Current numerical methods for simulating biophysical processes in aquatic environments are typically constructed in a grid-based Eulerian framework or as an individual-based model in a particle-based Lagrangian framework. Often, the biogeochemical processes and physical (hydrodynamic) processes occur at different time and space scales, and changes in biological processes do not affect the hydrodynamic conditions. Therefore, it is possible to develop an alternative strategy to grid-based approaches for linking hydrodynamic and biogeochemical models that can significantly improve computational efficiency for this type of linked biophysical model. In this work, we utilize a new technique that links hydrodynamic effects and biological processes through a property-carrying particle model (PCPM) in a Lagrangian/Eulerian framework. The model is tested in idealized cases and its utility is demonstrated in a practical application to Sandusky Bay. Results show the integration of Lagrangian and Eulerian approaches allows for a natural coupling of mass transport (represented by particle movements and random walk) and biological processes in water columns which is described by a nutrient-phytoplankton-zooplankton-detritus (NPZD) biological model. This method is far more efficient than traditional tracer-based Eulerian biophysical models for 3-D simulation, particularly for a large domain and/or ensemble simulations.

Stimulated by excess levels of phosphorus, the attached, filamentous green alga Cladophora grows to nuisance proportions in Lake Michigan, one of the Laurentian Great Lakes. While nearshore waters impacted by local sources of the nutrient continue to support nuisance conditions, offshore waters have undergone oligotrophication in response to reductions in phosphorus loading and benthification of phosphorus cycling by invasive dreissenid mussels. A concept termed the Dual Challenge recognizes that implementation of more stringent phosphorus-loading objectives (to control Cladophora in the nearshore) stands in conflict with a foreseen need to mitigate oligotrophication in the offshore (to sustain a healthy fishery). Attention to this nearshore–offshore dynamic calls into play the role of cross-margin phosphorus transport in mediating both endmembers of the conflict. We applied a biophysical model simulating soluble reactive (SRP) and particulate (PP) phosphorus, mussel biokinetics, and cross-margin mass transport in addressing the Dual Challenge. Pre- and post-dreissenid monitoring results suggest that a reduction in offshore PP levels (food web nutrition) in excess of 40% (2.4 to 1.4 mgP·m⁻³) has driven oligotrophication and attendant food web dysfunction. Yet, in the absence of local sources, model-predicted nearshore SRP levels remain at or below those required to prevent nuisance growth. These findings indicate that there is a margin of ~1 mgP·m⁻³ over which offshore PP levels could be increased (to the benefit of the food web and the fishery) without hindering efforts to reduce nuisance algal growth through local source control.