PAGES 2019: 0-30N Proxies

Next, the PAGES2019 0-30N latband. Their CPS reconstruction (CPS) for the 0-30N latband (extracted from the global reconstruction) looks almost exactly the same as reconstructions for the 0-30S and 30-60S latbands. However, none of the actual proxies in this latband look remotely like the latband reconstruction, as I’ll show below. In the course of examining the proxies in this latband, I looked back at 0-30N latband in prior PAGES compilations (2013 and 2017) and Mann et al 2008. The evolution of the proxy network is quite fascinating: the most notable feature is the increasing dominance of short (1-200 year) coral series in a network supposedly reconstructing the past 2000 years.

PAGES2019 Proxies with Values Prior to AD1200

The primary purpose of “2000 year” proxy reconstructions of temperature is to compare modern temperature to estimates of medieval and first millennium temperatures. There are 41 proxies in the 0-30N network, but only three proxies with values before AD1200 and only one (!?!) proxy with values prior to AD925 (see diagram below).

The single long proxy with values through the first millennium is a temperature reconstruction from Mg/Ca values from an ocean core offshore northern Africa. Its values decline erratically through the past two millenia, with very minor recovery in 20th century. If this is the ONLY data for the 0-30N latband through most of the first millennium, how can PAGES2K say with any confidence that modern values are higher than first millennium values? They can’t. My guess is that their algorithm(s) somehow paste 20th century trends in coral d18O onto non-descript or declining long proxies, but that is, at present, just a surmise. All one can say for sure is that, based on the PAGES2019 0-30N proxy network, it’s impossible to assert that modern temperatures in this latband exceed first millennium values (or vice versa.)

Three “long” proxies from 0-30N network. y-axis shows values of proxy, which are not necessarily converted to a temperature estimate. The ring width series is a “dimensionless” chronology; the coral series is d18O (multiplied above by -1 for orientation.)

Evolution of PAGES19 0-30N Proxies

The evolution of the PAGES2K network in the 0-30N latband is really quite remarkable: the major proxy classes are tree ring and coral; secondary classes are ocean cores, lake cores, speleothem with a single ice core retained in three versions. (For comparison, I’ve also included the Mann et al 2008 network). The evolution of the proxy selections in each successive network reveals a great deal about decision-making of PAGES2K authors – much more than is stated in the articles themselves.

Almost every detail in the above graphic gives rise to commentary, requiring a lengthy article to elucidate each detail. I have considerable work in inventory on these details, on which I’ll try to follow up. In this article, I’ll focus commentary on the PAGES 2019 network.


First and foremost, notice the “rise of corals” in successive PAGES versions, even though they are extremely short. As a proportion of the network, corals went from 1.7%, 1 of 57 proxies in the PAGES13 network, to 71% of the PAGES2019 network (29 of 41). All except three of these coral series begin after 1775, with many not beginning until the late 19th or even 20th centuries. The one coral series beginning before AD1000 is intermittent. (It is from Palmyra Island, located on a very narrow portion of the ITCZ in the eastern Pacific and may well be a rainfall proxy – see earlier CA discussion here.

It’s not that new coral series were added in PAGES 2019. The reason for the increased dominance of corals in PAGES2019 is that the 0-30N network was cut from 125 proxies in PAGES17 to 41 proxies in PAGES19 (see left panel above), with nearly all of the cutback falling on ocean sediments and tree rings, all of which were much longer than the retained coral proxies.

Tree Ring Chronologies (Mostly Asian)

PAGES2013 had 54 tree ring chronologies in the 0-30 latband; 52 of the 54 came from the Asia network of Anchukaitis and Cook, for which the chronology calculation method remains unknown (and hard to reconcile with data – see recent post on this issue here ^); the other two from Mexico. This network remained almost entirely unchanged in PAGES2017 which had 53 tree ring chronologies: 52 from Asia network and one from Mexico.

In PAGES2019, the network of Asian tree ring series chronologies is cut back to eight (see below). Mostly these chronologies are nondescript; none are similar to the eventual reconstruction. Two chronologies (CENTIB, MAXSIC) have very late upspikes – a phenomenon examined recently in connection with another Asian tree ring chronology for which underlying measurement data had become available. In that examination, it was impossible to replicate the upspike with usual chronology techniques; further, there did not appear to be any basis for the upspike in the underlying measurement data. In response to a recent inquiry, the PAGES2019 authors were unable to identify how the chronology was calculated and refused to find out.

Ocean Cores

The number of ocean cores in the 0-30N network was cut even more dramatically: from 21 series in PAGES2017 (nearly all of which had been added from the Ocean2K compilation subsequent to PAGES2013) to only three in PAGES2019, one of which is the only “long” proxy in the PAGES2019 network.

The diagram below shows eight PAGES2017 ocean proxies with values prior to AD1000, with the single series retained into PAGES2019 shown in red. With the exception of the Dry Tortugas series of Lund et al 2006, the other series show declining or stable values through the last millennium, consistent with the Ocean2K aggregate that PAGES2019 and IPCC seem to have been distancing themselves from. (In addition to the Kuhnert 2011 series shown in red below, the PAGES2019 network contains two other shorter ocean series – neither of which reach prior to AD1200. One of these two series is a shorter (15 on) version of the Tierney P-178-15P series at top left below. The shorter version of the series has distinct HS blade not present in the version shown below.

The removal of 18 of 21 ocean cores removed the vast majority of PAGES2017 “long” proxies from the PAGES2019 network.

d18O Proxies

During the past 20 years, there has been a vast increase in the population of high-resolution d18O proxies from speleothems and lakes. A few were included in the Mann et al 2008 collection, but these proxies have not been included in the PAGES2K collections. This is too bad, as, in my opinion, these show considerable promise of consistent high-resolution proxy information.

PAGES 2019 contained two “non-short” 0-30N d18O proxies (in addition to a myriad of short coral dq8O series): Palymra coral (6N, 160W) in heart of heavy ITCZ rainfall band; and a short version of the Dasuopu ice core. d18O values of Palmyra core have declined over past millennium and especially in 20th century and are interpreted as inversely correlated to temperature; d18O values at Dasuopu have increased over the past 100 years and especially in 20th century and are interpreted as positively correlated to temperature. Thus, the two d18O series in the same latband go in opposite directions in 20th century, but, for multiproxy purposes. PAGES2K (and other authors) orient them oppositely, so that each goes up in the 20th century.

For comparison, I’ve also shown two long d18O series – a speleothem (Dongge, China) and a lake sediment series (Yucatan, Mexico) from longer series included in Mann et al 2008. Both series show somewhat declining values in the last two millennia.


A major reason for looking at the underlying data in proxy reconstructions, aside from being sound statistical practice in general, is that, (1) by definition, a temperature proxy is supposed to be linearly related to temperature; and therefore (2) proxies in a network of actual temperature proxies, according to the definition, should (a) have a reasonably consistent appearance; and (b) look like the reconstruction. This obviously doesn’t occur in the PAGES2019 0-20N network.

