Methods of Estimating Time of Concentration: A Case Study of Urban Catchment of Sungai Kerayong, Kuala Lumpur

Abstract

Characterization of hydrologic processes of a catchment in relation to water resources structures design requires estimation of time-response characteristics which is used in hydrologic models. The time of concentration (T_c) is an essential component in hydrological modelling which is used in predicting the response time of a catchment to a storm event. There are many approaches in the estimation of time of concentration from literature. At gauged watersheds, T_c can be estimated using rainfall and a runoff hydrograph, while for ungauged catchments, empirical equations are used. In this study, variability of empirical methodologies and hydrograph separation method for evaluating T_c using data from past study on Sungai Kerayong, Kuala Lumpur is presented. Results of the study showed Gundlach, Carter and NAASRA methods are suitable for estimating T_c in the study area while Bransby-Williams and Ventura methods were the poorest in estimation of T_c in the study.

1 Introduction

Determination of runoff characteristics in a catchment has always been a critical subject in hydrological analysis. The time of concentration (T_c) is a basic catchment response time criteria needed for forecasting of the peak discharge rate and the timing of the flood event [1]. Nearly all hydrologic analyses depend upon one or more time-scale parameters as input. The time of concentration (T_c) is the most commonly used time parameter [2] because it is a key parameter in runoff estimation. Time parameters describe the accumulation of excess rainfall over a watershed and, as such, they have a direct and significant impact on the peak discharge and shape of the hydrograph. Time parameters are linked to the physical characteristics and the morphology of the watershed. Time parameters are an important part of rainfall-runoff hydrologic design and modelling [3]. T_c cannot be defined precisely, and likely differs from season to season and from storm to storm [4]. The time of concentration is the time necessary for water to flow from the remotest part of the outlet once the soil has become saturated and small depressions filled to the watershed outlet. On the other hand, time of concentration t_c can be evaluated from a rainfall hyetograph and the resulting runoff hydrograph. From this perspective, the time of concentration is the time between the centre of mass of rainfall excess and the inflection point on the recession curve of the direct runoff hydrograph [3]. A lot of empirical methods have been developed and used by several authors in estimating the time of concentration in a catchment. Precision in the estimation of T_c is very important to avoid overestimation in peak discharge result and vice versa [5]. Still, modelers are having problems in ascertaining the level of accuracy of these empirical methods. There has been previous effort in evaluating the accuracy of these methods. Nagy et al. [6] found out that Wisnovszky-equation underestimated T_c when they used HEC-HMS to model runoff using T_c as one of the input parameters. Salimi et al. [7] used 22 methods in estimating T_c and applied the values obtained in HEC-HMS. Their findings showed that peak runoff values estimate from Bransby-Williams method were the most consistent and displayed hydrologic condition of the watershed well. Almeida et al. [8] applied hierarchical cluster analysis (Cluster) to 30 empirical methods prioritizing those methods that incorporated rainfall intensity to evaluate the rate of similarity amongst the methods. Pasini’s and Ventura’s method presented the highest similarity while Arizona DOT (Arizona Department of Transportation) showed strong dissimilarities. Sharifi and Hosseini [2] established that California, Kirpich and Arizona DOT equations performed outstandingly when seven T_c equations were modified to reduce their bias. Almeida et al. [9] used graphical method to analyze T_c and compared the results to the results of T_c obtained using twenty empirical equations from past references. Findings showed that the graphical method was efficient and dependable in determining T_c, and Ventura’s equation was outstanding for a rural catchment in a tropical climate region.

Understanding the role of a catchment in relation to T_c is crucial for determining rainfall and peak flow [9]. Substantial errors in peak runoff quantification at catchment scales can be attributed to errors in the estimation of catchment response times like T_c and eventual false estimation of peak runoff [10]. Techniques for estimating time parameters generally need one or more watershed characteristics. For example, a method might require channel length or channel slope [11]. This paper provides in-depth analysis into the variability of accuracy of the various methods used for estimation of T_c for Sungai Kerayong Catchment in Kuala Lumpur, Malaysia. The study will use more referenced empirical methods to estimate value of T_c. The additional methodologies will be explained and results with be compared and discussed.

1.1 Objectives

The main objective of this study is to estimate the value of T_c by using Carter, Johnstone-Cross, Hakatnir-Sezen, Gundlach, revised CUHP (Colorado Urban Hydrograph Procedure), Papadakis-Kazan, Ventura and Arizona DOT methods. The eight methods are used and the results of T_c evaluated was compared to the T_c estimated from direct runoff hydrograph (DRH) for the Sungai Kerayong Catchment in previous study by Abustan et al. [12], Baharudin [13]. In order to evaluate the reliability of the results obtained from the DRHs and the extended empirical formulas, Nash–Sutcliffe efficiency index (NS) method was applied using an objective function.

