Retrieval of the attenuation coefficient

Kd() 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

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)=

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()=(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

)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()) 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

Kd()

Rrs(443)

Rrs(490)

Rrs(510)

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

RMS (m-

1)Relative error (%)

Slope r

NN 0.175 10.35 1.01 0.98

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

RMS Relative error (%)

Slope

r

Kd(450) NN 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

dz

zdE

zEzK d

dd

),(

),(

1),(

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:

w

][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() in open and coastal waters from SeaWiFS ocean color images

Jamet, C., H., Loisel and D., DessaillyLaboratoire d’Océanologie et de Géosciences

32 avenue Foch, 62930 Wimereux, Francecedric.jamet@univ-littoral.fr

IGARSS 11’25-29 July 2011

Vancouver, Canada