What was "First" About MBH98?

The NAS Panel claimed that MBH98 was the "first systematic" multiproxy study. It wasn’t; it didn’t even claim to be, citing Bradley and Jones 1993 and several other studies of the same vintage as predecessors. Crowley was a peer reviewer for the NAS panel, who presumably relied on him to catch this sort of mis-step. He should have caught this, but didn’t. So what was the distinctive contribution of MBH98 – if it wasn’t the “first” multiproxy study?

Rather than going at this from the point of view of statistical methods as I’ve spent most of my time doing recently, I’ve gone back to basics and looked at proxy selection. When you look at the proxy series in the studies leading up to MBH98 (and in the contemporary and somewhat rival Jones et al 1998), it’s remarkable to see how many series were taken directly from Bradley and Jones 1993 and the degree of overlap between the proxy selections. There are a couple of surprising conclusions that emerge from a simple parsing and comparison of selections.

Summary of Proxy Selections
The table below summarizes proxies by class for Bradley and Jones 1993, Barnett et al 1995 (coauthored by Jones), Jones et al 1998, Mann, Park and Bradley 1995 and MBH98. It’s curious that Bradley and Jones join forces in 1993, then seem to fall somewhat competitive paths over the next few years, before Mann and Jones re-joining forces in Mann and Jones 2003. Diaz and Bradley 1992 is reported in the NAS 1995 volume about which I posted a couple of days ago. Rob Wilson wrote me offline objecting to the fact that the chronologies discussed in the NAS 1995 volume were "limited", but, as you will see, these were nonetheless the core of the 1998 studies that were relied upon by IPCC TAR.

I’ve summarized the number of proxies in each study by different proxy classes. Most lables are self explanatory. I’ve distinguished ice cores into two classes: melt percentage and isotopic (dO18). Isotopic dO18 series were not used in Bradley and Jones 1993 and some concerns about dO18 as as a temperature proxy were expressed in the earlier literature (and have re-surfaced in recent literature for tropical ice cores); they became incresingly used.

I’ve divided tree ring series into 4 different classses: "tree ring temperature reconstructions" are series where tree ring site chronologies have been used to reconstruct gridcell temperatures. These reconstructions are linear combinations of one or a small number of site chronologies, but there has been at least a pretence of linking the site chronology to temperature. "Precipitation reconstructions" are self-explanatory. I’ve shown "site chronologies" and "PC series" separately, as in these cases, these are merely chronologies and do not themselves indicate any prior attempt to link the site chronology (or PC series) to temperature. I’ve provided separate summaries for the total network and the 15th century networks, after which I’ll comment on the choices and evolution.

Quickly, you’ll see that Bradley and Jones 1993 used 23 proxies. The majority continued in use in Barnett et al 1995, Jones et al 1998 on the one hand and Mann et al 1995 and MBH98. MBH98 differs from the other studies in that the coverage is far less homogeneous with the number of proxies going from 22 in the AD1400 step to 112 in the AD1820 step; while MBH98 uses virtually all the Bradley and Jones series, it introduces many new series – and these selections are interesting to consider.


Table 1. Proxy Types in 1990s Multiproxy Studies

Proxy Type DB92 BJ93 Barn95 JB98 MPB95 MBH98
Coral 0 0 2 3 2 2
Documentary 1 9 5 2 7 2
Instrumental Temperature 0 0 0 0 0 11
Instrumental Precipitation 0 0 0 0 0 11
Ice Core Melt/Accum 2 4 4 2 4 4
Ice Core dO18 4 0 0 2 2 5
Sediments 0 1 0 0 1 0
Tree Ring Temperature Recons 10 9 9 8 8 9
Tree Ring Precipitation Recons 0 0 0 0 0 3
Tree Ring Site Chronologies 0 0 0 0 11 27
Tree Ring PCs 0 0 0 0 0 31
Total 17 23 20 17 35 112

