Rrs Modeling and BRDF Correction

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Rrs Modeling and BRDF Correction
ZhongPing Lee1, Bertrand Lubac1, Deric Gray2,
Alan Weidemann2, Ken Voss3, Malik Chami4
1Northern Gulf Institute, Mississippi State
University 2Naval Research Laboratory 3University
of Miami 4Laboratoire Oceanographie de
Villefranche
Ocean Color Research Team Meeting, May 4 6,
2009, New York.
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(No Transcript)
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Outline

1. Background
2. Decision on particle phase function shape
3. Rrs model
4. IOP-centered BRDF correction validation
5. Summary

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1. Background

Why BRDF Correction?
Bidirectional Reflectance Distribution Function
Water-leaving radiance, Lw, is a function of
angles. BRDF correction Correct this angular
dependence
?S
?v
?
O(10, 20, 30) measured photons going further
away from Sun (forward scatter) O(10, 20, 150)
measured photons going closer to Sun
(backscatter)
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1. Background (cont.)

Rrs is a function of angles, too.
Define subsurface remote-sensing reflectance as
Cross-surface parameter
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1. Background (cont.)

further
From radiative transfer equation (Zaneveld 1995)
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1. Background (cont.)

The angular component
Phase function shape is the key on the model
parameter!
But not necessarily the bb/b number!
bb/b 0.01 0.015 0.02
0.025
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1. Background (cont.)

• Only two ideal condidtions can we precisely
  correct BRDF effects
• Completely diffused distribution (Lambertian).
• The phase function shape and IOPs are known
  exactly.

Remote sensing is not in ideal conditions
BRDF correction is an approximation!
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1. Background (cont.)

In general
Case-1 approach
a f1(Chl) b f2(Chl) ß f3(Chl)
g(O) Table(Chl, O)
Advantages need Chl only.
Caveats 1. For Case-1 waters only. 2.
Remotely it is difficult to know if a pixel
belongs to Case-1 or not. 3. (minor) large table
when (more spectral bands, more Chl) are required.
(Loisel et al 2002)
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1. Background (cont.)

Objectives of IOP-based BRDF Correction 1.
reduce or minimize the dependency on empirical
bio-optical relationships. 2. avoid the Case-1
assumption. 3. coefficients vary with angular
geometry only.
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2. Decision on particle phase function shape
Distribution of bbp (wide range)
Locations of VSF measurements
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2. Decision on particle phase function shape
(cont.)
Examples of newly measured phase function shape
Phase function normalized at 120o
Scattering angle deg
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2. Decision on particle phase function shape
(cont.)
Cruise average of measured shape
They are not the same! But very similar.
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2. Decision on particle phase function shape
(cont.)
Distribution of the shapes
Apparently there is a dominant appearance for
wide range of bbp!
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2. Decision on particle phase function shape
(cont.)
An average shape is determined from the
measurements
Phase function normalized at 120o
Scattering angle deg
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3. Rrs model
Hydrolight simulations ?s 0, 15, 30, 45,
60, 75 ?v 0, 10, 20, 30, 40, 50, 60, 70
? 0 180o with a 15o step ? 400 760
nm bb/(abb) 0 0.5
With the new average phase function shape
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3. Rrs model (cont.)
Note This G includes the cross-surface effect
and the subsurface model parameter.
Model parameters for gO are also available.
(Gordon 2005)
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3. Rrs model (cont.)
Example of G parameter variation

1. G is not a monotonic function of bb/(abb)
2. G flats out when bb/(abb) gets large (saturation)

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3. Rrs model (cont.)
Analytical G models
Gordon et al formulation (1988)
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3. Rrs model (cont.)
Other formulations
Albert and Mobley (2003)
Park and Ruddick (2005)
Van Der Woerd and Pasterkamp (2008)
Caveats
1. Not resolving the non-monotonic dependency
(contribution of molecular scattering) 2.
High-order polynomials do not behave smoothly
outside the range
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3. Rrs model (cont.)
Lee et al (2004)
Caveats
Cannot invert abb algebraically.
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3. Rrs model (cont.)
A practical choice for algebraic inversion
Global distribution of Rrs(443)
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3. Rrs model (cont.)
Retrieved Chl and bbp(555) of North Pacific Gyre
(from SeaWiFS)
After the separation of molecular and particle
scatterings on the model parameter, derived bbp
compared much better with in situ measurements.
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3. Rrs model (cont.)
Impact of wind speed
Distribution of Rrs difference between 0 m/s and
10 m/s
94.4 within 5!
distribution
impact of wind speed is small (consistent with
earlier studies).
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3. Rrs model (cont.)
(with 5 m/s wind)
Table ((7x131)x4x6) array, 2208 elements) of
G(O)
(if based on Chl, it is 6x13x7 546 elements per
band per Chl)
0.0593 0.0584 0.0586 0.0585 0.0588 0.0583 0.0586 0.0583
0.012 0.0177 0.0177 0.0176 0.0176 0.0163 0.0169 0.0131
0.0529 0.0502 0.0504 0.0503 0.0506 0.0502 0.0504 0.05
0.1277 0.1402 0.14 0.14 0.1404 0.1392 0.1398 0.1397
0.0581 0.0601 0.06 0.0598 0.06 0.059 0.0587 0.0577
0.0178 0.0157 0.0177 0.0176 0.0113 0.0123 0.0146 0.0178
0.0483 0.0527 0.0525 0.0514 0.0504 0.0489 0.0482 0.047
0.1511 0.1324 0.1342 0.138 0.1445 0.1481 0.1535 0.1569
0.0575 0.0598 0.0599 0.0598 0.0596 0.0584 0.0581 0.057
0.0178 0.0176 0.0176 0.0123 0.0137 0.0178 0.0158 0.0179
0.0463 0.0506 0.0505 0.0496 0.0488 0.0474 0.0466 0.0455
0.1642 0.1438 0.1456 0.1488 0.1547 0.1578 0.165 0.1709

