Hydrological wavelet analysis

Author: Wang Wensheng Ding Jing Li Yueqing
Publisher:
Publish Date: 2005-05-01
Features: This book briefly introduces the basic theory and main methods of wavelet analysis, with a focus on discussing the various applications of wavelet analysis methods in hydrology. The main contents include: the basic theory of wavelet analysis, wavelet functions and their construction, wavelet fast algorithms, filtering and denoising of hydrological sequences, complexity description of hydrological processes, multi-time-scale analysis of hydrological systems, singularity and trend analysis of hydrological sequences, hydrological prediction and forecasting, and hydrological random simulation. This book is a monograph in the field of wavelet analysis in domestic hydrology. Its characteristics are novel content, theoretical connection with practice, easy to understand, and convenient for practical analysis and calculation. This book can be used as a textbook and teaching reference for senior undergraduate and graduate students majoring in hydrology, water resources, and environment in universities. It can also be read by senior students, graduate students, and teachers in relevant majors of science and engineering colleges, as well as suitable for use and reference by relevant scientific and technological workers.
Introduction This book briefly introduces the basic theory and main methods of wavelet analysis, with a focus on discussing the various applications of wavelet analysis methods in hydrology. The main contents include: the basic theory of wavelet analysis, wavelet functions and their construction, wavelet fast algorithms, filtering and denoising of hydrological sequences, complexity description of hydrological processes, multi-time-scale analysis of hydrological systems, singularity and trend analysis of hydrological sequences, hydrological prediction and forecasting, and hydrological random simulation. This book is a monograph in the field of wavelet analysis in domestic hydrology. Its characteristics are novel content, theoretical connection with practice, easy to understand, and convenient for practical analysis and calculation. This book can be used as a textbook and teaching reference for senior undergraduate and graduate students majoring in hydrology, water resources, and environment in universities. It can also be read by senior students, graduate students, and teachers in relevant majors of science and engineering colleges, as well as suitable for use and reference by relevant scientific and technological workers.
Table of Contents
Table of Contents
Chapter 1 Introduction 1
1.1 Hydrology and Wavelet Analysis 1
1.2 Brief Introduction to the Development of Wavelet Analysis 1
1.3 Research on the Application of Wavelet Analysis in Hydrology 4
1.4 Content of This Book 8
Chapter 2 Basic Theory of Wavelet Analysis 9
2.1 Continuous Wavelet Transform 9
2.2 Discrete Wavelet Transform 16
2.3 Dyadic Wavelet Transform 17
2.4 Multi-Resolution Analysis 19
Chapter 3 Wavelet Functions and Their Construction 24
3.1 Introduction to Several Basic Wavelet Functions 24
3.2 Introduction to a Class of Dyadic Wavelet Functions 26
3.3 Construction of Orthogonal Wavelet Bases 27
3.4 Biorthogonal Wavelets and Their Construction 37
3.5 Summary 42
Chapter 4 Fast Wavelet Transform Algorithms and Filter Bank Design 43
4.1 Mallat Algorithm 43
4.2 Fast Algorithm Based on Quadratic Splines 48
4.3 ATrous Algorithm 51
4.4 Wavelet Packet Algorithm 53
4.5 Two-Channel Multi-Sampling Filter Bank 56
Chapter 5 Application of Wavelet Analysis in Hydrological Sequence Filtering and Denoising 60
5.1 Application of Wavelet Analysis in Hydrological Sequence Filtering 60
5.2 Wavelet Denoising Methods 63
5.3 Bias-Reduced Least Squares Regression Model Based on Wavelet Denoising 68
5.4 Application of Wavelet Denoising in Estimating the Fractal Dimension of Hydrological Sequences 75
Chapter 6 Research on the Application of Wavelet Analysis in Hydrological Sequence Complexity 79
6.1 Overview 79
6.2 Calculation of Information Coefficient of Hydrological Sequences Based on Wavelet Analysis 80
6.3 Fractal Dimension Estimation Method of Hydrological Sequences Based on Discrete Wavelet Transform 82
6.4 Fractal Dimension Estimation of Hydrological Sequences Based on Continuous Wavelet Transform 87
6.5 Wavelet Estimation of Hurst Coefficient of Hydrological Sequences 89
6.6 Research on the Complexity of Hydrological Sequences Based on Wavelet Denoising 92
6.7 Identification of Chaos in Hydrodynamic Systems Based on Wavelet Transform 95
Chapter 7 Application of Wavelet Analysis in Hydrological Sequence Singularity Detection and Trend Identification 100
7.1 Diagnosis of Hydrological Sequence Singularity Based on the Fractal Dimension Variation Curve of Wavelet Transform Coefficients 100
7.2 Principle of Wavelet Singular Point Identification and Its Application in Hydrological Sequence Singularity Detection 103
7.3 Application of Wavelet Analysis in Trend Component Identification of Hydrological Sequences 110
7.4 Summary 114
Chapter 8 Application of Wavelet Analysis in Multi-Time-Scale Analysis of Hydrological Systems 115
8.1 Wavelet Analysis Method for Multi-Time-Scale Analysis of Hydrological Systems 115
8.2 Multi-Time-Scale Variation Characteristics of Precipitation Time Series 116
8.3 Multi-Time-Scale Variation Characteristics of Annual Runoff 120
8.4 Multi-Time-Scale Analysis of Monthly Runoff 131
8.5 Multi-Time-Scale Analysis of Annual Maximum Flood Peak Flow 134
8.6 Multi-Time-Scale Analysis of Drought and Flood Classification Data 138
Chapter 9 Hydrological System Prediction Methods Based on Wavelet Analysis 142
9.1 Overview 142
9.2 Random Model Based on Wavelet Denoising 143
9.3 Combined Random Model Based on Wavelet Analysis 148
9.4 Combined Model Based on Wavelet Transform and k-Nearest Neighbor Sampling Regression 151
9.5 Wavelet Artificial Neural Network Combined Model 154
9.6 Wavelet Network Model 164
9.7 Chaotic Wavelet Network Model 168
Chapter 10 Application of Wavelet Analysis in Hydrological System Random Simulation 173
10.1 Overview 173
10.2 Introduction to Common Random Models 176
10.3 Random Combined Simulation Method Based on Wavelet Transform 180
10.4 Combined Random Model Based on Wavelet Transform 184
10.5 Kernel Density Estimation Random Model Based on Wavelet Analysis 187
10.6 Nonparametric Solution Set Model Based on Wavelet Analysis 195
10.7 Summary 199
References 201