On record-breaking events

Yet, there is a volume of statistical literature on the subject of record-statistics, and the underlying theory for the likelihood of a record-breaking event taking place in a stable system is remarkably simple (Benestad, 2003, 2004). In fact, the simplicity and the nature of the theory for the null-hypothesis (for an stable behaviour/stationary statistics for a set of unrelated observations, referred to as independent and identically distributed data, or ‘iid’, in statistics) makes it possible to test whether the occurrence of record-events is consistent with the null-hypothesis (iid). I will henceforth refer to this as the ‘iid-test’ (unlike many other tests, this analysis does not require that the data is normally distributed as long as there are no ties for the record-event). The results for such a test on monthly absolute minimum/maximum temperatures in the Nordic countries and monthly mean temperatures worldwide are inconsistent with what we would see under a stable climate. Further analysis showed that the absolute monthly maximum/minimum temperature was poorly correlated with that of the previous month, ruling out depeendency in time (this is also true for monthly mean temperature – hence, ‘seasonal forecasting’ is very difficult in this region). Additional tests (Monte Carlo simulations) were used to check whether a spatial dependency could explain the deviation from the iid-rule, but the conclusion was that it could not explain the observed number of records. A similar conclusion was drawn from a similar analysis applied to a (spatially sparse) global network of monthly mean temperatures, where the effect of spatial dependencies for inter-annual and inter-decadal variations could be ruled out (Benestad, 2004). Thus, the frequent occurrence of record-high temperatures is consistent with a global warming.

It is not possible to apply the iid-test to one single event, but the test can detect patterns in a series of events. The test requires a number of independent observations of the same variable over a (sufficiently long) period of time. Since climate encompasses a large number of different parameters (temperature, precipitation, wind, ice extent, etc), it is probable that a climate change would affect the statistics of a number of different parameters simultaneously. Thus, the iid-test can be applied to a set of parallel series representing different aspects of one complex system to examine whether its general state is undergoing a change. Satellite observations tend to be too short for concluding whether they are consistent with null-hypothesis saying there is no climate change (i.e. it being iid) or the alternative hypothesis that the climate is in fact changing (or the observations are not independent). Nevertheless, the record-low sea ice concentration is consistent with a shrinking ice-cap due to a warming. Rainfall observations tend to be longer and therefore more appropriate for such tests, but, such an analysis has not yet been done on a global scale to my knowledge. Results of an iid-test on series of maximum monthly 24-hour rainfall within the Nordic countries (Norway, Sweden, Finland, Denmark & Iceland) could not rule out the null-hypothesis (i.e. the possibility that there is no change in the rainfall statistics), but this case was on the border line and the signal could also be too weak for detection. In a recent publication, however, Kharin & Zwiers (2005) analysed extreme values from model simulations of a changing climate and found that an enhanced greenhouse effect will likely lead to ‘more extreme’ precipitation. This would imply an anomalously high occurrence of record-high rainfall amounts. They discussed the effect of variables being non-iid on the extreme value analysis, and after taking that into account, propose that changes in extreme precipitation are likely to be larger than the corresponding changes in annual mean precipitation under a global warming. Thus, new record-high precipitation amounts are consistent with the climate change scenarios.

Theory for the mathematically minded

Page 2 of 3 | Previous page | Next page