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absolute change. Using the simple equation for the surge on a constant- 

 depth shelf, Eq. (5.2), in the Mehta et al . report to which this discussion 

 refers , the relative changes can be shown as 



d^ ^ r -h^ dh^ ] r Bi di ] 



which shows that the relative change in total water level at the shoreline, 

 dCr? + h^y/irj + hg) , is roughly equal to the relative change in mean water 

 depth, dho/hQ; while the influence of relative change in shelf length, 

 di/i, is much smaller, since dJl/2 is small in itself and is multiplied by a 

 small number. Therefore the surge is most affected by the change in depth. 

 For the sloping- shelf case, using Eq. (5.7) in the Mehta et al . report 

 discussed herein for the surge height at the shoreline, the relative change 

 in shoreline surge, drj/r], is 



^ = nzl £ JlsL. ^ (A 3) 



n n n hg-x h^ 



where r is the dimensional ratio, B/m. For r small (note that for the 

 example with 150-km shelf and h^, = 10 m, r = 0.666), the relative change 

 dr]/ri is much less than the change dho/hQ, as 



^- - ^ (A.4) 



Note that with the assumption of a constantly sloping shelf depth, the 

 increase in shelf width due to the increase in water depth is implicitly 

 assumed. In fact, the difference between the surge height before the sea 

 level rise and the height after the rise can be seen conceptually as simply 

 extending the continental shelf in the first problem farther out to sea 

 until the new water depth due to the sea level rise is met. This extends 

 the shelf at the offshore end of the shelf, where there is little 

 hydrostatic response, so the total effect of the increase in water level 

 is small. 



