Numerical Modeling of Tides in Hudson Bay

Abstract

A two-dimensional numerical model is developed to study the cooscillating and independent tides in Hudson Bay. Using centered differences (forward differences for the dissipative term) and conjugate Richardson lattices, the Laplace Tidal Equations in spherical polar coordinates are integrated in time until cyclic equilibrium is reached. For the cooscillating tide, the direct tidal forcing term is set to zero, and the observed tidal constituent is specified at the mouth of Hudson Bay. Separate runs are made for M2, S2, N2, and K1. For the independent tide, the closed mouth boundary condition of zero water transport is imposed, and the model run for the M2 and K1 direct tidal forcing. A number of experiments are carried out to test the sensitivity of the model to uncertainties in the input data and parameterization of some of the terms. It is shown that the tidal propagation is relatively insensitive to friction coefficient and island schematization, but very sensitive to depth representation in the Belcher Islands area and phase variation in the specified boundary conditions.Comparison of the results with previous work and shore-based gauge observations gives good amplitude and phase agreement for the M2, S2, and N2 cooscillating tidal constituents except in the vicinity of the degenerate amphidromic points in James Bay and the Belcher Islands where the amplitudes are very small. The amplitudes of the K1 independent tide, unlike the M2, are found to be upwards of 30% of the K1 cooscillating tide. The M2 cooscillating tidal currents, when compared with current meter results at two stations across the mouth of James Bay, show good agreement in west–east decrease in amplitude, reversal of direction of rotation, and increase in rotary character, but generally tended to underestimate the absolute magnitude of these single depth measurements. Overall, the model gives good qualitative agreement with shore-based data and can be used to interpret tidal propagation in the Hudson–James Bay system.