Angular-dependent model coefficients for Rrs(O)
are now available.
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4. IOP-centered BRDF correction validation
IOP approach
Rrs(O) ? abb ? G0 ? Rrs0
QAA, optimization, linear matrix, etc.
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4. IOP-centered BRDF correction validation
(cont.)
Algebraic algorithm (e.g., QAA, linear matrix)
Optimization algorithm (e.g. GSM01, HOPE)
(Lee et al. 2002, Hoge and Lyon 1996)
(Roesler and Perry 1996, Lee et al. 1996,
Maritorena et al. 2001)
Input-data focus
Input-model focus
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4. IOP-centered BRDF correction validation
(cont.)
Retrieval and correction examples
HL simulated data Sun at 60o, 10-70o view angles
and 0-180o azimuth
Wavelength 400 760 nm
Comparison of IOPs (via QAA)
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4. IOP-centered BRDF correction validation
(cont.)
Comparison of Rrs0
Before correction 63 38 are within 10 and
5, respectively. After correction 99 95 are
within 10 and 5, respectively
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4. IOP-centered BRDF correction validation
(cont.)
QAA vs Spectral optimization (HOPE)
Rrs(O) ? abb ? G0 ? Rrs0
Distribution
Via spectral optimization 70 55 are within
10 and 5, respectively. Via QAA 99 95 are
within 10 and 5, respectively.
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4. IOP-centered BRDF correction validation
(cont.)
Impact of wrong phase function shape
O(15, 10, 165)
120o-normalized part. phase function
Rrs(O)?QAA?Rrs0 sr-1
Scattering angle deg
Rrs0 sr-1
Rrs(O)?QAA?a m-1
Rrs(O)?QAA?bbp m-1
Absorption coefficient m-1
bbp m-1
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4. IOP-centered BRDF correction validation
(cont.)
Mediterian Sea, 2004 Sun at 30o
Field measured data
Blue from Rrs Red from NuRADS
486 nm, 60o view
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4. IOP-centered BRDF correction validation
(cont.)
Mont. Bay 20060915 Sun at 60o
Field measured data
a440 1.1 m-1, Zeu 6.8 m
Blue from Rrs Red from NuRADS Black Hydrolight
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4. IOP-centered BRDF correction validation
(cont.)
Remote-sensing domain
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5. Summary

1. Angular distribution of remote-sensing
   reflectance (Rrs) highly depends on particle
   phase function shape (PPFS).
2. PPFS is not a constant, but generally varies
   within a limited range. An average PPFS (and
   particle phase function) is derived based on
   recent measurements.
3. Without known PPFS precisely, BRDF correction is
   an approximation.
4. The model parameter for Rrs is not a monotonic
   function of bb/(abb). Separating the angular
   effects of molecule and particle scatterings are
   important for deriving particle scattering
   coefficient in oceanic waters.

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5. Summary (cont.)

• E. Models and procedures to derive IOPs from
  angular Rrs, and then to correct the angular
  dependence, are now developed. This approach can
  be applied to both multi-band and hyperspectral
  data, and not need to assume Case-1 waters.
• F. Excellent results (99 are within 10 error
  after BRDF correction) are achieved with HL
  simulated data.
• G. Reasonable results are achieved with field
  measured data, but more tests/evaluation are
  necessary.
• H. Impacts of wrongly assumed PPFS are mainly on
  the retrieval of particle backscattering
  coefficient, with minor impact on the retrieval
  of absorption coefficient. The total absorption
  coefficient is the least affected parameter from
  angles/PPFS!

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Thank you!
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2. Decision on particle phase function shape
(cont.)
Measurement of shape difference
(compared with average shape)
(Mobley et al 2002)
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4. IOP-centered BRDF correction validation
(cont.)
AOPEX 081404 Sun at 70o
Field measured data
a440 0.035 m-1, Zeu 82 m
486 nm, 60o view
Blue from Rrs Red from NuRADS
548 nm, 60o view