Abstract: An inverse analysis for the multispectral estimation of internal sources in natural waters, from the knowledge of the exit radiation at the water surface, is presented. The analysis involves a forward model that utilizes an analytical discrete-ordinates method for solving the radiative transfer equation [1-3], and an inverse model which contains an algorithm for least-squares estimation that is iteratively solved for retrieving the desired optical properties by using the Levenberg-Marquardt optimizer [4-6]. The experimental data are simulated with synthetic data corrupted with noise. The results show that the internal sources can be recovered with good accuracy, even for high noisy data.

References:

1. E.S. Chalhoub (1997): O Metodo das Ordenadas Discretas na Soluçao da Equaçao de Transporte em Geometria Plana com Dependencia Azimutal, Doctorate thesis, Universidade de Sao Paulo, Brazil.

2. E.S. Chalhoub, R.D.M. Garcia (2000): The Equivalence between Two Techniques of Angular Interpolation for the Discrete-ordinates Method, Journal of Quantitative Spectroscopy & Radiative Transfer, 64,517-535.

3. E.S. Chalhoub, R.D.M. Garcia (2001): Discrete-ordinates Solution for Radiative Transfer Problems, Journal of Quantitative Spectroscopy & Radiative Transfer, in preparation.

4. K. Levenberg (1944): A Method for the Solution of Certain Problems in Least Squares, Quarterly of Applied Mathematics, 2, 164-168.

5. D. Marquardt (1963): An Algorithm for Least-squares Estimation of Nonlinear Parameters, Journal of the Society for Industrial and Applied Mathatematics, 11, 431-441.

6. DBCLSF (1991): IMSL MATH/LIBRARY Users Manual, Version 2.0. IMSL, Houston.