Relevance of Radiative Transfer Model in Physical Inversion. Xu Liu and Richard Lynch AER Inc.

Transcription

1 eevance of adatve ranfer Mode n Phyca Inveron Xu Lu and chard Lynch AE Inc.

2 Outne of the Preentaton. equrement on radatve tranfer mode for phyca nveron 2. Overvew of radatve tranfer cacuaton n nhomogeneou atmophere 3. Cacuaton of Anaytca Jacoban 4. ranformaton of varabe ung EOF before phyca nveron 5. Overvew of how to mode channe radance 6. Appcaton of OSS forward mode to CrIS and AS-I ntrument 7. Concuon

3 What an dea Fat adatve ranfer Mode for Phyca Inveron F x ε δ Kδx Accurate Idea f the accuracy reatve to LL controabe Phyca parameterzaton Accuracy and phyca parameterzaton coey couped Ue eat non-phyca aumpton Fat Modern computer technoogy can accommodate arge mode parameter ILS SF convouton houd be done durng the tranng Perform cacuaton monochromatcay Cacuate Jacoban effcenty Cacuate downweng radance effcenty e abe to hande mutpe catterng reat Panck functon and urface properte propery e abe to mode non-ocazed ntrument ne hape functon effcenty ran the forward mode under varety of condton e abe to hande varabe obervaton attude for arcraft ntrument

4 adatve ranfer Equaton for Infrared Spectra egon he frt term the urface emon he econd term the upweng therma emon he thrd term the refected downweng radaton he at term the refected oar radaton un un p d p u F p dp p p p dp p p p ρ ε ε co * Θ Θ Θ

5 Defnng Atmopherc Layerng Schematc for atmopherc ayer conventon eve OA 2 * 2 * * ayer eve ayer 2 eve * - * -2 eve -2 ayer - eve - ayer eve SUFACE

6 ecurve adatve ranfer Cacuaton un v un un F p ρ ε ε co * * * ε un v un un F p ρ ε co If we defne:

7 Cacuaton of Anaytca Jacoban... ] [ Θ Θ Θ Θ O O O H O H O H ef O H O H fx p k q k p k p ω ω ω ob ec exp d * ec exp ec ec ec ec * un ob o d ob X X X X ε ε X X X d ob < < ec ec * *

8 Cacuaton of Jacoban ï dt/dq can be cacuated from the ookup tabe eay d Θ Θ Θ Θ Θ M m k m m K ω Θ Θ ε ε ε Σ o un un F ρ ρ / ec exp co ec o d ob δ Σ Θ Θ Θ

9 emperature and Moture Jacoban

10 emperature and Moture Jacoban

11 ranformaton of varabe he ayer dervatve can be converted to eve dervatve by: X ev X above ay X above ay X ev X beow ay X beow ay X ev he truncted EOF U obtaned from background covarance can be ued compre X and K: ~ x U x ~ K K U Λ U S x U ~ x ~ K S ~ K Λ ~ K y ~ K ~ x y y S y If the fu correaton of noe covarance S y can be compreed ung truncated EOF obtaned from PCA of radance pectra he nveron of the tranformed matrx w be more effcent

12 Dffcute of Modeng Channe adance or ranmttance Φ d Φ d where Φ normazed ILS SF LL cacuaton of monochromatc ayer tranmttance or OA radance very tme conumng Convovng monochromatc radance or tranmttance wth ILS SF ao tme conumng he eer Law no onger vad It dffcut to hande nhomogeneou path and mutpe gae z z z φ v d φ v d φ v d ga ga2 ga ga2 z z z φ v d φ v d φ v d ayer ayer2 ayer ayer 2

13 Comparon of Dfferent Fat Mode Mode ype Charactertc Lmtaton and Mode eura net Correated k Dtrbuton CKD Exponenta Sum Fttng ranmon ESF Optran OV SAAGatropd. Optma Spectra Sampng OSS Smpe parameterzaton Fat Curt Godon approxmaton can be ued to hande nhomogeneou atmo. Smpe Fat Monochromatc g-v mappng Leve to eve k correaton approxmate Overappng gae treatment approxmate Monochromatc eect few k term or v pont Leve to eve k correaton approxmate method ext to hande t Overappng gae treatment approxmate Poychromatc Smart way to treat overappng gae eat nhomogeneou path Monochromatc reat nhomogeneou path and overappng gae we Parameterzaton phyca Lmted accuracy ot accurate to extend to mutpe gae Jacoban cacuaton? on-phyca parameterzaton ot perfect for nhomogeneou path and overappng gae Standard method perfect for nhomogeneou path and overappng gae Effectve ayer optca depth depend on ayer above t Very good treatment of nhomogeneou path and overappng gae

