The General Circulation of the Atmosphere

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19.1 Introduction - Historical Background

Historically, there must been a time when people had little idea of a circulation in the earth's atmosphere. Few were aware that the wind at their locality was related to the wind at another location on the face of the earth. It appears that the first to visualize a circulation in the atmosphere was the British scientist, Halley (1686), who made a detailed study of the wind systems over the tropical belt with the data then available and hypothesized that the observed trade winds at the surface were part of a direct thermally-driven vertical circulation between a heat source and a heat sink, which reversed direction between the lower and the upper levels and between winter and summer. About half a century later, George Hadley (1735), also a distinguished and well-known British scientist, investigated the same problem and offered an explanation for the cause of the trade winds as well as their observed direction on the basis of differential heating between the equatorial and the higher latitudes and rotation of the earth. He argued that a general equatorward drift of the tradewinds at low levels required a compensating poleward drift at high levels in order to prevent an undue accumulation of mass near the equator. Further, a general westward drag by the tradewinds due to the rotation of the earth on the earth's surface at low latitudes required a compensating eastward drag by the westerlies at high latitudes so as to prevent a general slowing down of the earth. It was found later that the general westward or eastward component of the wind could be easily explained on the basis of the principle of conservation of absolute angular momentum of the earth. A parcel of air moving equatorward from high latitudes in order to conserve the angular momentum of its original latitude would acquire an increasingly westward drift, while a poleward-moving parcel would acquire an increasingly eastward drift. This was due to the fact that the earth's surface at the equator moved faster than at higher latitudes. A change of wind direction from easterly at low levels to westerly at high levels also follows from thermal-wind considerations due to equator-to-pole horizontal temperature gradient. Hadley's idealized single-cell circulation model, shown schematically in Fig. 19.1 held ground and went unchallenged for nearly a

Fig. 19.1 Schematic of a single-cell Hadley circulation model

century and it was once thought that Hadley's model was representative of mean meridional circulation over all parts of the globe at all times of the year. However, later observations called for a modification of Hadley's idealized single-cell model. The new observations revealed the presence of a well-marked high pressure belt over the subtropics and a low pressure belt further poleward near 60o latitude, which suggested a meridional pressure gradient and a poleward drift of air, instead of an equatorward drift near surface, and a compensating equatorward drift at some height, over the midlatitudes. Further, the westerly wind over the midlatitudes were found to be baroclinically unstable and characterized by large-scale eddy motion. Amongst the early attempts made to modify Hadley's original scheme were those of Thomson (1857) and Ferrel (1859) who introduced a shallow indirect cell, characterized by a poleward flow near the surface and equatorward flow at some height, over the midlatitudes, within the framework of the idealized single-cell Hadley circulation model, as shown schematically in Fig. 19.2.

Further modifications to the meridional circulation model were made in the light of later observations. Of these, one proposed by Rossby (1947), is shown in

The three-cell meridional circulation model shows a direct circulation cell over the tropical belt, an indirect circulation cell over the midlatitudes and a direct circulation cell over the polar latitudes, with a polar front located at a latitude of about 60o. The Rossby model has, by and large, stood the test of time and found general

circulation model as modified by Thomson (1857) and Ferrel (1859)

Fig. 19.2 The Hadley

Fig. 19.3 Schematic of a three-cell meridional circulation model proposed by Rossby (1947)
Rossby Cell

acceptance by the scientific community to this day. In this model, it is the tropical cell which is identified as the classical Hadley circulation.

Palmen (1951), however, found that the use of the zonally-averaged data often tended to obscure or wipe out some of the more important features of the mean meridional circulation. He showed that the mean meridional circulation during winter differs significantly from the Rossby three-cell model. He found that over the high latitudes the meridional drifts of air were very slow compared to the zonal flow and concluded that the major part of the heat transfer over these high latitudes was effected by horizontal waves, whereas that over the tropics was accomplished by the tropical Hadley circulation.

Mintz (1951) presented a composite picture of the zonally-averaged observed mean zonal winds over the globe in a vertical cross-section extending from pole to pole and from m.s.l. to 50 mb during winter and summer, which is shown in Fig. 19.4.

The profiles of the zonal wind shown by Fig. 19.4 reveal the presence of deep easterlies over the tropics and westerlies over the middle and high latitudes in both the seasons though with some seasonal shifts in their latitudinal boundaries but considerable uncertainty appears to exist in the latitudinal extent and depth of the easterlies over the polar belt. However, the mean zonal wind over the Antarctic during southern summer appears to be easterly throughout the whole troposphere.

