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. Blank Page......Page 1 Preface......Page 4 Contents......Page 6 List of Figures......Page 15 List of Tables......Page 21 I Software, Statistics, and Data......Page 23 1.1 Hurricanes......Page 24 1.2 Climate......Page 27 1.3 Statistics......Page 28 1.4 R......Page 31 1.5 Organization......Page 32 2 R Tutorial......Page 35 2.1.1 What is R?......Page 36 2.1.2 Get R......Page 37 2.1.3 Packages......Page 38 2.1.4 Calculator......Page 39 2.1.5 Functions......Page 40 2.1.7 Assignments......Page 41 2.1.8 Help......Page 42 2.2.1 Small Amounts......Page 43 2.2.2 Functions......Page 44 2.2.3 Vectors......Page 46 2.2.4 Structured Data......Page 50 2.2.5 Logic......Page 51 2.2.6 Imports......Page 53 2.3.1 Tables and Summaries......Page 57 2.3.2 Quantiles......Page 59 2.3.3 Plots......Page 60 13.1.2 Conditional losses......Page 0 Scatter Plots......Page 62 2.4 R functions used in this chapter......Page 65 3.1 Descriptive Statistics......Page 67 3.1.1 Mean, median, and maximum......Page 68 3.1.2 Quantiles......Page 71 3.1.3 Missing values......Page 72 3.2.1 Random samples......Page 73 3.2.2 Combinatorics......Page 75 3.2.3 Discrete distributions......Page 76 3.2.4 Continuous distributions......Page 78 3.2.6 Densities......Page 80 3.2.7 Cumulative distribution functions......Page 82 3.2.8 Quantile functions......Page 84 3.2.9 Random numbers......Page 85 3.3 One-Sample Tests......Page 87 3.4 Wilcoxon Signed-Rank Test......Page 94 3.5 Two-Sample Tests......Page 96 3.6 Statistical Formula......Page 99 3.8 Two-Sample Wilcoxon Test......Page 102 3.9 Correlation......Page 103 3.9.2 Spearman's rank and Kendall's correlation......Page 107 3.9.3 Bootstrap confidence intervals......Page 108 3.10 Linear Regression......Page 110 3.11 Multiple Linear Regression......Page 119 3.11.1 Predictor choice......Page 124 3.11.2 Cross validation......Page 125 4.1 Learning About the Proportion of Landfalls......Page 127 4.3 Credible Interval......Page 134 4.4 Predictive Density......Page 136 4.5 Is Bayes Rule Needed?......Page 139 4.6 Bayesian Computation......Page 140 4.6.1 Time-to-Acceptance......Page 141 4.6.3 JAGS......Page 148 4.6.4 WinBUGS......Page 153 5 Graphs and Maps......Page 159 5.1.1 Box plot......Page 160 5.1.2 Histogram......Page 162 5.1.3 Density plot......Page 165 5.1.5 Scatter plot......Page 170 5.1.6 Conditional scatter plot......Page 173 5.2.1 Time-series graph......Page 175 5.2.3 Dates and times......Page 179 5.3.1 Boundaries......Page 181 Point data......Page 185 Field data......Page 194 5.4 Coordinate Reference Systems......Page 197 5.6.1 lattice......Page 203 5.6.2 ggplot2......Page 204 6.1 Best-Tracks......Page 210 6.1.1 Description......Page 211 6.1.2 Import......Page 213 6.1.3 Intensification......Page 216 6.1.4 Interpolation......Page 217 6.1.5 Regional activity......Page 220 6.1.7 Regional maximum intensity......Page 222 6.1.8 Tracks by location......Page 224 6.2.1 Annual cyclone counts......Page 229 6.2.2 Environmental variables......Page 230 6.3.1 Description......Page 238 6.3.2 Counts and magnitudes......Page 240 6.4 NetCDF Files......Page 242 II Models and Methods......Page 246 7.1 Counts......Page 247 7.1.2 Inhomogeneous Poisson process......Page 251 7.2 Environmental Variables......Page 254 7.3 Bivariate Relationships......Page 255 7.4.1 Limitation of linear regression......Page 257 7.4.3 Method of