
Research Article


An Investigation of Efficiency of Outlet Runoff Assessment Models: Navroud Watershed, Iran 

H. Mojaddadi,
M. Habibnejad,
K. Solaimani,
M. Z. Ahmadi
and
M. A. HadianAmri



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 km^{2} 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 abovementioned methods, first 6 equivalent
rainfallrunoff 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 km^{2} 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 rainfallrunoff events
considered 6 tantamount rainfallrunoff 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 km^{2} 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 K^{2} and
three artificial unit hydrographs of Snyder, NRCS/SCS and Gray, compared the
shapes of hydrographs in two subwatersheds with 114 and 350 km^{2}
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, KhaleSara 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 rainfallrunoff events in nonmelting
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 oneevent
(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 14:
where, Q_{p} is peak of flow (m^{3} sec^{1}),
A is area (km^{2}), t_{p} is time to peak flow (h), D
is effective time of rainfall (h), t_{l} is lag time (h) and t_{c}
is time of concentration (the time needed to reach out let) (h).
To solve equation of dimensionless unit hydrograph, calculation of t_{c}
of watershed is necessary. In this research t_{c} is 11 h (equal to
660 min) based on observed hydrographs. As the rainfallrunoff data dose not
exist in watersheds of without hydrometric stations, t_{c} is estimated
by other characters and compared with its real value. Based on existing parameters
of watershed 11 relationships are used to calculate t_{c} (Mobaraki,
2006). In this research among these methods, EspyVintslo, time of concentration
(601 min) with relative error of 8.95% is acceptable.
Gray unit hydrograph: Gray (1961) found the relationship
5 for t/P_{R}:
So, that Q_{t}/P_{R}, flow percentage in 0.25P_{R},
for t/P_{R}, q and λ are shape parameter and scale, Г, gama function
q equal to (q1)! (! = factorial), P_{R} 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:
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 79,
(RodriguezIturbe and Valders, 1979; Erfanian,
1998).
where, Q_{p} is peak discharge rate (m^{3} sec^{1}),
T_{p} is peak time (h), L_{Ù} is length of channel
of highest order (km), R_{B} is branch ratio, R_{L} is
length ratio, V is maximum velocity (m sec^{1}) and T_{b}
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 RodriguezIturbe
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 1013:
The formulas 14 and 15 were used from the same researches:
where, Q_{p} is peak discharge rate (m^{3} sec^{1}),
T_{p} is peak time (h), A_{Ω} is catchment area (km^{2}),
L_{Ω} is length of channel of highest order of drainage (km),
i_{r} is mean of effective rainfall intensity (m sec^{1})
calculated from hyetograph, R_{L} is length ratio, α_{Ω}
kinetic wave parameter with dimension L^{2/3}, t_{r} is
travel time (h) and T_{b} 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 P_{e} 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 m^{3} sec^{1} based on relationship
16:
where, IUH_{(t)} is dimensions of instantaneous unit hydrograph
in t (h) and P_{e} 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 1720, (Zehtabian
et al., 2001; Erfanian, 1998; Nash,
1958; Smith et al., 2004; Sadeghi
et al., 2005).
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, Se_{i}
is sum of squares of errors between observed and calculated hydrographs
in each time interval, Q_{oi} is dimension of observed hydrograph
and Q_{ci }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).
(MSE_{2}/MSE_{1})x100 = Ratio of estimating (1)
percentage efficiency of estimating (2)

(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. 27.

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 25
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 36 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 (t_{c})
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).

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