Guest post by Pat Frank
It’s become very clear that most published proxy thermometry since 1998 [1] is not at all science, and most thoroughly so because Steve McIntyre and Ross McKitrick revealed its foundation in ad hoc statistical numerology. Awhile back, Michael Tobis and I had a conversation here at WUWT about the non-science of proxy paleothermometry, starting with Michael’s comment here and my reply here. Michael quickly appealed to his home authorities at, Planet3.org. We all had a lovely conversation that ended with moderator-cum-debater Arthur Smith indulging a false claim of insult to impose censorship (insulting comment in full here for the strong of stomach).
But in any case, two local experts in proxy thermometry came to Michael’s aid: Kaustubh Thimuralai, a grad student in proxy climatology at U. Texas, Austin and Kevin Anchukaitis, a dendroclimatologist at Columbia University. Kaustubh also posted his defense at his own blog here.
Their defenses shared this peculiarity: an exclusive appeal to stable isotope temperature proxies — not word one in defense of tree-ring thermometry, which provides the vast bulk of paleotemperature reconstructions.
The non-science of published paleothermometry was proved by their non-defense of its tree-ring center; an indictment of discretionary silence.
Nor was there one word in defense of the substitution of statistics for physics, a near universal in paleo-thermo.
But their appeal to stable isotope proxythermometry provided an opportunity for examination. So, that’s what I’m offering here: an analysis of stable isotope proxy temperature reconstruction followed by a short tour of dendrothermometry.
Part I. Proxy Science: Stable Isotope Thermometry
The focus is on oxygen-18 (O-18), because that’s the heavy atom proxy overwhelmingly used to reconstruct past temperatures. NASA has a nice overview here. The average global stable isotopic ratios of oxygen are, O-16 = 99.757%, O-17 = 0.038 %, O-18 = 0.205 %. If there were no thermal effects (and no kinetic isotope effects), the oxygen isotopes would be distributed in minerals at exactly their natural ratios. But local thermal effects cause the ratios to depart from the average, and this is the basis for stable isotope thermometry.
Let’s be clear about two things immediately: first, the basic physics and chemistry of thermal isotope fractionation is thorough and fully legitimate. [2-4]
Second, the mass spectrometry (MS) used to determine O-18 is very precise and accurate. In 1950, MS of O-18 already had a reproducibility of 5 parts in 100,000, [3] and presently is 1 part in 100,000. [5] These tiny values are represented as “%o,” where 1 %o = 0.1% = 0.001. So dO-18 MS detection has improved by a factor of 5 since 1950, from (+/-)0.05%o to (+/-)0.01%o.
The O-18/O-16 ratio in sea water has a first-order dependence on the evaporation/condensation cycle of water. H2O-18 has a higher boiling point than H2O-16, and so evaporates and condenses at a higher temperature. Here’s a matter-of-fact Wiki presentation. The partition of O-18 and O-16 due to evaporation/condensation means that the O-18 fraction in surface waters rises and falls with temperature.
There’s no dispute that O-18 mixes into CO2 to produce heavy carbon dioxide – mostly isotopically mixed as C(O-16)(O-18).
Dissolved CO2 is in equilibrium with carbonic acid. Here’s a run-down on the aqueous chemistry of CO2 and calcium carbonate.
Dissolved light-isotope CO2 [as C(O-16)(O-16)] becomes heavy CO2 by exchanging an oxygen with heavy water, like this:
CO2 + H2O-18 => CO(O-18) + H2O-16
This heavy CO2 finds its way into the carbonate shells of mollusks, and the skeletons of foraminifera and corals in proportion to its ratio in the local waters (except when biology intervenes. See below).
This process is why the field of stable isotope proxy thermometry has focused primarily on O-18 CO2: it is incorporated into the carbonate of mollusk shells, corals, and foraminifera and provides a record of temperatures experienced by the organism.
Even better, fossil mollusk shells, fossil corals, and foraminiferal sediments in sea floor cores promise physically real reconstructions of O-18 paleotemperatures.
Before it can be measured, O-18 CO2 must be liberated from the carbonate matrix of mollusks, corals, or foraminifera. Liberation of CO2 typically involves treating solid CaCO3 with phosphoric acid.
3 CaCO3 + 2 H3PO4 => 3 CO2 + Ca3(PO4)2 + 3 H2O
CO2 is liberated from biological calcium carbonate and piped into a mass spectrometer. Laboratory methods are never perfect. They incur losses and inefficiencies that can affect the precision and accuracy of results. Anyone who’s done wet analytical work knows about these hazards and has struggled with them. The practical reliability of dO-18 proxy temperatures depends on the integrity of the laboratory methods to prepare and measure the intrinsic O-18.
The paleothermometric approach is to first determine a standard relationship between water temperature and the ratio of O-18/O-16 in precipitated calcium carbonate. One can measure how the O-18 in the water fractionates itself into solid carbonate over a range of typical SST temperatures, such as 10 C through 40 C. A plot of carbonate O-18 v. temperature is prepared.
Once this standard plot is in hand, the temperature is regressed against the carbonate dO-18. The result is a least-squares fitted equation that tells you the empirical relationship of T:dO-18 over that temperature range.
This empirical equation can then be used to reconstruct the water temperature whenever carbonate O-18 is known. That’s the principle.
The question I’m interested in is whether the complete physico-chemical method yields accurate temperatures. Those who’ve read my paper pdf on neglected systematic error in the surface air temperature record, will recognize the ‘why’ of focusing on measurement error. It’s the first and minimum error entering any empirically determined magnitude. That makes it the first and basic question about error limits in O-18 carbonate proxy temperatures.
So, how does the method work in practice?
Let’s start with the classic: J. M. McCrea (1950) “On the Isotopic Chemistry of Carbonates and a Paleotemperature Scale“[3], which is part of McCrae’s Ph.D. work.
McCrae’s work is presented in some detail to show the approach I took to evaluate error. After that, I promise more brevity. Nothing below is meant to be, or should be taken to be, criticism of McCrae’s absolutely excellent work — or criticism of any of the other O-18 authors and papers to follow.
McCrae made truly heroic and pioneering experimental work establishing the O-18 proxy temperature method. Here’s his hand-drawn picture of the custom glass apparatus used to produce CO2 from carbonate. I’ve annotated it to identify some bits:
Figure 1: J. McCrae’s CO2 preparative glass manifold for O-18 analysis.
I’ve worked with similar glass gas/vacuum systems with lapped-in ground-glass joints, and the opportunity for leak, crack, or crash-tastrophe is ever-present.
McCrae developed the method by precipitating dO18 carbonate at different temperatures from marine waters obtained off East Orleans, MA, on the Atlantic side of Cape Cod, and off Palm Beach, Florida. The O-18 carbonate was then chemically decomposed to release the O-18 CO2, which was analyzed in a double-focusing mass spectrometer, which they apparently custom built themselves.
The blue and red lines in the Figure below show his results (Table X and Figure 5 in his paper). The %o O-18 is the divergence of his experimental samples from his standard water.
Figure 2, McCrae, 1950, original caption (color-modified): “Variation of isotopic composition of CaCO3(s) with reciprocal of deposition temperature from H2O (Cape Cod series (red); Florida water series (blue)).” The vertical lines interpolate temperatures at %o O-18 = 0.0. Bottom: Color-coded experimental point scatter around a zero line (dashed purple).
The lines are linear least square (LSQ) fits and they reproduce McCrae’s almost exactly (T is in Kelvin):
Florida: McCrae: d18O=1.57 x (10^4/T)-54.2;
LSQ: d18O=1.57 x (10^4/T)-53.9; r^2=0.994.
Cape Cod: McCrae: d18O=1.64 x (10^4/T)-57.6;
LSQ: d18O=1.64 x (10^4/T)-57.4; r^2=0.995.
About his results, McCrae wrote this: “The respective salinities of 36.7 and 32.2%o make it not surprising that there is a difference in the oxygen composition of the calcium carbonate obtained from the two waters at the same temperature.(bold added)”
The boiling temperature of water increases with the amount of dissolved salt, which in turn affects the relative rates that H2O-16 and H2O-18 evaporate away. Marine salinity can also change from the influx of fresh water (from precipitation, riverine, or direct runoff), or from upwelling, from wave-mixing, and from currents. The O-16/O-18 ratio of fresh water, of upwelling water, or of distant water transported by currents, may differ from a local marine ratio. The result is that marine waters of the same temperature can have different O18 fractions. Disentangling the effects of temperature and salinity in a marine O-16/O-18 ratio can be difficult to impossible in paleo-reconstructions.
