Download Global Warming - Scientific Controversies in Climate

The concepts of Detection
and Attribution
Hans von Storch
Institute for Coastal Research
GKSS Research Center, Geesthacht, Germany
and Meteorological Institute, Hamburg University
Global Warming - Scientific Controversies in Climate Variability International seminar meeting at The
Royal Institute of Technology (KTH), Stockholm, Sweden, September 11-12th 2006
Detection and attribution
• Detection means – finding in a record of
observations evidence for a contamination of
the „natural variability“ by man-made signals.
A statistical problem.
• Attribution means – finding the most plausible
explanation for the cause of the detected
contamination. A plausibility argument.
Concept introduced by Klaus Hasselmann, first in 1979, and later in a framework
geared towards the problem of anthropogenic climate change in 1993.
Hasselmann, K., 1979: On the signal-to-noise problem in atmospheric response studies. Meteorology over the
tropical oceans (B.D.Shaw ed.), pp 251-259, Royal Met. Soc., Bracknell, Berkshire, England.
Hasselmann, K., 1993: Optimal fingerprints for the detection of time dependent climate change. J. Climate 6, 1957
- 1971
The detection problem:
Test of the nullhypothesis:
„considered climate signal is consistent with natural climate variability“
St ~Po , o 
with St representing the signal to be examined, whether it is consistent
with natural climate variability or not, and P o ,  o  describing the
distibution of the present climate with parameters  o and  o .
Problem is to determine
St and its distribution P.
The attribution problem
After we have found a signal to lie outside the range of natural
variations, the question arises whether this signal can be causally
related to an external factor.
Usually, there are many factors, but climatological theory reduces the
candidates to just a few (e.g., greenhouse gases, volcanic aerosols,
solar effects).
Then, that mix of processes is attributed to the signal, which fits best
to the a-priori assumed link between cause and effect. This may take
the form of a best-fit or as the result of a non-rejection of a null
hypothesis.
S t    k Fk  N t
k
Detection is a strictly statistical problem.
Attribution is based on a plausibility argument.
The attribution problem
If the theory / knowledge claims provide numerically accurate
“responses”, then also the coefficients γk are „known“. Then instead
of a best-fit approach, a test using the hypothesis
H0: γk = expected value
can be formulated – and attribution is considerd to be achieved when H0 is
NOT rejected.
Where does the stochasticity
come from?
• Observational data: irregular spatial coverage,
observational errors, limited observation time
span. And natural unforced variability.
• Simulation data: internally generated by a very
large number of chaotic processes.
Stochasticity as mathematical construct to allow
an efficient description of the simulated (and
observed) climate variability.
• Dynamical “cause” for natural unforced variability
as in models.
Mathematical
construct of
randomness – an
adequate concept
for description of
features resulting
from the presence
of many chaotic
processes.
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Noise or
deterministic
chaos?
IfK
Noise as
nuisance:
masking
the signal
The 300 hPa geopotential height fields in the Northern Hemisphere: the mean 1967-81
January field, the January 1971 field, which is closer to the mean field than most others,
and the January 1981 field, which deviates significantly from the mean field. Units: 10 m
How do we determine the
control climate P o , o  ?
• With the help of the limited empirical evidence from
instrumental observations, possibly after suitable
extraction of the suspected „non-natural“ signal.
• By projection of the signal on a proxy data space, and
by determining the stats of the latter from
geoscience indirect evidence (e.g., tree rings).
• By accessing long „control runs“ done with quasirealistic climate models
Signal or noise?
Trend in air
temperature
1965-1994
1916-1945
Formulation the null hypothesis
• Reduction of dimension be projection of the full fields on „guess
pattern(s)“ Gk.
St   k G k
k
• Guess patterns represent our expectations about the
anthropogenic signals. (They may be false, but the test is still
correct, but with little power.)
• Guess patterns may originate from numerical experiments on the
suspected mechanisms, or from other reasoning
(paleoclimatic/historical analogues; theoretical considerations).
• Test whether αk consistent with natural variability.
Expected
anthropogenic GHG signal
• … emerges most clearly in the last
decades
• … accelerates with time
• … manifests itself in a strong increase
of temperature, not with an
unprecedented level of temperature.
• The detection variable is “change of T”,
not “state of T”.
From:
Hadley Center,
IPCC TAR, 2001
attribution
Detection –
does it depend on
the hockeystick?
