Examples of using long term memory in climate analysis Hans von Storch and Eduardo Zorita GKSS Research Centre, Geesthacht, Germany

Goals Is it possible to identify an unnatural climate change in the 20th century by statistical methods alone? We need to characterize natural variations = define what is normal Estimate the probability that the 20th century climate belongs to normal variations

Possible statistical models for natural variations Autoregressive: x(t+1)= S ai x(t-i) + white noise (t) i=1,N Fractional differencing : x (t+1)= S ai x (t-1 ) + white noise (t) 0.5 (short memory) <fractional differencing d < 1 (non-stationary) Hurst coeff. = 0.5 +d i=1, Random walk (more generally unit root process) : x(t+1)= x(t) + stationary process (t)

a1= 0.7 d=0.4 Autocorrelation function Spectrum

Estimated d in millennial climate simulations With historical external forcing Global mean, d=0.65 Control: constant external forcing Global mean, d< 0.5 0.5 1 0.5 1

Long memory in proxy based reconstructions of Northern H. annual mean temperature Mann et al 1998 Briffa 2000 Esper et al 2003 Moberg et al 2005 Jones et al 1998 0.47 0.43 0.54 0.36 0.32

Generation of synthetic time series with the same memory properties

Ratio between temperature deviations from long-term mean and standard deviation expected from long memory

Probability of clustering of record years at global spatial scale From Zorita et al., GRL 2008

Probability of clustering of record years at local spatial scale From Zorita et al., GRL 2008