Transcript PowerPoint-Präsentation

An assessment of global, regional and
local record-breaking statistics in
annual mean temperature
Eduardo Zorita1 and Hans von Storch12
1Institute
for Coastal Research, GKSS Research Center, Geesthacht, Germany
2Meteorological
Institute, Hamburg University, Hamburg, Germany
and
Thomas Stocker
Climate and Environmental Physics, Physics Institute, University of Bern ,
Switzerland
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Global analysis
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?
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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?
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Assumed autocorrelation functions of stationary series
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.
1+2d drawn
from a
distribution with
mean 0.5 and
stdev 0.18
 drawn from a
distribution
with mean 0.7
and stdev 0.4
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d
Global analysis
Best guesses
  0.8
d  0.3 (??)
Prob(E|,d)
AR-1
long-memory
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
Global analysis
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.
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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
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Regional analysis
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!)
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Regional analysis
5%-significant
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Local analysis: prior to 2001
Temperature series at European stations
as described by CRU – AR(1) coefficients
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Local analysis: prior to 2001
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Local analysis: prior to 2001
5%-significant
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Conclusions
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.
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Generation of synthetic series with long-rangecorrelation 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.
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