The horizontal green line at %o O18 = zero intersects the Florida and Cape Cod lines at different temperatures, represented by the vertical drops to the abscissa. These show that the same dO-18 produces a difference of 4 C, depending on which equation you choose, with the apparent T covarying with a salinity change of 0.045%o.
That means if one generates a paleotemperature by applying a specific dO18:T equation to paleocarbonates, and one does not know the paleosalinity, the derived paleotemperature can be uncertain by as much as (+/-)2 C due to a hidden systematic covariance (salinity).
But I’m interested in experimental error. From those plots one can estimate the point scatter in the physico-chemical method itself as the variation around the fitted LSQ lines. The point scatter is plotted along the purple zero line at the bottom of Figure 2. Converted to temperature, the scatter is (+/-)1 C for the Florida data and (+/-)1.5 C for the Cape Cod data.
All the data were determined by McCrae in the same lab, using the same equipment and the same protocol. Therefore, it’s legitimate to combine the two sets of errors in Figure 2 to determine their average, and the resulting average uncertainty in any derived temperature. The standard deviation of the combined errors is (+/-)0.25 %o O-18, which translates into an average temperature uncertainty of (+/-)1.3 C. This emerged under ideal laboratory conditions where the water temperature was known from direct measurement and the marine O18 fraction was independently measured.
Next, it’s necessary to know whether the errors are systematic or random. Random errors diminish as 1/sqrtN, where N is the number of repetitions of analysis. If the errors are random, one can hope for a very precise temperature measurement just by repeating the dO-18 determination enough times. For example, in McCrae’s work, 25 repeats reduces the average error in any single temperature by 1.3/5 => (+/-)0.26 C.
To bridge the random/systematic divide, I binned the point scatter over (+/-)3 standard deviations = (+/-)99.7 % certainty of including the full range of error. There were no outliers, meaning all the scatter fell within the 99.7 % bound. There are only 15 points, which is not a good statistical sample, but we work with what we’ve got. Figure 3 shows the histogram plot of the binned point-scatter, and a Gaussian fit. It’s a little cluttered, but bear with me.
Figure 3: McCrae, 1950 data: (blue points), binned point scatter from Figure 2; red line, Two-Gaussian fit to the binned points; dashed green lines, the two fitted Gaussians. Thin purple points and line: separately binned Cape Cod point scatter; thin blue line and points, separately binned Florida point scatter.
The first thing to notice is that the binned points are very not normally distributed. This immediately suggests the measurement error is systematic, and not random. The two Gaussian fit is pretty good, but should not be taken as more than a numerical convenience. An independent set of measurement scatter points from a different set of experiments may well require a different set of Gaussians.
The two Gaussians imply at least two modes of experimental error operating simultaneously. The two thin single-experiment lines are spread across scatter width. This demonstrates that the point scatter in each data sets participates in both error modes simultaneously. But notice that the two data sets do not participate equivalently. This non-equivalence again indicates a systematic measurement error that apparently does not repeat consistently.
The uncertainty from systematic measurement error does not diminish as 1/sqrtN. The error is not a constant offset and does not subtract away in a difference between data sets. It propagates into a final value as (+/-)sqrt[(sum of N errors)^2/(N-1)].
The error in any new proxy temperature derived from those methods will probably fall somewhere in the Figure 3 envelope, but the experimenter will not know where. That means the only way to honestly present a result is to report the average systematic error, and that would be T(+/-)1.3 C.
This estimate is conservative, as McCrae noted that, “The average deviation of an individual result from the relation is 0.38%o.”, which is equivalent to an average error of (+/-)2 C (I calculated 1.95 C; McCrae’s result). McCrae wrote later, “The average deviation of an individual experimental result from this relation is 2°C in the series of slow precipitations just described.”
The slow precipitation experiments were the tests with Cape cod and Florida water, shown in Figure 2, and McCrae mentioned their paleothermal significance at the end of his paper, “The isotopic composition of calcium carbonate slowly formed from aqueous solution has been noted to be usually the same as that produced by organisms at the same temperature.”
Anyone using McCrae’s standard equations to reconstruct a dO-18 paleotemperature must include the experimental uncertainty hidden inside them. However, they are invariably neglected. I’ll give an example below.
Another methodological classic is Sang-Tae Kim et al. (2007) “Oxygen isotope fractionation between synthetic aragonite and water: Influence of temperature and Mg2+ concentration“.[6]
Kim, et al., measured the relationship between temperature and dO-18 incorporation in Aragonite, a form of calcium carbonate found in mollusk shells and corals (the other typical form is calcite). They calibrated the T:dO-8 relationship at five temperatures, 0, 5, 10, 25, and 40 C which covers the entire range of SST. Figure 4a shows their data.
Figure 4: a. Blue points: Aragonite T:dO-18 calibration experimental points from Kim, et al., 2007; purple line: LSQ fit. Below: green points, the unfit residual representing experimental point-scatter, 1-sigma = (+/-)0.21. b. 3-sigma histogram of the experimental unfit residual (points) and the 3-Gaussian fit (purple line). The thin colored lines plus points are separate histograms of the four data sub-sets making up the total.
The alpha in “ln-alpha” is the O-18 “fractionation factor,” which is a ratio of O-18 ratios. That sounds complicated, but it’s just (the ratio of O-18 in carbonate divided by the ratio of O-18 in water): {[(O-18)c/(O-16)c] / [(O-18)w/(O-16)w]}, where “c” = carbonate, and “w” = water.
The LSQ fitted line in Figure 4a is 1000 x ln-alpha = 17.80 x (1000/T)-30.84; R^2 = 0.99, which almost exactly reproduces the published line, 1000 x ln-alpha = 17.88 x (1000/T)-31.14.
The green points along the bottom of Figure 4a are the unfit residual, representing the experimental point scatter. These have a 1-sigma standard deviation = (+/-)0.21, which translates into an experimental uncertainty of (+/-)1 C.
In Figure 4b is a histogram of the unfit residual point scatter in part a, binned across (+/-)3-sigma. The purple line is a three-Gaussian fit to the histogram, but with the point at -0.58,3 left out because it destabilized the fit. In any case, the experimental data appear to be contaminated with at least three modes of divergence, again implying a systematic error.
Individual data sub-sets are shown as the thin colored lines in Figure 4b. They all spread across at least two of the three experimental divergence modes, but not equivalently. Once again, that means every data set is uniquely contaminated with systematic measurement error.
Kim, et al., reported a smaller analytical error (+/-)0.13, equivalent to an uncertainty in T = (+/-)0.6 C. But their (+/-)0.13 is the analytical precision of the mass spectrometric determination of the O-18 fractions. It’s not the total experimental scatter. Residual point scatter is a better uncertainty metric because the Kim, et al., equation represents a fit to the full experimental data, not just to the O-18 fractions found by the mass spectrometer.
Any researcher using the Kim, et al., 2007 dO-18:T equation to reconstruct a paleotemperature must propagate at least (+/-)0.6 C uncertainty into their result, and better (+/-)1 C.
I’ve done similar analyses of the experimental point-scatter in several studies used to calibrate the T:O-18 temperature scale. Here’s a summary of the results:
Study______________(+/-)1-sigma______n_____syst err?____Ref.
McCrae________________1.3 C_________15_____Y________[3]
O’Neil_________________29 C_________11______?________[7]
Epstein_______________0.76 C________25______?_________[8]
Bemis________________1.7 C_________14______Y________[9]
Kim__________________1.0 C_________70______Y________[6]
Li____________________2.2 C__________5______________[10]
Friedman______________1.1 C__________6______________[11]
O’Neil’s was a 0-500 C experiment
All the Summary uncertainties represent only measurement point scatter, which often behaved as systematic error. The O’Neil 1969 point scatter was indeterminate, and the Epstein question mark is discussed below.
Epstein, et al., (1953), chose to fit their T:dO-18 calibration data with a second-order polynomial rather than with a least squares straight line. Figure 5 shows their data with the polynomial fit, and for comparison a LSQ straight line fit.
Figure 5: Epstein, 1953 data fit with a second-order polynomial (R^2 = 0.996; sigma residual = (+/-)0.76 C) and with a least squares line (R^2 = 0.992; sigma residual = (+/-) 0.80 C). Insets: histograms of the point scatter plus Gaussian fits; Upper right, polynomial; lower left, linear.
The scatter around the polynomial was pretty Gaussian, but left a >3-sigma outlier at 2.7 C. The LSQ fit did almost as well, and put the polynomial 3-sigma outlier within the 3-sigma confidence limit. The histogram of the linear fit scatter required two Gaussians, and left an unfit point at 2.5-sigma (-2 C).
