Models of Harmful Algal Blooms

Models used to study harmful algal blooms are a subset of those used to examine more general planktonic processes. Most models have been heuristic, examining the likelihood of certain processes generating a harmful algal bloom. Several models have been more closely coupled to field data and have been used to gain insights into the dynamics underlying the observations. As better physical and biological models are developed, models may play an increasingly important role in harmful algal bloom research. Techniques such as data assimilation may increase the predictive power of models, suggest strategies for improving field sampling, and better constrain poorly known parameters and processes. Beginning with Kierstead and Slobodkin's (1953) model of the opposing effects of growth and diffusion in the formation of a bloom, models have served useful purposes in the study of bloom dynamics. These range from the testing of theoretical hypotheses to the identification and quantification of processes contributing to bloom formation. More recent advances in modeling techniques may allow models to play an increasingly important role in understanding and predicting blooms. Models of harmful algal blooms (HABs) are a small subset of models used in biological oceanography or plankton ecology in general. However, HABs present a particular set of problems that makes them interesting, socially relevant, and possibly excellent models for more general plankton dynamics. The most obvious aspect of HABs is that they often consist of a single species that grows toxic or unusually dense. To describe the dynamics of this species we must be able to adequately describe the dynamics of the ecosystem in which the species is embedded. In the sections below, I present many of the models used to explore HABs (Table 1). I have arranged the models by degree of complexity, beginning with highly aggregated biological models with no physical dynamics. These models segue into biological models with more resolution of taxa or species-less aggregation, more complexity, and more unknown parameters and processes. I then explore coupled physical-biological models used to study HABs, beginning with those using only simple physics (e.g. diffusion or swimming) and then examining those with more detailed physical dynamics. Throughout he presentation of these models, I emphasize the similarities of model structure, the way in which the models have been used, and the aspects of the models that might help us understand the dynamics underlying harmful algal blooms. Finally, I discuss some of the directions that I feel might be most fruitful for models of HABs, including a closer coupling with field programs and the use of data assimilation to better dissect the dynamics of the blooms. Acknowledgments I thank Sharon Franks for constructive comments on this manuscript. This work was supported by the Gulf of Maine Regional Marine Research Board. Model review Aggregated models-One of the earliest models of a red tide is that of Wyatt and Horwood (1973). In this simple model, the reduction of grazing pressure as the concentration of cells increases due to swimming allows the cells to grow relatively unchecked. The equations governing their model are basically dPn, I'Y dt rnC -Pn, (1)