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Processes with the influence on Earth ’s temperature and their modelling

Processes with the influence on Earth ’s temperature and their modelling. Ing. Pavel Oupick y Institute of P la s ma Physics AV ČR ,v.v.i. Department of O ptic al D iagnos tic Turnov. K eywords :

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Processes with the influence on Earth ’s temperature and their modelling

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  1. Processes with the influence on Earth’s temperature and their modelling Ing. Pavel Oupicky Institute of Plasma Physics AV ČR ,v.v.i. Department ofOpticalDiagnostic Turnov Keywords: TSI (total solar irradiation), black andgreybody, albedo, greenhouse effekt ,effektive temperature, climate modeling, Daisyworld, Greenhouseworld , Wimovac,Moses radiometers, spectroradiometers, satellites

  2. Procesyovliňující teplotu Zeměa jejich modelování Klíčová slova: TSI (total solar irradiation), černé a šedé těleso, albedo, skleníkový efekt ,efektivní teplota, klimatické modely, Daisyworld, Greenhouseworld , Wimovac,Moses radiometry, spektroradiometry, satelity Ing. Pavel Oupický Ústav fyziky plazmatu AV ČR ,v.v.i. Oddělení optické diagnostiky Turnov

  3. Sun + Earth Earth reflection + irradiation -> ….. <- Solar irradiation [1]

  4. Energy comming <=> Enegry leaving Climate Change and Greenhouse Effect. A briefing from the Hadley Centre for Climate Prediction Professor John Mitchell et al, Chief Scientist, Met Office December 2005

  5. Black body - Planck law (for wavelength) I is irradiation of black body of temperature T on wavelength λ

  6. Planck law (for wave number) I is irradiation of black body of temperature T on wave number ν l=1/ν[lin meters ] l=10000/ν[lin micrometers ]

  7. Stefan-Boltzman law derivation I is total irradiation of black body of temperature T

  8. Prof. Mike Barnsley, University of Wales Swansea

  9. Sun and Earth as black bodies Earth irradiation (T effective~ 14ºC) = 385W/m2

  10. Earth radiation The amount of energy radiated by the surface of the Earth depends only on the temperature of the surface of the Earth. The type of radiation is also determined by the temperature of the Earth, most of the energy it loses is in the form of infrared radiation. The quantity of radiation lost is proportional to T ^4, where T is the Earth’s temperature in kelvins (K).

  11. Black,greyand realbody Black body: EBB= σ T s4 Grey body: EGB= εσ T s4 ε (or α) < 1 Emisivity (or absorbance) ε (λ) = const Real Body: ERB= ε(λ)σ T s4

  12. Sun <---> Earth Power Balance PDISK = PSR ~PEI= PKOULE

  13. Sun + {geothermal + fosil} power π r 2 ETSI{+ 4 π r 2EGI + 4 π r2EFI}

  14. Earth outgoing power (Earth as real body) PEI (λ)= 4 π r 2ε(λ)ETEI ε(λ) = ( 1-G (λ) ) / (1–A(λ)) PEI (λ) = 4 π r 2(( 1-G (λ) ) / (1–A(λ))) ETEI

  15. Sun <---> Earth Power Balance π r 2 ETSI + {4 π r 2EGI + 4 π r2EFI} = 4 π r 2 (( 1-G ) / (1–A)) ETEI Next: dividing by 4 π r 2 and multipling by (1-A) :

  16. Sun <=> Earth Radiation Balance (1-A) ( ETSI/ 4 + {EGI + EFI} ) = (1-G) ETEI where : ETEI= σ T e4 A(l,φ,t,h,etc.) is albedo, A<1 G(l,φ,t,etc.) is greenhouse “albedo”, G<1 Teis effective temperature in Kelvins

  17. Sun <=> Earth Radiance Balance EGI= 0 , EFI = 0 (1 -A) ETSI/ 4 = (1-G) σ T e4 Basic equation of Solarworld (of black and grey bodies)

  18. Effective (emissive) temperature definition Te ~ ETSI / 4 ESI (φ) = ETSI cos2(φ)/ 2 (change between day and night, φis latitude) on equator(φ = 0 ) ESI (0) = ETSI / 2 ETSI cos2(φ)/ 2 = ETSI / 4 => φ cos 2(φ) = 1/2 => cos(φ) = 0.707 => 45º~ Te

  19. Effective and global temperature Temperature is monitored on the many places on Earth for the long time “Global temperature” is the average from many measurement

  20. On earth globe temperature Observed mean temperature from January to December 1961 - 1990

  21. TSI data from NASA Nextdata wereobtained from the NASA Langley Research Center AtmosphericScience Data Center.

  22. TSI on the top of earth orbit on the earth distance from Sun and re-count on A.U. TSI data from SORCE / TIM

  23. TSI on the top of earth orbit in A.U. and earth distance from Sun TSI data from SORCE / TIM / detail

  24. TSI on the top of earth orbit in A.U. TSI data comparison from ACRIM and SORCE satelites

  25. TSI on the top of earth orbit in A.U. TSI data comparison from ACRIM and SORCE satelites - detail

  26. TSI on the top of earth orbit in A.U. Data Quality Description (updated 13 December 2005) To date the TIM is proving very stable with usage and solar exposure, and long-term relative uncertainties are estimated to be less than 0.014 W/m2/yr (10 ppm/yr). Present absolute accuracy is estimated to be 0.48 W/m^2 (350 ppm), largely determined by the agreement between all four TIM radiometers. There remains an unresolved 4.5 W/m2 difference between the TIM and other space-borne radiometers, and this difference is being studied by the TSI and radiometry communities.