Secondly, proxies covering the medieval period and earlier are disturbingly sparse in the PAGES2019 0-30N network. Although such series have become much more widely available in the past 15 years or so, PAGES 2019 0-30N contains only one (!) proxy with values prior to AD925. Indeed, it actually reduced the representation of longer (ocean core, speleothem, lake sediment) proxies from Mann et al 2008 and PAGES2017, while dramatically increasing the proportional representation of very short coral proxies. Madness.

Finally, the network is wildly inhomogeneous over time. In the past two centuries, it is dominated by trending coral proxies, with only a few nondescript or declining long proxies. Any form of regression (or like multivariate method) of trending temperatures against a large network in the instrumental period will yield an almost perfectly fitting reconstruction in the calibration period if the network is large enough. But when the network is limited to the few long proxies (and especially the singleton proxy extending to the first century), the fit of the regression (or multivariate method) will be very poor and the predictive value of any reconstruction negligible.

Briffa rightly sneered at Mann’s hyperventilating claims in respect to the few uninformative tropical (0-30N) proxies in the Mann et al 1998-99 network. The same criticism applies to the PAGES 2019 0-30N network.

PAGES19: 0-30S

In a Climategate email. Keith Briffa famously sneered at Michael Mann’s claim that a temperature reconstruction could represent a hemisphere, including the tropics, by regressing a “few poorly temperature respresentative tropical series” against “any other target series” – even the trend of Mann’s own “self-opinionated verbiage” as follows:

I am sick to death of Mann stating his reconstruction represents the tropical area just because it contains a few (poorly temperature representative ) tropical series. He is just as capable of regressing these data again any other “target” series , such as the increasing trend of self-opinionated verbage he has produced over the last few years , and …  (better say no more)

People frequently say that the PAGES2K reconstruction has “vindicated” Mannian reconstructions – but neglect to mention that PAGES2K similarly regressed a “few poorly temperature representative tropical series” onto an increasing trend – thus, repeating, rather than vindicating, (one of) Mann’s erroneous methodologies.

In today’s article on the Hockey Stick featured in the new IPCC Hockey Stick diagram, I’ll look at proxies in the southern tropics (0-30S latband). The proxy network turns out to be defective in bizarre, unexpected ways, not reported on or discussed in the original article.

The 0-30S Network

The 0-30S latitude band is mostly Indo-Pacific tropical ocean, but includes most of Australia and South America and the lower part of Africa.

The PAGES2K 0-30S proxy network has 46 proxies (as compared to 8 proxies in the 60-30S network). It has oneyes, one – proxy from an ocean cores and two proxies from land. 43 of 46 series are very short coral series.

The 0-30S network only has two (!?!) proxies with values prior to AD1500: the ocean core (a temperature estimate from Mg/Ca at Makassar Strait, Indonesia [Oppo et al, Nature 2009] and the classic ice core d18O series from Quelccaya, Peru (as updated in 2013) that had been staple of Mann et al 1998-99, Jones et al 1998 and many other studies. Neither of these series contains a hockey stick; if you squint, you can discern lower values in each in a generalized LIA period.

Indeed, there are only two other 0-30S proxies that begin prior to AD1600: the Hendy (2002) Great Barrier Reef temperature reconstruction that does not have a HS; an Indonesian tree ring series (INDO0005) that is non-descript in the underlying measurement (rwl) data at NOAA, but which, according to a thus far undisclosed calculation, closes on a late spike – like numerous other sites in the PAGES2K Asia tree ring calculations. I’ve sought information on this chronology from the lead authors of PAGES2K 2019 but they don’t know and have refused to bother finding out.

The rest of the 0-30S network consists of 42(!) short and micro-short coral series. Below is a histogram of start dates for the 43 (including Hendy GBR) coral proxies. Half of them start after AD1850 and no less than 30% after AD1890. One series (Clipperton Atoll, Wu [2014]) begins in AD1942 !?! None of these short series shed any light on whether the medieval period, for example, was warmer than modern period or not.

Most of the coral proxies show substantial change in d18O and/or Sr/Ca in the 20th century. Here is a random sample of 9 (which, by chance, included the Hendy series shown above). The Hendy series is very different than typical series: PAGES2K is primarily populated with d18O series – which, in specialist articles, are seldom, if ever, used as temperature proxies, as Sr/Ca is usually preferred. Changes in 20th century coral d18O are nearly always much more pronounced than corresponding changes in coral Sr/Ca. Perhaps that’s why they were selectively chosen into the PAGES2K network.

Coral d18O is very responsive to rainfall amount and many 0-30S coral series are located along convergence zones where there is very strong latitudinal or longitudinal gradient in rainfall (and thus d18O). This is a large topic that ought to have been discussed by PAGES2K in explanation of their preference for d18O series. (I have extensive notes on this issue and will try to re-visit.) That these series go “down” doesn’t matter as more negative values are (ex ante) believed to represent higher temperatures (as opposed to the too prevalent ex post cherry picking).


How the PAGES2K authors obtained a big-bladed Hockey Stick from this data cannot be determined without examining their code, which, to my knowledge, has not been archived. (Nor have it been provided to me upon tweet request.) My surmise is that they use some sort of “stepwise” method in which successive steps incorporate the proxies available in that step. Such techniques will effectively splice the coral blade onto the two non-descript non-bladed long proxies to present a sort of hockey stick. The failure of the two long proxies to record the proposed blade means that the confidence levels prior to AD1800 or so extend from the “floor to the ceiling” – an apt phrase used by Rosanne d’Arrigo many years ago. I.e. with this set of information, we know essentially nothing about 0-30S temperatures prior to AD1800 or so. This does not mean that we actually know nothing. There are many interesting proxies in the 0-30S latband and many fascinating discussions in technical literature that does not appear to be reflected in the IPCC report.

Consolidating some of the information in this post with my prior post on the 30-60S latband, which consisted almost entirely (~96%) of ocean, PAGES2K only used one ocean core in the 0-60S latband, totally omitting high resolution alkenone series. Only four PAGES2019 series in the 0-60S latband start prior to AD1100 and none of them have a HS shape.

Overall, I think that it’s fair to say that Briffa’s criticism of Mann remains just as appropriate for the IPCC in 2021, as it did in 2001. Like Mann’s network, PAGES 2019 “contains a few (poorly temperature representative ) tropical series”. And PAGES 2019 authors “were just as capable [as Mann] of regressing these data again any other “target” series , such as the increasing trend of self-opinionated verbage he has produced over the last few years”. Indeed, if anything, the new generation of climate activists have proved themselves more than capable of continuing Mann’s “trend of self-opinionated verbiage” to, shall we say, “unprecedented” levels.

