Lots of interesting things to find when you turn over the rocks of Hansen et al 2006. These are comments on work in progress, but, to say the least, there appear to be some curious decisions and methodologies.
Reviewing briefly, the key figure in Hansen et al 2006 is its Figure 5 comparing recent SST measurements in the Pacific Warm Pool to Mg/Ca reconstructions.
Figure 1. Original Caption: Hansen et al 2006 Fig. 5. Modern sea surface temperatures (5, 6) in the WEP compared with paleoclimate proxy data (28). Modern data are the 5-year running mean, while the paleoclimate data has a resolution of the order of 1,000 years.
Now I don’t have any objection to focussing on the Western Equatorial Pacific. In fact, I think that there’s much to be said for focussing on a region that’s both extremely important and with relatively uniform temperature. It’s how it’s done that concerns me. In order to derive the above SST reconstruction, a transfer function relating Mg/Ca to SST is required. The transfer function used in Hansen et al 2006 is taken from Medina-Elizalde and Lea 2005 and is as follows:
(1) SST (deg C) = ln (Mg.Ca(m)/ 0.3) / 0.089 or equivalently
(2) Mg.Ca = 0.3 exp [ 0.089* SST]
Medine-Elizalde and Lea 2005 (see Legend to Medina-Elizalde and Lea Figure 2) cited Lea et al 2000 as authority for this transfer function. Now Lea et al 2000 is a relatively early paper in Mg/Ca paleo-calculations. It noted, but did not adjust for, preferential dissolution of Mg at depth in the Ontong Java Plateau (OJP); they noted that failure to account for such dissolution would result in colder paleo-temperature estimates. A more complicated formula with an adjustment method for dissolution was presented in Dekens et al 2002 (including Lea). However, for some reason, the updated formula was not applied in either Medina-Elizalde and Lea 2005 or Hansen et al 2006. Had the Dekens et al formula been used, the reconstruction would have been a little bit warmer as shown in Figure 2 below. (The 29.2 deg C benchmark is taken from Dekens et al 2002). I show this figure with a big asterisk as it seems to me that there’s an elementary algebraic error in the calculation of the formula in Dekens et al 2002 – which I will present for discussion below.
Figure 2. Re-stated Paleo-reconstruction using formula of Dekens et al 2002 – red.
Update Oct. 3 I wrote to David Lea asking why the older formula was used and he replied:
Hi Steve: the adjustment based on the Dekens 2002 equation is quite small at the location and depth of Hole 806b (~0.3 deg in SST), and, in the absence of time-varying dissolution corrections, only serves to change the absolute SST value. For that reason we chose to maintain the earlier calibration to be consistent with the published data in the 2000 study.
However, there’s a lot more than this going on, which I’ll try to summarize here.
Lea et al 2000
Let’s start with Lea et al 2000, beginning with their key Figure 2.
Figure 3. Lea et al 2000 Fig. 2. (A) Pacific core-top G. ruber calibration for Mg/Ca versus mean annual SST (43). Each point is the average of two or more analyses. The range of core-top water depths is 1625 to 3200 m. The standard error of the exponential fit is 60.6¡C. Dashed lines indicate the 95% conàÆà ⽤ence intervals for the curve fit.(B) Mg/Ca in G. ruber shells from core-tops on the Ontong Java Plateau as a function of water depth. The àÆà ⽬led diamond at 0 m is the Mg/Ca value for a plankton tow sample taken at SST 5 27.2¡C off southwest Puerto Rico. The filled circle at 0 m is the same sample corrected for the 2 deg C warmer temperature of the WEP. The data indicate that shell Mg/Ca decreases by about 12% per 1 km increase in water depth. See text for details.
The left panel shows the derivation of their calibration equation – the one used above. The right panel shows the effect of increasing core-top depth on dissolution of Mg/Ca with the effect on foraminifera shells reported by the authors as being visible. The points used to calibrate the left panel equation come from two locations – the “warmer” cores are from the Western Equatorial Pool (WEP) including core ODP806B; the “cooler” cores are from the Eastern Equatorial Pacific, all around the Galapagos. The core top Mg/Ca measurements are all dated through radiocarbon and dates of 4000-6000 BP are assigned to the core top measurements. The SST measurements are modern SST measurements from Levitus 1994.
