Abstract: This research has been carried out for investigation and comparison of the amount of precision and correctness of SCS unit hydrograph, GRAY, G.I.U.H and Gc.I.U.H models in determination of the shape and dimensions of outlet runoff hydrograph in Navroud watershed with 266 km2 area, located in Giulan Province of Iran and use of these models for the similar watersheds and without any data. To investigate the amount of efficiency of above-mentioned methods, first 6 equivalent rainfall-runoff events were selected and for each, hydrograph of outlet runoff were calculated. Then the models were compared with together, for peak time, base time, peak flow and volume of outlet runoff and the most efficient model in estimation of hydrograph of outlet flow for similar regions was proposed. Comparison of calculated hydrographs obtained from models under research and observed hydrographs of selected events showed that SCS unit hydrograph method had the most direct agreement in three parameters of peak time, base time and volume of direct runoff. On the other hand, the geomorphoclimatic instantaneous unit hydrograph, with the highest mean relative error of 16%, had highest harmony in estimation of peak flow direct runoff.
INTRODUCTION
Data and observed information are very important and basic for investigation and estimation of hydrologic events and if are recorded regularly and from old time, can be used in control structures and decrease of flood damages. Many watersheds do not have hydrometric stations, limnigraph and rain gauges (Bonta and Roa, 1991) and no data and lack of hydrological information are encountered, that is why for calculation of peak flood flow, time of concentration, peak time and watershed hydrograph, empirical formula and artificial hydrographs are used. Hydrograph is a curve which shows the variations of runoff discharge rate with respect to time and on the other hand, the dimensions of hydrograph of outlet discharge rate, shows quantitative and final responses of watershed to inlet rainfall. So, knowledge of the relationship between rainfall and runoff is one of the important issues in the hydrology (Alizadeh, 2006). One of the common methods in flood estimation is the use of unit hydrograph which not only is used in peak flow estimation, but also for creation of complicated flood hydrographs (Heshmatpour et al., 2002). Unit hydrograph and flood hydrograph which is obtained from rainfall and discharge rate of a watershed is used for that watershed and river only. For other points of river or watersheds having similar characteristics, artificial hydrograph method is used (Zehtabian et al., 2001). Among common methods for artificial unit hydrographs, Gray (1961) and NRCS/SCS (1972) models and for instantaneous unit hydrographs G.I.U.H. (Geomorphologic Instantaneous Unit Hydrograph), (1993) and Gc.I.U.H. (Geomorphoclimatic Instantaneous Unit Hydrograph), (1982) models can be cited.
About efficiency of artificial unit hydrographs and instantaneous unit hydrographs in the world and in Iran, many researches have been carried out. Bahadori Khosroshahi (1989) in Jajrood Watershed with 426 km2 areas and Rezaee (1994) in 9 watershed of Zanjan, Guilan, Mazandaran and Tehran Provinces, studied NRCS/SCS unit hydrograph and Snyder method in determination of flood in these watersheds, concluded that NRCS/SCS method has better agreement than Snyder in construction of unit artificial hydrograph with the observed hydrograph. Shahmohammadi (1994) in Khersan Watershed in southern part of Karoon Watershed, compared observed flood hydrograph with calculated flood hydrograph and by studying three methods of unit hydrograph (Snyder, NRCS/SCS and triangular), proposed the NRCS/SCS method for this watershed. Rahimian and Zare (1995) in Paskoohak Watershed in Shiraz concluded that Geomorphologic method had more agreement than SCS, Snyder and triangular methods with observed hydrograph. Ghahraman (1995), based on his studies on Kasilian and Emameh Representative Watersheds, concluded that for estimation of flood hydrograph, the Geomorphoclimatic instantaneous unit hydrographs are better than Geomorphologic artificial unit hydrograph. Ghiasi (1996) in Emameh Watershed, 6 rainfall-runoff events considered 6 tantamount rainfall-runoff events with Geomorphologic, NRCS/SCS, Snyder and triangular methods and concluded that efficiency of Geomorphologic method is similar to NRCS/SCS method and is less than that of Snyder method. Erfanian (1998) concluded in Jezin Watershed of Semnan by comparison of statistical indices of sum of squares errors that the percentage of efficiency of Geomorphologic model with respect to Geomorphoclimatic, Roso, Nash and NRCS/SCS methods were 134.2, 160.6, 295.18 and 210.2, respectively. Also, the efficiency percentage of Geomorphoclimatic method with respect to Roso, Nash and NRCS/SCS methods are 119.7, 294.7, 156.5%, respectively. Heshmatpour et al. (2002) after