by Richard Tol
There has been some brouhaha over a guest post by Lüdecke, Link, and Ewert. I think the quality of work is so bad that Judith should never have spotlighted these papers. Publicly berating Judith, I of course drew more attention to their work, and her response added to that.
So why I do think this work is so bad it should be ignored?
There are two papers. The first is by Lüdecke, Link, and Ewert (LLE). It opens with: “It is widely accepted that global surface air temperatures have increased in the past 100 years, with a pronounced rise in the last 50 years. However, the question is not yet answered which forcings cause the actual global temperature change. One assumes [people have blamed] natural fluctuations, the Atlantic and Pacific Multidecadal Oscillations, increasing green house gases, urban heat island effects (UHI), natural impacts as volcanic eruptions, condensation nuclei generated by cosmic rays in which their concentration is governed by the sun’s magnetic field, anthropogenic aerosols from insufficiently altered coal power plants and further impacts.”
This is an important question: Why has the world warmed?
LLE address this question using statistical methods. Their analysis uses one particular model and one particular method. The model is persistence. Some time series are uncorrelated: An anomaly at time t has no effect in later periods. Other time series are autocorrelated: An anomaly at time t is repeated in later years, but its magnitude fades away at an exponential rate. Yet other series are integrated (or order one): An anomaly at time t remains forever. And some series are somewhere in between autocorrelation and integration: Anomalies fade but only slowly. This is called persistence, long term memory or fractional integration, and is associated with such people as Hurst and Mandelbrot. Persistence was first analyzed in the temperature record by Bloomfield and Nychka and more recently by Rea, Reale and Brown. It is a perfectly respectable line of inquiry.
As their method, LLE use detrended fluctuation analysis (DFA). DFA is a perfectly respectable method to estimate the correlation function, power spectrum and Hurst exponent in one go.
So far so good. Unfortunately, fluctuation analysis does not work on trending variables. Therefore, LLE use DETRENDED fluctuation analysis. That is, they first fit a polynomial of order two to the data, remove this trend, and study the deviations from the trend.
Having removed the trend from their data, LLE cannot answer the question: What caused the warming? They eliminated from their analysis the very thing in which they are interested.
There are other flaws. You need a lot of data to reliably estimate the Hurst exponent. 100 years of data is not enough. Therefore, LLE switch to monthly data. Although this increases the number of observations to 1200, it simultaneously reduces the time step of their analysis by a factor 12. 1200 months is still only 100 years. No information was added. They cannot estimate the annual Hurst exponent with 100 years of data. With 1200 months of data, they can estimate the monthly Hurst exponent – but they still do not know the annual Hurst exponent.
In fact, in a further act of pre-analysis data manipulation, LLE removed the seasonal cycle. Such data manipulation is known to affect the later analysis, perhaps substantially so. LLE do not provide any detail, however, so the impact is hard to assess.
LLE then estimate the Hurst exponent. The paper omits information on the adequacy of the statistical fit. No indication is given on the precision of the estimates.
LLE then use the estimated model to create a large number of synthetic temperature records, and thus compute the probability of observing the actual temperature record. They find that the observed trend is actually not that rare, which is in line with their Hurst exponent of about 0.65. Again, confidence intervals are not provided, but as they cannot reliably estimate the annual Hurst exponent, confidence must be low.
Crucially, LLE use the 20th century record to define natural variability. That is, they use the observations of the 20th century to assess whether or not the 20th century was natural or otherwise. This is tautological.
LLE do not test the hypothesis of “natural variation” against any other possible explanation of the warming of the 20th century.
The second paper, by Lüdecke, addresses some of the concerns. Instead of 2250 100-year temperature records, 5 200-year records are used, again in monthly time steps. Furthermore, 2 2000-year proxy records (annual time steps) are used. The same procedure is used: The trend (of interest) is removed, and DFA is used to estimate the Hurst exponent. In the temperature records, the Hurst exponent is about 0.6. In the proxy records, the Hurst exponent is about 0.9.
There can be various reasons for this. Maybe something changed in the last 200 years, maybe you cannot compare annual and monthly Hurst exponents, maybe the proxy records are bad proxies. No confidence interval is given for the monthly Hurst exponents, so it may be that the difference is not even statistically significant.
Lüdecke then computes the Hurst exponents of the sunspot cycle, using annual observations for the period 1700-2000, and decadal reconstructions for the period 9,500 BC-1900 AD. Again, the long-term record shows a higher Hurst exponent (1.0) than the medium-term record (0.6). As sun spots follow an irregular 11-year cycle, chances are that the difference is caused by different resolution of the two sunspot records. Lüdecke argues that sun has caused the difference in the Hurst exponent between the temperature observations and the temperature proxies. However, he does not compute the long-range cross correlation (the bivariate generalization of the Hurst exponent), so this is speculation.
Oddly, Lüdecke omits carbon dioxide.
In sum, these two papers are badly done. We do not learn anything. The authors argue that natural variability may well have caused the observed warming in the 20th century, but the first paper does not test this and the second paper is inconclusive. The second paper makes a link to the sun, but fails to bivariately test this hypothesis, let alone against other hypotheses. No conclusions can be drawn from this work.
JC note: This is a technical thread that will be moderated for relevance. Make your general comments on EIKE or disinformation brouhaha on one of the previous threads. I invited Richard Tol to make this post, based upon his comments made in the previous threads.