2 Study Area

Sungai Kerayong catchment is located in Kuala Lumpur of Peninsular Malaysia. It has an area of 48.3 km² and consists of four major districts namely Kuala Lumpur, Ampang, Salak Selatan and Pekan Batu Sembilan. The elevation ranges between 30 and 175 m above mean sea level. The study area has year-round equatorial climate which is warm and sunny, along with heavy rainfall, especially during the southwest monsoon from April to September and has a record of 2266 mm mean annual precipitation. Urbanization has been vast throughout the years whereby continuous developments and increased population occurs in the study area. This has made Sungai Kerayong catchment an ideal selection as an experimental urban catchment to monitor the hydrological characteristics and time response parameters of the area. The study area is shown in Fig. 1 and the Stream network and subcatchments are shown in Fig. 2.

Fig. 1

Map of the Sungai Kerayong catchment area

Fig. 2

Stream network and sub catchment map

2.1 Previous Studies

There have been various and extensive studies on T_c estimation. There are two common approaches developed to estimate T_c, first is the velocity-based method [3]. (i) The hydraulics aspect wherein empirical equations that are regression based can be used in the analysis. (ii) The second approach is based on time-lag method where T_c can be computed from time difference between the end of rainfall excess and the inflection point. For this study various empirical methods will be explained and summarized here. A review of study of rainfall-runoff characteristics by Abustan et al. [12], Baharudin [13] for Sungai Kerayong will be conducted and eight more empirical approach will be used for further analysis to check the most suitable method for the study area (Table 1).

Table 1 Summarized empirical methods

3 Materials and Methods

The data used in this study are retrieved from study of rainfall-runoff characteristics of Sungai Kerayong [13]. Rainfall and water level data from Malaysia Department of Irrigation and Drainage (DID) and parameters for cross sections of the channels from channel survey and satellite images for assessing initial condition of channels were used to establish discharge for the storm events using Manning’s equation. The study area was delineated into three sub-catchments namely the Kg. Cheras Baru, Taman Miharja and the Taman Desa. A summary of catchment parameters used for T_c estimation is presented in Tables 2 and 3. The elevation map of Sungai Kerayong catchment is shown in Fig. 3. Runoff co-efficient value C of 0.60 was used for the three sub-catchments for revised CUHP because of the level of urbanization of the study area.

Table 2 Summary of parameters required for estimation of T_c using empirical equations

Table 3 Summary of additional parameters required for estimation of T_c using empirical equations

Fig. 3

Elevation map

Estimation of T_c for the sub-catchments were done after establishing all needed parameters for each equation. Five new empirical equations are selected to evaluate T_c for the study area based on the characteristics of the study area and suitability of the empirical methods relative to their past recommendations. Rainfall intensity of 150 mm/h was adopted for the study from MSMA [39]. The formula T_R was adopted for the revised CUHP as the percentage of impervious surface for the study area was 76.2%.

The previous work by Baharudin [13] used direct runoff hydrographs (DRH) to estimate the time of concentration of the catchments for 20 storm events. The DRH of a storm event for each catchment is shown in Fig. 4 and other storm events are presented in the Appendix.

Fig. 4

T_c = 150 min (Taman Desa, 30-09-2001)

The results for estimated T_c by Baharudin [13] and eight new methods are summarized in Table 4.

Table 4 Summary of estimated Tc for the study area by Baharudin [13] and newly included methods

4 Results and Discussions

Nash–Sutcliffe efficiency index (NS) method was used to evaluate the reliability of results from the DRH plots and the empirical formulas. This was done between the estimated T_c and the observed T_c. The results for the newly estimated Tc and previous study results are summarized in Table 5 for the three catchments in the study area.

Table 5 NS values obtained for the Tc empirical equation in comparison to observed Tc

The results of the NS values varied for all the three catchment areas. The methods which presented the best values for the three sub-catchment areas were highlighted in red in Table 5. Among the eleven empirical formulas used to evaluate T_c for Kg. Cheras Baru, Carter equation showed the best agreement with the T_c value of 57.14 min when compared to average observed T_c of 52.5 min while the Ventura method performed worst. The Gundlach equation performed best in Taman Miharja catchment area with T_c value 76.65 min compared to the average observed T_c of 79.5 min and Ventura still maintained worst performance for the catchment. The NAASRA equation maintained its best position of evaluating T_c for Kg. Cheras Baru from previous study of the catchment area and the Ventura and Bransby-Williams equation performed worst for this catchment as well. The reason for this poor output is because both methods have been recommended for estimation of time of concentration rural basins from previous studies.

5 Conclusion

Identifying the sensitivity of time of concentration is very crucial in evaluating the response time of runoff generation in an urban catchment. In this review study, Gundlach, Hakatnir-Sezen, Carter, Johnstone-Cross, revised CUHP, Papadakis-Kazan, Ventura and Arizona DOT empirical methods were used to further estimate the value of time of concentration of Sungai Kerayong urban catchment area of Kuala Lumpur, Malaysia. Previous study used rainfall-runoff hydrograph analysis and four empirical methods in estimation of T_c. From the findings of the study Gundlach, Carter and NAASRA methods performed best in estimating T_c and can be adopted in the region. Gundlach, NAASRA and Carter methods level of performance can be attributed to the method incorporating impervious fraction, area, length, roughness coefficient and slope which are important parameters in an urban catchment while the Bransby-Williams and Ventura can be concluded not suitable for evaluating T_c for an urban catchment. It can be recommended from this study findings that further data of time of concentration from several catchments by different methods can be gathered for machine learning like SVM, ANN which can help in predicting time of concentration of various catchment characteristics.

