Chapter I INTRODUCTION

Transcription

1 Chapter I INTRODUCTION 1.1. Atmosphere and its Dynamics The atmosphere can be regarded as a fluid medium held around the earth, in an approximately hydrostatic equilibriu~n condition, by the gravitational force of the earth. Dynamics of the atmosphere deals with the study of motions of the atmosphere. For such motions, the discrete molecular nature of the atmosphere can be ignored and can be regarded as a continuous fluid medium or continuum. Statistical description of atmospheric motions over earth, their role in transporting the constituents of the atmosphere and the transformations of different forms of energy constitute the subject of atmospheric dynamics. This is studied with various experimental techniques and analysed using different models of atmospheric general circulation. The atmosphere is characterised by certain physical quantities. like pressure, density, temperature and wind velocity. These quantities have unique values at each point in the atmospheric continuum. These properties are called field variables. The field variables and their derivatives are assumed to be continuous functions of space and time. The atmospheric motions are governed by the fundamental laws of fluid mechanics and thermodynamics. These laws are (i) law of conservation of mass (continuity equation) (ii) law of conservation of niomentum (momentum equation) (iii) law of conservation of energy (first law of thermodynamics) There are different forces, which influence the atmospheric motions. The forces, which are of primary concern, are the pressure gradient force, gravitational force, the frictional force and apparent forces (pseudo force and the Coriolis force. -,I

2 In the atmosphere we can find many kmds of wave motions with various spatial and time scales, such as general and global circulations, planetary waves, tides, gravity waves and turbulence. All these motions coexist and interact with each other, which make the measurements, interpretations and understanding of atmospheric motions, a complex and challenging task Composition of the Atmosphere Air is a mechanical mixture of gases. The atmosphere can be divided into two regions by considering the composition of air. The homosphere or turbosphere extending up to about 100 km is referred to as one region of the atmosphere where the composition of air is practically the same because of the dominant effect of turbulence. The heterosphere is the region of atmosphere of varying composition where molecular diffusion dominates over turbulence to cause decrease in molecular weight of air with height. Average co~mposition of dry air shows that four gases viz., nitrogen, oxygen, argon and carbon dioxide account for 99.98% of the air by volume. These gases are mixed with remarkably constant properties up to 100 krn.. Other gases such as ozone, hydrogen, methane and the rare gases like neon, helium, krypton, xenon etc., account for the remaining 0.02% of the air (Wallace and Hobbs, 1977). Of special significance, despite their relative scarcity, is the presence of greenhouse gases. which play an important role in the thermodynamics of the atmosphere, by trapping long-wave terrestrial radiation, producing the greenhouse effect. These gases include c:arbon dioxide, methane, nitrous oxide, ozone and chloroflourocarbons (CFC). In addition to these gases, water vapour, the major greenhouse gas. is a vital atmospheric constituent. It averages about one percent by volume but is variable both in space and time, being involved in a complex global hydrological cycle. Water vapour plays a dominant role in thermodynamic and radiative processes There are also significant quantities of aerosols in the atmosphere. Aerosols are suspended minute particles of sea salt, dust, organic matter and smoke. Aerosols

3 enter the atmosphere from a variety of natural and anthropogenic sources. They play a considerable role in the radiative properties of the atmosphere and cloud condensation process. There are variations, which occur in composition with height, latitude, longitude and time. Water vapour comprises up to 4% of the atmosphere by volume near the surface and only 3-6 ppm (parts per million by volume) above km. Ozone is concentrated mainly between 15 and 35 km with maximum ozone concentration occurring between km in low latitudes and km in high latitudes. Ozone content is low over the equator and high in subtropical latitude in spring. The water vapour content of the atmosphere is closely related to the temperature of the air and is therefore, greatest in summer in low latitudes. The carbon dioxide content of the air has a large seasonal change in higher latitudes in the northern hemisphere associated with photosynthesis and decay of biosphere. The amount of carbon dioxide and other greenhouse gases in the atmosphere are subject to long term variations and these are of special significance because of their possible effect on the radiation budget Vertical Structure of the Atmosphere The temperature, pressure and density of the atmosphere vary significantly with altitude. Pressure and density always decrease with height and nearly at the same rate in both summer and winte!r. But temperature changes are not uniform. The atmosphere can be conveniently divided into four layers according to the vertical structure of the atmospheric temperature (Figure 1.1). The lowest layer is the troposphere, where the temperature decreases with altitude at a nearly constant lapse rate of about of 6.5 Klkm. It is. the zone where the weather phenomena and atmospheric turbulence are mostly observed. The decrease in temperature ceases at the tropopause, which is located at 8-16 km, depending on the latitude and season. The minimum temperature at che tropospause level can be between 200 K to 220 K in the tropics. The stratosphere exists a.bove the tropopause, where the temperature increases with altitude up ro about km. The upper limit of the stratosphere is called the stratopause. corresponding to a local maximum of the temperature profile

4 Figure 1.1. Thermal structure of the (earth's atmosphere. (Globally averaged temperatures are given.)

5 caused by the absorption of solar ultraviolet radiation in the ozone layer. The temperature again decreases in the height region above the stratopause, which is called the mesosphere. The minimum temperature is detected at the mesopause height of around 90 krn. The thermosphere lies above the mesopause, where the temperature of the neutral atmosphere rapidly increases because of the absorption of solar extreme ultraviolet radiation and X-rays. While the layer from surface to the tropopause is known as the lower atmosphere, the layer between tropopause and lower thermosphere is commonly referred to as middle atmosphere, with the upper atmosphere designating the regions above 100 km altitude. Above 100 km the atmosphere is increasingly affected by cosmic radiation, solar X-rays and u11:raviolet radiation, which cause ionization or electrical charging (Watson Wan. 1929). The term ionosphere is commonly applied to the layers above 80 km although sometimes it is used only for the region of high electron density between 100 and 300 km Radiative Processes The thermal structure of the atmosphere is determined to a large extend by radiative processes. especially, in the upper reaches of the atmosphere. Above the tropopause the absorption of solar radiation plays a dominant role in the energy balance. Most of the absorption occurs in association with photo-ionisation and photo-dissociation of various gaseous iconstituents of the upper atmosphere by ultra violet and X-ray radiations. There are three distinct bands of wavelengths, which are absorbed in three distinct regions of the atmosphere. The solar radiation with wavelengths less than 0.1 pm is totally absorbed above about 90 km primarily due to photo-ionisation of atmospheric species (e.g., N2, 0 and 02). Radiation in the band 0.1 to 0.2 pm is absorbed primarily due to photo-dissociation of oxygen molecule between km. The maximum absorption of solar radiation in the wavelength band 0.2 to 0.3 pm takes place in a layer near 50 km in the photo-dissociation of ozone into molecular and atomic oxygen.

