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

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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/(.'!. ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern