SEASONAL PREDICTION OF GROUNDWATER LEVELS USING ANFIS … 1... · SEASONAL PREDICTION OF GROUNDWATER LEVELS USING ANFIS AND RADIAL BASIS NEURAL NETWORK *Amutha R and Porchelvan P

International Journal of Geology, Earth and Environmental Sciences ISSN: 2277-2081 (Online) An Online International Journal Available at http://www.cibtech.org/jgee.htm 2011 Vol. 1 (1) September-December, pp.98-108/Amutha and Porchelvan Research Article

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SEASONAL PREDICTION OF GROUNDWATER LEVELS USING ANFIS AND RADIAL BASIS NEURAL NETWORK

*Amutha R and Porchelvan P School of Mechanical and Building Sciences, VIT University, Vellore – 632014

*Author for Correspondence

ABSTRACT In Indian subcontinent the source of ground water is mainly from rainfall and partially due to the river flow, lakes, and reservoirs, which is highly nonlinear and dynamic. In this paper, the seasonal ground water levels are predicted using the Adaptive Neuro-Fuzzy Inference Systems (ANFIS) and Radial Basis Function (RBF) based on previous seasonal rainfall and ground water levels. The study is carried out in Malattar sub-watershed, located in Vellore district, Tamilnadu, India. The results show that both the models are able to predict the seasonal ground water levels with sufficient accuracy. However, it is observed that the ANFIS model is able to capture the dynamics of the surface water and ground water interactions better when compared to RBF and thus able to predict the seasonal ground water levels accurately. Key Words: Ground Water Recharge, Artificial Neural Network, Adaptive Neuro-Fuzzy Inference Systems, Radial Basis Function, Ground Water Levels INTRODUCTION In a watershed basin, the seasonal modeling of ground water fluctuations is very useful in planning and management of both the surface water and ground water resources. This is important in regions where there is depleting surface water resources and increase in water demand due to industrialization and urbanization. Further change in climatic trends results in the variation of rainfall quantities. Thus, ground water resources are becoming an alternate solution to meet the increase in demands. In case of Indian subcontinent, where rainfall patterns are changing due to change in climatic conditions, the over exploitation of ground water has become inevitable. The major source of ground water in most of the watersheds in India is through recharge from rainfall. The physical interaction between the hydrological variables (such as rainfall, evapotranspiration) with ground water is highly nonlinear, stochastic, and complex. The groundwater prediction models can be divided into two groups, namely, i) physical and ii) system theoretic. The main drawback of the physical model is the complexity of the models, which increases with increase in model parameters. Further, the development of these models is based on understanding of the physical processes in the system. On the other hand, the system theoretic model is based on data driven techniques, where the mapping or learning of the models is done through data itself. Here, the understanding of the physical process in model building is avoided to a large extent (Srivastav et al., 2007). In recent years, the system theoretic models have gained recognition in the field of surface as well as sub-surface hydrology. The application of the data driven models to hydrological models can be found in: for rainfall-runoff model (Sajikumar & Thandaveswara, 1999; Shamseldin, 1997), stream flow prediction (ASCE Task Committee. 2000,Campolo, et.al, 1999; Clair & Ehrman, 1998; Zealand, Burn, & Simonovic, 1999), groundwater level forecasting (Daliakopoulos, Coulibaly, & Tsanis, 2006; Nayak, Rao, & Sudheer, 2006; Yang, et.al, 2008; Srikanth et al., 2009). For more details on application of data driven models to hydrologic models, the readers are requested to refer to Maier et al. (2010). Among the data driven models, artificial neural network (ANN) model has been successfully applied to a wide variety of hydrologic problems (Maier et al., 2000). The application of a more promising data driven technique, the fuzzy inference system (FIS), has recently been increasing in hydrology. Lu and Lo (2002) used self-organizing maps (SOM) and fuzzy theory for diagnosing reservoir water quality. Tayfur et al.


