Simultaneous Retrieval of

1

• 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
• 1RT Solutions Inc., Cambridge, MA 02138, USA
• 2Stevens Institute for Technology, Hoboken NJ
  07030, USA
• 3University of Bergen, Allegaten 55, N-5007
  Bergen, Norway

2
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

3
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

4
Introduction

• Existing algorithms
• Take atmospheric correction --gt 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.

5
Simultaneous aerosol and ocean color retrieval as
a classic inverse problem

• Next Guess

errors
1)
2)
3)
4)

• Optimal Estimation (Rodgers 2000) least squares
  fitting with regularization
• xn retrieval state vector at iteration n, b
  model parameter vector (not retrieved)
• xa a priori state vector, error covariance Sa
• Ymeas vector of radiances at satellite, error
  covariance Se derived from enoise
• F(xn,b) forward (RT) simulation of Y, Kn are
  weighting functions w.r.t elements of x
• Gain matrix Gn, matrix of averaging kernels An
• Minimize c2, proceeding iteratively until
  convergence is reached.
• Four sources of Error
• Smoothing Error
• Model parameter error, Jacobians Kb 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)

6
Simultaneous aerosol and ocean color retrieval as
a classic inverse problem

• 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
• taer(l) NaerFe1(l) (1-F)e2(l)
• Improved Oceanic Medium Bio-optical model, C
  Chlorophyll concentration, W CDOM absorption
  Poster at this meeting, K. Zhang et al.
• tocean(l) awater(l) bwater(l)
  a(l)Cb(l) g(l)Cd(l) We-q(l-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.

7
Ocean Color Retrieval Flow Chart

First Guess
start
Biooptical Model Atmospheric model
Reference data
Linearized RT Forward Model
Update Guess
measurements
Inverse Fitting
NO
Converge?
YES
Write results
finish
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CAO-LDISORT Radiative Transfer Model

• Layer optical property inputs Dn, wn, bnl
• total optical thickness Dn
• single scattering albedo wn
• Layer phase function expansion coefficients bnl
• ANALYTIC weighting or sensitivity functions
  (Jacobians)
• K(t,m,f) ?I(t,m f) / ?x
• x AOT taer in planetary boundary layer
• x Chlorophyll C in uppermost ocean layer
• Coupled discrete ordinate model is completely
  differentiable with respect to any x
• Start derivatives of optical property inputs
• ?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

• Extension of multiple scattering DISORT radiative
  transfer model to coupled atmosphere-ocean
  system
• Reflection by and transmission through air-water
  interface determined by Fresnels equations
  Snells law
• Sufficient layers in atmosphere and ocean to
  resolve dependence of scattering properties --gt
  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.

9
Jacobians for AOT t555
Weighting Function Examples for 6 Sea WiFS
channels Contour graphs, with x-axis AOT
values, y-axis Chlor values
Jacobians for Chlorophyll C
10
Retrievals using SeaWiFS data
Example 1 Validation with SeaBASS data
Example 2 East Coast USA

• Approach 1 CAO-DISORT (LUT). Old method.
• LUT approach to fix aerosol model, t(865) and
  CK. 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.

11
Match-ups with SeaBASS validation Data

• Is the new approach making sense?
• Contrast 3 retrievals
• SeaDAS algorithm
• CAO-DISORT/LUT (Approach 1)
• CAO-LDISORT/OE (Approach 2)
• Retrieved aerosol t865
• 137 Aeronet match-ups
• Spread/bias in SeaDAS results notably worse
• Retrieved t865
• 1378 match-up cases
• R2 values similar

12
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)
13
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
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Model parameter errors GnKbdb Example effect
on retrieved chlorophyll accuracy
(1) (2) (3) (4) (5)
(6) (7)

• 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

CAO-LDISORT will deliver weighting functions with
respect to all these parameters
15
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