where he is the desired value, 2.0 feet (0.9804 units), h+ and h_ the tabulated values 

 immediately above and below lie, and P+ and P_ the cumulative probabilities corresponding 

 to h+ and h_. Substitution from Table 10 into equation (28) yields: 



P(h > he) 



he - h_ 



- ^- h^ - h_ ^^+ ^-^ 





= — 5lif^^ <»•-—> 





— 5:sS<— > 





= 0.1004 - 0,0066 



P(h > he) 



= 0.0938 



Thus, the probability that the tide will be above 2.0 feet at Atlantic City is 0.0938; i.e., the 

 tide level wiU be above 2.0 feet an average of about 822 hours per year [0.0938 (365)(24)] . 

 Applying the same calculation to the values for Atlantic City, tabulated in Appendix B, 

 yields a probabUity of 0.1025 that the hourly value will exceed 2.0 feet. Thus, in this case, 

 the error committed in basing the estimate for Atlantic City on tabulated probabihties for 

 the reference station, Sandy Hook, would be 0.0087; i.e., about 9 percent of the value com- 

 puted from the reference station tables or about 76 hours per year. 



A similar calculation of the fraction of aU high waters above 2.0 yields a value of 0.5055 

 when the Sandy Hook tables are used, and 0.4886 when the Atlantic City tables are used. 

 Both results indicate that about one-half of all high waters are above 2.0 feet. The error 

 resulting from basing the calculation on the reference station is 0.0169 or about 3 percent 

 of the value computed from reference station tables. The above calculations and similar 

 calculations for the remaining parts of this first problem are summarized in Table 11. 



Tidal heights are tabulated by NOS in units of tenths of feet; i.e., with somewhat less 

 resolution than is provided by the probability tables in Appendix B. The interpolation 

 formula (eq. 28) can be used for estimating the probabihty tliat any tide parameter wiU fall 

 into any one-tenth of a foot increment. Interpolation should be based on tlie cumulative 

 form of the distribution function. The probability that the actual water level will fall within 

 any increment is then determined by subtracting the cumulative probabilitj' for the next 

 lower interval from the cumulative probability for the interval of interest. The probability 

 that the lii^ tide at the Atlantic City Steel Pier wUl fall within specified one-tenth of a foot 

 increments above MSL is shown in Table 12 as a further illustration of tliese calculations. 

 Calculations based on primary tide calculations for Atlantic City as well as calculations 



77 



