Stacey F.D., Davis P.M. Physics of the Earth

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drift almost to the last section of this text is not

an indication of a minor role but recognition

that it is background information that passes

as common knowledge. Over no more than a

decade or two, paleomagnetism was trans-

formed from an exciting new sub-discipline,

overturning the standard view of the Earth, to

a basic tool.

–30

–60

300

330

Lower

Cambrian

Upper

Carboniferous

FIG U R E 25.12 The continents

of Gondwanaland reassembled

around Antarctica, to give a

common pole path for South

America, Africa, India and

Australia for Carboniferous to

Cambrian periods. Redrawn part

figure from Van der Voo (1992).

FI G U R E 25.13 Glaciation of the southern continents during the Late Carboniferous period. Arrows indicate

directions of ice movement. The glaciation and directions of ice movement are consistent with the clustering of these

land masses around Antarctica as a single super-continent, Gondwanaland, as in Fig. 25.12. Reproduced, by

permission, from Holmes (1965).

25.6 POLAR WANDER AND CONTINENTAL DRIFT 437

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‘Alternative’ energy sources and

natural climate variations: some

geophysical background

26.1 Preamble

Solid Earth geophysics offers assessments of

energy sources alternative to fossil fuels. We

gain some insight on the accessibility and geo-

physical effects of exploiting any particular

energy source by comparing the contemplated

scale of its use with the corresponding natural

dissipation. The analyses and discussions of ear-

lier chapters are used to address these issues. We

consider also the astronomically induced climate

variations that must be distinguished from the

consequences of fossil fuel use. This is back-

ground material to the environmental questions

that are primarily problems for atmospheric sci-

ence and to the resource question of fossil fuel

exhaustion that is a central problem for explora-

tion geophysicists. Energy sources considered are

solar, wind, tidal, ocean wave, hydroelectric and

geothermal, but not nuclear. We neglect also the

possibilities of biofuel, merely noting that if it

is to make a major contribution it will require a

large fraction of the land area to be devoted to

appropriate crops.

The energy dissipations by various natural

processes (Section 26.2), give an indication of

their availability for exploitation, and especially

the magnitudes of their potential contributions.

The comparison with the human use of energy

draws attention to the fact that human activity is

a global geophysical scale phenomenon. This

means that major adjustments to it cannot be

made easily in a controlled way. But major

adjustments to energy use are inevitable and if

they are uncontrolled they are likely to be pain-

ful. We examine here some of the basic facts that

are needed for informed judgements of the pro-

blems and potential solutions. Our discussion is

restricted to fundamental questions of energy

availability in principle and does not address

technical problems of exploitation.

Energy production and use are well docu-

mented because most of the production of fuels

and electricity occurs in industrial scale opera-

tions that are monitored by government author-

ities. The components of global energy use,

itemized in Tables 26.1 and 26.2, are tabulated

by the United Nations Statistical Division, the US

Department of Energy and others. The original

data appear in several forms and in some cases

there are significant discrepancies. Generally

fuels are assessed in petajoules (1 petajoule/

year ¼3.1688 10

W). In American usage an

alternative is quads (1 quad ¼10

British thermal

units ¼1055 petajoules). Notional equivalents are

1 barrel (159 litres) of oil ¼6.1 10

J and 1 tonne

(10

kg) of ‘standard’ coal  4.3 10

J (variable).

Electricity generation is quoted in millions

or billions of kilowatt-hours/year (10

kW-h/

year ¼1.14 10

W). All values are here con-

verted to average use in terawatts (10

W) for

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convenience of comparison. Care is required

in some cases, such as the production of electri-

city by means other than the combustion of

fossil fuels. Some tabulations include multiply-

ing factors to give estimates of the fuel that

would be required for the same generation

rather than electric power itself. That is not

done here. Pumped storage generation is also

excluded because that is produced from energy

otherwise accounted for.

The significance of possible alternative

energy sources must be judged against the

energy demand in Tables 26.1 and 26.2. The

least certain of these numbers is the ‘traditional’

fuels entry in Table 26.1, which is mainly wood

and animal wastes collected for heating and

cooking. Their use is still increasing by about

4% per year. The total energy demand is increas-

ing at about the same rate and is probably

limited only by a combination of availability

and affordability. Availability poses scientific

questions to which we draw attention; any active

control of demand requires political and social

decisions.

