Clusterization of Synthetic Unit Hydrograph Methods Based on ...

International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 06

76

Clusterization of Synthetic Unit Hydrograph Methods Based on Watershed Characteristics Ariani Budi Safarina1,*, Hang Tuah Salim2, Iwan K Hadihardaja2, M Syahril BK2 1

Faculty of Engineering,Civil Engineering Departement, Jendral Achmad Yani University, Cimahi, 40531,Indonesia 2 Faculty of Civil and Environmental Engineering, Institut Teknologi Bandung, Bandung 40132, Indonesia *Corresponding author: [email protected] Abstract— The aim of this study is to determine the appropriate method of synthetic unit hydrograph for various ungauge watershed characteristics, where each method specified in range of validity based on characteristics parameter and will be presented in the form of synthetic unit hydrograph methods clusterization. Characteristics of the watershed that is used as a parameter are watershed area, the length of the main river and the slope. Watershed as the study site is 32 watersheds located in Java Island, Indonesia. Based on rainfall and river water level data, the observation unit hydrograph is determined for each watershed using the convolution method. Synthetic method validation is done by calculating the comparison parameters between observation and synthetic unit hydrograph with the specified tolerance value. Comparison parameter measure the similarity of the unit hydrograph’s shape and the unit hydrograph parameters of the peak discharge, peak time and time base. The analyzed synthetic method is Snyder, SCS, Nakayasu and Gama-1. The results showed each synthetic method has a validity range of the watershed area, the length of the main river and the slope. Index Terms—Clusterization, Convolution Method, Comparison Parameter, Unit Hydrograph, Watershed Characteristic

I. INTRODUCTION

H

analysis is a method to estimate the river flow in gauge and ungauge watershed, ie by simulating the rainfall becomes runoff in a rainfall runoff model. The first rainfall-runoff model used is in the form of empirical equations developed from a region to some other regions. The method developed after it is rational method, which is used to predict the peak discharge. After that Sherman (1932) of Chow [10] found unit hydrograph which is the first method YDROGRAPH

Manuscript received November 10, 2011. This work was supported in part by the Indonesian. Directorate General of Higher Education under Grant Doctoral Student. Ariani Budi Safarina is with the Jenderal Achmad Yani University,Department of Civil Engineering, Cimahi, 40531, Indonesia (corresponding author to provide phone: 622-22-6641743; fax: 622-226641743; e-mail: arianibudis@ yahoo.com). Hang Tuah Salim., is with Faculty of Civil and Environmental Engineering ITB, Bandung 40132, Indonesia (e-mail: [email protected]). Iwan K Hadihardaja is with Faculty of Civil and Environmental Engineering ITB, Bandung 40132, Indonesia (e-mail: [email protected]). M Syahril BK is with Faculty of Civil and Environmental Engineering ITB, Bandung 40132, Indonesia (e-mail: [email protected]).

that does not only determine the peak discharge. [23]. Further research is synthetic unit hydrograph which started by Snyder (1938) and Gray (1961) of Chow [10] that gives some hydrograph characteristics such peak discharge, peak time and time base. Then the addition of parameters that is characteristic of watersheds reservoirs which was pioneered by Clark, (1943), of Chow [10]. In 1972, Soil Conservation Service (SCS) produces dimensionless synthetic unit hydrograph. In 1940, Dr.Nakayasu from Japan promote synthetic unit hydrograph based on rivers in Japan, which until recently widely used and known as a Nakayasu synthetic unit hydrograph. [40]. A study by Woodward et al (1980), from Solanki [42] gives a correction to SCS synthetic unit hydrograph with the proposed value of C = 284 for a named Delmarva peninsula. While the University of Florida (1986) set the value of C between 75 to 100 for a flat watershed. Himat Solanki and Stephen M Suau from the Southwest Florida Water Management found that C = 256 and 323 to the watershed in southwest Florida. In Indonesia, Suharto [15] suggested that four basic properties of synthetic unit hydrograph is time of rise,TR, peak discharge, QP, timebase,TB and storage coeffisien,K. Harto promote the synthetic unit hydrograph as Gama-1 synthetic unit hydrograph, and found that the rivers in the Java island has the straight line rising curve and exponential recession curve. Usul and Kupçu [46] determines unit hydrograph of Kumdere watershed, Turkey, with SCS unit hydrograph and with watershed parameters such as area, length of main rivers, the length of the central watershed to the outlet, and the slope of the watershed which is obtained with the geographic information systems (GIS). In this way his found that the discrepanty was 0.75% for the 5 minutes rainfall duration and 4.01% for a 10 minutes duration . Unit hydrograph of Clark [14] is an instantaneous unit hydrograph (IUH) with route technique. Clark is the first researcher to use the concept of IUH. To get his synthetic unit hydrograph, Clark split in two phases. The first stage is to determine the IUH of observe rainfall and runoff data. The second stage is converting the IUH to the unit hidrograph. For this aim Clark requires time of concentration, tc, storage constants, K and the time – area curve. IUH later developed into the more detailed data collection for watershed geomorphology by Gupta, Waymire and Wang [13], as Geomorphologi Instantaneous Unit Hydrograph (GIUH). GIUH parameters such as channel parameters, area, shape of the watershed, etc., is currently developed with GIS as

