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

2. 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

3. 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)

4. a1= 0.7
d=0.4
Autocorrelation function
Spectrum

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

6. 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

7. Generation of synthetic time series with the same memory properties

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

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

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