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The Physics of
Climate and
Climate Change
A/Professor Michael Box
Dr. Gail Box
School of Physics, UNSW
Radiation and Climate
 Thermal
radiation laws
The Greenhouse Effect
 Global
energy budget
 Simple models
Climate Forcing
 Aerosol
and gas forcings
Feedback Mechanisms
 Ice-albedo
Global Climate Models
 Strengths
and weaknesses
Climate Prediction
 Scenarios
and uncertainties
Radiation and Climate
The Earth’s climate, at both global and
regional scales, is the result of dynamic
balances (equilibrium) in the flows of
energy (heat), when averaged over
sufficiently large time and space scales.
 The only energy exchange mechanism
between the Earth and space is via
thermal (electromagnetic) radiation,
so we’ll start our physics lesson here.
Radiation laws: 1.
In order to understand radiation exchange, we
need to know the laws of (thermal) radiation.
Law 1: All bodies with temperatures above 0 K
(absolute zero) emit electromagnetic radiation.
A ‘black body’ is an ideal body which absorbs all
radiation incident on it, and reflects none. (Thus
it appears black!) A black body is also the most
efficient emitter of radiation. We will start be
examining the physics of blackbody radiation.
Radiation laws: 2.
Law 2: A blackbody at temperature T (°K)
emits radiation from its surface at the rate
I  T4
Watts per square metre
Here   5.67 x108 is the Stephen-Boltzmann
For a body which is not ‘black’, we may interpret
this temperature as an ‘effective temperature’.
Energy balance
The Earth’s climate is governed by the balance
solar radiation, S, minus the fraction, α,
which is reflected (both are measured by satellite);
 and the emission of ‘terrestrial’ radiation.
 incoming
If we assume that the Earth is a blackbody with
an unknown (effective) temperature T, then we
can determine T by ensuring this balance:
Radiative equilibrium
Incoming Radiation
(1 - )SR2
Outgoing Radiation:
T4 4R2
Energy balance
To determine the effective temperature of
the Earth, we balance these two terms:
1    S  R 2   T 4 4 R 2
T 
1    S
 255 K  18 C
where we have used F = 1368 Wm-2 and α = 0.3.
Seems a bit cold! (Average surface temp is 14.5° C.)
Is the physics wrong? No, it’s just incomplete.
Radiation laws: 3.
Law 3. The emission spectrum of blackbody
radiation follows Planck’s law. (This law has a
very interesting history, and was in fact the first
step in the development of Quantum Physics.)
Law 4. The wavelength at which this spectrum
peaks is inversely proportional to temperature.
(This is known as Wien’s law, and was actually
discovered some years before Planck’s law.)
Planck curve for different T
Planck's Law
Wavelength microns
The Greenhouse Effect
An examination of the spectra for 5750 K (the
sun’s temperature ), and 250 K (the Earth’s
effective temperature), shows quickly that
of sunlight has wavelength less than 4.0 μm;
known as shortwave radiation:
 99% of ‘earthlight’ has wavelength more than 4.0 μm;
known as longwave radiation.
 99%
Our atmosphere contains a number of gases
which absorb in the longwave region: these are
greenhouse (or ‘radiatively active’) gases.
These include H2O, CO2, CH4, N2O, O3, CFCs.
Atmospheric absorption: 1.
Atmospheric absorption: 2.
Infrared atmospheric absorption and absorption cross-sections
for halocarbons in the infrared atmospheric window
Radiation laws: 4.
A body which is not ‘black’ (any gas) will absorb
a fraction, aλ of the radiation incident upon it:
this usually varies (strongly) with wavelength, λ.
It will also emit a fraction, eλ of the radiation that
a black body would emit at that wavelength.
Law 5. Fractional absorptivity equals fractional
emissivity, at all wavelengths (Kirchhoff’s law):
a  e
for all 
Because of its temperature, the Earth’s surface
emits radiation in the 4.0 to 100.0 μm region.
Most of this is absorbed by greenhouse gases.
But the atmosphere is at a similar temperature,
so by Kirchhoff’s law these gases will re-emit
much of this radiation, some to space, but more
back to the surface, making the surface warmer.
This is known as the greenhouse effect, or more
correctly, the ‘atmosphere effect’. I now display it
both qualitatively, and quantitatively.
Measuring the greenhouse effect
There are two ways of measuring the greenhouse effect.
The first is the 33° difference between the effective temp
(-18°C) and the actual (average) surface temp (15°C).
The second is the difference between the 390 Wm-2
surface emission and the 237 Wm-2 emission to space.
Of this 153 Wm-2, H2O accounts for about 95, CO2 for
about 50, and N2O, CH4, O3 and CFCs about 2 each.
The interesting question which now confronts us is: how
are these numbers changing, as a result of our actions?
A simple one-layer model
We can construct a very simple model of an
absorbing atmosphere as follows:
 Assume
that the incoming shortwave radiation (after
removing the reflected component) is transmitted by
the atmosphere, and is all absorbed at the ground.
 Assume that the ground emits as black body with Tg.
 Assume the atmosphere absorbs all of this energy,
and re-emits energy, as a black body with Ta, from
both surfaces: i.e. to space; and back to ground.
 Ta4
E  1   S / 4   Ta4
Energy balance at the surface, and
at the top-of-atmosphere, gives
 Tg4
When these equations are solved
for the two temperatures we obtain
E   Ta4   Tg4
Ta = 255 K
Tg = 300 K = 27 C
This time it is a little too warm, but
it is an improvement.
More realistic models
For teaching purposes we use a model which
allows some solar radiation to be absorbed in
the atmosphere, and also allows some
longwave radiation to pass right through the
atmosphere (i.e. fractional emissivity < 1.0).
A radiative-convective model allows for an
atmosphere with many layers, each with it’s own
temperature and gas concentration (and hence
fractional emissivity). This model can only be
solved iteratively, but it serves as a first step in
realistic modelling of radiation flows.
Modified one layer greenhouse model
 E
a E
(1 – a - )E
Solar Radiation
 reflected
a absorbed in atmosphere
(1 – a - ) absorbed at surface
Modified one layer greenhouse model
 E
(1-e) Tg4
a E
(1 – a - )E
 Tg4
Terrestrial Radiation
e Tg4 absorbed in atmosphere
(1 – e) Tg4 emitted to space
Modified one layer greenhouse model
 E
a E
(1 – a - )E
(1-e) Tg4
e Ta4
 Tg4
e Ta4
Terrestrial Radiation
e Tg4 absorbed in atmosphere
(1 – e) Tg4 emitted to space
e Ta4 emitted to space AND to ground
 E
a E
(1 – a - )E
(1-e) Tg4
e Ta4
 Tg4
e Ta4
For radiative balance:
Incoming absorbed = Outgoing emitted
In atmospheric layer
aE + eTg4 = 2eTa4
(1 – a – )E + eTa4 = eTg4
Solve the simultaneous equations for two unknowns.
Climate Forcing
Any change in the radiation balance (at TOA)
caused by changes in atmospheric composition,
etc., is a called a “radiative forcing”.
We can evaluate radiative forcings with a very
high precision by running a 1D radiativeconvective model ‘before’ and ‘after’.
IPCC 4AR: “very high confidence” (>90%).
What forcings have been identified? The major
ones are greenhouse gases and aerosols.
Atmospheric aerosols
Atmospheric aerosols are small particles with
sizes ranging from ~10nm to ~10μm. They
have atmospheric residence times ~1 week.
They may be produced by both natural and
anthropogenic processes (or a combination).
Primary particles are directly injected into the
atmosphere (e.g. dust, sea salt, soot).
Secondary particles are created by gas-toparticle conversion, from precursor gases
(e.g. SO2 to sulphate aerosols).
Aerosol forcing: 1.
Aerosols are very efficient light scatterers, and
will reflect (some) sunlight back to space.
Increasing levels of (anthropogenic) aerosols
provide a negative forcing (cooling the surface).
This is known as the aerosol direct effect.
Some particles, mainly soot, but also mineral
dust, are efficient absorbers. They may affect the
vertical heating rate in the atmosphere.
Aerosol forcing: 2.
At the heart of every cloud droplet is an aerosol
particle (CCN), which is essential for it’s startup.
Increasing levels of aerosols may lead to more,
but smaller, cloud droplets (for fixed l.w.c.).
Such a cloud will be more reflective (brighter) –
this is the first aerosol indirect effect.
Smaller droplets also take longer to grow large
enough to precipitate, so a longer-lived cloud –
this is the second aerosol indirect effect.
These shiptracks,
seen from space,
are an example of
the indirect effect.
Ships sailing beneath
these clouds have
released particles
which have seeded
them with more CCN,
creating lines of
enhanced reflectivity.
Feedback Mechanisms
A radiative-convective model is only a first step
in understanding climate change, as we must
now allow the climate system to respond. This
involves ‘simple’ dynamics, plus feedbacks.
Feedbacks can be positive, enhancing any initial
warming (or cooling), or negative, damping out
any initial climatic change.
Unfortunately, many of the feedbacks which
have been identified are positive.
Feedback examples
The simplest feedback involves water vapour.
Warmer ocean temperatures lead to increased
evaporation, hence more water vapour in the
atmosphere. This is a powerful greenhouse gas,
which leads to more warming, which leads to….
Other feedbacks involve the carbon cycle and
the biosphere – both positive and negative.
As the oceans warm, their ability to dissolve CO2
decreases, so more will stay in the atmosphere.
Ice-albedo feedback
Surface warming at high latitudes leads to the
melting of ice and snow.
Ice has a much higher albedo (reflectivity) than
ocean: 80% vs. 5%. Less snow cover means
more solar energy is absorbed, causing more
warming, and hence more ice melting, etc.
This is the reason polar regions are warming
faster than the rest of the globe.
It is also a key to the glacial/interglacial cycle.
(The Milankovitch ice-age mechanism.)
Climate Models
Climate models are an attempt to encapsulate
everything we know about the Earth System.
This involves the atmosphere, the oceans and
sea ice, vegetation, biogeochemistry, aerosols
and atmospheric chemistry…. along with all of
the interconnections and feedbacks involved.
The growth of computer power, plus of our
knowledge of planetary systems, has allowed
these models to become increasingly powerful.
Atmospheric models
An atmospheric General Circulation Model
(GCM), like a numerical weather model, solves
the equations of motion for the fluid, plus
equations for conservation of energy (including
radiative transfer), mass and water vapour.
To do this the (continuous) atmosphere is
replaced by a collection grid-boxes:
maybe 20 vertical layers, and a horizontal
spacing of around 100 km (or more).
Climate models: impossible dream?
Sub-grid-scale phenomena
All processes which take place on scales smaller
than the grid scale must be ‘parameterized’.
This is one of the major sources of uncertainty in
using these models.
Major examples include clouds (still the main
problem), topography and coastlines.
This is one reason why global predictions are
more reliable than regional predictions.
Sometimes we run ‘nested models’.
Planetary heat transport
Both the atmosphere and ocean act to transport
heat from equatorial regions to polar regions.
Temperature gradients drive the weather.
For day-to-day weather forecasting, we can
ignore the ocean, as it’s conditions will not
change in the next week.
For longer time-scales we need to understand
how the atmosphere affects the oceans, and
how changes in ocean circulation (e.g. El Nino)
can feed back to affect weather patterns.
Climate Prediction
To predict the climate in the year 2100, we run
the best climate models available.
To do this, we need to decide on the conditions
which are significant – e.g. the composition of
the atmosphere – over the next 100 years, and
run the model for 100 years of computer time.
Since we can’t know in advance what will be the
atmospheric conditions, we use ‘scenarios’.
Climate scenarios
The CO2 content of the atmosphere in 2050
depends on inputs and outputs between now
and 2050. Thus we need ‘emissions scenarios’,
and a good understanding of the carbon cycle.
The IPCC asks modelers to run their models for
a range of emissions scenarios, which are
based on assumptions about technological
changes and economic decisions.
The main focus is usually on what used to be
called the business-as-usual scenario.
Changing climate statistics
What do we look for in model predictions?
 A major
focus is on global mean temperature.
 However other, statistical, predictions are studied (we
extract both means and variation from model runs):
 Rainfall: how is it distributed spatially and seasonally;
does it come as more intense downpours; is it likely to
rapidly re-evaporate due to higher temperatures?
 Changes in winter storms or tropical cyclones?
 Temperature: will there be more heatwaves (periods
of several days that are ‘too hot’) or other extremes?
Prediction uncertainties
Predictions of our ‘climatic future’ naturally
contain many uncertainties.
 Emissions
scenarios are clearly an uncertainty,
but one which we understand (and control).
 Models are never perfect – for example, sub-gridscale phenomena; or simplified chemistry.
 There are always processes (and feedbacks) which
are missing from the models, for different reasons.
What’s missing?
There will always be processes missing from the
models, and for a variety of reasons:
 Processes
which are just too complex:
e.g. a full atmospheric chemistry/aerosol package.
 Feedbacks we are not sure just when they’ll ‘kick in’:
e.g. icecaps being lubricated, and sliding off;
permafrost melting, releasing trapped methane.
 Processes that haven’t even entered our thinking yet.
For this reason, we must always monitor as many
aspects of the climate system as possible, and be on
the lookout for the unexpected (eggs and baskets).