James I.N. Introduction to Circulating Atmospheres

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8.2 Teleconnection patterns

269

(a)

ijV/.v//iv//™v.y.tpv-Y"V:"«^^^^^^^

Fig. 8.6. The Rossby wave source 5 for DJF, 1979-89 at 15kPa. (a) Contours of

absolute vorticity

£>

contour interval 2 x

10~

, and vectors of the divergent wind

The sample vector indicates 2ms"

. (b) S, contour interval 5 x 10~

, with

shading indicating negative values.

only short time series of analyses are available, making a statistically secure

identification of

low

frequency phenomena more difficult. This is exacerbated

since any southern hemisphere teleconnections have smaller amplitudes, and

do not stand out from the irregular background noise provided by synoptic

scale fluctuations.

270 Low frequency variability of the circulation

So,

although a number of attempts have been made to identify recurrent

teleconnection patterns in recent years, the various studies are not consistent

in detail. However, two results do appear to be robust, and to be common

to several independent studies. Here, a few results from a study by Mo and

White (1985), based on monthly mean 50kPa height and surface pressure

fields, are summarized.

The first major feature is a general negative correlation between either the

surface pressure or the 50kPa geopotential height in the polar regions and

the tropics, with a node around

°S.

This implies a related fluctuation in

the strength of the midlatitude westerlies. The other major feature is a rather

regular zonal wavenumber 3 pattern. Such a pattern is a feature of the

mean fields (see Fig. 6.1

(b)),

but there appears to be an index cycle whereby

midlatitude flow switches between a more zonal state and a state with a

pronounced wavenumber 3 steady wave. Correlation analysis reveals the

presence of three maxima of correlation around the southern midlatitudes.

The anomaly at the centre of these maxima can be used to construct an

index of the strength of this three-wave pattern. Figure 8.7 illustrates the

wave 3 pattern. It is based on a composite of fields for which the wave

3 index is largest, and a similar composite of fields with small wave three

index. The diagram shows the difference between these two extremes. The

diagram also suggests that the pressure correlation between high and low

latitudes may also be at least partly related to this wave 3 oscillation, since

it shows generally higher pressure over Antarctica than over the subtropics.

EOF analyses based on monthly mean fields also pick out these patterns.

They dominate the first two EOFs, which account for 37% of the total

variance in the monthly means.

This section has emphasized the propagation of Rossby waves from the

tropics into the midlatitudes. A significant part of

the

low frequency variance,

including persistent flow anomalies in the midlatitudes, can be related to

such propagation, and hence to anomalies in the tropical ocean circula-

tion. However, it should be remembered that most of the observed low

frequency and steady Rossby wave activity originates in the midlatitudes and

propagates mainly towards the tropics. This is clearly demonstrated by the

steady momentum

fluxes

which are predominantly poleward. The midlatitude

sources of Rossby waves are orography and ocean-land contrasts, as well as

excitation of Rossby waves by maturing transient baroclinic systems.

8.3 Stratospheric oscillations

271

Fig. 8.7. The difference between composites of

kPa height fields for the southern

hemisphere with maximum wave 3 index, and composites with minimum wave 3

index. Contour interval

with shading indicating negative values. (After Mo

and White 1985.)

8.3 Stratospheric oscillations

A number of rather regular oscillations of the zonal wind are observed

in the tropical stratosphere. They provide examples of some of the most

regular fluctuations of the atmospheric circulation and are generally thought

to be generated internally by the intrinsic dynamics of the atmosphere rather

than by some external forcing. We will discuss two such oscillations in this

section. One is called the 'quasi-biennial oscillation' (or 'QBO'); the other is

the 'semi-annual oscillation' (or 'SAO'). The QBO is observed in the lower

and middle stratosphere and can be detected by conventional radiosonde

observations. The SAO occurs higher in the atmosphere and is much more

difficult to observe. Above the ceiling of radiosondes, the main data sources

are satellite soundings of temperature. But near the equator there is no

suitable balance condition which can relate these temperature observations

to the wind field. Most of the observations of the SAO come from rather

272 Low frequency variability of the circulation

limited series of rocket borne measurements, launched from certain tropical

stations.

