A GENERAL PROCEDURE FOR DETERMINING A SYNTHETIC UNIT HYDROGRAPH BASED ON MASS CONCERVATION PRINCIPLE.
DEVELOPMENT OF ITB-1 AND ITB-2 SYNTHETIC UNIT HYDROGRAPH METHOD
D.K. Natakusumah
1, W. Hatmoko
2and D. Harlan
11Faculty of Civil and Environmental Engineering Institute of Technology Bandung
Bandung 40132 INDONESIA
2Research Center Water Resources, Agency for Research and Development Ministry of Publick Works
Bandung 40135 INDONESIA
E-mail: [email protected],[email protected],[email protected]
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-1 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-1 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-1 and ITB-2 SUH, flood hydrograph, hydrology.
1. INTRODUCTION
Synthetic unit hydrograph method (SUH), initially proposed by Sherman in 1922, 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-1 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, 2010. This one year research project was aimed to develop a General Procedure Calculation of Synthetic Unit Hydrograph (SUH) and Development of ITB ITB-1 and SUH-2 Synthetic Unit Hydrograph". This general procedure was initially proposed by Natakusumah (2009) and later implemented by Natakusumah, Hatmoko and Harlan (2010) for developing ITB-1 and ITB-2 Synthetic Unit Hydrograhps.
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 1) Basin Lag (TL) and Time to Peak (Tp), 2) Basic shape of SUH and 3) adjustable peak discharge (Qp) per unit rainfall depth.
2.1. 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 inTable-1.
Table 1 :Time lag Formulas and its relation to time to peak
Method Time Lag Time To Peak Remarks
Kirpich
835 . 0
77 . 0 S 0.01947 L Tc
For small chatcment (A < 2 km2)
Tc 3 / 2 Tp
Tc = Ttime lConcentration (hr) L = River Lenght (km) Te = Eff rainfall duration (hr) S = Ccatchment slope (m/m) Tp = ttime to peak (hr)
Snyder
3 . L=(LLc)0 T
5 . 5 / T Te p
Tr 0.50 + tp
= Tp Tr
<
Te
Te) - (Tr 0.25 + tp
= Tp Tr Tp Te
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)
Nakayasu
15km) (L L 0.058 + 0.527
km) 15
<
(L L
= 0.21 T
0.7
L Tp1.6TL
TL = time lag (hours) L = River Lenght (km) Tr = unit duration (hour) Tp = ttime to peak (hour)
SCS
5 . 0 0.7 8
. 0
S CN 14104
CN 22.86 - L 2540
= TL
Tr 5 . 0 T Tp L
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-1 SUH) or two simple functions (ITB-2 SUH) as follows.
a) Single Function (ITB-1)
Cp
t t 1 2 exp ) t ( q
(t > 0) = 1.500 (1)
b) Two Functions (ITB-2)
Rising Limb : q(t)t (0t1) = 2.500 (2.a)
Recession Limb : q(t)exp
1tCp
(t>1) = 1.000 (2.b)Value of α and β coefficients can be change by changing Cp (Peak Coefficient). Figure 1 shows the relation of the peak discharge parameter q=Q/Qp and t=T/Tp from equation of ITB-1 and ITB-2 SUH.
0.00 0.20 0.40 0.60 0.80 1.00 1.20
0.00 2.00 4.00 6.00 8.00 10.00 12.00
q=Q/Qp
t=T/Tp
ITB-2 SUH ITB-2 SUH
Figure 1 : Typical shape of ITB-1 and ITB-2 SUH (dimensionless)
2.3. 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.bandFigure 2.d.
Tb=8 s 0
= 1/2*(8 s)*(5 m3/s) =20 m3
(a) Triangular SUH
Tp=2 s 0 4
= (5 m3/s)*(2 s)*(2) = 20 m3 1
1
= Qp*Tp*
A Qp=5 m3/s
= 1/2*(4*1) = 2 (exact)
SUH
ASUH
VSUH VSUH
Tb
0 Tp 0 Tb/Tp
1
1 Qp
(b) Triangular SUH (dimensionless)
(c) Curvilinear SUH (d) Curvilinear SUH (dimensionless)
= Qp*Tp*
ASUH= Area of SUH (Computed Numerically) ASUH
VSUH
= Volume of SUH (m3) VSUH
Non-Dimensionalized by Qp and Tp
Non-Dimensionalized by Qp and Tp
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.