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(2003) developed fuzzy logic algorithms for estimating sediment loads from bare soil surface. Wong et al. (2003) predicted volume of rainfall using SOM, BPNN (Back propagation neural networks), and Alvisi et al.(2006) predicted water level using fuzzy logic and ANN. Further, in recent years many advancements of ANN, which includes, Radial Basis Function (RBF), Generalized Regression Neural Network (GRNN) And Adaptive Neuro-Fuzzy Inference Systems (ANFIS) has been adapted to hydrologic problems. The combination of ANN and FIS into the adaptive neuro-fuzzy inference system (ANFIS) has advantages in a computational framework. The learning capability of ANN can be used effectively for automatic fuzzy if-then rule generation and parameter optimization (Nayak et al., 2004). Several researchers have used ANFIS in hydrology. Ponnambalam et al. (2003) used ANFIS for minimizing variance of reservoir systems operation. Nayak et al. (2004) applied it to hydrologic time series modeling. Kisi (2005) investigated the ability of ANFIS and ANN to model the relationship between streamflow and suspended sediment. Chang and Chang (2007) used it to construct a water level forecasting system for flood periods. Tutmez et al. (2006) developed an ANFIS model for groundwater electrical conductivity, based on the concentration of positively charged ions in water. Pankaj and Deo (2006) have applied various advancements of ANN to forecast daily river flows on a continuous basis with the purpose of understanding how ANFIS, Generalized Regression Neural Networks (GRNN) and RBF compared with traditional ANN for the forecasts at Rajghat along river Narmada in India. They have found that both ANFIS and RBF are able to predict the river flows more accurately than ANN and GRNN model. In case of groundwater literature only few studies have been carried out using the above data driven models (Azhar and Watanabe, 2007; Sreekanth et.al 2009; Mansouret.al.2010; Zahra et al. 2010; Pankaj Singh, and Deo 2007; Sethi et.al 2010). Azhar and Watanabe,( 2007) developed a adaptive neuro-fuzzy inference system (ANFIS) and artificial neural networks (ANN) model based on Levenberg-Marquardt (LM) for forecasting daily groundwater level fluctuation (GLF).It was found that the algorithms produced no significant differences in prediction results. Overall, the results suggest that the soft computing algorithms can predict daily groundwater level with high accuracy using time lag as inputs networks. Coppola et.al (2009) adopted ANN for three types of groundwater prediction and management problems. In this paper the problem of hydrologic predictive modelling of a watershed is characterized by precipitation and observed water levels. Most of the previous papers analyzed the ground level predictions are either at hourly or daily level. Moreover, there is a limited application of the ANN advancements in prediction of seasonal groundwater levels. In this study, we compare the performance of the two advancements of the ANN models, namely, ANFIS and RBF to predict the seasonal groundwater levels. The seasonal ground water level from three observation wells in Malattar watershed were used as a case study. The main objective of this paper is to develop a reliable groundwater level fluctuation forecasting system to generate trend forecasts. The forecasts, based on ANFIS and RBF techniques, are then compared to actual measurements recorded during a subsequent monitoring period .The remainder of the paper is organized as follows. In Section 2, the details of the ANFIS and RBF models are presented. Following this, the results and discussion are presented in Section 3 aiming to the efficacy of both the ANFIS and RBF models through application to seasonal ground water levels at Malattar basin. Section 4 outlines the summary and conclusions of the present study and the scope for further research work. MATERIALS AND METHODS Adaptive Neuro-Fuzzy Inference System ANFIS was originally proposed by Jang (1993) ANFIS is a fuzzy system trained by an algorithm derived from neural network theory. Further, ANFIS is a new improved tool and a data-driven modeling approach for determining the behavior of imprecisely defined complex dynamical systems . The ANFIS model has human-like expertise within a specific domain it adapt itself and learns to do better in changing environments (Kurian et al. 2006). An ANFIS aims at systematically generating unknown fuzzy rules


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from a given input/output data set (Abraham et al. 2004).The algorithm is a hybrid training algorithm based on back propagation and the least squares approach. In this algorithm, the parameters defining the shape of the membership functions are identified by a back propagation algorithm, while the consequent parameters are identified by the least squares method. An ANFIS can be viewed as a special three-layer feed forward neural network. The first layer represents input variables, the hidden layer represents fuzzy rules, and the third layer is an output. Figure 1 represents a typical ANFIS architecture that is based on:

