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Climate Change A 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

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Climate change a simple climate model

Climate ChangeA simple climate model

Dudley Shallcross and Tim Harrison, Bristol University


Simple climate model
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 [email protected] or [email protected]


Granny s model of climate 1
Granny’s model of climate 1

Earth Sun

Temperature of the Earth ~ 10o C


Big problema clouds and ice
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
Granny’s model of climate 2

Earth Sun

With clouds and ice

Temperature of the Earth ~ - 18o C


Granny is now very cold
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
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).


Model 1 heat in heat out balanced flux model
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 4R2 (i.e. from the entire surface).


Area of Earth normal to Solar Radiation S =πRE2

Surface area of Earth = 4πRE2

Solar Flux, per unit area, S

Energy OutEnergy In

Out = TE4 4RE2 IN = S x Area

IN = 1370 πRE2W m-2


Surface temperature looks ok
Surface temperature looks OK

  • Energy in = Energy out

  • 1370 x RE2 = TE4 x 4 RE2

  • TE4 = 13704 x 5.67x10-8

  • TE =279 K

  • (note for later we will call 1370/4 = FS)


Big problema clouds and ice1
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 t e
Re-calculate TE

24% of solar flux is reflected by clouds

6% Scattered by surface

TE = 255 K (- 18 o C) Cold


Solar Radiation 5900 K Terrestrial Radiation 288 K

Wavelength m

Terrestrial Radiation

The Earth also acts as a blackbody radiator

TE = 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.

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



Model 2 one layer atmosphere
Model 2: One layer atmosphere

  • FS(1-A) FgIR

  • Fa

  • Atmosphere

  • FS(1-A)VIS Fa Fg

  • Ground

VIS

IR


Fs energy flux from the sun 1370 4 a albedo or reflectivity of earth typically 0 3
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 Fa Fg

  • Ground

VIS

IR


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 Fa Fg

  • Ground

VIS

IR


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 Fa Fg

  • Ground

VIS

IR


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 Fa Fg

  • Ground

VIS

IR


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 Fa Fg

  • Ground

VIS

IR


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 Fa Fg

  • Ground

VIS

IR


Fg the ir energy flux from the earth s surface
Fg= The IR energy flux from the Earth’s surface.

  • FS(1-A) FgIR

  • Fa

  • Atmosphere

  • FS(1-A)VIS Fa Fg

  • Ground

VIS

IR


Fluxes at the top of the atmosphere must balance
Fluxes at the top of the atmosphere must balance

  • FS(1-A) FgIR

  • Fa

  • Atmosphere

  • FS(1-A)VIS Fa Fg

  • Ground

VIS

IR


Fluxes at the ground must balance
Fluxes at the ground must balance

  • FS(1-A) FgIR

  • Fa

  • Atmosphere

  • FS(1-A)VIS Fa Fg

  • Ground

VIS

IR


Simply balance energy fluxes
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
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
Example calculations

  • TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25

  • FS /Wm-2 336 336 336 336

  • A 0.3 0.0 0.0 0.3

  • VIS 1.0 1.0 1.0 1.0

  • IR 1.0 1.0 0.0 0.0

  • TE /K 254 278 330 302


Example calculations1
Example calculations

  • TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25

  • FS /Wm-2 336 336 336 336

  • A 0.3 0.0 0.0 0.3

  • VIS 1.0 1.0 1.0 1.0

  • IR 1.0 1.0 0.0 0.0

  • TE /K 254 278 330 302


Example calculations2
Example calculations

  • TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25

  • FS /Wm-2 336 336 336 336

  • A 0.3 0.0 0.0 0.3

  • VIS 1.0 1.0 1.0 1.0

  • IR 1.0 1.0 0.0 0.0

  • TE /K 254 278 330 302


Example calculations3
Example calculations

  • TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25

  • FS /Wm-2 336 336 336 336

  • A 0.3 0.0 0.0 0.3

  • VIS 1.0 1.0 1.0 1.0

  • IR 1.0 1.0 0.0 0.0

  • TE /K 254 278 330 302


Example calculations4
Example calculations

  • TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25

  • FS /Wm-2 336 336 336 336

  • A 0.3 0.0 0.0 0.3

  • VIS 1.0 1.0 1.0 1.0

  • IR 1.0 1.0 0.0 0.0

  • TE /K 254 278 330 302


Quick QuestionsTE = [ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0.25 Assuming FS = 336 Wm-2 A = 0.3VIS = 0.8IR = 0.1TE = 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 QuestionsTE = [ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0.25 Assuming FS = 336 Wm-2 A = 0.3VIS = 0.8IR = 0.1TE = 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
Secrets in the Ice

  • Snow accumulation lays down record of environmental conditions

  • Compacted to ice preserving record

  • Drill ice core & date



Milankovitch cycles
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 cycles1
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



Indicators of the Human Influenceon the Atmosphere during the Industrial Era

Source: IPCC TAR 2001



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 CO2

Source: The Met Office. Hadley Center for Climate Prediction and Research


Temperature projections
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
Model simulation of recent climate

Natural forcings only(solar, volcanic etc. variability)

Anthropogenic forcings only(human-induced changes)

The Met Office


1.0

Observed

simulated by model

0.5

Temperature rise o C

0.0

Hadley Centre

1850 1900 1950 2000

Simulated global warming 1860-2000:Natural & Man-made factors


Factors affecting climate system
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
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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