Modelling, Analysis and Simulation Population dynamics of sinking phytoplankton in stratified waters

We analyze the predictions of a reaction advection di usion model to pinpoint the nec essary conditions for bloom development of sinking phytoplankton species in strati ed waters This reveals that there are two parameter windows that can sustain sinking phytoplankton a turbulence window and a thermocline depth window The two win dows are delimited by four critical parameters a minimal and maximal turbulence and a minimal and maximal thermocline depth Simple analytical expressions for these four critical parameters are presented and their relation to critical parameters previously introduced by Riley Sverdrup and others are explained Both parame ter windows disappear if the phytoplankton sinking velocity becomes too high This indicates the existence of a maximal phytoplankton sinking velocity that can be sus tained We derive that this maximal sinking velocity is inversely proportional to the background turbidity of the water column In other words clear waters can sustain species with high sinking rates whereas turbid waters can sustain species with low sinking rates only We demonstrate that this prediction is both qualitatively and quantitatively supported by empirical data An intriguing implication is that export production of sinking phytoplankton can be very sensitive to the turbidity of the water column The theory presented here o ers a new framework for a better understanding of the population dynamics of sinking phytoplankton species in strati ed waters Mathematics Subject Classi cation D M ACM Computing Classi cation System I J G and G