6 The structure and dynamics of the troposphere are profoundly influenced by the underlying surface through the fluxes of latent and sensible heat which penetrate upward all the way to the tropopause. These fluxes are absorbed by water vapour, CO, and to some extent by ozone Thermal Equilibrium in the Atmosphere and Atmospheric Motions The prime source of energy injected into the atmosphere is the sun, which is continually shedding pans of its mass by radiating waves of electro-magnetic energy and high-energy particles into space. The amount of energy received by the earth, is affected by the, intensity of incoming solar radiation and length of day, factors that are related directly to spherical shape of the earth, the tilt of the earth's axis and the rotation of earth about the sun. Because the earth is a sphere and is tilted by 23.5" to the solar plane. different regions of the globe are subjected to a strong annual cycle of incoming solar radiation. Thus the long days of the summer polar regions (up to 24 hours of day light) and intense solar heating of low latitudes (but with only 12 hours of day light). combine to produce an almost constant and very high input to solar heat over entire summer hemisphere. The sun-earth distance, altitude of the sun and day length illustrate the relative roles of atmosphere, clouds and the earth surface in reflecting and absorbing solar radiation at different latitudes. All motions in the atmosphere are the result of solar heating. The ultimate forcing mechanism of atmosphere is the pole to equator gradient of radiative heating of the planet. Atmospheric motions are produced by fluxes of heat at the lower boundary and by radiative cooling to :space generally from higher levels in the atmosphere. The forcing is manifested as pressure gradient force fields or body force that do work on fluid parcels. thus producing fluid motion. The ultimate purpose of the motion is to keep the planet in thermal balance. Excessive heat collected in the equatorial regions is transported to the polar regions. Fluid motions transport heat, moisture and momentum between the equator and the poles in order to maintain balances within the system.

7 1.6. Atmospheric Waves One of the most important dynamical properties of the atmosphere is its ability to support wave motions. These waves are of many different types. Atmospheric waves can be classified in various ways, according to their physical or geometrical properties. They can be categorised according to their restoring mechanisms, thus buoyancy or internal gravity waves owe their existence to stratification while inertia-gravity waves result from a combination of stratification and Coriolis force. Planetary waves results from the beta-effect (change of Coriolis force with latitude). A second type of classification is to distinguish forced waves, which must continually be maintained by an excitation mechanism of given phase speed and wave number, from free waves, which are not so maintained. Examples of forced waves include thermal tides, which are induced by the diurnal variations in solar heating, while free waves include global normal modes. A further classification results from the tact that some waves can propagate in all directions, while others may be trapped in some directions. Thus under some circumstances horizontally propagating planetary waves can be trapped in the vertical, while equatorial waves can propagate vertically and zonally but evanescent with increasing distance from the equator. Waves can also be separated into stationary waves, whose surfaces of constant phase are tixed with respect to the earth and travelling waves, whose phase surfaces move. Since information propagates with the group velocity, and not with the phase spee:d, propagation can still occur in stationary waves. The final general fomk of classification that we shall mention distinguishes waves that do not lead to any meanflow acceleration from those that do. The former category includes waves that are lineal:, steady, frictionless and adiabatic while the latter usually includes any waves that is transient. To produce oscillations, including wave motions in a material medium, a restoring mechanism is needed, under which each tiny element of the medium is returned towards equilibrium after being displaced. The most familiar fluid dynamical wave is the sound wave, in which the restoring mechanism is due to the compressibility of the gas. C)n the other hand, there are many other fluid wave motions, with quite different physics, which do strongly influence atmospheric

8 behaviour. The restoring mechanisms for the wave are associated with physical properties such as the density stratification of the atmosphere, which give rise to buoyancy forces. the rotation of the earth (leading to Coriolis force) and more subtly, the fluid dynamics of vorticity coupled with the near-spherical geometry of the planet. Moreover, these waves carry information over thousands of kilometres horizontally and tens of kilometres ver~:ically, so that forces imposed, say, at ground level may ultimately lead to deviations of the flow in the stratosphere and even the mesosphere. Planetary waves, tides and gravity waves are the three most important wave types that result from the various forces in the atmosphere. Depending upon the wave parameters it is possible to understand the physics of each class of waves by suitably neglecting the forces which art: relatively unimportant. Gravity waves in the atmosphere arise from the coupling of gravity with the continuous vertical density stratification. Atmospheric gravity waves can exist only when the atmosphere is stably stratified, so that a fluid parcel displaced vertically will undergo buoyancy oscillations. The buoyancy force is the restoring force responsible for gravity waves. These waves are also called buoyancy waves. Theoretical and observational studies have emphasised that upward propagating gravity waves which carry energy anti momentum flux from lower atmosphere to middle atmosphere and play an important role in maintaining the general circulation by providing dynamical stress due to breaking of gravity waves (e.g., Lindzen, 1981; Holton, 1982: Matsuno, 1982; Tsuda et al., 1990). The name planetary wave is generic for all waves having periods equal to or greater than half a day and horizontal dimensions comparable to the radius of the earth. These waves can be classified on the basis of their distinct characteristics, such as, extra tropical modes and equatorially trapped modes, free modes and forced modes, external modes and internal modes and modes that interact with the meanflow through wave transience and those that interact by wave dissipation. The most significant forced vertically propagating extratropical modes are the Rossby

9 waves, while the most significtant forced vertically propagating equatorial modes are the Kelvin wave and the Rossby-Gravity (RG) wave. Both the extra tropical modes and the equatorial modes are capable of changing the meanflow through the wavemeanflow interaction processes. These waves transport momentum from the tropospheric source region to the middle atmosphere. In the equatorial region, the most fascinating example of the product of the wave-meanflow interaction process is the Quasi Biennial Oscillation (QBO) of the mean zonal wind in the lower stratosphere and Semi Annual Oscillation (SAO) in the upper stratosphere and mesosphere. QBO in the mean zonal winds are zonally symmetric easterly and westerly wind regimes alternate regularly with a period varying from about 24 to 30 months. Successive wind regimes first appear above 30 km, but propagate downward at a rate of 1 km month-' and decays at about 20 km altitude. SAO is a dominant component of wind in the equatorial upper stratosphere (30-50 km) and the mesosphere (50-90 km). Figure 1.2 illustrates the dissipation of various wave types at different altitudes in the low latitude middle atmosphere, generating the QBO and SAO at particular altitudes. Both the sun and the moon exert periodic external forces upon the earth's atmosphere. In the case of the moon these forces are wholly gravitational, except for the minute heating effect from the reflected radiation at the full moon. The sun, however, exerts a strong thennal effect as well as a much weaker gravitational effect. The earth's atmosphere will respond to these forces in a manner analogous to forced mechanical vibrations. As it is possible to analyse the forcing term into harmonic components. the steady-state responses of the atmosphere to these forces are known as atmospheric tides. They will have periods that are submultiples of the solar or lunar day. In this thesis studies are carried out on two important atmospheric wave types viz., equatorial waves and atmospheric!:ides. The zonal wavelength of both of the above waves are comparable. i.e., they are planetary scales. In the case of equatorial waves the wave modes are latitudinally trapped, i.e., their propagation, which is zonal in the horizontal plane. are confined to about &20 latitude but the atmospheric tides

10 L 060 (20-35 km) W Figure 1.2. Schematic diagram showing wave dissipation at different altitudes in the low latitude middle atmosphere, generating very large period wind oscillations like QBO and SAO at particular altitudes (Raghava Reddi, 1998)

