ANEXAMPL EO FA RAINFALL-RUNOF F MODELFO RDESIG NFLOO DCOMPUTATIO N

PUBLICATION 74

StefanIgna r

Departmento fHydrauli cStructure s WarsawAgricultura lUniversit y 02-766Warsa w Poland

September198 6 CONTENTS

Page

1. INTRODUCTION 02

2. DESCRIPTIONO FTH EWATERSHE D 02

3. TOTALRAINFAL L 03

4. EFFECTIVERAINFAL L 05

5. RAINFALLRUNOF FTRANSFORMATIO N 09

6. WACKERMANNMODE LPARAMETER SEVALUATIO N 12

7. DESIGNFLOO DSIMULATIO N 16

8. RESULTSAN DDISCUSSION S 21

REFERENCES 23

LISTO FTABLE S 25

LISTO FFIGURE S 26 1. INTRODUCTION

Mathematicalmodel s in are often used as a tool for analysis. Such an analysis is carriedou tt odetermin e themagnitud eo f extremeflow swit ha lo wprobabilit yo foccurrence , the so called design discharges. The mainproble mo fmathematica lmodellin go fsmal lagricultura lwatershed s isth elac ko f recorded data. It requires research to apply simple, conceptual rainfall-runoffmodel swit honl ya fe wparameters .Parameter so f thesemodel sca nb edetermine dfro mcorrelatio nformulae , topographic maps andpublishe dtables . This report describes the practical application of aconceptua lmode l developedb yWackerman nfo rdesig nfloo devaluatio nwit hassume dprobabilit y of occurrence. Themetho dassume sth eequalit yo fprobabilitie s fordesig n precipitationan ddischarge . The described alghorithm consists of four stagesleadin gt oevaluation : a) totalrainfal l -P b) effectiverainfal l -H c) directflo whydrograp h -Q p d) totalfloo dflo whydrograp h -Q

The first three of them willb edescribed .Th efourt hstag econsist so f summationo ftw ohydrographs :direc tflo wQ pan dgroundwate r flow Qg. The values ofQ gar erelativel yver ysmal lcompare dt oQ pan di ti spossibl et o assume that direct flow can be treated as a total flow hydrograph. A practical application of the method was carried out for a small agriculturalwatershe d (area- 6. 5km 2)i neas tHolland .

2. DESCRIPTIONO FTH EWATERSHE D

TheHupsels eBee krun sfro meas tt owes tthroug ha slightl yundulatin grura l landscape inth eeaster npar to fTh eNetherlands .Thi sregio no fsand ysoil s iswel labov ese alevel .Th ecatchmen tare ai smainl y covered with grass. The topo fth eunderlyin g thicktertior yformatio no fmarin eclay si sfoun d ofshallo wdepth s inth eeas tan dslope sdow n to the west. These marine clays are covered with youngersan ddeposits .Th ethicknes so fthi ssan d aquifervarie sbetwee n1 an d 8 m from east to west. Consequently the transmissivity and the storagecapacit yo fth esoi lar erelativel ysmall , thegroundwate r tablei nthi sregio ni sshallow ,abou t5 0 cm below ground surface in winter whereas insumme rtim ei tma ydeclin et oabou t1.3 0m . Locallygroundwate r levelsma yris et o the surface during prolonged wet periods.

3. TOTALRAINFAL L

The described method utilizes as aninpu ta desig no rcritica lrainfal l histograph that imitates some severe future or historical event. If rainfall records are unavailable, design histographs are found from empirical formulae describing relationships between probability of occurrence, duration and intensityo fth erain .Fo rregion swit hrainfal l recordssuc ha relationship sca nb edevelope dfo rparticula rstations . Inorde rt odetermin e theinpu thistograp h it is necessary to assume a probability of occurrencean dt odetermin eth eduratio no fcritica lstorm . Thenex tste pi st oobtai nstor mintensit ybase do nth eselecte dprobabilit y and duration. Durationo finpu trainfal li susuall yequate dt oth etim eo f concentrationo fth ewatershed .Th etim eo fconcentratio ni sassume d to be equal to flow timefro mth emos tremot epoin ti nth edrainag eare at oth e outleto finteres t (Viessmane tal. , 1977). TheKirpic hequatio nca nb euse d forth etim eo fconcentratio ndetermination :