Scientific input is essential also to the other

problem discussed in this chapter: natural cli-

mate variations. We make only fleeting refer-

ence to the greenhouse gas problem, but

discuss the whole Earth/astronomical consider-

ations. The Earth’s closest approach to the Sun

on its elliptical orbit occurs on 4 Januar y, t he

height of the southern hemisphere summer. At

this time 7% more sunlight falls on the Earth

than at the height of the northern hemisphere

summer. The annual cycle of global average

temperature does not fully reflect this differ-

ence for several reasons, but especially because

the ratios of land to sea areas are quite differ-

ent over the two hemispheres. The precession

of the Earth (Section 7.2) is slowly changing

this situation, so that in 10 000 years time

the Earth will be closest to the Sun in the

northern hemisphere summer (as it was

10 000 years ago). Then the northern hemi-

sphere will experience hotter, shorter sum-

mers and colder, longer winters. Even if there

are no other changes, this fact alone will have

a major impact on the climatic pattern. It is

the most obvious of the astronomically driven

climate variations, the Milankovitch cycles

(Section 26.4).

We have another perspective on astronomi-

cal effects by noting that the Earth–Sun distance

oscillates with the lunar month. The Earth and

Moon are orbiting their common centre of mass

and it is this centre of mass that follows an

elliptical path about the Sun. The motion of the

Earth about this path is slight compared with the

annual oscillation of the Earth–Sun distance

caused by the ellipticity of the orbit, but its

period cannot be confused with any other. The

fact that a lunar period has been detected in

satellite observations of tropospheric tempera-

ture (see Section 26.4) provides unambiguous

evidence that this monthly oscillation has a

climatic effect. The atmospheric response is

complicated and not a simple radiative balance,

but involves changes in atmospheric circulation.

It presents a challenge to atmosphere–climate

modelling.

Table 26.1 Average global use, in year

2005, of primary energy sources (terawatts)

and annual percentage increase

Solids (coal, lignite, peat) 3.98 4.5%

Oil, liquefied gas 5.21 1.9%

Gas 3.42 2.0%

Primary electricity (see Table 26.2) 0.69 2.3%

‘Traditional’ fuels

1.1 4.0%

Total 14.40 2.8%

wood, animal waste, etc.

Table 26.2 Global electricity generation

(terawatts), year 2005, and annual

percentage increase

Primary: hydroelectricity 0.34 4.0%

nuclear 0.32 0

other

0.034 7.3%

Secondary: thermal

1.24 3.3%

Total 1.93 2.9%

geothermal, wind, solar, tidal, wave

generation

coal, oil and gas-fired generation

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26.2 Natural energy dissipations

That the human use of energy (Table 26.1) is of

geophysically significant magnitude is seen by

comparing it with the natural dissipations in

Table 26.3. Some of the quantities in this table

are well measured; others are guesstimates

based on assumptions that merit scrutiny and

are discussed below, but they are accurate

enough for the essential conclusion to be clear.

Only the solar radiative power completely

dwarfs our energy use and wind is a clear second.

Harnessing a few terawatts of solar energy could

have no significant impact on it, but the same is

not true for the other entries in the table, with

the probable exception of wind energy. Inclusion

in the table is not an implication that any parti-

cular form of energy is exploitable, even in prin-

ciple; accessibility and consequences of use are

considered in the next section.

The deep global processes in Table 26.3 are

subjects of Chapters 20, 22 and 24 and tidal

friction is discussed in Chapter 8. The listed

solar power is the product of the solar constant

and the cross-sectional area of the Earth, with

the fraction reaching the surface 0.56 of the total

at the top of the atmosphere. This leaves four

entries in the table that require some explana-

tion, especially as they are the least certain.

For the purpose of estimating the energy

dissipation by wind we are interested only in

friction with the Earth’s surface and not internal

dissipation by atmospheric turbulence. The

ocean wave energy in the table is wind energy

transferred via the oceans to shorelines, but we

cannot infer that the transfer of wind energy

to land areas is similar, because topography has

a strong influence. We need an independent

measure of the atmosphere–land coupling. An

indication of this is obtained by considering the

length of day variations caused by the atmos-

pheric circulation (Fig. 7.4). From the close par-

allelism of the two curves in this figure it is

evident that the coupling of the Earth to the

atmospheric motion is tight enough to cause

changes of order 1 millisecond in the length of

the day over a period as short as 15 days.

