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Air-Sea Interaction
(ASL712)
Flow Characteristics of the Marine Atmosphere
Solar energy powers the atmosphere. This energy warms the air and drives the
motions we feel as winds. The seasonal distribution of this energy depends on the orbital
characteristics of the earth around the sun.
The earth's rotation about its axis causes a daily cycle of sunrise, increasing solar
radiation until solar noon, then decreasing solar radiation, and finally sunset. Most of this
solar radiation is absorbed at the earth's surface, and provides the energy for photosynthesis and life.
Downward infrared (IR) radiation from the atmosphere to the earth is usually
slightly less than upward IR radiation from the earth, causing net cooling at the earth's
surface both day and night. The combination of daytime solar heating and continuous IR
cooling yields a diurnal (daily) cycle of net radiation.
In the marine atmosphere the lower boundary is formed by the sea surface, which is
distinguished from the relevant conditions prevailing over land. On the continents, shape
and size of the elements of surface roughness are linearly defined and comparatively easy
to determine. Generally, their nature and locality are fixed and neither vary with time nor
depend strongly on the wind. Their aerodynamics are relatively well defined and known.
Contrary to the conditions found over land the surface roughness encountered at sea is
composed of a great variety of ocean waves, i.e., moving elevations which are different in
size, shape, velocity as well as subject to continuous and irregular changes. The
dimensions, the spatial distribution, and the temporal variation of the ocean waves, are
governed by dynamical laws wherein the character and speed of the air flow play a
decisive role. Besides, orbital motion and drift current are present in the sea and it is quite
obvious that these water movements will react on the air flow. With increasing wind
speed, finally, the formation of foam and sea spray, which implies a disintegration of the
sea surface, affects large areas and extends to a certain height, thus creating a transition
zone between air and sea. Bearing all this in mind, we can hardly speak of the sea surface
being simply the lower boundary of the air flow as if it were a solid wall. More important,
we must realize that there is an extremely variable and, therefore, ill-defined and hardly
accessible boundary zone where the coupling between atmosphere and ocean occurs in a
very complicated manner.
These dynamic properties of the sea surface considerably increase the difficulties
inherent in any investigation concerned with the mechanism of the air-sea boundary layer.
This is the reason that so little is known, for instance, about the pattern of the air-flow
around moving water waves. With a view to this severe handicap it is only of little
comfort that the difficulties mentioned above are more or less the same in all oceanic
regions, thus enabling us to draw general conclusions from studies executed in a certain
area.
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We now describe the nature of the air flow over the sea. Before investigating the behavior
of the wind in detail we shall try to collect some additional information on the essentials
of the sea surface which are, or may be, related to wind structure.
Examples for air-sea interaction:
Any hurricane comes from water vapor, as it ascends the “eye-walls” that
surround a hurricane’s core, condensing and releasing its latent heat of evaporation. The
heat makes the moist air buoyant, turning the eye-walls into a giant chimney with an
incredibly strong draft. The draft sucks in sea-level air, causing it to spiral toward the
core in destructive winds and to drive waters against nearby coasts in storm surges. The
fast air flow over warm water also ensures intense heat and vapor transfer to the air,
sustaining the hurricane’s strength. Over colder water, where not enough water
evaporates, the hurricane dies: The lifeblood of a hurricane is intense sea to air transfer of
heat and water vapor. On the other hand, as hurricane winds whip the waters along, they
transfer some of their momentum downward. The loss of momentum acts as a brake on
the hurricane circulation, keeping the winds from completely getting out of hand.
A hurricane also mimics on a small-scale the global atmospheric circulation,
which is similarly “fueled” by latent heat released from condensing water vapor. This
happens in “hot towers,” concentrated updrafts of the Inter Tropical Convergence Zone
(ITCZ), and also in somewhat less vigorous updrafts within extra tropical storms. Many
of the latter draw their vapor supply from the warm Gulf Stream and its Pacific
counterpart, the Kuroshio, ocean currents transporting massive amounts of heat from
warm to cold regions. Hot towers make their presence known to travelers crossing the
equator, and wake them from their slumber when updrafts toss around their jetliner, as
high as 10 or 12 km above sea level. Heat release in the updrafts, and compensating
cooling and subsidence, are part of a thermodynamic cycle that energizes various
atmospheric circulation systems, including the easterly winds of the tropics and
subtropics, and the westerlies of mid-latitudes. The winds in turn sustain sea to air heat
and vapor transfer, supplying the fuel, moist air, for the updrafts. The associated air to sea
transfer of momentum from the winds is again the control on the strength of the
atmospheric circulation.