CLl 0-77 tc -0.066 3 •^ J ... [1] where:

tc -tim eo fconcentratio n(h ) L -th e horizontal projection of thechanne llengt hfro mth emos t distantpoin tt oth ebasi noutle t(km ) I =slop ebetwee nth etw opoint s (-) Because this formula gives only a rough estimation of tc, iti snecessar y to find thecritica l rainfall duration bya trial method, computing the flood fora few,usually longer, durations. For the Hupselse Beek watershed therelatio n between probability, duration and intensity of rainfall was assumed as for station De Bilt (Buishand, Velds, 1980). Developed relations for an assumed 1% probability lead to the intensity-duration curve shown inFig .1 .

I (mrn/h)

20.0

10.0

8.0

6.0

4.0

20

2 4 6 8 10 12 14 16 18 20 22 24 MM Fig. 1. Intensity .duration curve for station De Bilt. (p = 1%)

Time of concentration from Kirpich formula is2.7 5h . Duration used inth e calculations were: 2, 4, 6, 8, 12, 14 and 16 hours. Rainfall time distribution was uniform. 4. EFFECTIVERAINFAL L

Effective rainfall isa par to ftota lrainfal lremainin gafte rwithdrawin g oflosse sconsistin go finfiltratio n ,évapotranspiration ,interceptio n and depression storage. This rainfalli stransforme db yth esurfac ewatershe d intodirec trunoff . Amongth eman ymethod suse d inengineerin ghydrolog yfo reffectiv e rainfall determination, the SCS (SoilConservatio nService )Curv eNumbe rmetho di s oneo fth emos tofte nused . According tothi smethod ,th evolum eo feffectiv erainfal l is subjected to the CN (Curve Number) parameter depending onsoi ltype ,lan duse ,soi l conservationpractice san danteceden tmoistur econditions .Thi sparamete ri s relatedt oth emaximu m retention,S i nmm :

S«25. 4 •(±|° - lo) ... [2]

and effective rainfall after timet^-i-A t canb e calculated from the formula:

l '° forP ti-0.2-S<0 Hti =S AHj j-l [3]

where: Hti" effectiverainfal l intim efro mt gt o tj_(mm ) S - maximumpotentia lretentio no f the watershed,i.e . difference betweentota lrainfal lan ddirec trunof fafte ra lon gtim e(mm ) CN» methodparamete r (-)

Pt^= totalrainfal l intim efro mt Qt ot ^(mm ) AHj= effectiverainfal l inj-tim e interval (mm) AP-j= totalrainfal l inj-tim e interval (mm) Using this formula it ispossibl et odetermin eth eeffectiv erainfal li n subsequent timeintervals .Th evalu eo fth eC Nparamete r can be evaluated fromtable sdevelope db y SCS.I nthi smetho dsoil sar eclassifie da sA ,B ,C orD accordin gt oth efollowin gcriteria : A. (Lowrunof fpotential )Soil shavin g high rates even in thoroughly wetted and consisting chieflyo fdee pwel lt oexcessivel y drainedsand san dgravels .The yhav ea hig hrat eo fwate rtransmission . B. Soilshavin g moderate infiltration rates if thoroughly wetted and consisting chiefly of moderately deep to deep, moderatelywel lt o well-drainedsoil swit hmoderatel yfin et omoderatel y coarse textures. Theyhav ea moderat erat eo fwate rtransmission . C. Soilshavin gslo winfiltratio nrate si fthoroughl ywette dan dconsistin g chieflyo fsoi lwit ha laye r that impedes the downward movement of water, or soilswit hmoderatel y finet ofin etexture .The yhav ea slo w rateo fwate rtransmission . D. (Highrunof fpotential )Soil shavin gver y slow infiltration rates if thoroughly wetted and consisting chiefly of claysoil swit ha hig h swellingpotential ,soil swit ha daypa no rcla ylaye r at or near the surface, andshallo wsoil sove rnearl y imperviousmaterial .The yhav ea veryslo wrat eo fwate rtransmission .