19.2 Zonally-Averaged Mean Temperature and Wind Fields Over the Globe

19.2.1 Longitudinally-Averaged Mean Temperature and Wind Fields in Vertical Sections

Results of a computation of the zonally-averaged fields of temperature and zonal wind in the northern hemisphere troposphere and lower stratosphere for January and July are presented in Figs. 19.5(a) and (b) respectively.

The salient features of Figs. 19.5(a, b) may be summarized as follows:

Mintz General Circulation Atmosphere

Fig. 19.4 The profile of the observed mean zonal wind in a vertical section of the global atmosphere during winter and summer: Sections with easterlies are shaded (Mintz, 1951)

Fig. 19.4 The profile of the observed mean zonal wind in a vertical section of the global atmosphere during winter and summer: Sections with easterlies are shaded (Mintz, 1951)

In January (Fig. 19.5a, lower panel), the mean temperature decreases continuously from equator to pole with strongest horizontal temperature gradient over the midlatitudes and from surface upward. A minimum temperature of about —800C is found at the tropopause level over the equatorial belt at about 100 mb at altitude about 16 km a.s.l. The tropopause level breaks over the subtropical belt and suddenly lowers poleward of about 30N and gradually descends to about 300 mb at an altitude of about 10 km over the polar belt. The stratospheric temperature increases with height over the tropical and subtropical belts but decreases with height over the polar region.

The wind field shows two belts of light easterly winds in the troposphere, one over the tropics equatorward of 30N with depth increasing towards the equator and the other, a shallow one, over the polar belt, north of about 70N. Light easterly winds also appear over the tropical stratosphere. A strong westerly jet of velocity about 40 m s—1 prevails at an altitude of about 12 km over the subtropical belt and a westerly wind maximum about 20 m s—1 appears in the stratosphere over the latitudes between about 60N and 70N.

Circulation Earth Atmosphere Images
LATJTUDE f°N)

LATITUDE C*m

Fig. 19.5 Meridional cross-sections of longitudinally-averaged temperature in degrees Celsius (____) and zonal wind in meters per second ( ) for the northern hemisphere in (a) January, and (b) July. Zonal winds positive westerly, negative easterly. Heavy lines denote the tropopause and the Arctic inversion. (From U.S. Navy Weather Research Facility Arctic Forecast Guide, 1962)

LATITUDE C*m

Fig. 19.5 Meridional cross-sections of longitudinally-averaged temperature in degrees Celsius (____) and zonal wind in meters per second ( ) for the northern hemisphere in (a) January, and (b) July. Zonal winds positive westerly, negative easterly. Heavy lines denote the tropopause and the Arctic inversion. (From U.S. Navy Weather Research Facility Arctic Forecast Guide, 1962)

In July (Fig. 19.5b, upper panel), though the temperature field looks somewhat similar to that in January, there are significant differences. The warmest temperatures are now near surface over the tropical belt with temperatures decreasing both poleward and upward as in January but the horizontal temperature gradient is now much smaller.

A major change appears to have taken place in July in the thermal structure of the stratosphere over latitudes north of about 50N, with significant warming of the polar atmosphere by more than 300C.

Significant changes may also be noticed in the wind field in July. The westerly jet over the subtropical belt has weakened and moved poleward, while the easterly wind dominates the whole tropical belt and extends to great heights. The westerly wind maximum in the stratosphere over the high latitudes has disappeared and is replaced by light easterlies.

19.2.2 Idealized Pressure and Wind Fields at Surface Over the Globe in the Three-Cell Model

A general view of the mean sea-level pressure and wind systems consistent with the three-cell model is shown in Fig. 19.6.

Fig. 19.6 shows the tradewinds of the two hemispheres over the tropical belts blowing equatorward and converging into a well-marked trough of low pressure known as the equatorial trough and forming an intertropical convergence zone (ITCZ) at the equator, the westerly winds over the midlatitudes poleward of a well-marked ridge of high pressure over the subtropical belt; and a belt of easterlies poleward of the polar front.

The current view is that neither the original single-cell Hadley circulation model nor any of the above-mentioned modified models truly represents the actual circulation in the atmosphere which varies with time and longitude.

However, a three-cell model consisting of two direct Hadley-type cells, one over the tropics between the equator and about 30° parallels and the second over the polar belt poleward of about 60° parallels, and an indirect Thomson-Ferrel cell over the midlatitudes is, perhaps, the closest to what is observed in the real atmosphere over trough of low pressure along the equator

Fig. 19.6 Idealized pressure and wind belts at the earth's surface in a three-cell circulation model. Note that in this model, the tradewinds converge at the equatorial

Fig. 19.6 Idealized pressure and wind belts at the earth's surface in a three-cell

Earth Latitude Lines And Wind Belts

any part of the globe at any time of the year. This appears to be well borne out by a study of Starr (1968) who computed the mean northward wind component from a dataset of 700 stations spread over 5 years from all parts of the globe and later revised his earlier estimates by adding data of another 100 stations.

