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An Example of a Rainfall-Runoff Model For 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 hydrology are often used as a tool for flood 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 hydrograph 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 hydrographs 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 infiltration 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-seeded legumes 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.
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