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"Dynamics of the Tropical Middle Atmosphere: A Tutorial Review* Kevin Hamilton GFDL/NOAA, Princeton University, Princeton, New Jersey 08542, U.S.A. [Original manuscript received 27 March 1998; in revised form 5 August 1998] abstract The general circulation of the tropical stratosphere, mesosphere and lowermost thermosphere is discussed at a tutorial level. Observations of the quasi-biennial and semiannual oscillations by both in situ and satellite techniques are first reviewed. The basic dynamics controlling the zonal-mean component of the circulation are then discussed. The role of radiative diabatic cooling in constraining the zonal-mean circulation in the middle atmosphere is emphasized. It is shown that the effectiveness of this radiative constraint is reduced at low latitudes, allowing for the sustained mean flow accelerations over long periods of time characteristic of the quasi-biennial and semiannual oscillations in the tropics. The current view is that the dominant driving for the equatorial mean flow accelerations seen in the middle atmosphere derives from vertically-propagating waves. This process is illustrated here in its simplest context, i.e. the Plumb (1977) model of the interaction of monochromatic internal gravity waves with the mean flow (based on earlier work of Lindzen and Holton, 1968; Holton and Lindzen, 1972). It is shown that the dynamics illustrated by this simple model can serve as the basis for an explanation of the quasi-biennial oscillation. The paper then describes some of recent developments in the theory of the quasi-biennial and semiannual oscillations, including aspects related to the interaction between tropics and midlatitudes in the middle atmosphere. The paper concludes with a discussion of the effects of the long period dynamical variations in the tropical circulation on the chemical composition of the stratosphere. résumé D'un point de vue pédagogique, on discute, dans cet article, de la circulation générale de la stratosphère, de la mésophère et de la plus basse couche de la thermosphère dans la zone tropicale. D'abord, on passe en revue les observations des oscillations semestrielles et quasi biennales de deux façons, soient par des techniques satellitaires et in situ. On discute ensuite de la dynamique de base qui contrôle la composante zonale moyenne de la circulation. On met l’accent sur les contraintes que le refroidissement radiatif diabatif impose à la circulation zonale moyenne de la moyenne atmosphère. On montre que l'efficacité de cette contrainte radiative est réduite aux basses latitudes. Ceci tient compte des accélérations on an invited tutorial lecture at the Canadian Middle Atmosphere Modelling Project Summer School held in August 1997 at Cornwall, Ontario. *Based ATMOSPHERE-OCEAN 36 (4) 1998, 319–354 0705-5900/98/0000-0319$1.25/0 © Canadian Meteorological and Oceanographic Society 320 / Kevin Hamilton soutenues de la circulation moyenne sur de longues périodes de temps, propres aux oscillations semestrielles et quasi biennales dans les tropiques. Il est de notoriété que l'élément dominant entraînant des accélérations de la ciculation moyenne équatoriale dans l'atmosphère moyenne provient de la propagation verticale des ondes. Ce processus est illustré ici dans son plus simple contexte, i.e., le modèle Plumb (1977) de l'interaction des ondes gravitationnelles internes monochromatiques avec la circulation moyenne (basé sur les travaux précédents de Lindzen et Holton, 1968; Holton et Lindzen, 1972). On montre que la dynamique illustrée par ce simple modèle peut servir de base pour l'explication de l'oscillation quasi biennale. Cet article décrit enfin quelques développements récents de la théorie des oscillations semestrielles et quasi biennales, comprenant les aspects reliés à l'interaction entre les tropiques et les latitudes moyennes dans l’atmosphère moyenne. En conclusion, on discute des effets des variations dynamiques à longue pèriode dans la circulation tropicale sur la composition chimique de la stratosphère. 1 Introduction There are a number of features that distinguish the dynamics of the tropical stratosphere and mesosphere from the dynamics elsewhere in the atmosphere and hence justify the separate discussion of the tropical circulation that is presented here. The small Coriolis parameter at low latitudes leads to a breakdown of the validity of the geostrophic approximation for the wind and invalidates the quasi-geostrophic theory that is so useful in explaining the large-scale circulation of the extratropical atmosphere. Another consequence of the small Coriolis parameter is that temperature observations (e.g., from satellite radiometers) are of limited use in inferring winds at low latitudes. Thus, it is much harder in the tropics to diagnose the detailed dynamics from available observations, leading to more reliance on indirect theoretical and modelling approaches to study the general