11 are global oscillations. Both equatorial waves and tides are forced vertically propagating wave disturbances. The basic state of the atmosphere is governed by the equations expressing conservation of momentum and energy, the continuity equation and the hydrostatic equation. Ignoring sources and sinks, the governing equations of the atmosphere can be written in terms of perturbations in the velocity and geopotential fields. These equations are then linearised by neglecting the second order terms of products of perturbations. The different modes of atmospheric oscillations are assumed to be wavelike and are obtained as eigen solutions of the linearised perturbation equations. General solutions to these equations are complex. The complexity of the equatxons describing the different scales of atmospheric oscillations can be simplified by makin,g dynamical and geometrical approximations to exclude the oscillations lover some :parts of the globe and give solutions of the oscillations over a limited range of periods, so that we can have a clear physical understanding of these equations. The mathematical equations of equatorial wave modes are solved in the equatorial beta plane, which limits the description of the flow field in the rneridional extent. In the equatorial beta plane approximation, cose (0 is the latitude) is replaced by 1 and sine is replaced by yla where y is the distance in the meridional directions from the equator and a is the earth's radius. In the case of atmospheric tides. the tidal perturbation in any parameter is assumed to have sinusoidal variations in time with a fundamental period of 24 or 12 hours and sinusoidal variations with longitude (d), with longitude wave numbers s=0,1,2,..., the tidal perturbation is proportional to e"w'"' where w = 2nlT, T is the tidal wave period of one solar day or one lunar day. After these assumptions the linear perturbation equations are further simplified by separating the variable, wherein, each dependent variable is assumed to depend on the independent variables and the independent variables are not coupled. Each variable is separated into vertical and horizontal (latitudinal) parametric equations. The horizontal structure of the field variables of the wave motion is given by the Laplace's tidal wave equation and the vertical structure by the vertical Structure equation. Both the equations are dependent on a variable called the separation variable 'h' often referred to as equivalent depth. 11 I"',' /%+ \>.. \t_ \\.' -- ~ ~ e'

12 1.7. Equatorial Waves The equatorial atmospheric dynamics differ significantly from the middle and high latitude atmosphere. 'The Coriolrs parameter is very small in the equatorial (+20 ) latitudes. The solar insolation i,s maximum in the equatorial region resulting in the maximum heating of the low latitude atmosphere. The sea and land mass in different longitudes in the equatorial region produces uneven heating and results in east-west circulation along the equator. Particularly the Indonesian region is spread out in longitude along the equator. Similarly the African subcontinent and American subcontinent in the equatorial region are heated up more than the ocean areas in between. These localised heat sources generate the localised circulation cells in the vertical plane along the equator. The release of latent heat in cumulus convection is considered as a primary energy source for the maintenance of the equatorial disturbances. There is an interaction between the cumulus scale and large-scale disturbances. wherein. the large-scale convergence provides moisture for the convection and cumulus cells provide the large-scale heat source (Horel and Wallace, 1981). Because of the special nature of the driving force, as well as, the smallness of the Coriolis parameter. the large-scale equatorial atmospheric dynamics have certain distinct characteristic structural features, which are quite different from those of the mid-latitude system. The energy transport and dispersal in the equatorial region are through wave motions. Adopting the quasi-geostrophic approximation, which is suitable for midlatitudes Charney and Drazin (1961) have shown that the disturbances can propagate only when their phase speed was westward relative to the mean zonal flow. There is a limit to the maximum westward speed of the disturbance and this limiting value decreases rapidly for larger horizontall wave numbers. In the development of the theory under quasi-geostrophic approximation, it is shown that planetary scale waves generally will be 'trapped' (i.e., they can not propagate energy vertically) unless the frequency of the wave is greater than the Coriolis frequency V). Thus at middle latitudes waves with periods in the range of several days are generally not able to propagate significantly into the stratosphere. However, as the equator is approached, the Coriolis frequency allows these longer period waves to become

13 untrapped and propagate vertically. The large period waves propagate vertically as internal gravity waves and the energy they transport from their source region, the troposphere, is upwards; while the direction of their vertical phase propagation is downwards. Detailed theoretical studies (Matsuno, 1966). which are borne out to a very large extent by the observational data, show that in the equatorial latitude, there are two significant forced oscillations, one propagating eastward (westerly mode) and another westward (easterly mode). The westerly mode, known as the Kelvin wave is symmetric about the equator. The easterly mode is antisymmetric about the equator and is called RG waves. Both the wave modes are latitudinally trapped, i.e., their propagarion which is essentially zonal in the horizontal plane are confined to about?2o0 latitude. The observed characteristics of equatorial waves are summarised in Table I. 1. (Raghava Reddi, 1998). Conventionally, Kelvin and RG waves have been studied using radiosonde data. Since these waves have small vertical wavelengths. radiosondes may not reveal their structure adequately. As MST radar can collect high time resolution data, they have the potential to become a significant tool for mesoscale research. In addition, these radars can be operated almost continuously unattended and consequently, data sets are available for analysing longer period wave motions such as equatorial waves Theoretical Understanding of the Equatorial Wave Characteristics Theoretically the vertically propagating wave disturbances in the tropical middle atmosphere can be classified into two kinds (Matsuno, 1966; Holton, 1975). One kind is the free or natural modes. which are characteristics of the atmosphere. The second kind is the forced modes having periods dependent on the excitation source function. The forced modes can again be classified as external or vertically trapped oscillation having very large vertical wavelengths, and the internal or vertically propagating oscillations having relatively short vertical wavelength. The internal modes have a vertical component of the group velocity and can transport energy and momentum vertically. Some of the wave modes are trapped in one of the horizontal directions and propagate horizontally in the other direction only. The equatorial waves are trapped horizontally in latitude and propagate both zonally and vertically.

14 Table 1.1 Observed characteristics of the dominant planetary-scale waves in the equatorial lower stratosphere (Raghava Reddi, 1998) S1. No. Characteristics Kelvin waves RG waves 1 Zonal wave number Period (days) Phase speed (m s~') Direction of propagation Westerly (Eastward) Easterly (Westward) 5 Horizontal wavelength (km) 30,000 10,000 6 Latitudinal wavelength (km) 1,000 1,000 7 Vertical wavelength (km) Amplitude (a) Zonal w~nd 'u' (m s-i) 8 (b) Mer~dional wind 'v' (rn s-i) 0 (c) Vertical wind 'bv' (cm s-') 15 (d) Geopotential height 'z" (m) 4 (e) Temperature 'T' ("K) Symmetry about the equator (a) Zonal wind Even (b) Meridional wind. (c) Geopotential height Even Odd Even Odd 10 Phase relat~on between the perturbat~on parameters (a) Pressure 'P' and 'u' Out of phase In phase (b) Pressure 'P' and 'T' 'T leads 'P' by 90" 'T leads 'P' by 90" (c) Pressure 'P' and 'v' - 'P' leads 'v' by 90" (d) 'u' and 'w' In phase In phase

15 Atmospheric Kelvin Waves As already mentioned, an important property of the equatorial zone is that it acts as a waveguide, that is, disturbances are trapped in the vicinity of the equator (Mafsuno, 1966). The simplest wave that illustrate this property is the equatorial Kelvin waves so named because it is very similar in character to the coastally trapped Kelvin wave in the ocean. In atmospheric Kelvin wave, the motion is everywhere parallel to the equator and the perturbation in the meridional wind is identically zero. Horizontal Structure Using the linearised equations of motion, continuity and thermodynamic energy on an equatorial beta plane for zonally propagating waves the meridional distribution of zonal wind fluctuation is obtained as (Holron, 1979) The solution of equation (1.1) is expressed as Notations used uo u' 2' Y P R zonal wind velocity at the equator zonal wind fluctuation geopotential height distance northward of the equator 2nIa angular frequency of the earth radius of the earth wave frequency zonal wavenumber