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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 06 practiced by Jennifer Leigh Kilgore , and I. M. Hubail Ajward Muzik [2], Vikrant Jain, R Sinha [20], Ashour [3] and ME Noorbakhsh, MB Rahnama, S Montazeri [32]. In his research, Noorbakhsh et al get the parameters of Clark synthetic unit hidrograf using geographic information systems. Obtained synthetic unit hydrograph is closed to the observed unit hydrograph. Other researchers developed spatially distributed unit hydrograph ( SDUH) are Francisco Olivera and David Maidment R [34], M Hubail Ajward and I Muzik [2] In his research, Maidment use S-hidrograf to obtain SDUH. This SDUH is convoluted with hyctograf rainfall hourly and get direct runoff hidrograph for a rainfall event. The model developed is applied to five events rainfall and is observed that flood hidrograph is closed to the data flow from the watershed. In this research, digital elevation model (DEM) is used to the contours map of watershed and make cells for flow lines, flow direction, flow length and slope. SCS-CN method is used to calculate the rainfall of every cell. Direct runoff from each cell is routed to the watershed outlet through a river network. Kinematic wave equation is used to calculate overland flow and drainage time of each cell in the watershed. Isokhrone of the watershed is obtained by summing the time of concentration of each cell in the watershed. SDUH methods with the distributed rainfall-runoff model requires of computer equipment with a high specification [21]. In addition, to apply the method is also required topographic maps that are already integrated with GIS. For developing countries like Indonesia, this condition becomes severe enough constraint, so that this method is not aplicable. Existing synthetic unit hydrograph methods, such as method of Snyder, SCS, Nakayasu, and Gama-1 in its application for a ungauge watershed is often produce variation peak discharge, peak time, time base and the shape of hydrograph unit. This difference provides a considerable impact in the determination of peak discharge to be used. To determine the validity of the of synthetic unit hydrograph method against criteria of watershed characteristics, need to do a study [6]. Research done by creating an analysis model to compare the observation unit hydrograph with unit hydrograph obtained from synthetic unit hydrograph methods. II. WATERSHED CHARACTERISTIC A. Watershed as a Linear Model of a Hydrology System Assuming the watershed as a lumped linear system, the amount of water stored in a system hydrology associated with the inflow and outflow, can be written in the continuity equation as follows, where S is hydrologi system, I is inflow and Q is outflow,

dS = I −Q dt

(1)

The hydrology system is described as a reservoir and store large amounts of water that can be reduced and increased by a function of time from the I and Q Changes in I and Q as a function of time can be expressed as a function of storage of

77

Chow [10] as follows:

 dI d 2 I dQ d 2 Q  S = f  I , , 2 ,..., Q. , ,... dt dt 2  dt dt 

(2)

The continuity equation and storage functions in the above equation can be solved simultaneously so that the output Q can be calculated if I is given. This solution can be done in two ways. The first way by differentiating the function of storage and substituted results for dS/dt in equation (1), then look for solutions of differential equations in the I and Q by integration. B. Physical Characteristic of Watershed The main physical characteristics of a watershed is the area, shape, elevation, slope, orientation, soil type, channel networks, water storage capacity and land cover. Effect of type of characteristics are different. Soil type can control l infiltration, surface water capacity, and groundwater. The combined influence of all factors is the classification for small and large watersheds [14]. Large watershed is a watershed with the dominant influence of storage capacity, so the effect of rainfall on the reservoir is small. Large watershed is insensitive to variations in rainfal intensity and land use. Generally, a large watershed has a large size with the main river.Small watershed is controlled by overland flow, land use, slope, etc., have a peak flow variation is very large. Influence of the storage capacity is small, and watersheds are very sensitive to rainfall, so the response to it quickly. Watershed in a swamp which the area is slightly smaller, has the characteristics of the watershed as a large watershed. Area of the watershed is a physical characteristics that is always used in the analysis of hydrological basin. The area represent a watershed storage capacity.Uhlenbrook Stefan [47] in his paper defines that, according to the area, watershed is divided into small watershed (Area < 1 km2), meso scale watershed (10 km2 < Area < 1000 km2) and macro watersheds (> 1000 km2). Sosrodarsono and Kensaku [43] and Hundecha [19] gives the shape coefficient of the watershed, F, as a comparison between area (A) and square of main river length (L), with the equation: F = A/L2

