A comparative study for prediction of direct runoff for a river basin using geomorphological approach and artificial neural networks
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Abstract
Traditional techniques for estimation of flood using historical rainfall–runoff data are restricted in application for small basins due to poor stream gauging network. To overcome such difficulties, various techniques including those involving the morphologic details of the ungauged basin have been evolved. The geomorphologic instantaneous unit hydrograph method belongs to the latter approach. In this study, a gamma geomorphologic instantaneous unit hydrograph (GGIUH) model (based on geomorphologic characteristics of the basin and the Nash instantaneous unit hydrograph model) was calibrated and validated for prediction of direct runoff (flood) from the catchment of the DulungNala (a tributary of the Subarnarekha River System) at Phekoghat station in the state of West Bengal in the eastern part of India. Sensitivity analysis revealed that a change in the model parameters viz., n, R_{A} and R_{B} by 1–20% resulted in the peak discharge to vary from 1.1 to 27.2%, 3.4 to 21.2% and 3.4 to 21.6%, respectively, and the runoff volume to vary from 0.3 to 12.5%, 2.1 to 2.6% and 2.2 to 2.7%, respectively. The Nash–Sutcliffe model efficiency criterion, percentage error in volume, the percentage error in peak, and net difference of observed and simulated time to peak which were used for performance evaluation, have been found to range from 74.2 to 95.1%, 2.9 to 20.9%, 0.1 to 20.8% and −1 to 3 h, respectively, indicating a good performance of the GGIUH model for prediction of runoff hydrograph. Again, an artificial neural network (ANN) model was prepared to predict ordinates of discharge hydrograph using calibrative approach. Both the ANN and GGIUH models were found to have predicted the hydrograph characteristics in a satisfactory manner. Further, direct surface runoff hydrographs computed using the GGIUH model at two map scales (viz. 1:50,000 and 1:250,000) were found to yield comparable results for the two map scales. For a final clarification, the probability density function of the actual and predicted data from the two models was prepared to compare the pattern identification ability of both the models. The GGIUH model was found to identify the distribution pattern better than the ANN model, although both the models were found to be ably replicating the data patterns of the observed dataset.
Keywords
GGIUH ANN Direct surface runoff hydrograph Morphological parameters Probability density functionIntroduction
Streamflow synthesis from ungauged catchments has long been recognized as a subject of scientific investigations. In this regard, many empirical, conceptual and physically based models were developed during the last century. Sherman (1932) first introduced the unit hydrograph model based on the rainfall and runoff data for gauged watershed as a means to develop a runoff hydrograph for any given storm hyetograph. The geomorphologic instantaneous unit hydrograph (GIUH) approach was initiated by RodriguezIturbe and Valdes (1979) to relate rainfall–runoff process in ungauged basins. This was further developed by Valdes et al. (1979) and RodriguezIturbe and Valdes (1979).
In the international front, various authors used the GIUH approach to formulate the rainfall–runoff transformation process under different conditions (RodriguezIturbe et al.1982; Troutman and Karlinger 1985, Chutha and Dooge 1990; Sorman 1995). Wooding (1965) determined the geomorphologybased runoff hydrograph using the kinematic wave theory for flow on a catchment and along the stream, assuming the rainfall of constant intensity and finite duration. Yen and Lee (1997) derived the GIUH using the kinematic wave theory and streamlaw ratios for computation of travel times for the overland and channel flows in a stream ordering subbasin system.
In the national front, Bhaskar et al. (1997) derived the GIUH from the watershed geomorphologic characteristics, based on the approaches of Valdes et al. (1979) and RodriguezIturbe and Valdes (1979), and used Nash instantaneous unit hydrograph (IUH) model to develop the gamma geomorphologic instantaneous unit hydrograph model (GGIUH) for Jira sub basin (under Mahanadi basin). Jain et al. (2000) applied geographical information system (GIS)supported GIUH approach for the estimation of design flood for the Gambhiri subcatchment (under Chambal basin) in India and reported the suitability of the approach for the estimation of the design flood particularly for the ungauged catchment. The derivation of the GIUH based on kinematic wave theory and geomorphologic parameters of the Gagas and Chaukhutia watersheds of the Ramanga catchment (under Ganga River basin in Uttaranchal, India) has been reported by Kumar and Kumar (2004) and Kumar and Kumar (2007). Sahoo et al. (2006) reported reasonably accurate computation of direct surface runoff hydrographs by the GIUHbased Clark and Nash models for Ajoy River (tributary of the BhagirathiHugli—a distributary of the River Ganga) at Jamtara in India.
