8 hydrograph analysis

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ERT 246 Hydrology and Water Resources1HYDROGRAPH ANALYSISRiver gauging produces discharge (flow) data of a cross-sectional area of an outlet point of a watershedContinuous recording of discharge data with respect to time will produce a discharge-time (Q-t) relationship of the watershedHydrographA record and graphical representation of discharge (Q) as a function of time (t) at a specific location, for example, the discharge at a point in a river or the discharge from a pumping wellDischarge of a river are fluctuated (up and down) due to the rainfall condition. How river response to rainfall.The shape of hydrograph is depending on the shape of the watershed & the rainfall pattern

1ERT 246 Hydrology and Water Resources2Effect of Watershed shape on Hydrograph shapeABCBACQtDifferent shape would produce different Tc2ERT 246 Hydrology and Water Resources3Natural HydrographA natural hydrograph: An observed Q-t relationship of a watershed due to rainfall eventA rainfall event produces a single hydrographA natural hydrograph has important characteristics:Rising point (abrupt) (a)Rising limb (b)Peak flow (c)Falling limb (d)Inflection point (e)

Time (hr)Q(m3/s)bcead3ERT 246 Hydrology and Water Resources4Main Component of HydrographDirect flow (quick flow, effective flow) (Qe)That part of the flood hydrograph that represents the fastest response to rainfall and that is distinct from the base flow. Base flow (slow flow) (Qb)That part of the stream discharge that is not attributable to direct runoff from rainfall or melting snow, it is usually sustained by groundwater. Basin lag (tL) The time difference between the centroids of rainfall excess and its corresponding peak surface runoff produced in the watershed

t(jam)Q(m3/s)i(mm/j) Effective Rainfall, PeIndek QptL Inflection point QeQbQbBaseflow line4ERT 246 Hydrology and Water Resources5Base flow separation techniqueNatural hydrograph consists of two main components, i.e. Direct flow, Qe (quick flow) & Base flow (slow flow) (Qb).The quantity of Qe is important to know because it represents the volume flood and fresh water supply produced by individual rainfallTherefore it is important to separate the base flow from the total flowVarious techniques.Empirical formula: N = b A 0.2A = area (km2)b = constant = 0.8, depending on watershed characteristicsN = time lag after Qp (day) Constant-discharge methodConstant-slopeMaster Depletion CurveDigital filter for continuous hydrograph t(jam)Q(m3/s)QpTitik infleksiN5Master depletion curve method

use when the most accurate model of hydrograph recessions is needed combine data from several recessions to make general recession model from this an equation of the form can be derived, which gives discharge at any time after discharge is measured

ERT 246 Hydrology and Water Resources6

Eg: Total volume of Effective Runoff = Total Surface area under the curveERT 246 Hydrology and Water Resources8IIIIIIIVVVIERT 246 Hydrology and Water Resources9Baseflow Separation lineQuick/fast/direct flowSlow/base flowTotal Volume of direct flow = Total surface area = Qe * dt = 33 m3/s * 3600 s ERT 246 Hydrology and Water Resources10Unit Hydrograph (UH)Hydrograph of one unit surface runoffUnit hydrographThe discharge at a point, expressed as a function of time, due to a unit of effective rainfall that is applied uniformly over the contributing area during a specified period of time (D). Hydrograph resulted from one unit of effective rainfall spread uniformly over the watershed for a given durationAssumptions:Effective rainfall is directly proportional to direct runoff2 Unit Effective rainfall will produce 2 unit hidrographSuperposition:2 effective rainfall successively produce 2 successive UH with time lag TWhy need to establish Unit Hydrograph?

