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Simulation of runoff in ungauged catchments has always been a challenging issue, receiving significant attention more importantly in practical applications. This study aims at calibration of an Artificial Neural Network (ANN) model which is capable to apply in an ungauged basin. The methodology is applied to two sub-catchments located in the Northern East of Iran. To examine the effect of physical characteristics of the catchment on the capability of the model generalization, it is attempted to synthesize effective parameters using empirical methods of runoff estimation. Firstly, the model was designed for a pilot sub-catchment and the statistical comparison between simulated runoff, and target depicted the capability of ANN to accurately estimate runoff over a catchment. Then, the calibrated model was generalized to another sub-catchment assumed as an ungauged basin while there are runoff data to compare the result. The result showed that the designed model is relatively capable to estimate monthly runoff for a homogenous ungauged catchment. The method presented in this study in addition to adding effective spatial parameters in simulation runoff and calibration of model by using empirical methods and the integration of any useful accessible data, examines the adaptability of model to an ungauged catchment.

Uncertainty in hydrologic predictions makes it difficult to accurately estimate runoff which is a key factor in terms of catchment hydrology researches as well as practical management of water resources. Different types of the modern rainfall-runoff models which need complex parameters and data have been developed to provide reliable results whereas the feasibility of these models has been almost always concerned with ungauged or scarcely gauged catchments. Hence, application of data-driven techniques such as data mining and computational intelligence to describe dynamics and nonlinear process of rainfall-runoff has become the subject of increasing attention. Accordingly, Artificial Neural Network (ANN) has been widely applied as an efficient technique which is capable to capture the nonlinearity of rainfall-runoff process and represent the complexity of converting rainfall to runoff process over a catchment. So far, extensive researches have been done to examine the efficient performance of ANN models in simulation and prediction of stream flow. The efficiency of artificial neural network and multivariate regression was compared in prioritizing climate factors affecting runoff generation and concluded that multi-layer perceptron artificial neural network models are more accurate than multivariate regression models [

The model was applied in two sub-catchments of Samalghan River located in the East North region of Iran where the boundaries can be given by longitudes from 37˚24'39'' to 37˚29'07'' east and latitudes 56˚59'60'' to 56˚37'46'' north. The river is a tributary of Atrak River which flows into the Caspian Sea. Two sub catchments were delineated based Digital Elevation Model (DEM) in GIS software (

Physical Characteristics | Pilot Catchment | Ungauged Catchment |
---|---|---|

Area (km^{2}) | 118 | 175 |

Perimeter (m) | 48 | 58 |

The Maximum Height (m) | 2455 | 2500 |

The Minimum Height (m) | 1028 | 955 |

The Average Height (m) | 1824 | 1773 |

Main River Length (m) | 21 | 22 |

The Main River Gradient | 5 | 5.3 |

Compactness Coefficient^{a} | 1.3 | 1.2 |

^{a}Calculated by

temperature data series which span the period of 35 years from 1978 to 2013. Rivers in the study area are fed by spring discharge and individual rain events. There are also two hydrometric stations which provide monthly runoff data in the mentioned period (

the mean and dividing by the standard deviation. As mentioned above, one specific basin was considered as the pilot basin where the model was trained and calibrated and the other one regarded as an assumed ungauged catchment where the calibrated model applied to estimate runoff and the result compared with the observed data.

The most commonly used ANN structure in hydrological applications is the feed-forward multilayer perceptron (MLP) (

It is interesting to note that, in ANN simulation coupled with Levernberg-Marquardt training algorithm and hyperbolic tangent transfer functions, the appropriate choice of data set for training and testing stages is the most sensitive issue bringing about an efficient model which is capable to estimate monthly runoff in different seasons. In the present study, the standardized data series for two catchments are categorized into three data subsets, 60% of the entire data series for training set, the 20% of the data is considered as cross-validation set and the 20% of remaining data is used for testing set, considered based on the MATLAB tutorial.

The most important controller feature in forming of surface runoff over a catchment is the physiographic characteristics including slope, main waterway length, soil type and vegetation cover which can be regarded as the spatial parameters. To improve the capability of the model generalization, it is attempted to make a connection between the spatial parameters and temporal rainfall events in form of synthetic input variables of ANN.

This is investigated by using empirical methods of runoff estimation which consider some spatial parameters and connect them with the average rainfall. Empirical models include relationships and equations which have been determined using analysis of limited data and the region characteristics, and the models are used to estimate some special probabilistic parameters. Most of these methods are useful for a special zone so, it is not possible to use them for other areas. But, some of these methods have more expanded domain and can be used for some same regions by applying some corrections and choosing proper coefficients [

portant conventional equations were evaluated in regional conditions of the study area and the results were com- pared with observations runoff hence four methods that provide the most acceptable results in the study area were selected as the major equations, employing to synthesize the input data of ANN model as spatial-temporal variables. These equations are presented in the following:

Khosla proposed Equation (1) to calculate runoff using temperature and rainfall parameters [

Lacy presented Equation (2) for estimating annual runoff based on reviews in several catchments [

Justin investigated extensively on the relationships between annual rainfall and runoff in many catchments with different climatic conditions and presented their results as Equation (3) [

The Irrigation Department of India presented following equation between average rainfall and river runoff [

All variables in above equations are defined as the following:

P: average rainfall (cm); R: the corresponding runoff; T: average air temperature; A: catchment area (km); ΔH: maximum elevation difference of catchment; F: rainfall duration parameter; Z: coefficient for vegetation.

