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Downstream Prediction Using a Nonlinear Prediction Method Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Open Access Hydrol. Earth Syst. Sci. Discuss., 10, 14331–14354, 2013 Hydrology and www.hydrol-earth-syst-sci-discuss.net/10/14331/2013/ Earth System doi:10.5194/hessd-10-14331-2013 HESSD © Author(s) 2013. CC Attribution 3.0 License. Sciences Discussions 10, 14331–14354, 2013 This discussion paper is/has been under review for the journal Hydrology and Earth System Downstream Sciences (HESS). Please refer to the corresponding final paper in HESS if available. prediction N. H. Adenan and Downstream prediction using a nonlinear M. S. M. Noorani prediction method Title Page N. H. Adenan1 and M. S. M. Noorani2 Abstract Introduction 1Universiti Pendidikan Sultan Idris, Perak, Malaysia 2Universiti Kebangsaan Malaysia, Selangor, Malaysia Conclusions References Received: 1 October 2013 – Accepted: 6 November 2013 – Published: 22 November 2013 Tables Figures Correspondence to: N. H. Adenan ([email protected]) J I Published by Copernicus Publications on behalf of the European Geosciences Union. J I Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion 14331 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Abstract HESSD The estimation of river flow is significantly related to the impact of urban hydrology, as this could provide information to solve important problems, such as flooding down- 10, 14331–14354, 2013 stream. The nonlinear prediction method has been employed for analysis of four years 5 of daily river flow data for the Langat River at Kajang, Malaysia, which is located in Downstream a downstream area. The nonlinear prediction method involves two steps; namely, the prediction reconstruction of phase space and prediction. The reconstruction of phase space in- volves reconstruction from a single variable to the m-dimensional phase space in which N. H. Adenan and the dimension m is based on optimal values from two methods: the correlation dimen- M. S. M. Noorani 10 sion method (Model I) and false nearest neighbour(s) (Model II). The selection of an appropriate method for selecting a combination of preliminary parameters, such as m, is important to provide an accurate prediction. From our investigation, we gather Title Page that via manipulation of the appropriate parameters for the reconstruction of the phase Abstract Introduction space, Model II provides better prediction results. In particular, we have used Model 15 II together with the local linear prediction method to achieve the prediction results for Conclusions References the downstream area with a high correlation coefficient. In summary, the results show Tables Figures that Langat River in Kajang is chaotic, and, therefore, predictable using the nonlinear prediction method. Thus, the analysis and prediction of river flow in this area can pro- vide river flow information to the proper authorities for the construction of flood control, J I 20 particularly for the downstream area. J I Back Close 1 Introduction Full Screen / Esc Urbanization and urban growth are essential factors for planners and policy makers be- cause the urbanization pattern has major implications for the hydrological processes. Printer-friendly Version Urbanization can have various effects on certain hydrological problems, such as flood Interactive Discussion 25 prevention in urban areas, allocation of adequate resources in terms of water qual- ity and quantity, and waterborne waste disposal (Hall, 1984). Thus, the problems of 14332 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | urban hydrology involve flood and pollution prevention. However, our study only con- siders flood prevention based on the river flow prediction. If an undeveloped area is HESSD then transformed into a developed area, the conditions of the soil structure will be dis- 10, 14331–14354, 2013 turbed (Hall, 1984). These factors can change the magnitude of the river flow. The 5 volume of runoff will increase significantly with the increase in the magnitude of the river flow due to the impervious areas and the lack of drainage. Hence, downstream Downstream flooding problems exist in urban areas. There are several methods that can be used prediction to estimate the river flow in a watershed that is located in an urban area, such as the empirical and physical process methods. Referring to the empirical method for urban N. H. Adenan and M. S. M. Noorani 10 hydrology research, the behaviour of river flow in the downstream area is important to provide accurate information for the whole river flow (Viesmann and Lewis, 1996). This information can help in planning, development and flood prevention of the downstream Title Page area. The Langat River, which is one of the longest rivers in the state of Selangor, Malaysia, Abstract Introduction 15 is used as a case study. This research focuses on the downstream area at Kajang, which is well-known for experiencing flood hazards. Figure 1 shows the four gauging Conclusions References stations along the Langat River. The Langat River flows from east to southeast, which Tables Figures is from