent to C) and phase angle (right) for the SCR top channel (B12: peaking at about 43.5 km) during the period from December 21, 1972 to January 20, Fig. 9 shows the day-to-day variation of amplitude and phase angle of transient wave 1 obtained from the SCR top channel (Ch. B 12) radiance which is representative of the upper stratospheric temperature field in a layer between the meridional distribution of radiance wave amplitude of wavenumber 1 for one-month period from December 21, 1972 to January 20, In this analysis the daily values of wavenumber 1 amplitude for each channel are averaged during the period without making separation of traveling waves and standing waves. Therefore, it should be noted that Fig. 10 differs from the wave amplitude distribution of one-month average radiance field. One of the most interesting aspects of this figure is that there are two maxima of planetary wave amplitude in the stratosphere : one is at degrees latitude in the Northern (winter) Hemisphere and the other is at degrees latitude in the Southern (summer) Hemisphere. The ratio of the maximum amplitude between two hemispheres is about 1/5 `1/10. The planetary wave predominant in the winter hemisphere is regarded as a stationary forced Rossby wave which propagates vertically through the polar-night westerlies, since the day-to-day

11 February 1975 Isamu Hirota 43 variation of phase angle is very weak. On the other hand the wave in the summer hemisphere is essentially a traveling wave since it does not appear in the monthly mean radiance field. The reason why the wave amplitude maximum cannot be seen in the equatorial stratosphere may be because the vertical wavelength of equatorial waves such as Kelvin waves and mixed Rossbygravity waves is too small to be detected from the single channel radiance of SCR. 5. Summary and remarks penetration of traveling planetary waves into the summertime mesospheric easterlies, unless a critical level is encountered somewhere near the the easterly core. On the other hand, however, the penetration of eastward traveling waves into the easterlies cannot be explained since the relative zonal wind velocity is negative. Therefore the eastward traveling waves of wavenumber 2 and 3 may be evanescent modes. Generally speaking, there are some possibilities for the excitation of westward traveling planetary waves in the summer stratosphere and mesosphere. One is the lateral interaction between the winter and summer hemispheres crossing over the equator. This may be supported by the fact that the most predominant period in the winter hemispheric stratosphere is almost the same as that in the summer hemisphere (e.g. Miller, 1974). Another possibility is the vertical propagation of wave energy originated in the summer hemispheric Throughout the spectral analysis of meteorological rocket and satellite observations, following conclusions are obtained : in the summertime stratospheric and mesospheric easterlies in the subtropics and middle latitudes, planetary-scale waves with east-west wavenumber 1 to 3 are predominant, and can be detected from temperature, wind and isobaric height. The wave 1 is a westward traveling wave and the wave 2 and troposphere. If this is the case, we have to give 3 are eastward traveling waves. Characteristic an explanation for the selectivity of preferred time-scale of these waves is about two weeks, but periods of the subtropical upper circulation, along the waves in the mesosphere show rather wide a similar way as discussed by Murakami and range of oscillation. i.e., from 10 to 20 days, Frydrych (1974). In view of the particular feature partly due to the inaccuracy of rocket data. of the Indian monsoon, there may be a considerable At present, it is impossible to make a zonal difference between the summer stratospheric harmonic analysis of planetary waves in the mesosphere with the use of meteorological rocket data circulation spheres. of the northern and southern hemi- because of a lack of observation stations in a To give an answer to these questions, further hemispheric scale. In the near future, however, diagnostic study based on global synoptic observations the progress of meteorological satellite soundings should be continuously made together with of the temperature field with the aid of the Pressure theoretical investigations of the dynamics of Modulator Radiometer (PRM) and the Limb planetary waves in the summertime easterly Radiance Inversion Radiometer (LRIR) will current. provide us with more detailed information about the upper atmospheric circulation on a global Acknowledgements scale. When global observations with sufficiently The present author wishes to express his hearty high accuracy become available, it will be quite thanks to Dr. T. Maruyama for his helpful instructions interesting to estimate various kinds of transport in a power spectral analysis, and to Dr. J. J. quantities such as heat and momentum associated Barnett and the members of the Clarendon with planetary waves for the purpose of understanding Laboratory, Oxford, for their courtesy to supply the nature of the general circulation of him with the original data of the Nimbus-5 the upper atmosphere. Concerning the dynamics of planetary waves in Selective Chopper Radiometer. due to Messrs. M. Ishikawa Thanks are also and T. Sakurai for the summer mesospheric easterlies, in contrast to that in the polar-night westerlies, no theoretical their assistance in data arrangement, and to Miss M. Ohta for typing the manuscript. investigation has been so far made to explain the origin and nature of the waves. As indicated in References Table 2, the relative zonal wind velocity U-c is Angell, J. K., G. F. Cotton and J. Korshover, 1973: positive for the westward traveling wave of wavenumber 1. This fact suggests a possibility of the A climatological analysis of oscillations of Kelvin wave period at 50 mb. J. atmos. Sci.,30,

12 44 Journal of the Meteorological Society of Japan Vol. 53, No. 1 Barnett, L J., M. J. Cross, R. S. Harwood, J. T. Houghton, C. G. Morgan, G. E. Peckham, C. D. Rodgers, S. D. Smith and E. J. Williamson, 1972: The first year of the selective chopper radiometer on Nimbus 4. Quart. J. Roy. Met. Soc., 98, Deland, R. J., 1973a: Analysis of Nimbus 3 SIRS radiance data: traveling planetary-scale waves in the stratospheric temperature field. Mon. Wea. Rev., 101, b: -, Spectral analysis of planetaryscale waves: vertical structure in middle latitudes of Northern Hemisphere. Tellus, 25, Fritz, S. and S. D. Soules, 1972: Planetary variations of stratospheric temperatures. Mon. Wea. Rev., 100, , Hirota, I., 1968: Planetary waves in the upper stratosphere in early J. meteor. Soc. Japan. 46, Justus, C. G. and A. Woodrum, 1973: Upper atmospheric planetary wave and gravity-wave observations. J. atmos. Sci., 30, Maruyama, T., 1968: Time sequence of power spectra of disturbances in the equatorial lower stratosphere in relation to the quasi-biennial oscillation. J. meteor. Soc. Japan, 46, Miller, A. J., 1974: Periodic variation of atmospheric circulation at days. J. atmos. Sci., 31, Muench, H. S., 1968: Large-scale disturbances in the summertime stratosphere. J. atmos. Sci., 25, Murakami, T. and M. Frydrych, 1974: On the preferred period of upper wind fluctuations during the summer monsoon. J. atmos. Sci., 31, Scherhag, R., 1960: Stratospheric temperature changes and the associated changes in pressure distribution. J. meteor., 17,