RUNOFF HYDROGRAPHS USING SNYDER AND SCS
Journal of Ecological EngineeringVolume 18, Issue 1, Jan. 2017, pages 25–34Research ArticleDOI: 10.12911/22998993/66258RUNOFF HYDROGRAPHS USING SNYDER AND SCS SYNTHETIC UNITHYDROGRAPH METHODS: A CASE STUDY OF SELECTED RIVERS INSOUTH WEST NIGERIAAdebayo Wahab Salami1, Solomon Olakunle Bilewu1,Adeoye Biliyamin Ibitoye2, Ayanniyi Mufutau Ayanshola1Department of Water Resources and Environmental Engineering, University of Ilorin, Ilorin, Nigeria, e-mail:bilewuk@yahoo.com; engramayanshola@gmail.com2Department of Civil and Environmental Engineering, Kwara State University, Malete, Nigeria, e-mail:bilyamin@yahoo.comCorresponding Author‘s e-mail: awsalami2009@gmail.com1Received: 2016.10.01Accepted: 2016.10.23Published: 2017.01.01ABSTRACTThis paper presents the development of runoff hydrographs for selected rivers in theOgun-Osun river catchment, south west, Nigeria using Snyder and Soil ConservationService (SCS) methods of synthetic unit hydrograph to determine the ordinates. TheSoil Conservation Service (SCS) curve Number method was used to estimate the excess rainfall from storm of different return periods. The peak runoff hydrographs weredetermined by convoluting the unit hydrographs ordinates with the excess rainfall andthe value of peak flows obtained by both Snyder and SCS methods observed to varyfrom one river watershed to the other. The peak runoff hydrograph flows obtainedbased on the unit hydrograph ordinate determined with Snyder method for 20-yr, 50yr, 100-yr, 200-yr and 500-yr, return period varied from 112.63 m3/s and 13364.30m3/s, while those based on the SCS method varied from 304.43 m3/s and 6466.84 m3/sfor the eight watersheds. However, the percentage difference shows that for values ofpeak flows obtained with Snyder and SCS methods varies from 13.14% to 63.30%.However, SCS method is recommended to estimate the ordinate required for the development of peak runoff hydrograph in the river watersheds because it utilized additional morphometric parameters such as watershed slope and the curve number (CN)which is a function of the properties of the soil and vegetation cover of the watershed.Keywords: unit hydrograph, runoff hydrograph, storm duration, watershed, return periodsINTRODUCTIONBasic stream flow and rainfall data are notadequately available for planning and designingwater management facilities and other hydraulicstructures in ungauged watershed. This situation is common in Nigeria due to lack of gauging stations along most of the rivers and streams.However, techniques have been evolved that allow generation of synthetic unit hydrographs.This includes Snyder, Soil Conservation Service(SCS), Gray and Clark’s Instantaneous Unit Hydrograph methods. The peak discharges of streamflow from rainfall can be obtained from the de-sign runoff hydrographs developed from unit hydrographs ordinates determined from establishedmethods. Warren et al. [1972] described hydrograph as a continuous graph showing the properties of stream flow with respect to time, normally obtained by means of a continuous striprecorder that indicates stages versus time andis then transformed to a discharge hydrographby application of a rating curve. Wilson [1990]observed that with an adjustment and well measured rating curve, the daily gauge readings maybe converted directly to runoff volume. He alsoemphasized that catchment properties influencerunoff and each may be present to a large or small25
