A Wavelet-ANFIS Hybrid Model for Groundwater Level Forecasting for Different Prediction Periods

Artificial neural network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) have an extensive range of applications in water resources management. Wavelet transformation as a preprocessing approach can improve the ability of a forecasting model by capturing useful information on various resolution levels. The objective of this research is to compare several data-driven models for forecasting groundwater level for different prediction periods. In this study, a number of model structures for Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), Wavelet-ANN and Wavelet-ANFIS models have been compared to evaluate their performances to forecast groundwater level with 1, 2, 3 and 4 months ahead under two case studies in two sub-basins. It was demonstrated that wavelet transform can improve accuracy of groundwater level forecasting. It has been also shown that the forecasts made by Wavelet-ANFIS models are more accurate than those by ANN, ANFIS and Wavelet-ANN models. This study confirms that the optimum number of neurons in the hidden layer cannot be always determined by using a specific formula but trial-and-error method. The decomposition level in wavelet transform should be determined according to the periodicity and seasonality of data series. The prediction of these models is more accurate for 1 and 2 months ahead (for example RMSE = 0.12, E = 0.93 and R2 = 0.99 for wavelet-ANFIS model for 1 month ahead) than for 3 and 4 months ahead (for example RMSE = 2.07, E = 0.63 and R2 = 0.91 for wavelet-ANFIS model for 4 months ahead).

[1]  G..  A Theory for Multiresolution Signal Decomposition : The Wavelet Representation , 2004 .

[2]  Ozgur Kisi,et al.  Precipitation Forecasting Using Wavelet-Genetic Programming and Wavelet-Neuro-Fuzzy Conjunction Models , 2011 .

[3]  Mehdi Vafakhah,et al.  Application of Several Data-Driven Techniques for Predicting Groundwater Level , 2012, Water Resources Management.

[4]  A Asghari Moghaddam,et al.  FORECASTING SPATIOTEMPORAL WATER LEVELS BY NEURAL KRIGING METHOD IN TABRIZ CITY UNDERGROUND AREA , 2009 .

[5]  Sheng-Tun Li,et al.  Clustering spatial-temporal precipitation data using wavelet transform and self-organizing map neural network , 2010 .

[6]  N. S. Loboda,et al.  Using non-decimated wavelet decomposition to analyse time variations of North Atlantic Oscillation, eddy kinetic energy, and Ukrainian precipitation , 2006 .

[7]  Liang-Cheng Chang,et al.  Application of Optimal Control and Fuzzy Theory for Dynamic Groundwater Remediation Design , 2009 .

[8]  Soichi Nishiyama,et al.  Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool. , 2007, Journal of environmental management.

[9]  Hafzullah Aksoy.  Storage Capacity for River Reservoirs by Wavelet-Based Generation of Sequent-Peak Algorithm , 2001 .

[10]  Ozgur Kisi,et al.  Two hybrid Artificial Intelligence approaches for modeling rainfall–runoff process , 2011 .

[11]  Kourosh Mohammadi,et al.  Groundwater Table Estimation Using MODFLOW and Artificial Neural Networks , 2009 .

[12]  M. Sharp,et al.  Wavelet analysis of inter‐annual variability in the runoff regimes of glacial and nival stream catchments, Bow Lake, Alberta , 2003 .

[13]  Ozgur Kisi,et al.  Stream flow forecasting using neuro‐wavelet technique , 2008 .

[14]  E. Mizutani,et al.  Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence [Book Review] , 1997, IEEE Transactions on Automatic Control.

[15]  Henry C. W. Lau,et al.  A fuzzy multi-criteria decision support procedure for enhancing information delivery in extended enterprise networks , 2003 .

[16]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[17]  Faming Liang,et al.  Explicitly integrating parameter, input, and structure uncertainties into Bayesian Neural Networks for probabilistic hydrologic forecasting , 2011 .

[18]  Chuen-Tsai Sun,et al.  Neuro-fuzzy modeling and control , 1995, Proc. IEEE.

[19]  M. Castellano-Méndez,et al.  Modelling of the monthly and daily behaviour of the runoff of the Xallas river using Box-Jenkins and neural networks methods , 2004 .

[20]  Paul M. Mather,et al.  The use of backpropagating artificial neural networks in land cover classification , 2003 .

[21]  Linda See,et al.  Applying soft computing approaches to river level forecasting , 1999 .

[22]  Jan Adamowski,et al.  Development of a coupled wavelet transform and neural network method for flow forecasting of non-perennial rivers in semi-arid watersheds. , 2010 .

[23]  Turgay PartalT. Partal.  River flow forecasting using different artificial neural network algorithms and wavelet transform , 2009 .

[24]  Vahid Nourani,et al.  Forecasting Spatiotemproal Water Levels of Tabriz Aquifer , 2008 .

