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Chapter 2 Literature Review
This chapter provides a review of the literature relevant to the study presented in this thesis. Firstly, it introduces the background of the multi-model approach which is relevant to its application in the context of rainfall-runoff modelling for river flow forecasting. Secondly, the combination methods and the number of rainfall-runoff models applied in multi-model combination systems are presented. Then, it discusses the uncertainty analysis of the ANN multi-model. Finally, the literature review reveals research gaps which motivated the current research.
Multi-model approach background
Bates and Granger (1969) published their application of combination techniques to economic forecasting. They presented the weighted average methods of combining two separate sets of forecasts. The results show that the combination of forecasts can outperform the individual forecasts. Since then, the advantages of the combination method for improving forecasts have been demonstrated in many fields (e.g. Armstrong, 1989; Palm and Zellner, 1992; Deutsch et al., 1994; Ridley, 1997; Armstrong, 2001; Timmermann, 2005; Atiya, 2008; Coulibaly, 2008; Velázquez et al., 2011; Demargne et al., 2013). Their results indicated that the technique of combination methods can lead to significantly reduced forecast error when compared with that of a single model. No single forecasting method proves to be the most accurate for every data time series, and the best forecasts are often produced by combining forecasting models.
In hydrology, the first combination techniques were investigated by Cavadias and Morin (1986). They applied the three different methods of Granger and Newbold (1977) to the combination of simulated discharges of ten hydrological models. Their results found that combining discharges improved performance by approximately 80% more than the individual simulated discharges. In the combination river flow forecasting system, Shamseldin et al., (1997) compared three combination methods: the simple average method (SAM), the weighted average method (WAM) and the artificial neural network (ANN) method to combine the results obtained from five rainfall-runoff models. The results based on the Nash-Sutcliffe criteria found that the combined outputs were more accurate than the best single individual model and the ANN combination method performed better than the other combination methods. Shamseldin and O’Connor (1999) later developed a real-time model output combination method (RTMOCM) and tested it using three rainfall-runoff models on five watersheds. Their results showed that the combined streamflow output was generally better than the individual models. See and Openshaw (2000) applied a hybrid multi-model approach for river flow forecasting. Four different approaches, namely the hybrid neural network, the simple rule-based fuzzy logic model, the ARMA model and the naive predictions (which use the current value as the forecast) were developed on a time series data from the River Ouse in northern England to provide a hybridized solution for six hours ahead flood prediction. Results show that their purposed approaches were superior to the other individual model developed on the same data set. Xiong et al. (2001) developed the RTMOCM further by introducing a novel concept combination method of the first-order Takagi-Sugeno fuzzy based system, comparing it with three other combination methods (i.e. SAM, WAM and ANN). Abrahart and See (2002) evaluated six alternative methods for river flow forecasting based on two contrasting catchments, namely the River Ouse located in northern England and the Upper River Wype located in Central Wales to improve the multi-model data fusion. These methods are the arithmetic-averaging, the probabilistic method, two different neural network operations and two different soft computing methodologies. They were applied to perform the data fusion. Each set of single model forecasts used in the fusion operation comprised a six-hour-ahead prediction. Their results found that all data fusion methodologies produced improvements and the multi-model data fusion operated better in overall terms in comparison to their individual modelling. Ajami et al. (2006) applied four multi-model combination techniques for streamflow forecasting, namely the simple model average (SMA), the multimodel superensemble (MMSE), modified multi-model superensemble (M3SE), and the weighted average method (WAM). Four model combination techniques were evaluated using the results from the Distributed Model Intercomparison Project (DMIP) for hourly streamflow forecasting. Results revealed that the multi-model approach provides superior to the current single-model simulation.
To improve the rainfall-runoff model performance, Kim et al. (2006) reviewed the combination methods which have been commonly applied in economic forecasting and examined their applicability to hydrologic forecasting. The combination methods were used to improve the accuracy of the existing ensemble streamflow prediction (ESP) forecasting system for forecasting the monthly inflow to the Daecheong Dam in Geum River, Korea. Their results revealed that the combination techniques improved the probabilistic forecasting accuracy of the existing ESP system.