Think about what is illustrated here (and it took me a long time to understand it): the left panel shows a regression relationship between Holocene Optimum G. ruber Mg/Ca and modern SST!?! At most, this could illustrate a general geographic relationship but it can’t be used to calibrate anything, especially if it’s supposed to be calibration within a degree for the Framework Convention. But it’s worse. The right hand values from the WEP are “net” Mg/Ca values after dissolution. So the regression relationship is between partially dissolved Holocene Optimum foraminifera Mg/Ca and modern SST, with no accounting for the degree of dissolution!?!
Now there has been considerable discussion in the specialist literature about dissolution. I’ve spent a couple of days trying to replicate the above diagram in order to test the effect of applying different approachs to allowing for dissolution. The cores used in the above diagram appear almost certainly to be (from left to right) the following 11 cores: TR163-32; TR163-27; TR163-28; TR163-20B;TR163-22; TR163-18; TR163-19; ODP806B; MW91-9 08; MW91-9 34; MW91-9 38. (See Data Digression below). Figure 4 below shows my emulation of Lea et al Figure 2, using data from various publications – see Data Data Digression.
Figure 4. Emulation of Lea et al 2000 Figure 2.
The right panel indicates the presumed “original” Mg/Ca ratios prior to dissolution en route to sediments. (The dissolution occurs strongly at depth and Lea mentions that Mg is completely dissolved in OJP cores at 3500 m and below. The dissolution pertains to pCO2 values at depth. BTW there is some discussion about changing pCO2 values at depth over time in this literature which should be considered by people interested in carbon cycle and depp ocean exchange.) The “original” Mg/Ca values at surface, that gave rise to the WEP core top values, are approximately 5.42, a indicated by the surface intercept of the line on the right panel.
Figure 5 below shows these adjusted values in red in the same format as Lea et al Figure 2 (together with one modern measurement from the Atlantic in orange). Obviously the “adjusted” Mg/Ca values don’t fit the Lea et al 2000 curve at all. (BTW it’s my impression that the foraminifera in the EEP were not dissolved to the same extent as the OJP samples and adjustment is not as important there, but it’s something that needs to be verified.) So where does this leave us? The transfer equation in Lea et al 2000, used in Medina-Elizalde and Lea 2005 and Hansen et al 2006, appears to be completely inappropriate and without any logical basis, let alone statistical basis. So let’s go back to Dekens et al 2002 and see how they handled dissolution and see what can be salvaged.
Figure 5. Mg/Ca values adjusted for dissolution shown in red in same format as Figure 3.
Dekens et al 2002
It’s hard to see why the formula in Dekens et al 2002 wasn’t used in the later studies rather than the primitive methodology of Lea et al 2000. As noted above, perhaps it was because the reported adjustment in Dekens et al 2002 didn’t appear to be very large – but it’s still large enough to make a difference especially if we’re talking about half a degree or so. The actual expression in Dekens et al 2002 was:
which expressed in the same form as (1) is obviously:
(4) SST = ln ( Mg.Ca/0.38) +0.61*km +1.6
Dekens et al 2002 state, but do not derive this formula. In order to develop a rational transfer function, one obviously has to get away from regressing partially-dissolved Holocene Optimum core tops against modern SST and it appears that this was attempted in Dekens et al, but with some odd algebra.
Barker et al 2005 have a recent and sensible survey of Mg/Ca proxy calibration based on modern sediment trap data for calibration resulting in the following formula:
(5) Mg/Ca = 0.38 exp [ 0.09* SST]
This formula is shown in their Figure 2 as shown below:
Figure 5. Barker et al 2005 Fig. 2. Mg/Ca calibration results of Anand et al. (2003) for several species of planktonic foraminifera. Temperatures shown here are the isotopically derived calcification temperatures of Anand et al. (2003). A single temperature equation may be used to describe all data àÆà°r ¼ 0:93àÆà ⼺ Modified after Anand et al. (2003).