AC Nvalu e isextracte d fromTabl e1 .A composit eC Nfo ra watershe d having more than one land use,treatmen to rsoi ltyp eca nb efoun db yweightin g eachcurv enumbe raccordin g toit sarea .Th ecurv enumber s in Table 1 are applicablet oaverag eanteceden tmoistur econditions . Table1 RunoffCurv eNumber sfo rhydrologi esoil-cove rcomplexe s

(Antecedentmoistur econditio nII ,an dI a=0.2S)

Cover Hydrologie SoilGrou p

Landus eo rcove r Treatmento rPractic e Hydrologie Condition A

Fallow Straightro w -- 77 86 91 94 Rowcrop s Straightro w Poor 72 81 88 91 Straightro w Good 67 78 85 89 Contoured Poor 70 79 84 88 Contoured Good 65 75 82 86 Contouredan d terraced Poor 66 74 80 82 Contouredan d terraced Good 62 71 78 81 Smallgrai n Straightro w Poor 65 76 84 88 Good 63 75 83 87 Contoured Poor 63 74 82 85 Good 61 73 81 84 Contouredan d terraced Poor 61 72 79 82 Good 59 70 78 81 Close-seededlegume s Straightro w Poor 66 77 85 89 orrotatio nmeado w Straightro w Good 58 72 81 85 Contoured Poor 64 75 83 85 Contoured Good 55 69 78 83 Contouredan d terraced Poor 63 73 80 83 Contouredan d terraced Good 51 67 76 80 Pastureo rrang e Poor 68 79 86 89 Fair 49 69 79 84 Good 39 61 74 80 Contoured Poor 47 67 81 88 Contoured Fair 25 59 75 83 Contoured Good 6 35 70 79 Meadow Good 30 58 71 78 Woods Poor 45 66 77 83 Fair 36 60 73 79 Good 25 55 70 77 Farmsteads 59 74 82 86 Roads (dirt) 72 82 87 89 (hardsurface ) 74' 84 90 92

Otheranteceden tmoistur econdition s (AMC)are : AMCI : A condition of watershed soilswher eth esoil s aredr ybu tno t wiltingpoint ,an dwhe nsatisfactor yplowin go rcultivatio n takes place. AMCI I : Theaverag ecas efo rannua lfloods . AMCIII : When heavy rainfall orligh trainfal lan dlo wtemperature shav e occurreddurin gth e5 day spreviou st oth egive nstorm .

Table2 give stota l5-da yanteceden trainfal lfo rdifferen tAMC . Conversion ofth ecurv enumber st omoistur ecategorie sI o rII Ii sgive ni nTabl e3 .

Table2 Classificationo fAnteceden tMoistur eConditions .

Condition 5-dayanteceden trainfall ,m m Dormantseaso n Growingseaso n

I upt o1 3 lesstha n3 5 II 13-28 35t o5 3 III over2 8 over5 3

Table3 Curve Numbers (CN) for wet (AMCIII )an ddr y (AMCI )Anteceden t MoistureCondition scorrespondin gt oa naverag eAnteceden tMoistur e Condition.

CN for CorrespondigCN' s

AMCI I AMCI AMCII I

100 100 100 95 87 98 90 78 96 85 70 94 80 63 91 75 57 88 70 51 85 65 45 82 60 40 78 55 35 74 50 31 70 45 26 65 40 22 60 35 18 55 30 15 50 25 12 43 20 9 37 15 6 30 10 4 22 5 2 13 For a gauged watershed the CNvalu e canb e evaluated frommeasure d rainfall and runoffb y iterative methods (Banasik, Ignar, 1983). For theHupsels e Beekwatershe d the average CN value calculated using 10 flood events was91.8 . CN value determined for thewatershe d applying thehydrologi e soil-cover complex procedure with theus e of the data about type of soil and land use was much lower andwa s equal to73.6 .

