1. Inclusion of the surface reflection into the radiative transfer equation.

Transcription

1 Lectue. Methos fo sovg the aatve tasfe equato wth utpe scatteg. Pat : cuso of suface efecto a essvty. Exact ethos: Dscete-oate Ag-oubg a Mote Cao.. cuso of the suface efecto to the aatve tasfe equato.. cuso of the suface essvty to the aatve tasfe equato. 3. Dscete-oate etho fo hoogeeous a hoogeeous atosphee. 4. Pcpes of vaace a Ag-oubg etho. 5. Mote Cao etho. eque eag: L: cchazz P. S.. Yag et a. SBDA: A eseach a teachg softwae too fo Pae-paae aatve tasfe the eath's atosphee. Buet of the Aeca Meteooogca Socety Avace eag: hoas G.E. a K. Staes aatve tasfe the atosphee a ocea Chapte Lu Q. a. Weg Avace Doubg Ag Metho fo aatve asfe Paetay Atosphees. Joua of Atosphec Sceces Staes K. S. say W. Wscobe a K. Jayaweea Nuecay stabe agoth fo sceteoate-etho aatve tasfe utpe scatteg a ettg ayee ea." App. Opt he teatoa tecopaso of 3D aato Coes 3C: Cahaa.. et a. 5: he teatoa tecopaso of 3D aato Coes 3C: Bgg togethe the ost avace aatve tasfe toos fo couy atosphees. Bu. Ae. Meteo. Soc Davs A. B. a A. Mashak : Soa aato taspot the couy atosphee: a 3D pespectve o obsevatos a cate pacts. epots o pogess Physcs o:.88

2 . cuso of the suface efecto to the aatve tasfe equato. he ocea a a sufaces ca ofy the atosphec aato fe by a efectg a poto of the cet aato back to the atosphee; b tasttg soe cet aato; c absobg a poto of cet aato Kchhoff s aw; ettg the thea aato Kchhoff s aw; NCDEN ADAON ELECED ADAON EMED ADAON ANSMED ADAON ABSOBED ADAON ANSMED ADAON ypes of efecto gue. Scheatc ustato of ffeet types of suface scatteg. he obes ae poa agas of the scattee aato: a specua b quas-specua c Labeta quas-labeta e copex.

3 wo extee types of the suface efecto: specua efectace a ffuse efectace. Specua efectace s the efectace fo a pefecty sooth suface e.g. a o: Age of cece =Age of efectace efecto s geeay specua whe the "oughess" of the suface s sae tha the waveegth use. the soa spectu.4 to efecto s theefoe specua o sooth sufaces such as poshe eta st wate o os. NOE: Whe cog soa ght s upoaze efecte waves ae geeay poaze a ese's aws ca be use to etee poazato. Pactcay a ea sufaces ae ot sooth a the suface efecto epes o the cet age a the age of efecto. efectace fo such sufaces s cae the ffuse efectace. B-ectoa efectace stbuto fucto BD s touce to chaacteze the agua epeece the suface efecto a efe as the ato of the efecte testy to the eegy fux the cet bea: [.] NOE: Each type of sufaces has a specfc specta BD. ecpocty aw: Upweg aace s a tega ove BD a owweg aace [.] 3

4 Suface abeo s efe as the ato of the suface upweg to owweg fux: su NOE: Eq.[.3] s sa to Eq.[.4] except that the atte s wtte fo the coate ect cet fe. [.3] A suface s cae the Labet suface f t obeys the Labet s Law. Labet s Law of ffuse efecto: the ffusey efecte ght s sotopc a upoaze epeety of the state of poazato a the age of the cece ght. o the Labet suface BD s epeet o the ectos of cet a obseve ght bea. o the Labet suface fo Eq.[.] we have a fo Eq.[.3] we have [.3] L L [.4] su [.5] L efectace fo ocea sufaces Ocea efecto epes o the ocea suface a ea suface cotos: waves whtecaps a suspee patcuates. May oes have bee eveope to accout fo these factos by toucg coectos to the ese efecto. Oe of the ost wey use oes s the Cox a Muk 954 oe. efectace fo a sufaces sos vegetato: BDs ae cotoe by the physca stuctue of the suface e.g. the esty a theeesoa aageet of pat eaves a stes a the suface oughess of the so substate a the optca popetes of ts copoet eeets e.g. the specta efectace a tasttace of eaves stes a so facets. Nueous oes have 4

