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Inverse Ocean Color Retrieval with CAO-LDISORT Model

Explore simultaneous retrieval of aerosols and ocean color using a linearized radiative transfer model. Enhance accuracy and efficiency in atmospheric remote sensing tasks with analytic weighting functions and coupled atmosphere-ocean modeling.

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Inverse Ocean Color Retrieval with CAO-LDISORT Model

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  1. Simultaneous Retrieval of Aerosols and Ocean Color A classic inverse approach with the Linearized CAO-LDISORT Model Knut Stamnes1, Robert Spurr2, Wei Li1, Kexin Zhang1, Hans Eide1, Matteo Ottaviani1, Wenying Su3, Warren Wiscombe4, Jakob Stamnes5 1Stevens Institute for Technology, Hoboken, NJ 07030, USA 2RT Solutions Inc., Cambridge, MA 02138, USA 3NASA Langley RC, Hampton VA 23681, USA 4NASA Goddard SFC, Greenbelt, MD 20771, USA 5University of Bergen, Allegaten 55, N-5007 Bergen, Norway

  2. Outline of Presentation • Motivation: Problems with existing methods • Ocean color as classic inverse problem • CAO-LDISORT linearized radiative transfer • Analytic weighting functions from the model • Retrieval Examples using SeaWiFS data • Error budgeting for ocean color retrieval • Conclusion MODIS STM January 4-6, 2006

  3. Motivation • Reliable Ocean Color data requires accurate knowledge of distributions in overlying atmosphere (especially aerosol). • Existing algorithms (MODIS/SeaWiFS), 2-step approach: • Atmospheric correction --> water-leaving radiances (“ocean color”) • Visible: typically 10% of signal from ocean. Atmospheric correction very difficult unless infra-red black pixel assumption (BPA) holds • NIR channel to fix aerosol optical depth, 2 visible channels and semi-empirical model with regression to get chlorophyll • Ocean/atmosphere decoupled; not using all information; difficult to determine uncertainties and derive error budgets • The atmosphere is not a nuisance to be got rid of! MODIS STM January 4-6, 2006

  4. Ocean Color Retrieval Inverse approach (1) • Direct comparison of measured satellite data with simulated values using chi-square minimization in an iterative inversion scheme • Simultaneous retrieval of atmospheric and marine parameters combined in one state vector • Well-established error budgeting procedures giving clear divisions between sources of uncertainty. • Common in atmospheric remote sensing tasks. MODIS STM January 4-6, 2006

  5. Ocean Color RetrievalInverse approach (2) • More accurate and suitable Forward Modeling: • Fully coupled atmosphere-ocean radiative transfer model • Use the discrete ordinate model CAO-LDISORT with linearization facility to deliver analytic Jacobians • Use all available channels in visible and NIR • Continuously varying set of bimodal aerosol distributions: Naer = total loading, F = bimodal weighting factor • Improved bio-optical model for marine constituents: C = Chlorophyll concentration, Y = CDOM absorption • State vector = {Naer, F, C} or {Naer, F, C, Y} MODIS STM January 4-6, 2006

  6. Ocean Color Retrieval Flow Chart start First Guess Biooptical Model Linearized RT Forward Model Reference data Update Guess measurements Inverse Fitting NO Converge? YES Write results finish MODIS STM January 4-6, 2006

  7. The CAO-LDISORT Model (1) • Extension of multiple scattering DISORT radiative transfer model to coupled atmosphere-ocean system: • Reflection by and transmission through air-water interface determined by Fresnel’s equations + Snell’s law ; • Sufficient layers in atmosphere and ocean to resolve dependence of scattering properties --> stratification into optically uniform layers; • Solar beam source: primary and secondary rays in the atmosphere, transmitted solar ray in ocean; • Pseudo-spherical approximation: transmittance of solar beam in curved spherical shell atmosphere (not ocean!) • Jin and Stamnes (1994), Yan and Stamnes (2002). Validated against Monte-Carlo code (Gjerstad et al., 2003); MODIS STM January 4-6, 2006

  8. The CAO-LDISORT Model (2) • Radiances I(,)=∑mIm(,)cos (m). Fourier azimuth series. • RTE: for each Im(,), multiple scattering integral replaced by Gaussian quadrature --> N1 discrete ordinates in half space [0,90o] (atmosphere) • In ocean, these N1 streams transmitted to reduced half space [0,qcrit], due to refraction at air/water interface. Refractive index mr = 1.33 (ocean), qcrit~ 49o • In ocean, non-illuminated area of total internal reflection: N2 streams • Boundary conditions at interface (Fresnel), at TOA and ocean deep • Layer optical property inputs: • total optical thickness Dn; single scattering albedo wn; • Layer phase function expansion coefficients bnl; MODIS STM January 4-6, 2006

