Bidirectional Reflectance Function in
Coastal Waters And its Application to the
Validation of the Ocean Color Satellites
Alexander Gilerson1, Soe Hlaing1, Tristan Harmel1, Alberto Tonizzo1,
Robert Arnone2, Alan Weidemann2, Samir Ahmed1
1Optical
Remote Sensing Laboratory, City College, New York
2 Naval Research Laboratory, Stennis Space Center
1
Bidirectional Reflectance Distribution Function
(BRDF)
Above water
radiometer
Water Body
• Radiance emerging from the sea, in general, is not isotropic.
• Varies directionally depending on viewing and illumination conditions.
• Bi-directionality property depends on Inherent Optical Properties (IOP) of the water
constituents which are highly variable, especially in coastal environment
 This bidirectional effect needs to be corrected to get standardized parameters
suitable for :
Oceanic and Coastal waters monitoring
Calibration-validation of ocean-color satellite data
2
Correction for Bidirectional Reflectance Distribution
 Adjust the remote-sensing reflectance for
Hypothetical configuration of :
• Nadir Viewing
• Sun at zenith
Current standard BRDF correction algorithm [Morel & Gentili 2002 et. al] :
Optimized for the open ocean water conditions.
Correction is based on the prior estimation of chlorophyll
concentration.
But, inappropriate for typical coastal waters usually dominated by
sediment or by colored dissolved organic matters (CDOM)
3
BRDF-CORRECTION
Algorithm
4
Outline
To analyze Case 2 BRDF, a dataset of remote sensing reflectances typical for
coastal (Case 2) water conditions was generated through radiative transfer
simulations for a large range of viewing and illumination geometries.
Based on this simulated dataset, a Case 2 water-focused remote sensing
reflectance model is proposed to correct above-water and satellite water leaving
radiance data for bidirectional effects.
Proposed model is validated with a one year time series of in situ above-water
measurements acquired by collocated multi- and hyperspectral radiometers
which have different viewing geometries.
With the use of proposed BRDF correction, match-up comparisons of in situ
time series and the MODIS satellite data has been improved.
5
Theoretical Background
Fundamental equation which relates Rrs to optical properties [Morel 2002 et. al]:
Rrs( s ,v ,  ,  ,W , IOP)  ( s ,v,W ) 

f
f ( s ,  ,W , IOP)
  
Q( s ,v,  ,  ,W , IOP)
merges reflection and refraction effects that occur when downward irradiance and
upward radiance propagate through the air-water interface
relates the magnitude of the irradiance reflectance just below the surface to IOP
Q= bidirectional function
W = wind speed
ω = single back-scattering albedo ω = bb / ( a + bb )  determined by IOP
BRDF correction:
Rrs(W,IOP)_corrected
Rrs
_ corrected (W , IOP)  ( s ,v,W ) 
Angular Coordinate Convention
θv ~ Viewing angle
θs ~ solar Zenith
φ ~ solar-sensor relative azimuth
f ( s  0,  ,W , IOP)
  ( )
Q( s  0,v  0,   0,  ,W , IOP)
Set f and Q for Sun at zenith and nadir view
6
Bio-optical model and radiative transfer simulation
Obtain Rrs(λ) & equivalent ω(λ) from 500 sets of IOPs to
investigate Rrs – ω relatioships for large sets of viewing and
illumination geometries.
500 sets of IOP
Four Components
Bio-optical Model
Inherent Optical
Properties (IOP)
Algal Particles [Chl]
Absorption (a)
Non - Algal Particles [CNAP]
ω = b b / ( a + bb )
can be directly
connected to Rrs
through modeling
Scattering (b, bb)
Radiative
transfer
simulations
CDOM
(Hydrolight)
Pure Sea-water
Generated as random variables in the
prescribe ranges typical for coastal
water conditions
Range of input parameters
[Chl] = 1 to 10mg/m3
CNAP = 0.01 to 2.5mg/m3
aCDOM = 0 to 2m-1
Particle Scattering Phase
Function Varied with
particle Concentration &
Composition
Remotesensing
Reflectance
Rrs(λ)
1053 sets of Viewing & illumination
geometries
Viewing angle ( θv ) 0o ~ 80o
solar Zenith ( θs )
0o ~ 800
relative azimuth ( φ ) 0o ~ 180o
Wavelength:
412,443, 491, 551, 668 nm
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Rrs (λ) vs Single back-scattering albedo (ω) at various
illumination and viewing geometries
bb [Gordon 1988, Lee 2002
Rrs ~ function(ω) with  
& Park 2005 ].
a  bb
s = 0
s = 0
0.025
s = 30
 =45
0.015
0.01
0.005
0
s = 30
s = 60
0.02
Rrs(551nm) (Sr-1)
Rrs(551nm) (Sr-1)
s = 30
s = 60
0.02
0.1
0.2
 =90
0.015
0.01
0
0.3
(551nm)
s = 60
0.02
0.005
0
s = 0
0.025
Rrs(551nm) (Sr-1)
0.025
 =180
0.015
0.01
0.005
0
0.1
0.2
0
0.3
(551nm)
0
0.1
0.2
0.3
(551nm)
 Rrs~f(ω) relationship also depends on the viewing and illumination geometries.
