Comparison of Artificial Neural Network and regression models for sediment loss prediction from Banha watershed in India

Transcription

1 Agricultural Water Management 78 (2005) Comparison of Artificial Neural Network and regression models for sediment loss prediction from Banha watershed in India A. Sarangi *, A.K. Bhattacharya Water Technology Centre, IARI, Pusa Campus, New Delhi , India Accepted 2 February 2005 Available online 24 February 2005 Abstract Two Artificial Neural Network (ANN) models, one geomorphology-based (GANN) and another non-geomorphology-based (NGANN) for the prediction of sediment yield were developed and validated using the hydrographs and silt load data of for the Banha watershed in the Upper Damodar Valley in Jharkhand state in India. The sediment loads predicted by these models were compared with those predicted by an earlier developed regression model for the same watershed. It was revealed that the feed-forward ANN model with back propagation algorithm performed well for both the GANN and NGANN models. However, the GANN predicted better with highest coefficient of determination (R 2 ) of 0.98, model efficiency (E) of 0.96 and absolute average deviation (AAD) of in comparison to NGANN (R 2 = 0.94, E = 0.81, AAD = 0.006). The regression model performance was inferior (R 2 = , E = 0.72, AAD = 0.023) to the ANN models. The Neuralwork-ProII-plus and MATLAB software were used for development of the ANN models. It was also revealed that association of geomorphological parameters viz. relief factor, form factor and drainage factor with runoff rate resulted in a better prediction of sediment loss. # 2005 Elsevier B.V. All rights reserved. Keywords: ANN; Hydrology; Runoff rate; Sediment Loss; Geomorphology; Regression model; Model efficiency * Corresponding author. Tel.: address: arjamadutta.sarangi@elf.mcgill.ca (A. Sarangi) /$ see front matter # 2005 Elsevier B.V. All rights reserved. doi: /j.agwat

2 196 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) Introduction In the past decades, great strides have been made in conceptualizing the runoff and sediment yield processes from watersheds through modeling. Models are classified based on their comprehensiveness in representing the physical processes involved. With increasing comprehensiveness, models are classified as black-box models, conceptual models and physically based distributed models. The last of the three can be considered the better choice in a rigorous theoretical sense. However, the significant data need of such models and their marginally superior results compared to the others make them an unfavorable choice in operational hydrology (Gautam et al., 2000). Lumped conceptual models are favoured, as they can be based on a sound conceptual framework due to their limited data need. But they require lengthy calibration and parameterization processes. Amongst the soft computing tools viz. Genetic Algorithm (GA), Simulated Annealing (SA), Multivariate Adaptive Regression Splines (MARS) and Artificial Neural Networks (ANNs), the ANNs are most frequently used for hydrological modeling. The first fundamental concepts related to neural computing were developed by McCulloch and Pitts (1943), and much of the ANN activities have been centered on back-propagation and its extensions (Salas et al., 2000). The ANN technique mimics the cognitive response of the human brain. The ANN functions as a data-mining tool, in which the input and output data set has to be fed to the software and trained before validating the model. The network function is determined by the connections between elements. The neural networks need to be trained to perform a particular function by adjusting the values of the connections (weights) between elements. The weights are adjusted based on a comparison of ANN output and the target, until they match. ANNs have an advantage over deterministic models in that the data needs are usually less and they are well suited for long-term forecasting. The disadvantage of the ANN is that it is based on a black box approach since the internal structure of the model is generally not known and must be developed by a trial and error process. There has been a growing trend for the use of ANNs in the areas of hydrologic and water quality modeling (Sharma et al., 2003; Yu et al., 2004; ASCE, 2000a,b; Maier and Dandy, 2000), and land drainage engineering (Yang et al., 1996; Shukla et al., 1996). Despite the black-box nature of the ANN, it has the flexibility in inclusion of parameters and in capturing the non-linearity of rainfall-runoff-sediment yield processes, making it more attractive for modeling hydrological processes (Hsu et al., 1995). The main advantage of the ANN approach over traditional methods is that it does not require an explicit description of the complex nature of the underlying process in a mathematical form (Sudheer et al., 2002). Cannon and Whitfield (2002) suggested ANNs to be superior to stepwise linear regression procedures while conducting a study on predicting runoff from 5-day mean stream flow atmospheric data from 21 watersheds of British Columbia, Canada. Nagy et al. (2002) used a feed-forward three-layer back propagation (BP) ANN model to predict the sediment concentration in rivers using eight input parameters reflecting sediment and riverbed information. The ANN approach provided better results than other formulas used for estimation of sediment concentration. Sudheer et al. (2002)

