Application of ANN and ANFIS model on monthly groundwater level fluctuation in lower Bhavani River Basin

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(1)Indian Journal of Geo Marine Sciences Vol. 46 (10), October 2017, pp. 2114-2121. Application of ANN and ANFIS model on monthly groundwater level fluctuation in lower Bhavani River Basin Vetrivel N * & Elangovan K Department of Civil Engineering, PSG College of Technology, Coimbatore – 641 004, India. *. [E. Mail: vetrivel.nagarajan@gmail.com]. Received 05 April 2016 ; revised 28 November 2016 The present study is carried out to perform the comparative prediction between ANN, ANFIS, CWTFT-ANN (Continuous Wavelet Fast Fourier Transform), CWTFT-ANFIS, WT-ANN (Wavelet Transform) and WT-ANFIS on Groundwater Level prediction at different reaches (Top, Middle and End) of Lower Bhavani River Basin (LBRB) on monthly stress basis (from 2009 to 2015). From the results, the performance of CWTFT–ANFIS is 9.36%, 13.3% and 4.45% better than the ANFIS prediction and the performance of CWTFT-ANN is 47.17%, 25.6% and 47.45% better than the ANN prediction at Top, Middle and End reaches of LBRB respectively. Overall the prediction of CWTFT-ANN is about15.3% better than the other identified models, which is further fed for the forecasting of groundwater level to next one time stress level. [Keywords: Groundwater; ANFIS; CWTFT; Wavelet Transform; Lower Bhavani River Basin; Prediction and Forecasting]. Introduction ANN and ANFIS models are in need of data pre-processing of input and/or output data in order to perform the best prediction as possible1. By considering other types of data pre-processing, Wavelet transforms provide useful decompositions from the original time series. This will improve the ability of a forecasting model at different resolution levels2, 3. In hydrologic system development, many applications of wavelets and continuous wavelets are notices, i.e., temporal variability analysis in rainfall and runoff data4. Continuous wavelet transforms is used to identify the temporal variability of rainfall and runoff data5. Continuous wavelet and discrete orthogonal multi-resolution analysis is used to predict the non-stationarity of karstic watersheds6. The wavelet-based nonlinear rainfall-runoff modeling to forecast floods in a river basin is also studied7. Investigation is carried out on neural-wavelet network for the prediction of groundwater level8. An attempt made on comparative study between ANN and ANFIS model in the prediction of groundwater level of the thurinjapuram watershed9. From the detailed literature and to the. best of our knowledge, no research has been published on CWTFT with ANN and ANFIS for groundwater level prediction and forecasting with various hydrological input parameters. The main objective of this research work is to compare the hybrid CWTFT-ANFIS model with ANFIS, ANN, WT-ANFIS, WT-ANN and CWTFT-ANN models on monthly groundwater level prediction and forecasting at Top, Middle and End reaches of Lower Bhavani River Basin, Tamilnadu, India. Materials and Methods Bhavani Basin is the fourth largest sub basin in a Cauvery Basins with cumulative area of 6500km2.The western part is fully covered with hilly terrain boundary, northern side of the basin is surrounded by discontinuous hills boundary, south-eastern part is covered with flat terrain boundary. It has two sub basins, upper bhavani with 4100 km2 area and lower bhavani with 2400 km2area coverage, observed annual average precipitaiton is about 750 mm. The present study area is coming under heavy abstracting of groundwater for the irrigation,.