Again, physical, topographical and hydroclimatological features vary from river basin to river basin and to the best of our knowledge, no work related to (GGIUH) approach for computation of direct surface runoff hydrographs has been carried out for the Subarnarekha River basin which is the smallest of the fourteen major river basins of India and which drains sizeable portions of the three States of Jharkhand, Orissa and West Bengal in the eastern part of India. Therefore, it is appropriate to evaluate the GGIUH model for the basin of DulungNala (an important tributary of the Subarnarekha River System in India).
Hence, the present study was carried out (1) to assess the performance of the GGIUH model (as developed by Bhaskar et al. 1997) for the basin of DulungNala by computing the direct surface runoff hydrographs (DSRO) and (a) comparing them with observed DSRO hydrographs and with those derived by artificial neural network (ANN) model and (b) using statistical methods (in terms of probability density function) to identify the pattern replication ability of both the models; (2) to evaluate the effect of basin map scale (viz. 1:50,000 and 1:250,000) on the performance of the GGIUH model (which is based on geomorphological parameters of the basin).
It is worth mentioning that over the last two decades, neural networks have become very popular mathematical modeling tools in hydrology and water resources. The application of ANN modeling is widely reported in various hydrological literatures (Neelakantan and Pundarikanthan 2000; Ray and Klindworth 2000; Zhang and Govindaraju 2003; Ahmad and Simonovic 2005; Hong and Feng 2008; Zhang et al. 2008). Furthermore the use of the probability density function in hydrology has been found to be successful in solving many problems considering the hydrological laws and the quantity evaluation of the many characteristics of different hydrological regimes.
Study area
Data acquisition
The Survey of India toposheets (73J/10, 73J/14, 73J/15) (1:50,000) and 73J (1:250,000) were collected from the office of The Survey of India at Kolkata. Historical rainfall data spanning over the years 1995–2004 of the rain gauge stations (viz., Belpahari, Jhargram and Phekoghat) located in the basin (Fig. 1) were collected from the Dept. of Agriculture, GoWB. The discharge and flow velocity data at the Phekoghat gauging site (where stage is measured by water level stage recorder and flow velocity is measured by current meter) were collected for 1995–2004 from Central Water Commission, Govt of India, Bhubaneswar. The direct runoff which was estimated from the observed runoff data after deducting the baseflow was used to evaluate the Фindex. The effective rainfall intensity was computed using this Фindex. Sixteen isolated storm events (encompassing variety of sizes) were selected for study.
Methodology
GGIUH model
RodriguezIturbe and Valdes (1979) presented a probabilistic description of the movement of runoff through the drainage network of the catchment. In this approach, the initial state probability of one drop of rainfall was expressed in terms of geomorphologic parameters as well as the transition probability matrix and the final probability density function (PDF) of droplets leaving the highest order stream into the trapping state yielded the GIUH.
Artificial neural network model
 1.
Information must be processed at many single elements called nodes.
 2.
Signals are passed between nodes through connection links and each link has an associated weight that represents its connection strength.
 3.
Each of the nodes applies a nonlinear transformation called as activation function to its net input to determine its output signal.
Network building procedure
Selection of network topology
Neural networks can be of different types, like feed forward, radial basis function, time lag delay etc. The type of the network is selected with respect to the knowledge of input and output parameters and their relationship. Once the type of network is selected, selection of network topology is the next concern. Trial and error method is generally used for this purpose but many studies now prefer the application of genetic algorithm. Genetic algorithms are search algorithms based on the mechanics of natural genetic and natural selection. The basic elements of natural genetics—reproduction, crossover, and mutation—are used in the genetic search procedure (Majumdar et al. 2009).
Training phase
To encapsulate the desired input output relationship, weights are adjusted and applied to the network until the desired error is achieved. This is called as “training the network”.
Testing phase
After training is completed, some portion of the available historical dataset is fed to the trained network and known output is estimated out of them. The estimated values are compared with the target output to compute the MSE. If the value of MSE is less than 1%, the network is said to be sufficiently trained and ready for estimation. The dataset is also used for crossvalidation to prevent overtraining during the training phase.
Generally 70% of the available dataset used for training and rest is equally divided for testing and validation purpose (15% each). In the present study 70, 15, and 15% were used, respectively, for training, testing and validation purpose.
