ATMS 321: Science of Climate Practice Mid Term Exam - Spring 2008 page 1 Atmospheric Sciences 321 Science of Climate Practice Mid-Term Examination: Would be Closed Book Data and formulas at the end. Exam would be Weds. May 8, 2008 Multiple Choice Questions: 1. What fraction of the solar radiation that arrives at the top of the atmosphere is absorbed in the atmosphere? a) 70%, b) 50%, c) 30%, d) 20%, e) 10% Answer: d 2. What fraction of the solar radiation that arrives at the top of the atmosphere is absorbed at the Earth's surface? a) 70%, b) 50%, c) 30%, d) 20%, e) 10% Answer: b 3. What fraction of the solar radiation that is absorbed at the Earth's surface is used to evaporate water? a) 70%, b) 50%, c) 30%, d) 20%, e) 10% Answer: b 4. How large is the rate of terrestrial radiation emission from the Earth's surface compared to the solar radiation that arrives at the top of the atmosphere, globally averaged? a) 150%, b) 110%, c) 70%, d) 50%, e) 10% Answer: b 5. What fraction of the terrestrial radiation emission from the Earth's surface escapes to space without being absorbed by the atmosphere? a) 70%, b) 50%, c) 30%, d) 20%, e) 10% Answer: e 6. At what latitude and during what season is the daily-averaged insolation at the top of the atmosphere the greatest? a) Equator at Equinox, b) Equator on Jan. 5, c) South pole on Dec. 21, d) North pole on June 21, e) South Pole on June 21. Answer: c 7. The two most important greenhouse gases are: a) CO 2 and CFCs, b) CO 2 and CH 4, c) CO 2 and H 2 O, d) CO 2 and SO 2 Answer: c Problems: 1. A volcanic eruption produces a cloud of aerosols at 20 km altitude. The cloud of aerosols reflects 0.5% and absorbs 0.5% of the direct downward solar radiation incident on it. Use global mean radiative equilibrium calculations to estimate how much the surface temperature would change in response to the introduction of the stratospheric aerosol cloud. You may assume that the troposphere can be represented by two layers that are black bodies for terrestrial radiation, but transparent for solar radiation.
ATMS 321: Science of Climate Practice Mid Term Exam - Spring 2008 page 2 The trick here is to realize that the part that is absorbed in the stratosphere is effectively lost to the surface because it does not get under the greenhouse gases, but is absorbed wave above them. 2. What is the solar zenith angle at noon at winter solstice at 30N? At noon, zenith angle equals latitude minus declination. 5. Why are peat bogs so common in high latitudes? Use the water balance. Rain falls from warm air infusions, but surface is cold so Bowen Ratio is high. Available heat is lost by sensible flux. 6. What is potential evapotranspiration? 7. What does Penman s equation tell you? See Eqn. (5.12) 8. A rectangular 10 m 2 solar panel is inclined at an angle of 30 to the direct solar beam, the direction toward the sun. The panel has an albedo for solar radiation of 0.1 and an emissivity for thermal infrared radiation of 0.9. If the panel is such a good heat conductor that both its faces always have equal temperature, calculate the temperature of the solar panel at radiative equilibrium if the total solar irradiance is 1367 Wm -2. (10 pts) sun 30 Solar Panel IN = OUT Solar flux x shadow area x absorptivity = longwve emission x emission area. 9. Suppose the net radiative heat balance at the top of the atmosphere averages over the Northern Hemisphere to 5 Wm -2, and averages over the Southern Hemisphere to -5 Wm - 2, over a long period of time. Calculate the northward heat flux across the equator in Joules per second necessary to balance this radiative heating difference and maintain a steady equilibrium. (10pts) To get J/s = W, you need to multiply by the area over which energy is being lost. Pay attention to the sign. 10. The Gulf Stream off the East Coast of North America loses heat to the atmosphere at the rate of 300 Wm -2 during winter. If the Gulf Stream current is 500 meters deep, at what rate does the water temperature change with time as a result of this heat loss through the surface? Assume all influences on the temperature except the heat flux through he