Variations in the atmospheric motion are rapidly

communicated to the surface. We can use this

observation to estimate the rate of energy dissi-

pation by the frictional contact.

The change in total rotational energy result-

ing from a transfer of angular momentum

between the atmosphere and the solid Earth,

moments of inertia C

and C

, with angular

speeds !

and !

, subscripted 1 and 2 for initial

and final states, is

E ¼ð1=2ÞC

ð!

 !

Þþð1=2ÞC

ð!

 !

Þ:

(26:1)

Applying conservation of angular momentum,

ð!

 !

ÞþC

ð!

 !

Þ¼0; (26:2)

we can rewrite DE in two alternative ways that

are useful to the present discussion:

E ¼ð1=2ÞC

ð1 þ C

Þð!

 !

 C

ð!

 !

Þð!

 !

Þ; (26:3)

E ¼ð1=2ÞC

=ðC

þ C

ð!

 !

ð!

 !

: ð26:4Þ

Table 26.3 Natural energy dissipations

(terawatts)

Deep global processes:

Geothermal flux global 44.2

land areas 9.6

Tectonics 8.0

Geodynamo 0.3

Surface/atmospheric processes:

Solar power top of

atmosphere

1.75 10

surface 9.8 10

land surface 2.8 10

Tides 3.7

Wind global 434

land 126

Waves

5

River flow 6.5

Atmospheric

electric current

9 10

4

Assumes rms peak-to-peak wave height of

2 m on 10

m of coastline

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The first term of Eq. (26.3) gives the energy

dissipation if the final state is one of precise co-

rotation of the Earth and atmosphere, that is,

¼!

. Then, with !

¼7.292 10

5

rad s

1

¼8.036 10

kg m

, C

¼1.38 10

kgm

(Table A.4, Appendix E) and j!

!

j/ !

¼1

millisecond/24 hours ¼1.16 10

8

, we have

DE ¼1.67 10

J. Noting that the phase lag

between the curves of Fig. 7.4 is no more than

15 days (1.3 10

s), we assume that the rate

of energy dissipation is at least 1.67 10

J/1.3 10

s ¼12.9 10

W. The second term in

Eq. (26.3) may have either sign. The reason is

clearer in Eq. (26.4), which shows that the energy

change is simply proportional to the change in

the square of the zonal wind speed. However, its

magnitude is more readily calculated from

Eq. (26.3), using the length of day observations.

The speed of a zonal wind of strength sufficient

to dissipate the 13 terawatts estimated from

Eq. (26.3) is

 j!

 !

jðp=4ÞR

Earth

¼ !

ð1 þ C

ðp=4ÞR

Earth

¼ 2:5ms

1

; ð26:5Þ

where (p/4) is a factor to allow for the latitude

variation.

Equation (26.5) gives the zonal wind fluctua-

tion, averaged over the whole atmosphere, that

is required to cause the length of day fluctua-

tions in Fig. 7.4. The corresponding energy dis-

sipation, calculated above, is 12.9 terawatts. This

is the measure of the atmosphere–earth cou-

pling that we need: a global average wind speed

of 2.5 m s

1

dissipates about 13 terawatts by

its interaction with the Earth. We use this as a

calibration of the energy dissipation by interac-

tion of the overall global wind pattern with the

body of the Earth. The 2.5 m s

1

estimate is not

the surface wind speed but the average zonal

motion of the atmosphere as a whole. Noting

that the energy varies as the square of wind

speed in Eq. (26.4), we need only a value of the

rms wind speed of the whole atmosphere to

estimate the energy dissipation that wind turb-

ines could, in principle, intercept. It is obviously

much more than 2.5 m s

1

and we adopt, from

Archer and Jacobson (2005), 14.3 m s

1

as an

approximate value. On this basis the dissipation

is (14.3/2.5)

12.9 terawatts ¼434 terawatts.