In the pilot catchment, in fact, the input factor of ANN model is the monthly runoff calculated based on the equations mentioned above in a period of 35 years and the output target is also monthly runoff values recorded by the hydrometric station at the outlet of Darkesh sub-catchment (

ANN Variables (monthly runoff) | |
---|---|

Variable | Description |

Input Variable 1 (Vi1) | Runoff calculated based on Equation (1) |

Input Variable 2 (Vi2) | Runoff calculated based on Equation (2) |

Input Variable 3 (Vi3) | Runoff calculated based on Equation (3) |

Input Variable 4 (Vi4) | Runoff calculated based on Equation (4) |

Output Variable (Vo) | Runoff recorded in the outlet of basin |

The accuracy of ANN model performance is commonly evaluated with some efficiency terms. Each term is estimated from the predicted values of the model and the observed targets as follows:

1) The correlation coefficient (R-value) has been widely used to evaluate the goodness-of-fit of hydrologic and hydrodynamic models. This is obtained by performing a linear regression between the ANN-predicted values and the targets and is computed by Equation (4).

where R is correlation coefficient, N is the number of samples,

The correlation coefficient provides a direct measure of the ability of a model to reproduce the recorded flows with R = 1.0 indicating that all the estimated flows are the same as the recorded flows [

2) The ability of the ANN-predicted values to match observed data is also evaluated by the Mean Square Error (MSE) defined as Equation (5) [

The ANN responses are more precise if R, MSE are found to be close to 1, 0, respectively. In the present study, R and MSE, which demonstrate the performance efficiencies of each trial, have been recorded and compared to attain the more accurate results. The results of the three-layer feed-forward MLP model with synthesized input vectors for the pilot (Darkesh) catchment is shown in Figures 4-6. The comparison of calculated runoff by ANN model and the observed runoff (for stages of training, validation and testing) is also shown in Figures 7-9.

Regression between the network result and the recorded monthly runoff in the pilot basin presents an appropriately satisfactory correlation between the observed runoff data and simulated ones. The results are quite ac- ceptable and represent the satisfactory performance of the ANN model for the first catchment that means the model was successfully designed. Visual comparison of the estimated monthly runoff with actual values convince that the model capable to simulate the natural regime of stream.

Application of Calibrated Model in an Ungauged CatchmentThe goodness-of-fit measures point out a satisfactory robustness for the ANN model over the first catchment. This ability of the ANN which in fact can be trained by available effective data and estimate monthly runoff opens new opportunities to dealing with the ungauged catchment issues. In the last part of the study, with regard to the capability and efficiency of the ANN model to simulate the monthly runoff in DARKESH sub-catchment

as the pilot study area, the important step is to apply the calibrated model to the SHIRABAD sub-catchment regarded as an ungauged basin. In order to apply the method, similar to the pilot catchment, the rain data and the physical characteristics of SHIRABAD basin were synthesized by empirical equations and entered to the calibrated model based on pilot catchment’s dataset and run the model.

The correlation parameter and the regression equation between the result of model and the observed runoff on SHIRABAD catchment (the observed runoff data are only used for assessment of result since the catchment is regarded as a ungauged catchment in terms of runoff data) is presented in the

The procedure outlined in the study in addition to examining the capability of a MLP structure of ANN model, analyzed the effectiveness of synthesizing input vectors (using empirical methods) to simulate rainfall-runoff process on a catchment. The result indicates that if the effective parameters are entered to the model as the synthesized vectors, network learning process can be accelerated and improved so that the model becomes more capable to identify system and provide the more accurate result in face of new data. This ability is of great importance in generalization of model in an ungauged basin where there are no runoff data to training and validating the network. The result of this study represents the efficiency of ANN network in rainfall-runoff modeling, providing the accurate result in a pilot basin. In addition, in terms of application of model in an ungauged catchmenteven if the accuracy of results in comparison to the pilot catchment was declined, calibration of a model with appropriate cover of accessible climatic and spatial data which can be employed in adjacent and homogenous catchments would be an asset to estimate runoff in the absence of hydrological stations by considering the model estimating error.

The authors gratefully acknowledge the North Khorasan Water Regional Authority to provide data which have been used in this study. The corresponding author would like to express her great appreciation to Dr. FarshadKouhian, who made invaluable comments to conduct the study.

Shahrbanou Firouzi,Mohamad B. Sharifi, (2015) Calibration of a Rainfall-Runoff Model to Estimate Monthly Stream Flow in an Ungauged Catchment. Computational Water, Energy, and Environmental Engineering,04,57-66. doi: 10.4236/cweee.2015.44006