VUH= Qp Tp AUH= Qp Tp 3600 AUH (m3) (4)
Where VHU= volume of UH (m3), Qp = peak of UH (m3/s), AUH= area of UH (dimensionless). Please note that AUHcan be computed exactly or numerically (e.q. using trapeziodal rule),
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
VRE =ACAR 1000 (m3) (3)
Where VRE= total volume of unit excess rainfall (m3), ACA= Area of the wathershed (km2), R= unit excess rainfall depth (mm).
By applying principle of mass conservation VRE =VUH, we obtained Qp Tp 3600 AUH= ACAR 1000
Therefore the peak discharge can be writtes as follows
UH CA
p A
A Tp 6 . 3
Q R (m3/s) (5)
In which Qp = the peak discharge in m3/s; R= unit excess rainfall depth (mm); ACA= the catchment area (km2); AUH = the area of unit hydrograph (dimensionless), computed exactly or numerically (e.q.
using trapeziodal rule).
3. APPLICATION
3.1. Flood hydrograph of a Small Cathment
The first example application of ITB method is on a small wathershed with cathment area of 1.2 km2, river Length of 1.570 km and catchment Slope of 0001. To show flexibibility of the proposed method in adopting basic shape of UH, a triangular UH shown in Figure 3 was used to generate flood hydrograph due to excess rainfall of 10 mm, 70 mm and 30 mm (half-hour interval).
tb=5
0 tp=1
qp=1
qp=1/3
t=2
AHSS1/2*1*1+1/2*(1+1/3)*1+1/2*3*1/3=5/3
Figure 3 : Abritrary Triangular SUH (Dimensionless) a) Compute Time to Peak (Tp) and Time Base (Tb)
For small cathment, time Concentration is computed using Kirpirch formula hour 34 . 1 ute min 80.58 001
. 0
575 0.01947 1 S
0.01947 L
t 0.835
77 . 0 835
. 0
77 . 0
c
Time Peak (Tp) dan Time Base (Tb) hour 893 . 0 34 . 1 tc
Tp32 32
hour 2.382 893 . 0 tp
Tb38 38
b) Compute Triangular SUH
1. Compute Area of Triangular SUH
value Exact 5/3
= 1/3)
* 3
* (1/2 + 1}
* 1/3) + (1
* {1/2 + 1)
* 1
* (1/2 A A A
AHSS 1 2 3
2. Compute Peak Dicharge of SUH
1.667 0.224m /s 2. 1 893 . 0 6 . 3
1 A
A Tp 6 . 3
Qp R 3
SUH
CA
3. Dimesionalised SUH by mutiplying absis and ordinate of dimensionless SUH inFigure 3by Tp and Qp, and the resut is shown inFigure 4. Ordinates of SUH between 0 and Tp and between Tp and Tb (obtained using linear interpolation) is shown in table below.
