Simulation techniques for the population dynamics of sinking phytoplankton in light-limited environments

Phytoplankton use light for photosynthesis, and the light fluxdecreases with depth. As a result of this simple light-dependence,reaction-advection-diffusion models describing the dynamics ofphytoplankton species contain an integral over depth. That is, models thatsimulate phytoplankton dynamics in relation to mixing processes generallyhave the form of an integro-partial differential equation (integro-PDE).Integro-PDEs are computationally more demanding than standard PDEs. Here,we outline a reliable and efficient technique for numerical simulation ofintegro-PDEs. The simulation technique is illustrated with several exampleson the population dynamics of sinking phytoplankton, a species group thatis most relevant in the context of the global carbon cycle. Our resultsconfirm recent findings that Sverdrup's critical-depth theory breaks downif turbulent mixing is reduced below a critical turbulence. We thereforeconclude that models that do not carefully consider the population dynamicsof phytoplankton in relation to the turbulence structure of the watercolumn may easily lead to erroneous predictions.