Frequency Models

Abstract

Here in Part II, we focus on statistical models for understanding and predicting hurricane climate. This chapter shows you how to model hurricane occurrence. This is done using the annual count of hurricanes making landfall in the United States. We also consider the occurrence of hurricanes across the basin and by origin. We begin with exploratory analysis and then show you how to model counts with Poisson regression. Issues of model fit, interpretation, and prediction are considered in turn. The topic of how to assess forecast skill is examined including how to perform cross-validation. Alternatives to the Poisson regression model are considered. Logistic regression and receiver operating characteristics (ROCS) are also covered. You use the data set US.txt which contains a list of tropical cyclone counts by year (see Chapter 2). The counts indicate the number of hurricanes hitting in the United States (excluding Hawaii). Input the data, save them as a data frame object, and print out the first six lines by typing . . . > H = read.table("US.txt", header=TRUE) > head(H) . . . The columns include year Year, number of U.S. hurricanes All, number of major U.S. hurricanes MUS, number of U.S. Gulf coast hurricanes G, number of Florida hurricanes FL, and number of East coast hurricanes E. Save the total number of years in the record as n and the average number hurricanes per year as rate. . . . > n = length(H$Year); rate = mean(H$All) > n; rate [1] 160 [1] 1.69 . . . The average number of U.S. hurricanes is 1.69 per year over these 160 years. First plot a time series and a distribution of the annual counts. Together, the two plots provide a nice summary of the information in your data relevant to any modeling effort. . . . > par(las=1) > layout(matrix(c(1, 2), 1, 2, byrow=TRUE), + widths=c(3/5, 2/5)) > plot(H$Year, H$All, type="h", xlab="Year", + ylab="Hurricane Count") > grid() > mtext("a", side=3, line=1, adj=0, cex=1.1) > barplot(table(H$All), xlab="Hurricane Count", + ylab="Number of Years", main="") > mtext("b", side=3, line=1, adj=0, cex=1.1) . . . The layout function divides the plot page into rows and columns as specified in the matrix function (first argument).