NASA’s Earth Observatory reports that there was a record low Arctic sea ice concentration in June 2005. There was a record-number of typhoons over Japan in 2004. In June, there were reports of a number of record-breaking events in the US. And on July 28, the British News paper The Independent reported on record-breaking rainfall (~1 m) in India, claiming hundreds of lives. These are just a few examples of recent observations. So, what is happening?
Whenever there is a new record-breaking weather event, such as record-high temperatures, it is natural to ask whether the occurrence of such an event is due to a climate change. Before we proceed, it may be useful to define the term ‘statistically stationary’, the meaning here being that statistical aspects of the weather (means, standard deviation etc.) aren’t changing. In statistics, there is a large volume of literature on record-breaking behaviour, and statistically stationary systems will produce new record-breaking events from time to time. On the other hand, one would expect to see more new record-breaking events in a changing climate: when the mean temperature level rises new temperatures will surpass past record-highs. This is illustrated in Fig. 1.
Fig. 1. An example showing two different cases, one which is statistically stable (upper) and one that is undergoing a change with a high occurrence of new record-events. Green symbols mark a new record-event. (courtesy William M Connolley)
Record-events and extremes are closely related. Record-high and low values define the limits (bound or the range) between which observed values lie, and extremes are defined as those values in the vicinities of these limits. The third assessment report (TAR) of the IPCC reported some studies that have found regional trends in temperature extremes (particularly low temperatures). There have also been some reports on trends of more extreme precipitation, although The International Ad Hoc Detection and Attribution Group (IDAG, 2005) did not manage to attribute trends in precipitation to anthropogenic greenhouse gases (G) – a quote from their review article is: “For diurnal temperature range (DTR) and precipitation, detection is not achieved”, here ‘detection’ implying the signal of G. A high occurrence of new record-events is an indication of a change in the ‘tails’ of the frequency distribution and thus that values that in the past were considered extreme are becoming more common.
But how does one distinguish between the behaviour of a stable system to one that is undergoing a change in terms of record-events? This kind of question has traditionally not been discussed much in the climate research literature (e.g. record-events are not discussed in DIAG, 2005 or the IPCC TAR), perhaps because it has been perceived that analysis on record-breaking events is difficult if not impossible. There are many different types of record-events related to climatic and weather phenomena. One hurdle is that the number of record-/extreme-events is very low and there is not enough data for the analysis. Another problem is the data quality: does the sensor give a good reading near the ranges of their calibrated scales?
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
The simple theory behind the iid-test is that we have a number of N observations of the same object. If all the values represent a variable that follows the same distribution (i.e. exhibits the same behaviour), then the probability that the last observation is a record-breaking event (the highest number) is 1/N. It is then easy to estimate the expected number of record-events (E) for a series of length N: E = 1/1 + 1/2 + 1/3 + 1/4 + … + 1/N (the first observation being a ‘record-event’ by definition). It is also easy to estimate the likelihood that the number deviated from E by a given amount (i.e. using an analytical expression for the variance of E or so-called ‘Monte-Carlo’ simulations). The probability for seeing new record-events diminishes for an iid variable as the number N increases.
Benestad, R.E. (2004) Record-values, non-stationarity tests and extreme value distributions Global and Planetary Change vol 44, issue 1-4, p.11-26
DIAG (2005) Detecting and Attributing External Influences on the Climate System: A Review of Recent Advances, J. Clim., vol 18, 1291-1313, 1 May
Kharin & Zwiers (2005), Estimating Extremes in Transient Climate Change Simulations, J. Clim., 18, 1156-1173