0 Q p=0.224
H our m 3/s
Q =0.075
T=1.786
Tp=0.893 Tb=4.466
0.000 0.000 0.500 0.125
0.893 0.224 Tp
1.000 0.206 1.500 0.123
1.786 0.075 2*Tp
2.000 0.069 2.500 0.055 3.000 0.041 3.500 0.027 4.000 0.013
4.466 0.000 Tb = 5 Tp 4.500 0.000
Note T (hour) Q (m3/s)
Figure 4 : Triangular SUH (Dimensionalised)
c) The superposition process of 10 mm, 70 mm and 30 mm rainfall excess (half-hour intervals), is shown inTable 2and the final hydrograph result is shown inFigure 5.(Note : Ratio of DRO/RE <
100% was caused by the exlusion of peak discharge (Qp,Tp) from superposition process) Table 2 : Superposition of Triangular SUH
0.5 1.0 1.5 Total (mm)
10.0 70.0 30.0 110.0
0.000 0.000 0.000 0.000 0
0.500 0.125 1.253 0.000 1.253 1,127
1.000 0.202 2.024 8.769 0.000 10.792 10,841 1.500 0.122 1.224 14.167 3.758 19.149 26,948 2.000 0.069 0.687 8.571 6.072 15.330 31,031
2.500 0.055 0.550 4.811 3.673 9.034 21,927
3.000 0.041 0.412 3.849 2.062 6.323 13,821
3.500 0.027 0.275 2.886 1.649 4.811 10,020
4.000 0.014 0.137 1.924 1.237 3.299 7,299
4.500 0.000 0.000 0.962 0.825 1.787 4,577
5.000 0.000 0.000 0.412 0.412 1,979
5.500 0.000 0.000 0.000 371
Total Volum (m3) 129,570 C. Area (km2) 1.200
DRO (mm) 107.98
DRO/RE (%) 98.16%
Time (Hour)
Q SUH (m3/s)
Volume (m3) SUH Convolution
0.0
50.0
100.0
150.0
200.0
250.0
300.0 0.0
5.0 10.0 15.0 20.0 25.0 30.0
0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 5.500 6.000
R(mm)
Q(jm3/s)
T (Hour)
Reff 10.0 70.0 30.0 Total
Figure 5 : Superposition process of flood hydrograph from Triangular SUH
3.2. 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= 1.7), Limantara and GAMA-1 method. Input requirement for each methods are shown in Table 3. Calculation procedure for generating ITB-1 and ITB-2 SUH are shown in Table 5 and Table 6. In this example, time lag for ITB-1 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 inTable 7andTable 8.
Comparison of flood discharge of Cibatarua River calculated by ITB-1, ITB-2, Nakayasu, Snyder- Alexeyev, Limantara and GAMA-1 as well as software HEC-HMS results are shown in Figure 6. This figure show that the results of SUH ITB-1 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-1 and ITB-2 SUH are simple and the calculation process is eassy, but the final results agree well with other methods developed earlier.
Table 3 : Input requirement for each methods Table 4 : Rainfall Excess and Infiltration
Value Unit
A Catchment area 56.920 km2 Ct 1.000
L River Lenght 12.150 km Cp 0.620
Lc River Lenght from Centre to Outlet 6.075 km
A Catchment area 56.920 km2 α 1.700
L River Lenght 12.150 km
A Catchment area 56.920 km2
L River Slope 12.150 km
S River Lenght 0.080 m/m
J1 Number of 1'st Order River 63 river Js Number of River (all order) 112 river L1 First order river lenght 75.310 km Ls Over all River lenght (all Order) 130.200 km WL Cathment Width at 0.25L 9.700 km WU Cathment Width at 0.75L 6.110 km AU CA Upstream of Centroid 20.900 km2
A Catchment area 56.920 km2
L River Lenght 12.150 km
n River Roughness (Manning) 0.034
S River Slope 0.080
A Catchment area 56.920 km2 Ct 1.000
L River Lenght 12.150 km Cp 1.000
HSS ITB-1 dan HSS ITB-2 HSS Limantara
Physical Data Non-Physical
HSS Gama-1 HSS Nakayasu
HSS Snyder Alexeyey Time Reff (mm) Inf (mm) Total
1.000 55.400 89.267 178.534
2.000 16.100 23.202 46.405
3.000 11.700 16.276 32.552
4.000 9.200 12.957 25.914
5.000 7.200 10.942 21.884
6.000 5.700 9.564 19.129
0.0
100.0
200.0
300.0
400.0
500.0
600.0 0.0
50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0
0.0 6.0 12.0 18.0 24.0 30.0 36.0
R(mm)
Q(jm3/s)
T (Jam)
Inf (mm ) Reff (mm ) ITB-1 ITB-2 Alexeyev (Cp=0.62) Nakayasu (α = 1.70) Gam a-1 Limantara HEC-HMS (Cp=0.62)
Figure 6 : Comparison Results of ITB-1 SUH and ITB-2 SUH with the Results of Snyder- Alexeyev (Cp=0.62), Nakayasu (α= 1.7), Limantara, GAMA-1 and HEC-HMS Results
Table 5 : ITB-1 SUH Calculation For Cibatarua C.A (T.L Snyder)
Table 6 : ITB-2 SUH Calculation For Cibatarua C.A (T.L Nakayasu)
I. Characteristic of Watershed and Rainfall Excess
1. River Name = Cibatarua
2. Cathment Area (A) = 56.92 Km2
3. River Lenght (L) = 12.15 Km
4. Unit Rainfall Excess (R) = 1.00 mm
5. Unit Rainfall Duration (Tr) = 1.00 Hour II. Computation of Time Peak (Tp) and Time Base (Tb)
1. Time Coefficient (Ct) = 1.00
2. Time Lag --> Snyder 2
LC = 0.5*L = 6.075 km
TL = Ct(LxLC)n = 3.634 Hour
Te = tp/5.5 = 0.661 Hour
TP = TL+0.25(Tr-Te)Te > Tr TP = TL+0.50Tr Te < Tr 3. Time to Peak
Tp = = 4.134 Hour
4. Time Base
TB/TP = 10 (Ratio TB/TP)
TB = 41.34 Hour
III. Peak Discharge (QP)
1. Peak Coefficient (Cp) = 1.000
2. Alpha = 1.500
3. Area of SUH (Sum Col-4 Part IV) = 1.613 4. Qp = 1/(3.6Tp)*(ADAS/ASUH) = 2.370 m3/s 5. Rainfall Volum (=R*ACA*1000) = 56,920 m3 6. Vol. of SUH (VSUH)Sum of Col 6 = 56,920 m3 7. DRO Depth (VSUH/ACA/1000) = 1.000 mm IV. Computatuion of ITB-1 SUH :
t=T/Tp q=Q/Qp A Q(m3/s) V(m3)
( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 )
0.00 0.00000 0.00000 0.00000 0.00000 0.0000 1.00 0.24187 0.02831 0.00342 0.06711 120.7954 2.00 0.48374 0.43760 0.05635 1.03725 1987.8489 3.00 0.72561 0.85587 0.15643 2.02866 5518.6460 4.00 0.96748 0.99836 0.22424 2.36641 7911.1317 4.13 1.00000 1.00000 0.03249 2.37029 1146.1919 5.00 1.20936 0.94709 0.20382 2.24488 7190.5209 6.00 1.45123 0.81022 0.21252 1.92046 7497.6064 7.00 1.69310 0.65338 0.17700 1.54870 6244.4931 8.00 1.93497 0.50780 0.14043 1.20364 4954.2235 9.00 2.17684 0.38507 0.10798 0.91273 3809.4690 10.00 2.41871 0.28701 0.08128 0.68030 2867.4530 11.00 2.66058 0.21126 0.06026 0.50075 2125.8966 12.00 2.90245 0.15405 0.04418 0.36514 1558.6070 13.00 3.14432 0.11152 0.03212 0.26434 1133.0651 14.00 3.38620 0.08028 0.02320 0.19028 818.3158 15.00 3.62807 0.05752 0.01667 0.13635 587.9357 16.00 3.86994 0.04107 0.01192 0.09734 420.6509 17.00 4.11181 0.02923 0.00850 0.06929 299.9368 18.00 4.35368 0.02075 0.00604 0.04919 213.2601 19.00 4.59555 0.01470 0.00429 0.03485 151.2732 20.00 4.83742 0.01040 0.00304 0.02464 107.0893 21.00 5.07929 0.00734 0.00215 0.01740 75.6814 22.00 5.32116 0.00518 0.00151 0.01227 53.4067 23.00 5.56303 0.00365 0.00107 0.00864 37.6401 24.00 5.80491 0.00257 