In an ensemble forecast, Georgakakos et al. (2004) developed the multi-model river flow forecasting ensembles employing the simulations produced for the Distributed Model Intercomparison Project (DMIP). Results based on the root mean squared error (RMSE) confirmed that multi-model ensembles are more sophisticated and reliable than the single model ensemble. Ajami et al. (2006) later extended the work of Georgakakos et al. (2004) and Shamselding et al. (1997) by applying several multi-model combination techniques to the streamflow simulation results from the DMIP models. Their study revealed that the multi-model simulations are generally better than any single model simulations and the more sophisticated combination techniques may further improve simulation accuracy.
Since then, many studies have applied this technique (to take advantage of it for improving modelling results (e.g. Duan et al., 2007; Fenicia et al., 2007; Shamseldin et al., 2007; Vrugt and Robinson, 2007; Devineni et al., 2008; Weigel et al., 2008; Viney et al., 2009; Velázquez et al., 2010; Exbrayat et al., 2011; Evsukoff et al., 2012; Fernando et al., 2012; Liang, 2013).
Combination method
The early work of Bates and Granger (1969) demonstrated that combination techniques can help to improve forecast accuracy. More than 200 applications of the combination techniques were reviewed and summarized by Cleman (1989). To date, various combination methods have been applied in many fields (i.e. economics, statistics, business, management, science, industry and, meteorology). In hydrology, there are various linear, fuzzy based, Bayesian model averaging (BMA), non-linear neural network and symbolic regression methods, which have been used for producing the combined discharges. In a recent application, Dae and Kim (2009) have developed and reviewed useful guidelines for selecting an appropriate method for combining river forecasts.
Linear combination methods
Two linear combination methods: SAM (Shamseldin et al., 1997; Timmermann, 2005; Wang et al., 2005; Ajami et al., 2006; Kim et al., 2006; Goswami and O’Connor, 2007; Jeong and Kim, 2009) and WAM (Cavadias and Morin, 1986; Shamseldin et al., 1997; Shamseldin and O’Connor, 1999; Shamseldin and O’ Connor, 2003; Coulibaly et al., 2005; Ajami et al., 2006; Goswami and O’Connor, 2007; Jeong and Kim, 2009; Exbrayat et al., 2011) are the most popular combination techniques used for river flow forecasting. They are also used as a benchmark for comparing the results with other combination methods (e.g. ANN methods, fuzzy based method, and regression methods).
SAM is the simplest method for combining the outputs by weight of the forecast outputs of the individual models. Its accuracy depends on the fact that the different models have the same level of performance results of each individual model, and the number of models involved. Many published studies show that SAM provides an alternative which can perform better than individual forecasts (Makridakis et al., 1982; Makridakis and Winkler, 1983; Cleman, 1989; Shamseldin et al., 1997, Timmermann, 2005).
WAM was first discussed by Bates and Granger (1969). It utilizes the multiple linear regression technique to combine the results obtained from different models, where each model has a different model weight. Cavadias and Morin (1986) in an early application applied the WAM to river flow simulations where they found that the combination method improved the performance of the simulated discharge results. Shameseldin and O’Connor (1999) developed a Real-Time Model Output Combination Method (RTMOCM) based on the structure of the Linear Transfer Function Model (LTFM) and the WAM for three rainfall-runoff models output combinations. Their results indicated that the combined model output of the RTMOCM were generally better than the individual rainfall-runoff models. Coulibaly et al. (2005) found that using WAM for combining three different models can significantly improve the accuracy of the daily reservoir inflow forecast.
Bayesian model averaging method
The Bayesian model averaging (BMA) method has recently been applied as an alternative for combining the forecast outputs. BMA is a technique of statistical postprocessing that reduces the overall model predictions by weighing each individual prediction based on their probabilistic likelihood measures. The better performing prediction receives higher weights than the worse predictions (Duan et al., 2007). Duan et al. (2007) applied the Bayesian averaging model to develop the probabilistic hydrological predictions from a nine-member ensemble of hydrological predictions. The results showed that the BMA model has the advantage of generating more skilful and equally reliable probabilistic predictions than original ensembles. Vrugt and Robinson (2007) applied the BMA method for probabilistic ensemble streamflow forecasting. The results demonstrated that BMA produces more accurate and reliable predictions than other individual watershed models. Recently, Liang et al. (2013) applied the use of BMA in ensemble hydrologic forecasting from two hydrological models, for the Dongwan Basin, China. The results showed that the multi-model ensemble hydrological forecast based on BMA can provide a robust forecast of flood events.