10ERT 246 Hydrology and Water Resources11Establishing UH from Natural HydrographObtain a natural hydrograph from a known effective rainfall (D) and duration (T)Separate its base flowObtain the ordinate of the direct runoffCompute the total volume (depth)of the direct runoffCompute the ordinate of UH by dividing the ordinate of direct runoff to that the total depth of direct runoffPlot UH having 3 important parameters, Peak flow(Qp), Time to peak (Tp), base time (Tb)

11ERT 246 Hydrology and Water Resources12Eg: Unit HydrographColumn (1) and (2) is the coordinateof a natural Hydrograph generatedby 2 hour effective rainfall of 100 Hawatershed. Establish its Unit Hydrograph.

t (hr)Qt (m3/s)Qb(m3/s)Qe(m3/s)UH (m3/s/cm)05500.0016510.0829540.34314590.764155100.84510550.4268530.2576510.0885500.0033 m3/s12ERT 246 Hydrology and Water Resources13Eg: Unit HydrographEffective rainfall duration, T=2hrSeparate its baseflow (column 3)Obtain ordinate of the effective hydrograph (Column 4)Compute total depth of runoff (11.88 cm or 11.88 unit)Compute the ordinate of UH by dividing the ordinate of direct runoff to that the total depth of direct runoffPlot UH having 3 important parameters, Peak flow(Qp), base time (Tb)

13ERT 246 Hydrology and Water Resources14Changing the duration of UHS-Curve methodThe established T-UH is not always applicable because of different duration of effective rainfallS-Curve: method of deriving a UH for a desired duration from one of another durationEg: 2Hr - UH to 3 Hr-UHProcedures: An S-curve is constructed from a series of UH of several T by the simple process of successive displacement by T and summing up the ordinatesWhy need to change the duration of UH?

14ERT 246 Hydrology and Water Resources15Eg: S-Curve methodConvert the 2Hr-UH in the previous example (page 10) to 3Hr-UH, using S-Curve methodSteps (refer to Table pg.13):Obtain the ordinate of the original 2Hr-UH (column 2)Lagged the 2Hr-UH ordinate for 2 hours several times (column 3, 4, 5, 6, )Summing-up all the ordinate (column 2+3+4+..) to form S-curve ordinate (Column 6)The plots of the lagged ordinates and S-curve is shown in Figure.

S-Curve15ERT 246 Hydrology and Water Resources16Eg: S-Curve method (cont.)

(1) (2) (3) (4) (5) (6) 16ERT 246 Hydrology and Water Resources17Eg: S-Curve method (cont.)Steps (Cont.) (Refer Table on the right)Obtain ordinate S-Curve (column 2)Lagged ordinate S-curve 3 Hrs (column 3)Subtract ordinate S-curve to 3Hr lagged Curve (Column 4=column 2- column 3)Obtain a new UH-3Hr by multiplying column 4 with 2/3 (column 5) Plot the UH-2 Hr and UH-3Hr in one graph to see the different

(2)(3) (4) (5)

17ERT 246 Hydrology and Water Resources182Hr-UH to 3Hr-UH

2Hr-UHQp=1.39Tb=7Hrs

3Hr-UHQp=1.12Tb=8.5 hrs2Hr-UH3Hr-UH18ERT 246 Hydrology and Water Resources19Obtaining natural hydrograph from multiple rainfall from UHHaving UH, natural hydrograph from multiple rainfall (many rainfall) can be obtainedEg. Using 1Hr-UH, obtain natural hydrograph generated by 4 rainfall events as shown below

19ERT 246 Hydrology and Water Resources20multiple rainfall from UH

20ERT 246 Hydrology and Water Resources21

2.54.5 01.021ERT 246 Hydrology and Water Resources22Synthetic Unit HydrographA make-up (artificial) UH based on empirical relationship of key UH parametersNot all watersheds has their own UHMany watersheds are ungauged (no flow data)Many methods: Snyder, SCS, Epsey5 important key parameters: Qp (peak flow), Tp (time to peak), Tb (base time), D (duration of rainfall)

