where Sj^ = aHg is the wave setup at the shore due to breaking waves , Hg 

 is the height of the breaking wave, and ot is a coefficient which norm- 

 ally ranges from about 0.1 to 0.2. The local setup or setdown Sl is 

 the deviation of the water surface, from the computed water level due to 

 a local effect such as inland runoff or shape of the hydrography in the 

 nearshore region. Figure 2 shows a profile of the various components 

 of set over the Continental Shelf at a typical coastal region. 



Since numerical calculation of V is based on a repeating formula, 

 it is subject to the round-off errors, that is, each computed value will 

 influence the values which are yet to be determined. To ensure that the 

 value does not exceed the maximum possible value, it is useful to employ 

 the following derived relationship. Equation (12) can be written 

 incrementally as 



AV = k W^sine At - K V^D"^ At 

 or 



K v2d-2 At = k W^sine At - AV. 



For small AV, K V^D-^ < k W^ sin6i. 



Thus, the y-component of volume transport becomes 



D2k W2sine 



V 



2 K 



At the new time level, the above equation can be written as 



|Vi.lsl = O — C24) 



Thus, the absolute value of the flux must never exceed the term on the 

 right-hand side of the equation. This relation should always be used 

 as a check, and if it exceeds this value, the flux at the new time level, 

 as an estimate, can be set equal to the value given by right-hand side 

 of Equation (24) . 



8. Com.putational Formulas 



Here, we shall give the formulas in a more compact and generally 

 more usable form by absorbing invariant coefficients and values caused 

 by inconsistency of units into a constant for each equation. Thus, in 

 the United States, wind speeds associated with hurricanes are usually 

 reported in miles per hour while distances taken from hydrographic maps 



19 



