Efficiency of the geomorphologic instantaneous unit hydrograph method in flood hydrograph simulation

Catena 87 (2011) 163–171

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Catena j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c a t e n a

Efficiency of the geomorphologic instantaneous unit hydrograph method in flood hydrograph simulation M.R. Khaleghi a,⁎, V. Gholami b, J. Ghodusi c, H. Hosseini a a b c

Department of Range and Watershed Management, Torbat-e-Jam Branch, Islamic Azad University, Torbat-e-Jam, Iran Department of Range and Watershed Management, University of Guilan, Faculty of Natural Resources, Sowmeh Sara, Iran Islamic Azad University, Science and Research Branch, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 23 May 2010 Received in revised form 13 April 2011 Accepted 25 April 2011 Keywords: Rainfall-runoff model Flood hydrograph Geomorphologic and Geomorphoclimatic instantaneous unit hydrographs Kasilian Watershed

a b s t r a c t Several methods and models to simulate rainfall-runoff processes have been presented, and each of them has its own advantages and disadvantages. In the present study, different methods were applied to simulate the rainfall–runoff process over the Kasilian Watershed located in northern Iran, including Snyder, SCS, Trianglar, Rosso and Geomorphoclimatic unit hydrographs. The study was intended to compare the accuracy and reliability of a geomorphologic model with Snyder, SCS, Trianglar, Rosso and Geomorphoclimatic Unit hydrographs. In addition, this study attempted to determine the shape and dimensions of outlet runoff hydrographs in a 68.8 km 2 area in the Kasilian Basin, which is located in the Mazandaran Province of Iran. The first twenty-one equivalent rainfall–runoff events were selected, and a hydrograph of outlet runoff was calculated for each. The peak time and peak flow of outlet runoff in the models were then compared, and the model that most efficiently estimated hydrograph of outlet flow for similar regions was determined. The comparison of calculated and observed hydrographs showed that the geomorphologic model had the most direct agreement for the parameters of peak time and peak flow of direct runoff. Statistical analyses of the models demonstrated that the geomorphological model had the smallest main relative and square error. The study's results confirm the high efficiency of the Geomorphoclimatic Unit Hydrograph and its ability to increase simulation accuracy for runoff and hydrographs. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Many hydrologists have undertaken simulations of rainfall–runoff processes to estimate the volume of runoff and the pick discharge value of watersheds. The determination of the pick discharge value and the runoff volume of a watershed are crucial in managing natural disasters and designing and constructing water structures. Therefore, different methods have been developed. Each of these methods has their own merits and demerits. Human activities have always been accompanied by changes in land structure, the destruction of natural resources and urban developments. Cosmopolitan developments on the surface of the watershed will be included in the increase in peak discharge and runoff volume of the watershed (Burns et al., 2005; Brilly et al., 2006; Pappas et al., 2008). Iran is the second largest country in the Middle East, and almost 87% of the country is located in arid and semi-arid regions (Rangavar et al., 2004). The average annual rainfall is 240 mm, which is less than one-third of the global average value, making the region among the world's driest. Recent studies in Iran have shown that, the total volume of annual precipitation is

⁎ Corresponding author: Tel.: + 98 05282210222; fax: + 98 05282210080. E-mail address: [email protected] (M.R. Khaleghi). 0341-8162/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.catena.2011.04.005

almost 430 billion m 3 but that more than 20% is lost in the form of flash floods (Foltz, 2002). In watershed planning and flood management, estimating the maximum flood discharge is necessary for predicting watershed hydrological behavior. Flood management in a basin will not be successful unless the watershed's hydrological behaviors are predicted (Bhadra et al., 2008). Major problems concerning hydrological predictions include a lack or low accuracy of rain data, high cost, lack of information about catchments and the length of time required to obtain study results (Maheepala et al., 2001; Vaes et al., 2001; Lopez et al., 2005; Vahabi and Ghafouri, 2009). Knowledge of the relationship between rainfall and runoff is important to understand hydrology. A common method in flood estimation is the unit hydrograph, which is not only applied in peak flow estimation but also in the creation of complicated flood hydrographs. Catchments and storm characteristics are the primary parameters that affect complex watershed responses to rainfall events (Agirre et al., 2005). The production and behavior of runoff are functions of land use types and changes. The hydrological response of a river basin is based on the relationship between basin geomorphology (catchments area, shape of basin, topography, channel slope, stream density and channel storage) and its hydrology (Loukas et al., 1996; Shamseldin and Nash, 1998; Ajward and Muzik, 2000; Hall et al., 2001; Jain and Sinha, 2003; Nourani et al., 2009). Many studies