5. RAINFALL RUNOFF TRANSFORMATION

Among the many rainfall-runoffmodel s whichhav e been developed for flood flow evaluation, practical use is constrained to simple models with few, easy to determine parameters.On e suchmode l is theWackerman n (1981)mode l of two parallel cascades of linear reservoirs consisting of two reservoirs (Fig. 2).I t is a special case of themor e general Diskinmodel . Parameters of these model (i.e.Kl , K2-retention coefficients for first and second cascade, and ^-dividing coefficient for input effective rainfall) canb e evaluated from formulae developed by Thiele (1981) from data recorded in over 90watershed s fromWes t Germany:

fT ï0.2175 Kl - 0.7308- jj ... [5] .

rT ï0.2814 K2 - 2.0246- jY ... [6]

fT VO.5078 ß - 2.0188-Ij^ l ... [7]

where:

L,I - like in formula 1 10

-> -•%

Fig.2 .Conceptua l rainfall. runof fmode lb yWackermann .

Instantaneous Unit Hydrograph (IUH)ordinate scause db yuni to feffectiv e rainfall intim e- +0 ca nb edetermine dfro mequation :

ut- ^•"l(t)+( 1-^)-u2(t) [8] t-1,2 ...m where: ul(t)> u2(t)" ordinates of IUH for first and second cascade, respectively (1/h),calculate d fromth erelationship :

t "K j UJ(t)* K j •e [9] 11

where: j =1, 2 -fo rfirs tan dsecon dcascad e Kj= retentio ncoefficien tfo rj cascad e t -tim efro mth estar to fIU H

Ordinateso fth euni thydrograp hcause db y1 m mo feffectiv e rainfall with Atduratio nfo rwatershe dare aF an duse dfo rrainfall-runof ftransformatio n arecalculate d fromth eequation :

F F ht "37 6 "U t - 772 '(U t + Ut-l) '•• [10] 1-1,2.. .m where: 3 ht =uni thydrograp hordinate s (m /s-mm)

ut —lik ei nequatio n8 F -are ao fth ewatershe d (km2)

ût - 1/2 •(u t+ut.x)i n(1/h ) 1/3.6 -uni tcoefficien t

Calculationo fdirec tflo w from effective rainfall histograph and unit hydrograph isshow ni nFig .3 .I tca nb ewritte ni ngenera lform :

min(i.n) Qp(i)- s hk>AHj k-i-j+1,i-1, 2.. .m+n- 1 ... [11] 12

0At, 2 3 4 i i*1 i*2 m (m«n-1)At •m » Fig.3 . Direct flow calculation.

6. WACKERMANNMODE LPARAMETER SEVALUATIO N

Parameters of the Wackerraann model forth eHupsels eBee kwatershe dwer e calculated intw oways .Firs tthe ywer e obtained from formulae 5 to 7, applying L-4 kman d1- 10/00 .Calculate dvalue swer eyS—.173 ,Kl-2.094 ,an d K2-7.904. Thesecon dmetho dwa sbase do n the optimalization method. The procedure basedo nth edirec tsearc htechniqu ewit hconstraint spropose db yRosenbroc k wasadopte d (Kuester,Mize ,1973 )fo r the automatic calibration of the model parameters. This method is the most commonlyuse d inhydrologi e researchworks .Th esu mo fth esquare so fth edifference sbetwee n simulated andobserve ddirec tflo wordinate swa schose na sa nobjectiv efunctio namon g manyform sdescribe d inth eliteratur eabou tmode lcalibration :

N F- 2 (Qo(i)-Qc(i))2 [12] i-1 13

where:

F -objectiv efunctio n QO(i)™th ei-t hvalu eo fth eobserve dflo w (m3/s) Qc(i)= t*ie1-t hvalu eo fth ecompute dflo w(m 3/s) N -number so fvalue s inth eflo wserie s

Thecompute rprogra mwhic hcontain sdescribe dmethod swa sdevelope d in the Departmento fHydrauli cStructures ,a tth eWarsa wAgricultura lUniversity . Ten rainfall-runoff events were taken from the recorded datafo rth e optimizationcalculations .Th eresult sar eshow ni nTabl e 4. The recorded events were dividedint otw oset s (1t o6 an d7 t o10 )i norde rt omak ei t possible toverif yth emode lparameter swit hth e set of independent data (events 7t o 10). Soth eoptimize dparameter swer ecalculate da sa naverag e foral levent san dfo r1 t o6 events .