This is the global value in Table 26.3. It is not

immediately clear how this total is divided

between land and sea areas. The land is rougher,

but wind speed over it is generally lower. The land

value in Table 26.3 assumes a fraction propor-

tional to its area. It exceeds the human use of

energy by a factor of nearly 9.

We turn now to wave energy. Waves of peak-

to-peak amplitude a propagating in deep ocean

have energy per unit area

E=A ¼ a

g=4; (26:6)

where  ¼1025 kg m

3

is sea water density and

g ¼9.8 m s

2

is gravity. Waves of frequency f

travel in deep water with phase speed v ¼g/2pf

(obtained by putting kh  1 in Eq. (14.53) and

substituting k ¼2pf/v), but the wave energy trav-

els with the group speed u ¼v/2,

u ¼ g=4pf : (26:7)

For a dominant wave period 1/f ¼10s, which is

common for ocean swells, u ¼7.8 m s

1

. Thus the

rate at which wave energy reaches unit length of

shore line parallel to the wave fronts is

ðE=AÞu ¼ a

g

=16pf : (26:8)

Assuming that reflected energy is negligible, but

that waves in the deep ocean are randomly ori-

ented with respect to the nearest coastline (intro-

ducing a factor 2/p), and that the total global

coastline exposed to open ocean waves is

L ¼10

m (2.5 great circles), the global total

power dissipated by waves of rms peak-to-peak

amplitude 2 m is

Wave dissipation ¼ðE=AÞð2u=pÞL ¼ 5  10

(26:9)

as in Table 26.3. This appears to be a generous

estimate.

The equations for wave energy and speed

used here apply to open ocean situations, that

is to water depth much greater than wavelength.

As waves approach shallow water and slow up,

they are refracted so that the wave fronts are

more nearly parallel to the bottom contours

and adjacent coastline. However, this complica-

tion does not affect the calculation because we

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have calculated the flux of wave energy from

deep ocean into shallow water, where it all

turns on to the coastline. We have not consid-

ered the dissipation of energy in the open ocean,

regarding it as inaccessible, and conclude that

the wave energy reaching coastlines cannot

become a major contributor to usable power.

To the extent that it is available, hydro-

electricity is an ideal power source. The energy

is stored indefinitely in a convenient form and

its use can be continuously adjusted. The global

total rainfall on land is about 10

/year

and the fraction that flows to the sea in rivers

and streams is about 25%, giving a mass flow

dm/dt ¼2.5 10

kg/year ¼7.9 10

kg s

1

.Ifwe

make the simple assumption that this flows

from an average elevation h ¼840 m, the mean

height of all land, then the gravitational energy

release is

River power ¼ðdm=dtÞgh ¼ 6:5  10

W: (26:10)

This is probably an underestimate because rain-

fall is generally greater at higher elevations. But

the striking conclusion is that the current hydro-

electric power generation (Table 26.2) is already

5% of this hypothetical limit. The limit itself is

less than half of the current energy use.

Thunderstorms maintain an electric charge

on the Earth that continuously leaks to the iono-

sphere, with a global current of about 2000 A.

The potential difference between the ground

and the ionosphere is about 450 000 V, so that

the ohmic dissipation by this fine weather cur-

rent is 9 10

W. This is only a very small frac-

tion of the energy of the storms that maintain it

and is of no interest here.

Rough as some of these numbers are, energy

dissipation by wind must be seen as a clear sec-

ond to solar energy, with the other contenders

more than an order of magnitude smaller.

26.3 ‘Alternative’ energy sources:

possibilities and consequences

The variation of solar radiation with the sunspot

cycle is about 0.15% (see Section 26.4). Although

this effect appears to be slight, and evidence of

an 11-year cycle in climate is unconvincing, the

variation in radiation received by the Earth on

account of solar variability is 20 times the 14 tW

of human energy use. There are several implica-

tions; an important one is that the thermal effect

of energy use is inconsequential when consid-

ered in a global perspective. Concerns about

global warming have nothing to do with heat

release but only with changes to the infra-red

opacity of the atmosphere. It is also clear that

no conceivable harnessing of solar energy would

have a direct climatic implication. We examine

the other entries in Table 26.3 in the light of the

principle that natural dissipations give a meas-

ure of the availability of ‘alternative’ energies.

We consider also the consequences of use.