Journal of Ecological Engineering Vol. 18(1), 2017degree. The catchment properties include area,slope, orientation, shape, altitude and also streampattern in the basin. The unit hydrograph (UH) ofa drainage basin, according to Varshney [1986] isdefined as the hydrograph of direct runoff resulting from one unit of effective rainfall of a specified duration, generated uniformly over the basinarea at a uniform rate. Arora [2004] defined 1-hrunit hydrograph as the hydrograph which gives1 cm depth of direct runoff when a storm of 1-hrduration occurs uniformly over the catchment.A vast amount of literature exists treating thevarious unit hydrograph methods and their development. Jones [2006] reported that Sherman in1932 was first to explain the procedure for development of the unit hydrograph and recommended that the unit hydrograph method be used forwatersheds of 2000 square miles (5000 km2) orless. Chow et al. [1988] discussed the derivationof unit hydrograph and its linear systems theory.Furthermore, Viessman et al [1989], Wanielista[1990] and Arora [2004] presented the history andprocedures for several unit hydrograph methods.Ramirez [2000] reported that the synthetic unithydrograph of Snyder in 1938 was based on thestudy of 20 watersheds located in the AppalachianHighlands and varying in size from 10 to 10 000square miles (25 to 25 000 km2). Ramirez [2000]reported that the dimensionless unit hydrographwas developed by the Soil Conservation Serviceand obtained from the UH’s for a great number ofwatersheds of different sizes and for many different locations. It was also stated by Ramirez [2000]that the SCS dimensionless hydrograph is a synthetic UH in which the discharge is expressed asa ratio of discharge, Q, to peak discharge, Qp andthe time by the ratio of time, t, to time to peakof the UH, tp. Wilson [1990] also reported thatin 1938, McCarthy proposed a method of hydrograph synthesis but in that same year Snyder proposed a better known method by analyzing a larger number of basins in the Appalachian mountainregion of the United States. Ogunlela and Kasali[2002] applied four methods of unit hydrographsgeneration to develop a unit hydrograph for anungaged watershed. The outcome of the study revealed that both Snyder and SCS methods werenot significantly different from each other. Salami[2009] applied three unit hydrograph methods forrunoff hydrograph development of lower NigerRiver basin at downstream of the Jebba Dam. Themethods considered were Snyder, SCS and Graymethods. The statistical analysis, conducted at26the 5% level of significance, indicated significantdifferences in the methods except for Snyder andSCS methods which have relatively close values.In this study Snyder and SCS methods were usedto determine the ordinate of unit hydrographs andwas subsequently used to generate peak runoffhydrographs of rainfall depth of various returnintervals through convolution for selected riversin south west, Nigeria. The outcome of the studywill make the selection of peak runoff flows ofthe desire return period for design of hydraulicstructures in the region possible.MATERIALS AND METHODSStudy AreaThe river catchments under consideration areFawfaw, Oba, Awon, Opeki, Ogunpa, Osun, Otinand Ogun located in the Ogun – Osun River basin, South West Nigeria as presented in Figure 1.Development of Unit HydrographThe methods of unit hydrographs used to determine the peak runoff ordinates are; Snyder’sand Soil Conservation Service (SCS) methods.Snyder’s methodIn adopting Snyder’s method, the followingparameters were determined: the peak discharge,lag time and the time to peak, rainfall duration,the peak discharge per unit of watershed area, q’p,the basin lag t’l, the base time, tb, and the widths,w (in time units) of the unit hydrograph at 50 and75 percent of the peak discharge. The parameterswere estimated in accordance to Ramirez [2000]and Arora [2004] using equations (1) to (8).Lag time, tltl Ct (L * Lc )0.3(1)Where Ct is a coefficient representing variations of watershed slope and storage. Values ofCt range from 1.0 to 2.2 [Arora, 2004]. An average value of 1.60 is assumed for this catchment.Equation (1) gives the lag time for the watershed.Unit-hydrograph duration, tr (storm duration)tr tl5.5(2)From equation (2) the duration of the stormwas obtained. However, if other storm durationsare intended to be generated for the watershed,
