A hybrid neural network and ARIMA model for water quality time series prediction

https://doi.org/10.1016/j.engappai.2009.09.015Get rights and content

Abstract

Accurate predictions of time series data have motivated the researchers to develop innovative models for water resources management. Time series data often contain both linear and nonlinear patterns. Therefore, neither ARIMA nor neural networks can be adequate in modeling and predicting time series data. The ARIMA model cannot deal with nonlinear relationships while the neural network model alone is not able to handle both linear and nonlinear patterns equally well. In the present study, a hybrid ARIMA and neural network model is proposed that is capable of exploiting the strengths of traditional time series approaches and artificial neural networks. The proposed approach consists of an ARIMA methodology and feed-forward, backpropagation network structure with an optimized conjugated training algorithm. The hybrid approach for time series prediction is tested using 108-month observations of water quality data, including water temperature, boron and dissolved oxygen, during 1996–2004 at Büyük Menderes river, Turkey. Specifically, the results from the hybrid model provide a robust modeling framework capable of capturing the nonlinear nature of the complex time series and thus producing more accurate predictions. The correlation coefficients between the hybrid model predicted values and observed data for boron, dissolved oxygen and water temperature are 0.902, 0.893, and 0.909, respectively, which are satisfactory in common model applications. Predicted water quality data from the hybrid model are compared with those from the ARIMA methodology and neural network architecture using the accuracy measures. Owing to its ability in recognizing time series patterns and nonlinear characteristics, the hybrid model provides much better accuracy over the ARIMA and neural network models for water quality predictions.

Introduction

The water quality is a subject of ongoing concern. Deterioration of water quality has initiated serious management efforts in many countries. Most acceptable ecological and water related decisions are difficult to make without careful modeling, prediction and analysis of river water quality for typical development scenarios. Accurate predictions of future phenomena are the lifeblood of optimal water resources management in a watershed. Computer science and statistics have improved modeling approaches for discovering patterns found in water resources time series data. Much effort has been devoted over the past several decades to the development and improvement of time series prediction models. One of the most important and widely used time series model is the autoregressive integrated moving average (ARIMA) model (Shahwan and Odening, 2007).

Over the past several years, nonlinear models have been proposed as alternative techniques, as i.e. in Pisoni et al. (2009), where nonlinear autoregressive models (NARX) and artificial neural networks (ANNs) have been applied for environmental prediction. Zhang and Hu (1998) summarized the different applications of neural networks for predictions. There are a number of studies in which neural networks are used to address water resources problems. Maier and Dandy (2000) reviewed recent papers dealing with the use of neural network models for the prediction and forecasting of water resources variables. Flood and Kartam (1994), Hassoun (1995) and Rojas (1996) have used feedforward networks with sigmoidal-type transfer functions for the prediction and forecasting of water resources variables. Chau (2006) has reviewed the development and current progress of the integration of artificial intelligence into water quality modeling. Hatzikos et al. (2005) utilized neural networks with active neurons as a modeling tool for the prediction of seawater quality indicators like water temperature, pH, dissolved oxygen (DO) and turbidity. Palani et al. (2008) demonstrated the application of ANNs to model the values of selected seawater quality variables, having the dynamic and complex processes hidden in the monitored data itself.

Most of the studies reported above were simple applications of using traditional time series approaches and ANNs. Many of the real-life time series are extremely complex to be modeled using simple approaches especially when high accuracy is required. There have been several studies suggesting hybrid models, combining the ARIMA model and neural networks. Su et al. (1997) used a hybrid model to predict a time series of reliability data with growth trend. Their results showed that the hybrid model produced better predictions than either the ARIMA model or the neural network by itself. Zhang (2003) proposed a hybrid ARIMA and ANN model to take advantage of the two techniques and applied the proposed hybrid model to some real data sets. He concluded that the combined model can be an effective way to improving predictions achieved by either of the models used separately. Jain and Kumar (2006) proposed a hybrid approach for time series forecasting using monthly stream flow data at Colorado river. They indicated that the approach of combining the strengths of the conventional and ANN techniques provides a robust modeling framework capable of capturing the nonlinear nature of the complex time series and thus producing more accurate forecasts.

In the present paper, a hybrid approach, combining seasonal ARIMA model and neural network backpropagation model, is developed to predict water quality time series data. The use of combined models in water quality time series data could be complementary in capturing patterns of data sets and could improve the prediction accuracy. The motivation behind this hybrid approach is largely due to the fact that a water quality problem is often complex in nature and any individual model may not be able to capture different patterns equally well. The objectives of the present study are to: (1) develop a hybrid model, an ANN and an ARIMA model, to predict water quality time series data, (2) assess the performance of each modeling approach using observed data versus predicted data and (3) evaluate the predictive performance of hybrid model in comparison to ANN architecture and ARIMA model using accuracy measures.

Section snippets

Study area and water quality data

The Büyük Menderes basin, 3.2% of the total area of the country, is located in southwest Turkey and it drains a total area of 25,000 km2 into the Aegean Sea (Fig. 1). Annual rainfall ranges between 350 and 1000 mm and total mean annual evaporation, measured by Class A pans, is 2122 mm. Precipitation occurs mainly in the winters while during the summer irrigation period, there is very little rain. The main river of the basin is the Büyük Menderes river. The land use in the Büyük Menderes river

ARIMA modeling

In the present study, several trails were made to choose the optimal ARIMA model parameters. The model parameters that satisfy the statistical residual diagnostic checking were chosen in the ARIMA forecasting model. The ARIMA models were used to predict monthly water quality time series over the period between 1996 and 2004. The water quality data for the period between 1996 and 2001 were used for model calibration and to obtain the best model fit for each water quality parameter. The data for

Conclusions

A new approach of modeling water quality time series, capable of exploiting the advantages of both the conventional methods and the ANNs, was proposed. An empirical comparative evaluation of the performance of hybrid model to the ANN and ARIMA modeling approach was presented for river water quality predictions. The proposed modeling framework gradually receives the data filtered using the ARIMA models and then the residuals from the ARIMA approach were analyzed by ANNs to capture the

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