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have been carried out on the efficiency of artificial unit hydrographs and instantaneous unit hydrographs (IUHs) in Iran and around the world (Wang and Chen, 1996; Jeng and Coon, 2003). An IUH is defined as the probability density function (PDF) of the droplet travel time from the source to the basin outlet, in which the time spent in each state (the order of the stream in which the drop is located) is taken as a random variable with an exponential PDF (Liu et al., 2003). The concept of the GIUH was first introduced by Rodriguez-Iturbe and Valdes (1979) and later generalized by Gupta et al. (1980). In this approach, excess rainfall is assumed to follow different probabilistic flow paths in the channel and on overland areas to reach the basin outlet (Bhadra et al., 2008). Rodriguez-Iturbe et al. (1982) proposed a geomorphoclimatic instantaneous unit hydrograph (GCIUH) as a link between climate and the geomorphologic structure and hydrologic response of a basin. The authors derived a set of basic equations for a third-order watershed. This quantitative conceptualization allowed for the creation of a GIUH for an ungauged small watershed. Based on the results of the study, the GIUH model was applied in semi-arid regions and the results were compared with the traditional SCS approach to further verify the model. The authors concluded that there was a correlation between the simulated runoff hydrograph and the recorded flows. Cudennec et al. (2004) investigated the geomorphologic aspect of the unit hydrograph concept and concluded that the use of geomorphologic parameters explained the unit hydrograph and geomorphologic unit hydrograph theories. Sorman (1995) applied the GIUH model to estimate peak discharges resulting from various rainfall events for basins in Saudi Arabia and concluded that the length ratio (RL) significantly influenced the hydrologic response of a river basin and must be considered for flood-forecasting studies of any river. Hall et al. (2001) conducted a regional analysis using the GCIUH (Geomorphoclimatic Instantaneous Unit Hydrograph) in southwestern England. In this study, the rainfall excess duration was divided into several time increments, and separate IUHs were generated for each interval. The results showed that fine time intervals capture the shape of runoff hydrographs. Jain et al. (2000) investigated rainfall–runoff modeling using GIUH in the Gambhiri catchment in western India. The results indicated that peak characteristics of the design flood are more sensitive to various storm patterns. The purpose of the study was to compare different methods of flood hydrograph simulation for the purpose of analyzing floods in similar ungauged watersheds. The current study has been conducted to determine the most appropriate method of creating flood hydrographs in the Kasilian watershed. 2. Study area The Kasilian watershed encompasses an area of about 68 km² and is located in northern Iran within the limits of eastern longitude from 53°18′ to 53°30′ and northern latitude from 35 °58′ to 36 °07′ in the eastern part of the Mazandaran province (Fig. 1). The area's climate is semi-humid and cold, with an average annual precipitation of 791 mm and average temperature of 11 °C. The average, maximum and minimum heights of the watershed are 3349, 1120 and 1672 m, respectively. The average slope of the watershed, the average slope of the main channel and the length of the main channel are 15.8%, 13% and 16.5 km, respectively. A hydrometric station is located at the outlet of the watershed (Valikben Station), and a rain recorder station (Sangdeh Station) is located upstream of the station. This study was conducted from Winter (October) 2007 to Winter (June) 2009. 3. Materials and methods In this study, an attempt has been made to compare the performance of the GIUH and GCIUH methods and validate the models with recorded data from the watershed. Twenty-one single rainfall–

runoff events (which were collected among other data, including snow melt, which had no effect on the obtained flood) were selected for the creation of a geomorphologic instantaneous unit hydrograph. Data and information on equivalent rainfall–runoff events in which snow did not melt were collected from graphs. After separating the base flow and calculating curve areas from each event, the direct runoff was obtained by dividing the value by the total area of the watershed. The excess rainfall for 1 h was obtained in this way. Arcview GIS software was used extensively to prepare model input data, such as the area, slope and length of the main river basin, and geomorphologic characteristics, such as Ra (area ratio), Rb (bifurcation ratio) and Rl (length ratio). Strahler's ordering system was applied to determine stream order (Strahler, 1957). The model was relatively parsimonious in its data requirements, and most parameters could be obtained from DEM (Digital Elevation Model) data. Flow velocity was obtained by calibrating historical data or with methods appropriate for ungauged basins. 3.1. Model description 3.1.1. SCS model The method of hydrograph synthesis employed by the Soil Conversion Service (SCS), U. S. Department of Agriculture, uses an average number of natural UHs for watersheds varying widely in size and geographical location (Chow et al., 1988; Nourani et al., 2009). In the SCS model, the lag time, Tl, shall be determined using watershed physical properties such as the area, main river length, average slope and CN (Curve Number). The synthetic unit hydrograph can then be computed. The SCS model permits computing the UH for a watershed that has insufficient observed rainfall–runoff data. A Unit Hydrograph (UH) is defined as the direct runoff hydrograph (DRH) produced by 1 unit (inch) of effective rain (runoff) uniformly distributed over a basin. Unit hydrographs can be combined with precipitation data and basin data to determine the DRH for a particular basin. The curve number was determined with respect to land use and soil hydrological group maps in different antecedent moisture conditions (dry, average and moist) and hydrological conditions. The losses estimation is the sum of the interception, infiltration, and transmission of the soil and surface (in mm). The runoff calculation is given below: S=

25400 −254 CN

ð1Þ

Runoff was calculated using the following formula (2): Q =

ðP−0:25Þ2 P + 0:85

Q S P

ð2Þ

Run off (mm) Losses (mm) Maximum precipitation in 24 h (mm).

