# Presentation: 185923

**Simultaneous Retrieval of**
** ****Aerosols and Ocean Color **
** ****A classic inverse approach with **
**the Linearized CAO-LDISORT Model **
- Robert Spurr1, Knut Stamnes2, Hans Eide2,
- Wei Li2, Kexin Zhang2, Jakob Stamnes3
*1**RT Solutions Inc., Cambridge, MA 02138, USA*
*2**Stevens Institute for Technology, Hoboken NJ 07030, USA*
*3**University of Bergen, Allegaten 55, N-5007 Bergen, Norway*

- OCRTM, Newport RI, 04/11/06

## Outline of Presentation

- Context and Introduction
- Simultaneous aerosol and ocean color retrieval as a classic inverse problem
- CAO-LDISORT _*linearized*_ radiative transfer
- Retrievals using SeaWiFS data
- Validation against SeaBASS data set
- USA East Coast example
- Error budget first results
- Summary and Outlook

- OCRTM, Newport RI, 04/11/06

## Context

- Need for improvement in accuracy of retrieved ocean color products from existing (SeaWiFS, MODIS on Terra and Aqua) and future instruments (VIIRS on NPP and later NPOESS)
- Need to evaluate VIIRS ocean color products for eligibility as Climate Data Records (CDRs), and also the aerosol product over oceans
- Need not only for improved bio-optical models, but also new algorithm ideas to deal with inadequacies in existing retrievals
- Need for a real examination and budgeting of errors of all types associated with ocean color retrievals
- 3-year project funded under NASA EOS program NRA-03-OES-02: ”Earth System Science Research Using Data and Products from Terra, Aqua, & ACRIM satellites". Award to Stevens Institute for Technology (SIT), sub-award to RT Solutions Inc.
- Work based on findings in our Report for Year 1 as part of this NASA grant

- OCRTM, Newport RI, 04/11/06

## Introduction

- Existing algorithms:
- Take atmospheric correction --> water-leaving radiances (“ocean color”)
- In 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

- This Algorithm:
- Direct comparison of measured satellite radiance data with simulated values using chi-square minimization in an iterative inversion scheme.
- Simultaneous retrieval of atmospheric and marine parameters in one state vector
- Comprehensive radiative transfer with analytic weighting functions
- Well-established error budgeting procedures giving clear divisions between sources of uncertainty (measurement errors, model parameter errors, modelization errors...)
- Technique is standard practice in atmospheric remote sensing tasks.

- OCRTM, Newport RI, 04/11/06

## Simultaneous aerosol and ocean color retrieval as a classic inverse problem

- Optimal Estimation (Rodgers 2000) = least squares fitting with regularization
**x***n* = retrieval state vector at iteration *n*, **b** = model parameter vector (not retrieved)
**x***a* = a priori state vector, error covariance **S***a*
**Y***meas* = vector of radiances at satellite, error covariance **S***e* derived from *****noise*
**F**(**x***n*,**b**) = forward (RT) simulation of **Y**, **K***n* are weighting functions w.r.t elements of **x**
- Gain matrix **G***n*, matrix of averaging kernels **A***n*
- Minimize 2, proceeding iteratively until convergence is reached.
- Four sources of Error
- Smoothing Error
- Model parameter error, Jacobians **K**b w.r.t. parameters** b. **Random or systematic.
- Forward model error. Usually systematic
- Measurement error (random and systematic)
- Error budget and sensitivity studies: Linearize about a given state (1 iteration)

- Next Guess

- errors

- 1)

- 2)

- 3)

- 4)

- OCRTM, Newport RI, 04/11/06

## Use all available channels in visible and NIR to maximize information e.g. 8 SeaWiFS channels: 412,443,490,510,555,670,765,865 nm
Multilayer atmosphere with Rayleigh scattering and gaseous absorption, plus bi-modal maritime-type aerosol in lowest layer:
Continuously varying set of bimodal aerosol distributions: Naer = total loading, F = bimodal weighting factor. Scattering properties from Mie theory;
             aer() = Naer[Fe1() + (1F)e2 
Improved Oceanic Medium Bio-optical model, C = Chlorophyll concentration, W = CDOM absorption : [Poster at this meeting, K. Zhang et al.]
ocean() = awater() + bwater + C + C + We[-q(-443]
State vector x = {Naer, F, C} (Case I) or {Naer, F, C, W} (Case I/II)
Forward Model = Fully coupled atmosphere-ocean radiative transfer (RT) model
Use the discrete ordinate RT model CAO-LDISORT with linearization facility to deliver analytic Jacobians Kn and Kb
Atmospheric correction and water-leaving radiance: use RT model to deliver these quantities at each step of iteration. They are diagnostics.

