Rainfall-Runoff plays a major role in Hydrology and Water Resources. ANNs are a physical-based and black box model which is a useful tool in hydrology ^{1, 2}. Nowadays, Artificial Neural Networks (ANNs) have become one of the vital tools for modeling of complex hydrological processes. ANNs draw the relationship among the variables particularly inputs and outputs values ^{3, 4, 5}.

In hydrology, the research work is to develop the model to find out the future basin discharge which is a safe and economical tool for hydrological engineering design ^{6, 7, 8}. The water resources management using ANNs which involves the estimation of Rainfall-Runoff event, river discharge forecasting, Climate Change, river inflow modeling and estimation of groundwater, etc

From a review of previous researches, several researchers have investigated and studied the different aspects of this area over the last century, but did not arrive with clear signals. Then, this study has started to research in the district of Bankura.

The study area is located on Lower Gangetic Plain (Zone no-III, as per Planning Commission of India) in between 22° 38’00’’ and 23°38’00’’ N latitude and 86°36’00’’ and 87°46’00’’ E longitude. The area of the district Bankura is 688200 hectares. The district consists of different groundwater potential and water table contour (shown in^{2}. Sali is one of the tributaries of Damodar River located in district Bankura. ii) Darakeswar sub-basin: The catchment area of this basin is 4292 km^{2}. The tributaries of Darakeswar River are Arkasha, Kansachor, Gangheswari, Berai, Khukra, and Shankari. iii) Shilabati sub-basin: The catchment area of the basin is 4088 km^{2}. The tributaries of Shilabati River are Jaiponda, Puratan, Champyan, and Ketia. iv) Kangsabati sub-basin: The catchment area of this basin in West Bengal is 6324 km^{2}. The tributaries of Kangsabati River are Jam, Jhinuk, and Kumari. Damodar River is originated from Palamau hill range in Jharkhand State. Darakeswar, Shilabati, and Kangsabati are originated from upland of Chhota Nagpur Plateau in district Purulia, West Bengal.

For this research, the data have been collected from India Meteorological Department, Pune, for six meteorological station located in the district Bankura such as i) Bankura, ii) Bankura (Central Water Commission), iii) Joypur, iv) Kangsabati dam, v) Ranibandh, vi) Indus. The researches have been considered for predicting runoff by using ANNs model. The following five input variables are Rainfall, Average Temperature, Cloud Cover, Potential Evapotranspiration and Relative Humidity. In the present investigation, the rainfall intensity pattern is used having three different types of intensity i.e. 30mm/hr, 60mm/hr and 90mm/hr.

For physiographical data, viz. Land Use, Slope and Roughness have been collected from the chief soil survey officer, soil and land use survey of India, Pusa, New Delhi and Natural Resources Data Centre, Bankura, W.B. which is shown in

Land Use details of the district are 59.54 % under cultivation, 12.36% cultivable wasteland, 8.48% barren land, and 19.61% cover with forest. The land utilization pattern of the district reveals that Saltora, Mejia, Gangajalghati, Bankura, Bishnupur, and Patrasayer all have more than 57% of land under cultivation. The Joypur block has the highest cultivation (66%) whereas India has 83.01% highest cultivation. All these blocks are located in the central and eastern parts of the district. In the western and south-western part of the district have a less cultivated area. In Chhatna, Ranibandh and Raipur have more than 30% barren land and other 30% cover by forest. The percentage is covered by the forest of the following blocks – Barjora 23%, Ranibandh 32.87%, Taldangra 31.00%, and Bishnupur 35%. Researches have collected the all land use data from Soil and Land Use Survey of India, Pusa, New Delhi.

