Runs of No Hurricanes

James B. Elsner & Thomas H. Jagger

In order to quantify the run of no hurricanes a model consisting of a Markov Chain in which the annual counts are coded as 1 or 0 depending on hurricanes or no hurricanes.

Read in the data.

setwd("~/Dropbox/Hurricanes")
US = read.table("US.txt", header = TRUE)
US$W = as.integer(US$MUS > 0)
w = US$W

w0 = c(NA, w)
w1 = c(w, NA)
w01 = cbind(w0, w1)[2:length(w), ]

t0 = table(w01[, 1], w01[, 2])
t1 = t0/rowSums(t0)
ww = rep(0, 100000)
tp = t1[, 2]
for(i in 2:100000){
  ww[i] <- rbinom(1, prob = tp[ww[i - 1] + 1], size = 1)
  }

tmp = rle(ww)
tmp2 = tmp$lengths[tmp$values == 0]
csy = sum(tmp2 >= 9)/length(ww) * 100
cy = sum(tmp2[tmp2 >= 9])/length(ww) * 100

The first states that there is a 0.36% that any year is the start of a sequence. The second states that there is a 3.82% chance that any year is in a sequence of at least 9 years with no storms.

cy = numeric()
for(i in 8:16){
  cy = c(cy, sum(tmp2[tmp2 >= i])/length(ww) * 100)
}
df = data.frame(nY = as.factor(8:16), cy)
library("ggplot2")
ggplot(df, aes(nY, cy)) +
  geom_bar(stat = "identity") +
  ylab("Chance (%) Any Year Is In a String\nof At Least N Years Without A Major Hurricane\nin the United States sans Hawaii") +
  xlab("String of N Years Without a Major U.S. Hurricane")

cy = numeric()
J = 100
for(j in 1:J){
  ww = rep(0, 100000)
  tp = t1[, 2]
  for(i in 2:100000){
    ww[i] <- rbinom(1, prob = tp[ww[i - 1] + 1], size = 1)
  }
  tmp = rle(ww)
  tmp2 = tmp$lengths[tmp$values == 0]
  for(k in 8:16){
    cy = c(cy, sum(tmp2[tmp2 >= k])/length(ww) * 100)
  }
}
df = data.frame(j = rep(1:J, each = 9), nY = rep(as.factor(8:16), J), cy)

library("dplyr")

## 
## Attaching package: 'dplyr'
## 
## The following object is masked from 'package:stats':
## 
##     filter
## 
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

df2 = df %>%
  group_by(nY) %>%
  summarize(cyM = mean(cy),
            cySE = sd(cy))
ggplot(df2, aes(nY, cyM)) +
  geom_bar(stat = "identity", fill = "blue", alpha = .3) +
  geom_errorbar(aes(ymin = cyM - 2 * cySE, ymax = cyM + 2 * cySE), width = .05) +
  ylab("Chance (%) Any Year Is In a String\nof At Least N Years Without A Major Hurricane\nin the United States sans Hawaii") +
  xlab("String of N Years Without a Major U.S. Hurricane")