Discussion of use of statistical methods in palaeo-reconstructions

1. Photo: F. Zwiers 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

2. 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. 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. 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. 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. 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

7. The calibration problem Photo: F. Zwiers

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

9. 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. Reconstruction techniques • Ordinary Least Squares • Total Least Squares • Variance Matching CPS • Inverse Regression • Kalman Filter/Smoother • MBH (1998) CFR • RegEM

11. Improved parameter estimation technique Kalman filter estimates known known Proxy data (Pt) State process: NH temperature (Tt) unknown known Estimated influence of external forcings (Ft) known known 2007 1000 1850 Lee et al, 2008, 2010

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

13. 100 pseudo proxies – 1860-1970 calibration – mean abs deviation

14. Reconstruction techniques  • Ordinary Least Squares  • Total Least Squares  • Variance Matching CPS  • Inverse Regression  • Kalman Filter/Smoother

15. Photo: F. Zwiers Thanks