circulation. Perhaps the most distinctive features of the circulation in the tropical middle atmosphere are the large-amplitude, long-period oscillations seen in the zonallyaveraged ow. In particular, the winds and temperatures of the equatorial stratosphere undergo a very strong quasi-biennial oscillation (QBO) while the region from the near stratopause to lowermost thermosphere displays a prominent semiannual oscillation (SAO). These are such spectacular phenomena that their study has dominated the þeld of tropical middle atmospheric dynamics. The present tutorial will begin by reviewing some of the detailed observations of the QBO and SAO (Section 2). This is then followed in Section 3 by a consideration of the role of eddy forcing and diabatic effects in controlling the zonal-mean circulation. This will provide a basic explanation for the existence of long-period uctuations in the tropical mean ow. Section 4 will introduce a very simple version of a model of wave-mean ow interaction in the tropical middle atmosphere and will show that this can be used as the basis for an understanding of the QBO. Section 5 then brie y reviews extensions of the simple model of the QBO and application of similar ideas to the explanation of the SAO. Section 5 concludes with a consideration of the effects of the QBO and SAO on long-lived trace constituents in the stratosphere. A brief summary is given in Section 6. Dynamics of the Tropical Middle Atmosphere: A Tutorial Review / 321 This paper does not aim to be a comprehensive review, and many signiþcant papers dealing with the tropical middle atmosphere will not be referenced. The discussion assumes that the reader has a familiarity with the governing equations of meteorology, the notion of mean ow/eddy decomposition, and other basics that are covered, for example, in the þrst few chapters of Holton (1992). Also assumed is a knowledge of the \transformed-Eulerian" formalism for the mean circulation (e.g., Chapter 12 of Holton, 1992). The intent of this paper is to present both observations and theoretical considerations at an introductory tutorial level, and also to indicate brie y the scope of more recent developments in the subject. 2 Observed features of the tropical circulation a Historical Introduction The þrst scientiþc knowledge of the winds in the tropical stratosphere was obtained from observations of the motion of the aerosol cloud produced by the eruption of Mt. Krakatoa (modern-day Indonesia) in August 1883. The optical phenomena caused by the aerosol were remarkable enough that their þrst appearance was widely noted. Russell (1888) collected observations from over 30 locations in the tropics and plotted the motion of the edge of the aerosol cloud (see Fig. 1). The regular westward motion is evident, and Russell computed a mean easterly wind velocity between about 31 and 34 m s 1 . The wind in the tropical lower stratosphere was þrst measured with pilot balloons in 1908 by von Berson at two locations in equatorial East Africa. Over the next three decades these observations were followed by sporadic measurements at a number of tropical locations (see Hamilton (1998a) for a review of these early observations). The results sometimes indicated easterly winds and sometimes westerly winds, a state of affairs reconciled at the time by assuming that there was a narrow ribbon of westerlies (the \Berson westerlies") embedded in the prevailing easterly current revealed by the Krakatoa observations (e.g., Palmer, 1954). Regular balloon observations of the lower stratospheric winds in the tropics began at a number of stations in the early 1950s. By the end of the decade it was obvious that both the easterly and westerly regimes at any height covered the entire equatorial region, but that easterlies and westerlies alternated with a roughly biennial period (Veryard and Ebdon, 1961; Reed et al., 1961). Initially it was thought that the period of the oscillation might be exactly two years, but as measurements accumulated it soon became clear that the period of oscillation was somewhat irregular and averaged over 2 years. By the mid-1960s the term \quasi-biennial oscillation" (QBO) had been coined to denote this puzzling aspect of the stratospheric circulation. b Modern Observations of the QBO Figure 2 shows the raw time series of monthly-mean 30-mb zonal wind computed simply by averaging daily balloon observations at Singapore (1.3 N) over a period of 8 years. This illustrates many of the key features of the QBO. Note that the time series is clearly dominated by an alternation between easterly and westerly 322 / Kevin Hamilton Fig. 1 The spread of the optical phenomena observed after the eruption of Mt. Krakatoa on 26 August 1883. The dotted lines give the western boundary of the region where the phenomena had been observed on successive days, 26 August, 27 August . . . 