ATMS 321: Science of Climate Practice Mid Term Exam - Spring 2008 page 3 surface and the storage capacity can be neglected in this calculation. Give your answer in C per day. (10pts) density x specific heat x depth x dt/dt = flux 11. Which continent do you think has the highest Bowen ratio? Explain your reasoning. (5pts) Australia ( over Antarctica, I think) 12. In Oklahoma, the winds at the surface are often stronger during the day than at night. Explain. (10pts) See discussion related to Fig. 4.9. 13. The tropical upper troposphere around 12-15 km contains a large amount of high, thin cirrus cloud that is almost invisible, but which contains enough water to be mostly opaque to IR. How do you think this type of cloud affects the temperature of the planet? Explain your reasoning. (10pts) Think about albedo contrast and OLR contrast and their balance. 14. What is potential evapotranspiration? Explain thoroughly. (10pts) 15. Discuss the unusual features of this diurnal heat budget plot and speculate about what might cause these unusual features. (10pts) 1000 800 9 July Watts/Square Meter 600 400 200 R sfc G LE 0-200 0 2 4 6 8 SH 10 12 14 16 18 20 22 24 Local Time This figure appears in text. 16. A gigantic volcanic eruption takes place. The radiative properties of the atmosphere change such that the planetary albedo is changed to 0.2, and the disposition of the absorbed solar radiation is changed so that 50% of the radiation that is absorbed is absorbed into the atmosphere and 50% is absorbed at the surface. Assume that the
ATMS 321: Science of Climate Practice Mid Term Exam - Spring 2008 page 4 atmosphere can be represented with two layers at 2.5 and 5 km that are black bodies for infrared. The solar radiation is evenly distributed 25%/25% between the two atmospheric layers. a) Draw a diagram showing all of the radiative energy fluxes (be neat): (5pts) This is exactly like one of the HW problems. T1 T2 Tsurface b) Write down the radiative energy balance equations for the top of the the atmosphere, the two atmospheric layers, and the surface. (5pts) TOA Layer 1 Layer 2 Surface. c) Manipulate the 4 equations for the radiation energy balance to provide formulas for the temperature of each layer. Check to make sure that your 4 equations are consistent for the 3 temperature. (5pts) T1 = T2 = Tsurf = Tsurf = d) Solve for four temperatures, assuming that the solar constant is 1367 Wm -2. (5pts) Te = T1 =
ATMS 321: Science of Climate Practice Mid Term Exam - Spring 2008 page 5 T2 = Tsurf = e) Is this radiative equilibrium temperature profile convectively stable? Do you expect more or less rainfall than for the current climate? (5pts) 17. A planet orbits about the sun in an elliptical orbit so that its closest approach to the sun(perihelion) is 80% of the mean Earth-Sun distance, and its farthest distance from the sun(aphelion) is 120% of the mean Earth-Sun distance. Calculate the total solar irradiance (solar radiation energy flux in Wm -2 ) at this planet at the time of perihelion and aphelion. (15pts) 18. Mt. Fuji is a conical mountain at 38N with a side slope of 20. Calculate the insolation on the south side at local solar noon on Dec 22. Ignore absorption by the atmosphere. (15pts) 19. What is the Bowen Ratio and why is it important. (10pts) 20. Describe a situation in which the Bowen ratio might be negative. (10pts) 21. Boundary layer clouds over the ocean have a different effect on the radiation balance at the top of the atmosphere than cirrus clouds over desert. Explain thoroughly. (10pts) 22. In the high desert, days can be 40 C and nights <0 C. Explain thoroughly using radiation and boundary layer physics. (10pts) Think about surface heat capacity, greenhouse effect above your head, radiation heating and sensible heating. Data and Formulas: = 5.68x10-8 Wm -2 K -4 = 3.1415926 c T t G = R s LE SH F eo I = T 4 T e 4 = S o 4 (1 p) Area of circle = r 2 Area of Sphere = 4 r 2 Density of water = 1000 kg m -3 Specific heat of water = 4218 J K -1 kg -1 average radius of Earth = 6.37x10 6 m cos s = sin sin + coscos cosh S o =1367Wm 2 E = Mc 2 = 0.622 q * = 611Pa p = Q exp L 1 R v 273 1 T
ATMS 321: Science of Climate Practice Mid Term Exam - Spring 2008 page 6 R v = 461JK 1 kg 1 R = 287 JK 1 kg 1 Q = d 2 cos d s L = 2.5x10 6 J kg -1