where, u_i is the velocities; c is the tracer concentration; k_ir and k_is are the horizontal dispersion coefficients caused by the gravity residual circulation and the vertical shear effect of the tidal current oscillation in the tidal period respectively; k_it is the vertically integrated turbulent coefficient. In the numerical model, the tracer flux normal to the solid boundary is set to zero. The tracer concentration is also set to be zero on the open boundary when there is inflow. Providing the initial tracer concentration is c(t₀) in the bay, the water exchange rate R(x, y, t) can be calculated in terms of the tracer concentration c(x, y, t) as follow:

The TRIM model is accepted as the hydrodynamic model and its numerical scheme is applied in the numerical tracer model. Generally, the stability and the conservation of tracer mass of the numerical model can satisfy the requirement of the water exchange study in the estuary and the embayment. Because the water exchange model is 2-dimensional, a lot of time is saved in calculation. As the main vertical mixing mechanisms are included, the model simulates well the water exchange process.