PAGES2019: 30-60S

The 30-60N latitude band gets lots of attention in paleoclimate collections – probably more proxies than the rest of the world combined. The 30-60S latitude band is exactly the same size, but it is little studied. It is the world of the Roaring Forties and Furious Fifties, a world that is almost entirely ocean. The only land is New Zealand, Tasmania and the southern coast of Australia facing Antarctica, the tip of South Africa and the narrow part of South America: southern Chile and Argentina. But 96% or so is ocean.

No Ocean Proxies

Although the 60-30S is almost entirely ocean, PAGES 2019 did not use a single ocean proxy in its data. They used only eight series (out of 19 PAGES 2017). Seven tree ring series: two from New Zealand (both less than 500 years), three from Tasmania (one long, two less than 500 years), two from southern South America (both less than 500 years) and one weird lake sediment from Chile (a “singleton” proxy using pigments in the sediments).

Only One Long Proxy

Only one proxy in the network has values prior to AD750 and only two proxies have values prior to AD1450. Thus, the only information directly comparing medieval and modern values comes from these two proxies: Mt Read, Tasmania (a series used as long ago as Mann et al 1998 and Jones et al 1998) and many times since and the Laguna Aculeo pigment series – neither of which have shapes remotely similar to the PAGES2K 60-30S latband reconstruction – see below. (The latband reconstruction was calculated from the enormous file at NOAA here).

Take a look at the underlying data (converted to SD Units) – more commentary below.

PAGES 2019 20-60S Proxies (SD Units). Red dots show year 2000 values. Together with PAGES 2019 CPS 60-30S reconstruction.

Comments on the PAGES 60-30S HS

Quite aside from many issues about the PAGES2019 selection of 60-30S proxies, obvious questions arise about how they derived their latband reconstruction.

  • the blade of the reconstruction HS goes from -1 sigma in early 20th century to more than 4 sigma in 2000. Yet there is no comparable deviation in any of the underlying proxies. The three South American proxies and the long Mt Read, Tasmania tree ring chronology don’t have anything like a blade; the four short tree ring chronologies (two Tasmania and two New Zealand) have increase sharply in 20th century, but not enough to yield the PAGES 2019 HS. (These tree chronologies have been selected from a much larger candidate populaion – a screening process that already imparts a serious bias.)
  • the only 30-60S proxy with a value in the year 2000 is Mount Read, which has a value of ~1 sigma. Yet the PAGES 2019 30-60S (CPS) reconstruction has a value of over 4 sigma. How did they do that?
  • PAGES 2019 provide code for the generation of figures from reconstructions, but didn’t archive the code for the generation of the reconstructions. (At least in the links provided in any of the articles.) So it’s impossible to precisely diagnose what’s going on.
  • although PAGES proclaim the importance of public archiving as a selection criterion, only one of the tree ring chronologies (the long Mount Read chronology) can be firmly associated with ITRDB measurement data archives. Both South American tree ring chronologies derive from lead author Neukom’s calculation on unarchived South American data. D’Arrigo’s 1995 data remains unarchived, as does the Duncan New Zealand data. At the time of the PAGES 2013 publication of the two Allen tree ring chronologies from Tasmania, no relevant measurement data was archived; since then, Allen has archived measurement data from Tasmania, but PAGES 2019 doesn’t contain any citation.
  • the Laguna Aculeo series is a purported temperature reconstruction from pigments. At present, there are no other similar temperature reconstructions, leaving this series as a sort of ad hoc singleton.

High-Resolution Ocean Proxies

But most of all, given that the 60-30S latband is almost entirely (~96%) ocean, it seems bizarre that PAGES 2019 did not use any ocean core proxies, especially since there are physical formulas for estimating SST from alkenone or Mg/Ca measurements. Any conversion of tree ring widths to temperature in deg C is the result of ad hoc statistical fitting, not a universal formula. Alkenone values have been measured all over the modern ocean and nicely fit known ocean temperatures. In addition, alkenone values for ocean cores going back to deeper time (even to the Miocene) give a consistent and reproducible narrative. So there’s a lot to like about them as a candidate for a “good” proxy.

While there are numerous high-resolution (10 year resolution) alkenone and Mg/Ca measurements in the North Atlantic with values through the last millennium and up to the present, to my knowledge, there were not any such series as of PAGES 2013 or PAGES 2017. (In my opinion, IPCC AR5 ought to have noted this and suggested that this deficiency be remedied.)

PAGES 2017 included three ocean core proxy series in the 30-60S, all from offshore Chile. Their resolutions ranged from 24 to 83 years. There are some thus far undiscussed puzzles in the PAGES 2017 version of these series – as, in each case, modern values available in the underlying archive series were deleted. In each case, unsurprisingly, the effect of the deletion was to hide a decline. I will discuss this series below.

Subsequent to PAGES2017, the very first high-resolution (less than 10 years) 30-60S ocean core alkenone (or Mg/Ca) proxy was published: MD07-3093. [Collins, JA et al. (2019): Centennial-scale SE Pacific sea surface temperature variability over the past 2300 years. Paleoceanography and Paleoclimatology link.] It has values dated from 372 BC to 1992 AD, with a resolution of 5.4 years. The appearance of the high-resolution MD07-3093 is obviously very different – even opposite – to the PAGES 2019 reconstruction.

The three 30-60S ocean cores that were in PAGES 2017 (and dropped from PAGES 2019) are shown below. In each case, I’ve compared the NOAA or Pangaea original archive data (black) to the PAGES 2017 version (red). In each case, the PAGES2017 version was shortened by removal of a few closing values: CF7-33 was shortened from AD1874 close to AD1784; GeoB 3313-1 shortened from AD1884 to AD1650; and GeoB 7186-3 shortened from AD1938 to AD1900.

Although each of these series is lower resolution than the new MD07-3093 series, they tell the same story: a 1-1.5 deg C decrease in temperatures from the first millennium to the 20th century. And MD07-3093 indicates that the decrease has been maintained into the late 20th century (at least in these offshore Chile ocean core datasets.)


Given that the 60-30S latband is almost entirely ocean, it seems logical that IPCC and PAGES2K should use data from ocean proxies to estimate past temperature in this latitude band. But this isn’t what they’ve done. Instead, they’ve purported to estimate past temperature from a few scattered tree ring chronologies, only one of which reaches earlier than AD1850; and an idiosyncratic singleton pigment series. Ironically, the only 30-60S proxy series in PAGES 2019 that reaches back into the first millennium – the Mount Read, Tasmania tree ring series – was used by Mann et al 1998-1999, Jones et al 1998 and numerous other supposedly “independent” multiproxy studies. Neither of the two series reaching back to the medieval period permit the conclusion that modern period is warmer than medieval period. Caveat: I’m not saying that it isn’t; only that this data doesn’t show it, let alone support the big-bladed HS cited by IPCC. High-resolution alkenone measurements from ocean cores offshore Chile show a consistent decrease in ocean temperatures over the past two millennia that is neither reported nor discussed by IPCC (or PAGES 2019).