3 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) developed a new approach for designing the network structure in an ANN-based rainfall-runoff model. The method used the statistical properties, such as an autocorrelation function and a partial autocorrelation function of the data series in identifying a unique input vector that best represented the process for the basin, and a standard algorithm for training. The methodology was validated using data from a river basin in India. The results of the study were highly promising. Yitian and Gu (2003) developed a mass-conservation transfer function for flow and sediment yield of rivers incorporating the models into a real river network architecture using the soft computing tool and expanding hydrological applications of the ANN technique for sediment yield prediction. They applied the model in the Jingjiang reach of the Yangtze River and Dongting Lake, China, and demonstrated the capability of the ANN technique for real-time prediction of flow and sediment transport in a complex river network. Zhang and Govindaraju (2003) developed a geomorphology-based ANN (GANN) for prediction of watershed runoff. Several morphological parameters needed for developing the Geomorphologic Instantaneous Unit Hydrograph (GIUH) were used for development of flow path probabilities. Path probabilities were used as connection weights between the hidden and output layers. They concluded that the GANNs offered a scope of elevating the ANNs from purely empirical status to a platform where they could be considered more rational and realistic. With the added flexibility provided through the connection weights between input and hidden-layer nodes, they performed better than the GIUH model. Sudheer et al. (2002) used soft computing tools to develop a new approach for designing the network structure in an ANN-based rainfall-runoff model. The method utilizes an auto correlation function and partial auto correlation function of the data series in identifying a unique input vector that best represents the process in the basin and a standard algorithm for training. The methodology has been validated using the data for a river basin in India. Reddy (2003) used ANN and GIS tools in three watersheds of Daman Ganga Catchments, Maharashtra and two watersheds in Lower Bhavani catchments, Tamil Nadu State, India, for prediction of runoff. The feed-forward neural network with back propagation algorithm performed better with five hidden layers and nonparametric statistical test revealed a close match between the predicted and observed runoff values. Sarangi and Bhattacharya (2000) developed a regression model for prediction of sediment concentration from runoff rate, in association with certain geomorphological parameters and achieved a high R 2 value. Kaur et al. (2003) used the Soil and Water Assessment Tool (SWAT), a physically based, basinscale continuous event model to estimate runoff and sediment loss from Nagwan Watershed in the Upper Damodar Valley, India. They also developed a Spatial Decision Support System (SDSS) to identify the priority areas for soil and water conservation measures. The above review suggests that there is no ANN model available for prediction of sediment yield rate from the runoff rate from watersheds of India considering the geomorphological parameters of the watershed. The objective of this study was to develop geomorphology-based ANN models, non-geomorphology-based ANN models and compare their performance with the geomorphology-based regression models for prediction of sediment yield rate using runoff rate of the study watershed.

4 198 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) Study area The study area was the 1751 ha Banha watershed in the Itkhori block of Chatra district of Chhotnagpur Plateau in Jharkhand state in India, and falls within N latitude and E longitude (Fig. 1). The climate of the area is tropical and humid with average annual rainfall 1119 mm and average annual maximum and minimum temperature 43.4 and 5 8C, respectively. The soils vary from red and brown sandy loam to clay type. Of the total watershed area, 29.4% was under forest and the net sown area was 30.8% (Sarangi and Bhattacharya, 2000). The data of rainfall depth (mm), runoff rate (m 3 / s) and sediment loss (g/l) are recorded and maintained by the Damodar Valley Corporation (DVC) authority, Jharkhand. Four years ( ) of such data at the outlet of the Banha watershed and relevant maps were acquired from the office of the DVC and from the Indo German Bilateral Project (IGBP) office, New Delhi. In the present study, selected Fig. 1. Location map of the Banha watershed under DVC, Jharkhand, India.