In this chapter, we use the term 'general circulation' to mean generally a zonally-symmetric annual-mean basic background circulation which is assumed to be present at all longitudes at all times of the year, with a clear understanding that it may be influenced by several regional or local meteorological factors, such as large thermal contrasts between continents and oceans, or between one part of the ocean and another part, or by large-scale orography.The deviations from the general circulation as defined above may be particularly large over the tropics where along with surface thermal contrasts, an extra source of diabatic heating may be introduced by release of latent heat of condensation and its effects on convection and subsidence.

19.3 Observed Distributions of Mean Winds (Streamlines) and Circulations Over the Globe During Winter and Summer

Fig. 19.7 shows maps of mean low-level winds and circulations over the globe during (a) January, and (b) July.

It is evident from Fig. 19.7 that the observed low level circulations over the globe are to a large measure consistent with the fields of surface pressures shown in Figs. 2.1. Oceans and continents appear to have their own characteristic circulation systems and that they respond differentially to the seasonal movement of heat sources and sinks across the equator, as evident from the seasonal movement of the ITCZ (indicated by a double-dashed line). For example, the ITCZ sweeps out nearly 45°-50° of latitude between the hemispheres over the Asia-Australia region as well as between North and South America, whereas it moves through only about 10° of latitude over most of the Pacific and the Atlantic oceans. Further, circulations over continents are influenced by topographic features such as high mountain ranges, while those over oceans are affected by the distribution of warm and cold ocean currents. Over broad expanses of the eastern Pacific and eastern Atlantic, the ITCZ remains confined to the northern hemisphere only, since its movement to the southern hemisphere is prevented by the effect of the powerful cold ocean currents, viz., the Humbolt or Peruvian current in the South Pacific Ocean and the Benguela current in the South Atlantic Ocean, which keep the equatorial ocean surface cold.

The dominating features of low level wind systems over both continents and oceans in both seasons are the tradewinds which diverge anticyclonically from the subtropical high pressure cells and blow towards the equator to converge at the cyclonic circulation around the equatorial trough of low pressure and form the ITCZ. In this regard, a special situation appears to exist over the Asian continent. During winter, the lofty Himalaya Mountain ranges and the Tibetan plateau divide the subtropical high pressure system over Asia into two parts, one to the north of the

0 60 E 120 180 120 W 60~~~ $
Fultz Dishpan
Fig. 19.7 Streamlines showing mean low level (900 hPa) circulations over the globe during January, and July. H-High, L-Low Arrow shows direction of airflow

mountain ranges to be centered over the Mongolian region, and the other to the south broken up into three sub-cells over southern Asia, one over the Arabian peninsula, the second over India and the third over upper Myanmar. During northern summer, the high pressure sub-cells over southern Asia are replaced by low-pressure cells to which winds diverging from the southern hemisphere subtropical high pressure cells converge, thereby ushering in the southwest monsoon over the Indian subcontinent. Poleward of the subtropical high pressure belt, winds are generally westerly to latitude about 60o.

19.4 Maintenance of the Kinetic Energy and Angular Momentum of the General Circulation

We now enquire how the observed circulation and some of its important properties, such as kinetic energy and absolute angular momentum, etc., are maintained in the atmosphere. The list is not exhaustive, for one could also investigate into the global balances of potential energy, internal energy, water vapour, etc. In this section, we review the physical processes by which the atmosphere gains or loses some of these properties and the transfer mechanisms by which a balance is achieved between the source and the sink. Let us first look into the kinetic energy balance of the atmosphere.

19.4.1 The Kinetic Energy Balance of the Atmosphere

An expression for the kinetic energy of the atmosphere can be obtained from the horizontal momentum equation (11.4.7) by multiplying it scalarly by the velocity vector V. Thus,

V-dV/dt = V • (—« Vp — 2 Q x V — V ® + F) Or, P d (V2/2)/dt = —V • Vp + p V • g + p V-F (19.4.1)

Using the relationship, pd (V2/2)/dt = d (p V2/2)/dt — (p V2/2p) dp/dt and the vector identity V • Vp = V • pV — pV • V, in (19.4.1), we obtain, after rearranging, d(pV2/2)/dt = —(pV2/2)V • V — V • P V + pV • V + pV • g + pV • F

Or, dE/dt = —VEV — V^pV + pV^V + pV • g + p V • F (19.4.2)

where we have put E for pV2/2 which represents kinetic energy per unit volume and used the relationship, dE/dt = dE/dt + V • VE.