The land of the district consists of nine slope categories. The slopes of the district according to their area are as per

Sl no | Slopes classes | Area in hectare | Area in percentage (%) |

1. | Level slope | 23614.00 | 3.430 |

2. | Level – Very Gently slope | 371351.00 | 53.960 |

3. | Very Gently slope | 669.00 | 0.100 |

4. | Very Gently – Gently slope | 238513.00 | 34.660 |

5. | Gently – Moderately slope | 6301.00 | 0.920 |

6. | Strongly – Moderately steep slope | 8088.00 | 1.180 |

7. | Moderately steep – Steep slope | 1561.00 | 0.230 |

8. | Steep – Very steep slope | 995.00 | 0.140 |

9. | Miscellaneous slope | 37108.00 | 5.390 |

Total | 688200.00 | 100.000 |

*Sources: Soil and Land Use Survey of India, Pusa, New Delhi.

Input parameters
Output parameters
Slope (%)
Rainfall intensity (mm/hr)
Rainfall duration (Sec)
Runoff (mm)
Minimum
1
30
0
0
Maximum
3
90
1140
958.90

The research has used the equation of Kothyari and Garde (1991) which is more suitable for Lower Gangetic Basin, district Bankura, West Bengal. This equation is recommended by the International Water Management Institute (IWMI) in working Paper-130 which is published in 2008. Simultaneously this is also recommended by the National Institute of Hydrology, Roorkee, India in 2008. The equation is the following-

Where, R_{m} = Annual mean runoff in cm, P_{m} =the average annual rainfall in cm, T_{m} = the average annual temperature in ^{0}C, and F_{V} = vegetal cover factor.

Where, ɑ_{1}, ɑ_{2} , ɑ_{3}, ɑ_{4} are the weighting factors, F_{F} is the percentage area of forest, F_{G} is the percentage area of grass and scrub land, F_{A} is the percentage area of arable land, and F_{W} is the percentage area of waste land only.

In Hydrological research, ANN is a recognized tool to construct a structure between multiple input variables and specific output ^{12, 13, 14}. This technique is more suitable for forecasting and runoff analysis ^{15, 16}. In this investigation, ANNs consist of five input layers, a single hidden layer, and an output layer. Hidden layers may be increased in case of a complex situation.

Firstly, ANNs are trained with a series of observed inputs data set viz. Rainfall, Average Temperature, Cloud Cover, Potential Evapotranspiration, and Relative Humidity, denoted as X_{1}, X_{2}, X_{3}, X_{4}, and X_{5} respectively and output data, Runoff denoted as Y_{i}. In the training process, the coefficients (denoted as W_{k} and W_{kj}) are obtained. The first process carries out exploration for the optimum nonlinear correlation among input variables and output. In linear regression, the network involves input variables (X_{j}) linear functions operated by transfer function as shown in equation (iii). Where, the hidden unit receives from each and every input variable. We are writing mathematically by the following equations:

Where, X_{1}, X_{2}, …… X_{m} are input variables; φ denotes the hyperbolic transfer function; W_{k1}, W_{k2},… W_{km} and W_{1}, W_{2},… W_{k} are the coefficients (weights) of the network; u_{1}, u_{2}, ….u_{k} denotes hidden units; b_{kj} and b_{k} are the constants to linear regression, and Y_{i} is the output signal. Hidden units linear function along constant obtains final output of the network as shown in equation (iv). At first, normalization of the data series are performed as per equation (v) within ±1.

In equation (iii), P_{o}, P_{nor}, P_{min}, and P_{max} denotes observed data, normalized data, minimum observed data, and maximum observed data respectively. During ANNs modeling, complete data series were randomly distributed into training, testing, and validation in 70% / 15% /15% format. Initially, the network was trained with training data series, and after that testing, data series was utilized to calibrate the behavior of trained models. After calibration and testing finally, the data series was used to validate and to complete the ANNs model.

During the training the network, Gradient Decent (GD) algorithm was applied to reduce the network error by a function minimization routine and to improve the network output.

Where t_{j} = desired error and y_{i } = calculated output.

*Sources: https://www.researchgate.net / Publication / 282903935

For estimating the model performance, the Nash-Sutcliffe Efficiency (NSE) is an important measure that is expressed by the equation (vii).

Nash-Sutcliffe Efficiency (NSE) in percentage (%),

Where, Y_{O} = Observed flow at time t, Y_{K} = Predicted flow (Kinematic flow) at time t, and Y_{m} = Mean observed flow.

Nash-Sutcliffe Efficiency (NSE) measures the variability of the model (Legates and McCabe, 1999). NSE ranges from -∞ at a worst-case to +1 for a perfect correlation. According to Shamseldin (1997), the value of NSE 0.9 and above is very satisfactory, 0.8 to 0.9 represents a fairly good model and 0.8 is an unsatisfactory result ^{6}.

Where, Q_{k} = Observed flow, Ǭ_{k} = Predicted flow, and K = Total number of year considered (Validation data).

The value of RMSE measures the accuracy of the model, and as minimum as possible. The value of RMSE and MAE more or less similar (near about same) and represents the good satisfactory model (C. W. Dawson and R. L. Wilby, 2015).

Where, Q_{k} = Observed flow, Ǭ_{k} = Predicted flow, and K = Total number of year considered (Validation data).

The value of MAE measures the accuracy of the model and as minimum as possible.

The error in Runoff for the present investigation was estimated by,

Where, Y_{o} = Observed Runoff, and Y_{K} = Predicted Runoff.

The value of Error in Runoff computation measures the accuracy of the model and as lower as possible.

Where, X_{i} = Observed flow, _{i} = Predicted flow,

The ANNs model (Rainfall-Runoff model) is a machine learning process for flow (discharge) evaluation using Microsoft Excel. The researcher has collected the real-time data series (1901 – 2016) from India Meteorological Department (IMD), Pune, for the district Bankura. The data were taken from IMD station located six places and equally distributed in the entire district viz. i) Bankura, ii) Bankura (Central Water Commission), iii) Joypur, iv) Kangsabati dam, v) Ranibandh, vi) Indus. The data were taken at various slopes and various intensities. The studies have been considered for predicting runoff for five major climatic variables. The five input variables are Rainfall, Average Temperature, Cloud Cover, Potential Evapotranspiration, and Relative Humidity. The database used for ANNs model development is mentioned in

The behavior of the ANNs during training, testing, and validation are shown in

Model | Observed Runoff in mm | Predicted Runoff in mm | Error in Runoff in % | Correlation Coefficient “r” | Testing of model performance | Remarks | ||

NSE | RMSE | MAE | ||||||

A | 764.85 | 759.74 | 6.590 | 0.9736 | 81.38 | 43.495 | 38.788 | Model “C” is the Best fitted model and very satisfactory. |

B | 789.80 | 792.38 | 1.092 | 0.9746 | 87.925 | 46.521 | 38.574 | |

C | 787.46 | 769.31 | 0.062 | 0.9782 | 97.492 | 44.008 | 40.477 | |

D | 783.53 | 773.32 | 0.290 | 0.9897 | 95.245 | 62.759 | 45.792 |

The predicted result is useful in the field of water resources management and planning for decision-making ^{4}. Apart from that, the modeling can also be useful for rural as well as urban planners to take necessary measures.

The predicted result should be more useful in the field of water resources management and planning in the future.

First time, the study has been used Kothyari and Garde equation (recommended by National Institute of hydrology, Roorkee, India) in which the most important factor i.e. the Vegetal Cover Factor (Fv) was considered over this area.

For all events, model “A”, “B”, “C”, and “D”, correlation coefficient “r” and the Nash-Sutcliffe Efficiency (NSE) (for model “C”) greater than 97% (shown in

KKD expresses gratitude, and respect to Dr. Supriya Pal, Associate Professor, Department of Civil Engineering, NIT Durgapur, for his valuable advice, and guidance throughout the work. Also thanks Dr. A. K. Kar, Professor, Dream Institute of Technology, for his guidance.