Reconstruction of Dynamical Forecasting Model between Western Pacific Subtropical High Area Index and Its Summer Monsoon Impact Factors Based on the Improved Self-Memorization Principle

Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2014, Article ID 867632, 12 pages http://dx.doi.org/10.1155/2014/867632 Research Article Reconstruction of Dynamical Forecasting Model between Western Pacific Subtropical High Area Index and Its Summer Monsoon Impact Factors Based on the Improved Self-Memorization Principle Mei Hong,1 Ren Zhang,1 Xi Chen,1 Shanshan Ge,1 Chengzu Bai,1 and Vijay P. Singh2,3 1 Research Center of Ocean Environment Numerical Simulation, Institute of Meteorology and Oceanography, PLA University of Science and Technology, P.O. Box 003, No. 60, Shuanglong Road, Nanjing 211101, China 2 Department of Biological and Agricultural Engineering, Texas A & M University, College Station, TX 77843, USA 3 Zachry Department of Civil Engineering, Texas A & M University, College Station, TX 77843, USA Correspondence should be addressed to Mei Hong; Received 19 June 2014; Accepted 15 November 2014; Published 10 December 2014 Academic Editor: Stefan Balint Copyright © 2014 Mei Hong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. With the objective of tackling the problem of inaccurate long-term western pacific subtropical high (WPSH) forecasts, based on the concept of dynamical model reconstruction and improved self-memorization principle, a new dynamical forecasting model of WPSH area (SI) index is developed. To overcome the problem of single initial prediction value, the largest Lyapunov exponent is introduced to improve the traditional self-memorization function, making it more appropriate to describe the chaotic systems, such as WPSH; the equation reconstruction by actual data is used as its dynamical core to overcome the problem of relatively simple dynamical core. The developed dynamical forecasting model of SI index is used to predict WPSH strength in the long term. Through 10 experiments of the WPSH abnormal years, forecast results within 25 days are found to be good, with a correlation coefficient of about 0.80 and root mean square error under 8%, showing that the improved model has satisfactory long-term forecasting results. In particular the aberrance of the subtropical high can be drawn and forecast. It is acknowledged that mechanism for the occurrence and development of WPSH is complex, so the discussion in this paper is therefore exploratory. 1. Introduction The western pacific subtropical high (WPSH) is one of the most important components of the East Asian Summer Monsoon (EASM) system [1]. The intensity and position of WPSH show complex seasonal evolutions and the changes in them greatly affect the occurrence of rainy season in China, including floods, droughts, and heavy rains [1]. For example, when WPSH reaches the northernmost position, especially in summer, it significantly influences rainfall over China and Japan [2]. Owing to its dominance on the East Asian climate, WPSH has become one of the leading topics of interest in atmospheric sciences [3–5]. Over the past decades, much effort has gone into uncovering the forecast of the WPSH [6], especially the forecast of abnormal WPSH [7, 8]. Current forecasts for the WPSH can be divided into two categories: numerical forecasts and statistical forecasts. Numerical forecasts are widely used throughout the world; examples include the numerical forecast products of the European Centre for Medium-Range Weather Forecasts Model [9] and the Japanese FUFE502 numerical forecast products. However, numerical forecasts require field boundaries and the complex computations and low efficiency mean that the results are very unstable. Numerical forecast products have better results for large-scale weather systems, but for mesoscale weather systems, such as the WPSH, the results are less good and the forecast time is short. Statistical methods, in contrast, have achieved some success in forecasting the WPSH. These methods can use historical data and the computation is simple. However, there are some inherent flaws in statistical methods. Using neural 2 networks as an example, it is difficult to objectively determine the number of hidden layer neurons and the training process tends to predict a local optimum, which will limit the forecast accuracy [10]. Moreover, the reliability of all these methods is gradually reduced with increasing forecast time, so the forecast results and credibility become very low after two weeks [11]. Statistical forecasting products and numerical forecasting products both have some degrees of bias. In particular, error is more obvious in WPSH anomalies and longterm forecasting [3]. So the prediction of unusual activities of WPSH within season and the long-term trend forecast of WPSH has become difficult problems in recent years. A statistical-dynamical model of a weather system is reconstructed from actual data and can be used to describe the physical mechanisms of a complex weather system. Concerning the questions of local convergence of errors, Zhang et al. [12] introduced genetic algorithms (GA), which is widely used in a lot of fields [13, 14], to improve the determination of root efficiency of model parameters. On that basis, Bai et al. [15, 16] carried out research on the reconstruction of a nonlinear statistical-dynamical forecast model of the WPSH and achieved good results. However, the dynamical prediction equations derived by Zhang et al. [12] and Bai et al. [15, 16] greatly depend on the initial value, so the long-term forecast over 15 days diverged significantly and the results were not satisfactory. For the long-term forecast, the model should be improved. Cao [17] proposed the self-memorization principle, transforming the dynamical equation into memorization equation in a broader sense, named a differential-integral equation, wherein the memory coefficients can also be determined by actual data. This method has been widely used in prediction problems in meteorology, hydrology, and environmental field [18–20]. Because this method avoids the problem of initial condition in differential equations, it can be introduced to improve the proposed dynamical forecast model. The set of self-memory function is relatively simple [17] and is suitable for cyclical and linear systems. For nonlinear systems, especially chaotic systems, forecast results are unsatisfactory [20]. As the atmosphere and ocean are nonlinear systems, the self-memory function is needed to be modified for nonlinear system modeling. The largest Lyapunov exponent is introduced to improve the traditional self-memorization function. Finally, the improved dynamical forecasting model of WPSH with a new self-memorization function is developed. The improved function not only takes into account the chaotic characteristics of the nonlinear system, but also absorbs the information of past observations. In our study, we (...truncated)