Characteristic properties of models for the vertical distribution of phytoplankton under stratification

Steady-state solutions are described for a variety of two-layer models of the vertical distributions of phytoplankton and a nutrient under stratification and constant grazing. The different versions incorporate: a variable nutrient cell quota, multiple forms of the nutrient (e.g. nitrate and ammonia), chemical storage of light energy, and photoadaptation. In each case the mixed layer is assumed to be nutrient limited while the thermocline is light-limited. The solutions demonstrate that a wide range of models may be examined in this way, and reveal common properties which illustrate the interaction of these processes in a stratified environment. In such models, daily mean values may approach steady conditions within days, even when a diurnal cycle is present. Analysis shows that, as a result of the phytoplankton balance within the thermocline, all the models have four characteristic properties. These featurses, which can also be derived when there are several species each limited by a different nutrient, are shown to be part of the dynamics of a complex ecosystem model (MULES) even though this system does not achieve steady conditions. This suggests that the phytoplankton and nutrients in this model are often close to being in equilibrium with the grazers that are present at any time. General expressions are also derived when self-shading is considered and these give an improved representation of the MULES results. Steady-state analysis using layers provides a theoretical understanding of the dynamical behavior of such models. The relationships presented, e.g. the response to changing light and the treatment of self-shading, appear sufficiently universal to be sought observationally.