Figure .1. Structure of Adaptive Neuro-Fuzzy Inference System network

Layer 1 Every node in this layer is an adaptive node with a node function that may be a generalized bell membership function (Eq. 1), a Gaussian membership function (Eq. 2), or any membership functions:

Where ai, bi, and ci are premise parameters. Also, x is the input to node i and Ai is the linguistic label (for example, low and high) associated with this node function. Premise parameters change the shape of the membership function. Layer 2 Every node in this layer is a fixed node labeled, representing the firing strength of each rule, and is calculated by the fuzzy and connective of “product” of the incoming signals by using (Eq. 3) Eq. (3) i = 1,2 Where µAi (x) and µBi (x) are the membership grades of fuzzy sets A and B and also Wi is the firing strength of each rule. Layer 3 Every node in this layer is a fixed node labeled N, representing the normalized firing strength of each rule. The i th node calculates the ratio of the i th rule’s firing strength to the sum of the two rules’ firing strengths by using (Eq. 4):

i = 1,2 Where Wi is the normalized firing strength that is the ratio of the ith rule’s firing strength

Eq. (4)

Eq. (1)

Eq. (2)


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(Wi) to the sum of the first and second rules’ firing strengths (w1, w2). Layer 4 Every node in this layer is an adaptive node with a node function (Eq. 5), indicating the contribution of i th rule toward the overall output

Eq. (5) Where zi is equal to pi, qi, and ri are consequent parameters.

Layer 5 The single node in this layer is a fixed node labeled ∑, indicating the overall output as the summation of all incoming signals calculated by (Eq. 6)

where Z is the summation of all incoming signals. The Radial basis function (RBF) Radial basis function (RBF) networks have been widely used for nonlinear system identification because of their simple topological structure and their ability to reveal in an explicit manner how the learning is proceeding (Lin & Chen, 2004). RBF networks have increasingly attracted interest for engineering applications due to their advantages over traditional multilayer perceptrons, namely faster convergence, smaller extrapolation errors, and higher reliability (Moradkhani et al., 2004). The architecture and training algorithms for radial basis function networks (RBF) are simple and clear. Further, RBF is considered a good candidate for approximation problems because of its faster learning capability compared with other feed forward networks. In RBF networks, the Gaussian function and the least squares (Chen et. al., 2006) criterion are selected as the activation function of network and the objective function, respectively. A network adjusts parameters of each node iteratively by minimizing the least squares criterion according to gradient descent algorithm. Since a neural network can accomplish a highly nonlinear mapping from input space to output space. The radial basis function (RBF) network also consists of three layers, namely an input layer, a hidden layer or radial basis layer, and an output layer or linear layer. The input layer collects the input information. The hidden layer consists of a set of basic functions performing nonlinear transformations of the inputs. The most common transformation is Gaussian function as the nonlinearity of the hidden nodes. The response of the j-th hidden node to xi is given by (Eq. 7)

Eq. (7)

Where is Euclidean norm, c is the center of the basis function and α is a positive constant that determines the width of the symmetric response of the hidden node. j The output values of the network are computed as linear combination of these basis functions (hidden nodes),(Eq. 8)

Eq. (8) where wj is the network connection weights and K is the number of hidden nodes. Assume that N samples of the signal are available for training. The center, cj , 1 ≤ j ≤ K, can be selected from the network training input xi , 1 ≤ i ≤ N. The weights can then be solved using the least squares method. Modelling Exercise Split-sample training is a common method to train ANN models; in this method, collected data are divided into training and testing set. However, recent works have found that the better-trained model is not always coupled with better performance in the testing. A practical way to find a point of better generalization and avoid over training is to set aside a small percentage of the training data set, which then can be used for cross validation. Monitoring the errors in the training set and the validation set should be carried out during the training process. When the error in the validation set increases, the

Eq. (6)


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training should stop because the point of best generalization has reached. This cross validation approach was adopted for the training of ANFIS and RBF models in this study. Accordingly, 25years data (1982

