Effect of Time-Area Percent Curves in Development of Clark Model Unit Hydrograph

: This paper describes the effect of time – area percent curves in the development of Clark model unit hydrograph. This hydrology modelling study refers to event base modeling in order to derive the unit hydrograph from Clark instantaneous unit hydrograph. For this study, Kelani river basin up to Hanwella gauging site has been represented as the study area. Hydrologic Modelling System software developed by HEC, USA (HEC-HMS) has been used for the development of unit hydrographs under the Clark UH transform model. Three numbers of different time – area percent curves of Kelani river basin have been asynchronously used as input to the Clark UH transform model in order to obtain different simulations. The parameters, time of concentration T c and storage coefficient R values were calibrated and validated individually, against the various percent curves for the future analysis. The best suitable percent curve is identified based on the goodness of fit criteria, Nash-Sutcliffe Efficiency (NSE) with high accuracy. For the Loss model, initial and constant rate method was preferred. In the Meteorological Model, Gaged weight was considered for rainfall analysis. For the Transform Model or Direct Runoff Model, Clark UH is considered. For the Base flow model Recession, constant option was preferred. The Calibration (manual and automatic) was conducted for the storm events of May 2017, December 2014 and November 2012.Validation was conducted for the storm event of June 2014. The calibration and validation process was conducted for analyzing the hourly rainfall-runoff data for storm events observed during the monsoon seasons of the relevant years. The conclusions of the study would be very much applicable for the key personnel for taking structural and non-structural measures against the flood menace which is a frequent challenge over the study area concerned.


General
The fundamental theory of derivation of UH is very much useful in hydrological modeling studies. The direct runoff modeling also referred to as transform modeling -plays a significant role in the modeling studies. The program HEC-HMS used in this study, conceptually facilitates two options for the Transform models. These models are (i) Empirical models also known as system theoretical models and (ii) Conceptual models. The Clark UH Transform model, employed in this study-also falls under the empirical models. These empirical approaches follow the traditional UH theories [1]. Clark introduced his model and improved the concept and understanding of physical characteristics which influence runoff and flood producing capacity of streams [2]. Clark's method of deriving synthetic unit hydrograph(SUH) deals with instantaneous unit hydrograph (IUH).

ENGINEER 30
2 IUH mathematically conveys the excess precipitation into runoff to the outlet through two components such as (i) a translation hydrograph and (ii) attenuation [3] [4]. The translation flow is the function of time-area relations whereas attenuation is the effect of channel storage [5].
In this concept, the channel storage is treated as a linear reservoir storage for routing process. The Clark IUH can be derived by routing the unit excess rainfall with the conversion from time-area diagram of the watershed through a single linear reservoir [6].
The time-area histogram is developed in order to translate water volume in each area to the outlet considered, using corresponding time of travel of its translation. Development of the time-area relation of a basin is a complicated task unless software is used. Preparation of isochrone maps is essential to derive timehistograms. Isochrone defines that the imaginary line connecting equivalent time of travels to the outlet of a particular watershed. In this study, the isochrone map for the Kelani river basin up to Hanwella outlet is prepared in three different approaches. The first approach is synthetic time area relation. Other two approaches are carried out using two interpolation techniques such as Inverse distance weighted (IDW) and Kriging, which are available in ArcGIS software.
The application of synthetic time -area relation is described in the technical manual of HEC-HMS [7]. The interpolation techniques in ArcGIS obligatorily require certain inputs to produce isochrone maps. The inputs are the coordinates of remote points which are available with known time of travels to the outlets considered. Those remote points and their time of travels are computed with the application of HEC-GeoHMS which an extension package of ArcGIS is and is used to import the basin characteristics from ArcGIS to HEC-HMS. Coverage Geographical Informatics System (ArcGIS) is simultaneously employed with such modeling tasks nowadays [10]. representation of watershed characterization used in hydrological modeling in order to carryout flood assessment [11]. Flood estimation studies nowadays mainly deal with hydrological modelling software which are being updated with latest algorithms of computer application language [12].
GIS application enables to provide a digital

Figure 1 -Study Area
Kalani river basin up to Hanwella outlet, having an area of 1836 square kilometers, has been chosen for this study (Figure 1). Kelani river basin is located within the northern latitudes from 6° 45' to 7° 14' and eastern longitudes from 80° 04' to 80° 47'. The river basin lies in the districts of Colombo, Gampaha, Kegalle, Ratnapura and Nuwara-Eliya. Kelaniriver is the fourth largest river in Sri Lanka.

Data Availability and Data Processing
The Digital Elevation Model (DEM)of 30m resolution, which is freely available, was downloaded from the United States Geological Survey (USGS) website. DEM is the fundamental need of the HEC-Geo HMS tool to create the basin model. The soil data and land use -land cover maps are obtained to from a recent past study [8].
Meteorological data (hourly rainfall) for selected extreme flood events and hourly studies ENGINEER 31 3 Hydrological data (discharge & water level for selected extreme flood events) at six (06) gauging stations were obtained. These stations (shown in Figure 3) are Hanwella, Norwood, Deraniyagala, Kithulgala, Holombuwa and Glencourse located in the upper basin This data was obtained from the Department of Irrigation, Colombo, Sri Lanka for model calibration and validation. The event-based model calibration and validation is carried out by considering the extremely heavy rainfall events that occurred in the recent past (Table  1). To obtain the average rainfall of the basin, the Theisen polygon is processed in ArcGIS to obtain the gauge weights.