(2) 2115. INDIAN J. MAR. SCI., VOL. 46 , NO. 10, OCTOBER 2017. domestic and industrial usage. The past trend of groundwater fluctuation is clearly indicate that the demand increases with decline in groundwater table which is further leads in heavy distress conditon to the exisiting aquifer system. It is essential to understand the pattern of the groundwater potential and supply towards the demands. This shows the importants of. management policies towards the effective utilization of groundwaer system in the study area. The layout of the study area is shown in Fig.1. This research work is carried out through detailed literature reviews and collection of data pertaining to model development from Public shown in Fig.2 in order to predict the groundwater distribution based on the duration of prediction, groundwater discharge and groundwater recharge during 2009 to 2015. The data set collected are groundwater level fluctuation for the design period on monthly basis, lithological data, meteorological data, land use pattern and discharge in the basin at different reaches of the study area.. Fig. 1 – Study Area: Lower Bhavani River Basin. Works Department (Groundwater and Surface water Data centre, Tharamani, Chennai). After collecting the required monthly stress data from 2009 to 2015, it is scrutinized based detailed study, field application and sub basin information of groundwater system in LBRB. Based on the field constraints the input paramters are considered as, Duration in which the data collected, precipitaion, Groundwater discharge and Groundwater recharge. Groundwater fluctuation at particular duration is predicted as a output parameter by the identified soft computing techniques like ANN, ANFIS, WT-ANN, WTANFIS, CWTFT-ANN and CWTFT-ANFIS. Statistical indices are included to identify the best prediction possible by the each techniques. Based on the performance of each model during the prediction process, one such model is identified as a optimum, which is further used for forecasting process to next one time stress level. The main sources for groundwater recharge is through surface water, precipitation, stream flow, lakes storage, reservoirs storage, artificial recharge occurs through excess irrigation and seepage from canals. For modeling of groundwater system, hydrological variables like rainfall, evapo-transpiration, humidity, wind speed, runoff with the groundwater fluctuation and its physical interaction are play a vital. So these variables are considered for the model development which is highly nonlinear, stochastic and complex in nature10. Nine observation wells were identified (three per reach) at different reaches of the study area as. Fig. 2 – Location of Rain gauge stations and observation well. To evaluate the best prediction of all identified soft computing models, statistical indices R-Squared (R2), mean squared error (MSE), Root mean square error (RMSE), Pearson correlation coefficient (PCC) and Mean Absolute Error (MAR) are performed. These indices are useful to understand the goodness fit between the observed and calculated values of groundwater level fluctuation at different reaches of the study area. This measure indicates the ratio between the explained variations to the total variation. It deviates from 0 < r2 < 1, which depicts the strength of the linearity associated between observed and calculated variables. The mathematical relationship is given by the following formula: 2  1   (1) R 2    * x  x  * ( y  y) / ( *  )   N . . i. i. x. x.  . Where N is the number of observations made, xi is the observed value yi is the predicted value at the time level of i, y is the mean of predicted values, σx is the standard deviation of observed values, and σy is the standard deviation of predicted values..

(3) 2116. VETRIVEL & ELANGOVAN: APPLICATION OF ANN AND ANFIS ON MONTHLY GROUNDWATER LEVEL. It measures on centre of distribution of variables is associated with an error. The mathematical relationship is given by the following formula: MSE (t ) . k 1 k f i ( xi  t ) 2   pi ( xi  t ) 2  n i 1 i 1. sum of inputs to a processing layers are arrived and compared with threshold value. Working process of ANN is detailed in the following Fig.4.. (2). MSE(t) is a weighted average of the squares of the distances between t according to the relative frequencies of weight factors. It measures the difference between values of predicted by a model and the values actually observed from the field. The mathematical relationship is given by the following formula: n. RMSE . (X i 1. obs,i. Fig. 4 – Graphical Representation of neurons in ANN.  X mod el ,i ) 2. (3) n. Where Xobs is observed values and Xmodel is modeled values at time i. It measures the strength and the direction of a linear relationship between observed and calculated variables. The mathematical relationship is given by the following formula: n xy  ( x)( y ) (4) r n(. x. 2. )(.  x). 2. n(. y. 2. )(.  y). 