Rainfall estimation based on artificial neural network (ANN) models for monsoon season

CONTENTS

1. INTRODUCTION

2. REVIEW OF LITERATURE
2.1 Artificial Neural Networks (ANNs)
2.2 Sensitivity Analysis

3. MATERIALS AND METHODS
3.1 Description of Study Area
3.1.1 Physiographic description
3.1.2 Soil characteristics
3.1.3 Cropping pattern
3.1.4 Climatology
3.2 Data Acquisition
3.2.1 Pre-analysis and formulation of input and output data
3.3 Development of Models
3.3.1 Artificial neural networks (ANNs)
3.3.1.1 General
3.3.1.2 Description and application of ANNs
3.3.1.3 The biological basis of ANNs
3.3.1.4 Basic concept of artificial neural network
3.3.1.5 Network architecture
3.3.1.6 Neurons and layers
3.3.1.7 Output of the nodes
3.3.1.8 Propagation law
3.3.1.9 The Back-propagation algorithm
3.3.1.10 Activation functions
3.3.1.11 Sigmoid axon function
3.3.1.12 Hyperbolic tangent axon function
3.3.2 Selection of network architecture
3.4 Development of ANN Models
3.4.1 Pattern I
3.4.2 Pattern II
3.4.3 Pattern III
3.4.4 Training and testing of ANN models
3.5 Sensitivity Analysis
3.6 Performance Evaluation Indicators
3.6.1 Statistical indices
3.6.1.1 Mean square error (MSE)
3.6.1.2 Correlation coefficient (CC)
3.6.1.3 Akaike’s information Criterion (AIC)
3.6.2 Hydrological indies
3.6.2.1 Coefficient of efficiency (CE)
3.6.2.2 Pooled average relative error (PARE)

4. RESULTS AND DISCUSSION
4.1 Development of Rainfall Prediction Models
4.1.1 Artificial neural network (ANN) models
4.1.1.1 ANN models with nine input parameters and one output parameter (Pattern I)
4.1.1.2 ANN models with six input parameters and one output parameter (Pattern II)
4.1.1.3 ANN models with three input parameters and one output parameter (Pattern III)
4.2 Performance Assessment of Developed Models
4.2.1 Qualitative evaluation
4.2.2 Quantitative evaluation
4.2.2.1 Statistical indices
4.2.2.2 Hydrological indices
4.3 Sensitivity Analysis
4.3.1 Sensitivity analysis of the artificial neural network (ANN) model

5. SUMMARY AND CONCLUSIONS

LITERATURE CITED

VITAE

ABSTRACT (English)

ABSTRACT (Hindi)

ACKNOWLEDGEMENT

“ I deals are like stars: you will not succeed in touching them by your hands, but like seafaring man on the ocean desert of waters, you choose them as your guides and following them, you reach your destiny.”

Carl Schurz (1829-1906)

It is my proud privilege to express my profound sense of gratitude and veneration to Dr. Pravendra Kumar, Associate Professor, Department of Soil and Water Conservation Engineering and chairman of my Advisory Committee for his sincere exhortation, constructive criticism, meticulous guidance, and affectionate interaction, immense patience, parental care and supporting attitude throughout the course of this study and preparation of the manuscript.

I express my deepest sense of reverence and indebtedness to the esteemed member of my Advisory Committee Dr. Devendra Kumar, Professor & Head, Dr. Anil Kumar, Professor, Department of Soil and Water Conservation Engineering, and Dr. Sanjay Kumar, Assistant Professor, Department of Mathematics, Statistics and Computer Science for giving their valuable suggestions and help at various stages of the research work.

With a deep sense of gratitude and immense pleasure, I also acknowledge the whole hearted cooperation extended by the teachers of the Department of Soil and Water Conservation Engineering.

The author expresses his gratefulness to Dr. N.S. Murthy, Dean, College of Post Graduate Studies and Dr. H.C. Sharma, Dean, College of Technology, G. B. Pant University of Agriculture and Technology, Pantnagar for providing necessary facilities for providing necessary facilities to carry out present study.

The author is highly thankful to Dr. Kanhaiya Singh, Senior Scientist, IARI, New Delhi and Dr. I. S. Solanki, Head, IARI research station, Pusa, Samastipur for their painstaking effort in providing daily Weather data.

The whole hearted thanks for the cooperation and stupendous contribution of Mr. P.C. Bhandari, typist and Mr. M.R. Yadav, lab technician, Department of Soil and Water Conservation Engineering throughout the period of this investigation.

With my heartfelt enthusiasm, I dedicate this study to my beloved grandmother Late Smt. Lalita Devi. I cannot ever pay for the inspiration and opportunity provided to work for the profession of Soil and Water Conservation Engineering.

I would like to avail this opportunity to express my heartiest sense of reverence and love to my parents, especially my mother Smt. Pramila Singh and father Dr. Ravi Prakash Singh for their endless love, trust and sacrifices for me. Lots of love and blessings from my grandfather Shree Shiv Pujan Singh, loving sister Pallavi Singh, and love affection from my younger brother Dinkar Pratap Singh are greatly appreciated and acknowledged, at every walk of life.

A special word of appreciation is due to my elder brother like senior, Rupesh Ranjan Yadav, sister Neha Kumari and special friends like Garima Yadav, Kumar Saurav, Ankit Tiwari, Ajit Kumar Patel for their encouragement and moral support during my study period.

I find myself lucky to have seniors like Ravish Chandra, Kyada Pradip M., Saurabh Singh, Ghanshyam Singh Yerubam, Ajit Singh, Raghu Nandan, Manish Kumar Mishra, Sachin Kumar, Ram Kumar, Shikha Anand and friends like Tripti Srivastava, Dharmendra Kumar, Anurag Malik, Ramesh Abhishek, Manish Bhendura, Kamal Singh Rawat, Navin Kumar Navnit, Shiv Shankar Verma, Rahul Singh, Himanshu Khulve, Lalit Ranakoti, Omprakash Kumar, Ankit Singhal, Govind Singh Bhandari, Mukesh Rana, Umesh Yadav, Subhashis Nandi and loveable juniors like Prateek Singh, Vijay Kumar Singh, Bhaghwat Saran and Satrughan Jaiswal for their constant encouragement and time to time help during my research work.

The author is also highly thankful to the Technical Education Quality Improvement Programme- II (TEQUIP- II) for providing me the assistantship for pursuing the M. Tech. Degree Programme.

Last but not the least; I express my thanks to Almighty for giving me courage and company of so many wonderful persons without whom I could not have succeeded in my pursuit.

Pantnagar

July, 2014

Bhaskar Pratap Singh

Author

LIST OF TABLES

3.1 Details of various types of activation functions

3.2 Year wise daily meteorological data (i.e. mean temperature, relative humidity, vapour pressure and rainfall) of Pusa, Samastipur

3.3 Input-output pairs in training and testing data (Pattern I) for ANN models of both activation functions

3.4 Input-output pairs in training and testing data (Pattern II) for ANN models of both activation functions

3.5 Input-output pairs in training data and testing (Pattern III) for ANN models of both activation functions

4.1 Comparison of different sigmoid axon function based ANN models to choose the best model for Pattern I

4.2 Comparison of different hyperbolic tangent axon function based ANN models to choose the best model for Pattern I

4.3 Comparison of different sigmoid axon function based ANN models to choose the best model for Pattern II

4.4 Comparison of different hyperbolic tangent axon function based ANN models to choose the best model for Pattern II

4.5 Comparison of different sigmoid axon function based ANN models to choose the best model for Pattern III

4.6 Comparison of different hyperbolic tangent axon function based ANN models to choose the best model for Pattern III

4.7 Performance evaluation of developed ANN models during training period for the best selected networks

4.8 Performance evaluation of developed ANN models during training period for the best selected networks

4.9 Performance indices of ANN model (3-23-1) for sensitivity analysis during testing period

LIST OF FIGURES

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LIST OF ABBREVIATIONS

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Introduction

1. INTRODUCTION

All aspects of human life are, affected by climatic processes. This effect is especially noticeable in such fields as agriculture, irrigation, economy, telecommunications, transportation, traffic, air pollution and military industries (Haltiner and Williams, 1980).