Notice that the key outside parameters of the Barker et al transfer function are identical to the corresponding parameters used in Dekens et al 2002: the “preexponent” parameter of 0.38 occurs in both as does the inside parameter of 0.09. So it’s evident that Dekens et al 2002 applied the relationship later articulated in Barker et al 2005, the relationship presumably available in the community in 2002. Dekens et al appear to have used this relationship on reconstructed “original” Mg/Ca values, after allowing for dissolution.
Now the adjustment for dissolution from the right panel of Lea et al 2000 (with denoting the surface (original) Mg/Ca values prior to dissolution – the value appropriate for the Barker et al 2005 equation.
The parameter 0.58 for the depth relationship is obviously very close to the figure of 0.61 in the Dekens et al 2002 equation; I will apply this parameter in the following calculations in place of the value of 0.58. Thus:
Substituting this relationship into (5) and using baby steps, we get:
This is similar in appearance, but materially different from the formula of Dekens et al 2002:
Equation (8) follows logically from the literature, but the Dekens et al 2002 equation only appears possible by dropping a bracket or some other error in the simple algebra.
So what happens if formula (8) is applied to actual data – doing the algebra in baby steps:
gives the following reconstruction:
Figure 6. Hole ODP806B Reconstruction using varied transfer function. Blue – amended calculation.
Where does this leave us? In paleoclimate terms, using the adjustment for dissolution as calculated above, the temperature differences in the Pacific Warm Pool are less than one would expect. My guess is that the dissolution adjustment in glacial times will be less than in warm times – there’s substantial evidence at modern sites that dissolution is not as serious a problem at cooler sites. However, as long as one is speculating on the proportion of dissolution in the foraminifera, there are layers of uncertainties that are not even hinted at in Hansen et al 2006. We don’t know what the pre-dissolution values of Mg/Ca for the Holocene Optimum were and so comparing modern instrumental values to core top values is little more than speculation. Having said that, Mg/Ca levels in the Holocene Optimum were relatively warm within the Pleistocene – reinforcing the observation that the Holocene is a relatively mild period within the Pleistocene. Prior to the last few years, this was usually believed to be a “good thing” in human terms.
For calibration, the Barker et al 2005 equation pertains to calcification temperature. G ruber grows in the mixed layer – I’ve seen a figure of 0-50 m quoted in the South China Sea. Presumably it would grow deeper in the WEP with its very deep mixed layer. So the temperature that’s being measured is some sort of average temperature in the mixed layer; how does this compare with the instrumental measurement? Well, consider all the energy that went into adjusting between canvas and wooden buckets in order to make the HadSST data set. If those adjustments are worth making, then surely a little inquiry is required before splicing calcification temperature integrated over the mixed layer in some manner with instrumental temperatures.
Update (Oct. 2, 2006)
In some comments, I pointed out that there was evidence [McClain et al,. JGR 1999] that the top part of the Warm Pool was nutrient poor and that plankton growth optimized at lower depth, which presumably would be cooler by about 2 deg C. David Stockwell posited that the unexplained 1.6 deg C adjustment in Dekens et al 2002 plausibly came from this. Here’s some documentation of this effect and a diagram of its impact.
Tian et al 2005 say of the South China Sea:
G. ruber is a mixed layer dweller that lives at depths between ~30–60 m in the upper mixed layer of the modern ocean [Hemleben et al., 1989],
Peeters et al 2002 say of the Arabian Sea:
The calcification temperatures of G. ruber mirrored the seawater temperatures near the DCM, at 11 m during upwelling (at station 313). Although calcification temperatures during non-upwelling ranged between the sea surface temperatures and those found at 80 m, the average calcification temperatures suggest that most calcite precipitated between 50 and 80 m, i.e. between the DCM and the upper thermocline. On average, the calcification temperature of G. ruber was 1.7 deg C lower than the sea surface temperature.