Epstein had no good statistical reason to choose the polynomial fit over the linear fit, and didn’t mention his rationale. The poly fit came closer to the high-temperature end-point at 30 C, but the linear fit came closer to the low-T end-point at 7 C, and was just as good as through the internal data points. So, the higher order fit may have been an attempt to save the point at 30 C.
Before presenting an application of these lessons, I’d like to show a review paper, which compares all the different dO-18:T calibration equations in current use: B. E. Bemis, H. J. Spero, J. Bijma, and D. W. Lea, Reevaluation of the oxygen isotopic composition of planktonic foraminifera: Experimental results and revised paleotemperature equations. [9]
This paper is particularly valuable because it reviews the earlier equations used to model the T:dO18 relationship.
Figure 6 below reproduces an annotated Figure 2 from Bemis, et al. It compares several T:dO-18 calibration equations from a variety of laboratories. They have similar slopes but are offset. The result is that a given dO-18 predicts a different temperature, depending on which calibration equation one chooses. The Figure is annotated with a couple of very revealing drop lines.
Figure 6: Original caption”Comparison of temperature predictions using new O. universa and G. bulloides temperature:dO-18 relationships and published paleotemperature equations. Several published equations are identified for reference. Equations presented in this study predict lower temperatures than most other equations. Temperatures were calculated using the VSMOW to VPDB corrections listed in Table 1 for dO-18w values.”
The green drop lines show that a single temperature associates with dO-18 values ranging across 0.4 %o. That’s about 10-40x larger than the precision of a mass spectrometer dO-18 measurement. Alternatively, the horizontal red extensions show that a single dO-18 measurement predicts temperatures across a ~1.8 C range, representing an uncertainty of (+/-)0.9 C in choice of standards.
The 1.8 C excludes the three lines, labeled 11-Ch, 12-Ch, and 13-Ch. These refer to G. bulloides with 11-, 12-, and 13-chambered shells. Including them, the spread of temperatures at a single dO-18 is ~3.7 C (dashed red line).
In G. bulloides, the number of shell chambers increases with age. Specific gravity increases with the number of chambers, causing the G. bulloides to sink into deeper waters. Later chambers sample different waters than the earlier ones, and incorporate the ratio of O-18 at depth. Three different lines show the vertical change in dO-18 is significant, and imply a false spread in T of about 0.5 C.
Here’s what Bemis, et al., say about it (p. 150), “Although most of these temperature:d18O relationships appear to be similar, temperature reconstructions can differ by as much as 2 C when ambient temperature varies from 15 to 25 C.”
That “2 C” reveals a higher level of systematic error that appears as variations among the different temperature reconstruction equations. This error should be included as part of the reported uncertainty whenever any one of these standard lines is used to determine a paleotemperature.
Some of the variations in standard lines are also due to confounding factors such as salinity and the activity of photosynthetic foraminiferal symbionts.
Bemis, et al., discuss this problem on page 152: “Non-equilibrium d18O values in planktonic foraminifera have never been adequately explained. Recently, laboratory experiments with live foraminifera have demonstrated that the photosynthetic activity of algal symbionts and the carbonate ion concentration ([CO32-]) of seawater also affect shell d18O values. In these cases an increase in symbiont photosynthetic activity or [CO32-] results in a decrease in shell d18O values. Given the inconsistent SST reconstructions obtained using existing paleotemperature equations and the recently identified parameters controlling shell d18O values, there is a clear need to reexamine the temperature:d18O relationships for planktonic foraminifera.”
Bemis, et al., are thoughtful and modest in this way throughout their paper. They present a candid review of the literature. They discuss the strengths and pitfalls in the field, and describe where more work needs to be done. In other words, they are doing honest science. The contrast could not be more stark between their approach and the pastiche of million dollar claims and statistical maneuvering that swamp AGW-driven paleothermometry.
When the inter-methodological ~(+/-)0.9 C spread of standard T:dO-18 equations is added as the rms to the (+/-)1.34 C average measurement error from the Summary Table, the combined 1-sigma uncertainty in a dO-18 temperature =(+/-)sqrt(1.34^2+0.9^2)=(+/-)1.6 C. That doesn’t include any further invisible environmental confounding effects that might confound a paleo-O18 ratio, such as shifts in monsoon, in salinity, or in upwelling.
A (+/-)1.6 C uncertainty is already 2x larger than the commonly accepted 0.8 C of 20th century warming. T:dO-18 proxies are entirely unable to determine whether recent climate change is in any way historically or paleontologically unusual.
Now let’s look at Keigwin’s justly famous Sargasso Sea dO-18 proxy temperature reconstruction: (1996) “The Little Ice Age and Medieval Warm Period in the Sargasso Sea.” [12] The reconstructed Sargasso Sea paleotemperature rests on G. ruber calcite. G. ruber has photosynthetic symbionts, which induces the T:dO-18 artifacts mentioned by Bemis, et al. Keigwin is a good scientist and attempted to account for this by applying an average G. ruber correction. But removal of an average bias is effective only when the error envelope is random around a constant offset. Subtracting the average bias of a systematic error does not reduce the uncertainty width, and may even increase the total error if the systematic bias in your data set is different from the average bias. Keigwin also assumed an average salinity of 36.5%o throughout, which may or may not be valid.
More to the point, no error bars appear on the reconstruction. Keigwin reported changes in paleotemperature of 1 C or 1.5 C, implying a temperature resolution with smaller errors than these values.
Keigwin used the T:dO-18 equation published by Shackleton in 1974,[13] to turn his Sargasso G. ruber dO-18 measurements into paleotemperatures. Unfortunately, Shackleton published his equation in the International Colloquium Journal of the French C.N.R.S., and neither I nor my French contact (thank-you Elodie) have been able to get that paper. Without it, one can’t directly evaluate the measurement point scatter.
However in 1965, Shackleton published a paper demonstrating his methodology to obtain high precision dO-18 measurements. [14] Shackleton’s high precision scatter should be the minimum scatter in his 1974 T:dO-18 equation.
Shackleton, 1965 made five replicate measurements of the dO-18 in five separate samples of a single piece of Italian marble (marble is calcium carbonate). Here’s his Table of results:
Reaction No. _1____2____3____4____5____Mean____Std dev.
dO-18 value__4.1__4.45_4.35__4.2__4.2____4.26%___0.12%o.
Shackleton mistakenly reported the root-mean-square of the point scatter instead of the standard deviation. No big deal, the true 1-sigma = (+/-)0.14%o; not very different.
In Shackleton’s 1965 words, “The major reason for discrepancy between successive measurements lies in the difficulty of preparing and handling the gas.” That is, the measurement scatter is due to the inevitable systematic laboratory error we’ve already seen above.
Shackleton’s 1974 standard T:dO-18 equation appears in Barrera, et al., [15] and it’s T = 16.9 – 4.38(dO-18) + 0.10(dO-18)^2. Plugging Shackleton’s high-precision 1-sigma=0.14%o into his equation yields an estimated minimum uncertainty of (+/-)0.61 C in any dO-18 temperature calculated using the Shackleton T:dO-18 equation.
At the ftp site where Keigwin’s data are located, one reads “Data precision: ~1% for carbonate; ~0.1 permil for d18-O.” So, Keigwin’s independent dO-18 measurements were good to about (+/-)0.1%o.
The uncertainty in temperature represented by Keigwin’s (+/-)0.1%o spread in measured dO-18 equates to (+/-)0.44 C in Shackleton’s equation.
The total measurement uncertainty in Keigwin’s dO-18 proxy temperature is the quadratic sum of the uncertainty in Shackleton’s equation plus the uncertainty in Keigwin’s own dO-18 measurements. That’s (+/-)sqrt[(0.61)^2+(0.44)^2]=(+/-)0.75 C. This represents measurement error, and is the 1-sigma minimum of error.
And so now we get to see something possibly never before seen anywhere: a proxy paleotemperature series with true, physically real, 95% confidence level 2-sigma systematic error bars. Here it is:
Figure 7: Keigwin’s Sargasso Sea dO-18 proxy paleotemperature series, [12] showing 2-sigma systematic measurement error bars. The blue rectangle is the 95% confidence interval centered on the mean temperature of 23.0 C.
Let’s be clear on what Keigwin accomplished. He reconstructed 3175 years of nominal Sargasso Sea dO-18 SSTs with a precision of (+/-)1.5 C at the 95% confidence level. That’s an uncertainty of 6.5% about the mean, and is a darn good result. I’ve worked hard in the lab to get spectroscopic titrations to that level of accuracy. Hat’s off to Keigwin.
