by Horst-Joachim Lüdecke, Rainer Link, and Friedrich-Karl Ewert
In his comments R. L. Tol argues that our paper LU and LL should be ignored. We will respond following the order of R. Tol’s objections. We refer to the same shortcuts and references as in our guest post – LU resp. LL, and -.
R. Tol claims “However, the question is not yet answered which forcings cause the actual global temperature change”. Actually, this was not at all what our work was aimed for. Everyone who is familiar with persistence, HURST exponents, DFA etc. knows very well that these methods cannot give any information about the nature of trends or persistence (if trends are found). See also the appropriate remark in LL on page 5 where we denote “… neither Eq. (2) nor a power law of the fluctuation of the FA or DFA says anything about its origin”. We assume that this statement is clear enough, but it was not percieved by R. Tol. Consequently, we did not eliminate anything as Tol argues in “They eliminated from their analysis the very thing in which they are interested.”
Principally, our papers are neither predominantly interested in nor can give any answers about the forcings. Regarding Figure 10 on page 17 of LL, only the UHI and elevation warming can be clearly identified. Without doubt, there is a leftover of many possible further forcings that could have caused the 20th century warming – even so the anthropogenic CO2 that is haunting so many people. However, our applied method cannot distinguish between these forcings. Our main task was to show that the 20th century warming was predominantly a natural fluctuation. This answer was given by an elaborated statistical method, which of course like all statistical analyses have its limits.
R. Tol argues “Therefore, LL 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. “This statement is completely wrong, to be polite. There is no annual HURST exponent in favour of a monthly or daily one. Autocorrelation of temperature records provokes that the autocorrelation function fades with a power law. It is self evident by basic maths that this law, and as a consequence, the exponent of the power law is not effected by the time unit, be it day, month or year (see in LU the beginning of the last segment on page 5. See also in LL on page 2, Eq. 2 and on page 4, Eq. 5 and Eq. 6). R. Tol should first read , , then the papers cited therein, then our papers and then criticize, not the other way around.
R. Tol notes “data manipulation” in the context of monthly means. However, LL reports about removing the seasonal dependence of monthly means on page 4 in the last phrase of the section above Eq. (3). Removing seasonal effects is indispensable for a correct application of the DFA and has nothing to do with “data manipulation”. It can be found in every paper that uses monthly means with DFA, for instance in ,  and all appropriate papers cited therein.
R. Tol bemoans “Crucially, LL 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.” Unfortunately, also this statement is dauntingly wrong. The definition of the naturality of a temperature record is given in detail in Chapter 3 of LL. There is nothing you may find in this chapter that can be associated with Tol’s absurd allegation. We did not use any 20th record to define natural variability. The main item is connected with Figure 3. R. Tol should read this chapter more carefully to understand the procedure.
R. Tol says “LU and LL 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.” In our papers LU and LL the HURST exponents are calculated by an established method, not “estimated”. We give in LU the uncertainty of Alpha values in the last section of page 13. By the way, in Tol’s objections once again the nonsense of an annual HURST exponent in opposite to a monthly one is brought forward.
In the statement “LL 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.” R. Tol confounds in addition two quite differerent topics. The confidence interval (better the confidence limit) for the assessment that a “trend” in a record is either external or a natural fluctuation caused by persistence has nothing to do with the error in the value of HURST exponents.
The only substantial and really interesting item that we could find in Tol’s critique refers to LU when R. Tol objects “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.” The paper cited by R. Tol analyzes cross correlation between two monofractal time series that have HURST exponents H1 and H2. However, as Figure 8 (right panel) of LU clearly shows, the sun spot series is not monofractal, i.e. it has no unique HURST exponent. The consequences of this fact and the applied method are dealt with in chapter 6. of LU. R. Tol is completely right that the hypothesis about the sun’s influence on the HURST exponents of tree rings and stalagmite proxies in LU is a speculation. The header of chapter 6 in LU “A hypothesis on the sun’s influence” expresses this clearly. It is common in scientific papers to sometimes add a speculation.
We regret that R. Tol – as he bemoans – does not learn anything from our papers. We are not responsible for this deficit. R. Tol criticizes predominantly the state of the art of persistence analysis. We did not develop these methods, we used them. Further, we assume that R. Tol’s critique is caused by his inadequate knowledge about the whole persistence and DFA methods. Therefore, we take the liberty to recommend him politely to read the book of Jens Feder “Fractals” for studying the basics. In addition, a closer look on the many papers about FA, DFA and their applications might be helpful. We will willingly provide him with most of the relevant papers (Judy can give him the E-Mail-adress of Lüdecke). It should be stressed that we used an elaborated new method , . If R. Tol likes to criticize this method – after beeing better informed about it – we recommend him to write directly to the authors of , .
We would like to answer on the many comments on our guest post. However, more than 500 comments – so far – are too much. Most comments have the same shortcoming as Tol’s critique – a fundamental deficit of knowledge about persistence and DFA. However, we found also some important and very interesting objections and comments. For those we prepare a follow-up to our guest post and will publish it on Judy’s Blog. She has already agreed. No paper is free of failings. Therefore, we welcome – as good practice in science – every critique if it is substantial.
JC note: I invited Ludecke et al. to respond to the comments made in the previous two posts. I would like to thank Horst-Joachim Lüdecke, Rainer Link, and Friedrich-Karl Ewert, Richard Tol, and those that have made thoughtful and constructive comments on these two threads. This has been an interesting, albeit controversial, experiment in “blog” science.
Moderation note: This is a technical tread, comments will be moderated for general relevance. The “debate” surrounding disinformation, etc. can be continued on the original thread, or at collide-a-scape.