These admittedly do not specifically cover the Pacific Warm Pool. McClain et al 1999 discuss the Pacific Warm Pool and, while they do not specifically discuss G. ruber, they have information that bears on the problem. They report on model output for plankton production in the Warm Pool at 165E, not too far from the Ontong Java Plateau. Here is a graphic showing levels of plankton productivity:
Plate 5. Depth-time contour plots for simulated (a) NO3 2, (b) NH4 1, (c) Z, and (d) P (or chlorophyll) in mgatN m23 derived from the diffusion-only (w 5 0) simulation. McCl;ain et al JGR 1999.
They also provide the following graphic showing the temperature output from their model while noting in their text that
“The temperatures replicate the observed temperatures within the upper 100 m to within ~1 deg C but are generally warmer at depth by 1–2 deg C, on average. (p 18311) “
Plate 2. Depth-time contour plot of … (d) temperature (8C) from the ocean general circulation model. Texr:
Thus, as David Stockwell suggests, it seems quite plausible that the adjustment of 1.6 deg C in the Dekens et al 2002 equation describes the difference between SST and the average calcification temperature for G. ruber. If so, then the above equations should read, allowing for the algebraic
This produces the following rather troubling graphic:
Figure x. SST Reconstruction using equation (10), which assumes that the Mg/Ca reconstruction estimates a mixed layer that is 1.6 deg C cooler than the surface SST.
I think that what this latest calculation is saying is that a linear adjustment for relative dissolution is probably not very accurate, but it obviously highlights the impact of assumptions on Mg/Ca dissolution in trying to carry out a Hansen splice.
Now for a little digression on the data in this diagram. As usual in matters paleoclimate, it’s never easy to reconcile data and I’ve spent a couple of days trying to sort this out. Lea et al 2000 Table 1 and Dekens et al 2002 Table 4 (both shown below) show core top Mg/Ca and SST for a variety of cores, including cores shown here. Lea has archived a couple of holes (notably ODP806B and TR163-19 at WDCP – excerpts below). The trouble is that the data does not reconcile exactly and doesn’t reconcile clearly with the figure. Now it’s close enough that probably not much turns on it, but it’s very frustrating when you’re trying to figure out what they did.
For example, the left panel of Lea et al 2000 Figure 2 has two points at 26.2 deg C with Mg/Ca values just below 3. These cores are almost certainly TR163-18 and TR163-19, but the values in Lea et al 2000 Table 1 are a little bit higher than in Figure 2. The values for TR163-18 in Dekens et al 2002 are different: these might be the values used in Lea et al 2000, but what is in Table 1? What is the connection between the archived values and the reported core top values? They are close in both cases – but don’t match. I’ve experimented with different combinations but haven’t been able to determine what was done. Other puzzling points: why is TR163-22 shown in Lea et al 2000 Table 1 not carried forward to Dekens et al 2002 Table 4? However aside from these questions, the cores used for the fitting appear almost certainly to be (from left to right) the following 11 cores: TR163-32; TR163-27; TR163-28; TR163-20B;TR163-22; TR163-18; TR163-19; ODP806B; MW91-9 08; MW91-9 34; MW91-9 38.
Excerpt from Lea et al 2002 – Table 1
Excerpt from Dekens et al 2002 Table 4
Excerpt from Table S2 Medina-Elizalde and Lea 2005 SI. http://www.sciencemag.org/cgi/content/full/1115933/DC1 for ODP806B (also at WDCP here . For data on TR163-19 see WDCP here
Lea et al 2000. Science
Dekens et al 2002. Paleoceanography.
Barker et al 2005. QSR.
Hansen et al 2006. PNAS.
Tian et al 2005 GRL
Frank J.C. Peeters, Geert-Jan A. Brummer, Gerald Ganssen, 2002, The effect of upwelling on the distribution and stable isotope composition of Globigerina bulloides and Globigerinoides ruber (planktic foraminifera) in modern surface waters of the NW Arabian Sea Global and Planetary Change 34 (2002) 269–291
S. Levitus and T. P. Boyer, World Ocean Atlas 1994, Volume 4: Temperature, NOAA Atlas NESDIS (U.S. Department of Commerce, Washington, DC, 1994).Accessed at http://ingrid.ldgo.columbia.edu/SOURCES/.LEVITUS94/