Table 1, 



Calculation procedure for locating bounds of 

 the shoal zone , 



Bound 



Procedure 



Landward 



Required site parameters: y' and Hg, 

 0, Tg, and g in consistent units. 



Find dimensionless root (2'iTdj/L) of 

 equation (5) , either by iteration 

 using the calculator program in the 

 Appendix or from Figure 3 after cal- 

 culating the value of the abscissa 

 {2Tr (Hs + 5.6 a)/gT|}. 



Calculate 



'.■(^)(-(?^)l(§)- 



Seaward 



Additional required site parameter: 

 D in consistent units at water 

 depth of (1.5 dj^). 



Find the dimensionless value of 

 (2Tidi/L) specified by equation (9), 

 using either the calculator program 

 in the Appendix or Figure 4 after 

 calculating the value of the ordinate 

 fTt2 (H3 - 0.3 a)2\"-5 



i 8Y'gDT2 1 

 Calculate 



provide results usually consistent in accuracy with the critical values given in 

 equations (1) and (7) to one significant digit. To allow for possible effects 

 of tides, it is recommended that the calculated d^ and d-;^ be taken as being 

 with respect to mean lower low water (MLLW) at a locality, giving conservative 

 (farther seaward) locations for the shoal zone boundaries. Also, it seems ap- 

 propriate to use calculated results in U.S. customary units (feet), rounded to 

 the nearest integer unit. 



III. APPLICATIONS OF d^ AND d^ 



The shoal zone is an objectively defined buffer area of moderate wave effects 

 on the submerged beach profile throughout the year. Where wave and sand charac- 

 teristics are known, the two calculated water depths are useful in various 

 coastal engineering activities requiring a seaward-limit estimate. The possible 

 applications in the following list are discussed in detail in Hallermeier (1981), 

 and further evaluations of shoal zone uses are being conducted. 



(a) Fathometer surveys of customary vertical resolution (±0.5 foot 

 or ±0.15 meter) may not be expected to resolve usually small bottom 

 changes during the year seaward of d£ . Nearshore surveys extending 

 to d^ are needed to define seasonal conditions at a site. 



(b) Gages to record waves incident on the littoral zone may be 

 placed just seaward of the anticipated value of dj^, so that the meas- 

 ured waves will not be modified differently through the year due to 

 significant changes in the bottom seaward of the gage site. 



12 