Table 2. For the Fifteenth Century

Proxy Type DB92 BJ93 Barn95 JB98 MPB95 MBH98
Coral 0 0 0 0 0 0
Documentary 0 3 2 0 2 0
Instrumental Temperature 0 0 0 0 0 0
Instrumental Precipitation 0 0 0 0 0 0
Ice Core Melt/Accum 1 3 3 1 1 3
Ice Core dO18 2 0 0 1 1 3
Sediments 0 1 0 0 1 0
Tree Ring Temperature Recons 4 4 4 5 3 4
Tree Ring Precipitation Recons 0 0 0 0 0 3
Tree Ring Site Chronologues 0 0 0 0 0 6
Tree Ring PCs 0 0 0 0 0 3
Total 7 11 9 7 8 22

<

PROXIES WHERE MBH98 IS MOSTLY SIMILAR

In many of the proxy classes, MBH98 selections are virtually identical to the other studies; I’ll consider these first and then consider proxy classes where major differences arise.

Tree Ring Temperature Reconstructions
The tree ring temperature reconstructions selected in Bradley and Jones 1993 provide a common core to all these studies. All 9 temperature reconstructions in Bradley and Jones 1993 are used either directly in MBH98 (8 cases) or, in the case of the Jacoby treeline reconstruction, by splitting the reconstruction into 11 component chronologies.

The tree ring temperature reconstructions in Bradley and Jones 1993 are mostly familiar to readers of this blog: Polar Urals, Tornetrask (Briffa), Jacoby’s North American treeline composite, Briffa’s North American reconstruction (MXD), Fritts North American reconstruction(RW), Cook’s Tasmania reconstruction, Norton and Palmer’s New Zealand reconstruction and two South American reconstructions from Villalba from Patagonia and Rio Alerce.

The basic selection framework was already set out in Diaz and Bradley 1992. The only Bradley and Jones 1993 series not in Diaz and Bradley 1992 is the Norton and Palmer series; otherwise, the only other change is the consolidation of 3 regional Fritts series listed in Diaz and Bradley 1992 into one series in Bradley and Jones 1993.

Barnett et al 1995 used the identical set of tree ring proxies as Bradley and Jones 1993.

Mann et al 1995 used 8 of the 9 Bradley and Jones tree ring reconstructions — they only dropped the Fritts reconstruction (re-inserted in MBH98). They added one new tree ring series — Kolyma River, Russia, also carried forward into MBH98. However, Mann et al 1995 made one major change presaging MBH98 — instead of using the Jacoby temperature reconstruction as one series, they split them into 11 component site chronologies. The listing in Mann’s thesis shows all the versions as extending from 1515-1982 (but this is probably not correct as a number of chronologies don’t start that early. A 1515 start is also later than some series – Gaspé, in particular, start in MBH98.)

Jones et al 1998, one of the “independent” reconstructions in most spaghetti graphs, used 6 of the 9 tree ring reconstructions of Bradley and Jones 1993. It added the Jasper, Alberta reconstruction of Luckman et al, which becomes used in nearly every subsequent study (but is not used in MBH98), and a Lenca, Chile reconstruction which is not used in subsequent studies. (One has HS, the other doesn’t). Discontinued between Bradley and Jones 1993 and Jones et al 1998 are the Fritts reconstruction and the Northern Patagonia (araucaria) reconstruction. Also, the Briffa et al 1995 version of Polar Urals replaced the Graybill and Shiyatov version (a switch also made in MBH98).

MBH98 did not use any tree ring temperature reconstructions not used in previous studies. The only tree ring temperature reconstruction not used in Bradley and Jones 1993 is the Kolyma River reconstruction. As noted above, the Jacoby treeline reconstruction is replaced by 11 individual site chronologies, themselves not individually calibrated to temperature. The Polar Urals version of Briffa et al 1995 is substitued for the earlier Graybill and Shiyatov version. Otherwise, my surmise is that identical digital versions were used in both studies.

As noted above, Rob Wilson complained that the temperature reconstructions discussed in the NAS1995 were not necessarily constructed according to methods better suited to extracting millennial information. Maybe so. But there was NO material change in the versinos used in MBH98 and Jones et al 1998. So the better question is: if these studies don’t capture centennial variation, why was MBH98 able to extract a HS from them?

Corals
Corals have very short coverage – none go back to the MWP. They merely enhance the appearance of being "multiproxy".