After calculating runoff caused by a storm event, the maximum flood discharge was calculated using the following formula (3): Q max =

Qmax A Q tp

2:083AQ tp

ð3Þ

maximum flood discharge (m 3/s) Basin area (km 2) Run off (mm) time of flood crest which is evaluated by time of concentration (tc) in minute.

M.R. Khaleghi et al. / Catena 87 (2011) 163–171

165

Fig. 1. The location of study area (Kasilian Watershed).

3.1.2. Snyder synthetic unit hydrograph Snyder (1938) was the first to propose a unit hydrograph technique that could be used on ungauged basins. His method was based on a number of watersheds in the Appalachian Highlands ranging in size from 10 mi 2 to 10,000 mi 2. Snyder's equations are: 0:3

Tp = Ct ðLLc Þ

ð4Þ

where tp is basin lag, L is length of the main stream from the outlet to the divide, Lc is Length along the main stream to a point nearest the watershed centroid and Ct is coefficient usually ranging from 1.8 to 2.2 (Ct has been found to vary from 0.4 in mountainous areas to 8.0 along the Gulf of Mexico). Q p = 640CpA=tp

ð5Þ

Where Qp is peak discharge of the unit hydrograph, A is drainage area and Cp is storage coefficient ranging from 0.4 to 0.8 where larger values of Cp are associated with smaller values of Ct. Tb = 3 + tp=8

ð6Þ

Where Tb is the time base of the hydrograph. For small waterheds, Eq. 6 should be replaced by multiplying tp by a value of from 3 to 5 as a better estimate of Tb. Eqs. 4–6 define points for a unit hydrograph produced but an excess rainfall odf duration D = tp/5.5. For other rainfall excess durations D′, an adjusted formula for tp becomes:
0  0 Tp = tp + 0:25 D  D

ð7Þ

3.1.3. Instantaneous unit hydrograph G.I.U.H Rodriguez-Iturbe and Valdes (1979) obtained expressions for the time to peak, tp, and peak discharge, Qp, of the IUH, which are functions of geomorphology, and the dynamic parameter represented by the peak velocity. The results obtained through the numerical integration of the full GIUH and multiple regression analyses are simple and straightforward. The equations are: qp =

tp =

1:31 0:43 R V LΩ L   0:44LΩ RB 0:55 −0:38 RL V RA

ð8Þ

ð9Þ ð10Þ

Q p:tb = 2

where qp is the discharge peak (m 3/s), tp is time to peak (hr), LΩ is the length of the highest order stream channel in the basin (km), Rl is the length ratio, v is the maximum velocity for peak flow (m/s), RB is the branch ratio, RA is the area ratio and tb is base flow time. If the discharge obtained from Eq. 4 is multiplied by the area of the watershed basin and the height of effective rainfall, ir, then the pick discharge of each cloud burst is calculated on the basis of relation in Eq. 7: Qp =

, qp 3600

ir A 100

ð11Þ

where A is a basin area (m 2), ir is the height of effective rainfall (cm), and Qp is the flow discharge (m 3/s). Rodriguez-Iturbe and Valdes (1979) has presented relation 5 for the calculation of time to peak for effluent hydrographs.

where tp′ is the adjusted lag time for duration D′. Once the three quantities tp, Qp, and tb are known, unit hydrograph can be sketched so that the area under the curve represents 1,0 in of direct runoff from the watershed. In this application the two items of data are:

Tp = tp + 0:75tr

Cp Tp

where Tp is the time to peak of effluent hydrograph (hr), tp is the time to peak in hr, and tr is the time of effective rainfall (hr).