(3)

According to Sharma [39], the shape of a watershed can be represented by a river network The slope of the watershed is generally represented by the slope of the main river. The slope of the major rivers in a watershed affects the water drainage in the watershed and the magnitude of time of concentration. Sharma define the slope (S) of watershed as the function of contour interval (D), number of contours that cut watershed boundary (N) and watershed perimeter (P) with the equation, S = DN/P

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III. HYDROGRAPH ANALYSIS A. Basic Concept of Hydrograph Hydrograph is a graph that represents the stream discharge versus time [11] Flow hydrograph is the result of the runoff , which consists of the overland flow, interflow and base flow which is generated from rainfall. Discharge,Q(m3/s)

t p = C1Ct ( LLc ) 0.3

(5)

2) Peak discharge per unit area of watershed in m3/s.km2 from standard unit hidrograph is the function of watershed coefficient (C2,Cp) and time lag, Tp

Rainfall

qp =

Flow Hydrograf

C 2C p

(6)

tp

3) The relation between qp and qpR is

Time,t (s)

q pR =

q pt p

(7)

t pR

Fig 1 Flow Hydrograph

B. Unit Hydrograph Unit hydrograph is a simple linear model that can be used to obtain hydrograph which can be determined from any effective rainfall [10] The basic assumption used in this linear model is • Effective rainfall has a constant intensity over the effective duration. • Effective rainfall is distributed uniformly at every point in the watershed. • Hidrograph time base direct runoff from a rainfall effectively with a specific duration is constant. • Ordinate of direct runoff hidrograph from a basic flow is proportional to the total amount of effective rainfall for each hidrograph. • For a watershed, hidrograph generated for each specific effective rainfall, describe the same watershed characteristics C. Snyder Synthetic Unit Hydrograph Synthetic unit hydrograph used at ungauge watershed. The main factor influencing the accuracy of synthetic unit hydrograph is in determining the watershed characteristics parameters so the synthetic unit hydrograph is closed to the observation unit hydrograph [8,9]. Snyder (1938), from Chow [10], conducting studies in several watersheds in the Appalachian highlands, United States, with watershed area variations between 30 km2 up to 30,000 km2. In his study he found a synthetic relation to some of the characteristics of standard unit hydrograph. From these relationships, the five characteristics of a unit hydrograph that will be determine for given effective rainfall duration, can be calculated. The Equation of Snyder Method 1) Time lag (Tp) is the function of the length of main river (L), watershed characteristic (C1 and Ct), and the distance from the centre of watershed to the outlet (Lc). The equation of Tp,is shown below,

4) Time base, Tb in hour,is the function of watershed coefficient (C3) and qpR,

tb =

C3 q pR

(8)

5) The width of unit hydrograph, is

W = C w q −pR1.08

(9)

tr tp qp

Time (a)

tR tpR qpR W75 W50 Tb

Time

(b) Fig 2. Snyder.Synthetic Unit Hydrograph (a) Standard Unit Hydrograph (tp=5,5tr). (b) Required Unit Hidrograph (tpR ≠ 5,5tR)

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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 06 D. SCS Synthetic Unit Hydrograph SCS dimensionless synthetic unit hydrograph is expressed discharge as the ratio q/qp and time t/Tp. If the peak discharge and lag time for a duration of effective rainfall is given, then the unit hydrograph can be estimated. Figure below shows SCS imensionless hidrograph, which is determined of several varied watershed. The Equation of SCS Method 1) Time lag (Tp) is the function of the time of concentration (tc) and duration of effective rainfall (Tr). The equation of Tp,is shown below, (10)

tp = 0.6 tc

Tp =

Tr +tp 2

(11)

2) Peak discharge (qp) is the function of the area of watershed (A), watershed characteristic coefficient (C) and time lag (Tp) The equation of qp,is showed below,