Appendix

See Figs. 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60 and 61.

Fig. 5

T_c = 195 min (Taman Desa, 01-07-2001)

Fig. 6

T_c = 135 min (Taman Desa, 30-07-2001)

Fig. 7

T_c = 135 min (Taman Desa, 06-10-2001)

Fig. 8

T_c = 165 min (Taman Desa, 16-10-2001)

Fig. 9

T_c = 120 min (Taman Desa, 28-10-2001)

Fig. 10

T_c = 120 min (Taman Desa, 09-11-2001)

Fig. 11

T_c = 120 min (Taman Desa, 19-11-2001)

Fig. 12

T_c = 165 min (Taman Desa, 01-12-2002)

Fig. 13

T_c = 135 min (Taman Desa, 21-02-2002)

Fig. 14

T_c = 135 min (Taman Desa, 23-04-2002)

Fig. 15

T_c = 90 min (Taman Desa, 27-04-2002)

Fig. 16

T_c = 120 min (Taman Desa, 20-05-2002)

Fig. 17

T_c = 180 min (Taman Desa, 02-06-2002)

Fig. 18

T_c = 120 min (Taman Desa, 16-06-2002)

Fig. 19

T_c = 195 min (Taman Desa, 08-10-2002)

Fig. 20

T_c = 135 min (Taman Desa, 07-10-2002)

Fig. 21

T_c = 150 min (Taman Desa, 13-11-2002)

Fig. 22

T_c = 135 min (Taman Desa, 13-01-2003)

Fig. 23

T_c = 150 min (Taman Desa, 06-01-2003)

Fig. 24

T_c = 90 min (Taman Miharja, 19-07-2001)

Fig. 25

T_c = 75 min (Taman Miharja, 14-08-2001)

Fig. 26

T_c = 75 min (Taman Miharja, 15-09-2001)

Fig. 27

T_c = 90 min (Taman Miharja, 19-09-2001)

Fig. 28

T_c = 105 min (Taman Miharja, 30-09-2001)

Fig. 29

T_c = 75 min (Taman Miharja, 16-10-2001)

Fig. 30

T_c = 75 min (Taman Miharja, 27-12-2001)

Fig. 31

T_c = 75 min (Taman Miharja, 19-01-2002)

Fig. 32

T_c = 90 min (Taman Miharja, 21-02-2002)

Fig. 33

T_c = 90 min (Taman Miharja, 22-04-2002)

Fig. 34

T_c = 75 min (Taman Miharja, 23-04-2002)

Fig. 35

T_c = 90 min (Taman Miharja, 26-04-2002)

Fig. 36

T_c = 90 min (Taman Miharja, 27-04-2002)

Fig. 37

T_c = 90 min (Taman Miharja, 20-05-2002)

Fig. 38

T_c = 120 min (Taman Miharja, 26-05-2002)

Fig. 39

T_c = 45 min (Taman Miharja, 07-06-2002)

Fig. 40

T_c = 90 min (Taman Miharja, 11-06-2002)

Fig. 41

T_c = 75 min (Taman Miharja, 16-06-2002)

Fig. 42

T_c = 75 min (Taman Miharja, 07-11-2002)

Fig. 43

T_c = 75 min (Taman Miharja, 06-01-2003)

Fig. 44

T_c = 45 min (Kg. Cheras Baru, 01-07-2001)

Fig. 45

T_c = 60 min (Kg. Cheras Baru, 09-07-2001)

Fig. 46

T_c = 30 min (Kg. Cheras Baru, 30-07-2001)

Fig. 47

T_c = 60 min (Kg. Cheras Baru, 14-08-2001)

Fig. 48

T_c = 60 min (Kg. Cheras Baru, 15-09-2001)

Fig. 49

T_c = 60 min (Kg. Cheras Baru, 30-09-2001)

Fig. 50

T_c = 60 min (Kg. Cheras Baru, 19-01-2002)

Fig. 51

T_c = 30 min (Kg. Cheras Baru, 21-02-2002)

Fig. 52

T_c = 75 min (Kg. Cheras Baru, 06-05-2002)

Fig. 53

T_c = 30 min (Kg. Cheras Baru, 20-05-2002)

Fig. 54

T_c = 30 min (Kg. Cheras Baru, 26-05-2002)

Fig. 55

T_c = 60 min (Kg. Cheras Baru, 02-06-2002)

Fig. 56

T_c = 45 min (Kg. Cheras Baru, 11-06-2002)

Fig. 57

T_c = 75 min (Kg. Cheras Baru, 16-06-2002)

Fig. 58

T_c = 30 min (Kg. Cheras Baru, 05-11-2002)

Fig. 59

T_c = 75 min (Kg. Cheras Baru, 07-11-2002)

Fig. 60

T_c = 45 min (Kg. Cheras Baru, 14-11-2002)

Fig. 61

T_c = 75 min (Kg. Cheras Baru, 08-12-2002)