Hurricane Climatology: A Modern Statistical Guide Using R

542 Pages·2013·13.45 MB·English

by  James B. Elsner, Thomas Herbert Jagger

H U R R I C A N E
C L I M AT O L O G Y
A Modern Statistical Guide Using R
JAMESB.ELSNER&THOMASH.JAGGER
TheFloridaStateUniversity
Climatek
NewYork Oxford
OXFORDUNIVERSITYPRESS
2012
1

Preface
“Thegoalistoprovideanalyticaltoolsthatwilllaststudents
alifetime.”
—EdwardTufte
Ahurricaneisnature’smostdestructivestorm. Violentwind,flood-
ingrain,andpowerfulsurgeposehazardstolifeandproperty. Changes
inhurricaneactivitycouldhavesignificantsocietalconsequences.Hurri-
canesarealreadytheleadingsourceofinsuredlossesfromnaturalcatas-
trophesworldwide.
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 to learn. The goal is to
show you how to analyze, model, and predict hurricane climate using
data. Itshowsyouhowtocreatestatisticalmodelsfromhurricanedata
thatareaccessibleandexplanatory.
The book is didactic. It teaches you how to learn about hurricanes
from data. It uses statistics. Statistics is the science of organizing and
interpretingdata. StatisticshelpsyouunderstandandpredictandtheR
programminglanguagehelpsyoudostatistics.Thetextiswrittenaround
codethatwhencopiedtoanRsessionwillreproducethegraphs,tables,
and maps. The approach is different from other books that use R. It
i
focusesonasingletopicandshowsyouhowtomakeuseof Rtobetter
understandthetopic.
The first five chapters provide background material on using R and
doingstatistics.Thismaterialisappropriateforanundergraduatecourse
onstatisticalmethodsintheenvironmentalsciences.Chapter6presents
details on the data sets that are used in the later chapters. Chapters 7,
8,and 9 layout the buildingblocksof models forhurricaneclimate re-
search.Thismaterialisappropriateforgraduatelevelcoursesinclimatol-
ogy. Chapters10–13giveexamplesfromourmorerecentresearchthat
couldbeusedinaseminaronmethodsandmodelsforhurricaneclimate
analysisandprediction.
The book benefited from research conducted with our students in-
cluding Robert Hodges, Jill Trepanier and Kelsey Scheitlin. Editorial
assistance came from Laura Michaels with additional help from Sarah
Strazzo. Our sincere thanks go to the R Core Development Team for
maintainingthissoftwareandtothemanypackageauthorswhoenrich
thesoftwareenvironment.WethankRichardMurnaneandTonyKnap
of the Risk Prediction Initiative for their unwavering support over the
years.
GratitudegoestoSvetlaforherwryhumorthroughout.
JamesB.Elsner&ThomasH.Jagger
Tallahassee,Florida
March2012
ii
Contents
Preface i
Contents iii
ListofFigures xii
ListofTables xviii
I Software,Statistics,andData 1
1 Hurricanes,Climate,andStatistics 1
1.1 Hurricanes . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Climate . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Organization . . . . . . . . . . . . . . . . . . . . . . . . 9
2 RTutorial 12
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 WhatisR? . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 GetR . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.3 Packages . . . . . . . . . . . . . . . . . . . . . . 15
iii
2.1.4 Calculator . . . . . . . . . . . . . . . . . . . . . 16
2.1.5 Functions . . . . . . . . . . . . . . . . . . . . . 17
2.1.6 Warningsanderrors . . . . . . . . . . . . . . . 18
2.1.7 Assignments . . . . . . . . . . . . . . . . . . . . 18
2.1.8 Help . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 SmallAmounts . . . . . . . . . . . . . . . . . . 20
2.2.2 Functions . . . . . . . . . . . . . . . . . . . . . 22
2.2.3 Vectors . . . . . . . . . . . . . . . . . . . . . . 23
2.2.4 StructuredData . . . . . . . . . . . . . . . . . . 27
