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Open Boundary Conditions

  Open boundary conditions are required for elevation, temperature, salinity and tracer concentration (used here to represent effluent). Because the elevation field at each time step is solved for with a fully implicit scheme, the boundary condition must be specified as part of the matrix solution for the elevation field. In addition, the matrix solver used in this code requires the matrix to be symmetric and positive definite, which puts further restraints on the type of boundary condition imposed. The partially clamped boundary condition of Blumberg and Kantha (1985) can be shown to satify these conditions, and is expressed as

where is specified from data. If is very large a pure radiation condition is approached, and if is very small a purely clamped (specified) condition is approached. In the Massachusetts Bay model, the offshore boundary elevation was clamped while the southern boundary radiated gravity waves. The values for elevation used along the offshore boundary were a combination of , , and tidal elevations derived from the tidal model of Lynch and Naimie (1993) and low-frequency fluctuations obtained from the adjunct Gulf of Maine model described in chapter 2.9. The tidal elevations obtained from Lynch (personal communication, 1993) were used to synthesize and constituents by scaling the amplitudes by the observed and ratios at the Boston Buoy and shifting the and phases by the amount observed at the Boston Buoy. This is a reasonable approximation since the , and amplitude and phase vary in much the same manner in the Gulf of Maine (e.g. Moody et al, 1984).

Temperature, salinity and effluent are also specified along the open boundaries. If the flow is directed out of the domain, the interior values are simply advected out of the domain. When outflow turns to inflow, the water property values slowly move toward specified values over a defined relaxation time to avoid artificial fronts from developing. In the Massachusetts Bay model, the relaxation time was specified to vary linearly from 3 days at the most northern boundary cell to 30 days at the southern boundary cell.

Initially the temperature and salinity values along the boundary were specified by climatology interpolated from the Bedford Institute of Oceanography AFAP database (Drinkwater, 1992), while the effluent concentration field was set to zero. Although it was hoped that most local river effects would be due to the Merrimack and the Charles, early runs showed that the gross salinity picture for Massachusetts Bay could not be adequately specified by parameterizing the other Gulf of Maine rivers by seasonal climatology. To address this problem, an adjunct model of the western Gulf of Maine was developed to provide better salinity boundary conditions for the Massachusetts Bay model.