2) Peak discharge is the funtion of watershed area (A), watershed characteristic coefficient (C), unit rainfall (Ro), tame lag (Tp) and time required to discharge reduction up to 30% peak discharge (T0.3). The equation is,

Qp =

CARo 3,6(0,3T p + T0,3 )

(12)

(14)

3) Rising limb curve,Qa, is the function of peak discharge (Qp), time (t) and time lag (Tp). The equation is,

Qa = Q p (

t 2, 4 ) Tp

(15)

4) Decreasing limb curve, Qd, is the function of peak discharge (Qp), time(t), time lag (Tp) and time required to discharge reduction up to 30% peak discharge (T0.3).The equation is, t −T p

Qd>0,3 Qp :

CA qp = Tp

79

Qd = Q p .0,3

T0 , 3

(16) t −T p + 0 , 5T0 , 3

0,3Qp>Qd>0,32Qp :

Qd = Q p .0,3

1, 5T0 , 3

(17)

t −T p +1, 5T0 , 3

E. Nakayasu Synthetic Unit Hydrograph Dr. Nakayasu doing research on rivers in Japan and he produces a synthetic unit hydrograph [40] The synthetic unit hydrograph are as follows, Q(m3/s)

tr 0.7 tr tg

Qp

Decreasing Limb Rising Limb

0.32Qp

0.3Qp

t Tp

T0.3

1.5T0.3

Fig 3 Nakayasu Synthetic Unit Hydrograph

The Equation of Nakayasu Method 1) Time lag (Tp) is the function of the time of concentration (tg) and duration of effective rainfall (tr). The equation of Tp,is showed below, Tp = tg + 0,8 tr

(13)

2

0,3 Qp>Qp

Qd = Q p .0,3

2T0 , 3

(18)

F. Gama-1 Synthetic Unit Hydrograph Gama 1synthetic unit hydrograph from Sri Harto [15] is the result of 30 research watersheds in Java Island. According to Sri Harto, the results of his research was obtained several important factors that greatly affect the unit hydrograph of a watershed. The properties are: • Source factor, (SF), ie sum of the lengths of all river orde compared with the sum of the lengths of the river all orde. • Source frequency,( SN) is the number first orde of the river compared to all orde of the river. • Width factor, (WF) is the ratio between the width watershed at the point in the0.75 river length with the width watershed at the point in the river which is 0.25 length. • Upstream catchment area, (Rua), which is relatively width of the watershed in upstream line drawn through a point on the river closest to the centroid of watershed, perpendicular to the line connecting these points with the outlet. • Symmetri factor, (SIM) is the product of the width factor (WF) and watershed area upstream (Rua). • Number of junctions, (JN) is the total number of river crossing point in the watershed The Equation of Gama-1 Method 1) Time lag (TR) is the function of SF and SIM. The equation is,

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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 06 3

 L  TR = 0,43  +1,0665SIM + 1,2775  100SF 

(19)

and direct runoff, so the value of output of the system at time intervals to n (t = n∆t) is Qn = Q(n∆t)

Q (m3/s)

80

n = 1,2,3,…

(25)

tr

Qn is the instantaneous value of flow at the end of time interval to n (in cfs or m3/s). Thus the input and output variables for watershed system recorded with different dimensions and uses a different representation of discrete data as well. Effect of pulse input of duration ∆t starting at time (m-1) ∆t and the output at time t = n ∆t measured by the value of the unit pulse response function h [t-(m-1) ∆t] = h [n∆t-(m1 ) ∆t] = h [(n-m +1) ∆t], then equation (1) becomes

TR Qp

t(hour)

Tb

1 h[(n − m + 1)∆t ] = ∆t

Fig 4 Gama-1 Synthetic Unit Hydrograph

2) Peak discharge (Qp) is the function of watershed area (A), JN and TR. The equation is,

QP = 0,1836A0,5886 JN 0, 2381TR −0, 4008

(20)

3) Decreasing curve, Qt, is the function of peak discharge (Qp), time (t) and storage capacity (K). the equation is,

Qt = QPe − t / K

(21)

4) Time base is the function of TR, slope (S), SN and RUA. The equation is,

TB = 27,4132TR0,1457S −0,0986SN0,7344RUA0,2574

(22)

(23)

IV. CONVOLUTION METHOD An impulse, either step or pulse response function, is defined to have a continuous time domain. If the domain of time discrete with ∆t duration interval, then there are two ways to describe the function of continuous time in discrete time domain, the system of pulse data and sampled data systems. Pulse data systems used for precipitation and the value of discrete input function according to Chow (1988) are:

Pm =

(26)

By discretizing convolution integral at t = n ∆t and subtitute, the importance of the convolution equation with the input and output pulse Pm in Qn as a function of time sampled data: Qn= P1h[(n∆t)]+P2h[(n-1)∆t]+... +Pmh[(n-m+1)∆t]+... +PMh[(n-M+1)∆t]

(27)

Continuous pulse response function h(t) can be represented into discrete time domain as a function of sample data U. Thus the discrete convolution equation for the linear system:

Qn = ∑ PmU n − m +1

V. VALIDATION AND CLUSTERIZATION A. Validation Validation of the model is the justification that a model, in the domain of application, appropriate and consistent with the objective of the Model and Simulation. Validation of the model makes the true model [4,5]. In this research, synthetic methods are validated against observation unit hydrograph by using the comparison parameters. Comparison parameters consists of the error shape of hydrograph (E) and discrepanty ratio (d) of the peak discharge, peak time and time base [1,12,50]. Error magnitude is meant to measure the the similarity of the synthetic hydrograph curve and observation curve. The equation developed from the method of Sum Square Error as follows:

∑

(24)

( m −1) ∆t

(28)

m =1

m∆t

∫ I (τ )dt m=1,2,3...

∫ u(l )dl

( n − m ) ∆t

n≤ m

5) Storage capacity (K) is the function of watershed area (A), slope (S), SF and drainage density (D). the equation is,

K = 0,5617A0,1798S −0,1446SF −1,0897D0,0452

( n − m +1) ∆t

(qobs − q sin) 2

E=

Pm is the depth of precipitation during the interval of time (in inches or centimeters). Sampled data system used for flow

N Qp obs

(29)

The discrepanty ratio of hydrograph unit parameters is, 116106-7878 IJCEE-IJENS © December 2011 IJENS

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d (Qp) =

Qpsin Qp0bs

(30)

d (Tp ) =

Tpsin Tp 0bs

(31)

d (Tb) =

Tbsin Tb0bs

(32)

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The first name of watershed indicate the name of the main river, and the second is the name of the outlet. B. Watershed Characteristic The watershed area, the main river length and the slope of each watershed, is shown below

TABLE 2

B. Clusterization Value of E is greater than or equal to zero. If E smaller, synthetic unit hydrograph curve is closed to the observation curve, and if E = 0, the synthetic curve is fit with the observation.The magnitude of d (Qp), d (Tp) and d (Tb) is positive. If discrepanty ratio equal to one, it means the synthetic is fit with the observation. In this research, clusterization is carried out against watershed area (A), the main river length (L) and the slope (S). All synthetic methods will be classified based on this caharacteristic.

WATERSHED CHARACTERISTIC

Watershed

Area (Km2)

Slope (%)

L (Km)

1

1762.59

0.611

82.00

2

203.38

4.850

34.00

3

112.13

0.500

33.09

4

254.00

3.650

78.00

5

151.00

11.150

23.00

6

450.68

0.030

42.00

7

115.76

0.060

30.00

8

628.86

0.295

55.17

9

324.38

0.020

33.00

10

131.00

1.400

65.17

11

347.00

6.400

51.29

12

506.00

7.400

38.95

13

2666.00

0.015

140.19

TABLE I

14

1099.00

0.600

42.59

NUMBER OF WATERSHED

15

22.00

4.000

23.00

16

113.00

0.300

47.45 22.52

VI. RESULT AND DISCUSSION A. Number of Watershed There are 32 watersheds studied in this research. The number and the name of those watersheds is shown below,

