, pp.88-95 http://dx.doi.org/10.14257/astl.2017.146.17 Snyder Unit Hydrograph Parameters for Malasian Catchments Hazalizah bt Hamzah¹, Jer Lang Hong² and Kee An Hong 3 ¹ Drainage and Irrigation Department, Malaysia ² Evault Technologies 3 Hong & Associates Abstract. Synthetic unit hydrograph models such as the Snyder unit hydrograph usually used lag time and peaking coefficient as input to estimate flood peaks and flood hydrographs for the design of water structures. As not all the streams are gauged lag time for ungauged catchments has to be estimated using relationships of the physical characteristics of the gauged catchments and the lag time derived from streamflow and rainfall data. In this study, a lag time formula using data from 30 rural catchments in Peninsular Malaysia ranging from 20 to 1450 km² was derived. 15 minutes interval rainfall and runoff data formed the basis for this study. In addition, daily read rainfall data were also used in aiding the estimation of catchment rainfall. A total of more than 500 significant storm events were chosen for lag time study. Stepwise multiple regression analysis was performed to relate average lag time to the catchment characteristics. The formula derived is: t p = 1.1789 A 0.254 L 0.5771 S 0.5608 Where t p is the lag time in hours, L is the main stream length in km and S is the weighted slope in m/km. The peaking coefficients for the gauged catchments range from 0.43 to 0.67, with a mean value of 0.59. The peaking coefficient is not significantly related to any of the catchment characteristics, therefore a mean value of 0.59 is recommended for use for ungauged catchments in the peninsula. 1 Introduction The objective of this study is to use local rainfall and runoff data from gauged stations operated and maintained by the Drainage and Irrigation Department to derive the Snyder lag time and peaking coefficient for use for ungauged catchments in Peninsular Malaysia. As the study area covered the whole peninsula, data available from autographic rainfall and streamflow stations and daily rainfall stations throughout the State are obtained from the Department of Drainage and Irrigation. In parallel with the expansion of the data base, there have been advances in hydrological methods and computer modeling, especially the powerful HEC-HMS model, which made this study simpler and time saving. ISSN: 2287-1233 ASTL Copyright 2017 SERSC
2 Literature Review 2.1 Time Parameters in Flood Hydrology Lag time is the time parameter which is an essential input to common flood discharge models. This stream flow response time is related to physical features of the catchment such as drainage area, stream slope and stream length. Estimated catchment lag time is needed to develop a synthetic unit hydrograph (UH) by the methods of Snyder and the Natural Resources Conservation Services(formally known as Soil Conservation Services (SCS). Lag time (t p ) has been defined in several different ways. In this study, lag time is defined as the time difference from the centroid of the net(excess) rainfall to the peak discharge of the catchment outlet. This definition is the one used in Snyder and SCS synthetic UH models. 2.2 Unit Hydrograph Peaking Coefficient A description of the shape of a unit hydrograph is the peaking coefficient Cp. The peaking coefficient is a dimensionless parameter represented by the formula: Q p = C p U A t p (1) In which Qp is the peak discharge, U is the unit depth of net rainfall, A is the catchment area and tp is the lag time. The value of Cp is usually between 0.4 and 0.8(McEnroe and Zhao 1999). In the SCS synthetic UH method, Cp is assigned a constamt value of 0.75. Snyder gave Cp value in the range 0.56 to 0.69 (Ponce 1989). The Snyder synthetic UH method requires Cp as an input. The peak discharge of the synthetic UH is directly proportional to Cp. 2.3 Previous Studies In flood hydrology, the lag time of a catchment is normally considered as constant, independent of the magnitude of the flood. Lag time is related to the travel time for the flood wave. In this section, some well-known formulas for lag time are presented. The SCS formula(1972) is: t p = 0.0057 ( 100 CN 9)0.7 L0.8 S In which t p is catchment lag time in hours,l is the longest flow path in km, S is the catchment slope in m/m, and CN is the SCS runoff curve number. This formula was developed from rainfall and streamflow data of agricultural catchments (SCS 1972) Snyder s formula(1938) is: t p = C t (L ca L) 0.3 (3) (2) Copyright 2017 SERSC 89