For the present investigation, a linear equation of the relationship between peak discharge and the duration of the extreme event can be estimated by Eq. 8. The present problem used the pattern recognition ability of neural models to predict the constant α of Eq. 8.
Input and output of ANN model
Input  Output 

Sub model I (to find the value of α, β)  
Q, t (when β = 0)**  α 
Q, t (when α = 0)**  β 
Sub model II (to find the value of Q)  
α, t, β  Q 
Neural network model was prepared and trained with training algorithm Conjugate Gradient Descent (CGD) to compute discharge hydrograph using effective rainfall and observed discharge hydrograph as input for five storm events.
The correlation coefficient, standard deviation and mean square error were used to evaluate the efficiency of the training algorithm. After that, α was predicted for all the events and Q was estimated from Eq. 8.
Estimation of geomorphologic parameter
Geomorphological characteristics of the DulungNala River basin
Scale  Stream order (u)  total number of streams (N_{ u })  mean stream length (L_{ u }) (km)  Mean stream area of order u (\( \overline{{A_{u} }} \)) (km^{2})  Geomorphologic parameters (dimensionless) 

1:250,000  1  32  3.4  8.74  R_{B} = 3.5 
2  14  2.9  39.9  R_{L} = 2.2  
3  3  7.9  213.5  R_{A} = 4.5  
4  1  22.6  802  
1:50,000  1  201  0.6  2.2  R_{B} = 3.4 
2  58  1.1  11.9  R_{L} = 2.4  
3  18  2.8  35.8  R_{A} = 3.9  
4  2  13.3  380.3  
5  1  22.1  802.2 
Estimation of flow velocity
RodriguezIturbe and Valdes (1979) in their studies have assumed that at any given instant during the storm, flow velocity can be taken as more or less constant throughout the catchment and have taken this flow velocity as the velocity corresponding to the peak discharge for a given rainfall–runoff event for the derivation of the GIUH. However, the peak discharge is not known for ungauged catchments. In such cases, the velocity may be estimated using relationship developed between velocity and excess rainfall in the following manner.
Assuming average excess rainfall intensity for a storm (with the assumption that storm will continue up to the time of equilibrium), the resulting equilibrium discharge may be given by the following equation: Q_{e} = 0.2778 × i_{r} × A where i_{r} = P/Δt; P = depth of rainfall excess (in mm); A = catchment area in km^{2}; and Δt = duration of excess rainfall.
Excess rainfall of constant intensity (i_{r}), corresponding to observed discharge data was calculated using above equation. The observed velocity (V) corresponding to the above discharge data was also picked up from the dataset. From the pairs of such observed V and estimated i_{r}, a relationship between i_{r} and V was developed using power regression and this was used for flow velocity estimation.
Evaluation of the model
The model evaluation process included calibration, sensitivity analysis and validation. Critical parameters were identified by sensitivity analysis for the event of 16/8/2002 and the model was calibrated for the identified parameters.

Percentage error in simulated volume (PEV)

Percentage error in simulated peak (PEP), and

Net difference of observed and simulated time to peak (NDTP), as given below:
After model prediction, the dataset was grouped into 10 classes. Each class represents the values that fall into the incremental domains which are determined by dividing the difference of highest and lowest data value with 10. The probability of these periods are plotted and matched with common distribution functions to identify the better matched one which was taken as the representative of the dataset. Predictions from the two models and actual data were used to identify the best fit density function.
Result and discussion
Morphometric analysis of the basin
The geomorphologic parameters were computed graphically by plotting number of streams, stream length and stream area versus the order of the stream and finding the slope of the best fit equation. The values of bifurcation ratio (R_{B}), length ratio (R_{L}), area ratio (R_{A}) and length of highest order stream (L_{Ω}) were estimated as R_{B} = 3.5, R_{L} = 2.2 and R_{A} = 4.5, L_{Ω}= 22.6 km and R_{B} = 3.4, R_{L} = 2.4, R_{A} = 3.9 and L_{Ω} = 22.1 for the two scales (1:250,000) and (1:50,000), respectively (Table 2). It may be noted that these ratios lie in the ranges of values observed for natural basins wherein R_{B} ranges between 3 and 5, R_{L} ranges between 1.5 and 3.5 and R_{A} ranges between 3 and 6 (Smart 1972).
