James I.N. Introduction to Circulating Atmospheres

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9.2 Wave propagation and mean flow interactions

319

90W

- 90E

Fig. 9.8. Ertel's potential vorticity on the

850

K isentropic surface on 3 Decem-

ber 1981, showing an example of planetary wave 'breaking', Contour interval

10~

kg~

(i.e.,

100

PVU),

with shading indicating values between 300 and

400

PVU.

The outer latitude circle is

°N.

(Data kindly supplied by A. O'Neill.)

propagation of mainly wavenumber

or 2 Rossby waves. Over the Pacific, a

long streamer of high potential vorticity has apparently been pulled off the

main vortex, and is being wrapped into a huge spiral. This large region of

small and irregular potential vorticity gradient is the so-called 'surf zone'.

As well as mixing potential vorticity in midlatitudes, Rossby wave break-

ing tends to sharpen the gradients of potential vorticity around the polar

vortex

itself.

This occurs as small distortions on the vortex are pulled out

into long thin streamers, which are mixed into the surf zone, leaving the

edge of the vortex smoother and sharper than previously. The effect is

rather analogous to a plane removing the projections from a rough piece of

wood, leaving the wood/air interface smoother and sharper. This process is

particularly important in the southern hemisphere winter, where the vortex

is less distorted. The sharpening of gradients around its periphery inhibits

the exchange of matter and heat between the centre of the vortex and the

surf

zone.

During the winter, the temperatures become very cold, and trace

constituents can accumulate and take place in various chemical reactions,

320 The stratosphere

without mixing down to lower latitudes where they would be photolysed by

sunlight. The formation of this cold 'containment vessel' is an important

element in generating the infamous ozone hole.

Now let us return to a consideration of the vertical propagation of Rossby

waves in the stratosphere. We can use the work of Section 6.5 which set

up a framework for discussing the propagation of Rossby waves on a zonal

flow U = U(y,z

). By making a 'slowly varying' approximation, we can

follow the propagation of wave activity into regions where U is different.

As we saw in Section 6.5, the Eliassen-Palm flux vector is parallel to the

local group velocity. But in frictionless, steady and adiabatic conditions,

the Eliassen-Palm theorem must hold, and so the Eliassen-Palm flux must

have zero divergence. But now consider the situation depicted in Fig. 9.9, in

which the zonal wind changes sign at some level in the stratosphere. Steady

Rossby waves cannot propagate in easterly conditions. They are evanescent

and, as we saw in Eq. (6.54), their poleward temperature flux is zero. In this

region, both

V •

F and F itself

will

be zero. In the westerly flow,

V •

F must be

zero,

but F itself will generally be nonzero. In the simplest example of the

Charney-Drazin model, F will be vertical and constant with height. In the

vicinity of the 'critical level' where (7 = 0, there must be a large convergence

of F, and, consequently, the Eliassen-Palm theorem must break down there.

Assuming that friction and heating remain small, the simplest solution is

to predict that the flow will become unsteady at this level. Equation (9.6)

suggests that this unsteadiness will be manifested as an easterly acceleration

at the critical level. Thus, if there is a constant flux of wave activity into the

base of the stratosphere, the region of easterly flow will descend until it fills

the stratosphere.

This kind of

process

is the basis of current theories of sudden stratospheric

warmings. Once easterly flow is established at some upper level (where the

assumptions of frictionless, adiabatic flow may become invalid so that the

atmosphere is not constrained by the Eliassen-Palm theorem), the region

of easterlies can descend on a relatively fast dynamical timescale. Once

the easterly regime is established, wave activity will virtually die away, and

the usual westerly regime can only be re-established on a slower radiative

timescale. The associated large temperature rises result from meridional

circulations which maintain thermal wind balance as the zonal wind changes.

It is easy to show that in the stably stratified stratosphere, quite small vertical

displacements of air can result in large temperature changes.

9.3 The production and transport

ozone

321

easterly

westerly

troposphere

Fig. 9.9. Schematic illustration

steady Rossby waves propagating vertically into

a region of easterly flow.