[25]  A. Grossmann,et al.  DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE , 1984 .

[26]  Eloise Kendy,et al.  Groundwater depletion: A global problem , 2005 .

[27]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[28]  Jeffrey L. Elman,et al.  Finding Structure in Time , 1990, Cogn. Sci..

[29]  Ioannis K. Nikolos,et al.  Optimal selection of artificial neural network parameters for the prediction of a karstic aquifer's response , 2009 .

[30]  J. Adamowski,et al.  A wavelet neural network conjunction model for groundwater level forecasting , 2011 .

[31]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[32]  Mustafa M. Aral,et al.  Aquifer parameter and zone structure estimation using kernel-based fuzzy c-means clustering and genetic algorithm , 2007 .

[33]  Wensheng Wang,et al.  Wavelet Network Model and Its Application to the Prediction of Hydrology , 2003 .

[34]  Chien-ming Chou.  A Threshold Based Wavelet Denoising Method for Hydrological Data Modelling , 2011 .

[35]  J. Adamowski,et al.  Forecasting Urban Water Demand Via Wavelet-Denoising and Neural Network Models. Case Study: City of Syracuse, Italy , 2012, Water Resources Management.

[36]  E. B. Christopoulou,et al.  The "a trous" nvantelet transform versus clasical methods for the improvement of solar images , 2002, 2002 14th International Conference on Digital Signal Processing Proceedings. DSP 2002 (Cat. No.02TH8628).

[37]  Mahmut Firat,et al.  Comparative analysis of fuzzy inference systems for water consumption time series prediction. , 2009 .

[38]  Paulin Coulibaly,et al.  Groundwater level forecasting using artificial neural networks , 2005 .

[39]  Hitoshi Tanaka,et al.  Developing a hybrid multi‐model for peak flood forecasting , 2009 .

[40]  Holger R. Maier,et al.  The effect of internal parameters and geometry on the performance of back-propagation neural networks: an empirical study , 1998 .

[41]  Hojjat Ahmadi,et al.  Prediction of Daily Pan Evaporation using Wavelet Neural Networks , 2012, Water Resources Management.

[42]  K. Carpenter.  District Chief U.S. Geological Survey , 1985 .

[43]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[44]  J. Adamowski.  Development of a short-term river flood forecasting method for snowmelt driven floods based on wavelet and cross-wavelet analysis , 2008 .

[45]  Robert J. Abrahart,et al.  Letter to the Editor on “Precipitation Forecasting Using Wavelet-Genetic Programming and Wavelet-Neuro-Fuzzy Conjunction Models” by Ozgur Kisi & Jalal Shiri [Water Resources Management 25 (2011) 3135–3152] , 2012, Water Resources Management.

[46]  Ozgur Kisi,et al.  REPLY to Discussion of “Precipitation Forecasting Using Wavelet-Genetic Programming and Wavelet-Neuro-Fuzzy Conjunction Models” , 2012, Water Resources Management.

[47]  L. Shu,et al.  Assessment of Sustainable Yield of Karst Water in Huaibei, China , 2011 .

[48]  Fi-John Chang,et al.  Adaptive neuro-fuzzy inference system for prediction of water level in reservoir , 2006 .

[49]  Shakeel Ahmed,et al.  Forecasting groundwater level using artificial neural networks. , 2009 .

[50]  Ka-Ming Lau,et al.  Wavelets, Period Doubling, and Time–Frequency Localization with Application to Organization of Convection over the Tropical Western Pacific , 1994 .

[51]  A. Cohen,et al.  Wavelets: the mathematical background , 1996, Proc. IEEE.

[52]  O. Kisi,et al.  Wavelet and neuro-fuzzy conjunction model for precipitation forecasting , 2007 .

[53]  O. Kisi.  Neural Networks and Wavelet Conjunction Model for Intermittent Streamflow Forecasting , 2009 .

[54]  Alessandra Fanni,et al.  River flow forecasting using neural networks and wavelet analysis , 2005 .

[55]  Taher Rajaee,et al.  Wavelet and ANN combination model for prediction of daily suspended sediment load in rivers. , 2011, The Science of the total environment.

[56]  F. Anctil,et al.  An exploration of artificial neural network rainfall-runoff forecasting combined with wavelet decomposition , 2004 .

[57]  Vahid Nourani,et al.  A COMBINED NEURAL-WAVELET MODEL FOR PREDICTION OF WATERSHED PRECIPITATION, LIGVANCHAI, IRAN , 2008 .

[58]  Inmaculada Pulido-Calvo,et al.  Improved irrigation water demand forecasting using a soft-computing hybrid model , 2009 .

[59]  Pedro J. Depetris,et al.  Discharge trends and flow dynamics of South American rivers draining the southern Atlantic seaboard: An overview , 2007 .