Velocity and effective rainfall intensity relationship
Calibration and sensitivity analysis of the model
The moderately high value of PEV (4.7%), high value of PEP (21.2%) and low value of Nash–Sutcliffe model efficiency (58.2%) for simulation of runoff with precalibrated model indicates the precalibrated model performance is poor.
Thus, in the present study critical parameters were identified by sensitivity analysis and the model was calibrated for the identified parameters
Sensitivity analysis of calibrated parameters (n, R_{A}, R_{B}) of GGIUH model for the basin
% Deviation of peak discharge and runoff volume from observed  

+1  +5  +10  +15  +20  −1  −5  −10  −15  −20  
Peak discharge (cumec)  
n  −1.1  −5.84  −15.1  −21.3  −27.2  1.6  5.9  8.8  14.95  21.15 
R_{A}  −10.1  −8.1  −5.5  −4.7  −3.4  −11.2  −13.1  −16.3  −19.39  −21.24 
R_{B}  −11.2  −12.9  −15.5  −19.9  −21.6  −10.1  −7.9  −5.0  −4.38  −3.36 
Runoff volume (m^{3})  
n  2.0  0.3  −2.2  −4.5  −6.8  3.1  4.7  7.3  9.75  12.48 
R_{A}  2.4  2.5  2.5  2.6  2.6  2.4  2.4  2.3  2.2  2.1 
R_{B}  2.4  2.4  2.3  2.2  2.2  2.4  2.5  2.6  2.6  2.65 
It is evident from Table 3 that both the peak discharge and runoff volume are more sensitive to the Nash model parameter n than to bifurcation ratio (R_{B}), and area ratio(R_{A}) as could be seen by either increasing or decreasing these parameters by ±1, ±5, ±10, ±15 and ±20%, respectively.
A change in the parameter n, R_{A} and R_{B} by 1–20% exhibited the peak discharge to vary from 1.1 to 27.2%, 3.4 to 21.2% and 3.4 to 21.6%, respectively. Corresponding runoff volume was found to vary from 0.3 to 12.5%, 2.1 to 2.6% and 2.2 to 2.7%, respectively.
It is evident from Fig. 3 that there is a close similarity in shape parameters of the hydrograph, such as peak discharge, time base and overall shape of the hydrograph. However, the time to peak of the predicted direct runoff hydrograph (DRH) occurred 2 h before that of the observed one. The low PEV, PEP and NDTP values (2.5%, 10.6% and 0) and the high value (79.1%) of the Nash–Sutcliffe model efficiency (EFF) for the storm event indicate that the model can be well adopted for simulation of direct runoff.
Thus the results indicate that overall prediction of DSRO by the GGIUH model during the calibration period is satisfactory and therefore may be accepted for further analysis.
Verification of the model
Performance measures of GGIUH model for storm events (basin map scale 1:50,000)
Events  PEP  PEV  NDTP  EFF 

14/9/1994  10.5  20.6  2  84.5 
6/9/1995  20.7  20.9  3  77.7 
11/10/1995  −0.1  17.1  3  83.2 
21/7/1999  −4.4  10.5  2  85.2 
28/8/1997  −3.5  12.8  3  74.6 
16/8/1999  5.3  9.1  3  79.4 
6/9/2002  −6.2  7.7  2  84.6 
24/8/2002  −9.6  5.4  3  74.2 
8/6/1997  −16.2  15.0  3  82.1 
20/9/2000  −3.2  19.6  3  90.6 
25/7/1999  −7.2  15.5  4  87.3 
7/8/1999  −7.1  18.3  3  88.5 
23/6/1996  1.7  20.1  3  80.6 
19/7/1998  6.8  20.7  1  84.1 
23/6/1999  −3.3  −10.9  1  95.2 
25/6/2004  −14.9  2.9  −1  80.9 
It is observed from Table 4 that PEV, PEP and NDTP values vary from (2.9–20.9%), (0.1–20.8%) and (−1 to 3 h; only for the event of 25/7/1999 the deviation was 4 h), respectively, indicating a close agreement between observed and simulated runoff. The prediction limits for the simulation model for peak discharge and runoff volume have been found to be within ±20% (which is considered as acceptable levels of accuracy for simulations models) from measured values. The reasonably high (74.2–95.1%) values of the Nash–Sutcliffe model efficiency (EFF) show satisfactory performance of the model. A close similarity in peak discharge, time base and overall shape of the hydrographs are evident from Figs. 4, 5, 6 and 7.
