# Presentation: 832697

**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
*1**Stevens Institute for Technology, Hoboken, NJ 07030, USA*
*2**RT Solutions Inc., Cambridge, MA 02138, USA*
*3**NASA Langley RC, Hampton VA 23681, USA*
*4**NASA Goddard SFC, Greenbelt, MD 20771, USA*
*5**University of Bergen, Allegaten 55, N-5007 Bergen, Norway*

- MODIS STM January 4-6, 2006

## 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

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## 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!

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## 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.

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## Ocean Color RetrievalInverse 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}

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## Ocean Color Retrieval Flow Chart

- start

- Biooptical Model

- Linearized RT Forward Model

- Inverse Fitting

- Converge?

- Write results

- Update Guess

- finish

- First Guess

- measurements

- Reference data

- YES

- NO

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## 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);

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## 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,crit], due to refraction at air/water interface. Refractive index mr = 1.33 (ocean), crit~ 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 n;  single scattering albedo n;
- Layer phase function expansion coefficients nl;

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## The CAO-LDISORT Model (3):

- _ANALYTIC_  weighting or sensitivity functions (Jacobians):
-                     K() =  ∂I() / ∂
-   = aerosol optical thickness aer in planetary boundary layer;
-   = chlorophyll concentration C in uppermost ocean layer;
*CAO RT theory completely differentiable w.r.t any ***
- Starting points = derivatives of the optical property inputs w.r.t. 
-                        ∂n / ∂n      ∂n / ∂n           ∂nl / ∂n
- 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

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## Jacobians for Aerosol optical thickness 555First  6 SeaWiFS Channels

-                              432
- |
- Chlor
- |
-                                                    -- AOT--

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## Jacobians for Chlorophyll concentrationFirst  6 SeaWiFS Channels

- |
- Chlor
- |
-                                                                  -- AOT--

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## SeaWiFS Retrieval ExamplesModel 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:
-            aer() = Naer[Fe1() + (1F)e2
- Bio-optical model: [Poster: K. Zhang et al.]
- ocean() = awater() + bwater +
-                         C + C + Ye[-q(-443]
- Retrieving: {Naer, F, C, Y}

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##  SeaWiFS Retrieval ExamplesTwo approaches compared

- Approach 1: “CAO-DISORT (LUT)”. Old method.
- Look-up table approach to fix aerosol model, (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.

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## Example 1: SeaBASS Validation Data 

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## Retrieved aerosol  (3 methods)137 Aeronet data match-up cases

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## Retrieved Chlorophyll (3 methods)1378 Match-up cases

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## Example 2: SeaWiFS Image US East Coast

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## Radiance Residuals, Channels 1-4(blue) CAO-DISORT(LUT); (black) CAO-LDISORT(OE)

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## Radiance Residuals, Channels 5-8(blue) CAO-DISORT(LUT); (black) CAO-LDISORT(OE)

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## 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)

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## 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

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