Bulletin of Mathematical Biology

, Volume 61, Issue 2, pp 239–272 | Cite as

A physical-biological coupled model for algal dynamics in lakes

  • Ulrich Franke
  • Kolumban HutterEmail author
  • Klaus Jöhnk


A coupled model is presented for simulating physical and biological dynamics in fresh water lakes. The physical model rests upon the assumption that the turbulent kinetic energy in a water column of the lake is fully contained in a mixed layer of variable depth. Below this layer the mechanical energy content is assumed to vanish. Additionally, the horizontal currents are ignored. This one-dimensional two-layered model describes the internal conversion of the mechanical and thermal energy input from the atmosphere into an evolution of the mixed layer depth by entrainment and detrainment mechanisms. It is supposed to form the physical domain in which the simulation of the biological processes takes place.

The biological model describes mathematically the typical properties of phyto-and zooplankton, their interactions and their response to the physical environment. This description then allows the study of the behaviour of Lagrangian clusters of virtual plankton that are subjected to such environments. The essence of the model is the dynamical simulation of an arbitrary number of nutrient limited phytoplankton species and one species of zooplankton. The members of the food web above and below affect the model only statically.

The model is able to reproduce the typical progression of a predator-prey interaction between phyto-and zooplankton as well as the exploitative competition for nutrients between two phytoplankton species under grazing pressure of Daphnia. It suggests that the influence of the biological system on the physical system results in a weak increase of the surface temperature for coupled simulations, but a considerably higher seasonal thermocline in spring and a lower one in autumn.


Water Column Loss Rate Mixed Layer Turbulent Kinetic Energy Mixed Layer Depth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Society for Mathematical Biology 1999

Authors and Affiliations

  1. 1.Darmstadt Institute of Technology, Institute of MechanicsDarmstadtGermany
  2. 2.Limnological InstituteUniversity of ConstanceKonstanzGermany

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