5 bee eveope to escbe a accout fo these eatoshps. hese oes ae geeay fouate as foows f so f geok geo f vo whee k geo a k vo ae the oe `kees' a f so f geo a f vo ae spectayepeet weghtg factos. he `kees' ae tgooetc fuctos that escbe the shape of the BD tes of the soa uato a seso vew ages. hey ae eve fo appoxatos to a spfcatos of the pcpes of geoetcaoptcs k geo a aatve-tasfe theoy k vo. Each kee s utpe by a facto f that weghts the eatve cotbuto of suface-scatteg f geo a voue-scatteg f vo to the easue BD. he te f so s cue to accout fo sotopc scatteg fo the suface pactce ths cues cotbutos fo both sgescatteg a utpe-scatteg. hus the oe s fouate so that bectoa efectace s a ea cobato of thee tes weghte by thee paaetes: a sotopc fucto accoutg fo bectoa efectace wth a vewg a the ovehea su; a geoetc fucto accoutg fo the effects of shaows a the geoetca stuctue of potusos fo a backgou suface; a a voue scatteg fucto base o aatve tasfe accoutg fo efectace by a coecto of aoy-spese facets. k vo ustato of thee tes cue to the BD oes: sotopc geoetca a voue scatteg 5

6 A otabe featue of the BD fo atua sufaces s the hot spot - a peak efectace fo ect backscatte =8. Hot spot ae cause by: the ack of obseve shaows a specua efecto fo oete eaves geea the suface efectace s a fucto of waveegth. Exapes of the suface abeo at about 55 : fesh sowce =.8-.9; eset=.3 sos=.-.5; ocea=.5. Exapes of the specta suface efectace. gue. ypca shotwave specta efectaces of vaous atua sufaces. 6

7 cuso of the suface efecto to the aatve tasfe equato: Let s cue the cotbuto fo the Labet suface. Labet suface: cost [.6] su Geeazg the eftos fo the efecto a tassso fuctos.e. Eqs.[.] [.] we ay expess the efecte ffuse testy a tastte ffuse testy as t c [.7] [.8] t c he efecte testy at the top of the aye cug the suface efecto ay be wtte as exp su su [.9] NOE: he seco te o the ght-ha se gves the cotbuto fo the suface efecte testy whch s ffusey tastte to the top of the aye wheeas the th te gves the cotbuto fo the suface efecte testy whch s the ecty tastte. We ca e-wte Eq.[.9] as [.] whee exp t su Now et s cose the ffuse tastte testy. sotopc testy su popagatg upwa the aye afte beg scattee by the Labeto suface ca be patay efecte back to the suface a hece cotbute to the owwa testy the atoa aout 7

8 8 su su a hus the tastte testy cug the suface cotbuto s su su [.] Both Eqs.[.] a [.] have su. hus we ee to f su. fux Dowwa x abeo Suface su he owwa fux has thee copoets: astte ect fux = exp astte ffuse fux= t 3 acto of su efecte by the atosphee back to the suface = su a heefoe t su o su su exp a eaagg te we have su su su heefoe the ffuse efecte a tastte testes accoutg fo the suface cotbuto ae su su [.a] su su [.b]

9 tegatg Eq.[.a b] ove the so age we f ffuse fuxes whee t exp su [.3a] su su [.3a] su NOE: t a wee efe Lectue see Eq.[.8] a [.9]. NOE: o o-labet suface the cuso of the suface efecto s a copex bouay pobe.. cuso of the suface essvty to the aatve tasfe equato. geea essvty epes o the ecto of esso suface tepeatue waveegth a soe physca popetes of the suface e.g. the efactve ex. the thea > 4 eay a sufaces ae effcet ettes wth the essvty >.8 a the essvty epes tte o the ecto about -3% agua vaato 9

10 gue.3 Exapes of specta essvty MODS UCSB Essvty Lbay cuso of the suface essvty to the aatve tasfe equato: eca the geea souto of the upweg aace the thea : B exp exp ; ; whee ; s the cotbuto fo the suface.

