1. Climate Research Branch / CCCma Discussion of use of statistical methods in palaeo-reconstructions Photo: F. Zwiers Francis Zwiers Climate Research Division, Environment Canada, Toronto, Ontario 11 IMSC, 12-16 July 2010, Edinburgh

2. 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).

3. 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)

4. 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

5. 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

6. Climate Research Branch / CCCma 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 Statistical considerations

7. Climate Research Branch / CCCma The calibration problem Photo: F. Zwiers

8. Climate Research Branch / CCCma The Calibration Problem NH mean temperature Proxy series Need to reconstruct Known 1860 2000 1000 Known2000 10001860Known Calibration period Year Training period Identify a statistical relationship between a collection proxies and NH temperature Apply that relationship to reconstruct past NH temperature Reconstruction period

9. 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

10. Climate Research Branch / CCCma Reconstruction techniques Ordinary Least Squares Total Least Squares Variance Matching MBH (1998) Inverse Regression Kalman Filter/Smoother RegEM CPS CFR

11. Climate Research Branch / CCCma Improved parameter estimation technique Kalman filter estimates known Proxy data (P t ) unknownknown State process: NH temperature (T t ) known 1850 2007 1000 Estimated influence of external forcings (F t ) Lee et al, 2008, 2010

12. Climate Research Branch / CCCma 15 point network – 11 year moving average – CSM - SNR = 0.5 One particular reconstruction from the sample of 100

13. Climate Research Branch / CCCma 100 pseudo proxies – 1860-1970 calibration – mean abs deviation

14. Climate Research Branch / CCCma Reconstruction techniques Ordinary Least Squares Total Least Squares Variance Matching Inverse Regression Kalman Filter/Smoother CPS  

15. Climate Research Branch / CCCma Thanks Photo: F. Zwiers