Hurricane Climatology: A Modern Statistical Guide Using R

Description

Hurricanes are nature's most destructive storms and they are becoming more powerful as the globe warms. Hurricane Climatology explains how to analyze and model hurricane data to better understand and predict present and future hurricane activity. It uses the open-source and now widely used R software for statistical computing to create a tutorial-style manual for independent study, review, and reference. The text is written around the code that when copied will reproduce the graphs, tables, and maps. The approach is different from other books that use R. It focuses on a single topic and explains how to make use of R to better understand the topic. The book is organized into two parts, the first of which provides material on software, statistics, and data. The second part presents methods and models used in hurricane climate research. Cover......Page 1 Preface......Page 4 Contents......Page 6 List of Figures......Page 14 List of Tables......Page 19 I Software, Statistics, and Data......Page 21 1.1 Hurricanes......Page 22 1.2 Climate......Page 25 1.3 Statistics......Page 26 1.4 R......Page 29 1.5 Organization......Page 30 2 R Tutorial......Page 33 2.1.1 What is R?......Page 34 2.1.2 Get R......Page 35 2.1.3 Packages......Page 36 2.1.4 Calculator......Page 37 2.1.5 Functions......Page 38 2.1.7 Assignments......Page 39 2.1.8 Help......Page 40 2.2.1 Small Amounts......Page 41 2.2.2 Functions......Page 42 2.2.3 Vectors......Page 44 2.2.4 Structured Data......Page 48 2.2.5 Logic......Page 49 2.2.6 Imports......Page 51 2.3.1 Tables and Summaries......Page 55 2.3.2 Quantiles......Page 57 2.3.3 Plots......Page 58 12.1.2 Conditional losses......Page 0 Scatter Plots......Page 60 2.4 R functions used in this chapter......Page 63 3.1 Descriptive Statistics......Page 65 3.1.1 Mean, median, and maximum......Page 66 3.1.2 Quantiles......Page 69 3.1.3 Missing values......Page 70 3.2.1 Random samples......Page 71 3.2.2 Combinatorics......Page 73 3.2.3 Discrete distributions......Page 74 3.2.4 Continuous distributions......Page 76 3.2.6 Densities......Page 78 3.2.7 Cumulative distribution functions......Page 80 3.2.8 Quantile functions......Page 82 3.2.9 Random numbers......Page 83 3.3 One-Sample Tests......Page 85 3.4 Wilcoxon Signed-Rank Test......Page 92 3.5 Two-Sample Tests......Page 94 3.6 Statistical Formula......Page 97 3.8 Two-Sample Wilcoxon Test......Page 100 3.9 Correlation......Page 101 3.9.2 Spearman's rank and Kendall's correlation......Page 105 3.9.3 Bootstrap confidence intervals......Page 106 3.10 Linear Regression......Page 108 3.11 Multiple Linear Regression......Page 117 3.11.1 Predictor choice......Page 122 3.11.2 Cross validation......Page 123 4.1 Learning About the Proportion of Landfalls......Page 125 4.3 Credible Interval......Page 132 4.4 Predictive Density......Page 134 4.5 Is Bayes Rule Needed?......Page 137 4.6 Bayesian Computation......Page 138 4.6.1 Time-to-Acceptance......Page 139 4.6.3 JAGS......Page 146 4.6.4 WinBUGS......Page 151 5 Graphs and Maps......Page 157 5.1.1 Box plot......Page 158 5.1.2 Histogram......Page 160 5.1.3 Density plot......Page 163 5.1.5 Scatter plot......Page 168 5.1.6 Conditional scatter plot......Page 171 5.2.1 Time-series graph......Page 173 5.2.3 Dates and times......Page 177 5.3.1 Boundaries......Page 179 Point data......Page 183 Field data......Page 192 5.4 Coordinate Reference Systems......Page 195 5.6.1 lattice......Page 201 5.6.2 ggplot2......Page 202 6.1 Best-Tracks......Page 208 6.1.1 Description......Page 