and time (Kraus 1983, Kraus and Harikai 1983, Kraus , Hanson, and Harikai 1984, 

 Hanson and Kraus 1986a, Hanson 1987, Hanson and Kraus 1989, Gravens and Kraus 

 1989). Despite the assumption of constancy of beach profile shape alongshore, 

 the shoreline change model has proven to be robust in predictions and provides 

 a complete solution of the equation governing shoreline change. Because the 

 profile shape is assumed to remain constant, in principle, onshore and off- 

 shore movement of any contour could be used to represent beach change . Thus , 

 this type of model is sometimes referred to as a "one-contour line" model or, 

 simply, "one-line" model. Since the mean shoreline position (zero-depth 

 contour) is conveniently measured and such data are usually available, the 

 representative contour line is taken to be the shoreline. 

 Multi -contour line / schematic three-dimensional (3D) models 



Three-dimensional beach change models describe the response of the bottom 

 to waves and currents, which can vary in both horizontal (cross -shore and 

 longshore) directions. Therefore, the fundamental assumptions of constant 

 profile shape used in shoreline change models and constant longshore transport 

 in beach change models are relaxed. Although 3D models are the ultimate goal 

 of deterministic calculation of sediment transport and beach change, achieve- 

 ment of this goal is limited by our capability to predict sediment transport 

 processes and wave climates. In practice, simplifying assumptions are made to 

 produce schematic 3D-models, for example, to restrict the shape of the profile 

 or calculate global rather than point transport rates. Perlin and Dean (1978) 

 introduced an extended version of the "2-contour line model" of Bakker (1968) 

 to an n-contour line model in which depths were restricted to monotonically 

 increase with distance offshore. 



Schematized 3D beach change models have not yet reached the stage of wide 

 application; they are limited in capabilities due to their complexity and 

 require considerable computational resources and expertise to operate. 

 Introduction of these models into engineering practice is expected in the near 

 future , however . 