Water is the most essential and precious gift provided by the almighty to the human beings in the form of rain, river, sea etc. One cannot imagine the life without water. Rainwater is major sources which live up to a number of significant functions. Distinct, from the most other natural resources, rainwater do not has a substitute in its main usages. Some of the most vital concerns of comprehensive climatic erraticism are its consequence on water wealth. Practically no activity in culture or process in the land-living or in the atmosphere would be possible in the absence of water. It is one of the key constituents of our everyday requirement whose dearth can harshly constrain our economic progression. In emerging countries like India, covering about two-third of the world’s population, the industrialized and unindustrialized growth, which is profoundly dependent upon water demand, is possible to be in a fragile position with the non-availability of water. All the other spreading out activities in some or the last way seems to show a bent to centre on the main water resources system. Raindrops are one of the most complex and difficult elements of the hydrological cycle to know and to model due to the complication of the atmospheric processes. Moreover precipitation is the outcome of complicated physical processes taking place in nature.

The precipitation as a weather parameter stands multi-layered nonlinear occurrences and varies along with time and space. Typical extent of rain is not easily known until it takes place. The continuous fluctuations in overall climate and the irregular spatial and temporal distribution of rainfall are causes for severe problems like floods and droughts. In 2002, significant drop in the monsoon rains during July, results in a seasonal rainfall deficit of 19% and causes profound loss of agricultural production with a drop of over 3% in India’s GDP. Hence, the prediction of the rainfall in Indian monsoon season remains an important concern (Parthasarathy et al., 1995). Taking example of the study area for this research, in 2004 the heavy rain results in a flood prone area almost everywhere in Bihar state. Pusa is the most affected area by this flood in Bihar. Thus it is very much necessary to know the nature of rain prior it happens and results in a disaster.

Groundwater and shallow water are the two different fonts from which water is utilized for irrigation purposes. These two sources are mainly replenished by rainfall and stream flow. Since, Rajendra Agricultural University is also located, so, it is necessary to know the real timed occurrence of rainfall for the area, as the productivity and development of agriculture in the area is mostly dependent on the precipitation. The above facts lead to conclusion that rainfall forecasting is very essential for planning and management of water resources. In the urban areas, rainfall has a strong influence on traffic, sewer system, water logging and other human activity.

During June and September, south-west monsoon contributes more than 75% of the annual rainfall of India (Singh, 2006). The angle of Indian agriculture is very much hooked on onset/withdrawal of monsoon and depth of rainfall during rainy season. Average area under rain fed crops in India is about 75% of the total cultivable land (Roy et al., 2009). Therefore, it is vital to forecast the monsoon rainfall, which administers the major crop production/productivity of Indian agriculture.

Forecast of any natural and usual event call for information regarding its phase of occurrence as well as nature, based on sound and analytical study. It may be more or less impossible, unmanageable and unbearable to carry out manual assimilation of such a massive amount of data being continuously acquired by the automatic or mindless measuring device. Physical analysis may also generate further inconsistencies due to issues, such as fatigue, contradiction of personal sensitivities, etc. At the same stage, prediction of a natural happening would be most effective, operative and accurate only if it is timely done and based on the complete information available for analysis or study at any point of time. Soft Computing is an emerging field and its main ingredients are fuzzy logic, neural computing, evolutionary computation, machine learning and probabilistic reasoning. Strong learning, cognitive ability and good tolerance of uncertainty and imprecision of these constituents make them the best suited for wide applications. Resemblance to human intellectual is the striking property of soft computing techniques than outmoded techniques which were largely based on conventional analytical systems, such as sentential logic and predicate logic, or rely heavily on the mathematical capabilities of a computer.

In observance of the above circumstances, the artificial neural network is the most proficient rainfall forecasting methods for bringing the more agricultural productions from the inadequate land and water resources. Artificial Neural Networks (ANNs) are non-linear mapping structures based on the functions of human brain. ANNs imitate the learning process of the human brain and can process problems involving non-linear and complex data even if the data are imprecise and noisy. Thus, the accurate rainfall prediction is one of the greatest challenges in hydrology. Although, many mathematical models have been developed by researchers, the popular models of recent times are based on artificial neural networks. Over the last decade or more, neural networks have become a very popular mathematical modelling tool in hydrology and water resources. They are generally employed as alternatives to the traditional models (e.g. Karunanithi et al., 1994; Hsu et al., 1995; Hu et al., 2005 and Keskin et al., 2006). However, despite justifiable claims that the neural network models are very flexible and versatile, it has not been convincingly demonstrated that they are universally superior to the traditional models. Moreover, there is no denying the fact that the “black-box” NNMs are generally non-parsimonious and hence prone to “over-fitting” and the phenomenon of “equifinality” (Beven and Binley, 1992).

An ANN is a flexible scientific structure having an inter-connected muster of simple processing elements or nodes, which follows the functioning of neurons in the human brain. It has many individual advantages and enjoys the capability of representing the arbitrary complex non-linear relationship between the input and the output of any system. ANN models have been extensively used by hydrologists mostly in modelling of the rainfall-runoff process (e.g Lorrai and Sechi, 1995; Minns and Hall, 1996; Tokar and Johnson, 1999; Rajurkar et al., 2002; Wilby et al., 2003; Giustolisi and Laucelli, 2005 and Jain and Srinivasulu, 2006). ANN is also a powerful tool in solving complex nonlinear river flow forecasting problems (Thirumalaiah and Deo, 1998a , b; Atiya et al., 1999; Hsu et al., 2002; Toth, 2009; Birikundavyi et al., 2002 and Kar et al., 2010) and in particular when the time required generating a forecast is very short. Mathematically, an ANN can be treated as a universal approximation technique having an ability to learn from examples without the need of explicit physics (ASCE, 2000a, b). Previous research by (Karunanithi et al., 1994; Dawson and Wilby, 1998; Campolo et al., 1999; Zealand et al., 1999 and Imrie et al., 2000), have demonstrated the capability of ANNs in stream flow forecasting.

Timely rainfall forecasting is used to deliver judicious warning to people residing in rain affected area and flood prone plains and can lighten a lot of distress and flood damage. Rainfall forecasting correspondingly provide useful information to water management personnel for making prime decisions related to flood control structures, drought management and reservoirs operation. Rains are natural phenomena and are inherently complex to model. Conventional methods of flood forecasting are based on either simple empirical black box which do not try to mimic the physical processes involved or use complex models which aim to recreate the physical processes and the concept about the behaviour of a basin in complex mathematical expressions (Lohani et al., 2005a). Keeping in view the above facts, an attempt has been made to estimate daily monsoon rainfall at Pusa, which is located in district Samastipur of Bihar state, India. The generalized feed forward back propagation ANN algorithm with two different activation functions, namely sigmoid axon and hyperbolic tangent axon have been employed in this study. The comprehensive explanation of feed forward neural network (FFNN) with error- back propagation (EBP) is well organised in the literature (Herz et al., 1991; Muller and Reinhardt, 1991; Bishop, 1994 and Haykin, 1994). The main purpose of the study is to analyse the performance of mentioned activation functions for daily monsoon rainfall using the current day rainfall data as output variable and one, two and three lag days rainfall; one, two lag days and current day mean temperature, relative humidity and vapour pressure data as input variables. Sensitivity analysis is also carried out in this study to show the effect of most sensitive input variable on daily monsoon rainfall at Pusa.

