cific case under consideration. Selection of a particular framework for a specific component varies from facility to facility, is usually based on theoretical developments associated with that component, and is usually proprietary. Determination of the numerical constants associated with the framework is called *identification*. A discussion of both the selection of a framework and identification of its constants for each major component of the computer model is presented in the following sections.

In order to determine the forces that act on a ship, it is necessary to determine the bathymetry (depths, contours) of the waterway in the neighborhood of any position the ship might assume during its passage. The framework typically consists of a data base that stores the waterway depth at specific locations and an interpolation scheme for these data that allows estimation of the water depth at an arbitrary point in the waterway. The structure of these data bases varies considerably. No clear advantage has been demonstrated for any particular scheme. Usually selection is a tradeoff between size of the database and ease of interpolation, which translates into a tradeoff between the storage capacity and computational speed of the computer used for the simulation. The presentation of the data in the original source is a strong influence on the selection of framework.

A typical framework for the data base is a grid on a chart of the waterway (either a rectangular grid or curvilinear grid fitted to the channel). Entries in this matrix correspond to water depth at each node of the gird. Data points must be specified with sufficient density to capture the underwater geometry of the waterway. Of the various choices, the rectangular grid (normally based on latitude and longitude) requires the largest number of data points but is simplest for interpolation. Data bases that use a waterway-fitted grid (for instance, one that uses the channel centerline as one coordinate) are much smaller but require more complex interpolation.

In any of the grid data base systems, different levels of interpolation can be used. Linear interpolation is the easiest and has the advantage of being most computationally robust. However, linear interpolation is also the least accurate because the interpolated values always lie within those data base values used as input to the interpolation. Higher order schemes, such as parabolic interpolation or cubic spline interpolation, require fewer data base points. However, if the data base points do not correspond to a smooth surface, anomalous interpolations can occur. Consequently, linear interpolation is most often used.

Some facilities use a different system altogether, one in which the numbers stored in the waterway data base correspond to polygonal contours of equal draft. Although this scheme results in an extremely compact repre-