carrying research in Kasilian Watershed and comparison by statistical indices of sum of squares errors, that efficiency percentage of Geomorphologic model with respect to Geomorphoclimatic, Nash, Roso and NRCS/SCS methods were 106.56, 171.12, 106.79 and 112.64, respectively. Also, the efficiency percentage of Geomorphoclimatic method with respect to Nash, Roso and SCS methods are 160.57, 100.21, 105.69%, respectively. Barkhirdari (2006), concluded that in Sikhoran Watershed of Hormozgan Province to determine ability and efficiency of artificial unit hydrograph (Snyder, triangular and Clark), including determination of natural and artificial unit hydrographs using morphologic, rainfall and hydrometric data and comparison of four methods of construction of artificial and observed (natural) unit hydrographs, Snyder method in mountainous steep watersheds and NRCS/SCS and triangular methods in plain and low slope watersheds had better estimation. Gary (1961) concluded in his research called artificial unit hydrograph for small watersheds that Gray unit artificial hydrograph in watershed with 243.5 km2 areas in Iowa, Illinois, Wisconsin, Nebraska and Missouri with specific local coefficients, had acceptable results. Zeiazinski (1986), in his research by expressing this case that theory of Geomorphologic unit hydrograph to estimate parameters of 2 conceptual models of cascade Liner and model of the type Laurenson, using the two models for flood control, expressed Geomorphologic unit instantaneous hydrograph for Vistola Watershed of Poland. Ghioto (1991), in a research compared NRCS/SCS, Snyder and Santa barba hydrographs and showed that in big watersheds, NRCS/SCS model has better estimation. Bonta and Roa (1991) by using four statistical distributions of Gamma, Beta, Weibul and K2 and three artificial unit hydrographs of Snyder, NRCS/SCS and Gray, compared the shapes of hydrographs in two sub-watersheds with 114 and 350 km2 in India. Among methods of estimation of unit artificial hydrographs, the percentage of relative error in time to peak and peak discharge rate of hydrographs obtained from NRCS/SCS method had 20 and 3% and standard error of 2.95% which shows that this method is suitable for watersheds of without data.
MATERIALS AND METHODS
Study area: Navrood representative watershed (Table 1) is located between 48° 36’-48°36’ E and 48°36’-48° 36’ N and located between Gorganrood Watershed from north, Khale-Sara Watershed from east, Arpachay Watershed from west and Dinachal Watershed from south. About 83% of the Watershed is as forest and the rest is as rangeland and bare land. Figure 1 shows some morphometric characters of Navrood Watershed. This study was conducted in Winter (June) 2008.
Data and methods: To reach the aims of this research, the following
should be carried out:
| • | Physiographic parameters of watershed are prepared (Table 1) |
| • | Data and information of equivalent rainfall-runoff events in non-melting season of snow are collected from graphs |
| Table 1: | Physiographic parameters of Navrood watershed region |
| Fig. 1: | Navroud Watershed, North of Iran |
| • | After selection of events, the 1 h rainfall and then cumulative rainfall of each duration from rainfall recording gages are obtained. The base flow of each flood is obtained from different methods (Chow et al., 1988; Viessman and Lewis, 2003). Here, the direct line method is used which is usually used in most hydrologic works (Mahdavi, 2005; Alizadeh, 2006). After separation of base flow and calculation of under curve area, the direct runoff is obtained by dividing it by watershed area. The excess rainfall for 1 h is obtained which is NRCS/SCS method which is a model of one-event (Karvonen, 1999; Chow, 1964; USACE, 2000; Mahdavi, 2005; Alizadeh, 2006) |
| • | Preparation of unit hydrograph and instantaneous unit hydrograph with different models: |
NRCS/SCS unit hydrograph: In this method it is sufficient to calculate the time to peak and the amount of peak flow. The coordinate of unit hydrograph is obtained from a table (Mahdavi, 2005; Alizadeh, 2006). The relationships in NRCS/SCS hydrograph are 1-4:
(1) |
(2) |
(3) |
(4) |
where, Qp is peak of flow (m3 sec-1), A is area (km2), tp is time to peak flow (h), D is effective time of rainfall (h), tl is lag time (h) and tc is time of concentration (the time needed to reach out let) (h).
To solve equation of dimensionless unit hydrograph, calculation of tc of watershed is necessary. In this research tc is 11 h (equal to 660 min) based on observed hydrographs. As the rainfall-runoff data dose not exist in watersheds of without hydrometric stations, tc is estimated by other characters and compared with its real value. Based on existing parameters of watershed 11 relationships are used to calculate tc (Mobaraki, 2006). In this research among these methods, Espy-Vintslo, time of concentration (601 min) with relative error of 8.95% is acceptable.
