James I.N. Introduction to Circulating Atmospheres

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7.5 The global transport of water vapour

249

Fig. 7.21. Vertically integrated water vapour abundance for (a) December 1991

—

February 1992; and (b) June, July and August 1991. Contour interval 5kgm~

, with

shading denoting values in excess of

kg m~

. (Based on an unpublished analysis

of ECMWF data by J. Dodd.)

the fluctuations of sea surface temperature, and hence to E. As mentioned

above, this effect is especially marked over central and north-eastern Asia,

which is extremely dry in winter.

A major feature is seen in JJA over south-east Asia. The largest values of

f are found over the Bay of

Bengal,

with an extended region where it exceeds

50kgm~

over India and south-east Asia. This maximum is an important

fP* dp

= / vr^-. (7.33)

h g

250 Three-dimensional aspects of the global circulation

part of the monsoon circulation. It reflects a mean convergent flux of low

level moisture into this region from the surrounding ocean areas, especially

the Arabian Sea. The availability of this moisture leads to convection and

latent heat release. A marked maximum in the atmospheric heating rate was

shown in Fig. 3.8(b); such heating in turn drives the motions responsible

for the monsoon. These processes were described in Section 7.2. Such a

feedback between latent heat release and the large scale motion field is a

crucial aspect of many tropical circulation systems.

The fluxes of atmospheric water vapour are shown in Figs. 7.22 and 7.23.

The first shows the mean vertically integrated flux of water vapour by the

atmospheric flow, that is:

The transport of water vapour by the zonal winds is dominant, with a strong

westward transport throughout the tropics and an eastward transport in the

midlatitudes that is only about half as strong as that in the tropics. The

zonal flow is stronger in the midlatitudes, but the typical values of r are

considerably smaller. Throughout the tropics, there is a general divergence of

over the oceans and convergence over the continents. In the midlatitudes,

maxima of the eastward and poleward transport of water vapour are associ-

ated with the storm tracks. The total flux is roughly parallel to the storm

track axis. Especially notable is the strong flux of water vapour in the JJA

season from the Indian Ocean into south-east Asia, reflecting the low level

wind pattern associated with the monsoonal circulation.

The depth integrated transient flux F

defined as

F, =

[

'W^

(7.34)

Jo g

is shown in Fig. 7.23. This is dominated by the midlatitude storm tracks. The

transient fluxes in the midlatitudes are in a quite different direction from the

total fluxes. Instead of being roughly parallel to the storm track axes, they

are nearly at right angles to it, with strong poleward and westward fluxes

along the storm tracks. Although the transient fluxes are nearly an order

of magnitude smaller than the mean fluxes, the divergence of the transient

water vapour fluxes is only slightly less than that of the mean fluxes in

the midlatitude storm track regions. The moisture flux by the baroclinic

eddies at the start of the storm tracks tends to import moisture to the

continental interiors of North America and eastern Asia from the warm

oceans to the south and east. These transient fluxes are more than offset

by the mean fluxes, so that there is net divergence of water vapour out of

7.5 The global transport of water vapour

251

300.0

(a)

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300.0

(b)

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S \ '•, S!

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j—.

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Fig. 7.22. The total fluxes of water vapour, F

(see Eq.(7.33)) for (a) December 1991

- February 1992; and (b) June, July and August 1991. The sample arrow represents

300 kg m"

. (Based on an unpublished analysis of ECMWF data by J. Dodd.)

northern Canada and central Asia. Such a mean circulation is consistent

with the mean circulations induced by the concentration of transient activity

in the storm tracks, as shown in Fig. 7.15, and undoubtedly plays a role in

supplying heat, in the form of latent heat, which is needed to maintain the

storm tracks.

Finally, notice that these generalizations do not extend to the southern

252

Three-dimensional aspects

the global circulation

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Fig. 7.23.

The

fluxes

water vapour

transient eddies,

(

see

Eq.(7.34))

for (a)

December 1991-February 1992;

and (b)

June, July

and

August 1991.

The

sample

arrow represents lOkgm"

(Based

on an

unpublished analysis

ECMWF data

Dodd.)

hemisphere storm track.

The

transient fluxes

are

indeed

maximum

the region

the southern hemisphere storm track,

but

they

are

eastwards

and polewards throughout. There

some evidence

of a

flux

moisture

out

South America

due

the

midlatitude transients. This

fed

a mean flux convergence, chiefly from

the

tropics.

may

well

that

the southern hemisphere storm track

formed

rather different physical

7.6

Problems

253

mechanisms from the two northern hemisphere storm tracks. On the other

hand, we should recall that the accuracy of these moisture fluxes over the

southern hemisphere oceans is probably very poor, and better observations

are urgently needed before such conclusions can be established with any

certainty.