Important to the operation of hurricanes and to large-scale atmospheric and ocean
circulation systems is therefore in what amount, and by what mechanisms, momentum,
heat and vapor pass from one medium to the other. The rates of transfer, per unit time and
unit surface area, depend on a variety of conditions and processes; relationships between
the rates and the variables influencing them are the “transfer laws” of the air sea interface
that we seek in this chapter. As all laws of physics, these too are distilled from
observation, and, as most such laws, they are more or less accurate approximations. Their
establishment requires painstaking work, hampered by difficulties of observation at sea.
After nearly a century of research by many scientists from a variety of nations, there are
still many uncertainties affecting the transfer laws
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How the Ocean-Atmosphere System is Driven
This is about winds, currents, and the distribution of heat in the atmosphere and
ocean. Since these are due to the Sun, we look at some of the essential processes that
determine how the atmosphere and ocean respond to radiation from the Sun. Ideally, one
would like to be able to deduce this response in all its details from knowledge of the
appropriate properties of the earth and of its ocean and atmosphere, but this is not a
simple matter. The nearest approach to a solution of this problem is by means of
numerical models, but these still rely to some extent on observations of the real system,
e.g., for determining the effects of processes (like those associated with individual clouds)
that have a scale small compared with the grid used in the model.
The aim of the numerical models is to include the effects of all processes that play
a significant part in determining the response of the ocean-atmosphere system. The aim
of this section, on the other hand, is to consider only the most basic processes and to
show how an equilibrium state can be reached. One such basic process is the absorption
of radiation by certain gases (principally water vapor, carbon dioxide, and ozone), and so
the "greenhouse" effect is discussed. The density field that results from radiation
processes acting in isolation is not in dynamical equilibrium, because air near the ground
is so warm that it is lighter than the air above. Consequently, vertical convection takes
place and stirs up the lower atmosphere. Calculations of the equilibrium established when
convective and radiative processes are both active is discussed later. These calculations,
however, neglect variations in the horizontal, which are, of course, extremely important
since they are responsible for the winds and currents that are the main subject of this
notes. A brief discussion of the effects of horizontal variations is given in the subsequent
lectures. Finally, since radiation is the source of energy for the atmosphere-ocean system,
variations in the radiative input are discussed further.
1.2
The Amount of Energy Received by the Earth
Energy from the sun is received in the form of radiation, nearly all the energy
being at wavelengths between 0.2 and 4 µm. About 40% is in the visible part of the
spectrum (0.4-0.67 µm). The average energy flux from the sun at the mean radius of the
earth is called the solar constant S and has the value (Hickey et al., 1980)
S = 1.376 kW m-2
(1)
(A great variety of units is used for energy flux). In other words, a 1-m-diameter dish in
space could collect enough energy from the sun to run a 1-kW electric heater! Since the
earth's orbit is elliptical rather than circular, the actual energy received varies seasonally
by ± 3.5%, the maximum amount being received at the beginning of January.
The total energy received from the sun per unit time is
π R2S,
(2)
where R is the radius of the earth. Since the area of the earth's surface is 4π R2, the
average amount of energy received per unit area of the earth's surface per unit time is
3
1
S  344W m  2
4
(3)
if the earth's axis were not tilted, the average flux received would vary from π -1S at the
equator to zero at the poles. However, the tilt of the earth (23.5°) results in seasonal
variations in the distribution of the flux received. When account is taken of these
variations, the average flux received in 1 yr is found to vary with latitude as shown in Fig.
1.
Not all the energy impinging on the earth is absorbed. A fraction  is reflected or
scattered, so the average flux actually absorbed is


1
1   S  240W m  2
4
(4)
The amount reflected or scattered is about 100 W m- 2 at all latitudes, as shown in Figure.
