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<br />EM 1116-2-1405 <br />31 Aug 59 <br /> <br />e <br /> <br />21. S.CURVE HYDROGRAPHS. a. Aeeording to thp uuit h~'drograph ('oneept, if the ullit rate of <br />rainfall ('X('('SS OYt'l' a orainagr arC's should eontinut' indefinitply with tll(' sump nfeal distribution and <br />intf'nsity ('haraelpristi('s: SlH'('("ssiv(' units of rainfall {'xe('ss would contriblltp runoff at rates l"on('spond- <br />ing to the busi(' unit hydrograph. An 8("('umulation of runoff ordinates, ('orrpsponding to a particular <br />timp would give tJl(' total ralt' of runoff produ(O('d by th(' uniform, ('ontinuous rat(' of raillfall ('X("('SS <br />antf'("e-deut th(,l'('to. At a tirnl' ('qual to thf' bast' of th(' unit hydrograph, 1('58 tll(' duration of onp <br />unit-rainfall incn-m('ntf HIl' ralC' of runoff would b("('ome ("qual to the' ralt' of rainfall ('x("('ss and would <br />fe-main constant tllPreaftpr. The hydrograph gr--Ileratpd ill this fashion will be rpff'ned to IJt'I"(.in as an <br />S~urve Hydro!Jraph, (See plate 1\'0, 9.) The S~urve hydrograph, as defi,U'd above, should not I", <br />confused with mass curv{'s of runoff th8;t simply rppresent accumulative volurnps, <br />b. An S-curve hydrograph Ina~' be comput{'d by tabulating a series of identical unit hydrographs, <br />arranged with origins spaced progress: vely one unit-rainfall duration apart on the time scale and <br />accumulating the ordinates for specific times" A more convenipnt proeedurt, is illustrated in plates <br />;'\os. R alld 9. With the unit hydrograph values known, the S-curve hydrograph would he eomputed <br />by steps. During the firsl 12-hour unit-rainfall duration, the ullit hydrograph (column 2, plate 1\'0. R) <br />and S-curve values (column 4) are- identical. The S-curve val liPS shown ill ('olumn 4 of plate No, 8 for <br />the first 12-hour period are transferred to eA)lumn 3 and added to unit hydrograph diseharges for tl", <br />second 12-hour interval to obtain corresponding S-curve ordinait's. Th(' pro('('ss is rontilHH'd until the <br />S-curt'e discharge rate is equal to the basic rate of rainfall ('xcess. Tin' OpPI"UtiOIlS involved al'C mon' <br />apparent if the reverse proc{'dure is considered, assuming- that the S-cunf hydrograph val ups tahulated <br />in column 4 were originally known, Disf'hargp valuC's shown in (~olumn 4 rf'pn'st'flt tlU' ratt.s of runoff <br />that would result from a uniform continuous ratC' of rainfall ('x("pss of 1 inch in 12 hour5, beginning at <br />timp zero. If the discharge va]ues shown in column 4 arc entered ill column ~, with the origin tillle <br />12 hours later, the differcll('e betw{'cn values ill columns 4 and :3 will rf'pn's{'1l1 thp ralt' of runoff from <br />I ineh of rainfall exe,'ss in 12 hours (eolumn 2). (See platl' Xo, 9.) <br />c. I n accordance with the unit hydrograph principlf'J Hl(' ordinal.('s or all S-curvf; hydrog-raph <br />representing runoff from a uniform continuous rainfall excess rah~ of 1 inch pt'r 12 hOllI'S may' he multi- <br />plied by 2 in ordf'r to obtain values applicable to a rainfall ('xepss rate of 1 inch 1)('1' 6 hours. Aecordingly, <br />S-CUl've hydrographs developed from runoff data for unit. storms of various durations ma,\' he adjuslt.d <br />to apply to any unit rainfall dura.tion desired, within praetica] limit::'i. 'I'll<' ('omputation of a 6-honr <br />unit hydrograph from a 12-hour S~urve hydrograph is illustrated in l'o]umns 5 to 7 of pial!' :-.io. 8. <br />d, In addition to the applications referred to above, the S-curve procC'dure is us{'ful in modifying <br />unit hydrographs to represent more eonservative peak valtH's, or to reflect moderate changes in rainfall <br />distribution, as discussed hereinafter. <br /> <br />e <br /> <br />22. SUMMARY OF SYNTHETIC UNIT HYDROGRAPH COMPUTATION. III developing unil <br />hydrographs for use in eomputing hypothetieal hydrographs of runoff from major storms, without <br />the henefit of reliable and adequate rainfall-runoff data, the following general procedure is reeommended: <br />a. Analyze sueh hydrologic data as are available for portions of the draillage area havillg stream- <br />flow reeords to determine approximately the peak discharge, lag, and general shape of ullit hydrographs. <br />In many instances, fragmentary hydrologic data that an~ not adcquatc for unit hydrog-raph derivation <br />in the usual manner may be v(':y useful in eonnectioTl with synthetic analyses. <br />b. If adequate hydrologic records are availahle for a representative portion of the draina.gp ha.sin, <br />evaluate coefficients 640 Cp and (\ in equations 1 and [) of paragraph 19b and use t.h(~s(' "31tH'S in ('sti- <br />mating the peak discharge of a synthetic unit hydrograph for thC' ~iv(>1I drainag-t' arra. LIH'king <br />,h."drologic [('cords in the immpdiate drainagC' basill for ('valuating- 640 ep and ('I' adoptNI vahH's should <br />he basf'd on recorus for adjacent strcams \",'ilh similar chaI'3('1pristies. <br />c. By a g'('rH'ral compeloison of runoff charu('lt'l'!sti('s ir:p.ln'rl, l'stinuu{' \\'iliotjl('; lhi' 1JI!i! ilydl'oe:raph <br />ppuk disf'llal'g-p nt-lu('s ('ornpu1pd for tl~(' par:j"tdul' ltn'il hn' \'n~lsistl'nt ",illt \"11:IW": for l'oIllpnrflhl{' husi;;,;, <br /> <br />12 <br /> <br />e <br />