# 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

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.ukd.e.shallcross@bris.ac.uk

Grannys model of climate 1 Earth Sun Temperature of the Earth ~ 10 o C

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/waterIce 30% of incoming solar radiation reflected back out to space without being absorbed (Earths albedo A = 0.3)

Grannys model of climate 2 Earth Sun With clouds and ice Temperature of the Earth ~ - 18 o C

Granny is now very cold What can she do to warm herself up? Move closer? (Earths 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)

CO 2 O3O3

Grannys model of climate 3 (with blankets) Earth Sun with clouds and iceand greenhouse gases Temperature of the Earth ~ 16 o C

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 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 R E, in this very simple model we can see that the Earth absorbs solar radiation over an area R 2 (i.e. a flat atmosphere) but emits energy from an area 4 R 2 (i.e. from the entire surface).

Energy OutEnergy In Out = T E 4 4R E 2 IN = S x Area IN = 1370 πR E 2 W m -2 Area of Earth normal to Solar Radiation S = π R E 2 Surface area of Earth = 4 π R E 2 Solar Flux, per unit area, S

Surface temperature looks OK Energy in=Energy out 1370 x R E 2 = T E 4 x 4 R E 2 T E 4 = 1370 4 x 5.67x10 -8 T E =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/waterIce 30% of incoming solar radiation reflected back out to space without being absorbed (Earths albedo A = 0.3)

Re-calculate T E 24% of solar flux is reflected by clouds 6% Scattered by surface T E = 255 K (- 18 o C) Cold

Terrestrial Radiation The Earth also acts as a blackbody radiator T E = 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 Earths 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)Fg IR Fa Atmosphere FS(1-A) VISFaFg Ground IR VIS

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) VISFaFg Ground IR VIS

VIS = Transmittance of UV/Vis light from the Sun through the Earths 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) VISFaFg Ground IR VIS

IR = Transmittance of IR light from the Earth through the Earths 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) VISFaFg 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)Fg IR Fa Atmosphere FS(1-A) VISFaFg Ground IR VIS

Fg IR = The IR energy flux from the ground modified by the transmittance properties of the Earths atmosphere that now escapes to space. FS(1-A)Fg IR Fa Atmosphere FS(1-A) VISFaFg 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 Earths atmosphere. FS(1-A)Fg IR Fa Atmosphere FS(1-A) VISFaFg Ground IR VIS

Fg = The IR energy flux from the Earths surface. FS(1-A)Fg IR Fa Atmosphere FS(1-A) VISFaFg Ground IR VIS

Fluxes at the top of the atmosphere must balance FS(1-A)Fg IR Fa Atmosphere FS(1-A) VISFaFg Ground IR VIS

Fluxes at the ground must balance FS(1-A)Fg IR Fa Atmosphere FS(1-A) VISFaFg 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 = T E 4 =FS(1-A)(1 + VIS) / (1 + IR ) T E =[ FS(1-A)(1 + VIS) / σ(1 + IR ) ] 0.25 Assuming FS = 336 Wm -2 A = 0.3 VIS =0.8 IR=0.1 T E =287 K

Example calculations T E =[ FS(1-A)(1 + VIS) / σ(1 + IR )] 0.25 FS /Wm -2 336336 336336 A0.30.00.00.3 VIS 1.01.01.01.0 IR1.01.00.00.0 T E /K 254278330302

Example calculations T E =[ FS(1-A)(1 + VIS) / σ(1 + IR )] 0.25 FS /Wm -2 336336 336336 A0.30.00.00.3 VIS 1.01.01.01.0 IR1.01.00.00.0 T E /K 254278330302

Example calculations T E =[ FS(1-A)(1 + VIS) / σ(1 + IR )] 0.25 FS /Wm -2 336336 336336 A0.30.00.00.3 VIS 1.01.01.01.0 IR1.01.00.00.0 T E /K 254278330302

Example calculations T E =[ FS(1-A)(1 + VIS) / σ(1 + IR )] 0.25 FS /Wm -2 336336 336336 A0.30.00.00.3 VIS 1.01.01.01.0 IR1.01.00.00.0 T E /K 254278330302

Example calculations T E =[ FS(1-A)(1 + VIS) / σ(1 + IR )] 0.25 FS /Wm -2 336336 336336 A0.30.00.00.3 VIS 1.01.01.01.0 IR1.01.00.00.0 T E /K 254278330302

Quick Questions T E =[ FS(1-A)(1 + VIS) / σ(1 + IR ) ] 0.25 Assuming FS = 336 Wm -2 A = 0.3 VIS =0.8 IR=0.1 T E =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 Earths 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 T E =[ FS(1-A)(1 + VIS) / σ(1 + IR ) ] 0.25 Assuming FS = 336 Wm -2 A = 0.3 VIS =0.8 IR=0.1 T E =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 Earths 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 Earths 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 Earths 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 Earths 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 Influence on the Atmosphere during the Industrial Era Source: IPCC TAR 2001

Climate Change

Source: IPCC TAR 2001 Variations of the Earths Surface Temperature* *relative to 1961-1990 average

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

Global average temperature is projected to increase by 1.0 to 10 °C from 1990 to 2100 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 Temperature 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 Observed simulated by model Temperature rise 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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