Improving forecasting accuracy of medium and long-term runoff using artificial neural network based on EEMD decomposition
Introduction
One of the important tasks of hydrologists and water resource engineers is to assess and forecast the quantity of water available in a basin over longer periods, for example, months and years, and manage the water resource for many practical applications involving conservation, environmental disposal and efficient water supply (Wang et al., 2013). For such purposes, understanding runoff processes at longer time scales and constructing a long-term runoff forecasting model, for example, are much more important than those at smaller time scales (daily or hourly) (Yang et al., 2005). In the past few decades, mathematical modelling of runoff series, for reproducing the underlying stochastic structure of this type of hydrological process, has been performed extensively (Remesan et al., 2009). For example, the Box-Jenkins time series analysis method comprises auto-regressive (AR), moving average (MA), autoregressive moving average (ARMA), etc. (Box et al., 1994). In recent years, non-linear data-driven models have been introduced and widely used as surrogate in hydrological studies as powerful alternative modelling tools, such as artificial neural network (ANN) (Budu, 2014, Chua and Wong, 2011, Dawson et al., 2002, Dibike and Solomatine, 2001, Lu et al., 2004, Minns and Hall, 2006, Wang et al., 2009). A comprehensive review by ASCE Task Committee on Application of Artificial Neural Networks in Hydrology shows the acceptance of ANN technique among hydrologists (Govindaraju and Artific, 2000a, Govindaraju and Artific, 2000b). ANN has certain advantages in practical applications. For example, ANN models require less information than physically-based models (Sohail et al., 2008a), and they are not like physically-based models which are usually more complex, relying on the skill and experience of the modeler in model calibration (de Vos and Rientjes, 2005). Therefore, the use of ANNs is attractive especially if the interest is solely on making accurate runoff forecasts at a particular location and if the only data available are the time series of flow (Pulido-Calvo and Portela, 2007).
However, despite the good performance of ANN technique when used on their own, there is still room for further improving their accuracy. One new trend is to extract trends and harmonics and eliminate noise from hydrological time series using appropriate data preprocessing techniques (Wu et al., 2010). Hu et al. (2007) developed a rainfall-runoff neural network (RRNN) model using principal component analysis (PCA) as an input data-preprocessing tool, which was found to provide a generally better representation of the rainfall-runoff relationship. Wu et al. (2009) used three data-preprocessing techniques, namely, moving average (MA), singular spectrum analysis (SSA), and wavelet multi-resolution analysis (WMRA), to couple with ANN to improve the estimate of daily flows. Sang et al. (2009) developed wavelet analysis (WA) and maximum entropy spectral analysis (MESA) to identify periods of hydrologic series data. Wu and Chau (2011) employed ANN coupled with SSA for rainfall-runoff modeling. Kisi (2009) proposed the application of a conjunction (neuro-wavelet) for forecasting monthly lake levels, and the results indicated that the suggested model could significantly increase the short and long-term forecast accuracy. Sang et al. (2013) used the improved continuous wavelet transform (CWT) method to reveal the periodic characteristics of several typical hydrological series. Wang et al. (2014) developed sample entropy-based adaptive wavelet de-noising approach for meteorologic and hydrologic time series. Nourani et al. (2013) used wavelet transform to extract dynamic and multi-scale features of the nonstationary runoff time series and to remove noise in nerual network based rainfall-runoff modeling. Wei et al. (2013) developed a wavelet-neural network (WNN) hybrid modelling approach for monthly river flow estimation and prediction.
Recently, an ensemble empirical mode decomposition (EEMD) has been developed by Wu and Huang (2009), which is a new noise assisted data analysis method, and which can overcome the mode mixing drawback of the original empirical mode decomposition (EMD), first introduced by (Huang et al., 1998). EEMD method is different from other traditional decomposition techniques such as the Fourier decomposition and wavelet decomposition, and is an empirical, intuitive, direct and self-adaptive data processing method created especially for non-linear and non-stationary signal sequences (Hu et al., 2013, Huang and Wu, 2008). The hydrologic times series (rainfall processes, runoff processes) have characteristics of nonlinear and non-stationary (Karthikeyan and Nagesh Kumar, 2013). Hence, EMD method can be used to analyze the nonlinear data of hydrology. Several successful applications have been reported in the literature that addressed the use of EMD or EEMD to hydrologic time series. Napolitano et al. (2011) discussed the aspects of artificial neural network in hindcasting of daily stream flow data through EMD. Sang et al. (2012) developed empirical mode decomposition (EMD) and maximum entropy spectral analysis (MESA) in combination to identify periods in hydrologic time series. Motivated by the idea of “decomposition and ensemble”, the original time series can be decomposed into several sub-series, and each sub-series can be forecasted with the purpose of easy prediction tasks, and the final forecasted value can be obtained by summing the forecasted value of each sub-series (Guo et al., 2012, Wang et al., 2013). EEMD has been employed for decomposing rainfall series in rainfall-runoff model based on support vector machine (SVM) (Wang et al., 2013). Di et al. (2014) proposed a new method with four stages, EMD-EEMD-RBFNN-LNN for predicting the hydrological time series, and the results of six cases show that the proposed hybrid prediction model improves the prediction performance significantly and outperforms some other popular forecasting methods.
