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<br />.to <br /> <br />'l <br /> <br />3-05. <br /> <br />b. In ardinary hydralogic frequency work, 'exceedence 1're- <br />q~enc~es are express~d in' percent or in terms o? events per h~~dred. <br />years, as shown on ex.'U.bit 37,w!;ichgives, plotting positions far <br />arrays up to 100 events in size. For arrays larger than 100, the <br />plotting positian,P, can be obtained as were those of exhibit 37 <br />by lAse of the fallO'..ing equation: ' <br /> <br />1 - Pl '" (O.5)1/N (1) <br /> <br />ix. .'ilicb Pl i.6 the. plottiI:g positian for thelargsst event, and. N <br />is the number of years of record. The plottillg position for the <br />s=11est event is. the cOIllJlle=nt of this ,value, and. alJ. other <br />plotting positio!lS are interpolated l1nearlybetween these Wa. <br />For. plU'tial-.illl'ation ., c'll.-ves, pa.rt;icu.la.rly where theree.re more <br />events thij.n years (N), plottillg positions larger than' 50 percent <br />e.re,obtained by use .01' thetollowinS equation: .. <br /> <br />P '" (2m - 1) j2N. <br /> <br />(la) <br /> <br />i~ whichm is tbe order number 01' the event. <br /> <br />3-06. <br /> <br />l'LO'ITD.'G GRID <br /> <br />IfhylUoQlogic frequency data are ;plotted with Ca.l:'tesi= coo~'- <br />d:inateis,. the resulting frcq,uencyrelationship will curve rather <br />abruptly attbe up;pE!r end and possibly at the lower end also. Fu~ <br />therJllOre, the extreme values in which there is the greatest interest <br />would be.cOIllJlressed into a very slllal1 area, and extrapolation at <br />the cun'e;roll1d beditticult. Accordingly, it has been found desir- <br />able to use a plotting grid on which a trequency curve of hydrologic <br />data. 'Will usualJ.y approx:1mate a straight line. A grid that has been <br />found to be suitable tor this se is the ob 11 <br />grid is desig/lea. so that theeumula'tive frequency curve of a va.rl.able <br />that is distributed in accardance with the no:rms.l prObability curve <br />will plot as a straight line. The grid i.s illustra'ted on exhibit <br />10. It has been found that items such as air temperature or river <br />staee that either do not have a fixed lower limit 01' zero or whose <br />lower limit is ter removed tromthe range of experience, will o:t'ten <br />yield frequency curves 'J.pproximating a straight line when plotted <br />or.: this grid. Variables such as streamflow where a lower limit of <br />zeN is often approached in ex;perie:c.ce will ordinarily yield an <br />apj;ororimately straight trequency curre only Uthe logarithms are <br />:plot.ted on this grid. For convenience, the. ~oge.r1tblllic probability <br />grid illustrated on exhibit 2 bas been devised so that flows can <br />be plotted directly to yield an approx:l.mlLtely straight line. <br /> <br /> <br />-13- <br /> <br />Rev 26 Oct 64 <br />