Chlorophyll concentration profiles from in situ radiances by ant colony optimization

A methodology for the reconstruction of vertical profiles of the absorption (a) and scattering (b) coefficients in natural waters is presented. Reconstruction is performed using single-wavelength in situ radiance measurements at several depths. The depth is discretized by a multi-region approach assuming that absorption and scattering coefficients are constant in each region. The inverse problem is iteratively computed employing the radiative transfer equation as direct model, and bio-optical models to correlate the chlorophyll concentration to these coefficients. At every iteration, the inverse solver generates a candidate solution that is a set of discrete chlorophyll concentration values. For each region, the concentration is mapped to the values of absorption and scattering coefficients. The radiative transfer equation is then solved by a parallel version of the Laplace transform discrete ordinate (LTSN) method considering polar and azimuthal scattering angles. An objective function is given by the square difference between reconstructed and experimental radiances. In order to compensate the nearly exponential radiance decay with depth, that unbalances the influence of the radiance at different depths, a depth correction factor is applied to weight radiance values at each level. This objective function is minimized by an Ant Colony System (ACS) implementation. A new regularization scheme pre-selects candidate solutions based on their smoothness quantified by the Tikhonov’s norm. A new chlorophyll candidate profile is then generated and iterations proceed. Synthetic and real data show the suitability of the proposed method.