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Retrieval of the attenuation coefficient Kd(λ) in open and coastal waters using a neural
network inversionJamet, C., H., Loisel and D., Dessailly
Laboratoire d’Océanologie et de Géosciences32 avenue Foch, 62930 Wimereux, France
IGARSS 11’25-29 July 2011
Vancouver, Canada
Purpose of the study (1/2)• Diffuse attenuation coefficient Kd(λ) 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(λ) 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)=
with X=log10(Rrs(490)/Rrs(555)) (SeaWiFS/MODIS standard algorithm)
– Zhang, 2007: • If (Rrs(490)/Rrs(555)) ≥ 0.85,
Kd(490)=
with X=log10(Rrs(490)/Rrs(555)
• If (Rrs(490)/Rrs(555)) < 0.85, Kd(490)=
with X=log10(Rrs(490)/Rrs(665)
0166.010 )811.0101.0459.1843.0( 32
+−−−− XXX
0166.010 )0690.14414.28714.18263.18515.0( 432
+−−+−− XXXX
0166.010 )021.0247.0302.1094.0( 32
+−+− XXX
State-of-the art (2/3)• Two-step empirical algorithm with
intermediate link– Morel, 2007:
• chl-a= 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(λ)=(1+0.005*θs)*a(λ) + 4.18*(1-0.52*e-10.8.a(λ))bb(λ)
with a(λ) and bb(λ) calculated from Rrs(λ) through radiative transfer equations
)X*0.5683-X*1.2259-X*2.7218X*2.9940-(0.3272 432
10 +
•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
State-of-the art (3/3)
Way to improve the estimation
• Use of artificial neural networks Multi-Layer 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
x1
x2
y1
y2
y3
f
• 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)
Advantages:
• Universal approximators of any non-linear continuous and derivable function • Multi-dimensional function•More accurate and faster in operational mode
Limits and drawbacks:
• 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(λ)) per wavelength– IOCCG synthetical dataset (http://ioccg.org/groups/lee.html):
• 1500 set of (Rrs, Kd(λ)) 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
Kd(λ)
Rrs(443)
Rrs(490)
Rrs(510)
Rrs(555)
Rrs(670)
λ
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(λ)) per wavelength– IOCCG synthetical dataset (http://ioccg.org/groups/lee.html):
• 1500 set of (Rrs, Kd(λ)) 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
0.175
RMS (m-1)
10.35
Relative error (%)
1.01
Slope
0.98NN
r
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)
0.34
0.33
1.28
48.83
0.695
Morel
0.87
-0.08
1.34
29.81
0.337
Zhang
0.81
0.03
0.92
38.06
0.351
Lee
-0.000.57Intercept
0.940.19r
1.060.14Slope
36.0744.96Relative error (%)
0.2040.924RMS
NNWerdell
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)
0.38
0.47
0.47
61.47
1.026
Morel
0.79
0.13
0.68
47.34
0.625
Lee
0.080.83Intercept
0.960.22r
0.940.22Slope
29.0449.55Relative error (%)
0.2791.113RMS
NNWerdell
Flexibility of the NN
• NN learned for λ=443, 490, 510, 555, 670 nm
• But λ is an input parameter• Is it possible to forecast a Kd at another
wavelength ?• Test for Kd(456) with the COASTLOOC
database
0.250
RMS
31.65
Relative error (%)
0.96
Slope
0.96Kd(450) NN
r
Conclusions and Perspectives• On the used dataset:
– Net overall improvement of the estimation of the Kd(λ)
– 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
dz
zdE
zEzK d
dd
),(
),(
1),(
λλ
λ =
State-of-the art (1/3)• Direct one-step empirical relationship:
– Mueller, 2000:• Kd(490)=0.1853.X-1.349 with X=Rrs(490)/Rrs(555)
– Werdell, 2005:• Kd(490)=0.016 + 0.1565.X-1.540 with X=Rrs(490)/Rrs(555)
– Werdell, 2009:• Kd(490)=
with X=log10(Rrs(490)/Rrs(555)) (SeaWiFS/MODIS standard algorithm)
– Zhang, 2007: • If (Rrs(490)/Rrs(555) ≥ 0.85,
Kd(490)=
with X=log10(Rrs(490)/Rrs(555)
• If (Rrs(490)/Rrs(555) < 0.85, Kd(490)=
with X=log10(Rrs(490)/Rrs(665)
0166.010 )811.0101.0459.1843.0( 32
+−−−− XXX
0166.010 )0690.14414.28714.18263.18515.0( 432
+−−+−− XXXX
0166.010 )021.0247.0302.1094.0( 32
+−+− XXX
Impact of the estimation of the inherent optical properties of seawater
• Equation:
α = (− 0.83 + 5.34 η − 12.26 η2) + µw(1.013 − 4.124 η + 8.088 η2)
δ = (0.871 + 0.4 η − 1.83 η2)
δα><= ][101b rsd RKb
• Loisel et al. Model:
Estimation of the inherent optical properties of the seawater: absorption, scattering coefficients
New model with previous Kd parameterizations
New model with Kd estimated fromNeural Network
The Kd-NN allows to decrease the RMSE of bbp and atot-w by a factor of 1.92and 1.6, respectively.
Performance of the new model at 490 nm using the IOCCG synthetic data set.
New model with Kd estimated from Neural Networks on the NOMAD data set
Monitoring the diffuse attenuation coefficient Kd(λ) in open and coastal waters from SeaWiFS ocean color images
Jamet, C., H., Loisel and D., DessaillyLaboratoire d’Océanologie et de Géosciences32 avenue Foch, 62930 Wimereux, France
IGARSS 11’25-29 July 2011
Vancouver, Canada