In Bradley and Jones 1993, no coral series were used. Two series were introduced in Barnett et al 1995 (Great Barrier Reef, Galapagos). The same two series were used in Mann et al 1995 and were carried forward to MBH98 and Jones et al 1998. Jones et al 1998 added a coral series from New Caledonia, also used in MBH98. MBH98 added 6 other coral series, including a C-13 series with a very strong HS.

None of the coral series affect 15th century results.

Documentary
Here there is somewhat of a change from Bradley and Jones 1993, with a de-emphasis of documentary series in the later studies.

Bradley and Jones 1993 had 9 documentary series – the most of any of the studies, even MBH98. In addition to the Central England and Central Europe series (used by all subsequent studies), they used one Russian, five Chinese and one Japanese documentary series.

Barnett et al cut back to 5 documentary series, dropping the Russian, Japanese and two Chinese series. Mann et al 1995 cut back to 7, dropping the Russian and Japanese series. Both Jones et al 1998 and MBH98 cut back further, just to the two European series, both of which had annual resolution, whereas the others were reported in decadal versions.

Two Chinese series made a re-appearance in Jones and Mann 2004. I’ve only been able to locate digital versions of 4 documnetary series – these two and the two European series.

Ice Cores
Bradley and Jones 1993 used 4 ice core series based on melt percentage (Agassiz, Devon, Greenland (Kameda) and Svalbard) and did not use any isotopic dO18 series. This was a departure from Diaz and Bradley 1992 which used two melt series (Agassiz, Devon), but also used 4 isotopic series (Camp Century and Milcent, Greenland; Quelccaya, Dunde).

Barnett et al 1995 used the same 4 melt series as Bradley and Joens 1993, as did Mann et al 1995, which additionally used two isotopic series (Quelccaya, Dunde).

Jones et al 1998 dropped two ice core melt series (Agassiz, Devon) both of which had 5-year resolution; and used two different isotope series (Fisher’s Greenland stack, which included Milcent, and Law Dome, Antarctica).

MBH98 also dropped the two ice core melt series with 5 year resolution; also added Fisher’s Greenland stack. Strangely, where Mann et al 1995 had used one Quelccaya series, MBH98 used 4 different series from the same site: different dO18 series from two nearby cores; and two accumulation series from the same cores. These were not pre-processed into one index. Why would 4 different series from Quelccaya be used? Isn’t the theory of "teleconnections" being taken to its reducito ad absurdum if two cores only tens of meters apart can be taken to record different teleconnections with climate fields all over the world?

The Dunde series continued in use in later studies as a strong component of the Yang Chinese composite. The Agassiz melt series, after falling out of favor, re-emerged in Moberg et al 2005, where it is one of the largest single contributors to 20th century HS.

Sediments
A low-frequency temperature reconstruction from sediments (Cloud Lake) in Bradley and Jones 1993, is not used further except in Mann et al 1995. Some sediment series recur in later studies (Crowley and Lowery 2000; and especially Moberg et al 2005)

PROXIES WHERE MBH98 IS DIFFERENT
So far the proxy usage in MBH98 is remarkably similar to the other sites and within the range of variability of the other studies. Now it gets interesting – here are the differences.

Instrumental Temperature
Unlike the other studies, MBH98 included a large number of long instrumental temperature series (although the Central England “documentary” series, used in many studies, is, through most of its history, an instrumental series, and, in this case, the distinction between documentary and instrumental is a bit arbitrary.) In addition to the Central England series, MBH98 included 11 long instrumental series as “proxies”.

This has always caused a bit of controversy, even among pliant climate scientists. However, the impact of using instrumental temperature series is a little different than people thinkg, though I will only allude to it here. Although actual instrumental results for 12 gridcells are available to it, MBH98 methods do not really "peek" at the answer. If I recall correctly, the North American PC1 is weighted more strongly in (say) the reconstruction of 18th century Vienna gridcell reconstruction than the available local instrumental measurements. Some instrumental temperature series actually have negative coefficients in contributing to the final reconstruction (which are more strongly influenced by tree ring PC1s.)

The use of instrumental temperature series as a “proxy” is an MBH innovation and one that has not been followed in other studies (other than the continued use of the Central England series as a "proxy").

