Coastal ocean forecasting presents important practical constraints on the limits of the forecast domain, the available data, the missing data, and the means for estimating the state of the ocean. The domain must contain all the relevant dynamics; the data must force same; and the real-time forecast must be fast. Here we are concerned with limited-area forecasts of 3-D transient dynamics, with necessarily extensive open boundaries and concomitant boundary conditions. The importance of inferred wind-band barotropic pressure at the open boundary is discussed, and the necessity for its inference by fitting a hindcast simulation to observations. The twin problems of dimension of the inversion, and its persistence through the forecast, potentially limit the forecast skill.

On the physical hypothesis that the missing boundary conditions are the import of non-local wind-band dynamics: we develop a procedure for deducing boundary pressure as a convolution of observed (local) wind. This significantly reduces the rank of the inversion, leading to accelerated convergence of the conjugate gradient method iterative inverse. A test case is developed and studied to illustrate these ideas and their realization in software.

The method is applied to the problem of forecasting coastal water level in the South Atlantic Bight (SAB). The forecast system, consists of a far field wind response model of the North Atlantic, a prognostic simulator for the continental shelf, and an inverse model which estimates the errors in the far field boundary conditions using data from NOS tide gages. The forecast procedure rests on the assumption that the boundary condition features estimated in the hindcast period persist into the forecast period. Lagged convolution coefficients are estimated from the NOS data during the hindcast period relative to the locally observed wind. A forecast wind product is then convolved with the estimated coefficients to estimate the boundary conditions for the forecast period. Forecast skill is evaluated at the NOS tide gages and the locations of other available data.