Terrestrial infrared radiative processes. Part 4: IR radiative heating/cooling rates.

Transcription

1 Lectre. erretrial inrare raiative procee. Part : R raiative heating/cooling rate.. R raiative traner reviite.. nrare raiative heating/cooling rate in the clo-ree atmophere. 3. Concept o the broaban lx emiivity. Reqire reaing: L:...5,.7 Avance reaing: Clogh, S.A., M.J. acono, an J.-L. Moncet, Line-by-line calclation o atmopheric lxe an cooling rate: Application to water vapor.j. Geophy. Re., 97, , 99. Clogh, S.A. an M.J. acono, Line-by-line calclation o atmopheric lxe an cooling rate : Application to carbon ioxie, ozone, methane, nitro oxie, an the halocarbon. J. Geophy. Re.,, 6,59-6,535, R raiative traner reviite. Recall Lectre 8, the oltion o the raiative traner eqation or the monochromatic pwar an ownwar intenitie in the R or a plane-parallel atmophere coniting o aborbing gae no cattering are exp exp exp an in term o tranmiion nction

2 Recall that the above oltion were erive or the entire atmophere with the optical epth or two bonary conition: Srace: ame to be a blackboy in the R emitting with the race temperatre,, race i not a blackboy:, where i the race emiivity. op o the atmophere OA, = : no ownwar emiion, =============================================================== NOE: Conier an atmophere that i repreente by a ingle layer with the eective temperatre o e e.g., an iothermal atmophere. Uner thi amption, the Planck nction i contant = e o that a impliie expreion or the raiance at the top o the atmophere i ] exp [ exp e ==============================================================

3 3 n Lectre 3, pwelling an ownwelling lxe were eine a [.] NOE: Eq.[.] ame that there i no epenency on in a plane-parallel atmophere. h, we can re-write the raiative traner eqation an it oltion in term o the monochromatic pwar an ownwar lxe exp exp [.a] an exp [.b] Let introce the tranmiion nction or the raiative lx calle ie tranmiion nction or lab tranmiion nction or lx tranmiion nction a [.3] where i the monochromatic tranmiion nction. Spectral ie tranmiion nction or tranmittance may be eine a: [.]

4 Uing the einition o monochromatic ie tranmittance an oltion o the raiative traner eqation expree via the tranmittance, the oltion or lxe can be written a [.5a] an [.5b] NOE: On the right ie o Eq.[.5a] or the pwar lx, the irt term give the race emiion that i attenate to the level an the econ term give the emiion rom the atmopheric layer characterize by the Planck nction mltiplie by the weighting nction /. Likewie, the ownwar lx at a given layer Eq.[.5b] i proce by the emiion rom the atmopheric layer.. nrare raiative heating/cooling rate in the clo-ree atmophere. Raiative procee may aect the ynamic an thermoynamic o an atmophere throgh the generation o raiative heating/cooling rate. he raiative heating or cooling rate i eine a the rate o temperatre change o the layer z e to raiative energy gain or lo: t c z p net g c p p net [.6] where c p i the peciic heat at the contant prere c p =.67 J/kg/K an i the air enity in a given layer.

5 NOE: he thermoynamic eqation or the temperatre change in the atmophere i.e. the irt law o thermoynamic or moit air incle the raiative energy exchange term i.e. total raiative heating/cooling rate which are a m o olar an inrare heating/cooling rate. n thi lectre we ic R raiative rate only olar will be ice later in the core. Recall the einition o the monochromatic net lx net power per area at a given height ee Lectre 3: z z z [.7] Similar, we can eine the total net lx: z z z [.8] ntrocing the net lx z+z at the level z+z ee igre below, we in the net lx ivergence or the layer z a z z z z+z < z hence < => a layer gain raiative energy => heating z+z > z hence > => a layer loe raiative energy => cooling p-p z z z z z+z + p z z z p 5

