snyder unit hydrograph parameters for malasian...

Snyder Unit Hydrograph Parameters for Malasian

Catchments

Hazalizah bt Hamzah¹, Jer Lang Hong² and Kee An Hong3

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:

𝑡𝑝 = 1.1789 ∗ 𝐴0.254 ∗ 𝐿0.5771 ∗ 𝑆−0.5608

Where 𝑡𝑝 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.

Advanced Science and Technology Letters Vol.146 (FGCN 2017), pp.88-95

http://dx.doi.org/10.14257/astl.2017.146.17

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 (𝑡𝑝) 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:

𝑄𝑝 =𝐶𝑝∗𝑈∗𝐴

𝑡𝑝 (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:

𝑡𝑝 = 0.0057 ∗ (100

𝐶𝑁− 9)

0.7

∗𝐿0.8

√𝑆 (2)

In which 𝑡𝑝 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:

𝑡𝑝 = 𝐶𝑡 ∗ (𝐿𝑐𝑎 ∗ 𝐿)0.3 (3)

Advanced Science and Technology Letters Vol.146 (FGCN 2017)

Copyright © 2017 SERSC 89

In which 𝑡𝑝 is catchment lag time in hours , 𝐿𝑐𝑎 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:

𝑡𝑝 = 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:

𝑡𝑝 = 0.086 ∗ (𝐿

√𝑆)0.64 (5)

In which 𝑡𝑝 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

𝑡𝑝 = 0.0044 ∗ (𝐿

√𝑆)1.2282 (6)

Where 𝑡𝑝 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



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∗ ∑ (𝑄𝑜 − 𝑄𝑐)2 ∗ 𝑊𝑇𝑖

𝑛𝑖=1 (7)

In which Qo and Qc are observed and computed discharges at time index i, 𝑊𝑇𝑖 is

the weighting factor for time index i, and n is the number of ordinates of the hydrograph.

The weighting factor ,𝑊𝑇𝑖 (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.



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



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:

𝑡𝑝 = 1.1789 ∗ 𝐴0.254 ∗ 𝐿0.5771 ∗ 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.



The formula derived is:

𝑡𝑝 = 1.1789 ∗ 𝐴0.254 ∗ 𝐿0.5771 ∗ 𝑆−0.5608

Where 𝑡𝑝 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



snyder unit hydrograph parameters for malasian...

Documents