Ministry of Publick Works Bandung INDONESIA

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1 A GENERAL PROCEDURE FOR DETERMINING A SYNTHETIC UNIT HYDROGRAPH BASED ON MASS CONCERVATION PRINCIPLE. DEVELOPMENT OF ITB- AND ITB-2 SYNTHETIC UNIT HYDROGRAPH METHOD D.K. Natakusumah, W. Hatmoko 2 and D. Harlan Faculty of Civil and Environmental Engineering Institute of Technology Bandung Bandung 402 INDONESIA 2 Research Center Water Resources, Agency for Research and Development Ministry of Publick Works Bandung 405 INDONESIA dantje2009@gmail.com, dhemi70@yahoo.com, whatmoko@yahoo.com Abstract: Synthetic unit hydrograph methods are popular and play an important role in many water resources design and analysis of ungagged watersheds. These methods are simple, requiring only an easy determination of watershed characteristics such as catchment area and river length. In some cases it may also include land use characteristics. Therefore, these methods serve as useful tools to simulate runoff from watersheds undergoing land use change. In this paper a simple and accurate approach for determining a consistent Synthetic Unit Hydrograph (SUH) based on mass conservation principles and its application in the development of ITB- and ITB-2 SUH is presented. Some applications of the method in computing design flood of small and medium size catchment are also presented. The results show that, although input data required by ITB- and ITB-2 SUH are simple and the calculation is eassy, but the final results agree well with other methods developed earlier. Keywords: Synthetic Unit Hydrograph (SUH), mass conserving SUH calculation procedure, ITB- and ITB-2 SUH, flood hydrograph, hydrology.. INTRODUCTION Synthetic unit hydrograph method (SUH), initially proposed by Sherman in 922, is still a widely used tool in hydrologic analysis and synthesis especially for ungagged watershed. The term synthetic in synthetic unit hydrograph denotes the unit hydrograph (UH) derived from watershed characteristics rather than rainfall-runoff data.these methods are popular and play an important role in many water resources design and analysis of ungagged watersheds. These methods are simple, requiring only an easy determination of watershed characteristics such as catchment area and river length. These methods serve as useful tools to simulate runoff from ungagged watersheds. When land use characteristics are included, these methods serve as useful tools to simulate runoff from watersheds undergoing land use change. To develop a synthetic unit hydrograph, several techniques are available. Several most popular unit hydrographs models such as HEC-HMS, Nakayasu, Snyder-Alexeyev, SCS, and GAMA- are available and commonly used in Indonesia for developing either peak discharge rate, volume or a runoff hydrograph. Some of the parameters used in the UH equations are empirical; the model is limited to physiolographic conditions of the catchment. Therefore, model should be evaluated with the local data. This paper presents one of the results of research in the Program for Research Capacity Building at Institute Technology Bandung (ITB), Indonesia, 200. This one year research project was aimed to develop a General Procedure Calculation of Synthetic Unit Hydrograph (SUH) and Development of ITB ITB- and SUH-2 Synthetic Unit Hydrograph". This general procedure was initially proposed by Natakusumah (2009) and later implemented by Natakusumah, Hatmoko and Harlan (200) for developing ITB- and ITB-2 Synthetic Unit Hydrograhps.

