HW_2 - MPO 551 Homework #2: Due Sep 28 Problem#1: One way...

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Unformatted text preview: MPO 551 Homework #2: Due Sep 28 Problem#1: One way of deducing past climate changes and present climate trends is to examine variations in the mountain snowline altitude, which is roughly indicative of the height of the freezing level. Paleoclimate evidence suggests that tropical mountain snowlines were about 1 km lower at the Last Glacial Maximum (LGM) than at present. How much cooler the oceans were is controversial, with estimates ranging from 1.5-6.5C. For our purposes, let's take an intermediate value of 2.8C based on analysis of planktonic foraminifera (Lea et al., 2000, Science 289, 1719) as a reasonable guess. Assume that in the tropics, = m, and consider a typical current-day surface temperature of 25C. a.) Estimate the height of the freezing level in the tropics. The moist adiabatic lapse rate is variable with height since it depends on T, which makes an actual calculation difficult to do by hand, so to make life easier for you, let's use the value of m at 15C (~800 mb), which is a decent estimate of its mean value over the lower half of the troposphere, to make a simple linear calculation of distance to the freezing level. b.) The actual freezing level in the tropics is a little lower than 5 km. What does this imply (qualitatively) about the actual lapse rate in the tropical lower troposphere relative to m (assuming that our simple linear estimate in (a) is OK)? Offer a specific explanation for the sign of the discrepancy (based on concepts we have discussed). c.) Ignoring the complication of part (b), derive an expression for the change in freezing height Hf that would accompany a change in surface temperature Ts. If the 800 mb level was 3.5C cooler at the LGM than at present (we'd expect the 800 mb level to have cooled by a little more than the surface if = m), is the observed snowline descent approximately consistent with the surface LGM cooling inferred by Lea et al.? d.) There has been considerable controversy about how temperature at the surface and in the troposphere has been changing in recent decades, but after exhaustive attempts to account for all biases in satellite instruments and radiosondes (weather balloons), a consensus appears to be emerging that the troposphere warmed a little more than the surface did over the past half a century. Are these changes (qualitatively) consistent with the ideas used to reconcile inferred changes at the LGM? Explain. Problem #2: Consider dry air in a closed container with a volume of 1 m3, a pressure of 1000 mb, and a temperature of 25oC. (a) What is the density and specific volume v? (b) How many molecules are in the container? (c) If the container is surrounded by a vacuum, what would be the total force exerted on the interior walls (assume the container is a cube)? (d) How many molecules would leave the volume in 1 s if a hole 1 mm2 is made in the container? (e) If instead of a vacuum, the container is surrounded by air at a temperature of 30 oC and a pressure of 1000 mb, would the number of molecules in the container initially increase, decrease or remain the same? Explain. Problem #3: Write an expression for the sensitivity of evaporation rate to surface temperature (dE/dT). Based on this, if the radiative forcing of CO2 is balanced by an increase in evaporation, would you expect a larger surface temperature change in the tropics or polar regions? p c pd Problem #4: Show that potential temperature, = 0 , and dry static energy, p c p T + , are conserved for dry adiabatic processes. Rd ...
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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.

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