The result is in agreement with an earlier study carried out for Chaukhutia watershed in India by Kumar and Kumar (2007), for Ajoy River basin in India by Sahoo et al. (2005), for Gagas watershed of Ram Ganga River, India by Kumar and Kumar (2004) and by Bhaskar et al. (1997) for Jira River subcatchment in eastern India.
Thus, the results confirm that GGIUH model predicts fairly well the peak discharge, time to peak and time base and runoff volume of the DRH for various storm events of the studied basin with marginal deviation as discussed earlier.
Since the GGIUH model utilizes only geomorphologic parameters of the basin and does not require the flow data, this model can be applied for predicting DRH for ungauged basins.
Comparative performance analysis of GGIUH model for two topographic map scales of 1:50,000 and 1:250,000
Peak discharge and time to peak of the observed and the GGIUH model DSRO hydrographs at two basin map scales 1:250,000 and 1:50,000
Event date  Observed  GGUIH model  

Scale 1:50,000  Scale 1:250,000  
Q_{P} (cumec)  T_{P} (h)  Q_{P} (cumec)  T_{P} (h)  Q_{P} (cumec)  T_{P} (h)  
14/9/1994  220.9  8  197.7  6  179.9  7 
6/9/1995  175.8  8  139.1  5  126.8  6 
11/10/1995  160.9  8  161.1  5  145.8  6 
21/7/1999  154.8  9  161.6  7  146.7  8 
28/8/1997  288.9  8  298.9  5  277.6  6 
16/8/1999  146.9  10  139.1  7  126.6  7 
6/9/2002  156.8  9  166.6  7  151.2  8 
24/8/2002  139.3  8  152.7  5  138.5  6 
6/8/1997  549.5  10  638.5  7  602.5  8 
20/9/2000  165.0  9  170.4  6  153.8  6 
25/7/1999  133.8  9  143.5  5  130.5  6 
7/8/1999  703.6  10  753.7  7  690.6  7 
23/6/1996  59  8  57.9  5  52.9  5 
19/7/1998  30  7  27.9  6  23.6  6 
23/6/1999  60.9  7  62.9  6  57.5  6 
25/6/2004  20.2  8  23.2  9  18.5  9 
It is observed that the peak flow (q_{p}) as estimated by the model is higher (ranges between 7.1 and 20.3%) at map scale 1:50,000 than that at map scale 1:250,000. While Time to peak (t_{p}) as estimated by the model is lower (ranges between 0 and 16.7%) at map scale 1:50,000 than that at map scale 1:250,000.
Performance measures of GGIUH model for storm events (basin map scale 1:250,000)
Events  PEP  PEV  NDTP  EFF 

14/9/1994  18.6  29.4  1  86.8 
6/9/1995  27.9  23.4  2  69.7 
11/10/1995  9.4  15.8  2  83.6 
21/7/1999  5.3  9.1  1  95.9 
28/8/1997  3.9  11.3  2  77.3 
16/8/1999  13.8  7.3  3  92.1 
6/9/2002  3.6  6.4  1  96.3 
24/8/2002  0.6  3.7  2  73.4 
6/8/1997  −9.7  14.4  2  84.8 
20/9/2000  6.8  18.1  3  87.5 
25/7/1999  2.5  13.9  3  86.2 
7/8/1999  1.9  17.2  3  85.8 
23/6/1996  10.2  19.2  3  82.3 
19/7/1998  21.4  18.2  1  87.5 
23/6/1999  5.6  −12.3  1  92.2 
25/6/2004  8.4  8.3  −1  79.3 
It may be noted that Sahoo et al. (2005) in course of their study in Ajoy River basin in India concluded that smaller basin map scales can be used to estimate geomorphological parameters and correspondingly DSRO hydrographs.
Comparative performance analysis of GGIUH model and ANN
It is evident from the figures that both the models have predicted the hydrograph characteristics uniformly, where slope of both GGIUH and ANN predicted hydrographs were found to be nearly equal for rising as well as recession curve, though a significant difference in time to peak was observed for both the hydrographs.