If we integrate (19.4.2) over a finite volume 5v, we obtain, after applying Gauss's theorem to the first two terms on the right-hand side, the following relationship:

d(J E 8v) / dt = — J EVn 5a — J pVn 5a+J p VV 5v+J p V • g 5v+J pV • F 5v

where 5a is the surface area of the volume 5v, and Vn is the velocity component normal to the surface.

If we now replace the volume element by the whole atmosphere and apply (19.4.3) to it, the first two terms on the right-hand side of (19.4.3) disappear and we are left with the relation dK/dt =JpV-V 5v + J pV • g 5v + J pV • F 5v (19.4.4)

where we have replaced / E 5v by K, which we call the global kinetic energy.

Further, if we consider the kinetic energy of horizontal motion only, the second term on the right-hand side of (19.4.4) which represents the work done by gravity against vertical displacements disappears and we are finally left with the relation

The Eq. (19.4.5) states that if the Kinetic energy of horizontal motion is to remain constant in the atmosphere, the dissipation of kinetic energy by frictional forces (the second term on the right-hand side of the equation) must be continually replaced or balanced by the generation of kinetic energy by pressure forces. In the atmosphere, areas of high pressure with anticyclonic divergent circulation, such as those found at surface over most parts of the subtropical belt act as sources of kinetic energy, while those of low pressure with cyclonic convergent circulation, such as the equatorial trough or the polar low, act as sinks.

The frictional dissipation of kinetic energy occurs only in molecular motion and small-scale turbulent flow. In flow involving large-scale eddies and waves, however, the frictional effect may be reversed in that instead of dissipating the energy, it may actually add to the kinetic energy of the time-mean flow. This reversal is often referred to as a phenomenon of 'negative viscosity'.

19.4.2 The Angular Momentum Balance - Maintenance of the Zonal Circulation

The principle of conservation of absolute angular momentum requires that a parcel of air at rest relative to the rotating surface of the earth at a latitude acquires from, or loses to, the underlying earth's surface angular momentum according as it moves to lower or higher latitudes. Thus, the equatorward-moving easterly tradewinds over the tropics and easterly winds over the polar belt pick up angular momentum from the earth's surface, while the poleward-moving westerly winds lose angular momentum to the surface. Since all these zonal winds are maintained over long periods of time, it follows that the excess angular momentum picked up over the tropics and the polar belt must be transported so as to meet the deficit over the midlatitudes.

The following analysis shows how the zonal winds are maintained in the atmosphere.

Let u be the zonal wind velocity of a parcel of air of unit mass at a latitude ^ relative to the earth's surface. Its absolute angular momentum denoted by M is then given by

M =(u + a Q cos a cos ^ = u a cos ^ + Qa2 cos2 ^ (19.4.6)

where Q denotes the angular velocity and 'a' the mean radius of the earth.

In (19.4.6), the first term stands for relative momentum and is positive or negative according as the relative velocity is eastward or westward, while the second denotes the earth's angular momentum and is called the Q-momentum.

The forces which can change the absolute angular momentum M of a unit mass of air at latitude ^ are those due to torques exerted by the pressure gradient and frictional forces.

Thus, according to Newton's second law, the equation of absolute angular momentum for zonal motion may be written dM/dt =(-adp/dx + Fx)r (19.4.7)

where r = a cos p is pressure, a is specific volume and Fx is the zonal component of the frictional force per unit mass.

Since a = 1/p, we may write (19.4.7) in the form p dM/dt = (—dp/dx + p Fx)r and simplify it, by using the flux form of the equation of continuity (12.2.6) and noting that r does not vary with x, to obtain an expression for the rate of change of absolute angular momentum per unit volume in the form d(pM)/dt = -Vp M V - d (pr) /dx + p Fx r (19.4.8)

The interpretation of (19.4.8) is simple. It states that the absolute angular momentum of the atmosphere poleward of a latitude can change as a result of (1) convergence of the meridional transport of absolute angular momentum across the latitude wall, (2) the torque exerted by the pressure gradient force across mountain ranges, and (3) the torque exerted by the frictional drag of the earth on the atmosphere within the polar cap. In (19.4.8), the term (1) on the right-hand side acts as a source of absolute angular momentum, while the terms (2) and (3) act as sinks. Thus, for balance, it is required that the source (1) should equal the combined effects of the sinks at (2) and (3).

Palmen (1951) has given a more convenient expression for the source term (1). If v be the poleward component of the wind velocity, the total poleward transport of the absolute angular momentum, &, through the vertical cross-section at latitude c|) is

& = J j pMv (a cos ^ bX) 5z where bX and 5z are small increments along longitude and vertical respectively.