5 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) Table 1 Geomorphological parameters of Banha watershed Sl. no. Name of the dimensionless geomorphological parameter Value 1 Relief ratio Relative relief Elongation ratio Basin shape factor Form factor Length width ratio Circulatory ratio Compactness coefficient Drainage density Stream frequency Drainage factor Hypsometric integral Source: Sarangi and Bhattacharya (2000). geomorphological parameters of the watershed (Table 1) were used for the development of GANN models. 3. ANN model development steps The most commonly used ANN in hydrological predictions is a feed-forward network with the BP training algorithm (Govindaraju and Rao, 2000). Back propagation algorithm is a first-order gradient search method, which is capable of non-linear pattern recognition and memory association. Standard multi-layer feed forward networks are capable of approximating any measurable function to any desired degree of accuracy. The term bias used in ANN models represents an adjustable parameter of the neurons that is basically the difference between the ANN-estimated and the observed output. For better model development, the sum of the biases (Figs. 2 and 3) for the entire data should be small. In the present study, the feed forward neural network with BP training algorithm is used for development of the ANN models Neural network architecture In practice, the ANN architecture consists of input layer, intermediate layers (hidden layer) and output layer. The hidden layers may be one or more depending on the data type and the model error statistics. Also, the numbers of nodes in the hidden layer play a significant role in ANN model performance. Zhang and Govindaraju (2003) used the number of flow paths as the number of nodes in the hidden layer of a GANN. The maximum number of flow paths in a watershed drainage network is given by 2 V 1, where V is the highest stream order. In Strahler s stream ordering system (Strahler, 1957), the first-order stream is the smallest unbranched stream and originates at a source. The secondorder stream is generated from the joining of two first-order streams and similar sequence is followed in ordering the streams within a watershed system leading to the highest order

6 200 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) Fig. 2. The flow chart of data training in NGANN. stream appearing at the watershed outlet (Ritter et al., 2002). For this analysis, the drainage networks were extracted from the digital elevation map of the Banha watershed using the Watershed Morphology Estimation Tool (WMET) as an interface in ArcGIS 1 (Sarangi et al., 2003). The flow path and path probabilities, responsible for translating runoff Fig. 3. The flow chart of data training in GANN.

7 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) towards the outlet were evaluated from the drainage network parameters. In this study, the stream order concept in selecting the optimal number of nodes in the hidden layer was adopted. The number of nodes in the hidden layer was estimated to be 8 (2 (4 1) =2 3 =8)as Banha is a fourth-order watershed (Sarangi and Bhattacharya, 2000). An unresolved issue in applying ANNs to the modelling of the rainfall-runoff process is the architecture that should be used to map the process effectively (Sudheer et al., 2002). The input vectors to the selected ANN model and the number of hidden layers, the learning rule and the number of output vectors have impact upon the model s performance. There are no fixed rules for developing an ANN and a general framework is followed based on previous successful applications in engineering. Based on such successes, the trial and error approach was adopted to select the optimal ANN architecture in the present analysis, using the data of Banha watershed. Different combinations of input parameters and the number of hidden layers with a single output (sediment yield) were tried. The root mean square error (RMSE) of the ANN model was chosen as the criterion for selection of optimal architecture. The architectures for GANN and NGANN are shown in Figs. 2 and 3, respectively. Each neuron has a number of input arcs connected (Figs. 2 and 3), u 1 to u n, and associated with each i, there is a weight W ij, which represents a factor by which a value passing to the neuron is multiplied. A neuron sums the values of all inputs as: S j ¼ X W u þ b In the Figs. 2 and 3, W u corresponds to the summation of weights W ij. The term b is called bias. Finally, an activation function is applied to S j to provide final output from the neuron. When a BP training algorithm is used for training a network, the sigmoid activation function is most often used (Sivakumar et al., 2002). The sigmoid function is bounded above and below (0 and 1), is continuous and differentiable everywhere (Dawson and Wilby, 1998). The sigmoid function (w) is given by ðs j Þ¼ 1 1 þ e S (2) J where S j is the value of the neuron at jth location Data preparation and standardization Out of the 96 data sets available for the runoff rate and sediment yield in 4 years, about 60% were used for ANN model development and the remaining 40% (40 sets) were used for model validation. Out of the data used for model development, 60% of the data (30 sets) were used for training and 40% (20 sets) were used for model testing. The Neural Works Professional II + version 5.23 and Neural Network toolbox of MATLAB 6.5 tools were used for developing the ANN models. The regression model (Eq. (3), Sarangi and Bhattacharya, 2000) was used for comparison with the GANN and NGANN models that were developed in the study. The regression model is associated with three geomorphological parameters as given by: p S ¼ 13:756 17:5R ffiffiffiffi R f p þ 7:30R ffiffiffiffi F f p 3:23R ffiffiffiffi D f (1) (3)