Instrumental Precipitation
An unusual and undiscussed MBH98 innovation is the use of instrumental precipitation series in a temperature reconstruction. I guess this is part of theory of "teleconnections". In introducing instrumental precipitation as a temperature proxy, MBH98 did not require that any evidence of a relationship to gridcell temperature be proved. Proving such connections would have been difficult as MBH98 had incorrect gridcell assignments for most of its instrumental precipitation series – sometimes bizarrely so. The Paris precipitation series was re-located to the New England gridcell (“The rain from Maine falls mainly in the Seine”). The Toulouse series was re-located to South Carolina. Identifying these mislocations was not easy as MBH provided incorrect data citations and, even in the Corrigendum, have refused to provide sources for their precipitation data (other than "NOAA"). Their series attributed to Bombay comes from somewhere else – perhaps Philadelphia. Teleconnections indeed.

The MBH98 innovation of using instrumental precipitation series in a temperature reconstruction was not continued in later studies, other than studies by Mann or Ammann continuing the use of the MBH98 network (Rutherford et al 2005, Wahl and Ammann 2006).

Tree Ring Precipitation Reconstructions
Another MBH98 innovation, related to their use of instrumental precipitation records, was their use of tree ring precipitation reconstructions. Here I’m not talking about site chronologies which may be affected by precipitation, but by series actually denominated in mm of precipitation, calculated by relating tree ring chronologies to instrumental precipitation records. Three such series were used in MBH98, all of which were in the 15th century network.

Again, this innovation was not continued other than in Rutherford et al 2005 and Wahl and Ammann 2006.

Tree Ring Site Chronologies
In addition to the 11 Jacoby site chronologies used individually, MBH98 used 16 individual site chronologies – here I’m contrasting the direct use of a chronology with a tree ring temperature reconstruction where the site chronology has been related to gridcell temperature and the resulting series is expressed in deg C. I’m also distinguishing the direct use of a site chronology from its use as part of a tree ring regional network.

In some cases, the individual chronologies have been identified in the literature as precipitation-related (e.g. the Moroccan site chronologies.)

It’s hard to see why some sites are used individually, while others are included in tree ring networks for principal component summarization and some are used more than once. The sites used in the precipitation reconstructions mentioned above are also used in the NOAMER principal components network. The Gaspé site is used individually and in the NOAMER network. Spruce Canyon is used in the NOAMER and STAHLE networks. There’s no obvious rhyme or reason to the methods. Some sites listed as being used are not used and the explanation in the Corrigendum is false.

The use of uncalibrated site chronologies also opens up other potential problems – non-normality, nonlinearity. There was surely an impression attached to MBH98 that some process of checking for the validity of proxies had taken place and some series had had such checking. But then there was the vast unflux of uncalibrated site chronologies. This is the first such use. After MBH98, one starts to see more use of uncalibrated site chronologies, reserving a "check" only for the final answer.

Tree Ring Principal Component Series
The other big innovation of MBH98 was simply throwing vast populations of disparate tree ring chronologies into a hopper, applying an unsupervised algorithm to them (which in their case was the biased MBH principal components method) and then using the resultant PC series without verifying that they had any connection to temperature. Prior to MBH98, there was no suggestion that something like this could be done. The relevant test for a temperature series is not whether it is "significant" under Preisendorfer’s Rule N as a pattern within a network, but whether it is a temperature proxy. This point has been debated at length in the past 2 years. However, here, I’m just noting that, prior to MBH98, even climate scientists made some attempt to ensure that proxies were temperature proxies.

Although MBH purported to rely on prior peer-reviewed literature, the grab-bag of series in the principal component networks and the PC series themselves were never reviewed prior to their use in MBH98. We made this point in our EE 2005 article as follows (and the associated illustration is worth reviewing):

Despite the reliance of MBH98 on the North American PC1, the validity of this series as a temperature proxy was not independently established in peer-reviewed literature….The strong negative bias of the MBH98 PC1 is evident in comparison to the Briffa reconstruction. The strong negative bias of the MBH98 PC1 is also evident in periods where we have instrumental records in North America. There is no reason to believe that average temperatures in the 18th century were negative 3 standard deviation units.