QpTpDTb22ERT 246 Hydrology and Water Resources23a.Tempoh mencapai Qp, tp

tp= Ct (L*Lca)0.3Ct = pekali empirikal (bergantung kepada kawasan tadahan) 0.2 2.2L = panjang sungai (km)Lca= panjang sungai dari titik tumpuan ke pusat graviti kawasan tadahanc.g.LcaERT 246 Hydrology and Water Resources24b.Tempoh hujan berkesan, trtr = tp/5.5c.Kadar alir puncak, QpQp = Cp A/tpCp = pekali empirikal = 2.0 6.5A = keluasan tadahan (km2)tp = tempuh puncakd.Tempoh aliran dasar (base time), TbTb = 3 + 3 (Tp/24) hari atau Tb = 5 TpERT 246 Hydrology and Water Resources25Synthetic Unit Hydrograph (Snyder Method)Qp = (640 Cp A )/Tp (cfs)Tp = Ct (L Lc)0.3 (hr) A = watershed area (mile2)Tb = 3 + Tp/8 (days)Cp = storage coefficient (0.4-0.8)Ct = watershed coefficient (1.8-2.2)Lc = length along channel to watershed centroid (miles)L = length of main stream (miles)

25Problem SetERT 246 Hydrology and Water Resources26Time0306090120150180210240270300330360390Runoff (m3/s)01.22.81.71.41.21.10.910.740.610.500.280.170The 30-min Unit Hydrograph for a 2.25 km2 catchment is given by:Determine the S-hydrographCalculate the 40-min unit hydrographVerify that the 40-min unit hydrograph correspond to a 1-cm rainfall excessChart60000000.099206349211110.09920634920.396825396802220.39682539681.19047619050.09920634923331.28968253971.38888888890.39682539680441.78571428570.79365079371.19047619050.0992063492552.08333333330.39682539681.38888888890.3968253968062.182539682500.79365079371.19047619050.099206349272.083333333380.39682539681.38888888890.396825396802.1825396825900.79365079371.19047619050.09920634922.083333333310100.39682539681.38888888890.39682539682.1825396825

Original Ordinate UH-2Hr1st 2Hr lag2nd-2Hr lag3rd- 2Hr lag4th 2-Hr lagS-Curve Ordinate (1)+(2)+(3)+Time (Hrs)Q (m3/s)

Sheet1t (j)012345678932.53.559107531.5t (Hr)03300Time(Hr)Original Ordinate UH-2Hr1st 2Hr lag2nd-2Hr lag3rd- 2Hr lag4th 2-Hr lagS-Curve Ordinate (1)+(2)+(3)+1330000.000.0023.530.50.099206349210.100.1035320.396825396820.400.000.4049361.190476190531.190.101.29510371.388888888941.390.400.001.7967340.793650793750.791.190.102.0875320.396825396860.401.390.400.002.188330070.000.791.190.102.089330080.401.390.400.002.187740090.000.791.190.102.0821.5100.401.390.402.185.04t (Hr)031323.5354951067758393

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Sheet1t (j)012345678932.53.559107531.5t (Hr)03300Time(Hr)Original Ordinate UH-2Hr1st 2Hr lag2nd-2Hr lag3rd- 2Hr lag4th 2-Hr lagS-Curve Ordinate (1)+(2)+(3)+1330000.000.0023.530.50.099206349210.100.1035320.396825396820.400.000.4049361.190476190531.190.101.29510371.388888888941.390.400.001.7967340.793650793750.791.190.102.0875320.396825396860.401.390.400.002.188330070.000.791.190.102.089330080.401.390.400.002.187740090.000.791.190.102.0821.5100.401.390.402.185.04t (Hr)031323.5354951067758393

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Sheet2000.09920634920.39682539681.19047619051.38888888890.79365079370.396825396800


