Record-breaking temperatures reveal a warming climate

Abstract

Abstract. -We present a mathematical analysis of records drawn from independent random variables with a drifting mean. To leading order the change in the record rate is proportional to the ratio of the drift velocity to the standard deviation of the underlying distribution. We apply the theory to time series of daily temperatures for given calendar days, obtained from historical climate recordings of European and American weather stations as well as re-analysis data. We conclude that the change in the mean temperature has increased the rate of record breaking events in a moderate but significant way: For the European station data covering the time period 1976-2005, we find that about 5 of the 17 high temperature records observed on average in 2005 can be attributed to the warming climate.Introduction. -In current media coverage the occurrence of record-breaking temperatures and other extreme weather conditions is often associated with global climate change. However, record breaking events occur at a certain rate in any stationary random process. In mathematical terms, a record is an entry in a time series that is larger (upper record) or smaller (lower record) than all previous entries [1][2][3]. If the entries are independent and identically distributed random variables drawn from a continuous probability distribution, the probability P n to observe a new record after n steps, hereafter referred to as the record rate, is simply P n = 1/n, because all n values are equally likely to be the largest. Applying this result to maximal temperatures measured at a specific calendar day over a time span of n years, it follows that the expected number of records per year is 365/n, i.e. about 12 records for an observation period of 30 years. Remarkably, this prediction is entirely independent of the underlying probability distribution, which may even differ for different calendar days.Despite considerable current interest in extreme climate events [4][5][6][7][8][9][10][11][12][13][14], the subject of climate records has received relatively little attention. It is intuitively obvious that an increase in the mean temperature will lead to an increased occurrence of high temperature records, but attempts to detect this effect in observational data have long remained inconclusive [15][16][17][18]. Only very recently an empirical study of temperature data from the US found a significant effect of warming on the relative occurrence of

Records in stochastic processes—theory and applications

“…In 2009, Meehl et al [8] analyzed a large number of U.S. weather stations with respect to the occurrence of heat and cold records and found a significant effect of global warming in the ratio of the two of them. In 2010, Wergen and Krug [9] confirmed these findings in an independent study of European station and re-analysis data [57,80]. The work of Newman et al [10], Anderson and Kostinski [79], Elguindi et al [11] as well as Rahmstorf and Coumou [12] lead to similar results.…”

“…In a previous study, they analyzed historical temperature measurements from U.S. weather stations [57] that were recorded in whole degrees of Fahrenheit. They observed that this discreteness had a significant effect on the record statistics of the temperature data that could, in principle, disguise a possible effect of global warming on the occurrence of record-breaking events [9,40]. The problem is more general: In all applications, experimental measurements can only be recorded up to a certain accuracy.…”

“…Clearly, this is exactly the Linear Drift Model (LDM) we discussed in section 3 for Gaussian RV's. The work of Redner and Peterson motivated many others to study both the statistics of record breaking temperatures [8,9,10,79,11,12] and also the simple LDM [31,32,33]. In 2009, Meehl et al [8] analyzed a large number of U.S. weather stations with respect to the occurrence of heat and cold records and found a significant effect of global warming in the ratio of the two of them.…”

“…This effect is also found in measurement from European and U.S. weather stations and re-analysis data. Over the same period, the standard deviation of the daily and monthly temperatures around their moving mean value remained more or less constant [69,4,9]. Since the magnitude of the warming in recent years is still much smaller than the average standard deviation of daily temperatures, one can compare the temperature measurements with a Gaussian LDM in the regime of small c ≪ σ/ √ n (see section 3).…”

“…These predictions are in good agreement with the data found in the literature. For instance, Wergen et al [9] considered daily maximum temperatures measured at 202 European stations [80] between 1975 and 2005 and found an increase of around 40% in the number of heat records along with a normalized drift ofc ≈ 0.015 y −1 . For monthly mean temperatures the normalized drift is usually larger, since the standard deviation of these averaged values is much smaller than in the case of daily measurements.…”