Power generation from tides is very limited,

although a tidal power station has operated in

the Rance estuary at St. Malo, on the Atlantic

coast of France, for many years. Even at the few

sites around the world with comparably large

tides, the available head of water is very small

by the standards of hydroelectric power genera-

tion. The requirement for very large turbines and

multiple impoundments of water, or an ancillary

pumped storage facility if power is to be main-

tained through the tidal cycle, make the econom-

ics of tidal power doubtful, but such situations

can change, so we examine the possibility.

Tidal power has appeared attractive in prin-

ciple because it has been assumed that the local

environmental impact is the only negative con-

sequence and that there is no global effect.

However, tidal energy is derived from the

Earth’s rotation. As discussed in Chapter 8, tidal

friction slows the rotation and causes the Moon

to recede from the Earth. Natural tidal friction

dissipates rotational energy at a rate that is about

a quarter of the present human use of energy, so,

if a major conversion to tidal power were possi-

ble, it would have a first order effect on the rota-

tional slowing. This would still be very gradual

(tides are causing the length of day to increase by

2.4 milliseconds per century), and, even with

serious harnessing, the time scale for major

change would be hundreds of millions of years.

There is a remote possibility that accelerated

slowing of the rotation would affect the geody-

namo (on a time scale of thousands of years), but

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motions in the core are so rapid compared with

any contemplated rotational change that we con-

sider this to be unlikely.

Tidal friction causes a phase lag, ,ofthe

tide, relative to the position of the Moon or

Sun (Fig. 8.4), and dissipation is proportional

to sin 2d. The satellite-measured phase lag is

2.98. The maximum possible dissipation would

occur for  ¼458 (sin 2 ¼1) and if the tidal

amplitude were unaffected the dissipation

would be 1/sin 5.88 ¼9.9 times the present

rate, giving 36 10

W. But a reduction in

tidal amplitude would accompany energy ext-

raction and the theoretical limit is nearer to

20 10

W. Although the energy reservoir is

extremely large, it is accessible only in a very

limited way. It is not a super-abundant power

source, even i n principle.

The harnessing of tides would be ‘mining’

energy in the sense of a permanent and irrever-

sible extraction of energy from a finite, although

vast, source. The harnessing of wind, waves and

river flow is qualitatively different. All three are

by-products of solar energy and all of the energy

that is available, in principle, is dissipated natu-

rally anyway. We may intercept and make use of

some of it, with local environmental consequen-

ces but no effect on the global energy balance.

Wind energy is conveniently exploitable at ele-

vations up to 100 m or so, in an atmospheric boun-

dary layer, within which wind speed increases

with height. This layer is responsible for the nat-

ural dissipation estimated in Section 26.2 and

energy is carried down into it from greater

heights. The consequence of extracting wind

energy, with turbines in the boundary layer, is

subtly different from the effect of obstacles, such

as buildings and trees, but the difference is not

important. It is obviously impossible to remove

all of the energy from the boundary layer

because that would completely stop it, leaving

no energy to be extracted and causing a new

boundary layer to form above it. This confirms

two earlier points. The wind energy is generated

high in the atmosphere and is dissipated any-

way, with or without man-made structures and

there is no global environmental consequence to

dissipation in man-made structures. The second

point applies to all of the energies in Table 26.3:

it is possible to ‘capture’ only a fraction and for a

viable source the required fraction needs to be

small. In response to the question ‘How small?’,

we note that, in the case of wind, by our esti-

mates, 12% would suffice to satisfy global energy

demand if energy extraction is confined to land

areas. Archer and Jacobson (2005) made a more

direct estimate of available wind energy from

records of wind speeds at 80 m elevation, a stand-

ard height for wind turbines. They concentrated

attention on continental areas of high average

wind speeds, v, because extractable energy

depends on v

(the rate at which air mass passes

through a turbine is proportional to v and

its kinetic energy per unit mass is proportional

to v

). The essential conclusion of Archer and

Jacobson is that sufficient energy is indeed acc-

essible, with existing technology, for wind to

become the dominant world energy source.