14 Overvew of Dfferent Fat Mode K dtrbuton KD v ω φ v v v ω dv g exp[ k g ω] v ω g { Θ g [ Θ g]exp[ k g ω] g z v g and k obtaned by groupng kv Correated-K dtrbuton CKD Correaton between the pectra hape and poton dfferent ayer approxmate KD made for a et of P ndependenty Method ext to correct th approxmaton Ue ame g-v mappng for a ayer e.g Mayer et a. eference ayer add-ubtract method e.g. Ona Edward.

15 Overvew of Dfferent Fat Mode Correated-K dtrbuton Contnued reatment of overappng gae approxmate Aume gae are uncorreated: z 2 2 v v ω ω φ vv v ω v ω dv v ω v ω g exp[ k g ω ] g exp[ k g ω ] 2 2 j 2 j 2 j 2 j M Introduce ω or functon of ω ga ga2. a addtona factor when generatng k kgpω

16 Overvew of Dfferent Fat Mode Exponenta Sum Fttng of ranmon ESF v ω φ v v v ω dv w exp[ k v ω] v ω w{ Θ v [ Θ v]exp[ k g ω] w z v w and the pectra ocaton of k obtaned by a eecton/regreon proce reatment of nhomogeneou atmophere Ue w and obtaned for a reference ayer and cae exponenta term wth approprate functon of P and Incude a ayer n the regreon and eecton proce Armbruter and fher 996 OA v p ω w v exp[ k v p ω p ] L L L

17 Overvew of Dfferent Fat Mode ESF contnued reatment of mxng gae Smar to CKD aume uncorreated z v v ω ω φ v v[ δ v ω ][ δ v ω ] dv wδ v ω δ v ω z z v v φ vv v ω dv φ vv v ω dv Equvaent extncton tter and Geeyn Edward Addtona nterpoaton varabe a a functon of ω or functon of ω ga ga2. Frequency ampng method or radance ampng method Sneden et a. 975 jemke and Schmetz 997

18 Overvew of the OSS forward mode Optma Spectra Sampng OSS approxmate channe radance or tranmttance accordng to: Φ d w ε Channe radance are a near combnaton of monochromatc radance at pre-eected frequence Spectra ocaton/weghtng coeffcent are obtaned through a eecton/regreon proce he computatona gan more than 3 order of magntude reatve to the ne-by-ne cacuaton done monochromatcay Monochromatc ookup tabe ued to cacuate the tranmttance for varou gae and dfferent atmopherc ayer no approxmate need to be made Cacuate Jacoban anaytcay very effcent reat refected radance accuratey Can be eay couped wth mutpe catterng code

19 Appcaton of OSS to AS-I

20 Expanded Vew of the MS of the Forward Mode

21 umber of Pont Per Channe Average of 2.59 monochromatc pectra cacuaton are needed for each AS-I channe AS-I Spectra and umber of Channe umber of Monochromatc Pont Average Pont per Channe LWI MWI SWI

22 Vadaton of OSS Forward Mode Accuracy he radance error derved from ndependent profe et foow a Gau dtrbuton

23 Oberved and Modeed AS-I adance for 7/4/ CLAM Campagn

24 Expanded Vew of the Oberved and Cacuated AS-I adance

25 Oberved v. Cacuated AS adance for Cryta-Face AIS Underfght

26 CrIS etreva Agorthm wa ued etreved Profe For the CAMEXIII Campagn ear Andro Iand

27 etreved emperature Profe from AS-I Intrument

28 Concuon Jacoban provde entvty of radance wth repect to the retreved parameter ecurve cacuaton gve nght Mot term needed for the radance cacuaton can be ued for Jacoban cacuaton tme avng ranformaton of varabe acceerate nveron proce It ao provde tabty to the nveron he fat radatve tranfer mode bet done at monochromatc frequence Phyca parameterzaton Effcent n cacuatng Jabcoban matrx needed for nveron Can ncude mutpe catterng cacuaton It bet to tran a atmopherc ayer and a major gae mutaneou OSS mode ha been deveoped to mode AS-I radance and wa ncorporated nto ASA retreva agorthm OSS ha been ued to muate the CrIS ED retreva performance and the retreva agorthm ha been vadated ung AS-I data