answer is greater or less than your answer to part g, and whether that agrees withwhat 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 theplanetary 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 thanyour answer to part h, and whether that agrees with what you would physicallyexpect to result from an increase in latent heat flux.(j) With an increase in latent heat flux, would you expect global mean precipitationto increase or decrease? Why?(k) Physically explain why we expect global mean latent heat flux to increase as thesurface warms.ap)LHOT SEOTAεσΤΑAtmospheric layerEarth'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 asingle blackbody atmospheric layer with temperature T₁ and emissivity = 0.9. Thesurface is a perfect blackbody with temperature T. The atmospheric layer is assumedto 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 fluxassociated with this evaporation is taken to be LH = 55 W m-2. The solar constantis 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 thatthe Earth system is in a steady-state, which implies that the Earth system is in thermalequilibrium.(a) Write an expression for the energy balance of the surface in terms of T, TA and theother given parameters. Keep your expression algebraic, using the notation givenabove.(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 expressionthat solves for T. Keep your expression algebraic, and simplify your expression asmuch as possible.(d) Use your answers to previous parts to obtain an expression that solves for TA. Keepyour expression algebraic, and simplify your expression as much as possible.(e) Use your answers to previous parts to obtain an expression that solves for theemission temperature, Te, in terms of given quantities. (That is, your expressionshould not contain T, or TA.) Keep your expression algebraic, and simplify yourexpression 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 watervapour cause the atmospheric emissivity to increases to 0.93. Obtain new valuesfor T, TA and Te. Comment on whether your answers are greater than, less thanor equal to your answers to part f, and whether that agrees with what you wouldphysically 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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