Number

Watershed

17

66.00

9.000

1

Citarum-Nanjung

18

29.00

7.000

26.00

2

Cisangkuy-Kamasan

19

162.00

0.700

33.27

3

Cikapundung-Pasirluyu

4

Ciliwung-Sugutamu

20

19.00

3.500

12.00

5

Ciliwung-Katulampa

21

58.63

0.400

33.27

6

Cimanuk-Leuwidaun

22

47.00

0.700

31.59

7

Cikeruh-Jatiwangi

23

13.06

8.000

14.00

8

Cilutung-Damkamun

9

Cilutung-Bantarmerak

24

236.00

4.000

34.00

10

Cokroyasan-Winong

25

440.00

5.900

27.36

11

Bogowonto-Pungangan

26

572.00

3.200

48.00

1256.37

0.020

71.00

12

Progohulu-Badran

13

Serayu-Banyumas

27

14

Klawing-Pegandegan

28

547.00

2.380

44.80

15

Gajahwong-Papringan

29

4382.00

0.009

182.56

16

Bedog-Guwosari

17

Tambakbayan-Pulodadi

30

1297.00

3.700

67.00

18

Code-Pogung

31

8089.00

0.006

248.93

19

Progo-Duwet

32

981.00

0.200

64.00

20

Gajahwong-Wonokromo

21

Code-Koloran

22

Winongo-Padokan

23

Winongo-Sinduadi

24

Amprong-Mahdyopuro

25

Lesti-Tawangrejeni

26

Brantas-Gadang

27

Brantas-Sengguruh

28

Paritraya-Bendo

29

Brantas-Jeli

30

Widas-Lengkong

31

Brantas-Ploso

32

Brangkal-Sooko

C. Cluster of Snyder Method Snyder method only be used in the watershed that has sub watershed to obtain the coefficient from the main watershed. There are 12 watersheds analyzed with this method and Snyder method performance is shown in Table 3. Based on this table, Snyder method has average 23% error of hydrograph’s shape and 25% error of peak discharge. Clusterization of this Error and d(Qp) is shown in Fig 5.In this

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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 06 research, most of the data located in the first cluster. This figure show both value of E and d(Qp) of each cluster. Discrepanty ratio of peak discharge assumed to represent the unit hydrograph. This figure is allowed users to choose the suitable method based on watershed characteristic. Direct runoff volum (Vol DRO) in table 3 is shown to control the unit hydrograph if it is accordance to the basic concept of unit hydrograph where the volume of direct runoff is equal to one (millimeter depht)

of hydrograph’s shape and 182% error of peak discharge. Clusterization of this Error and d(Qp) is shown in Fig 6. SCS method show very high Error and discrepanty ratio of peak discharge and this applies for all watershed characteristics. TABLE 4 PERFORMANCE OF SCS METHOD Watershed

TABLE 3 PERFORMANCE OF SNYDER METHOD Snyder

Watershed Esnyd

Vol DRO(mm)

SCS d(Tp)

d(Tb)

Vol DRO(mm)

