7. Energy, Power
and Climate Change
Chapter 7.2 - The greenhouse effect
and global warming
The black-body law
• All object that are kept at some absolute
temperature T (kelvin scale) radiate energy in
the form of electromagnetic waves.
• Depending on the temperature of the object, it
will radiate different types of energy.
• Some objects only emit IR
radiation, like people but others
can emit visible radiation, like a
hot piece of iron.
Stefan-Boltzmann Law
• The power radiated by a body is governed by the StefanBoltzmann Law.
The amount of energy per second radiated by a
body depends on its surface area A, absolute
temperature T and the properties of the surface
P  eAT
4
where
 = 5.67x10-8 W m-2 K-4 (Stefan-Boltzmann constant)
e is the emissivity of the surface. It has no dimensions (units) and
varies between 0 and 1). For a perfect emitter (black body) e =1.
Black-body
• A black body is an object that absorbs all electromagnetic
radiation that falls on it. No electromagnetic radiation passes
through it and none is reflected. Because no light (visible
electromagnetic radiation) is reflected or transmitted, the object
appears black when it is cold.
• If the black body is hot, these properties make it an ideal source of
thermal radiation.
• A black body is thus an object that is a ‘perfect’ emitter of
radiation.
• A real body can be a good approximation to a black body if its
surface is black and dull.
Black-body
• But a shiny and silver object is clearly the opposite to a
black body as it reflects radiation rather that absorbing it.
• Dark dull surfaces have e close to 1  they are almost
perfect emitters and are a good approximation to a black
body
• Shiny silver surfaces have e close to 0  they cannot be
considered black bodies.
Black-body
• A body of emissivity e that is kept at temperature T1 will radiate
power at a rate
Pout = e A T1 4
but will also absorb power at a rate
Pin = e A T2 4
if the surroundings are kept at temperature T1.
• Hence the net power lost by the body is
Pnet = Pout - Pin = e A (T1 4 -T2 4)
• At equilibrium, Pnet = 0, i.e., the body loses as much energy as it
gains, and so the body’s temperature stays constant a equals that
of the surroundings: T1 = T2.
Black-body
• The energy that is radiated by a body is electromagnetic
radiation and is distributed over an infinite range of
wavelengths.
• However, most of the energy is radiated at a specific
wavelength that is determined by the temperature of the
body:
The higher the temperature of the body, the shorter the
wavelength for maximum emission.
• For a body at room temperature (20ºC or 293K) the
wavelength at which most radiation is emitted is an infrared
wavelength.
Black-body spectrum
•
Very hot objects will
radiate at short
wavelengths. Ex: the
sun’s temperature is
around 5500 K and
its  for maximum
emission
corresponds to
green/yellow light.
•
Cold objects will
radiate at long
wavelengths. Ex: the
human body radiates
in the infrared region.
Black-body radiation and Wien’s law
• The relationship between the max  and the object’s
temperature is given by Wien’s law :
max T  2.9010 m K
3
Power emission and emissivity
For different surfaces at the same temperature (300K), the power
emitted will be different and will depend of the surface’s emissivity
e = 1.0
power
emitted
e = 0.8
e = 0.2
0.5
1.0
1.5
2.0
2.5
3.0
 /x10-5 m
Solar radiation
• The sun may be considered to radiate as a perfect emitter, that
is, as a black body.
• The total power emitted by the Sun is P = 3.9 x 1026 W
• The power received per unit area on earth is called intensity
and given by:

P
I
4r 2
PIA
• Substituting the numerical values gives
I
3.91026

4 1.5 10

11 2
 1400W/m2
• This is the intensity of the solar radiation at the top of earth’s
atmosphere. It’s called solar constant and denoted by S.
Albedo
• The albedo, , of a body is defined as the ratio of the power of
radiation reflected or scattered from the body to the total
power incident on the body.
t ot alscat t ered/reflect edpower

t ot alincident power
• The albedo is a dimensionless number. Snow (white shiny surfaces)
has an albedo of 0.85. It reflects almost all radiation. Charcoal (dark
dull surface) has an albedo on 0.04. It reflects very little radiation.
• The earth as a whole has a global average albedo of about 0.3. The
variations depend on:
- the time of the year (many or few clouds)
- latitude (amount of snow or ice)
- whether one is over desert land (=0.3-0.4), forests
(=0.1) or
water (=0.1).
Albedo
• At any one moment in time, the earth offers a ‘target’ area
R2, where R is the radius of the Earth.
• As the target area is ¼ of the total surface area of the earth,
the power radiation received per square metre of the Earth’s
surface is S/4 = 350 W/m2.
disc of
• Since 30% is reflected
(albedo), this means that
the earth receives a net
radiation intensity of
245 W/m2.
solar radiation
area R2
sphere of
surface
area 4R2
R
radiation
Energy balance
• The earth has a constant average temperature and behaves
as a black body. So the energy input to the earth must equal
(balance) the energy output by the earth.
• Taking account of the albedo, the power delivered to surface
area A is P = (1 - ) IA
• If the atmosphere
is not taken into
account, we can
consider this
energy diagram for
earth (energy
balance
equation).
incoming
intensity = I
reflected =  I
radiation back into
space = (1 – ) I
received by the earth = (1 -- ) I
The Greenhouse effect
• Any planet with an atmosphere experiences this effect.
• Most radiation that reaches earth’s surface is in the visible region
of the EMS, with small amounts of IR and UV.
• About 30% is reflected back into space.
• The rest of the radiation is absorbed by earth's atmosphere and
surface.
• Earth's average temperature is about 288K which means that it
will radiate energy in the IR region.
• Unlike Visible light, IR light does not pass through the
atmosphere as it is strongly absorbed by various gases
(greenhouse gases).
The Greenhouse effect
• This means that some of this radiation is received by the earth’s
surface again, causing additional warming.
• This is radiation that would be lost in space were it not for the
greenhouse gases.
• Without this greenhouse effect, the earth’s temperature would
be 32K lower than what it is now (TEarth = 256K or -17°C).
The Greenhouse effect
incoming
intensity
radiated back
into space
greenhouse effect
reflected
absorbed IR
radiation
re-radiated back
to earth
earth’s
surface
received by earth and atmosphere
The Greenhouse effect
The greenhouse effect is the warming of the earth
caused by infrared radiation, emitted by the earth’s
surface, which is absorbed by various gases in the
earth’s atmosphere and is then partly re-radiated
towards the surface.
The gases primarily responsible for this absorption
(the greenhouse gases) are water vapour, carbon
dioxide, methane and nitrous oxide.
The Greenhouse effect
The Greenhouse effect
• The greenhouse effect is a natural consequence of the
presence of the atmosphere.
• However, there is an enhanced greenhouse effect which
refers to additional warming due to increased quantities of
the greenhouse gases in the atmosphere.
• This increase is due to human activity.
• Greenhouse gases can have natural or anthropogenic
(man-made) origins.
The Greenhouse effect
• But there are also ways of reducing the concentrations of
these gases:
- CO2 is absorbed by plants during photosynthesis and dissolved in
oceans;
- CH4 (methane) is destroyed in the lower atmosphere by chemical
reactions involving free hydroxyl radicals (HO·)
- nitrous oxide is also destroyed in the lower atmosphere by
photochemical reactions.
• It must be noticed that most radiation coming from the sun is
visible light which is not absorbed by the gases in the
atmosphere. Therefore, the incident radiation passes through
the atmosphere and arrives the earth’s surface.
Sources of greenhouse gases
Greenhouse
gas
H2O (g)
Natural sources
Anthropogenic causes
Evaporation of water
from oceans, rivers and
lakes
CO2
Forest fires, volcanic
Burning fossil fuels in power plants
eruptions, evaporation of and cars, burning forests
water from oceans
CH4
Wetlands, oceans, lakes
and rivers
Flooded rice fields, farm animals,
termites, processing of coal, natural
gas and oil, and burning biomass
N 2O
Forests, oceans, soils
and grasslands
Burning fossil fuels, manufacture of
cement, fertilizers, deforestation
(reduction of nitrogen fixation by
plants)
Mechanism of photon absorption
• Electrons within atoms can absorb have quantized
energies.
• In the same way, molecules can absorb discrete amounts
of energy related to their vibrational and rotational
motion.
• Just like electrons exit in energy levels in atoms, there are
vibrational and rotational energy levels.
• The difference, however, is that the energy difference
between rotational/vibrational energy levels is the same as
the energy of IR photons (atomic levels have difference in
energies related to UV, Vis and IR
Mechanism of photon absorption
• This means that when IR photons travel through a greenhouse gas,
they will be absorbed.
• As the excited state is an unstable one, the radiation absorbed will
be emitted again, but this time in all directions.
• That is, the photons are not all emitted outwards into space. Some
are emitted back towards the earth, thereby warming the earth’s
surface.
incoming
intensity
radiated back
into space
greenhouse effect
reflected
absorbed IR
radiation
re-radiated back
to earth
received by earth and atmosphere
earth’s
surface
Mechanism of photon absorption
• Consider two atoms forming a diatomic molecule.
• The force between atoms may be loosely modelled as a massspring system.
• Simple harmonic oscillations take place when the atoms are
disturbed from their equilibrium positions.
• The frequency of oscillations is given by:
1
f 
2
k
m
where m is related to the mass of the 2 atoms
m1 and m2, through:
m1m2
m
m1  m2
Mechanism of photon absorption
• For CO2, k=1900 N/m and m=1.14x10-26 kg. So f = 6.5x1013 Hz.
• This is the natural frequency of the molecule.
• Photons travelling through this gas will be in resonance with the
molecule if they have a frequency equal to the natural
frequency.
• A typical IR photon as E = 0.25eV and, therefore, f = 6.1x1013
Hz.
• This means that the photon will be absorbed by the molecule
Transmittance curves
• Consider IR radiation passing through the atmosphere.
• Some of this radiation will be absorbed so the intensity of
the radiation after passing through the atmosphere will be
reduced.
• A transmittance curve shows how percentage of radiation
transmitted by the gas varies with the wavelength.
T/%
100
6
12
/m
Transmittance curves
• The black-body
spectrum of the sun
is not a perfect
curve (doted line) as
the gases present in
the atmosphere
absorb part of the
radiation.
H2O
CO2
Transmittance curves
Surface heat capacity
• We define CS, the surface heat capacity of the body, as
the energy required to increase the temperature of 1m2 of
the surface by 1 K.
• The concept is useful in the context of bodies radiating and
absorbing energy, since it is the surface that is responsible
for the energy lost or gained.
• The units of CS are J m-2 K-1.
• Thus, for a surface of surface heat capacity CS and area A,
the amount of thermal energy needed to increase its
temperature by T is given by:
Q  ACS T
Surface heat capacity – example question Q4
Show that CS is related to c (specific heat capacity).
Q  ACS T
and
Q  m cT
ACS T  mcT
But
m  V  Ah
and hence:
ACS T  AhcT
CS  hc
so:
Global warming
• The next figure shows the variation of the deviations of the earth’s
average T from the expected long-term average since 1880.
Global warming
Global warming – concentration of CO2 over the years
• CO2 concentration has doubled since the
nineteenth century (pre-industrial times).
• There seems to be a connection between global warming and
greenhouse gases but some say that the data collected does not
cover a large enough time span.
Global warming – concentration of CO2 over the years
• However, analysing samples from
ice cores in Antarctica and
Greenland it is possible to measure
the concentration of different gases
at the time of freezing.
• The results show that there is a very
close link between global warming
and increased greenhouse gas
concentrations.
• Some of the Antarctic ice cores are
extracted form a depth of about
3600m over the frozen lake Vostok.
• They reveal a connection between
temperature changes and changes
in CO2 and CH4 concentrations.
Global warming – concentration of CO2 over the years
• The ice cores give a detailed account of global climate conditions
over a time period spanning some 420 000 years. The figure
below shows how T and [CO2] have varied over time.
Global warming – concentration of CO2 over the years
• The figure below shows that the earth was warmest
whenever the levels of CO2 in the atmosphere increased.
• Looking at the present concentration of CO2 it is certain that
temperature will increase.
• What is uncertain is the detailed effect of this temperature
increase on the global climate – in magnitude and in time
scale.
Global warming
Global warming
Global warming
• The majority of experts tend to agree that the enhanced
greenhouse effect is behind global warming.
• But some say that GW may be due to an increase solar
power output as solar activity has a periodic variation.
• However, the pattern of GW is not consistent with this
variation.
• Other theories include the increase of volcanic activity,
variations of eccentricity of the earth’s orbit around the sun
as well as ‘tilt’ of the orbit with respect to the sun.
• These orbital phenomena occur over time scales ranging
from 20 000 to 100 000 years which means that they are
not so relevant when only the last 200 years are
considered.
Sea level
• The level of water is always varying due to changes in
atmospheric pressure, plate tectonic movements, wins, tides, flow
of large rivers into the sea, changes in water salinity and others.
• But the problem is when sea level changes because of climate
changes. It is know that climate changes affect sea level through
the fact that the temperature determines how much ice melts or
how much water freezes.
• During the last ice age (about 18 000 years ago), the sea level
was about 100m lower than it is today.
Changes in sea level affect the amount of water that can
evaporate and the amount of thermal energy that can be
exchanged with the atmosphere. In addition, changes in sea
level affect ocean currents which are vital in transferring thermal
energy from the warm tropics to colder regions
The melting of ice
• To melt a mass m of ice requires an amount of thermal energy
Q=mLf.
• When it comes to discuss sea level, we must distinguish
between land ice (ice supported on land) and sea ice (ice
floating in sea water).
• When sea ice melts, there is no change in sea level. This is a
consequence of Archimedes’ principle – the weight of the ice
equals to the weight of the displaced water. So when ice melts,
the resulting water will occupy the place of ice and no change
will take place.
• However, when land ice melts, the water will eventually flow to
the sea and will increase the sea level.
Estimating changes in sea level
• Another important aspect of the melting of land ice is that it will
expose the dark land underneath the ice. The dark land absorbs
light very easily and will radiate IR radiation that will contribute to
the increase of global temperature.
• Sea level will increase because
- more land ice will melt;
- warmer water occupies a larger volume.
• However, water expansion is anomalous. Water:
- contracts in volume when it goes from 0ºC to 4ºC
- expands as the temperature is increased further from 4ºC.
• This means that the density of water is highest at T=4ºC and this
fact has a great importance for life in lakes, rivers and oceans.
• Given a volume V0 at a temperature 0, the volume after a
temperature increase of  will increase by V given by
Estimating changes in sea level
• Given a volume V0 at a temperature 0, the volume after a
temperature increase of  will increase by V given by
V =  V0 
where  is a coefficient known as coefficient of volume expansion
• The coefficient of volume expansion is defined as the
fractional change in volume per unit temperature change.
• For water, the coefficient  actually depends on temperature,
and so a given volume of water will change by different
amounts even for the same temperature changes 
depending on the initial temperature of water.
Effects of global warming on climate
• A higher average earth temperature implies a rising sea level.
• One effect on climate of a rising sea level is the change in the
albedo of the surface (more water as opposed to dry land).
• The change in the albedo will not change significantly the
temperature.
• However, warmer water at higher temperature evaporates more
easily and more water vapour will be released to the
atmosphere.
• This means:
- cooling of the earth’s surface,
- more cloud cover (and more reflected radiation)
- more precipitation (rain may not fall in the region of interest)
Effects of global warming on climate
• Another effect of higher T is that the solubility of CO2 in the
oceans decreases. This means more CO2 is left in the
atmosphere.
• Deforestation is a controversial issue.
• Rain forests produce CH4 and thus contribute to increased
concentrations of greenhouse gases
• They absorb CO2 from the atmosphere during
photosynthesis but return that CO2 when they die and
decompose.
Measures to reduce global warming
• Using fuel-efficient cars and developing hybrid cars further;
• Increasing the efficiency of coal-burning power plants;
• Replacing coal-burning power plants with natural gas-fired
plants;
• Considering methods of capturing and storing the CO2
produced in power plants;
• Increasing the amounts of power produced by wind and solar
generators;
• Considering nuclear power;
• Being energy conscientious, with buildings, appliances,
transportation, industrial processes and entertainment;
• Stopping deforestation.
The Kyoto protocol and the IPCC (intergovernmental panel on climate change)
• An extremely important agreement towards cutting
greenhouse gas emissions was reached in 1997, in Kyoto,
Japan.
• The industrial nations agreed to reduce their emissions of
GG by 5.2% from 1990 levels between 2008 and 2012.
• The protocol allowed mechanisms for developed nations
to use projects aimed at reducing emissions in developing
nations as part of their own reduction targets.
• Endorsed by 160 countries, the protocol would become
legally binding if at least 33 countries signed it.
• The non-ratification by the USA and Australia has
weakened the impact of the agreement.
The Kyoto protocol
Participation in the Kyoto Protocol
Signed and ratified
Signed, ratification pending
Signed, ratification declined
Non-signatory
The Kyoto protocol and the IPCC (intergovernmental panel on climate change)
• Unlike Kyoto protocol, which imposed mandatory limits for
GG emissions, the Asia-Pacific Partnership on Clean
Development and Climate asked for voluntary reductions
of these emissions.
• It was signed by the USA, Australia, India, China, Japan
and South Korea in 2005.
• It is an agreement in which the signatory nations agree to
cooperate in reducing emissions.
• It has been criticized as worthless because the reductions
are voluntary but defended because it includes China and
India, major GG producers, who are not bond by the Kyoto
protocol.
The Kyoto protocol and the IPCC (intergovernmental panel on climate change)
• A major, comprehensive, detailed and scientifically impartial
analysis of global climate has been undertaken by IPCC.
• The IPCC was created by the World Meteorological
Organization and the United Nations Environment
Programme in 1988.
• It does no research of its own but it collects information from
scientific material to report on technical and socio-economic
aspects of climate change.
• Its 4 reports (1990, 1997, 2001 and 2007) have been
instrumental in providing an accurate analysis of the global
situation.