Figure.2. Structure of Radial basis function network

to 2006) of seasonal rainfall records and groundwater levels are selected to train both the models, in which 70% of the data is set as a training set, 10% of the data is set aside to use for cross validation and 20% of the data is set as a testing data. The training set is used to calibrate the weights of the network; the cross validation is used to monitor the progress of training process. The testing data set have no effect on training and so provide an independent measure of network performance during and after training.. In order to avoid the level difference between the sample data and eliminate errors by different dimension and unit, we need to normalize the data. Further, in order to fit within the range of the transfer function the data has to be scaled. In this study the following equations are adopted for normalization and scaling by using (Eq. 9). Eq (9)

Where y is the normalized data, x is the actual data, X is the mean of the actual data and X is the standard deviation of the actual data (Eq. 10) Eq (10)

where zi , yi are variables before and after normalization respectively; ymax and ymin are maximum and minimum of variable y, respectively. Further, the data are appropriately scaled between 0 and 1 to fall within the limits of transfer function which in this study is log sigmoid function. The trial and error procedure started with two hidden neurons initially, and the number of hidden neurons was increased up to 10 with a step size of 1 in each trial. For each set of hidden neurons, the network was trained in batch mode (offline learning) to minimize the mean square error at the output layer. Selection of Inputs and Outputs Development of the network was based on the idea that if a sufficient length of the previous observations were given, the network would recognize the hidden pattern in between them and accordingly produce the forecast. Sudheer et al. (2002) has suggested a methodology based on autocorrelation and cross correlation for the selection of input variables. In this study, based on the examination of the auto-correlation and cross-correlation function of the measured seasonal rainfall and groundwater level quantities found that an input of three previous lags/observations is sufficient for the network to understand the unknown pattern in the outcome. The inputs identified for the ANFIS and RBF models


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are: R(t-3), R(t-2), R(t-1), GW(t-3), GW(t-2), GW(t-1), where R(t) represents the rainfall and GW(t) represents the groundwater levels at any time period t. The output of the network was considered as GW(t). Performance criteria The values of the ground water levels estimated by the models and the observed ground water level tested using four performance criteria such as mean bias error (MBE), Root Mean Square error (RMSE), Correlation coefficient (R) and Nash-Sutcliffe efficiency or coefficient of efficiency (CE) (Nash and Sutcliffe, 1970). The following are the equations for the above performance measures ( Eq.11 – Eq.14)

Coefficient of Correlation (R) R Eq. (11)

Coefficient of Efficiency (CE) CE Eq. (12)

Root Mean Square Error (RMSE) RMSE

Mean Bias Error (MBE) MBE Eq. (14) where subscripts are observed and predicated levels respectively n_total number of data pairs considered; and mean value of the observed and predicated data respectively.

Description of Study area The chosen study area is Malattar sub-watershed is a major tributary of Palar river lies between north latitude from 78º39’ to 79º56’ and east longitude from 12º48’ to 12º56’, covers a geographical area about 162Sq.Km and covered part of Survey of India toposheets of 55L/13 55L/9, 55L/ 11. The study area of Malattar sub-watershed is shown in Figure 3 Malattar River originates in the hilly regions of Venkatagrikotta in Andra Pradesh and flows Niakeneri forest of Palamanar Taluk. This river confluences Palar River 5 Km east of Ambur near Sathampakkam village on the left side and flows through Pernampet block of Vellore District. Daily rainfall data of Gudiyattam from 1982 to 2006, 26 years was collected from the meterological data station, Chennai. Table.1 shows the annual rainfall gauge location (latitude and longitude) of the study area used in this research. Similarly the seasonal data for five wells within the study area were available for the study. RESULTS AND DISCUSSION As discussed earlier, this paper investigates two types of soft computing techniques, ANFIS and RBF model, for the prediction of ground water level. Records of seasonal (once in three months) were compiled from observation wells in the case study area for 25 years (1982 to 2010). Three observation wells were analyzed to ensure that all variables received equal attention during the calculation process; they were normalized (Maier & Dandy, 2000). By this consideration, the inputs and output desired were

Eq. (13)


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scaled in the range of 0 to1 by scaling with respect to minimum and maximum data before being fed into the calculation model. The comparison of ANFIS and RBF models based on the performance measures for all the three well data considered in this study are presented in Table 2. Table.1. Location of rain gauge stations in the studyarea.