We now integrate & around the latitude wall with heights extending from surface to infinity and obtain

where p0 is surface pressure and we have used the hydrostatic approximation, p§z = —§p/g.

Let us now divide the observed wind components u and v into their zonally-averaged values u and v and the respective eddy components u' and v' which are deviations from the zonal average. Since, by perturbation theory, uv = uv + u'v', (19.4.9) may be written

&=[(2na2 cos2 6)/gl P (Qvacos 6 + uv + uV) 5p (19.4.10)

The terms within the integral on the right-hand side of (19.4.10), from left to right, are: (1) the Q-transport term, (2) the drift term, and (3) the eddy-transport term. It may be seen that if v = 0, the only mechanism left to effect northward transfer of the absolute angular momentum of the atmosphere is that through the eddies. If v = 0, the condition implies the existence of a mean meridional circulation at the latitude under consideration p0

since a northward drift of mass is balanced by a southward drift over a long period of time. The same remark applies to the Q-transport term, a northward transport of which at some level or latitude will be balanced by a southward transport at some other level or latitude over a long period of time. However, the integral of the drift term /u v dp is positive if u and v are positively correlated in the vertical.

Palmen and Alaka (1952) applied (19.4.10) to study the angular momentum balance in the mean January atmosphere over the tropical belt between 20N and 30N. The results of their evaluation of the three terms of the equation are presented in Fig. 19.8.

The fluxes computed were of the Q-transport term, the drift term and the eddy-flux term in each 5-deg latitude boxes shown. Since the tropical atmosphere has the NE-trades at low levels and the SW-ly flow aloft, it was divided into two layers, the lower between 1010 mb and 700 mb and the upper extending from 700 mb to the top of the atmosphere where the pressure was assumed to be 0 mb. In the Figure, the solid arrows represent the drift term, and the broken arrows the eddy-transport term. The large amounts by the side of the solid arrows represent the amount of the Q-transport term, while the small amounts represent the momentum transfer arising from the tendency of the meridional circulation to move north or south the whole isotach pattern in the mean cross-section. The zonally-averaged values of the fluxes for each block are shown at the latitude walls for both the layers. The direction of the

Fig. 19.8 Computed angular momentum balance for the latitude belt between 20N and 30N in January. The units of the angular momentum fluxes in the diagram are in 1025 g cm2 s~2 (After Palmen and Alaka, 1952)

meridional transport is indicated by the arrows, while the circled numbers represent the net total flux out of the box in either the meridional or the vertical direction.

Note that the meridional circulation is responsible for the largest part of the meridional transport and this is accomplished almost entirely by the Q-transport term. The drift term makes only a minor contribution, while the eddy-flux term becomes important only in the upper layer. An important point to note is that there is a divergence of the southward flux of angular momentum in the lower layer and convergence of northward flux in the upper layer and the balance is restored by the downward flux into the box immediately below.

The validity of the balance may be checked by comparing the circled numbers appearing on opposite sides of the 700 mb partition line. Also, it is noteworthy that a large amount of angular momentum that is transported poleward in the upper layer across the latitudinal wall at 30N is available for maintenance of angular momentum of the midlatitude westerlies. It is likely that part of this tropical contribution may be transported poleward by the breakthrough extension of the tropical cell in the vicinity of about 30N. However, it appears that over the midlatitudes the contribution made by the eddy-flux term far exceeds that due to the Q- transport and the drift terms.

The tropical circulation cell also plays an important role in the meridional transport of water vapour in the tropics. Over most of the tradewind region, evaporation exceeds precipitation, while reverse is the case near the equator where precipitation exceeds evaporartion. The required water vapour transport to the equatorial region for net precipitation is provided by the meridional circulation.

19.5 Eddy-Transports

We now turn to the latitudes where wave activity dominates the air flow and most of the poleward transports of sensible heat, angular momentum and water vapour are effected by large-scale eddies.

Wiin-Nielsen (1967) showed that maximum kinetic energy is transported across midlatitudes by eddies of circumpolar wave numbers about six, i.e., wavelengths around 6500 km.

Starr (1968) computed the direction and magnitude of the eddy- transfer of annual mean zonally averaged heat, angular momentum and water vapour across the different latitudes. Some of the results of his computations were reviewed by Lorenz (1969). Here, we summarize some of the important findings of the studies.

19.5.1 Eddy Flux of Sensible Heat

The maximum northward eddy-flux of sensible heat occurs across midlatitudes where there is strong northward gradient of temperature and where baroclinic waves dominate. A northward flux requires that the zonal fluctuations in v and T are positively correlated, i.e., v/T/ > 0. [Here, the underlining denotes a zonal average].