But it’s clear that changes in SSTs on the order of 1-1.5 C can’t be resolved in those data. The most that can be said is that it’s possible Sargasso Sea SSTs were higher 3000 years ago.
If we factor in the uncertainty due to the (+/-)0.9 C variation among all the various T:dO-18 standard equations (Figure 6), then the Sargasso Sea 95% confidence interval expands to (+/-)2.75 C.
This (+/-)2.75 C = (uncertainty in experimenter d-O18 measurements) + (uncertainty in any given standard T:dO-18 equation) + (methodological uncertainty across all T:dO-18 equations).
So, (+/-)2.75 C is probably a good estimate of the methodological 95% confidence interval in any determination of a dO-18 paleotemperature. The confounding artifacts of paleo-variations in salinity, photosynthesis, upwelling and meteoric water will bring into any dO-18 reconstruction of paleotemperatures, further errors that are invisible but perhaps of analogous magnitude.
At the end, it’s true that the T:dO18 relationship is soundly based in physics. However, it is not true that the relationship has produced a reliably high-resolution proxy for paleotemperatures.
Part II: Pseudo-Science: Statistical Thermometry
Now on to the typical published proxy paleotemperature reconstructions. I’ve gone through a representative set of eight high-status studies, looking for evidence of science. Evidence of science is whether any of them make use of physical theory.
Executive summary: none of them are physically valid. Not one of them yields a temperature.
Before proceeding, a necessary word about correlation and causation. Here’s what Michael Tobis wrote about that, “If two signals are correlated, then each signal contains information about the other. Claiming otherwise is just silly.”
There’s a lot of that going around in proxythermometry, and clarification is a must. John Aldrich has a fine paper [16] describing the battle between Karl Pearson and G. Udny Yule over correlation indicating causation. Pearson believed it, Yule did not.
On page 373, Aldrich makes a very relevant distinction: “ Statistical inference deals with inference from sample to population while scientific inference deals with the interpretation of the population in terms of a theoretical structure.”
That is, statistics is about the relations among numbers. Science is about deductions from a falsifiable theory.
We’ll see that the proxy studies below improperly mix these categories. They convert true statistics into false science.
To spice up the point, here are some fine examples of spurious correlations, and here are the winners of the 1998 Purdue University spurious correlations contest, including correlations between ice cream sales and death-by-drowning, and between ministers’ salaries and the price of vodka. Pace Michael Tobis, each of those correlated “signals” so obviously contains information about the other, and I hope that irony lays the issue to rest.
Diaz and Osuna [17] point out that distinguishing, “between alchemy and science … is (1) the specification of rigorously tested models, which (2) adequately describe the available data, (3) encompass previous findings, and (4) are derived from well-based theories. (my numbers, my bold)”
The causal significance of any correlation is revealed only within the deductive context of a falsifiable theory that predicts the correlation. Statistics (inductive inference) never, ever, of itself reveals causation.
AGW paleo proxythermometry will be shown missing Diaz and Osuna elements 1, 3, and 4 of science. That makes it alchemy; otherwise known as pseudoscience.
That said, here we go: AGW proxythermometry:
1. Thomas J. Crowley and Thomas S. Lowery (2000) “How Warm Was the Medieval Warm Period?.” [18]
They used fifteen series: three dO-18 (Keigwin’s Sargasso Sea proxy, GISP 2, and the Dunde Ice cap series), eight tree-ring series, the Central England temperature (CET) record, an Iceland temperature (IT) series, and two plant-growth proxies (China phenology and Michigan pollen).
All fifteen series were scaled to vary between 0 and 1, and then averaged. There was complete and utter neglect of the physical meaning of the five physically valid series (3 x dO18, IT, and CET). All of them were scaled to the same physically meaningless unitary bound.
Think about what this means: Crowley and Lowry took five physically meaningful series, and discarded the physics. That made the series fit to use in AGW-related proxythermometry.
There is no physical theory that coverts tree ring metrics into temperatures. That theory does not exist and any exact relationship remains entirely obscure.
So then how did Crowley and Lowery convert their unitized proxy average into temperature? Well, “The two composites were scaled to agree with the Jones et al. instrumental record for the Northern Hemisphere…,” and that settles the matter.
In short, the fifteen series were numerically adjusted to a common scale, averaged, and scaled up to the measurement record. Then C&L reported their temperatures to a resolution of (+/-)0.05 C. Measurement uncertainty in the physically real series was ignored in their final composite. That’s how you do science, AGW proxythermometry style.
Any physical theory employed?: No
Strictly statistical inference?: Yes
Physical content: none.
Physical validity: none.
Temperature meaning of the final composite: none.
2. Timothy J. Osborn and Keith R. Briffa (2006) The Spatial Extent of 20th-Century Warmth in the Context of the Past 1200 Years.” [19]
Fourteen proxies — eleven of them tree rings, one dO-18 ice core (W. Greenland) — were divided by their respective standard deviation to produce a common unit magnitude, and then scaled into the measurement record. The ice core dO-18 had its physical meaning removed and its experimental uncertainty ignored.
Interestingly, between 1975 and 2000 the composite proxy declined away from the instrumental record. Osborn and Briffa didn’t hide the decline, to their everlasting credit, but instead wrote that this disconfirmation is due to, “the expected consequences of noise in the proxy records.”
I estimated the “noise” by comparing its offset with respect to the temperature record, and it’s worth about 0.5 C. It didn’t appear as an uncertainty on their plot. In fact, they artificially matched the 1856-1995 means of the proxy series and the surface air temperature record, making the proxy look like temperature. The 0.5 C “noise” divergence got suppressed and looks much smaller than it really is. Actual 0.5 C “noise” error bars scaled onto the temperature record of their final Figure 3 would have made the whole enterprise theatrically useless, no matter that it is bereft of science in any case.
Any physical theory employed?: No
Strictly statistical inference?: Yes
Physical uncertainty in T: none.
Physical validity: none.
Temperature meaning of the composite: none.
3. Michael E. Mann, Zhihua Zhang, Malcolm K. Hughes, Raymond S. Bradley, Sonya K. Miller, Scott Rutherford, and Fenbiao Ni (2008) “Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia.” [20]
A large number of proxies of multiple lengths and provenances. They included some ice core, speleothem, and coral dO-18, but the data are vastly dominated by tree ring series. Mann & co., statistically correlated the series with local temperature during a “calibration period,” adjusted them to equal standard deviation, scaled into the instrumental record, and published the composite showing a resolution of 0.1 C (Figure 3). Their method again removed and discarded the physical meaning of the dO-18 proxies.
Any physical theory employed?: No
Strictly statistical inference?: Yes
Physical uncertainty in T: none.
Physical validity: none.
Temperature meaning of the composite: none.
4. Rosanne D’Arrigo, Rob Wilson, Gordon Jacoby (2006) “ On the long-term context for late twentieth century warming .” [21]
Tree ring series from 66 sites, variance adjusted, scaled into the instrumental record and published with a resolution of 0.2 C (Figure 5 C).
Any physical theory employed?: No
Strictly statistical inference?: Yes
Physically valid temperature uncertainties: no
Physical meaning of the 0.2 C divisions: none.
Physical meaning of tree-ring temperatures: none available.
Temperature meaning of the composite: none.
5.Anders Moberg, Dmitry M. Sonechkin, Karin Holmgren, Nina M. Datsenko and Wibjörn Karlén (2005) “Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data.” [22]
Eighteen proxies: Two d-O18 SSTs (Sargasso and Caribbean Seas foraminiferal d-O18, and one stalagmite d-O18 (Soylegrotta, Norway), seven tree ring series. Plus other composites.
The proxies were processed using an excitingly novel wavelet transform method (it must be better), combined, variance adjusted, intensity scaled to the instrumental record over the calibration period, and published with a resolution of 0.2 C (Figure 2 D). Following standard practice, the authors extracted the physical meaning of the dO-18 proxies and then discarded it.
Any physical theory employed?: No
Strictly statistical inference?: Yes
Physical uncertainties propagated from the dO18 proxies into the final composite? No.
Physical meaning of the 0.2 C divisions: none.
Temperature meaning of the composite: none.