  9. The CAO-LDISORT Model (3): • ANALYTIC weighting or sensitivity functions (Jacobians): K(,,) = ∂I(,) / ∂x; • x = aerosol optical thickness taer in planetary boundary layer; • x = chlorophyll concentration C in uppermost ocean layer; • CAO RT theory completely differentiable w.r.t any x; • Starting points = derivatives of the optical property inputs w.r.t. x ∂Dn / ∂xn ∂wn /∂xn ∂bnl /∂xn • Single call produces radiances and all Jacobians simultaneously • Fast and accurate, no need for repeated finite-difference estimates • Linearization based on LIDORT models (Spurr et al., 2001-2005) for atmosphere and surface remote sensing retrieval MODIS STM January 4-6, 2006

  10. 432 | Chlor | -- AOT-- Jacobians for Aerosol optical thickness t555First 6 SeaWiFS Channels MODIS STM January 4-6, 2006

  11. | Chlor | -- AOT-- Jacobians for Chlorophyll concentrationFirst 6 SeaWiFS Channels MODIS STM January 4-6, 2006

  12. SeaWiFS Retrieval ExamplesModel setup • 8 SeaWiFS channels: (412,443,490,510,555,670,765,865) • 13-layer Rayleigh atmosphere with bi-modal maritime-type aerosol in lowest layer: taer(l) = Naer[Fe1(l) + (1-F)e2(l)] • Bio-optical model: [Poster: K. Zhang et al.] tocean(l) = awater(l) + bwater(l) + a(l)Cb(l) + g(l)Cd(l) + Ye[-q(l-443] Retrieving: {Naer, F, C, Y} MODIS STM January 4-6, 2006

  13. SeaWiFS Retrieval ExamplesTwo approaches compared • Approach 1: “CAO-DISORT (LUT)”. Old method. • Look-up table approach to fix aerosol model, t(865) and Chlorophyll • K. Stamnes et al., Applied Optics 42, 939 (2003) • Approach 2: CAO-LDISORT (OE). This Work. • Iterative chi-square minimization using linearized RT model; • Optimal Estimation with loose a priori constraint (aids convergence) • Continuum approach to bimodal aerosol, new bio-optical model • Retrieval is stable and fast (3-6 iterations), no matter what the initial state vector guess. Solutions constrained for C > 0. MODIS STM January 4-6, 2006

  14. Example 1: SeaBASS Validation Data MODIS STM January 4-6, 2006

  15. Retrieved aerosol t865 (3 methods)137 Aeronet data match-up cases MODIS STM January 4-6, 2006

  16. Retrieved Chlorophyll (3 methods)1378 Match-up cases MODIS STM January 4-6, 2006

  17. Example 2: SeaWiFS Image US East Coast MODIS STM January 4-6, 2006

  18. Radiance Residuals, Channels 1-4(blue) CAO-DISORT(LUT); (black) CAO-LDISORT(OE) MODIS STM January 4-6, 2006

  19. Radiance Residuals, Channels 5-8(blue) CAO-DISORT(LUT); (black) CAO-LDISORT(OE) MODIS STM January 4-6, 2006

  20. Ocean Retrieval Inverse Problem Error budgets Four types of error: (Rodgers, 2001) • Smoothing Error • Model parameter error, Jacobians Kb • Forward model error Gy f. Usually systematic • Measurement error (random and systematic) Linearize about a given state (1 iteration) MODIS STM January 4-6, 2006

  21. Conclusion • Summary of the present work • Iterative inverse techniques applied to simultaneous aerosol and ocean color retrievals, SeaWiFS retrievals Improved residuals • Linearized forward model CAO-LDISORT for radiative transfer simulation of satellite radiances and analytic weighting functions • Facility for extensive error budget studies • Outlook • Extend range to include NIR channels (e.g. MODIS 1240/1640) • Turbid/coastal waters - improved bio-optical models (poster, Zhang et al.) • More retrievals for real data from SeaWiFS and MODIS • Comprehensive error budget planned for first half of 2006 • Improved sunglint corrections (see poster, Ottaviani et al.) This work was funded through NASA EOS program MODIS STM January 4-6, 2006

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