Original caption. Figure 6. Solid: North American temperature reconstruction of Briffa et al. [1992a]. Dashed: the MBH98 North American PC1. All series smoothed with a 25-year Gaussian filter. Both series are standardized by subtracting the 1902-1980 mean and dividing by the 1902-1980 standard deviation (re-scaling is not an issue here, since the PC calculations have already been done.)

A hidden result of the tree ring grab-bag networks in which anything could be dumped in was the introduction of bristlecones into temperature reconstructions – a definite MBH98 innovation. Caveats had been expressed about CO2 fertilization at the highest levels of the climate reconstruction world (even IPCC 2AR). There were explicit cautions about them in the specialist literature. None of the predecessor studies used bristlecones. This in itself is an extraordinary and remarkable finding that even I had not explicitly considered before. think about it - none of the temperature reconstructions in any multiproxy reconstruction prior to MBH98 used bristlecones (or foxtails).

Afterwards, bristlecones (and foxtails) became commonplace – Crowley and Lowery 2000, Esper et al 2002, Cook et al 2004, Moberg et al 2005, Rutherford et al 2005, Hegerl et al 2006, Osborn and Briffa 2006. These weren’t recent collections (they were mostly done in the mid-1980s by Graybill); but they were introduced into multiproxy studies by MBH98. They were not re-introduced explicitly but through these "networks" and principal component analysis applied to the networks – deep cover indeed.

Conclusion
Overall, what’s new about the proxies in MBH98? Many of the proxies overlap with Bradley and Jones 1993 and Jones et al 1998. Indeed, 14 of 17 proxies in Jones et al 1998 are also used in MBH98. The distinctive features of MBH98 proxy selection appear in retrospect to be the following:

· the use of proxies without any effort to ensure that they were temperature proxies, including even using instrumental precipitation series, taken to the extreme of even using grab-bag "networks";
· the ignoring of specialist warnings about bristlecones, previously excluded from every multiproxy study, and their introduction into multiproxy studies under deep cover.

References:
Diaz and Bradley 1992 Documenting Natural Climatic Variations: How Different is the Climate of the Twentieth Century from That of Previous Centuries?in National Academy of Sciences 1995. Natural Climate Variability on Decade-to-Century Time Scales (1995) http://darwin.nap.edu/books/0309054494/html/17.html
Barnett, T. P., Santer, B., Jones, P. D., Bradley, R. S. & Briffa, K. R. Estimates of low frequency natural variability in near-surface air temperature. Holocene 6, 255–263 (1996).
Mann, M. E., Park, J. & Bradley, R. S. Global interdecadal and century-scale oscillations during the past five centuries. Nature 378, 266–270 (1995). Series are listed in chapter 3 of Mann’s thesis available from Mann’s FTP site.
Bradley, R. S. & Jones, P. D. “‹Å“Little Ice Age’ summer temperature variations: their nature and relevance to recent global warming trends. Holocene 3, 367–376 (1993).
Hughes, M. K. & Diaz, H. F. Was there a “‹Å“Medieval Warm Period’ and if so, where and when? Clim. Change 26, 109–142 (1994).
Diaz, H. F. & Pulwarty, R. S. An analysis of the time scales of variability in centuries-long ENSO-sensitive records in the last 1000 years. Clim. Change 26, 317–342 (1994).

30 Comments

  1. Posted Jul 2, 2006 at 11:08 AM | Permalink | Reply

    It was the first study to have redneck Republicans, led by faux-Canadian-scientists, bashing it ad infinitum.

  2. Steve McIntyre
    Posted Jul 2, 2006 at 12:01 PM | Permalink | Reply

    I’ve deleted three posts.

    R.C.H., unfortunately, at the suggestion of readers, we’ve had to introduce blog rules to stop the sort of insult-hurling that you’ve started. You are hereby issued a yellow card; I request that you do not post here for 24 hours. TCO, you’re issued a warning which will be followed by a yellow card.

  3. TCO
    Posted Jul 2, 2006 at 12:29 PM | Permalink | Reply

    On topic:
    a. Nice post, Steve.
    b. Do the instrumental series get negative weighting in the recon or in a PC? (Just checking to be double sure.)

