Application of PCRTM to Hyperspectral Data

Transcription

1 Appication of PCTM to Hyperspectra Data Xu Liu NASA Langey esearch Center, Hampton, VA W. L. Smith, D. K. Zhou, A. M. Larar, P. Schuesser, M. Godberg,. Sauders, P. D. Giroamo, A. Cough, L. Zhou, W. Wof, J-L. Moncet, L. Strow Advanced High Spectra esoution Infrared Observations University of Wisconsin - Madison, Wisconsin Apri 26 28,

2 Outine Chaenges of modeing hyperspectra data Description of PCTM Comparisons of PCTM with AIS and NAST-I observations, and other T modes etrieva agorithms reated to hyperspectra data Appying PCTM retrieva methodoogy to NAST-I data Summary and concusions 2

3 Chaenges deaing with hyperspectra data Modern hyperspectra sensors have thousands of channes AIS: 2378 CrIS: 1305 NAST-I: 8632 IASI: 8461 Commony used methods for deaing with arge amount of channes Channe seection According to information content (Cive odgers) Used by IASI, NAST-I, AIS Sub-bands Good for chemica species retrievas Used by TES Superchannes Uses smaer number of channes to capture information from measurements Optran AIS IASI Perform radiative transfer cacuation in transformed EOF space Principa Component base adiative Transfer Mode (PCTM) Used for NAST-I 3

4 adiative Transfer Equation Infrared Spectra egion Monochromatic adiance needs to be verticay integrated: 0 ν = ε ν B ν (T s )t s,ν + B ν (T( p)) t (p,θ ) ν u dp p p s The first term is the surface emission p s +(1 ε ν )t s,ν B ν (T(p)) t * ν ( p,θ d ) dp + ρ ν t s,ν t ν (p s,θ sun )F 0,ν cosθ sun p 0 N top * = ε νs t ν,nbot B ν,s + (t ν,i 1 t ν,i )B ν,i + (1 ε νs )t ν,nbot (t ν,i i= N bot +ρ s t ν,nbot t sun ( p s,θ sun )F 0,v cosθ sun The second term is the upweing therma emission The third term is the refected downweing radiation The ast term is the refected soar radiation Channe radiance is a spectra integra of monochromatic radiances: N bot i= N top * t ν,i 1 )B ν,i Δν ( ν ) = Δν ' φ( ν ν ) ( ν ) dν ' Δν ' φ( ν ν ) dν ' 4

5 Description of PCTM PCTM is not a channe-based TM predicts PC scores (Y) instead of channe radiances () The reationship is derived from the properties of eigenvectors and instrument ine shape functions: r r Y Channe radiances (or transmittances ) can be obtained by mutipying the PC scores with pre-stored Principa Components (PCs): r chan r Y = A r mono Yi X = chan i = U N mono = 1 T = a mono ( ) X N k = 1 φ chan N k = 1 r N EOF r = U Y = yiu k i= 1 φ mono k k i + r ε 5

6 Description of PCTM (continued) Y is a non-inear function of atmospheric state Can be thought as super channes contains essentia information about the spectrum U captures spectra variations from channe to channe Capture detais on instrument functions does not change from one spectrum to another No need to incude it in inversion process Y can be predicted from monochromatic radiances directy Linear reationship due to the properties of U and φ More than an order of magnitude reduction in dimension Jacobian can be cacuated in EOF domain directy Great advantage to perform retrieva in EOF domain T done monochromaticay at very few representative frequencies Easy couping with mutipe scattering modes Can efficienty dea with any instrument ine shape functions e.g ILS with negative side obes 6

7 Forward Mode Fowchart 7

8 8 adiative Transfer Cacuation is Simpe adiative Transfer coding is very simpe (see exampe for cacuating upweing radiances): Enddo = nbot,ntop,-1 Do Initiaize ) ( ) (1 ) ( ) (1 ) sec( ] ) ( [ ) ( : up up up up up up up up s v up up T B t t O H O H T T B t t T T t T B T B ν ν ν ν ν ν ν ν ν ν ν ν ν ν τ τ τ τ θ τ ε + = = + = = =

9 Exampes of PCTM Jacobian for AIS Instrument Jacobians for AIS Instrument 9

10 Comparison of Observed AIS adiance and PCTM Cacuated adiance Ozone truth is from ECMWF mode which may not be accurate Spikes are due to instrument popping noise which have not been removed 10

11 Comparison of NAST-I Observation with PCTM 11

12 Location of Cear AIS Observation 12

13 Differences between AIS Observed and PCTM- Cacuated Spectra 13

14 Comparison of PCTM Jacobian with other forward mode (thanks to oger et a.) Jacobians for AIS Instrument H 2 O Jacobian for AIS instrument 14

