Record-values, nonstationarity tests and extreme value distributions

The chance of seeing new record-values in a stationary series is described by a simple mathematical expression. The expected probability for new record-values is then used to estimate the expectation number for new parallel records in N independent stations at a given time. This probability is then compared with the observed number of new records. A confidence interval about the theoretical expectation number is estimated using Monte-Carlo integrations, and a χ2-type test can be used to assess whether the rate of observed new records is higher than expected for a number of stationary series. The results of this record-statistics test suggest that the observed rate of record-warm monthly mean temperatures at 17 stations around the world may be unexpectedly high. In addition to testing N independent series as a group, it is also possible to examine the number of records set in a single series of a given length. An expression is derived for how the number of records varies with the length of the series, and a confidence interval is estimated using Monte-Carlo integrations. Taking the mean number of records from 17 climate stations spread around the globe, it is shown that by the end of the 20th century, it is higher than expected if the series had been stationary. The record-statistics tests can be used to identify nonstationarities which are problematic for extrapolations of return-periods and return-values from fitting the tails of extreme value distributions. The results for the monthly mean temperature from 17 stations worldwide point to the presence of nonstationaries, implying that a projection will underestimate the future return-values while overestimating the return-periods for the monthly mean temperature if the warming trend continues.