R.P. Souto, H.F. de Campos Velho, S. Stephany (2004): Reconstruction of Ocean Water Chlorophyll Concentration Using a Parallel Implementation of the Ant Colony Meta-heuristic, Brazilian Congress on Computational and Applied Mathematics (CNMAC-2004), 13-16 September, Porto Alegre (RS), Brazil.

Abstract: A methodology to reconstruct vertical profiles of the absorption and scattering coefficients in offshore ocean waters is presented, using in situ radiance measurements in several depths, single wavelength, and azimuthal symmetry is assumed. Bio-optical models [2] are employed to correlate the Chlorophyll concentration to these coefficients. The inverse problem is formulated as an optimization problem and iteratively solved using the radiative transfer equation. The Laplace transform discrete ordinate (LTSN) [1] method is used to compute the radiances. An objective function is given by the square difference between computed and experimental radiances at every iteration. This objective function is minimized by an Ant Colony System (ACS) meta-heuristic [3]. A parallel implementation of the ACS is used and executed in a distributed memory machine. A recent regularization scheme [4] pre-selects candidate solutions based on their smoothness, using the classical Tikhonov regularization. As radiance intensity decays exponentially with depth, a depth correction factor must be employed to weight the influence of the depth-depend radiances [5]. In this work, another correction factor is used. This factor is given by the ratio between the mean radiance - related to the polar angle - at each level and the mean radiance at the surface. Good results were obtained even for very noisy radiance data.

References:

[1] L.B. Barichello and M.T. Vilhena (1993): A general Approach to One-group One-dimensional Transport Equation, Kerntechnik, 58(3), 182-184.

[2] C.D. Mobley (1984): Light and Water: Radiative Transfer in Natural Waters, Academic Press.

[3] M. Dorigo, V. Maniezzo and A. Colorni (1996): The Ant System: Optimization by a Colony of Cooperating Agents, IEEE Transactions on Systems, Man, and Cybernetics--Part B, 26(2), 29-41.

[4] A.J. Preto, H.F. Campos Velho, J.C. Becceneri, N.N. Arai, R.P. Souto, S. Stephany (2004): A New Regularization Technique for an Ant-colony Based Inverse Solver Applied to a Crystal Growth Problem, 13th Inverse Problem in Engineering Seminar (IPES-2004), 14-15 June 2004, University of Cincinnati, Ohio, USA.

[5] Z. Tao, N.J. McCormick, R. Sanchez (1994): Ocean Source and Optical Property Estimation from Explicit and Implicit Algorithms, Applied Optics, 33(5), 3265-3275.