Table4 OptimizedWackerman nmode lparameter s

No Date ß Kl K2

1 22-08-77 .295 3.073 7.312 2 11-12-77 .144 1.664 5.781 3 20-03-78 .159 6.053 4.090 4 02-02-80 .230 1.222 3.589 5 17-12-80 .333 2.620 6.528 6 09-01-81 .323 .999 4.862 7 14-01-81 .341 1.130 4.958 8 31-12-81 .357 5.124 2.429 9 06-06-82 .499 3.984 2.199 10 21-03-83 .444 7.344 2.428

Average1: 6 .226 2.616 5.339 Average1:1 0 .270 3.132 4.521 Thieleformula e .173 2.094 7.904

Parametervalue sfro mth eThiel eformula ear eshow nfo rcomparison .I norde r 14

to compare the effecto fdifferen tmethod so fparamete revaluation ,thre e instantaneousuni thydrograph sar eshow ni nFigur e4 for three calculated setso fparameters . Next, the verification was doneusin gparameter scompute di na differen t way,fo rfou rfloo devent s (7t o 10). The criterion proposed by Delleur, Sarma and Rao (1973) was used forcompariso no fobserve dan dsimulate d hydrographs.I twa sth eso-calle dspecia l correlation coefficient in the form:

N N 1/2 2 2 2 Q0(i)-Qc(i)- S (Qc(i) R - i-1 i-1 [13] S N S (Q0(i))2 i-1 where:

Q0(i)> Qc(i) N likei nfor m1 2

Theauthor so fth ecriterio ndetermine dfiv einterval smakin g itpossibl et o evaluateth eagreemen tbetwee nth eobseve dhydrograph san dth eon e computed by the model, by usingfiv egrade sfro mexcellen t (denotedb y5 )t opoo r (denotedb y 1). Theseinterval sare :

0.99< R s< 1.0 excellent= 5

0.95< R s< 0.99 verygoo d- 4

0.90< R s< 0.95 good —3

0.85< R s< 0.90 fair -2

0.00< R s< 0.85 poor -1

Theresult so fth everificatio nar egive ni nTabl e5 . 15

o

CU O vO -1- a + z> E TD T3 o dl o» **— IM rsi 'E 'Ë JV ~a> CL o. IE O o t—

Ol E o

ai

CL o en o TD

O

c a c

-4- en 16

Table5 Resultso fWackerman nmode lverification .

Optimization 1:10 Optimizlatio n1: 6 Thiele formulae No RS grade RS grade RS grade

7 .963 4 .955 4 .896 2 8 .973 4 .956 4 .876 2 9 .952 4 .935 3 .863 2 10 .978 4 .976 4 .927 3

7. DESIGNFLOO DSIMULATIO N

Thedescribe drainfall-runof fmode lwa suse dfo rdesig nfloo dsimulatio nfo r theHupsels eBee kwatershed .Th eC Nparameter ,assesse da sth eaverag eo f1 0 observedevent swa sequa lt o 91.8. Eight total rainfall durations were applied tochec kthei rinfluenc eo nfloo dmagnitude .Ther ewer e2 ,4 ,6 ,8 , 10,12 ,1 4an d1 6hours,tim eo fconcentratio nevaluate dfro mKirpic hformul a was2.7 5 hours).Tota lrainfal lintensitie swer etake nfro mth erelationshi p showni nFigur e1 .Th esimulate dhydrograph sar epresente di nFigur e 5 for CN equal to 91.8 and in Figure6 fo rCN-73.6 .Rainfal lintensitie san d amountstogethe rwit hpea kflow sar eshow ni nTabl e6 .