Fuzzy rule-based model
In the combining of models, See and Openshaw (2000) introduced a fuzzy rule-based model in the application of river flow forecasting. This method is based on fuzzy if-THEN rules which transform the individual model forecasts into the multi-model forecasts. Their results are based on the root mean squared error (RMSE) and show that the performances of fuzzy rule-based models were better than other individual model forecasts and integrated approaches. Later, Xiong et al. (2001) applied the fuzzy rule-based model (the first-order Takagi-Sugeno fuzzy system) as a combination method to produce the combination forecasts of five different conceptual rainfall-runoff models. The results demonstrated that the fuzzy rule based model was efficient in enhancing the flood forecasting accuracy. They recommended the use of the fuzzy rule-based model in the combination system for flood forecasting. Abrahart and See (2002) applied six data fusion strategies, including the fuzzy rule-based models, to combine data-driven and physically based hydrological models. These methods were used to produce forecast outputs in two contrasting catchments. The results indicated that the fuzzy rule-based multi-models were better suited to the estimation of flashier behaviour and their operations were better in overall terms, than their individual hydrological modelling.
Artificial neural networks model
Recently, ANN has become a very popular modelling tool in hydrological modelling, generally being used as a competing alternative to the nonlinear rainfall-runoff modelling (e.g. Hsu et al., 1995; Sajikumar and Thandaveswara, 1999; Tokar and Markus, 2000; Shamseldin et al., 2002; Ancil et al., 2004; Jeong and Kim, 2005; Kerem and Kisi, 2006; Ki, 2007; Wang et al., 2009; Izadifar and Elshorbagy, 2010; Wei et al., 2012; Singh et al., 2013). However, there are a small number of studies which intensively consider the development and application of combining simulated river flows (e.g. Shamseldin et al., 1997 and 2007; Xiong et al., 2001; See and Abrahart, 2001; Abrahart and See, 2002; Kim et al., 2006; Jean and Kim, 2009).
ANN was inspired by biological research; its origins are based on the human brain which consists of billions of neural cells that process information. It is a non-linear black-box model and its adaptability and ability to handle complex modelling problems make it very useful. ANNs can help to identify complex non-linear relationships between input and output and can provide rapid and reliable solutions. Their use in combination methods also differs from their other hydrological applications, as the ANNs work synergistically but not competitively with the integral models to produce better river flow simulation. There are various ANN types which can be used in river flow simulations.
Chapter 1 Introduction
1.1 Objectives of the research
1.2 Layout Organisation
Chapter 2 Literature Review
2.1 Multi-model approach background
2.2 Combination method
2.3 Number of rainfall-runoff models applied in multi-model approach
2.4 Uncertainty analysis of the ANN multi-model
2.5 Research Gaps
2.6 Motivations for the Thesis
2.7 Summary
Chapter 3 Study areas and Data
3.1 Catchment description
3.2 Data and sources
3.3 Summary
Chapter 4 Rainfall-runoff models and model efficiency criteria
4.1 Rainfall-runoff models
4.2 Evaluation of model performance
4.3 Summary
Chapter 5 Multi-model approach using ANNs and GEP
5.1 Study areas, data, and rainfall-runoff models
5.2 The combination methods
5.4 Methodology
5.5 Evaluation of model performance
5.6 Results and Discussion
5.8 Summary
Chapter 6 The optimal number of rainfall-runoff models used in ANN combinations
6.1 Introduction
6.2 Knowledge extraction from artificial neural network
6.3 The optimal number of rainfall-runoff models
6.4 Results and discussions
6.5 Summary
Chapter 7 Uncertainty analysis in ANN multi-model combination systems
7.1 Uncertainty analysis
7.2 Modelling performance evaluation
7.3 Results and discussions
7.4 Summary
Chapter 8 Summary, Conclusion and Future Work
8.1 Multi-model approach using ANNs and GEP
8.2 The optimal number of rainfall-runoff models used in ANN combinations
8.3 Uncertainty analysis in ANN multi-model combination systems
8.4 Future Research Directions
References .
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