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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
Article
  • 105 Downloads

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 profiles.

Keywords

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

References

  1. Barichello LB, Vilhena MT (1993) A general approach to one-group one-dimensional transport equation. Kerntechnik 58(3):182–184Google Scholar
  2. Chandrasekhar S (1960) Radiative transfer. Dover, New YorkzbMATHGoogle Scholar
  3. Cherkasheva A, Nöthig EM, Bauerfeind E, Melsheimer C, Bracher A (2013) From the chlorophyll a in the surface layer to its vertical profile: a greenland sea relationship for satellite applications. Ocean Sci 9(2):431–445. doi: 10.5194/os-9-431-2013 CrossRefGoogle Scholar
  4. Cullen JJ (1982) The deep chlorophyll maximum: comparing vertical profiles of chlorophyll a. Can J Fish Aquatic Sci 39(5):791–803CrossRefGoogle Scholar
  5. Dorigo M, Maniezzo V, Colorni A (1996) The ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B 26(2):29–41CrossRefGoogle Scholar
  6. Gordon HR, Morel A (1983) Remote assessment of ocean color for interpretation of satellite visible imagery, a review. In: Lectures Notes on Coastal Estuarine Studies. Springer-Verlag, New York, p 114Google Scholar
  7. Iott J, Haftka RT, Adelman HM (1985) Selecting step sizes in sensitivity analysis by finite differences. NASA Technical Memorandum 86382 . http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19850025225.pdf
  8. Lavigne H, D’Ortenzio F, Ribera D’Alcalà M, Claustre H, Sauzède R, Gacic M (2015) On the vertical distribution of the chlorophyll a concentration in the mediterranean sea: a basin scale and seasonal approach. Biogeosci Discuss 12(5):4139–4181. doi: 10.5194/bgd-12-4139-2015 CrossRefGoogle Scholar
  9. Matsumura S, Shiomoto A (1993) Vertical distribution of primary productivity function phi, 2: For the estimation of primary productivity using by satellite remote sensing. Bulletin-National Research Institute of Far Seas Fisheries (Japan)Google Scholar
  10. Mignot A, Claustre H, D’Ortenzio F, Xing X, Poteau A, Ras J (2011) From the shape of the vertical profile of in vivo fluorescence to chlorophyll-a concentration. Biogeosciences 8(8):2391–2406CrossRefGoogle Scholar
  11. Morel A (1991) Light and marine photosynthesis: a spectral model with geochemical and climatological implications. Prog Oceanogr 26(3):263–306CrossRefGoogle Scholar
  12. Muñoz-Anderson M, Millán-Núñez R, Hernández-Walls R, González-Silvera A, Santamaría-del Ángel E, Rojas-Mayoral E, Galindo-Bect S (2015) Fitting vertical chlorophyll profiles in the california current using two gaussian curves. Limnology and Oceanography: MethodsGoogle Scholar
  13. Platt T, Sathyendranath S (1988) Oceanic primary production: estimation by remote sensing and regional scales. Science 241:1613–1620CrossRefGoogle Scholar
  14. Preto AJ, CamposVelho HF, Becceneri JC, Arai NN, Souto RP, Stephany S (2004) A new regularization technique for an ant-colony based inverse solver applied to a crystal growth problem. In: Proceedings, Inverse Problem in Engineering Seminar, Cincinnati. pp 147–153Google Scholar
  15. Segatto CF, Vilhena MT (1994) Extension of the ltsn formulation for discrete ordinates problem without azimuthal symmetry. Ann Nucl Energy 21(11):701–710CrossRefGoogle Scholar
  16. Segatto CF, Vilhena MT, Gomes MG (1999) The one-dimensional ltsn solution in a slab with high degree of quadrature. Ann Nucl Energy 26(10):925–934CrossRefGoogle Scholar
  17. Souto RP, Dias PLS, CamposVelho HF, Stephany S, Kampel M (2012) Reconstruction of chlorophyll-a vertical profiles with enhanced resolution. In: Proceedings of 10th World Congress on Computational Mechanics. São PauloGoogle Scholar
  18. Souto RP, Kampel M, Brandini F, CamposVelho HF, Stephany S (2005) Análise comparativa de medições in situ e orbital de radiâncias do oceano na estimativa de concentração de clorofila-a. In: Anais do XII Simpósio Brasileiro de Sensoriamento Remoto, São José dos Campos. pp 3679–3686. URL http://marte.dpi.inpe.br/rep-/ltid.inpe.br/sbsr/2004/11.30.22.29
  19. Stephany S, Becceneri J, Souto R, de Campos Velho H, Silva Neto A (2010) A pre-regularization scheme for the reconstruction of a spatial dependent scattering albedo using a hybrid ant colony optimization implementation. Appl Math Model 34(3):561–572Google Scholar
  20. Ward BA, Waniek JJ (2007) Phytoplankton growth conditions during autumn and winter in the irminger sea, north atlantic. Marine Ecol Prog Ser 334:47–61CrossRefGoogle Scholar

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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