Storage coefficient plus catchment lag

ð12Þ

M.R. Khaleghi et al. / Catena 87 (2011) 163–171

Therefore, the presence of flow velocity as an important factor in determining peak discharge and time to peak flow necessitates unique instantaneous unit hydrographs for each rainfall event. 3.1.4. Instantaneous unit hydrograph G.C.I.U.H Comprehensive descriptions of the derivation of the GIUH and its extension to the GCIUH have already been provided by Gupta et al. (1980). qp = 1:97ðΠÞ

0:4

ð13Þ

0:4

tp = 0:2587ðΠÞ Πi =

ð15Þ

10

 0:4 + 0:75tr Tp = 0:2587 Πj

ð16Þ

ð17Þ

Estimated instantaneous unit hydrograph, has been a one-hour instantaneous unit hydrograph and if rainfall duration is more than one hour, instantaneous unit hydrographs are extracted for the duration of effective rainfall. 3.1.5. Instantaneous unit hydrograph ROSSO Recent research has demonstrated that the hydrologic and geomorphologic approaches in defining watershed hydrologic response functions are converging and may be expressed through the gamma function. The similarities between the geomorphologic and hydrologic approaches has led to the development of a geomorphologic method for estimating unit hydrograph shapes and scale parameters, as is represented by the Nash model (Nash, 2009). ! −t  a−1 t ek k kΓðaÞ

RA K = 0:7 RB RL

0:48

Rosso

4

Observative 3

Snyder GIUH

2

Triangular GCIUH

1 0 1

3

5

7

9

11

13

15

LΩ ðV Þ

 0:78 R 0:07 α = 3029 B RL RA

ð18Þ

−1

17

19

21

23

25

27

29

31

33

Time(hr) Fig. 2. Comparison of observed and simulated hydrographs of different methods for the storm event of 2 October 2009.

1

0:4927t C B A i t r CB Q p = 5:475@ Ω r 0:4 A@1−  0:4r A Πj Πj



SCS

3.2. Extraction of the unit hydrograph from the instantaneous unit hydrograph

And for estimating direct runoff hydrograph, we use:

hð t Þ =

5

ð14Þ

ðLΩ Þ2:5 ir AΩ RL ðαΩ Þ1:5

0

6

Discharge(m3/s)

166

If the aim is the extraction of 1-hour unit hydrographs from Pe units of excess water, then one should obtain the extracted instantaneous unit hydrograph from models that are obtained from the inverse of time (h-1), expressed in m 3/s based on relationship in Eq. 21: Ut = ðIUH ðt ÞÞðPeÞðΑΩÞ

where IUH (t) is a dimension of instantaneous unit hydrograph in t (h) and Pe is excess water (m). 3.3. Model performance measures To evaluate a method's suitability for the study basin, two criteria were chosen to analyze the degree of goodness of fit. These criteria are Mean Relative Error (MRE) and Mean Square Error (MSE), which are based on the following equations: REi =

O−P × 100 O

ð22Þ

1 n ∑ R n i = 1 Ei

ð23Þ

RME =

SE = ½ðQ oi −Q ci Þ=Q oi  ð19Þ MSE = ð20Þ

where LΩ is the length of the highest-order stream channel in the basin (km), v is the average cross-sectional stream flow velocity at the outlet during peak discharge for the given flood wave, Γ is the gamma function, and α and k are the shape parameter and scale parameter of the Nash model IUH, respectively. 3.1.6. Trianglar unit hydrograph Since the height and base-width of the triangle are constrained to be simple functions of its time to peak, Tp, the triangular UH is a 1parameter model. Employing a statistical relationship between Tp and catchment characteristics, the triangular UH can be applied in regionalisation mode for catchments ungauged for flow. The triangular UH is widely employed for flood hydrology. For hydrological analysis of lower flows, or for characterizing whole flow regimes, the 1-parameter triangular UH is, not surprisingly, limited by its conceptual simplicity (e.g. hydrograph recessions are not characteristically linear).

ð21Þ

2

ð24Þ

1 n ∑ S n i = 1 Ei

ð25Þ

where MRE is mean relative error percentage, n is number of estimations, and RE is the percentage of relative error in each estimation of the related parameter (here, 4 parameters have been considered: peak time, base time, peak volume and discharge rate of flood). O is the observed values, P is the calculated values, MSE is the Mean Square Error, SEi is the sum of squares of errors between observed and calculated hydrographs in each time interval, Qoi is the dimension of the observed hydrograph and Qci is the dimension of calculated hydrographs. Table 1 Base values used in the sensitivity analysis. Parameter channel velocity (m/s) Precipitation parameters Geomorphologic ratios

Value Rainfall intensity (cm/hr) Rainfall duration (hr) Bifurcation Ratio (RB) Length ratio (RL) Area ratio (RA) Rainfall intensity (cm/hr)

1.05 2.54 2 4/02 1/3 3/9

M.R. Khaleghi et al. / Catena 87 (2011) 163–171 Table 2 Geomorphologic characteristics of the Kasilian watershed. Order

No. of streams

Average length (km)

Average area (km2)

Value of constants

1 2 3 4 5 6

595 148 34 12 3 1

0.31171 0.4545 1.05625 1.3942 0.885 8.55936

0.21897 1.1298 4.4640 6.3501 24.7790 67.8

Rb = 4.02 Rl = 1.3 Ra = 3.9

Mean Square Error (MSE) of efficiency for each model was used to determine potential of each model in effectively estimating outlet hydrograph dimensions. The calculation was based on the following equation: ðMSE2 = MSE1 Þ × 100

