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Saturday, August 21, 2010
Hockey Sticky Wicket
This is further analysis of the infamous attempts by climate scientists to use historical proxies to predict climate. As I posted form the very beginning of this blog, this was a suspect enterprise if only because the actual variation range during the Holocene is 2 degrees. How do you tell the difference? The fact is that you do not and end up stacking guess on guess.
The good news is that everyone has sobered up and is applying their skills with great energy.
After reading through all this, it seems likely that we should be able to produce a fine and reliable random number generator from the daily weather data. This is of some use in digital applications.
New paper makes a hockey sticky wicket of Mann et al 98/99/08
Oh, my. There is a new and important study on temperature proxy reconstructions (McShane and Wyner 2010) submitted into the Annals of Applied Statistics and is listed to be published in the next issue. According to Steve McIntyre, this is one of the “top statistical journals”. This paper is a direct and serious rebuttal to the proxy reconstructions of Mann. It seems watertight on the surface, because instead of trying to attack the proxy data quality issues, they assumed the proxy data was accurate for their purpose, then created a bayesian backcast method. Then, using the proxy data, they demonstrate it fails to reproduce the sharp 20th century uptick.
Now, there’s a new look to the familiar “hockey stick”.
Multiproxy reconstruction of Northern Hemisphere surface temperature variations over the past millennium (blue), along with 50-year average (black), a measure of the statistical uncertainty associated with the reconstruction (gray), and instrumental surface temperature data for the last 150 years (red), based on the work by Mann et al. (1999). This figure has sometimes been referred to as the hockey stick. Source: IPCC (2001).
FIG 16. Backcast from Bayesian Model of Section 5. CRU Northern Hemisphere annual mean land temperature is given by the thin black line and a smoothed version is given by the thick black line. The forecast is given by the thin red line and a smoothed version is given by the thick red line. The model is fit on 1850-1998 AD and backcasts 998-1849 AD. The cyan region indicates uncertainty due to t, the green region indicates uncertainty due to β, and the gray region indicates total uncertainty.
Not only are the results stunning, but the paper is highly readable, written in a sensible style that most laymen can absorb, even if they don’t understand some of the finer points of bayesian and loess filters, or principal components. Not only that, this paper is a confirmation of McIntyre and McKitrick’s work, with a strong nod to Wegman. I highly recommend reading this and distributing this story widely.
We find that the proxies do not predict temperature significantly better than random series generated independently of temperature. Furthermore, various model specifications that perform similarly at predicting temperature produce extremely different historical backcasts. Finally, the proxies seem unable to forecast the high levels of and sharp run-up in temperature in the 1990s either in-sample or from contiguous holdout blocks, thus casting doubt on their ability to predict such phenomena if in fact they occurred several hundred years ago.
Here are some excerpts from the paper (emphasis in paragraphs mine):
This one shows that M&M hit the mark, because it is independent validation:
In other words, our model performs better when using highly autocorrelated noise rather than proxies to ”predict” temperature. The real proxies are less predictive than our ”fake” data. While the Lasso generated reconstructions using the proxies are highly statistically significant compared to simple null models, they do not achieve statistical significance against sophisticated null models.
We are not the first to observe this effect. It was shown, in McIntyre and McKitrick (2005a,c), that random sequences with complex local dependence structures can predict temperatures. Their approach has been roundly dismissed in the climate science literature:
To generate ”random” noise series, MM05c apply the full autoregressive structure of the real world proxy series. In this way, they in fact train their stochastic engine with significant (if not dominant) low frequency climate signal rather than purely non-climatic noise and its persistence. [Emphasis in original]
Ammann and Wahl (2007)
On the power of the proxy data to actually detect climate change:
This is disturbing: if a model cannot predict the occurrence of a sharp run-up in an out-of-sample block which is contiguous with the insample training set, then it seems highly unlikely that it has power to detect such levels or run-ups in the more distant past. It is even more discouraging when one recalls Figure 15: the model cannot capture the sharp run-up even in-sample. In sum, these results suggest that the ninety-three sequences that comprise the 1,000 year old proxy record simply lack power to detect a sharp increase in temperature. See Footnote 12
On the other hand, perhaps our model is unable to detect the high level of and sharp run-up in recent temperatures because anthropogenic factors have, for example, caused a regime change in the relation between temperatures and proxies. While this is certainly a consistent line of reasoning, it is also fraught with peril for, once one admits the possibility of regime changes in the instrumental period, it raises the question of whether such changes exist elsewhere over the past 1,000 years. Furthermore, it implies that up to half of the already short instrumental record is corrupted by anthropogenic factors, thus undermining paleoclimatology as a statistical enterprise.
