Atmospheric Correction of Satellite OceanColor Imagery

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Atmospheric Correction of Satellite Ocean-Color
Imagery
Robert Frouin Scripps Institution of
Oceanography La Jolla, California
OCRT Meeting, Newport, RI, 11 April 2006
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Collaborators Pierre-Yves Deschamps, University
of Lille Lydwine Gross-Colzy, Capgemini,
Toulouse Bruno Pelletier, University of
Montpellier
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• Approaches to Atmospheric Correction
• 1. Linear Combination of Observations (Frouin
  et al., JO, in press)
• 2. Decomposition in Principal Components
  (Gross and Frouin, SPIE, 2004)
• 3. Fields of Nonlinear Regression Models
  (Frouin and Pelletier, RSE, in revision)

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1. Linear Combination of Observations -Perturbing
signal expressed as a polynomial or a linear
combination of orthogonal components -TOA
Reflectance in selected spectral bands linearly
combined to eliminate perturbing
signal -Progressive atmospheric correction from
near-infrared to visible
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2. Decomposition in Principal Components -TOA
reflectance decomposed in principal
components -Components sensitive to the ocean
signal combined to retrieve the principal
components of marine reflectance, allowing
reconstruction of the marine reflectance.
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3. Fields of Non-Linear Regression Models
Problem   To estimate marine reflectance rw from
top-of-atmosphere reflectance rTOA and angular
variables t without knowing the other variables x
that influence the radiative transfer in the
ocean-atmosphere system
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Methodology   Explanatory variables (rTOA) are
considered separately from the conditioning
variables (t). An inverse model is attached to
each t, and the attachment is continuous, i.e.,
the solution is represented by a continuum of
parameterized statistical models (a field of
non-linear regression models) indexed by t   rw
zt(rTOA) e   where e is the residual of the
modeling.  
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Methodology (cont.)   Ridge functions, selected
for their approximation properties, especially
density, are used to define the statistical
models explaining rw from rTOA and t   ztj(rTOA)
Si 1, , n cijh(ai. rTOA bi)   rwj
ztj(rTOA) ej where ai(t), bi(t), and cij(t)
are the model parameters.
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Simulated Data Sets   62,000 joint samples of
rTOA and rw split in two data sets, D0e and D0v,
for construction and validation. Noisy versions
D1e, D1v, D2e, and D2v generated, by adding 1 and
2 of noise to rTOA. The noise is defined
by   rTOAj rTOAj ncrTOAj
nucjrTOAj   where nc and nucj are random
variables uniformly distributed on the interval
-n/200, n/200, where n is the total amount of
noise in percent.  
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Simulated data Sets (cont.) rTOA simulated in
SeaWiFS spectral bands using radiative transfer
code of Vermote (1997). Marine reflectance
assumed to be isotropic and to depend only on
chlorophyll-a concentration (Case 1 waters).
Wide range of aerosol optical thickness and
models, including absorbing aerosols, wind speed,
chlorophyll-a concentration and sun and viewing
angles considered.
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Function Field Construction   The free
parameters of the field, i.e., the maps ai(t),
bi(t), and cij(t), are estimated by multi-linear
interpolation on a regular grid covering the
range of t.   The adjustment is considered in the
least-square sense, and minimization of the mean
squared error is carried out using a stochastic
gradient descent algorithm.  
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Function Field Construction (cont.)    A
sufficient number of n 15 basis functions was
selected via simulations, and three fields of
this kind, z0, z1, and z2 were constructed for 0,
1, and 2 of noise.   Since the components ztj
take their values in the same vector space (the
vector space spanned by the linear combinations
of ridge functions), the approach is not
equivalent to separate retrievals on a
component-by-component basis.
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Table 1. Root Mean Squared error (RMS) and Root
Mean Squared Relative error (RMSR) for the models
z0, z1, and z2 evaluated on the construction and
validation data sets (D0e and D0v) and on 1 and
2 noisy versions of them (D1e, D1v, D2e, and
D2v).
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Figure 1. Estimated versus expected marine
reflectance for model z0 adjusted on non-noisy
data.
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Figure 2. Estimated versus expected marine
reflectance for model z1 adjusted on 1 noisy
data.
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Figure 3. Conditional quantiles (of order 0.1,
0.25, 0.5, 0.75, and 0.9) of the residual rw
error distributions as a function of aerosol
optical thickness at 550nm for model z1 applied
to 1 noisy data.
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Figure 4. Conditional quantiles (of order 0.1,
0.25, 0.5, 0.75, and 0.9) of the residual rw
error distributions at 412 and 555 nm as a
function of the fraction of one aerosol model in
a mixture of two for model z1 applied to 1 noisy
data.
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Figure 5. rw(443)/rw(555) and rw(490)/rw(555) as
a function of Chl-a for theoretical rw, for rw
estimated by z0 from non-noisy data, and for rw
estimated by z1 from 1 noisy data.
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Figure 6. Estimated Chl-a using rw(443)/rw(555)
and rw(490)/rw(555) obtained by z0 on D0 and z1
on D1 versus expected Chl-a.
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Application to SeaWiFS Imagery   Function field
methodology tested on SeaWiFS imagery acquired on
day 323 of year 2002 over Southern California.
  zt2 gives large differences in ?w compared
with SeaDAS values, resulting in 78 difference
in chlorophyll-a concentration on average.  
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Application to SeaWiFS Imagery (cont.)   Differen
ces may be explained by large noise level on rTOA
(e.g., 14 at 412 nm), due to RT modeling
uncertainties.   Noise distribution estimated on
2,000 randomly selected pixels of the imagery,
and introduced during the execution of the
stochastic fitting algorithm, yielding function
field zt.
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Figure 7. Marine reflectance rw estimated by z
for SeaWiFS imagery acquired on day 323 of year
2002 over Southern California.
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Figure 8. Marine reflectance rw estimated by
SeaDAS for SeaWiFS imagery acquired on day 323 of
year 2002 over Southern California.
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Figure 9. Histograms of marine reflectance rw
retrieved by SeaDAS and z.
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Figure 10. Marine reflectance spectra retrieved
by SeaDAS and z.
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Figure 11. Chl-a retrieved by SeaDAS and z,
fractional difference, and histograms for SeaWiFS
imagery acquired on day 323 of year 2002 over
Southern California. Average difference is 19.6.
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Conclusions   Fields of non-linear regression
models emerge as solutions to a continuum of
similar statistical inverse problems. They match
well the characteristics of the remote sensing
problem, allowing separation of the explanatory
variables (rTOA) from the conditioning variables
(t).   The inversion is robust, with good
generalization, and computationally efficient.
The retrievals of rw are accurate, with an error
uniform over the entire range of rw values.
Situations of absorbing aerosols are handled
well.
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Conclusions (cont.)   For noise levels up to a
few percent, a general noise scheme may be
appropriate, but for large noise levels, the
noise distribution needs to be estimated. A
plug-in approach may be reasonable.   Extension
of the methodology to atmospheric correction over
optically complex waters is possible.