atmo324-07-asmt3 - T = 288 K air temperature T a is fixed...

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ATMO 324: Problem Set 3 ( due Oct. 22 ) Chapter 4: Energy Balance of the Surface 1. What is the planetary boundary layer? Why does it exist? What are the different types of planetary boundary layer? 2. (Hartman) If the top 100 m of ocean warms by 5 o C during a 3-month summer period, what is the average rate of net energy flow into the ocean during this period in units of W m -2 ? If the atmosphere warms by 20 o C during the same period, what is the average rate of net energy flow into the atmosphere? 3. (Hartman) The blackbody emission from the surface can be linearized about some reference temperature T 0 . ... ) ( 4 3 4 4 + ! + " o s o o s T T T T T # # # And the sensible cooling of the surface can be written as SH = C p " C D U T s # T a ( ) Calculate and compare the rates at which longwave emission and sensible heat flux vary with surface temperature, T s . In other words, if the surface temperature rises by 1 o C , by how much will the longwave and sensible cooling increase? Assume that
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Unformatted text preview: T = 288 K, air temperature T a is fixed, ρ = 1.2 kg m-3 , C p = 1004 J kg-1 K-1 , C D = 2 x 10-3 , and U = 5 m s-1 . 4. (Hartman) Air with a temperature of 27 o C moves across a dry parking lot at a speed of 5 m s-1 . The insolation at the surface is 600 W m-2 and the downward longwave radiation at the ground is 300 W m-2 . The longwave emissivity of the surface is 0.85, and the albedo of the asphalt surface is 0.10. What is the surface temperature in equilibrium ? What is the surface temperature if the asphalt is replaced with concrete with an albedo of 0.3 and the same emissivity ? The air density and drag coefficient are as in Problem 3. Hint : Linearize the blackbody emission around the air temperature T a and use the surface energy equation to show that T s " T a = S # (0) • (1 " $ s ) + % F # (0) " & T a 4 ( ) C p ’ C D U + 4 T a 3...
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