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Consider a planet where the surface emits radiation as a perfect blackbody, and the atmosphere has an absorptivity of as for incoming solar radiation, and a, for outgoing long- wave infrared radiation. a) Draw a diagram to illustrate the contributions to the radiation budget above the atmosphere and directly above the surface. b) Show that the radiative equilibrium surface temperature of the planet is increased by the presence of the atmosphere if a₁ > a, and decreased if α₁ < aç.

Consider a planet where the surface emits radiation as a perfect blackbody, and the atmosphere has an absorptivity of as for incoming solar radiation, and a, for outgoing long- wave infrared radiation. a) Draw a diagram to illustrate the contributions to the radiation budget above the atmosphere and directly above the surface. b) Show that the radiative equilibrium surface temperature of the planet is increased by the presence of the atmosphere if a₁ > a, and decreased if α₁ < aç.

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
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Earth-Sun mean distance: 149.598 x 10⁰ m Radius of Sun: 6.96 x 10⁰ m Radius of Earth: 6371 x 10³ m Effective temperature of Sun: 5770 K Cross sectional area of a sphere: R² Surface area of a sphere: 4+R² Solid Angle: = Area on sphere/R²; d = sin0d0 dø Albedo of the Earth: A = 0.3 Plank Function: B(λ,T) = 2hc² hc 25 ekλT-1 Plank's constant: h = 6.626 × 10-34 Js Boltzmann's constant: k = 1.381× 10-23 J/K Speed of light: c = 3 × 108 m/s Flux: F = I cose d Watts Stephan-Boltzmann Law: F = 6T4 m² Stephan's constant: = 5.67 × 108 W m²2 K-4 Net flux upward or downward for isotropic radiation: F=nl Wien's displacement Law: Ap=2898/T µm Kirchoff's Law: absorptivity = emissivity Watts m².um.sr Run Flux of solar Radiation at Earth: F = Tsun = 1370 Watts/m² D²-s Optical cross section: k in Effective Radiating Temperature for the Earth (current climate): T₂ = 255 K Beer's Law: 1(X) = 1(0) exp[-x]; x = · S² kpdx = fondx m² kg or o in m² molecule Ideal Gas Law: P = pRT; R = 287 J Kg¹ K-¹ Ideal Gas Law: P = n k T; k = 1.381 × 10-²³ J/K Ideal Gas Law for Water Vapour: e=py Ry T; R = 461.5 J Kg¹ K-¹ Hydrostatic Equation: Barometric Law: P(z) = P(0) exp (− ²); H = RT/g; P₁ = 100 × 10³ Pa ; g = 9,81 m/s² dP dz ,(Po-P). Force of buoyancy: FB = 9- ·=g₁ P =-pg Adiabatic Lapse! dT Rate: =- dz g Cp First Law of Thermodynamics: dq = c₂dT + P da or Sq = ₁₂ dT - ² dp Joules kg-deg C Specific Heat Capacity for Air: Potential Temperature: 0 = T (T-To) To = -9.8 °C/km =1005 Cp Brunt-Vaisala Frequency, or Buoyancy Frequency: N² = g de 0 dz R Latent Heat of Condensation for water: 2535 J/g Latent Heat of Sublimation for water: 2834 J/g CAPE = -R des Les Clausius-Clapeyron Equation: dT R₂T² Solution to C-C equation: - = exp es(T) eso LFC dT Saturated (Wet) Adiabatic Lapse Rate: T = -- = dz EL [(T-To) dinPo Ry To LWS Equivalent Potential Temperature: 0 ~ 0 exp CpT - })}; at To = 0 °C (273 K), es = 611 Pa Velocity: v²v² = 2a(z-z₁); a is acceleration - 1+ Id Adiabatic liquid/ice water content: x = − 4w₁ (2); or x = − 4ps (1) - L dws T dz Cp đồ
Transcribed Image Text:Earth-Sun mean distance: 149.598 x 10⁰ m Radius of Sun: 6.96 x 10⁰ m Radius of Earth: 6371 x 10³ m Effective temperature of Sun: 5770 K Cross sectional area of a sphere: R² Surface area of a sphere: 4+R² Solid Angle: = Area on sphere/R²; d = sin0d0 dø Albedo of the Earth: A = 0.3 Plank Function: B(λ,T) = 2hc² hc 25 ekλT-1 Plank's constant: h = 6.626 × 10-34 Js Boltzmann's constant: k = 1.381× 10-23 J/K Speed of light: c = 3 × 108 m/s Flux: F = I cose d Watts Stephan-Boltzmann Law: F = 6T4 m² Stephan's constant: = 5.67 × 108 W m²2 K-4 Net flux upward or downward for isotropic radiation: F=nl Wien's displacement Law: Ap=2898/T µm Kirchoff's Law: absorptivity = emissivity Watts m².um.sr Run Flux of solar Radiation at Earth: F = Tsun = 1370 Watts/m² D²-s Optical cross section: k in Effective Radiating Temperature for the Earth (current climate): T₂ = 255 K Beer's Law: 1(X) = 1(0) exp[-x]; x = · S² kpdx = fondx m² kg or o in m² molecule Ideal Gas Law: P = pRT; R = 287 J Kg¹ K-¹ Ideal Gas Law: P = n k T; k = 1.381 × 10-²³ J/K Ideal Gas Law for Water Vapour: e=py Ry T; R = 461.5 J Kg¹ K-¹ Hydrostatic Equation: Barometric Law: P(z) = P(0) exp (− ²); H = RT/g; P₁ = 100 × 10³ Pa ; g = 9,81 m/s² dP dz ,(Po-P). Force of buoyancy: FB = 9- ·=g₁ P =-pg Adiabatic Lapse! dT Rate: =- dz g Cp First Law of Thermodynamics: dq = c₂dT + P da or Sq = ₁₂ dT - ² dp Joules kg-deg C Specific Heat Capacity for Air: Potential Temperature: 0 = T (T-To) To = -9.8 °C/km =1005 Cp Brunt-Vaisala Frequency, or Buoyancy Frequency: N² = g de 0 dz R Latent Heat of Condensation for water: 2535 J/g Latent Heat of Sublimation for water: 2834 J/g CAPE = -R des Les Clausius-Clapeyron Equation: dT R₂T² Solution to C-C equation: - = exp es(T) eso LFC dT Saturated (Wet) Adiabatic Lapse Rate: T = -- = dz EL [(T-To) dinPo Ry To LWS Equivalent Potential Temperature: 0 ~ 0 exp CpT - })}; at To = 0 °C (273 K), es = 611 Pa Velocity: v²v² = 2a(z-z₁); a is acceleration - 1+ Id Adiabatic liquid/ice water content: x = − 4w₁ (2); or x = − 4ps (1) - L dws T dz Cp đồ
Consider a planet where the surface emits radiation as a perfect blackbody, and the atmosphere has an absorptivity of as for incoming solar radiation, and a for outgoing long- wave infrared radiation. a) Draw a diagram to illustrate the contributions to the radiation budget above the atmosphere and directly above the surface. b) Show that the radiative equilibrium surface temperature of the planet is increased by the presence of the atmosphere if a₁ > a, and decreased if a₁ < as.
Transcribed Image Text:Consider a planet where the surface emits radiation as a perfect blackbody, and the atmosphere has an absorptivity of as for incoming solar radiation, and a for outgoing long- wave infrared radiation. a) Draw a diagram to illustrate the contributions to the radiation budget above the atmosphere and directly above the surface. b) Show that the radiative equilibrium surface temperature of the planet is increased by the presence of the atmosphere if a₁ > a, and decreased if a₁ < as.
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