To be clear, some of the technical articles on 30-60S ocean core proxies by specialist authors are truly excellent and far more magisterial than the IPCC mustered, in particular, several articles on offshore Chile. Here are a few:

Mohtadi et al, 2007. Cooling of the southern high latitudes during the Medieval Period
and its effect on ENSO link

Killian and Lamy 2012. A review of Glacial and Holocene paleoclimate records from southernmost Patagonia (49-55degS) link

Collins et al 2019. Centennial‐Scale SE Pacific Sea Surface Temperature Variability Over the Past 2,300 Years link

PAGES19 Asian Tree Ring Chronologies

About 20% of the PAGES 2019 proxies are 50 Asian tree ring chronologies, all of which were originally published as chronologies in PAGES (2013). At the time, none of these series (and certainly not in these digital versions, had ever been published in technical literature, peer reviewed or otherwise. Nothing in the Supplementary Information to any of these articles says who calculated these chronologies or how they were calculated. PAGES (2017) does cite a couple of academic articles (especially Cook et al 2013) for many of these series, but none of these chronologies actually appears in any of these academic articles or their supplementary information.

PAGES (2013) was originally rejected by Science in 2012, because peer reviewers (including Michael Mann) objected to the introduction of so many new proxies in what was ostensibly a review paper; they sensibly recommended that components first be peer reviewed in relevant specialist journals. However, PAGES2K results had already been incorporated into a pending IPCC assessment (AR5), so the authors, now under a very short deadline, submitted to Nature, which was confronted by the same review problems that led to the rejection by Science. Keith Briffa had a clever, too clever, solution: publish the PAGES2K submission as a “Progress Article” – a classification that did not require the peer review procedure required for a Research Article. This would qualify the article for IPCC and nobody would notice the sleight-of-hand. (Even I didn’t notice it at the time; someone told me.)

One of the consequences of the 2013 manoeuvring was that several hundred Asian tree ring chronologies were introduced to paleoclimate archives with no technical publication or technical peer review, no information on how they were calculated or even who among the PAGES2K (2013) authors had calculated them.

Having been introduced through the back door, so to speak, nearly all of the 200+ Asian tree ring chronologies were carried forward into the PAGES (2017) compilation, and then a subset of 50 chronologies (more or less the most hockey stick shaped) was screened to become a substantial component of PAGES (2019) – the source of the IPCC Summary for Policy-makers Hockey Stick.

In an earlier post, I had commented on the extreme closing uptick in one of these series (Asia_207). In 2013, despite PAGES2K’s professed insistence on using proxies with public archives, measurement data for this chronology was not available, so it was impossible to see what was going on at the time.

In the SI to PAGES (2017), the data is cited to the site denoted by NOAA as paki033, a site located in a mountainous region in northern Pakistan near Gilgit. As a short editorial digression, I visited Gilgit briefly in 1968 and was there when we learned, via shortwave radio, that Bobby Kennedy had been assassinated. Twenty years later (1988), Osama bin Laden, then a CIA protege, announced himself by slaughtering the Shia population of Gilgit. (In today’s US intel nomenclature, since they were Shia, the murdered Shia would presumably be labeled as “Iran-backed” as though that were both justification and sufficient explanation.)

But back to main programming.

Measurement Data and Chronology Construction

From the measurement data for paki033.rwl at NOAA, I calculated a site chronology using the rcs function from Andy Bunn’s dplR package. The resulting chronology does NOT have the huge uptick of PAGES2019 – indeed it declines over the 20th century. (Diagram below used dplR function – see script below).

Code for this diagram is as follows:

rwi=rcs(rwl,po=Po) #646 18
crn=chron(rwi, prefix = “033”)
plot(crn,main=”Mushkin PIGE – paki033″)

I got an almost identical chronology by fitting a single Hugershoff curve (rw = A+B* (x^D)*exp(-C*x) to allow for growth prior to chronology calculation.

An observation here: although the overall appearance of the chronologies is very different, there is a high correlation (~0.5) between the PAGES version and the other versions – that high a correlation strongly indicates to me that they are representing the same data. (Also the start and end dates of the PAGES2K version exactly match the measurement data.)

What could possibly account for the huge uptick in the PAGES version? It turns out that the paki033 dataset consists of only 10 trees (18 cores). Only two of the trees are dated prior to the 18th century – well below usual minimums for calculating a chronology. Only 6 trees have cores extending to the last year (2007). This is a very small total – indeed, so small that it’s possible to plot actual measurements for all 6 trees very easily so we can look for ourselves at what’s going on.

Here is a plot of actual measurements for the two cores from each of six trees for the period 1700-2007. One tree (MUSP04) is relatively old and slow-growing. Most of the trees were relatively young (dating from 19th century) and showed characteristic decline in measured ring width as the tree got older (and diameter increased.) Nothing in this data shows an upspike in 2007.

So who calculated the Asia_207 chronology? And how was it calculated?

At the time (2013), Briffa and Melvin of the University of East Anglia were hyping a method that they called “signal-free” tree ring chronology calculation, which, in the examples that they showed, resulted in a more HS-shaped chronology than produced by ordinary chronology. It’s possible that the PAGES2K chronology was produced with some variation of this method. Melvin’s article does not provide a clear description of the mathematical procedure in their algorithm. They used ugly Fortran code that might be possible to figure out. But it takes time to parse this stuff and, without knowing for sure that this technique was used in PAGES2K, I’ve got other things to do.

But, even if the chronology calculation can be determined to be Melvin’s method (or some equivalent), this example ought to raise serious issues about the validity of the method- whatever it was. There is nothing in the actual ring width measurements that justifies the huge upspike in the archived PAGES2K Asia_207 chronology. The implication is that there is something wrong with the chronology algorithm used by PAGES2K (2013) authors. If so, the defect would affect not just the Asia_207 chronology, but a vast swathe of other PAGES2K chronologies relied upon in the IPCC diagram. I checked a couple of others and was unable to replicate them either.

As a caveat, I’m not saying that “everything” in the IPCC diagram stands or falls with this particular issue. There are many issues with this diagram – I listed many in my first post on this topic and am aware of many aware. It’s possible that I’ve overlooked something. If a possible error in this analysis is identified, I’ll promptly evaluate and amend if required.

The IPCC AR6 Hockeystick

Although climate scientists keep telling that defects in their “hockey stick” proxy reconstructions don’t matter – that it doesn’t matter whether they use data upside down, that it doesn’t matter if they cherry pick individual series depending on whether they go up in the 20th century, that it doesn’t matter if they discard series that don’t go the “right” way (“hide the decline”), that it doesn’t matter if they used contaminated data or stripbark bristlecones, that such errors don’t matter because the hockey stick itself doesn’t matter – the IPCC remains addicted to hockey sticks: lo and behold, Figure 1a of its newly minted Summary for Policy-makers contains what else – a hockey stick diagram. If you thought Michael Mann’s hockey stick was bad, imagine a woke hockey stick by woke climate scientists. As the climate scientists say, it’s even worse that we thought.