8 202 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) where S = sediment yield in g/l; R = runoff rate in m 3 /s; R f = relative relief; F f = form factor and D f = drainage factor. The regression model was validated again with the validation data set. For developing the GANN, the three dimensionless geomorphological parameters p used ffiffiffiffiffi in p Eq. ffiffiffiffiffi (3) (Table pffiffiffiffiffi 1) R were mathematically associated with the observed runoff rate as R f F, R f D, and R f, which were inputted to the ANN model (Fig. 2). For developing the NGANN, the runoff rate is used as the only input parameter and sediment yield is used as only output parameter, with one hidden layer having eight nodes (Fig. 3). The back propagation (BP) feed-forward neural network model with different learning rules and transfer functions resulted in a better RMSE for all the randomized data sets. The data set was randomized and 20 such shuffled sets were prepared for input to the ANN architecture and the RMSEs were calculated for all. The randomized data sets were also used for cross validation. The final model was developed keeping in view both the RMSE and the cross-validation statistics (i.e., R 2 value). The data shuffling was performed within Excel TM spreadsheet to nullify the presence of any existing trend and inherent properties within the data. The delta-learning rule with sigmoid transfer function resulted in a better RMSE for all the randomized data sets. Moreover, due to the nature of the sigmoid function (Eq. (2)), it was necessary to standardize the data in a range between 0 and 1. The ANN would require extremely small weighting factors causing computational inaccuracies due to floating point calculations, sluggish training and the near-zero gradient of sigmoid function at extreme values (Dawson and Wilby, 1998). Therefore, in the present study, the input values were standardized with respect to the maximum and minimum values in the range (Eq. (4)), as this provided better model predictions than other approaches of standardization. N i ¼ R i Min i (4) Max i Min i where R i is the real value applied to node i; N i the respective standardized value for the node; Max i and Min i are, respectively, the maximum and minimum of all values applied to the node. Finally, the standardized output values were reconverted to give the predicted values of sediment yield for comparison with the corresponding observed values Training the neural networks The training of ANN model is similar to the calibration of conceptual models. ANNs are trained with a set of known input and output data. The training process was repeated with different sets of shuffled data. The RMSE was noted for each analysis and cross validation was done to estimate the R 2 values. The learning process was terminated when an optimum prediction statistic was obtained in relation to epoch size and cross-validation results. Epoch is the number of training data sets presented to the learning cycles between weight updates and it should be less than the number of vectors of the input file. In the present study, the Normalized Cumulative Delta Rule (NCDR) was implemented with the sigmoid transfer function. This NCDR was independent of the epoch size due to its normalized function. To substantiate this concept, epochs ranging from 10 to 15 were considered.

9 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) Changes in epoch had no significant effect on ANN performance. Once the training process was satisfactorily completed, the network was saved, the test and validation data sets were recalled and the model-predicted values were compared with observed values of sediment yield. The validation was done using those data sets, which were not used in the model development. As the ANN is of empirical nature, once developed for a watershed, it cannot be applied to others. However, the steps and procedures used for ANN development can be replicated for different watersheds Model evaluation The model efficiency factor (E), coefficient of determination (R 2 ) and absolute average deviation (AAD) between the observed and the predicted values were estimated for different predictions on validation data sets. The best model was selected based on the highest R 2 and E values (James and Burgess, 1982) and AAD estimate approaching zero (Sarangi and Bhattacharya, 2000). The efficiency factor was estimated for all the 20 validation sets using the relation: P ni¼1 ðp E ¼ 1 i o i Þ 2 P ni¼1 ðo i ōþ 2 (5) where N = total number of observations; o i = ith observed value; ō = mean of observed values; p i = ith predicted value. 4. Results and discussions The developed models based on regression equation and neural network approaches were tested for predictability using the unseen validation data sets Regression models for sediment yield The best regression models developed by Sarangi and Bhattacharya, 2000 using the runoff rates (m 3 /s) and sediment concentrations in runoff water (g/l) for different rainfall events over the 4 years were re-validated using the data set. The validation statistics yielded a R 2 of 0.78, model efficiency E of 0.72 and average absolute deviation (AAD) of (Table 2). Ideally, the E and R 2 should be close to 1 and AAD should be close to 0 for reliable model prediction. Table 2 The validation statistics of different models for randomized data sets Models Maximum R 2 Minimum R 2 Maximum E Minimum E AAD GANN NGANN Regression model 0.78 NA * 0.72 NA * * Regression model validated for one data set.

