The Analysis of Directional Time Series: Applications to Wind Speed and Direction

ISBN-13: 9780387971827 / Angielski / Miękka / 1989 / 238 str.

Jens Breckling

Opis

Given a series of wind speeds and directions from the port of Fremantle the aim of this monograph is to detect general weather patterns and seasonal characteristics. To separate the daily land and sea breeze cycle and other short-term disturbances from the general wind, the series is divided into a daily and a longer term, synoptic component. The latter is related to the atmospheric pressure field, while the former is studied in order i) to isolate particular short-term events such as calms, storms and oscillating winds, and ii) to determine the land and sea breeze cycle which dominates the weather pattern for most of the year. All these patterns are described in detail and are related to the synoptic component of the data. Two time series models for directional data and a new measure of angular association are introduced to provide the basis for certain parts of the analysis.

Spis treści

I: Wind Data Analysis.- 1. Introduction.- 1.1. Surface Wind Observation.- 1.2. General Weather Pattern.- 1.3. Outline of this Monograph.- 2. The Initial Decomposition.- 2.1. General Background.- 2.2. Robust Filtering.- 2.3. Univariate Filter Study.- 2.4. Multivariate Filter Study.- 2.5. Application to Wind Series.- 2.6. Appendix: Mathematical Details.- 3. The Geostrophic Component.- 3.1. The Geostrophic Wind.- 3.2. Estimation of the Geostrophic Wind.- 3.3. Comparison with the Geostrophic Component.- 3.4. Synoptic States.- 3.5. Appendix: Derivation of the Geostrophic Wind Equation.- 4. The Land and Sea Breeze Cycle.- 4.1. The Nature of the Circulation.- 4.2. Statistical Approach.- 4.3. Land and Sea Breeze Pattern.- 5. Short-Term Events.- 5.1. Meteorological Patterns.- 5.2. Wind Classification.- 5.3. Characteristics of Short-Term Events.- 5.4. Appendix: Removal of Storms.- II: Time Series of Directional Data.- 6. Time Series Models for Directional Data.- 6.1. Circular Variables.- 6.2. The von Mises Process.- 6.3. The Wrapped Autoregressive Process.- 7. Measures of Angular Association.- 7.1. Desirable Properties.- 7.2. Bivariate Angular Distributions.- 7.3. Review of Measures of Association.- 7.4. A Proposal for Vector Valued Time Series.- 7.5. Appendix: Non-von Mises Marginals.- 8. Comparison of Different Measures of Association.- 8.1. Independent Bivariate Directional Data.- 8.2. Time Series of Directional Data.- 9. Inference from the Wrapped Autoregressive Process.- 9.1. Introduction.- 9.2. Equating Theoretical and Empirical Circular Variance (EQ).- 9.3. Corrected EQ-Estimation (EC).- 9.4. Bayes Estimation (BA).- 9.5. Maximum Likelihood Estimation (ML).- 9.6. Characteristic Function Estimation (CF).- 9.7. Numerical Comparison of Estimators.- 10. Application to Series of Residual Wind Directions.- 11. Conclusions and Summary of Results.- List of Symbols.