9 September. Reproduced from Russell (1888). wind regimes roughly every other year. The extremes in the prevailing winds vary from cycle to cycle, but the peak easterly (in the monthly mean) usually exceeds 30 m s 1 , while the westerly extreme is usually between 10 and 20 m s 1 . The time series has a rough square-wave character with rapid transitions (2{4 months) between periods of fairly constant prevailing easterlies or westerlies. The height-time evolution of the monthly-mean wind near the equator for over four decades is shown in Fig. 3 (an updated version of the þgures in Naujokat, 1986; Marquardt and Naujokat, 1997). The wind reversals invariably appear þrst at high levels and then descend. At any level the transition between easterly and westerly regimes is rapid so that the transitions are also associated with strong vertical shear. These near-equatorial data suggest that the mean period of the oscillation is about 28 months and varies between about 20 months and 36 months (Marquardt and Naujokat, 1997). Much of the variability in period is associated with the changes in the length of the easterly phase, particularly above about 50 mb. The maximum amplitude occurs near 30 mb and the amplitude drops off to small, but apparently still detectable (Hitchman et al., 1997) values near the tropopause (17 km). The dropoff in QBO amplitude above 30 mb is very gradual and the oscillation is still Dynamics of the Tropical Middle Atmosphere: A Tutorial Review / 323 Fig. 2 Time series of the monthly-mean zonal wind measured by balloons at Singapore during the period 1980{88. very strong at the 10-mb level. At almost all levels and all times the easterly-towesterly transitions are more rapid than vice versa, and the associated westerly shear zones are considerably more intense than the easterly shear zones. There is only a very limited network of radiosonde stations near the equator regularly reporting stratospheric winds. An assumption implicit in most observational studies is that the prevailing winds near the equator are essentially zonallysymmetric. Belmont and Dartt (1968) tried to check this with available radiosonde data and concluded that the QBO was indeed very nearly zonally-symmetric up to 50 mb (above this level they felt they had inadequate data for veriþcation). Among the complications in determining the details of the QBO signal is the fact that the annual cycle becomes strong off the equator and itself has considerable geographical variability (Hitchman et al., 1997). Recently the advent of Doppler-radiometer observations of horizontal winds by the High Resolution Doppler Imager (HRDI) instrument on the Upper Atmosphere Research Satellite (e.g., Ortland et al., 1996) has provided another opportunity to examine this issue. Ortland (1997) þnds that there may be some modest (10 m s 1 ) zonal asymmetries in the monthly-mean wind at the equator in the westerly phase of the QBO, particularly at and above 10 mb. This issue will be discussed further in Section 5b, but, to þrst order, the assumption of a zonally-symmetric QBO is appropriate. Figure 4 shows a determination of the amplitude (solid contours) and phase (dashed contours) of the QBO in zonal wind as a function of height and latitude in the tropical stratosphere. It was derived by Reed (1965b) who þt a simple 26-month harmonic to about 8 years of zonal wind data at a number of low latitude stations. 324 / Kevin Hamilton Fig. 3 Time-height section of the monthly-mean wind at stations near the equator. Results represent observations from Canton Island (2.8 S, 171.7 W) during 1957{1967, Gan (0.7 S, 73.1 E) during 1967{1975, and Singapore (1.4 N, 103.9 E) during 1976{1998. Westerly winds are shaded and the contour interval is 10 m s 1 . Figure provided by B. Naujokat. Dynamics of the Tropical Middle Atmosphere: A Tutorial Review / 325 Fig. 4 Latitude-height section of the amplitude and phase of the QBO in zonal wind determined from radiosonde observations. Amplitude contours are solid and the contour interval is 2.5 m s 1 . The Northern Hemisphere is shown on the left. Phase contours are dashed and the contour interval is 1 month. The thin tick marks on the axis show the latitude of each of the stations used in the analysis. The scale on the right is a standard height (in km). Adapted from Reed (1965b). The result for the amplitude shows a peak centred squarely on the equator and a roughly Gaussian dropoff in latitude with an e-folding width of between 13 and 15 degrees of latitude. The phase lines are remarkably regular indicating a steady downward propagation of about 2 km month 1 and very little phase variation in latitude. Similar results for the observed height-latitude structure of the QBO are given by Belmont et al. (1974). A QBO in temperature has also been clearly observed. Reed (1962) used balloon observations to show that the QBO in temperature has a peak amplitude of 2{ 3 C. In general the usefulness of the geostrophic approximation breaks down at low latitudes, of course, but in fact the zonal-mean component of the circulation should be close to geostrophic