16 If we assume that k > 0, then a > 0 corresponds to an eastward moving wave. In that case equation (1.2) indicate that field of u' will have a Gaussian distribution about the equator with an e-folding width (Y,) given by For a westward movlng wave (o < O), the solution given by equation (1.2) increases in amplitude exponentially away from the equator. The solution does not satisfy the boundary condition at the poles and must be rejected. Therefore there exist only an eastward propagating atmospheric Kelvin wave. The horizontal distribution of pressure and velocity characteristics of Kelvin waves is shown in figure 1.3 adapted from Matsuno (1966). In figure 1.3 the continuous lines are the constant pressure contours and the arrows represent the wind velocity vectors. For Kelvin wave zonal velocity perturbations (u') and pressure perturbations (P) have even symmetry about the equator. The Kelvin wave has essentially no meridional velocity component, i.e., v' = 0. Vertical Structure The vertical structure of zonal w~nd fluctuation is given by ' 1 du' k', - + u = 0 where H N scale height Brunt Vaisala frequency Solution of the equation (1.4) can be wrrtten in the form with

17 . Figure 1 ;3. Pressure and wind fields of Kelvin waves. (Matsuno, 1966)

18 Here C, and C, are constants to be determined by appropriate boundary conditions. For /I2 > 0, the solution (1.5) is a vertically propagating wave. For waves in the equatorial stratosphere which are forced by disturbances in the troposphere, the energy propagation (i.e. group velocity) must have an upward component, therefore the phase velocity of Kelvin wave must be downward which is identical to an eastward propagating gravity wave. For this reason, Kelvin wave can be considered as a gravity wave in the (x. :) plane. A typical vertical section is demonstrated in the figure 1.4. Figure 1.4 shows the longitude-height section along the equator showing pressure, temperature and wind perturbations of a thermally damped Kelvin wave. The heavy wave lines indicate the material lines and short blunt arrows show the phase propagation. The areas of high pressure are shaded. The length of the small thin arrows is proportional to the wave amplitude, which are shown to decrease with altitude due to wave damping. The large shaded arrow indicates the net mean flow acceleration due to the divergence of the wave stres:s Rossby Gravity Waves For the RG waves the solutions correspond to (Holton, 1979) where v' Q meridional wind fluctuation geopotential height Horizontal Structure It is obvious from equation (1.7) that for this wave mode, v' has a Gaussian distribution about the equator. The e-folding width (Y,) of the oscillation in this case

19 -W LONGITUDE E- Figure 1.4. Longitude-height section showing the field variables of Kelvin wave (Holron, 1979).

20 This solution is valid for westward propagating waves (a<o) provided that I+ku//3 > 0. Noting that s = ka where s is the number of wavelengths around a latitude circle, this condition may be written as For frequencies which tio not satisfy equation (1.9) the wave amplitude will not decay away from the equator and it is not possible to satisfy boundary conditions at the poles. Waves with the properties described above are called RG waves. The horizontal distribu1:ion of pressure and velocity characteristics of RG waves is shown in figures 1.5. In figure 1.5. the continuous lines are the constant pressure contours and the arrows represent the wind velocity vectors. In the RG mode, u' and P are antisymnetric with respect to the equator. Vertical Structure The vertical structure YI~z*) of the three variables is given by with and the constants C, and C2 are determined by boundary conditions. Figure 1.6. shows the longitude height section along a latitude circle north of equator showing pressure, temperature and wind perturbations for a thermally damped RG wave. Areas of high pressure are shaded. Small arrows show the zonal wind and vertical wmnd perturbations with lengths proportional to the wave amplitude. Meridional wind perturbations are shown by arrows pointed into the

21 Figure 1.5. Pressure and wind fields for RG waves (Marsuno, 1966)

22 - W LONGITUDE E- Figure 1.6. Longitude-height sectiorl showing the field variables of RG waves (Holton, 1979).

23 paper (northward) and out of the paper (southward). The large shaded arrow indicates the net mean flow acceleration due to the wave stress divergence Generation Mechanisms of Equatorial Waves Both the Kelvin and RG waves are excited by sources in the troposphere. Since the vertical fluxes of energy and momentum carried by the waves depend on the nature and strength of the sources, it is clear that an understanding of these sources and their variation in time and space are essential for modelling the general circulation of the equatorial middle atmosphere. Spectral studies have shown that tropospheric variables in rhe tropics have a very broad range of frequencies (Wallace, 1973). Three pc~ssibilities have been proposed for the generation of equatorial waves. One is the generation of tropical waves from lateral forcing at subtropical latitudes (Mak. 1969). Many studies do suggest that mid-latitude circulations have large impacts on tropical waves (Zangvil and Yanai, 1980; Yanai and Lu, 1983; Iroh and Ghi!, 1988). The second theory assumes tropical waves to be forced by variable tropical convective heating (Holron, 1972; Salby and Garcia, 1987). The third theory is that of wave conditional instability of second kind (Wave- CISK). Here it is considered that waves are self-maintained by the latent heat released in convection associated with the wave convergence fields. The relative roles of these three mechanisms in generating the observed variances in the tropics are still uncertain. Lateral forcing from mid-latitudes could excite RG waves. Mak (1969) examined the response of the tropical atmosphere to lateral boundary forcing. In his model, westward moving resonant waves had a large response at wavenumber 3 and with a period of 4 days. A theoretical study of meridional propagation of large-scale waves in mid-latitudes revealed that the disturbances with phase velocity less than the mean zonal velocity on the path can propagate and transport momentum toward the equator (Bennen and Young, 1971). Experiments using GFDL general circulation model shows that both mid-latitude forcing and interaction with cumulus convection are important for the excitation of RG waves (Hayashi and Golder, 1978; Lamb, 1973: Iroh. 1978).

24 Another mechanism for the generation of tropical waves is a forced heating of the atmosphere. Equatorla1 waves are explained as a response to the heating due to cumulus convection. Latent heat released within the Inter Tropical Convergence Zone (ITCZ) is a possible sclurce for equatorial waves (Hayashi, 1970; Holton, 1972; Murakaml, 1972: Haycrshi, 19'74; Salby, 1984; Salby and Garcia, 1987; Bergman and Salby. 1994). Equatorial waves are excited by the diabatic heating of the atmosphere (Holron. 1973; Salby and Garcia, 1987; Manzini and Hamilton, 1993). Analyses of diabatic forcing (Chang, 1976; Hayashi, 1976; Itoh, 1977) indicate a preference for vertical wavelengths which are twice the depth of the heating. Using results of radiosonde observation at the Marshall Islands, Nitta (1972) showed that the heating rate had a maximum around 500 hpa with a period of 5 days. Hendon and Liebmann (1991) pursued convective coupling as a mechanism for the generation of the 4-5 day period RG waves by examining the relationship between the wavefields and tropical convection. Shimizu and Tsuda (1997) observed Kelvin wave charactenstics with radiosondes over Indonesia. They found that wave act~vitles were enhanced when tall, convective clouds passed over the site, suggesting that cuniulus convection seems to play a key role in generating these waves in the equatorial region. Wave-Conditional Instability of Second Kind (CISK) was also introduced as a generation mechanism for equatorial waves (Hayashi, 1970; Chang and Lim, 1988; Gill, 1982: Zhang and Geller. 1994). The release of latent heat in cumulus convection is considered to be the primary energy source for the maintenance of finite amplitude equatorial waves. It might be thought that such waves are merely a direct result of the release of conditional instability in a saturated atmosphere. The cumulus convection and the large-scale motion must be viewed as co-operatively interacting. The cumulus convection supplies the heat necessary to drive the largescale motions and the large-scale motions thus produced will generate the moisture convergence necessarq to drive the cumulus convection. When co-operative interaction between the cumulus convection and a large-scale perturbation lead to unstable growth of the system. the process is named as a CISK. There is recent observational evidence of convectively coupled Kelvin waves with phase speeds of