2.2.5 Logic . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.6 Imports. . . . . . . . . . . . . . . . . . . . . . . 30
2.3 TABLESANDPLOTS . . . . . . . . . . . . . . . . . 34
2.3.1 TablesandSummaries . . . . . . . . . . . . . . 34
2.3.2 Quantiles. . . . . . . . . . . . . . . . . . . . . . 36
2.3.3 Plots . . . . . . . . . . . . . . . . . . . . . . . . 37
BarPlots . . . . . . . . . . . . . . . . . . . . . . 38
ScatterPlots . . . . . . . . . . . . . . . . . . . . 39
2.4 Rfunctionsusedinthischapter . . . . . . . . . . . . . 42
3 ClassicalStatistics 44
3.1 DescriptiveStatistics . . . . . . . . . . . . . . . . . . . 44
3.1.1 Mean,median,andmaximum . . . . . . . . . . 45
3.1.2 Quantiles. . . . . . . . . . . . . . . . . . . . . . 48
3.1.3 Missingvalues . . . . . . . . . . . . . . . . . . . 49
3.2 ProbabilityandDistributions . . . . . . . . . . . . . . . 50
3.2.1 Randomsamples . . . . . . . . . . . . . . . . . 50
3.2.2 Combinatorics . . . . . . . . . . . . . . . . . . . 52
3.2.3 Discretedistributions . . . . . . . . . . . . . . . 53
3.2.4 Continuousdistributions . . . . . . . . . . . . . 55
3.2.5 Distributions . . . . . . . . . . . . . . . . . . . 57
3.2.6 Densities . . . . . . . . . . . . . . . . . . . . . . 57
3.2.7 Cumulativedistributionfunctions . . . . . . . . 59
3.2.8 Quantilefunctions . . . . . . . . . . . . . . . . 61
3.2.9 Randomnumbers . . . . . . . . . . . . . . . . . 62
iv
3.3 One-SampleTests . . . . . . . . . . . . . . . . . . . . . 64
3.4 WilcoxonSigned-RankTest . . . . . . . . . . . . . . . 71
3.5 Two-SampleTests . . . . . . . . . . . . . . . . . . . . . 73
3.6 StatisticalFormula . . . . . . . . . . . . . . . . . . . . . 76
3.7 CompareVariances . . . . . . . . . . . . . . . . . . . . 78
3.8 Two-SampleWilcoxonTest . . . . . . . . . . . . . . . . 79
3.9 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.9.1 Pearson’sproduct-momentcorrelation. . . . . . 81
3.9.2 Spearman’srankandKendall’scorrelation. . . . 84
3.9.3 Bootstrapconfidenceintervals . . . . . . . . . . 86
3.9.4 Causation . . . . . . . . . . . . . . . . . . . . . 87
3.10 LinearRegression . . . . . . . . . . . . . . . . . . . . . 87
3.11 MultipleLinearRegression . . . . . . . . . . . . . . . . 96
3.11.1 Predictorchoice . . . . . . . . . . . . . . . . . . 101
3.11.2 Crossvalidation . . . . . . . . . . . . . . . . . . 103
4 BayesianStatistics 104
4.1 LearningAbouttheProportionofLandfalls. . . . . . . 104
4.2 Inference . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.3 CredibleInterval . . . . . . . . . . . . . . . . . . . . . . 111
4.4 PredictiveDensity . . . . . . . . . . . . . . . . . . . . . 113
4.5 IsBayesRuleNeeded? . . . . . . . . . . . . . . . . . . . 116
4.6 BayesianComputation . . . . . . . . . . . . . . . . . . 117
4.6.1 Time-to-Acceptance . . . . . . . . . . . . . . . 118
4.6.2 MarkovchainMonteCarloapproach . . . . . . 124
4.6.3 JAGS . . . . . . . . . . . . . . . . . . . . . . . . 125
4.6.4 WinBUGS . . . . . . . . . . . . . . . . . . . . . 130
5 GraphsandMaps 136
5.1 Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.1.1 Boxplot . . . . . . . . . . . . . . . . . . . . . . 137
5.1.2 Histogram . . . . . . . . . . . . . . . . . . . . . 140
5.1.3 Densityplot . . . . . . . . . . . . . . . . . . . . 142
5.1.4 Q-Qplot . . . . . . . . . . . . . . . . . . . . . . 145
5.1.5 Scatterplot . . . . . . . . . . . . . . . . . . . . 147
v
5.1.6 Conditionalscatterplot . . . . . . . . . . . . . . 150
5.2 Timeseries . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.2.1 Time-seriesgraph . . . . . . . . . . . . . . . . . 153
5.2.2 Autocorrelation . . . . . . . . . . . . . . . . . . 153
5.2.3 Datesandtimes . . . . . . . . . . . . . . . . . . 156