maximum likelihood......Page 258 7.4.4 Model fit......Page 260 7.4.5 Interpretation......Page 261 7.5 Model Predictions......Page 263 7.6.1 Metrics......Page 265 7.6.2 Cross validation......Page 266 7.7 Nonlinear Regression Structure......Page 268 7.8 Zero-Inflated Count Model......Page 271 7.9 Machine Learning......Page 275 7.10 Logistic Regression......Page 278 7.10.1 Exploratory analysis......Page 280 7.10.3 Fit and interpretation......Page 283 7.10.4 Prediction......Page 285 7.10.5 Fit and adequacy......Page 287 7.10.6 Receiver operating characteristics......Page 289 8.1 Lifetime Highest Intensity......Page 293 8.1.1 Exploratory analysis......Page 294 8.2.1 Exploratory analysis......Page 308 8.2.3 Extreme value theory......Page 311 8.2.6 Intensity and frequency model......Page 317 8.2.7 Confidence intervals......Page 318 8.2.8 Threshold intensity......Page 320 8.3.1 Marked Poisson process......Page 323 8.3.2 Return levels......Page 324 8.3.3 Covariates......Page 326 8.3.4 Miami-Dade......Page 328 9.1 Track Hexagons......Page 331 9.1.1 Spatial points data frame......Page 332 9.1.2 Hexagon tessellation......Page 334 9.1.3 Overlays......Page 335 9.1.4 Maps......Page 337 9.2 SST Data......Page 339 9.4.1 Moran's I......Page 345 9.4.2 Spatial lag variable......Page 347 9.5 Spatial Regression Models......Page 350 9.5.2 Geographically-weighted regression......Page 353 9.5.3 Model fit......Page 360 9.6.1 Preliminaries......Page 363 9.6.2 Empirical variogram......Page 365 9.6.4 Kriging......Page 370 10 Time Series Models......Page 377 10.1 Time Series Overlays......Page 378 10.2.1 Count variability......Page 380 10.2.2 Moving average......Page 382 10.2.3 Seasonality......Page 383 10.3.1 Counts......Page 388 10.3.2 Covariates......Page 391 10.4 Continuous Time Series......Page 393 10.5.1 Time series visibility......Page 399 10.5.2 Network plot......Page 401 11.1 Time Clusters......Page 409 11.1.1 Cluster detection......Page 410 11.1.2 Conditional counts......Page 412 11.1.3 Cluster model......Page 414 11.1.4 Parameter estimation......Page 415 11.1.5 Model diagnostics......Page 416 11.1.6 Forecasts......Page 420 11.2 Spatial Clusters......Page 422 11.2.2 Spatial density......Page 427 11.3 Feature Clusters......Page 433 11.3.1 Dissimilarity and distance......Page 434 11.3.2 K-means clustering......Page 437 11.3.3 Track clusters......Page 439 11.3.4 Track plots......Page 442 12.1.1 Poisson-gamma conjugate......Page 446 12.1.2 Prior parameters......Page 448 12.1.3 Posterior density......Page 449 12.3.1 Bayesian model averaging......Page 459 12.3.3 Model selection......Page 463 12.3.4 Consensus hindcasts......Page 471 12.4 Space-Time Model......Page 473 12.4.1 Lattice data......Page 474 12.4.2 Local independent regressions......Page 481 12.4.3 Spatial autocorrelation......Page 486 12.4.4 BUGS data......Page 487 12.4.5 MCMC output......Page 488 12.4.6 Convergence and mixing......Page 491 12.4.7 Updates......Page 496 13.1 Extreme Losses......Page 500 13.1.1 Exploratory analysis......Page 501 13.1.3 Industry loss models......Page 504 13.2.1 Historical catalogue......Page 505 13.2.2 Gulf of Mexico hurricanes and SST......Page 510 13.2.3 Intensity changes with SST......Page 511 13.2.4 Stronger hurricanes......Page 514 A.1 Functions......Page 516 A.2 Packages......Page 527 A.3 Data Sets......Page 528 B Install Package From Source......Page 530 References......Page 532