Gray unit hydrograph: Gray (1961) found the relationship 5 for t/PR:
(5) |
So, that Qt/PR, flow percentage in 0.25PR, for t/PR, q and λ are shape parameter and scale, Г, gama function q equal to (q-1)! (! = factorial), PR is peak time of natural unit hydrograph of 1 h to minute and t is time in minute (Singh, 2000).
Instantaneous unit hydrograph G.I.U.H: The hydrologic function of Navrood representation watershed, order based on 5 based on Strahler classification, is given by the following relationship 6:
(6) |
where, GIUH(t) is ordinate instantaneous unit hydrograph in time t, θ1(o) to θ5(o) are probability of primary conditions, dΦ17(t)/dt to dΦ57(t)/dt are the variations of probability of transfer of time interval. Knowing velocity of flow and the average length of channels, the inverse of time of expectance (λ) is determined and having this criterion probability of transfer to (dΦ/dt) is obtained. Having (dΦ/dt) and probability of initial condition θi(o), the coordinate of instantaneous unit hydrograph is determined (Bhaskar, 1996; Ganjkhanlou, 2002). In theory of G.I.U.H., the discharge rate, peak time and base time are calculated from relationships 7-9, (Rodriguez-Iturbe and Valders, 1979; Erfanian, 1998).
(7) |
(8) |
(9) |
where, Qp is peak discharge rate (m3 sec-1), Tp is peak time (h), LÙ is length of channel of highest order (km), RB is branch ratio, RL is length ratio, V is maximum velocity (m sec-1) and Tb is base flow time (h). So, the presence of flow velocity as an important factor in determining peak discharge and time to peak flow causes that for each rainfall, unit instantaneous hydrograph is different.
Instantaneous unit hydrograph Gc.U.I.H: Theory of Geomorphoclimatic Instantaneous Unit Hydrograph was submitted by Rodriguez-Iturbe and Bars (1982) by accepting bases of Geomorphologic instantaneous unit hydrograph and accepting the results of there studies about velocity, based on the fact that peak velocity is a function of excess rain intensity and kinetic wave. They used the relationship 10-13:
(10) |
(11) |
(12) |
(13) |
The formulas 14 and 15 were used from the same researches:
(14) |
(15) |
where, Qp is peak discharge rate (m3 sec-1), Tp is peak time (h), AΩ is catchment area (km2), LΩ is length of channel of highest order of drainage (km), ir is mean of effective rainfall intensity (m sec-1) calculated from hyetograph, RL is length ratio, αΩ kinetic wave parameter with dimension L2/3, tr is travel time (h) and Tb is base flow time (h). So, the presence of flow velocity as an important factor in determining peak discharge and time to peak flow causes that for each rainfall, unit instantaneous hydrograph is different.
Extraction of unit hydrograph from instantaneous unit hydrograph: The dimensions of 1 h instantaneous unit hydrograph of Geomorphologic and Geomorphoclimatic in terms of inverse of time (h-1) in terms of one unit excess water for selected storms were calculated. If the aim is the extraction of 1 h unit hydrograph from Pe units of excess water, one should obtain extracted instantaneous unit hydrograph from models that are obtained from inverse of time (h-1) and should be expressed in m3 sec-1 based on relationship 16:
(16) |
where, IUH(t) is dimensions of instantaneous unit hydrograph in t (h) and Pe is excess water (m).
Extraction of outlet hydrograph from selected events: To calculate dimension of outlet hydrograph of selected events for different methods under research, due to non uniformity of time distribution of rain in hydrograph of each storm and allocation of different excess rainfall in different time periods, the matrix method and simultaneous solution of equations are used (Heshmatpour et al., 2002).
Determination and assessment of outlet hydrograph dimensions of watershed by comparison of calculated and observed hydrographs and by Mean Relative Error (MRE) and Mean Square Error (MSE) based on relationship 17-20, (Zehtabian et al., 2001; Erfanian, 1998; Nash, 1958; Smith et al., 2004; Sadeghi et al., 2005).
(17) |
(18) |
(19) |
(20) |
where, MRE is mean relative error percentage, n is number of estimation, RE (%) is the percentage of relative error in estimation of the related parameter (here 4 parameters of peak time, base time, peak volume and discharge rate of flood have been considered). O is the observed values, P is the calculated values, MSE is mean of power 2 error, Sei is sum of squares of errors between observed and calculated hydrographs in each time interval, Qoi is dimension of observed hydrograph and Qci is dimensions of calculated hydrograph.