2. In recent year’s application of ANN have been widely used to time series forecasting process, pattern recognition and process control in many areas of science and engineering11. Based on the literature, ANN has served as an effective tool in modeling virtually for any nonlinear function with a minimum expected degree of accuracy. ANN does not require the complex nature or constrained behavior of the fundamental process for the analysis. This creates ANN is a smart tool for modeling of groundwater table fluctuations. A systematic architecture for ANN is shown in the following Fig.3 for the model development.. Where X is the input units, W is the weighting factors and f(Y) is the output obtained from the input vectors. Further the activation signal is passed through a mathematical transformation function in order to create a proceeding signal to processing units in the next layer. Supervised Training of an ANN is a mathematical practice to optimize the weights and threshold values of interconnection by using limited available data. The process of optimization routines is used to determine the required number of hidden layer and its transfer functions. Back propagation algorithm serve as a most popular network for hydrological modeling in multi-layer perception (MLP). Systematic back propagation algorithm has used to estimate the network parameters12. A more number of empirical relationships between the training samples and the connection weights need to be evaluated in order to ensure a good generalization ability of an ANN model13. A sigmoid function is used as an activation function for both hidden and output layers for the model development. This function f(x) is given by the following relationship: 1 (5) f ( x)  1  exp(  x) a. x   w ji mi   j. j= 1 to n. (6). x   w jk p j   k. k= 1 to I. (7). i 1 a. Fig. 3 – ANN Architecture for model development. j 1. This type of network is associated with interconnected group of artificial neurons / processing units are arranged in a layered system like input layer, hidden layer and an output layer. Input layer is consisting of normalized values of identified input values. The hidden and output layers are well connected with the preceding layer by weighting factors. Cumulative of all weighted. Where, ‘a’ is number of input nodes, ‘n’ is number of hidden nodes, ‘i' is number of output nodes, ‘m’ is input node value, ‘p’ is hidden note value, ‘w’ is synaptic weight and ‘σ’ is threshold. In addition, ability of ANN is used to explore the nonlinearity between the input and output data and then to generalize the results to the other parameters under consideration14. Present study is.

(4) INDIAN J. MAR. SCI., VOL. 46 , NO. 10, OCTOBER 2017. employed with three layer feed forward neural network with a standard back propagation algorithm for training, and the number of hidden neurons is optimized based on trial and error approach. Back-propagation neural network has two phases. Phase I : training input pattern is presented to the network input layer, Phase II: The network then propagates the input pattern from layer to layer until the output pattern is generated by the output layer. If the generated pattern is different from the desired output, an error is calculated and then propagated backwards through the network from the output layer to the input layer. The weights are modified according to the fitness and error propagation. Data pertaining to model development is divided in to three phases: calibration/training, validation and testing. Data validation and test data are used to determine the structure of the neural network15. The network is trained with Levenberg-Marquardt back propagation algorithm (trainlm) or scaled conjugate gradient back propagation (trainscg) according to the enough memory condition. Mean squared error and Regression R values are used to correlate between output and targets values. Training process is automatically get stop when increase in the mean square error of the validation samples. Basically the structure of Adaptive neuralfuzzy network is the combined form of neural networks (NN: capable of training property) and fuzzy Inference systems (FIS: capable of inference ability during uncertain situations)14. ANFIS was originally created by Jang (1993), it has human-like proficiency with in a specific constraints and the training process is derived from the neural network concept16. The main advantage of fuzzy logic is explicit knowledge representation with simple if-than relationships between the constrained parameters9. ANFIS consist of two distinct Fuzzy inference system i.e., Mamdani and Sugeno. Sugeno-type of FIS is integrated with neural networks and serves to be the best efficient system and perform well in optimization process, adaptive techniques, and control problems, especially for dynamic non-linear system of interconnected constrains17. ANFIS is a data driven approachthrough neural network for the approximate solution to the hydrological anlaysis. ANFIS structure consist of veriety of layers like, fuzzification, inferences process, defuzzification and cumulative output aredetailed in the Fig.5.. 