209 6.1.2 Import......Page 211 6.1.3 Intensification......Page 214 6.1.4 Interpolation......Page 215 6.1.5 Regional activity......Page 218 6.1.7 Regional maximum intensity......Page 220 6.1.8 Tracks by location......Page 222 6.2.1 Annual cyclone counts......Page 227 6.2.2 Environmental variables......Page 228 6.3.1 Description......Page 236 6.3.2 Counts and magnitudes......Page 238 6.4 NetCDF Files......Page 240 II Models and Methods......Page 244 7.1 Counts......Page 245 7.1.2 Inhomogeneous Poisson process......Page 249 7.2 Environmental Variables......Page 252 7.3 Bivariate Relationships......Page 253 7.4.1 Limitation of linear regression......Page 255 7.4.3 Method of maximum likelihood......Page 256 7.4.4 Model fit......Page 258 7.4.5 Interpretation......Page 259 7.5 Model Predictions......Page 261 7.6.1 Metrics......Page 263 7.6.2 Cross validation......Page 264 7.7 Nonlinear Regression Structure......Page 266 7.8 Zero-Inflated Count Model......Page 269 7.9 Machine Learning......Page 273 7.10 Logistic Regression......Page 276 7.10.1 Exploratory analysis......Page 278 7.10.3 Fit and interpretation......Page 281 7.10.4 Prediction......Page 283 7.10.5 Fit and adequacy......Page 285 7.10.6 Receiver operating characteristics......Page 287 8.1 Lifetime Highest Intensity......Page 291 8.1.1 Exploratory analysis......Page 292 8.2.1 Exploratory analysis......Page 306 8.2.3 Extreme value theory......Page 309 8.2.6 Intensity and frequency model......Page 315 8.2.7 Confidence intervals......Page 316 8.2.8 Threshold intensity......Page 318 8.3.1 Marked Poisson process......Page 321 8.3.2 Return levels......Page 322 8.3.3 Covariates......Page 324 8.3.4 Miami-Dade......Page 326 9 Time Series Models......Page 329 9.1 Time Series Overlays......Page 330 9.2.1 Count variability......Page 332 9.2.2 Moving average......Page 334 9.2.3 Seasonality......Page 335 9.3.1 Counts......Page 340 9.3.2 Covariates......Page 343 9.4 Continuous Time Series......Page 345 9.5.1 Time series visibility......Page 351 9.5.2 Network plot......Page 353 10.1 Time Clusters......Page 361 10.1.1 Cluster detection......Page 362 10.1.2 Conditional counts......Page 364 10.1.3 Cluster model......Page 366 10.1.4 Parameter estimation......Page 367 10.1.5 Model diagnostics......Page 368 10.1.6 Forecasts......Page 372 10.2 Spatial Clusters......Page 374 10.2.2 Spatial density......Page 379 10.3 Feature Clusters......Page 385 10.3.1 Dissimilarity and distance......Page 386 10.3.2 K-means clustering......Page 389 10.3.3 Track clusters......Page 391 10.3.4 Track plots......Page 394 11.1.1 Poisson-gamma conjugate......Page 398 11.1.2 Prior parameters......Page 400 11.1.3 Posterior density......Page 401 11.3.1 Bayesian model averaging......Page 411 11.3.3 Model selection......Page 415 11.3.4 Consensus hindcasts......Page 423 11.4 Space-Time Model......Page 425 11.4.1 Lattice data......Page 426 11.4.2 Local independent regressions......Page 433 11.4.3 Spatial autocorrelation......Page 438 11.4.4 BUGS data......Page 439 11.4.5 MCMC output......Page 440 11.4.6 Convergence and mixing......Page 443 11.4.7 Updates......Page 448 12.1 Extreme Losses......Page 452 12.1.1 Exploratory analysis......Page 453 12.1.3 Industry loss models......Page 456 12.2.1 Historical catalogue......Page 457 12.2.2 Gulf of Mexico hurricanes and SST......Page 462 12.2.3 Intensity changes with SST......Page 463 12.2.4 Stronger hurricanes......Page 466 A.1 Functions......Page 468 A.2 Packages......Page 479 A.3 Data Sets......Page 480 B Install Package From Source......Page 482 References......Page 484