0.00075 0.00608 26.4988 25.00 6.04678 0.00180 0.00053 0.00427 18.6371 26.00 6.28865 0.00127 0.00037 0.00300 13.0967 27.00 6.53052 0.00089 0.00026 0.00211 9.1963 28.00 6.77239 0.00062 0.00018 0.00148 6.4531 29.00 7.01426 0.00044 0.00013 0.00104 4.5255 30.00 7.25613 0.00031 0.00009 0.00073 3.1720 31.00 7.49800 0.00021 0.00006 0.00051 2.2222 32.00 7.73987 0.00015 0.00004 0.00036 1.5561 33.00 7.98175 0.00011 0.00003 0.00025 1.0892 34.00 8.22362 0.00007 0.00002 0.00017 0.7621 35.00 8.46549 0.00005 0.00002 0.00012 0.5331 36.00 8.70736 0.00004 0.00001 0.00009 0.3728 37.00 8.94923 0.00003 0.00001 0.00006 0.2606 38.00 9.19110 0.00002 0.00001 0.00004 0.1821 39.00 9.43297 0.00001 0.00000 0.00003 0.1273 40.00 9.67484 0.00001 0.00000 0.00002 0.0889 41.00 9.91671 0.00001 0.00000 0.00001 0.0621 42.00 10.15859 0.00000 0.00000 0.00000 0.0255 43.00 10.40046 0.00000 0.00000 0.00000 0.0000 44.00 10.64233 0.00000 0.00000 0.00000 0.0000 45.00 10.88420 0.00000 0.00000 0.00000 0.0000 Area SUH 1.6134085 Vol (m3) 56920.000
DRO (mm) 1.000 Remark
Col-1 : Given Time Interval (Hour)Ti=Ti-1+ Tr Col-2 : Dimensionless Time t=T/TpKolom-1 /Tp
Col-3 : Dimensionless Ordinate q=Q/Qp from ITB-1 Equation Curve Col-4 : Area of SUHAi=½ × (ti-ti-1) × (qi+ qi-1) (dimensionless)
: Sum of Column-4 = ASUH(Important for Computing Qp) Col-5 : Dimensionalised QiQi= qi× Qp (Kolom 3 x Qp) Col-6 : Area of SUH (m3)Ai=½ × 3600 x (Ti-Ti-1) × (Qi+ Qi-1)
: Sum of Column-6 (VSUH) if divided by ACAshoild be = 1 Hour 4.134
T (hour)
SUH (dimensionless) SUH (dimensionalised)
I. Characteristic of Watershed and Rainfall Excess
1. River Name = Cibatarua
2. Cathment Area (A) = 56.92 Km2
3. River Lenght (L) = 12.15 Km
4. Unit Rainfall Excess (R) = 1.00 mm
5. Unit Rainfall Duration (Tr) = 1.00 Jam II. Computation of Time Peak (Tp) and Time Base (Tb)
1. Time Coefficient (Ct) = 1.00
2. Time Lag --> Nakayasu 1
TL = Ct*0.21*L0.7 < 15 km
= Ct*(0.527 + 0.058*L) ≥15 km
TP = 1.6 TL = 1.930 Hour
3. Time to Peak
Tp = = 1.930 Hour
4. Time Base
TB/TP = 20 (Ratio TB/TP)
TB = 38.60 Hour
III. Peak Discharge (QP)
1. Peak Coefficient (Cp) = 1.000
2. Alpha = 2.500
3. Betha = 1.000
4. Area of SUH (Sum Col-4 Part IV) = 1.359 5. Qp = 1/(3.6Tp)*(ADAS/ASUH) = 6.028 m3/s 6. Rainfall Vol. (=R*ACA*1000) = 56,920 m3 7. Vol. of SUH (VSUH)Sum of Col 6 = 56,920 m3 8. DRO Depth (VSUH/ACA/1000) == 1.000 mm IV. Computatuion of ITB-2 SUH :
t=T/Tp q=Q/Qp A Q(m3/s) V(m3)
( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 )
0.00 0.00000 0.00000 0.00000 0.00000 0.0000 1.00 0.51815 0.19326 0.05007 1.16501 2097.0267 1.93 1.00000 1.00000 0.28749 6.02821 12040.6104 2.00 1.03630 0.96435 0.03566 5.81328 1493.4139 3.00 1.55446 0.57438 0.39865 3.46251 16696.4199 4.00 2.07261 0.34211 0.23744 2.06234 9944.7238 5.00 2.59076 0.20377 0.14143 1.22837 5923.2777 6.00 3.10891 0.12137 0.08424 0.73164 3528.0234 7.00 3.62707 0.07229 0.05017 0.43578 2101.3618 8.00 4.14522 0.04306 0.02988 0.25956 1251.6134 9.00 4.66337 0.02565 0.01780 0.15460 745.4861 10.00 5.18152 0.01528 0.01060 0.09208 444.0265 11.00 5.69967 0.00910 0.00631 