2117. Fig. 5 – A Typical ANFIS architecture. Where I1, I2 and I3 are the inputs and Y is the final output, C1, C2, C3 and C4are the linguistic label (Low, Medium, High and Very High) associated with the node function. The present study is carried out with supervised learning as shown in Fig. 6, in which each input vector has a corresponding desired output vector. During training process, the input vectors are presented to the network which further results in output vector. The actual output vector is compared with the target output in order to find the existance of error signals which is used for adjustment of weights between the parameters until the actual output matches the desired (target) outputs.. Fig. 6 – Network Representation of Supervised Learning. The process of ANFIS is processed from layer 1 to layer 5 movement. The input data for the present study are in qualitative form, so these data must be fuzzified by relative membership functions. In Layer 1, Input values are fuzzified according to the mebmership fucntions (Mfs: Triangular, Trapezoidal, Gaussian,Gbell and splin-based etc.,). During this, the data are fuzzified in to fuzzy subset in order to cover the whole deviation of collected data. The subset is based on the seasonal variation and hydrological cycle of the study area. On the basis of inter relation between fuzzy inputs and outputs, fuzzy rules for the analysis are generated. In Layer 2&3: Inference process in which the rules and member ship function are applied.The result obtained from.

(5) 2118. VETRIVEL & ELANGOVAN: APPLICATION OF ANN AND ANFIS ON MONTHLY GROUNDWATER LEVEL. the analysis is in the form of fuzzy set. This is defuzzified to get a required output by centroid method of defuzzification. In Layer 4&5: cumulative output is defuzzified to bring know output for further prediction and correlation process. Wavelet transform is a mathematical function which is used to decompose the continuous time signal in to a time scale illustration process with their relationships18. Here the data series is broken down by the transformation functions to its ‘wavelets’19. It is well suitable for long time intervals with low-frequency information and shorter intervals with high-frequency information. It is adaptable to data like trends, breakdown point, and discontinuities signal analysis techniques. Groundwater level fluctuation is one of such time series data which is to be decomposed in order to obtain the best performance of identified models during preprocessing of data. Continuous Wavelet Transform is the sum of all time of the signal multiplied by scaled, shifted form of wavelet function ‘’. Mathematical representation of CWT is given by, . . M(x.y) f(t) x,y (t ) dt. (8). -. where f (t ) is the signal pertaining to model analysis. (t) is the mother wavelet. In 1 * t  y  which, x,y (t )  (9)    x  x  where * represents complex conjugation. This equation give a details on how a function f (t ) is decomposed into a set of basis functions called as wavelets. is a window. A(k ) . 1 n. i 0 x(i)e n 1. k  j 2 i n. (12). Where k=0,1,2,…n-1 This allows the computation of the spectra from discrete-time data of N samples by satisfying the Nyquist criterion. Fast Fourier Transforms (FFT) are fast Discrete Fourier Transform algorithms which is useful if ‘n’ is a regular power of 2 (n=2p). Combined effect of Continuouts Wavelet Transformation with Fast Fourier Transform (CWTFT) result in high performance during data pre-processing. Results and Discussion This section analyzes the results obtained from data pre-processing, ANN, ANFIS, WTANN, CWTFT-ANN, WT-ANN and CWTFTANFIS models. 70% of collected data are used for calibration / Training process through which weighted sum and threshold values are optimized and remaining dataset is used for testing process. In order to develop the optimum performance of ANN and ANFIS models, the original data was decomposed into a series of details by using a discrete wavelet transformation which turns the original time series data in to a many lower resolution components2. All the identified parameters are decomposed with various wavelets i.e., Haar, Daubechies (db2, db4) and imported to ANN and ANFIS model prediction process. After many trials it was found that, for groundwater fluctuation time series data, the optimum denoised signals are obtained by using Wavelet db4 at 5th level under Rigorous SURE thresholding method is detailed in the Fig.7.. function called the mother wavelet, ‘x’ is a scale and ‘y’ is a translation.If  is given by,.    M   d ( )      . 2. (10). then ‘f’ is reconstructed by inverse wavelet transform which is givenby, . f (t )  M  1. . . . 0. M ( x, y )  x, y (t ) dy. dx x2. (11). The results of the CWT are consist of many wavelet coefficientswhich is function of scale and position. The Fourier Transform for the discrete signal is known as Discrete Fourier Transform (DFT) which is repsented by the follwing mathematical relationships.. Fig. 7 – Wavelet approximations and details of groundwater level fluctuation time series decomposed using db4 wavelet at level 5.

