in one formulation. Therefore, to obtain a closed-form solution to shoreline 

 change, a simple mathematical formulation has to be used, but one which still 

 preserves the important mechanisms involved. The one-line (denoting the 

 shoreline) theory was introduced by Pelnard-Considere (1956), and it has been 

 demonstrated to be adequate in this respect. Considerable numerical modeling 

 of long-term shoreline evolution (time-scale on the order of years) has been 

 done on the basis of this work. However, not many analytical approaches have 

 been published, probably because of their limited applicability for describing 

 the finer details of shoreline change. Contributors in this field include 

 Bakker and Edelman (1965), Bakker (1969), Bakker, Klein-Breteler , and Roos 

 (1971), Bakker (1970), Grijm (1961, 1965), Le Mehaute and Brebner (1961), 

 Le Mehaute and Soldate (1977, 1978, 1979), and Walton and Chiu (1979). 



One-Line Theory 



4. The aim of the one-line theory is to describe long-term variations 

 in shoreline position. Short-term variations (e.g., changes caused by storms 

 or by rip currents) are regarded as negligible perturbations superimposed on 

 the main trend of shoreline evolution. In the one-line theory, the beach pro- 

 file is assumed to maintain an equilibrium shape, implying that all bottom 

 contours are parallel. Consequently, under this assumption it is sufficient 

 to consider the movement of one line in studying the shoreline change, and 

 that line is conveniently taken to be the shoreline, which is easily observed 

 (Figure 1) . 



5. In the model, longshore sand transport is assumed to occur uniformly 

 over the whole beach profile down to a certain critical depth D called the 

 depth of closure. No sand is presumed to move alongshore in the region sea- 

 ward of this depth. If the beach profile moves only parallel to itself 

 (maintaining its shape) , a change in shoreline position Ay at a certain 

 point is related to the change in cross-sectional area AA at the same 

 point according to Equation 1: 



AA = AyD (1) 