25 10-20 m s-' (e.g.. Dunkerton (2nd Crum, 1995; Wheeler and Kiladis, 1999). Kelvin wave-cisk theory may be relevant to these waves Interaction of Equatorial Waves with the Mean Flow to Generate QBO Many of the middle atmospheric phenomena can be regarded as involving the interaction of a meanflow with disturbances such as waves or eddies; that are superimposed upon it. QBC) in the lower stratosphere over equatorial latitudes are produced by the equatorial wave-meanflow interaction. Equatorial waves transfer momentum upward and are thus potentially capable of generating mean zonal motion within the stratosphere. Steady waves cannot, however, force meanflow accelerations unless they are dissipated either via mechanical or thermal damping or via absorption at a critical level where the Doppler-shifted phase speed relative to the local meanflow vanishes (e.g., Holton, 1975; Andrews and Mc Intyre, 1976; Mc Infyre, 1980). The vertically propagating equatorial wave modes apparently provide the momentum sources necessary to drive the QBO. The necessity for such momentum sources was shown by Wallace and Holton (1968) who used a diagnostic model for the zonal mean circulation to demonstrate that no reasonable distribution of radiative sources alone could account for the observed wind oscillation. Mechanistic models which demonstrate that the momentum fluxes due to vertically propagating equatorial wave modes can acc:ount for. the observed wind oscillation have been formulated by Lindzen and Holton (1968) and Holton and Lindzen (1972). Theoretical calculations show that the equatorial waves are absorbed by radiative damping and that this damping is strongly dependent on the Doppler-shifted frequency of the waves so that the waves should be completely damped out well below any critical level. Holton and Lindzen (1972) showed that, the Kelvin waves are absorbed as a result of infrared radiative cooling i.e. the waves are damped primarily by infrared radiation to space which tends to smooth out the temperature perturbations associated with the waves. Such absorption leads to a divergence of the wave momentum flux and consequent mean flow acceleration.

26 The basic mechanism of QBO m the theoretical model of Plumb (1977) is illustrated in figure 1.7a and 1.7b (Plumb, 1984). In his model, Plumb considered a vertically unbounded stratified fluid subject to standing wave forcing at its lowest boundary by two travelling waves of equal amplitude and oppositely directed phase speeds. This forcing generates vertically propagating internal gravity waves which propagate upward into the fluid wherein they dissipate by a weak Newtonian cooling with constant rate a. In figure 1.7a a westerly meanflow perturbation has been introduced. In the regions of westerly flow, the Doppler shifted phase speed (c-i!?) of the westerly wave is reduced (c is the phase velocity of the wave and O' is the mean zonal flow velocity). The vertical group velocity is proportional to (c -??)I. When the Doppler shifted phase speed decreases the vertical group velocity decreases and there will be a larger time available for the energy to be damped for a given vertical propagation distance. Conversely the easterly wave is attenuated less rapidly, since c+ C is increased. Therefore westerly acceleration dominates in this region, as shown in figure 1.7a. As a result of this selective attenuation of the westerly wave, however, at high levels, the easterly wave dominates and therefore the net acceleration become:$ easterly there. Plumb (1977) showed that the level of maximum acceleration is below the level of maximum O', consequently the level of maximum O' must descent with time. This instability can lead to a finite amplitude mean wind oscillation resembling QBO is shown in figure 1.7b. The subsequent evolution of the flow is depicted schematically in figure 1.8. The shear zone separating the: low-level westerly regime from the easterly flow above becomes increasingly narrow with time, (figure 1.8a) so that viscous diffusion across the shear zone destroys the low-level westerly. This has the effect of destroying the westerly regime from above and therefore 'switching' the low-level flow into an easterly regime (figure 1.8b). When this occurs, the westerly wave is no longer attenuated at low levels and penetrates to greater heights. Consequently a high level westerly acceleration of the meanflow takes place. Eventually (figure 1.8~) a westerly regime develops there, which moves downward until the interior shear layer again becomes narrow enough for diffusion to act (figure 1.8d). The

27 Figure 1.7. Schematic representation of the instability of zonal flow in a stratified fluid with standing wave forcing applied at a lower boundary. Zonal mean velocity (c) vs. height (z) (Plumb, 1984). (a) Onset of instability from a small zonal flow perturbation. (b) Early stages of subsequent evolution Double arrows: Approximate location and direction of mawimum acceleration. Wavy lines: Schematic representation of penetration of wave components

28 Figure 1.8. Schematic representation of evolution and structure of fully developed flow (following from Figure 1.7). Six stages in one complete cycle of the mean flow oscillation (Plumb, 1984) Single arrows: acceleration arising from viscous forces. Double arrows: acceleration arising from wave attenuation. Wavy lines: Schematic representation of penetration of wave components

29 easterly waves can then penetrate to higher levels (figure 1.8e), where it initiates a new easterly plane of oscillation (figure 1.8D. Thus the interaction between upward propagating dissipating waves and the meantlow generates a new oscillation with finite amplitude which depends primarily on the momentum flux and vertical decay scale of the waves. This mechanism was demonstrated in a laboratory experiment by Plumb and McEwan (1978). A detailed study of the vertical and horizontal (latitudinal) structure and properties of equatorial Kelvin and RG waves undergoing thermal and mechanical dissipation and consequent rneanflow acceleration and the evolution of the mean flow producing a realistic QUO in the lower stratosphere, was done by Plumb and Bell (1982 a, b). Dunkerton (1985) simulated some features of the 2-D structure of QBO by using a WKB approach for fbrcings caused by Kelvin waves and RG waves. He could simulate some of the observed features of QBO near the equator and its variation with latitude. Takahashi (1987) developed a 2-D mechanistic model, which verified the importance of wave damping in driving the QBO. However, the model required unrealistically high wave amplitudes in order to produce a QBO consistent with observations. Takahashi anal Holton (1991) noted the inability of RG waves to provide sufficient momentum to drive the easterly phase of the QBO. Takahashi and Boville (1992) in their 3-D simulation of the QBO, inferred that to have a QBO-like oscillation the amplitude of the RG wave had to be about five times as large as the observational values and that of Kelvrn wave also had to be larger than the observational values. Boville and Randel (1992) examined the ability of a General Circulation Model (GCM) to sin~ulatequatorial waves and investigated the changes in the wave properties as a function of the vertical resolution of the model. The simulated wave amplitudes were as large as observed and the waves were absorbed in the lower stratosphere. as required in order to force the QBO. However, the momentum flux divergence associated with equatorial waves was not sufficient to explain the zonal flow accelerations found in the QBO. The probable candidates for the carriers of zonal momentum in addition to equatorial waves are gravity waves of

