We describe a Eulerian–Lagrangian–agent method (ELAM) for mechanistically decoding and forecasting 3-D movement patterns of individual fish responding to abiotic stimuli. A ELAM model is an individual-based model (IBM) coupling a (1) Eulerian framework to govern the physical, hydrodynamic, and water quality domains, (2) Lagrangian framework to govern the sensory perception and movement trajectories of individual fish, and (3) agent framework to govern the behavior decisions of individuals. The resulting ELAM framework is well suited for describing large-scale patterns in hydrodynamics and water quality as well as the much smaller scales at which individual fish make movement decisions. This ability of ELAM models to simultaneously handle dynamics at multiple scales allows them to realistically represent fish movements within aquatic systems. We introduce ELAMs with an application to aid in the design and operation of fish passage systems in the Pacific Northwest, USA. Individual virtual fish make behavior decisions about every 2.0 s. These are sub-meter to meter-scale movements based on hydrodynamic stimuli obtained from a hydraulic model. Movement rules and behavior coefficients are systematically adjusted until the virtual fish movements approximate the observed fish.
The ELAM model introduced in this paper is called the Numerical Fish Surrogate. It facilitated the development of a mechanistic biological-based hypothesis describing observed 3-D movement and passage response of downstream migrating juvenile salmon at 3 hydropower dams on 2 rivers with a total of 20 different structural and operational configurations. The Numerical Fish Surrogate is presently used by the U.S. Army Corps of Engineers and public utility districts during project planning and design to forecast juvenile salmon movement and passage response to alternative bypass structures.