Retrieval of the attenuation
coefficient Kd() in open and
coastal waters using a neural
network inversion
Jamet, C., H., Loisel and D., Dessailly
Laboratoire d’Océanologie et de Géosciences
32 avenue Foch, 62930 Wimereux, France
cedric.jamet@univ-littoral.fr
IGARSS 11’
25-29 July 2011
Vancouver, Canada
Purpose of the study (1/2)
• Diffuse attenuation coefficient Kd() of
the spectral downward irradiance plays a
critical role:
– Heat transfer in the upper ocean (Chang and
Dickey, 2004; Lewis et al., 1990; Morel and
Antoine, 1994)
– Photosynthesis and other biological processes in
the water column (Marra et al., 1995; McClain et
al., 1996; Platt et al., 1988)
– Turbidity of the oceanic and coastal waters
(Jerlov, 1976; Kirk, 1986)
Purpose of the study (2/2)
• Kd() is an apparent optical property
(Preisendorfer, 1976)  varies with solar
zenith angle, sky and surface conditions,
depth
• Satellite observations: only effective
method to provide large-scale maps of
Kd(490) over basin and global scales
• Ocean color remote sensing: vertically
averaged value of Kd(490) in the surface
mixed layer
State-of-the art (1/3)
• Direct one-step empirical relationship:
– Werdell, 2009:
•
Kd(490)=
10
(  0 . 8515  1 . 8263 X  1 . 8714 X
2
 2 . 4414 X
3
 1 . 0690 X
4
)
 0 . 0166
with X=log10(Rrs(490)/Rrs(555)) (SeaWiFS/MODIS standard algorithm)
– Zhang, 2007:
• If (Rrs(490)/Rrs(555))  0.85,
Kd(490)=
10
(  0 . 843  1 . 459 X  0 . 101 X
2
 0 . 811 X
2
 0 . 021 X
3
)
 0 . 0166
)
 0 . 0166
with X=log10(Rrs(490)/Rrs(555)
• If (Rrs(490)/Rrs(555)) < 0.85,
Kd(490)=
10
( 0 . 094  1 . 302 X  0 . 247 X
with X=log10(Rrs(490)/Rrs(665)
3
State-of-the art (2/3)
• Two-step empirical algorithm with
intermediate link
– Morel, 2007:
2
3
4
(0.3272 - 2.9940 * X  2.7218 * X -1.2259 * X - 0.5683 * X )
• chl-a= 10
with X=max(Rrs(443),Rrs(490),Rrs(510)) (OC4V6)
• Kd(490)=0.0166 + 0.0733[chl-a]0.6715
• Semi-analytical approach:
– Lee, 2005 AOPs determined by IOPs:
• Kd()=(1+0.005*s)*a() + 4.18*(1-0.52*e-10.8.a())bb()
with a() and bb() calculated from Rrs() through radiative
transfer equations
State-of-the art (3/3)
•Open ocean (Lee, 2005) :
• All methods give accurate
estimates
• Coastal waters (Lee, 2005) :
•Empirical methods: significant
errors except for Zhang (2007)
•Semi-analytical: not such
limitation but accuracy still low
Way to improve the estimation
• Use of artificial neural networks  MultiLayer Perceptron (MLP)
–
–
–
–
Purely empirical method
Non-linear inversion
Universal approximator of any derivable function
Can handle “easily” noise and outliers
• Method widely used in atmospheric sciences
but rarely in spatial oceanography
Principles of NN
•
•
•
A MLP is a set of interconnected neurons
that is able to solve complicated problems
Each neuron receives from and send
signals to only the neurons to which it is
connected
Applications in geophysics:
– Non-linear regression and inversion
(Badran and Thiria, J. Phys. IV, 1998;
Cherkassky, Neural Networks, 2006)
– Statistical analysis of dataset
(Hsieh, W.W, Rev. Geophys., 2004)
y1
x1
x2
f
y2
y3
Advantages:
Limits and drawbacks:
• Universal approximators of any nonlinear continuous and derivable
function
• Multi-dimensional function
•More accurate and faster in
operational mode
• Need adequate database
• Learning phase is time consuming
• Number of hidden layers and
neurons unknown: need to determine
them
Dataset
• Learning/testing datasets  Calibration of the NN
– NOMAD database (Werdell and Bailey, 2005):
• 337 set of (Rrs,Kd()) per wavelength
– IOCCG synthetical dataset (http://ioccg.org/groups/lee.html):
• 1500 set of (Rrs, Kd()) per wavelength
• Three solar angles: 0°, 30°, 60°
• 80% of the entire dataset randomly taken for the learning
phase (e.g., determination of the optimal configuration of
the artificial neural networks)
• The rest of the dataset used for the validation phase
Rrs(443)
Rrs(490)
Rrs(510)
Kd()
Rrs(555)
Rrs(670)

Architecture of the Multi-Layered Perceptron:
Two hidden layers with four neurons on each layer
Dataset
• Learning/testing datasets  Calibration of the NN
– NOMAD database (Werdell and Bailey, 2005):
