APPENDIX I 



The published tables are based on the finding that peak flow is a function of mean 

 water yield. The equation is: 



In (P/4) = a+b [1.5708 - arc tan (sinh F/A)] (1) 



in which P, A, and F are, respectively, peak flow (c.f.s.), area (square miles), and 

 mean flow (c.f.s.). The constant 1.5708 is the angle 90° expressed in radians. 



Equation (1) is based on data found in Thomas, Broom, and Cummans (1963) and 

 Bodhaine and Thomas (1964). Only those rivers were analyzed whose records indicated 

 no diversions, impoundments, or poor data. The equation was derived as follows: For 

 each streamflow record, the annual peak flow data were arranged in a descending order 

 of magnitude. If N represents the total number of items in the series, and M. is the 

 ordered position in the series (i.e., 1 , 2 . . .M • . . ./I?) , then the probability of occurrence 

 {F-p) (or percent chance) for a peak flow equal to or smaller than that in ordered 

 position M . is 



(M. - 0.5) 



100 X - ^ 



N 



This probability was calculated for each ordered position, and defined the plotting 

 position of the associated peak flow on log-normal paper. A smooth line was drawn 

 through the plotted data, but was not extended beyond the range of the plotted data. 

 We then read the adjusted peak flows for the selected recurrence periods: 2.33; 5; 10; 

 and 20 years. (The recurrence period is 100 divided by the probability of occurrence; 

 e.g., if = 20, = 5.) 



Data drawn from the smooth curves formed four new sets of data, one for each 

 selected recurrence period. Each set of data was then analyzed to obtain the values 

 of a and b in equation (1). We have listed below these values, as well as the correla- 

 tion coefficient (/?) relating the dependent and independent variables. 



Reaurrenae period a b R 

 (Years) 



2.33 3.3434 -1.9693 0.966 



5 3.6653 -2.0440 .950 



10 3.7141 -1.8908 .938 



20 3.8733 -1.8324 .902 



Values for tables 1 and 2 were calculated for selected values of mean flow (F/A) 

 using the equation p 



P _ a+&[1.5708 - arc tan (sinh y )] (2) 



A~ ^ ^ 



where e is 2.71828, base for Naperian logarithms. 



11 