    Off topic: Steve, please don’t apply the rules too much against me. Favoritism is good.

  4. Steve McIntyre
    Posted Jul 2, 2006 at 1:40 PM | Permalink | Reply

    Some series go into PC pre-processing; some don’t. Instrumental temperatures don’t. Weights here are weights in the NH recon.

  5. TCO
    Posted Jul 2, 2006 at 1:47 PM | Permalink | Reply

    Ok. Just to make sure. “The NH reconstruction” is the hockey stick graph?

  6. Pat Frank
    Posted Jul 2, 2006 at 1:56 PM | Permalink | Reply

    “prior to MBH98, even climate scientists made some attempt to ensure that proxies were temperature proxies. (emphasis added)”

    Jeez, Steve, can it be that your experiences have made you cynical? :-D

    More to the general point, I’d wonder how climate scientists objectively know that *any* proxy is in fact a temperature proxy, and not something else.

    Really an excellent post, Steve. Your table helps enormously for climate dilettantes like myself to get a grip on what what was done.

    For reconstructing temperature, every one of those proxies would have to be transformed onto an explicit temperature/time grid before they could be combined. Otherwise, combining intensities would be meaningless. I can see how a d-O18 proxy might be converted into a temperature history (ignoring for now the “rainout” complication). But how does one convert tree rings into temperature? Or precipitation proxies, or ice-melt records? What physical theory makes the transformation? If the transformation into a common unit is impossible, then where is the physical justification for making a proxy reconstruction at all?

  7. Larry Huldén
    Posted Jul 2, 2006 at 1:57 PM | Permalink | Reply

    Dear Steve !
    I feel that this overview was very important. I am thinking of the big amount of details that you have accumulated in recent times. It takes a lot of work for me to follow the stats (it is, however, possible, even for a stat layman like me) but for now I would not be able to present the results in public. I feel that it would be very important to present somehow your results and observations for media in Finland but extremely few people are that interested in details. People (like Timmy) are only interested in the conclusions and not the proofs.
    However, the scientific community needs people like you (and also people like John A.), otherwise most of them would think that earth (=human brains) is flat (like Timmy thinks).
    Larry Huldén, Finnish Museum of Natural History

  8. Steve McIntyre
    Posted Jul 2, 2006 at 2:38 PM | Permalink | Reply

    #6. One of the things that I found instructive (for myself) is doing this post was really assessing what MBH98 did differently now that I know the field so well.

    Think about the debate on PCs – Mann’s justification is by using things like Preisendorfer’s Rule N – which is just a pattern recognition, not a scientific justification. Yet this is presented as though it’s a “mathematical” necessity and climate scientists don’t think twice about it. It’s all about the “right” way to make PC summaries, not whether any of it makes any sense.

  9. TCO
    Posted Jul 2, 2006 at 2:39 PM | Permalink | Reply

    Well right a paper on it. Do some good.

  10. Tim Ball
    Posted Jul 2, 2006 at 5:55 PM | Permalink | Reply

    #6
    It is very difficult to attibute a temperature or any other cause to a proxy series. Some, like Joel Guiot, tried to take a tree ring record and compare it with a modern instrumental record to create a regression formula, which is then used to infer pre-instrumental temperatures from tree rings. Of course, the problem that correlation does not guarantee causation is ever present.

  11. Steve Sadlov
    Posted Jul 2, 2006 at 8:18 PM | Permalink | Reply

    Wow. Since RCH was apparently monitoring you, witness the rapidity of his ad hom attack, there must be a real hot button regarding looking at the proxy selections with this degree of detail. Given that, I would say, keep looking!

  12. David Smith
    Posted Jul 2, 2006 at 8:33 PM | Permalink | Reply

    Interesting recent article from NASA on solar irradiance (link). If I remember correctly, the estimated decrease in solar irradiance during the sunspot minimum several hundred years ago was about 0.3%, so the current 0.05% per decade increase is not insignificant.

    Question, and my apology for drifting away from the main topic: does anyone know if earth irradiance satellite images are available online? NASA offers many products, and I believe they have a satellite that generates this data, but I cannot find it.

