author = "Souto, Roberto P. and Dias, Pedro L. Silva and Campos Velho, 
                         Haroldo Fraga de and Stephany, Stephan and Kampel, Milton",
          affiliation = "{Laborat{\'o}rio Nacional de Computa{\c{c}}{\~a}o 
                         Cient{\'{\i}}fica (LNCC)} and {Laborat{\'o}rio Nacional de 
                         Computa{\c{c}}{\~a}o Cient{\'{\i}}fica (LNCC)} and {Instituto 
                         Nacional de Pesquisas Espaciais (INPE)} and {Instituto Nacional de 
                         Pesquisas Espaciais (INPE)} and {Instituto Nacional de Pesquisas 
                         Espaciais (INPE)}",
                title = "New developments on reconstruction of high resolution 
                         chlorophyll-a vertical profiles",
              journal = "Computational and Applied Mathematics",
                 year = "2017",
               volume = "36",
               number = "3",
                pages = "1195--1204",
                month = "Sept.",
             keywords = "Radiative transfer equation  Ant colony system  
                         Levenberg-Marquardt  Hydrologic optics  Chlorophyll-a profile.",
             abstract = "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 
                  doi = "10.1007/s40314-016-0318-8",
                  url = "http://dx.doi.org/10.1007/s40314-016-0318-8",
                 issn = "2238-3603",
             language = "en",
           targetfile = "souto_new.pdf",
        urlaccessdate = "22 jan. 2021"