By Andy May
I’m reviewing the Pages 2k temperature proxies one-by-one as I once reviewed Marcott’s proxies (May, 2018). There are 647 Pages 2k proxies, so this is a big job. This reconstruction is prominently displayed and used in the IPCC AR6 report (IPCC, 2021, pp. 211, 432) so it is worth the time to investigate it. Their proxies can be downloaded as one R data file (RData format) from here. This post will just cover six of the Greenland ice core proxies, but the full ensemble median Pages 2k global temperature reconstruction is shown in figure 1.
Figure 1 resembles the well-known “hockey stick” reconstruction (Mann et al., 1998), which has been the subject of substantial methodological criticism regarding proxy selection, principal-component methodology, and uncertainty estimation. It was featured prominently in the third report or “TAR” (IPCC, 2001). We will not get into the problems with the previous hockey stick here, they are well covered by Steve McIntyre (McIntyre, 2011), (McIntyre & McKitrick, 2005), (Wegman et al., 2010), and Andrew Montford (Montford, 2010).
Pages 2k Statistical Methods
Some of the problems with figure 1 are statistical and similar to the problems with Mann’s hockey stick. This post is about selected and well-known Greenland ice core proxies and the technical problems using them to compute temperatures over the past 2,000 years, but it is worthwhile to briefly list the statistical problems and provide references for more details.
The Pages 2k consortium uses seven different temperature reconstruction methods, including principal component regression, arguing that by using multiple methods and getting broadly similar results, confidence in the outcome is increased (Pages2K, 2019). However, if all seven methods are fed the same data and calibrated to the same instrumental data from ~1850 to 2014, agreement among the methods is not independent evidence nor surprising. The real problem is the calibration period is short, only about 150 to 170 years and it lies at the end of the proxy records. This is the same problem Mann had, calibration points at only one end assume that proxy sensitivity to temperature has not changed over the past 2,000 years, which is unlikely.
In addition, 392 of the 647 proxies are tree-ring proxies. I’ll deal with the problems with using tree rings as temperature proxies in another post, but for now just remember that tree ring records are detrended, which “results in a loss of multi-century variance” (Briffa et al., 1998b). This is the “segment-length curse” (Cook et al., 1995), which means that recoverable climatic information can be limited to the lengths of the individual tree-ring series used to build a reconstruction. The Pages 2k team tries to get around this by using “Regional Curve Standardization” (Esper et al., 2003), but in order for this to work properly all trees in the chosen standardization region must belong to the same “biological growth” population, something that cannot be verified 2,000 years ago, or even several hundred years ago. “This problem still remains largely unsolved.” (Cook et al., 1995)
The Pages 2k database paper (Pages 2K, 2017) admits that less than half of the proxies they studied correlated with HadCRUT4.2 over the instrumental period (1850-2014). Proxy records that did not significantly correlate with instrumental era measurements were rejected (Pages 2K, 2017) & (Pages2k, 2013). Screening proxies based on correlations during the short modern calibration interval may preferentially retain proxies that share characteristics of the late twentieth-century climate trend, potentially introducing selection bias. This selection bias can have the effect of forcing a hockey stick shape (Wegman et al., 2010). Further, the use of principal components, and some other dimensionality reduction techniques can cause similar problems. Principal component methods reduce many proxy series into a smaller number of composite indices. Depending on preprocessing choices and network composition, these methods may emphasize certain patterns of variability (such as modern warming) while suppressing others.
Pages 2k is attempting to produce a global mean temperature, but their spatial proxy coverage is uneven, even sparse in the Southern Hemisphere. Overall, their methodology is overly complicated and as methodological complexity increases, transparency decreases.