6. B.H. Luckman, K.R. Briffa, P.D. Jones and F.H. Schweingruber (1997) “Tree-ring based reconstruction of summer temperatures at the Columbia Icefield, Alberta, Canada, AD 1073-1983.” [23]
Sixty-three regional tree ring series, plus 38 fossilwood series; used the standard statistical (not physical) calibration-verification function to convert tree rings to temperature, overlaid the composite and the instrumental record at their 1961-1990 mean, and published the result at 0.5 C resolution (Figure 8). But in the text they reported anomalies to (+/-)0.01 C resolution (e.g., Tables 3&4), and the mean anomalies to (+/-)0.001 C. That last is 10x greater claimed accuracy than the typical rating of a two-point calibrated platinum resistance thermometer within a modern aspirated shield under controlled laboratory conditions.
Any physical theory employed?: No
Strictly statistical inference?: Yes
Physical meaning of the proxies: none.
Temperature meaning of the composite: none.
7. Michael E. Mann, Scott Rutherford, Eugene Wahl, and Caspar Ammann (2005) “Testing the Fidelity of Methods Used in Proxy-Based Reconstructions of Past Climate.” [24]
This study is, in part, a methodological review of the recommended ways to produce a proxy paleotemperature made by the premier practitioners in the field:
Method 1: “The composite-plus-scale (CPS) method, “a dozen proxy series, each of which is assumed to represent a linear combination of local temperature variations and an additive “noise” component, are composited (typically at decadal resolution;…) and scaled against an instrumental hemispheric mean temperature series during an overlapping “calibration” interval to form a hemispheric reconstruction. (my bold)”
Method 2, Climate field reconstruction (CFR): “Our implementation of the CFR approach makes use of the regularized expectation maximization (RegEM) method of Schneider (2001), which has been applied to CFR in several recent studies. The method is similar to principal component analysis (PCA)-based approaches but employs an iterative estimate of data covariances to make more complete use of the available information . As in Rutherford et al. (2005), we tested (i) straight application of RegEM, (ii) a “hybrid frequency-domain calibration” approach that employs separate calibrations of high (shorter than 20-yr period) and low frequency (longer than 20-yr period) components of the annual mean data that are subsequently composited to form a single reconstruction, and (iii) a “stepwise” version of RegEM in which the reconstruction itself is increasingly used in calibrating successively older segments. (my bold)”
Restating the obvious: CPS: Assumed representative of temperature; statistical scaling into the instrumental record; methodological correlation = causation. Physical validity: none. Scientific content: none.
CFR: Principal component analysis (PCA): a numerical method devoid of intrinsic physical meaning. Principal components are numerically, not physically, orthogonal. Numerical PCs are typically composites of multiple decomposed (i.e., partial) physical signals of unknown magnitude. They have no particular physical meaning. Quantitative physical meaning cannot be assigned to PCs by reference to subjective judgments of ‘temperature dependence.’
Scaling the PCs into the temperature record? Correlation = causation.
‘Correlation = causation is possibly the most naive error possible in science. Mann et al., unashamedly reveal it as undergirding the entire field of tree ring proxy thermometry.
Scientific content of the Mann-Rutherford-Wahl-Ammann proxy method: zero.
Finally, an honorable mention:
8. Rob Wilson, Alexander Tudhope, Philip Brohan, Keith Briffa, Timothy Osborn, and Simon Tet (2006), “Two-hundred-fifty years of reconstructed and modeled tropical temperatures.”[25]
Wilson, et al, reconstructed 250 years of SSTs using only coral records, including dO-18, strontium/calcium, uranium/calcium, and barium/calcium ratios. I’ve not assessed the latter three in any detail, but inspection of their point scatter is enough to imply that none of them will yield more accurate temperatures than dO-18.
However, all the Wilson, et al., temperature proxies had real physical meaning. What a great opportunity to challenge the method, and discuss the impacts of salinity, biological disequilibrium, and how to account for them, and explore all the other central elements of stable isotope marine temperatures.
So what did they do? Starting with about 60 proxy series, they threw out all those that didn’t correlate with local gridded temperatures. That left 16 proxies, 15 of which were dO-18. Why didn’t the other proxies correlate with temperature? Rob Wilson & co., were silent on the matter. After tossing two more proxies to avoid the problem of filtering away high frequencies, they ended up with 14 coral SST proxies.
After that, they employed standard statistical processing: divide by the standard deviation, average the proxies together (they used the “nesting procedure,” which adjusts for individual proxy length), and scale up to the instrumental record.
The honorable mention for these folks derives from the fact that they used only physically real proxies, and then discarded the physical meaning of all of them.
That puts them ahead of the other seven exemplars, who included proxies that had no known physical meaning at all.
Nevertheless,
Any physical theory employed?: No
Strictly statistical inference?: Yes
Any physically valid methodology? No.
Physical meaning of the proxies: present and accounted for, and then discarded.
Temperature meaning of the composite: none.
Summary Statement: AGW-related paleo proxythermometry as ubiquitously practiced consists of composites that rely entirely on statistical inference and numerical scaling. They not only have no scientific content, the methodology actively discards scientific content.
Statistical methods: 100%.
Physical methods: nearly zero (stable isotopes excepted, but their physical meaning is invariably discarded in composite paleoproxies).
Temperature meaning of the numerically scaled composites: zero.
The seven studies are typical, and representative of the entire field of AGW-related proxy thermometry. As commonly practiced, it is a scientific charade. It’s pseudo-science through-and-through.
Stable isotope studies are real science, however. That field is cooking along and the scientists involved are properly paying attention to detail. I hereby fully except them from my general condemnation of the field of AGW proxythermometry.
With this study, I’ve now examined the reliability of all three legs of AGW science: Climate models (GCMs) here (calculations here), the surface air temperature record here (pdf downloads, all), and now proxy paleotemperature reconstructions.
Every one of them thoroughly neglects systematic error. The neglected systematic error shows that none of the methods – not one of them — is able to resolve or address the surface temperature change of the last 150 years.
Nevertheless, the pandemic pervasiveness of this neglect is the central mechanism by which AGW alarmism survives. This has been going on for at least 15 years; for GCMs, 24 years. Granting integrity, one can only conclude that the scientists, their reviewers, and their editors are uniformly incompetent.
Summary conclusion: When it comes to claims about unprecedented this-or-that in recent global surface temperatures, no one knows what they’re talking about.
I’m sure there are people who will dispute that conclusion. They are very welcome to come here and make their case.
References:
1. Mann, M.E., R.S. Bradley, and M.S. Hughes, Global-scale temperature patterns and climate forcing over the past six centuries. Nature, 1998. 392(p. 779-787.
2. Dansgaard, W., Stable isotopes in precipitation. Tellus, 1964. 16(4): p. 436-468.
3. McCrea, J.M., On the Isotopic Chemistry of Carbonates and a Paleotemperature Scale. J. Chem. Phys., 1950. 18(6): p. 849-857.
4. Urey, H.C., The thermodynamic properties of isotopic substances. J. Chem. Soc., 1947: p. 562-581.
5. Brand, W.A., High precision Isotope Ratio Monitoring Techniques in Mass Spectrometry. J. Mass. Spectrosc., 1996. 31(3): p. 225-235.
6. Kim, S.-T., et al., Oxygen isotope fractionation between synthetic aragonite and water: Influence of temperature and Mg2+ concentration. Geochimica et Cosmochimica Acta, 2007. 71(19): p. 4704-4715.
7. O’Neil, J.R., R.N. Clayton, and T.K. Mayeda, Oxygen Isotope Fractionation in Divalent Metal Carbonates. J. Chem. Phys., 1969. 51(12): p. 5547-5558.
8. Epstein, S., et al., Revised Carbonate-Water Isotopic Temperature Scale. Geol. Soc. Amer. Bull., 1953. 64(11): p. 1315-1326.
9. Bemis, B.E., et al., Reevaluation of the oxygen isotopic composition of planktonic foraminifera: Experimental results and revised paleotemperature equations. Paleoceanography, 1998. 13(2): p. 150Ð160.
10. Li, X. and W. Liu, Oxygen isotope fractionation in the ostracod Eucypris mareotica: results from a culture experiment and implications for paleoclimate reconstruction. Journal of Paleolimnology, 2010. 43(1): p. 111-120.
11. Friedman, G.M., Temperature and salinity effects on 18O fractionation for rapidly precipitated carbonates: Laboratory experiments with alkaline lake water ÑPerspective. Episodes, 1998. 21(p. 97Ð98
12. Keigwin, L.D., The Little Ice Age and Medieval Warm Period in the Sargasso Sea. Science, 1996. 274(5292): p. 1503-1508; data site: ftp://ftp.ncdc.noaa.gov/pub/data/paleo/paleocean/by_contributor/keigwin1996/.
