Paul Linsay continued his look at the statistics of hurricanes by looking at the entire record, which I present here:
I went back and repeated the analysis for the Atlantic hurricane data but this time used all the data back to 1851. There is some question about undercounts prior to 1944 but I ignored that issue and used the data as is. The principal change is that the mean number of hurricanes dropped to 5.25 per year from 6.1 for the period 1944 – 2006. The plot of the yearly counts again looks trendless ( Figure 3).
Figure 3. All hurricane counts from 1851 to 2006. The dashed line is the mean of 5.25 hurricanes per year.
The distribution of counts and a calculated Poisson distribution with an average of 5.25 are plotted in Figure 4. The error on the bin height, sqrt(bin height), is also plotted. Just like the 1944 – 2006 data, there is good agreement between the two.
Figure 4. Histogram of annual hurricane counts(red), 1851 to 2006 and associated Poisson distribution(blue). The errors on the bin heights are plotted in black.
Once there are a large number of events it becomes possible to start looking for rare events predicted by a Poisson distribution. With an average of 5.25 hurricanes per year and 156 years of data the probability is high that there will be at least one year with no hurricanes. This is calculated as follows. The probability of no hurricanes in a particular year is exp(-5.25) = 5.2e-3. In 156 years we then expect 156*exp(-5.25) = 0.82 years when there were no hurricanes. Referring to Figure 3, there were no hurricanes observed in 1907 and 1914.
Poisson processes also have the property that the time interval, T, between events is distributed as C*exp(-T/T_o) where T_o and C are constants. (See for example, L. G. Parrett, Probability and Experimental Errors in Science, Dover, 1971).
Using the Atlantic data that SteveM archived here I computed the time in days between hurricanes for all the data from 1851 to the present and histogramed the time differences. The result is in Figure 5.
Figure 5. Histogram of the time interval between hurricanes, semilog plot. The distribution is in red, the error bars are plotted in black, and the best fit exponential is plotted in blue.
It is quite obvious from the plot that the time intervals are distributed exponentially for intervals between 3 and 51 days. There is a deficit for time intervals shorter than three days, probably due to physical limitations of hurricane formation. There is also a very long tail beyond 50 days.
I performed a least squares fit of the distribution to an exponential using sqrt(bin height) as the one sigma error (Poisson!). The result is the blue line in the plot with a time constant, T_o, of 11.6 +- 0.5 days. Overall, the chi-square was 47.5 for 47 degrees of freedom(49 data points – 2 parameters), a very good fit.
The evidence seems quite clear that hurricanes are the result of a stochastic process that obeys Poisson statistics. The annual counts are distributed as a Poisson distribution and matches the distribution computed from the average of the annual counts. Rare events, years with no hurricanes, are seen at a rate predicted from the distribution properties. And the time between hurricanes follows an exponential distribution.
A final note: If I were to do more analysis of hurricane counts I wouldn’t do a global analysis but group them by area of origin to see if is different for the Atlantic, the eastern Pacific, western Pacific, and so on. There might be interesting information there.