(There is no obvious reason that this amount should vary so little with latitude.) The
number  is called the albedo of the earth and has a value (Stephens et al., 1981) of
about
 = 0.3.
(5)
Similarly, the albedo  can be defined for a particular place and particular time as the
fraction of the impinging radiation that is reflected or scattered. The reflected light is the
light by which the earth may be photographed from space, and such photographs, which
is effectively the result of combining many such photographs to give the mean
reflectivity) show that the albedo can vary enormously with such factors as the amount of
cloud, and whether the ground is covered by ice or snow. Mars, with no cloud cover, has
about half the albedo of the earth, whereas Venus, with total cloud cover, has about twice
the albedo of the earth. A quantitative estimate of the degree to which clouds, ice, and
snow affect the albedo can be obtained from satellite measurements. The minimum
albedo is presumably close to the value in the absence of clouds and of snow-free
conditions where these occur. On land, the value is usually about 0.15, with higher values
in desert regions (0.2-0.3) and in icy regions, reaching 0.6 in parts of the Antarctic.
Comparison of the minimum albedo with the average albedo shows the effect of clouds.
For instance, most of the ocean within 40° of the equator has minimum albedo below 0.1,
but the average albedo is normally between 0.15 and 0.3. It is clear that the factors that
determine albedo are very important in determining the energy balance of the earth.
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1.3
Radiative Equilibrium Models
Since the ocean-atmosphere system is driven by the sun's radiation, it is important
to know how radiation is affected by the atmosphere and ocean. Only the most basic
elements will be discussed here. To begin with, consider the equilibrium that would be
established if the earth had no fluid envelope. The surface would reflect a fraction  of
the incoming radiation and absorb the remainder. The absorption of energy would cause
the surface to warm up until it radiated to space as much energy as it absorbed. When the
surface reaches temperature T, the amount of energy E radiated per unit time is given by
Stefan's law
E = σ T4
(6)
σ = 5.7 × 10-8 W m-2 K-4.
(7)
where
For the radiation actually absorbed by the earth (see Fig), such an equilibrium would be
achieved when the temperature at the equator reached 270 K, the temperature at the
South Pole 150 K, and the temperature at the North Pole 170 K. In fact the earth's surface
is much warmer, and the contrast in temperature between the equator and the poles is
much less. The difference from the observed surface temperature must be due to the
existence of the fluid cover of the earth. This can affect the equilibrium reached in two
ways. First, radiation can be absorbed within the atmosphere itself. Second, the
atmosphere and ocean can carry heat from one area to another, thereby affecting the
balance. In this section, the first effect will be considered in isolation from the second. In
subsequent sections, the effect of fluid motion on the equilibrium will be discussed. This
fluid motion consists of winds, ocean currents, etc., which will be the main concern.
The radiative equilibrium that would be established in the absence of fluid motion
has been calculated by Moller and Manabe (1961). The average temperature profile thus
obtained is shown by the solid line in the Fig. In some ways the left-hand version of the
figure is more appropriate because it gives equal weight to equal masses of air. In the
lower 70% (by mass) of the atmosphere, the main physical factor responsible for the
equilibrium reached is the absorption of radiation by the water vapor present in the
atmosphere. For their calculations, Moller and Manabe used the observed distribution of
water vapor with height. At higher levels, other absorbers such as carbon dioxide and
ozone become important. Figure shows that the presence of the atmosphere results in
much higher ground temperatures than would otherwise be achieved. This is due to the
“greenhouse” effect, which will be discussed.
1.4
The Greenhouse Effect
The radiative equilibrium solution shown in Fig has much higher ground
temperatures than would exist in the absence of the atmosphere. This is caused by the
“greenhouse” effect, the principle of which can be explained as follows. Consider a
greenhouse formed by placing a horizontal sheet of glass above the ground as shown in
Fig. The glass used is transparent to radiation with wavelengths below 4 µm, but partially
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absorbs radiation of longer wavelengths. Suppose the glass and ground are initially cold,
and then a downward flux I of solar radiation is “switched on.” This radiation will pass
through the glass unattenuated and be absorbed by the ground. The ground will warm up
to a temperature Tg and emit long-wave radiation with an upward flux U given by
Stefan's law:
U = σ T4g
(8)
Practically, all the radiation emitted at temperatures typical of the atmosphere has
wavelengths above 4 µm (the range is 4-100 µm), so a fraction e of this radiation will be
absorbed by the glass. Thus the glass will also warm up and emit radiation. Suppose the
flux emitted in each direction is B.
