Figures 1 and 2 show that at many locations the tide level remains near the high or low 

 water values longer than it remains near MSL. Thus, the distribution of tide levels cannot be 

 adequately described by the Gaussian distribution function which is unbounded and 

 uninodal. Wherever the ampUtude of each tide wave is a large fraction of the mean range, 

 the distribution of hourly tidal heights wiU be distinctly binodal (Fig. 28). A Gaussian 

 distribution function with the same total area is plotted in the figure for comparison. This is 

 the most prominent form of the distribution function for hourly tides along the U.S. 

 Atlantic coast. 



At some locations, such as Pensacola, Florida, and Mobile, Alabama, the range of spring 

 tides is several times as large as the range at neap tides. This variabiUty in the ampUtude of 

 the tide wave yields a distribution function that is nearly uninodal with a peak near MSL 

 (Fig. 29). 



Galveston, Texas, and San Francisco, Cahfornia, show another common type of tide 

 where the water level remains above MSL much longer than below MSL. The lowest 

 predicted tide levels for these locations are farther below MSL than the maximum tide levels 

 are above MSL. In these cases, the distribution function for hourly tidal heights is definitely 

 skewed as shown in Figure 30. 



The comparison of empirical distribution functions with theoretical models is often 

 facilitated by plotting the cumulative form of the empirical distribution function on a graph 

 where one axis has been stretched so that the theoretical distribution, appears as a straight 

 Une. 



Althou^ the distribution of astronomical tides cannot be Gaussian, graph paper 

 designed so that the cumulative form of Gaussian distiibution wiU appear as a straight line 

 has many advantages for displaying distiibution functions for astronomical tides. This is the 

 standard form for showing distribution functions in this report. A sample display of this 

 type is shown in Figure 31. Each curve is of the form 



9 

 P(y>y) = / p(y)dy (25) 



yo 



where p(y)dj is the probability that 



[j-y) ^y^ (y-y) (26) 



as Ay ->• 0, and y^ is the lowest value of y . 

 For a Gaussian distribution, 



where a is the standard deviation of y and the mean value of y is zero. 



67 