13. Shackleton, N.J., Attainment of isotopic equilibrium between ocean water and the benthonic foraminifera genus Uvigerina: Isotopic changes in the ocean during the last glacial. Colloq. Int. C.N.R.S., 1974. 219(p. 203-209.
14. Shackleton, N.J., The high-precision isotopic analysis of oxygen and carbon in carbon dioxide. J. Sci. Instrum., 1965. 42(9): p. 689-692.
15. Barrera, E., M.J.S. Tevesz, and J.G. Carter, Variations in Oxygen and Carbon Isotopic Compositions and Microstructure of the Shell of Adamussium colbecki (Bivalvia). PALAIOS, 1990. 5(2): p. 149-159.
16. Aldrich, J., Correlations Genuine and Spurious in Pearson and Yule. Statistical Science, 1995. 10(4): p. 364-376.
17. D’az, E. and R. Osuna, Understanding spurious correlation: a rejoinder to Kliman. Journal of Post Keynesian Economics, 2008. 31(2): p. 357-362.
18. Crowley, T.J. and T.S. Lowery, How Warm Was the Medieval Warm Period? AMBIO, 2000. 29(1): p. 51-54.
19. Osborn, T.J. and K.R. Briffa, The Spatial Extent of 20th-Century Warmth in the Context of the Past 1200 Years. Science, 2006. 311(5762): p. 841-844.
20. Mann, M.E., et al., Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia. Proc. Natl. Acad. Sci., 2008. 105(36): p. 13252-13257.
21. D’Arrigo, R., R. Wilson, and G. Jacoby, On the long-term context for late twentieth century warming. J. Geophys. Res., 2006. 111(D3): p. D03103.
22. Moberg, A., et al., Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data. Nature, 2005. 433(7026): p. 613-617.
23. Luckman, B.H., et al., Tree-ring based reconstruction of summer temperatures at the Columbia Icefield, Alberta, Canada, AD 1073-1983. The Holocene, 1997. 7(4): p. 375-389.
24. Mann, M.E., et al., Testing the Fidelity of Methods Used in Proxy-Based Reconstructions of Past Climate. J. Climate, 2005. 18(20): p. 4097-4107.
25. Wilson, R., et al., Two-hundred-fifty years of reconstructed and modeled tropical temperatures. J. Geophys. Res., 2006. 111(C10): p. C10007.
any chance of resurrecting the links embedded HERE:
“We’ll see that the proxy studies below improperly mix these categories. They convert true statistics into false science.
To spice up the point, HERE are some fine examples of spurious correlations, and HERE are the winners of the 1998 Purdue University spurious correlations contest, including correlations between ice cream…”
Tomwys, sorry for the trouble. I posted a set of fixed links in the comment section here
Frank, I have never once directed any ad hominem against you in our conversation. Pointing out that you began your criticisms not knowing anything about mass spec or how the dO-18 proxy works, etc., were not ad hominem statements. They assessed your expertise, not you personally, and they were factual.
It’ll take a while to answer your points; other duties call. But I’ll get to them.
Pat: After 10 days of [stunned?] silence regarding the presentation showing how to do uncertainty analysis when using a standard curve, it seems obvious that this methodology was unknown to you. Your ignorance of my scientific expertise is even worse: I used a mass spec several times a week, if not several times a day, for decades and am aware of why one should (or shouldn’t) get a linear plot for the logarithm of isotope ratio vs 1/T (Figure 4a).
I certainly didn’t understand all of the practical aspects of O18 dating when we began this conversation, but the green and brown lines on Figure 6 immediately suggested that you were confusing random and systematic errors when translating uncertainty in isotope ratio into uncertainty in temperature. Furthermore, I was taught to show error bars of one SEM so that your audience’s eye would immediately be drawn to data with differences that were likely to be statistically significant. (See Figures 5 and 6 at http://jcb.rupress.org/content/177/1/7.full) With 95% CI’s you showed, error bars overlap until p = 0.01, an absurd requirement in a scientific discipline that absurdly considers p<0.33 "likely" and p<0.05 "virtually certain". If the editor of the Journal of Biological Chemistry thinks his readers need an article on interpreting of error bars, I suspect the readers of WUWT may also.
Frank, in your paragraph 3, you drew attention to the wrong slide. The relevant comparisons are following slide 30, assessments of residuals.
These later slides describe random and non-random residuals. This distinction, not sensitivity, is relevant to the post analysis.
Post Figures 3-5 show the fit residuals are non-random. That implies systematic error. Systematic error is also present in the data of Kim & O’Neil and Zhou & Zhang, as later posted here and here.
Regarding your suggestion about calculating total uncertainty using the uncertainty in fitted parameters, I’ve already dealt with that in item 2, here. You gain nothing by it. Fitted e.s.d.s are, in any case, one step removed from a more straight-forward error analysis using the data scatter itself.
Lea doesn’t say from where he gets his estimates. Your speculation sheds no light.
The Shakelton calibration curve can be used to calculate temperatures for any dO-18 ratios that fall within its data bounds. “Decades” has nothing to do with it.
I truly regret having to observe this, Frank, but every time you sally forth into some area you demonstrate a lack of understanding.
You wrote, concerning all those systematic effects, “The uncertainty contributed by all of these factors to the standard error of the mean temperature diminishes with the square root of the number of samples analyzed.” No, it does not.
Only random error diminishes as 1/sqrtN, Frank. Systematic error does not. Here’s a reasonable Wiki discussion. When systematic error varies with time, locale, and/or experimenter it’s magnitude is unknown and unknowable. The only way to get a measure of it is to run a known standard through the method, measure the systematic error, and report that error as the minimum uncertainty in any result. And even that assumes the systematic effects of time and location are nil.
Your a-c: My uncertainty estimate for Keigwin’s chart has nothing to do with “site variability.” It has strictly to do with measurement error. You’ve now expressed that same mistaken view five times running; the four times already pointed out here.
You wrote, “If Keigwin analyzed 100 control samples, the standard error of the mean control isotope ratio would be very low…” That would be true only if Keigwin’s measurement errors were randomly distributed. Do you know they are so-distributed?
All the measurements I’ve investigated show evidence of systematic error. Shackleton mentioned them as plaguing even his high-precision results. You’ll have to demonstrate that Keigwin’s measurements include only random error before being justified in deploying the statistics of random error.
Shackelton’s and Keigwin’s respective measurement errors are independent. They each contribute independently to the total uncertainty in Keigwin’s final result. Such errors should always be added in quadrature.
Frank, I’m distracted by work and will be more so as May progresses. These responses take time, and after today I probably won’t have that time until at least mid-June.
What seems obvious to you is worthless without demonstration. So far, you have demonstrated a repeated tendency to be incorrect.
You wrote, “I used a mass spec several times a week, if not several times a day, for decades…
Right. That’s how you knew that, “The absolute size of peaks in a mass spectrum is irrelevant; only ratios are reported.”
That claim was demonstrated as incorrect here, showing that the output of a mass spectrometer is absolute peak height; but the tinypic has been removed, unfortunately. A more permanent demonstration picture is here.
And your decades-long knowledge of mass spectrometry led you to write that, “Stable isotopes are much more accurate describing temperature change, rather than absolute temperature. Most publications plot stable isotope ratios, rather than derived temperatures, on the vertical axis for precisely this reason,” which is also wrong.
Whereas in fact, stable isotope ratios for climatology are used to reconstruct temperature, not temperature differences. The temperature of the past is basically caculated as T_past = [(O-18_ratio)_past]/[(O-18_ratio)_present] times T_present plus a constant, where the ratio is vs standard sea water. Frank, you aren’t fooling anyone.
95% error bars are equivalent to p<0.05, Frank. The statistical p<0.01 represents 3 SD's or about 99.7% certainty (of including the correct value). You're once again mistaken.
Your comments concerning mass spec on April 29 reply are wrong: 1) The vertical scale on a mass spectrum originally was a measure of the ion current carried from the source to the collector by ions of analyte. Since different molecules ionize with very different efficiencies, ion current (or the output from newer detectors) is normally not reported quantitatively. For that reason, the vertical axis of a mass spectrum is traditionally labeled “relative abundance” or “arbitrary units”. The biggest signal is called the base peak and assigned a size of 100%; all other peaks are listed as percentages of that base peak, ie as RATIOS. Different isotopes of the same molecule do ionize with same efficiency; their difference is in the nuclei, not the electron orbitals involved in ionization. However, when too much sample is introduced in an attempt to strengthen the signal of minor isotopes, isotope ratios can be distorted. 2) The permanent link to the output of a mass spec you provided does NOT show a real mass spectrum. The output on this page characterizes a beam of oxygen ions probably intended to ionize samples during secondary ion mass spectroscopy. Based on your faulty information, it’s beginning to look as if I might know more about mass spec than you do. It takes Mannian guts to question the knowledge of someone who claims to have routinely used mass spec for decades when you make silly mistakes like these. Stick with unsubstantiated insults; they are safer.