Equilibrium will be reached when the upward fluxes balance the downward fluxes,
i.e., when
I = (l - e)U + B = U – B
(9)
Solving (8) and (9), the result for the ground temperature is
σ T4g = U = I/(1 – e/2)
(10)
Thus Tg is higher (by up to 19%) than it would be in the absence (e = 0) of the glass. This
is the principle on which a greenhouse operates.
The effect can be most easily understood in the extreme case of glass that absorbs
all the long-wave radiation (e = 1). Then (ref figure) I = B, which implies that the glass
reaches the same temperature that the ground would have in the absence of glass. Since
the underside of the glass is at the same temperature, it radiates a downward flux B of
long-wave radiation downward, so the ground receives a total flux of I + B = 21. Thus by
Stefan's law the ground reaches a temperature that is higher than in the absence of glass
by a factor 21/4 = 1.19. For other nonzero values of e, the ground still receives a back
radiation flux B in addition to the short-wave flux I, so it reaches a higher temperature
than it would otherwise.
In the atmosphere, the absorbing material is distributed continuously in the
vertical rather than being confined to a thin sheet. Generalization of the above ideas to
this case is straightforward and gives temperature profiles for the lower atmosphere that
are similar to those of Moller and Manabe. More accurate calculations require the
radiative energy to be divided up into many wavebands rather than just two (i.e., “long”
and “short” waves), and to take account of the absorption in each band separately. Also,
reflection and scattering must be allowed for. This depends on the distribution and albedo
of clouds and on the albedo of the underlying surface.
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An estimate of the radiation balance for the atmosphere is summarized in figure.
Setting the incident flux at 100 units, the reflected and scattered flux of short-wave
radiation is 100  ≈ 30 units. This leaves 70 units of net downward flux of short-wave
radiation at the top of the atmosphere, of which 19 units are absorbed in the atmosphere,
leaving only 51 units to be absorbed at the surface. There is also a large amount [London
and Sasamori (1971) estimate 98 units] of long-wave radiation absorbed at the surface,
this representing back radiation from the atmosphere (it is possible for the back radiation
to exceed the incident radiation, as a generalization of Fig to several sheets of glass can
readily show). The net surface emission (excess of upward over downward radiation) of
long-wave radiation is 21 units, the remaining upward flux of 30 units being by
convection. The upward flux at the top of the atmosphere is 70 units, as required to
balance the short-wave radiation received. The mean surface temperature is that
corresponding to the 98 + 51 = 149 units of radiated energy flux at the ground rather than
that corresponding to the 70 units emitted at the top of the atmosphere. The latter flux can
be more closely identified with a temperature at “cloud-top” height.
1.5
Effect of Convection
The radiative equilibrium solution was described in Section 1.3 as the solution
that would be obtained in the absence of fluid motion. This statement is not strictly true,
however, because the radiative equilibrium solution is based on the observed distribution
of water vapor. This distribution is not predetermined, but is the result a balance that
involves fluid motion.
To see how fluid motion can affect the balance, consider an atmosphere that, at
some initial time, contained no water vapor, but was in radiative equilibrium. If the
atmosphere absorbed no radiation at all, the ground would warm up as in the absence of
an atmosphere (see Section 1.3), but the air above would remain cold. Although the
system would be in radiative equilibrium, it would not be in dynamic equilibrium because
the air warmed by contact with the surface could not remain below the cold air above
without convection occurring, as it does in a kettle full of water that is heated from below.
The vigorous motion produced carries not only heat up into the atmosphere, but also
water vapor produced by evaporation at the surface. The water vapor then affects the
radiative balance because of its radiation-absorbing properties, so the final equilibrium
depends on a balance between radiative and convective effects and is called radiativeconvective equilibrium.