5.3 Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
5.3.1 Boundaries . . . . . . . . . . . . . . . . . . . . . 159
5.3.2 Datatypes . . . . . . . . . . . . . . . . . . . . . 162
Pointdata . . . . . . . . . . . . . . . . . . . . . 162
Arealdata . . . . . . . . . . . . . . . . . . . . . 168
Fielddata . . . . . . . . . . . . . . . . . . . . . 171
5.4 CoordinateReferenceSystems . . . . . . . . . . . . . . 174
5.5 Export . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.6 OtherGraphicPackages . . . . . . . . . . . . . . . . . . 180
5.6.1 lattice . . . . . . . . . . . . . . . . . . . . . . . . 180
5.6.2 ggplot2 . . . . . . . . . . . . . . . . . . . . . . . 181
5.6.3 ggmap . . . . . . . . . . . . . . . . . . . . . . . 185
6 DataSets 187
6.1 Best-Tracks . . . . . . . . . . . . . . . . . . . . . . . . . 187
6.1.1 Description . . . . . . . . . . . . . . . . . . . . 188
6.1.2 Import . . . . . . . . . . . . . . . . . . . . . . . 190
6.1.3 Intensification . . . . . . . . . . . . . . . . . . . 193
6.1.4 Interpolation . . . . . . . . . . . . . . . . . . . . 194
6.1.5 Regionalactivity . . . . . . . . . . . . . . . . . . 197
6.1.6 Lifetimemaximumintensity . . . . . . . . . . . 198
6.1.7 Regionalmaximumintensity . . . . . . . . . . . 199
6.1.8 Tracksbylocation . . . . . . . . . . . . . . . . . 201
6.1.9 Attributesbylocation . . . . . . . . . . . . . . . 204
6.2 AnnualAggregation . . . . . . . . . . . . . . . . . . . . 206
6.2.1 Annualcyclonecounts . . . . . . . . . . . . . . 206
6.2.2 Environmentalvariables . . . . . . . . . . . . . 208
6.3 CoastalCountyWinds . . . . . . . . . . . . . . . . . . 215
6.3.1 Description . . . . . . . . . . . . . . . . . . . . 215
6.3.2 Countsandmagnitudes . . . . . . . . . . . . . . 217
vi
6.4 NetCDFFiles . . . . . . . . . . . . . . . . . . . . . . . 219
II ModelsandMethods 223
7 FrequencyModels 224
7.1 Counts . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
7.1.1 Poissonprocess . . . . . . . . . . . . . . . . . . 227
7.1.2 InhomogeneousPoissonprocess . . . . . . . . . 228
7.2 EnvironmentalVariables . . . . . . . . . . . . . . . . . 231
7.3 BivariateRelationships . . . . . . . . . . . . . . . . . . 232
7.4 PoissonRegression . . . . . . . . . . . . . . . . . . . . 233
7.4.1 Limitationoflinearregression . . . . . . . . . . 234
7.4.2 Poissonregressionequation . . . . . . . . . . . 235
7.4.3 Methodofmaximumlikelihood . . . . . . . . . 236
7.4.4 Modelfit . . . . . . . . . . . . . . . . . . . . . . 237
7.4.5 Interpretation . . . . . . . . . . . . . . . . . . . 238
7.5 ModelPredictions . . . . . . . . . . . . . . . . . . . . . 240
7.6 ForecastSkill . . . . . . . . . . . . . . . . . . . . . . . . 242
7.6.1 Metrics . . . . . . . . . . . . . . . . . . . . . . . 242
7.6.2 Crossvalidation . . . . . . . . . . . . . . . . . . 243
7.7 NonlinearRegressionStructure . . . . . . . . . . . . . 245
7.8 Zero-InflatedCountModel . . . . . . . . . . . . . . . . 248
7.9 MachineLearning . . . . . . . . . . . . . . . . . . . . . 252
7.10 LogisticRegression . . . . . . . . . . . . . . . . . . . . 255
7.10.1 Exploratoryanalysis . . . . . . . . . . . . . . . . 257
7.10.2 Logitandlogisticfunctions . . . . . . . . . . . . 259
7.10.3 Fitandinterpretation . . . . . . . . . . . . . . . 260
7.10.4 Prediction . . . . . . . . . . . . . . . . . . . . . 262
7.10.5 Fitandadequacy . . . . . . . . . . . . . . . . . 264
7.10.6 Receiveroperatingcharacteristics . . . . . . . . 266
8 IntensityModels 270
8.1 LifetimeHighestIntensity . . . . . . . . . . . . . . . . 270
8.1.1 Exploratoryanalysis . . . . . . . . . . . . . . . . 271
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