1

0.72

2.06

0.54

1.11

1.01

2

3.11

6.11

0.25

0.29

1.01

3

2.12

9.03

0.10

0.22

1.01

4

1.01

2.53

0.42

0.50

1.01

5

1.54

3.58

0.23

0.22

1.01

6

1.56

3.20

0.49

0.45

1.01

7

0.11

1.09

0.83

1.00

1.01 1.01

1.46

0.97

0.68

0.93

3

0.25

3.80

0.21

0.25

0.82

8

0.70

2.51

0.74

0.62

5

0.13

0.89

0.87

0.47

0.92

9

0.30

0.76

2.16

1.30

1.01

9

0.18

0.73

1.46

0.73

0.91

10

0.37

1.60

1.25

0.48

1.01

14

0.43

0.34

0.60

1.56

0.98

11

1.09

3.25

0.48

0.27

1.01

24

0.25

12

1.28

3.71

0.61

0.34

1.01

13

0.34

0.52

3.47

3.47

1.01

25

0.35

1.51

0.40

0.34

0.90

14

1.16

3.14

0.42

0.31

1.01

26

0.19

1.58

0.57

0.36

0.91

15

0.94

2.43

0.55

0.29

1.01

27

0.24

0.53

2.65

0.53

0.93

16

0.24

1.30

0.83

0.76

1.01

17

1.94

5.07

0.23

0.15

1.01

18

1.76

5.15

0.26

0.11

1.01

0.57

1.38

0.61

0.92

28

0.17

0.98

1.51

0.94

0.92

29

0.24

1.37

0.76

0.75

0.94

19

0.89

2.39

0.34

0.41

1.01

30

0.22

1.29

0.92

0.71

0.92

20

1.48

3.50

0.37

0.20

1.01

21

1.03

2.68

0.55

0.29

1.01

22

0.71

1.96

0.50

0.27

1.01

23

2.27

6.53

0.27

0.09

1.01

24

0.57

1.68

0.66

0.39

1.01

Average

0.23

1.25

1.02

0.66

0.92

Max

0.43

3.80

2.65

1.56

0.98

Min

0.13

0.34

0.21

0.25

0.82

25

1.59

3.60

0.25

0.26

1.01

S

0.08

0.91

0.66

0.35

0.04

26

0.80

2.45

0.55

0.44

1.01

27

0.17

1.19

1.12

0.45

1.01

28

0.65

2.40

0.58

0.72

1.01

29

0.21

0.80

1.21

2.38

1.01

30

1.25

2.84

0.38

0.60

1.01

31

0.29

0.21

4.53

9.43

1.01

32

0.18

0.82

1.55

1.01

1.01

Average

1.01

2.82

0.84

0.90

1.01

Max

3.11

9.03

4.53

9.43

1.01

Min

0.11

0.21

0.10

0.09

1.01

S

0.72

1.92

0.95

1.70

0.00

E = 0.18 d(Qp)= 1.28

500

5

E = 0.28 d(Qp)= 0.9

A (Km2)

1000

E = 0.23 d(Qp)= 0.91

50 E = 0.23 d(Qp)= 1.27

0

d(Tb)

d(Qp)

0.17

E = 0.24 d(Qp)= 1.32 0

d(Tp)

Escs

2

E = 0.24 d(Qp)= 1.49 0

d(Qp)

82

E = 0.24 d(Qp)= 1.37

L (Km)

100 E = 0.35 d(Qp)= 1.51

E = 0.13 d(Qp)= 0.89

E = 1.23 d(Qp)= 3.37

S (%)

500

0

10

D. Custer of SCS Method SCS method is asimplest method in this research. Influence of this dimensionless method that is the formula becomes stiff and difficult to modify [9]. In most of watershed, SCS method produces high peak discharge, so the discrepanty ratio is much larger than one. SCS method performance is shown in Table 4. Based on this table, SCS method has average 101 % error

50

0

5

0

A (Km2)

E = 0.28 d(Qp)= 0.51

L (Km)

E = 1.54 d(Qp)= 3.58

S (%)

100 E = 1.86 d(Qp)= 4.77

E = 0.74 d(Qp)= 2.2

E = 0.59 d(Qp)= 1.54 1000

E = 0.69 d(Qp)= 2.1

E = 1.24 d(Qp)= 3.5

Fig 5 Cluster of Snyder Synthetic Unit Hydrograph

E = 0.72 d(Qp)= 2.38

10

Fig 6 Cluster of SCS Synthetic Unit Hydrograph

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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 06 E. Cluster of Nakayasu Synthetic Unit Hydrograph Nakayasu method is the method used the time of concentration formula. This method also analyze decreasing curve more detail then the others and has both rising and decreasing equation separately. Nakayasu method performance is shown in Table 5 Based on this table, Nakayasu method has average 22 % error of hydrograph’s shape and 9% error of peak discharge. Clusterization of this Error and d(Qp) is shown in Fig 7 Nakayasu method show average 20% error for all cluster and all watershed characteristics. TABLE 5 PERFORMANCE OF NAKAYASU METHOD Watershed

Nakayasu

TABLE 6 PERFORMANCE OF GAMA-1 METHOD

Watershed

Gama-1 Egama

d(Qp)

d(Tp)

d(Tb)

Vol DRO(mm)

1

1.45

0.29

12.04

7.19

1.28

2

0.21

1.57

0.47

1.82

1.18

3

1.49

5.17

0.12

1.64

2.59

4

0.36

0.25

20.18

4.44

1.53

5

0.21

0.86

0.73

3.33

2.70

6

0.24

0.96

1.02

1.82

2.96

d(Qp)

d(Tp)

d(Tb)

Vol DRO(mm)