11 geea cotbuto fo the suface = esso + efecto o a specua suface: ; B s [.4] whee s the suface essvty suf = - a s the owweg aaces eachg the suface. the wow suf s eggby sa fo the a a ocea sufaces => t s coo the aatve tasfe oeg to keep oy the fst te Eq.[.4]. abe. Boaba essvty of soe sufaces the wow -to. Suface Essvty Wate ce.98 Gee gass Sa oze so.93 Cocete.94 Sow Gate.898 NOE: hee ae sevea atabases that have bee eveope to pove the specta esso ata of atua sufaces. Both suface essvty a efectace BD a abeo ca be eteve fo satete obsevatos sesos ffe the spata footptcoveage a specta esouto Exape: ASE specta bay cues ata fo thee othe specta baes: the Johs Hopks Uvesty JHU Specta Lbay the Jet Popuso Laboatoy JPL Specta Lbay a the Ute States Geoogca Suvey USGS - esto Specta Lbay. Cuet Veso. of the ASE specta bay cues ove 4 specta of atua a aae ateas.

12 3. Dscete-oate etho fo hoogeeous a hoogeeous atosphee. st cose a hoogeeous atosphee. eca the aatve tasfe equato Lectue 9 fo azuthay epeet ffuse testy: exp 4 ' ' ' P P o sotopc scatteg the scatteg phase fucto s. Hece we have exp 4 ' ' [.5] Let s appy the Gaussa quaatues to epace the tega Eq.[.5] exp 4 a [.6] whee =- tes a a ae the Gaussa weghts costats a ae quaatue ages o pots. Eq.[.6] s a syste of hoogeeous ffeeta equatos: Souto of Eq.[.6] = geea souto + patcua souto whee the geea souto s a souto of the hoogeeous pat of the Eq.[.6] Deotg = the geea souto of Eq.[.6] ca be fou as exp k g [.7] setg Eq.[.7] to Eq.[.6] we obta g a k g [.8] We ca f g the fo L k g whee L s a costat to be etee. Substtutg ths expesso fo g Eq.[.8] we have k a k a [.9] Eq.[.9] gves soutos fo +-k =.

13 hus geea souto s L exp k [.] k whee L ae costats. he patcua souto ca be fou as h exp [.] 4 whee h ae costats. setg Eq.[.] to Eq.[.6] we have h a h [.3] o Eq.[.3] h s fou as whee s etee fo h { } [.4] a Ag the geea souto Eq.[.] a the patcua souto Eq.[.] we have L exp k exp [.5] k 4 whee L ae costats to be etee fo the bouay cotos. H-fucto has bee touce by Chaasekha as H... k [.6] Expessg the H-fucto Eq.[.5] becoes L H H exp k exp [.6] k 4 3

14 4 Eq.[.6] gves a spe souto fo the se-fte sotopc atosphee see L:6.. 4 H H [.7] Geeazato of the scete-oate etho fo a hoogeeous atosphee. Let s cose the atosphee wth o-sotopc scatteg. We ca expa the ffuse testy the cose sees cos N So we ee to sove exp 4 4 P P P P o N N he geea souto ay be wtte as k L exp k L ae coeffcets to be etee. he patcua souto ay be wtte as exp p Z Whee Z s the foowg fucto 4 N P H H P Z

15 he copete souto of the aatve tasfe s L exp k Z exp [.8] =- Let s geeaze the copete souto Eq.[.8] of the aatve tasfe fo the hoogeeous atosphee. he atosphee ca be ve to the N hoogeeous ayes each s chaacteze by a sge scatteg abeo phase fucto a optca epth. NOE: f a atosphec aye has gases aeosos ao cous oe ees to cacuate the effectve optca popetes of ths aye. o -th aye we ca wte the souto usg Eq.[.8]. o spfy otatos et s cose the azutha epeet case.e. = so we have L exp k Z exp [.9] Now we ee to atch the bouay a cotuty cotos betwee ayes. At the top of the atosphee OA: o owwa ffuse testy [.3] At the aye s bouay: upwa a owwa testes ust be cotuous [.3] At the botto of the atosphee assug the Laeta suface: N su N [ N exp N ] Eqs.[.3]-[.3] pove ecessay equatos to f the ukow coeffcets. [.3] Nueca peetato of the scete-oate etho: DSO DSO s a OAN ueca coe base o the scete-oate etho eveope by Staes Wscobe et a. DSO s opey avaabe a has a goo use-gue. 5

