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(a) Write an expression for the energy balance of the surface in terms of T5, T₁ and the other given parameters. Keep your expression algebraic, using the notation given above. (b) Write an expression for the energy balance of the atmospheric layer in terms of T., TA, and the other given parameters. Keep your expression algebraic. (c) Combine your answers to previous parts to eliminate T₁ and obtain an expression that solves for T. Keep your expression algebraic, and simplify your expression as much as possible. (d) Use your answers to previous parts to obtain an expression that solves for T₁. Keep your expression algebraic, and simplify your expression as much as possible. (e) Use your answers to previous parts to obtain an expression that solves for the emission temperature, Te, in terms of given quantities. (That is, your expression should not contain T, or T₁.) Keep your expression algebraic, and simplify your expression as much as possible. (f) Using the given parameter values, determine numerical values for T₁, T₁ and Te. (g) Assume that increasing concentrations of atmospheric carbon dioxide and water vapour cause the atmospheric emissivity to increases to 0.93. Obtain new values for T, TA and Te. Comment on whether your answers are greater than, less than or equal to your answers to part f, and whether that agrees with what you would physically expect to result from an increase in atmospheric emissivity. (h) Assume that, in addition to the atmospheric emissivity increasing to 0.93, the plan- etary albedo reduces to 0.27. Obtain a new value for T,. Comment on whether your

(a) Write an expression for the energy balance of the surface in terms of T5, T₁ and the other given parameters. Keep your expression algebraic, using the notation given above. (b) Write an expression for the energy balance of the atmospheric layer in terms of T., TA, and the other given parameters. Keep your expression algebraic. (c) Combine your answers to previous parts to eliminate T₁ and obtain an expression that solves for T. Keep your expression algebraic, and simplify your expression as much as possible. (d) Use your answers to previous parts to obtain an expression that solves for T₁. Keep your expression algebraic, and simplify your expression as much as possible. (e) Use your answers to previous parts to obtain an expression that solves for the emission temperature, Te, in terms of given quantities. (That is, your expression should not contain T, or T₁.) Keep your expression algebraic, and simplify your expression as much as possible. (f) Using the given parameter values, determine numerical values for T₁, T₁ and Te. (g) Assume that increasing concentrations of atmospheric carbon dioxide and water vapour cause the atmospheric emissivity to increases to 0.93. Obtain new values for T, TA and Te. Comment on whether your answers are greater than, less than or equal to your answers to part f, and whether that agrees with what you would physically expect to result from an increase in atmospheric emissivity. (h) Assume that, in addition to the atmospheric emissivity increasing to 0.93, the plan- etary albedo reduces to 0.27. Obtain a new value for T,. Comment on whether your

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
Section: Chapter Questions
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answer is greater or less than your answer to part g, and whether that agrees with what you would physically expect to result from a decrease in planetary albedo. (i) Assume that, in addition to the atmospheric cmissivity increasing to 0.93, and the planetary albedo decreasing to 0.27, the latent heat flux increases to 62 W m-². Obtain a new value for T.. Comment on whether your answer is greater or less than your answer to part h, and whether that agrees with what you would physically expect to result from an increase in latent heat flux. (j) With an increase in latent heat flux, would you expect global mean precipitation to increase or decrease? Why? (k) Physically explain why we expect global mean latent heat flux to increase as the surface warms. ap) LH OT S EOTA εσΤΑ Atmospheric layer Earth's surface
Transcribed Image Text:answer is greater or less than your answer to part g, and whether that agrees with what you would physically expect to result from a decrease in planetary albedo. (i) Assume that, in addition to the atmospheric cmissivity increasing to 0.93, and the planetary albedo decreasing to 0.27, the latent heat flux increases to 62 W m-². Obtain a new value for T.. Comment on whether your answer is greater or less than your answer to part h, and whether that agrees with what you would physically expect to result from an increase in latent heat flux. (j) With an increase in latent heat flux, would you expect global mean precipitation to increase or decrease? Why? (k) Physically explain why we expect global mean latent heat flux to increase as the surface warms. ap) LH OT S EOTA εσΤΑ Atmospheric layer Earth's surface
