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Unformatted text preview: MPO 551 Homework #3: Due Wednesday, October 26 Problem#1: (a) Starting with the solar constant, So=1367W/m2, how much solar radiation is absorbed by the Earth if 30% of the sky has an optical depth of 0 (due to scattering by clouds, and with no absorption), the clear sky has an infinitely deep optical depth (i.e. zero extinction of solar radiation by either scattering or absorption), and the surface of the Earth is a perfect blackbody? If the atmosphere an isothermal layer that is perfectly opaque to infrared radiation, what is the surface temperature? What is the brightness temperature of the Earth (i.e. the temperature that the Earth would look from space)? (b) Let us replace this opaque layer with a layer that has the same albedo and some effective emissivity that is less than 1 (i.e. a non-perfect blackbody). In this case, some fraction (1- where is the emissivity) of the radiation passes directly from the surface to space, and the rest is absorbed by the atmosphere and then reradiated back down. What would this emissivity have to be in order to explain the observed equilibrium surface temperature (288 K)? What is the temperature of this atmosphere? Does the brightness temperature change from the previous case? How do you explain the relationship between the surface temperature, atmospheric temperature, and brightness temperature? Problem #3: Exercise 4.43 in W&H Problem#4: Find a satellite image related to your research topic/interest, and explain the principles of radiation that are used to make this image. Send your results to Honghai who will post your image and explanation on the class website so everyone can learn from the various applications. You should be able to explain this in person to the class as well. Please post your answers BEFORE class on OCT 26. Problem #5: Low clouds and high clouds have a different effect on the net radiation at the top of the atmosphere. Cloud radiative effect is generally defined as the different in net radiative flux (absorbed solar radiation outgoing longwave radiation) between the total sky and the clear sky: QnetCLOUD = QnetTOTALSKY - QnetCLEAR . Explain why low clouds over the ocean have a different net radiative effect than high clouds as shown in the picture on the following page. Assume the albedo of the high and low clouds is approximately the same. This figure shows the net cloud forcing of high clouds (top panel), and low clouds (bottom panel). This is Figure 21 from Hartmann et al. (1992)- which you can find on our class website- if you want more details about how this is calculated. ...
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This note was uploaded on 01/08/2012 for the course MPO 551 taught by Professor Zhang,c during the Summer '08 term at University of Miami.
- Summer '08