In which t p is catchment lag time in hours, L ca is the distance along the main stream from the outlet to the point nearest the centroid of the catchment in km, L is the total length in km of the main stream, and Ct is a coefficient that varies geographically.. Snyder applied the synthetic UH relationships to catchments ranging from 10 to 10000 mi²(30 to 30000 km²) [Chow 1988]. Carter s formula (1961) is: t p = 0.098 ( L S )0.6 (4) In which tp is the catchment lag time in hours, L is the main stream length in km, S is the average slope of the main stream length. This formula was developed from urban catchments in Washington D. C. with storm sewers and natural channels. The Kansas formula (McEnroe and Zhao,1999) is: t p = 0.086 ( L S )0.64 (5) In which t p is the lag time in hours, L is the main stream slope in Km,and S is the main channel slope in m/m. It is applicable for rural catchments up to 50 km² in Kansas Kum river formula (Jeong S. et al (2001)) is t p = 0.0044 ( L S )1.2282 (6) Where t p is the lag time in hours, L is the main stream slope in Km,and S is the main channel slope in m/m. In using the method of McEnroe and Zhao (1999) for the Kum river in Korea, Jeong et. al., (2001) derived the above equation for catchment area ranging from 134 to 902 km². 3 Hydrological and Geospatial Data There are 30 autographic gauged catchments in Peninsular Malaysia. Data at 15 minutes interval for all the stations in the peninsula (including rainfall data) were obtained from the Drainage and Irrigation Department. Figure 1 show the locations of the gauging stations and the periods of record for the stations are generally ranging from 1970 to 2016. For recorded flows at stations regulated by upstream storage, only pre dam data were be used for analysis. The catchment parameters adopted are catchment area, stream length, stream slope for this study. The catchment characteristics were measured for the catchments studied using geo-spatial method. 90 Copyright 2017 SERSC
4 Method of Approach 4.1 Selection of Rainfall runoff Events Floods with estimated return periods of 2 years or greater were identified and used for further study. Some smaller floods were also considered if the record is of acceptable quality. Single storm and multi-period storm events were selected provided that the Copyright 2017 SERSC 91
resulting hydrographs are well defined. There are no fixed rules in choosing the rainfall runoff events and the choice depends also on data availability. The quality of hydrograph data can be evaluated and selected using graphic printout and visual inspection. The rainfall runoff events were discarded if.the hydrographs were multipeaked.. the hydrographs started before the hyetographs..the hydrograph started after the hyetograph ended..the events presented a negative lag time.. direct runoff is greater than total rainfall for a storm event. 4.2 Computation of Lag Times and Peaking Coefficients The calibration feature in the HEC-HMS(2016) flood hydrograph program was used to determine the lag times for the individual events. Each catchment was modeled as a single basin. catchment rainfall was estimated using records from the catchments. The computation of lag times from rainfall and flow data requires the separation of base flow and the computation of net or excess rainfall. We use the exponential recession module of HEC-HMS to calculate base flow and direct runoff of the catchments. The initial and uniform loss model was used to compute the excess rainfall. 4.3 Parameter Estimation in HEC-HMS HEC-HMS used a numerical index to measure the closeness of fit of the computed and observed hydrographs. The objective function that is minimized by optimization routine is a discharge weighted root-mean square error. This objective function is: STDER= 1 n (Q n i=1 o Q c ) 2 WT i (7) In which Qo and Qc are observed and computed discharges at time index i, WT i is the weighting factor for time index i, and n is the number of ordinates of the hydrograph. The weighting factor,wt i (Qo+Qc)/2*Qave, in which Qave is the average observed discharge. This objective function provides an index of how closely the observed hydrograph is replicated. 4.4 Catchment Average Lag Time The lag time from the individual events were averaged to obtain a single lag time for each catchment. The average peaking coefficients were also calculated. Table 1 shows the average lag time and peaking coefficients for the 30 catchments. Lag time that differs greatly from the median value for the catchment were not used to compute the average lag time. Only minority of these events are excluded for individual catchments. 92 Copyright 2017 SERSC