Journal of Ecological Engineering Vol. 18(1), 2017Figure 1. Map of Nigeria showing location of the selected riversthe new unit hydrograph storm duration (t’r), thecorresponding basin lag time ((t’l) can be obtainedfrom equation (3). t ' tr (3)tl' ' t'l r tr'tr' t t (3)(3)tltl tlt l 4 r r 44 The output from the equations and the measured physical parameters of each of the basinsare presented in Table 1.Soil Conservation Service (SCS)In adopting the method of US Soil ConservaPeakdischarge,Q’The peakdischarge(Q’) pwas obtained from' p Q’tionServicePeakdischarge, tr tr(Q’ p p) was obtained from equationdischarge(4)(SCS) for constructing synthetic unit'equation: The tpeak (3)t graphs (4)was based on a dimensionless hylp C 4* A 2.l78 *p' CA**(4)drograph,whichrelates ratios of time to ratios ofQ p ' 2.78(4)pQ p tl' '(4)flow[Viessmanetal. 1989] and Ramirez [2000].tl Q’Peakpiscoefficientthe coefficientaccountingfor floodwaveandstorage conditions.(Valuesof Cpwererange from 0.3whereCp discharge,Where Valuesthe time to peakp wherethe coefficientaccountingforfloodwave forandstorageof Cp range from 0.3Cp ion(4)thisp) flood wave andtostorageconditions. withValuesof Cp ofdeterminedin accordancewith [Viessman et al.0.93, Aroraan average0.62 is assumedfor this catchment).Cp * A2.78 *[2004]'range from 0.3 to rez2000, SCS 2002, (4)p (days) 'Base timetage of 0.62 is hunath2006] byTheBasebase timetime (days)was obtained from equation econditions.(Valuesof Cp range from 0.3whereCThe base timeobtainedfromequationadoptingequations (9) to (12).Thewasbaseobtainedfrom(5)equation(5)ptime was' tArora to hment).tb 3 3 l tl' (5)(5)3 tb 3 24(5)Peak discharge24 Base time (days)The time width W50 and W75 of the hydrograph at 50% and 75% of the height of the peak flow ordinateTheWbaseandtimewasobtainedequation (5)peakisthe flowandW75fromof theat50%dischargeandin75%of obtainedthe heightoftheArmypeakThetimewidthWThe uations(6) hydrographand amirez2000]: tat 50% and 75%oftheheightofthepeakfloworEngineer [Arora,l 2004]. The unit of the time width is hr. Also the peak discharge per area (cumec/km ) is2 2004]. The unit (5)tb 3 hargeperarea(cumec/km)isdinate were givenobtainedbased24onequations (6) andby equation0.208 * A * Qd . (8). (8).givenbyequation(9)Q p(7) respectively in accordanceU.S Army5.9 width Wwithand W75 of thetimep the height of the peak flow ordinateW50 The [Arora,(6)hydrograph at 50% and 75% tof5.92004].50The1.08Corps of Engineerunitofthe' obtained based on equations (6)W (6)wereand(7)respectivelyinaccordancewith U.S Army Corps of50 q1.083Qp –ispeakdischarge(mdischarge/s)time width is hr.EngineerAlsop thepeak dischargeperunitareaof the where:q 'p[Arora,2004]. Thetime widthhr. Alsothe peakper area (cumec/km2) is223.4A–watershedarea(km)(cumec/km )Wis givenby3equationequation(8).given by(8).(7).475 Qd– quantity tof runt r offW75 q ' 1.085.19.08(7) t(mm)'ppl(6)W50 q p 1.08(6)t–timetopeak(hr)2p''qQp ' pTime to peak (tp) and lag time (tl):Qpq 'p '(8)3.4q p A (8)t 0.133t ct(7) (7)W75 A 1.08t p r tl t p c(10)q 'p1.7of the basins are presentedThe output from the equations and the measured physical2parameters of eachThe outputof each of the basins are presentedin Table1.Q p'Q p'from the equations and the measured physical parameters(11)t l 0.6t c'inq 'pTable1. (8) (8)qp t c of0.concentration133t cAAwhere: ttc – time(min)Soil Conservation Service (SCS)p1.7SoilConservationService(SCS)In adopting the method of US Soil Conservation Service (SCS) for constructing synthetic unitTheadoptingoutput fromtheequationsand Soilthe measuredphysicalparametersofforeachconstructingof the basinssyntheticare presentedInmethodof USConservationService(SCS)hydrographswas thebasedon a dimensionlesshydrograph, whichrelatesratiosof time to ratiosof flowunit27ratiosin Table1. was based on a dimensionless hydrograph, which relates ratios of time tohydrographsofinflow[Viessman et al., 1989] and Ramirez [2000]. The peak discharge and the time to peak were nce with [Viessman et al., 1989, Wanielista, 1990, Ramirez, 2000, SCS, 2002, Ogunlela and inSoil ConservationService (SCS)accordance[Viessmanet byal.,adopting1989, Wanielista,1990,Ramirez, 2000, SCS, 2002, Ogunlela andKasali,2002 andwithRaghunath,2006]equations (9)to (12).In adoptingthe Raghunath,method of2006]US bySoilConservation(SCS) for constructing synthetic unitKasali,2002 andadoptingequationsService(9) to (12).