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Sheet1t (j)012345678932.53.559107531.5t (Hr)03300Time(Hr)Original Ordinate UH-2Hr1st 2Hr lag2nd-2Hr lag3rd- 2Hr lag4th 2-Hr lagS-Curve Ordinate (1)+(2)+(3)+Time(Hr)S-Curve OrdinateLagged 3Hr SCurve OrdinateS-Curve Ordinate - Lagged 3HrsNew UH-3HrOriginal Ordinate UH-2HrNew UH-3Hr1330000.000.0000.000.000.000.00023.530.50.099206349210.100.1010.100.100.070.100.066137566135320.396825396820.400.000.4020.400.400.260.400.264550264649361.190476190531.190.101.2931.290.001.290.861.190.8597883598510371.388888888941.390.400.001.7941.790.101.691.121.391.124338624367340.793650793750.791.190.102.0852.080.401.691.120.791.124338624375320.396825396860.401.390.400.002.1862.181.290.890.600.400.59523809528330070.000.791.190.102.0872.081.790.300.200.000.19841269849330080.401.390.400.002.1882.182.080.100.070.06613756617740090.000.791.190.102.0892.082.18-0.10-0.07-0.066137566121.5100.401.390.402.18102.182.080.100.070.06613756615.04t (Hr)031323.5354951067758393

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Chart8000.09920634920.06613756610.39682539680.26455026461.19047619050.85978835981.38888888891.12433862430.79365079371.12433862430.39682539680.595238095200.198412698480.06613756619-0.0661375661100.0661375661

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Sheet1t (j)012345678932.53.559107531.5t (Hr)03300Time(Hr)Original Ordinate UH-2Hr1st 2Hr lag2nd-2Hr lag3rd- 2Hr lag4th 2-Hr lagS-Curve Ordinate (1)+(2)+(3)+Time(Hr)S-Curve OrdinateLagged 3Hr SCurve OrdinateS-Curve Ordinate - Lagged 3HrsNew UH-3HrOriginal Ordinate UH-2HrNew UH-3Hr1330000.000.0000.000.000.0000.00023.530.50.099206349210.100.1010.100.100.0710.100.066137566135320.396825396820.400.000.4020.400.400.2620.400.264550264649361.190476190531.190.101.2931.290.001.290.8631.190.8597883598510371.388888888941.390.400.001.7941.790.101.691.1241.391.124338624367340.793650793750.791.190.102.0852.080.401.691.1250.791.124338624375320.396825396860.401.390.400.002.1862.181.290.890.6060.400.59523809528330070.000.791.190.102.0872.081.790.300.2070.000.19841269849330080.401.390.400.002.1882.182.080.100.0780.06613756617740090.000.791.190.102.0892.082.18-0.10-0.079-0.066137566121.5100.401.390.402.18102.182.080.100.07100.06613756615.04t (Hr)031323.5354951067758393

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Sheet1t (j)012345678932.53.559107531.5t (Hr)03300Time(Hr)Original Ordinate UH-2Hr1st 2Hr lag2nd-2Hr lag3rd- 2Hr lag4th 2-Hr lagS-Curve Ordinate (1)+(2)+(3)+Time(Hr)S-Curve OrdinateLagged 3Hr SCurve OrdinateS-Curve Ordinate - Lagged 3HrsNew UH-3HrOriginal Ordinate UH-2HrNew UH-3Hr1330000.000.0000.000.000.0000.00023.530.50.099206349210.100.1010.100.100.0710.100.0661375661Time (hr)Ordinate 1Hr-UH35320.396825396820.400.000.4020.400.400.2620.400.26455026460049361.190476190531.190.101.2931.290.001.290.8631.190.8597883598150510371.388888888941.390.400.001.7941.790.101.691.1241.391.1243386243216067340.793650793750.791.190.102.0852.080.401.691.1250.791.1243386243322575320.396825396860.401.390.400.002.1862.181.290.890.6060.400.595238095241858330070.000.791.190.102.0872.081.790.300.2070.000.198412698451259330080.401.390.400.002.1882.182.080.100.0780.06613756616807740090.000.791.190.102.0892.082.18-0.10-0.079-0.066137566174521.5100.401.390.402.18102.182.080.100.07100.06613756618205.0490t (Hr)031323.5354951067758393

