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Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University
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Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Mar 28, 2015

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Page 1: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Climate ChangeA simple climate model

Dudley Shallcross and Tim Harrison, Bristol University

Page 2: 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• Ideas and questions e-mail [email protected] or

[email protected]

Page 3: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Granny’s model of climate 1

Earth Sun

Temperature of the Earth ~ 10o C

Page 4: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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)

Page 5: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Granny’s model of climate 2

Earth Sun

With clouds and ice

Temperature of the Earth ~ - 18o C

Page 6: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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)

Page 7: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

CO2 O3

Page 8: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Granny’s model of climate 3 (with blankets)

Earth Sun

with clouds and ice and greenhouse gases

Temperature of the Earth ~ 16o C

Page 9: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Thanks to Mike Stuart 2008 www.disphoria.co.uk

For the granny cartoons

Page 10: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 11: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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).

Page 12: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Energy Out Energy In

Out = TE4 4RE

2 IN = S x Area

IN = 1370 πRE2 W m-2

Area of Earth normal to Solar Radiation S = πRE

2

Surface area of Earth = 4πRE2

Solar Flux, per unit area, S

Page 13: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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)

Page 14: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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)

Page 15: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Re-calculate TE

48(5.6

13

7

7

10 ) 4

0 0.7ET

24% of solar flux is reflected by clouds

6% Scattered by surface

TE = 255 K (- 18 o C) Cold

Page 16: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Terrestrial RadiationThe 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.

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

Page 17: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Atmospheric Window (C-F bonds absorb ir energy)

Page 18: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Model 2: One layer atmosphere

FS(1-A) FgIRFa

Atmosphere

FS(1-A)VIS Fa Fg

Ground

IR VIS

Page 19: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 20: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 21: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 22: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 23: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 24: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 25: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

FS(1-A) FgIRFa

Atmosphere

FS(1-A)VIS Fa Fg

Ground

IR VIS

Page 26: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Fluxes at the top of the atmosphere must balance

FS(1-A) FgIRFa

Atmosphere

FS(1-A)VIS Fa Fg

Ground

IR VIS

Page 27: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Fluxes at the ground must balance

FS(1-A) FgIRFa

Atmosphere

FS(1-A)VIS Fa Fg

Ground

IR VIS

Page 28: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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 )

Page 29: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 30: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 31: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 32: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 33: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 34: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 35: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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.

Page 36: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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)

Page 37: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Secrets in the Ice

Snow accumulation lays down record of environmental conditions

Compacted to ice preserving record

Drill ice core & date

Page 38: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Climate Change

Page 39: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 40: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 41: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Source: OSTP

Page 42: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 43: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Climate Change

Page 44: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 45: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Page 46: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

21002100

Projected 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

Page 47: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

Model simulation of recent climate

Natural forcings only(solar, volcanic etc.

variability)

Anthropogenic forcings only(human-induced changes)

The Met Office

Page 48: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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

Observed

simulated by model

Tem

pera

ture

ris

e

o C

0.0

0.5

1.0

1850 1900 1950 2000

Hadley Centre

Page 49: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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?

Page 50: Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University.

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