The numerical model used for the Tampa Bay Coastal Prediction System (CPS) is the three dimensional Estuarine Coastal Ocean Model (ECOM-3D).
This model is a close relative of the Princeton Ocean Model (POM) which was pioneered by Alan Blumberg and George Mellor starting in 1977. Extensive details of this model can be found in Blumberg and Herring (1987), Blumberg and Mellor (1987), Blumberg (1990), Blumberg and Mellor (1980), and Mellor (1998).
ECOM-3D solves the time dependant, three dimensional equations for the conservation of mass, momentum, salt, heat and turbulence quantities in an incompressible hydrostatic fluid. Parameterization of vertical mixing is provided by a 2.5 order turbulence closure sub-model that solves prognostic equations for turbulence macroscale and turbulence kinetic energy (Mellor and Yamada, (1974), Mellor and Yamada (1982), Galperin et. al (1988)). Parameterization of the horizontal sub-grid scale mixing is provided by a Smagorinsky (1963) Laplacian type formulation, which computes the local mixing coefficients based upon the grid spacing and velocity shears.
To resolve the surface and bottom boundary layers, the vertical equations of the model are restructured in a bottom and surface following sigma coordinate system. First developed by Phillips (1957) for atmospheric applications, the sigma coordinate scales the vertical coordinate by the depth, thereby preserving all model layers as the bathymetry and surface elevation change. In addition, the vertical layers can be focused near the bed and surface to better resolve the important boundary layers. The horizontal equations are recast in a curvilinear orthogonal coordinate system that allows variable grid sizing and grid cell focusing in the model domain.
The model equations are discretized on a staggered Arakawa-C (Arakawa and Lamb, 1977) finite difference grid. A mode splitting technique is used that separates the fast external gravity waves and the slow moving internal gravity waves (Blumberg and Mellor, 1987), thereby allowing greater efficiency of computation. The external mode shallow water equations, which are obtained from vertically integrating the three-dimensional equations, are solved by a leap-frog explicit scheme. The vertical terms are solved less frequently using an implicit scheme.
The model can be forced with time series of high frequency boundary conditions. In a test bed like Tampa Bay, the typical forcing at the open boundary includes: water level, temperature and salinity, while typical free surface forcing includes wind stress, and the flux of heat and moisture. Along the lateral boundaries, rivers are prescribed with temperature, salinity and flow rates. When needed, mass, temperature and salinity can be added or removed from interior cells to simulate source and sinks such as municipal intakes and outfalls. In the configuration used for Tampa Bay, the model uses a Blumberg-Kantha (Blumberg and Kantha, 1985) radiation type scheme for the open boundary conditions.
Previous applications of this model family (POM and ECOM-3D) range from large ocean and lake systems to much smaller bays and estuaries. A small subset of specific deployments include: the Atlantic East Coast of the United States (Aikman et al., 1996), the North Atlantic (Ezer and Mellor, 1994), Lake Erie (Schwab and Bedford, 1999); (New York Bight (Oey, et al., 1995); Chesapeake Bay (Blumberg and Goodrich, 1990), Yellow Sea (Lewis et al., 1999) and Boston Harbor (Signell et al., 2000). In Tampa Bay, the ECOM-3D model was initially deployed in work by Galperin , Blumberg and Weisberg (1992 a,b).
For the Tampa Bay CPS research, the model was redeployed with a finer resolution grid, revised forcing data, the addition of evaporation and precipitation surface fluxes and revised output formats that are more conducive to operational simulations in nowcast and forecast modes. Evaporation and precipitation was incorporated by the addition of mass flux boundary conditions to the two dimensional external equations (subroutine EXTERNL) and the surface layer of the three dimensional internal equations (subroutine VERTVL). The evaporation fluxes were computed external to the model using a standard bulk evaporation formula.
The Tampa Bay ECOM-3D uses a high resolution grid with 70 by 100 cells in the horizontal and 10 sigma layers in the vertical. A total of 2,244 cells are computationally active. The dimensions of active cells range from 2240 meters to 307.67 meters, with a mean of 668.34 meters. The mean cell area is 0.425 square kilometers. The maximum, mean and minimum depths of the grid cells are 13.93, 3.62 and 1.3 meters mean lower low water (mllw) respectively.