tp t l 0.6t c1.7(11)Journal of EcologicalWhereEngineering Vol. 18(1), 2017tc time of concentration (min)runoff hydrographs for selected return periods L0.77 (12)t c 0.0195 0.385 (12)(20yr, 50yr, 100yr, 200yr and 500yr) were devel Soped through convolution. The maximum 24-hrL lengthof channelwhere: L – lengthof channel(m);(m); S slope of channelrainfall depths of the different recurrence intervalS – slope of channel.for the catchment under consideration are 174.2The estimated values of both the peak discharge and time to peak were applied to the dimensionless205.0 mm,232.3262.73weremm and309.0[Raghunath ,hydrographratiosin accordanceSCS andmm,the pointsfor theunit mm,hydrographobtainedThe estimatedvaluesof boththe toandusedto develophydrograph curve. The calculated values for parametersThetp and qp werecharge and timepeakwereappliedtheto unitthe dirunoff hydrographwasderived froma hydrographmultiperi- phtoobtainthecorrespondingunitmensionless hydrograph ratios in accordance toof rainfallinexcesshydrographconvoluThe estimated unit hydrograph ordinates odis presentedTable called2 basedon the valuesof time to peakSCS and the points for the unit hydrograph weredischarge (tp) and peak discharge (qp) for eachcatchment.tion.riverIt involvesmultiplying the unit hydrographobtained [Raghunath 2006] and used to developordinates (Un) by incremental rainfall excessthe unit akRunoff Hydrographs(Pn), adding and lagging in a sequence to producefor parameters tp Theand qestablishedwere appliedthe SCS ordinates were used to develop the runoff hydrographs due tounit tohydrographspa resulting runoff hydrograph. The SCS type IIdimensionlessunit hydrographobtaincorre- Peakactualrainfall eventtooverthethecatchment.runoff hydrographs for selected return periods (20yr, 50yr,curve wasused toThedividethe differentrainfallsponding unit100yr,hydrographordinates.200yr and500yr) Thewereestimatdeveloped throughconvolution.maximum24-hr rainfalldepths of tionare174.2mm,205.0mm,232.3 mm,ed unit hydrograph ordinates is presented in hydrographwasderivedfrom2 based on the values of time to peak discharge n.Itinvolvesmultiplyingtheunitand peak discharge (qp) for each river catchment.hydrograph ordinates (Un) by nproduce a resulting runoff hydrograph. TheTheSCSincrementaltype II curverainfallwas usedtodividethedifferentrainfalldataexcess was obtained byDevelopmentofsuccessivePeak RunoffHydrographsintoequalshort time events andthe SCS sequentially,Curve Numberthemethodusedfromto estimate thesubtractingrainfallwasexcesscumulative rainfall for storm depth of evious time events. The equations that ap-incrementalThe established unit hydrographs ordinatesrainfall excess was obtained by subtracting sequentially, the rainfall excess from the previous time events.ply to the SCS Curve Number method are givenwere used toThedevelopthe runoffhydrographsdueequationsthat applyto the SCSCurve Number method are given below [SCS, 2002].to actual rainfall event* over 2the catchment. Peakbelow [SCS 2002].P Ia*Qd *for P 0.2SP 0.8S for generating unit (14)Table 1. Watershed characteristicshydrograph (Snyder’s method)*Q 0forP 0.2SRiver watershed dL (km)L (km)t (hr)t (hr)Q (m3/s)T (hr)A (km2)S (%) cFaw-FawIa initialabstraction11.806.40Ia 70375.000.3925400S 23.50 07With the CN 75 based on soil group B, small grain and good condition, S is estimated as 84.67 mm,20.0012.192.22108.570.21while Ia43.50is 16.94 mm.This impliesthat anyvalue of81.31rainfall lessthan 16.94575.00mm is regardedas 47.5015.0011.48175.66106.441170.000.21P* accumulatedprecipitation(mm) 2.09OpekiOtinOsunOgunTable 2. Unit hydrograph ordinates for US Soil Conservation Service (SCS) methodFaw-Faw RiverOba RiverAwon RiverOgunpa RiverOpeki RiverOtin RiverOsun RiverOgun Rivert (hr) Q (m3/s) t (hr) Q (m3/s) t (hr) Q (m3/s) t (hr) Q (m3/s) t (hr) Q (m3/s) t (hr) Q (m3/s) t (hr) Q (m3/s) t (hr) Q .0551.90.028