Table 1. Average lag time and peak coefficient for selected catchments Basin ID Name Area Stream Length Stream Slope Lag time Peaking coeff. 1 Sg Arau at Ldg Tebu 20.6 9.1 4.4 3.35 0.43 2 Sg Kulim at Ara Kuda 129 30 6.7 9.58 0.57 3 Sg Krian at Selama 629 46.7 12.4 18.1 0.51 4 Sg Kinta at Tg Rambutan 246 33.8 33.3 3.63 0.5 5 Sg Raia at 182 37.8 33.8 4.04 0.48 6 Sg Bidor at Malayan Tin Bhd 210 34.9 21.1 6.85 0.51 7 Sg sungkai at Sungkai 289 44.6 19.7 10 0.51 8 Sg Bernam at TG Malim 186 20.2 45.8 3.88 0.53 9 Sg Selangor Rasa 321 37.8 23.9 5.87 0.5 10 Sg Selangor at R. Panjang 1450 75.2 8.3 38.69 0.53 11 Sg Batu at sentul 145 28.2 17.2 5.88 0.6 12 Sg Semenyih at Kg Rinching 225 36 10 8.19 0.49 13 Sg Langat at Dengkil 1240 48.5 7.7 21.7 0.47 14 Sg Linggi at Sua Betong 523 59.7 7.4 26.4 0.46 15 Sg Kepis at Jam Kepis 21 9.7 11.4 3.92 0.52 16 Sg Melaka at Pantai Belimbing 350 43.8 2.1 17.1 0.59 17 Sg Durian Tunggal at Air Resam 72.5 15.63 3.4 7.1 0.59 18 Sg Kesang at Chin Chin 161 34 2.4 19.4 0.46 19 Sg Sayong at Jam Johor Tenggara 624 47.1 1.3 58.7 0.62 20 Sg Johor at R Panjang 1130 61.4 1.2 69.2 0.65 21 Sg Kahang at 587 58.8 3.6 40 0.52 22 Sg Bentong at Kg Marong 241 25 16.2 5.13 0.51 23 Sg Lepar at Gelugor 560 69.5 3.2 39.1 0.63 24 Sg Kuantan at Bt Kenau 582 36.2 12.7 6.92 0.59 25 Sg Cherul at Kg Ban Ho 505 53.6 6 21.3 0.67 26 Sg Berang 140 30 23.7 6.1 0.59 27 Sg Telemong at 100 42.4 9.3 8.35 0.59 28 Sg Nerus at 393 48.5 2.3 27.7 0.62 29 Sg Chalok at Chalok 20.5 7.1 2.2 5.7 0.54 30 Sg Kemasin at Peringat 47.9 17.53 0.64 22.7 0.62 Copyright 2017 SERSC 93
4.5 Regression Analysis Regression analysis was carried out to quantify the relationship of lag time and catchment characteristics. This is to derive synthetic UH for ungauged catchments. A multiple linear regression analysis shows that lag time is highly correlated to catchment area, stream length and stream slope in the form of Equation 8: t p = 1.1789 A 0.254 L 0.5771 S 0.5608 (8) R=0.961715 R²=0.924896 And in the form tp=0.80037(l/ S) 1.06618 (9) R=0.95207 R²=0.90645 Where R is the correlation coefficient and R²is the coefficient of determination. Regression analysis was also performed to correlate lag time with catchment,slope and L/ S but no better correlation coefficients can be obtained. The results are: R=0.668 for tp ~ L in log form R=0.6709 for tp~s in log form R=0.909 for tp~ L S in log form As equation 8 gives a higher R²,it is recommended for use to estimate the lag time for ungauged catchments 4.6 Analysis of Peaking Coefficients Correlation analysis shows that Cp is not strongly related to any catchment characteristics. In other words when plotted against any catchment parameter, a flat slope exists and shows only a small amount of scatter for the regression line, therefore use of an average value for Cp may be just as reliable as the use of a regression equation. A Cp value of 0.59 is recommended for use for ungauged catchments. 5 Conclusion Synthetic unit hydrograph models such as the Snyder unit hydrograph usually used lag time and peaking coefficient as input to estimate flood peaks and flood hydrographs for the design of water structures. As not all the streams are gauged, lag time for ungauged catchments has to be estimated using relationships of the physical characteristics of the gauged catchments and the lag time derived from streamflow and rainfall data. In this study, a lag time formula using data from 30 rural catchments in Peninsular Malaysia ranging from 20 to 1450 km² was derived. 15 minutes interval rainfall and runoff data formed the basis for this study. In addition, daily read rainfall data were also used in aiding the estimation of catchment rainfall. A total of more than 500 significant storm events were chosen for lag time study. Stepwise multiple regression analysis was performed to relate average lag time to the catchment characteristics. 94 Copyright 2017 SERSC
The formula derived is: t p = 1.1789 A 0.254 L 0.5771 S 0.5608 Where t p is the lag time in hours, L is the main stream length in km and S is the weighted slope in m/km. The peaking coefficients for the gauged catchments range from 0.43 to 0.67, with a mean value of 0.59.The peaking coefficient is not significantly related to any of the catchment characteristics, therefore a mean value of 0.59 is recommended for use for ungauged catchments in the peninsula. Acknowledgement: The permission of the Drainage and Irrigation Department to use the data for this study is gratefully acknowledged. References 1. Carter R. W. (1961) Magnitude and frequency of floods in suburban area USGS prof paper 424-B 2. Chow V. T. Maidment D. R. and Mays L. W (1988) Applied hydrology McGraw Hill 3. Hydrology Engineering Centre (2016) Hydrologic modeling system version 5.2.1 user manual 4. Jeong S Park S. C. and Lee J H (2001) A study on the parameter estimation of Snyder-type synthetic unit hydrograph development in Kum river basin Water engineering research vol 2 No 4 5. McEnroe B. M and Zhao H(1999) Lag time and peak coefficients for rural watersheds in Kansa Kansas 6. University 7. Ponce V. M. (1989) Engineering hydrology, principles and practice Prentice Hall Englewood Cliff, New Jersey 8. Snyder F. F. (1938) Synthetic unit hydrograph Trans AGU 19 9. Soil Conservation Services (1972) national Engineering Handbook 10. Viessman Warren Jr. and Levis G L (1995) Introduction to hydrology Copyright 2017 SERSC 95