(6) 2119. INDIAN J. MAR. SCI., VOL. 46 , NO. 10, OCTOBER 2017. All the identified parameters are decomposed with Continuous Wavelet Fast Fourier Transform in order to derive the best performance of ANN and ANFIS models to predict the groundwater fluctuation time series data. Various CWTFT wavelets are incorporated to identify the best decomposition level i.e., morl, morlex, mexh and paul at different parameters from 1 to 6. After many trials, it was found that, the CWTFT using morl6 performs better under dyadic synthesis method which results in least relative error. The details of decomposition are shown in Fig.8.. Fig. 8 – CWTFT approximations and details of groundwater level fluctuation time series decomposed using morl6. Comparative Prediction of Groundwater Level by the models The comparative prediction by the conventional ANN, ANFIS, over WT-ANN, WTANFIS, CWTFT-ANN and CWTFT-ANFIS models are derived based on average error of prediction of each identified model. The correlation statistics are used to evaluate the linear correlation between the observed and the computed water table. Table 1 details the average error of each model under different membership functions. Table 2 represents the overall goodness fit to the observed and predicted values of groundwater fluctuation by the each model at different reaches during prediction process. From the results, in order to find the best model for forecasting process, a comparative prediction and overall percentage of improvement on one model over conventional are evaluated. Higher end of CWTFT-ANN prediction were observed in top and middle reaches of the study area and best performance by CWTFT-ANFIS were observed in end reach prediction is shown in Fig.9.. Table 1 – Average Error during prediction process by the models (ANFIS). Model. Well Number. Membership Functions trimf. trapmf. gbellmf. gauss2mf. ANFIS. 63103. 0.90676. 0.64293. 0.77866. 0.50405. CWTFTANFIS. 63103. 0.87045. 0.51591. 0.46288. 0.55979. WTANFIS. 63103. 0.79395. 0.45443. 0.41197. 0.45872. ANFIS. 63104. 1.2548. 1.0121. 0.98401. 0.82422. CWTFTANFIS. 63104. 1.0378. 0.89292. 0.74513. 0.66282. WTANFIS. 63104. 0.88232. 0.79903. 0.49705. 0.58775. ANFIS. 63105. 0.8792. 0.73359. 0.98322. 0.72849. CWTFTANFIS. 63105. 0.78496. 0.60302. 0.45912. 0.55412. WTANFIS. 63105. 0.7987. 0.56259. 0.37269. 0.48389. ANFIS. 63325. 1.3183. 1.4604. 2.6055. 1.2374. CWTFTANFIS. 63325. 1.3183. 1.4604. 2.6055. 1.2374. WTANFIS. 63325. 0.62502. 0.63972. 1.181. 0.54074. ANFIS. 63328. 1.3475. 1.5007. 1.6961. 1.5549. CWTFTANFIS. 63328. 1.0867. 1.1475. 1.6668. 1.022. WTANFIS. 63328. 1.0168. 1.0781. 2.3543. 1.0028. ANFIS. 63006. 0.89301. 1.2558. 1.041. 1.3054. CWTFTANFIS. 63006. 0.74698. 1.0609. 0.66222. 1.0651. WTANFIS. 63006. 0.7153. 1.0905. 1.1046. 0.89. ANFIS. 63321. 1.527. 1.2714. 1.67. 1.512. CWTFTANFIS. 63321. 1.3306. 1.2071. 1.4851. 1.2259. WTANFIS. 63321. 1.1735. 1.1185. 1.3717. 1.1382. ANFIS. 63326. 1.6008. 1.255. 1.2704. 1.28. CWTFTANFIS. 63326. 1.5267. 1.2869. 2.1861. 1.204. WTANFIS. 63326. 1.4295. 1.2426. 1.5378. 1.2212. ANFIS. 63327. 1.3183. 1.4604. 2.6055. 1.2374. CWTFTANFIS. 63327. 1.4883. 1.1507. 1.0872. 1.1288. WTANFIS. 63327. 1.3583. 1.058. 0.998. 1.0387.

