Hurricane Climatology

Transcription

1 Hurricane Climatology Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page i #1

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3 Hurricane Climatology A Modern Statistical Guide Using R James B. Elsner and Thomas H. Jagger 1 Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page iii #3

4 3 Oxford University Press is a department of the University of Oxford. It furthers the University s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trademark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY Oxford University Press 2013 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. Library of Congress Cataloging-in-Publication Data Elsner, James B., author. Hurricane climatology : a modern statistical guide using R / James B. Elsner and Thomas H. Jagger. pages ; cm Includes bibliographical references and index. ISBN (hardcover : alk. paper) 1. Hurricanes Forecasting Statistical methods. 2. R (Computer program language) I. Jagger, Thomas H., author. II. Title. QC944.E dc Printed in the United States of America on acid-free paper Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page iv #4

5 CONTENTS Preface xiii Part One: Data, Statistics, and Software 1. Hurricanes, Climate, and Statistics Hurricanes Climate Statistics R Organization 8 2. R Tutorial Introduction What Is R? Get R Packages Calculator Functions Warnings and Errors Assignments Help Data Small Amounts Functions Vectors Structured Data Logic Imports Tables and Plots Tables and Summaries Quantiles Plots 28 Bar Plots 28 Scatter Plots 29 v Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page v #5

6 vi Contents 3. Classical Statistics Descriptive Statistics Mean, Median, and Maximum Quantiles Missing Values Probability and Distributions Random Samples Combinatorics Discrete distributions Continuous Distributions Distributions Density Cumulative Distribution Functions Quantile Functions Random Numbers One-Sample Test Wilcoxon Signed-Rank Test Two-Sample Test Statistical Formula Two-Sample Wilcoxon Test Compare Variances Correlation Pearson s Product-Moment Correlation Spearman s Rank and Kendall s τ Correlation Bootstrap Confidence Intervals Causation Linear Regression Multiple Linear Regression Predictor Choice Cross-validation Bayesian Statistics Learning about the Proportion of Landfalls Inference Credible Interval Predictive Density Is Bayes s Rule Needed? Bayesian Computation Time-to-Acceptance Markov Chain Monte Carlo approach JAGS WinBUGS 94 Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page vi #6

7 vii Contents 5. Graphs and Maps Graphs Box Plot Histogram Density Plot Q Q Plot Scatter Plot Conditional Scatter Plot Time Series Time Series Graph Autocorrelation Dates and Times Maps Boundaries Data Types 116 Point Data 116 Areal Data 120 Field Data Coordinate Reference Systems Export Other Graphic Packages lattice ggplot ggmap Data Sets Best-Tracks Data Description Import Intensification Interpolation Regional Activity Lifetime Maximum Intensity Regional Maximum Intensity Tracks by Location Attributes by Location Annual Aggregation Annual Cyclone Counts Environmental variables Coastal County Winds Description Counts and Magnitudes NetCDF Files 156 Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page vii #7

8 viii Contents Part Two: Models and Methods 7. Frequency Models Counts Poisson Process Inhomogeneous Poisson Process Environmental Variables Bivariate Relationships Poisson Regression Limitation of Linear Regression Poisson Regression Equation Method of Maximum Likelihood Model Fit Interpretation Model Predictions Forecast Skill Metrics Cross-Validation Nonlinear Regression Structure Zero-Inflated Count Model Machine Learning Logistic Regression Exploratory Analysis Logit and Logistic Functions Fit and Interpretation Prediction Fit and Adequacy Receiver Operating Characteristics Intensity Models Lifetime Highest Intensity Exploratory Analysis Quantile Regression Fastest Hurricane Winds Exploratory Analysis Return Periods Extreme Value Theory Generalized Pareto Distribution Extreme Intensity Model Intensity and Frequency Model Confidence Intervals Threshold Intensity Categorical Wind Speeds by County Marked Poisson Process Return Levels 216 Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page viii #8

