Effects of different levels of solar radiation and depth-varying vertical diffusion on the dynamics of a reaction–diffusion NPZ model

Abstract

ABSTRACT Although the effects of solar radiation, diffusion and mixed layer depths on plankton populations have been studied extensively, it is not intuitive what the equilibrium states of a plankton system should be in the absence of seasonal forcing, nor what are the prime determiners of the attracting equilibrium states. In this study, the linear stability of a nutrient–phytoplankton–zooplankton (NPZ) model in reaction–diffusion form is analyzed to understand how solar radiation, diffusion and mixed layer depth influence the predicted equilibrium states. We incorporate parameters that control the response of the phytoplankton growth rate to solar radiation, control the depth of the upper mixed layer and control the strength of the diffusion. The combined effect of the constant in time parameters for these quantities is shown to significantly influence the stability properties of the NPZ reaction–diffusion model. In our parameter range, we find that diffusion and light are stronger determinants of the equilibrium state than mixed layer depth. This linear stability study gives insight into how these quantities affect the stability states of marine planktonic ecosystems and reinforces the importance of understanding light and upper mixed layer turbulence as important factors in determining the state of the plankton system.