climate change a simple climate model
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Climate ChangeA simple climate model
Dudley Shallcross and Tim Harrison, Bristol University
Simple climate model
A simple climate model• 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 Sun
Temperature of the Earth ~ 10o C
Big problema: clouds and iceFrom sun (100)
Scattered out to spaceby clouds (24)
Scattered out to space by the surface (6) (skiing)
Surface Land/water Ice30% 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 Sun
With clouds and ice
Temperature of the Earth ~ - 18o C
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 Sun
with clouds and ice and greenhouse gases
Temperature of the Earth ~ 16o C
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 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).
4)( TTI
Model 1: Heat in, heat outBalanced 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 4R2 (i.e. from the entire surface).
Energy Out Energy InOut = TE
4 4RE2 IN = S x Area
IN = 1370 πRE2 W m-2
Area of Earth normal to Solar Radiation S = πRE
2Surface area of Earth = 4πRE
2
Solar Flux, per unit area, S
Surface temperature looks OK
Energy in = Energy out
1370 x RE2 = TE
4 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 iceFrom sun (100)
Scattered byClouds (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
48(5.6
1377
10 ) 40 0.7
ET
24% of solar flux is reflected by clouds
6% Scattered by surface
TE = 255 K (- 18 o C) Cold
Terrestrial RadiationThe Earth also acts as a blackbody radiatorTE = 288 K so most of the irradiance from the Earth is in the infra-red part of the spectrum and peaks at about 10 m.
Solar Radiation 5900 K Terrestrial Radiation 288 K
Wavelength m
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
Atmospheric Window (C-F bonds absorb ir energy)
Model 2: One layer atmosphere
FS(1-A)FgIRFa
Atmosphere
FS(1-A)VIS Fa Fg
Ground
IR VIS
FS = Energy Flux from the Sun (1370/4)A = Albedo or reflectivity of Earth typically ~ 0.3
FS(1-A)FgIRFa
Atmosphere
FS(1-A)VIS Fa Fg
Ground
IR VIS
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)FgIRFa
Atmosphere
FS(1-A)VIS Fa Fg
Ground
IR VIS
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)FgIRFa
Atmosphere
FS(1-A)VIS Fa Fg
Ground
IR VIS
Fa = Energy flux from the atmosphere, in a balanced flux model the flux upwards and the flux downwards are the same.
FS(1-A)FgIRFa
Atmosphere
FS(1-A)VIS Fa Fg
Ground
IR VIS
FgIR = 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)FgIRFa
Atmosphere
FS(1-A)VIS Fa Fg
Ground
IR VIS
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)FgIRFa
Atmosphere
FS(1-A)VIS Fa Fg
Ground
IR VIS
Fg = The IR energy flux from the Earth’s surface.
FS(1-A)FgIRFa
Atmosphere
FS(1-A)VIS Fa Fg
Ground
IR VIS
Fluxes at the top of the atmosphere must balance
FS(1-A)FgIRFa
Atmosphere
FS(1-A)VIS Fa Fg
Ground
IR VIS
Fluxes at the ground must balance
FS(1-A)FgIRFa
Atmosphere
FS(1-A)VIS Fa Fg
Ground
IR VIS
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) (b)
If the two fluxes are in balance
Fg = FS(1-A)(1 + VIS) / (1 + IR )
Finally
Fg = TE4 = FS(1-A)(1 + VIS) / (1 + IR )
TE = [ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0.25
Assuming FS = 336 Wm-2 A = 0.3
VIS = 0.8 IR = 0.1
TE = 287 K
Example calculations
TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25
FS /Wm-2 336 336 336 336A 0.3 0.0 0.0 0.3VIS 1.0 1.0 1.0 1.0IR 1.0 1.0 0.0 0.0
TE /K 254 278 330 302
Example calculations
TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25
FS /Wm-2 336 336 336 336A 0.3 0.0 0.0 0.3VIS 1.0 1.0 1.0 1.0IR 1.0 1.0 0.0 0.0
TE /K 254 278 330 302
Example calculations
TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25
FS /Wm-2 336 336 336 336A 0.3 0.0 0.0 0.3VIS 1.0 1.0 1.0 1.0IR 1.0 1.0 0.0 0.0
TE /K 254 278 330 302
Example calculations
TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25
FS /Wm-2 336 336 336 336A 0.3 0.0 0.0 0.3VIS 1.0 1.0 1.0 1.0IR 1.0 1.0 0.0 0.0
TE /K 254 278 330 302
Example calculations
TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25
FS /Wm-2 336 336 336 336A 0.3 0.0 0.0 0.3VIS 1.0 1.0 1.0 1.0IR 1.0 1.0 0.0 0.0
TE /K 254 278 330 302
Quick Questions TE = [ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0.25
Assuming FS = 336 Wm-2 A = 0.3
VIS = 0.8 IR = 0.1 TE = 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 = 336 Wm-2 A = 0.3
VIS = 0.8 IR = 0.1
TE = 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. 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 Earth-sun distance is less 100,000 years
Source: OSTP
Indicators of the Human InfluenceIndicators of the Human Influenceon the Atmosphere during the Industrial Eraon the Atmosphere during the Industrial Era
Source: IPCC TAR 2001
Climate Change
Source: IPCC TAR 2001
Variations of the Variations of the Earth’s Surface Earth’s Surface Temperature*Temperature*
*relative to 1961-1990 average*relative to 1961-1990 average
Projected Changes in Annual Temperatures for the 2050sProjected Changes in Annual Temperatures for the 2050s
The projected change is compared to the present day with a ~1% increase per year in equivalent COThe projected change is compared to the present day with a ~1% increase per year in equivalent CO 22
Source: The Met Office. Hadley Center for Climate Prediction and Research
Global average temperature is projected Global average temperature is projected to increase by 1.0 to 10 °C from 1990 toto increase by 1.0 to 10 °C from 1990 to 21002100Projected temperature increases are Projected temperature increases are greater than those in the SAR (1.8 to greater than those in the SAR (1.8 to 6.3°C)6.3°C)Projected rate of warming is Projected rate of warming is unprecedented for last 10,000 yearsunprecedented for last 10,000 years
Temperature ProjectionsTemperature Projections
Source: IPCC TAR 2001
Model simulation of recent climate
Natural forcings only(solar, volcanic etc.
variability)Anthropogenic forcings only(human-induced changes)
The Met Office
Simulated global warming 1860-2000:Natural & Man-made factors
Observedsimulated by model
Tem
pera
ture
ris
e o
C
0.0
0.5
1.0
1850 1900 1950 2000
Hadley Centre
Factors affecting climate system
The global mean radiative forcing of the climate system for the year 2000, relative to 1750 (IPCC, 2001).
Establishing a link between
global warming and man-made greenhouse gas
pollution?
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
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