19.5.2 Eddy-Flux of Angular Momentum

Starr (1968) computed the northward eddy-flux of angular momentum by using observed winds in the eddy-transport term of (19.4.10). About his results, Lorenz (1969) remarks as follows:

'Since the transport of angular momentum has been computed from observed winds rather than analysed maps, it presumably includes the contribution of most of the spectrum. It can be shown, however, that the transport is mainly due to the larger scales. In any band of the spectrum, the maximum possible angular momentum transport is limited by the kinetic energy. The contribution of the small scales, even if the eastward and northward components of the wind were correlated in these

Fig. 19.9 Trough-ridge tilt by an angle, 9, from the meridian for poleward eddy-transport of angular momentum

scales, could not match the observed contribution of the large scales, which results generally from correlations of about 0.2. Similar considerations apply to the transport of sensible heat, since the temperature spectrum has somewhat the character of that of kinetic energy.' The validity of Lorenz's remarks becomes evident from at least two considerations, viz., (1) asymmetry, or tilt from the meridian, of troughs and ridges in zonal flow, and (2) the Index cycle, shown in Fig. 19.9 and Fig. 19.10 respectively.

Machta showed in 1949 that a northward eddy-transport of angular momentum is proportional to the tangent of the angle of tilt 9 from the meridian, i.e., when the troughs and ridges are aligned in a NE-SW direction, as shown in Fig. 19.9. A tilt in the opposite direction, i.e., in a NW-SE direction, will result in a southward eddy-transfer.

The alternation between strong and weak westerlies over the midlatitudes is usually described as an Index cycle. In the meridional distribution of the zonal

Circulation Earth Atmosphere Images

Wind speed (ms-1)

Wind speed (ms-1)

Fig. 19.10 Meridional profile of westerlies during (a) low-index (L.I), and (b) high index (H.I) phase of the Index cycle. J denotes the W'ly Jet. (After Riehl et al., 1954)

winds, a high-index phase is characterized by a single strongly peaked maximum, while in a low-index situation, the zonal winds are relatively weaker over the midlatudes and may have two maxima in winter, one at a latitude near 25N and the other at about 45N, as shown in Fig. 19.10. The two maxima, one in the form of a strong subtropical jet and the other a somewhat weaker midlati-tude jet was also apparent in Palmen's model of mean meridional circulation in winter.

A high-index situation arises when a strong meridional temperature gradient develops over the midlatitudes. The thermal wind builds up a strong westerly jet in the upper troposphere. The flow becomes baroclinically unstable and breaks down into waves which transport heat rapidly northward. The result is a weakening of the meridional temperature gradient, a weakening of the jet, and the beginning of a low-index phase of the cycle. The waves draw kinetic energy from the available potential energy of the zonal flow during the transition from high-index to low-index phase and return kinetic energy to the zonal flow during the transition from the low-index to the high-index phase.

19.5.3 Eddy-Flux of Water Vapour

An estimate of the northward eddy-transport of water vapour as computed from annual mean zonally-averaged distribution of specific humidity in the northern hemisphere was made by Peixoto and Crisi (1965) from one year of data. Since the transport of water vapour implies a transport of latent heat of condensation, it plays a role similar to that of sensible heat, in the energy balance. Further, it plays an important role in the global hydrological cycle, as qualitatively suggested by Fig. 19.11 which shows the meridional distribution of zonally averaged annual evaporation and precipitation over the globe and the sense of water vapour flux required for moisture balance.

NORTH LATTITUDE SOUTH

Fig. 19.11 Average annual evaporation and (—) precipitation (----) per unit area expressed in meters per year. Arrows represent the sense of the water vapour flux in the atmosphere (Sellers, 1965)

NORTH LATTITUDE SOUTH

Fig. 19.11 Average annual evaporation and (—) precipitation (----) per unit area expressed in meters per year. Arrows represent the sense of the water vapour flux in the atmosphere (Sellers, 1965)

19.5.4 Vertical Eddy-Transports

The above considerations certainly do not apply to the vertical transports of atmospheric properties by eddies. The vertical kinetic-energy spectrum is difficult to determine and there is no evidence that the energy is concentrated in the larger-scale eddies as in horizontal transfers. In fact, the observed upward and downward motions inside and outside some of the small-scale towering clouds may be many orders of magnitude larger that the averaged large-scale vertical motion computed in the atmosphere. Regarding the reliability of vertical transports evaluations, Lorenz (1969) writes:

"It is doubtful that the large-scale vertical motion fields deduced by one means or another from more readily observable quantities are sufficiently accurate for evaluating reliable vertical transports of sensible heat, angular momentum and water vapour. Thus, even if we knew the small-scale contributions, we could not readily compare them with the large-scale contributions. However, it is easy to see how convective-cloud circulations can carry significant amounts of energy upward." As an example of possible vertical transport of energy, Lorenz refers to the work of Riehl and Malkus (1958) who estimated that the entire vertical transport of energy in the equatorial zone could be effected by one giant cumulonimbus cloud per square degree. Palmen and Newton (1969) have indicated that a large part of the angular momentum also can be transported vertically by cumulonimbus clouds, or by squall lines along which they are organized. Comparing the evaluated vertical eddy-transports of energy and angular momentum by eddies of all scales; they conclude that the vertical transport of angular momentum appears to be rather small, while that of energy can be quite large.

19.6 Laboratory Simulation of the General Circulation

From about the middle of the eighteenth century, there have been several attempts by many an experimental physicist (e.g., Wilcke, 1785; Vettin, 1857, 1884; Taylor, 1921; Fultz, 1949, 1950, 1951; Long, 1951) to simulate the essential features of the general circulation of the atmosphere by using differentially heated rotating fluids in the laboratory, with encouraging results. Earlier experiments used air as the working fluid, but in most of the later experiments, it has been replaced by water, since by putting tracer elements in water one could follow fluid motions better than in air. The early experiments of the latter type were carried out with rotating dishpans and as such came to be known as 'dishpan experiments'. In these experiments, the fluid in the dishpan was supposed to represent the atmosphere over one hemisphere with the bottom curved surface of the pan representing the curved surface of the earth. The pan was heated at the rim which was supposed to correspond to the equator and cooled at the center which was assumed to correspond to the pole. One may note that in the laboratory experiments, the scales of several characteristic parameters of the fluid, such as density, velocity, length, time, pressure fluctuations, etc., were many orders of magnitude different from those in the atmosphere. For example, (a) the density of the working fluid was almost a thousand times greater than that of air; (b) gravity has the same direction throughout the fluid, whereas in the atmosphere it varies with latitude; (c) the angular velocity of the dishpan is constant horizontally, whereas in the atmosphere the vertical component of the angular velocity varies with latitude. However, despite these differences, for certain combinations of differential heating and rate of rotation, the fluid was observed to circulate forming patterns which appeared to bear close resemblance to those observed in the atmosphere. For example, Fultz found that at low speeds of rotation, there was simple overturning of the fluid with heated water rising at the rim and cooled water sinking at the center, thus forming a mean meridional circulation which closely resembled the Hadley circulation of the atmosphere. At higher rate of rotation, the rotating fluid appeared to develop jet streams and wave motions in patterns which closely resembled the baro-clinic waves in the atmosphere over the midlatitudes. Another series of experiments called the 'annulus experiments' was carried out using two co-axial cylinders of different radii and the annular space between the two filled with the working fluid. Differential heating was created between the outer and the inner walls of the annulus by heating the outer surface and cooling the inner surface and maintaining a precise temperature difference across the fluid. The inner cylinder was rotated at different speeds which simulated the rotation of the earth and the motion of the fluid in the annular region was observed. It was found that for certain combinations of heating and rotation, the different flow patterns that evolved were very similar to those that were observed with the dishpan experiments.

Phillips (1963) showed that the flow patterns observed in the annular experiments could be interpreted within the framework of the quasi-geostrophic theory, since the geostrophy of a flow did not depend upon the scaling parameters, but upon the nondimensional ratio of these parameters called the Rossby number, Ro, defined in the case of the annular fluid by where Q is the angular velocity of the rotating cylinder, U is a typical velocity of the fluid, and (b - a) is the width of the annulus, b and a being the radii of the outer and the inner cylinders respectively.

Since water is nearly incompressible, adiabatic temperature changes are negligible following the motion. So the density p varies with the temperature T according to the relation where G is the thermal expansion co-efficient (= 2 x 10-4 per degree Celsius for water) and p0 is the density at the mean temperature T0. Using the hydrostatic approximation

and the geostrophic relationship

where Vg is the geostrophic wind velocity, We obtain an expression for the thermal wind dVg/dz = -(g e /2Q)kxVT (19.6.5)

If we now let U denote the scale of the geostrophic wind, H the depth of the fluid, and AT the radial temperature difference across the annulus, (19.6.5) may be written

Substituting the value of U from (19.6.6) in (19.6.1), we obtain an expression for the thermal Rossby number

For typical values of the parameters involved in (19.5.7), we may use (b - a) ~ H ~ 10cm, AT = 10C, and Q ~ 1s-1