Application of ArcGIS and Preparation of Isochrone Maps
Application of ArcGIS is mainly involved in the spatial data processing. Watershed delineation, Digital elevation map, Theisen polygon map and Isochrone maps using different interpolation techniques are outputs of the application of ArcGIS. Accurate raw DEM is essential to feed as input to prepare a watershed and digital elevation map. Rain gauge stations and their coordinates are required as input to produce the 'Theisen' polygon map. Remote points with known time of travels and the coordinates of those points are required for preparing isochrone maps of the basin using different interpolation techniques.
To prepare the isochronal map of the basin, some points, located on the Kelani river and its tributaries in the basin are identified using HEC-GeoHMS. The time of travels from all these points up to Hanwella gauging site are required to be estimated. In this regard, the time of travels of all the segments, obtained from considering the two consecutive points on the streams, are taken to be directly proportional to L/ √s. This can be demonstrated by the Manning's equation as follows To prepare the isochronal maps, the following interpolation methods, available in the ArcGIS, are used: ▪ Inverse Distance Weighted (IDW) Interpolation ▪ Kriging Interpolation The Time-Area curve is developed using the above methods. It is presented in the form of a Time-Area Histogram as well as cumulative Time-Area Percent curves. In addition to this, a synthetic Time-Area curve is developed within the HEC-HMS program, considering the diamond shape of the basin. It provides an option for using the inbuilt time area curve in place of user defined time area curve. The HEC-HMS software has a predefined typical time-area relationship which has been built in the program as shown in Eq. (4) by considering the shape of the basin as diamond shape in order to make the time -area relationship smooth. where At = Cumulative watershed area contributing at time t; A= total watershed area; and Tc=time of concentration of the watershed.

Application of HEC-GeoHMS and HEC-HMS
HEC-GeoHMS is Geospatial Hydrological Modelling System, the extended supplementary application tool of ArcGIS and used to develop basin model and its characteristics from the raw digital elevation model (DEM) in a convenient manner. Basin Model is created by HEC-GeoHMS with two sub basins and used for the calibration and verification process.
The required basin characteristics such as longest flow path, river lengths, upstream & downstream elevations and slopes of each river segments are obtained via this HEC-GeoHMS application process [13]. The element network of the basin which represented in HEC-HMS desktop is also performed by HEC-GeoHMS.
Subsequently, the developed basin model representing element network in HEC-GeoHMS is imported to HEC-HMS for further application. HEC-HMS is the simulation software developed to simulate all types hydrological processes of watershed [9]. The software is user friendly and available as an open source. It is designed by USACE with updated versions and treats manner. The entire modeling process mainly is executed by the software HEC-GeoHMS and HEC-HMS. Figure 2 illustrates the calibration and validation process of the modelling of this study.
Meteorological Model is created by selecting gage weight option available in this HEC-HMS model.
Gage weights, estimated from Thiessen polygon method, are used for this option. There are three options available in the HEC-HMS program for the computation of baseflow. Those are: ▪ Constant, Monthly -varying value ▪ Exponential recession model ▪ Linear-reservoir accounting model In this study, the exponential-recession model and constant monthly varying value model are used to separate the base flow from the flood hydrographs resulting from different storm events in order to estimate the direct surface runoff hydrographs for the Hanwella net basin and Kithulgala sub basin respectively. The initial parameter values of the above two base flow models are obtained from the available observed flood hydrographs data. These initial parameter values are required to set up the HEC-HMS model for validation and calibration [1].

Figure 2 -Flow Diagram for Methodology
There are numerous runoff volume models also known as loss models, available in HEC-HMS modelling.
▪ where R is a constant linear reservoir parameter (storage coefficient). From the above equations (5) and (6), the following relationships are yielded.
Ot = CAIt + CBOt-1 …. (7) where CA and CB are routing coefficients. computation of these coefficients is given below: Since the cumulated effects of all basin storage are represented in this Clark UH model, the reservoir may be considered to be located conceptually at the outlet considered. In addition to this lumped model of storage, the Clark UH model computes the time required for water to move outlet from the basin. It carries this out with a linear channel model, in which water is routed from remote points to the outlet with delay (translation) but without attenuation. This delay is implicitly related to time and area, so called time-area histogram. This specifies the basin area contributing flow at the outlet as a function of time. If the area is multiplied by the unit depth of excess rainfall and divided by the time step ∆t, the result is inflow, It, to the outlet (linear reservoir).  . . (11) where Qobs, Qcom, and Q̅ are the observed, simulated and observed mean discharge over the n hours respectively. The most optimal value of NSE is 1. Volume deviation (DV) where Vobs and Vcom are the observed and simulated volume of runoff over the n hours respectively. The most optimal value of DV is 0 (zero). Percent error in peak (Z) Z = | Qobs(peak) − Qcom(peak) Qobs(peak) | x 100% . . (13) where (peak) and (peak)are the observed and simulated peak discharge of runoff over the n hours respectively. The most optimal value of Z is 0 (zero).
NSE has been reported as the best performance criterion of simulation [14]. However, in addition to the NSE, percent error in peak, percent error in time to peak, percent error in discharge volume of each direct runoff model were compared individually for each of the flood events considered for calibration and validation[8].