Curiously, this leading diagram of the Summary of Policy-Makers does not appear in the Report itself. (At least, I was unable to locate it in Chapter 2.) However, it is clearly the progeny of PAGES2K Consortium (Nature 2019) and Kaufman et al (2020), both of which I commented on briefly on Twitter (see here).

It’s hard to know where to begin.

The idea/definition of a temperature “proxy” is that it has some sort of linear or near-linear relationship to temperature with errors being white noise or low-order red noise. In other words, if you look at a panel of actual temperature “proxies”, you would expect to see series that look pretty similar and consistent.

But that’s not what you see with the data used by the IPCC. You’d never know this from the IPCC report or even from the cited articles, since authors of these one- and two-millennium temperature reconstructions scrupulously avoid plotting any of the underlying data. It’s hard for readers unfamiliar with the topic to fully appreciate the extreme inconsistency of underlying “proxy” data, given the faux precision of the IPCC diagram.

Many of the series discussed in this post, including nearly all of any HS-shaped series, have been previously discussed in Climate Audit blog posts (tag/pages2k) from 2, 5, 10 or even 15 years ago or in tweets from 2019 and 2020 (see here).

The PAGES2019 is not a “random” selection of proxies, but winnowed through ex post criteria. As Rosanne d’Arrigo explained to the NAS panel many years ago: if you want to make cherry pie, you first have to pick cherries.

The PAGES2019 dataset consists of 257 proxies, selected from the prior PAGES2017 dataset consisting of 692 proxies, which had previously been selected from thousands of proxy series accumulated by many authors over the years.

In order to give readers an overview of the underlying data – not the massaged final product, I’ve plotted three batches of 11 randomly selected series from each of PAGES2017, PAGES2019 and then PAGES2019 North American tree rings and then commented on each batch. (The samples were selected by R formula sample(1:K, 11) where K is the size of dataset being sampled.) In each case, there were usually series that I had already studied plus numerous non-descript series, which are notable and important to show precisely because the majority of proxies are non-descript and you need to see this to understand it.

This post will be a work in progress for a few days, as I have some sections on special issues that I will try to add as I have time.

A First Batch: PAGES2017 Proxies

As a first illustration, below is a random sample of 11 PAGES2017 series. The series carried forward to PAGES2019 are in blue. For reference, the IPCC curve is shown in red. As you can easily see, most of the series are non-descript and short. Only one series in this sample (Cape Ghir temperature alkenones) has a hockey stick shape, but it goes down.

The Cape Ghir series, shown above, is in deg C, but has an obvious problem: it goes down. (See prior Climate Audit discussion of Cape Ghir alkenone series here). And this is not a case where the raw proxy measurement has an inverse relationship to temperature (e.g. coral Sr or coral d18O), but a case where the temperature estimate from the proxy goes down. Alkenones are a very unique proxy because there are widely accepted formulas for converting alkenone measurements directly to deg C. Alkenones are widely used to estimate ocean temperature in deep time, yielding consistent estimates for millions of years. This is totally different than tree ring measurements, where ring widths have first to be adjusted for age and location, prior to trying to develop an ad hoc local formula to estimate local temperature from a sort of average of ring widths.

Precisely why local Cape Ghir (offshore Morocco) temperatures were going down is somewhat of a quandary. Rather than figuring out this quandary, Neukom and the woke just turn the series upside down, following the example of Upside Down Mann by orienting the series according to its correlation with target instrumental temperature, even in their “CPS” reconstruction – a technique that is normally resistant to opportunistic flipping of proxies to enhance HS-ness of a final reconstruction.

Watch what Neukom et al did with their “CPS” method:

CPS (to my knowledge) in all prior reconstructions by non-woke authors is an average of scaled data that has been oriented ex ante by known properties of the proxy. I.e. it won’t flip over an alkenone temperature estimate simply because it goes the wrong way. But this salutary property is not maintained in Neukom’s bastardized implementation of CPS – a bastardization that ought to have been resisted by reviewers somewhere along the line. PAGES2K produced temperature reconstructions by seven different methods, all of which yielded somewhat similar results to CPS – strongly suggesting that these other methods also flip series like Cape Ghir.

A Second Batch: PAGES2019 Proxies

Here’s a second random sample of proxies, this time all from the additionally screened PAGES2019 subset. Take a look, comments below.

It’s not as though PAGES2K made a composite from 257 series that are two millennia long, all or a majority having a HS shape. One series in this sample does look a lot like the IPCC stick and will be discussed at length below, but the others look very different.

Four of the series in the sample are very short – three of them are actually shorter than the instrumental record. These are all coral Sr or coral d18O series, which make up 25% of the PAGES2019 data set. The extremely short records illustrated above are typical, indeed almost universal, in this class of proxy. They do have a pronounced trend in the instrumental period. This contrasts with the lack of trend that one sees in the two long proxies in the middle column above – a tree ring series from Mt Read, Tasmania (also used in MBH98) and a 1983 ice core series by Fisher from Devon Ice Cap on Baffin Island (also available to 1990s vintage multiproxy studies).

The short coral series do not contribute information to the medieval and earlier periods which one is trying to compare to the modern period. So what is their function? Do they contribute anything other than painting a moustache on the non-descript longer series?

The tree ring series in this sample are rather short; the screening procedures have somewhat concentrated series with slight upticks. (The stripbark bristlecone chronologies that were so prominent in the Mann et al Hockey Stick continue to be used in PAGES2019 – as discussed below.) I discussed the series in the left column with large uptick (Asi_MUSPIG aka paki033) in a 2019 tweet thread here. I located the underlying ring width measurements at NOAA and re-calculated the tree ring “chronology” using standard methodology – see below. The high-frequency details match, showing that the underlying measurement data is apples-to-apples. No chronology from original authors is archived at NOAA: so how did PAGES2K manage to get such a hockey stick? I have no idea.

The most “interesting” series in this sample batch is the borehole temperature reconstruction that has such an uncanny resemblance to the eventual IPCC reconstruction. By coincidence (or not), I wrote about this borehole temperature reconstruction (from WAIS Divide, Antarctica) in February 2019, a few months before publication of PAGES 2019 – see here – scroll down – for a more thorough analysis.

I’ve written multiple posts on the mathematics of borehole inversion calculations, which purport to estimate temperatures for thousands of years into the past from modern day temperatures measured downhole. These calculations require the inversion of a multicollinear matrix (with determinant close to 0). As far as I’m concerned, nearly all the details that specialists pontificate about are a sort of Chladni pattern artifact.

