adding the Iiighest tide to the highest surge. The probability of this combination, assuming 

 that tlie probability of each is independent of the other, is tlie product of the separate 

 probabilities. Thus, 



p(lO.lft) - p(6.4 + 3.7) = p(6.4) X p(3.7) 



(surge) (tide) 



= O.OOIl X 0.0005 

 = 5.50 X 10-' 



p(10.0 ft) = p(6.4 + 3.6) = p(6.4) x p(3.6) 



(surge) (tide) 



= 0.0011 X 0.0033 

 = 3.63 X 10-6 



p(9.9ft) = p(6.4 + 3.5) + p(6.2 + 3.7) 

 = p(6.4)p(3.5) + p(6.2)p(3.7) 



(surge) (tide) (surge) (tide) 



= 0.0011 X 0.0082 + 0.0013 x 0.0005 

 = 9.02 X 10"* + 0.650 X 10"* 

 = 9.67 X 10"* 



Further hand calculations are tedious, but a few should be made to be certain tliat the 

 principle is fuUy understood. 



IX. SUMMARY AND RECOMMENDATIONS 



This report has presented a compilation of material from various sources designed to 

 provide the engineer with an understanding of the problems involved in the estabUshment of 

 reference datums for the measurement of elevations and of tlie various phenomena that 

 should be considered in estimating the extreme high or low water that might reasonably be 

 expected at any given location during a period measured in decades. 



A study of the statistical properties of astronomical tides has also been presented (Sees. 

 VII and Vni), which, so far as the author is aware, has not been previously reported. 

 Experience in using the tables, acquired during preparation of the report, has indicated that 

 some changes may be necessary in the original calculations. However, the principal purpose 

 of the work has been to provide the practicing engineer with the tools needed to estimate 

 the contribution of astronomical tides to hydraulic or hydrologic phenomena when the 

 estimate should be considered in a probability sense. 

 Recommendations for Revision of the Probability Tables. 



A more rational statistical study of daily high and low water and daily ranges apparently 

 would have been obtained if the lunar day rather than the solar day had been chosen for 

 summarizing diurnal characteristics of the tide. 



85 