Lui River to Kajang. The total length of the upstream and downstream is about 34.4 km and the downstream area has been identified as a flood risk area (Mohammed J I 20 et al., 2011). Checkpoint 1 (station number 3118445) is located at the Lui River gaug- ing station (upstream) and Checkpoint 2 (station number 2917401) is located at the J I Kajang gauging station (downstream). The Langat River at the Kajang gauging station Back Close has been used for the river flow analysis and prediction using the nonlinear prediction method. This area had a population of 229 655 people in 2000, which increased to Full Screen / Esc 25 342 657 people in 2010 (Department of Irrigation and Drainage Malaysia, 2005). The increase in population in this area reflects the development in the Kajang area. Further- Printer-friendly Version more, the study area is adjacent to an industrial area and pig farms. Flooding in this area can cause damage to the industrial area and pollution in the Langat River basin. Interactive Discussion Thus, studies of the downstream area (Kajang) are important to provide information 14333 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | about the flow downstream. This study was conducted at this point so that the release of water from Checkpoint 2 could be estimated for a certain length of time. The results HESSD of this study could help to identify the preventive measures that could be undertaken in 10, 14331–14354, 2013 this downstream area. 5 The analysis and prediction of river flow could provide the information about the dy- namics of the river flow system. However, the flow of the river is not dependent on Downstream rainfall alone. The characteristics of an area, such as shape, slope, land, soil struc- prediction ture and climate change, can also affect the flow of the river in an area (Viesmann and Lewis, 1996). Thus, the application of stochastic methods is often used to anal- N. H. Adenan and M. S. M. Noorani 10 yse complex natural conditions, such as the river flow. Developments in the study of nonlinear time series analysis is growing with some revolutionary methods. One partic- ular method that provides important findings is known as chaos theory, which explains Title Page that a complex system can be analysed by deterministic methods that use a minimum number of the system’s variables (Islam and Sivakumar, 2002). Several decades ago, Abstract Introduction 15 a number of studies were performed to obtain information on characterizing, modelling and predicting hydrological phenomena as a deterministic system (e.g. Jayawardena Conclusions References and Lai, 1993; Sivakumar, 2000; Ghorbani et al., 2010). The results showed that the Tables Figures river flow prediction and other hydrological processes are in good agreement with the actual data values (Sivakumar, 2003; Regonda et al., 2005; She and Yang, 2010; Khat- J I 20 ibi et al., 2012). In addition, prediction using chaos theory can reveal the number of variables that affect the dynamics of the river flow. J I Studies on river flow analysis and prediction in Malaysia have been done and im- Back Close proved for a variety of purposes, such as providing information for flood prevention. Several methods, such as support vector machine method (Shabri and Suhartono, Full Screen / Esc 25 2012), neural network model (Ahmad and Juahir, 2006) and hydrodynamic modelling (Ghani et al., 2010), have been used for river flow prediction. However, several meth- Printer-friendly Version ods have yet to be explored for the purpose of river flow prediction in Malaysia, such as chaos theory, Bayesian methods and wavelet methods. River flow prediction using Interactive Discussion chaos theory involves a single variable (river flow data) albeit there are other dominant 14334 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | variables affecting river flow prediction. Meanwhile, the Bayesian and Wavelet meth- ods are dependent on a number of dominant variables, such as rainfall, temperature HESSD and soil type. To the best of our knowledge, this is the first attempt to use the for the 10, 14331–14354, 2013 analysis and prediction of river flow in Malaysia. Downstream 5 2 Nonlinear prediction method prediction The nonlinear prediction method (NLP) of chaos theory is used to analyse river flow N. H. Adenan and and predict the future value of the flow. There are two steps in NLP – phase space M. S. M. Noorani reconstruction and prediction. Reconstruction of the phase space uses observed data (one-dimensional) to build the m-dimensional phase space that reflects the dynamics 10 of the river flow (Abarbanel, 1996; Adenan and Noorani, 2013). A scalar time series Title Page x(t) forms a one-dimensional time series: Abstract Introduction {x } = {x ,x ,x ,...,x } (1) i 1 2 3 N Conclusions References where N is the total number of points in the time series that can be transformed into Tables Figures m-dimensional vectors: J I 15 Y t = xt,xt+τ,xt+2τ,...,xt+(m−1)τ (2) J I where τ is an appropriate time delay and m is a chosen embedding dimension (Abar- banel, 1996; Tongal and Berndtsson, 2013).
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