15 Comparison of PCTM Jacobian with other forward mode (Thanks to oger et. a.) Ozone Jacobians for AIS Instrument 15

16 Inversion for atmospheric profie etrieva agorithm based on optima estimation X T 1 + X a = ( K S y K + λi + S ) + K( X Levenberg Marquardt method used to hande non-inearity Cimatoogy background and covariance matrix as constraints Either cimatoogy or regression as first guess Time consuming to perform physica retrieva using a channes [( y 3 T mode generated for NAST-I (PFAST, OSS, PCTM) ) Y X 1 1 T 1 n 1 a y n m n a K S )] etrieva Configuration /Matrix Dimensions adiance/prof Y 8632 X 100 K S y -1 S x 8632x x x100 16

17 EOF transformation of Observed adiances educes Inversion Time EOF transformation converts observations (y rad ) into PC scores (Y PC- ) educe dimension for K and S y -1 educe forward mode computationa time educe matrix mutipication time Y PC prof K = rad PC PCTM provides both Y and K in EOF space directy No need to perform EOF transformations of Y and K at each iteration A information from measurements used in inversion U = T rad Y U rad T prof K rad etrieva Configuration /Matrix Dimensions adiance PC Score/Profie Y 100 X 100 K S y -1 S x 100x x x100 17

18 Use subset of Channes may not be optima Use subset of channes aso reduces computationa time educes dimensions of Y, K, and S y educes forward mode time Sub-optima Uses ess than 4% of a avaiabe channes (300 channes out of 8632) More susceptibe to noise What if the chosen channe has arge spectroscopic error? etrieva Configuration /Matrix Dimensions Seected adiance/profie Y 300 X 100 K S y -1 S x 300x x x100 18

19 EOF transformation of state vector reduces inversion time further PC P PC P r X K PC P PC = r X a Prof = K Prof Eigenvectors generated from cimatoogica atmospheric profies eguarize the retrieva Make S a ess singuar for highy correated eves Minimize vertica eve instabiity in the retrieva Much smaer matrix dimension for (K T S -1 y K + λ I + S -1 a ) -1 U PC T Prof prof U r X etrieva Configuration /Matrix Dimensions adiance/profie PC Y 100 X 32 K S y -1 S x 100x32 100x100 32x32 19

20 Advantages of PCTM etrieva Methodoogy A channes incuded PC scores contains information from a channes The dimension of S y is much smaer Noise correation incuded Good to hande interferometer with strong apodization functions Good to incude correated forward mode errors Good to incude correated bias correction covariance The dimension of S x is much smaer Inversion is faster EOF transformation stabiize state vector inversions Easy to increase state vector size when mutipe pixes are used PCTM provides K and Y in PC domain directy No need to convert Jacobian and radiance to PC space at each iteration Big computationa saving Fast speed and sma matrix sizes are good for Coud handing Use spatia and tempora information etr. Config/Matrix Dim. adiance/prof Subset adiance/prof ad PC/ Prof PC Y X K 8632x x x32 S -1 y 8632x x x100 S x 100x x100 32x32 Time for cac. K and Y ~2 sec 0.1 sec 0.02 sec 20

21 Appication of PCTM to NAST-I etrieva 100 adiance PC used 32 parameters retrieved: 1 surface skin temperature 19 Temperature EOF 8 moisture EOF 4 ozon EOF Emissivity fixed Ocean emissivity= measured vaues from JH database Land emissvity either set to 0.98 (very approximate) or set to regression generated emissivity Background covariance generated from NOAA88 database Goba variations etrieva starts from goba cimatoogy Wi try regression first guess ater Levenberge-Marguardt non-inear inversion with cimatoogy background constraint incuded Very robust Converges in 3-4 iteration 21

22 PCTM etrieved Ts, PWV, T and H (09/09/2004) 22

23 Coud Properties from NAST-I Standard egression etrieva 23

24 Time Series of Vertica Profies from PCTM 24

25 Vertica Temperature and H variations from adosonde and LIDA 25

26 Comparison of PCTM EOF etrieved Profies with adiosonde and LIDA 26

27 Appication of PCTM EOF retrieva agorithm to EAQUATE NAST-I Data Upper pane: Mean NAST-I and PCTM radiances Midde: MS difference between NAST-I and PCTM fitting Bottom: Mean difference between NAST-I and PCTM 27

28 Summary and Concusions on PCTM Physica parameterization The radiance variation as a function of T, H 2 O, O 3, CH 4, N 2 O, CO, T skin, ε, ρ, sec (Θ), P obs. is captured via monochromatic T cacuations PC score predicted by simpe a inear mode The redundant spectra information is captured via EOF representation Can dea with any ILS or SF Super channe magnitudes are a inear combination of a few hundred monochromatic radiances Channe radiances are a inear combination of EOFs with super channes as weights! Provides forward mode and Jacobians in both spectra and EOF domain No need to seect sub-set of channes Sma dimensions, fast speed Correated noise and error sources can be incuded A preiminary appication of PCTM to NAST-I data show good resuts Wi be tested with more NAST-I datasets Further improvements wi be made CO,CH4 and N2O retrievas Surface emissivity retrievas etrieva under coudy condition Characterize forward mode errors and incude them in retrievas PCTM has good potentia for hyperspectra remote sensing IASI, NWP data assimiation, coud parameter retrievas 28