Pages 2k is not a simple repeat of Mann 1998, but its use of multiple statistical methods does not automatically eliminate shared biases, especially if all non-correlating proxies in the very short calibration period (~1850-2014) are rejected. If all methods use the same proxy network, the same calibration period, and similar assumptions about proxy stationarity, then agreement among methods is not proof that the reconstruction is correct. “Proxy stationarity” is the assumption that the relationship between the proxy and the target variable observed in the calibration period remains constant over time. For a good discussion of some of the problems with Pages 2k, see Steve McIntyre’s South American proxies, North American tree ring proxies, and Antarctic proxies.
Greenland
The main goal of this post is to help the reader appreciate why proxy temperatures are uncertain, even though ice core proxies are probably the best temperature proxies. A “proxy” can be a singleton, for example a single ice core, or a small region “reconstruction” or “aggregate” based on multiple cores from the same area that have been carefully correlated. Thus, the term is somewhat vague. In this post we will use “proxy” as synonymous with a small region reconstruction, since many ice core records are constructed from multiple cores taken in a small area.
The Pages 2k dataset contains six Vinther proxies (Vinther et al., 2009) from the Agassiz area in northeastern Canada and Greenland that we will focus on here. They are mapped in figure 2 and all were used in the Pages 2k final global reconstruction.
The Vinther Greenland proxies are well studied and have been used to make a Greenland temperature reconstruction that, in my opinion, is the best. This is the Vinther 2009 (Vinther et al., 2009) reconstruction shown alongside the Rosenthal Makassar Strait reconstruction in figure 3. In this post we will treat the Vinther 2009 reconstruction as the ideal for Greenland.
The two reconstructions shown in figure 3, Vinther’s 2009 Greenland reconstruction (the orange line) and Rosenthal’s 500-meter depth Makassar Strait reconstruction (Rosenthal et al., 2013) of the North Pacific SSTs (black line) are high-quality and have high temporal resolution (~20 years). They are also 9,500 miles apart.
Vinther’s 2009 Greenland Reconstruction
In 2009, Bo Vinther published a now-classic paper that explains a lot of problems with Greenland ice-core proxies and his solution for some of them. The oxygen-18 (“18O”) to oxygen-16 (“16O”) ratio from ice cores used in climate studies is a comparison of the measured ratio to the VSMOW2 standard ratio in ‰ (per thousand) difference. The standard is conceptually based on the mean seawater 18O /16O ratio. In reality, VSMOW2 is comprised of a mixture of lake water samples and is formulated to match the original seawater standard (SMOW) developed by Harmon Craig in the 1960s (Craig, 1961).
Vinther recognized that the 18O /16O ratio (or more simply, δ18O) was not simply a function of temperature, but also a function of the elevation of snow deposition, which varies substantially over time as a result of tectonic changes and the rate of snow deposition and glacier melting or movement. In figure 2 the current elevation is posted at each proxy site. Vinther recognized that the δ18O records from the Agassiz and Renland sites are similar, and dissimilar to the other sites. The four Agassiz cores are compared to the Renland core and the NCDC high resolution versions of the proxy records in figure 4.
The Agassiz A77 core is over two kilometers from the other three Agassiz cores and down slope from them, as a result its δ18O record is offset 1-1.5 ‰ negative as shown in the left graph in figure 4. This is likely due to scouring of winter snow off the Agassiz dome and ridge, where the other three cores are located, and the deposition of excess winter snow on the A77 site (Fisher et al., 1995) & (Fisher et al., 1983). This causes the mean annual δ18O to be lower at A77, a systematic seasonal effect. The plot of the offsets in the right-hand graph supports this idea, the offsets are similar and they became more negative in the Little Ice Age when the winters were colder, that is the summer/winter difference was more extreme in the Little Ice Age. This was a factor in the increased storminess observed in the Little Ice Age (Behringer, 2010), (Parker, 2012) & (Costas et al., 2016).
Unlike the ice cores taken deep into the Greenland ice sheet, the smaller Agassiz and Renland icecaps have reasonably accurate elevation histories available and their δ18O records can be corrected. Once this was done, they were very similar even though the sites are 1,500 km apart and they are on opposite sides of the Greenland Ice Sheet (Vinther et al., 2009). Vinther’s corrected δ18O Greenland temperature reconstruction is shown in figure 3 with the orange line.
Converting δ18O to ΔT
Creating an accurate and defensible temperature anomaly (ΔT) from ice core δ18O is challenging. The list of things that affect ice core δ18O besides temperature is long, it includes elevation, wind-blown snow, topography, and location. There are two methods, one is to correlate δ18O to local instrumental temperatures when they are available and fit an ordinary least squares (OLS) or other linear best line to the data and use the resulting slope to compute ΔT for the whole record. In Greenland this methodology produces very poor regression statistics as shown in figure 5 for the NCDC/Pages 2k one-year Agassiz δ18O record (R2 = 0, p=0.92) and the 5-year Renland record (R2 = 0.267, p = 0.01).
Figure 5 is constructed from Pages 2k δ18O high-resolution data and local NOAA GlobalTemp version 6. The correlations are very poor. It doesn’t get any better using the original Vinther 20-year sample version of the same ice core data. GlobalTemp data from the closest grid cell is used on the y axis and the site δ18O is on the x axis. These correlations are not unique, nearly all the Greenland Pages 2K proxies produce poor R2 values as shown in table 1.
Besides the poor R2 and p values in table 1, the slopes are odd, especially considering that Agassiz A87 (slope = -20 ‰/°C) and Agassiz A84 (slope = 0.369 ‰/°C) are only about 30 meters apart and A79 (slope = 0.8 ‰/°C ) is only a km away. These regressions do not provide a robust basis for estimating temperature sensitivity. We used the fits to compute ΔT and the result is plotted in the right-hand graphs in figure 5. The Agassiz plot is essentially a horizontal line, and the Renland plot is close to a horizontal line. Pages 2k explains that extratropical winter variability is a better predictor of the annual average, so when given a choice (as they are here) they use winter values (Pages 2K, 2017). The proxies used by Pages 2k, in table 1, have an “NCDC” prefix.
The Pages 2k documentation (Pages 2K, 2017) indicates that instrumental correlations played a role in calibration of the proxy to temperature relationship and in screening the proxies. I was unable to locate sufficient information to fully reproduce their calibration process. They do not supply the calibration datasets or the proxy-by-proxy correlation statistics that I could find and the explanation they do provide (Pages 2K, 2017) suggests the process is quite complex. In my work, I used all points between 1870 and 2020 to do the calibrations.
NOAA GlobalTemp
The NOAA GlobalTemp instrumental record for the grid cell identified in figure 2 is compared to the SW Greenland instrumental record (Vinther et al., 2006) in figure 6.
Figure 6 compares the land only SW Greenland temperature record and the corresponding record for the closest NOAA GlobalTemp grid cell located in figure 2. The grid cell contains a lot of sea surface area, that have temperatures that warm more slowly than the land-based temperatures in the SW Greenland record, which probably accounts for the 20th century difference.
Using “standard” δ18O to local temperature conversions
The problem with using an ice-core proxy δ18O to local temperature correlation for predicting temperature was recognized in the 1960s and Dansgaard and colleagues developed local correlations between δ18O in precipitation and temperature where both measurements are from the same sample. Their data is plotted in figure 7. Isotopic fractionation of precipitation versus condensation temperature is a real thing and atmospheric δ18O does decrease with condensation temperature. However, it is not a simple correlation and there are many confounding local factors when comparing regional temperatures to δ18O proxies. These include wind speed, relative humidity, topography, storm tracks, sea ice extent, elevation, and seasonality of precipitation. Thus, using a conversion from δ18O to ΔT varies from location to location.
Below is a blow up of Greenland points away from the coast shown in green in figure 7.
Figure 8 shows just the points in the interior of Greenland. All temperatures and δ18O value are measured from the same samples in the same conditions. The correlation is excellent and the resulting slope of 0.63 ‰/°C is very close to the generally accepted Greenland conversion of 0.62 ‰/°C used for the curves in figure 9.