The QBO consists of an oscillation of the zonal wind, from easterly to

westerly, at upper levels in the deep tropics. The wind oscillates with a

maximum amplitude of around

20-30

ms"

near 2kPa, and the oscillations

become small below 5kPa; the easterlies are generally rather stronger than

the westerlies. The latitudinal variation is roughly Gaussian with a half

width of 12° of latitude. The period is rather irregular, being in the range

of 22 to 34 months; over a long period, the mean period of the oscillation

is around 27 months. This indicates that the oscillation is definitely not

related to the annual cycle, though there is some evidence that there is a

tendency for the wind reversal to take place preferentially in the northern

hemisphere summer. During the westerly phase, the strongest zonal westerlies

are actually on the equator; this is a clear sign that eddy fluxes of angular

momentum are implicated in the QBO, since this westerly air current has

greater angular momentum per unit mass than any part of the Earth's

surface. Such a maximum could not be acheived by purely axisymmetric,

inviscid circulations. Further discussion of this point will be given in Section

10.3.

An important clue about the nature of the mechanisms driving the QBO is

contained in Fig. 8.8. This shows a height-time plot of the zonal component

of the wind observed at a number of tropical stations. The oscillation

originates at high levels, and propagates slowly downwards. There are some

significant asymmetries. For example, the switch from easterly to westerly

flow propagates downwards more quickly than does the switch from westerly

to easterly. It is easy to see that the QBO cannot simply be a downward

propagating wave. Dissipation would quickly damp it, and the exponential

decrease of density with height would demand that the amplitude should

be largest in the forcing region, but reduce exponentially as the wave prop-

agated downwards. In any case, it is difficult to envisage what mechanisms

could excite such a low frequency wave at high levels in the stratosphere.

The currently accepted theories of the QBO suggest that the flow is forced

from the troposphere, and that it involves interactions between upward

propagating waves and the mean flow.

A simulation of the way this might work was provided in an elegant

laboratory experiment by Plumb and McEwan (1978). Their apparatus,

illustrated in Fig. 8.9, consisted of a cylindrical tank containing stratified

brine, with a mechanism for exciting a standing wave, frequency co and

zonal wavenumber /c, on the lower boundary. Such a standing wave can be

decomposed into two travelling waves, of equal amplitude, but travelling in

8.3 Stratospheric oscillations

273

Fig. 8.8. Time-height plot of the monthly mean zonal wind based on observations

from various equatorial stations, namely, Canton Island (January 1953 to August

1967),

Maldive Islands (September 1967 to December 1975) and Singapore (January

1976 to May 1992). Contour interval

ms"

westerlies shaded. (Updated from

Naujokat 1986.)

274 Low frequency variability of the circulation

opposite directions with phase speeds c = +co/k. The brine solution supports

internal gravity waves, with zonal wavenumber k and vertical wavenumber

m. The dispersion relation for vertically propagating internal gravity waves

is:

co = U

k+ _ (8.9)

where U is the zonal wind, presumed constant, or at least only a slowly

varying function of height z, and N is the Brunt-Vaisala frequency. A

theory for the vertical propagation of internal gravity waves through a

medium where the zonal wind changes slowly with height can be developed,

based on this dispersion relation. The steps are the same as those developed

in Section 6.2 for the horizontal propagation of Rossby

waves.

The frequency

and zonal wavenumber are conserved by the propagating wave packet, while

Eq. (8.9) can be rearranged to give a diagnostic relationship between m and

the local value of the zonal wind U:

(d^-

fc2

(810)

The sign of

is determined by the condition that the group velocity of gravity

waves be upward. From the dispersion relation, the vertical component of

the group velocity,

dco/dm,

may be written:

(c-Ufkm

- ^

(8.1

Thus,

to ensure upward energy propagation, the negative root for m must

be chosen when U > c, and the positive root when U < c. Equation (8.10)

also shows that there must be restrictions on the value of U for there to be

any vertical propagation. The vertical wavenumber becomes imaginary, i.e.

the waves are evanescent in the vertical, unless:

- U)

< N

. (8.12)

Vertical propagation is possible only for a range of flow speeds centred upon

±c.

