UV/VIS Limb Retrieval

Transcription

1 UV/VIS Limb Retrieval Erkki Kyrölä Finnish Meteorological Institute 1. Data selection 2. Forward and inverse possibilities 3. Occultation: GOMOS inversion 4. Limb scattering: OSIRIS inversion 5. Summary 6. Dessert: MCMC ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 1

2 Occultation Limb scattering ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 2

3 Data selection for retrieval Many locations All spectral data One location All spectral data Tomography Spectral calibrated data Spectral normalised data Radiance comparisons One z All λ Spectrally global inversion All z All λ One step inversion λ -windows DOAS inversion ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 3

4 Data normalisation UV/VIS instruments are difficult to calibrate. Add ageing and stray light. Big trouble. Observations Occultation T(λ)= I occ(λ) I ref (λ) I ref (λ) I occ (λ) Modelling T(",z) = exp(# ' & $ j (",T(z(s))% j (z(s))ds) ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 4

5 Limb scattering R obs (z,") = I obs (z,") I ref (z ref,") R mod (z,") = ref I mod I mod(#, z,") (# ref,z ref,") A priori information + radiance difficult to calculate Additional bonuses: Ratio is insensitive to albedo ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 5

6 Retrieval choices Forward model 1. Forward model 2. Inverse modelling target instrument data 3. Estimation Inverse model ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 6

7 Hierachy of forward models True nature G(x,z) + " z=all other pertinent variables G known (x,z known = z fix ) + " The best forward model available. Uninteresting variables fixed. G app (x,z known = z fix ) + " Model used in signal simulation G inv (x,z known = z fix ) + " Model used for inversion ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 7

8 Forward modelling levels (draft only) Forward model Nature Photon vs classical? Best Simulation Inversion GOMOS Light propagates through turbulent 3-D atmosphere. Refraction, absorption, scattering, emissions. Light propagates through 2-D layered but fluctuating atmosphere. Refraction, absorption, scattering, emissions. Light propagates through phase screen, where refraction takes place. Turbulence seen as scintillations. Removed as noise. OSIRIS Light propagates in 3-D atmosphere with absorptions and multiple scatterings. Polarisation, clouds, ground surface, emissions. Light propagates in 3-D atmosphere with absorption and multiple scattering. Polarisation, simple broken, clouds and albedos, emissions. Multiple scattering in 3-D. Clouds as an elevated surface albedo. Polarisation. Single scattering. Multiple scattering only by LUT. ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 8

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10 Inverse modelling choices Model transformation Original nonlinear Linearised Noise also transformed Model factorisation to spatial x spectral No factorisation One-step inversion Separate spatial and spectral Need to iterate to correct the approximation Cross sections Absolute DOAS Spectrally smooth constituents neglected A priori information None Smoothness Active profile (optimal est.) Contamination must be controlled Initial values ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 10

11 Bayesian method P(x y)p(y) = P(y x)p(x) P(x y) = P(y x)p(x) P(y) = " P(y x)p(x) P(y x)p(x)dx P(x y) = Conditional probability distribution for model parameters x given data y P(x) = A priori probability for model parameters P(y x) = Conditional pdf for data y when x given. Also called as likelihood. P(y) = The normalization. It can usually be ignored. ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 11

12 Wiki: Thomas Bayes was born in London. In 1719 he enrolled at the University of Edinburgh to study logic and theology: Because he was a Nonconformist, Oxford and Cambridge were closed to him. A systematic basis for inversion theory is given by the Bayesian approach Model parameters are random variables Probability distribution of model parameters is retrieved Prior information is needed. This has led to many controversies about the Bayesian approach. ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 12

13 Estimation choices P(x y) = P(y x)p(x) Whole distribution max of Point estimation Maximum likelihood max of MAP Gaussian errors MCMC method LSQ LM method Linear model Closed solution ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 13

14 Prior information Discrete grid: Assume that profile has only a finite number of free parameters Smoothness: Tikhonov constraint A priori profile Positivity constraint or similar ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 14

15 Literature and a reference Tarantola: Inverse problem theory, Methods for data fitting and model parameter estimation, Elsevier, 1987 Rodgers: Inverse Methods for Atmospheric Sounding: Theory and Practice, World Scientific, 2000 Menke: Geophysical data analysis: discrete inverse theory, Academic Press, 1984 ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 15

16 OCCULTATION I ref I occ calibration free principle ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 16

17 GOMOS: Measured Sirius reference spectrum ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 17

18 GOMOS: Measured Sirius transmitted spectrum ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 18

19 GOMOS: Calculated Sirius transmissions ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 19

20 Occultation inversion Occultation inversion is simple because... T(",z) = exp(# ' $ j (",T(z(s))% j (z(s))ds) Beer-Lambert law & s z(s) " = cross section " = number density T = temperature But... ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 20

21 Stellar occultations: dilution & scintillations Strong scintillations: multiple stars Density fluctuation Weak scintillations: intensity maxima and minima ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 21

22 Chromatic effects Different colors different refraction angles Same det. times different altitudes Same altitude Different det. times ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 22

23 We can, however, write T(z,") = T ref T ext Transmission from refractive effects can be estimated from ray tracing calculations (dilution, chromatic effects). In addition, we need photometer measurements to estimate the random part (scintillations). ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 23

24 GOMOS: Horizontal transmissions km O3 in mesosphere O3 in stratosphere NO2 in stratosphere ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 24

25 Occultation inversion using Beer-Lambert: Two step T(",z) = exp(# % $ j (")N (z)) j Spectral inversion N j (z) = # " j (z(s))ds Vertical inversion This separation is not true if cross sections depend on temperature. In these cases we can use iteration over spectral and vertical inversion or one-step inversion. ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 25