Ocean waves represent a more concentrated

form of energy than the wind that drives them,

but we are interested only in the dissipation that

occurs at coastlines. The calculation leading to

Eq. (26.9) gives an energy flux of 50 kW per metre

of wavefront for waves of 2 m peak-to-peak

amplitude and 10 s period. This concentration

of mechanical energy makes it appear attractive

from the perspective of small-scale engineering,

but on a global scale the 5 tW entry in Table 26.3

makes it evident that, irrespective of technical

problems, waves have no prospect of becoming a

major player in the energy game.

As pointed out in the previous section, if

every drop of water that flows to the sea in rivers

and streams were to flow all the way through

turbines of 100% efficiency, the total power gen-

eration (Table 26.3) would be less than half of the

present total energy use and only 20 times the

current hydroelectric power generation (which

continues to increase). This is a comment on the

ready accessibility of river power, but it is also an

indication that the most favourable sites are

already in use. The total capacity of the world’s

hydroelectric dams is about 7 10

and this

water storage on land has lowered sea level by

about 2 mm (perhaps 10% of the effect of all the

smaller dams). This is inconsequential. The

increased moment of inertia of the Earth is far

below the level that would cause an observable

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effect on rotation. The environmental consequen-

ces of harnessing river power are local, not global.

But, although the energy of river flow is very

accessible, in an engineering sense, the total in

Table 26.3 makes it clear that this cannot, in

principle, become a dominant energy source.

Geothermal power stations in Iceland, Italy,

New Zealand and California use steam from

ground water in volcanic areas. Although they

areavaluablesourceofpower in these areas,

they require very special geological conditions.

Interest in the wider use of deep heat assumes

that it is possible to extract heat from hot, dry

rock at depth in the crust. In geologically stable

continental regions the ambient heat flux averages

about 0.065 W m

2

and the temperature gradient is

typically 25 K/km, so that prohibitively deep drill-

ing would be required to reach anything more

than very low-grade heat. Only areas with unusu-

ally high temperature gradients offer any prospect

of economic heat extraction and, as in Fig. 20.4,

these are restricted to geologically young igneous

regions. We can take a closer look at this problem

by modifying Eqs. (20.15) and (20.16) to model an

area with a uniform crust, having a layer of gran-

ite extending from the surface to depth z

.We

assume heat generation

q ¼ 2:8  10

6

3

(corresponding to 1.05 10

9

Wkg

1

,asin

Table 21.3), conductivity  ¼2.5 W m

1

and a

heat flux

¼ 0:025 W m

2

from the mantle.

Relative to the surface value T

, the temperature

at depth z is

TðzÞT

z= þð

q=Þðz

z  z

=2Þ: (26:11)

At a suitable drilling depth of 3 km this gives

Tð3kmÞT

¼ 25K þ 3:36K  z

ðkmÞ; (26:12)

so that 20 km of granite would give an equili-

brium temperature only 90 K above that at the

surface (or 150 K at 5 km depth). We see that rock

in thermal equilibrium at accessible depths

could be usefully hot only if it is far more radio-

active than normal granite or if it extends to

implausible depths.

The conclusion from these equations is that

hot dry rock geothermal power projects are pos-

sible only in areas of high heat flux arising from

the residual heat of igneous activity. The heat

generation in the rock itself is only marginally

relevant and we can note that, without loss of

heat, the temperature rise in granite due to its

own radioactivity would be only about 40 K per

million years. Moreover, a prodigious thickness

would be required to stop it diffusing out. But the

geological requirement is not as restrictive as

that for conventional geothermal power genera-

tion, which taps ground water superheated by

more recent (or current) volcanic activity.

We can also look at the energy balance of a

hot dry rock project. If we suppose that circula-

tion of water between boreholes in fractured

rock extracts sufficient heat to cool 1 km

rock by 100 K, before the heat degrades too far

to be effective, and that the average thermody-

namic efficiency of power generation over the

usable temperature range is 20%, then it would

produce 100 megawatts for 16 years. That vol-

ume of rock would then be thermally exhausted.

On a time scale of 10

to 10

years, partial recov-

ery by diffusion of heat from hot surroundings,

including deeper rock, is possible but not

assured. Like the conventional ‘hot wet rock’

geothermal power generation, this would be

mining heat of igneous origin, not exploitation

of the geothermal flux listed in Table 26.3 and

discussed in Section 20.3. But the heat is abun-

dant in restricted areas and the fundamental

limitation is its distribution. Hot dry rock could

provide geothermal power in geologically youth-

ful igneous provinces, although these are suffi-

ciently limited to keep it out of the big league in

the energy game.

By a process of elimination we reach the con-

clusion that, disallowing nuclear power, the only

replacement sources that can, in principle, sup-

ply energy on the scale of the current use of fossil

fuels are solar and wind. That they are also the

most widely distributed sources is not inciden-

tal; we are not considering concentrated sources

and wide distribution is necessary simply to

meet the total requirement. It follows that, as

‘alternative’ sources come into play, power gen-

eration will become increasingly localized in

smaller scale operations than has been conven-

tional. Barring some unanticipated discovery,

these two sources must, between them, eventu-

ally take over. The perceived difficulty of

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discontinuous or erratic availability is a techni-

cal problem, to which solutions are at hand,

including the already well established pumped

storage system.

26.4 Orbital modulation of

insolation and

solar variability

Precise satellite observations of the luminosity

of the Sun now extend over more than two 11-

year cycles of sunspot numbers. Willson and

Hudson (1991) appear to have been first to dem-

onstrate that it varies by about 0.15%, with max-

ima coinciding with sunspot maxima. Although

the record is short, we have independent evi-

dence that sunspots correlate with, and can be

used as an indicator of, solar output. The

Maunder minimum in activity (1645–1715),

when sunspots were virtually absent for 70

years, coincided with the ‘little ice age’ of low-

ered global temperature, and we note a report by

Zhang et al. (1994) of correlated luminosity and

magnetic activity of ten solar type stars.

Although clear reports of an 11-year cycle in

global temperature are lacking, variability of

the Sun must be allowed as an important con-

tributor to climate change, perhaps the most

important one, although not understood. The

enhanced greenhouse effect of carbon dioxide

and other gases must be seen against a back-

ground of such natural effects.

As mentioned in the preamble, the Earth’s

orbit about the Sun is eccentric (e ¼0.016 73),

giving a ratio of perihelion (closest) to aphelion

(most remote) distances of 0.967 09. The inten-

sity of radiation received by the Earth varies

inversely as the square of this factor, being stron-

ger on January 4 than six months later by a factor

1.069. If we make the simple assumption that the

Earth behaves as a radiative black body, emitting

energy proportional to T

, the variation in insola-

tion would imply a global average temperature

oscillation of 4.6 K. An effect as big as this would

be very obvious, but, apart from atmospheric feed-

back mechanisms, it is mitigated and obscured by

the asymmetry of continents and oceans, with a

much greater oceanic area in the south. The con-

sequences include greater cloudiness there, but

this state of affairs is not permanent. The Earth’s

axis of rotation precesses (Section 7.2) and the

alignment of the hemispheres with maximum

insolation interchanges. This is one aspect of the

Milankovitch cycles, discussed below.

Surprisingly, one of the weakest of the astro-

nomical cycles has an observed effect. This is the

lunar modulation of the tropospheric tempera-

ture (roughly the lowest 6 km of the atmosphere)

as seen by satellite measurements of thermally

excited microwave radiation from molecular

oxygen. The Earth and Moon orbit the Sun

together and it is the centre of mass of the

combination that follows the elliptical orbit

about the Sun. The shared centre of mass is a

point within the Earth 4671 km from the centre

(assuming the Moon to be at its mean distance,

3.844 10

km). Thus, there is a monthly oscil-

lation in the Earth–Sun distance amounting

to 2 4671 km, a variation of 6.2 parts in 10

causing a monthly oscillation in insolation of

1.24 10

4

. There is also a contribution by

moonlight, which is strongest at full Moon,

when the Earth is closest to the Sun, and so

reinforces the variation. For this purpose we

can assume the albedo (reflectivity) of the

Moon to be unity, because absorbed radiation is

re-radiated in the infra-red and intercepted by

the Earth. (Most of this infra-red radiation is

emitted from the hotter, sunlit side of the

Moon.) Allowing for the slightly smaller angular

size of the Moon than the Sun, as seen from the

Earth, the moonlight peak is 2.0 10

5

of the

solar radiation. This makes the total monthly

variation in insolation 1.44 10

4

A monthly cycle of tropospheric temperature

was identified by Balling and Cerveny (1995) in

records of satellite-monitored radiation from

molecular oxygen. The global average tropo-

spheric temperature is 269 K and oscillates by

about 0.01% of this, but does not have a simple

phase relationship with the cycle of insolation.