Whether or not convection will occur depends on the “lapse” rate, i.e., the rate at,
which the temperature of the atmosphere decreases with height. Convection will only
occur when the lapse rate exceeds a certain value. This value can be calculated by
considering the temperature changes of a parcel of air that moves up or down
“adiabatically,” i.e., without exchanging heat with the air outside the parcel. As such a
parcel rises, the pressure falls, the parcel expands, and thus its temperature falls. The rate
at which the temperature falls with height, due to expansion, is called the dry adiabatic
lapse rate and has a value of about 10 K/km. If the temperature of the surroundings fell
off more quickly with height, a rising parcel would find itself warmer than its
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surroundings, and therefore would continue to rise under its own buoyancy. In other
words, the situation would not be a stable one, and so convection would occur.
Convection carries heat upward and thus will reduce the lapse rate until it falls to the
equilibrium value, for then convection can no longer occur. Another way of expressing
the same ideas is in terms of potential energy. When the lapse- rate exceeds the adiabatic
value, the potential energy can be reduced by moving parcels adiabatically to different
levels. Thus energy is released and is used to drive the convection.
If the atmosphere contained only small amounts of water vapor, convection would
only occur if the dry adiabatic lapse rate were exceeded. In practice, the situation is
complicated by the fact that air at a given temperature and pressure can only hold a
certain amount of water vapor. The amount of water vapor relative to this saturation
value is called the relative humidity. When the relative humidity reaches 100%, water
droplets condense out of the air, thereby forming clouds. The condensed water ultimately
returns to the earth’s surface as precipitation.
This hydrological cycle affects the energy balance of the atmosphere in a number
of important ways. First, clouds have an important effect on the total amount of energy
absorbed by the atmosphere because they reflect and scatter a significant amount of the
incoming radiation (see Section 1.2). Second, the radiation-absorbing properties of water
vapor are important in determining the temperature of the lower atmosphere, as discussed
in Section 1.3. Third, cooling takes place upon evaporation because of the latent heat
required. This heat is released back into the atmosphere when condensation takes place in
clouds. The heat transferred by this means is, on average, about 75% of the convective
transport (see Fig).
The release of latent heat in clouds also affects the conditions under which convection can take place. The amount of water vapor a parcel of air rising adiabatically can
hold decreases with height. Thus if the parcel is already saturated with water vapor, latent
heat will be released as the parcel rises, so the rate of decrease of temperature with height
will be less than for dry air. The rate of decrease with height is called the moist adiabatic
lapse rate and has a value that depends on the temperature and pressure. In the lower
atmosphere, the value is about 4 deg km-1 at 20º and 5 deg km-1 at 10º. The appropriate
lapse rate may also be different if ice is formed instead of liquid water. A fuller
discussion is given in Section 3.8.
The moist adiabatic lapse rate is appropriate for ascending air, but for descending
air the story is different. The amount of water vapor a parcel of air can hold increases as
the parcel descends, so the parcel is always unsaturated and the dry adiabatic lapse rate is
appropriate. Thus in a convecting atmosphere, potential energy may be released where
the air is ascending, whereas work is being done against gravity where the air is
descending.
Another consequence of the nature of moist convection is the distribution of
relative humidity in the atmosphere. The mean value must lie between the 100% of the
moist air in rising regions and the lower values of the descending regions. A rough
approximation to the observed mean distribution is a relative humidity that decreases
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linearly with pressure from 77% at the ground to zero at the top of the atmosphere. The
relative humidity does not change very much from one season to another, whereas the
actual amount of water vapor present varies a great deal.
A problem in modeling the atmosphere is to find a satisfactory way to represent
the effects of convection without modeling details of the ascending and descending
parcels of air. Radiative-convective models represent the effects of convection in a very
simple way. First, they ignore horizontal variations, so that the temperature and other
quantities are functions only of altitude (or, equivalently, of pressure). Distributions of
the radiation-absorbing gases, carbon dioxide and ozone, of clouds, and of either relative
humidity or absolute humidity are fixed, as is the downward flux of short-wave radiation
at the top of the atmosphere. An initial temperature distribution is allowed to adjust
toward equilibrium, taking account not only of radiative fluxes but also of convective
fluxes. Convection is assumed to occur only when the radiative fluxes are tending to
increase the lapse rate above a certain critical value. Then an opposing convective flux is
introduced that redistributes (but does not add or remove) heat in such a way as to keep
the lapse rate at the critical value. The difficulty lies in the choice of the critical value.