ð26Þ

3.4. Sensitivity Analysis Further work is required to analyze the influence of individual morphometric parameters on flood characteristics. A series of sensitivity analyses were performed to assess the GIUH model's sensitivity regarding different parameters. A sensitivity analysis identifies input parameters that have the most significant impact on model predictions. As each variable was allowed to vary, all others were held constant. The base scenario used for the sensitivity analyses is summarized in Table 6. As each parameter was evaluated, the impacts on the peak flow rate, the time to peak and the overall hydrograph shape were examined. Channel flow velocities and geomorphologic ratios were calculated by multiplying the ‘base’ value by 0.5, 1.0, 1.5 and 2.0 to evaluate how changes in parameters affected the peak flow rate, time to peak and general hydrograph shape. To test the GIUH model's responsiveness to different excess rainfall intensities, unit hydrographs were developed for 0.03 cm/hr, 0.05 cm/hr, 0.1 cm/hr, and 0.15 cm/hr. 4. Results and discussions Simulated hydrographs were compared to observed hydrographs in 1-hour time durations using different methods (Fig. 2). The model

167

results for peak discharge (qp) and the time to peak (tp) of different storm events were also confirmed. Detailed geomorphologic factors of the basin, which are listed in Table 1, were calculated by applying a DEM using a 20 m-resolution raster elevation data set. Table 2 presents the physiographic and geomorphologic parameters of the basin that was studied. The study basin was discovered to be a sixth-order basin. For the study basin, the bifurcation, length and area ratios, which are non-dimensional characteristics, are 4.2, 1.03 and 3.9, respectively. These values are similar to results reported in previous studies. Table 3 depicts the rates of excess rainfall and duration time for selected floods in the study basin. Along with increased excess rainfall, peak flow and flow velocity also increased. These results may result from the fact that peak flow and flow velocity are functions of excess rainfall intensity. Table 4 illustrates the hydrograph dimensions in the study basin using the SCS, Snyder and Trianglar methods. The results demonstrate that a comparable level of performance was achieved for all methods. Peak discharge hydrographs were similar and showed negligible errors, but the hydrographs differed more noticeably for peak flow. This fact may be related to the dependence of peak flow on excess rainfall intensity. Table 5 shows the values of MSE and MRE for each method. The results illustrate the efficiency of extracted hydrographs using different methods though these two indices (MSE and MRE). These methods are most effective for the largest rainfall events. The MSE values for the Geomorphologic, Snyder, SCS, Trianglar, Rosso and GCIUH models in the study basin are 0.215, 19.634, 21.37, 19.11, 10.39 and 1.065 percent, respectively. The RME values for the Geomorphologic, Snyder, SCS, Trianglar, Rosso and GCIUH models in the study basin are 8.524, 72.04, 77.64, 73.63, 56.73 and 21.57 percent, respectively. Table 6 presents the relative efficiency of each method in estimating the dimensions of outflow in the study basin. For this purpose, the MSE of each model was used. The results highlight the efficiency of the GIUH method ratio compared to other models. A comparison between the estimated hydrographs and the observed hydrographs of the models studied showed that the ratio of the efficiency of the geomorphologic model to that of the Snyder, SCS, Trianglar, Rosso and GCIUH models in the study basin are 91.06, 99.11, 88.642, 48.195 and 4.94, respectively. This study has determined that, compared to other models, the geomorphologic model is the most efficient model to use in determining pick discharge. In addition, similarities were observed for the outlet runoff volume parameter in

Table 3 Rates of excess rainfall and their duration for selective floods in the Kasilian watershed. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Date 1991/05/12 1992/06/20 1993/06/04 1994/03/27 1994/07/22 1995/08/27 1996/07/02 1996/07/12 1999/05/10 2001/09/26 2002/08/20 2003/07/07 2004/06/20 2004/09/20 2005/04/30 2005/07/12 2005/09/21 2006/07/02 2006/08/05 2007/08/08 2007/09/02

Excess rainfall (mm)

Duration of Excess rainfall (hr)

Qp(m3/s) Qp = qp = 3600 ×

7.31 0.0421 0.12 8.58 6.39 0.121 1.33 1.28 2.17 0.36 0.19 0.6618 0.47 0.11 0.1565 0.5198 0.22 0.1041 1.3371 0.1731 0.49

8.00 2 2 7.00 4.50 2 5.50 2.25 3.25 2 3 3 4 2.15 2 6 9 1.5 3 1.45 6

12.1 1.68 2.043 12.55 11.7 2.85 2.12 3.89 5.81 1.75 3.66 11.5 10.68 1.9 2.2 8.3 3.3 1.9 1.38 1.86 13.05

ir 100

V = 0.7859Q0.3864

Qp(hr− 1) 0:43 qp = 1:31 V LΩ RL

tp

Time to peak(hr) Tp = tp + 0.75tr

2.06 0.960 1.035 2.09 2.03 1.177 1.05 1.33 1.55 0.97 1.297 2.019 1.96 1.007 1.065 1.78 1.24 1.007 0.89 0.998 2.12