Performance measures of GGIUH model with respect to ANN model for storm events
Event Date  PEV  PEP  NDTP  EFF 

14/9/1994  2.7  −12.9  1  86.5 
6/9/1995  10.4  −17.8  2  78.6 
11/10/1995  −9.4  6.2  2  88.8 
21/7/1999  −10.5  3.6  2  85.9 
28/8/1997  −13.9  4.3  1  84.7 
16/8/1999  −8.9  −6.1  3  77.5 
6/9/2002  −7.1  5.2  2  86.1 
24/8/2002  −0.9  12.2  2  83.8 
6/8/1997  15.1  −14.6  2  87.4 
20/9/2000  7.3  4.0  2  88.4 
25/7/1999  13.9  5.9  1  82.4 
7/8/1999  24.4  −5.4  2  81.4 
23/6/1996  10.3  5.8  1  86.5 
19/7/1998  19.1  3.1  1  83.2 
23/6/1999  −29.3  −2.5  0  88.3 
25/6/2004  2.1  −5.4  2  73.9 
It is observed from Table 7 that PEV, PEP and NDTP values range between 0.9 and 29.3%, 2.5 and 17.8% and 0 and 3 h, respectively, which indicates a good correlation between runoff computed by both ANN and GGIUH models. It may be noted that ‘Time to Peak discharge’ as estimated by both the models was found to be identical for the event of 23/6/1999. The reasonably high (73.9–88.8%) values of the Nash–Sutcliffe model efficiency (EFF) further supports this fact.
Probability distribution function (PDF) for observed data, GGIUH and ANN model
Events  Distribution  Parameters  

24/8/2002  
ANN  Fatigue Life  α = 3.2654, β = 28.749  
GGIUH  Weibull  α = 0.22344, β = 15.016  
Observed  Beta  α_{1} = 0.16874, α_{2} = 0.47736  
a = −6.6232E−15, b = 588.4  
6/9/2002  
ANN  Fatigue Life  α = 3.6349, β = 8.6044  
GGIUH  Weibull  α = 0.30488, β = 13.028  
Observed  Johnson SB  γ = 0.59908, δ = 0.21162  
λ = 217.9, ξ = 0.93392  
16/8/1999  
ANN  Fatigue Life  α = 2.5668, β = 9.4388  
GGIUH  Power Function  α = 0.17764, a = 4.5807E−15, b = 142.73  
Observed  Power Function  α = 0.21961, a = 4.1899E−16, b = 182.6  
28/8/1997  
ANN  LogLogistic  α = 0.57772, β = 3.7588  
GGIUH  Fatigue Life  α = 4.2451, β = 3.5755  
Observed  Fatigue Life  α = 3.4199, β = 6.4133  
21/7/1999  
ANN  Power Function  α = 0.32396, a = −0.64668, b = 163.93  
GGIUH  Kumaraswamy  α_{1} = 0.23789, α_{2} = 1.1198  
a = −2.0097E−15, b = 230.0  
Observed  Beta  α_{1} = 0.21517, α_{2} = 0.47141  
a = −1.0805E−14, b = 154.79  
11/10/1995  
ANN  Fatigue Life (3P)  α = 3.9516, β = 6.8613, γ = −0.73036  
GGIUH  Weibull  α = 0.21076, β = 3.527  
Observed  Fatigue Life  α = 13.571, β = 0.86118  
6/9/1995  
ANN  Gamma (3P)  α = 0.36791, β = 129.07, γ = −0.64668  
GGIUH  Fatigue Life  α = 3.3682, β = 6.3866  
Observed  Dagum  k = 9.2903E−4, α = 415.48, β = 173.02  
14/9/1994  
ANN  Fatigue Life  α = 3.5593, β = 4.6599  
GGIUH  Fatigue Life  α = 5.8549, β = 1.9698  
Observed  Fatigue Life  α = 4.2997, β = 3.5658  
23/6/1996  
ANN  Fatigue Life (3P)  α = 1.7423, β = 0.86005, γ = −0.23972  
GGIUH  Fatigue Life  α = 7.4294, β = 0.34316  
Observed  Fatigue Life  α = 9.425, β = 0.09984  
23/6/1999  
ANN  Pearson 5 (3P)  α = 0.86984, β = 0.48389, γ = −0.32166  
GGIUH  Dagum  k = 0.00438, α = 84.816, β = 64.218  
Observed  Beta  α_{1} = 0.26942, α_{2} = 0.82488  
a = −1.0362E−14, b = 60.935  
25/6/2004  
ANN  Burr (4P)  k = 1.5494, α = 0.78285  
β = 0.65279, γ = −0.1497  
GGIUH  Fatigue Life  α = 10.027, β = 0.07886  
Observed  Fatigue Life  α = 9.425, β = 0.09984  
19/7/1998  
ANN  Beta  α_{1} = 0.16686, α_{2} = 0.36355  
a = −0.00203, b = 4.1239  
GGIUH  Fatigue Life  α = 6.6484, β = 0.29246  
Observed  Kumaraswamy  α_{1} = 0.21312, α_{2} = 0.8398  
a = −1.9339E−14, b = 30.0  
25/7/1999  
ANN  Beta  α_{1} = 0.22439, α_{2} = 0.58132  
a = −1.6000E−4, b = 6.5758  
GGIUH  Fatigue Life  α = 9.4625, β = 0.99786  
Observed  Weibull  α = 0.30715, β = 10.867  