As for error bars, you didn’t bother to read the reference I provided (or weren’t capable of understanding it). Error bars display descriptive statistics, but the paper was concerned with drawing statistical inferences about the DIFFERENCE between two or more data points from the appearance of their error bars. In Figures 5 and 6, the authors have illustrated how the error bars will appear (overlapping or not) when a t test shows the significance of the DIFFERENCE in means is borderline (p = 0.05). One can look at the error bars for a reconstruction and visually estimate whether or not any difference in temperature (for example, between the MWP and the LIA) is likely to be statistically significant. It is easy to spot insignificant differences when the error bar displays one SEM; the error bars touch or overlap. A error bars showing 95% ci can overlap and still represent meaningful differences in mean. Of course, the significance of any difference should be confirmed by a t test, but there is no easy way to display the results for all possible differences.
Unfortunately, you don’t seem to realize that science is mostly about CHANGE and DIFFERENCE: Is the recent rise in temperature bigger than natural variation? Is the treatment group different from the control? Is the difference between theory and observation significant enough to invalidate the theory? No one gives a #$*!%* whether the mean annual temperature in the Sargasso Sea was 21.2+/-0.7 or 22.6+/-1.6 degC during the LIA; we are interested in knowing the magnitude of natural variation and how much of the reconstructed variation might be attributable to random experimental error. You are capable of addressing issues more complicated than the mean temperature and its confidence interval, aren’t you?
(Figure 3 in your post suggests the answer to this question is yes. However, you should have performed a test to reject the (null) hypothesis that the data are consistent a single Gaussian distribution before making claims of systematic error.)
You wrote: “Whereas in fact, stable isotope ratios for climatology are used to reconstruct temperature, not temperature differences. The temperature of the past is basically calculated as T_past = [(O-18_ratio)_past]/[(O-18_ratio)_present] times T_present plus a constant, where the ratio is vs standard sea water. Frank, you aren’t fooling anyone.”
One can define a T_past_1 and a T_past_2 and calculate their difference:
[(O-18_ratio)_past_2 – O-18_ratio)_past_1]/[(O-18_ratio)_present] times T_present
AND eliminate of the uncertainty inherent in that inconvenient constant. Figure 6 vividly demonstrates the wide range of values this constant can have in different situations. I’ve made this point before and refuse to accept the unnecessary inflation in uncertainty associated with calculating temperature differences from absolute temperature. If I add 1.0 mg of sample to a 15.4531 g vial on an analytical balance, the uncertainty in that 1.0 mg doesn’t depend on the uncertainty in the actual weight of the vial. It depends on the sensitivity of the balance to an addition 1 mg when loaded with 15 g.
If you search google images for “core” and “O18”, you will find hundreds of graphs with delta O18 on the vertical axis instead of a temperature. When uncertainty in local seawater O18 or factors affecting the y-intercept of the calibration curve make it unreasonable to report absolute temperature reconstructions, the changes in O18 provide an estimate of changes in temperature (roughly 4.8 degC per 1 %o for O18 in calcium carbonate).
Finally, please acknowledge that I provided a reference showing that at least one analytical chemistry professor teaches students to calculate the uncertainty arising from use of a standard curve from the uncertainty in the parameters obtained during the least-squares fit to the calibration data. This procedure uses regression bands calculated for the desired degree of confidence to determine “sensitivity”: the minimum CHANGE that can be reliably detected. When you have time to study this unfamiliar method, you can explain why it is or is not appropriate for O18 dating.
I don’t know how Shakelton, Keigwin or Lea actually assess uncertainty, but this method doesn’t require Shakelton’s calibration uncertainty to be added in quadrature to Keigwin’s. Nor does it require the resulting uncertainty in temperature to be added in quadrature again when considering temperature change/variability. Unless you can demonstrate why sensitivity is an inappropriate measure of uncertain, Lea’s figure of +/-0.5 degC is more sensible than yours.
I should have listened when Steve Mosher warned another commenter above not to waste pointing out possible problems with your post. So, I won’t waste more time responding to further comments about my alleged ignorance or putative mistakes. However, I am seriously interested in the proper treatment of uncertainty in this situation and whether a sensitivity derived from the calibration curve is the best answer.
Frank, where to start? Maybe with your “2) because it will lead to your “1).”
The legend to the mass spectrum here says, “Mass spectrum of the Hyperion ion source operating with oxygen.” Ie., it’s a real mass spectrum of the oxygen ions produced by an oxygen ion plasma source used, for example, to micromill surfaces. Anyone with even the most basic understanding of mass spectrometry would have recognized that.
Notice that the ordinate is “counts.” That’s detector counts, representing absolute intensity. Detector counts, typically ion current, is what all mass spectrometers measure. That does not change if someone later rescales the spectrum, setting the most intense peak to 1.00 relative height.
Later processing to produce peak ratios does not mean that mass spectra themselves consist of peak ratios. You’re completely mixed up about what spectrometers detect (ion current) and how people process spectra afterwards (what is “reported”).
The text of your “1)” has the stilted language of a formal presentation, suggestive that it was largely copied from elsewhere.
You may, “[claim] to have routinely used mass spec for decades” but your extemporaneous comments here provide no evidence that you understand anything important about mass spectrometry. As I’m responding to your statements here, and not your purported experience, there’s no difficulty in sustaining the point.
You wrote, “Stick with unsubstantiated insults; they are safer.” Let’s see you quote any post of mine in which I have written an insult. I claim you won’t be able to do it, and therefore that your statement itself is an unsubstantiated canard.
Your whole paragraph starting with, “As for error bars,…” merely shows that you still don’t understand the difference between systematic and random errors. Further, for the umpteenth time, the errors I derived have nothing to do with differences between values.
When error is systematic, the mean value is not the most probable value. The mean is merely one among all the possible values between the systematic uncertainty limits. The unknown true value may not lay near the mean value. Statistical t-tests no longer make physically relevant comparisons between sets of means.
You wrote, “Unfortunately, you don’t seem to realize that science is mostly about CHANGE and DIFFERENCE:.” Science is about replicable fact in a context of falsifiable theory. Energy flux defines a gradient, which one supposes may be what you mean by change and difference.
You may not care whether systematic error is (+/-)0.7 C or (+/-)1.6 C, but any scientist would care about that difference. My interest was to explore the accuracy of proxy temperature methods. Both Kaustubh Thirumalai and Kevin Anchukaitis focused on dO-18 as their sole defense of proxy climatology, despite that the field largely relies on tree rings.
As the dO-18 proxy is truly based in physics (in contrast to tree-ring thermometry) and is acknowledged as the most well-developed and most accurate of all physically valid proxy methods, I decided to examine the errors in that method.
The measurement errors represent the lower limit of accuracy in the dO-18 method itself. In turn, since dO-18 proxies provide the most accurate proxy temperature reconstructions, their lower limit of accuracy sets the lower limit of resolution in the entire field of proxy thermometry.
In light of the envelope of data points, your parenthetical comment about Figure 3 is ludicrous.
You wrote, “One can define a T_past_1 and a T_past_2 and calculate their difference: [(O-18_ratio)_past_2 – O-18_ratio)_past_1]/[(O-18_ratio)_present] times T_present AND eliminate of the uncertainty inherent in that inconvenient constant.”
First, the error in the constant (the intercept) is determined solely by the error in the slope. Second, the first order error in the slope is due to measurement error (my concern here). Third, taking a difference does not eliminate systematic error because one does not know where the true value lies in the distribution of error and every single measured value has its own unique bias due to its own unique level of systematic error. Hence the variety of point scatter.
Look at Figures 2, 4, & 5: the residual scatter is not constant. The error is not constant. Error is not a constant offset in each point. Subtracting two data points does not eliminate the error inherent in them. The difference may even have a larger error than the points themselves if the systematic errors have the same sign.
Regarding your paragraph starting, “Finally, please acknowledge…,” as already noted, I dealt with that issue in item 2, paragraphs 3-5 here. Calculating an over all uncertainty using regression uncertainties gets you nothing. As already noted, using regression uncertainties is one step away from the more fundamental uncertainty calculated using the measurement errors in the data set itself.