 Spectral dependency of the ω ~ Rrs relationship can be also observed [Gilerson 2007 et.al].
 Rrs can be fitted to ω with a third order polynomial:
s = 0
i
Rrs(412nm) (Sr-1)
0.02
s = 60
0.025
s = 0
0.025
s = 30
s = 0
s = 30
Rrs()  1()  2 2 ( )  33 ( )
0.02
s = 60
0.02
Rrs(412nm) (Sr-1)
s = 30
Rrs(412nm) (Sr-1)
0.025
s = 60
 =90of viewing / illumination geometries
=180
 =45 are generated for each set
coefficients
as well as for
0.015
0.015
0.015
each wavelength.
8
0.01
0.01
These coefficients
are applicable to0.01
typical coastal water conditions.
CCNY-BRDF correction algorithm
Optimized for typical Case-2 water conditions
Use of third order polynomial parameterization based on radiative transfer
computation for large range of optical properties
3
Rrs( s , v ,  ,  ,  )   i ( s , v ,  ,  ) i ( )
 generalized expression
i 1
Tabulated
coefficients based on
radiative transfer
computation
ω – single backscattering albedo
θs – Solar zenith angle
θv – Viewing zenith angle
φ – Solar-sensor relative azimuth
λ – Wavelengths
CCNY algorithm in 2 steps:
(1) From the measured Rrs(θs, θv, φ, λ): Solve and retrieve ω(λ) with the use of the least mean
square fitting & tabulated αi (θs, θv, φ, λ) coefficients.
(2) Use the retrieved ω(λ ) in the equation with αi (θs=0, θv=0, φ=0, λ ) coefficients for nadir
viewing and illumination to calculate the BRDF-corrected Rrs(θs=0, θv=0, φ=0, λ )
9
Statistical Analysis/Comparison of the standard MG (Morel/Gentili) and
proposed CCNY Algorithms Based on Simulated Dataset (1/2)
Standard Algorithm
CCNY Algorithm
Regression lines
y = 0.93*x – 8.4e-5 (Standard)
y = 1.00*x – 8.5e-6 (CCNY)
Dispersion
100 N Rrs _ actuali  Rrs _ retrievedi
AAPD 

N i 1
Rrs _ actuali
AAPD(Standard Algo)=9.5%
AAPD(CCNY Algo)=0.6%
 The standard use of Case 1-water based BRDF MG correction induce
almost 10% uncertainty in the remote sensing reflectance retrieval in typical
coastal waters.
 The proposed algorithm permit to reduce this dispersion below 1% without
10
adding any bias
Statistical Analysis of the Algorithms Based on Simulated
Dataset (2/2)
CCNY
algorithm
Standard
algorithm
Without
correction
 Up to 26% in bi-directional variation
is observed addressing the need for a
BRDF correction.
 Standard MG algorithm: helps, but
57% of the dataset still have relative
percent difference more than 5%
which is the required accuracy for
Ocean Color Sensor
 CCNY algorithm: ~98% of the
cases
have
relative
percent
difference less than 5%
Rrs _ actual  Rrs _ retrieved in %
Rrs _ actual
 Important need to incorporate Case-2 water based BRDF correction in the current
data processing
 Possible suitability of CCNY-algorithm to fulfill the Ocean Color
Radiometry requirements
11
ASSESSMENT OF BRDFCORRECTION
APPLICATION TO ABOVE-WATER DATA
AT LONG ISLAND SOUND COASTAL
OBSERVATORY
12
LISCO Site Characteristics
LISCO Multispectral SeaPRISM system
as part of AERONET – Ocean Color network
LISCO
[Zibordi et al., 2006]
 Identical measuring systems and protocols, calibrated using a single reference source
and method, and processed with the same code;
 Standardized products of exact normalized water-leaving radiance and
aerosol optical thickness
13
LISCO Site Characteristics
Location and Bathymetry
Depth in meters (GEBCO data)
Water type: Moderately turbid and very productive (Aurin et al. 2010)
Bathymetry : plateau at 13 m depth
14
LISCO site Characteristics
Platform: Collocated multispectral SeaPRISM and hyperspectral
LISCOHyperSAS
Tower instrumentations since October 2009
Instrument Panel
12 meters
Retractable Instrument Tower
15
LISCO Instrumentation
SeaPRISM instrument
HyperSAS Instrument
 Sea Radiance
 Sea Radiance
 Direct Sun Radiance and Sky Radiance  Sky Radiance
 Bands: 413, 443, 490, 551, 668, 870  Downwelling Irradiance
and 1018 nm
 Linear Polarization measurements
 Hyperspectral: 180 wavelengths [305,900] nm
Data acquisition every 30 minutes for high time resolution time series
16
16
Features of the LISCO site
Unique Capability of Making Near-Concurrent WaterLeaving Radiance From Different Viewing Geometries
HyperSAS
SeaPRISM
N
W
Instrument
Panel
Both instrument makes measurements with viewing angle, θv = 40o.
