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<br />In add1t10n to the observed. valuu. table 2 also shows the <br />theoret1cal probab111t;y correspondins to each ot the observed. <br />probab111t1es. Fortunate13 tor 1.18. the theoretical probab111t;Y does <br />not require a looo-;year strelllll now record tor 11;8 deteminat10n. It <br />may be computed tor Bl:q t1me period and for a rrr 1II&X1mum .nnuel peak <br />rate proVided the average tnquenc;y ot that peak 1.. known. I't 18 equal <br />to l-(l-p)l'f, \/here p 1s the average tnquenc;y and N 18 the t1me period <br />10 years. For example, suppose we wished to detenn.l.ne the probab111t;y <br />that a 50-year peak wouJ.d be equalled or exceeded at least once 10 .~ <br />10-;year period. The average frequenc;y ot a 50-year pee.k. is 1/50 or 0.02 <br />and the time period is 10 ;years. The des1red probabil1 t;y is, theretore, <br />equal to 1-(1-0.02)10 or to 0.18. <br /> <br />Conclusions <br /> <br />In the foregoing discussion an attempt bas been llIlIlie to create a <br />bettllr lllldersta.nd1ng among high.~ engineers of some of the "roblems <br />inherent in ~ high~ stream crosa1ns. The va.r1ous strel\lll character- <br />istics that have been demonstrated have led to the conclusions that are <br />sUlllluari zed as follovs:- <br /> <br />(1) Knowing the instantaneous peak rate of runoff at the <br />crest ot an indiVidual strelllll nse tells the highway engineer onl;y that <br />this peak rate ill one of an alJIIoat infinite nUlllber ot possible pee.k. rates. <br /> <br />(2) fee.k. rates are not spaced unifo1"lllly 10 time but appear as <br />random events. <br /> <br />(3) Averae;e recurrence intervals for may" mUm annual peaks above <br />any min1mum do exist but are consistent onl;y when detemined for long <br />periolls of time such as 500 or 1000 ;years or IIIOre. <br /> <br />(4) The average recurrence interval tor 1II&X1J1111Dl Ann".l peaks <br />above some miJ:l1mUlll. when co1lS1dered by 1 tselt. 1s ot 11 ttle value to <br />the high~ ens1neer as 1t g1ves him no 1nf'o%lll&t1on on the ~tude of <br />the peaks that might be expected to be greater than th1s min1lllum or ~ <br />info%lll&t1on as to when they Ill1ght be expected. <br /> <br />(5) It the average recurrence loterval for ~ may"""" umual <br />peak rate 1s Imown. then the probabil1ty of obtaining one or IIIOre that <br />are equal to or greater than that peak in ~ desired time interval <br />may be computed. SUch into%lll&t1on covering a su1'1'ic1ent range 1n the <br />~tude of 111&>''''''''' annual pee.k.s and 1n the length of time 1ntervals is <br />the first requirement of the h1gh~ engineer for the design ot a sate <br />and economical stream crossing. <br /> <br />3-6 <br /> <br />e <br /> <br />,. <br /> <br />~- <br /> <br />e <br /> <br />. <br /> <br />i <br /> <br />e <br />