6 ============================================================= EXAMPLE Calclate longwave cooling at night or an atmopheric layer rom to km ing the pwelling an ownwelling lxe calclate with MODRAN or the US Stanar Atmophere 976. SOLUON: Altite km Nee to in net lxe at each altite z z z At km: net = = 5 W/m At km: net = = 5 W/m h = W/m R Upwelling lx W/m R Downwelling lx W/m t R c z p net.7kg/ m 3 J m Jkg K m /t = -.7x -5 K/ = -.5 K/ay =============================================================== hermal inrare region: Each part o the atmophere emit an aborb raiation. Where aborption ominate, there i the net raiative heating where emiion ominate, there i net cooling. he latter i more common. h one can talk abot R raiative cooling rate giving poitive vale o. t R t R or R raiative heating rate giving negative vale o 6

7 Altite, km o calclate the R heating/cooling rate one nee to know: i Proile o R pwelling an ownwelling lxe to calclate the proile o the R net lxe o compte the R ownwar an pwar lxe one nee to know: Atmopheric characteritic: vertical proile o, P an air enity an he vertical proile o R raiatively active gae, clo an aerool. ii Uing the proile o net lxe an air enity, one calclate the R raiative heating/cooling rate a t R z c z p Eect o the varying amont o a ga on R raiation ner the ame atmopheric conition Conier the tanar tropical atmophere an ry tropical atmophere: ame atmopheric characteritic, except the amont o H O ee igre below HO g/kg 7

8 Altite, km Calclate R lxe or tropical otte line an ry tropical atmophere oli line m k 6, e 5 3 ltit A lx, W/m p w p, ry w, ry H O increae in a layer => increae becae more R raiation emitte in a layer => race increae H O increae in a layer => ecreae becae more R raiation aborbe bt reemitte at the lower temperatre => OA ecreae ncreae o an R aborbing ga contribte to the greenhoe eect. Calclate R net lxe or tropical otte line an ry tropical atmophere oli line lx, W/m net net, ry he larger change o the net lx rom one level to another i.e., the larger lope o Z v Z, the larger R cooling rate. 8

9 Calclate R cooling rate or tropical otte line an ry tropical atmophere oli line Heating rate, K/ay NOE: he larget R cooling rate or the tanar tropical atmophere are occrre in the race layer. R cooling rate o inivial gae: igre. he thermal R heating rate proile in a clo-ree tanar tropical atmophere, egregate accoring to main aborbing gae. Note that negative vale repreent cooling. 9

10 NOE: CO ha very mall raiative heating rate. Raiation emitte at one level i aborbe at nearby level having almot the ame temperatre. Only at the tropopae near 5 km, where the temperatre proile ha a minimm, there i a mall amont o heating. At higher altite, prere broaening i mch weaker allowing emitte raiation to ecape to pace with little compenating raiation ownwar rom higher level. H O i concentrate in the lower atmophere relting in the high cooling rate between 3 an km. he two peak in the proile are aociate with ierent aborption ban, the tronger o thee being aociate with the higher altite peak. H O continm aborption i very enitive to prere. he ma aborption coeicient all o rapily with height. Coneqently, the atmophere in the pper tropophere an abot i eectively tranparent in thi pectral ban, while lower altite ee airly trong aborption. O3 i reponible or only intance o igniicant R warming in the atmophere below 3 km, with the peak warming between an 3 km. hi heating i e to the aborption at the bae o the ozone layer o raiation emitte by the gron in the 9.6 m ban. R cooling rate in ierent clo-ree atmophere: igre. he total R heating rate proile calclate or three ierent moel atmophere.

11 3. Concept o the broaban lx emiivity he broaban lx emiivity approach allow calclation o inrare lxe an heating/cooling rate tilizing the temperatre in term o the Stean-oltzmann law intea o the Planck nction. ae on Eq.[.5 a, b], the total pwar an ownwar lxe in the path length coorinate may be expree a [.9a] an [.9b] rom the Stean-oltzmann law, we have Let eine the iothermal broaban emiivity a, [.] Uing the iothermal broaban emiivity, Eq.[.9a, b] may be approximate a,, [.a]

12 an, [.b] NOE: the iothermal broaban emiivity i known, the broaban lxe an heating/cooling rate can be eaily calclate rom Eq.[.a, b].