The size of this range depends upon the selected values of N and k.

An illustration of these restrictions on the value of U is shown in Fig. 8.10,

which gives the vertical component of group velocity as a function of the

flow speed U. The values of N, k and

are those used by Plumb and

McEwan in their experiment. Vertical propagation is possible only for | U \

less than 57 mm s"

. Suppose U is westerly, and of such a magnitude that

vertical propagation can take place. The slope of the lines of constant phase

is simply m/k; the requirement that c

be upward means that m takes the

8.3 Stratospheric oscillations

275

Critical level

Stratified brine

Rubber membrane

Fig. 8.9. The apparatus used by Plumb and McEwan as a model of the QBO.

opposite sign from c

—

U. So the phase tilt is westward with height when

U > c. This implies that

[u*w*]

is negative, that is, there must be an upward

flux of easterly momentum. Near levels where the waves are dissipated, by

internal diffusion, for example, there must be

convergence of this easterly

momentum flux, and

so an

easterly acceleration will be imparted

the

flow. Around these levels, U will gradually be reduced, and will eventually

approach the value

which vertical propagation ceases.

the forcing

the base is maintained, the zero wind level will therefore gradually descend

through the fluid. Eventually, easterlies will reach the base. Then waves for

which U < c can propagate in the vertical. All the above arguments reverse,

so that these waves will carry westerly momentum aloft, and bring about

a flow reversal, first

upper levels, then

lower levels. The apparatus

exhibits

low frequency oscillation of its zonal wind, driven by nonlinear

interactions between the upward propagating gravity waves and the zonal

flow.

It is now generally accepted that the atmospheric QBO is driven in this

kind

way. Motions

the troposphere, particularly those associated

with clusters of cumulus convection in the tropics, can force

spectrum of

disturbances at the tropical tropopause. Vertically propagating gravity waves

are probably much less important to the QBO than larger scale vertically

propagating waves; the prime candidates are likely

to be

the planetary

scale Kelvin waves, which can propagate into the stratosphere

easterly

276

Low frequency variability of the circulation

-60

-40

-20 0

U (mm/s)

Fig. 8.10. The dependence of the vertical components of the group velocity on zonal

flow U for the Plumb-McEwan laboratory model of the QBO. The solid curves

show cases where U < c, and hence for which

[u*w

]

> 0. The dashed curves show

cases where U > c and

[u*w*]

< 0.

conditions, and the mixed Rossby-gravity waves which can propagate in

westerly conditions. Section 7.1 gives a brief account of equatorially trapped

planetary scale waves. The different characteristics of these waves help to

account for the observed asymmetry between the easterly and westerly phases

of the QBO; the chaotic nature of the forcing, which itself has considerable

low frequency variability, explains why the QBO is only quasi-periodic.

The confinement of the QBO to tropical latitudes reflects the meridional

confinement of the equatorial modes which drive it.

The semi-annual oscillation (SAO) has many features in common with

the QBO. Like the QBO, it consists of an oscillation of the zonal wind in

the tropics. The oscillation has maximum amplitude near the stratopause

and the mesopause; it seems likely that the mesopause oscillation is rather

distinct from the stratopause oscillation, and may be driven by different

mechanisms. Below 40 km, the oscillation becomes weaker and is swamped

by the QBO. The stratopause oscillation has an amplitude of

ms"

and

a half width of

25 °

of latitude. The maximum of westerly wind at the

tropopause occurs just after the equinox, and the maximum of easterly wind

just after the solstice. It is sometimes said that the SAO is global in extent,

not merely confined to the tropics. However, it is likely that the extratropical

SAO is simply a first harmonic of the annual cycle of zonal wind.

The westerly acceleration of the stratospheric SAO appears to start at the

8.4 Intraseasonal oscillation 277

stratopause and to propagate downwards, at a rate of around

km per

month. This is quite similar to the QBO, and there is strong evidence that

vertically propagating Kelvin waves are associated with the westerly accel-

eration. However, there does not appear to be sufficient Kelvin wave activity

to account for the magnitude of the acceleration; it may be that gravity

waves also play a role. The easterly acceleration is quite different. It occurs

almost simultaneously at all levels, and so vertically propagating waves

must play, at most, a subsidiary role in driving it. Horizontal transports of

angular momentum are needed to provide a simultaneous acceleration at all

levels.

The zonal mean advection of the summer easterlies across the equator

probably accounts for a large fraction of the easterly acceleration, with

horizontal momentum transports associated with breaking Rossby waves in

the winter hemisphere possibly playing a secondary role. More details about

these aspects of the stratospheric circulation are discussed in Chapter 9.

The SAO at the mesopause is not well observed. It has been suggested

that it is primarily driven by upward propagating gravity waves, as in the

Plumb-McEwan analogue of the QBO.

8.4 Intraseasonal oscillation

Apart from the regular seasonal cycle, quasi-periodic fluctuations of the

tropospheric circulation are rather unusual. So it came as a considerable

surprise in the early 1970s when a quasi-periodic oscillation of the tropical

zonal wind was discovered, with a period of between 40 and 50 days. Since

then, the oscillation has been well documented in studies of a number of

tropospheric variables. The period is quite variable, and the range has now

been extended to 30-60 days. Variously called the 30-60 day oscillation,

the 40-50 day oscillation and Madden-Julian oscillation, the best name is

perhaps the 'intraseasonal oscillation', that is, a somewhat irregular oscilla-

tion whose timescale is long compared to synoptic timescales, but shorter

than the seasonal timescale. Figure 8.11 shows the surface pressure record

from a single station, Canton Island (3°S,

172

°W);

the oscillation shows

even in the raw station data, and is very clear when a suitable band pass

filter is employed to remove high frequencies and the seasonal cycle.

Comparison of the records from many tropical observing stations suggests

that the oscillation is an eastward moving, zonal wavenumber 1 disturbance,

centred on the equator with a half width of about

10 °

of latitude. It is most

pronounced in the surface pressure, tropospheric temperature and zonal

wind fields, and more recently has also been identified in the patterns of

convective cloud distribution and in the distribution of rainfall. The oscilla-

278 Low frequency variability of the circulation

MAR

1958

MAY

Fig. 8.11. The surface pressure record from Canton (3°S,

172

°W).

The upper curve

is the raw data and the lower curve the result of applying a band pass filter centred

around 45 days to the data. (From Madden & Julian, 1972.)

tion varies both in intensity and phase speed. It is strongest in DJF and

weakest in JJA, but can be detected at all times of the year. Longitude-time

plots show that intraseasonal disturbances move eastwards over the Indian

Ocean, and reach their largest amplitude over Indonesia. Over the central

and western Pacific, they become rather weaker, and take on the character of

a standing oscillation. Figure 8.12 gives an indication of the structure of the

intraseasonal oscillation, based upon eight DJF periods from the ECMWF

archived analyses. EOF analysis has been used to isolate the oscillation in

the field of the velocity potential. A numerical filter which isolates periods

of 30-60 days was applied to a time series of the velocity potential at

kPa

and

kPa.

The resulting band pass filtered time series was used as the basis

of an EOF analysis. Figure 8.12(a,b) show the first two EOFs at 15kPa. The

most intense feature of EOF 1 is over Indonesia, with upper level divergence

over Indonesia and low level convergence. EOF2 is almost out of phase with

EOF1,

and the corresponding principal component time series (Fig. 8.12(c))

fluctuate in quadrature. Combining the fields of EOF1 and EOF2 gives

a generally eastward propagating disturbance with largest amplitude over

Indonesia.

The velocity potential is often used, as it was in Fig. 8.12, to diagnose such

convectively driven motions in the tropics. It provides a graphic picture of

the outflow from strongly convecting regions, and suggests that the global