You wrote, “I don’t know how Shakelton, Keigwin or Lea actually assess uncertainty…,” but you nevertheless do know that your unknown method doesn’t require adding errors in quadrature and that your inference is “more sensible” than my calculation. And you meant that to be convincing.
Here’s Shackleton’s equation: T = 16.9-4.38*(dO-18)+0.1*(dO-18)^2. We know from the Table of Shackleton’s precision analytical method that his minimal dO-18 error is (+/-)0.14%o.
Put that error into the equation, and one calculates that the minimal uncertainty of any calculated temperature is (+/-)0.61 C, when applying a proxy dO-18 measurement to Shackleton’s line.
That (+/-)0.61 C is the inherent uncertainty residing in Shackleton’s equation itself. We know from Shackleton’s comments that the error is from uncontrolled systematic causes.
Let’s see if I can explain this in words. If you, as an expert in mass spectrometry, managed to obtain a dO-18 measurement with zero experimental error, so that you knew the true exact dO-18 value, i.e., measurement uncertainty = (+/-)zero, then plugging that perfect dO-18 value into Shackleton’s equation would yield a proxy temperature with an uncertainty of T(+/-)0.61 C; i.e., the pure uncertainty in Shackleton’s equation.
But suppose you report that your dO-18 measurement error is (+/-)0.1%o (i.e., Keigwin’s average error). That means the dO-18 value you plug into Shackleton’s equation has its own independent error. Your error is in addition to Shackleton’s error, and it’s of the same magnitude, and it’s also systematic.
Your (+/-)0.1%o dO-18 measurement error produces an equivalent (+/-)0.44 C uncertainty in temperature when run through Shackleton’s equation.
But again, Shackleton’s equation has its own separate and independent error of (+/-)0.61 C. Any temperature calculated using Shackleton’s equation has a high uncertainty of +0.61 C and a low uncertainty of -0.61 C, from use of the equation alone.
The (+/-)0.44 C of your own measurement error is independent of Shackleton’s and additive. The +0.44 C portion of your uncertainty sits on top of (adds to) the +0.61 C portion of Shackleton’s uncertainty. Likewise, the -0.44 C of your measurement error adds to the -0.61 C of Shackleton’s uncertainty.
More analytically, Shackleton’s equation can be represented with the dO-18 measurement uncertainties left visible: T(+/-)sigma = 16.9-4.38*((+/-)0.14%o)+0.1*((+/-)0.14%o)^2.
Now we add in your measurements, which I’ll label as capital-DO-18. T(+/-)sigma = 16.9-4.38*[((+/-)0.14%o)+(DO-18(+/-)0.1%o)]+0.1*[(+/-)0.14%o)+(DO-18(+/-)0.1%o)]^2.
Rearranging: T(+/-)sigma = 16.9-4.38*[(DO-18(+/-)0.14%o)(+/-)0.1%o)]+0.1*[DO-18(+/-)0.14%o)(+/-)0.1%o)]^2. The errors now combine.
And so, T(+/-)sigma = 16.9-4.38*[DO-18(+/-)(total%o error)]+0.1*[DO-18(+/-)(total%o error)]^2.
Here we see explicitly that the dO-18 measurement uncertainty inherent within Shackleton’s equation adds directly to the error in your particular DO-18 measurements and, specifically, combines with your measurement error.
Errors in added quantities combine in quadrature. See “Addition and Subtraction” here.
Applying that statistical rule, “total %o error” = sqrt[(Shackleton error)^2+(Keigwin error)^2]. That’s QED, so let’s finish with this.
You wrote, “I am seriously interested in the proper treatment of uncertainty in this situation and whether a sensitivity derived from the calibration curve is the best answer”
Page 4 in your calibration presentation shows “sensitivity” to be the same as measurement accuracy when the uncertainty limits represent systematic error.
In that light, both my post and everything I’ve written here are about accuracy in the dO-18 calibration tests. That makes “sensitivity” the center of the discussion. And you have unfailingly argued against it. One is led to wonder about the seriousness of your interest.
Finally, you wrote, “I should have listened when Steve Mosher warned another commenter above not to waste pointing out possible problems with your post.”
Steve Mosher claimed that I ‘refuse to engage the argument.’ He had visited the pages at tAV (here and here) and must have known his charge was untrue when he wrote it.
You also visited at least one of those pages and must have noted my extensive engagement of the argument there.
You’ve also experienced my extensive engagement with your argument here — no matter that you’ve disagreed with me (though to no end).
So you knew that Steve Mosher’s criticism was untrue on its face, and you know that it’s untrue here as well. But you’ve repeated it and then applied it. Why aren’t you guilty of a double Mosher?
Pat:
Page 4 of the calibration presentation does NOT show sensitivity to be the same as measurement accuracy. Sensitivity is calculated from the separation between the regression bands calculated from the least-squares fit to the calibration data. I anticipate that the sensitivity will improve if the temperature range of the calibration is wider and if more samples are used in calibration, even though the uncertainty in each sample remains unchanged. The sensitivity near the ends of the calibration is poorer than in the middle. This is NOT simply measurement accuracy. A least-squares fit allow one to go beyond the uncertainty of single measurements at one temperature (0.14%o for Shakelton, according to you) particularly when calculating slope. It is the uncertainty in the slope (dT/dO18) that makes the uncertainty in temperature differences bigger than the uncertainty in individual temperature measurements. When the uncertainty in slope is small, your ability to reliably detect temperature differences should improve.
Nowhere in the presentation are two uncertainties added in quadrature to produce an overall uncertainty and then added again when one is interested in the difference between two results. You are not doing what this professor teaches.
Read about the units on the y-axis of a mass spectrum here: http://en.wikipedia.org/wiki/Mass_spectrum
Except in the case of isotopes, variable ionization prevents development of a useful relationship between the number of analyte molecules entering the mass spec and the number ions detected at a particular m/z. Sometimes the signal from minor, easily ionized impurities overwhelms the signal from the major component.
Read about the use of a BEAM of oxygen ions to ionize SAMPLES during secondary ion mass spectroscopy (SIMS) here:
http://en.wikipedia.org/wiki/Secondary_ion_mass_spectroscopy
The m/z ratio of the beam is displayed, not a mass spectrum of a typical sample.
No one runs a mass spectrum under conditions that break roughly half of the oxygen molecules into the oxygen ions which you can see at m/z = 16. If you did that with CO2 samples, you’d get a massive primary isotope effect enriching the O18 signal because the C-O16 bond is weaker than the C-O18 bond. (Sometimes chemists do want to fragment molecular ions to identify subunits, but they certainly wouldn’t use conditions that blow apart a simple oxygen molecule.) I’m certainly being picky about the oxygen beam, but you did say I knew nothing about mass spec.
You ignored the whole subject of using error bars to draw inferences about the significance of differences. You continue to mix discussion of random/experimental error – which is disclosed via error bars – with systematic error – which can’t easily be quantified. The possibility of systematic error is high. If you want to destroy O18 proxies, reliable estimates of systematic error could do it.
No, I didn’t plagiarize my comment. I revised in an to attempt to avoid misunderstanding.
I understood Mosher to be warning me that no matter what I said, what ideas I provided (concerning the obvious importance of uncertainty in temperature CHANGE), what alternatives I might present (a method for using uncertainty from least-squares calibrations), what alternative ways of looking at a issue I might propose (inferences from error bars), references I might present (Lea’s 0.5 degC); everything would be rejected as being unambiguously wrong; right down to the originality of my words and my experience with mass spec. You could have quickly checked any online source about the use of relative abundant, base peak, and a beam of oxygen ions in SIMS. You could have acknowledged that 1 sigma error bars can be used to draw inferences about climate change in a manner that you didn’t recognize when you decided to use 2 sigma error bars. 2 Sigma wasn’t WRONG, after all. ENGAGEMENT requires an open mind – I don’t mean Tamino’s – not a just error-ridden replies indiscriminately saying WRONG, WRONG, WRONG before you’ve really considered anything. From my perspective, your attitude is no different than the Hockey Team responding to McIntyre. An open-mind: “Frank, could you provide a reference showing how analytical chemists use the uncertainty in the least-squares fit to assess uncertainty in assays using a standard curve?” “Frank, I was focused on the uncertainty in absolute temperature, but the uncertainty in temperature change is also important and does become ridiculously large by adding in quadrature. Your method does produce temperature differences with less uncertainty, but I’m skeptical that one can eliminate the uncertainty inherent in the y-intercept by eliminating that term algebraically.” Which bring me back to Feynman and the easiest person to fool.