Transcript The speakers

Climate Research Branch / CCCma
Discussion of use of statistical
methods in palaeo-reconstructions
Francis Zwiers
Climate Research Division, Environment Canada, Toronto, Ontario
11 IMSC, 12-16 July 2010, Edinburgh
Photo: F. Zwiers
Climate Research Branch / CCCma
The speakers
• Wanner
– Have satisfactory physical process understanding on the
millennial time scale over past 6K years, but are challenged
on shorter timescales
– What would have happened in absence of ANT forcing?
• Haslett
– Rapid progress is being made on developing a suitable
(Bayesian) framework for characterizing uncertainty in
palaeo-reconstructions
– Demonstrated via SUPRAnet and implemented in Bclim
– Key observation is that our interest is in non-linear
functionals of climate change
– Issue that is illustrated by contrasting these two talks is how
to bring in our understanding of the physics of climate
change (how do we constrain the inversion to also account
for the physics of rapid non-linear change – need to do more
than describe the data and associated uncertainty).
Climate Research Branch / CCCma
The speakers
• Mann
– Spatial reconstructions more interesting than simply the
hemispheric means
– Underscored the importance of imposing physical
constraints on interpretation and validation of reconstructions
– External forcing response detectable and understandable
(see also Hegerl et al, 2003)
– Points out palaeo-evidence for Bjerknes “tropical thermostat”
feedback mechanism (seen in a few some full models)
• Osborne
– Explores whether reconstructions can help constrain key
climate system parameters by studying behaviour of mle’s of
the parameters
– Potential exists, provided forcing well enough known
– Points out benefit of imposing physical constraints on
parameter estimates, although this should be done in a
suitable statistical framework (otherwise, this could lead to
undesirable traits, such as bias)
Climate Research Branch / CCCma
The speakers
• Edwards
– Biomization approach to vegetation model allows
alternative approach to reconstruction climate that
is less dependent upon modern analogues
– Uncertainties include lack of a linear relationship
between pollen and plant abundance (includes
long-range transport issues for some species),
lack of sufficient data
Climate Research Branch / CCCma
Statistical considerations
• Apparent in virtually every step of the reconstruction
process
– Identification of suitable proxies for the target of
interest (e.g., temperature, precipitation, …)
– Development of local chronologies
– Interpretation of a field of chronologies
– Applications
Climate Research Branch / CCCma
Statistical considerations
• Bayesian methods increasingly apparent
– Allows characterization of the chain of uncertainty
– Computing perhaps no longer a large impediment
– Incorporating process understanding does still
remain an impediment
• Statistical technique should not impede
interpretability of the reconstruction
• User (climate scientist) requires
– Traceable behaviour
– An understanding of how to apply posterior
The calibration problem
Climate Research Branch / CCCma
Photo: F. Zwiers
Climate Research Branch / CCCma
The Calibration Problem
Reconstruction period
Training period
Calibration period
NH mean
temperature
Known
Need to reconstruct
1000
2000
1860
Proxy series
Year
1000
Known
Apply that
relationship to
reconstruct past NH
temperature
1860
Known
2000
Identify a statistical
relationship between
a collection proxies
and NH temperature
Climate Research Branch / CCCma
Two types of reconstruction techniques
• CPS – composite plus scale
– Average (or composite) proxies into some index
(e.g., just average, and make dimensionless)
– Calibrate the composite to hemispheric mean
temperature from instrumental data
• CFR – climate field reconstruction
– EOF regression, or other technique, to reconstruct
hemispheric temperature field
• Used, for example, to reconstruct SSTs back
into 1800’s using sparse instrumental data
– Spatially average the reconstructed field to
estimate hemispheric mean temperature
Climate Research Branch / CCCma
Reconstruction techniques
CPS
• Ordinary Least Squares
Tt  Pt   t
• Total Least Squares
Tt   ( Pt  t )   t
• Variance Matching
Tt  Pt   t
ˆ  [V (T ) / V ( P)]1/ 2
• Inverse Regression
Pt  Tt   t
• Kalman Filter/Smoother
• MBH (1998)
CFR
• RegEM
Pt   Tt   t
Tt  φ Tt-1  Ft  t
Tt 
  u
k
NH
k
t ,k
vk dA   t
Climate Research Branch / CCCma
Improved parameter estimation technique
Kalman filter estimates
Proxy data (Pt)
State process:
NH temperature (Tt)
Estimated influence
of external forcings (Ft)
Lee et al, 2008, 2010
1000
known
known
unknown
known
known
known
1850
2007
Climate
Research
15 point network – 11 year moving average
– CSM
- Branch
SNR /=CCCma
0.5
One particular reconstruction from the sample of 100
Climate
Research
Branch
/ CCCma
100 pseudo proxies – 1860-1970 calibration
– mean
abs
deviation
Climate Research Branch / CCCma
Reconstruction techniques
CPS
• Ordinary Least Squares
Tt  Pt   t
• Total Least Squares
Tt   ( Pt  t )   t


• Variance Matching
Tt  Pt   t
ˆ  [V (T ) / V ( P)]1/ 2

• Inverse Regression
Pt  Tt   t

• Kalman Filter/Smoother
Pt   Tt   t
Tt  φ Tt-1  Ft  t

Photo:
F. Zwiers
Climate Research Branch
/ CCCma
Thanks