7.6

Problems

7.1 The forced solution to the shallow water equations shown in Fig. 7.4 is

linear, and therefore there is no interaction between the forced disturbance

and the mean flow. Use the diagram to discuss qualitatively the momentum

flux associated with the forced pattern, and hence deduce the zonal flow that

you might expect to be forced.

7.2 From Fig. 7.3, estimate the group velocities of Kelvin waves and

planetary waves. If the drag timescale is taken to be five days, estimate the

eastward and westward scales of disturbances induced by a tropical heating

anomaly situated on the equator.

7.3 Use Fig. 7.17 to estimate the typical divergence of E near the start

and near the end of the Atlantic storm track. Hence, estimate the typical

acceleration of the zonal wind in these regions (in units ofms"

day"

7.4 Using the information of Fig. 7.18, estimate the typical gradient of

the three-dimensional E-vector in (a) the zonal direction, (b) the meridional

direction.

7.5 Suppose that temperature varies sinusoidally around a latitude circle

between temperature To

—

AT and To + AT, but that the relative humidity

is a constant

RQ.

Show that the apparent zonal mean relative humidity

Ra, based on the zonal mean temperature and specific humidity, can exceed

100%.

7.6 Estimate typical midlatitude values of

Jp'

The typical variance of humidity mixing ratio, [r

] , is 10~

in the mid-

latitudes. Use this value to estimate the typical displacement of air masses

if the fluctuations of water vapour are due solely to: (a) poleward motions;

(b) vertical motions. Discuss the relationship between your values and the

typical properties of midlatitude weather systems.

254 Three-dimensional aspects of the global circulation

7.7 It is believed that air is mostly exchanged between the troposphere and

stratosphere in the tropics, where the tropopause is extremely cold, perhaps

200

Estimate the saturated vapour pressure at

200

K and hence predict

typical values of r in the stratosphere.

Low frequency variability of the circulation

8.1 Low frequency transients

In the preceding chapter, Fig. 7.14 compared the eddy correlation tensor for

the higher frequency eddies, whose periods are less than around ten days,

with the lower frequency transients. The high frequency eddy statistics have

a well-defined structure in the midlatitudes, with maxima in the storm track

regions. The high pass filter used in Chapter 7 served to isolate a specific

family of dynamical processes, namely, those associated with baroclinic

instability and the subsequent evolution of baroclinically unstable waves. The

low frequency eddy kinetic energy is much less clearly structured. Figure 7.14

shows some evidence of maxima downstream of the high frequency maxima,

as well as some correlation between the jet centres and maxima of low

frequency variability. But none of these patterns is especially marked.

One reason for this is that the low frequency band covers a very wide range

of frequencies. There are disturbances whose periods are very little longer

than those of the baroclinic disturbances; indeed, the maxima downstream

of the storm track centres are at least partly due to the occlusion and decay

of midlatitude cyclones, which become slower moving as they fill. But there

are also transients of significant amplitude with very much longer periods.

Indeed, a spectral analysis of any long sequence of atmospheric data reveals

that variability is observed on as long a period as one cares to specify.

Furthermore, the spectrum tends to be red, with amplitude increasing as

frequency decreases down to very low frequencies. Within such a range

of frequencies, many different physical mechanisms are operating. It is

little wonder that their combined signal is rather confused. In studying

low frequency variability, it is not enough simply to look at the total low

frequency signal. We will need to isolate particular frequency ranges and

spatial structures.

255

256 Low frequency variability of the circulation

One way to do this would be to use spectral analysis or time series filtering

to isolate particular narrow ranges of frequencies. This could then lead to the

spatial structures of oscillations of different frequency. A difficulty with this

approach is the amount of data required to draw reliable conclusions. More

seriously, a characteristic of many low frequency phenomena is that they

are only quasi-periodic. This means that although they recur, their period

can vary, and their structure can vary between one maximum and another.

In spectral terms, periodic fluctuations are characterized by broad, rather

than sharp, peaks. These features indicate that we are generally dealing with

highly nonlinear phenomena, rather than normal modes of oscillation which

would emerge from some linear analysis of atmospheric motions.