• 337 set of (Rrs,Kd()) per wavelength
– IOCCG synthetical dataset (http://ioccg.org/groups/lee.html):
• 1500 set of (Rrs, Kd()) per wavelength
• Three solar angles: 0°, 30°, 60°
• 80% of the entire dataset randomly taken for the learning
phase (e.g., determination of the optimal configuration of
the artificial neural networks)
• The rest of the dataset used for the validation phase
NN
RMS (m-1) Relative
Slope
error (%)
r
0.175
0.98
10.35
1.01
Statistics on the test dataset
Comparison with other methods
• COASTLOOC DATABASE (Babin et al., 2003)
– Observations in European coastal waters between
1997 and 1998
– Entirely independent dataset from NOMAD and IOCCG
– Kd(490) ranging from 0.023 m-1 and 3.14 m-1 with a
mean value of 0.64 m-1
– Nb total data: 132
• Comparison of Kd(490), Kd(443)
Werdell Zhang
Morel
Lee
NN
RMS
0.924
0.337
0.695
0.351
0.204
Relative
error (%)
44.96
29.81
48.83
38.06
36.07
Slope
0.14
1.34
1.28
0.92
1.06
Intercept
0.57
-0.08
0.33
0.03
-0.00
r
0.19
0.87
0.34
0.81
0.94
Comparison for Kd(443)
• Werdell
– Empirically extrapolated from Kd(490) following
approach of Austin and Petzold (1986):
• Kd(443)=0.0178 + 1.517*(Kd(490) – 0.016)
• Morel:
– Kd(443) is calculated like Kd(490) with only difference
being the spectral values: 0.0085 for Kw(443),
a0(443)=0.10963 and a1(443)=0.6717
• Lee:
– Kd(443) calculated same way that for Kd(490), a(443)
and bb(443) being calculated from Rrs(443)
Werdell
Morel
Lee
NN
RMS
1.113
1.026
0.625
0.279
Relative
error (%)
49.55
61.47
47.34
29.04
Slope
0.22
0.47
0.68
0.94
Intercept
0.83
0.47
0.13
0.08
r
0.22
0.38
0.79
0.96
Flexibility of the NN
• NN learned for =443, 490, 510, 555, 670
nm
• But  is an input parameter
• Is it possible to forecast a Kd at another
wavelength ?
• Test for Kd(456) with the COASTLOOC
database
Kd(450) NN
RMS
Relative error
(%)
Slope r
0.250
31.65
0.96
0.96
Conclusions and Perspectives
• On the used dataset:
– Net overall improvement of the estimation of the
Kd()
– Same quality for the very low values of Kd(490), i.e. <
0.2 m-1
– Huge improvement for the greater values, especially
for very turbid waters (Kd(490) > 1 m-1)
• More tests of the useful inputs parameters: solar
zenithal angle?
• Duplicate work for MODIS and MERIS sensors
Acknowledgments
• CNRS and INSU for funding
• Marcel Babin for providing the
COASTLOOC database
• IOCCG for providing the synthetical
database
• NASA for providing the NOMAD
database
K d ( , z ) 
1
dE d (  , z )
E d ( , z )
dz
State-of-the art (1/3)
•
Direct one-step empirical relationship:
– Mueller, 2000:
•
– Werdell, 2005:
•
– Werdell, 2009:
•
Kd(490)=0.1853.X-1.349 with X=Rrs(490)/Rrs(555)
Kd(490)=0.016 + 0.1565.X-1.540 with X=Rrs(490)/Rrs(555)
(  0 . 8515  1 . 8263 X  1 . 8714 X
Kd(490)= 10
2
 2 . 4414 X
3
4
 1 . 0690 X
)
 0 . 0166
with X=log10(Rrs(490)/Rrs(555)) (SeaWiFS/MODIS standard algorithm)
– Zhang, 2007:
• If (Rrs(490)/Rrs(555)  0.85,
Kd(490)=
10
(  0 . 843  1 . 459 X  0 . 101 X
2
 0 . 811 X
3
)
 0 . 0166
2
 0 . 021 X
3
)
 0 . 0166
with X=log10(Rrs(490)/Rrs(555)
• If (Rrs(490)/Rrs(555) < 0.85,
Kd(490)=
10
( 0 . 094  1 . 302 X  0 . 247 X
with X=log10(Rrs(490)/Rrs(665)
Impact of the estimation of the inherent
optical properties of seawater
• Loisel et al. Model:
Estimation of the
inherent optical
properties of the
seawater: absorption,
scattering coefficients
• Equation:
b b   K d  1 10
a
[ R rs ]
d
a  ( 0.83  5.34 h  12.26 h2)  mw(1.013
 4.124 h  8.088 h2)
d  (0.871  0.4 h  1.83 h2)
Performance of the new model at 490 nm using the IOCCG synthetic data set.
New model with previous Kd
parameterizations
New model with Kd estimated from
Neural Network
The Kd-NN allows to decrease the RMSE of bbp and atot-w by a factor of 1.92
and 1.6, respectively.
New model with Kd estimated from Neural Networks on
the NOMAD data set
Monitoring the diffuse
attenuation coefficient Kd() in
open and coastal waters from
SeaWiFS ocean color images
Jamet, C., H., Loisel and D., Dessailly
Laboratoire d’Océanologie et de Géosciences
32 avenue Foch, 62930 Wimereux, France
cedric.jamet@univ-littoral.fr
IGARSS 11’
25-29 July 2011
Vancouver, Canada