Turbulent mixing and phytoplankton life history: A Lagrangian versus Eulerian model comparison

Abstract

Phytoplankton dynamics models follow either an Eulerian or a Lagrangian approach. The Eulerian formulation assumes that all individuals of a population living in homogeneous environmental conditions, i.e. within a model grid cell, are in a single average physiological state, which generally depends on local conditions. By tracking each individual cell or cluster of cells, the Lagrangian formulation allows population behaviour to emerge from a broader range of individual physiological states inherited from different life histories. In order to determine in which mixing conditions the widely used Eulerian approach differs from a more representative but also more computationally costly Lagrangian formulation, we compared the results obtained from a simple 1-dimensional phytoplankton growth model using both formulations under various mixing conditions. The chosen model is based on Droop kinetics, where growth is a function of light and an internal nutrient cell quota. It is applied in cases with constant and uniform diffusivity, and in more realistic cases of wind-induced and tidal mixing. The 2 main outcomes of our study are: (1) results from both formulations converge in weakly stratified environments for any level of turbulent mixing, and (2) results diverge in stratified environments and intermediate mixing up to a diffusivity value above which the environment appears homogeneous to moving cells, and both formulations converge. These results suggest that in heterogeneous and dynamic marine environments, strong variability among individuals may prevent Eulerian models from accurately predicting phytoplankton production.