To determine percentage of superiority of the models under research in estimation of outlet hydrograph dimensions in the watershed under study, the mean of power 2 of error of each model with respect to other model have been used based on the relationship 21, (Erfanian, 1998; Sadeghi et al., 2005).
|
(MSE2/MSE1)x100 = Ratio of estimating (1) |
(21) |
RESULTS
Dimensions of calculated outlet hydrographs by different methods were compared with observed hydrograph in 1 h time duration and have been shown in Fig. 2-7.
| Fig. 2: | Comparison of observed and calculated hydrographs of different models for storm 14th Oct. 1994 |
| Fig. 3: | Comparison of observed and calculated hydrographs of different models for storm 21st Oct. 1994 |
| Fig. 4: | Comparison of observed and calculated hydrographs of different models for storm 23rd Apr. 1995 |
| Fig. 5: | Comparison of observed and calculated hydrographs of different models for storm 21st Jun 1995 |
| Fig. 6: | Comparison of observed and calculated hydrographs of different models for storm 13th Aug. 1995 |
| Fig. 7: | Comparison of observed and calculated hydrographs of different models for storm 10th Nov. 1998 |
The results show the efficiency of extracted hydrographs in different methods by two indices of MRE and MSE. Table 2-5 show amounts of peak time, base time, peak flow and peak discharge rate, estimated runoff volume of out let runoff, percentage of their differences with observed values and mean error (MRE) of these characters in different methods for selective events. Table 6 shows observed amounts of characters and Table 7 shows MSE in different methods for different events.
Table 8 shows the percentage of efficiency of models compared to each other in estimating dimensions of outflow in Navrood Watershed. For this purpose MSE of each model was used.
| Table 2: | Estimated amounts of characters in NRCS/SCS method for selective events and percentage of their differences with observed values and mean error (MRE) of them |
| Table 3: | Estimated amounts of characters in GRAY method for selective events and percentage of their differences with observed values and mean error (MRE) of them |
| Table 4: | Estimated amounts of characters in GIUH method for selective events and percentage of their differences with observed values and mean error (MRE) of them |
| Table 5: | Estimated amounts of characters in Gc.I.U.H method for selective events and percentage of their differences with observed values and mean error (MRE) of them |
| Table 6: | Observed amounts of parameters |
| Table 7: | MSE in different methods for different events |
| Table 8: | Relative efficiency (1) with respect to estimator (2) in estimating runoff in Navrood representative watershed |
DISCUSSION
An investigation of the obtained results, showed high agreement of NRCS/SCS, GRAY, G.I.U.H and Gc.I.U.H methods with observed hydrograph in three parameters of peak time, runoff volume and outlet runoff. This is in agreement results obtained later (Barkhirdari, 2006; Bahadori Khosroshahi, 1989). But these methods show higher peak discharge rate than that observed values which is due to influencing factors on the shape of hydrograph in the watershed under study like vegetation (dense forest) and long watershed (Habibnejad et al., 2004). Overall, the comparison of obtained results of the methods under study shows that efficiency of NRCS/SCS method is more efficient than GRAY, Geomorphologic and Geomorphoclimatic methods by 134.6746, 144.277 and 106.7506%, respectively. As a result, NRCS/SCS is more efficient than other method, the difference with Geomorphoclimatic is sight and one can say that the two methods have similar efficiencies. This is in agreement results obtained later (Heshmatpour et al., 2002). As the Geomorphoclimatic method can not estimate peak and base times precisely, its MSE becomes higher, so that the efficiency of model has been reduced. But as Table 3-6 show the MRE of peak flow in this method is higher with respect to other models and these show a high precision in estimation of peak flow of outlet runoff. Ghahraman (1995) and Heshmatpour (1999) got same results in their researches.
It is suggested that in this research two models of NRCS/SCS and Geomorphoclimatic methods have similar efficiencies, due to lower number of parameters required in NRCS/SCS model and simplicity of calculation of this method with respect to other methods in flood estimation and also in cases lower risk in designs is important, this method can be used for watersheds of no data. Also, in case for a specific region with respect available data, all types of models should be evaluated, one can obtain safer and more reliable results. Increase on number of events, calculation of excess water with more efficient methods which can calculate rain loss as a function of time and in case of using SCS model for excess rain estimation, calculation of precise CN of the region, calibration of time of concentration (tc) formula and peak flow coefficients for the region under study, etc. is a factor of increase in precision in NRCS/SCS unit hydrograph, whose result is the more precise of dimensions of outlet runoff.
In general, this research is in agreement with the results of Bahadori Khosroshahi (1989), Rezaee (1994), Shahmohammadi (1994), Ghiasi (1996), Heshmatpour (1999) and Barkhirdari (2006) but differs from the results of Rahimian and Zare (1995) and Erfanian (1998).