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Chapter 4

Chapter 4 Problems.pdf

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CHEM 302
Michael Wheeler

69 PROBLEMS 4. 1 Dilution of power plant plumes Match each power plant plume (1-4) to the corresponding atmospheric lapse rate on each case.ines; the dashed line is the adiabatic lapse rate Γ). Briefly comment 1 2 3 4 z z z z T T T T AB CD 70 4. 2 Short questions on atmospheric transport 1. Pollutants emitted in the United States tend to be ventilated by vertical transport in summer and by horizontal transport in winter. Explain this seasonal difference. 2. Solar heating of the Earth’s surface facilitates not only the upward but also the downward transport of air pollutants. Explain. 3. A monitoring station measures the vertical concentration profiles of a pollutant emitted at a constant and uniform rate at the surface. The profiles measured on two successive days are shown below: z Day 1 Day 2 C Which of these two profiles is consistent with a one-dimensional turbulent diffusion parameterization of turbulence? How would you explain the other profile? 4. A power plant in a city discharges a pollutant continuously from a 200-m tall stack. At what time of day would you expect the the surface air concentrations of the pollutant in the city to be highest? 5. In a conditionally unstable atmosphere (-dT/dz < ΓW), is a cloudy air parcel stable or unstable with respect to sinking motions? Can these "downdraft" motions lead to rapid vertical transport of air from the upper to the lower troposphere? Briefly explain. 6. For a gas that is well mixed in the atmosphere, is there any turbulent transport flux associated with turbulent motions? Briefly explain. 71 4. 3 Seasonal motion of the ITCZ The mean latitude of the ITCZ varies seasonally from 5 S in January to 10 Nin July, following the orientation of the Earth relative to the SBy using a two-box model for transfer of air between the northern and the southern hemispheres, with the ITCZ as a moving boundary between the two boxes, calculate the fraction of hemispheric mass transferred by this process from one hemisphere to the other over the course of one year. Does this process make an important contribution to the overall interhemispheric exchange of air? 4. 4 A simple boundary layer model We construct a simple model for diurnal mixing in the planetary boundary layer (PBL) by dividing the PBL vertically into two superimposed domains: (1) the mixed layer and (2) the remnant PBL (see figure below). These two domains are separated by an inversion, and a second inversion caps the remnant PBL. We assume that the domains are individually well mixed and that there is no vertical exchange across the inversions. 2 2. REMNANT PBL Temperature 1 inversions Altitude, km 1. MIXED LAYER 0 0 6 12 18 24 Time of day, hours 1. Provide a brief justification for this model, and for the diurnal variation in the sizes of the two domains. Why is there a mixed layer at night? (Hint: buoyancy is not the only source of vertical turbulent mixing). 2. Consider an inert pollutant X emitted from the surface with a constant emission flux beginning at t = 0 (midnight). Plot the change in the concentration of X from t =0t t = 24 hours in domains (1) and (2), starting from zero concentrations at t = 0 in both domains. 4. 5 Breaking a nighttime inversion A town suffers from severe nighttime smoke pollution during the winter months because of domestic wood burning and strong temperature inversions. Consider the following temperature profile measured at dawn: 72 z, km 1 0.5 0 o -5 0 T, C We determine in this problem the amount of solar heating necessary to break the inversion and ventilate the town. 1. Show on the figure the minimum temperature rise required to ventilate the town. 6 2. Show that the corresponding heat input per unit area of surface is Q = 2.5x10 J m -. Use ρ=1gm -3for the density of air andpC = 1x10 gk -1K-1for the specific heat of air at constant pressure. 3. Solar radiation heats the surface after sunrise, and the resulting heat flux F to the atmosphere is approximated by 2π(t)t—noon FF= maxcos---------------------a-- .
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