A laterally averaged two-dimensional trajectory model for estimating transport time scales in the Alafia River estuary, Florida

This paper presents a laterally averaged two-dimensional trajectory model for narrow rivers and estuaries and its use for estimating transport time scales in the Alafia River estuary, Florida. The model simulates trajectories of conservative particles in narrow rivers and estuaries with variable width. In the model, the advective movement of the particle is calculated using a high order approach involving multiple sub-timesteps, while the diffusive movement of the particle is modeled using a random walk procedure. A reflection routine is used to prevent particles from crossing the bottom and free surface boundaries. The trajectory model was validated against the analytical solution for an idealized advection-diffusion case before it was applied to the Alafia River estuary. The velocity field at each time step was provided by a hydrodynamic mode model named LAMFE that has been well calibrated for the Alafia River estuary. The trajectory model was run for 16 constant freshwater flow rates at the upstream boundary to calculate both the estuarine residence time (ERT) and the age of fresh water entering the system from the upstream boundary. Depending on the rate of the freshwater inflow, it was found that the ERT of the estuary varies roughly between 2 and 10 days, while the age of water at the most downstream cross section varies between <2 days to about 7 days. An empirical relationship between ERT and the freshwater inflow at the upstream boundary is obtained to be ERT=49.8+226.5e−0.0113Q.