actual rainfall event over the catchment. Peak runoff hydrographs for selected return periods (20yr, 50yr,100yr, 200yr and 500yr) were developed through convolution. The maximum 24-hr rainfall depths of thedifferent recurrence interval for the catchment under consideration are 174.2 mm, 205.0 mm, 232.3 mm,262.73 mm and 309.0 mm respectively [Olofintoye et al, 2009]. The runoff hydrograph was derived froma multiperiod of rainfall excess called hydrographconvolution.It involvesmultiplyingthe unitJournal of EcologicalEngineeringVol. 18(1),2017hydrograph ordinates (Un) by incremental rainfall excess (Pn), adding and lagging in a sequence toproduce a resulting runoff hydrograph. The SCS type II curve was used to divide the different rainfall data2RESULTSANDDISCUSSIONS*equalshort time events andthe SCSCurveNumber method was used to estimate thePinto successiveIa*Qd cumulativeforP 2 S depth of 20yr, 50yr, 100yr, 200yr and 500yr return period. The incrementalrainfallfor0.storm*Prainfall 0.8excessSTwo methodsof syntheticunit thehydrograph(13)was obtained by subtractingsequentially,the rainfallexcess fromprevious time events.*wereadoptedtodeterminetheordinatesfor theQd 0 Thefor equationsP 0.2thatS apply to the SCS Curve Number method are given below [SCS, 2002].developmentofpeakrunoffhydrographforeight2P * precipitationIawhere: P* – accumulated* (mm)catchments listed. The values of the ordinate fromQd *for P 0.2SQd – cumulativeexcess, runoff (14)the synthetic unit hydrograph methods were preP 0rainfall.8S(mm) Q 0 for P * 0.2Ssented in Tables 1 and 2 while the runoff hydrodIa – initial abstraction, Ia 0.2S.graph peak flows (m3/s) for the eight river catchIa initial abstraction Ia 0.2Sments are presented in Table 3.25400(14)S 254(15)It was observed for Faw-Faw river catchCNment that the values obtained for SCS methodWith the WithCN the75CNbasedsoilongroupB, B,is smallhighergrainby 63.31%thanthat of Snydermethod. 75onbasedsoil groupand goodcondition,S is estimatedas 84.67 mm,small grain andgoodis estimatedObariver catchment,the mmvaluesobtainedwhileIa iscondition,16.94 mm. SThisimplies that anyForvalueof rainfallless than 16.94is regardedas Zero.as 84.67 mm, wherewhile Ia is 16.94 mm. This impliesfor SCS method is higher by 45.88% than thatthat any valueP*of rainfallless than16.94 mmisaccumulatedprecipitation(mm)of Snyder. Also for Awon river catchment, theregarded as Zero.values obtained for SCS method is higher byThe runoff hydrograph peak flows obtained40.66% than that of Snyder. Likewise, for Ogunfor the catchments of Fawfaw, Oba, Awon,pa river catchment, the value obtained for SCSOgunpa, Opeki, Otin, Osun and Ogun Riversmethod is higher by 54.46% than that of Snyderbased on the two methods of synthetic unit hymethod. For Opeki river catchment, the valuesdrographs and various return periods are preobtained for SCS method is higher by 23.20%sented in Table 3.than that of Snyder. For Otin river catchment,() Table 3. Peak runoff hydrograph (m3/s)MethodsStorm return periods20yr, 24hr50yr, 24hrSnyder112.63143.70SCS304.43388.06100yr, 24hr200yr, 24hr500yr, 24hr171.28203.15352.34464.59556.52699.89Faw-Faw River catchmentOba River S1240.541581.351893.192267.812852.03Awon River 96Ogunpa River catchmentOpeki River 99.022513.93Otin River catchmentOsun River 92.725142.166466.84Ogun River catchment29
Journal of Ecological Engineering Vol. 18(1), 2017a)b)Figure 2. Runoff hydrograph of different return periods for Faw-faw River: a) SCS method, b) Snyder methoda)b)Figure 3. Runoff hydrograph of different return periods for Oba River: a) SCS method, b) Snyder method30
Journal of Ecological Engineering Vol. 18(1), 2017a)b)Figure 4. Runoff hydrograph of different return periods for Awon River: a) SCS method, b) Snyder methoda)b)Figure 5. Runoff hydrograph of different return periods for Ogunpa River: a) SCS method, b) Snyder method31
Journal of Ecological Engineering Vol. 18(1), 2017a)b)Figure 6. Runoff hydrograph of different return periods for Opeki River: a) SCS method, b) Snyder methoda)b)Figure 7. Runoff hydrograph of different return periods for Otin River: a) SCS method, b) Snyder method32
Journal of Ecological Engineering Vol. 18(1), 2017a)b)Figure 8. Runoff hydrograph of different return periods for Osun River: a) SCS method, b) Snyder methoda)b)Figure 9. Runoff hydrograph of different return periods for Ogun River: a) SCS method, b) Snyder method33
Journal of Ecological Engineering Vol. 18(1), 2017the values obtained for SCS method is higherby 39.11% than that of Snyder. For Osun rivercatchment, the values obtained for SCS methodis higher by 13.14% than that of Snyder method.For Ogun river catchment, the values obtainedfor Snyder method is higher by 52.06% thanthat of SCS method. This implies that, the percentage difference shows that for values of peakflows obtained by Snyder and SCS methods varies from 13.14% to 63.30%.The runoff hydrograph for the river catchmentbased on the unit hydrograph obtained with SCSmethod are presented in Figures 2a to 9a, whilethose obtained with Snyder method are presentedin Figures 2b to 9b for adoption at the study area.CONCLUSIONThe percentage difference for values of peakflows obtained with Snyder and SCS methodsvaries from 13.14% to 63.30%. However, SCSmethod is recommended because it utilized additional morphometric parameters such as watershed slope and the curve number (CN) which isa function of the properties of the soil and vegetation cover of the watershed in the estimationof ordinate required for the development of peakrunoff hydrograph in the river watersheds.REFERENCES1. Arora K.R. 2004. Irrigation, water power and waterResources Engineering. Standard Publishers Distributions, 1705-B, NAI SARAK, Delhi, 79–106.2. Chow V.T., Maidment D.R. and Mays L.W. 1988.Applied Hydrology: McGraw – Hill Publishingcompany, New York.3. Jones B.S. 2006. Five – minute unit hydrographsfor selected Texas Watersheds. M.Sc Thesis in Civil Engineering submitted to the Graduate Facultyof Texas Tech. University.344. Murray R.S and Larry J.S. 2000. Theory and Problems of Statistics. Third edition. Tata, McGrawHill Publishing Company Limited, New Delhi.5. Ogunlela A.O and Kasali. M.Y. 2002. Evaluationof four methods of storm hydrograph developmentfor an ungaged watershed. Published in NigerianJournal of Technological development. Faculty ofengineering and Technology, University of Ilorin,Ilorin, Nigeria (2), 25–34.6. Olofintoye O.O, Sule B.F and Salami A.W. 2009.Best-fit Probability Distribution model for peakdaily rainfall of selected Cities in Nigeria. NewYork Science Journal, 2(3).7. Ramirez J.A. 2000. Prediction and Modeling ofFlood Hydrology and Hydraulics. Chapter 11 of Inland Flood Hazards: Human, Riparian and AquaticCommunities. Edited by Ellen Wohl; CambridgeUniversity Press.8. Raghunath H.M. 2006. Hydrology: Principles,Analysis and Design. New Age International (P)Limited, Publishers, New Delhi. 2nd edition.9. Salami A.W. 2009. Evaluation of Methods of StormHydrograph Development. International EgyptianEngineering Mathematical Society IEEMS, Zagazig University Publications. International e-Journalof Egyptian Engineering Mathematics: Theory andApplication (6), 17–28 (http://www.ieems.net/iejemta.htm).10. SCS 2002. Soil Conservation Service. Design ofHydrograph. US Department of agriculture, Washington, DC.11. Varshney R.S. 1986 Engineering Hydrology. NEMChand & Bros, Roorkee (U.P), India.12. Viessman W., Knapp J.W. and Lewis G.L. 1989.Introduction to Hydrology, Harper and Row Publishers, New York, 149–355.13. Wanielista M.P. 1990. Hydrology and Water Quantity Control. John Willey and Sons. Inc.14. Warren V., Terence E.H. and John W.K. 1972. Introduction to hydrology. Intext Educational Publishers, 2nd edition, New York, 106–141.15. Wilson E.M. 1990. Engineering Hydrology. Macmillan Press Ltd. 2nd edition Houndmills, Basingstoke, Hampshire and London, 172–180.