7

0.29

1.10

0.51

4.76

3.24

1

0.15

0.86

0.85

5.29

0.97

2

0.20

1.80

0.63

1.59

0.99

8

0.24

1.27

1.51

3.33

1.91

0.33

1.15

0.77

4.00

3.23

3

1.24

4.90

0.14

0.64

1.00

9

4

0.20

0.61

1.14

2.38

1.00

10

0.12

0.92

3.17

1.54

1.36

5

0.22

1.03

0.63

1.19

1.06

6

0.06

0.93

1.21

2.00

0.98

11

0.29

0.96

1.52

1.85

1.38

7

0.17

1.18

0.59

1.43

1.00

12

0.27

0.78

2.23

3.89

1.64

8

0.12

1.45

0.88

1.33

1.01

13

Time to rise = 356 hour

9

0.16

1.19

1.04

1.20

0.99

10

0.22

0.54

2.49

1.92

1.07

14

0.25

1.27

0.62

2.25

2.15

11

0.14

0.78

1.39

1.85

1.01

15

0.12

0.32

5.88

5.79

1.90

12

0.20

0.95

1.73

1.94

0.99

13

0.19

0.73

1.56

4.00

1.04

16

0.10

0.87

0.81

2.27

1.42

14

0.26

1.53

0.61

1.00

0.99

17

0.20

1.26

0.75

1.61

2.23

15

0.14

0.85

1.27

1.32

1.09

18

0.13

1.17

0.82

1.06

1.63

16

0.06

0.77

0.99

1.82

0.98

17

0.31

1.52

0.63

1.00

1.10

19

0.21

1.44

0.38

1.40

1.52

18

0.24

1.54

0.68

0.73

1.05

20

0.15

0.56

0.83

1.32

0.73

19

0.16

1.17

0.52

1.20

0.99

20

0.12

1.26

0.95

1.11

1.38

21

0.55

0.38

6.46

2.25

0.93

0.17

0.90

0.54

1.08

1.24

21

0.17

0.70

0.78

1.58

0.99

22

22

0.15

0.97

0.76

1.00

1.00

23

0.38

1.11

2.27

2.33

3.71

23

0.33

2.35

0.67

0.49

1.36

24

0.19

0.52

1.59

1.76

0.99

24

0.04

0.19

2.00

3.53

0.76

25

0.14

1.00

0.70

2.11

1.04

25

0.14

0.30

0.59

3.16

0.74

26

0.32

0.44

1.99

2.00

0.98

27

0.21

0.33

2.66

2.40

1.03

26

0.08

0.17

2.70

3.00

0.59

28

0.18

0.78

1.27

3.33

0.99

27

0.04

0.12

0.11

0.01

0.83

29

0.30

0.46

1.31

6.09

0.78

28

30

0.12

0.72

1.02

3.75

1.05

31

0.36

0.38

1.56

8.33

0.65

29

0.06

0.18

5.02

5.22

0.42

32

0.10

0.52

1.64

2.39

1.05

30

0.11

0.25

1.65

3.75

0.38

3.04

0.56

Average

0.22

1.09

1.12

2.19

1.02

Max

1.24

4.90

2.66

8.33

1.38

Min S

0.06 0.20

0.33 0.83

0.14 0.57

0.49 1.69

0.65 0.12

E = 0.18 d(Qp)= 0.83

500

0

50

E = 0.22 d(Qp)= 1.02 5

E = 0.23 d(Qp)= 0.72

A (Km2)

E = 0.28 d(Qp)= 0.52

L (Km)

E = 0.22 d(Qp)= 1.03

S (%)

1000 E = 0.16 d(Qp)= 0.73

E = 0.24 d(Qp)= 1.3

0

F. Cluster of Gama-1 Synthetic Unit Hydrograph Gama-1 method is developed based on the study of watersheds in Java Island, Indonesia [15,16,17].

Enkys

E = 0.23 d(Qp)= 1.28

0

83

100

E = 0.23 d(Qp)= 1.36 10

Fig 7 Cluster of Nakayasu Synthetic Unit Hydrograph

31 32

Time to rise = 196 hour

Time to rise = 146 hour 0.05

0.21

1.92

This method use a lot of watershed characteristics and quite difficult to get the parameters. Fortunately, this study used the GIS map, so that these parameters can be obtained more easily. Based on calculations of this research, there are some peculiarities in this method. For watershed number 13, 28 and 31 is obtained very high time lag, as is shown in Table 6. Moreover, most of the watersheds have volume of direct runoff not equal to one milimeter.The equations in this method is easily modified so that the volume of direct runoff can be equal to one and time lag is not unsual [9]. But the problem is, how to fix the volume of direct runoff so that it still equal to one although the equations is modified. In this research, clusterization of Gama-1 method will be

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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 06 done untill there is a study so that could answer the problem.

VII. CONCLUSION Based on this study can be concluded that the synthetic unit hydrograph methods are not always valid to use in each watershed. Snyder method has sufficient accuracy, but this method can only be used in sub-watersheds based on major watershed that has observe data. SCS method in general always produces a very large peak discharge, so that if this method is used without calibration, can lead to over-design. Nakayasu method is a method that has the precision shape of hydrograph and the parameters, so this method is safe to use in the ungauge watershed . Gama-1 method requires a watershed parameters very much, so it needs to be simplified. In addition, the equations in this method need to be evaluated in order to produce a correct peak time and the volume of direct runoff. In order to obtain more precise results in the design flood, dams and other water resources planning for the ungauge watershed is suggested using synthetic unit hydrograph Nakayasu method.

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