. 4
( 16)


tion can be pieced together. Indirect sources, such as are provided by ice cores,
tree rings and records of lake levels, of glacier advance and retreat, and of pollen
distribution (found in sediments in lakes for instance), can also yield informa-
tion to assist in building up the whole climatic story. From a variety of sources,
for instance, it has been possible to put together for China a systematic atlas of
weather patterns covering the last 500 years.
Similarly, from direct and indirect sources, it has been possible to deduce
the average temperature over the northern hemisphere for the last millennium
(Figure 4.5). Suf¬cient data are not available for the same reconstruction to be
carried out over the southern hemisphere. Because of the uncertainties underly-
ing the precise interpretation of proxy data and because of the sparsity of data
and coverage especially for earlier periods, there are large uncertainties associ-
ated with the reconstructions shown in Figure 4.5 “ as is illustrated also by the
range within the ten different reconstructions. However, it is just possible to
identify the ˜Medieval Warm Period™ associated with the eleventh to fourteenth

centuries and a relatively cool period, the ˜Little Ice Age™, associated with the ¬f-
teenth to nineteenth centuries. There has been much debate about the extent of
these particular periods that only affected part of the northern hemisphere and
are therefore more prominent in local records, for instance those from central
England. The increase in temperature over the twentieth century is particularly
striking and the 1990s are likely to have been the warmest decade of the millen-
nium in the northern hemisphere.
Although there is as yet no complete explanation for the variations that
occurred between 1000 and 1900, it is clear that greenhouse gases such as car-
bon dioxide and methane cannot have been the cause of change. For the millen-
nium before 1800 their concentration in the atmosphere was rather stable, the
carbon dioxide concentration, for instance, varying by less than 3%. However,
the in¬‚uence of variations in volcanic activity can be identi¬ed especially in
some of the downturns of temperature in the record of Figure 4.3. For instance,
one of the largest eruptions during the period was that of Tambora in Indonesia
in April 1815, which was followed in many places by two exceptionally cold
years; and 1816 was described in New England and Canada as the ˜year without
a summer™. Although the effect on the climate even of an eruption of the mag-
nitude of Tambora only lasts a few years, variations in average volcanic activity
have a longer-term effect. It is likely also variations in the output of energy from
the Sun provide some part of the explanation.3 Although accurate direct meas-
urements of total solar radiation are not available (apart from those made during
the last two decades from satellite instruments), other evidence suggests that the
solar output could have varied signi¬cantly in the past. For instance, compared
with its value today it may have been somewhat lower (by a few tenths of a watt
per square metre) during the Maunder Minimum in the seventeenth century
(a period when almost no sunspots were recorded; see also box on page 166).
There is no need, however, to invoke volcanoes or variations in solar output as
the cause of all the climate variations over this period. As with the shorter-term
changes mentioned earlier, such variations of climate can arise naturally from
internal variations within the atmosphere and the ocean and in the two-way
relationship “ coupling “ between them.
The millennial record of Figure 4.5 is particularly important because it pro-
vides an indication of the range and character of climate variability that arises
from natural causes. As we shall see in the next chapter, climate models also
provide some information on natural climate variability. Careful assessments
of these observational and model results con¬rm that natural variability (the
combination of internal variability and naturally forced, e.g. by volcanoes or
change in solar output) is very unlikely to explain the warming in the latter half
of the twentieth century.
82 C L I M AT E S O F T H E PA S T

Scientists in Antarctica use a hand drill to take 10-metre ice cores. Chemical analyses
of the cores will reveal changes in climate and the composition of the atmosphere.

The past million years
To go back before recorded human history, scientists have to rely on indirect
methods to unravel much of the story of the past climate. A particularly valu-
able information source is the record stored in the ice that caps Greenland and
the Antarctic continent. These ice caps are several thousands of metres thick.
Snow deposited on their surface gradually becomes compacted as further snow
falls, becoming solid ice. The ice moves steadily downwards, eventually ¬‚ow-
ing outwards at the bottom of the ice-sheet. Ice near the top of the layer will
have been deposited fairly recently; ice near the bottom will have fallen on the
surface many tens or hundreds of thousands of years ago. Analysis of the ice at
different levels can, therefore, provide information about the conditions pre-
vailing at different times in the past.
Deep cores have been drilled out of the ice at several locations in both Greenland
and Antarctica. At Russia™s Vostok station in east Antarctica, for instance, drilling
has been carried out for over 25 years. The longest and most recent core reached a
depth of over 3.5 km; the ice at the bottom of the hole fell as snow on the surface
of the Antarctic continent well over half a million years ago (Figure 4.6b).
Small bubbles of air are trapped within the ice. Analysis of the composition of
that air shows what was present in the atmosphere for the time at which the ice

Figure 4.6 (a) Variations over 700
the last 160 000 years of polar
CO2 in 2100
temperature and atmospheric (with business as usual)
carbon dioxide concentrations
derived from the Vostok ice core
from Antarctica. It is estimated
Double pre-industrial CO2
that the variation of global
average temperature is about

CO2 concentration (ppm)
half that in the polar regions.
Also shown is the current carbon Lowest possible CO2
stabilisation level by 2100
dioxide concentration of about
380 ppm and the likely rise during 400
CO2 now
the twenty-¬rst century under
Temperature difference from now (°C)

various projections of its growth.
(b) Variations of deuterium (δD), a
proxy for local temperature; ‚18O, 300
a proxy for global ice volume
¬‚uctuations; and the atmospheric
concentrations of CO2 and CH4
derived from air trapped within
ice cores from Antarctica. Shading
indicates interglacial periods.
160 120 80 40 Now
Time (thousands of years)

Benthic ( 18O)
Deuterium ( D)
300 CO2
CO2 (ppm)


CH4 (ppb)


“360 300
D (°)


“440 2.8


600 500 400 300 200 100 0
Time (before 2005)
84 C L I M AT E S O F T H E PA S T

Palaeoclimate reconstruction from isotope data
The isotope 18O is present in natural oxygen at a concentration of about 1 part in 500 compared with the
more abundant isotope 16O. When water evaporates, water containing the lighter isotope is more easily
vaporised, so that water vapour in the atmosphere contains less 18O compared with sea water. Similar
separation occurs in the process of condensation when ice crystals form in clouds. The amount of separ-
ation between the two oxygen isotopes in these processes depends on the temperatures at which evapor-
ation and condensation occur. Measurements on snowfall in different places can be used to calibrate the
method; it is found that the concentration of 18O varies by about 0.7 of a part per 1000 for each degree
of change in average temperature at the surface. Information is therefore available in the ice cores taken
from polar ice caps concerning the variation in atmospheric temperature in polar regions during the whole
period when the ice core was laid down.
Since the ice caps are formed from accumulated snowfall which contains less 18O compared with sea
water, the concentration of 18O in water from the oceans provides a measure of the total volume of the
ice in the ice caps; it changes by about 1 part in 1000 between the maximum ice extent of the ice ages
and the warm periods in between. Information about the 18O content of ocean water at different times is
locked up in corals and in cores of sediment taken from the ocean bottom, which contain carbonates from
fossils of plankton and small sea creatures from past centuries and millennia. Measurements of radioactive
isotopes, such as the carbon isotope 14C, and correlations with other signi¬cant past events enable the
corals and sediment cores to be dated. Since the separation between the oxygen isotopes which occurs as
these creatures are formed also depends on the temperature of the sea water (although the dependence is
weaker than the other dependencies considered above) information is also available about the distribution
of ocean surface temperature at different times in the past.

was formed “ gases such as carbon dioxide or methane. Dust particles that may
have come from volcanoes or from the sea surface are also contained within the
ice. Further information is provided by analysis of the ice itself. Small quantities
of different oxygen isotopes and of the heavy isotope of hydrogen (deuterium)
are contained in the ice. The ratios of these isotopes that are present depend
sensitively on the temperatures at which evaporation and condensation took
place for the water in the clouds from which the ice originated (see box). These
in turn are dependent on the average temperature near the surface of the Earth.
A temperature record for the polar regions can therefore be constructed from
analyses of the ice cores. The associated changes in global average temperature
are estimated to be about half the changes in the polar regions.
Such a reconstruction from a Vostok core for the temperature and the car-
bon dioxide content is shown in Figure 4.6a for the past 160 000 years, which
includes the last major ice age that began about 120 000 years ago and began
to come to an end about 20 000 years ago. Figure 4.6b extends the record to

650 000 years ago. The close connections that exist between temperature, car-
bon dioxide and methane concentrations are evident in Figure 4.6. Note also
from Figure 4.6 the likely growth of atmospheric carbon dioxide during the
twenty-¬rst century, taking it to levels that are unlikely to have been exceeded
during the past 20 million years.
Further information over the past million years is available from investiga-
tions of the composition of ocean sediments. Fossils of plankton and other small
sea creatures deposited in these sediments also contain different isotopes of oxy-
gen. In particular the amount of the heavier isotope of oxygen (18O) compared
with the more abundant isotope (16O) is sensitive both to the temperature at
which the fossils were formed and to the total volume of ice in the world™s ice
caps at the time of the fossils™ formation that is linked to the global sea level. For
instance, from such data it can be deduced that the sea level at the last glacial
maximum, 20 000 years ago, was about 120 m lower than today and that dur-
ing the last interglacial period, about 125 000 years ago, it was likely between
4 and 6 m higher than today due to some melting of the polar ice caps in both
Greenland and Antarctica.
From the variety of palaeoclimate data available, variations in the volume of
ice in the ice caps can be reconstructed over the greater part of the last million
years (Figures 4.6b, lower curve, and 4.7c). In this record six or seven major ice
ages can be identi¬ed with warmer periods in between, the period between
these major ice ages being approximately 100 000 years. Other cycles are also
evident in the record.
The most obvious place to look for the cause of regular cycles in climate is
outside the Earth, in the Sun™s radiation. Has this varied in the past in a cyclic
way? So far as is known the output of the Sun itself has not changed to any large
extent over the last million years or so. But because of variations in the Earth™s
orbit, the distribution of solar radiation has varied in a more or less regular way
during this period.
Three regular variations occur in the orbit of the Earth around the Sun
(Figure 4.7a). The Earth™s orbit, although nearly circular, is actually an ellipse.
The eccentricity of the ellipse (which is related to the ratio between the greatest
and the least diameters) varies with a period of about 100 000 years; that is the
slowest of the three variations. The Earth also spins on its own axis, the axis
of spin being tilted with respect to the axis of the Earth™s orbit, the angle of tilt
varying between 21.6° and 24.5° (currently it is 23.5°) with a period of about
41 000 years. The third variation is of the time of year when the Earth is closest
to the Sun (the Earth™s perihelion). The time of perihelion moves through the
months of the year with a period of about 23 000 years (see also Figure 5.19); in
the present con¬guration, the Earth is closest to the Sun in January.
86 C L I M AT E S O F T H E PA S T

Figure 4.7 Variations in the Earth™s
21.6 degrees orbit (a), in its eccentricity, the
orientation of its spin axis (between
24.5 degrees 21.6° and 24.5°) and the longitude
of perihelion (i.e. the time of year
Sun Earth
when the Earth is closest to the
Sun; see also Figure 5.19), cause
changes in the average amount of
summer sunshine (in millions of
joules per square metre per day)
near the poles (b). These changes
(b) (c)
appear as cycles in the climate
record in terms of the volume of ice
in the ice caps (c).


As the Earth™s orbit changes
its relationship to the Sun,
Thousands of years ago

although the total quantity of
solar radiation reaching the
Earth varies very little, the dis-

tribution of that radiation with
latitude and season over the
Earth™s surface changes consid-
erably. The changes are espe-
cially large in polar regions

where the variations in sum-
mer sunshine, for instance,
reach about 10% (Figure 4.7b).
2.2 2.4
James Croll, a British scientist,
Ice volume
Summer sunshine
¬ rst pointed out in 1867 that
the major ice ages of the past
might be linked with these regular variations in the seasonal distribution
of solar radiation reaching the Earth. His ideas were developed in 1920 by
Milutin Milankovitch, a climatologist from Yugoslavia, whose name is usu-
ally linked with the theory. Inspection by eye of the relationship between the
variations of polar summer sunshine and global ice volume shown in Figure
4.7 suggests a signi¬cant connection. Careful study of the correlation between
the two curves con¬ rms this and demonstrates that 60% of the variance in the
climatic record of global ice volume falls close to the three frequencies of regu-
lar variations in the Earth™s orbit, thus providing support for the Milankovitch

More careful study of the relationship between the ice ages and the Earth™s
orbital variations shows that the size of the climate changes is larger than might
be expected from forcing by the radiation changes alone. Other processes that
enhance the effect of the radiation changes (in other words, positive feedback
processes) have to be introduced to explain the climate variations. One such
feedback arises from the changes in carbon dioxide in¬‚uencing atmospheric
temperature through the greenhouse effect, illustrated by the strong correla-
tion observed in the climatic record between average atmospheric temperature
and carbon dioxide concentration (Figure 4.6). Such a correlation does not, of
course, prove the existence of the greenhouse feedback; in fact part of the cor-
relation arises because the atmospheric carbon dioxide concentration is itself
in¬‚uenced, through biological feedbacks (see Chapter 3), by factors related to
the average global temperature.5 Further, since Antarctic temperature started
to rise several centuries before atmospheric carbon dioxide during past glacial
terminations, it is clear that carbon dioxide variations have not provided the
trigger for the end of glacial periods. However, as we shall see in Chapter 5,
climates of the past cannot be modelled successfully without taking the green-
house feedback into account.6
An obvious question to ask is when, on the Milankovitch theory, is the next
ice age due? It so happens that we are currently in a period of relatively small
solar radiation variations and the best projections for the long term are of a
longer than normal interglacial period leading to the beginning of a new ice age
perhaps in 50 000 years™ time.7

How stable has past climate been?
The major climate changes considered so far in this chapter have taken place
relatively slowly. The growth and recession of the large polar ice-sheets between
the ice ages and the intervening warmer interglacial periods have taken on
average many thousands of years. However, the ice core records such as those in
Figures 4.6 and 4.8 show evidence of large and relatively rapid ¬‚uctuations. Ice
cores from Greenland provide more detailed evidence of these than those from
Antarctica. This is because at the summit of the Greenland ice cap, the rate of
accumulation of snow has been higher than that at the Antarctica drilling loca-
tions. For a given period in the past, the relevant part of the Greenland ice core
is longer and more detail of variations over relatively short periods is therefore
The data show that the last 8000 years have been unusually stable com-
pared with earlier epochs. In fact, as judged from the Vostok (Figure 4.6) and
the Greenland records (Figure 4.8) this long stable period in the Holocene is a
88 C L I M AT E S O F T H E PA S T

Figure 4.8 Variations in Arctic temperature over the past 100 000 years as
Present 0
day deduced from oxygen isotope measurements (in terms of d18O) from the
˜Summit™ ice core in Greenland. The quantity d18O plotted in Figures 4.6 and
Time (thousands of years before present)

4.7 is the difference (in parts per thousand) between the 18O/16O ratio in
the sample and the same ratio in a laboratory standard. The overall shape
of the record is similar to that from the Vostok ice core shown in Figure 4.6
but much more detail is apparent in the ˜Summit™ record™s stable period over
the last 8000 years. A change of 5 parts per 1000 in d18O in the ice core
corresponds to about a 7 °C change in temperature.

unique feature of climate during the past 420 000 years. It has been
suggested that this had profound implications for the development
of civilisations.8 Model simulations (see Chapter 5) indicate that the
detail of long-term changes during the Holocene is consistent with
the in¬‚uence of orbital forcing (Figure 4.7). For instance, some north-
“ 45 “ 40 “ 35
ern hemisphere glaciers retreated between 11 000 and 5000 years ago
and were smaller during the later part of this period than they are
today. The present-day glacier retreat cannot be attributed to the same natural
causes as the decrease in summer insolation due to orbital forcing during the
past few millennia has tended to glacier increase.
It is also interesting to inspect the rate of temperature change during the
recovery period from the last glacial maximum about 20 000 years ago and com-
pare it with recent temperature changes. The data indicate an average warming
rate of about 0.2 °C per century between 20 000 and 10 000 years before present
(BP) over Greenland, with lower rates for other regions. Compare this with a
temperature rise during the twentieth century of about 0.6 °C and the rates
of change of a few degrees Celsius per century projected to occur during the
twenty-¬rst century because of human activities (see Chapter 6).
The ice core data (Figure 4.8) demonstrate that a series of rapid warm and cold
oscillations called Dansgaard“Oeschger events punctuated the last glaciation.
Comparison between the results from ice cores drilled at different locations
within the Greenland ice cap con¬rm the details up to about 100 000 years ago.
Comparison with data from Antarctica suggests that the ¬‚uctuations of tem-
perature over Greenland (perhaps up to 16 °C) have been larger than those over
Antarctica. Similar large and relatively rapid variations are evident from North
Atlantic deep sea sediment cores.
Another particularly interesting period of climatic history, more recently, is
the Younger Dryas event (so called because it was marked by the spread of an
arctic ¬‚ower, Dryas octopetala), which occurred over a period of about 1500 years
between about 12 000 and 10 700 years ago. For 6000 years before the start of
this event the Earth had been warming up after the end of the last ice age. But

“35 “30
“38 “36 “34 “32 “30 “28 °

8500 yrs BP
Deep ice core

9000 yrs BP

9500 yrs BP
Lake Gerzen sediments
“10 “8 “6°

˜50 yrs
Depth of sediment (m)

1 1786
10 700 yrs BP

Younger Dryas
1800 7 °C


Younger Dryas

Depth of
ice core (m) 1850

Figure 4.9 Records of the variations of the oxygen isotope d18O from lake sediments from
Lake Gerzen in Switzerland and from the Greenland ice core ˜Dye 3™ showing the Younger
Dryas event and its rapid end about 10 700 years ago. Dating of the ice core was by counting
the annual layers down from the surface; dating of the lake sediment was by the 14C method.
A change of 5 parts per 1000 in d18O in the ice core corresponds to about a 7 °C change in

then during the Younger Dryas period, as demonstrated from many different
sources of palaeoclimatic data, the climate swung back again into much colder
conditions similar to those at the end of the last ice age (Figure 4.9). The ice core
record shows that at the end of the event, 10 700 years ago, the warming in the
Arctic of about 7 °C occurred over only about 50 years and was associated with
decreased storminess (shown by a dramatic fall in the amount of dust in the ice
core) and an increase in precipitation of about 50%.
Two main reasons for these rapid variations in the past have been suggested.
One reason particularly applicable to ice age conditions is that, as the ice-
sheets over Greenland and eastern Canada have built up, major break-ups have
occurred from time to time, releasing massive numbers of icebergs into the
North Atlantic in what are called Heinrich events. The second possibility is that
the ocean circulation in the North Atlantic region has been strongly affected
by injections of fresh water from the melting of ice. At present the ocean circu-
lation in this region is strongly in¬‚uenced by cold salty water sinking to deep
ocean levels because its saltiness makes it dense; this sinking process is part of
90 C L I M AT E S O F T H E PA S T

the ˜conveyor belt™ which is the major feature of the circulation of deep ocean
water around the world (see Figure 5.18). Large quantities of fresh water from
the melting of ice would make the water less salty, preventing it from sinking
and thereby altering the whole Atlantic circulation.
This link between the melting of ice and the ocean circulation is a key feature
of the explanation put forward by Professor Wallace Broecker for the Younger
Dryas event.9 As the great ice-sheet over North America began to melt at the
end of the last ice age, the melt water at ¬rst drained through the Mississippi
into the Gulf of Mexico. Eventually, however, the retreat of the ice opened up a
channel for the water in the region of the St Lawrence River. This in¬‚ux of fresh
water into the North Atlantic reduced its saltiness, thus, Broecker postulates,
cutting off the formation of deep water and that part of the ocean ˜conveyor
belt™.10 Warm water was therefore prevented from ¬‚owing northward, resulting
in a reversal to much colder conditions. The suggestion is also that a reversal of
this process with the starting up of the Atlantic ˜conveyor belt™ could lead to a
sudden onset of warmer conditions.
Although debate continues regarding the details of the Younger Dryas event,
there is considerable evidence from palaeodata, especially those from ocean
sediments, for the main elements of the Broecker explanation which involve
the deep ocean circulation. It is also clear from palaeodata that large changes
have occurred at different times in the past in the formation of deep water
and in the deep ocean circulation. Chapter 3 mentioned the possibility of such
changes being induced by global warming through the growth of greenhouse
gas concentrations. Our perspective regarding the possibilities of future cli-
mate change needs to take into account the rapid climate changes that have
occurred in the past.


In this chapter we have learnt that:
• Records of temperature, atmospheric composition and sea level from ice
cores from Greenland and Antarctica, from ocean and lake sediment cores
and other proxy records have provided a wealth of information about past
climates over much of the past million years.
• The current levels of carbon dioxide and methane concentrations in the
atmosphere and their rate of increase is unprecedented in the palaeoclimate
record over the last half million years and probably for much longer.

• It is likely that the 50-year period of the second half of the twentieth cen-
tury was the warmest northern hemisphere period in the last 1300 years.
• It is very likely that the warming of 4 to 7 °C since the last glacial maximum
18 000 years ago occurred at an average rate about ten times slower than
the warming of the twentieth century.
• The main trigger mechanism for the series of ice ages over the last million
years or more has been the variations in the distribution of solar radia-
tion especially in the polar regions arising from the regular variations in
parameters of the Earth™s orbit around the Sun “ called Milankovitch cycles.
Variations in greenhouse gases have served to add a positive feedback to
this forcing. These orbital variations are well understood and the next ice
age is not expected to begin for at least 30 000 years.
• For the ¬rst half of the last interglacial period (∼130 000“123 000 years
ago), a large increase in summer solar radiation due to orbital forcing led to
higher temperatures in polar regions 3 to 5 °C warmer than today and melt-
ing in polar regions that led to 4 to 6 metres higher sea level than today.
• Some of the abrupt events during the last 100 000 years that have been
identi¬ed in the records from ice core and other data may have been asso-
ciated with large fresh water inputs into the ocean due for instance to large
ice discharges that resulted in large-scale changes to the ocean circulation.
Having now in these early chapters set the scene, by describing the basic
science of global warming, the greenhouse gases and their origins and the
current state of knowledge regarding past climates, I move on in the next
chapter to describe how, through computer models of the climate, predictions
can be made about what climate change can be expected in the future.

1 Given that the sea level at the end of the last glacial maximum was 120 m
lower than that today, estimate the volume of ice in the ice-sheets that
covered the northern parts of the American and Eurasian continents.
2 How much energy would be required to melt the volume of ice you
have calculated in Question 1? Compare this with the extra summer
sunshine north of latitude 60° which might have been available between
18 000 and 6000 years before the present according to the data in
Figure 4.7. Does your answer support the Milankovitch theory?
92 C L I M AT E S O F T H E PA S T

3 It is sometimes suggested that the large reserves of fossil fuels on Earth
should be preserved until the onset of the next ice age is closer so that some
of its impact can be postponed. From what you know of the greenhouse
effect and of the behaviour of carbon dioxide in the atmosphere and the
oceans, consider the in¬‚uences that human burning of the known reserves of
fossil fuels (see Figure 11.2) could have on the onset of the next ice age.

James Hansen et al., Climate Change and Trace Gases, Phil. Trans. R. Soc.A (2007),
365, 1925“1954. Summarises in¬‚uence of greenhouse gases on paleoclimates of
different epochs.
Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, R. B., Tignor, M.,
Miller, H. L. (eds.) 2007. Climate Change 2007: The Physical Science Basis.
Contribution of Working Group I to the Fourth Assessment Report of the
Intergovernmental Panel on Climate Change. Cambridge: Cambridge University Press.
Technical Summary (summarises basic information about greenhouse gases and
observations of the present and past climates)
Chapter 3 Observations: Surface and atmospheric climate change
Chapter 4 Observations: Changes in snow, ice and frozen ground
Chapter 5 Observations: Oceanic climate change and sea level
Chapter 6 Palaeoclimate

in Solomon et al. (eds.) Climate Change 2007: The
1 In Solomon, S. et al, (eds.) Climate Change 2007: The
Physical Science Basis.
Physical Science Basis expressions of certainty such as
6 See, for instance, James Hansen, Bjerknes
very likely were related so far as possible to quantita-
Lecture at American Geophysical Union, 17
tive statements of con¬dence as follows: virtually
December 2008 at www.columbia.edu/njeh1/2008/
certain >99% probability of occurrence, extremely
likely >95%, very likely >90%, likely >66%, more likely
7 Berger, A., Loutre, M. F. 2002. Science, 297, 1287“8.
than not >50%, unlikely <33%, very unlikely <10%,
The IPCC 2007 Report states that ˜it is very unlikely
extremely unlikely <5%. When these ˜likely™ words,
that the Earth would naturally enter another ice age
employed in this way, appear in the text they are
for at least 30,000 years™. (Chapter 6 Summary, in
Solomon et al. (eds.) Climate Change 2007: The Physical
2 Smith, D. M. et al., 2007. Science, 317, 796“9.
Science Basis).
3 See, for instance, Crowley, T. J. 2000. Causes of
8 Petit, J. R. et al. 1999. Nature, 399, 429“36.
climate change over the past 1000 years. Science,
9 Broecker, W. S., Denton, G. H. 1990. What drives
289, 270“7.
glacial cycles? Scienti¬c American, 262, 43“50.
4 Raymo, M. E., Huybers, P. 2008. Nature, 451, 284“5.
10 More information in Chapter 5, see especially
5 For a discussion of what caused the low CO2 concen-
Figure 5.18.
trations during glacial times see Box 6.2, Chapter 6,
Modelling the climate

This supercell thunderstorm (the largest and most severe class of thunderstorm) caused widespread damage
in northwest Colorado, June 2006.

C HAPTER 2 looked at the greenhouse effect in terms of a simple radiation balance. That gave
an estimate of the rise in the average temperature at the surface of the Earth as greenhouse
gases increase. But any change in climate will not be distributed uniformly everywhere; the climate
system is much more complicated than that. More detail in climate change prediction requires very
much more elaborate calculations using computers. The problem is so vast that the fastest and largest
computers available are needed. But before computers can be set to work on the calculation, a model
of the climate must be set up for them to use. A model of the weather as used for weather forecasting
will be used to explain what is meant by a numerical model on a computer, followed by a description
of the increase in elaboration required to include all parts of the climate system in the model.
94 M O D E L L I N G T H E C L I M AT E

Modelling the weather
An English mathematician, Lewis Fry Richardson, set up the ¬rst numerical
model of the weather. During his spare moments while working for the Friends™
Ambulance Unit (he was a Quaker) in France during the First World War he car-
ried out the ¬rst numerical weather forecast. With much painstaking calculation
with his slide rule, he solved the appropriate
equations and produced a six-hour forecast. It
took him six months “ and then it was not a very
good result. But his basic methods, described
in a book published in 1922,1 were correct. To
apply his methods to real forecasts, Richardson
imagined the possibility of a very large concert
hall ¬lled with people, each person carrying
out part of the calculation, so that the integra-
tion of the numerical model could keep up with
the weather. But he was many years before his
time! It was not until some forty years later
that, essentially using Richardson™s methods,
the ¬rst operational weather forecast was pro-
duced on an electronic computer. Computers
more than one trillion times faster than the
one used for that ¬rst forecast (Figure 5.1) now
run the numerical models that are the basis of
all weather forecasts.
Numerical models of the weather and the
climate are based on the fundamental math-
ematical equations that describe the physics
Lewis Fry Richardson (11 October 1881“30
and dynamics of the movements and processes
September 1953).
taking place in the atmosphere, the ocean, the
ice and on the land. Although they include
empirical information, they are not based to any large degree on empirical
relationships “ unlike numerical models of many other systems, for instance in
the social sciences.
Setting up a model of the atmosphere for a weather forecast (see Figure 5.2)
requires a mathematical description of the way in which energy from the Sun
enters the atmosphere from above, some being re¬‚ected by the surface or by clouds
and some being absorbed at the surface or in the atmosphere (see Figure 2.7). The
exchange of energy and water vapour between the atmosphere and the surface
must also be described.

100 T = 10 to power 14 Earth Simulator
10 T
Cray T3E NEC SX6
100 G
Cray C916
10 G
Peak performance (FLOPS)

ETA 10
Cray YMP 8
Cyber 205
100 M

10 M
IBM 360/195

100 K
10 K

1950 1960 1970 1980 1990 2000
Year of first use

Figure 5.1 The growth of computer power available at major forecasting centres.
The computers are those used by the UK Met Of¬ce for numerical weather prediction
research, since 1965 for operational weather forecasting and most recently for
research into climate prediction. Richardson™s dream computer of a large ˜human™
computer mentioned at the beginning of the chapter would possess a performance of
perhaps 500 FLOPS (¬‚oating point operations per second). The largest computer on
which meteorological or climate models are run in 2007 is the Earth Simulator in Japan.
The straight line illustrates a rate of increase in performance of a factor of 10 every
¬ve years.

Figure 5.2 Schematic illustrating Solar Thermal
radiation radiation
the parameters and physical
processes involved in atmospheric
Top of atmosphere

Density depends on temperature and pressure
Motion horizontal and vertical

Composition water vapour, carbon dioxide,
clouds, etc.


Surface exchange of heat, momentum (friction)
and water vapour
96 M O D E L L I N G T H E C L I M AT E

˜500 km ˜500 km
(a) (b)

Figure 5.3 Illustration of the horizontal model grid over Europe as in a typical global climate model (a) in 1990
employed for the IPCC 1st Assessment Report and (b) in 2007 as employed for the IPCC 4th Assessment
Report. Note the large improvement from the coarse grid of 1990.

Water vapour is important because of its associated latent heat (in other words,
it gives out heat when it condenses) and also because the condensation of water
vapour results in cloud formation, which modi¬es substantially the interaction
of the atmosphere with the incoming energy from the Sun. Variations in both
these energy inputs modify the atmospheric temperature structure, causing
changes in atmospheric density (since warmed gases expand and are therefore
less dense). It is these density changes that drive atmospheric motions such as
winds and air currents, which in their turn alter and feed back on atmospheric
density and composition. More details of the model formulation are given in
the box below.
To forecast the weather for several days ahead a model covering the whole
globe is required; for example, the southern hemisphere circulation today will
affect northern hemisphere weather within a few days and vice versa. In a glo-
bal forecasting model, the parameters (i.e. pressure, temperature, humidity,
wind velocity and so on) that are needed to describe the dynamics and physics
(listed in the box below) are speci¬ed at a grid of points (Figure 5.3) covering
the globe. A typical spacing between points in the horizontal would be 100 km
and about 1 km in the vertical; typically there would be 20 or 30 levels in the
model in the vertical. The ¬neness of the spacing is limited by the power of the
computers available.
Having set up the model, to generate a forecast from the present, it is started
off from the atmosphere™s current state and then the equations are integrated
forward in time (see box below) to provide new descriptions of the atmospheric
circulation and structure up to six or more days ahead. For a description of the
atmosphere™s current state, data from a wide variety of sources (see box below)
have to be brought together and fed into the model.

Setting up a numerical atmospheric model
A numerical model of the atmosphere contains descriptions, in appropriate computer form and with nec-
essary approximations, of the basic dynamics and physics of the different components of the atmosphere
and their interactions.2 When a physical process is described in terms of an algorithm (a process of step-
by-step calculation) and simple parameters (the quantities that are included in a mathematical equation),
the process is said to have been parameterised.
The dynamical equations are:

• The horizontal momentum equations (Newton™s Second Law of Motion). In these, the horizontal accel-
eration of a volume of air is balanced by the horizontal pressure gradient and the friction. Because the
Earth is rotating, this acceleration includes the Coriolis acceleration. The ˜friction™ in the model mainly
arises from motions smaller than the grid spacing, which have to be parameterised.
• The hydrostatic equation. The pressure at a point is given by the mass of the atmosphere above that
point. Vertical accelerations are neglected.
• The continuity equation. This ensures conservation of mass.

The model™s physics consists of:

• The equation of state. This connects the quantities of pressure, volume and temperature for the
• The thermodynamic equation (the law of conservation of energy).
• Parameterisation of moist processes (such as evaporation, condensation, formation and dispersal of
• Parameterisation of absorption, emission and re¬‚ection of solar radiation and of thermal radiation.
• Parameterisation of convective processes.
• Parameterisation of exchange of momentum (in other words, friction), heat and water vapour at the

Most of the equations in the model are differential equations, which means they describe the way in
which quantities such as pressure and wind velocity change with time and with location. If the rate of
change of a quantity such as wind velocity and its value at a given time are known, then its value at a later
time can be calculated. Constant repetition of this procedure is called integration. Integration of the equa-
tions is the process whereby new values of all necessary quantities are calculated at later times, providing
the model™s predictive powers.

Since computer models for weather forecasting were ¬rst introduced,
their forecast skill has improved to an extent beyond any envisaged by those
involved in the development of the early models. As improvements have
been made in the model formulation, in the accuracy or coverage of the data
98 M O D E L L I N G T H E C L I M AT E

Data to initialise the model
At a major global weather forecasting centre, data from many sources are collected and fed into the
model. This process is called initialisation. Figure 5.4 illustrates some of the sources of data for the forecast

150°W 120°W 90°W 60°W 30°W 0° 60°E 90°E 120°E 150°E





Surface Observations (23158)





Satellite soundings (33640)

Figure 5.4 Some of the sources of data for input into the UK Met Of¬ce global weather forecasting model on a
typical day. Surface observations are from land observing stations (manned and unmanned), from ships and from
buoys. Radiosonde balloons make observations at up to 30 km altitude from land and from ship-borne stations.
Satellite soundings are of temperature and humidity at different atmospheric levels deduced from observations
of infrared or microwave radiation. Satellite cloud-track winds are derived from observing the motion of clouds in
images from geostationary satellites. The number of observations of each type is given in brackets.

beginning at 0000 hours Universal Time (UT) on 20 May 2008. To ensure the timely
receipt of data from around the world a dedicated communication network has been
set up, used solely for this purpose. Great care needs to be taken with the methods
for assimilation of the data into the model as well as with the data™s quality and

150°W 120°W 90°W 60°W 30°W 30°E 60°E 90°E 120°E 150°E





Radiosonde balloons (1586)





Satellite cloud-track winds (7779)

Figure 5.4 Continued
100 M O D E L L I N G T H E C L I M AT E



Root mean square forecast error

Persistence (T + 72)

(T + 72)
(T + 48)
(T + 24)





1970 1975 1980 1985 1990 1995 2000 2005
Figure 5.5 Errors (root mean square differences of forecasts of surface pressure in
hPa compared with analyses) of UK Met Of¬ce forecasting models for the north
Atlantic and Western Europe since 1966 for 24-hour (blue), 48-hour (green) and
72-hour (red) forecasts compared with assuming no change (purple). Note that
1 hPa = 1 mbar.

used for initialisation (see box) or in the resolution of the model (the distance
between grid points), the resulting forecast skill has increased. For instance,
for the British Isles, three-day forecasts of surface pressure today are as skil-
ful on average as two-day forecasts of ten years ago, as can be seen from
Figure 5.5.
When looking at the continued improvement in weather forecasts, the ques-
tion obviously arises as to whether the improvement will continue or whether
there is a limit to the predictability we can expect. Because the atmosphere is
a partially chaotic system (see box below), even if perfect observations of the
atmospheric state and circulation could be provided, there would be a limit
to our ability to forecast the detailed state of the atmosphere at some time in
the future. In Figure 5.6 current forecast skill is compared with the best esti-
mate of the limit of the forecast skill for the British Isles (similar results would
be obtained with any other mid latitude situation) with a perfect model and
near-perfect data. According to that estimate, the limit of signi¬cant future
skill is about 20 days ahead.

Figure 5.6 Potential improvements in forecast skill 200

if there were better data or a better model. The

Measure of forecast error
ordinate (vertical axis) is a measure of the error of
model forecasts (it is the root mean square
differences of forecasts of the 500 hPa height ¬eld
compared with analyses). Curve (a) is the error of 100
1990 UK Met Of¬ce forecasts as a function of (b)
forecast range. Curve (b) is an estimate showing (c)
how, with the same initial data, the error would be
reduced if a perfect model could be used. Curve
(c) is an estimate showing the further improvement 0
which might be expected if near-perfect data could 0 10 20 30
Forecast range (days)
be provided for the initial state. After a suf¬ciently
long period, all the curves approach a saturation
value of the average root mean square difference
between any forecasts chosen at random.

Forecast skill varies considerably between different weather situations or
patterns. In other words some situations are more ˜chaotic™ (in the technical
sense in which that word is used “ see box below) than others. One way of
identifying the skill that might be achieved in a given situation is to employ
ensemble forecasting in which an ensemble of forecasts is run from a cluster of
initial states that are generated by adding to an initial state small perturbations
that are within the range of observational or analysis errors. The forecasts pro-
vided from the means of such ensembles show signi¬cant improvement com-
pared with individual forecasts. Further, ensemble forecasts where the spread
amongst the ensemble is low possess more skill than those where the spread in
the ensemble is comparatively high (Figure 5.8).3

Seasonal forecasting
So far short-term forecasts of detailed weather have been considered. After 20
days or so they run out of skill. What about further into the future? Although
we cannot expect to forecast the weather in detail, is there any possibility of
predicting the average weather, say, a few months ahead? As this section shows,
it is possible for some parts of the world, because of the in¬‚uence of the distri-
bution of ocean surface temperatures on the atmosphere™s behaviour. For sea-
sonal forecasting it is no longer the initial state of the atmosphere about which
detailed knowledge is required. Rather, we need to know the conditions at the
surface and how they might be changing.
102 M O D E L L I N G T H E C L I M AT E

Weather forecasting and chaos
The science of chaos has developed rapidly since the 1960s (when a meteorologist, Edward Lorenz, was
one of its pioneers) along with the power of electronic computers. In this context, chaos4 is a term with
a particular technical meaning (see Glossary). A chaotic system is one whose behaviour is so highly sensi-
tive to the initial conditions from which it started that precise future prediction is not possible. Even quite
simple systems can exhibit chaos under some conditions. For instance, the motion of a simple pendulum
(Figure 5.7) can be ˜chaotic™ under some circumstances, and, because of its extreme sensitivity to small
disturbances, its detailed motion is not then predictable.
A condition for chaotic behaviour is that the relationship between the quantities which govern the motion of
the system be non-linear; in other words, a description of the relationship on a graph would be a curve rather
than a straight line.5 Since the appropriate relationships for the atmosphere are non-linear it can be expected
to show chaotic behaviour. This is illustrated in Figure 5.6, which shows the improvement in predictability that
can be expected if the data describing the initial state are improved. However, even with virtually perfect initial
data, the predictability in terms of days ahead only moves from about six days to about 20 days, because the
atmosphere is a chaotic system.
For the simple pendulum not all situations are chaotic (Figure 5.7). Not surprisingly, therefore, in a sys-
tem as complex as the atmosphere, some occasions are more predictable than others. A good illustration
of an occasion with particular sensitivity to the initial data is provided by the exceptionally severe storm
Lothar that crossed northern France in December 1999. It blew down hundreds of millions of trees and led
to economic losses estimated at over 5 billion euros. Figure 5.8 shows an ensemble of forecasts carried out

w (b) (c)
Forcing frequency w

frequency wo)
“2.5 0 2.5 “2.5 0 2.5
w x w
Chaotic w = 0.99766 wo
Stable w =1.00088 wo

Figure 5.7 (a) A simple pendulum consisting of a bob at the end of a string of length 10 cm
attached to a point of suspension which is moved with a linear oscillatory forcing motion at
frequencies near the pendulum™s resonance frequency f0. (b) and (c) show plots of the bob™s
motion on a horizontal plane, the scale being in centimetres. (b) For a forcing frequency just
above f0 the motion of the bob settles down to a simple, regular pattern. (c) For a forcing
frequency just below f0 the bob shows ˜chaotic™ motion (although contained within a given
region) which varies randomly and discontinuously as a function of the initial conditions.

by the European Centre for Medium Range Forecasting (ECMWF) starting from a set of slightly varying
initial conditions 42 hours earlier.6 The best-guidance deterministic forecast only predicts a weak trough in
surface pressure which is supported by a number of members of the ensemble. However, a minority of the
ensemble members show an intense vortex over France similar to what actually occurred, demonstrating
the value of the ensemble in its prediction of the risk of the severe event even though a precise determin-
istic forecast was not possible. It is interesting that more recent deterministic reforecasts with an improved
model have failed to predict this storm.

Deterministic predictions Verification


Forecast 1 Forecast 2 Forecast 3 Forecast 4 Forecast 5 Forecast 6 Forecast 7 Forecast 8 Forecast 9 Forecast 10
99 L

Forecast 11 Forecast 12 Forecast 13 Forecast 14 Forecast 15 Forecast 16 Forecast 17 Forecast 18 Forecast 19 Forecast 20


Forecast 21 Forecast 22 Forecast 23 Forecast 24 Forecast 25 Forecast 26 Forecast 27 Forecast 28 Forecast 29 Forecast 30

Forecast 31 Forecast 32 Forecast 33 Forecast 34 Forecast 35 Forecast 36 Forecast 37 Forecast 38 Forecast 39 Forecast 40

Forecast 41 Forecast 42 Forecast 43 Forecast 44 Forecast 45 Forecast 46 Forecast 47 Forecast 48 Forecast 49 Forecast 50


Figure 5.8 Isopleths of surface pressure from a 51-member ensemble forecast by the European Centre for
Medium Range Forecasting (ECMWF) of the storm Lothar based on initial conditions 42 hours before the
storm crossed northern France on 26 December 1999. The isobars are 5 mb apart and the thicker 1000 mb
isobar runs across the middle of the ¬gures. The top left shows forecasts made from the best estimate of
the initial conditions that did not indicate the presence of a severe storm. Nor did many members of the
ensemble. However, some of the ensemble members show an intense vortex indicating signi¬cant risk of its
occurrence. The top right shows the situation at the end of the forecast period.
Around Christmas 1999, storm front Lothar raced across France, Switzerland and Germany, and 100 people
died. (Also see Figure 5.8).

Figure 5.9 Monthly values of
the Southern Oscillation Index
2 (SOI) based on normalised Tahiti
minus Darwin sea level pres-
Standard deviations

1 sures. An 11-point low pass ¬lter
effectively removes ¬‚uctuations
with periods of less than eight
months. The thick black line rep-
resents a decadal ¬lter. Negative
values indicate positive sea level
pressure anomalies at Darwin
and thus El Ni±o conditions.
1860 1890 1920 1950 1980

In the tropics, the atmosphere is particularly sensitive to sea surface tem-
perature. This is not surprising because the largest contribution to the heat
input to the atmosphere is due to evaporation of water vapour from the ocean
surface and its subsequent condensation in the atmosphere, releasing its latent
heat. Because the saturation water vapour pressure increases rapidly with

A simple model of the El Ni±o
El Ni±o events are good exam- N
ples of the strong coupling which
occurs between the circulations
of ocean and atmosphere. The
stress exerted by atmospheric Equator Kelvin wave


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