Usually this is simply chosen to be the observed mean lapse rate of the lower atmosphere,
namely, 6.5 deg km-1. The result of such a calculation is shown in Fig and gives quite a
good approximation to the observed mean temperature profile. As such, it is an
improvement over the pure radiative equilibrium-model, but its limitations should not be
forgotten.
1.6
Effects of Horizontal Gradients
In the earlier section, it was seen that the large vertical temperature gradients that
would be produced by radiation acting in isolation result in convection that tends to
reduce gradients. In a similar way, the variations with latitude of the absorbed radiative
(Fig. 1.1) would lead to large horizontal temperature gradients if radiation acted in
isolation. Again fluid motion takes place that tends to reduce these gradients. The nature
of these motions depends on dynamical processes, which will be the subject of
subsequent chapters.
Intuitively, one might expect the non-uniform heating of the atmosphere to cause
rising motion in the tropics and descending motion at higher latitudes. Halley (1686)
Hadley (1735) proposed this type of circulation, which is now known as a Hadley cell. A
similar circulation might be expected to occur in the ocean, so that the excess heat
received in the tropics would be transported poleward in both atmosphere and ocean.
The circulation (in the meridional plane) that actually occurs is known
quantitatively (but with limited accuracy) for the atmosphere from observations and is
shown in Fig. 1.7. By comparison, the meridional circulation in the ocean is very poorly
known, but estimates have been made that at least give an order of magnitude. A brief
description of the atmospheric part of the circulation is as follows. The Hadley cell is
confined to the tropics. Moist air from the trade wind zone, where evaporation exceeds
precipitation, is drawn into the areas of rising motion, which, because they are wet and
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cloudy. Important regions of rising motion are over Indonesia and the Amazon and
Congo basins. Over the Atlantic and Pacific Oceans, the rising motions tends to be
concentrated in a fairly narrow band called the Inter-Tropical Convergence Zone (ITCZ),
usually found between 5 and 10° to the north of the equator. The regions of descending
air are dry, and include particular the desert regions, which are found between latitudes
20° and 30°.
In mid-latitudes, the picture is quite different. Because of the rotation of the earth,
the motion produced by the horizontal density gradients is mainly east-west, and there is
relatively little meridional circulation. However, the situation is not a stable one, and
large transient disturbances (which appear as cyclones and anticyclones on the weather
map) develop. These disturbances are very effective at transporting energy poleward.
The effectiveness of fluid motion in reducing horizontal gradients can be judged
from a comparison of the two lower curves in Fig. 1.1. The solid curve shows the
variation with latitude of the absorbed flux of radiative energy. In a pure radiative
equilibrium (or a radiative-convective equilibrium), the outgoing radiation would be
equal to the absorbed radiation at all latitudes. In practice, the outgoing flux of radiative
energy, shown by the dashed line in Fig. 1.1, is much more uniform. From the difference
between the two curves, the amount of energy that must be transported across each circle
of latitude by fluid motion can be calculated.
The curve so obtained for the northern hemisphere is shown in Fig. 1.8. This
curve can be compared with the one for the observed transport of energy by the
atmosphere. The difference between the two curves (the shaded region in Fig. 1.8)
provides an estimate of the energy transport by the ocean According to these results,
ocean and atmosphere are equally important in transporting energy, the atmosphere being
most important at 50° N and the ocean most important at 20°N. There is, however,
considerable uncertainty in the measurements, and probable errors are estimated by
Vonder Haar and Oort (1973). For instance, the probable error in the transport of energy
by the ocean at 20° N is about 70%.
In calculating the energy transport by the atmosphere from observations, a distinction can be made between the energy transported by the mean (time-averaged) circulation
and the energy transported by transient motions. If this calculation is done for each month
in turn and the results are averaged, the curve in the unshaded part of Fig. 1.8 is obtained.