Over the lunar month, the temperature peak

precedes the maximum in insolation (at full

Moon) and there is a complicated latitude var-

iation. At the equator, little effect is seen. At

high and low latitudes, in both hemispheres,

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the temperature variation follows the global

trend, but at mid-latitudes (roughly 408 to 608),

the oscillation is reversed. The pattern of atmos-

pheric circulation is varying slightly in a system-

atic way over the lunar month. Although the

possibility of a tidal influence cannot be securely

discounted, the obvious driver is radiative forc-

ing, but there is no theoretical explanation. It is

useful to note also that Gordon (1994) used the

same microwave observations to find a weekly

cycle in tropospheric temperature, amounting to

0.01 K (warmer on weekdays) in the northern

hemisphere, but not in the south.

The demonstrated sensitivity of tropospheric

temperature to very small variations in insolation

appears to conflict with the limited evidence for

a climatic response to ellipticity of the Earth’s

orbit, illustrating the complexity of the climate

system. Atmospheric feedback mechanisms,

compounded with the ocean/continent asymme-

try of the hemispheres, make it difficult to isolate

cause–effect relationships. This is a reason for

interest in the satellite microwave observations.

The lunar period is unique. There is no way

of attributing the appearance of this period in

tropospheric temperature to anything but the

Earth–Moon orbital motion. Similarly, the weekly

cycle, distinguishing weekdays from weekends,

has no astronomical or other natural basis and is

unambiguously identified with human activity.

The observations provide vital evidence that the

atmosphere responds in a comprehensible way to

both variations in insolation and the impositions

of human activity. We can keep these situations

in mind when trying to understand more compli-

cated effects with multiple causes.

Natural climate changes occur on all time

scales but variations with characteristic times

of a few tens of thousands of years have attracted

particular attention. This is the time scale of

the major advances and recessions of glaciers

and ice-sheets over the last million years or

so (the Quaternary period). The idea that ice

ages were brought on by diminished insolation

arising from orbital changes originated in the

1800s, especially with the work of James Croll,

and was given a sound theoretical basis by

M. Milankovitch in the early 1940s. With sub-

sequent improvements in dating Quaternary

geological events and in calculating details of

orbital motion, it has become clear that the astro-

nomical cycles expected by the Milankovitch

theory are seen in the observed climatic

changes (Berger, 1988; Berger and Loutre,

1992). There is even a report of geological evi-

dence of Milakovitch cycles 500 million years

ago (Williams, 1991). However, there are obvi-

ously other factors, including changes in the

Sun and probably ocean circulation, not all of

which are understood.

The precession of the Earth (Section 7.2)

causes the axis of rotation to cycle about the

normal to the ecliptic plane with a period of

25 700 years. If this were the only variation

then in half this time the Earth would be closest

to the Sun in the northern hemisphere summer

instead of the southern hemisphere summer, as

at present. But the orientation of the axis of the

orbital ellipse also changes and the combined

effect is a climatic precessional period of 21 000

years. It depends on the fact that the orbit is

elliptical, but this also changes. The eccentricity

varies with a period of about 96 000 years, and

when it is very small, climatic evidence of the

precession disappears. The other important orbi-

tal parameter is obliquity (inclination of the rota-

tional axis to the normal to the orbital plane),

which has a 41 000-year period. These effects

all interact to produce variations in insolation

with latitude as well as season and the Earth

responds in a non-linear manner, with varying

albedo due to snow and ice cover. Nevertheless,

climate indicators, such as oxygen isotope

ratios (Section 3.9), give sufficient evidence of

Milankovitch periods to convince us that they

account for a significant part of the climate

variations.

It is difficult to attribute to orbital variations

the prolonged extreme glaciations that occurred

in the Permian period and also in the late

Precambrian period. The possibility of major

changes to the greenhouse gas content of the

atmosphere must be allowed, but solar variabil-

ity is also implicated. If we attribute major

changes to the Sun itself, we must allow lesser

effects to have the same cause and with this

much freedom to blame the Sun, our theories

become very nebulous.

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