0.05485 264.4711 12.00 6.21783 0.00542 0.00376 0.03267 157.5243 13.00 6.73598 0.00323 0.00224 0.01946 93.8247 14.00 7.25413 0.00192 0.00133 0.01159 55.8839 15.00 7.77228 0.00115 0.00079 0.00690 33.2856 16.00 8.29043 0.00068 0.00047 0.00411 19.8255 17.00 8.80859 0.00041 0.00028 0.00245 11.8085 18.00 9.32674 0.00024 0.00017 0.00146 7.0334 19.00 9.84489 0.00014 0.00010 0.00087 4.1892 20.00 10.36304 0.00009 0.00006 0.00052 2.4952 21.00 10.88120 0.00005 0.00004 0.00031 1.4862 22.00 11.39935 0.00003 0.00002 0.00018 0.8852 23.00 11.91750 0.00002 0.00001 0.00011 0.5272 24.00 12.43565 0.00001 0.00001 0.00007 0.3140 25.00 12.95380 0.00001 0.00000 0.00004 0.1870 26.00 13.47196 0.00000 0.00000 0.00002 0.1114 27.00 13.99011 0.00000 0.00000 0.00001 0.0664 28.00 14.50826 0.00000 0.00000 0.00001 0.0395 29.00 15.02641 0.00000 0.00000 0.00000 0.0235 30.00 15.54457 0.00000 0.00000 0.00000 0.0140 31.00 16.06272 0.00000 0.00000 0.00000 0.0084 32.00 16.58087 0.00000 0.00000 0.00000 0.0050 33.00 17.09902 0.00000 0.00000 0.00000 0.0030 34.00 17.61717 0.00000 0.00000 0.00000 0.0018 35.00 18.13533 0.00000 0.00000 0.00000 0.0011 36.00 18.65348 0.00000 0.00000 0.00000 0.0006 37.00 19.17163 0.00000 0.00000 0.00000 0.0004 38.00 19.68978 0.00000 0.00000 0.00000 0.0002 39.00 20.20793 0.00000 0.00000 0.00000 0.0001 40.00 20.72609 0.00000 0.00000 0.00000 0.0000 41.00 21.24424 0.00000 0.00000 0.00000 0.0000 42.00 21.76239 0.00000 0.00000 0.00000 0.0000 43.00 22.28054 0.00000 0.00000 0.00000 0.0000 44.00 22.79870 0.00000 0.00000 0.00000 0.0000 45.00 23.31685 0.00000 0.00000 0.00000 0.0000 Area SUH 1.3590380 Vol (m3) 56920.000
DRO (mm) 1.000 Remark
Col-1 : Given Time Interval (Hour)Ti=Ti-1+ Tr Col-2 : Dimensionless Time t=T/TpKolom-1 /Tp
Col-3 : Dimensionless Ordinate q=Q/Qp from ITB-2 Equation Curve Col-4 : Area of SUHAi=½ × (ti-ti-1) × (qi+ qi-1) (dimensionless)
: Sum of Column-4 = ASUH(Important for Computing Qp) Col-5 : Dimensionalised QiQi= qi× Qp (Kolom 3 x Qp) Col-6 : Area of SUH (m3)Ai=½ × 3600 x (Ti-Ti-1) × (Qi+ Qi-1)
: Sum of Column-6 (VSUH) if divided by ACAshoild be = 1 1.206 Hour
T (jam) HSS Tak berdimensi HSS berdimensi
Table 7 : Superposition ofITB-1 SUH Table 8 : Superposition ofITB-2 SUH
1 2 3 4 5 6
55.40 16.10 11.70 9.20 7.20 5.70 105.300
0.0 0.00 0.00 0.00 0.0
1.00 0.07 3.72 0.00 3.72 6692.1
2.00 1.04 57.46 1.08 0.00 58.54 112071.6
3.00 2.03 112.39 16.70 0.79 0.00 129.87 339150.7
4.00 2.37 131.10 32.66 12.14 0.62 0.00 176.51 551496.0 5.00 2.24 124.37 38.10 23.74 9.54 0.48 0.00 196.23 670932.8 6.00 1.92 106.39 36.14 27.69 18.66 7.47 0.38 196.74 707335.3 7.00 1.55 85.80 30.92 26.27 21.77 14.61 5.91 185.27 687617.5 8.00 1.20 66.68 24.93 22.47 20.65 17.04 11.56 163.34 627501.7 9.00 0.91 50.57 19.38 18.12 17.67 16.16 13.49 135.38 537701.9 10.00 0.68 37.69 14.69 14.08 14.25 13.83 12.80 107.34 436897.7 11.00 0.50 27.74 10.95 10.68 11.07 11.15 10.95 82.54 341787.0 12.00 0.37 20.23 8.06 7.96 8.40 8.67 8.83 62.14 260434.1 13.00 0.26 14.64 5.88 5.86 6.26 6.57 6.86 46.07 194786.2 14.00 0.19 10.54 4.26 4.27 4.61 4.90 5.20 33.78 