0.35 0.1626 0.1754 0.35 0.34 0.199 0.18 0.23 0.262 0.1652 0.2197 0.3420 0.332 0.1705 0.1805 0.3015 0.2111 0.1705 0.1507 0.1691 0.3591

1.54 3.29 3.056 1.51 1.56 2.68 3.01 2.38 2.04 3.24 2.43 1.56 1.61 3.14 2.966 1.77 2.53 3.14 3.55 3.16 1.49

7.54 4.79 4.55 6.76 4.93 4.18 7.14 4.07 4.47 4.74 4.68 3.81 4.61 4.75 4.46 6.27 9.28 4.26 5.80 4.25 5.99

×A

168

M.R. Khaleghi et al. / Catena 87 (2011) 163–171

Table 4 Hydrograph dimensions in SCS, Snyder and Trianglar methods for the Kasilian watershed. No

Date

Methods Flood

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1991/05/12 1992/06/20 1993/06/04 1994/03/27 1994/07/22 1995/08/27 1996/07/02 1996/07/12 1999/05/10 2001/09/26 2002/08/20 2003/07/07 2004/06/20 2004/09/20 2005/04/30 2005/07/12 2005/09/21 2006/07/02 2006/08/05 2007/08/08 2007/09/02

SCS

Snyder

Trianglar

Qp

tp

Qp

tp

Qp

tp

Qp

tp

12.1 12.55 11.7 2.12 3.89 5.81 2.85 1.75 1.9 11.5 1.86 1.38 3.3 3.66 13.05 10.68 1.68 1.9 2.2 8.3 2.043

8.3 8.1 6.5 8.2 5.7 5.84 5.9 6.11 6.23 4.65 4.53 6.24 8.88 5.94 6.87 5.47 6.31 5.21 5.7 6.13 5.76

18.33 3.35 6.35 19.13 17.49 3.35 3.47 5.21 8.91 3.35 5.22 23.22 16.03 3.33 5.356 14.005 6.66 3.43 3.22 3.43 18.005

5.69 3.14 3.49 5.32 4.13 3.71 4.50 3.34 4.64 2.94 4.60 4.77 4.94 2.64 3.35 4.75 7.44 4.10 4.28 3.14 4.63

17.33 2.35 2.35 1.813 2.049 2.35 1.94 2.32 2.19 2.356 2.22 2.22 2.10 2.33 2.35 1.900 1.66 2.43 2.22 2.43 1.90

9.67 5.17 5.17 8.92 7.05 5.17 7.79 5.36 6.11 5.17 5.92 5.92 6.67 5.28 5.17 8.17 10.42 4.79 5.92 4.76 8.17

17.83 2.85 5.85 18.63 20.99 2.85 4.97 6.71 9.41 2.85 6.72 22.72 21.53 2.83 4.85 19.50 6.15 2.93 3.72 2.93 19.50

5.69 3.14 3.49 5.32 4.13 3.71 4.50 3.34 4.65 2.95 4.60 4.77 4.94 2.64 3.35 4.75 7.44 4.10 4.28 3.14 4.63

the GIUH, SCS, Snyder, Triangular and GCIUH methods, but comparisons have proven the GIUH method to be more efficient than other methods. In addition, because the difference between GIUH and GCIUH is not significant, the two methods are approximately similar in efficiency. Thus, the GIUH model can be adopted as a standard tool for modeling rainfall–runoff transformation processes in basins that lack data. These findings support the results of a study by Bhadra et al. (2008). The model developed here performed well and yielded estimated values that were reasonably close to observed values when used to predict storm runoff in the Kasilian watershed. A series of sensitivity analyses were conducted to identify the input parameters that had the most significant impact on the GIUH model. The flow velocity estimation is an important variable in calculating the time-area curve and the resulting runoff hydrograph. While keeping the geomorphic parameters fixed, the base flow

Table 6 Relative efficiency of estimator (1) to estimator (2) in estimating runoff in the Kasilian watershed. Estimator(2) Estimator(1)

