System for solving for the fully three-dimensional advection diffusion reaction (ADR) of dissolved or particulate tracers (biological or chemical materials) in aquatic environments including an input processor and an ADR tracer field processor. Results from a single execution of an ocean circulation model may be used to drive a separate ADR computer simulation and compute a tracer forecast. The velocity fields are not required to be from an ocean circulation model, they could be analysis fields derived from some other source, such as high frequency RADAR observations or satellite-based surface ocean velocity inversion/detection methods.