(7) 2120. VETRIVEL & ELANGOVAN: APPLICATION OF ANN AND ANFIS ON MONTHLY GROUNDWATER LEVEL. Table 2 – Goodness fit by the models during prediction process. 63327 0.8444. (a) Top Reach. 0.4332 0.3955. 0.2938. 0.8743. 0.8823. 63326 0.7744 0.3873 0.4226. 0.1402. 0.7824. 0.804. 63321 0.7643 0.4355 0.4355. 0.4203. 0.7911. 0.7918. 63006 0.917 0.7085 0.5969. 0.6906. 0.9432. 0.9573. 63328 0.807 0.5733 0.5548. 0.5588. 0.9048. 0.9143. 63325 0.8945 0.5906 0.5618. 0.5833. 0.9393. 0.9461. 63105 0.8729 0.2897. 0.9626. 0.9546. 63104 0.9526 0.7819. 0.9722. 0.9698. 63103 0.926 0.9403. 0.4264. ANNWT. 0.4008. ANNCWTFT. 0.8426. ANN. End Reach. 0.8. ANFISWT. 0.9333. ANFISCWTFT. 0.524. ANFIS. Middle Reach. 0.528. Well Number. Top Reach. 0.5128. Reaches. (b) Middle Reach. Fig. 9 – Overall Percentage of improvement by CWTFT over WT Prediction. Based on ratio of prediction performance by CWTFT and WT model, it was found that CWTFT-ANN has best performance during the prediction process (Training and Testing Process) which is further used for the forecasting process. Forecasting of Models From the detailed analysis during training and testing process, CWTFT-ANN found to be best optimum model for forecasting process. The results obtained in different reaches of the study area are detailed in the following Fig.10.The path traced by the predicted model was exactly follows the observed pattern both during training and testing process in top reach.. (c)End Reach Fig. 10 – Prediction and Forecasting of CWTFT-ANN model at different reaches. Conclusions The potential of coupled WT-ANN / ANFIS, CWTFT-ANN / ANFIS models are compared with the conventional ANN and ANFIS model in the process of prediction of groundwater fluctuation at different reaches in Lower Bhavani River Basin. ANFIS method shows a good potential to nonlinear and multivariate problems. ANN is largely dependent on architecture of the.