30 intermediate scales smaller than planetary scale. The significance of short-period gravity waves with intermediate scales in producing QBO is suggested observationally and theoretically. (e.g., Takahashi and Shiobara, 1995; Takahashi, 1996, 1999; Takahashi et al ; Mayr et al., 1997, 2000; Sato and Dunkerton, 1997; Dunkerton. 1997; Alexander and Holton, 1997; Horinouchi and Yoden, 1998) Role of Kelvin Wave in the Generation of SAO Kelvin wave also plays an important role in driving the SAO through wavemeanflow interaction. Holron (1975) was the first to suggest that Kelvin wave absorption could produce the necessary eddy momentum flux and observed downward propagation of the: SAO westerly phase. The latitudinal and vertical structure of equatorial Kelvin wave is fixed by their phase speed. Because of this property and because simple Kelvin waves are zonally nondispersive, Kelvin waves are often categorised according to their phase speed. For phase speeds of m s-', which are characteristic of the 'slow Kelvin wave' observed in the lower. stratosphere (Wallace and &bus@, 1968a), the latitudinal width and vertical wavelength are of order 30'' and 10 km respectively (e.g., Salby et al., 1984). For a phase speed of 60 m s'. which is characteristic of the 'fast Kelvin wave' observed in the middle and upper stratosphere (Hirota, 1978), the latitudinal width and vertical wavelength are of order 40' and 20 km, respectively. For a phase speed of 120 m s-i, which is characteristic of the 'Ultra Fast Kelvin (UFK)' wave observed in the upper stratosphere and mesosphere (Salby et al., 1984), the latitudinal width and vertical wavelength are of order 50" and 40 km, respectively. Observational studies of equatorial waves show that the long-period slow Kelvin waves which are predominant during the easterly phase of the QBO in the lower stratosphere are dissipated in the westerly shear zone of the QBO. Short-period fast and ultra fast Kelvin waves would experience relatively small damping in passing through the lower stratosphere, since their intrinsic phase speeds would remain large in the comparatively weak westerlies of the QBO. Thus such waves could easily propagate into upper stratosphere and mesosphere. The fast Kelvin waves drive the westerly phase of stratopause SAO (Hirota, 1978, 1979; Dunkerton, 1979; Mahlman and Umscheid, 1984: Sassi and Garcia, 1997). Similarly westerly accelerations

31 observed in the mesopause SAO may be provided by UFK waves (Dunkerton, 1982). Recently. the zonal momentum and eastward acceleration due to UFK are studied (Riggin et al., 1997; Lieberman and Riggin, 1997) and the results suggest that Kelvin waves are important sources of eastward momentum in the mesosphere and lower thermosphere and may contribute in part to the eastward momentum budgets of the mesopause SAO. It was reported that UFK activity in the mesospheric and lower thermospheric region showed a semi-annual variation (Vincent, 1993: Yoshida er a/, 1999) strongly suggesting a relation between the UFK and mesospheric SAO Observational Evidence of Equatorial Waves The observational evidence of the Kelvin waves was first reported by Wallace and Kousky (1968a). In thei~. analysis of radiosonde data, they noted a large day period oscillation in zonal wind with a vertical wavelength of about 10 km. The earliest observational evidence of RG waves was provided by Yanai and Mancyarna (1966) and Maruyarna and Yanai (1967). Using balloonsonde and rocketsonde data. at many low latitude stations. they noticed the westward and downward propagating fluchlations in meridional winds with periods of about 4-5 days and vertical wavelengths of about 6 km. They had odd symmetry about equator and were confined to within f 1.2" on either side of the equator. Subsequent studies revealed the existence of similar fluctuations in zonal wind also. Wallace describes this RG waves as one which 'behaves as gravity wave at low zonal wave number and as a quasi-geostrophic Rossby wave at high zonal wave number'. Hirora (1978) using rocketsonde data observed the existence of Kelvin and RG waves. The Kelvin wave identified by him had a vertical wavelength of km, period 10 days and had large amplitudes during the easterly phase of QBO. Devarajan et al. (1985) obtained considerable information on the characteristics of equatorial waves from rocket observations pertaining to the upper troposphere and lower stratosphere. The period of Kelvin waves were inferred to be in the range of 4-8 days with dominant vertical wavelengths in the range of km. The together with the shorter periods, indicated the.of< zonal "- wavenumber two. Dhaka er a/. (1995) detected -._

32 measured wind tn the 0-30 km altitude range and rocket-measured wind in the km altitude range. Their study revealed evidence of Kelvin waves with period days and vertical wavelength -10 km in the lower stratosphere, with period days and vertical wavelength of km in the stratospheric-lower mesospheric region and RG waves with periods days and vertical wavelength of 10 km in the upper troposphere and lower stratosphere. Tsuda et al. (1994) using radiosonde data over Indonesia obtained Kelvin waves of period days in the troposphere and 7 and 20 day period Kelvin waves in the lower stratosphere. Shimizu and Tsuda (1997) studied characteristics of Kelvin waves observed with radiosondes over Indonesia. Vincent (1993) observed 3-10 day period range Kelvin waves using MF radar located at Christmas Island. Riggin et al. (1997) used mesospheric radars to investigate the characteristic.^ of a Kelvin wave from two equatorial sites. A Kelvin wave with a period near 3 days was detected throughout the period of observation. Recently Yoshida er al. (1999) analysed the behaviour of the ultra-fast Kelvin waves using data from meteor wind radar in the upper atmosphere and from radiosonde in the lower atmosphere Satellite observations have revealed the global structure of the Kelvin waves. Using data from a nadir-viewing satellite, Hirora (1979) was able to show the evidence for 4-10 day Kelvin waves. Evidence that Kelvin waves exist at levels above 60 krn has come from the Limb Infrared Monitor of the Stratosphere (LIMS) experiment. Fast Kelvin waves are identified in temperature field derived from the LIMS (Salby et al., 1984; C0.y and H~tchman, 1984; Hitchman and Leovy, 1988). Using LIMS ozone mixing ratio data, 'ozone Kelvin waves' were detected in the upper stratosphere and Kelvin wave-induced oscillations were revealed in the other LIMS constituent fields such as water vapour and nitric acid (Randel, 1990). Hirota et al. (1991) and Randel and Gille (1991), using ozone mixing ratio data from the Solar Backscaner Ultra Violet (SBUV) sensor, also found 'ozone Kelvin waves' in the upper stratosphere. Randel (1992) found evidence for RG wave signatures in the tropical data fields produced by the European Centre for Medium

33 Range Weather Forecasts (ECMWF) and was able to further corroborate the signals with tropical rawinsonde observations. Canziani er al. (1994) have analysed several aspects of the Kelvin waves seen in the temperature and ozone data derived from the Microwave Limb Sounder (MLS) instrument onboard the Upper Atmosphere Research Satellite (UARS). The satell~te observational evidence of the slow Kelvin waves and RG waves was obtained using total column ozone data from the Total Ozone Mapping Spectrometer (TOMS) satellite instrument (e.g. Stanford and Ziemke, 1993: Ziemke and :?ranford, 1994a, b). Slow Kelvin waves were reported in UARS temperatures by Shioratzi er al. (1997). The results from the High Resolution Doppler Imager (HRDI) instrument aboard the UARS shows the evidence of Kelvin waves in the upper mesosphere and the lower thermosphere (Liebennan and Riggin, 1997; Smith, 1999) Atmospheric Tides Atmospheric pressure, temperature, density and winds are all subject to variations with 24-hour (diurnal) and 12-hour (semidiurnal) periods. The small but measurable, variations of atmospheric parameters with lunar semidiurnal period are caused by the gravitational attraction between the moon and the earth. But the variation of the atmospheric parameters with the solar diurnal and solar semidiurnal periods are caused predominaritly by the heating of the atmosphere due to the absorption of solar radiation by water vapour primarily in the troposphere (Lindzen, 1967 and Groves, 1982). ozone in the stratosphere and mesosphere (Lindzen, 1967) and ionised oxygen in the ionosphere (Harris and Mayr, 1975). The heating has a strong altitude variation anti latitude variation as well. The heating generated pressure variations have particular patterns of variation with latitude, longitude and height. If the distribution of the absorbing medium is zonally uniform around the globe, then the solar heating will produce diurnal oscillations that are sunsynchronous with their phase propagating to the west traversing the globe in one solar day (a zonal wavenumber of one). These oscillations represent the migrating tidal modes and have the feature that their local solar time phase is independent of longitude. The migrating rneridional and zonal pressure gradients generate accelerations of air parcels that are subject to Coriolis torque as they move. The

