Computational and Applied Mathematics

, Volume 36, Issue 3, pp 1195–1204 | Cite as

New developments on reconstruction of high resolution chlorophyll-a vertical profiles

  • Roberto P. SoutoEmail author
  • Pedro L. Silva Dias
  • Haroldo F. Campos Velho
  • Stephan Stephany
  • Milton Kampel


We present a methodology to vertical profiles of chlorophyll-a pigment concentration in open-ocean waters based on radiance values at different depths. The inverse problem is formulated here as an optimization problem and iteratively solved by an Ant Colony System (ACS) meta-heuristic. An objective function is given by the square difference between computed and experimental radiances at each iteration. The Laplace transform discrete ordinate (LTSN) method is used to solve the radiative transfer equation (direct problem) in order to compute the radiances. In a first approach, this methodology did not allow the reconstruction of profiles with two or more peaks of chlorophyll-a concentration. This limitation can be partially explained by the relatively low number (11) of sampling points at different depths, which limits the spatial resolution of the vertical profile to be reconstructed. Alternatively, we propose the such reconstruction of the profile by increasing the vertical resolution, in order to evaluate the ability of identifying any peak in the chlorophyll-a concentration. A hybrid methodology is adopted: initially, the original inverse ACS methodology is employed to retrieve high resolution profiles (41 and 81 points), and then these results are used as an initial guesses for the Lavenberg-Marquardt deteriministic optimization method in order to refine the vertical profiles.


Radiative transfer equation Ant colony system Levenberg-Marquardt Hydrologic optics Chlorophyll-a profile 


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016

Authors and Affiliations

  • Roberto P. Souto
    • 1
    Email author
  • Pedro L. Silva Dias
    • 1
  • Haroldo F. Campos Velho
    • 2
  • Stephan Stephany
    • 2
  • Milton Kampel
    • 2
  1. 1.National Laboratory for Scientific Computing-LNCCPetropolisBrazil
  2. 2.National Institute for Space Research-INPESao Jose dos CamposBrazil

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