As in the previous post about recent plummeting global temperatures, I want to look at the statistics of the drop, and determine its significance. The sort of questions of interest are, how improbable is a fall in temperatures of that magnitude of a 12 month period? After all, it is irresponsible to report alarming results without demonstrating the statistical significance. Unfortunately it is a common practice, for example, see record high temperatures from NASA.
The statistical setup for answering the question is encoded in the question. As we are only looking at falls in temperature, this should be a one-tailed test. The data we need are the twelve-month changes in global temperature anomalies, of which there are twelve every year to compare against the previous year. We then need the area of the distribution curve for these results, up to and including the value in question, -0.5906 in the case of the HadCRU data.
The raw temperature change datasets can be found in the second column of the file at the UK Hadley Climate Research Unit
Programming in R is then a case of adding to the length of the temperature anomalies, both at the beginning and the end, and then subtracting them. In R (I am sure there is a more elegant way to do this BTW):
d< -read.table("hadcrut-monthly.txt") d12f<-c(rep(NA,12),d$V2) d12b<-c(d$V2,rep(NA,12)) d12d<-d12f-d12b
From the vector d12d of 12 month differences we calculate the mean and variace below, remembering to omit the NA’s.
> mean(na.omit(d12d))  -0.005088594 > sd(d12d) Error in var(x, na.rm = na.rm) : missing observations in cov/cor > sd(na.omit(d12d))  0.201136
Hmmm… As the mean is negative it looks like falls tend to more negative than positive over the period (1850 to the present). Perhaps this is not a stationary process, and temperatures have been on a long term downward trend since the 19th century? Anyway, we then get the probability of the present fall from the R pnorm function.
> pnorm(mean=-0.005088594,sd=0.201136,-0.595)  0.00167907
This analysis, assuming the 12 month differences come from a normal distribution, suggests that there is a 0.00168 probability of a fall larger than 0.595C. In annual terms this is a one in 50 year event! Call the press!
However, being skeptical statisticians we suspect that the temperature differences are not from a normal differences. The most direct way to do this is to generate the actual histogram of differences and calculate the probability directly from the number of events with falling temperatures greater than 0.595C. The R code below gives us a histogram changes in global temperature:
h< -hist(d12d,breaks=seq(-1.1,1.3,0.1)) $breaks  -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2  0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 $counts  0 0 2 2 4 18 30 71 146 281 391 413 291 122 61 31 16 5  0 0 0 0 1 0
From the counts above we get the counts less than 0.6C.
> 26/1885  0.01379
A probability of 0.0139 translates into a one in 6 year event. The advantages of the histogram is that it prevents us from exaggerating the significance of the event where we do not have a normal distribution. A fall in temperatures of this magnitude is only expected once in every 6 years – an order of magnitude different to 50 years with the false assumption of normality in the data.