In latitudes where the transport by the atmosphere is important, the transient motions
account for most of the transport. This observation is the basis for simple equilibrium
models in which the radiative heat flux is balanced not by small-scale convection, as in
radiative-convective equilibrium models, but by energy fluxes due to large-scale transient
motions (such as cyclones and anticyclones). These motions transport heat vertically as
well as horizontally, so calculations of both vertical and horizontal gradients can be made.
The method of estimating the transports due to the large-scale transient motions is
beyond the scope of the present chapter, but the concept is important. The structure of the
atmosphere and ocean depends on the motions driven by radiation and their effectiveness
in redistributing heat. If the effect of the dominant energy-transporting mechanism can be
10
estimated in some simple way, one hopes that reasonable estimates of basic features such
as the mean horizontal and vertical temperature gradients of the atmosphere can be
obtained.
1.7
Variability in Radiative Driving of the Earth
Since the present state of the ocean and atmosphere is a result of their response to
the radiation received from the sun, one would like to know what variability there is in
this driving. The total amount of radiation incident on the earth in 1 year depends only on
the output of radiation from the sun, which is measured by the solar constant S, whose
present value is given by (1). Measurements since the 1920s show no variations larger
than the probable measurement errors, so S cannot have varied more than 1 or 2% in that
time. Thus the hypothesis that S is constant, as suggested by the name “solar constant,” is
consistent with observations to date, although other possibilities are not ruled out.
The amount of radiation incident at a particular point on the earth does, however,
vary enormously between day and night and from season to season, and these variations
are of obvious importance to life as we know it. The emphasis here is on periods larger
than a day, daily variations will not be discussed explicitly. However, it is important to
realize that the existence of daily variations can affect the state of the atmosphere over
longer periods, the magnitude of the effect depending on the amplitude of the daily
variations. An example of such an effect is the mixing of the lower atmosphere. In
summer especially, the ground can become very hot during the day, causing strong
convection that stirs up a considerable depth of air. The air is not “unmixed” at night, so
the net effect is substantially different from that which would be achieved with uniform
radiation.
Seasonal variations are due to (i) the tilt of the earth's axis relative to the plane of
its orbit (at present 23.5°) and (ii) the ellipticity of the earth's orbit. The ellipticity is such
that the total amount of radiation incident on the earth varies by ± 3.5%, with the
maximum in early January. The consequent changes with latitude and time of the incident
radiation are given by List (1951, Tables 132 and 134), whereas Stephens et al. (1981)
give the observed changes in outgoing radiation. These are smaller than the changes in
incident radiation, so there is a net gain of energy between October and March when the
earth is nearer the sun, and a net loss in the remainder of the year. The variations show a
marked asymmetry between the two hemispheres because of the different proportions of
land and sea, changes over the latter being relatively small.
The existence of seasonal variations has important effects on the mean state of the
atmosphere and ocean, the magnitude of the effect depending on the amplitude of the
variations. This fact has been demonstrated by numerical experiments of Wetherald and
Manabe (1972). They began with an ocean-atmosphere model driven by the annual mean
radiation and then changed to seasonal forcing. The mean state was changed thereby, e.g.,
surface temperatures in high latitudes were greater and the mean north-south temperature
gradient in the atmosphere was reduced. [The sensitivity, e.g., to changes in CO 2 content,
is also affected-see Wetherald and Manabe (1981).] The most important contributing
11
factor was found to be the melting of snow in high latitudes in summer, thus reducing the
net albedo. Another factor was found to be the development of a warm surface layer in
the ocean in summer, giving a higher mean sea-surface temperature.
The fact that seasonal variations affect the mean state of the ocean-atmosphere
system is the basis of an astronomical theory of climate change due to Milankovich (1930,
1941). Because of perturbations caused by other planets, the tilt of the earth's axis varies
between 22 and 24.5°, and the eccentricity of the earth's orbit changes, the time scales of
these changes being 104-105 years. The net radiation incident over a year is altered very
little, but the distribution in time and space is changed. The eccentricity varies
sufficiently for the amplitude of seasonal variations in the incident radiation to change
between 0 and 15% and the time of the maximum also changes.
12