But that’s another story. Here the problem was much stranger. A few years earlier, I had (circuitously) managed to obtain a copy of the code used to calculate this borehole inversion (which is not archived anywhere.) The code showed that they had deleted the top 15 meters of the core from their calculation.

I’ve had a LOT of trouble getting the underlying borehole temperatures for some famous series. (The 2006 NAS panel cited one such result, but the original author (a US government employee) refused to make the data available, and, to my knowledge, it remains unavailable.) However, in this case, the underlying downhole temperatures had been archived, including the values had been deleted. Needless to say, they went down. An inversion using all the data would not have resulted in the impressive Hockey Stick in the PAGES2019 dataset, but a substantial recent decline.

Prima facie, another example of “hide the decline”.

To be fair, as I observed in the earlier post, there is a dramatic seasonal fluctuation in temperatures in the top portion of the Antarctic ice sheet, which makes the already formidable (and probably impossible) inversion problem even more intractable. In my Feb 2019 post, I showed a diagram from van Ommen et al (1999) which showed the dramatic changes in downhole temperature as the seasons changed: a sort of damped sinusoidal pattern can be discerned. In the top 15 meters of the core, seasonal changes dominate.

Note that the blade on the hockey stick in this IPCC series is entirely dependent on the choice of 15 meters as a cutoff point for the borehole inversion. A choice of 20 meters would have probably eliminated the blade altogether.

The fact that the top portion of the core has to be excluded because of seasonal effects also creates a strange irony: the layers at 15 meters at WAIS date back to the 1960s. So IPCC has ended up relying on a series that purports to reconstruct temperature up to 2007, but without using any of the ice core dating from ~1965 to 2007. The calculation is entirely done from ice core layers dated prior to the 1960s. Does this seem reliable to any of you? Doesn’t to me.

Furthermore, the WAIS Divide borehole temperature reconstruction yields a totally different result than the widely replicated and well understood d18O isotope series.

Given the questions and defects surrounding the WAIS borehole inversion series, it is absurd that this series (a singleton, to boot) should be used in a policy-relevant document. That the final IPCC diagram is so similar to this garbage series also makes one wonder about what is happening under the hood of the multivariate calculations.

A Third Batch: PAGES2019 North American Tree Rings

North American tree rings (including some Arctic series) make up ~25% of PAGES2019 proxies. Here’s a random sample.

The majority are short and rather non-descript – nothing like the final IPCC diagram.

There are one series with an enormous hockey stick: Mackenzie Delta (Porter 2013); and two series (“GB [Great Basin]” and nv512) with noticeable closing upticks. Sharp-eyed readers may have already figured out some of this story.

I discussed the Mackenzie Delta super-stick of Porter et al (2013), a new entry to hockey stick fabrication technology, in July 2019 here on Twitter. It comes from Yukon, Canada, an area that, in a 2004 study by d’Arrigo et al, had been a type location for the classic “divergence problem” – ring widths going down, while temperatures went up. So how did Porter et al manage to get a super-stick that had eluded Jacoby and d’Arrigo, long-time searchers for hockey sticks in tree ring data and not shy about picking cherries in order to make cherry pie?

They took “hide the decline” to extremes that had never been contemplated by prior practitioners of this dark art. Rather than hiding the decline in the final product, they did so for individual trees: as explained in the underlying article, they excluded the “divergent portions” of individual trees that had temerity to have decreasing growth in recent years. Even Briffa would never have contemplated such woke radical measures.

To be fair, Porter et al’s original article showed both the actual (non-descript) chronology from all trees, together with superstick resulting from “hide the decline” on individual trees: the decision to use the spurious superstick belongs to Neukom and PAGES2019.

Stripbark Bristlecone Chronologies

As noted above, sharp-eyed readers may recall the identifier nv512. It is one of the classic Graybill stripbark bristlecone chronologies (Pearl Peak), which we had observed to dominate both the MBH98 PC1 and the final MBH98 reconstruction. It (and other key stripbark sites) was listed in McIntyre and McKitrick (2005 GRL) Table 1:

Readers will also recall that the 2006 NAS Panel recommended that “stripbark” chronologies be “avoided” in temperature reconstructions. Although the climate community has professed to implement the recommendations of the NAS Panel, they are addicted to stripbark chronologies, the properties of which are well known. Five different PAGES2019 series use stripbark bristlecones (three from original Graybill versions): nv512 (Pearl Peak); nv513 (Mount Washington); ca529 (Timber Gap Upper); SFP (an update of San Francisco Peaks, incorporating az510) and GB (a composite of Pearl Peak, Mount Washington and Sheep Mountain, using both Graybill and updated information).

In 2018, I looked at how North American tree ring networks had changed since MBH98. The one constant was the addiction of paleoclimatologists to stripbark chronologies- a phenomenon that I had commented on long before Climategate (citing Clapton et al and Paeffgen et al), much to the annoyance of dendros, but the comment remains as true now as it was then.

South American Proxies


Other Proxies



I discussed many of these problems in July 2019, within a couple of days of publication of the underlying article (see here). While I don’t necessarily expect IPCC reviewers to be paying rapt attention to my twitter feed, one surely presumes that IPCC climate scientists, who are employed full time on these topics, to be competent enough to notice things that I was able to observe in my first day or so of looking at PAGES2019. But their obtuseness never ceases to amaze.

Milankovitch Forcing and Tree Ring Proxies

Mar 2, 2021. This post was written in 2015 but, for some reason, I didn’t publish it at the time.  Seems just as valid today as when it was written.


Esper et al 2012, Orbital Forcing of Tree Ring Data pdf SI, is one of the few paleoclimate articles in past decade which really made me stop and think. It connected two obvious points:

  • high-latitude tree ring proxies are sensitive to summer (JJA, even JJ) temperature, not annual temperature.
  • high-latitude NH summer insolation, which has long had special interest as the “prime forcing” of Milankovitch theory of ice ages, had declined by ~6 w m-2 over the past 2000 years, the period covered by many popular IPCC temperature reconstructions. An amount that is approximately four times larger than anthropogenic forcing from CO2 since 1750 AD (~1.5 w m-2).

From these two points, they made plausible and compelling observation that the very large changes in high-latitude Holocene summer insolation should be visible in long high-latitude tree ring chronologies, especially those chronologies reaching back to the Roman period and earlier.

But it isn’t, as they demonstrated in an important graphic, which, unfortunately, was buried in the SI where it passed unnoticed. (One of the authors drew my attention to it several years ago or I too would have missed it.) Long tree ring chronologies have negligible millennial-scale variance – one more reason to distrust the temperature reconstructions of PAGES2K and IPCC.

Esper Figure S1

Here is the interesting figure S1 from Esper et al 2012. It compared three long tree ring width chronologies (grey-black) to Norwegian glacier equilibrium line (blue) and Yamal treeline (km north of present treeline.)  While the glacier equilibrium line (and Yamal tree line) have both migrated lower (southerly) with

However, as shown in Figure S1 of Esper et al 2012 (shown below), these long chronologies have more of less zero millennium-scale variability over the past 7000 years i.e. in addition to other defects in tree ring chronologies as temperature proxies, they only show high-frequency variability.  In contrast, Holocene-scale changes were visible in equilibrium lines of Norwegian glaciers and the treeline in Yamal.

Figure 2. Esper et al 2012 Figure S1. Original Caption: Showing multi-millennial TRW records from Sweden, Finland, and Russia (all in grey)
together with reconstructions of the glacier equilibrium line in Norway(blue), northern treeline in Russia (green), and JJA temperatures in the 60-70°N European/Siberian sector from orbitally forced ECHO-G7,8 (red) and ECHAM5/MPIOM9 (orange) CGCM runs10. All records, except for the treeline data (in km) were normalized relative to the AD 1500-2000 period. Resolution of model and TRW data were reduced (to ~ 30 years) to match the glacier data. Comment: 
Tree ring width chronologies (grey) are Grudd et al, 2002 (Tornetrask, northern Sweden); Helama et al 2010 (Finland); and Hantemirov and Shiyatov 2002 (Yamal); Norwegian glacier equilibrium lines (blue) are Aspvatnet (Bakke et al 2005a) and Lyngen (Bakke et al 2005b); treeline northing (in km) is from Yamal (Hantemirov and Shiyatov, 2002). 


In their important diagram in the Supplementary Information, Esper et al showed proxies back to 7000 BP, but neglected to show or discuss insolation changes earlier in the Holocene. These are even more dramatic as shown in figure below. Summer insolation at 50N has decreased by more than 35 w m-2 (!!!) since the early Holocene (10000 BP) and is presently at levels characteristic of the Last Glacial Maximum (19000 BP). The disintegration of the Laurentide ice sheet, previously covering Canada, took place primarily in the period of maximum summer insolation (12000-8000 BP). I’ve shown the scale of modern anthropogenic forcing in red for reference.

In older paleoclimate texts, paleoclimatologists reported signs of “neo-glaciation” during the past 4000 years, consistent with Milankowitch factors.  In the 19th century, ice-rafted debris (IRD) was observed at Hvitarvatn lake for the first time since the LGM due to expanded local glaciers. (This proxy has been repeatedly discussed at Climate Audit.) Varve thicknesses at Hvitarvatn also increased dramatically in the Little Ice Age, reaching their maximum in the 19th and early 20th century. BSi productivity at Hvitarvatn was at its maximum from 9000-5000 BP, slightly after the insolation maximum – presumably delayed until LGM glacier had sufficiently receded.

Climate Audit readers will recall that PAGES2K (2013) used Hvitarvatn data upside-down – interpreting wide varves at the height of the Little Ice Age – as evidence of warmth, rather than the opposite, as I noticed almost immediately – see ^. Aside from the use of data upside down being an embarrassing, almost Mannian, gaffe, one has to wonder at the apparent lack of understanding of underlying data on the part of the multiproxy collaters. I have an identical beef in respect to Baffin Island data. Glaciers in Baffin Island – a past center of Laurentide glaciation – similarly expanded in the Little Ice Age through the 19th century. 19th and early 20th century varve thicknesses from Baffin Island, where the time series data pattern is astonishingly similar to Iceland, are nonetheless interpreted by PAGES2K (and IPCC) as evidence of warmth.

Because tree ring width chronologies were unresponsive to large but slow changes in insolation, Esper et al observed that temperature reconstructions relying on long tree ring chronologies (most of the popular IPCC two millennium chronologies) would be similarly unresponsive. Esper stated this conclusion as follows:

an evaluation of long-term temperature reconstructions, even over the past 7,000 years from across northern Eurasia, demonstrates that TRW-based records fail to show orbital signatures found in low-resolution proxy archives and climate model simulations (Supplementary Fig. S1). These discrepancies not only reveal that dendrochronological records are limited in preserving millennial scale variance, but also suggest that hemispheric reconstructions, integrating these data, might underestimate natural climate variability.

This conclusion impacts PAGES2K, Mann et al 2008 and all other temperature reconstructions relied upon by IPCC.

Norwegian Glacier Equilibrium Lines

Details on the two Norwegian glacier equilibrium line series are shown below (slightly different horizontal scale).  At both locations, glaciers are believed to be absent in the early Holocene (during highest summer insolation) and to have formed around 5000-4000 BP (neo-glaciation).  During the late Holocene, the glaciers expanded until ~2000 BP with maximum Holocene extent in the Little Ice Age – a pattern that is characteristic in many locations. During the 20th century, there has been a noticeable retreat of the glaciers – back to levels characteristic of the early first millennium.

Yamal Treeline

The treeline series illustrated in Esper et al 2012 was derived from Hantemirov and Shiyatov Figure 2 (but excluding its Early Holocene portion). It showed mid-Holocene treelines extended approximately 30 km north of present treelines. However, this 30 km figure represented the northern limit of the survey, NOT the actual Holocene treeline. By the time of Hantemirov’s thesis in 2009, the survey – and the mid-Holocene treeline – had been extended nearly 120 km north of the current treeline (see middle panel). It appears that the Holocene treeline may have been even further north: in 1941, Tikhonov reportedly observed sub-fossil Holocene trees at 70N, approximately 275 km north of the present treeline. So, while Esper et al were right to note that Holocene treeline was further north, their diagram dramatically under-estimated the actual distance further north of the Holocene treeline, not just absolutely, but in respect to what was known in Russian literature at the date of their article.

Note that, in the 20th century, the Yamal treeline finally reversed its long march south, though still located far south of its Holocene location. This reversal corresponds to the 20th century reversal of the equilibrium line of Norwegian small glaciers – neither effect being apparent in the Esper et al figure.

Vinther et al 2009

The long decline in Holocene

Vinther et al 2009 (Nature) is a seminal article on the interpretation of Greenland d18O which makes the popular Alley (2000) temperature reconstruction from GISP2 totally obsolete.  Vinther observed that the elevation of the Greenland ice sheet had decreased substantially over the Holocene and that this had a material impact on d18O values at the summit (where GISP2 and GRIP are located): by flattening out the curve through the Holocene. Vinther observed that elevation changes through the Holocene were negligible at Renland (Greenland) and Agassiz (Ellesmere Island) and proposed (convincingly in my opinion) that the d18O records at these locations provided a more accurate record of climate change through the Holocene, and could even be used to estimate elevation changes at the summit of the ice sheet (where GISP2 was located.) Rather than being stable through the Holocene, Renland d18O showed a steady decline through the Holocene.