34 resulting equilibrium global distribution of the pressure and velocity fields associated with the tides is subject to the very important boundary conditions of the earth's poles, in addition to the usual conditions of hydrostatic balance, mass continuity and thermodynamic energy conservation. For example, the zonal motion has to vanish at the poles. The natural boundaries provided by the poles result in specific modes of oscillations with specific latitudinal structures only being possible for each tidal period. Tides, particularly ocean tides, were recognised as early as 320 B.C. Atmospheric tide has been studied in the modem sense for almost two centuries. The general study of tides is historically important, involving such names as Newton, Laplace and Kelvin. In the present time the role of atmospheric tides in explaining daily variations in the magnetic field (Tarpley, 1970 a, b; Richmond et al., 1976; Forbes and Lindzen, 1976 a, b), ionospheric electric fields (Forbes and Lindzen, 1977), latimdinal asymmetries in the F-region equatorial anomaly (Rush, 1972), composition variations (:May and Harris, 1977; Forbes, 1978; Peritdidier and Teitelbaum. 1977). the ;generation of mean winds (Miyahara, 1978) and mean heating of the thermosphere (Lindzen and Blake, 1970) are recognised. Tides can be decomposed mathematically into orthogonal functions with each component representing a particular mode of the total oscillation. The first mathematical approach to understand the generation and structure of tides was by Laplace ( ) who developed an equation describing their horizontal structure on a frictionless spherical earth. Studies by Hough (1897,1898), Wilkes (1949), Sieber? (1961) and Kato (1966) investigated the mathematical structure of atmospheric tides using assumptions about the structure of the earth's atmosphere which lead to the 'classical tidal theory' summarised in the monograph of Chapman and Lindzen (1970). Recent works have lead to an improved understanding of the structure of atmospheric tides using numerical models which do not have many of the limiting assumptions of the classical linear tidal theory (Lindzen and Hong, 1974; Forbes and Hagun, 1979; Walterscheid 1980, Forbes, 1982 a, b; Forbes and Groves, 1987).

35 Classical Tidal Theory In 'classical tidal theory' (Chapman and Lindzen, 1970) the equations of motion (considering the linearised equations for tidal perturbations on a basic state with neither meanflow nor horizontal temperature gradients in an inviscid nondissipative atmosphere with many other simplifying assumptions such as validity of local thermodynamic equilibrium, atmosphere being treated as a perfect gas in hydrostatic equilibrium) can be reduced to a single second order partial differential equation in a single dependent variable. This partial differential equation for the latitude dependence is Laplace's tidal equation whose solution consists in an infinite set of eigenfunctions (called Hough functions) and associated eigen values or separation constants (called equivalent depths). The forcing functions (thermotidal heating functions) are expanded in terms of these Hough functions and the vertical structure equation is used to calculate the response to the forcing for each Hough component. The equivalent depths determine the nature of the vertical structure of the tidal fields. The vertical (upward) propagation of tidal energy in an isothermal atmosphere is having a functional form exp(ik) (Chapman and Lindzen, 1970), where z is the vertical co-ordinate and where Y the ratio of specific heats H scale height '8 km h, the equivalent depth for a particular mode n Obviously. for h,i 0 and h, > 8 km, /1 becomes imaginary and tidal energy decays exponentially with height: i.e., tidal wave become evanescent. For the diurnal and semidiurnal rides values for all positive h,s are less than 8 km and hence these tides have a vertical propagation, whereas for the negative diurnal modes, energy becomes trapped vertically.

36 Development of More Realistic Models of Tides The 'classical' tidal theory was successful in interpreting many of the observed tidal features in the neutral atmosphere, though it was based on unrealistic assumption of a zero mean wind atmosphere with no horizontal temperature gradients and no dissipation of tidal waves. The tides were assumed to be produced exclusively by the solar thennal excitation of water vapour and ozone. Realistic modelling of atmospheric tides requires consideration of a number of physical processes beyond those considered in classical tidal theory. To undersrand tht: migrating diurnal tides, two-dimensional linear mechanistic and numerical models have been developed. In these models the effect of background winds and meridional temperature gradients are incorporated and their variation with altitude, latitude and season are taken into account. They have been quite successful in reproducing many of the observed features of the diurnal tides (e.g., Forbes 1982 a, b; ifso et al., 1981,1987; Vial 1986, 1989; Forbes and Hagan 1988; Hagan er al., 1995). Some tidal modelling efforts are done by Vial (1986). Aso er al., (1981,1987), Forbes and Hogan (1988), Forbes and Vial (1989) and Aso (1993). Two significant features of the tidal fields which have come out of these studies and could not be seen in classical theory are the so called 'mode coupling' produced by the mean winds and 'mode distcrtion' 01- 'mode broadening' produced by turbulent dissipative processes. The generation of higher order modes which is a direct consequence of the mean wind acting on the lower order modes is referred to as 'mode coupling' and they propagate into the upper atmosphere as any other thermally forced mode and may interfere with the thermally forced modes. Much effort has been devoted to the study and modelling of tidal perturbations in the mesosphere and lower thermosphere wind field (e.g., Hays er al., 1994; Burrage et al., 19'95; Hagan er al., 1995, 1997, 1999a; Mc Landress, 1997; Akmaev et o1.,1997; Wang er al., 1997; Wood and Andrews 1997 a, b, c; Yudin er al., 1997). Comprehensive three-dimensional (3-D) numerical models, such

37 as the thennosphere!ionosphereimesosphere electrodynamics general circulation model (TIME-GCM) (Robie and Ridley, 1994) have been developed which predict how the migrating tides affect observable quantities such as airglow emission brightness, atmospheric temperatures and wind as a function of local time, geographic location and altitude. A three-dimensional middle atmospheric model named as spectral mesosplierellower thermosphere model was developed, which been primarily used for sinlulations and diagnostics of the zonal mean climatology and which incorporates realistic parameterisations of radiative transfer and dissipation processes including eddy and molecular viscosity and thennal conductivity and ion drag (Akmaev er al., 1992; Akmaev. 1994; Akmaev et al. 1996). Using prescribed heating rates in the lower atmosphere and specified profiles of both the eddy diffusion coefficient and gravity wave drag in the mesosphere and lower thermosphere. Hagan et a[., (1995) developed the linear global scale wave model (GSWM) using series of background wind models (Groves, 1985,1987; Ponyagin and Solo'eva, 1992 a, b) and the MSIS-E-90 temperature model (Hedin, 1991). This model was updated incorporating the background wind field between -10 and 120 km with multi-year monthly averaged High Resolution Doppler Interferometer (HRDI) zonal mean zonal wind data and the ozone climatologies used to parameterise strato-mesospheric tidal forcing (Hagan, 1996; Hagan et al. 1999a, 1999b) Tidal Interactions The correlations and interactions between wave types in the mesosphere especially between gravity waves and tides had been studied both observationally (Walterscheid et al ; F,ritr.r and Vincent, 1987; Wang and Fritts, 1991; Hall et al., 1995 a, b: Thqapparan er al ) and theoretically (Walrerscheid, 1981; Forbes et al., 1991: Miyahara and Forbes, 1991; Mc Landress and Ward, 1994). Many aspects of gravity wave-tide interactions are adequately reviewed by Vial and Forbes (1989) and Miyuhara and Forbes (1994). It has become evident that a modulation of gravity wave fluxes at tidal periods may be a process whereby a tidal signal can be impressed upon1 the upper atmosphere, even at thennospheric heights (Fritts and Vincent. 1987; Wang and Fritts, 1991; Forbes et al., 1997). The tidal