9.3 The production and transport of ozone

The distribution of stratospheric ozone was described in the preceding sec-

tion. Figure 9.10 shows the global distribution

ozone as

function of

height and latitude, while Fig. 9.11 shows how the total ozone in

column

above the Earth's surface varies with latitude and time of year. The maxi-

mum concentration of ozone is generally at heights of 20-25 km and occurs

in the tropics. However, the layer

ozone

generally rather thicker

the winter and spring polar regions, with the result that the column total

ozone abundance reaches its maximum in the spring at high latitudes. The

notorious 'ozone hole' which has recently developed in the southern hemi-

sphere spring is a major depletion of this spring maximum at high southern

latitudes.

this section, we will consider how the major features

the

ozone distribution are to be understood, beginning with

consideration of

the photochemical processes which produce ozone. But in the lower strato-

sphere, the meridional advection timescales are quite short compared with

322

The stratosphere

.001 _

0 30N

LATITUDE

.001-

LATITUDE

Fig. 9.10. Latitude-height cross sections of ozone concentration for (a) January;

and (b) March, based on the CIRA climatology of Fleming et. a\. (1990). Contour

interval 10

molecules m~

, with values in excess of

x 10

molecules m~

indicated

by shading.

the photochemical equilibrium timescales, and so the ozone distribution is

strongly modified as a result of transport by atmospheric motions.

Ozone is formed as a result of photodissociation of ordinary diatomic

oxygen molecules by ultraviolet light, and the subsequent recombination

of free oxygen with diatomic oxygen. It is broken down by the action

93 The production and transport of ozone

323

Total column ozone

0123456789

Month of year

Fig. 9.11. Latitude-time plot of the column total abundance, in 'Dobson units'. The

shaded region is unobserved since it receives no sunlight. Plot based on TOMS data

for the period 1984-88, extracted from the SERC Geophysical Data Facility.

of sunlight and by the catalytic effect of certain trace constituents such

as hydroxyl radicals, nitrogen oxides and anthropogenic chlorine atoms.

Throughout much of the stratosphere, these creation and destruction rates

are comparable to the dynamical timescales, so the advection of ozone is very

important in generating concentration anomalies. This interaction between

photochemical processes and transport processes has provided an important

practical impetus for the study of stratospheric circulation in recent years.

In this book, we confine ourselves to a very elementary account of the

photochemistry of stratospheric ozone. The reader requiring greater detail is

referred to more specialist texts on atmospheric chemistry.

The primary mechanism for the generation of

ozone

is called the 'Chapman

scheme', being first suggested by Chapman in 1935. It involves a sequence of

reactions which are consequent upon the splitting of an ordinary diatomic

molecule of oxygen by a sufficiently energetic quantum of electromagnetic

radiation:

-• O + O. (9.11)

The energy required to photodissociate the oxygen molecule means that this

reaction can only take place for wavelengths less than

246

nm.

The single

oxygen radical produced by the reaction is highly reactive, and will readily

bind on to suitable molecules, including that of diatomic oxygen. The prime

324 The stratosphere

reaction for producing ozone is:

O + O

+ M -• O

+ M. (9.12)

where M is any third molecule, generally N2 or O2. This third molecule

plays a catalytic role. It is needed to carry off excess momentum, enabling

the O and O2 molecules to bind during a collision while conserving both

kinetic energy and momentum. Chapman also identified ozone destruction

reactions; the balance between the production and destruction processes

should define the observed ozone concentrations. The first process is the

photolysis of ozone, effectively reversing reaction (9.12) by solar radiation

with wavelengths of less than 1140nm:

O3 +

/1V

-»O

+ O. (9.13)

Finally, a reaction involving both O and O3 will destroy both forms of free

oxygen:

O3+O-+2O2. (9.14)

Because the concentrations of both O3 and O are low, this last reaction is

relatively slow.

