Variations in mean water depth, as a result of a storm, may alter the speed of the tide 

 wave as it advances inland from the open sea. An increase in river discharge may lead to a 

 decrease in tidal range at inland tide gages. An example of this effect is provided by Zeile 

 (1979). These interactions are complex and poorly documented. Interactions between 

 gravitational tides and meteorological effects on sea level are not considered in this report. 

 Example Problems. 



Applications of tide probability tables are demonstrated by two problems centered on 

 Atlantic City, New Jersey, which was selected for the following reasons: 



(a) Atlantic City is treated as a secondary station by NOS. Tide predictions for 

 Atlantic City are normally based on the reference station at Sandy Hook, New Jersey. 

 Thus, probability calculations may be derived from the Sandy Hook probability 

 tables and verified by referring to the calculations based on the harmonic constants 

 derived from Atlantic City observations. 



(b) Myers (1970) has provided frequency estimates for extreme storm surge 

 magnitudes at Atlantic City, thus permitting an illustration of the calculation of the 

 probabilities of the combined astronomical and meteorological effects on tlie water 

 level. 



The two problems considered are (a) to estimate tlie fraction of high tides and of hourly 

 tide levels above 2.0 feet MSL, and of the low tides and hourly levels 2.0 feet below MSL, 

 and (b) to estimate the liighest water level which has a probabUity of 0.01 of occurring in 

 any century; i.e., a probability of 10"* in any year. Secular changes in sea level (variations 

 in the annual mean sea levels) are neglected in developing these estimates. 



a. First Problem, Since the meteorological and astronomical events which control the 

 water level near the shore are nearly independent, it is assumed that meteorological events 

 can be neglected in estimating the frequencies of water levels between MLW and MHW. The 

 mean tidal range at Atlantic City Steel Pier (station 1703 in the tables as determined from 

 Appendix C or from the NOS tide tables) is 4.08 (4.1) feet. Thus, the scaling factor of one- 

 half the mean tidal range is 2.04 feet. Two feet, therefore, corresponds to 2.00/2.04 = 

 0.9804 units in the probabUity table. The part of the probability table for hourly tides 

 nearest this value for Sandy Hook, the appropriate reference tide station, is shown in Table 

 10. 



The probability that the water level will be above 2.0 feet (0.9804 normalization units) 

 can be estimated by linear interpolation according to the equation: 



P(h>hc) = P_ + 



hr - h 



K 



(P+-P_) 



(28) 



Table 10. Pari uf cumulative distribulioii table 

 for Sandy Hook, New Jersey. 



Qass No. 



Lower limit of height 



Cumulative frequency 



79 

 78 



0.9961 

 (0.9804) 

 0.9618 



0.0883 

 0.1004 



76 