(8) INDIAN J. MAR. SCI., VOL. 46 , NO. 10, OCTOBER 2017. network which is only obtained through trial and error procedure while such a process is not required in ANFIS model development. Waveletdecomposed data improved the efficiency of the ANN and ANFIS models. Small difference were observed in the process of prediction by CWTFTANFIS and CWTFT-ANN model, but based on the over performance among the models, ANNCWTFT prediction during training and testing process is 15.3% better than the conventional model and abruptly following the exact fluctuations pattern of groundwater in the study area, further this model is used to forecast the fluctuation for next one time step level. Acknowledgements Authors are grateful to Surface Water and Groundwater Data Centre, Public works department, Chennai, Government of Tamilnadu, India for providing necessary data pertaining to model development for the present research work.. 9.. 10.. 11.. 12.. 13.. 14.. References 1.. 2.. 3.. 4.. 5.. 6.. 7.. 8.. Cannas, B., Fanni, A., Sias, G., Tronei, S., Zedda, M.K., River flow forecasting using neural network and wavelet analysis. European Geosciences Union., 2006, pp:234-243. Adamowski, J., Sun, K., Development of a coupled wavelet transform and neural network method for flow forecasting of non-perennial rivers in semiarid watershed. Journal of Hydrology., 390(1-9) 2010:85-91. Hsu., K.C., Li, S.T., Clustering spatial temporal precipitation data using wavelet transform and selforganizing map neural network. Advanced Water Resources., 33(2) 2010: 192-200. Szilagyi, J., Parlange, M. B.,Katul, G. G., and Albertson, J. D., An objective method for determining principal time scales of coherent eddy structures using orthogonal wavelets. Advanced Water Resources., 22(6)199: 561–566. Nakken, M., Wavelet analysis of rainfall–runoff variability isolating climatic from anthropogenic patterns; Environmental. Modeling Software. 14 (4) 1999:283–295. Labat, D., Mangin, A., Ababou, R., Rainfall-runoff relations for karstic springs: multifractal analyses. Journal of Hydrology., 256(20) 2002:176–195 Chou, C.M., Efficient nonlinear modeling of rainfall-runoff process using wavelet compression. Journal of Hydrology., 332(3-4) 2007: 442-455. Nakhaeet, M., Saberi Nasr, A., and Farajzade, R., Investigate the neural-wavelet network in predicting the groundwater level. Fourth conference of water resources management., Amirkabir University of Technology, Tehran. (2011).. 15.. 16.. 17.. 18.. 19.. 2121. Kavitha Mayilvaganan, M., Naidu, K. B., Comparative Study on ANN and ANFIS for the prediction of Groundwater Level of a Watershed. Global Journal of Mathematical Science:Theory and Practical., Vol.3 (2011): 299-306. Amutha, R., Porchelvan, P., Seasonal Prediction of Groundwater Levels using ANFIS and Radial Basis Neural Network. International Journal of Geology, Earth and Environmental Sciences., Vol. 1(2011): 98-108. Nayak, P.C., Rao, Y.R.S., and Sudheer, K.P., Groundwater level forecasting in a shallow aquifer using artificial neural network approach. Water Resources Management., 20(2006): 77-90. Rumellhart, D. E., Hinton, G. E., and Wiliams, R. J., Learning representations by back propagating errors. Nature., 323(1986), 533-536. Maier, H. R., Dandy, G. C., Neural Networks for the prediction and forecasting of water resources variables. Environmental Modeling & Software., 15(1) 2000: 101-124. Zohreh Alipour., Ali Mohammad Akhund Ali., Feraydoun Radmanesh and Mahmoud Joorabyan., Comparison of three methods of ANN, ANFIS and Time series Models to predict groundwater level: (Case Study: North Mahyar plain), Bulletin of Environment, Pharmacology and Life Sciences.,Vol.3(2014) : 128-134. Semko Rashidi., Milad Mohammadan and Koorosh Azizi., Predicting of Groundwater Level Fluctuation Using ANN and ANFIS in Lailakh Plain. Journal of Renewable Natural Resources Bhutan., Vol. 3.1(2015) : 77-84. Kurian, C. P., George, V. I., Bhat, J., andAithal, R. S., ANFIs model for the time series prediction of interior daylight illuminance. AIML Journal., 6(3) 2006: 35-40. Arshdeep Kaur., Amrit Kaur., Comparison of Mamdani-Type and Sugeno-Type Fuzzy Inference Systems for Air Conditioning System. International Journal of Soft Computing and engineering., Vol.2(2012) : 323-325. Daubechies, I., The wavelet transform, timefrequency localization and signal analysis. IEEE transactions of Information, Univerisity of California at San Diego., (1990). Grossman, A., Morlet, J., Decompositions of hardy functions into square integral wavelets of constant shape. Journal of Mathematical Analysis., 15(1984): 723-736..

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