These reactions can be used to estimate a photochemical equilibrium

concentration of ozone. This is based on the law of mass action, which

states that the rate of reaction of two constituents is proportional to the

product of their concentrations. That is, for a simple reaction of the form:

A + B^C (9.15)

the rate of production of molecules of C is given by:

^ =

(9.16)

Here, n

, n

and n

are the so-called number densities, that is, the number

of molecules per unit volume, of the reactants A, B and C respectively, and

k is the reaction rate, which will generally be a function, possibly a rather

sharply varying function, of temperature. Applied to the Chapman scheme,

the law of mass action predicts the equilibrium number density of ozone

molecules,

713,

to be:

(9.17)

where n

and n

are the number density of the oxygen molecules and the

catalyst molecules M respectively, k

and k

are the reaction rates of re-

actions (9.12) and (9.14), respectively, and J

, J3 are the photodissociation

93 The production and transport of ozone 325

rates associated with reactions (9.11) and (9.13), respectively. These photo-

dissociation rates themselves depend upon the ozone distribution, since they

measure the amount of ultraviolet light of the appropriate wavelengths

reaching the location under consideration. Some of this ultra-violet light will

have been absorbed by O3 and O2 as it passes through higher layers of the

atmosphere. The rate J

increases more rapidly with height than does /

with the result that Eq. (9.17) predicts a maximum of the number density

of ozone molecules in the stratosphere. However, the scheme predicts rather

too much ozone generally, and certainly cannot account for features of the

distribution such as the spring maximum. Rather, photochemical arguments

alone would suggest that the ozone distribution should correlate strongly

with the distribution of short wave radiation.

Two important modifications to the simple photochemical equilibrium

theory need to be introduced. First, further chemical reactions, often involv-

ing trace atmospheric constituents, can modify the chemistry of

the

Chapman

scheme. Second, atmospheric transports can redistribute the ozone.

The most important modifications to the chemistry arise through catalytic

destruction of ozone by trace constituents. Denote such a constituent by X.

Then the ozone destruction process can be written:

X + O

->XO + O

, (9.18a)

O^X + O

. (9.18b)

The net effect is to combine O and

to form two molecules of

O2,

leaving X

unconsumed and ready to participate in further ozone destruction. The most

important catalysts are OH, NO and Cl. The OH is formed naturally by the

photodissociation of water vapour. The NO also has natural sources, such as

lightning and photodissociation of ammonia and other biologically produced

nitrogen compounds. It is also found in the exhaust gases of aircraft flying

in the stratosphere, and there have been concerns that unrestricted growth

in the number of commercial supersonic flights could have a significant

impact on the ozone layer. A much more serious threat to ozone is now

thought to come from Cl, which is almost entirely artificial in origin, being

formed by a complex sequence of heterogeneous reactions, starting with

the photodissociation of man-made chemicals such as chlorofluorocarbons.

It is responsible for the large ozone depletions observed in the southern

hemisphere spring and for the smaller depletion now becoming apparent in

the northern hemisphere.

A full quantitative account of

the

photochemical equilibrium concentration

326 The stratosphere

.001

.010

.100

100 _

100Q

—'—'—'—'—'—'—'—'—'—'—'—'—'—'—'—i—

-9DS -60S -30S 0 30N 60N SDN

LATITUDE

Fig. 9.12. The photochemical equilibrium distribution

ozone

for

March. Calcu-

lations kindly carried

out by J.

Haigh

(see

Haigh (1985)

for

details

the model

used).

Contouring

as in

Fig. 9.10.

of ozone, taking into account these catalytic destruction cycles,

rather

complex. The various photochemical processes which generate

the

catalysts

themselves need

to be

taken into account. Furthermore,

the

effects

of the

catalysts

ozone concentration

are not

simply additive,

but can

interact

with one another.

large number

reactions, many with widely different

rate constants, quickly becomes necessary. Figure

9.12

shows

the

zonal

mean photochemical equilibrium distribution

ozone during spring.

The

concentration

is a

maximum

at the

equator,

altitudes

40-50

km.

But

this

quite different from

the

actual distribution

stratospheric ozone

at this time

year, shown

Figs.

