R.P. Souto, H.F. de Campos Velho, S. Stephany (2004): Reconstruction of Chlorophyll Vertical Profiles from "in-situ" Radiances using the Ant Colony Meta-Heuristic, Iberain Latin American Congress on Computational Methods (CILAMCE-2004), 10-12 November, Recife (PE), BRAZIL.

Abstract: It is proposed a methodology to reconstruct vertical profiles of the absorption (a) and scattering (b) coefficients in natural waters from in situ radiance measurements in several depths and single wavelength. A multi-region (R=10) approach is employed and these coefficients are assumed as being constant in each region. The inverse problem is iteratively solved using the radiative transfer equation as direct model. A former work employed a step-by-step reconstruction methodology, estimating a and b in an alternate manner [4] (R=1). In the current work, bio-optical models [1] are employed to correlate the Chlorophyll concentration to a and b, and thus to the single scattering albedo w0. At every iteration, the inverse solver generates a candidate solution that is a set of discrete Chlorophyll concentration values for each region. The radiative transfer equation is solved using these values by the Laplace transform discrete ordinate (LTSn) method [2] for 20 polar angles and 174 azimuthal modes. An objective function is given by the square difference between reconstructed and experimental radiances at every iteration. This objective function is minimized by an Ant Colony System (ACS) [3] implementation. A new regularization scheme pre-selects candidate solutions based on their smoothness, in addition to the classical Tikhonov regularization. This scheme was proposed in a crystal growth inverse problem to reconstruct the diffusion coefficient [5]. Another Chlorophyll candidate profile is generated and iterations proceed. Test results show the suitability of the proposed method. As hundreds of iterations are typically demanded, a parallel implementation of the LTSn method [6] is used and executed in a distributed memory machine.

References:

[1] C.D. Mobley (1994): Light and water: radiative transfer in natural waters, Academic Press.

[2] L.B. Barichello, M.T. Vilhena (1993): A general approach to one-group one-dimensional transport equation, Kerntechnik, 58(3), 182-184.

[3] M. Dorigo, V. Maniezzo, 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] S. Stephany, H.F. Campos Velho, F. M. Ramos, C.D. Mobley (2000): Identification of inherent optical properties and bioluminescence source term in a hydrologic optics problem, Journal of Quantitative Spectroscopy & Radiative Transfer, 67(2), 113-123.

[5] 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, University of Cincinnati, Ohio, USA - accepted.

[6] R.P. Souto, H.F. Campos Velho, S. Stephany, A.J. Preto, C.F. Segatto, M.T. Vilhena (2003): A Parallel Implementation of the LTSn Method for a Radiative Transfer Problem, Proceedings of the 15th Symposium on Computer Architecture and High Performance Computing, Edited by: Liria M. Sato, Phillipe O. A. Navaux, Edson T. Midorikawa, p. 116-122, ISBN: 0-7695-2046-4, IEEE Computer Society.