    Thank you in advance, and my apology for getting away from the main topic.

    David

  13. David Smith
    Posted Jul 2, 2006 at 8:36 PM | Permalink | Reply

    John, please correct my clumsy attempt at providing a link in #12 and #13. Thanks

  14. Gerald Machnee
    Posted Jul 2, 2006 at 8:50 PM | Permalink | Reply

    Another question – When was cherry picking started? or re-phrasing it – not using a good representation of samples?

  15. John Creighton
    Posted Jul 2, 2006 at 10:56 PM | Permalink | Reply

    #10 Correlation doesn’t guarantee causation. However, a thought just occurred to me. For a given proxi we don’t know how much of the proxy is signal and how much of it is noise but what happens if we assume the proxy is all noise.

    Consider the problem of determining an average. Say we have a series of independent measurements y1…yn. We can estimate the standard deviation of y from these independent measurements. The correlation matrix:
    P=E[y y^T]
    Will be a diagonal matrix with the variance on the diagonal. The square root of this matrix S will be a diagonal matrix where the diagonal values are the standard deviation. To determine the average the data equation

    Y=AX

    can be use where the data matrix A is a vector of ones. This equation can be whitened as follows:

    S^-1 Y = S^-1 A X

    Taking the pseseudo inverse:

    X=(( S^-1 A)^T ( S^-1 A))^-1 (S^-1 A)^T Y
    X=(sigma^2 N)^-1 * sigma * sum(Y)
    X=average(Y)/sigma

    Thus our minimum mean squared error estimate of the average is not zero even if we assume the signal is entirely noise. By knowing the statistics of our estimate of sigma, our assumption that Y has noise of sigma we can compute the variance in our estimate of X. Since the mean of X:

    X=average(Y)/sigma

    and we know the variance of X we can do hypothesis testing to see if X is greater then zero. Or we can state our confidence that X is greater then zero. Applying this to proxies we can state our confidence that a proxy is a temperature proxy or equivalently that it is positively correlated with temperature. Of course proxies the measurements aren’t independent. Thus we have to de-trend them so to speak. De-treding sounds adhoc when what we really want to do is whiten our measurements. I have discussed that here:

    http://www.climateaudit.org/?p=696#comment-33232

  16. Nomad
    Posted Jul 3, 2006 at 2:49 AM | Permalink | Reply

    Steve,

    Excellent overview. This taps into an issue I’ve been troubled with for over a year now: the overlap of use of different proxies.

    You now have included a table outlining the overlap between different studies. My question: to your knowledge, is there a complete overview avaialble that tabulates proxy series AND the authors who have used that series? One could class the different proxies as you did (Corals, Sediment, Tree ring, etc), list the authors who reported the data and in a next column show the studies which have re-used those measurements. For a direct overview, you could select (cherry-pick?) the hockey team members and visualise the reliance of a recurring set of proxies. You could even add another column “Goes back to MWP Yes/No”.

    But has that kind of tabulating of series been done, and it has, would it be available? I’ve used GEOROC for isotope series in volcanic rocks and have long wondered whether there is a similar databse for proxies used in climate science.

  17. John Davis
    Posted Jul 3, 2006 at 7:35 AM | Permalink | Reply

    #12. Fascinating, and seemingly in direct contradiction to the RC line that recent solar changes (since the 1950’s?) have been insignificant. Just taking a broad brush view, the earth sits about 290K above absolute zero. Assuming this is all due to the sun, 0.05% per decade equates to about 0.15 degrees per decade. Not a million miles from the observed trend. Or am I being way too simplistic?

  18. Posted Jul 3, 2006 at 8:05 AM | Permalink | Reply

    #17. Yes I have wondered about this too. From the black body relationship (Stephan-Boltzmann law) puts T to the fourth power of radiant energy, so it should be a lot if that were the only process operating. I don’t discount positive feedbacks however creating a proportional effect at least within a limited range.

  19. John Davis
    Posted Jul 3, 2006 at 9:50 AM | Permalink | Reply

    Oops! Thanks for pointing that out. Way too simplistic indeed! Nearer 0.36 degrees/decade then. Back to the day job, methinks.