of unit hydrograph and its linear systems theory. Furthermore, Viessman et al [1989], Wanielista [1990] and Arora [2004] presented the history and procedures for several unit hydrograph methods. Ramirez [2000] reported that the synthetic unit hydrograph of Snyder in 1938 was based on the study of 20 watersheds located in the Appalachian .Cited by: 7Publish Year: 2017Author: Wahab Adebayo Salami, Solomon Olakunle Bilewu, Biliyamin Adeoye Ibitoye, Mufutau Ayanniyi Ayanshola
Average Several UHG’s It is suggested that several unit hydrographs be derived and averaged. The unit hydrographs must be of the same duration in order to be properly averaged. It is often not sufficient to simply average the ordinates of the unit hydrographs in order to obtain the final unit hydrograph. A numerical average o
v Agriculture Handbook 590 Ponds—Planning, Design, Construction Tables Table 1 Runoff curve numbers for urban areas 14 Table 2 Runoff curve numbers for agricultural lands 15 Table 3 Runoff curve numbers for other agricultural lands 16 Table 4 Runoff curve numbers for arid and semiarid rangelands 17 Table 5 Runoff depth, in inches 18 Table 6 I a values for runoff curve numbers 21
2 Unit-III 1) Runoff: Runoff, sources and component, classification of streams, factors affecting runoff, Estimation Methods. Measurement of discharge of a stream by Area-slope and Area-velocity methods. 2) Hydrograph: Flood hydrographs and its components, Base flow & Base flow separation, S-Curve technique, unit hydrograph, synthetic hydrograph.
v Agriculture Handbook 590 Ponds—Planning, Design, Construction Tables Table 1 Runoff curve numbers for urban areas 14 Table 2 Runoff curve numbers for agricultural lands 15 Table 3 Runoff curve numbers for other agricultural lands 16 Table 4 Runoff curve numbers for arid and semiarid rangelands 17 Table 5 Runoff depth, in
Clifford E. and Melda C. Snyder Loan Fund Application Revised April 27, 2018 1 Clifford E. and Melda C. Snyder Loan Fund APPLICATION DUE DATE IS APRIL 15 Purpose The Clifford E. and Melda C. Snyder Loan Fund was established under the Last Will and Testament of Melda C. Snyder who died on March 18, 1987. The income of the fund is
great it is the influence of the culture in this ancient oriental land on Snyder's works. Patrick D. Murphy reveals in his book A Place for Wayfaring—The Poetry and Prose of Gary Snyder that during college and the early years in San Francisco, Snyder's favorite poet was Ezra Pound according to Kerouac and other friends.
GARY SNYDER A Bibliography of Works By and About Gary Snyder Based in part on the Gary Snyder Papers and Other Holdings of the University of California, Davis. . SMOKEY THE BEAR SUTRA. 1969 A18a. "Merry Chri
Academic writing introductions tips with useful phrases Start the introduction by answering the question which you have been set or you have set yourself (“I believe that the government’s policy on ” etc). Start the introduction by setting out the background to the question that you have been set or have set yourself (“In our globalised society, ”, “Over the last few years .
