The document discusses using a neural network to estimate the diffuse attenuation coefficient Kd(λ) from satellite ocean color data. It finds that a neural network approach provides more accurate estimates of Kd(λ) than existing empirical and semi-analytical methods, especially for turbid coastal waters. The neural network is trained on two datasets and performs well at estimating Kd(λ) for wavelengths within the training range, as well as for untrained wavelengths. The improved Kd(λ) estimates allow decreasing errors when estimating inherent optical properties of seawater.

1. 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 [email_address] IGARSS 11’ 25-29 July 2011 Vancouver, Canada

2. Purpose of the study (1/2) Diffuse attenuation coefficient K d (  ) 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)

3. Purpose of the study (2/2) K d (  ) 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 K d (490) over basin and global scales Ocean color remote sensing: vertically averaged value of K d (490) in the surface mixed layer

4. 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)

5. 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: K d (  )=(1+0.005*  s )* a (  ) + 4.18*(1-0.52*e -10.8.a(  ) )b b (  ) with a(  ) and b b (  ) calculated from Rrs(  ) through radiative transfer equations

6. 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

7. 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

8. 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) 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 x 1 x 2 y 1 y 2 y 3 f

9. 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

10. 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

11. 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

13. Statistics on the test dataset 0.175 RMS (m -1 ) 10.35 Relative error (%) 1.01 Slope 0.98 NN r

14. 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)

17. 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 -0.00 0.57 Intercept 0.94 0.19 r 1.06 0.14 Slope 36.07 44.96 Relative error (%) 0.204 0.924 RMS NN Werdell

18. 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), a 0 (443)=0.10963 and a 1 (443)=0.6717 Lee: Kd(443) calculated same way that for Kd(490), a(443) and bb(443) being calculated from Rrs(443)

21. 0.38 0.47 0.47 61.47 1.026 Morel 0.79 0.13 0.68 47.34 0.625 Lee 0.08 0.83 Intercept 0.96 0.22 r 0.94 0.22 Slope 29.04 49.55 Relative error (%) 0.279 1.113 RMS NN Werdell

22. Flexibility of the NN NN learned for  =443, 490, 510, 555, 670 nm But  is an input parameter Is it possible to forecast a K d at another wavelength ? Test for K d (456) with the COASTLOOC database

24. 0.250 RMS 31.65 Relative error (%) 0.96 Slope 0.96 Kd(450) NN r

25. 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 (K d (490) > 1 m -1 ) More tests of the useful inputs parameters: solar zenithal angle? Duplicate work for MODIS and MERIS sensors

26. 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

28. 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)

29. 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:    w      

30. New model with previous Kd parameterizations New model with Kd estimated from Neural Network The Kd-NN allows to decrease the RMSE of b bp and a tot-w by a factor of 1.92 and 1.6, respectively. Performance of the new model at 490 nm using the IOCCG synthetic data set .

31. New model with Kd estimated from Neural Networks on the NOMAD data set

32. 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 [email_address] IGARSS 11’ 25-29 July 2011 Vancouver, Canada