Introducing Two-Dimensional Hydraulic Simulation as a Technique for Estimating the Time of Concentration

Introduction:

 Time of concentration (TC) is the time in which a water parcel travels from watershed divide to its outlet. Time of concentration is also the most important factor in selecting design discharge for an area, since the most severe floods are those caused by rainfalls with durations equal to the concentration time of a watershed. Time of concentration is necessary in the studies of water resources management, flow volume and discharge estimation, design of spillways and hydraulic structures, development of flood predicting models, flood alert systems, river management and drainage projects and many other water related studies. There are various empirical methods for calculation of concentration time. The focus of this study is to simulate the water parcel to calculate the time of concentration with a two-dimensional hydraulic model (HEC-RAS 5.0.7). To the knowledge of the authors this method has never been applied for estimation of time of concentration.

Currently there are two main methods to evaluate the time of concentration; applying empirical formulas or applying graphical methods with requires flood hydrograph and corresponding rainfall hyetographs. Due to the differences in the accuracy levels of empirical methods in different areas, along with the unavailability of graphical methods in most of the watersheds, this study aims to estimate TC, using the basic definition of time of concentration which is the travel time of a water parcel from basin divide to the outlet. Two-dimensional HEC-RAS model was used to navigate the runoff flow in the main channel of a watershed from the farthest hydrological point to the outlet. Besides, 48 different empirical equations were gathered from the literature and used to estimate the time of concentration. In order to validate the numerical method and the empirical formulas, the actual concentration time of the flow is measured by salt solution tracking. Then, the comparison of the measured data with the results of the numerical and experimental methods is made, using the percent of error index. Ali Abad watershed of Fars province has been considered as a case study due to the appropriate data availability and the possibility of various measurements as described in the following sections.

Results showed that only 5 methods indicate relative errors less than 20% of which 4 belong to the empirical formulas (8% of the total empirical methods) and one to the numerical simulation. The NRCS is also a well-known equation in which runoff flow in a watershed is divided into three parts: sheet flow, concentrated shallow flow and open channel flow. Flow velocity is estimated by the Manning's relation in the reach according to this method. This method’s accuracy is about 82%. In order to run the two-dimensional model, DEM of the area with 10 meters’ accuracy was used to define the bathymetry. Manning roughness coefficient was also calibrated for model tuning. Over ally the best results were obtained from the hydraulic simulation when applying bank-full discharge equal to 3.53 cms so that the error of this method was limited to 3%. Hence, it is wise to accept the computational costs of a two-dimensional hydraulic simulation to predict the time of concentration instead of empirical formulas, Since the results might be used to construct costly hydraulic structures.

Different methods of concentration time estimations were evaluated and compared with the actual concentration time obtained by salt solution tracing in Aliabad watershed of Fars province. Two-Dimensional simulation of the water parcel from the basin divide to the outlet was also performed by HEC-RAS 5.0.7. The results indicated that among empirical relations, the concentration time value obtained from the Simas and Hawkins equation is much closer to the actual value and is considered as the best empirical equation for Aliabad watershed. This equation involves river length and slope, watershed area and surface storage. Following Simas and Hawkins, equations developed by SCS, SCSlag, Yen and Chow, and NRCS gave closest estimations to the actual concentration time, respectively. However, the results of hydraulic simulation show the most accuracy depending on water parcel definition. That is because, the two-dimensional model takes the topography, local slope, roughness and geometry of the water body into account and is a reliable technique to estimate the time of concentration in any desired location. Nevertheless, for empirical relations it is necessary to realize the limitations of each method and compare it with the study area. Hence, it is recommended to apply hydraulic simulation instead of empirical formulas to estimate the time of concentration. Also, with the measurement data, the results of this study can be used as a criterion for measuring concentration time in similar hydrological studies.