Table6 Simulateddesig nfloods .

Totalrainfal l Totalrainfal l Peakflo wrm 3/sl No TP intensity amount [h] [mm/h] [mm] CN-73.6 CN-91.8

1 2 22.2 44.4 .94 4.10 2 4 13.1 52.4 1.47 5.13 3 6 9.3 55.8 1.74 5.48 4 8 7.4 59.2 1.97 5.70 5 10 6.2 62.0 2.15 5.76 6 12 5.3 63.6 2.21 5.66 7 14 4.6 64.4 2.18 5.42 8 16 4.1 65.6 2.19 5.20 17

Inorde rt oevaluat eth einfluenc eo fC N value on peak flows additional simulations were conductedfo rCN=60 ,7 0an d8 0an dfo rrainfal lduration s upt o2 0hours .Th erelationship sbetwee nfloo dpeak san drainfal l duration fordifferen tC Nar epresente d inFigur e7 .

19 20

CL t— C vO O oo o rn o O co r— C-» ii n II II z z z l—l l_l LJ

dE 21

8. RESULTSAN DDISCUSSION S

Calibration ofth eWackerman nmode lha sshow ndiscrepancie samon gparamete r valuesobtaine d intw odifferen tways .A si sshow ni nTabl e4 ,th eoptimize d seto fparameter s isscattered ,wit haverag evalue so f .270,3.13 2 and4.52 1 for ß, Klan dK 2 (foral levents) . Parameter values computed from Thiele formulae are respectively: .173,2.09 4an d7.904 .I norde rt oevaluat eth e influenceo fdifferen tparamete rvalue so n Instantaneous Unit Hydrograph, three hydrographs were generated from theseparameter san dar eshow ni n Figure4 .I tca nb esee ntha tal lthre ehydrograph spea ka tfou rhours , but peak values differ significantly (44%fo rThiel eformula eparameters ,an d 11% forparameter soptimize d for6 ,compare dt o1 0events) . This difference is probably caused byth ever ysmal lslop eo fth emai nriver ,compare dt o watershed inWes tGermany ,fo rwhic hth eThiel efomula ewer edetermined . Modelverificatio nresult swit hth eus eo ffou revent s (no. 7 to 10) are shown in Table5 .I tca nb esee ntha tfo rbot hoptimize dse to fparameter s verificationgav ever ygoo dresult s (withon eeven tgrade da sgood) . forth e Thiele methodparameter s theresult swer emuc hwors e (threegrade sfai ran d one good). Theaverag eC Nparamete rvalu e of ten events (calculated from observed rainfall-runoff data)wa s91.8 .Th evalu edetermine db yth ehydrologi esoi l covercomple xprocedur e (asdevelope db ySCS )include sdat ao ntyp eo f soil and land use andwa smuc hlowe r (73.6). Suchdifference sar edescribe di n theliteratur e (Bales,Berson ,1982) . Ifth esoi lcove rcomple xprocedur ei s used forungauge dwatersheds ,direc tflo wfo robserve drainfal levent sman y beunderestimated .However ,whe nth eprobabilit y of flooding is low, CN values obtained in thiswa yca nb eused .Thi smetho dha sth eadvantag eo f beingsimpl ean dthoug hi tca nb euse dfo rungauge dwatersheds ,bu t it can produce results in which less confidence may beplaced .A nadditiona l explanationfo rsuc hdiscrepanc ybetwee n CN values obtained by the two methods is shown in Table4 .Almos tal levent swer erecorde d inth ewet , winterperiod .S oAM CII Icondition swer emor elikel yt ooccur . Designfloo dhydrograph s forCN-91. 8an d 73.6 with 8 different rainfall durations are showni nth eFigure s5 an d6 .Critica lrainfal lduratio nfo r CN-91.8wa s10 han dfo rCN-73. 612 han dpea kflow swer e5.7 6m 3/s and 2.21 m3/s respectively. Floodhydrograph sfo rCN-73. 6ar eclos et oth eexpecte d 22

