A weighting function approach for neural network nonlinear time series analysis of satellite

remote sensing of rainstorms

Lisheng Xu, Jilie Ding , and Xiaobo Deng

Satellite Remote Sensing and Nonlinear Sciences Lab

China Meteorological Administration−Atmospheric Sounding Key Laboratory Chengdu University of Information Technology , Chengdu, SC610041, China

Abstract— One of frequently used neural networks, i.e., a radial-based function network (RBFN) with Gaussian activation functions is employed to study the nonlinear time series by carrying out the characterization experiments for a GMS-5 satellite 11μm IR observations of rainstorm process. The proposed methodology mainly uses RBFN to approximate the nonlinear time series signal first; then the characteristics of its weighting functions changed with time are analyzed. The difficulty due to the effects of high noise on the signal processing using neural networks is addressed. Thus, finally a more integrated method combining the neural network analysis with wavelet packet decomposition is introduced. The preliminary results show that the proposed approach for nonlinear time series analysis is efficient and promising.

I. INTRODUCTION

In recent years, extreme weather events, such as severe storms and extreme rainfalls, have been increased likely worldwide, especially over Europe and Asian monsoon regions [1], which have caused, and will still frequently cause great or sudden disasters, with terrible accidents of human lives and economic society in the world. The knowledge of formation and evolution of rainstorms, and their forecasting are crucial to studies of weather, climate, and environment problems. It is difficult to solve the satellite retrieval problems in cloudy atmospheres with rainstorms using the traditional and classical optical retrieval approach. Therefore, it is imperative to develop new and modern retrieval theories and methods for satellite optical remote sensing of storms.

We can imagine that the evolution of storm process is a nonlinear dynamic process, with chaos and fractal properties [2]. Thus, to develop a new and modern satellite remote sensing method to reveal the occurrence and evolution process of severe storms, we would like to combine satellite remote sensing with nonlinear sciences to study the issues.

Chaotic systems are an important class of dynamical systems. Often, the only information we have about such systems is in the form of a time series. The process of analyzing time series constitutes a field of science known as time-series analysis. Its objective is to build a model for the unknown dynamical system that generated the time series.

Chaotic time-series analysis, or nonlinear time-series analysis, cannot be studied satisfactorily by linear time series analysis, which fails to detect any nonlinear correlations present and cannot provide a complete characterization of the underlying dynamics and, thus, describe the nonlinear structure in chaotic time series. However, uncovering the deterministic structure is important because it allows for construction of more realistic and better models and thus improved predictive capabilities.

Over the last two decades many nonlinear time series methods have been developed in the theory of nonlinear dynamics, commonly known as chaos theory. Since artificial neural networks are a high complex nonlinear dynamical system with powerful signal processing capability and have all demonstrated superior performance in many engineering applications, in this paper we would like to use neural networks combined with wavelet analysis to study the nonlinear time series of satellite remote sensing of rainstorm process. The preliminary results show that the proposed approach of neural network weight series combined with wavelet packet decomposition has potential for nonlinear time series analysis with high noise effects.

II. Neural network nonlinear time series prediction

Neural networks have been applied to many areas of statistics, classification and pattern recognition, and time series analysis. In many areas of statistics, especially in time series analysis, neural networks play an important role. The historical development of neural computation is written in some books [3,4].

There are two kinds of time series, i.e., linear time series and nonlinear time series, or chaotic time series. For time series analysis, the very first object of the study is forecasting, which is one of controversial domain and the subject of a tremendous effort in research and development. Time series forecasting can be studied using well-established statistical models, which, however, have some drawbacks as pointed out by Hill et al. [5] and Kajitani et al. [6], thus, are not suitable for nonlinear time series forecasting. Some approaches for nonlinear time series forecasting are commonly used, for example, chaos model, neural network model, and random work model, etc.. Especially, since the last decade in 20 century, a considerable attention has been devoted to dynamical system theory for the study of nonlinear time series. It is worth pointing out that the starting point of dynamical system time series analysis is the determination of past series information to be