16 6 Soe featues: DSO appes to the hoogeeous othothea pae-paae atosphee. A use ay set-up ay ubes of the pae-paae ayes. 3 Each aye ust be chaacteze by the effectve optca epth sge scatteg abeo a asyety paaete f the Heyey-Geeste phase fucto s use. 4 A use ay use ay phase fucto by povg the Legee poyoa expaso coeffcets. 5 A use seects a ube of steas keepg that the coputato te vaes as 3. 6 A key pobe s to obta a souto fo fuxes fo stogy fowa-peake scatteg. 7 DSO aows pectg the testy as a fucto of ecto a posto at ay pot the atosphee.e. ot oy at the bouaes of the ayes. DSO s copoate to the SBDA aatve tasfe coe. 4. Pcpes of vaace a Ag-oubg etho. eca the eftos of efecto a tassso of a aye touce Lectue 9. f the soa fux s cet o a aye of optca epth : O the geea case: c c t he pcpe of vaace fo the se-fte atosphee Abatzua 94: the ffuse efecte testy caot be chage f a aye of fte optca epth havg the sae optca popetes as those of the oga aye s ae see L: 6.3..

17 7 he pcpes of vaace fo a fte atosphee Chaasekha 95: he efecte upwa testy at ay gve optca epth esuts fo the efecto of a the atteuate soa fux = exp a b the owwa ffuse testy at the eve exp [.33] he ffusey tastte owwa testy at the eve esuts fo a the tassso of cet soa fux a b the efecto of the upwa ffuse testy above the eve : [.33] ' '

18 8 3 he efecte upwa testy at the top of the fte atosphee = s equvaet to a the efecto of soa fux pus b the ect a ffuse tassso of the upwa ffuse testy above the eve : exp [.34] 4 he ffusey tastte owwa testy at the botto of the fte atosphee s equvaet to a the tassso of the atteuate soa fux at the eve pus b the ect a ffuse tassso of the owwa ffuse testy at the eve fo above: exp exp [.35] 5. Ag-oubg etho. ' '= o ' '

19 Ag-oubg etho s a exact etho fo sovg the aatve tasfe equato wth utpe scatteg. t uses geoetca ay-tacg appoach a the efecto a tassso of each vua atosphec aye. Stategy: kowg the efecto a tassso of two vua ayes the efecto a tassso of the cobe aye ay be obtae by cacuatg the successve efectos a tasssos betwee these two ayes. NOE: f optca epths of these two ayes ae equae ths etho s efee to as the oubg-ag etho. Cose two ayes wth efecto a a tota ect pus ffuse tassso a fuctos espectvey. Let s eote the cobe efecto a tota tassso fuctos by a a cobe efecto a tota tassso fuctos betwee ayes a by U a D espectvey. U D 9

20 he cobe efecto fucto s [...]... [.36] NOE: Eq.[.36] we use that x x he cobe tota tassso fucto s... [...] [.37] he cobe efecto fucto U betwee ayes a : U... [...] [.38] he cobe tota tassso fucto D betwee ayes a : D... [...] [.39] o Eqs.[.36]-[.39] we f that U; D; U D [.4] Let s touce S Usg that exp fo Eqs.[.39]-[.4] we f D D exp S exp S S exp exp [.4]

21 exp exp exp exp exp D D D [.4] hus we ca wte a syste of teatve equatos fo the coputato of ffuse tassso a efecto fo the two ayes the fo: D D U U D U S S D Q Q S Q exp exp exp exp exp [.43] NOE: Eq.[.43] the pouct of two fuctos pes tegato ove the appopate age so that a utpe-scatteg cotbutos ae cue. o stace Nueca poceue of the ag-oubg etho: As the statg pot oe ay cacuate the efecto a tassso fuctos of a ta aye of vey sa optca epth e.g. = -8 that the sge scatteg appoxato s appcabe. he usg Eq.[.43] oe coputes the efecto a tassso fuctos of the aye of. 3 Usg Eq.[.43] oe epeats the cacuatos ag the ayes ut a esabe optca epth s acheve.

22 5. Mote Cao etho. he absopto a scatteg pocesses the atosphee ca be cosee as stochastc pocesses. eca that eegy of oe photo s hc whee h = 6.66x -34 J s Soa fux at the top of the atosphee at 55 =.55x 5 photos c - s - hus the aatve fe ca be pecte by statstca aayss of taveg photos. he scatteg phase fucto ca be tepete as a pobabty fucto fo the estbuto of photos ffeet ectos. he sge scatteg abeo ca be tepete as the pobabty that a photo w be scattee gve a extcto evet. NOE: - s cae co-abeo a ca be cosee as the pobabty of absopto pe extcto evet. he cocept of the Mote Cao etho s to suate photo popagato a optcay effectve eu as a ao pocess. Geeato of ao ubes: Usg a ao ube geeato a ueca agoth the ao ubes betwee a wth a pobabty stbuto fucto PD ca be geeate. Usg ths we ca geeate aothe set of ao ubes as x = - wth PD = exp-x a x betwee a fty. Let s cose a hoogeeous eu chaacteze by the extcto coeffcet ext sge scatteg abeo a phase fucto P'. Mote Cao etho suates the taectoes of vua photos accog to the foowg schee: Detee statg posto x a ecto of a photo Geeate a photo path egth usg ao ubes x x = x 3 Cacuate a ew photo posto x +x cae the evet pot o coso pot

