estimate for tlie extreme combination of storm surge and astronomical tide. A lower and 

 more reliable estimate could be obtained by combining a probability distribution based on 

 complete surge hydrographs with tlie distribution function for hourly tide heights. 



Before proceeding to tlie demonstration calculation, it is necessary to consider the 

 difference between frequency expressed as a fraction of all possible cases which fall into a 

 specific class, and frequency expressed as a probability density. 



The average number of extratropical storm surges per year, with heights above 2.0 feet, 

 the lowest value considered by Myers (1970), can be obtained as the total of all frequencies 

 in Table 16 • The frequency values can be converted into probabihty densities by 

 dividing each frequency by the total frequency. The frequency with which each water level 

 is expected to occur per year, on the average, from each possible combination of extra- 

 tropical storm surge and astronomical tide can be recovered by multiplying the combined 

 frequencies by the number of surges expected each year (4.10). Since dividing one factor of 

 the multipUcation by a constant and multiplying the product by the same constant produces 

 no fundamental changes, these steps may be omitted in applying equations (29) and (30) to 

 the storm surge and tide data. The results of the calculation v«ll be a tabulation of the fre- 

 quencies per year of various water levels to be expected from a combination of astronomical 

 tides and extratropical tides. 



Table 17. Computation of joint probabilities for astronomical tides and extratropical 

 storm surges at Atlantic Qty, New Jersey. 



Combined 



Results from 



Product of 



Total combined 



Cumulative 



height^ 





probabilities 



probability 



probability 



(ft) 











10.1 



6.4 + 3.7 



5.50 X 10"'' 



5.50 X lO-'' 



5.50 X 10"' 



10.0 



6.4 + 3.6 



3.63 X 10-* 



3.63 X 10'* 



4.18 X 10-* 



9.9 



6.4 + 3.5 



9.02 X 10-* 









6.2 + 3.7 



0.650 X 10"* 



9.67 X 10-* 



1.803 X 10-5 



9.8 



6.4 + 3.4 



1.82 X lo-s 









6.2 + 3.6 



0.429 X 10-^ 



2.25 X 10-5 



4.053 X 10-5 



9.7 



6.4 + 3.3 

 6.2 + 3.5 



2.95 X lo-s 

 1.07 X 10-^ 









6.0 + 3.7 



0.105 X 10-^ 



4.13 X 10-5 



8.183 X 10-5 



9.6 



6.4 + 3.2 

 6.2 + 3.4 



4.53 X 10-^ 

 2.15 X 10"^ 









6.0 + 3.6 



0.693 X 10"^ 



7.37 X 10-5 



1.5553 X 10-^ 



'Based on Tables 12 and 16; all heights are in feet. 

 2 Referred to MSL. 



A sample calculation of the combined frequency of astronomical tides and storm surges 

 is shown in Table 17. Note that a combined height of 9.9 feet can be obtained only by 



84 