Over the past two millennia, the Norwegian glacier equilibrium line series in Esper et al Figure S1 (blue in excerpt at right) do have a sort of hockey stick shape that is not derived from ex post screening, stripbark bristlecone ring widths or other Mannian tricks. However, in a longer Holocene context, the reversal is both modest in scale and in a direction that mitigated intensifying neo-glaciation from Milankovitch factors.  One possible interpretation of this data is that anthropogenic CO2 has mitigated and even slightly reverse the Milankovitch forcing into potentially much expanded NH glaciation (compare to Ganopolski’s “near miss” article).


A “Good” Proxy on the Antarctic Peninsula?

Nearly all of the text of this article on an interesting ice core proxy series (James Ross Island) from the Antarctic Peninsula was written in June 2014, but not finished at the time for reasons that I don’t recall.  This proxy was one of 16 proxy series in the Kaufman 12K pdf. 60-90S reconstruction.

I originally drafted the article because it seemed to me that the then new James Ross Island isotope series exemplified many features of a “good” proxy according to ex ante criteria that I had loosely formulated from time to time in critiquing “bad” proxies, but never really codified (in large part, because it’s not easy to codify criteria except through handling data.)

Although this series is in the Kaufman 60-90S reconstruction, its appearance is quite different than the final 60-90S reconstruction: indeed, it has a very negative correlation (-0.61) to Kaufman’s final CPS reconstruction. I’ll discuss that in a different article.

Following is mostly 2014 notes, with some minot updating for context.

Continue reading

IPCC AR5 WG2 on Yield Sensitivity: Statistical Malpractice

This post was written on Aug 12, 2014, but not published until Mar 2, 2020 (today).

One of the signature findings of IPCC AR5 WG2 has been that climate change has already had a negative impact on crop yields, especially wheat and maize. These findings are prominent in the WG2 Summary for Policy Makers and were featured in WG2 press coverage. The topic of crop yields are a specialty of WG2 Co-Chair Christopher Field. Field’s frequent co-author, David Lobell, was a Lead Author of the chapter on Food (chapter 7), which in turn cited and relied on a series of Lobell articles, in particular, Lobell et al (Science 2011, Climate Trends and Global Crop Production Since 1980, pdf), which was a statistical analysis of crop yields from 1980 to 2008 (or to 2002 in some analyses) for four major crops (wheat, maize, rice, soy) for 185 countries.

In the period 1980-2008, both crop yields and temperatures have positive trends (notwithstanding the pause/hiatus in the 21st century). Because both series have positive trends, there is therefore a positive correlation between crop yields and temperatures for the vast majority of crop-country combinations.

Given that both series are going up, it is an entirely valid question to wonder who Lobell and coauthors arrived at their signature negative impact merely by applying elementary statistical methods to annual data of yields, temperature and precipitation. I’ll look at this question in today’s post.


In 2011, I obtained the data for Lobell et al 2011 from lead author Lobell (who undertook at the time to place both data and code online, neither of which appears to be done.) I had asked Lobell to archive code, because it wasn’t entirely clear what he had done. Lobell collated temperature and precipitation data from both UDel and CRU. (For the latter, Lobell used the CRU TS data made famous by the Harry Readme.) In the figure below, I’ve plotted Lobell’s yield and temperature data for the China-wheat combination (both standardised to SD units), as an example of both series going up.


Lobell regressed Yield (actually log Yield) against time, temperature and precipitation variables, describing the procedure as follows:

Translating these climate trends into potential yield impacts required models of yield response. We used regression analysis of historical data to relate past yield outcomes to weather realizations. All of the resulting models include T and P, their squares, country-specific intercepts to account for spatial variations in crop management and soil quality, and country-specific time trends to account for yield growth due to technology gains (6).

The precipitation and quadratic terms don’t appear to affect the regression very much, i.e. the main effects are delivered by the model in which Yield is regressed against time and temperature as follows:

(1) Yield ~ Year + Temperature

Using conventional regression nomenclature, the regression coefficient b is given by the formula

(2) b= (X^T * X)^{-1} X^T y

where the X matrix of independent variables if {Year; Temperature} and y is the Yield vector.

For convenience (and thus is irrelevant to the point that I’m working towards), normalize the data.

X^T y is simply the vector of correlations of Yield to Time (the normalized trend) and Temperature.

(X^T * X) is nothing more than the correlation matrix between Year and Temperature i.e. the off-diagonal element r is the temperature trend (normalized units) as follows:

| 1 r |
| r 1 |

The calculation of the OLS regression coefficients uses the inverse of this matrix,

| 1 -r | * 1/(1-r^2)
| -r 1 |

The negative term in the off-diagonal means that the OLS coefficient for the regression of Yield onto Time and Temperature is calculated as a function of the correlation between yield and temperature, the trend in yield, the trend in temperature as follows:

b_temperature = 1/(1-r^2) (-r*trend_yield + cor_yield_temp)

In other words, if the correlation between Yield and temperature is less than the product of the trend in yields and trend in temperature (both normalized), then the regression coefficient is negative. This has nothing to do with yields or temperatures, but is a trivial property of the matrix algebra.

As an example, for the Chinese wheat series shown above, although there is a positive correlation between yield and temperature (0.5096), the OLS regression coefficient of a regression of Yield against Year and Temperature results in a negative coefficient. Applying the above formula, the normalized trends (correlations between year and item) for yield and temperature are 0.984 and 0.548, yielding 0.5096- 0.984*0.584 <0.

Gregory et al 2019: Does climate feedback really vary in AOGCM historical simulations?

A guest post by Nic Lewis


The recent open-access paper Gregory et al 2019 “How accurately can the climate sensitivity to CO2 be estimated from historical climate change?” discusses, inter alia, the use of regression to estimate historical climate feedback. As I wrote in a previous article, Gregory et al. consider a regression in the form R = α T, where T is the change in global-mean surface temperature with respect to an unperturbed (i.e. preindustrial) equilibrium and R is the radiative response of the climate system to the change in T, however caused; α is thus the applicable climate feedback parameter for that cause. The corresponding effective climate sensitivity (EffCS) is then F2xCO2/α  where F2xCO2 is the effective radiative forcing (ERF) for a doubling of preindustrial atmospheric carbon dioxide concentration. Continue reading

Gregory et al 2019: Unsound claims about bias in climate feedback and climate sensitivity estimation

A guest post by Nic Lewis

The recently published open-access paper “How accurately can the climate sensitivity to CO2 be estimated from historical climate change?” by Gregory et al.[i] makes a number of assertions, many uncontentious but others in my view unjustified, misleading or definitely incorrect. Perhaps most importantly, they say in the Abstract that “The real-world variations mean that historical EffCS [effective climate sensitivity] underestimates CO2 EffCS by 30% when considering the entire historical period.” But they do not indicate that this finding relates only to effective climate sensitivity in GCMs, and then only to when they are driven by one particular observational sea surface temperature dataset.

However, in this article I will focus on one particular statistical issue, where the claim made in the paper can readily be proven wrong without needing to delve into the details of GCM simulations. Continue reading