10 204 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) Fig. 4. Observed and predicted sediment yield using regression model. In view of deviations from the desirable values, it was felt that there was a scope for improvement in the predictability as obtained using the above regression model. The observed and predicted values are shown in Fig. 4 depicting deviations from the line of best fit passing through the origin Neural network model for sediment yield The NGANN models developed without using the morphological parameters and with the sole output variable as the sediment yield were used in training with all the 20 datasets. The RMSE values varied from to For these RMSE values, the R 2 ranged from 0.87 to 0.94 and E ranged from 0.76 to The highest R 2 corresponded to the lowest RMSE, whereas the E was not the highest for the lowest RMSE. The observed and predicted values were in close proximity to the line of best fit (Fig. 5). In the GANN model, the three geomorphological parameters (viz. relative pffiffiffiffi relief, pffiffiffiffi R form factor and drainage factor) were associated with runoff rate values as R f F pffiffiffiffi, R f, D and R f, and three input node values were generated. The data for development of the model were standardized, randomized and split into training and testing data sets. The BP-ANN (Fig. 3) was tested on the 20 data sets. The resulting RMSEs ranged from to 0.076, R 2 valuesfrom0.91to0.98ande valuesfrom0.89to0.96. The highest R 2 of 0.98 occurred for the lowest RMSE (0.0564), while the highest E of 0.96 occurred for an RMSE of Finally, the ANN model with highest E value (0.96) was selected and the corresponding R 2 was estimated to be The observed and predicted values (Fig. 6) show a much closer cluster along the best-fit line.

11 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) Fig. 5. Observed and predicted sediment yield using NGANN model. The predicted values of the three models were plotted against the observed value of sediment loss corresponding to 40 selected validation data sets of runoff rate and sediment loss of the Banha watershed (Fig. 7). The GANN- and NGANN-based predicted values of sediment loss were in close proximity of the observed values, whereas the regression model predicted values indicated a poorer match with the observed values. Fig. 6. Observed and predicted sediment yield using GANN model.

12 206 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) Fig. 7. Observed and predicted sediment yield using all three models.

13 5. Conclusion A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) The field of neural networks has a history of some five decades but has found useful application only in the past 15 years, and the field is still developing rapidly. Thus, it is distinctly different from the fields of control systems or optimization where the terminology, basic mathematics, and design procedures have been firmly established and applied for many years. In the present study, association of watershed morphological parameters with the runoff rate measured at the watershed outlet and feeding to a BP- ANN with feed-forward learning approach resulted in a better prediction of sediment load when compared with the recorded data of the study watershed (Banha) and the results of an earlier regression approach for the same purpose. It is evident that the neural network and regression models developed for one watershed cannot be applied to watersheds at different location as such, and also the empirical association of geomorphological parameter with rainfall and runoff may differ from place to place. However, this study standardizes the ANN approaches, which can be applied to any watershed data for development of ANN models for subsequent prediction. The study results confirm that inclusion of morphological parameters in ANN models improves the model prediction. Acknowledgements The authors wish to acknowledge the support and technical guidance given by the Project Director and Principal Investigator of the in-house project of Water Technology Centre, IARI, New Delhi for undertaking this research. References ASCE, 2000a. Artificial neural networks in hydrology I: preliminary concepts. J. Hydrologic Eng., ASCE task committee on application of ANNS in hydrology. 5(2), ASCE, 2000b. Artificial neural networks in hydrology II: hydrologic applications. J. Hydrologic Eng., ASCE. 5(2), Cannon, A.J., Whitfield, P.H., Downscaling recent stream-flow conditions in British Columbia, Canada using ensemble neural networks. J. Hydrol. 259, Dawson, C.W., Wilby, R., An artificial neural network approach to rainfall-runoff modeling. Hydrol. Sci. J. 43 (1), Gautam, M.R., Watanabe, K., Saegusa, H., Runoff analysis in humid forest catchment with artificial neural network. J. Hydrol. 235, Govindaraju, R.S., Rao, A.R., Introduction. In: Govindraraju, R.S., Rao, A.R. (Eds.), Artificial Neural Networks in Hydrology. Kluwer, Dordrecht, Netherlands, pp Hsu, K.L., Gupta, H.V., Sorooshian, S., Artificial neural network modeling of the rainfall-runoff process. Water Resour. Res. 31, James, L.D., Burgess, S.J., Selection, calibration and testing of hydrologic models. In: Haan, C.T., Johnson, H.P., Brakensiek, D.L. (Eds.), Hydrological Modeling of Small Watersheds. American Society of Agricultural Engineers, St. Joseph, MI, pp Kaur, R., Srinivasan, R., Mishra, K., Dutta, D., Prasad, D., Bansal, G., Assessment of SWAT model for soil and water management in India. Land Use Water Resour. Res. 3, 1 7.