38 amplitude in the upper mesosphere are suppressed by tide-gravity wave interactions (Fritts and Vincent. 1987; Hunr, 1990: Miyahara and Forbes, 1991,1994, Lu and Frins, 1993). The breaking of gravity waves suppress the diumal tide and the momentum flux convergence induce tides having other frequencies (e.g., semidiurnal tides) (Forbes and Hagan, 1979, Forbes et al., 1991). Gravity wave breaking produces tidally modulated diffusivities which in turn produces diurnal variation in mesospheric ozone (Ejarson et al., 1987). The diffusivities produced by gravity wave breaking also alf.er the daily averaged mean flow acceleration (Hunt, 1986, 1990; Mc Landress and Ward, 1994). Eckermann and Marks (1996) analysed the interaction of a gravity wave with a solar tide using ray theory in order to assess whether the temporal oscillation of the tide has any significant effects on the interaction. Their amplitude calculations revealed that time-varying gravity wave momentum flux divergences were resulted from tidal reaction and consequently were highly phase coherent wirh the tidal oscillation. The non-linear interaction between the diumal and the semidiurnal tides is another kind of wave-wave inreraction modifying the tidal structure. Non-linear interactions were put forth to explain the observed structure of the terdiurnal tide (Glass and Fello+vs. 1975). The effect of nonlinearities on atmospheric tides have been studied by Kahler (1988) u:sing 3-D model. Quasi-Two-Day Waves (QTDW) dominate the horizontal winds and influence global circulation, mass transport, temperature profiles and electrical conductivity in the middle and upper atmosphere. It is suggested that the QTDW is a nearly resonant wave forced by the migrating diurnal tides through nonlinear interactions (e.g., Walrerscheid (znd Vincent. 1996). Recent modelling results have indicated that a large amplitude QTDW occurs at times when the diurnal tide is weak, suggesting that a possible interaction between the two may be causing the weak tidal amplitudes (Norton and Thurburn. 1996, 1997). Non-linear effects resulting from interactions with planetary waves is a possible source of variability for the diurnal tide (Teitelbaum and Vial, 1991).

39 Planetary waves interact with tides and modulate gravity wave fluxes (Manson er al., 1982; Teirelbaum and Vial, 1991: Ruster, 1992; Kamalabadi er al., 1997). There is evidence of gravity wave modulation at tidal periods at times of strong planetary wave and tidal activity (e.g., Manson and Meek, 1990; Manson et al., 1998). Pancheva (2000) reported considerable modulation of tidal amplitudes by planetary waves in the neutral wind, in the lower thermosphere Norunigrating Tides The amount of atmospheric minor constituents that absorb solar radiation can fundamentally be assumed :not to show a significant variation in the longitudinal distribution. Therefore, the corresponding tidal generation also becomes zonally homogeneous, so the tides propagate westward, synchronising with the apparent motion of the sun. This sun-synchronous component is commonly called the migrating tide. In addition tmo the sun-synchronous tides, nonmigrating tides can be generated by a localised excitation source, such as longitudinal non-uniformity of water vapour content and the cloud convective activity as well as a land-sea contrast in the heat transfer process within the planetary boundary layer (Mc Kenzie 1968; Karo er al., 1982; Forbes and Groves. 1987; Tsuda and Kato, 1989; Hsu and Hoskins, 1989: Williams and Avery, 1996 a, b; Ekanayake er al., 1997, Hagan er al., 1997). Two other sourc:es of exciting diurnal tides in the trpposphere include surface heat flux (Karo, 1989) and latent heat release of precipitating clouds (Lindzen, 1978; Hamilton, 1981, Williams and Avery, 1996 a). The zonal distribution of surface heat flux and precipitating clouds is not uniform around the globe and leads to the generation of nonmigrating tidal oscillations. Following classical tidal theory, the loc;alised distribution of a heat source can be expanded into a series of positive and negative longitudinal wave numbers. Therefore, the nonmigrating tides consist of various zonal wavenumbers, propagating both westward and eastward, or standing (Tsuda and Karo, 1989). Observationally. the existence of nonmigrating tides has been known for more than half a century as reviewed by Chapman and Lindzen, (1970). Haunvitz (1965) found nonmigrating tides in diurnal surface pressure oscillations whose

40 amplitudes are larger on land than over ocean. In his analysis of surface pressure data, he found not only the diurnal migrating tide that travels westward with the sun, but also other components (nomigrating tides) having various zonal wavenumbers propagating both westward and eastward. Haurwirz and Cowlq (1973) showed larger diurnal surface pressure oscillation over land areas than over ocean areas and attributed it to nomigrating modes. The global distribution of diurnal tidal winds in the troposphere and lower stratosphere has been examined by Wallace and Harrrunfr (1909) and Wallace and Tadd (1974). Their studies showed that although the spatial panerns of the diurnal tide are dominated by wavenumber one, higher order longitudinal modes are present throughout the troposphere and lower stratosphere. The distortions, which were present in the lower troposphere, seem to be associated with ropographic features and the placement of the continents. Above 200 mb. only the broadest scales were observed. The wind patterns showed strong seasonal variations in the midlatitudes. Further evidence for nonmigrating tides in the middle atmosphere appeared in radar and rocket profiles of wind and temperature (Marhe~vs, 19761; Kasrogi, 1981; Sasi and Krishnamunhy, 1990; Tsuda er al., 1994, 1997, 1999) and in forecast model analyses (Hsu and Hoskins, 1989). Fukao et al. (1980) and Mackawa er al. (1986) using radar data found diurnal wind variations in the lower stratosphere over Arecibo having short vertical wavelengths (less than 1Okm) which are due to nomigrating tides. Liebennan (1991) determined the behaviour of diurnal tides from satellite observations in the middle atmosphere, reported that nonmigrating tides could have larger amplitudes than migrating components and that the norunigrating tides could cause significant time variations of diurnal tides. Williams arid Avery (1996b) observed nomigrating tides in zonal and meridional winds using 50 MHz wind profilers over the equatorial Pacific. In an analysis of Upper Atmosphere Research Satellite (UARS) High-Resolution Doppler Imager (HRDI) mesosphere and lower thermosphere wind measurements, Kharratov et al. (1996) found longitudinal tidal variability, which they attributed to the presence of nonmigraring components. Chang and Avery (1997) reported a detailed long-term tidal analysis of horizontal winds measured over Christmas Island (2"N, 157" W) which included comparisons to GSW model predictions. They suggested that the GSWM underestimates of the diurnal tide that they observed may be