Hand in Question sheets with answer booklets Calculators allowed Mobile telephones or other devices not allowed

Transcription

1 York University Department of Earth and Space Science and Engineering ESSE 3030 Department of Physics and Astronomy PHYS 3080 Atmospheric Radiation and Thermodynamics Final Examination 2:00 PM 11 December 2016 Duration: 3 hours Hand in Question sheets with answer booklets Calculators allowed Mobile telephones or other devices not allowed 100 marks in total: Q1 40 marks Q2 15 marks Q3 15 marks Q4 10 marks Q5 10 marks Q6 10 marks Useful information is given on page 5. 1

2 1. Explain: (4 marks each, 40 in total) a) Blue sky, red sunset. b) On a clear still night, the surface temperature drops more rapidly when the air above is dry than when it is moist. c) Surface temperature and the effective radiating temperature for a planet are not equal. d) Two climate feedback processes. e) High altitude clouds tend to have a warming effect on climate while low clouds tend to have a cooling effect. f) Ice crystals grow most rapidly by vapour deposition when there are also liquid water droplets present. g) Chapman profile for absorption of solar radiation. h) The Earth s climate would be very different if the atmosphere did not contain particulate matter (aerosol). i) Atomic Oxygen is the most abundant constituent in the atmosphere above a height of 150 km. j) The dryness of the stratosphere is explained by the circulation pattern in which air enters by rising through the tropical tropopause. 2. a) Show that if the Earth were covered entirely with ice having an albedo of 0.75, it would be possible to remain in that state indefinitely if the composition of the atmosphere did not change. (5 marks) b) If the sun were somewhat bluer in colour, so that it s wavelength of maximum emission was 0.4 μm instead of μm, calculate the effective radiating temperature of the Earth under these conditions. (5 marks) c) Compute the temperature at the top of the troposphere (the skin temperature ) assuming that transfer of infrared radiation is the only important process. (5 marks) 2

3 3. Consider a simple climate model in which the Earth s atmosphere is represented as a single layer that is transparent to solar radiation, but has an absorptivity, a, in the infrared. The Earth s overall albedo is 0.3. a) Draw a diagram to illustrate the contributions to the radiation budget above the atmosphere and directly above the surface. (5 marks) b) Determine the IR absorptivity for the atmosphere that will result in a ground temperature that is equal to the current average of 288 K for the Earth. (5 marks) c) A doubling of carbon dioxide will cause the infrared absorptivity of the atmosphere to increase by 2.6 %. Calculate the resulting change in surface temperature. (5 marks) 4.) a) What fraction of incident radiation is absorbed in passing through the layer in the atmosphere extending from optical depth 0.2 to 4.0. (5 marks) b) Of the intensity that is emitted to space by an isothermal atmosphere, what fraction is emitted from the layer extending from an optical depth of 0.2 to 4.0. (5 marks) 5.) a) The spectra of intensity of infrared radiation measured from orbit above Antarctica and the Sahara Desert are shown in Figures 1a and 1b. Explain why there is a relative maximum for wavelengths in the range μm above Antarctica, but there is a relative minimum for the same wavelengths above the Sahara Desert. (5 marks) b) Figure 1c shows the spectrum of infrared radiation measured above the Pacific Ocean when the atmosphere was cloud free and also above a thick thunderstorm anvil outflow cloud. Estimate the height of the anvil cloud top assuming that the lapse rate was 6 o C per km throughout the troposphere. (5 marks) 6.) Consider a location in the tropics where the average flux of solar radiation at the top of the atmosphere is 400 W/m 2. A cloud scatters 50 % of the incident solar radiation back to space, and it has an infrared absorptivity of 1.0. a) Calculate the temperature of the cloud top for which the combined effects of the cloud on solar and infrared radiation would cancel. (5 marks) b) What is the lowest cloud top height for a net positive heating effect on climate? Assume the ground temperature is 30 o C and the lapse rate is 6 o C per km throughout the troposphere. (5 marks) 3

4 Figure 1. Spectra of infrared radiation intensity measured from an orbiting satellite above (a) the Sahara Desert (no clouds), (b) Antarctica (no clouds), and (c) the tropical western Pacific Ocean. (c) includes a spectrum measured above clear air as well as a specrum measured above a thick thunderstorm anvil outflow cloud (as labeled). Plank function curves at various temperatures are shown (dashed lines) for comparison. 4

5 Information Earth-Sun mean distance: x 10 9 m (one A.U.) Radius of Sun: 6.96 x 10 8 m Radius of Earth: 6371 x 10 3 m Effective temperature of Sun: 5770 K Cross sectional area of a sphere: πr 2 Surface area of a sphere: 4πR 2 Solid Angle: W = Area on sphere/r 2 ; dw = sinq dq df Flux of solar radiation at the Earth: Fs = 1370 W/m 2 Albedo of the Earth: A = 0.3 Plank Function: B(λ,T) = 2hc 2 /λ 5 (e hc/kλt 1) Plank s constant: h = J s Boltzmann s constant: k = J/K Speed of light: c = 3 x 10 8 m/s Stephan-Boltzmann Law: F = σt 4 Stephan s constant: σ = W m -2 K -4 For isotropic radiation: F = p I Wien s displacement Law: λp = 2898/T μm Beer s Law: I = Io exp(-χ); dχ = kρdz/cosθ Schwarzchild s equation:!" #$!% = I + J Ideal Gas Law: P = ρrt; R = 287 J Kg -1 K -1 Barometric Law: P(z) = Po exp(-z/h); H = RT/g; Po = Pa ; g = 9.81 m/s 2 Latent Heat of Sublimation for water ice at temperature 270 K: 2464 J/g 5