143730.6 15.00 0.14 7.55 3.06 3.09 3.36 3.61 3.88 24.55 104993.5 16.00 0.10 5.39 2.20 2.23 2.43 2.63 2.85 17.73 76107.9 17.00 0.07 3.84 1.57 1.60 1.75 1.90 2.08 12.74 54838.5 18.00 0.05 2.73 1.12 1.14 1.25 1.37 1.51 9.11 39324.6 19.00 0.03 1.93 0.79 0.81 0.90 0.98 1.08 6.50 28090.8 20.00 0.02 1.37 0.56 0.58 0.64 0.70 0.78 4.62 20002.7 21.00 0.02 0.96 0.40 0.41 0.45 0.50 0.55 3.27 14206.0 22.00 0.01 0.68 0.28 0.29 0.32 0.35 0.39 2.32 10067.0 23.00 0.01 0.48 0.20 0.20 0.23 0.25 0.28 1.64 7120.6 24.00 0.01 0.34 0.14 0.14 0.16 0.18 0.20 1.16 5028.5 25.00 0.00 0.24 0.10 0.10 0.11 0.13 0.14 0.81 3546.2 26.00 0.00 0.17 0.07 0.07 0.08 0.09 0.10 0.57 2497.9 27.00 0.00 0.12 0.05 0.05 0.06 0.06 0.07 0.40 1757.6 28.00 0.00 0.08 0.03 0.04 0.04 0.04 0.05 0.28 1235.6 29.00 0.00 0.06 0.02 0.02 0.03 0.03 0.03 0.20 867.9 30.00 0.00 0.04 0.02 0.02 0.02 0.02 0.02 0.14 609.2 31.00 0.00 0.03 0.01 0.01 0.01 0.02 0.02 0.10 427.4 32.00 0.00 0.02 0.01 0.01 0.01 0.01 0.01 0.07 299.6 33.00 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.05 209.9 34.00 0.00 0.01 0.00 0.00 0.00 0.01 0.01 0.03 147.0 35.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.02 102.9
36.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 72.0
37.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 50.4
38.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 35.2
39.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 24.6
40.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17.2
41.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 12.0
42.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 7.4
43.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.9
44.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.2
45.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.2
46.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.5
47.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.1
48.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
49.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
50.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
Vol Hydrograf m3 6E+06 Cathment Area km2 56.92 Direct Run Off mm 105.23
Rasio DRO/RE % 99.9%
Vol Hyd (m3) Time
(hour) ITB-1 SUH
Hydrograph Convolution Total 1 2 3 4 5 6
55.40 16.10 11.70 9.20 7.20 5.70 105.300
0.0 0.00 0.00 0.00 0.0
1.00 1.17 64.54 0.00 64.54 116175.3
2.00 5.81 322.1 18.76 0.00 340.81 729637.8
3.00 3.46 191.82 93.59 13.63 0.00 299.05 1151747.9
4.00 2.06 114.25 55.75 68.02 10.72 0.00 248.7 986005.6 5.00 1.23 68.05 33.20 40.51 53.48 8.39 0.00 203.64 814266.9 6.00 0.73 40.53 19.78 24.13 31.86 41.86 6.64 164.79 663169.4 7.00 0.44 24.14 11.78 14.37 18.97 24.93 33.14 127.33 525822.0 8.00 0.26 14.38 7.02 8.56 11.30 14.85 19.74 75.84 365714.9 9.00 0.15 8.56 4.18 5.10 6.73 8.84 11.76 45.17 217827.2 10.00 0.09 5.10 2.49 3.04 4.01 5.27 7.00 26.91 129742.3 11.00 0.05 3.04 1.48 1.81 2.39 3.14 4.17 16.03 77277.1 12.00 0.03 1.81 0.88 1.08 1.42 1.87 2.48 9.55 46027.8 13.00 0.02 1.08 0.53 0.64 0.85 1.11 1.48 5.69 27415.1 14.00 0.01 0.64 0.31 0.38 0.50 0.66 0.88 3.39 16329.0 15.00 0.01 0.38 0.19 0.23 0.30 0.39 0.52 2.02 9725.9 16.00 0.00 0.23 0.11 0.14 0.18 0.24 0.31 1.20 5792.9 17.00 0.00 0.14 0.07 0.08 0.11 0.14 0.19 0.72 3450.4 18.00 0.00 0.08 0.04 0.05 0.06 0.08 0.11 0.43 2055.1 19.00 0.00 0.05 0.02 0.03 0.04 0.05 0.07 0.25 1224.1 20.00 0.00 0.03 0.01 0.02 0.02 0.03 0.04 0.15 729.1 21.00 0.00 0.02 0.01 0.01 0.01 0.02 0.02 0.09 434.3 22.00 0.00 0.01 0.00 0.01 0.01 0.01 0.01 0.05 258.7 23.00 0.00 0.01 0.00 0.00 0.00 0.01 0.01 0.03 154.1