Rybski, D., A. Bunde, S. Havlin,and H. von Storch,
2006: Long-term persistence in climate and the
detection problem. Geophys. Res. Lett. 33,
L06718, doi:10.1029/2005GL025591
Historical Reconstructions – their significance for “detection”
• Statistics of ΔTL,m, which is the
difference of two m-year temperature
means separated by L years.
• Temperature variations are modelled as
Gaussian long-memory process, fitted
to the various reconstructions.
Historical Reconstructions – their significance for “detection”
Temporal development of
Ti(m,L) = Ti(m) – Ti-L(m)
divided by the standard
deviation (m,L) of the
considered reconstructed temp
record
for m=5 and L=20 (top), and
for m=30 and L=100 years.
The thresholds R = 2, 2.5 and 3
are given as dashed lines.
Conclusions
• Detection of anomalous conditions and attribution to specific causes is
a well defined and developed concept in climate change studies.
• Detection is a strictly statistical problem; attribution is a plausibility
argument.
• A-priori guidance by quasi-realistic models most helpful if not
mandatory.
• Improvement of data base for estimating variability with the help of
quasi-realistic models most helpful if not mandatory.
• Ongoing climate variations can not be explained by natural climate
variations alone. Detection has succeeded.
• A significant proportion of the detected signal can be attributed to
increased levels of carbon dioxide.
• All available historical reconstructions, from MBH to Moberg, lead to
a very small risk of rejecting the null hypothesis of only natural
variablity. Detection is independent of the hockey-stick claim.
Numerical experiment with ocean model: standard simulation with steady
forcing (wind, heat
and fresh water
fluxes) plus random
forcing
zero-mean
precipitation overlaid.
Example for
Stochastic Climate
Model at work.
response
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Noise as a constitutive element
IfK
Noise as constitutive element
 = (T)
Idealized energy balance
Integration of a zero–dimensional energy balance model
with constant transmissivity and
temperature dependent albedo
evolution from different initial
values
with noise
evolution with slightly randomized
transmissivity
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no noise
IfK
Example of a local detection study.
Pfizenmayer (2002)
Estimated wave energy impinging on the West Coast of Jutland (Sylt),
derived with a downscaling model from large scale monthly mean atmospheric states
in operational analyses („reconstruction“), in a control simulation (T42 control) and in
a climate change simulation (T42 transient).
The energy increases even though the storm activity does hardly so.
References
Zwiers, F.W., 1999: The detection of climate change. In: H. von Storch
and G. Flöser (Eds.): Anthropogenic Climate Change. Springer Verlag,
163-209, ISBN 3-540-65033-4
von Storch, H., J.-S. von Storch, and P. Müller, 2001: Noise in the
Climate System – ubiquituos, constitutive and concealing. In B.
Engquist and W. Schmid (eds.) Mathematics Unlimited – 2001 and
beyond. Part II. Springer Verlag, 1179-1194
Hegerl, G.C. , K.H. Hasselmann, U. Cubasch, J.F.B. Mitchell, E. Roeckner,
R. Voss and J. Waszkewitz, 1997: Multi-fingerprint detection and
attribution analysis of greenhouse gas, greenhouse gas-plus-aerosol
and solar forced climate change. Clim. Dyn. 13, 613-634
Pfizenmayer and H. von Storch, 2001: Anthropogenic climate change
shown by local wave conditions in the North Sea. Climate Res. 19, 1523
Rybski, D., A. Bunde, S. Havlin,and H. von Storch, 2006: Long-term
persistence in climate and the detection problem. Geophys. Res. Lett. 33,
L06718, doi:10.1029/2005GL025591
Specific problem in climate applications: usually very many
(>103) degrees of freedom, but the signal of change
resides on in a few of these degrees of freedom.
Example:
Signal = (2, 0, 0, ...0)
with all components
independent.
Power of detecting the
signal, if different
degrees of freedom
are considered.
Thus, the dimension of the problem must be reduced
before doing anything further. Usually, only very few
components are selected, such as 1 or 2.
2-patterns problem (Hegerl et al. 1997)
• guess patterns for climate change mechanisms taken as first EOFs of
a climate change simulation on that mechanism.
• only CO2 increase
• increase of CO2 and industrial aerosols as well.
• orthogonalisation of the two patterns
• estimation of natural variability through GCM control simulations done
at MPI in Hamburg, GFDL in Princeton and HC in Bracknell.
30 year trends
30 year trends
detection
50 year trends
attribution