Attempt to model the effect of increasing greenhouse gas concentration in Earth's at- mosphere using a simplified model as in the figure below. In this model, there is a single blackbody atmospheric layer with temperature T₁ and emissivity = 0.9. The surface is a perfect blackbody with temperature T. The atmospheric layer is assumed to be completely transparent to solar radiation. In addition to these radiative processes, evaporation also acts to cool the surface and warm the atmosphere. The latent heat flux associated with this evaporation is taken to be LH = 55 W m-2. The solar constant is So=1362 W m2, the Stefan-Boltzmann constant is o = 5.67 × 10-8 W m² K¯4, and the planetary albedo is taken to be ap = 0.29. For all questions below, assume that the Earth system is in a steady-state, which implies that the Earth system is in thermal equilibrium. (a) Write an expression for the energy balance of the surface in terms of T, TA and the other given parameters. Keep your expression algebraic, using the notation given above. (b) Write an expression for the energy balance of the atmospheric layer in terms of Ts, TA, and the other given parameters. Keep your expression algebraic. (c) Combine your answers to previous parts to eliminate T₁ and obtain an expression that solves for T. Keep your expression algebraic, and simplify your expression as much as possible. (d) Use your answers to previous parts to obtain an expression that solves for TA. Keep your expression algebraic, and simplify your expression as much as possible. (e) Use your answers to previous parts to obtain an expression that solves for the emission temperature, Te, in terms of given quantities. (That is, your expression should not contain T, or TA.) Keep your expression algebraic, and simplify your expression as much as possible. (f) Using the given parameter values, determine numerical values for T₁, TA and Te. (g) Assume that increasing concentrations of atmospheric carbon dioxide and water vapour cause the atmospheric emissivity to increases to 0.93. Obtain new values for T, TA and Te. Comment on whether your answers are greater than, less than or equal to your answers to part f, and whether that agrees with what you would physically expect to result from an increase in atmospheric emissivity. (h) Assume that, in addition to the atmospheric emissivity increasing to 0.93, the plan- etary albedo reduces to 0.27. Obtain a new value for Tg. Comment on whether your
Transcribed Image Text:Attempt to model the effect of increasing greenhouse gas concentration in Earth's at- mosphere using a simplified model as in the figure below. In this model, there is a single blackbody atmospheric layer with temperature T₁ and emissivity = 0.9. The surface is a perfect blackbody with temperature T. The atmospheric layer is assumed to be completely transparent to solar radiation. In addition to these radiative processes, evaporation also acts to cool the surface and warm the atmosphere. The latent heat flux associated with this evaporation is taken to be LH = 55 W m-2. The solar constant is So=1362 W m2, the Stefan-Boltzmann constant is o = 5.67 × 10-8 W m² K¯4, and the planetary albedo is taken to be ap = 0.29. For all questions below, assume that the Earth system is in a steady-state, which implies that the Earth system is in thermal equilibrium. (a) Write an expression for the energy balance of the surface in terms of T, TA and the other given parameters. Keep your expression algebraic, using the notation given above. (b) Write an expression for the energy balance of the atmospheric layer in terms of Ts, TA, and the other given parameters. Keep your expression algebraic. (c) Combine your answers to previous parts to eliminate T₁ and obtain an expression that solves for T. Keep your expression algebraic, and simplify your expression as much as possible. (d) Use your answers to previous parts to obtain an expression that solves for TA. Keep your expression algebraic, and simplify your expression as much as possible. (e) Use your answers to previous parts to obtain an expression that solves for the emission temperature, Te, in terms of given quantities. (That is, your expression should not contain T, or TA.) Keep your expression algebraic, and simplify your expression as much as possible. (f) Using the given parameter values, determine numerical values for T₁, TA and Te. (g) Assume that increasing concentrations of atmospheric carbon dioxide and water vapour cause the atmospheric emissivity to increases to 0.93. Obtain new values for T, TA and Te. Comment on whether your answers are greater than, less than or equal to your answers to part f, and whether that agrees with what you would physically expect to result from an increase in atmospheric emissivity. (h) Assume that, in addition to the atmospheric emissivity increasing to 0.93, the plan- etary albedo reduces to 0.27. Obtain a new value for Tg. Comment on whether your
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