The present study has been under taken with the following specific objectives:

1. To develop Artificial Neural Networks (ANNs) models with different activation functions to predict daily rainfall for monsoon season.
2. To verify developed models for the study area.
3. To compare the performance of developed models for the study area through qualitative and quantitative comparisons to identify the best suited model.
4. To observe the effect of the most and the least important factors responsible for rainfall based on sensitivity analysis.

Review Of Literature

2. REVIEW OF LITERATURE

Modelling in the field of hydrology is a significant expanse. Rainfall is reflected as one of the chief component of the hydrological development. The consideration of prior work is important to keep informed our acquaintance and analyse the systems applied in corresponding field. Hence, a review of relevant research works associated with rainfall forecasting, analysis and applications of artificial neural networks, and sensitivity analysis is presented in this chapter.

2.1 Artificial Neural Networks (ANNs)

Artificial neural networks are computational model enthused by the basic design of the human mind that mug up to perform tasks rather than having tasks encoded into it. The use of ANN has especially increased for climatic expectations in the last few years owing to the following reasons; firstly, advancements in computer technology and also, it can handle unstructured and noisy records/data. Moreover, ANNs have need of minor or no prior statistics and again, the ability to solve complex and nonlinear problems such as modelling of rainfall and other hydrological processes leads to the use of ANNs in hydrological modelling.

The obtainable works related to the use of artificial neural networks (ANNs) in the field of hydrology is reported in this section.

French et al. (1992) developed an ANN to forecast rainfall intensity field in space and time. Three layers ANN model with back propagation was used to model rainfall fields as the input and the output data. A trained network was used to forecast rainfall intensity with a lead time of one hour, using only the current field as the output. The rainfall intensity fields were generated using a mathematical rainfall simulation model, and the data was used for training and evaluating. The performance of the neural network was compared with the other two methods; persistence and forecasting of short term prediction. Persistence was applied by using the current time intensity field. The forecasting technique utilized the two latest fields, to determine the velocity of the events.

Buch et al. (1993) suggested that the neural network performance is superior as compared to the energy balance and multiple regression models. In addition, it was observed that neural network was faster in learning and exhibited excellent system generalization characteristics.

Kang et al. (1993) utilized three layered ANN model in predicting daily and hourly stream flow for Pyung Chang river basin in Korea. ANNs were found as useful tools for forecasting stream flow as compared to autoregressive moving average model.

Navone and Ceccatto (1994) linked output of two individual networks to a hybrid network to predict the summer monsoon rainfall over India.

Lorrai and Sechi (1995) developed and applied neural network to rainfall runoff transformation. A two hidden layer neural network with sigmoid response function and using back-propagation learning rule was developed. Monthly rainfall, runoff and temperature were used to develop the model by dividing the data into three ten year’s period and verified in rest ten year’s block. They found that artificial neural networks provide higher efficiency during model development and were superior to multivariate autoregressive model.

Carrierie et al. (1996) developed a virtual runoff hydrograph system that employed a recurrent back- propagation artificial neural network to generate runoff hydrograph. The author concluded that the neural network could predict runoff hydrograph accurately with good agreement of the observed and predicted values.

Shamseldin et al. (1997) suggested a method for combining the estimated output of different rainfall-runoff models to produce an overall combined estimated output to be used as an alternative to that obtained from a single individual rainfall-runoff model. Three methods of combining model outputs were considered as the simple average method (SAM), the weighted average method (WAM), and the neural network method (NNM). The results confirm that better discharge estimates can be obtained by combining the model output of different models.

Chen (1998) presented systematic derivations of setting up a nonlinear model predictive control based on the artificial neural network. The control law is mathematically developed in detail so that the performance of the ANN-based controller can be improved. A three-layer feed forward neural network with hyperbolic tangent functions in the hidden layer and with a linear function in the output layer is used. The two stage scheme including pseudo Gauss-Newton and least squares is proposed for training ANN. This training method is better than the traditional algorithm in terms of training speed. The Levenberg-Marquardt approximation is also utilized for the minimum of the predictive control criterion. Two typical chemical processes are simulated and the ANN model predictive control applications reached to fairly good results.

Dawson and Wilby (1998) discussed the development and application of Artificial Neural Networks (ANNs) to flow forecasting in two flood-prone UK catchments using real hydrometric data. Comparisons were made between the performance of the ANN and those of conventional flood forecasting systems. The results obtained for validation forecasts were of comparable quality to those obtained from operational systems for the River Amber. The ability of the ANN to cope with missing data and to learn from the event currently being forecast in real time makes it an appealing alternative to conventional lumped or semi-distributed flood forecasting models.

Thirumalaiah and Deo (1998) highlighted the use of artificial neural network in real time forecasting with a lead time 1 and 2 days of water levels at a given site continuously throughout the year based on the same levels at some upstream gauging station or using the stage time history recorded at the same site. The network was trained by using three algorithms, namely, error back-propagation, cascade correlation and conjugate gradient. The training results were compared with each other and found that error back-propagation gave better results than others.

Jain and Srivastava (1999) studied the application of ANNs for reservoir inflow forecasting and further development of reservoir operation policy. An auto-regressive integrated moving average time series model and an ANN based model were fitted to the monthly inflow data series and their performances were compared. The ANN was found to model the high flow better, whereas, the low flows were better predicted through the auto - regressive integrated moving average model. Reservoir operation policies were formulated through dynamic programming.

Zealand et al. (1999) investigated the utility of Artificial Neural Networks (ANNs) for short term forecasting of stream flow, explored the capabilities of ANNs and compared the performance of ANN tool to conventional approaches used to forecast stream flow. Perceived strengths of ANNs are the capability for representing complex, non-linear relationships as well as being able to model interaction effects. A very close fit was obtained during the calibration (training) phase and the ANNs developed consistently outperformed a conventional model during the verification (testing) phase for all of the four forecast lead-times. The average improvement in the root mean squared error (RMSE) for the 8 years of test data varied from 5 cms in the four time step ahead forecasts to 12.1 cms in the two time step ahead forecasts.

ASCE (2000a) described an introduction of ANNs and the role of ANNs in hydrology. Apart from description of various aspect of ANN, some guidelines on their uses were presented in the paper offered brief comparison of ANNs and other modelling philosophies in hydrology. A discussion on the strengths and the limitations of ANN brought out the similarities they have with other modelling approaches.

ASCE (2000b) examined the role of ANN in various branches of hydrology and found that ANNs are robust tool for modelling many of nonlinear hydrologic processes such as rainfall-runoff, stream flow, ground water management, water quality simulation and precipitation. There are still some questions about the application of this emerging technique in engineering, which needs further study on some important aspects such as physical interpretation of ANN architecture, optimal training data set, adaptive learning, and extrapolation. The merits and limitations of ANN applications have been discussed, and potential research avenues have been explored briefly.

Coulibaly et al. (2000) introduced an early stopped training approach (STA) to train multi-layer feed-forward neural networks (FNN) for real-time reservoir inflow forecasting. The proposed method takes advantage of both Levenberg–Marquardt Back- propagation (LMBP) and cross-validation technique to avoid under fitting or over fitting on FNN training and enhances generalization performance. The results show that the proposed method is effective for improving prediction accuracy.

