The seven curves shown in Figure 31 and similar graphs in Appendix B correspond to the 

 seven tide parameters. The abscissa of these graphs give the probability that eacli parameter 

 will exceed the value indicated by the ordinate. AU data have been scaled so that 98 percent 

 of the ordinate scale corresponds to the height difference between tlie maximum and 

 minimum predicted tidal heights within the metonic period of 19 years. The positions of 

 MSL, MHW, MHHW, MLW, and MLLW have been indicated on the ordinate scale. The 

 cumulative form of a Gaussian distribution function with the same standard deviation as the 

 completed hourly tides, has been superimposed as a straight line in all graphs. The graphs in 

 Appendix B show that, for some locations, the Gaussian curve provides a good 

 approximation to the computed values within one or two standard deviations from the" 

 mean. This is particularly true for Baltimore, Maryland, and several situations in tlie Gulf of 

 Mexico. The Gaussian distribution function, however, is a very poor approximation to the 

 real distribution function for the highest and lowest astronomical tides. 



At many locations, the astronomical tides are symmetrically distributed about the MSL. 

 It is not uncommon, however, to find that the distribution function is skewed with the 

 astronomical tide remaining above MSL longer than below, with greater departures below 

 the mean than above the mean. At Honolulu, Hawaii, the astronomical tide is below MSL 

 more than half the time, and the positive departures from the mean are larger than negative 

 departures. 



Although the actual distribution function is nearly identical to tlie Gaussian over the 

 central 90 to 95 percent of the actual distribution at a few locations, the most common 

 distribution is flatter than the Gaussian, with values on the order of one standard deviation 

 above or below the mean being more common, and values near the mean or more than two 

 standard deviation units above or below the mean being less common than in tlie Gaussian 

 distribution. Many stations have bimodal distribution functions. 



At a few locations, the annual range in MSL may be greater than the range of neap tides, 

 and it is not uncommon for the predicted tide level to remain on one side of MSL for longer 

 than a lunar day. 



The graphs of the distribution of computed tide parameters are presented to show the 

 character of the distribution function. The computer-controUed plotter does not always 

 place the various curves precisely. Therefore, numerical values for further work should be 

 taken from the tables in Appendix B, not from graphs. 



5. Probability Tables for Astronomical Tides. 



The curves in Figure 31 are based on similar data as presented in Tables 8 and 9. The 

 maximum and minimum values of each parameter were used to determine the range of 



70 