2.6
Model Calibration and Validation using Three Different Time-Area Relations Calibration of transform models is carried out using the automatic calibration (optimization) option available in HEC-HMS. However, for the optimization runs, the initial parameter values of the models are required to be estimated. In this regard, sensitivity analysis is carried out for estimating the parameters. The calibrations of the model are carried out based on the various goodness of fit measures derived from the observed and simulated hydrographs in HEC-HMS program. Based on these measures, the optimized parameters of the Clark UH model, are selected. Calibration is carried out for a selected number of events and the representative parameters are derived taking the average of the optimized parameters obtained for each event considered for the calibration. The representative parameters of the Clark UH model under the three-different consideration of time area percent curves are used in HEC-HMS for their validation over the selected storm events not considered for calibration.

Data Processing
Thiessen polygon map is developed using ArcGIS as shown in Figure 3. Hourly rainfall values were available for storm events at 6 rain-gauge stations located within the basin. The locations of these six rain gauge stations are considered to prepare this map. Gauge weights for the two sub basins are computed by using Thiessen polygon method. From Figure 3, it is observed that the Norwood rain-gauge station has the least Thiessen Gauge Weight for the Hanwella net basin compared to the other rain gauge stations. The Thiessen Gauge Weights for the six rain gauge stations influence the Hanwella net basin whereas only two Theisen gauge weights namely Kithulgala and Norwood, influence the Kithulgala sub basin. The corresponding Thiessen Gauge weights are considered as input to the Meteorological Model for HEC-HMS program to individually compute the average hourly rainfall over the sub basins for all four storm events using Thiessen Polygon Method.

Figure 3 -Thiessen Polygon
The isochrone map is prepared following the methodology under Section 2.2. The longest flow path and river reaches are identified using HEC-GeoHMS software.

Inverse Distance Weighted (IDW) Interpolation
Method (using ArcGIS): These isochrones are drawn using inverse distance weighted (IDW) interpolation technique of ArcGIS which helps to interpolate a raster surface from points with its known time of travel as shown in Figure 5.

Figure 5 -Points Identified Using HEC -GeoHMS and Their Time of Travel
The time of concentration (Tc) is considered as 18 hrs during the computations. Kelani river basin upto Hanwella is divided into 18 different subareas enclosed between the two consecutive isochrones having time of travels (∆tc) of 1 hour as shown in Figure 6. The time of travels associated with each isochrone and the area enclosed between the two consecutive isochrones are computed. Then, the cumulative area and time of travels are also computed. Subsequently, the value of t/Tc and At/A are computed.    Finally, the time-area percent curves obtained from three different methods are compared as shown in Figure 11. From this figure, it is observed that there is not much variation in the shape of the time-area percent curves developed by both the two interpolation methods.

3.2
Computation of Initial Model Parameters Barnes (1940) introduced the recession storage of a basin Qt = Q0.Kr = Q0.e -at ; where Q0 and Qt are discharge at time interval t days with Q0 being the initial discharge. Kr is the recession constant value less than unity; a = (-ln Kr). Figure 13. shows the recession curve obtained from the flood hydrograph of Hanwella gauging station during the event of May 2017. From this curve, the base flow model parameters for the Hanwella net basin are computed. The initial discharge, recession constant and the threshold discharge are computed to be 9.5 m 3 /s, 0.9 and 215 m 3 /s respectively. These initial values are also used for the other flood events for their simulations.             Figure  28 shows the comparison of percent errors in peaks, time to peaks and discharge volumes, with the three-different time-area percent curve applications for the Jun 2014 event . From these figures, it is observed that the overall model efficiency NSE value of Kriging interpolation case is quite higher than that of other two time-area percent curve cases.  Table 5 shows the NSE values resulted during the calibration and validation of Clark UH model using three time-area percent curves. Calibration of the three events yields a comparatively higher value for the synthetic time-area percent curve approach whereas validation of the single event results in a comparatively higher value for Kriging interpolated time-area percent curve case.

Conclusions
Only three of recent past flood events have been used for calibration and one event has been used for validation. However, the validation of the event of June 2014 yields a comparatively higher NSE value for the 'kriging' interpolated time-area percent curve method. Also, the more sensitive parameter Tc (= 13.4 hrs) basin significantly differs from the Tc of other cases. Tc is the one of the principal hydrograph properties of Clark UH. Hence, the kriging interpolated time-area percent curve is very much applicable in the use of Clark UH model of HEC-HMS compared to other types of time-area percent curves.