Geomorphologic Snyder SCS

Triangular Rosso

Geomorphologic Snyder SCS Triangular Rosso GCIUH

1 91.060 99.114 88.642 48.195 4.9438

0.0112 1.0272 1.1181 1 0.5437 0.0557

0.0109 1 1.0884 0.9734 0.529 0.0542

0.0100 0.9187 1 0.8943 0.4862 0.0498

GCIUH

0.0207 0.202 1.889 18.418 2.056 20.047 1.839 17.929 1 9.748 0.102 1

velocities calculated in Table 1 varied from 50% to 200%. Changes in flow velocity had a significant impact on hydrograph timing. As the flow velocity increased, the hydrograph shifted to the left and pick discharge occurred earlier. As the flow velocity increased, the time to the peak discharge decreased from 2.75 h to 2 h (Fig. 3). Lower velocities correspond to low stages, indicating the lean period. Higher velocities indicate higher stage periods. Fig. 3 illustrates that increases in average flow velocity cause significant increases in the hydrograph's peak (QP) and shortens the time to peak (tP). The flow velocity and rainfall excess intensity had the most influence on the peak flow rate, and these variables also had the greatest effect on the time to peak prediction. When a sensitivity analysis was performed, the flow velocity had the most influence on the time to peak. Changes in flow velocity seemed to affect the time to peak more than the peak flow rate. The higher the flow velocity is, the lower the cumulative travel time and, eventually, the lower the time to peak will be. However, changes in the overland flow velocity had more impact on the peak flow rate than on the time to peak. Hence, the geomorphologic unit hydrograph is not linear because its main characteristics, such as QP and tP, vary with the velocity (V) of the flow course of the main river. The effects of velocity on GIUH reflect the dynamics of the hydrological response of the basin. The study's findings support the results of Kilgore (1997) and Jain et al. (2000). Because there is a good deal of uncertainty in estimating rainfall excess intensity, the effects of different excess rainfall intensities were investigated by allowing the intensity to vary from 0.03 cm/hr to 0.15 cm/hr. As the intensity of excess rainfall increased, the resulting hydrographs showed less attenuation and a higher, faster peak flow rate (Fig. 4), while the time to peak decreased from 2.5 h to 1.5 h.

Table 5 MSE and MRE values for the Kasilian watershed. No.

Event

Geomorphologic

Snyder

SCS

Triangular

Rosso

GCIUH

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Sum RME MSE

1991/05/12 1992/06/20 1993/06/04 1994/03/27 1994/07/22 1995/08/27 1996/07/02 1996/07/12 1999/05/10 2001/09/26 2002/08/20 2003/07/07 2004/06/20 2004/09/20 2005/04/30 2005/07/12 2005/09/21 2006/07/02 2006/08/05 2007/08/08 2007/09/02

0.082 0.001 0.065 0.022 0.307 0.534 0.045 0.737 0.440 0.022 0.008 1.192 0.950 0.017 0.022 0.030 0.029 0.048 0.069 0.045 0.063 4.743 8.524 0.215

27.358 0.456 10.97 31.128 33.52 0.244 5.549 5.387 9.657 0.367 6.590 115.07 18.99 0.1891 4.647 22.139 5.569 0.279 3.395 0.3318 35.465 431.951 72.04 19.634

38.819 2.808 18.60 43.28 33.52 0.255 1.838 1.74 9.657 2.578 2.456 137.52 28.71 2.058 9.959 32.5 11.28 2.336 3.39 2.48 24.55 470.1 77.64 21.37

32.83 1.38 7.912 36.95 39.56 3.04 8.15 7.95 13.01 1.22 9.40 52.23 78.47 0.874 7.05 27.09 8.17 1.057 5.48 1.158 41.67 420.48 73.63 19.11

24.16 2.80 2.47 27.83 48.83 1.605 2.40 0.56 0.161 2.75 0.76 19.76 14.59 2.617 2.04 4.39 1.096 2.619 2.99 2.65 32.27 228.61 56.73 10.39

2.02 0.017 0.001 1.80 2.64 0.87 0.15 1.32 1.34 0.001 0.071 4.38 3.64 0.09 0.005 0.91 0.026 0.14 0.011 0.138 2.198 23.45 21.57 1.065

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Fig. 5. Sensitivity of model response to variations in the time to recession. Fig. 3. Sensitivity of model response to variations in channel flow velocity.

Excess rainfall intensity was found to have a large impact on both the time to peak flow rate and the peak flow rate. Increasing the excess rainfall intensity caused an earlier and larger peak flow rate. The excess rainfall intensity is an important parameter in estimating the peak flow rate and the time to peak. Care should be taken when selecting a technique to estimate the rainfall excess. These findings agree with the results of Kilgore (1997). The effects of different excess rainfall durations were investigated by allowing the duration to vary from 2 h to 8 h. As the duration of excess rainfall increased, the resulting hydrographs showed a higher, faster peak flow rate (Fig. 5), and the time to peak decreased from 2.5 h to 1.8 h. The effects of different geomorphologic ratios (RL, RA and RB) were investigated by allowing the geomorphologic ratios to vary from 1.5 to 6. Our preliminary results suggest that out of the three Horton's morph metric ratios, RL influenced the QP and tP most significantly. Our analysis predicts higher QP for higher RL. This fact demonstrates the influence of particular morphologic parameters on the flooding behavior of individual basins. As the length ratios (RL) increased, the resulting hydrographs showed a higher, faster peak flow rate (Figs. 6– 8). As the length ratio increased, the time to peak decreased from 2.5 h to 2.1 h. The length ratio (RL) is an important parameter for estimating the peak flow rate and the time to peak in the GIUH model and significantly influenced the hydrologic response of the study basin. The area ratio (RA) and bifurcation ratio (RB) are also important parameters for estimating the time to peak in the GIUH model. As the area ratio and bifurcation ratio increased, the time to peak increased from 2.5 h to 2.8 h. This study's findings are in agreement with the results of Sorman (1995) and Jain et al. (2000). All methods tested do not agree with the observed hydrographs for outlet runoff values. Due to the simplicity of the proposed method in comparison with other methods for flood estimation and because lower design risk is desirable, GIUH and GCIUH can be used for watershed with no data. Compared with synthetic unit hydrographs,

