# AOS145_HW05 - AOS 145 Homework#5 Winter 2017 Li Due Name ID...

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Unformatted text preview: AOS 145 Homework #5 Winter 2017 – Li Due 3/8/2017 Name: ______________________________ ID: _________________________________ 1. Dust and radiation Desert dust aerosols scatter solar radiation (no absorption) and absorb terrestrial radiation (no scatter). Consider our simple greenhouse model where the gaseous atmosphere consists of a single thin layer that is transparent to solar radiation but absorbs a fraction f of terrestrial radiation. We add to that layer some desert dust so that the planetary albedo increases from A to A + dA, and the absorption efficiency of the atmospheric layer in the terrestrial radiation range increases from f to f + df. Assume that dA and df are small increments so that dA << A and df << f. Show that the net effect of desert dust is to increase T0 if δf Fs > ≈ 1.8 δA 2σT04 and to decrease T0 otherwise. Here FS is the solar constant and s is the Stefan-Boltzmann constant. !"#\$%&#!'&#(&#)*+#!",##-..%"/#&0(&#&0/1/#(1/#!'#'&0/1#(&"'.20/134#(\$.'1\$/1.#'1# 2. Absorption in the atmospheric window .4(&&/1/1.#(&#/3&0/1#'5#&0/./#6(7/8/!9&0.,##:'!.3;/1#(!#(&"'.20/1/#63&0#(#&'&(8#<)# € radiation The water vapor dimer absorbs in the 8-12 µm >?atmospheric window. The resulting optical 4'8%"!#!"="'8/4%8/.#4" @#'\$./17/;#\$A#&0/#.(&/883&/#;31/4&/8A#'7/10/(;B#63&0#&0/# depth for an elemental atmospheric column of thickness dz is dt = krdz, where r is the mass density ;'6!6/883!9#.'8(1#1(;3(&3'!#"(C3!9#(!#(!98/##"#&'#&0/#7/1&34(8#=.'8(1#D/!3&0#(!98/@B# of air and k = 1´10-11 p2H2O m2 per kg of air is the mass absorption coefficient for the water vapor (.#.0'6!#'!#&0/#E39%1/,## dimer; pH2O is the water vapor a scale height of H = 4 km for the water # pressure in Pascals. Assuming -3 vapor mixing ratio, a surface m and p0H2O = 1000 Pa for the water vapor # air density r0 of 1.2 kgGHI J<KG .(&/883&/ LJFsurface air, calculate the total optical depth from absorption by the pressure in water vapor dimer. # I =%&" I S(\$) IRI(\$) S R=%&" How efficient is the dimer at ! absorbing radiation in the 8-12 µm window? ! 3. Measuring ozone from space ! Ozone columns have been measured from space continuously since 1979 by backscatter of solar UV ! radiation. Consider a simple satellite instrument measuring reflected solar radiation at 340 nm and ozone ! absorbs at 340 nm but not ! 380 nm wavelengths. Ozone at 380 nm. Assume that there are no other ! atmospheric absorbers or scatters at either of these wavelengths. Consider an atmosphere with a total # ozone column W (molecules! cm-2) observed by the z satellite directly overhead, with the downwelling A ! solar radiation making an angle q to the vertical (solar zenith angle) as shown F(1&0#.%15(4/# ! ##F(1&0#.%15(4/ %15(4/ ! ! Let IS(l) and IR(l) be the downwelling and reflected ! radiation at wavelength l, A the surface albedo M/&#IS=%& (!;#IR=%& \$/#&0/#;'6!6/883!9#(!;#1/58/4&/;#1(;3(&3'!#(&#6(7/8/!9&0# (assumed identical at 340 nm and 380 nm), and s %'"("&0/#.%15(4/#(8\$/;'#=(..%"/;#3;/!&34(8#(&#)N+#(!;#)*+#!"@B#(!;#)"&0/# the absorption cross-section of ozone (assumed (\$.'12&3'!#41'..>./4&3'!#'5#'D'!/#=(..%"/;#4'!.&(!&@,#G0'6#&0(&#&0/#'D'!/#4'8%"! constant). Show that the ozone column can be 4(!#\$/#;/137/;#51'"#&0/#.(&/883&/#"/(.%1/"/!&.#'5#1/58/4&/;#1(;3(&3'!#\$A## derived from the satellite measurements of reflected radiation by # I =% @ I * % & O !+ 8! R ? S O # , O - I S =%? @ I R * %O & )/ . O0 4'. # 1 2 where l1 = 340 nm and l2 = 380 nm. 60/1/#%O#P#)N+#!"#(!;#%?#P#)*+#!",# # 3. Stratospheric water vapor increase # G&1(&'.20/134#6(&/1#7(2'1#3!41/(./;#(&#(#1(&/#'5#OQ#(>O#;%13!9#&0/#ORR+.B#5'1#1/(.'!. ...
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• Winter '17
• Quinbin LI
• Atmosphere, Water vapor

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