Advertisement

Mathematical Modeling of Phosphorus Dynamics in Aquatic Ecosystems

  • Maibelin Castillo-AlvarezEmail author
  • Rolando Cárdenas
  • Roberto González-de Zayas
  • Yanelis Estrada-Hernández
  • Julio Antonio Lestayo
  • Dailé Ávila-Alonso
  • Lorgio Batar
Conference paper

Abstract

A basic framework for the elaboration of a model of the dynamics of phosphorus in Cuban coastal ecosystems is presented. We start from a zero-dimensional model, which includes several physical, chemical, and biological processes depending only on time. In this, first a relatively isolated ecosystem was considered, and then polluting loads from runoff were included. Then, the vertical space variable was introduced, given the importance of the interaction of phosphorus with the bottom in many coastal ecosystems. This resulted in a one-dimensional model of predominantly thermo-hydrodynamic model, coupled with a model of radiative transfer in atmosphere and ocean. The thermo-hydrodynamic frame of the model consists of a system of three partial differential equations whose solutions were found and turned out to be well behaved from a mathematical point of view. A preliminary application to a case study was done and analyzed. They were able to lay the foundations for the preparation of a Cuban hydrodynamic model.

Keywords

Phosphorus Aquatic ecosystems Differential equation Biogeochemical processes 

References

  1. 1.
    Abell JM, Ozkundakci D, Hamilton DP (2010) Nitrogen and phosphorus limitation of phytoplankton growth in New Zealand Lakes: implications for eutrophication control. Ecosystems 13(7):966–977CrossRefGoogle Scholar
  2. 2.
    Elser JJ, Marzolf ER, Goldman CR (1990) Phosphorus and nitrogen limitation of phytoplankton growth in the freshwaters of North America: a review and critique of experimental enrichments. Can J Fish Aquat Sci 47:1468–1477CrossRefGoogle Scholar
  3. 3.
    Ji Z-G (2008) Hydrodynamics and water quality. Wiley InterscienceGoogle Scholar
  4. 4.
    Márquez A, Senior W, Martínez G, Gonzalez Á (2007) Concentraciones de nitrógeno y fósforo en sedimentos recientes de la laguna Los Patos, Estado Sucre, VenezuelaGoogle Scholar
  5. 5.
    Montalvo JF et al (2010) Compuestos de nitrógeno y fósforo en las aguas superficiales de tres zonas de la plataforma marina cubana. Ser Oceanol 7Google Scholar
  6. 6.
    Robson BJ (2014) State of the art in modelling of phosphorus in aquatic systems: review, criticisms and commentary. Environ Model Softw 61:339–359CrossRefGoogle Scholar
  7. 7.
    González-De Zayas R, Merino-Ibarra M, Soto-Jiménez MF, Castillo-Sandoval FS (2013) Biogeochemical responses to nutrient inputs in a Cuban coastal lagoon: runoff, anthropogenic, and groundwater sources. Springer Environ Monit Assess 185(12):10101–10114CrossRefGoogle Scholar
  8. 8.
    Montalvo JF, Loza S (2006) Flujos de materiales conservativos y no conservativos en la Bahía de Jigüey (Archipiélago Sabana-Camagüey, Cuba) y el océano. Ser Oceanol 2:1–2Google Scholar
  9. 9.
    López-Monroy F, Troccoli-Ghinaglia L (2017) Modelaje de la interaccón entre la laguna costera tropical Los Mártires (Isla de Margarita, Venezuela) y el Mar Caribe Adyacente. Ciencias Básicas y Tecnología 29:534–545Google Scholar
  10. 10.
    Valiela I (2013) Marine ecological processes. Springer Science & Business MediaGoogle Scholar
  11. 11.
    Mellor GL, Yamada T (1974) A hierarchy of turbulence closure models for planetary boundary layers. J Appl Meteorol 13:1791–1806Google Scholar
  12. 12.
    Mellor GL, Yamada T (1982) Development of a turbulence closure model for geophysical fluid problems. Rev Geophys Space Phys 20:851–875CrossRefGoogle Scholar
  13. 13.
    Tageo (ed) (2018) Available (17/04/2018): http://www.tageo.com/index-e-cu-v-00-d-m2276714.htm
  14. 14.
    Alvarez-Salgueiro J (2015) Habitabilidad Primaria del Fitoplancton en el Golfo de Ana María. Departamento de Física, Universidad Central “Marta Abreu” de Las Villas Santa ClaraGoogle Scholar
  15. 15.
    Goddes TW (ed) (2018) Solstice and equinox dates 2010 to 2020. Available (18/01/18): http://www.thewhitegoddess.co.uk/the_wheel_of_the_year/solstice_and_equinox_dates_2010_to_2020.asp (Online)
  16. 16.
    Stewart RH (2006) Introduction to physical oceanography, Sept 2006 edition ed. Texas A & M UniversityGoogle Scholar
  17. 17.
    Mellor GL, Durbin PA (1975) The structure and dynamics of the ocean surface mixed layer. J Phys Oceanogr 5(7):18–728Google Scholar
  18. 18.
    Elgoltz L (1983) Ecuaciones diferenciales y cálculo variacional, 3ra edn. Editorial Mir, MoscúGoogle Scholar
  19. 19.
    Tijonov AA, Samarsky A (1972) Ecuaciones de la física matematica. Mir, MoscúGoogle Scholar
  20. 20.
    Arriaza L et al (2008) Corrientes Marinas estimadas en la plataforma suroriental cubana. Ser Oceanol 4Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maibelin Castillo-Alvarez
    • 1
    Email author
  • Rolando Cárdenas
    • 2
  • Roberto González-de Zayas
    • 1
  • Yanelis Estrada-Hernández
    • 2
  • Julio Antonio Lestayo
    • 1
  • Dailé Ávila-Alonso
    • 2
  • Lorgio Batar
    • 2
  1. 1.Coastal Ecosystem Research Center (CIEC)Cayo Coco, MorónCuba
  2. 2.Central University “Marta Abreu” of Las VillasSanta ClaraCuba

Personalised recommendations