Forecasting endangered fish migration and survival through an urbanized estuary using acoustic telmetry and stochastic modeling

Abstract:

Anadromous fish such as various salmonid species spawn in inland rivers and migrate at juveniles to the ocean to mature. The mechanisms and dynamics of this early life-stage migration are difficult to characterize and quantify owing to the difficulty of monitoring these very small fish through large riverine systems. Tagging, release and recapture studies provide spatially sporadic timeseries of tagged fish passing through telemetry stations that must be translated into usable forecast models aid in decision support in complex multipurpose water systems. Typically, owing to the sparse spatial coverage in such datasets, and the large scale-separation between experimentally observed body-scale behaviors and monitored river-reach scale migratory patterns, models of migration are largely phenomenological. Adding to this complexity is the fact that tagging experiments only record first detections at various telemetry stations along the river-course. This data-censoring effectively renders each telemetry station into a fully absorbing boundary condition along the river-flow. We present an analytical solution to the 1D advection-dispersion equation (1D-ADE) with general along-stream boundary conditions as a suitable candidate to forecast the dynamics of juvenile salmon migration through the ecologically fragile San Francisco Bay-Delta system in California. The 1D-ADE has been used to model a wide range of real‐world processes including groundwater contaminant transport, atmospheric plume deposition, and the movement of planktonic organisms and migratory animals through riverine systems. Imposing boundary conditions at upstream and downstream locations complicates the analysis of this equation. Here, we provide an analytical solution to a class of 1D-ADEs that are broadly applicable to the processes described above as well as many other physical and biological problems. Our solution makes it possible to incorporate any type of boundary conditions, making it a more flexible approach for modeling realistic field conditions. Our model is both mechanistic and is in excellent agreement with the tagging data along multiple, complex migration routes through this dendritic estuary.