DOI: 10.9790/2402-1007010115 www.iosrjournals.org 1 | Page IOSR Journal of Environmental Science, Toxicology and Food Technology (IOSR-JESTFT) e-ISSN: 2319-2402, p- ISSN: 2319-2399.Volume 10, Issue 7 Ver. I (July 2016), PP 01-15 www.iosrjournals.org Comparative Study of Wavelet-SARIMA and Wavelet- NNAR Models for Groundwater Level in Rajshahi District Md. Abdul Khalek * and Md. Ayub Ali * * Department of Statistics, University of Rajshahi, Rajshahi-6205, Bangladesh. Abstract: This study compared the application of time series methods for forecasting groundwater levels at nine upazila’s in Rajshahi district, Bangladesh. Accurate and reliable groundwater level forecasting models can help ensure the sustainable use of groundwater. A new method was proposed for forecasting groundwater level by combining the wavelet technique with seasonal autoregressive integrated moving average (SARIMA) and neural network autoregressive (NNAR) model applied to monthly groundwater level. The data were divided into a training dataset (January, 1991 to December, 2009) to construct the models and a testing dataset (January, 2010 to December, 2013) to estimate their performance. The relative performance of the proposed joined wavelet-seasonal autoregressive integrated moving average (W-SARIMA) and joined wavelet-neural network autoregressive (W-NNAR) models was compared to regular SARIMA and NNAR models for monthly groundwater level forecasting. The calibration and validation performance of the models is evaluated statistically, and the relative performance based on the predictive ability of out-sample forecasts is evaluated. The results indicate that the W-SARIMA model is more effective than the W-NNAR model, regular SARIMA and NNAR models. Keywords: Groundwater Level Forecasting; Rajshahi District; W-SARIMA; W-NNAR I. Introduction Water is the tonic of life and is crucial for sustainable development. Earlier, it was considered to be a limitless or at least fully renewable natural resource, but in the recent past, there has been a tremendous pressure on this valuable natural resource mainly due to rapid industrialization, population growth and using dimensionality of water. For an effective management of groundwater, it is important to predict groundwater level fluctuations. Groundwater systems possess features such as complexity, nonlinearity, being multi-scale and random, all governed by natural and/or anthropogenic factors, that complicates the dynamic predictions. Keeping in mind the scarcity of available water resources in the near future and it impending threats, it has become imperative on the part of water scientists as well as planners to quantify the available water resources for its judicial use. Thus, a ready reckoner to monitor the fluctuations in groundwater levels well in advance is the need of the hour to formulate and model the sustainable water management protocols. At the present, there are many groundwater modeling approaches have been applied to forecast groundwater level and its fluctuations, within which, conceptual and physically based models; are the main types, for depicting hydrological variables and characterizing the complex structures of aquifers. Nevertheless, these modeling approaches do have some limitations in practice; for instance, a large number of accurate data (Mohammadi, 2006) is necessary for modeling. Autoregressive moving average (ARIMA) model is one of empirical models with its particular properties allowing generalizations of the process being analyzed. It is a linear prediction method which assumes that the present data is a function of past data and errors (Faruk, 2010). However, the performance and accuracy of the ARIMA model are not always satisfactory, it is also not adequate to apply ARIMA model to forecast groundwater level as the climate and exploitation changes over time greatly. The variation of groundwater level is highly nonlinear because of interdependencies and uncertainties in the hydrogeological process (Suryanarayani et al., 2014). Artificial intelligence techniques have been proved to be the effective methods in virtually modeling for any nonlinear function. To sum up, artificial neural networks (ANNs) and seasonal autoregressive integrated moving average (SARIMA) techniques are all widely used for predicting groundwater level at present, and all these techniques have been proved to be effective methods (Daliakopoulos et al., 2005; Krishna et al., 2008; Adamowski and Chan, 2011).The NNAR model is a relatively innovative method which is computer intensive and generally yields satisfactory results in terms of in-sample and out-of-sample measures after some proper fine tuning of its parameters. It is important not to apply neural network models blindly in “black box” mode but rather to select the parameters of the neural network model wisely by means of traditional modeling skills (Faraway. and Chatfield, 1998). All these models should have been being compared and to be highlighted the better one. Thus, the purpose of this study is to build up several models SARIMA, NNAR and wavelet groundwater level time series data to forecast monthly groundwater level, and to compare their performances among the existing models.