26 Spectral inversion We aim to minimize S(N) = (T obs " T mod (N)) T C "1 ((T obs " T mod (N)) C = covariance matrix T = transmission vector (all wavelengths) N = column density vector (different constituents) Solution by Levenberg-Marquardt algorithm ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 26

27 Aspects of spectral inversion in UV-VIS Linearization Non-linear approach Spectrally global Spectral windows Absolute cross sections DOAS ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 27

28 Cross sections OClO NO3 Cross section (cm 2 ) O3 BrO O3 NO Wavelength (Å) 6000 ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 28

29 Transmission components at 27 km aerosol NO2 NO3 Rayleigh ozone ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 29

30 GOMOS vertical inversion Discretize N(z) = # "(z(s))ds N = K" where the kernel matrix is d 11 d22 d 21 " d 11 $ $ 2d 21 d 22 K = $ 2d 31 $ 2d 32 d 33 $ # $ % ' ' ' ' ' &' Onion peel solution ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 30

31 Tikhonov regularization ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 31

32 GOMOS level 1 ECMWF prediction /analysis MSIS90 Raw data Geolocation & ray tracing Instrumental corrections Data extraction Datation Geolocation (ECMWF+MSIS90) Wavelength assignment Spectrometer samples correction Photometer data processing Central band background estimation Star spectrum computation Transmission computation Products generation Calibration database Photometer data Transmission data Limb data ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 32

33 GOMOS level 2 Level 1 transmissions Dilution & scintillation corrections Spectral inversion Line densities Vertical inversion Local densities O3, NO2, NO3 aerosols, Air T, H2O, O2 Level 1 photometer data Cross sections ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 33

34 LIMB SCATTERING RETRIEVAL ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 34

35 OSIRIS radiances ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 35

36 OSIRIS radiance ratios ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 36

37 Scattered limb radiances I = I sun " T sun (s)(# a (s)$ a (%)P a + # R (s)$ R (%)P R )T det (s)ds + I ms s Total radiance= single scattering + multiple scattering ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 37

38 Single and multiple scattering ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 38

39 Difficulties in limb radiative transfer MS time consuming Albedo Clouds Aerosols Polarization Raman scattering ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 39

40 Modified onion peeling method Measured ratio spectra: R obs (z,") = I obs(z,") I ref (z ref,") Modelled ratio spectra: R mod (z,") = ref I mod I mod(#, z,") (# ref, z ref, ") Minimize S(") = [ R mod # R obs ] T $ C #1 $ [ R mod # R obs ] with onion peel type inversion or with one-step inversion ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 40

41 Multiple scattering ss I mod (", z,#) = I mod (", z, #) $ M(" apr,z,#) M = I total I ss tabulated from a full radiative transfer code like FMI s Monte Carlo model Siro. ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 41

42 GOMOS/OSIRIS limb processing scheme ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 42

43 Summary Occultation and limb scattering retrievals can be approached with similar methods. They are based on: -non-linear approach -using relative quantities, not directly measured quantities -original cross sections -all wavelengths Difficulties : Aerosol modelling, scintillations, multiple scattering Other methods DOAS with spectral windows Flittner for limb scattering; 3 wavelengths ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 43

44 This presentation has followed: References Kyrölä, E., E. Sihvola, M. Tikka, Y. Kotivuori T. Tuomi, and H. Haario, Inverse Theory for Occultation Measurements 1. Spectral Inversion, J. Geophys. Res., 98, , Oikarinen, L., E. Sihvola, and E. Kyrölä, Multiple scattering radiance in limb-viewing geometry, J. Geophys. Res., 104, , Auvinen, H., L. Oikarinen and E. Kyrölä, Inversion algorithms for limb measurements, J. Geophys. Res., 107, D13, 2001JD000407, ACH 7-1: 7-7, 2002 Tukiainen, S., S. Hassinen, A. Seppälä, E. Kyrölä, J. Tamminen, P. Verronen, H. Auvinen, C. Haley, and N. Lloyd, Description and validation of a limb scatter inversion method for Odin/OSIRIS, J. Geophys. Res 113, D04308, Haley, C., S. M. Brohede, C. E. Sioris, E. Griffioen,D. P. Murtagh, I. C. McDade,1 P. Eriksson, E. J. Llewellyn, A.Bazureau, and F. Goutail, Retrieval of stratospheric O3 and NO2 profiles from Odin Optical Spectrograph and Infrared Imager System (OSIRIS) limb-scattered sunlight measurements,j. Geophys. Res. 109, D16303, Numerical examples: FMI s GomLab and LimbLab ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 44

45 Ultimate estimators: Markov chain Monte Carlo Twin peaks drama Mr. Markov: Hold your horses Blind Mr. Levenberg: That s it! Top guy: Yes! Mean guy: <Sorry but...> Flatness dullness ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 45

46 Markov chain Monte Carlo Estimators from MCMC 1 N <x i >= Σ z t i N t ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 46

47 MCMC examples (GOMOS) Bright star Weak star Marginal posterior distributions at 30 km for different gases by J. Tamminen, FMI ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 47

48 MCMC example: Model selection: aerosols by M. Laine, FMI ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 48

49 ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 49

50 MCMC references Tamminen and Kyrölä, JGR, 106, 14377, 2001 Tamminen: Ph.D. thesis, FMI contributions 47, 2004 Laine and Tamminen: Aerosol model selection, ACPD 2008 ESA AATC Oxford 2008 Day 3 Limb retrieval - Erkki Kyrölä 50