2 2. PROPOSED PROCEDURE The most popular SUH method used is the Soil Conservation Service (SCS) curvilinear unit hydrograph. It is derived from the analysis of large number of natural UH s for the catchments of varying size and geographic locations. This method is based on the assumption that the same unit hydrograph shape applies to all catchments; only the scale differs. Following the approach developed by SCS and later followed by Nakayasu, Alexeyev and others, we also derived a unit hydrograph calculation procedure where the unit hydrograph is dimensionless with axis of q=q/qp and t=t/tp, in which Q equals the discharge rate at any time T, and Qp equal the peak discharge at peak time Tp. To define a complete shape of SUH, three characteristics of SUH are required. The three characteristics are ) Basin Lag (TL) and Time to Peak (Tp), 2) Basic shape of SUH and ) adjustable peak discharge (Qp) per unit rainfall depth. 2.. Basin Lag and Time To Peak The basin lag is an important parameter in computing unit hydrograph, but it is sometimes difficult to estimate its value in real world situations. Many empirical equations of time lag and its relation to time to peak have been proposed in the literatures. The proposed method is very flexible in adopting Time lag and Time to peak formula, and some of them are listed in Table-. Table : Time lag Formulas and its relation to time to peak Method Time Lag Time To Peak Remarks Kirpich Snyder Nakayasu SCS 0.77 L Tc S For small chatcment (A < 2 km 2 ) 0. TL =(L Lc) L TL = L (L <5 km) (L 5 km) CN TL = L CN S Tp 2 / Tc Te Tp / 5.5 Te Tr Tp = tp (Tr - Te) T p Te < Tr Tp = tp Tr Tp.6 TL Tp TL 0.5 Tr Tc = Ttime lconcentration (hr) L = River Lenght (km) Te = Eff rainfall duration (hr) S = Ccatchment slope (m/m) Tp = ttime to peak (hr) TL = time lag (hours) L = River Lenght (km) Lc = Center to outlet lenght (km) Te = Eff rainfall duration (hour) Tr = unit duration (hour) Tp = ttime to peak (hour) TL = time lag (hours) L = River Lenght (km) Tr = unit duration (hour) Tp = ttime to peak (hour) TL = time lag (hours) L = River Lenght (km) S = Ccatchment slope (m/m) CN = Curve number (50-95) Tr = unit duration (hour) Tp = ttime to peak (hour) 2.2. Basic Shape of SUH Unlike SCS, Nakayasu and Alexeyev methods that use specific UH Shape, the proposed method is very flexible in adopting any basic shape representing UH shape (triangular, cirvilinear etc). Although, the proposed method is equaly applicable to any basic shape for SUH, in this reseach, however, we proposed adjustable SUH shape synthesized by using either a simple single function (ITB- SUH) or two simple functions (ITB-2 SUH) as follows. a) Single Function (ITB-) C p q(t) exp2 t (t > 0) =.500 () t b) Two Functions (ITB-2) Rising Limb : C Recession Limb : q(t) exp t p q (t) t (0 t ) = (2.a) (t>) =.000 (2.b)

3 Value of α and β coefficients can be change by changing Cp (Peak Coefficient). Figure shows the relation of the peak discharge parameter q=q/qp and t=t/tp from equation of ITB- and ITB-2 SUH..20 ITB-2 SUH ITB-2 SUH q=q/qp t=t/tp Figure : Typical shape of ITB- and ITB-2 SUH (dimensionless) 2.. Peak Discharge of SUH Peak Discharge of UH was derived by following the definition unit hydrograph and the principle of mass conservation. Figure 2.a and Figure 2.c shows two typical shape of UH (triangular and culvilinear shape) of a catchment generated by rainfall excess R (mm). By dividing absis and ordinates of UH by Tp and Qp, we obtain dimensionless UH show Figure 2.b and Figure 2.d. Qp=5 m/s VSUH = /2*(8 s)*(5 m/s) =20 m ASUH= /2*(4*) = 2 (exact) VSUH = Qp*Tp* A SUH = (5 m/s)*(2 s)*(2) = 20 m Non-Dimensionalized by Qp and Tp 0 0 Tp=2 s 4 (a) Triangular SUH Tb=8 s (b) Triangular SUH (dimensionless) Qp VSUH = Volume of SUH (m) A SUH= Area of SUH (Computed Numerically) VSUH= Qp*Tp* ASUH Non-Dimensionalized by Qp and Tp 0 0 Tp Tb/Tp (c) Curvilinear SUH Tb (d) Curvilinear SUH (dimensionless) Figure 2 : Simple Approach for Calculating UH Volume from Dimensionless UH By referring to these figures, a simple approach for caculating UH volume from dimensionless UH is given as. V UH = Qp Tp A UH = Qp Tp 600 A UH (m) (4) Where V HU = volume of UH (m ), Qp = peak of UH (m /s), A UH = area of UH (dimensionless). Please note that A UH can be computed exactly or numerically (e.q. using trapeziodal rule),

4 The Unit Hydrograph (UH) of a catchment, according to Ramirez (2000) is defined as the direct runoff hydrograph resulting from a unit excess rainfall depth of constant intensity and uniformly distributed over the watersheed. Folowing this definition, volume of rainfall excess can be computed as V RE = A CA R 000 (m) () Where V RE = total volume of unit excess rainfall (m), A CA = Area of the wathershed (km2), R= unit excess rainfall depth (mm). By applying principle of mass conservation V RE = V UH, we obtained Qp Tp 600 A UH = A CA R 000 Therefore the peak discharge can be writtes as follows Q p R.6 Tp A A CA UH (m/s) (5) In which Qp = the peak discharge in m /s; R= unit excess rainfall depth (mm); A CA = the catchment area (km 2 ); A UH = the area of unit hydrograph (dimensionless), computed exactly or numerically (e.q. using trapeziodal rule).. APPLICATION.. Flood hydrograph of a Small Cathment The first example application of ITB method is on a small wathershed with cathment area of.2 km2, river Length of.570 km and catchment Slope of 000. To show flexibibility of the proposed method in adopting basic shape of UH, a triangular UH shown in Figure was used to generate flood hydrograph due to excess rainfall of 0 mm, 70 mm and 0 mm (half-hour interval). qp= AHSS /2**+/2*(+/)*+/2**/=5/ qp=/ 0 tp= t=2 tb=5 Figure : Abritrary Triangular SUH (Dimensionless) a) Compute Time to Peak (Tp) and Time Base (Tb) For small cathment, time Concentration is computed using Kirpirch formula t c L S min ute.4 hour Time Peak (Tp) dan Time Base (Tb) 2 2 Tp tc hour 8 8 Tb tp hour b) Compute Triangular SUH. Compute Area of Triangular SUH AHSS A A2 A (/2 * * ) + {/2 * (+ /) * } + (/2 * * /) = 5/ Exact value

5 2. Compute Peak Dicharge of SUH Qp R.6 Tp A A CA SUH m. Dimesionalised SUH by mutiplying absis and ordinate of dimensionless SUH in Figure by Tp and Qp, and the resut is shown in Figure 4. Ordinates of SUH between 0 and Tp and between Tp and Tb (obtained using linear interpolation) is shown in table below. m/s / s T (hour) Q (m/s) Note Qp=0.224 Q= Tp *Tp Tb = 5 Tp Tp=0.89 T=.786 Tb=4.466 Hour Figure 4 : Triangular SUH (Dimensionalised) c) The superposition process of 0 mm, 70 mm and 0 mm rainfall excess (half-hour intervals), is shown in Table 2 and the final hydrograph result is shown in Figure 5. (Note : Ratio of DRO/RE < 00% was caused by the exlusion of peak discharge (Qp,Tp) from superposition process) Table 2 : Superposition of Triangular SUH Time (Hour) Q SUH (m/s) SUH Convolution Total (mm Volume (m) , , , , , , , , , , Total Volum (m) 29,570 C. Area (km2).200 DRO (mm) DRO/RE (%) 98.6% Reff Total Q (jm/s) R (mm) T (Hour) Figure 5 : Superposition process of flood hydrograph from Triangular SUH