S.No. Rain gauge station Latitude Longitude Source

1 V.Kotta 260 25”N 300 6’14”E Indian Meteorological Department, Nungampakkam, Chennai 2 Modikuppam 780 39’ N 120 48’ E

3 Ambur 110 13’N 780 13’E

Figure.3. Study area of the Malattar Sub-watershed (4C2B2a)

It is observed that the correlation coefficient of both the ANFIS and RBF model is high in calibration. However, the correlation coefficient of the ANFIS model is better when compared to RBF model in case of validation. Similarly it is observed from Table 2 that the coefficient of efficiency of ANFIS model is better when compared to RBF in both calibration and validation. The root mean square error for the ANFIS is less when compared to RBF in both calibration and validation. Further, similar trend of results for mean bias error is observed. It is worth to be noted that the ANFIS model is able to show better


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performance in comparison to RBF model, in case of all the wells. The scatter plot showing trend line between predicted and observed groundwater levels and time series plot comparing the performance of both ANFIS and RBF models are presented in Figs. 4-6. For brevity only the result for Well No.1 is Table-2. Performance Measure of ANFIS and RBF Calibration And Validation model for well nos

1-3

Model Calibration Validation Calibration Validation Calibration Validation

ANFIS RBF ANFIS RBF ANFIS RBF ANFIS RBF ANFIS RBF ANFIS RBF WELL -1 WELL -2 WELL -3

CC 0.9999 0.9984 0.9415 0.8226 0.9999 0.9986 0.9619 0.9358 0.9999 0.9954 0.9398 0.6062 CE 0.9999 0.9967 0.8672 0.1496 0.9999 0.9969 0.8914 0.8666 0.9999 0.9907 0.5908 0.1671 RMSE 5E-06 0.5407 3.0527 7.723 5E-05 0.6189 3.9022 4.3343 0.0005 0.7106 7.3835 10.534

MBE 4E-06 --0.043 0.9762 2.0891 3.6E-

06 -0.0357 -1.893 -0.788 2E-05 0.0347 -4.080 1.4005

presented here. It is observed from the Fig. 4 that band of scatter plot is very narrow and close to the line of perfect fit in case of calibration. On the other hand ANFIS shows marginally better performance is compared to RBF model in validation. It is evident from Fig. 4 (and Table 2) that the performance of the ANFIS and RBF in case of calibration is almost similar. However, in case of validation (Fig. 5, and 6 ) the ANFIS outperforms the RBF model. It is to be envisaged that the ANFIS model is able to capture the dynamics of the rainfall-groundwater process better in compare to RBF model for all the three wells considered in this study.

Figure.4. Performance Measure of ANFIS and RBF Calibration and Validation model for well-1


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Figure.5. Performance Measure of ANFIS and RBF Calibration model for well -1

Figure.6. Performance Measure of ANFIS and RBF Validation model for well -1 Summary and Conclusion In this study the performance of the two advancements of ANN models, namely ANFIS and RBF model are compared for prediction of groundwater levels in Malattar watershed basin. The modeling exercise is carried out based on split-sample validation. The performance of the model is carried out based on performance measures such as correlation coefficient, coefficient of efficiency, root mean square error and mean bias error. It is observed that the performance of the ANFIS is quite satisfactory providing close or sometime superior performance when compared to RBF model in terms of the performance measures used in this study. It is envisaged from this study that ANFIS model can be a better alternate for modeling the seasonal rainfall-groundwater process. A few studies have been carried out and reported on the applications of RBF and ANFIS in hydrology, quite a few of them are related to ground water level forecasting. Further, more investigations needed on the application of the ANFIS and RBF techniques in ground water level forecasting to have a precise statement.