Imrie et al. (2000) presented a method for improved generalisation during training by adding a guidance system to the cascade- correlation learning architecture. Two case studies from catchments in the UK are prepared so that the validation data contains values that are greater or less than any included in the calibration data. The ability of the developed algorithm to generalise on new data is compared with that of the standard error back propagation algorithm. The ability of ANNs trained with different output activation functions to extrapolate beyond the calibration data is assessed.

Ren et al. (2000) demonstrated the usefulness of near-infrared (NIR) spectra and artificial neural network (ANN) in non-destructive quantitative analysis of Pharmaceuticals. Real data sets from near-infrared reflectance spectra of analgini powder pharmaceutical were used to build up an artificial neural network to predict unknown samples. A new network evaluation criterion, the degree of approximation, was employed. Owing to the good nonlinear multivariate calibration nature of ANN, the predicted result was reliable and precise. The relative error of unknown samples was less than 2.5 %.

Sahai et al. (2000) described the artificial neural network (ANN) technique with error-back propagation algorithm to provide prediction of Indian Summer Monsoon Rainfall on monthly and seasonal time scales. The ANN technique was applied to the five time series of June, July, August, September monthly means and seasonal mean (June + July + August + September) rainfall from 1871 to 1994 based on Parthasarathy dataset. The previous five years values from all the five time-series were used to train the ANN to predict for the next year. Various statistics were calculated to examine the performance of the model and it was found that the model could be used as a forecasting tool on seasonal and monthly time scales. It is observed by various researchers that with the passage of time the relationships between various predictors and Indian monsoon were changing, leading to changes in monsoon predictability. This issue is discussed and it was found that the monsoon system inherently has a decadal scale variation in predictability.

Toth et al. (2000) studied and compared the accuracy of the short-term rainfall forecasts obtained with time-series analysis techniques, using past rainfall depths as the only input information. The techniques proposed were linear stochastic auto-regressive moving average (ARMA) models, artificial neural networks (ANN) and the non- parametric nearest-neighbours method. The rainfall forecasts obtained using the considered methods were then routed through a lumped, conceptual rainfall–runoff model, thus implementing a coupled rainfall–runoff forecasting procedure for a case study on the Apennines Mountains, Italy. The study analysed and compared the relative advantages and limitations of each time-series analysis technique, used for issuing rainfall forecasts for lead-times varying from 1 to 6 h. The results also indicated how the considered time-series analysis techniques, and especially those based on the use of ANN, provide a significant improvement in the flood forecasting accuracy in comparison to the use of simple rainfall prediction approaches of heuristic type, which are often applied in hydrological practice.

Luk et al. (2001) presented the results of a study investigating the application of ANNs to forecast the spatial distribution of rainfall for an urban catchment. Three alternative types of ANNs, namely multi-layer feed-forward neural networks, partial recurrent neural networks and time delay neural networks, were identified, developed and found to provide reasonable predictions of the rainfall depth one time-step in advance.

Kumar et al. (2002) investigated the utility of ANNs for estimation of daily grass reference crop evapotranspiration. ANN was applied using standard back propagation with learning rates of 0.2 and 0.8 and back propagation momentum with learning rate of 0.2 and momentum term as 0.95. The results of ANN were compared with the results of the conventional method (Penman-Monteith). The results exhibited that ANN could predict ET0 better than conventional Penman-Monteith method for the data of Davis CIMIS (California Irrigation Management Information System).

Lee and Jeng (2002) presented an artificial neural network (ANN) model for forecasting the tidal-level using the short term measuring data. The ANN model can easily decide the unknown parameters by learning the input–output interrelation of the short term tidal records. Three field data with three types of tides will be used to test the performance of the proposed ANN model. The numerical results indicate that the hourly tidal levels over a long duration can be predicted using a short-term hourly tidal record.

Lonhde et al. (2004) outlined the basic principles of modelling, common network architectures and training algorithms in view of the application of ANN in rainfall-runoff modelling. They suggested that the future research might focus towards the development of ANN models, the assessment of the models for exciting the knowledge that is contained in the connection weights of trained ANNs.

Kumar and Vishwanath (2004) used ANN for rainfall- runoff modelling of Osman Sager catchments, Hyderabad. They applied SCS method for the estimation of the runoff. Special emphasis was given on the use of recurrent networks (Elman Network) for the modelling. The study revealed that runoff estimated by Elman networks had good correlation with the rainfall.

Kisi (2004) demonstrated the application of artificial neural networks (ANNs) in predicting mean monthly stream flow. This study is based on the monthly flow data obtained from the Turkey State of Water works. ANNs have been used to predict river flow. Autoregressive (AR) models have also been applied to the same data. The performance of neural network is compared with that of the Statistical methods.

Olsson et al. (2004) used neural networks for rainfall forecasting by atmospheric down scaling. Attempts were made to improve the performance of ANN by using two approaches: (1) two ANNs were coupled in series, the first to determine the rainfall occurrence, and the second to determine rainfall intensity during rainy periods, and (2) rainfall was categorized on the basis of intensity. The neural network was trained to reproduce categorized intensities rather than the actual intensities. The two ANNs in series greatly improved the performance while categorization was useful for probabilities.

Riad et al. (2004) developed and used an ANN to model the rainfall-runoff relationship, in a catchment located in a semiarid climate in Morocco. The multilayer perceptron (MLP) neural network was chosen for the study. The results and comparative study indicate that the artificial neural network method is more suitable to predict river runoff than classical regression model.

Tsanis et al. (2005) examined the performance of different neural networks in a groundwater level forecasting in order to identify an optimal ANN architecture that can simulate the decreasing trend of the groundwater level and provide acceptable predictions up to 18 months ahead. Messara Valley in Crete (Greece) was chosen as the study area as its groundwater resources have being overexploited during the last fifteen years and the groundwater level has been decreasing steadily. Seven different types of network architectures and training algorithms are investigated and compared in terms of model prediction efficiency and accuracy. The different experimented results show that accurate predictions can be achieved with a standard feed forward neural network trained with the Levenberg Marquardt algorithm providing the best results for up to 18 months forecasts.

Guo et al. (2007) developed a nonlinear perturbation model (NLPM) based on artificial neural network (ANN), defined as NLPM-ANN, for the purpose of improving the rainfall–runoff forecasting efficiency and accuracy. The NLPM-ANN model structure is similar to that of the linear perturbation model (LPM). The deference is that ANN, instead of the linear response function, was used to simulate the unknown relationship between the input perturbations and the output perturbations. The proposed model was also compared with the LPM, a nonlinear perturbation model considering catchment wetness (NLPM-API), and two different ANN models. It showed that the model efficiency of NLPM-ANN model is significantly higher than that of the LPM. The results demonstrated that the relationship between the perturbations is highly nonlinear though subtracting the seasonal means and ANN is capable to simulate this relationship. Comparing with the NLPM-API, the NLPM-ANN also showed advantages in simulating the nonlinear relationship between the rainfall and runoff. The results also indicated that consideration of the seasonal information can improve the model efficiency of not only the linear models but also the ANN models. Subtracting the seasonal means, which is adopted in the LPM, is also a feasible way to reduce the system complexity and improve the model efficiency of ANN models.

Kumar et al. (2007) presented an Artificial Intelligence approach for regional rainfall forecasting for Orissa state, India on monthly and seasonal time scales. The possible relation between regional rainfall over Orissa and the large scale climate indices like El-Niño Southern Oscillation (ENSO), EQ Uitorial Indian Ocean Oscillation (EQUINOO) and a local climate index of Ocean-Land Temperature Contrast (OLTC) are studied first and then used to forecast monsoon rainfall. They employed Artificial Neural Networks (ANNs) methodology to handle the highly non-linear and complex behaviour of the climatic variables for forecasting the rainfall,. To optimize the ANN architecture, Genetic Optimizer (GO) was used. After identifying the lagged relation between climate indices and monthly rainfall, the rainfall values were forecast for the summer monsoon months of June, July, August, and September (JJAS) individually, as well as for total monsoon rainfall. The models were trained individually for monthly and for seasonal rainfall forecasting. Then the trained models were tested to evaluate the performance of the model. The results show reasonably good accuracy for monthly and seasonal rainfall forecasting. The study emphasized the value of using large-scale climate teleconnections for regional rainfall forecasting and the significance of Artificial Intelligence approaches like GO and ANNs in predicting the uncertain rainfall.

Sh amseldin et al. (2007) compared the performances of three artificial neural network (NN) methods for combining simulated river flows, based on three different neural network structures. These network structures are: the simple neural network (SNN), the radial basis function neural network (RBFNN) and the multi- layer perceptron neural network (MLPNN). The results showed that the performances of all three combination methods are, on average, better than that of the best individual rainfall– runoff model utilized in the combination, i.e. that the combination concept works. In terms of the Nash- Sutcliffe model efficiency index, the MLPNN combination method generally performs better than the other two combination methods tested. For most of the catchments, the differences in the efficiency index values of the SNN and the RBFNN combination methods are not significant but, on average, the SNN form performs marginally better than the more complex RBFNN alternative. Based on the results obtained for the three NN combination methods, the use of the multi-layer perceptron neural network (MLPNN) is recommended as the appropriate NN form for use in the context of combining simulated river flows.

Chokmani et al. (2008) tested and compared artificial neural network (ANN) and regression models for estimating river stream flow affected by ice conditions. Three regression models are investigated including: multiple regression, stepwise regression and ridge regression. A case study conducted on the Fraser River in British Columbia (Canada) is presented in which various combinations of hydrological and meteorological explanatory variables were used. Discharge estimates obtained by statistical modelling were also compared to the official estimates made by Water Survey of Canada (WSC) hydrometric technologists. The case study shows that ANN models are relatively more successful than regression models for winter stream flow estimation purposes. However, due to data scarcity, it was difficult to make a definitive assessment. Stepwise regression was found to be the most effective of the three regressive approaches investigated. Statistical modelling is a viable approach for winter stream flow data estimation, but data completeness and reliability is a major limitation.

Elshorbagy and Parasuraman (2008) investigated the utility of the widely adopted data-driven model, namely artificial neural networks (ANNs), for modelling the complex soil moisture dynamics. Datasets from three experimental soil covers (D1, D2, and D3), with thickness of 0.50 m, 0.35 m, and 1.0 m, comprising a thin layer of peat mineral mix over varying thickness of till, are considered . Volumetric soil moisture contents at both the peat and the till layers were modelled as a function of precipitation, air temperature, net radiation, and ground temperature at different layers. Initial simulations illustrated that, in the absence of time-lagged meteorological variables, the ground temperature is the most influential state variable for characterizing the soil moisture, highlighting the strong link between the soil thermal properties and the corresponding moisture status. With the objective of extracting the maximum information from the most influential state variables (ground temperature), a higher-order neural networks (HONNs) model was developed to characterize the soil moisture dynamics. The HONNs resulted in relatively higher correlation coefficient, than traditional ANNs, for some of the soil moisture simulations. Time-lagged inputs were used to improve the model performance and obtain optimum results. The ANN models performed better than a previously developed conceptual model for estimating the depth averaged soil moisture content. Results indicated that modelling of soil moisture using ANNs is challenging but achievable, and its performance is largely influenced by the structure and formation of the soil covers, which in turn governed the dynamics of soil moisture variability.

Kalteh (2008) developed a rainfall-runoff model using an ANN approach, and described different approaches including Neural Interpretation Diagram, Garson’s algorithm, and randomization approach to understand the relationship learned by the ANN model. The results indicated that ANNs are promising tools not only in accurate modelling of complex processes but also in providing insight from the learned relationship, which would assist the modeller in understanding of the process under investigation as well as in evaluation of the model.

Lekkas (2008) developed and compared four artificial neural network (ANN) models in order to forecast river flow in the River Trent, UK. The first two are feed- forward networks and were trained with back-propagation and cascade- correlation algorithms; the third is an adaptive linear neuron network; and the fourth is an Elman network. Using observations of river flow for 1996–1998, the ANN models were satisfactorily trained and verified. A method that allows the explicit description of the variations in the lag of the system was also used and, when applied together with a real- time updating method, resulted in improved model performance. The research showed that using a parallel data-driven error prediction model to complement the ANNs produces much better flow predictions in comparison to using the ANNs alone.

Mar and Naing (2008) used neural network model as a forecasting tool. The major aim was to evaluate a suitable neural network model for monthly precipitation mapping of Myanmar. Using 3-layerd neural network models, 100 cases were tested by changing the number of input and hidden nodes from 1 to 10 nodes, respectively, and only one output node used. The optimum model with the suitable number of nodes was selected in accordance with the minimum forecast error. In measuring network performance using Root Mean Square Error (RMSE), experimental results significantly show that 3 inputs-10 hiddens-1 output architecture model gives the best prediction result for monthly precipitation in Myanmar.

Nasseri et al. (2008) developed feed-forward type networks to simulate the rainfall field and so called back propagation (BP) algorithm coupled with genetic algorithm (GA) used to train and optimize the networks. The technique was implemented to forecast rainfall for a number of times using rainfall hyetograph of recording rain gauges in the Upper Parramatta catchment in the western suburbs of Sydney, Australia. Results of the study showed the structuring of ANN network with the input parameter selection, when coupled with GA, performed better compared to similar work of using ANN alone.

Yadav et al. (2008) investigated the applicability of ANN for inflow forecasting of a salty lake known as Flat bay, situated on the northern side of port Blair in Andaman and Nicobar Islands, India. Two types of ANN architectures (1-5-1 and 2-5-1) were formulated and applied to surrounding catchments. A three layer feed forward ANN model trained by back propagation algorithm with log sigmoidal activation function was used. It was found that the formulated ANN architecture provided an efficient tool for inflow forecasting and proper lake management.

Hung et al. (2009) presented a new approach using an Artificial Neural Network technique to improve rainfall forecast performance. A real world case study was set up in Bangkok; 4 years of hourly data from 75 rain gauge stations in the area were used to develop the ANN model. The developed ANN model was being applied for real time rainfall forecasting and flood management in Bangkok, Thailand. Aimed at providing forecasts in a near real time schedule, different network types were tested with different kinds of input information. Preliminary tests showed that a generalized feed-forward ANN model using hyperbolic tangent transfer function achieved the best generalization of rainfall. Especially, the use of a combination of meteorological parameters (relative humidity, air pressure, wet bulb temperature and cloudiness), the rainfall at the point of forecasting and rainfall at the surrounding stations, as an input data, advanced ANN model to apply with continuous data containing rainy and non-rainy period, allowed model to issue forecast at any moment. Additionally, forecasts by ANN model were compared to the convenient approach namely simple persistent method. Results show that ANN forecasts have superiority over the ones obtained by the persistent model. Rainfall forecast s for Bangkok from 1 to 3 h ahead was highly satisfactory. Sensitivity analysis indicated that the most important input parameter besides rainfall itself is the wet bulb temperature in forecasting rainfall.

Kentel (2009) estimated future monthly river flows for Guvenc River, Ankara using various artificial neural network models. Success of artificial neural net - work models relies on the availability of adequate data sets. A direct mapping from inputs to outputs without consideration of the complex relationships among the dependent and independent variables of the hydrological process is identified. In this study, past precipitation, river flow data, and the associated month are used to predict future river flows for Guvenc River. Impacts of various input patterns, number of training cycles, and initial values assigned to the weights of the connections are investigated. One of the major weaknesses of artificial neural networks is that they may fail to generate good estimates for extreme events, i.e. events that do not occur at all or often enough in the training data set. It is very important to be able to identify such unlikely events. A fuzzy c-means algorithm is used in this study to cluster the training and validation input vectors into regular and extreme events so that the user will have an idea about the risk of the artificial neural network model to generate unreliable results.

Banerjee et al. (2011) evaluated the prospect of artificial neural network (ANN) simulation over mathematical modelling in estimating safe pumping rate to maintain groundwater salinity in island aquifers. Feed-forward ANN model with quick propagation (QP) as training algorithm has been used to forecast the salinity under varied pumping rates. The proposed ANN model has surfaced as a simpler and more accurate alternative to the numerical method techniques. The ANN methodology using minimal lag and number of hidden nodes, along with the optimal number of spatial and temporal variables consistently produced the best performing network based simulation models.

El - Shafie et al. (2011a) developed two rainfall prediction models and implemented in Alexandria, Egypt. These models are Artificial Neural Network (ANN) model and Multi Regression ( MLR) model. A Feed Forward Neural Network ( FFNN) model was developed and implemented to predict the rainfall on yearly and monthly basis. In order to evaluate the incomes of both models, statistical parameters were used to make the comparison between the two models. The data set that has been used in this study includes daily measurements for the rainfall and temperature. The FFNN model has shown better performance than the MLR model. The MLR model revealed a humble prediction performance. The linear nature of MLR model estimators makes it inadequate to provide good prognostics for a variable characterized by a highly nonlinear physics. On the other hand the ANN model was a nonlinear mapping tool which potentially was more suitable for rain (nonlinear physics) forecasts.

El-Shafie et al. (2011b) focused on investigating the potential of introducing a neural network that could address the temporal relationships of the rainfall series. Two different static neural networks and one dynamic neural network namely; Multi-Layer perceptron Neural network (MLP-NN), Radial Basis Function Neural Network (RBFNN) and Input Delay Neural Network (IDNN), respectively, have been examined. Those models had been developed for two time horizon in monthly and weekly rainfall basis forecasting at Klang River, Malaysia. Comprehensive comparison analyses were carried out to evaluate the performance of the proposed static and dynamic neural network. Results showed that MLP-NN neural network model able to follow the similar trend of the actual rainfall, yet it still relatively poor. RBFNN model achieved better accuracy over the MLP-NN model. Moreover, the forecasting accuracy of the IDNN model outperformed during training and testing stage which prove a consistent level of accuracy with seen and unseen data. Furthermore, the IDNN significantly enhance the forecasting accuracy if compared with the other static neural network model as they could memorize the sequential or time varying patterns.

Furman et al. (2011) examined the use of three different classes of artificial neural networks for modelling water flow in wet table and water repellent soils, using both synthetic numerical data and experimentally measured data. The 1D self-organizing maps (SOM) successfully rendered the moisture contour in the transition zone of the wetting plumes for all soil types at different flow rates. Due to SOMs inability to generate external output data, multilayer perceptron (MLP) and modular neural networks (MNNs), respectively, were combined with SOM to predict the moisture contour for both wet table and water- repellent soils. Due to dimensionality reduction, the 1D SOM failed to capture high moisture content classes of water-repellent soils with anomalous wetting patterns, whereas spatial moment analysis succeeded in providing an accurate, albeit indirect, description. Hence, the MLP and MNN networks were applied to predict the spatial moments. The comparison between the predicted and the experimental measures demonstrated the capability of the MLP and SOM to predict the spatial moments. Comparison of the two different artificial neural networks indicated no significant difference between their results.

Lee et al. (2011) developed two nonlinear time-series models for predicting groundwater level (GWL) fluctuations using artificial neural networks (ANNs) and support vector machines (SVMs). The models were applied to GWL prediction of two wells at a coastal aquifer in Korea. Among the possible variables (past GWL, precipitation, and tide level) for an input structure, the past GWL was the most effective input variable for this study site. Tide level was more frequently selected as an input variable than precipitation. The results of the model performance show that root mean squared error (RMSE) values of ANN models are lower than those of SVM in model training and testing stages. However, the overall model performance criteria of the SVM are similar to or even better than those of the ANN in model prediction stage. The generalization ability of a SVM model is superior to an ANN model for input structures and lead times. The uncertainty analysis for model parameters detects an equifinality of model parameter sets and higher uncertainty for ANN model than SVM in this case. These results implied that the model-building process should be carefully conducted, especially when using ANN models for GWL forecasting in a coastal aquifer.

Abbot and Marohasy (2012) used artificial intelligence to monthly and seasonal rainfall forecasting in Queensland, Australia. It was assessed by inputting recognized climate indices, monthly historical rainfall data, and atmospheric temperatures into a prototype stand-alone, dynamic, recurrent, time-delay, artificial neural network. Outputs, as monthly rainfall forecasts 3 months in advance for the period 1993 to 2009, were compared with observed rainfall data using time -series plots, root mean squared error (RMSE), and Pearson correlation coefficients. A comparison of RMSE values with forecasts generated by the Australian Bureau of Meteorology’s Predictive Ocean Atmosphere Model for Australia (POAMA) -1.5 general circulation models (GCM) indicated that the prototype achieved a lower RMSE for 16 of the 17 sites compared. The application of artificial neural networ ks to rainfall forecasting was reviewed. The prototype design is considered preliminary, with potential for significant improvement such as inclusion of output from GCMs and experimentation with other input attributes.

Chauhan and Shrivastava (2012) developed ANN models for estimation of reference crop evapotranspiration with climate data required for Penman -Monteith (P- M) method, to test artificial neural networks (ANNs) for estimating reference evapotranspiration (ET0) with limited climate data (ET0) and compares the performance of ANNs with P-M method. The ANNs are trained to estimate ET0 from weekly climate data as input and the Penman-Monteith (P-M) estimate as output. Using varied input combinations of climatic variables have been trained using the sam e training algorithms as mentioned above. For each class of inputs, the best ANN architecture for estimation of ET0 was selected on the basis of statistical parameters like square estimates of error (SEE) and model efficiency. The analysis suggest that the ET0 can be computed from limited climate data using the ANN approach in Mahanadi Reservoir Project (MRP) command area.

Chebud et al. (2012) developed a neural network model to quantify water quality parameters, namely chlorophyll-a, turbidity and phosphorus before and after ecosystem restoration and during the wet and dry seasons. The results demonstrate that the developed neural network model provided an excellent relationship between the observed and simulated water quality parameters. The root m ean square error values for phosphorus, turbidity and chlorophyll were below 0.03 mg L−1, 0.5 NTU, and 0.17 mg m−3, respectively, at the neural network training and validation phases. Using the developed methodology, the trends for temporal and spatial dyn amics of the selected water quality parameters were investigated. In addition, the amounts of phosphorus and chlorophyll stored in the water column were calculated.

Hardaha e t al. (2012) carried out an experiment in kaithal irrigation circle for prediction of farmers’ decisions on crop yields using artificial neural Network (ANN). Artificial Neural Network models have shown considerable potential for resolving some of the problems related with irrigated agricultural systems, which are complex, non-linear and ill defined. ANNs have shown potential uses in three type of applications in the field of irrigated agriculture including image analysis techniques for management, and predictions of various processes. It was found that radial basis function with spread constant 0.1 performed better for prediction of wheat and rice yields. It was also found that ANN algorithm predicted better for both wheat and rice crops in comparison to statistical regression model as obtained coefficient of determination in case of ANN was much higher for (r2=0.63) than regression model (r2=0.32).

Kumar (2012) presented neural network modelling, as a complimentary tool for modelling bed material load transport. The developed model demonstrated a superior performance compared to other traditional methods based on different statistical criteria, such as the coefficient of determination, Nash-Sutcliffe coefficient and discrepancy ratio.

Kumar et al. (2012) has attempted to establish a linear relationship between the input weather data and corresponding target data. There are many literatures in non - linear statistics for the weather forecasting; most of them required that the nonlinear model be specified before the estimation is done. But since the weather data is nonlinear and follows a very irregular trend, Artificial Neural Network (ANN) has evolved out to be a better technique to bring out the structural relationship between the various entries. The paper examines the applicability of ANN approach by developing effective and reliable nonlinear predictive models for weather analysis, also compared and evaluated the performance of the developed models using different transfer functions,, hidden layers and neurons to forecast maximum temperature for 365 days of the year.

Ojha and Bhakar (2012) developed artificial neural networks (ANNs) for comparison of daily reference evapotranspiration (ET0) estimated by Penman-Monteith (PM) method and that of estimated by ANNs during growing season of wheat crop, feed forward network has been used for predi ction of ET0 using resilient back- propagation method. For the purpose of the study, daily meteorological observations such as minimum and maximum temperature, minimum and maximum relative humidity, wind speed and solar radiation for the period of November 21, 1997 to March 2, 1998 were used as input and ET0 estimated by Penman-Monteith method for growing season of wheat crop as output. The crop evapotranspiration estimated by ANNs were compared with ETc estimated by crop coefficient approach and that of evapotranspiration measured by lysimeter. The correlation coefficients during training of ETc of wheat crop were found to be 0.994 and 0.915 respectively which were also found significant at 5% level. Based on these comparisons, it can be concluded that the ANN models is suitable for prediction of ET0 and ETc.

Sensoy et al. (2012) commented on “Catchment flow estimation using Neural Networks in the mountainous Euphrates basin” by A. G. Yilmaz, M. A. Imteaz, G. Jenkins (J. Hydrol. 410 (2011) 134-140) and concluded that ANN modelling should be used with care and enough data including topography and snow data especially when applied in a mountainous snow dominated basin.

Shrivastava et al. (2012) developed artificial neural networks (ANNs) model for weather forecasting, especially in rainfall forecasting a comprehensive literature review from 1923 to 2012 is done and presented in this paper, and it is found that architectures of ANN such as BPN, RBFN is the best established to be forecast chaotic behaviour and have efficient enough to forecast monsoon rainfall as well as other weather parameter prediction phenomenon over the smaller geographical region.

Singh et al. (2012) has developed radial basis neural network (RBNN) for Nagwa watershed for simulating monthly surface runoff and sediment yield. Different set of input were employed and it was observed that only average monthly rainfall was sufficient to estimate surface runoff, while average monthly rainfall and average monthly discharge were needed for estimating sediment yield. Result indicate that coefficient of determination, R2, Nash-sutcliffe simulation efficiency, NSE and root mean square error, RMSE values for RBNN model were 0.93, 0.92, and 1.25 during training, and 0.72, 0.73 and 0.77 during validation period respectively. The model performed well for simulation of sediment yield with R 2, NSE and RMSE values of 0.92, 0.92 and 1822 during training period and 0.80, 0.70 and 2288 during validation period respectively.

Chang et al . ( 2013) proposed a hybrid model (BD) that combines back- propagation neural networks (BPNN) and dynamic factor analysis (DFA) to precisely estimate pan evaporation at multiple meteorological stations in northern Taiwan through incorporating a large number of meteorological data sets into the estimation process. The BD model successfully inherited the advantages from the DFA and BPNN, and effectively enhanced its generalization ability and estimation accuracy. The results demonstrated that the proposed BD model has good reliability and applicability in simultaneously estimating pan evaporation for multiple meteorological stations.

Karatzas et al. (2013) used the Particle Swarm Optimization (PSO) algorithm to train a feed-forward multi-layer ANN for the simulation of hydraulic head change at an observation well at the region of Agia, Chania, Greece. Three variants of the particle swarm optimization algorithm are considered, the classic one with the inertia weight improvement, PSO-TVAC and GLBest-PSO. The best performance was achieved by GLBest-PSO when implemented using field data from the region of interest, providing improved training results compared to the back propagation training algorithm. The trained ANN was subsequently used for midterm prediction of the hydraulic head as well as for the study of three climate change scenarios. Data time series were created using a stochastic weather generator, and the scenarios were examined for the period 2010-2020

Mirlatifi et al. (2013) predicted the cumulative infiltration at specific time steps, using readily available soil data and Artificial Neural Networks (ANNs). 210 double ring infiltration data were collected from different regions of Iran. Basic soil properties of the two upper pathogenic layers (A and B horizons) including initial soil water content, soil water contents at field capacity (33 k Pa) and permanent wilting point (1500 k Pa), bulk density, particle-size distributions, organic carbon, gravel content (>2 mm size), and CaCO3 content were determined. The feed forward multilayer perceptron ANN model was used to predict the cumulative infiltration at 5, 10, 15, 20, 30, 45, 60, 90, 120, 150, 180, 210, 240, and 270 min after the start of the infiltration experiment and at the time of the basic infiltration rate. The developed ANN models were categorized to type I and type II ANN models. The basic soil properties of the first upper soil horizon were hierarchically used as inputs to develop type I ANN models. In contrast, the type II ANN models were developed while the available soil properties of the two upper soil horizons were implemented as inputs using principal component analysis technique. Results of the reliability test for the developed ANN models indicated that type I ANN models with a RMSE of 1.136–9.312 cm had the best performance in estimating the cumulative infiltration. Type I ANN models with the mean RMSD of 6.307 cm had the best performance in estimating the cumulative infiltration curve (CIC). Results indicated that at the 1% probability level, ANNs-derived CIC can be accepted as one of the replications of a reliable infiltration experiment. It was also concluded that compared to the Horton, Kostiakov, revised USDA-NRCS, Philip, and Green and Ampt infiltration models, the Kostiakov–Lewis model performed better to quantify the infiltration process.

Nastos et al. (2013) developed predictive models in order to forecast rain intensity (mm/day) in Athens, Greece, using Artificial Neural Network (ANN) models. The ANNs outcomes concern the projected mean, maximum and minimum monthly rain intensity for the next four consecutive months in Athens. The meteorological data used to estimate the rain intensity, were the monthly rain totals (mm) and the respective rain days, which were acquired from the National Observatory of Athens, for a 111 - year period (1899–2009). The results of the developed and applied ANN models showed a fairly reliable forecast of the rain intensity for the next four months. For the evaluation of the results and the ability of the developed prognostic models, appropriate statistical indices were taken into consideration. In general, the predicted rain intensity compared with the corresponding observed one seemed to be in a very good agreement at a statistical significance level of p less than 0.01.

Nia et al. (2013) investigated the abilities of Support Vector Machine (SVM) and Artificial Neural Network (ANN ) models to predict daily suspended sediment load (SSL) in Doiraj River, located in the west part of Iran. An 11-year data (1994–2004) was applied for predicting SSL. Stream flow and rainfall were used as the model inputs and SSL as the model output. The best input of SVM and ANN models was identified using combination of Gamma Test and Genetic Algorithm (GT GA). Its results accuracy was compared with the results of conventional correlation coefficient analysis between input and output variables and the best combination was identified. Also, the present study explored Gamma Test to identify the length of the training dataset. Finally, in order to predict SSL, they used the nu-SVR (using the four kernels including linear, polynomial, sigmoid and Radial Basis Function (RBF)) and ANN models (based on BFGS algorithm and Conjugate algorithm). The reliability of SVM and ANN models were evaluated based on performance criteria such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Efficiency Index (EI) and correlation coefficient (R 2). The obtained results show that ANN models and nu- SVR model using Gamma Test for input selection has better performance than regression combination. Also, the performance BFGS-ANN model were better than other models with RMSE value and R2 equal to 0.34 (ton) and 0.99, respectively. The nu-SVR model with RBF kernel has more capability in prediction of SSL than the other kernels (RMSE = 0.96 (ton) and R2 = 0.98). In addition, the results showed that M-test can be used as a new method to determine the number of required data for network training for creating a smooth model by nu-SVR and ANN models.

Alhashimi (2014) developed and implemented three rainfall prediction models based on past observations such as time series models based on autoregressive integrated moving average (ARIMA), artificial neural network (ANN) model and multi linear regression (MLR) model. A feed-forward neural network (FNN) model was applied to predict the rainfall on monthly basis. In order to evaluate the performance of three models, statistical parameters were used to make the comparison between these models. These parameters include the correlation coefficient (R) and root mean square errors (RMSE). The study reveals that ANN model can be used as an appropriate forecasting tool to predict the monthly rainfall, which is preferable over the ARIMA model and MLR model.

Yang et al. (2013) applied an artificial neural network (ANN) based southwest monsoon rainfall enhancement (AME) to improve the typhoon rainfall climate model (TRCM) rainfall forecasting for the Tsengwen Reservoir watershed in the south western Taiwan where maximum typhoon rainfall frequently occurred. The results indicated that the flux threshold is related to the topographic lifting of the moist air, with lower threshold in the upstream high altitude stations in the watershed. The lower flux threshold allows a larger rainfall amount with AME. They also incorporated the rainfall prediction with a state space neural network (SSNN) to simulate rainfall-runoff processes. Their improved method is robust and produces better flood predictions of total rai nfall and multiple rainfall peaks. The runoff processes in the watershed are improved in terms of coefficient of efficiency, peak discharge, and total volume.

Ay and Kisi (2014) proposed integration of k-means clustering and multi-layer perceptron (k-means-MLP) methods in modelling chemical oxygen demand (COD) concentration. The proposed method was tested by using daily measured water suspended solids, pH, temperature, discharge and COD concentration data of upstream of the municipal wastewater treatment plant system in Adapazari province of Turkey. Performance of the k-means-MLP method was compared with multi-linear regression, multi-layer perceptron, radial-based neural network, generalized regression neural network, and two different adaptive neuro-fuzzy inference system techniques (subtractive clustering and grid partition). Root mean square error, mean absolute error, mean absolute relative error and determination coefficient statistics were employed for the evaluation accuracy of each model. It was found that the k-means-MLP performed better than the other techniques in estimating COD.

He et al. (2014) studied the potential of three different data driven methods, artificial neural network (ANN), adaptive neuro fuzzy inference system (ANFIS) and support vector machine (SVM) for forecasting river flow in the semiarid mountain region, north-western China. The performance of the ANN, ANFIS and SVM models in training and validation sets are compared with the observed data. The model which consists of three antecedent values of flow has been selected as the best fit model for river flow forecasting. Four quantitative standard statistical performance evaluation measures, the coefficient of correlation (R), root mean squared error (RMSE), Nash Sutcliffe efficiency coefficient (NS) and mean absolute relative error (MARE), were employed to evaluate the performances of various models developed. The results indicated that the performance obtained by ANN, ANFIS and SVM in terms of different evaluation criteria during the training and validation period does not vary substantially; the performance of the ANN, ANFIS and SVM models in river flow forecasting was satisfactory. A detailed comparison of the overall performance indicated that the SVM model performed better than ANN and ANFIS in river flow forecasting for the validation data sets. The results also suggest that ANN, ANFIS and SVM method can be successfully applied to establish river flow with complicated topography forecasting models in the semiarid mountain regions.

Kashyap et al. (2014) developed a general numerical model for simulation of salt water transport induced by pumpage from a scavenger well system. The numerical model is invoked to develop two Artificial Neural Network (ANN) models of the relevant state variables viz. production well salinity and drawdown at well face. These ANN models were used for optimizing the scavenging discharge with respect to the position of the two screens and subjected to the constraint on production well salinity and the drawdown to ensure functionality of the production well screen.

Lopez-Lineros et al. (2014) proposed a new quality control method based on non- linear auto regressive neural networks (NARNN) for validating hydrological information, more specifically of 10 min river stage data, for automatic detection of incorrect records. To assess the effectiveness of the approach, a comparison with adapted conventional validation tests extensively used for hydro meteorological data was carried out. Different parameters of NARNN and their stability were also analysed in order to select the most appropriate configuration for obtaining the optimal performance. A set of errors of different magnitudes was artificially introduced into the dataset to evaluate detection efficiency. The NARNN method detected more than 90% of altered records, when the magnitude of error introduced was very high, while conventional tests detected only around 13%. In addition, the NARNN method maintained a similar efficiency at the intermediate and lower error ratios, while the conventional tests were not able to detect more than 6% of erroneous data.

Shiri et al. ( 2014) aimed to apply different methods to modelling energy dissipation in napped and skimming flow regimes over stepped spillway by using original experimental dataset through the artificial networks (ANNs) and Genetic Expression Programming (GEP) techniques. Subsequently, three kinds of data including the napped and skimming regimes data as well as combination of them are applied as models input– output variables. A preliminary investigation on various GEP operators is also carried out for selecting the proper operators. The obtained results indicated that machine learning techniques have reliable performance in predicting energy dissipation over stepped spillways.

Tayfur et al. (2014) quantitatively investigated the use of soil moisture measured at 10, 20, and 40 cm soil depths along with rainfall in predicting runoff. Rainfall plus soil moisture at 10, 20, and 40 cm formed the input vector while the discharge was the target output in the model of generalized regression neural network (GRNN). The model for each basin was calibrated and tested using October 2002–March 2003 data. The calibrated and tested GRNN was then employed to predict runoff for each basin for the period of January–April 2004. The model performance was found to be satisfactory with determination coefficient, equal to 0.87 and Nash–Sutcliffe efficiency, NS, equal to 0.86 in the validation phase for both catchments. The sensitivity analysis indicated that the use of soil moisture data at different depths allows preserving the memory of the system thus having a similar effect of employing the past values of rainfall, but with improved GRNN performance.

2.2 Sensitivity Analysis

Cannon and McKendry (2002) described a form of sensitivity analysis that illustrated the effects that inputs have on outputs of statistical models. The strength and sign of relationships, the types of non-linearity, and the presence of interactions between inputs can be diagnosed using this technique. As ANNs are increasingly being used for climate prediction, the discussion focuses on specific problems associated with their use in this context. The skill of multiple linear regression and ensemble ANNs are compared using a resampling procedure. Interpretation of the models is then conducted using traditional diagnostic tools and graphical sensitivity analysis. Sensitivity analyses suggest a mildly nonlinear relationship.

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