hans von storch & eduardo zorita institute for coastal research
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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. Motivation: the failed quest for low-dimensional nonlinearity in 1986. - PowerPoint PPT PresentationTRANSCRIPT
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Testing empirical methods for reconstructing temperature and sea level for times with insufficient instrumental coverage
Hans von Storch & Eduardo ZoritaInstitute for Coastal ResearchHelmholtz Zentrum Geesthacht, Germany
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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. Wallace initiated 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
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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.
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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?
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ECHO-G simulations „Erik den Røde” (1000-1990)
and “Christoph Columbus” (1550-1990)
with estimated volcanic, GHG and solar forcing
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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.
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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.
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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.
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pseudo-proxies: grid point SAT plus white noise(largest sample available to MBH)
Testing the MBH method
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Mimicking MBH?
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Discussion
• Claim: MBH was not built for such large variations as in ECHO-G
• But – the same phenomenon emerges in a control run.
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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.
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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”.
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CPS: simple average of normalized proxies,
then rescale to instrumental NHT variance
Comparison of MBH with Moberg’s method
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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?
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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.
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d (sea-level)/dt~temperature
sea-level rate 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
Testing Claims - #3
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.
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Semi-quantitative agreement between
CSM and ECHO-G simulations
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d (sea-level)/dt~temperature
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Variability of the regression coefficient in sliding time-windows:dH/dt ~ T
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Overall Conclusions
1.Millennial simulations are useful laboratories to test
empirical methods, which can not be really
validated with reliably recorded data.
2. The MBH method is associated with a systematic underestimation of long-term variability.
3. The McMc-phenomenon of “artificial hockey sticks” (AHS) due to unwise centering of EOFs does not cause harm for the overall process.
4. The straight-forward “composite and scaling” (similar to Moberg’s) method exhibits relatively little systematic errors.
5. 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.
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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.794ffvon 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.