1. 10 IMSC, 20-24 August 2007, Beijing Page 1 An assessment of global, regional and local record-breaking statistics in annual mean temperature Eduardo Zorita 1 and Hans von Storch 12 1 Institute for Coastal Research, GKSS Research Center, Geesthacht, Germany 2 Meteorological Institute, Hamburg University, Hamburg, Germany and Thomas Stocker Climate and Environmental Physics, Physics Institute, University of Bern, Switzerland

2. 10 IMSC, 20-24 August 2007, Beijing Page 2 Different datasets of global mean surface air temperature show consistently increasing values for the past 50 years. Since 1990, a large number of record warm years was detected: the 12 warmest years since 1880 have all occurred after 1990. The probability p of the event E of finding at least 12 of the largest values of a sequence of 126 random numbers (years 1880 to 2005) on the last 16 places (year 1990 to 2005) is 9.3·10 –14. However, annual mean surface air temperatures show serial correlations even in the absence of variations of external forcing. Two null-hypothesis have been used to calculate the probability that such series of warm record years may arise by chance in stationary, but serially correlated, series: an auto-regressive process of order 1 and long-memory process. The parameters of these processes are estimated from the observed data, using the complete record or just part of it. The resulting probabilities, estimated by Montecarlo realizations, hover over 10 -4 to 10 -3. A similar analysis has been performed for the annual temperature averaged in each of the 26 regions defined by Giorgi and Bi (2005), derived from the HadCRU3 data set. Some of these series start earlier than 1880. The autoregressive parameter is estimated for each of these series, as well as the number of warmest years occurring in 1990-2005. The probabilities of these number of record years arising by chance under this null-hypothesis varies widely. For some regions, it is as high as 0.1, but for other regions, notably East Asia and Alaska, they are remarkably small, of the order of 10 -6, indicating that for these regions the late series of warm years would lie even more clearly outside the range of random fluctuations than for the global annual temperature.

3. 10 IMSC, 20-24 August 2007, Beijing Page 3 Among the last 16 years, 1991-2006, there were the 12 warmest years since 1881 (i.e., in 126 samples) – how probable is such an event if the time series were stationary? Global analysis

4. 10 IMSC, 20-24 August 2007, Beijing Page 4 How probable is the event E = at least 12 of the largest values of a sequence of 126 random numbers are among the last 16 samples given that the generating process X is stationary?

5. 10 IMSC, 20-24 August 2007, Beijing Page 5 a)X is a “short memory” process, e.g., AR(1) with an exponentially decaying covariance functions  (k) =  -k b)X is a “long-memory” process with a power-law decaying auto-covariance function  (k) = k -(1+2d), with d being named fractional differencing parameter.  drawn from a distribution with mean 0.7 and stdev 0.4 1+2d drawn from a distribution with mean 0.5 and stdev 0.18 Assumed autocorrelation functions of stationary series

6. 10 IMSC, 20-24 August 2007, Beijing Page 6 Best guesses   0.8 d  0.3 (??) d  Prob(E| ,d) AR-1 long-memory Global analysis

7. 10 IMSC, 20-24 August 2007, Beijing Page 7 As a further test of the consistency of our result, we found that E never emerges in a historical model simulation during the pre-industrial period 1000-1850. Global analysis

8. 10 IMSC, 20-24 August 2007, Beijing Page 8 Extending this type of analysis to regional and local scales Less record-breaking years (-) Lower-autocorrelation (+) Longer time series (+) … so far only AR(1) simulations

9. 10 IMSC, 20-24 August 2007, Beijing Page 9 Giorgi-regions Top: AR(1)-memory Bottom: Number N of years in 1991-2006 with annual temperature T larger than maximum prior to 1991 (different time series lengths in different regions!) Regional analysis

10. 10 IMSC, 20-24 August 2007, Beijing Page 10 5%-significant Regional analysis

11. 10 IMSC, 20-24 August 2007, Beijing Page 11 Local analysis: prior to 2001 Temperature series at European stations as described by CRU – AR(1) coefficients

12. 10 IMSC, 20-24 August 2007, Beijing Page 12 Local analysis: prior to 2001

13. 10 IMSC, 20-24 August 2007, Beijing Page 13 5%-significant Local analysis: prior to 2001

14. 10 IMSC, 20-24 August 2007, Beijing Page 14 The anthropogenic warming on the global scale has been demonstrated using sophisticated statistical techniques since the mid 1990s. Since then the anthropogenic signal has strengthened, and straightforward probability arguments suffice to demonstrate the presence of non-stationary developments. The probability of finding the 12 warmest years among the last 16 years in a sequence of 126 years is extremely small, even if different, conservative assumptions concerning the long-term memory of the climate system are taken into account. Even for local and regional annual mean temperatures, the clustering of recent warmest years is inconsistent with the notion of stationarity. This “success of detection” is due to a blending of strength of signal + length of record + strength of memory. Conclusions

15. 10 IMSC, 20-24 August 2007, Beijing Page 15

16. 10 IMSC, 20-24 August 2007, Beijing Page 16 Generation of synthetic series with long-range- correlation is based on the Fourier Transform. A power-law decaying autocorrelation function is associated with a certain spectral density, which can be calculated analytically. Realizations of random Gaussian white noise are first Fourier-transformed, and the Fourier coefficients are then modified to achieve the desired spectral form. An inverse Fourier transformation yields a time series with the desired form of the autocorrelation function.