23 4 Aayze what ca happe wth the photo at ths evet pot by geeatg the ao ube a copag t wth f => the photo s absobe => go to fo a ew photo. f => the photo s scattee => go to 5 5 a ew ecto fo the scattee photo usg the phase fucto to cacuate the cuuatve pobabty fucto to eate the scatteg age to a ao ube. 6 he epeat statg wth 3 ut the a photos ae aayze. Mote Cao eques about 6 9 photos to pouce statstcay eabe esuts. Backwa Mote Cao etho: stats wth the photo at the pot of teest a taces back to the souce. Let's cose the hoogeeous atosphee. We ca spt t to the hoogeeous gs. Pot of teacto o evet pot x step step ext x y z whee step = step-sze each g 3

24 = ext s cae fee path-egth. exp exp x exp x [.44] ext aatve tasfe techques fo hoogeeous cous. Cous exhbt hgh vaabty space x y z => oe-esoa aatve tasfe has te appcatos gue.4 ustato of the souces of eos oe-esoa aatve tasfe couy cotos. 4

25 How to teat the hoogeety of cous: he spest etho: touce a cou facto f c f c s cooy epote fo eteooogca obsevatos f f c c whee c s the testy cacuate wth oe-esoa cou a cea s the testy of cea sky. But the pobe s that Aothe pobe s cou oveap. f c cea obseve f aatve c c epeet Cou Appoxato CA CA s coputatoa effcet techque to cacuate the aatve tasfe accoutg fo the cou hoogeety. A cou s subve to cous pae-paae aatve tasfe s appe to each cou a the ovea aatve tasfe effect s the suato fo the vua cous. hus CA cacuates the oa-aveage aatve popetes. CA eques the pobabty stbuto of optca epth PD the couy pat of the scee stea of ust the ea optca epth. CA cocept s we sutabe fo GCM oes but oes ot wok we the eote sesg of cou popetes. Mofcato of CA NCA ooca epeet cou appoxato has bee popose to accout fo aatve soothg effect.e. the teecy of hozota photo taspot to sooth the aatve fe pecte by CA. 5

26 gue.5 Soa fux.µ - 4µ at the Eath's suface cacuate wth CA a Mote Cao fo the cou fe show o the uppe paes. he su s shg fo the eft soa zeth age s 3. he ght age shows a coss secto aog the otte e Maye et a. 6

27 NOE g..5: he 3D shaows o ot appea beow the cous but of couse offset to the ecto of the ect soa bea. he 3D aato fe outse the cou shaows s ehace copae to the oe-esoa appoxato. he 3D fux se the cou shaows s coseaby ehace copae to the epeet pxe appoxato by oe tha a facto of. hs s cause by sewas scatteg of aato ue the cou. Bake et a. Assessg D Atosphec Soa aatve asfe Moes: tepetato a Hag of Uesove Cous. Joua of Cate vo. 6 ssue 6 pp he Mote Cao epeet Cou Appoxato McCA: cobes AC a Mote Cao copoate to the ECMW foecastg oe Spheca Haoc Dscete Oate Metho SHDOM: eveope by. Evas SHDOM s a hghy effcet a fexbe 3D atosphec aatve tasfe oe. SHDOM uses a teatve pocess to copute the souce fucto cug the scatteg tega o a g of pots space. he agua pat of the souce fucto s epesete wth a spheca haoc expaso. SHDOM ca copute upoaze oochoatc a boaba wth a k- stbuto shotwave a ogwave aatve fuxes. he eu popetes extcto phase fucto etc. ae specfe at each g pot a the suface abeo ay vay as we. Pcus. a K.. Evas 9: Coputatoa cost a accuacy cacuatg theeesoa aatve tasfe: esuts fo ew peetatos of Mote Cao a SHDOM. J. Atos. Sc