6 .2. Flood Hydrograph of Cibatarua Watersheed The second example application of ITB method is computation flood Hydrograph of Cibatarua River. The resulting flood hydrographs were compared with the results of Snyder-Alexeyev (Cp=0.62), Nakayasu (α =.7), Limantara and GAMA- method. Input requirement for each methods are shown in Table. Calculation procedure for generating ITB- and ITB-2 SUH are shown in Table 5 and Table 6. In this example, time lag for ITB- SUH was calculated using Snyder method, while for ITB-2 time lag was calculated using Nakayasu formula. The incremental rainfall excess shown in Table 4 used to generate the storm hydrograph was obtained by subtracting the incremental infiltration from the rainfall. Furthermore, the storm hydrograph was derived from a multiperiod of rainfall excess called hydrograph convolution. It involves multiplying the unit hydrograph ordinates by incremental rainfall excess, adding and lagging in a sequence to produce a resulting storm hydrograph. This process is shown in Table 7 and Table 8. Comparison of flood discharge of Cibatarua River calculated by ITB-, ITB-2, Nakayasu, Snyder- Alexeyev, Limantara and GAMA- as well as software HEC-HMS results are shown in Figure 6. This figure show that the results of SUH ITB- is very close to the resukys of Snyner-Alexeyev and HEC- HMS, while the ITB-2 SUH are very close to the method Nakayasu. This example results show that, although input data required by ITB- and ITB-2 SUH are simple and the calculation process is eassy, but the final results agree well with other methods developed earlier. Table : Input requirement for each methods Table 4 : Rainfall Excess and Infiltration Physical Data Value Unit Non-Physical HSS Snyder Alexeyey A Catchment area km2 Ct.000 L River Lenght 2.50 km Cp Lc River Lenght from Centre to Outlet km HSS Nakayasu A Catchment area km2 α.700 L River Lenght 2.50 km HSS Gama- A Catchment area km2 L River Slope 2.50 km S River Lenght m/m J Number of 'st Order River 6 river Js Number of River (all order) 2 river L First order river lenght 75.0 km Ls Over all River lenght (all Order) km WL Cathment Width at 0.25L km WU Cathment Width at 0.75L 6.0 km AU CA Upstream of Centroid km2 HSS Limantara A Catchment area km2 L River Lenght 2.50 km n River Roughness (Manning) 0.04 S River Slope HSS ITB- dan HSS ITB-2 A Catchment area km2 Ct.000 L River Lenght 2.50 km Cp.000 Time Reff (mm) Inf (mm) Total Inf (mm) Reff (mm) ITB- ITB-2 Alexeyev (Cp=0.62) Nakayasu (α =.70) Gama- Limantara HEC-HMS (Cp=0.62) Q (jm/s) R (mm) Figure 6 : Comparison Results of ITB- SUH and ITB-2 SUH with the Results of Snyder- Alexeyev (Cp=0.62), Nakayasu (α =.7), Limantara, GAMA- and HEC-HMS Results T (Jam)

7 Table 5 : ITB- SUH Calculation For Cibatarua C.A (T.L Snyder) I. Characteristic of Watershed and Rainfall Excess. River Name = Cibatarua 2. Cathment Area (A) = Km 2. River Lenght (L) = 2.5 Km 4. Unit Rainfall Excess (R) =.00 mm 5. Unit Rainfall Duration (Tr) =.00 Hour II. Computation of Time Peak (Tp) and Time Base (Tb). Time Coefficient (C t ) = Time Lag --> Snyder 2 LC = 0.5*L = km TL = Ct(LxLC) n =.64 Hour Te = tp/5.5 = 0.66 Hour TP = TL+0.25(Tr-Te) Te > Tr TP = TL+0.50Tr Te < Tr. Time to Peak 4.4 Hour Tp = = 4.4 Hour 4. Time Base T B /T P = 0 (Ratio T B /T P ) T B = 4.4 Hour III. Peak Discharge (QP). Peak Coefficient (C p ) = Alpha =.500. Area of SUH (Sum Col-4 Part IV) =.6 4. Qp = /(.6Tp)*(A DAS /A SUH ) = 2.70 m/s 5. Rainfall Volum (=R*A CA*000) = 56,920 m 6. Vol. of SUH (V SUH) Sum of Col 6 = 56,920 m 7. DRO