  20. John Davis
    Posted Jul 3, 2006 at 9:54 AM | Permalink | Reply

    Grrr.. 0.036 degrees/decade…

  21. John A
    Posted Jul 3, 2006 at 9:55 AM | Permalink | Reply

    re #18 I think the positive feedbacks must be small and easily saturated otherwise the climate system would have spiralled to one or other attractor well before now. Most likely anything else other than the solar forcing would be dominated by noise/chaotic behavior.

  22. jae
    Posted Jul 3, 2006 at 10:00 AM | Permalink | Reply

    Great post, Steve!

    I swear, I have never seen such lousy "science." The universities where these guys came from should retract their PhDs.

    How in the hell do you mix degrees and raw proxy data? The units are different. Some more magic statistics?

    So much for "independent studies."

    What is a "documentary" proxy?

    Instrumental "proxies?" LOL.

    Still no evidence that tree rings can serve as a proxy. Been waiting for over a year for someone to explain this nonsense.

    Maybe it would be valuable to publish this.

    Steve: To clarify, they don’t mix degrees and raw proxies in a trivial way. The things are scaled and re-scaled so the units are not an issue per se. My point is the use of data not demonstrated in peer-reviewed literature to be temperature proxies.

  23. Jean S
    Posted Jul 3, 2006 at 10:28 AM | Permalink | Reply

    An unusual and undiscussed MBH98 innovation is the use of instrumental precipitation series in a temperature reconstruction

    Hmmm, I wouldn’t be suprised if they used the Dow Jones Industrial Average as a new “instrumental series” in the next HT reconstruction :)

  24. Lee
    Posted Jul 3, 2006 at 10:30 AM | Permalink | Reply

    re 21.
    So JohnA, the only options are small and easily saturated feedbacks that don’t cause any significant effect, or unlimited feedbacks leading to a spiraling out of control? Really?

  25. Dave Dardinger
    Posted Jul 3, 2006 at 10:52 AM | Permalink | Reply

    re: #24

    the only options are small and easily saturated feedbacks that don’t cause any significant effect, or unlimited feedbacks leading to a spiraling out of control?

    Well, how does that differ from the warmer view that a moderate CO2 increase will produce a barren earth void of intelligent creatures? (Yes I’m exaggerating). What’s sauce for the goose should be sauce for the gander too.

  26. Lee
    Posted Jul 3, 2006 at 11:35 AM | Permalink | Reply

    OK, Dave, you go right ahead and make your arguments based on admittedly exaggerated misrepresentations of the other side’s arguments. Meanwhile, I’ll stand by my specific response to JohnA, based on JohnA’s specific statement.

  27. Steve McIntyre
    Posted Jul 3, 2006 at 11:51 AM | Permalink | Reply

    Please some other thread to discuss feedbacks.

  28. Dave Dardinger
    Posted Jul 3, 2006 at 1:12 PM | Permalink | Reply

    re: #27,

    Well, Steve, how about the OU thread? It’s discussing Solar, at least in the context of why we haven’t had run-away heating, etc. He discusses water feedbacks and so forth. Looks tailor-made.

  29. Peter D. Tillman
    Posted Jul 4, 2006 at 11:17 PM | Permalink | Reply

    #12. Fascinating, and seemingly in direct contradiction to the RC line that recent solar changes (since the 1950’s?) have been insignificant.
    .
    .
    .

    Well, Steve, how about the OU thread? It’s discussing Solar, at least in the context of why we haven’t had run-away heating, etc.

    C’mon guys, have pity on newcomers. WTH’s “RC”? “OU”?

    TIA & Cheers — Pete Tillman
    “It’s a sin to waste the reader’s time” — Larry Niven

  30. J. Sperry
    Posted Jul 5, 2006 at 3:30 PM | Permalink | Reply

    Pete,
    RC = RealClimate (another blog included in the “links” section of this site)
    OU = Hsien Wang Ou, a researcher discussed in Steve M’s June 17 blog entry (link not provided dut to technical reasons)

Post a Comment

Required fields are marked *

*
*

Follow

Get every new post delivered to your Inbox.

Join 3,179 other followers

%d bloggers like this: