Climate Change
A simple climate model
Dudley Shallcross and Tim Harrison, Bristol University
Simple climate model
A simple climate model
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Students can use an excel spreadsheet to run it
Simple factors to change
Can look at feedbacks on climate
Ideas and questions e-mail d.e.shallcross@bris.ac.uk or
t.g.harrison@bris.ac.uk
Granny’s model of climate 1
Earth
Temperature of the Earth ~ 10o C
Sun
Big problema: clouds and ice
From sun (100)
Scattered out to space
by clouds (24)
Scattered out to space
by the surface (6) (skiing)
Surface
Land/water
Ice
30% of incoming solar radiation reflected back out to space without
being absorbed (Earth’s albedo A = 0.3)
Granny’s model of climate 2
Earth
With clouds and ice
Temperature of the Earth ~ - 18o C
Sun
Granny is now very cold
What can she do to warm herself up?
Move closer?
(Earth’s distance to the Sun varies but not enough to
make up this loss in heat)
Get a blanket? (In effect this is what Greenhouse gases
do)
CO2
O3
Granny’s model of climate 3
(with blankets)
Earth
with clouds and ice and greenhouse gases
Temperature of the Earth ~ 16o C
Sun
Thanks to Mike Stuart 2008
www.disphoria.co.uk
For the granny cartoons
Essential Background Physics
Black Body Radiation
All bodies radiate energy as electro-magnetic radiation.
A black body absorbs all radiation falling on it. It emits
radiation as a function of its surface temperature without
favouring particular frequencies.
The Stefan-Boltzmann Law relates how the total energy
emitted by a black body relates to the temperature by
I (T )   T
4
Equation 1
where I is the energy per unit area emitted per second
(Watts m-2 s-1), T is the Absolute Temperature (K) and  is
the Stefan-Boltzmann constant (5.67 x 10-8 W m-2 K-4).
Model 1: Heat in, heat out
Balanced Flux model
• We know that the energy from the Sun reaching the top
of the atmosphere, the so-called solar constant S, is
1370 Wm-2.
• If we take the radius of the Earth to be RE, in this very
simple model we can see that the Earth absorbs solar
radiation over an area R2 (i.e. a flat atmosphere) but
emits energy from an area 4R2 (i.e. from the entire
surface).
Energy Out
Energy In
Out = TE4 4RE2
IN = S x Area
IN = 1370
Area of Earth normal to
Solar Radiation S = πRE2
πRE2 W m-2
Surface area of Earth = 4πRE2
Solar Flux, per unit area, S
Surface temperature looks OK
Energy in
=
Energy out
1370 x RE2
=
TE4 x 4 RE2
TE4
=
1370
4 x 5.67x10-8
TE
=
279 K
(note for later we will call 1370/4 = FS)
Big problema: clouds and ice
From sun (100)
Scattered by
Clouds (24)
Scattered by
the surface (6)
Surface
Land/water
Ice
30% of incoming solar radiation reflected back out to
space without being absorbed (Earth’s albedo A = 0.3)
Re-calculate TE
24% of solar flux is reflected by clouds
6% Scattered by surface
T
4
E

13 7 0  0.7
8
(5.6 7  10 )  4
TE = 255 K (- 18 o C) Cold
Terrestrial Radiation
The Earth also acts as a blackbody radiator
TE = 288 K so most of the irradiance from the Earth is in the infrared part of the spectrum and peaks at about 10 m.
Solar Radiation 5900 K
Terrestrial Radiation 288 K
little overlap between the
incoming solar radiation
and the outgoing infra-red
radiation from the Earth’s
surface.
separated by a gap at
around 4 m
shortwave (SW) radiation
longwave (LW) radiation
Wavelength m
Atmospheric Window (C-F bonds absorb ir energy)
Model 2: One layer atmosphere
FS(1-A)
FgIR
Fa
Atmosphere
FS(1-A)VIS
Ground
IR
VIS
Fa
Fg
FS = Energy Flux from the Sun (1370/4)
A = Albedo or reflectivity of Earth typically ~ 0.3
FS(1-A)
FgIR
Fa
Atmosphere
FS(1-A)VIS
Ground
IR
VIS
Fa
Fg
VIS = Transmittance of UV/Vis light from the Sun through the Earth’s
atmosphere to the ground. If all the light is absorbed VIS =
0.0 and if all the light passes through VIS = 1.0
FS(1-A)
FgIR
Fa
Atmosphere
FS(1-A)VIS
Ground
IR
VIS
Fa
Fg
IR = Transmittance of IR light from the Earth through the Earth’s
atmosphere to space. If all the ir light is absorbed IR =
0.0 and if all the ir light passes through IR = 1.0
FS(1-A)
FgIR
Fa
Atmosphere
FS(1-A)VIS
Ground
IR
VIS
Fa
Fg
Fa = Energy flux from the atmosphere, in a balanced flux model
the flux upwards and the flux downwards are the same.
FS(1-A)
FgIR
Fa
Atmosphere
FS(1-A)VIS
Ground
IR
VIS
Fa
Fg
FgIR = The IR energy flux from the ground modified by the transmittance
properties of the Earth’s atmosphere that now escapes to space.
FS(1-A)
FgIR
Fa
Atmosphere
FS(1-A)VIS
Ground
IR
VIS
Fa
Fg
FS(1-A)VIS = The UV/Vis energy flux reaching the ground from the Sun
modified by the transmittance properties of the Earth’s
atmosphere.
FS(1-A)
FgIR
Fa
Atmosphere
FS(1-A)VIS
Ground
IR
VIS
Fa
Fg
Fg = The IR energy flux from the Earth’s surface.
FS(1-A)
FgIR
Fa
Atmosphere
FS(1-A)VIS
Ground
IR
VIS
Fa
Fg
Fluxes at the top of the atmosphere
must balance
FS(1-A)
FgIR
Fa
Atmosphere
FS(1-A)VIS
Ground
IR
VIS
Fa
Fg
Fluxes at the ground must balance
FS(1-A)
FgIR
Fa
Atmosphere
FS(1-A)VIS
Ground
IR
VIS
Fa
Fg
Simply balance energy fluxes
At the surface
FS(1-A) VIS + Fa = Fg
(a)
And at the top of the atmosphere,
Fg IR + Fa = FS(1-A)
If the two fluxes are in balance
Fg =
FS(1-A)(1 + VIS) / (1 + IR )
(b)
Finally
=
FS(1-A)(1 + VIS) / (1 + IR )
TE
=
[ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0.25
Assuming FS
A
VIS
IR
=
=
=
=
336 Wm-2
0.3
0.8
0.1
=
287 K
Fg =
TE4
TE
Example calculations
TE
=
[ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25
FS /Wm-2
A
VIS
IR
336
0.3
1.0
1.0
336
0.0
1.0
1.0
336
0.0
1.0
0.0
336
0.3
1.0
0.0
TE /K
254
278
330
302
Example calculations
TE
=
[ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25
FS /Wm-2
A
VIS
IR
336
0.3
1.0
1.0
336
0.0
1.0
1.0
336
0.0
1.0
0.0
336
0.3
1.0
0.0
TE /K
254
278
330
302
Example calculations
TE
=
[ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25
FS /Wm-2
A
VIS
IR
336
0.3
1.0
1.0
336
0.0
1.0
1.0
336
0.0
1.0
0.0
336
0.3
1.0
0.0
TE /K
254
278
330
302
Example calculations
TE
=
[ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25
FS /Wm-2
A
VIS
IR
336
0.3
1.0
1.0
336
0.0
1.0
1.0
336
0.0
1.0
0.0
336
0.3
1.0
0.0
TE /K
254
278
330
302
Example calculations
TE
=
[ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25
FS /Wm-2
A
VIS
IR
336
0.3
1.0
1.0
336
0.0
1.0
1.0
336
0.0
1.0
0.0
336
0.3
1.0
0.0
TE /K
254
278
330
302
Quick Questions
TE
=
[ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0.25
Assuming FS
A
VIS
IR
TE
=
=
=
=
=
336 Wm-2
0.3
0.8
0.1
287 K
1 If the Earth were to move closer to the Sun such that the
solar constant increases by 10% calculate the effect on the
surface temperature of the Earth.
2 If the Earth’s ice caps were to grow such that 25% of the
surface was covered in ice (it is about 6% now) calculate the
effect on the surface temperature of the Earth.
Quick Questions
TE
=
[ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0.25
Assuming FS
A
VIS
IR
=
=
=
=
336 Wm-2
0.3
0.8
0.1
=
287 K
TE
1 If the Earth were to move closer to the Sun such that the
solar constant increases by 10% calculate the effect on the
surface temperature of the Earth. 294 K (up 7 K)
2 If the Earth’s ice caps were to grow such that 25% of the
surface was covered in ice (it is about 6% now) calculate the
effect on the surface temperature of the Earth. 265 K (- 8 C)
Secrets in the Ice
Snow accumulation lays down record of
environmental conditions
Compacted to ice preserving record
Drill ice core & date
Climate Change
Milankovitch Cycles
Climate shifts correspond to three cycles related to
Earth’s orbit
Effect intensity of solar radiation
Caused by gravitational attraction between the planets
(mainly Jupiter) and Earth
Predictions from cycles match major glacial/interglacial
periods and minor periodic oscillations in climate
record
Milankovitch Cycles
Obliquity of Earth’s axis of rotation (tilt) changes from
22° (currently23.5°) to 24.5°  41,000 years
Precession (wobble) changes the quantity of incident
radiation at each latitude during a season  22,000
years
Eccentricity of Earth’s orbit varies from nearly circular to
elliptical. At low eccentricity orbits the average Earthsun distance is less  100,000 years
Source: OSTP
Indicators of the Human Influence
on the Atmosphere during the Industrial Era
Source: IPCC TAR 2001
Climate Change
Variations of the
Earth’s Surface
Temperature*
*relative to 1961-1990 average
Source: IPCC TAR 2001
Projected Changes in Annual Temperatures for the 2050s
The projected change is compared to the present day with a ~1% increase per year in equivalent CO 2
Source: The Met Office. Hadley Center for Climate Prediction and Research
Temperature Projections
Global average temperature is projected
to increase by 1.0 to 10 °C from 1990 to
2100
Projected temperature increases are
greater than those in the SAR (1.8 to
6.3°C)
Projected rate of warming is
unprecedented for last 10,000 years
Source: IPCC TAR 2001
Model simulation of recent
climate
Natural forcings only
(solar, volcanic etc. variability)
The Met Office
Anthropogenic forcings only
(human-induced changes)
Simulated global warming 1860-2000:
Natural & Man-made factors
1.0
Observed
Temperature rise o C
simulated by model
0.5
0.0
Hadley Centre
1850
1900
1950
2000
Factors affecting climate system
Establishing a
link between
global warming
and man-made
greenhouse gas
pollution?
The global mean radiative forcing of the climate system for the year 2000,
relative to 1750 (IPCC, 2001).
Impacts of Climate on the UK
UK will become warmer
High summer temperatures
more frequent
Very cold winters increasingly
rare
Winters will become wetter
and summers may become
drier