Fig. 4. Sensitivity of model response to variations in excess rainfall intensity.

these methods (GIUH & GCIUH) provide more accurate estimations of time to peak and peak discharge. The prediction performance of the developed GIUH was evaluated by combining the peak discharge (qp) and time to peak (tp). Compared to traditional methods, the proposed method can be used for the precise investigation of morphogenetic characteristics and their effects on basin hydrology. Using the proposed method, the contributions and participations of different tributaries to flood hazards in a river basin can be well understood. Variation in GIUH parameters with respect to velocity reflects the dynamic behavior of the hydrological response of the Kasilian river basin in different periods. The effect of individual morphogenetic parameters on flood discharge can also be provided by the proposed method. In general, the studies' findings are in accordance with the results of Jain and Sinha (2003), Jain et al. (2000), Hall et al. (2001) and Cudennec et al. (2004). 5. Conclusions The Kasilian watershed, a forested area, is less exposed to destruction and land use changes compared to other areas within Iran. Human activities in the form of urban development and land use changes have increased the risk of flood events and heightened watershed sensitivity to the results of rainfall events such as the generation of runoff and periods of peak discharge. Increases in runoff generation and peak discharge will be more drastic for heavier rainfalls (Camorani et al., 2005). None of the tested methods agree with the outlet runoff values found using the observed hydrographs. The comparison between values indicates that the Geomorphoclimatic Unite Hydrograph increases the simulation accuracy of the hydrograph (Nourani et al., 2009). When the number of events increases, the estimation accuracy and the efficiency and precision of excess water estimation increase. The results are validated when compared to the results of the flood frequency analysis based on the observed data. Due to the simplicity of the proposed method and because a low design risk is desired, the proposed method may be the

Fig. 6. Sensitivity of model response to variations in the bifurcation ratio.

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were lacking. Thus, the present models could be applied to simulate flood hydrographs for the basins that were not studied. Acknowledgments The authors would like to thank the Mazandaran Regional Water Company and TAMAB (Research Organization of Water Resources) for providing rainfall data and flood hydrographs and for aiding in the preprocessing of data. References

Fig. 7. Sensitivity of model response to variations in the area ratio.

best method to use for watersheds that lack data. Compared to synthetic unit hydrographs, these methods (GIUH & GCIUH) most accurately estimate time to peak and peak discharge. Hence, the prediction performance of the developed GIUH was evaluated by comparing the observed peak discharge (qp) and time to peak (tp). Compared to traditional methods, the proposed method can be used for the precise investigation of morphogenetic characteristics and their effects on basin hydrology. Using the proposed method, the contributions of different tributaries to flood hazards in river basin can be well understood. The effects of individual morphogenetic parameters on flood discharge could also be provided by the proposed method. To identify the input parameters that had the most significant effect on the GIUH model, a series of sensitivity analyses were carried out. The flow velocity and excess rainfall intensity had the largest influence on the peak flow rate and the greatest effect on the time to peak prediction. A sensitivity analysis was performed, and the results indicated that the flow velocity had the most noticeable influence on the time to peak. The results indicated that changes in flow velocity had a greater effect on the time to peak than the peak flow rate. The higher the flow velocity, the lower the cumulative travel time and eventually the lower the time to peak. Contrarily, changes in the overland flow velocity had a greater impact on the peak flow rate than on the time to peak. Hence, the geomorphologic unit hydrograph is not linear because its main characteristics, QP and tP, vary with the velocity, V, of the main river course. The effect of velocity on the GIUH reflects the dynamics of the basin's hydrological response. This study presents an effective method for simulating the rainfall–runoff process and flood hydrographs. The lack of flood data is a basic problem for hydrological studies and hydrologic modeling in Iran. In fact, many past floods have not been recorded by hydrometric stations, and many basin areas lack stations. In this study, we found that errors exist in past datasets because skilled experts

Fig. 8. Sensitivity of model response to variations in the length ratio.

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