Model Grid
The numerical model used in this study is a time-dependent, three-dimensional, primitive equation, estuarine and coastal ocean circulation model described in detail by Blumberg and Mellor (1987). The original governing equations are first transformed from a Cartesian coordinate system into an orthogonal curvilinear coordinate system for the horizontal directions to increase model efficiency in regions of irregularly shaped river boundaries, and to obtain higher resolution in the harbor. Model grid covers the New York harbor from 74° 10' W to 73° 45' W and from 40° 24' N to 40° 52' N. The grid itself is completely orthogonal and is sufficiently so to minimize truncation errors. The horizontal spacial resolution varies from place to place, but in general, is approximate from 50 to 750 m in the long-harbor and across-harbor directions, resulting in 134 by 73 grid points in each direction.

A fine grid, covering the navigational critical waterways of Kill van Kull and Newark Bay, has been developed and embedded within the original (coarse) grid. The grid resolution for the nested grid is doubled from the coarse grid. The fine grid takes hydrodynamic information at the interface between the coarse and fine grids. Due to the a higher spatial resolution, the fine grid is then capable of resolving fine scale eddies in detail.

The bottom topography in the study area was deduced from a 15 second gridded bathymetric file of the NOS hydrographic data base. The data base was obtained from the National Geophysical Data Center. The bathymetric data, after smoothing, have been interpolated onto the model grids.

A topographically conformal coordinate system is used so that the number of grid points in the vertical is independent of the depth. The vertical resolution is resolved by seven level spacing in sigma coordinate wherein =(0.00, 0.17, 0.33, 0.50 0.67, 0.83, 1.0). The Courant-Friedrichs-Levy (CFL)computational stability condition requires the time step should not be longer than the length of time necessary for a gravity wave to move one grid interval.

Boundary conditions
In the early stage of model development, model boundary conditions are:

(1) at the sea surface:

Assuming free surface approximation, the momentum fluxes (wind stress) are set to zero.

(2) at the sea bottom:

The fluxes of heat and salt should vanish at the bottom, and for the u and v components of velocities, the computed solutions are matched with the turbulence law of the wall which extends the computed u and v into the viscous sub-layer where the non-slip bottom boundary condition is satisfied, i.e., The approach employed by Blumberg-Mellor(1987) is used here and is to assume where = 0.4 is the von Karman constant and z0 is a user specified roughness parameter. The value of z is equal to half the thickness of the bottom layer in the physical vertical space.

(3) at the lateral boundaries:

The values of u and v should vanish at material (closed) boundaries; while at non-material (open) boundaries surface elevations are prescribed as a single time series re-constructed from the harmonic constants of the water level observations and/or sub-tidal water level induced by meteorological effect.

Revised Friday March 29 2002by OCS Webmaster