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Sheet1t (j)012345678932.53.559107531.5t (Hr)03300Time(Hr)Original Ordinate UH-2Hr1st 2Hr lag2nd-2Hr lag3rd- 2Hr lag4th 2-Hr lagS-Curve Ordinate (1)+(2)+(3)+Time(Hr)S-Curve OrdinateLagged 3Hr SCurve OrdinateS-Curve Ordinate - Lagged 3HrsNew UH-3HrOriginal Ordinate UH-2HrNew UH-3Hr1330000.000.0000.000.000.0000.00023.530.50.099206349210.100.1010.100.100.0710.100.0661375661Time (hr)Ordinate 1Hr-UHTime (hr)Rainfall (cm)35320.396825396820.400.000.4020.400.400.2620.400.264550264600049361.190476190531.190.101.2931.290.001.290.8631.190.859788359815012.5510371.388888888941.390.400.001.7941.790.101.691.1241.391.1243386243216024.567340.793650793750.791.190.102.0852.080.401.691.1250.791.124338624332253075320.396825396860.401.390.400.002.1862.181.290.890.6060.400.59523809524185418330070.000.791.190.102.0872.081.790.300.2070.000.198412698451259330080.401.390.400.002.1882.182.080.100.0780.06613756616807740090.000.791.190.102.0892.082.18-0.10-0.079-0.066137566174521.5100.401.390.402.18102.182.080.100.07100.06613756618205.0490t (Hr)031323.5354951067758393

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Sheet1t (j)012345678932.53.559107531.5t (Hr)03300Time(Hr)Original Ordinate UH-2Hr1st 2Hr lag2nd-2Hr lag3rd- 2Hr lag4th 2-Hr lagS-Curve Ordinate (1)+(2)+(3)+Time(Hr)S-Curve OrdinateLagged 3Hr SCurve OrdinateS-Curve Ordinate - Lagged 3HrsNew UH-3HrOriginal Ordinate UH-2HrNew UH-3Hr1330000.000.0000.000.000.0000.00023.530.50.099206349210.100.1010.100.100.0710.100.0661375661Time (hr)Ordinate 1Hr-UHTime (hr)Rainfall (cm)Time (hr)Ordinate 1Hr-UH2.5*UH4.5*UH0*UH1*UHTotal (Natural)35320.396825396820.400.000.4020.400.400.2620.400.264550264600000049361.190476190531.190.101.2931.290.001.290.8631.190.859788359815012.515000510371.388888888941.390.400.001.7941.790.101.691.1241.391.1243386243216024.52160125012567340.793650793750.791.190.102.0852.080.401.691.1250.791.12433862433225303225400225062575320.396825396860.401.390.400.002.1862.181.290.890.6060.400.59523809524185414185562.5720001282.58330070.000.791.190.102.0872.081.790.300.2070.000.198412698451255125462.51012.505015259330080.401.390.400.002.1882.182.080.100.0780.0661375661680680312.5832.5016013057740090.000.791.190.102.0892.082.18-0.10-0.079-0.0661375661745745200562.50225987.521.5100.401.390.402.18102.182.080.100.07100.0661375661820820112.53600185657.55.04909050202.50125377.51009008017011004545t (Hr)Ordinate U12020200313001323.5354951067758393

Sheet1333.559107533

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Sheet2000.09920634920.39682539681.19047619051.38888888890.79365079370.396825396800


Sheet30000000.099206349211110.09920634920.396825396802220.39682539681.19047619050.09920634923331.28968253971.38888888890.39682539680441.78571428570.79365079371.19047619050.0992063492552.08333333330.39682539681.38888888890.3968253968062.182539682500.79365079371.19047619050.099206349272.083333333380.39682539681.38888888890.396825396802.1825396825900.79365079371.19047619050.09920634922.083333333310100.39682539681.38888888890.39682539682.1825396825


000.09920634920.06613756610.39682539680.26455026461.19047619050.85978835981.38888888891.12433862430.79365079371.12433862430.39682539680.595238095200.198412698480.06613756619-0.0661375661100.0661375661

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Chart11000000111012502212540022503625562.5720001282.5462.51012.50501525312.5832.501601305200562.50225987.5112.53600185657.550202.50125377.50900801701100454512120202013131300

2.5*UH4.5*UH0*UH1*UHTotal (Natural)Time (hr)Q (m3/s)


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8 hydrograph analysis

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