2000 Years Surface Temperatures Time Series Lag Plot

The NAS report has been chastised here and here for concluding that it is “plausible” that the “Northern Hemisphere was warmer during the last few decades of the 20th century than during any comparable period over the preceding millennium” while at the same time conceding that every statistical criticism of MBH is correct, disowning MBH claims to statistical skill for individual decades and years, and finding little confidence in reconstructions of surface temperatures from 1600 back to A.D. 900, and very little confidence in findings on average temperatures before then.

One of the main justifications for this plausibility was the “general consistency” of other studies.

The committee noted that scientists’ reconstructions of Northern Hemisphere surface temperatures for the past thousand years are generally consistent. The reconstructions show relatively warm conditions centered around the year 1000, and a relatively cold period, or “Little Ice Age,” from roughly 1500 to 1850. (NAS press release)

I want to show to what a vacuous motherhood statement this is. Previously I have shown that virtually any data, including random data, will produce a graph similar to the existing studies if you ‘cherry pick’ proxies for correlations with temperature and then you squint your eyes a bit here, here, and here. Today I thought I would run a simple statistical test see how consistent each of the reconstructions really is.

Below I have plotted up each of the reconstructions and CRU temperatures using a lag plot. A lag plot shows the value of a time series against its successive values (lag 1). A lag plot allows easy discrimination of three main types of series:

  • Random – shown as a cloud
  • Autocorrelated – shown as a diagonal, and
  • Periodic – shown as circles.

lag-plot.png

Millennial temperature reconstructions on a lag plot.

The data and reconstructions above are:

	CRU	Climate Research Unit
3	J98	Jones et al. 1998 Holocene
4	MBH99	Mann et al. 1999 Geophys Res Lett
5	MJ03	Mann and Jones 2003
6	CL00	Crowley and Lowery 2000 Ambio
7	BJ00	Briffa 2000 Quat Sci Rev
8	BJ01	Briffa et al. 2001 J Geophys Res
9	Esp02	Esper 2002 Science
10	Mob05	Moberg 2005 Science

The substantial differences between them are clear from the lag plots.

Two of the plots, MJ03 and CL00 have very strong diagonals, and look nothing like the CRU temperatures.

Two of the plots, CL00 and Mob05 have distinct circular patterns suggesting periodicity, a pattern not present in the CRU temperatures.

BJ01 appears random.

The ones that look a bit like temperatures are J98, MBH98, BJ00 and Esp02. Of these MBH98 uses a flawed methodology according to the NAS.

You have to squint very hard for the actual reconstructions of temperature to look consistent. The lag plot shows there is very little real consistency between the series in even the broad features of the underlying dynamics: random, autocorrelated and periodic. This proves what a generic motherhood statement “… generally consistent” really is.

Message:

For successful analytics you need to do more than make motherhood statements that can hardly be proved wrong, and squint your eyes very hard to see the similarity between things. You need to at least apply basic techniques and probe the underlying dynamics, carefully discriminating between things. It is no mistake that the term ” .. general consistency” is not found in the manual of scientific method. Seeking general consistency, like broad consensus, is just social constructivism, with objective fact playing a small role if any, and nicely summed up by the phrase “Hottest in Whatever Many Years”. There are hypotheses, there are tests, and there is falsification (and if you are a rabid Popperrite — corroboration — which is a form of falsification anyway).

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0 thoughts on “2000 Years Surface Temperatures Time Series Lag Plot

  1. Sorry for the lag. That’s fascinating how you could extract information from them in such a way that you get totally different pictures. This is exactly the type of stuff that should be done with the autocorrelations because such procedures are kind of the strongest constraints on a possible theory or a model. Congrats and keep on playing. Maybe you should publish an extended version of such a work. Best, Lubos

  2. Sorry for the lag. That’s fascinating how you could extract information from them in such a way that you get totally different pictures. This is exactly the type of stuff that should be done with the autocorrelations because such procedures are kind of the strongest constraints on a possible theory or a model. Congrats and keep on playing. Maybe you should publish an extended version of such a work. Best, Lubos

  3. Yes they are interesting, particularly as the process for generating them is so simple. I would like to see them animated. I like the comments about strength of constraints too. Makes me think of some sort of heirarchy of constraints that could be addressed systematically.

  4. Yes they are interesting, particularly as the process for generating them is so simple. I would like to see them animated. I like the comments about strength of constraints too. Makes me think of some sort of heirarchy of constraints that could be addressed systematically.

  5. MJ03 and Mob05 have the circular patterns in them, correct? 1st plot on 2nd row and last plot on 3rd row. Is it possible to determine what steps in MJo3 and Mob05 inject this sort of pattern into your plots? Presumably they, (MJ03 & Mob05), share some method(s) not found in the others? Would you consider this to be an artifact of their process and not something resulting from their selection of data?

    I am no mathematician and apologize in advance if these questions are nonsense or have trivial answers.

  6. MJ03 and Mob05 have the circular patterns in them, correct? 1st plot on 2nd row and last plot on 3rd row. Is it possible to determine what steps in MJo3 and Mob05 inject this sort of pattern into your plots? Presumably they, (MJ03 & Mob05), share some method(s) not found in the others? Would you consider this to be an artifact of their process and not something resulting from their selection of data?

    I am no mathematician and apologize in advance if these questions are nonsense or have trivial answers.

  7. Is it true that some slopes are favored in CRU and J98? If so, that doesn’t seem to be the case in BJ01. The slopes in BJ01’s plot seem to be more random. If this obsevation is correct, why would the CRU plot behave this way?

  8. Is it true that some slopes are favored in CRU and J98? If so, that doesn’t seem to be the case in BJ01. The slopes in BJ01’s plot seem to be more random. If this obsevation is correct, why would the CRU plot behave this way?

  9. Where are the charts? Do the charts say which lags are used? A lag of 1 is often used, but that doesn’t mean it’s always reasonable?  Are the data sets available? Tried partial autocorrelation functions?

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