Conclusions
As should be clear from figure 7, the slope of 0.62 ‰/°C is only appropriate for ice cores in the interior of Greenland. It is not appropriate for other ice cores, marine carbonates, foraminifera, corals, speleothems, or lake carbonates. In fact, from my OLS study of the Pages 2k δ18O proxies the average derived slope for 46 marine and lake sediment samples was -0.77 ‰/°C. All these OLS slopes are highly speculative with an average R2 of 0.16. The normal marine slope is negative and found by linear regression, no dataset like shown in figures 7 & 8 exists for marine sediments to my knowledge. These results suggest that temperature reconstructions or aggregates based solely on marine δ18O should be interpreted cautiously because non-temperature influences can be large and difficult to quantify. The Rosenthal reconstruction plotted figure 3 is a bit unique, since it is very well located, with an accurate depth that is corrected for sea level changes, and very well constrained (Rosenthal et al., 2013).
When a good correlation between δ18O and ΔT is available, and the relationship can be reasonably expected to persist into the past over the time span of the proxy record, δ18O can be a very good proxy. I think that is the case for Greenland ice cores from the interior (see figure 8), as long as elevation changes can be corrected for and the sites are well located. Agassiz 77 is a good example of a poorly located proxy.
Site specific problems
While δ18O in precipitation is differentiated by condensation temperature, there is no unique one-to-one relationship between proxy δ18O and temperature because multiple climatic and environmental variables influence the isotopic signal. In a nutshell, water molecules containing 18O are slightly heavier than those containing 16O. As moist air cools and condenses, the heavier 18O preferentially rains or snows out. As an air mass moves poleward or upslope, it becomes progressively depleted in 18O. Colder condensation temperatures therefore generally produce more negative δ18O values. This produces the familiar positive slope observed in figure 7.
Corals, foraminifera and other marine carbonates are different. Colder seawater causes carbonates to incorporate more 18O. Thus, colder water has a higher δ18O and the slope becomes negative, we normally expect a slope of about -0.2, but the Pages 2k average is much higher than this, so these slopes are highly uncertain. Ocean water 18O content is affected by evaporation, precipitation, river input, sea ice formation, and melting ice, so the 18O content in shells and corals is very hard to interpret. The relationship between δ18O and ΔT, everything else equal, is linear but the confounding factors of humidity, moisture source, storm tracks, seasonality, evaporation/precipitation balance, ice volume and proximity, and salinity make the relationship quite uncertain.
Transparent calibration procedures
The importance of the calibration of δ18O to ΔT is apparent. This makes the lack of specific proxy-by-proxy details in the Pages 2k documentation and papers unsettling. All I could find was the phrase “correlation with instrumental” deep in the RData documentation.[1] No statistics were stored in the record, and the conversion process is only vaguely described in the papers and other documentation (Pages 2K, 2017). Transparent calibration proxy-by-proxy details are critical because inferred temperatures depend strongly on the assumed δ18O-to-temperature conversion, and the conversion depends upon local conditions.
Combining multiple proxies into one global or hemispheric reconstruction is unlikely to work and hard to interpret. Each proxy is influenced by local conditions that are not necessarily related to temperature. All proxies are not equally accurate, especially over long periods of time, and the long-term accuracy is difficult to estimate. The correlation to modern instrumental temperature measurements may not persist into the past, and we could not verify that it does even if it did. It is easier to interpret proxies one at a time, each has unique problems, as we can see with the Greenland examples in this post. The only meaningful use of temperature proxies is to estimate the local temperature history around the proxy or aggregate proxy location, which should be carefully compared to local historical or archeological records (Soon & Baliunas, 2003) & (Soon et al., 2003b).
The R code to make these figures and perform the analysis is complicated so I will not provide a code supplement in this post, instead I will write a post or two describing the code and provide downloadable code and data with those posts.
Download the bibliography here.
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