RoT is then found to have a value of about 10-1, a value low enough to justify the application of the quasi-geostrophic theory to the problem. However, there is a difficulty in applying RoT directly to the annular flow problem in view of the existence of strong conduction boundary layers near the vertical walls of the annulus, in which the temperature changes rather rapidly away from the boundaries. For this reason, the thermal wind concept cannot be applied to these boundary layers but only to the interior region of the annular fluid. However, since the boundary layers are not separated from the interior by any rigid barrier, their temperatures are continually regulated by flow conditions in the interior. From this viewpoint, the temperatures measured at the walls are to be treated as externally imposed. We, therefore, talk of an imposed thermal Rossby number which is defined by

where Tb and Ta are the imposed temperatures at the outer and the inner walls of the annulus respectively. For reasons stated above, it follows that RoT* > RoT. This means that RoT * C 1. This condition fully justifies the application of quasi-geostrophic theory to the annular flow problem.

Figure 19.12 summarizes the results of Fultz's annular experiments, as presented by Phillips (1963). It shows, on a log-log plot, the Hadley and the Rossby regimes of flow for different combinations of the imposed thermal Rossby number, RoT*, and the non-dimensionalized rotation rate, (G*)-1 = ((b - a)Q2/g. The heavy solid line separates the axially-symmetric Hadley regime from the wavy Rossby regime.

Fultz Rossby
Fig. 19.12 Separation of Hadley and Rossby regimes in Fultz's annular experiments (After Phillips, 1963)

The interpretation of Fig. 19.12 is as follows: For very low values of thermal Rossby number, i.e., small differential heating across the annulus and high rate of rotation, there is only axially-symmetric Hadley-type circulation. But, as the thermal Rossby number is increased, there is an increase in the value of the thermal wind and a stage is reached when the flow becomes baroclinically unstable and baroclinic waves appear. This marks the beginning of the Rossby wave regime. However, in a baroclinic wave, heat is transported both horizontally and vertically, so that an increase in the value of RoT * will tend to increase the static stabity of the fluid. The strengthening of the static stability together with a lowering of the rotation rate leads to a decrease of the wave number or increase of the wavelength of the waves. Thus, with increasing RoT *, the flow undergoes transitions to longer and longer waves until the static stability becomes so strong that even the longest wave cannot change the character of the flow which then returns to the axially-symmetric Hadley regime.

19.7 Numerical Experiment on the General Circulation

The invention of the electronic computer and its application to solve meteorological problems from about the middle of the last century marked the beginning of a new era in studies of the general circulation of the atmosphere. At first, because of limited memory and working speed, the computers could be used to solve only simple time-dependent mathematical models of the atmosphere, like a single-level barotropic model or two-level baroclinic models, to produce short-term forecasts of atmospheric flow patterns. But, as time passed, there was rapid advance in the design of computers and large-memory high-speed computers became available to handle the more complete primitive equation models.

These developments led to rapid advance in the field of numerical weather prediction (NWP) and attempts were made to turn out reliable forecasts for larger areas and for longer periods. However, it was soon realized that the atmosphere was much too complicated a medium involving motions at various space and time scales to be modelled adequately for long-range forecasts without a better understanding of its physics and dynamics and associated computational problems than we could do at present. This need for a better understanding of the atmosphere led several meteorologists to undertake numerical experiments to simulate the general circulation of the atmosphere.

The first successful numerical experiment in this direction was carried out by Phillips (1956) who used a two-level quasi-geostrophic model for the numerical integration, starting from a state of rest. Diabatic heating and friction were externally prescribed. However, there were several shortcomings, the most serious of which was that the static stability of the atmosphere could not be determined since the temperature was computed at one level only. It was evident from the annular experiment in the laboratory that the static stability played an important role in determining the character of the flow. Also, the actual distribution of diabatic heating in the atmosphere differed considerably from what was prescribed in the model. There were also problems of computational instability which had to be overcome. But it is remarkable that inspite of all the limitations, the model turned out thermal and flow patterns which were found to be quite realistic over extratropical latitudes. Phillips' pioneering experiment was followed by several others (for example, Smagorinsky, 1963; Mintz, 1968; Hahn and Manabe, 1975) at many global meteorological centers to simulate the general circulation of the atmosphere under more realistic conditions.

The last few decades have witnessed emergence of comprehensive numerical models to simulate the general circulation of the atmosphere under conditions which can be prescribed and controlled at will in order to study different aspects of weather and climate. To-day, several such models are in operation at meteorological research centers in many parts of the globe.

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Renewable Energy 101

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  • hana
    Is earth's atmosphere deeper over the tropics?
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