Hans von Storch & Eduardo Zorita Institute for Coastal Research

1. Testing empirical methods for reconstructing temperature and sea level for times with insufficient instrumental coverage Hans von Storch & Eduardo Zorita Institute for Coastal Research Helmholtz Zentrum Geesthacht, Germany

2. Motivation: the failed quest for low-dimensional nonlinearity in 1986 • In the 19070s and 80s, scientists were eager to identify multi-modality of atmospheric dynamics – as a proof that low-dimensional system’s theory is applicable to atmospheric dynamics. • Hansen, A.R. and A. Sutera, 1986: On the probability density function of planetary scale atmospheric wave amplitude. J. Atmos. Sci. 43 – made widely accepted claims for having detected bimodality in data representative for planetary scale dynamics. • J.M. Wallaceinitiated a careful review – and found the claim exaggerated because of methodical insufficiencies:Nitsche, G., J.M. Wallace and C. Kooperberg, 1994, J. Atmos. Sci. 51. Alleged proof for bi-modality of extratropical atmospheric dynamics

3. Motivation: the failed quest for low-dimensional nonlinearity in 1986 • - From the case of 1986 the scientific community has learned that it is wise to be reluctant before accepting wide-reaching claims which are based on purportedly advanced and complex statistical methods. • - Statistical analysis does not provide magic bullets. After a real pattern has been detected with an allegedly advanced method, it must be identifiable also with simpler methods.

4. We have used millennial simulations to examine the questions … • Is the hockey stick method reliable in reconstructing low-frequency variability? • Is the phenomenon that an EOF analysis of a field of spatially incoherent, time wise red noise variables sometimes returns artificial hockey sticks when the time centering is done for a sub-period, relevant when applied to historical situations? • Can global mean sea level change be deduced from global mean temperature?

5. ECHO-G simulations „Erik den Røde” (1000-1990) and “Christoph Columbus” (1550-1990) with estimated volcanic, GHG and solar forcing

7. The millennial run generates temperature variations considerably larger than MBH-type reconstructions. The simulated temperature variations are of a similar range as derived from NH summer dendro-data, from terrestrial boreholes and low-frequency proxy data.

8. For the purpose of testing reconstruction methods, it does not really matter how „good“ the historical climate is reproduced by a millennial simulation. Such model data provide a laboratory to examine statistical diagnostic methods.

9. Testing Claims - #1 The historical development of air temperature during the past 1000 years resembles a hockey stick – with a weak ongoing decline until about 1850 and a marked increase thereafter.

10. Testing the MBH method pseudo-proxies: grid point SAT plus white noise(largest sample available to MBH)

12. Mimicking MBH?

13. Discussion • Claim: MBH was not built for such large variations as in ECHO-G • But – the same phenomenon emerges in a control run.

14. Training with or without trend • In our implementation of MBH, the trend in the calibration period is taken out. • When the trend during the calibration period is used as a critical factor in the empirical reconstruction model, then the contamination of the proxy trend by non-climatic signals must be mimicked. • Thus, apart of white/red noise also error on the centennial time scale. • Here: 50% centennial,75% white noise. • Again heavy underestimation of long-term variability.

15. Conclusion #1 • MBH algorithm does not satisfy the basic requirement R·S = 1 • Instead MBH underestimates long-term variability • But R(S(E)) ≈ M, with M representing MBH and E the millennial simulation “Erik de Røde”.

16. Comparison of MBH with Moberg’s method CPS: simple average of normalized proxies, then rescale to instrumental NHT variance

17. Testing Claims - #2 • McIntyre, M., and R. McKitrick, 2005: Hockey sticks, principal components and spurious significance. Geoph Res. Letters 32 • Claim: Partial centering generates PC coefficients with a hockey stick pattern from red-noise random time series fields. • Claim is valid – but does it matter when deriving historical reconstructions?

18. Conclusion #2 • Resulting from the application of the MBH98 algorithm to a network of pseudo-proxies. • The variance of the pseudoproxies contains 50% noise (top panel: white noise; bottom panel: red noise with one-year lag-autocorrelation of 0.8). • The pseudoproxies were subjected to separate PCA in North America, South America and Australia with full (1000-1980; red) or partial (1902-1980; blue) centering. • This specific critique of McIntyre and McKitrick is irrelevant for the problem of reconstructing historical climate.

19. Testing Claims - #3 d (sea-level)/dt~temperature Past sea-level evolution is not completely understood; predictions for the future are uncertain (new factors) An empirical approach was suggested, which was published as: Rahmstorf, S., 2007: science 315, 368-370 sea-level rate temperature We tested the link in the virtual reality of our millennial simulation of Erik den Røde. Models describe mostly only thermal expansion; not ice sheet growing and melting. Thus, a test of the methodology in such models is liberal.

20. Semi-quantitative agreement between CSM and ECHO-G simulations

21. d (sea-level)/dt~temperature

22. Variability of the regression coefficient in sliding time-windows: dH/dt ~ T

24. Millennial simulations are useful laboratories to test empirical methods, which can not be really validated with reliably recorded data. • The MBH method is associated with a systematic underestimation of long-term variability. • The McMc-phenomenon of “artificial hockey sticks” (AHS) due to unwise centering of EOFs does not cause harm for the overall process. • The straight-forward “composite and scaling” (similar to Moberg’s) method exhibits relatively little systematic errors. • Global mean temperature is not a good predictor for the thermosteric sea-level change The best predictor (among those tested in the simulation is surface heat-flux (but difficult to measure - no time series). The time derivative of temperature is a better predictor for sea-level variations. Overall Conclusions

25. Publications: MBH: von Storch, H., E. Zorita, J. Jones, Y. Dimitriev, F. González-Rouco, and S. Tett, 2004: Reconstructing past climate from noisy data, Science 306, 679-682, 22 October 2004 + comments + replies Zorita, E., and H. von Storch, 2005: Methodical aspects of reconstructing non-local historical temperatures, Memorie della Società Astronomica Italia 76, p.794ff von Storch, H., E. Zorita and J.F. González-Rouco, 2009: Assessment of three temperature reconstruction methods in the virtual reality of a climate simulation. International Journal of Earth Sciences McMc: von Storch, H., and E. Zorita, 2005: Comment to "Hockey sticks, principal components and spurious significance" by S. McIntyre and R. McKitrick, Geophys. Res. Lett. 32, L 20701 doi:10.1029/2005GL022753 + reply Sea level: von Storch, H., E. Zorita and J.F. González-Rouco, 2008: Relationship between global mean sea-level and global mean temperature and heat flux in a climate simulation of the past millennium, Ocean Dyn. doi 10.1007/s10236-008-0142-9, 10pp.