FIG 15. In-sample Backcast from Bayesian Model of Section 5. CRU Northern Hemisphere annual mean land temperature is given by the thin black line and a smoothed version is given by the thick black line. The forecast is given by the thin red line and a smoothed version is given by the thick red line. The model is fit on 1850-1998 AD.
We plot the in-sample portion of this backcast (1850-1998 AD) in Figure 15. Not surprisingly, the model tracks CRU reasonably well because it is in-sample. However, despite the fact that the backcast is both in-sample and initialized with the high true temperatures from 1999 AD and 2000 AD, it still cannot capture either the high level of or the sharp run-up in temperatures of the 1990s. It is substantially biased low. That the model cannot capture run-up even in-sample does not portend well for its ability
to capture similar levels and run-ups if they exist out-of-sample.
Research on multi-proxy temperature reconstructions of the earth’s temperature is now entering its second decade. While the literature is large, there has been very little collaboration with universitylevel, professional statisticians (Wegman et al., 2006; Wegman, 2006). Our paper is an effort to apply some modern statistical methods to these problems. While our results agree with the climate scientists findings in some respects, our methods of estimating model uncertainty and accuracy are in sharp disagreement.
On the one hand, we conclude unequivocally that the evidence for a ”long-handled” hockey stick (where the shaft of the hockey stick extends to the year 1000 AD) is lacking in the data.The fundamental problem is that there is a limited amount of proxy data which dates back to 1000 AD; what is available is weakly predictive of global annual temperature. Our backcasting methods, which track quite closely the methods applied most recently in Mann (2008) to the same data, are unable to catch the sharp run up in temperatures recorded in the 1990s, even in-sample.
As can be seen in Figure 15, our estimate of the run up in temperature in the 1990s has a much smaller slope than the actual temperature series. Furthermore, the lower frame of Figure 18 clearly reveals that the proxy model is not at all able to track the high gradient segment.Consequently, the long flat handle of the hockey stick is best understood to be a feature of regression and less a reflection of our knowledge of the truth. Nevertheless, the temperatures of the last few decades have been relatively warm compared to many of the thousand year temperature curves sampled from the posterior distribution of our model.
Our main contribution is our efforts to seriously grapple with the uncertainty involved in paleoclimatological reconstructions. Regression of high dimensional time series is always a complex problem with many traps. In our case, the particular challenges include (i) a short sequence of training data, (ii) more predictors than observations, (iii) a very weak signal, and (iv) response and predictor variables which are both strongly autocorrelated.
The final point is particularly troublesome: since the data is not easily modeled by a simple autoregressive process it follows that the number of truly independent observations (i.e., the effective sample size) may be just too small for accurate reconstruction.
Climate scientists have greatly underestimated the uncertainty of proxy based reconstructions and hence have been overconfident in their models. We have shown that time dependence in the temperature series is sufficiently strong to permit complex sequences of random numbers to forecast out-of-sample reasonably well fairly frequently (see, for example, Figure 9). Furthermore, even proxy based models with approximately the same amount of reconstructive skill (Figures 11,12, and 13), produce strikingly dissimilar historical backcasts: some of these look like hockey sticks but most do not (Figure 14).
Natural climate variability is not well understood and is probably quite large. It is not clear that the proxies currently used to predict temperature are even predictive of it at the scale of several decades let alone over many centuries. Nonetheless, paleoclimatoligical reconstructions constitute only one source of evidence in the AGW debate. Our work stands entirely on the shoulders of those environmental scientists who labored untold years to assemble the vast network of natural proxies. Although we assume the reliability of their data for our purposes here, there still remains a considerable number of outstanding questions that can only be answered with a free and open inquiry and a great deal of replication.
Commenters on WUWT report that Tamino and Romm are deleting comments even mentioning this paper on their blog comment forum. Their refusal to even acknowledge it tells you it has squarely hit the target, and the fat lady has sung – loudly.