14 208 A. Sarangi, A.K. Bhattacharya / Agricultural Water Management 78 (2005) Maier, H., Dandy, G.C., Neural networks for the prediction and forecasting of water resources variables: a review of modeling issues and applications. Environ. Modeling Software 15, McCulloch, W.S., Pitts, W.H., A logical calculus of the ideas immanent in neural nets. Bull. Math. Biophys. 5, Nagy, H.M., Watanabe, K., Hirano, M., Prediction of sediment load concentration in rivers using Artificial Neural Network Model. J. Hydraulic Eng. (ASCE) 128 (6), Reddy, S.B Estimation of watershed runoff using artificial neural networks. Ph.D Thesis in Agric. Engg. (unpubl.). Post Graduate School, IARI, New Delhi. Ritter, D., Kochel, F.R.C., Miller, J.R., Process Geomorphology. McGraw Hill, Boston. Salas, J.D., Markus, M., Tokar, A.S., Streamflow forecasting based on Artificial Neural Networks. In: Govindaraju, R.S., Ramachandra Rao, A. (Eds.),Artificial Neural Networks in Hydrology. Kluwer Publishers, London, pp Sarangi, A., Bhattacharya, A.K., Use of geomorphological parameters for sediment yield prediction from watersheds. J. Soil Water Conserv. 44 (1 2), Sarangi, A., Madramootoo, C.A., Enright, P., Development of user interface in ArcGIS for estimation of watershed morphological parameters. Presented in CSAE Conference, 6th to 9th July, Montreal, Canada. (last accessed on 31st January 2005). Sharma, V., Negi, S.C., Rudra, R.P., Yang, S., Neural networks in predicting nitrate-nitrogen in drainage water. Agric. Water Manage. 63, Shukla, M.B., Kok, R., Prasher, S.O., Clark, G., Lacroix, R., Use of artificial neural networks in transient drainage design. Trans. ASAE 39, Sivakumar, B., Jayawardena, A.W., Fernando, T.M.K.G., River flow forecasting: use of phase-space reconstruction and artificial neural networks approaches. J. Hydrol. 265, Strahler, A.N., Quantitative analysis of watershed geomorphology. Trans. Am. Geophys. Union 38 (6), Sudheer, K.P., Gosain, A.K., Ramasastri, K.S., A data-driven algorithm for constructing artificial neural network rainfall-runoff models. Hydrol. Process. 16, Yang, C.C., Prasher, S.O., Lacroix, R., Applications of artificial neural networks to land drainage engineering. Trans. ASAE 39, Yitian, L., Gu, R.R., Modeling flow and sediment transport in a river system using an artificial neural network. Environ. Manage. 31 (1), Yu, C., Northcott, W.J., McIsaac, G.F., Development of an artificial neural network model for hydrologic and water quality modeling of agricultural watersheds. Trans. ASAE 47 (1), Zhang, B., Govindaraju, R., Geomorphology-based artificial neural networks (GANNs) for estimation of direct runoff over watersheds. J. Hydrol. 273,