9.10 and

9.11.

The

maximum ozone

concentration

observed

high latitudes

in the

spring hemisphere,

levels below

km.

This result strongly suggests that transport

ozone

from production regions near

the

equator

to the

winter

and

spring polar

regions

is a

very important process. Note that Fig. 9.11 may

longer

an accurate picture

the southern hemisphere spring, since

it is

based

data that

are a few

years

old.

Ozone levels

in the

spring stratosphere

are

now severely depleted over Antarctica, thanks

anthropogenic pollution by

chlorine compounds.

In this book,

our

major concern

with

how

atmospheric motions will

modify

the

large scale distribution

ozone.

In the

upper stratosphere,

heights between

and

km,

the

answer

hardly

at all. At

these

9.3 The

production

and

transport

ozone

327

levels,

the ozone concentration reaches its photochemical equilibrium in

quite a short time, certainly short compared to the time for atmospheric

motions to advect ozone to regions where the temperature, pressure or

radiative regime is significantly different. In the lower stratosphere, the

photochemical reaction rates become small, and so the time required to

reach photochemical equilibrium becomes several weeks, much longer than

the typical dynamical timescale. In the lower stratosphere, then, ozone is

advected around almost as a conserved tracer. In fact, the largest abundances

of ozone are found in the lower stratosphere, suggesting that the transport

of ozone from production regions is a very important process. Furthermore,

the column integrated ozone amount is a maximum at high latitudes in the

spring, where photochemical production rates would be expected to be very

low; there are simply not enough sufficiently energetic photons available

to produce the observed abundances of ozone. Once more, there must be

significant transport of ozone from lower latitudes.

The 'Brewer-Dobson' circulation was proposed in the 1940s to account for

the observed distribution of ozone and other conserved trace constituents

in the lower stratosphere. It is illustrated in Fig. 9.13 and consists of a

meridional circulation in each hemisphere, with air rising into the strato-

sphere in the tropics, moving poleward, with descent and entrainment back

into the troposphere at high latitudes. Such a mass circulation will trans-

port ozone from the tropical production regions and accumulate it towards

the poles, accounting for the spring polar maximum. Of course, such a

circulation, deduced from the observed concentrations of trace constituents,

is a Lagrangian circulation. Attempts to deduce a meridional circulation

from observed heating rates and eddy fluxes of heat and momentum, as was

described in Chapter 4, yield quite a different Eulerian mean circulation.

Because of this misunderstanding, the 'Brewer-Dobson' circulation was re-

garded for a long time as incorrect. In more recent times, there has been

renewed interest in the Lagrangian mean circulation and in approximations

to it, such as the isentropic mean circulation or the residual circulation

introduced in the last section.

The concentration of ozone in an air parcel can be written in the form:

^ w^ = C

. (9.19)

Here,

c?,

denotes the mixing ratio of ozone, while C3 denotes the photo-

chemical production or destruction rate of ozone. Note that if

represents

a volume mixing ratio, it is proportional to the molecular number density

H3 given in Eq. (9.17). Conceptually, C3 could be written in terms of an

328

The stratosphere

troposphere

pole equator

Fig. 9.13. Schematic illustration

the Brewer-Dobson circulation, proposed

account for the observed distribution of various conserved trace constituents in the

lower stratosphere.

equilibrium concentration c

and

photochemical timescale x

(9.20)

which represents exponential decay of

towards c

timescale x

. This

will

adequate

not too different from

and could

be a

useful

approximation for pedagogical purposes. Note that Eq. (9.19) is identical in

form to the thermodynamic equation in terms of 9; the difference is that C3

does not directly affect the atmospheric motions in the way in which 9 does.

Let us take the zonal mean of Eq. (9.19):

It is difficult to see any way of simplifying this equation further. In particular,

the ozone concentration may vary very sharply with height,

we are not

justified in neglecting the vertical advection terms, as we did with the thermo-

dynamic equation under

quasi-geostrophic scaling. The various terms

this transport equation are difficult

estimate from observations, since [v]