Lecture 14. Review for Exam 1.

Transcription

1 Lecture 4. Review for Exa.

2 Eectroagetic radiatio exhibits the dua ature: wave properties ad particuate properties Wave ature of radiatio: Eectroagetic waves are characterized by waveegth or frequecy ~,or waveuber ad speed Reatio betwee, ad ~ : = ~ /c = / Particuate ature of radiatio: ca be described i ters of partices of eergy, caed photos. E photo = h ~ = h c/ = h c h is Pak s costat h = x0-34 J s.

3 Fux or irradiace is defied as radiat eergy i a give directio per uit tie per uit waveegth or frequecy rage per uit area perpedicuar to the give directio: df de dtdad UNITS: J sec = W -2 - The radiative fux is the itegratio of ora copoet of oochroatic itesity over soe soid age. F I cos d F 2 I d

4 Net radiative fux Moochroatic et fux is the itegratio of ora copoet of oochroatic itesity over the a soid ages over 4: d d I F F F et 2 0,, What is the et fux of the isotropic radiative fied?

5 Extictio scatterig +absorptio ad eissio. Extictio is a process that decreases the radiat itesity, whie eissio icreases it. Extictio or atteuatio is due to absorptio ad scatterig. Absorptio is a process that reoves the radiat eergy fro a eectroagetic fied ad trasfers it to other fors of eergy. Scatterig is a process that does ot reove eergy fro the radiatio fied, but ay redirect it.

6 Lecture 3 The fudaeta aw of extictio is the Beer-Bouguer-Labert aw: the extictio process is iear i the itesity of radiatio ad aout of atter, provided that the physica state i.e., T, P, copositio is hed costat. Extictio: di e Ids, Eissio: where e, is the voue extictio coefficiet LENGTH - J is the source fuctio. di e, Jds e, a, s, di I ds e, e, J ds

7 Lecture 3 The differetia for of radiative trasfer equatio di e, Ids e, di ds e, I J J ds Usig I d e s ds Eeetary soutio:, We have di d di d s I 0exp s0 exp s s Je, s 0 I ds I J J See p.2

8 Soutio of the radiative trasfer equatio i the pae-parae atosphere caed the itegra for d J I I exp exp 0 0 d J I I exp exp * * * Lecture 3

9 Lecture 4 Backbody eissio Pack fuctio, B T, gives the itesity or radiace eitted by a backbody havig a give teperature. B 2 2hc T 5 exp hc / k B T Stefa-Botza aw: F = s b T 4 = BT Wie dispaceet aw: Kirchhoff aw: = 2898 / T e = A

10 Moecuar Absorptio/Eissio Spectra

11 Loretz profie of a spectra ie is used to characterize the pressure broadeig ad is defied as: / f L T T P P T P 0 0 0, is the haf-width of a ie at the haf axiu i c -, ofte caed the ie width Dopper profie is defied i the absece of coisio effects i.e., o pressure broadeig as: exp D D f D D is the Dopper ie width 2 0 / / 2 T k c B D

12 Copariso of the Dopper ad Loretz profies for equivaet ie stregths ad widths.

13 Absorptio coefficiet is defied by the positio, stregth, ad shape of a spectra ie: k a, = S f 0 S k a, d f 0 d Depedecies: S depeds o T f 0, depeds o the ie hafwidth p, T, which depeds o pressure ad teperature.

14 Path egth or path is defied as the aout of a absorber aog the path If the aout of a absorber is give i ters of ass desity, path egth is u s 2 s s ds Hoogeeous absorptio path: whe k a, does ot vary aog the path => optica depth is = k a, u Ihoogeeous absorptio path: k a, varies aog the path u u 2 k a, du

15 Absorbig gas path egth u Absorptio coefficiet Lie itesity S c c - c -2 g c -2 c 2 g - c g - oecue c -2 c 2 /oecue c/oecue c at c at - c -2 at -

16 Moochroatic trasittace ad absorbace T exp A T exp

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18 Spectra itesity = itesity averaged over a very arrow iterva that B is aost costat but the iterva is arge eough to cosist of severa absorptio ies. Narrow-bad itesity= itesity averaged over a arrow bad which icudes a ot of ies Broad-bad itesity= itesity averaged over a broad bad e.g., over a whoe ogwave regio d u k d d T u T exp exp d u k d u T A exp exp

19 d T B I I exp exp * * * d T B I I exp exp 0 0 The soutios of the radiative trasfer equatio for the oochroatic upward ad dowward itesities i the IR for a pae-parae atosphere cosistig of absorbig gases o scatterig: d B B I exp exp * * * d B I exp 0

20 For isothera atosphere ad back body surface I 0 B * * exp B T eff [ * exp ] For fuxes see pp.54-57

21 Moochroatic et fux et power per area at a give height z F z F z F ad tota et fux z F z F z F Itroducig the et fux Fz+z at the eve z+z, the et fux divergece for the ayer z is z F z z F F

22 Fz+z < Fz hece F < 0 => a ayer gais radiative eergy => heatig Fz+z > Fz hece F > 0 => a ayer osses radiative eergy => cooig The IR radiative heatig or cooig rate is defied as the rate of teperature chage of the ayer dz due to IR radiative eergy gai or oss: dt dt IR c p df dz et g c p df where c p is the specific heat at the costat pressure et dp c p = J/kg/K ad is the air desity i a give ayer.

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24 Atitude, k Effect of the varyig aout of a gas o IR radiatio uder the sae atospheric coditio Cosider the stadard tropica atosphere ad dry tropica atosphere: sae atospheric characteristics, except the aout of H 2 O H2O g/kg

25 Atitude, k IR fuxes for tropica dotted ies ad dry tropica atospheres soid ies Fux, W/2 Fup Fdw Fup, dry Fdw, dry H2O icreases i a ayer => F icreases because ore IR radiatio eitted i a ayer => surface icreases H2O icreases i a ayer => F decreases because ore IR radiatio absorbed but reeitted at the ower teperature => F TOA decreases Icrease of a IR absorbig gas cotributes to the greehouse effect. F

26 Atitude, k IR et fuxes for tropica dotted ies ad dry tropica atospheres soid ies Fux, W/2 Fet Fet, dry

27 Atitude, k IR cooig rates for tropica dotted ies ad dry tropica atospheres soid ies Heatig Cooig rates, K/day Cooig rates Cooig rates, dry tropics

28 IR cooig rates of idividua gases:

29 IR cooig rates i differet coud-free atospheres:

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