9 ix Contents Covariates Miami-Dade Spatial Models Track Hexagons Spatial Points Data Frame Hexagon Tessellation Overlays Maps SST Data SST and Intensity Spatial Autocorrelation Moran s I Spatial Lag Variable Statistical Significance Spatial Regression Models Linear Regression Geographically Weighted Regression Model Fit Spatial Interpolation Preliminaries Sample Variogram Variogram Model Kriging Uncertainty Time Series Models Time Series Overlays Discrete Time Series Count Variability Moving Average Seasonality Change Points Counts Covariates Continuous Time Series Time-Series Network Time Series Visibility Network Plot Degree Distribution and Anomalous Years Global Metrics Cluster Models Time Clusters 275 Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page ix #9

10 x Contents Cluster Detection Conditional Counts Cluster Model Parameter Estimation Model Diagnostics Forecasts Spatial Clusters Point Processes Spatial Density Second-Order Properties Models Feature Clusters Dissimilarity and Distance K-Means Clustering Track Clusters Track Plots Bayesian Models Long-Range Outlook Poisson-Gamma Conjugate Prior Parameters Posterior Density Predictive Distribution Seasonal Model Consensus Model Bayesian Model Averaging Data Plots Model Selection Consensus Hindcasts Space-Time Model Lattice Data Local Independent Regressions Spatial Autocorrelation BUGS Data MCMC Output Convergence and Mixing Updates Relative Risk Maps Impact Models Extreme Losses Exploratory Analysis Conditional Losses Industry Loss Models 343 Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page x #10

11 xi Contents Future Wind Damage Historical Catalogue Gulf of Mexico Hurricanes and SST Intensity Changes with SST Stronger Hurricanes 350 Appendix A. R Functions 352 Appendix B. R Packages 361 Appendix C. Data sets 362 Bibliography 363 Index 370 Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page xi #11

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13 PREFACE The goal is to provide analytical tools that will last students a lifetime. Edward Tufte A hurricane is nature s most destructive storm. Violent wind, flooding rain, and powerful surge pose hazards to life and property. Changes in hurricane activity could have significant societal consequences. Hurricanes are the leading source of insured losses from natural catastrophes worldwide and global warming could make the strongest hurricanes ever stronger. Most of what we know about hurricanes comes from past storms. Hurricane climatology is the study of hurricanes as a collection of past events. It answers questions about when, where, and how often. This book is an argument that there is much more remains to learn. The goal is to show you how to analyze, model, and predict hurricane climate using data. It shows you how to create statistical models from hurricane data that are accessible and explanatory. The book is didactic. It teaches you how to learn about hurricane climatology from data. It uses statistics. Statistics is the science of organizing and interpreting data. Statistics is best done using R. The text is written around code that when copied to an R session reproduces the graphs, tables, and maps presented. The approach is different from other books that use R. Rather than showing you how to use R for a variety of purposes, this book focuses on a single topic and shows you how to better understand it by using R. The first five chapters provide background material on R and doing statistics. This material is appropriate for an undergraduate course on statistical methods in the environmental sciences. Chapter 6 presents details on the data sets that are used in the later chapters. Chapters 7, 8, and 9 lay out the building blocks of models for hurricane climate research. This material is appropriate for graduate-level courses in climatology. Chapters give examples from our more recent research that could be used in a seminar on methods and models for hurricane climate analysis and prediction. The book benefited from the research conducted with our students including Robert Hodges, Jill Trepanier, and Kelsey Scheitlin. Editorial assistance came from Laura Michaels with additional help from Sarah Strazzo. We thank Ian Elsner for the book s Web site design. Our sincere thanks go to the R Core Development Team xiii Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page xiii #13

14 xiv Preface for maintaining this software and to the many package authors who enrich the software environment. We thank Richard Murnane and Tony Knap of the Risk Prediction Initiative for their unwavering support over the years. Gratitude goes to Svetla for her wry humor. James B. Elsner and Thomas H. Jagger Tallahassee, Florida August 2012 Elsner: 00 ELSNER PRELIMS 2012/9/25 18:12 page xiv #14

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