balance. Reed (1962) showed that indeed, within observational error, the measured zonal-mean QBO temperature variations are in thermal wind balance with the zonal-mean zonal wind. In recent years observational studies of the general circulation of the tropical lower and middle stratosphere have focused on characterizing some of the details of the QBO. Examples include studies of the evolution of the meridional structure of the zonal wind þeld through the QBO cycle (Hamilton, 1984, 1985; Dunkerton and Delisi, 1985), and studies of the variability of the QBO period from cycle to cycle (Quiroz, 1981; Dunkerton and Delisi, 1985; Naujokat, 1986; Maruyama and Tsuneoka, 1988). Studies of the in uence of the QBO in the tropical upper stratosphere, mesosphere and lower thermosphere have been made using rocketsonde (e.g., Hamilton, 1981) and HRDI satellite observations (Burrage et al., 1996). 326 / Kevin Hamilton Fig. 5 The December{February zonal-mean zonal wind averaged over winters with easterly equatorial winds at 40 mb minus an average over winters with westerly equatorial winds at 40 mb. The data employed are for 1979{90. The dashed contours denote negative values and the contour interval is 2 m s 1 . The zonal winds here are determined geostrophically from global analyses of geopotential height. Results are not plotted at low latitudes where the observed geopotential analyses are of too poor quality for an accurate determination of the zonal wind. Adapted from Baldwin and Dunkerton (1991). The issue of QBO effects beyond the tropical middle atmosphere has been addressed in a number of studies and is still an issue of current investigation and controversy. The clearest remote effects appear to be in the extratropical northern hemisphere winter stratosphere (e.g., Holton and Tan, 1980, 1982; Dunkerton and Baldwin, 1991; Baldwin and Dunkerton, 1991). Figure 5 shows the December{ February zonal-mean zonal wind averaged over easterly phase QBO periods minus that averaged over periods of westerly QBO phase. Here the phase of the QBO used in the compositing is based on the sign of the 40-mb zonal wind measured at Singapore (1.3 N). The tendency for the polar vortex to be somewhat weaker in the easterly QBO phase is evident. Other studies have shown that midwinter sudden warmings of the northern hemisphere (NH) polar stratosphere are significantly more frequent during the easterly QBO phase than in the westerly phase (Dunkerton et al., 1988). The issue of extratropical QBO effects is discussed in more detail in Section 5b. c Observations of the Semiannual Oscillation The 10-mb level (approximately 30 km) is the usual ceiling for operational balloon soundings, and so knowledge of the wind þeld at higher levels was þrst obtained with rocket soundings. Figure 6 (from Reed, 1965a) shows all the zonal wind ob- Dynamics of the Tropical Middle Atmosphere: A Tutorial Review / 327 Fig. 6 Zonal wind measurements taken at Ascension island (7.9 S) during the period October 1962 through October 1964. The solid circles show individual measurements and the open circles are monthly means for months when there was more than one measurement available. Reproduced from Reed (1965a). servations from rocket soundings during a two-year period at Ascension Is. (7.9 S). In the middle stratosphere the QBO appears quite clearly (at least to 40 km; see also Hamilton, 1981). However, at upper stratospheric levels the QBO is dominated by a shorter period oscillation. We now know that this is a semiannual oscillation (SAO). Unlike the QBO, the SAO is very clearly phase-locked to the calendar. Near the stratopause the easterly extremes are reached in January and July and the westerly extremes around April and October. Figure 7 shows a climatological annual march of the zonal wind deduced from rocket observations at a number of sites. At the equator the semiannual variation clearly dominates in a thick layer around the stratopause. The vertical structure of the westerly accelerations displays a downward propagation that is similar to the QBO wind reversals. The easterly accelerations are more uniform in height. The stratopause SAO has been seen in rocket observations of zonal winds, rocket observations of temperatures (e.g., Garcia et al., 1997; Dunkerton and Delisi, 1997), satellite radiometer measurements 328 / Kevin Hamilton Fig. 7 (top) Latitude-time section of the climatological annual march of zonal-mean zonal winds at 50-km height determined from rocketsonde observations at several stations. Contour interval is 20 m s 1 and regions of westerlies are shaded. (bottom) Altitude-time section of the annual march of equatorial zonal wind determined from interpolation of observations at Kwajalein (8.7 N) and Ascension Island (7.9 S). Contour interval is 10 m s 1 and regions of westerlies are shaded. Reproduced from Delisi and Dunkerton (1988b) and based on an earlier þgure from Belmont et al...."

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