Thanks to the rotation feature of SeaPRISM, its relative azimuth angle, φ, is always
set 90o with respect to the sun (resulting in water scattering angle range of 132 ~ 145o).
HyperSAS instrument is fixed pointing westward position all the time, thus φ is
changing throughout the day and resulting scattering angle range from 110 -175o.
LISCO site instrumentations configuration permits to assess
accuracy of the bi-directionality correction of the water
leaving radiances.
17
Above-Water Data Processing
Above Water Signal decomposition
Total radiance
Sky radiance
Down-welling
Irradiance
Sun
Ed
Sun glint
radiance
Li
LT = Lw + ρ(W) Li + Lg
θ
Water leaving radiance
θ
Sea surface reflectivity
Li
Remote-sensing reflectance:
Rrs = Lw /Ed
Needs to be corrected for the
bidirectionality property
Lw
18
Comparison of SeaPRISM and HyperSAS
Both instrument pointing same direction
(within ±10° in Azimuth)
Rrs HyperSAS [sr-1]
Rrs HyperSAS [sr-1]
For all the viewing geometries
Rrs SeaPRISM [sr-1]
Rrs SeaPRISM [sr-1]
Increased dispersion in the right figure is mainly due to BRDF
 (filters exclude data from some geometries, specifically where relative azimuth angle, φ < 60° to
eliminate glint effects)
19
Comparison between the Standard MG and Proposed
CCNY Algorithm with the LISCO Dataset
Before BRDF Correction
Corrected with MG
Corrected with CCNY
 Current MG algorithm does not reduce significantly the dispersion and induces a
weaker correlation with R2
 The proposed CCNY algorithm reduce dispersion by 2% in
absolute value and by more than 3% in relative values
20
APPLICATION TO OCEAN
COLOR MODIS IMAGERY
21
Satellite Validation
Satellite Pixel Selection for Matchup Comparison
Validation of MODIS-Aqua against the LISCO Data
Satellite Data Processing: Standard NASA Ocean Color Reprocessing 2009
3km×3km pixel box for
matchup comparison
Exclusion of pixel box if presence
of cloud-contaminated pixels in
this 9km×9km pixel box
Also exclusion of any pixel flagged by the NASA data quality check
processing (Atmospheric correction failure, sun glint contamination,…)
22
Comparison between LISCO and MODIS Ocean
Color data
Rrs Time series for the match-up comparison
 Qualitative consistency in variations is observed between the in-situ and satellite
data.
How will the Satellite / in situ data comparison be improved
by application of the CCNY BRDF-correction ?
23
Application to the Satellite Data
Corrected with Standard Algo
AAPD (%)
Corrected with CCNY
Wavelength (nm)
412
443
491
551
667
Standard
46.43
38.85
16.68
13.61
24.54
CCNY
42.40
34.16
14.93
10.99
21.89
Improvement
4.03
4.69
1.75
2.62
2.65
Application of the CCNY algorithm induces stronger correlation (0.926)
Spectral average absolute percent difference is improved by more than 3%.
Suitability of CCNY BRDF-correction to significantly improve
24
OCR satellite data accuracy in coastal areas
Conclusions
 We proposed a new algorithm for BRDF correction of the remote-sensing
reflectance based on extensive radiative transfer calculations for typical coastal
(case-2) waters conditions
 Theoretical analysis showed that significant improvement are observed with the
proposed algorithm reducing the uncertainty of this correction below 1%
 This algorithm has been tested over the two years time series of LISCO
observations.
 It has been shown that the CCNY BRDF-correction algorithm improve the accuracy of
the above-water data by more than 3%
 Application of CCNY-algorithm to MODIS satellite data showed the same order of
improvement. Suitability of CCNY BRDF-correction to significantly improve OCR
satellite data accuracy in coastal areas
As a consequence of this work the operational application of this
algorithm to current and future (VIIRS) OCR satellite is planned
25
ACKNOWLEDGMENTS
NASA AERONET team for SeaPRISM calibration,
data processing and support of the site operations
NASA Ocean Color Processing Group for satellite
imagery
Partial support from:
Office of Naval Research (ONR)
National Oceanographic and Atmospheric
Administration (NOAA)
26