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Climate Change A simple climate model

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

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  1. Climate ChangeA simple climate model Dudley Shallcross and Tim Harrison, Bristol University

  2. 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

  3. Granny’s model of climate 1 Earth Sun Temperature of the Earth ~ 10o C

  4. 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)

  5. Granny’s model of climate 2 Earth Sun With clouds and ice Temperature of the Earth ~ - 18o C

  6. 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)

  7. CO2 O3

  8. Granny’s model of climate 3 (with blankets) Earth Sun with clouds and ice and greenhouse gases Temperature of the Earth ~ 16o C

  9. Thanks to Mike Stuart 2008 • www.disphoria.co.uk • For the granny cartoons

  10. 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).

  11. 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).

  12. 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

  13. 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)

  14. 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)

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

  16. 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

  17. Atmospheric Window (C-F bonds absorb ir energy)

  18. Model 2: One layer atmosphere • FS(1-A) FgIR • Fa • Atmosphere • FS(1-A)VIS Fa Fg • Ground VIS IR

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. Fluxes at the ground must balance • FS(1-A) FgIR • Fa • Atmosphere • FS(1-A)VIS Fa Fg • Ground VIS IR

  28. 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 )

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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.

  36. 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)

  37. Secrets in the Ice • Snow accumulation lays down record of environmental conditions • Compacted to ice preserving record • Drill ice core & date

  38. Climate Change

  39. 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

  40. 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

  41. Source: OSTP

  42. Indicators of the Human Influenceon the Atmosphere during the Industrial Era Source: IPCC TAR 2001

  43. Climate Change

  44. Variations of the Earth’s Surface Temperature* *relative to 1961-1990 average Source: IPCC TAR 2001

  45. 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

  46. 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

  47. Model simulation of recent climate Natural forcings only(solar, volcanic etc. variability) Anthropogenic forcings only(human-induced changes) The Met Office

  48. 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

  49. 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).

  50. 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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