Wallace J.M., Hobbs P.V. Atmospheric Science. An Introductory Survey

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454 Climate Dynamics

interval increases beyond the lifetime of the gas, the

GWP drops.

In addition to the direct GWP listed in Table 10.1,

each gas can be assigned an indirect GWP that

describes the radiative forcing due to changes in the

concentrations of other greenhouse gases or aerosols

induced by a small incremental increase in its con-

centration. For example, the injection of methane

into the atmosphere enhances the formation of tro-

pospheric ozone, thereby inducing an indirect warm-

ing amounting to 25% of the direct warming due to

the increase in methane itself.

Figure 10.42 shows the contributions of various

atmospheric constituents to the radiative forcing

at the top of the atmosphere, as defined in the

previous section, for the year 2000, relative to con-

ditions prior to the industrial revolution. Hence,

these values may be viewed as the contributions of

these constituents to the current human-induced

greenhouse effect. The left-most bar in Fig. 10.42

shows the contributions of greenhouse gases. The

combined warming due to CH

O and CFCs and

tropospheric ozone is roughly equivalent to that of

emissions. The contribution from stratospheric

ozone is negative because human activity has

resulted in decreased concentrations of stratos-

pheric ozone.

Also shown in Fig. 10.42 are estimates of the

contributions from aerosols to the human-induced

climate forcing. Sulfate aerosols cool because they

are highly reflective, whereas black carbon (soot)

has the opposing effect. The large and highly uncer-

tain aerosol indirect effect represents the effects of

increasing concentrations of aerosols upon the

properties of clouds. Visual evidence of the whiten-

ing of stratus cloud decks by the exhaust plumes

from the engines of ships (Fig. 6.9) has fueled spec-

ulation that emissions of cloud condensation nuclei

from power plants, aviation, biomass burning, and

other human activities might be affecting surface

air temperature indirectly by changing the optical

properties of low clouds andor by increasing their

areal coverage.

There are several ways in which aerosols could

conceivably affect the optical properties of clouds.

Greater numbers of cloud droplets competing for the

same amount of cloud water result in larger numbers

of smaller droplets, which favor more reflective

clouds. In contrast, carbon (soot) particles injected

into the atmosphere by human activities tend to

increase the absorptivity of clouds, thereby reducing

the fraction of the incident solar radiation that is

backscattered to space.

The aerosol indirect effect is believed to be

negative and potentially quite important, but its

magnitude is highly uncertain. Whether it is or is

not an important factor in the human-induced

radiative forcing has important implications for

estimates of climate sensitivity, as demonstrated in

Exercise 10.26.

Table 10.1 Greenhouse warming potentials for selected

greenhouse gases for 20, 100, and 500-year time intervals

Radiative Lifetime

Gas efficiency (year) GWP

GWP

100

GWP

500

0.0155 — 1 1 1

0.37 12 62 23 7

3.1 114 275 296 156

CFC-12 320 100 10200 10600 5200

HCFC-21 170 2 700 210 65

Radiative efficiency is expressed in W m

2

ppmv

1

. [Adapted from Inter-

governmental Panel on Climate Change, Climate Change 2001: The Scientific Basis,

Cambridge University Press, pp. 388–389 (2001).]

Fig. 10.42 Radiative forcing at the top of the atmosphere

due to the human-induced incremental change in atmos-

pheric concentrations of various species of trace gases

and aerosols based on present concentrations minus pre-

industrial concentrations. [Adapted from Intergovernmental

Panel on Climate Change, Climate Change 2001: The Scientific

Basis, Cambridge University Press, p. 8 (2001).]

Radiative forcing (W m

–2

)

Halocarbons

N O

Tropospheric

ozone

Stratospheric

ozone

Sulfate

Organic

carbon

from

fossil

fuel

burning

Biomass

burning

Aerosol

indirect

effect

Mineral

Dust

Black

carbon from

fossil fuel

burning

Aerosols

–1

–2

–3

P732951-Ch10.qxd 12/09/2005 09:12 PM Page 454

10.4 Greenhouse Warming 455

Condensation trails (contrails for short) are cloud-

like streamers that can form behind aircraft in

cold, humid air (Fig. 10.43). They are produced by

water vapor and cloud condensation nuclei (CCN)

from aircraft engines. Due to the large concentra-

tion of CCN in engine exhausts, recently formed

contrails contain large concentrations of small

droplets. Therefore, as in the case of continental

clouds discussed in Section 6.2, the boundaries of

recently formed contrails are usually well defined

(e.g., the brighter contrail in the center of the

photo). However, as a contrail ages and becomes

glaciated, the ice particles survive longer than

droplets as they mix with the surrounding subsatu-

rated air. Consequently, the boundaries of older

contrails are more diffuse, like the other contrails

in the photo.

In the vicinity of large airports, contrails can be

very numerous and may spread out to cover large

areas of the sky. Because contrails can reduce the

transfer of both incoming solar radiation and

outgoing infrared radiation, they have the poten-

tial to reduce the diurnal temperature range.

Following the terrorist attack on the Twin Towers

in New York City on 11 September 2001, all com-

mercial aircraft flights in the United States were

10.3 Evidence of an Indirect Aerosol Effect

Fig. 10.43 Condensation trails. [Photograph courtesy

of Art Rangno.]

stopped for 3 days. During this period there was

an statistically significant increase of 1.1 °C in the

average diurnal temperature range for ground

stations across the United States, relative to the

climatological mean.

Atmospheric concentrations of methane, tropo-

spheric ozone and CFCs respond much more rapidly

to changes in source strength than does CO

.Policy

decisions relating to the emissions of these gases

could substantially slow the rate of greenhouse

warming over the next 50 years. Restrictions man-

dated by the Montreal Protocol have already halted

the rapid buildup of CFCs; changes in land use and

oil extraction practices could potentially reduce

methane emissions, and tighter air pollution stan-

dards could reduce tropospheric ozone.

10.4.2 Is Human-Induced Greenhouse

Warming Already Evident?

The 20th century was marked by warming that is

reflected in records of surface air temperature over

both land and ocean, as shown in Fig. 10.44, in the heat

content of the upper oceans, in the retreat of moun-

tain glaciers (Fig. 10.45), the rise in global sea level

(Fig. 10.46), and in a variety of other indicators such as

melt and freeze dates on lakes and rivers, blooming

dates of flowering plants, timing of bird migrations,

and the poleward extent of plant, insect, and animal

species. To the extent that proxy evidence reflects the

true temperature trends during previous centuries, the

rate of warming observed during the 20th century

appears to be unprecedented in the past millennium.

The warming observed during the 20th century

was not uniform either in time or in space. The pro-

nounced warming of the 1920s and 1930s followed

by flattening of the temperature trace around

the middle of the century, shown in Fig. 10.44,

was mainly a northern hemisphere phenomenon.

Temperatures over parts of the Arctic rose by sev-

eral degrees Celsius during the 1920s and dropped

by a nearly comparable amount during the 1950s

and 1960s. Temperatures over the interior of the

Antarctic continent have risen little, if at all, since

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456 Climate Dynamics

Temperature anomaly (°C)

1880 1900 1920 1940 1960 1980 2000

1.2

–0.6

–0.3

0.0

0.3

0.6

–0.6

–0.3

0.0

0.3

0.6

0.9

–1.2

–0.6

0.0

0.6

Ye a r

Land

Land and Ocean

Ocean

Fig. 10.44 Time series of global-, ocean-, and land-averaged

surface temperature anomalies, defined as departures from

the 1880–2003 mean. The data are updated through

December of 2004. [Courtesy of NOAA’s National Climatic

Data Center.]

Fig. 10.45 Photographs documenting the retreat of snow

and ice on Mt. Kilimanjaro in equatorial Africa during the

20th century. [Courtesy of Lonnie G. Thompson.]

observations began in 1958, yet the Antarctic

Peninsula has warmed dramatically during this

period. For the globe as a whole and for many

regions, the rate of warming since 1970 has been

larger than for any period of comparable length ear-

lier in the record.

How much of the warming observed during the

20th century was human induced and how much was

Global-mean sea level varies in response to the

expansion and contraction of sea water as the

oceans warm and cool (the thermosteric effect).

Because of the temperature dependence of the

coefficient of expansion of sea water, the magni-

tude of the thermosteric effect depends not only

on the net amount of heating of the oceans, but

also on the heating distribution in relation to the

existing temperature distribution, as illustrated in

Exercise 10.28. Global-mean sea level also varies

in response to changes in the volume of water

that is stored in the oceans (the eustatic effect).

Changes in the volume of the ice sheets, in the

volume of water stored on land in lakes, rivers,

10.4 Global Sea Level Rise

reservoirs, soils and aquifers, changes in the shape

of the Earth’s crust, and (on timescales of millions

of years) exchanges of water between the oceans

and the mantle all contribute to the eustatic

effect.

On timescales of years to decades, local wind-

induced variations in sea level, such as the ENSO-

related variations shown in Fig. 10.23, are much

larger than thermosteric and eustatic changes

in global-mean sea level. On the basis of the exist-

ing sparse tide-gauge network it is difficult to

distinguish between the global greenhouse warm-

ing “signal” and the local, wind-induced “noise.”

On longer timescales, the deformation in the

Continued on next page

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10.4 Greenhouse Warming 457

a reflection of the natural variability of the climate

system cannot be known with certainty because there

is no way of obtaining multiple realizations of the

unperturbed climate of the 20th century to serve as a

basis for comparison. Natural variability on decadal

timescales was probably responsible for some of the

regional differences in the trends and the lack of uni-

formity of the global-mean temperature trend over the

course of the century. It may also have contributed to

(or detracted from) the net warming. However, the

warming of the past 30 years has been so pronounced

and the cumulative warming since 1900 so large as

to beg for an explanation. Thus far, the only plausible

and well-supported interpretation that has been put

forward is that they are early indications of a response

to the buildup of greenhouse gases.

10.4.3 Projections of Future Human-Induced

Greenhouse Warming

There are several ways of estimating how much

global-mean surface air temperature would rise in

response to a prescribed increase in the concentra-

tions of greenhouse gases. One approach is to rely on

the past history of the Earth system to estimate

the sensitivity of global mean surface air tempera-

tures to changes in radiative forcing, as illustrated in

Exercises 10.4 and 10.26. Empirical estimates of this

kind are subject to large uncertainties, as illustrated in

Exercise 10.26. Hence, most estimates of climate sen-

sitivity are based on models: either globally averaged,

one-dimensional, radiative-convective equilibrium

models with assumptions concerning water vapor,

cloud and ice-albedo feedbacks; or three-dimen-

sional, coupled atmosphere-ocean-cryosphere-land

surface models that explicitly compute water vapor

concentrations, ocean temperatures, and currents and

include parameterizations of clouds, sea ice, snow

cover, land vegetation, and soil wetness.

The advantage of radiative-convective models is

that they are simple and they yield results that are eas-

ily interpretable. These models predict that a doubling

of the atmospheric CO

concentration relative to its

preindustrial concentration would result in a down-

ward radiative forcing F at the top of the atmosphere

of 3.7 W m

2

, raising global mean surface air tempera-

ture by



F  0.96 K. If water vapor feedback is

included under the assumption that relative humidity

remains constant, the sensitivity to a prescribed forc-

ing roughly doubles, and if ice-albedo feedback is

included as well, the feedback factor, as defined in con-

nection with (10.8), increases to around 0.6, yielding

an increase in T

of around 2.5 K for a CO

doubling.

In comparison to the simpler radiative convective

models, three-dimensional, coupled climate models

10.3 Continued

Earth’s crust—in particular, the isostatic rebound

from the last ice age (i.e., the rising of the crust in

areas that were formerly depressed by the weight

of the continental ice sheet and the sinking of the

crust in the surrounding regions)—further com-

plicates the interpretation of local tide gauge

records.

Since 1992, sea level has been monitored on a

global basis using satellite altimeters capable of

detecting small changes relative to the Earth’s geoid

(surfaces of constant geopotential). These direct

measurements, shown in Fig. 10.46, indicate that sea-

level is currently rising at a rate of 3mmyear

1

(or 30 cm per century) about twice as rapidly as pre-

vious indirect estimates based on measurements of

the rate of warming of the world’s oceans, trends in

salinity over high latitudes (indicative of the the

melting of the ice sheets), and changes in the inven-

tory of water on land.

–20

–10

1996 1998

Year

2000 2002 2004

Change in mean sea-level

1994

TOPEX

Jason

60-day smoothing

Fig. 10.46 Measurements of 10-day mean and 60-day

running mean global-mean sea-level from the NASA

CNES

TOPEX Poseidon and Jason satellite-borne altimeters.

Changes are with respect to an arbitrary reference level.

The data have been corrected to remove the climatological-

mean seasonal variations. The sloping black line indicates

the linear trend in the data. [Courtesy of Steve Nerem.]

P732951-Ch10.qxd 12/09/2005 09:13 PM Page 457

458 Climate Dynamics

offer a number of significant advantages for making

projections of greenhouse warming,

•They provide a test bed for improving our

understanding of boundary layer, cloud,

cryospheric, and biospheric processes that have a

bearing on climate sensitivity.

•They enable the various components of the

atmosphere and the Earth system to interact in

ways that cannot be investigated empirically or

with the use of radiative-convective models. For

example, they allow for the possibility of changes

in the tropospheric temperature lapse rate, high

or low cloud cover, and surface wind speed in

different parts of the world, any of which might

have implications for climate sensitivity.

•They yield much more comprehensive predictions

of how climate would change in response to a

prescribed forcing, with regionally and seasonally

specific (as opposed to globally and annually

averaged) temperature projections, as well as

estimates of patterns of changes in rainfall,

snowfall, cloudiness, wind, and the statistics of

severe weather events such as tropical cyclones.

•They provide a framework for investigating the

impacts of climate change on the Earth system

as a whole (e.g., sea level rise, changes in

streamflow statistics for various watersheds,

desertification of marginally arid regions, and

changes in the range of various plant and animal

species and diseases).

• Unlike the simpler models, they provide a

timetable for the changes that explicitly takes

into account the role of the ocean in buffering

both the chemical and the thermal response to

the burning of fossil fuels.

Numerical simulations of the response to the buildup

of concentrations of greenhouse gases have been per-

formed with an array of coupled models. The simu-

lated responses vary somewhat from model to model,

but the gains tend to be in the same range as those

inferred from the radiative convective models (1.5 to

4.5). The simulated responses share a number of com-

mon characteristics that are in accord with simple

physical reasoning:

•a polar amplification of the warming, particularly

during winter and spring due, in large part, to the

positive feedback from the cryosphere. This

tendency is also clearly evident in historical

temperature records from paleoclimate

reconstructions.

•a gradual buildup of the warming due to the

large thermal inertia of the oceans.

• more rapid warming over the continents than over

the oceans during the early stages of the warming.

• an increase in atmospheric precipitable water,

leading to heavier precipitation events

(particularly during winter over higher latitudes

where the predicted warming is greatest).

• earlier spring snowmelt and enhanced

evaporation rates, leading to drying of some

continental regions during summer. In such

regions, positive feedback from the biosphere

amplifies the rise in daytime temperatures.

•a rise in global sea level due to the thermal

expansion of sea water as it warms (20–40 cm

during the 21st century, compared to 15 cm

during the 20th century). Present models are not

capable of predicting the extent of the additional

eustatic contribution dominated by the melting

of the continental ice sheets and alpine glaciers.

•a reduced rate of formation of North Atlantic deep

water in response to the freshening of the surface

waters as precipitation increases and ice melts.

There is considerable uncertainty as how the

cryosphere will respond to global warming. Will the

Arctic pack ice continue to retreat, offering the pos-

sibility of new trans-Arctic shipping routes? Will

Greenland become ice free, as it apparently was at

the time of the last interglacial? Will the melting of

the ice sheets be sufficiently rapid to accelerate the

rate of sea level rise, as illustrated in Exercise 10.28?

How serious is the risk of a “climate surprise” — for

example, a sudden disintegration of a major part of

one of the ice sheets or a reorganization of the

atmospheric andor ocean general circulation analo-

gous to those that caused the abrupt discontinuities

in ice core records? Such complex workings of the

Earth system are beyond the capability of the pres-

ent generation of coupled models to simulate.

10.5 Climate Monitoring

and Prediction

Early in the 20th century, understanding of weather

phenomena reached the point that many nations of

the world deemed it to be in the public interest to

establish weather services charged with the task of

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10.5 Climate Monitoring and Prediction 459

providing forecasts of changing weather conditions

and timely warnings of weather events that might pose

risks to life and property. In support of these activities,

a global observing system was established under the

auspices of the United Nations. Several nations and

international consortia established centers that collect

atmospheric and other relevant Earth system data and

assimilate it into models that diagnose the current

state of the atmosphere and predict how it will evolve

out to the limit of deterministic weather prediction.

This weather information is delivered to the public by

a distributed communications system involving both

government and private industry.

The global weather observing system is in the

process of being augmented to serve the additional

task of climate monitoring. Clouds, radiatively active

trace gases and aerosols are being added to the suite

of atmospheric measurements, and the observing sys-

tem is being expanded to encompass other compo-

nents of the Earth system that have a bearing on

climate. Many of the needed atmospheric and surface

observations can be obtained with complete global

coverage by means of remote sensing from satellites.

A number of other strategies are being used to moni-

tor subsurface temperatures, currents, and chemical

and biological properties of the oceans. Because it

deals with relatively weak, slowly evolving climate

anomalies, climate monitoring imposes much more

stringent requirements on the calibration and long-

term stability of measurements than observations in

support of numerical weather prediction.

Gridded atmospheric fields used in operational

numerical weather prediction are not well suited for

climate studies because they contain artificial discon-

tinuities due to changes in instrumentation, changes

in the availability of different kinds of measurements,

changes in the quality control procedures, and the

successive updating of the numerical weather predic-

tion models used to perform the data assimilation.

These inhomogeneities can be reduced substantially

by performing reanalysis of the archived observations,

using a single, state-of-the-art numerical weather

prediction model and uniform quality control proce-

dures, and correcting the data for known changes in

instrument characteristics.

Three-dimensional, coupled climate models were

first introduced in the 1970s and have gradually

expanded to include additional components of the

Earth system. Just as there is more to building a high-

performance automobile than merely assembling a

set of components designed independently by a

number of different manufacturers, there is more

to building a high-performance climate model than

merely coupling an atmospheric general circulation

model (GCM) with an ocean GCM, a sea-ice model,

or a land hydrology model.

Atmosphere-only GCMs are designed to produce

realistic simulations of the current observed climate

when run with climatological-mean sea-surface tem-

perature and sea ice. Ocean-only GCMs are designed

to produce realistic simulations of ocean temperatures

and currents when run with prescribed surface winds,

surface air temperatures, and precipitation, and similar

considerations apply to the models of other compo-

nents of the Earth system. When the models of the var-

ious components of the Earth system are coupled, the

observational constraints that were used in designing

and tuning them are removed. For example, the

observed sea-surface temperature is no longer pre-

scribed as part of the lower boundary conditions for

the atmosphere: in the coupled model, sea-surface tem-

perature is determined by the mutual adjustment of

the atmosphere and ocean GCMs to the insolation and

the interactions with the other model components.

The behavior of a coupled model is often quite

different from the composite behavior of the compo-

nent models from which it is constructed. Coupled

models may exhibit a pronounced climate drift, which

reflects the mutual adjustment of the various com-

ponents as the coupled system erratically wanders

away from the imposed initial conditions and estab-

lishes its own peculiar climatology. This equilibration

process proceeds rapidly at first, but it may take

centuries to complete, because of the large thermal

inertia of the oceans. Coupled models exhibit greater

internal variability than the component models of

which they are made up because of their ability

to simulated coupled phenomena such as ENSO.

Coupled climate models provide a physically consis-

tent framework for data assimilation, not only for the

atmosphere, but also for other components of the

Earth system.

Although the weather forecaster is still the object of

derision from time to time, the general public under-

stands and appreciates the value of weather forecasts

and makes routine use of them. The “market” for

climate forecasts on timescales ranging from seasons to

decades is much more limited: the main “customers”

being corporate enterprises in climate-dependent

sectors of the world economy, such as water, energy,

agriculture, fisheries, forestry, and outdoor recreation.

Managers in these fields are already accustomed to

P732951-Ch10.qxd 12/09/2005 09:13 PM Page 459

460 Climate Dynamics

using climatological mean data as a basis for decision

making, but many are reluctant to use climate forecasts

in the absence of a long track record, analogous to the

one that exists for weather forecasts. To attract users,

climate forecasts need to be tailored to their needs. For

example, a public utilities manager might need infor-

mation on precipitation and snow levels within a par-

ticular watershed; an operator of a wind power grid

might need statistics of wind speeds at specific sites.

For some applications the relatively coarse resolu-

tion atmospheric fields derived from the global models

need to be downscaled, that is, enhanced by incorporat-

ing information on the unresolved scales either statisti-

cally or with the help of regional mesoscale models

that include a detailed representation of the local

terrain. For other applications, variables such as stream

flow, crop yields, energy demand, or output from a

wind power grid can be related directly to the more

predictable indexes of the hemispheric scale circu-

lation, like those used to represent ENSO, using statis-

tical methods based on historical records.

Exercises

10.5 Explain or interpret the following.

(a) Global-mean surface air temperature is

below the radiative equilibrium temperature.

(b) In Fig. 10.1, the troposphere emits more

longwave radiation in the downward

direction than in the upward direction,

whereas the stratosphere emits more

longwave radiation in the upward direction

than in the downward direction

atmosphere is downward at low latitudes

and upward at high latitudes.

(d) The annual mean net flux of energy at the

air–sea interface is locally downward over

the eastern equatorial Pacific.

(e) Mars exhibits a larger diurnal temperature

range than Earth; there is almost no diurnal

cycle in surface temperature on Venus

(Table 2.6).

(f) Dust storms on Mars substantially reduce the

diurnal temperature range, but have little

influence on the daily average temperature.

(g) Summer insolation (Fig. 10.5) is up to 6%

stronger in the southern hemisphere than

in the northern hemisphere.

(h) The Earth system is nearly in equilibrium

with the annual mean net radiation at the

top of the atmosphere, but not with the

seasonal mean net radiation.

(i) The net radiation at the Earth’s surface

averaged over the spring or summer

hemisphere is downward.

(j) Climatological-mean insolation is greater at

the summer pole than on the equator, yet

surface air temperatures in the polar region

are lower than over the equator (Fig. 10.5).

(k) The net radiation at the top of the

atmosphere over the polar regions is

upward, even during summer (Fig. 10.6).

(l) The amplitude of the annual cycle in

surface air temperature is larger at high

latitudes than at low latitudes (Fig. 10.8).

(m) In middle latitudes the annual cycle in

surface air temperature is larger in the

northern hemisphere than in the southern

hemisphere.

(n) Net radiation at the top of the atmosphere

is upward over the Sahara, even during

summer, yet the surface is hot.

(o) The phase of the annual cycle in surface air

temperature tends to be earlier over the

continents than over the oceans.

(p) The ocean mixed layer deepens with time

during autumn and winter.

(q) During a single autumn storm the depth of

the oceanic mixed layer may deepen

dramatically.

(r) During July the equatorial thermocline tilts

upward toward the east in both the Pacific

and Atlantic Oceans, but not the Indian

Ocean. [Hint: consider the distribution of

surface winds in Fig. 1.18.]

(s) The subtropical oceanic anticyclones tend to

be stronger during summer than during

winter.

(t) Climate predictability is not subject to the

2-week limit of deterministic atmospheric

predictability.

(u) An atmospheric general circulation model

exhibits more interannual variability when

it is coupled to a slab mixed layer ocean

than when it is run with fixed sea-surface

temperature. The enhanced variability is at

low frequencies. The deeper the mixed

P732951-Ch10.qxd 12/09/2005 09:13 PM Page 460

Exercises 461

layer, the lower the frequency range of the

enhanced variability.

(v) When the easterly surface winds in the

central equatorial Pacific weaken, sea-

surface temperature rises on the eastern

side of the Pacific basin.

(w) A warming of sea-surface temperature over

the equatorial eastern Pacific favors a

weakening of the easterly surface winds

over the equatorial central Pacific.

(x) During summer over continental regions,

monthly mean surface air temperature

tends to be negatively correlated with the

previous month’s rainfall. (The correlation

derives mainly from daytime temperatures.)

(y) During the 20th century the upward trend

in daily minimum temperature was around

twice as large as the trend in daily

maximum temperature.

(z) A child is sleeping in a cold room and her

mother decides she needs an extra blanket.

The temperature of the topmost blanket is

being monitored with an infrared radiometer

mounted on the ceiling. (i) How does the

temperature sensed by the infrared

thermometer respond to the addition of the

extra blanket? Consider both the time-

dependent behavior and the new

equilibrium temperature after the “system”

has adjusted to the addition of the extra

blanket. Assume that the initial temperature

of the extra blanket is the same as that of the

blanket immediately below it and that the

child’s metabolism is constant. (ii) What

sensations of warmth or coolness would the

child experience if she were awake during

this period? (iii) Is the temperature recorded

by the infrared thermometer of any use in

diagnosing whether the child is comfortably

warm? (iv) In what ways is this situation

analogous to the response of global mean

surface air temperature to an incremental

change in radiative forcing at the top of the

atmosphere?

(aa) Describe how the net energy flux at the

air–sea interface would evolve in response

to an abrupt increase in radiative forcing

at the top of the atmosphere.

(bb) Global-mean surface air temperature at

high latitudes is more sensitive to external

forcing on millennial timescales than on

decadal timescales.

(cc) Despite the existence of positive water

vapor and ice-albedo feedbacks, the Earth

has not experienced a runaway greenhouse.

(dd) Cloud-albedo feedback could conceivably

be large and of either sign.

(ee) Water vapor is the most important

atmospheric greenhouse gas and is a product

of fossil fuel burning, yet it is not included

among the greenhouse gases in Fig. 10.42.

(ff) The relationship between greenhouse

warming and atmospheric CO

concentration is expected to be roughly

logarithmic, rather than linear (e.g., a

quadrupling of CO

is expected to produce

about twice, rather than four times, as

much warming as a CO

doubling).

(gg) The atmospheric concentration (by volume)

of methane is only roughly 1200 that of

, yet its present contribution to the

greenhouse effect is almost 13 as large as

that of CO

(hh) The greenhouse warming potential of

nitrous oxide is much higher than that of

methane, especially over a time interval of

a century or longer.

(ii) Human activities are believed to be

primarily responsible for the more than

20% increase in the concentration of

atmospheric CO

that has been observed

since monitoring began in the late 1950’s

and for the 35% increase since the time

of the industrial revolution.

(jj) Most scientists believe that human

activities are primarily responsible for the

warming observed during the 20th century.

(kk) Even if the rate of fossil fuel consumption

were to immediately level off and begin

declining, atmospheric CO

concentrations

would be expected to continue to rise

throughout the 21st century.

(ll) Processes within the oceans play an

important role in determining the level to

which atmospheric CO

concentrations

will ultimately rise in response to the

burning of fossil fuels.

(mm) The sea level rise projected to occur in

response to the buildup of greenhouse

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462 Climate Dynamics

gases develops more gradually and does

not peak until a few hundred years later

than the peak CO

concentrations.

(nn) The policy dimensions of greenhouse

warming are much more complex than

those surrounding the ozone hole.

10.6 Repeat Exercise 10.1 for the stratosphere.

10.7 Using data in Fig. 10.7 make a rough estimate

of the rate of energy loss through the ocean

surface during autumn and early winter, when

the ocean mixed later is cooling and

deepening. [Hint: Consider the top-most 100-m

layer, which cools from a vertically averaged

temperature of 18 °C in September to 15

°C in January, a drop of 3 °C in 100 days.]

10.8 If the time series of a climatic variable is

perfectly sinusoidal with amplitude A, prove

that its root mean squared amplitude or

standard deviation is .

10.9 (a) Prove that for standardized variables x

and y, the straight line passing through the origin

represents the least-squares best fit regression

line,where best fit is defined in the sense that

the quantity

is minimized. Here, as in the text, the overbar

represents the mean over all the data points. In

this expression, y

is the y coordinate of the ith

data point in a scatter plot like the ones shown in

Fig. 10.12, and rx

is the y coordinate of the

regression line where it passes through x  x

Hence, (y

 rx

) is the error in y

, as estimated or

predicted on the basis of its linear relationship

with x.

(b) Prove that r

is the variance of y that can be

explained in the basis of this least squares best fit

and (1  r

) is the error or unexplained variance.

Solution: (a) Q can be calculated for any

prescribed value of r. At the value of r for

which Q is minimized



 rx

)

 0

( )



 rx

)

r  x

y  rx

A

√

Expanding, we obtain

Differentiating and noting that the data x

and

are independent of r and that  1 yields

Based on this least squares best fit, we can write

where 

is the error. Squaring and averaging,

we obtain

The error 

and x

must be uncorrelated. If that

were not the case, y  rx would not be the line

of best fit. Because , this expression

reduces to

where r

is the explained variance and is

the unexplained variance. This relationship

can be extended to unstandardized variables,

in which case r

is the fraction of the variance

of y that can be explained in the basis of the

least-squares best fit and (1  r

) is the fraction

of the variance that remains unexplained. ■

10.10 The standard deviation of monthly mean

temperature at a certain station averaged over

the winter months December–March is 5.0 °C.

The standard deviation of winter seasonal

mean temperature is 3.0 °C.What is the

standard deviation of monthly mean

temperature about the respective seasonal

means for individual winters?

10.11 Prove that

[Hint: Make use of the fact that ]

10.12 Suppose that the Earth warms by 3 °C during

the 21st century and that the entire ocean warms

by the same amount. Assume that the

cryosphere remains unchanged. In the global

y  xy  0.

xy  xy  x y



1  r





 y

 1

 r

 2







 rx





r  x



 2rx

 r



 0

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Exercises 463

energy balance in Fig. 10.1, by how many W m

2

would the net incoming solar radiation have to

exceed the outgoing Earth radiation at the top

of the atmosphere? [Hint:The mass of the

oceans per unit area of the Earth’s surface is

given in Table 2.2.]

10.13 On the basis of the global energy balance in

Fig. 10.1, estimate what the surface

temperature of the Earth would be in the

absence of latent and sensible heat fluxes.

Assume that the fraction of the longwave

radiation emitted from the Earth’s surface that

is absorbed by the atmosphere and re-emitted

back to the surface remains unchanged.

10.14 Using data in Fig. 10.2, estimate the poleward

flux of energy by the atmosphere and oceans

across 38 °N, where the incoming and outgoing

radiation curves intersect. [Hint: Assume that

the energy transport across the equator is zero.

Assume that the energy transport across the

equator is zero.]

10.15 Compare the daily insolation upon the top of

the atmosphere (a) at the North Pole at the

time of the summer solstice and (b) at the

equator at the time of the equinox. The solar

declination angle (the astronomical analog of

geographic latitude; i.e., the latitude at which

the sun is directly overhead at noontime) at the

time of the summer solstice is 23.45° and the

Earth–Sun distances are 1.52 and 1.50  10

km, respectively.

10.16 Consider the response of the Earth’s equivalent

blackbody temperature T

to a volcanic

eruption that increases the planetary albedo,

resulting in a radiative forcing at the top of the

atmosphere of



F 2W m

2

. (a) Calculate

the equilibrium response. (b) Suppose that the

atmosphere is well mixed and thermally

isolated from the other components of the

Earth system; that the increase in planetary

albedo is instantaneous; and that the albedo

remains constant at the higher value after

the eruption. Show that T

drops toward its

new equilibrium value exponentially,

approaching it with an e-folding time equal to

the atmospheric radiative relaxation time

defined and estimated in Exercise 4.29.

[Hint: Consider the energy balance at the top

of the atmosphere. Make use of the fact that

that



FF  1 and



T

 1.]

10.17 Rework Exercise 10.16, but assuming that the

radiative flux at the top of the atmosphere

abruptly returns to its preeruption value

exactly a year after the eruption. Estimate the

drop in T

during the year after the eruption

(a) assuming that the atmosphere is well

mixed and thermally isolated from

the other components of the Earth system and

(b) assuming that the atmosphere remains

in thermal equilibrium with a 50-m-deep

ocean mixed layer that covers the planet.

the Earth system lose more energy during

the year that the volcanic debris are present

in the atmosphere? (d) Which of these

scenarios is more realistic, and why?

10.18 Which of the following has the largest impact

on the Earth’s equivalent blackbody

temperature. (a) The 0.07% variation sun’s

emission that is observed to occur in

association with the 11-year sunspot cycle.

(b) The flux of geothermal energy from

the interior of the Earth (0.05 W m

2

activities (10

W).

10.19 Two feedback processes capable of

amplifying greenhouse warming by factors

of 1.5 and 2.0, respectively, if each were

acting in isolation, would be capable of

amplifying it by a factor of ________ if they

were acting in concert.

10.20 (a) Without using Eq. (10.9) show that for a

case of a single auxiliary variable y, the change

in global mean surface air temperature T

resulting from an incremental climate forcing



F is given by

(10.16)

where f is the feedback factor. (b) Show that

(10.9) follows directly from (10.16).

10.21 For a planet with an atmosphere like the

Earth’s and covered by an ocean 50-m deep,

estimate the response time for global-mean

surface air temperature to adjust to an

instantaneous change in the climate forcing

at the top of the atmosphere. Assume that

the gain is 2.5.

10.22 Show that the net cloud radiative forcing

(i.e., the incremental change in downward net









F (1  f  f

 f

......)

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