  27. TSI on the top of earth orbit in A.U. TSI data from ACRIM / ACRIM3 satelite - detail

  28. TSI in three solar cycles TSI from the maxima of 21. solar cycle to the minima of 21.solar one

  29. Data from ACRIM3 - example

  30. Sun and Earth as ideal black body radiators Theoretical count of spectra

  31. Sun and Earth as ideal black body radiators Theoretical count of normalised spectra

  32. Solar irradiation measuring On the top of atmosphere and on the Earth in sea level

  33. Solar irradiation measuring Measuring on the Earth surface Malá Skála (near of Turnov city, Czech Republic)

  34. Earth reflection and absorption(Campbell and Norman 1998) Shortwave radiation budget [1] Reflection : a) Atmosphere c) clouds e) surface Absorption: b) atmosphere d) clouds f) surface

  35. Incoming Solar radiation 342 = 1368 / 4 [ W/m2]

  36. Reflected solar radiation Picture from NASA / Satellite Terra/Modis measuring

  37. Earth and atmosphereirradiation Longwave irradiation budget a) absorbed by atmospheric gases b) lost to space c) from atmospheric gases d) sensible heat flux e) from clouds f) latent heat flux

  38. Earth and atmosphere irradiation Satellite measuring (Modis) (Data from NASA, Earth Observatory)

  39. Total Sun <-> Earth radiation balance Radiation - all in W/m2

  40. Total Sun <-> Earth radiation balance Picture from NASA / Earth Observatory

  41. Total Sun <-> Earth radiation balance

  42. Earth incoming <-> outgoing energy balanceall in W/m2 What is the net energy at the top of the atmosphere? Incomming : 1368/4 = 342–77(clouds)–30(surface) = 235 W/m2 Outgoing: 165(a)+30(c) + 40(w) = 235 W/m2 The Earth (planet and atmosphere) receives as much energy from the Sun as it loses to space What is the net energy of the centre of the atmosphere? Incoming : 67(aa) + 78(vap) + 24(thermal) + 350(es) = 519 Outgoing: 324(back)+165(e)+30(c) = 519 The atmosphere receives as much energy from the Sun as it loses to Space What is the net energy of the surface of the Earth? Incoming: 168(Sun) + 324(gases) = 492 Outgoing: 390(surface) + 78(vap) + 24(thermal) = 492

  43. Earth incoming <-> outgoing energy balance Atmosphere

  44. Earth incoming <-> outgoing energy balance results • The surface of the Earth receives as much energy from the Sun as it loses to space • All the elements of the Earth/atmosphere system lose as much energy as they gain. • Therefore, their temperature stays stable.

  45. Climate models Zero-dimensional models Higher Dimension Models Radiative-Convective Models EMICs (Earth-system Models of Intermediate Complexity) GCMs (Global Climate Models or General Circulation Models

  46. Zero-dimensional models • A very simple model of the radiative equilibrium of the Earth is (1 − a) S πr2 = 4πr2ε σT4 • where • the left hand side represents the incoming energy from the Sun • the right hand side represents the outgoing energy from the Earth, calculated from the Stefan-Boltzmann law assuming a constant radiative temperature, T, that is to be found, • and

  47. Zero-dimensional models The constant πr2 can be factored out, giving (1 − a) S = 4 ε σ T 4 This yields an average earth temperature of 288 K. This is because the above equation represents the effective radiative temperature of the Earth (including the clouds and atmosphere).

  48. Zero-dimensional models • S is the solar constant - the incoming solar radiation per unit area - about 1367 W·m-2 • a is the Earth's average albedo, measured to be 0.3[1][2] • r is Earth's radius — approximately 6.371×106m • π is well known, approximately 3.14159 • σ is the Stefan-Boltzmann constant — approximately 5.67×10-8 J·K-4·m-2·s-1 • ε is the effective emissivity of earth, about 0.612

  49. Greenhouse effect EEI= ε(λ)σ T s4 EEI=(1-G(λ))σ T s4 ( 1/Ghf(λ) ) =1-G(λ) = ε(λ) EEI= σ T s4 ε < 1, G<1 , Ghf>1 Greenhouse factor or emissivity or Greenhouse “albedo” equivalents

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