6/8/1997  
ANN  Fatigue Life (3P)  α = 3.936, β = 1.8459, γ = −0.16067  
GGIUH  Beta  α_{1} = 0.15201, α_{2} = 0.46625  
a = −6.6606E−15, b = 638.52  
Observed  Pearson 6  α_{1} = 0.27404, α_{2} = 1167.2, β = 6.3967E+5  
7/8/1999  
ANN  Beta  α_{1} = 0.1366, α_{2} = 0.36814  
a = 0.12512, b = 73.993  
GGIUH  Fatigue Life  α = 19.612, β = 1.0723  
Observed  Power Function  α = 0.16874, a = 4.9068E−15, b = 705.33  
20/9/2000  
ANN  Johnson SB  γ = 0.83812, δ = 0.23763  
λ = 20.959, ξ = −0.17622  
GGIUH  Fatigue Life  α = 10.529, β = 0.75602  
Observed  Kumaraswamy  α_{1} = 0.19957, α_{2} = 1.0925  
a = 1.9191E−15, b = 253.34 
Conclusion
Based on the previous work of Bhaskar et al. (1997) and Singh (2004), a gamma geomorphologic instantaneous unit hydrograph (GGIUH) model was developed for prediction of direct runoff from the catchment of the DulungNala (the largest left bank tributary of the Subarnarekha River System) at Phekoghat station in the state of West Bengal in the eastern part of India.
The peak discharge and runoff volume were found to be quite sensitive to GGIUH model parameters viz., n, R_{A} and R_{B}. A change in these parameters by 1–20% resulted in the peak discharge to vary from 1.1 to 27.2%, 3.4 to 21.2% and 3.4 to 21.6%, respectively. On the other hand, for the same changes in the same three parameters, runoff volume was found to vary from 0.3 to 12.5%, 2.1 to 2.6% and 2.2 to 2.7%, respectively. Based on this sensitivity analysis, the calibration of the model was carried out for these parameters.
The Nash–Sutcliffe model efficiency (EFF) criterion, percentage error in volume (PEV), the percentage error in peak (PEP), and net difference of observed and simulated time to peak (NDTP) which were used for performance evaluation of the model for 16 storm events, have been found to range from 74.1 to 95.1%, 2.9 to 20.9%, 0.1 to 20.8% and −1 to 3 h (only for the event of 25/7/1999 the deviation was 4 h) respectively, indicating a good performance of the calibrated GGIUH model for prediction of runoff hydrograph.
Again, ANN models were prepared and trained with three different training algorithms to predict discharge hydrograph using observed rainfall and discharge hydrograph.
Analysis of performance measures of GGIUH model, with respect to predicted discharge hydrograph by ANN model, reveals that the PEV, PEP, NDTP and EFF values range between 0.9 and 29.3%, 2.5 and 17.8%, 0 and 3 h and 73.9 to 88.8%, respectively, indicating comparable performance of both ANN and GGIUH models.
Further, DSRO hydrographs computed using the GGIUH model at two map scales (viz. 1:50,000 and 1:250,000) were found to yield comparable performance indicating suitability of using lower map scale to estimate the DSRO hydrographs. Thus, lower map scales may also be employed for extraction of geomorphological parameters in case of nonavailability of larger map scales (1: 50,000). This would further minimize the extent of labor and time involvement in estimating parameters and this has a practical relevance to field engineers. In a study in the Ajoy River basin in India, Sahoo et al. (2005) reported that smaller basin map scales may be used to estimate DSRO with reasonable accuracy. As GGIUH model was found to predict the event distribution pattern more efficiently than the ANN model, the supremacy of the former over latter is evident. Thus, the GGIUH model which does not use historical runoff data can be used for the prediction of design floods from ungauged basins.
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