Depth (V SUH/A CA/000) =.000 mm IV. Computatuion of ITB- SUH : T SUH (dimensionless) SUH (dimensionalised) (hour) t=t/tp q=q/qp A Q(m/s) V(m) ( ) ( 2 ) ( ) ( 4 ) ( 5 ) ( 6 ) Area SUH Vol (m) DRO (mm).000 Remark Col- : Given Time Interval (Hour) T i =T i- + Tr Col-2 : Dimensionless Time t=t/tp Kolom- /Tp Col- : Dimensionless Ordinate q=q/qp from ITB- Equation Curve Col-4 : Area of SUH A i = ½ (t i -t i- ) (q i + q i- ) (dimensionless) : Sum of Column-4 = A SUH (Important for Computing Qp) Col-5 : Dimensionalised Qi Q i = q i Qp (Kolom x Qp) Col-6 : Area of SUH (m) A i = ½ 600 x (T i -T i- ) (Q i + Q i- ) : Sum of Column-6 (V SUH ) if divided by A CA shoild be = Table 6 : ITB-2 SUH Calculation For Cibatarua C.A (T.L Nakayasu) I. Characteristic of Watershed and Rainfall Excess. River Name = Cibatarua 2. Cathment Area (A) = Km 2. River Lenght (L) = 2.5 Km 4. Unit Rainfall Excess (R) =.00 mm 5. Unit Rainfall Duration (Tr) =.00 Jam II. Computation of Time Peak (Tp) and Time Base (Tb). Time Coefficient (C t ) = Time Lag --> Nakayasu TP =.6 TL TL = Ct*0.2*L 0.7 < 5 km = Ct*( *L) 5 km =.206 Hour.90 Hour. Time to Peak Tp = =.90 Hour 4. Time Base T B/T P = 20 (Ratio T B/T P) T B = 8.60 Hour III. Peak Discharge (QP). Peak Coefficient (C p ) = Alpha = Betha = Area of SUH (Sum Col-4 Part IV) = Qp = /(.6Tp)*(A DAS/A SUH) = m/s 6. Rainfall Vol. (=R*A CA*000) = 56,920 m 7. Vol. of SUH (V SUH) Sum of Col 6 = 56,920 m 8. DRO Depth (V SUH /A CA /000) =.000 mm IV. Computatuion of ITB-2 SUH : T (jam) HSS Tak berdimensi HSS berdimensi t=t/tp q=q/qp A Q(m/s) V(m) ( ) ( 2 ) ( ) ( 4 ) ( 5 ) ( 6 ) Area SUH Vol (m) DRO (mm).000 Remark Col- : Given Time Interval (Hour) T i =T i- + Tr Col-2 : Dimensionless Time t=t/tp Kolom- /Tp Col- : Dimensionless Ordinate q=q/qp from ITB-2 Equation Curve Col-4 : Area of SUH A i = ½ (t i -t i- ) (q i + q i- ) (dimensionless) : Sum of Column-4 = A SUH (Important for Computing Qp) Col-5 : Dimensionalised Qi Q i = q i Qp (Kolom x Qp) Col-6 : Area of SUH (m) A i = ½ 600 x (T i -T i- ) (Q i + Q i- ) : Sum of Column-6 (V SUH ) if divided by A CA shoild be =

8 Time (hour) Table 7 : Superposition of ITB- SUH ITB- SUH Hydrograph Convolution Total Vol Hyd (m) Vol Hydrograf m 6E+06 Cathment Area km Direct Run Off mm 05.2 Rasio DRO/RE % 99.9% Time (hour) Table 8 : Superposition of ITB-2 SUH ITB-2 SUH Hydrograph Convolution Total Vol Hyd (m) Vol Hydrograf m 6E+06 Cathment Area km Direct Run Off mm 0.50 Rasio DRO/RE % 98.% 4. ACKNOWLEDGMENT This research is supported through Capacity Building Reseach Program 200, funded by Institute of Technology Bandung. 5. CONCLUSION A new procedure for determining a SUH based on mass concervation principle has been derived. Its application on development of ITB- and ITB-2 SUH shows that, despite its simplicity on input data and overall calculation process, the final results agree well with other methods developed earlier. 6. REFFERENCES ) Natakusumah D.K, (2009), Prosedure Umum Penentuan Hidrograf Satuan Sintetis Untuk Perhitungan Hidrograph Banjir Rencana, Water Resources Conference, Bandung, August, 2009, pp ) Natakusumah D.K, Hatmoko W, Harlan D, (200), Prosedure Umum Perhitungan Hidrograph Satuan Sintetis (HSS) Untuk Perhitungan Hidrograph Banjir Rencana. Studi Kasus Pengembangan HSS ITB- Dan HSS ITB-2, Water Resources Conference, Bandung, November, 200. ) Ramírez, J. A., 2000: Prediction and Modeling of Flood Hydrology and Hydraulics. Chapter of Inland Flood Hazards: Human, Riparian and Aquatic Communities Eds. Ellen Wohl; Cambridge University Press.