24.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 91.8
25.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 54.7
26.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 32.6
27.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 19.4
28.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 11.5
29.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.9
30.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4.1
31.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.4
32.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.5
33.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.9
34.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.5
35.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.3
36.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.2
37.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.1
38.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.1
39.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
40.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
41.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
42.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
43.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
44.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
45.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
46.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
47.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
48.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
49.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
50.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0
Vol Hydrograf m3 6E+06 Cathment Area km2 56.92 Direct Run Off mm 103.50
Rasio DRO/RE % 98.3%
Vol Hyd (m3) Time
(hour) ITB-2 SUH
Hydrograph Convolution Total
4. ACKNOWLEDGMENT
This research is supported through Capacity Building Reseach Program 2010, 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-1 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
1) Natakusumah D.K, (2009), Prosedure Umum Penentuan Hidrograf Satuan Sintetis Untuk Perhitungan Hidrograph Banjir Rencana, Water Resources Conference, Bandung, 11 August, 2009, pp. 267-272.
2) Natakusumah D.K, Hatmoko W, Harlan D, (2010), Prosedure Umum Perhitungan Hidrograph Satuan Sintetis (HSS) Untuk Perhitungan Hidrograph Banjir Rencana. Studi Kasus Pengembangan HSS ITB-1 Dan HSS ITB-2, Water Resources Conference, Bandung, 11 November, 2010.
3) Ramírez, J. A., 2000:Prediction and Modeling of Flood Hydrology and Hydraulics. Chapter 11 of Inland Flood Hazards: Human, Riparian and Aquatic Communities Eds. Ellen Wohl; Cambridge University Press.