In this chapter, we will discuss some empirical techniques which have

been used to isolate particular low frequency components of the atmospheric

circulation. These structures are generally understood to result from local-

ized anomalies of heating or other types of forcing which in favourable

conditions can then propagate over substantial parts of the globe. The

ray tracing theories of Section 6.2 give a simple description of the ways

in which this can happen. We will also look at various quasi-periodic

oscillations of the stratospheric circulation and at an important oscillation

in the tropical Pacific which involves interactions between the atmospheric

and ocean circulations. Finally, we will stress that the atmospheric system

alone is sufficiently complex and nonlinear to generate unexpectedly low

frequency transients without recourse to any forcing from external systems.

8.2 Teleconnection patterns

Certain analyses of long time series of atmospheric circulation data reveal

large scale correlations between the flow at remote locations. These fluctua-

tions belong in the low frequency range of timescales, and they have been

dubbed 'teleconnections' to stress the correlation-at-a-distance aspect of their

nature. Teleconnections are located in particular places, and take the form of

'standing waves', with fixed nodes and antinodes of

low

frequency oscillation.

They are often orientated in a such a way as to indicate connections between

the tropical and midlatitude low frequency transients. The theory of such

teleconnections is incomplete, though we will relate them to meridionally

propagating Rossby waves. Much of this section will be concerned with the

description of empirical statistical techniques which are frequently used to

detect teleconnection patterns.

The most straightforward procedure is called correlation analysis. Con-

sider some meteorological field Q defined on a grid of N discrete points;

8.2

Teleconnection patterns

257

denote its value on the zth grid point

Qi(t).

In many analyses, Q is the field of

50kPa geopotential height; this field is observed reasonably accurately and

long time series of it exist, at least for the northern hemisphere extra-tropics.

It is usual to emphasize the low frequency teleconnection patterns by filtering

in some way to remove the higher frequency fluctuations. At its simplest,

such a filtering is accomplished by taking monthly mean values of Q

. The

heart of the method is to calculate, for each gridpoint, a correlation with the

values of

at every other gridpoint. Such a correlation is:

Point i is called the 'base point'. The correlation ry will be large in the neigh-

bourhood of the base point, with values tending towards 1 as j approaches

i. If no teleconnection patterns exist, ry will drop away towards zero when

points i, j are separated by a distance greater than the typical horizontal

scale of coherent circulation systems. Large positive or negative values of ry

when the points are well separated indicates some kind of teleconnection.

Some typical examples for the northern hemisphere winter are shown in

Fig. 8.1. These calculations were based on the mean 50kPa geopotential

height for 45 December, January and February months, beginning with the

1962-3 winter and finishing with the 1976-7 winter. The base point in

Fig. 8.1 (a) is

°N,

°W,

in the mid-Atlantic. An elliptical region of large

correlation, with a meridional width of some

2000

km,

is centred upon the

base point. The correlations over the Pacific and south-east Asia are small.

But large correlations are seen roughly strung along a great circle passing

through the base point, with alternating positive and negative correlations.

An even more impressive pattern is seen in Fig. 8.1(b). Here the base point is

°N,

160 °W

in the central Pacific Ocean. A train of alternating positive

and negative centres spreads north from the base point into North America.

In contrast, the correlations between this base point and points over the

Atlantic and Asia are generally small.

These particular base points were chosen because they lead to especially

well-defined teleconnection patterns. Other base points have correlations

which fall uniformly away to small values at any significant distance from

the base point. These patterns do not deserve to be distinguished as telecon-

nections. Figure 8.2 summarizes the most significant teleconnection patterns

identified in northern hemisphere winter data. The most well defined is the

Pacific-North American (PNA) pattern, which is epitomized by Fig. 8.1(b).

Another major pattern is the North Atlantic oscillation (NAO, sometimes

258

Low frequency variability of the circulation

(a)

Fig. 8.1. Correlation maps based on 50kPa monthly mean geopotential height data

for 45 winter (DJF) months from 1962/3 to 1976/7: (a) base point

°N,

°W.

subdivided into the west Atlantic and east Atlantic patterns). Other, weaker,

patterns are sometimes identified, though these are probably not statistically

significant. The character of the PNA and NAO patterns is essentially a

meridional connection between the tropics or subtropics and the midlatit-

udes.

They are remarkably similar to the Rossby wavetrains discussed in

Section 6.2, suggesting that the teleconnection patterns may be thought of as

a Rossby train emitted from some anomalous forcing region in the tropics.

The correlation analysis gives information about the spatial structure of

teleconnections, but does not give much information about the timescales

of teleconnection events. More sophisticated filtering of the time series be-

fore carrying out the analysis might help, but the method rapidly becomes

cumbersome and the conclusions statistically dubious. A more elegant ap-