An expanded Eulerian model of phytoplankton environmental response

An Eulerian approach to modeling plankton physiological responses to environmental factors is developed wherein the time history of cell exposure to two external environmental fields over specified time intervals are utilized as independent variables along with position and time to help characterize the cell population. We seek to find the concentration of cells per unit volume as a function of depth, time, and the time histories of exposure to PAR (photosynthetically active radiation) as it influences internal cellular carbon through phototsynthesis and to nitrate as it influences internal cellular nitrogen through nutrient assimilation. The response under consideration here, vertical swimming, is taken to depend on historical exposure to the external PAR and nitrate fields. The model can be readily extended to other external fields and to more than the one historical time scale here associated with each external field. This type of model joins Lagrangian models as most beneficial when phytoplankton physiology responds to environmental factors in a nonlinear fashion, i.e. when the mean response does not depend on the mean exposure. A simple example is discussed and the impact of wind-driven mixing is explored.