forth eHupsels eBee kwatershed .Figur e7 show stha tth e critical rainfall duration getsrapidl ylonge rwit hdecreasin gvalue so fth eC Nparameter .I t wasa fe wtime slonge r than the time of concentration calculated from Kirpich formulae. This confirms the idea that the critical rainfall durationsha st o be found by running simulation models for different rainfalldurations .Analysi so fth erelationship s inFigur e7 als oconfirme d adependenc eo ffloo d peak flows on CN parameter values. (Peak flows increasewit hincreasin gC Nvalues) . Presented results showtha tth edescribe dWackerman nmode lca nb euse dfo r designfloo dhydrograp hcomputation ;howeve rth euse rshoul db eawar e of a possible lower accuracy when using thismode lfo rungauge dbasins ,whe n applyingThiel eformulae . 23

REFERENCES

Bales,J. , R.P.Betson ,1982 . The Curve Number as a hydrologie index. Proceedings of Int. Symp. on Rainfall-Runoff Modeling. May18-21 . Mississippi StateUniversity .

Banasik,K. ,S . Ignar, 1983. Determination of effective rainfall from recorded rainfall and runoff bySC Smethod , (inPolish) .Preg .Geot . Vol.XXCIII ,no .3-4 .

Banasik,K. ,S .Ignar ,1986 .Analysi s of rainfall duration influence on flood magnitude. Proceedingso fth eInt .Conf ."Hydrologica lProcesse s inth eCatchment" .Craco wTechnica lUniversity ,Craco w8-1 1May .

Buishand, T.A., C.A. Velds, 1980. Neerslag en verdamping. Koninklij k NederlandsMeteorologisc h Instituut. (Royal Netherlands Meteorological Institute).

Delleur, J.W., P.B.S.Sarma ,A.R .Rao ,1973 .Compariso no frainfall-runof f modelsfo rurba nareas .J .Hyd .18 .

Kuester,J.L. , J.H. Mize, 1973. Optimization techniques with Fortran. McGraw-Hill.Ne wYork .

Soil Conservation Service,1972 .Nationa lEngineerin gHandbook ,Hydrology , sect.4 .USDA .Washingto nD.C .

Thiele, F, 1981. Vergleichende Untersuchung zur Ermittlung von Ubertragungsfunktionen aus Eizugsgebietsgrössen nach verschiedenen Methoden.DVWK .Bonn .

Viessman,W. ,J.W .Knapp ,G.L .Lewis ,T.E .Harbaugh ,1977 . Introduction to hydrology.Harpe r& Row .Ne wYork . 24

Wackermann, R., 1981. Eine Einheitsganglinie aus Charakteristiken Systemwerten ohne Niederschlag-Abfluss-Messungen. "Wasserun dBoden" , no.1 .

Warmerdam, P.M.M., 1982. The effect of improvement on the hydrologicalregim eo fa smal l representative catchment area in the Netherlands.Studie sReport si nHydrolog y 32.UNESCO . 25

LISTO FTABLE S

1. RunoffCurv eNumber sfo rhydrologi esoil-cove rcomplexes .

2. Classificationo fAnteceden tMoistur eConditions .

3. CurveNumber s (CN)fo rwe t (AMCIII )an ddr y (AMCI )Anteceden tMoistur e Conditionscorrespondin g toa naverag eAnteceden tMoistur eCondition .

4. OptimizedWackerman nmode lparameters .

5. Resulto fWackerman nmode lverification .

6. Simulateddesig nfloods . 26

LISTO FFIGURE S

1. Intensity-durationcurv efo rstatio nD eBil t (p-1%).

2. Conceptualrainfall-runof fmode lb yWackermann .

3. Directflo wcalculation .

4. Instantaneousuni thydrograph s forthre eset so fparameters .

5. Directrunof fhydrograph sfo rCN-91.8 .

6. Directrunof fhydrograph s forCN-73.6 .

7. Relationshipsbetwee nfloo dpeak sQ max andrainfal lduratio nTP .