- Multilayer atmosphere with Rayleigh scattering and gaseous absorption, plus bi-modal maritime-type aerosol in lowest layer:
- Continuously varying set of bimodal aerosol distributions: Naer = total loading, F = bimodal weighting factor. Scattering properties from Mie theory;
-              aer() = Naer[Fe1() + (1F)e2
- Improved Oceanic Medium Bio-optical model, C = Chlorophyll concentration, W = CDOM absorption : [Poster at this meeting, K. Zhang et al.]
- ocean() = awater() + bwater + C + C + We[-q(-443]
- State vector **x **= {Naer, F, C} (Case I) or {Naer, F, C, W} (Case I/II)
- Forward Model = Fully coupled atmosphere-ocean radiative transfer (RT) model
- Use the discrete ordinate RT model CAO-LDISORT with _*linearization facility*_ to deliver analytic Jacobians **K***n* and **K****b**
- Atmospheric correction and water-leaving radiance: use RT model to deliver these quantities at each step of iteration. They are *diagnostics*.

- Simultaneous aerosol and ocean color retrieval as a classic inverse problem

- OCRTM, Newport RI, 04/11/06

## Ocean Color Retrieval Flow Chart

- Biooptical Model Atmospheric model

- Linearized RT Forward Model

- Inverse Fitting

- Converge?

- Write results

- Update Guess

- finish

- First Guess

- measurements

- Reference data

- YES

- NO

- start

- OCRTM, Newport RI, 04/11/06

## CAO-LDISORT Radiative Transfer Model

- 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 shell atmosphere (not ocean!)
- Jin & Stamnes (1994), Yan & Stamnes (2002).
- Monte Carlo validation: Gjerstad et al., 2003.

- Layer optical property inputs = n, n, nl
- total optical thickness n
- single scattering albedo n
- Layer phase function expansion coefficients nl
- _ANALYTIC_  weighting or sensitivity functions (Jacobians):
-                     K() =  ∂I() / ∂
-   = AOT aer in planetary boundary layer;
-   = Chlorophyll C in uppermost ocean layer;
*Coupled discrete ordinate model is completely differentiable with respect to any ***
- Start: derivatives of optical property inputs:
-            ∂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

- OCRTM, Newport RI, 04/11/06

## Jacobians for AOT 555

- Weighting Function Examples for 6 Sea WiFS channels: Contour graphs, with x-axis – AOT values, y-axis – Chlor values

- Jacobians for Chlorophyll C

- OCRTM, Newport RI, 04/11/06

## Retrievals using SeaWiFS data:

- Approach 1: “CAO-DISORT (LUT)”. Old method.
- LUT approach to fix aerosol model, (865) and C;K. Stamnes et al., Applied Optics (2003)
- Approach 2: CAO-LDISORT (OE). This Work.
- Optimal Estimation with loose *a priori* constraint (aids convergence)
- Retrieval is stable and fast (3-6 iterations), no matter what the initial state vector guess.

- Example 1: Validation with SeaBASS data

- Example 2: East Coast USA

- OCRTM, Newport RI, 04/11/06

## Is the new approach making sense?
Contrast 3 retrievals
SeaDAS algorithm
CAO-DISORT/LUT (Approach 1)
CAO-LDISORT/OE (Approach 2)
Retrieved aerosol 
137 Aeronet match-ups
Spread/bias in SeaDAS results notably worse
Retrieved  
1378  match-up cases
R2 values similar

- Contrast 3 retrievals
- SeaDAS algorithm
- CAO-DISORT/LUT (Approach 1)
- CAO-LDISORT/OE (Approach 2)
- Retrieved aerosol 
- 137 Aeronet match-ups
- Spread/bias in SeaDAS results notably worse
- Retrieved  
- 1378  match-up cases
- R2 values similar

- Match-ups with SeaBASS validation Data

- OCRTM, Newport RI, 04/11/06

## Radiance residuals for USA East Coast scene

- Radiance Residuals, Channels 1-4

- Radiance Residuals, Channels 5-8

**(blue) CAO-DISORT(LUT)****                            ****(black) CAO-LDISORT(OE)**

- OCRTM, Newport RI, 04/11/06

## Radiance residuals summary: all scenes

- Approach 2 vs. Approach 1 (brackets)

- For all channels, greater percentage with under 5% error, large improvements especially for 490, 510, 550, 765, 865 nm

- OCRTM, Newport RI, 04/11/06

## Model parameter errors GnKbb: Example: effect on retrieved chlorophyll accuracy

_**Examples model parameters**_
- Atmospheric properties
- aerosol coefficients (extinction/scattering).
- Trace gas and Rayleigh scattering inputs
- Marine properties
- Pure water absorption and scattering coeffs. (1-2)
- Chlorophyll absorption coefficients (3-4)
- Chlorophyll scattering coefficients (4-5)
- CDOM absorption exponential gradient (7)
- Others

-    (1)       (2)        (3)       (4)      (5)       (6)       (7)

- CAO-LDISORT will deliver weighting functions with respect to all these parameters

- OCRTM, Newport RI, 04/11/06

## Summary and Outlook

- 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 - newer bio-optical models;
- More retrievals for real data from SeaWiFS and MODIS.
- Comprehensive error budget starting Spring 2006
- This work was funded through NASA EOS program

- OCRTM, Newport RI, 04/11/06