The purpose of this paper is to assess forecasting accuracy of artificial neural network (ANN) models coupled with ensemble empirical mode decomposition (EEMD) for annual runoff time series. Hence, EEMD is applied to decompose annual runoff time series, then different ANN models are constructed with each sub-series, and the final forecasted value can be obtained by conjunction of these models. The developed models were evaluated using goodness-of-fit statistics and visual comparison of the hydrograph predictions against actual values. To ensure wider applications of conclusions, two reservoirs annual runoff time series from Biuliuhe and Mopanshan in China are investigated.
The rest of the paper is organized as follows: Section 2 introduces the study areas and the background information. Section 3 gives a brief description to basic theories and algorithms of EEMD, ANN and hybrid EEMD-ANN. The model evaluation criteria of forecasting performance are presented in Section 4. The model development, application results, analysis and discussion are described in Section 5. Section 6 states the conclusions.
Section snippets
Study areas and background information
Two case studies are selected for the present model application. The first study area is Biliuhe River, which originates from Qipan Mountain in Liaoning Province, China, passes through Gaizhou, Zhuanghe and Pulandian, and ingresses into Yellow Sea near Xiejiatun. The river catchment approximately covers 2,184 km2, and the river is about 156 km long. The average annual rainfall of Biliuhe catchment is 742.8 mm. The annual runoff data for this study is from 1951 to 2007 at the dam site of Biliuhe
Ensemble empirical mode decomposition (EEMD)
Ensemble empirical mode decomposition (EEMD) (Wu and Huang, 2009) is an enhancement of the empirical mode decomposition (EMD), which is an empirical but highly efficient and adaptive method for processing non-linear and non-stationary time series (Huang et al., 1998, Huang and Wu, 2008). The major idea of EMD is to decompose the original time series data into a finite and small number of oscillatory modes based on the local characteristic time scale (Huang et al., 1998). Each oscillatory mode
Model performance evaluation
In order to evaluate the forecasting ability of the developed models, four main criteria, which have been widely used to evaluate the goodness-of-fit of hydrologic and hydro-climatic models (Legates and McCabe, 1999), are employed for evaluation of level prediction and directional forecasting, respectively.
- (1)
Root mean squared error (RMSE)where and are, respectively, the observed and forecasted runoffs, and N is the number data points considered.
As one of the
Decomposing annual runoff time series using EEMD
By employing the EEMD technique, the two original annual runoff time series are decomposed into several independent IMFs and one residue, respectively. The results are illustrated in Fig. 5, Fig. 6. As can be seen from Fig. 5, Fig. 6, the two original annual runoff time series are decomposed into four independent IMF components in the order from the highest frequency to the lowest frequency, and one residue component, respectively. The IMF1, IMF2 IMF3 and IMF4 components in Fig. 5, Fig. 6 show
Conclusions
In order to improve the forecasting accuracy of medium and long-term runoff, this paper proposes a hybrid forecasting model based on ensemble empirical mode decomposition (EEMD) and three-layer feed-forward ANN model to forecast the annual runoff time series. An ANN model based on the original annual runoff time series is also employed as a benchmark comparison. Based on annual runoff data from Biuliuhe and Mopanshan in China, the models are developed, and four statistical performance
Acknowledgements
This research was supported by Central Research Grant of Hong Kong Polytechnic University (4-ZZAD), Program for Science & Technology Innovation Talents in Universities of Henan Province (13HASTIT034), Science and technology innovation team in Colleges and universities in Henan Province (14IRTSTHN028) and the Henan Province key scientific and technological project (132102110046). We would like to thank the organizing committee of the 3rd International Conference of GIS/RS in Hydrology, Water
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