Theoretical Hindcast of Currents and Water Elevations Using Numerical Models
Authors: Mainville Charles R. , Evans Douglas J. , Earle Marshall D. 
Published: October 2008

ABSTRACT
Numerical hydrodynamic models may be used for the hindcasting of water elevations and currents in areas where data and predictions are lacking. A numerical hydrodynamic model has been set up, calibrated and applied to the Nova Scotia Shelf. Inputs to the model are deep water tidal records and wind fields determined from an analysis of synoptic weather charts. Boundary conditions are the coastlines and bathymetry of the area. Hindcasted storm and astronomical tides and currents for specific dates have been compared with measured elevations and currents at several locations on the shelf. The good agreement between measured and theoretical data establishes the model as a valuable tool for the determination of extreme and normal environmental criteria.

INTRODUCTION
An accurate prediction and hindcast of the currents and the sea water elevations over the continental shelves is important in offshore oil operations and for the determination of design criteria. The tides and currents are the resultant of several forces which include the wind, the astronomical tidal forces, the Coriolis force, frictional forces, and pressure gradient forces. While the currents and elevations are described theoretically, the irregular coastline and bathymetry of the continental shelves and estuaries create complex boundary conditions which make the solution of equations difficult. Large computers have made possible the solution of these equations through numerical modeling techniques which closely retain the physical characteristics of the area of interest. Several friction and stress coefficients must be evaluated from measured data. The accuracy of this numerical modeling technique is evaluated by comparison with independently determined current and water elevation data. If such comparisons are favorable, then the modeling technique is a strong tool for the prediction or hinc1cast of the wind and tidal currents and elevations over the continental shelves and thus can solve many design or operational problems. This paper describes a numerical model, its calibration and its application to the Nova Scotia Shelf.

THEORY
Tides and currents are the result of the meteorological and tidal forces which act on the ocean. These forces include the wind stress on the sea surface, the tidal forces, the pressure gradient force, the Coriolis force, the retarding force of friction at the bottom, and the internal frictional force or the horizontal eddy viscosity. The equations describing the flow are integrated vertically over the water column to yield:(Available In Full Paper)
Equations (1), (2) and (3) constitute a single layer mathematical description of the tides and currents. Models based on these equations have been used by Hansen1 and Laevastu3 If the area being modeled is of a regular shape and depth then the equations may be solved directly; but for an actual ocean offshore area where the coastlines and bathymetry are irregular a numerical solution may be necessary. For a numerical solution the equations are solved by finite difference methods2 Once the equations (1), (2) and (3) are approximated by finite difference techniques, they may be programmed for computer solution.3