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ACKNOWLEDGEMENTS We would like to thank Dr. Roshan Srivastav, VIT University for his suggestions and support. This research is supported by Shool of Mechanical and Building Sciences, VIT University, Vellore, Tamil Nadu, India. The authors are grateful to Ground Water Department PWD, Vellore, Central Ground Water (CGWB), Chennai and Indian Meteorological Department, Nungampakkam, Chennai, for providing the valuable data. REFERENCES Alvisi, .S., G. Mascellani., M. Franchini., and A. Bardossy., (2006). Water level forecasting through fuzzy logic and Artificial Neural Network approaches, Journal of Hydrology and Earth System Sciences 10, 1-17. Azhar K., Affandi and Kunio Watanabe (2007), Daily groundwater level fluctuation forecasting using soft computing technique, Nature and Science, 5(2).1-10. Campolo, M., P. Andreuss,i, and A. Soldati,, (1999). River flood forecasting with a neuralnetwork model. Water Resources Research, 35(4), 1191–1197. Chen,J., and B.J. Adam,, (2006). Integration of Artificial Neural Networks with conceptual models in rainfall-runoff modeling. Journal of Hydrology 318(1-4), 232-249. Chang, F.J., Chiang, Y.M., and Chang, L.C., (2007). Multi-step-ahead neural networks for flood orecasting. Hydrological Sciences Journal (Journal Des Sciences Hydrologiques) 52 (1), 114-130. Clair, T. A., & J.M. Ehrman., (1998). Using neural networks to assess the influence of changing seasonal climates in modifying discharge dissolved organic carbon, and nitrogen export in eastern Canadian rivers. Water Resources Research, 34(3), 447–455. Coppola, E., M. Poulton., E. Charles., J. Dustman., and F. Szidarovszky., (2003). Application of artificial neural networks to complex groundwater management problem. Natural Resources Research 12, 303-320. Dawson, C.W., Wilby, R.L., (2001). Hydrological Modelling Using Artificial Neural Networks Progress in Physical Geography 25 (1), 80-108. Hornik, K., M. Stinchcombe., and H. White., (1989). Multilayer feed forward networks are universal approximators, Neural Networks, 2,359–366. Ioannis N Daliakopoulos. , Paulin Coulibaly., & Ioannis K Tsanis (2005). Groundwater level forecasting using artificial neural networks. Journal of Hydrology, 309(1–4), 229–240. Jang, J.S.R., (1993). ANFIS: Adaptive network based fuzzy inference system, IEEE Trans. On System, Man, and Cybernetics 23(3), 665-685. Kisi, O., (2005). Suspended sediment estimation using neuro-fuzzy and neural network approaches. Hydrological Sciences Journal 50(4), 683-696. Kurian, C. P., V.I. George., J. Bhat., & R.S. Aithal., (2006). ANFIS model for the time series prediction of interior daylight illuminance. AIML Journal, 6(3),35–40. Lin, G.F., and L.H. Chen., (2004). A non-linear rainfall-runoff model using radial basis function network. Journal of Hydrology 289, 1-8. Maier, H.R., G.C. Dandy., (1999). Empirical comparison of various methods for training feed-forward neural networks for salinity forecasting. Water Resources Research 35(8), 2591-2596. Maier.H.R.,G.C.Dandy.,(2000).Neural networks for the prediction and forecasting of water resources variables:.Environmental Modeling & Software15(1), 101-124. Mansour Talebizadeh.,Ali Moridnejad.,(2010). Uncertainty analysis for the forecast of lake level fluctuations using ensembles of ANN and ANFIS models. Expert Systems with Applications,38 (4), 4126-4135. Moradkhani, H., K. Hsu., H.V. Gupta., S. Sorooshian., (2004). Improved streamflow forecasting using self-organizing radial basis function artificial neural networks.Journal of Hydrology 295 (1.4), 246-262.


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SEASONAL PREDICTION OF GROUNDWATER LEVELS USING ANFIS … 1... · SEASONAL PREDICTION OF GROUNDWATER LEVELS USING ANFIS AND RADIAL BASIS NEURAL NETWORK *Amutha R and Porchelvan P