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<br />EM 1111l-2,U05
<br />31 Aug 59
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<br />21. S-CURVE HYDROGRAPHS. a. Aecording to thr uuit hydrograph eonerpt, if tll(' unit rate of
<br />rainfall ('X('PSS oypr a drainage an'a should eontinup inddiIlitply with tlI(' same an'a] distrihution and
<br />intensity eharartHisti{>s, suc{'('ssivp ullits of rainfall pxeess would cOlltribut(, runoff at ratC's eOfl'Pspond-
<br />iug to the basic' ullit hydrograph. An accumulation of fllllOff ordinat('::; cOITPsponding to 8 particulur
<br />tim{> would giv<' tllp total rall' of runoff producNl by th(' uniform, ("ontinuOllS ralp of rainfall (,xC'pss
<br />antN"{,dpJlt the-reio. At a tirnC' <'qual to the' hasp of Hi(' ullit hydrograph, 1('58 t!It' duration of o[lr
<br />unit-rainfall inCI'em('Ill, tlH' ratp of runoff would b('('ome ('qual to tilt, ratp of rainfall rxc('ss and would
<br />remain eonstant tlu'reaftel'. The llydrograph gp_lwraled ill this fashion will hp r(.fprred to IWI"{'ln as an
<br />S-curl.'t Hydrogl'aph. (Sl'P plutp Xo. 9.) The S-cun:f' hydrograpll, as d('{illl'd ahovp, ghould lIot 1)('
<br />confused with mass curves of runoff th8;t simply represent a('cumulativp voluml's.
<br />b. An S-C1J,FVe hydrograph may be computed b.'T tahulatillg' a serif's of idpntiralullit hydrog-raphs,
<br />arranged ,\.ith origins spaced progrf'ss:vel.y 011(' unit-rainfall duration apart on thr time scale and
<br />accumulating the ordinates for specific times. A more convenient proccdul'(, is illustrated in plates
<br />:\os. 8 and 9. With the unit hydrograph valurs known, the S,curve hydl'ograph would be eompuled
<br />by steps. During the first 12-hour unit-rainfall duration, the unit hydrograph (column 2, platp !\o_ 8)
<br />and S-curce values (column 4) an" identical. The S-curve valu('s shown ill ('olumn 4 of plate f\o. 8 for
<br />the first 12-hour period arc transfrrrE'd to column ;{ and added to ullit hydrograph discharg'f's for thp
<br />second 12-hour interval to obta.in corresponding S-curve ordinatt.s. Thp pw{'pss is ('ontinm'd until the
<br />S-cuJ"re discharge rate is pqual to the basic rate of rainfall <,xe{'ss. TJIC' oppratio!ls in\'olv('d are morl'
<br />apparent if the rev('rse procedure is ('onsidered, assuming that tll(' S-CUI'/'f hydrograph vahH's taoulatrd
<br />in eolumn 4 were originally known. Dis('harg(' vahIPs shown in eolumn 4 !"('J)I'('SPllt tll<' ratt's of rllnoff
<br />that would result from a uniform continuous ratr of rainfall ex('('ss of 1 in('h ill 12 hOl1l'~, beginning at
<br />time zero. If the discharge values shown in column 4 arc entered ill ('olumlt J, with the origin time
<br />12 hours latrr, the difl'eren{'c between \Talu('s in ('olumns 4 and :~ ",ill f('(H'('S('llt tlw rat<. of runoff from
<br />I inch of rainlall rxerss in 12 hours (column 2). (See plat!' :\0. g.)
<br />c. I n accordance' "lith the unit hydrograph principleJ tlH' ordillat('S of all S-l.'uro(' hydrograph
<br />rrprpsf'Ilting runoff from a uniform continuous ralnfall execss rate of 1 in('1I ppr 12 hours may be muhi-
<br />plipd by 2 in ol'd('l' to obtain valu('s applicable to a. rainfall ('x('('ss rate of 1 in('h JH'r 6 hourR. Aeeordingly,
<br />S-C1ll'lle hydrographs devdoped from runoff data for unit storms of vurious durations may be adjustpd
<br />to apply to any unit rainfall duration desir{'d, within pmdical limits. 'I'1H' ('omputation of a f.-hour
<br />unit hydl'Ograph from a 12,hoUl' S,curve hydrograph is illustrated in columns 5 to 7 of plate :\0. 8.
<br />d. In addition to the applications referred to above, the S-curve procedure' is usC'ful in modifying-
<br />unit hydrographs to represent morC' eonservative peak vslups, or to fpflect modC'rate changes in rainfall
<br />distribution, as discussed hereinaftcr.
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<br />22. SUMMARY OF SYNTHETIC UNIT HYDROGRAPH COMPUTATION. In drveloping unit
<br />hydrographs for use in computing hypothetical hydrographs of runoff from major storms, without
<br />th(' benefit of reliable and adequate rainfall-runoff data, the following general proc~dure is recommended:
<br />a. Ana.lyze such hydrologic data as are available for portions of the drainage area having stream-
<br />flow records to determine approximatrly the peak diseharge, lag, and general shape of unit hydrographs.
<br />In many instanees, fragmentary hydrologic data that are not adequatp fOf unit hydrograph derivation
<br />in the usual manner may be v('~y useful in connection with synthetic analyses,
<br />b. If adc4uatf' hydrologic records are availahle for a representative portion of the drainag-p hasin,
<br />evaluate coefficients 640 (\, and (', in equations 1 and:) of paragraph 19b and usc these' val ups in rsti-
<br />mating the peak discharge of a sYIlthetic unit hydrograph for thr given drainage. ar{'ll. Lacking
<br />,hydrologic [('('onls in the immpdiatp drainage basin for f'nduatiflg- 040 (1p and ('r, ndopt('d YU[ll('S should
<br />be baspcj OIl rp('ords for a.djacent strrams \'v'ith similar ('hursderisti('s.
<br />c, By a g-f'tH'rnl comp2.rison of runoff chara.rl(>l'lstif's inHIJn'd, pst inHu (, \\ ill'ti!f'!" 1 ht, nllil il.nlrograph
<br />peak dis('har~f' n:dups computC'd for the pa,:i\'ul:ll' .1f'('H ilJ'i' l'oIl"iislt'llt with \"f1iu('~ for ('OnlJHlrahh' basin;.;.
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