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

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

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.

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?

ECHO-G simulations „Erik den Røde” (1000-1990)

and “Christoph Columbus” (1550-1990)

with estimated volcanic, GHG and solar forcing

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.

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.

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.

pseudo-proxies: grid point SAT plus white noise(largest sample available to MBH)

Testing the MBH method

Mimicking MBH?

Discussion

• Claim: MBH was not built for such large variations as in ECHO-G

• But – the same phenomenon emerges in a control run.

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.

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”.

CPS: simple average of normalized proxies,

then rescale to instrumental NHT variance

Comparison of MBH with Moberg’s method

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?

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.

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.

Semi-quantitative agreement between

CSM and ECHO-G simulations

d (sea-level)/dt~temperature

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

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.

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.