The Physical Basis of Proxy Development

Background

Michael Tobis (mt for short), a colleague of mine who works at the University of Texas Institute for Geophysics runs a very interesting online climate/energy/science magazine called Planet 3.0. Prior to this, he used to post on the science blog, Only in it for the Gold (which he has shifted under Planet 3.0). Mt was kind enough to feature my article refuting Fred Singer’s claims (Proxy Evidence for Recent Warming) on Planet 3.0. 

A person by the name of Pat Frank on WUWT responded to this post by saying this. He claims that there is no physical theory backing up proxy reconstructions, that paleoclimate variables thus obtained are not physically real and that paleoclimatologists are guilty of "statistical hokum" by scaling a measurement to a trend and calling it temperature. This post is motivated by the aforementioned accusation.

First of all, let me start by pointing out the irony of this situation. Fred Singer (who is confused with Patrick Michaels by the WUWT commenter – get your facts straight... Oh wait…) was the person to claim that proxies do not show 20^th century warming. He used this (false) hypothesis to claim that global warming was not happening. Therefore, it is clear that he puts faith in proxy reconstructions as he uses them to argue his point. Now, we have another denier claiming that proxy reconstructions have no physical meaning, which would nullify what Singer said in the first place! Oh the irony… In any case, let me bring you some scientific snippets (aka truth) on the topic.

Understanding Proxies

As you are all aware, a paleoclimate proxy is a tool that is used to infer geophysical variables from the past. Generalizing this concept, a proxy could be anything that reveals past information. For example, wet grass in your front lawn on a clear, cloudless, sunny morning tells you that it rained the night before. Despite not seeing or hearing the rain yourself, believing that it rained the night before is not a long shot. The fact that the previous night was a cloudy one can be inferred too. It is logical to subscribe to this stance because we have seen the grass become wet and seen clouds in the sky when it rains. But how can we be so sure that rain caused the grass to be wet? (What if it was a neighbor who accidentally watered your lawn? What if the grass was wet because a pack of dogs urinated all over your lawn last night?) There are ways to test this hypothesis, physically and statistically (Is the grass in the backyard wet too? What about the other houses in the neighbourhood? How likely is it that a pack of dogs could urinate uniformly over all the grass in the neighbourhood?) The philosophy behind proxy based reconstructions, just like geology, is rooted in uniformitarianism - the present is the key to the past. A chemical/physical measurement on a proxy variable (say, stable oxygen isotopes on a coral head that has grown for centuries) reveals a significant amount of information about past geophysical parameters as long as we know how the variable is affected by the relevant geophysical process (eg. the controls of temperature, salinity on the isotopes). Different proxy variables respond to different physical parameters and this can be tested, verified and validated by experiment. This procedure is rooted in physics and the scientific method.

The Physics of Proxies: Foraminifera & Stable Isotopes

Let me focus on a proxy that I am familiar with and well within my realms as a researcher to talk about: oxygen-18 isotopes in the calcium carbonate shells of planktic foraminifera. Foraminifera are small organisms that secrete calcium carbonate shells and live in the ocean. Oxygen-18, is a stable isotope (doesn’t undergo radioactive decay) of the more abundant oxygen-16 and contains two more neutrons than the latter (ie the atomic mass is more). The change in the ratio of ¹⁸O/¹⁶O in any system undergoing a physical/chemical process is termed as isotopic fractionation. We utilize mass spectrometers to measure this ratio of ¹⁸O/¹⁶O in the calcium carbonate of the small shells (reported as δ¹⁸O ‰ relative to a standard). We are sure of pinning down this measurement up to a very high precision (error ≈0.05‰ – an order of magnitude less than 0.05%, mind you).

Nobel laureate Harold Urey, in 1947, explained the behavior of these stable isotopes (¹⁸O) and their departure in chemical and physical properties from the more abundant isotope (¹⁶O), arising from a difference in atomic mass in his landmark paper, The Thermodynamic Properties of Isotopic Substances (Journal of the Chemical Society, 1947). He discovered that temperature is the dominant control on isotopic fractionation.

As a simple analogy, consider the oxygen you are breathing in right now - it is not pure ¹⁶O₂. It is a mixture of the molecules ¹⁸O-¹⁶O, ¹⁸O-¹⁸O & ¹⁶O-¹⁶O – quantified by a certain ¹⁸O/¹⁶O ratio or δ¹⁸O. If you isolated it (closed system) and subjected it to a physical process, say liquefaction, isotope fractionation would occur. You would have a δ¹⁸O for the oxygen vapor and a different δ¹⁸O value for the liquid oxygen (similar to elementary vapor-gas equilibria studies).  Now, suppose you wanted to obtain different ratios for the vapor and liquid? How can this be achieved? Urey discovered that by increasing the temperature of the system, preferentially, lighter isotopes in the liquid phase would tend to go into gas phase and hence the liquid would be more enriched in δ¹⁸O and the gas would be depleted in δ¹⁸O (or more enriched with ¹⁶O). Of course, one could also change the ratio by introducing a stream of pure ¹⁸O-¹⁸O vapor or liquid, but then, the system would no longer be closed.

Amazingly, Urey predicted that paleotemperatures may be teased out of stable isotopic measurements of old carbonates utilizing this same principle. In the 50s, his student, Cesare Emiliani, carried out isotopic experiments on foraminifera shells and established quantifiable controls for this proxy in terms of a physical transfer function. When the CaCO₃ is deposited by these creatures, the resultant δ¹⁸O is a function of the temperature at the time of fractionation. However since the system is not closed, the δ¹⁸O of seawater must also factor in – i.e. how much ¹⁸O is available for the organism in the first place? Foraminiferal δ¹⁸O is a function of temperature and the δ¹⁸O of the seawater at the time that it was deposited:

δ¹⁸O_foram = f(Temperature_seawater , δ¹⁸O_seawater)

In other words ONLY a change in temperature or a change in seawater δ¹⁸O can alter the δ¹⁸O ratio of foraminiferal calcite. If temperature and seawater δ¹⁸O stayed constant through time, the measured δ¹⁸O of would be constant too. This is not the case. Therefore, when we measure isotopes on foraminifera shells in a marine sediment core, and we see that they are not the same, we can infer that there had to have been a change in sea temperature or sea water δ¹⁸O (which is related to sea water salinity and ice volume). There is no doubt about this.

Since then, there have been thousands of experiments (laboratory based, culture experiments, sediment traps) to accurately quantify these estimates and to pin down uncertainties – 60 years is a long time! Even though quantitative estimates are refined every now and then due to progress in mass spectrometry and understanding the biology of these creatures, qualitative inference (trends, variability) of foraminiferal proxy records from as far backas the 50s still holds true (Milankovitch cycles, ice ages etc.)

In summary, a measurement in a geological artifact (speleothem isotopes, fossil content, paleosols composition, tree-rings width, ice-core bubble makeup etc.) known to respond to a climatic parameter (temperature, humidity, precipitation, pCO₂ etc.) in the present is utilized as a proxy for the past. These proxy measurements are independently verified and statistically validated by robust methods of comparison with instrumental data and should have a sound physical reason as to why they change with aforementioned climate parameter (correlation does not imply causation); only then are proxy reconstructions and their inherent quantitative and qualitative implications accepted by the community. Nobody merely matches trends and principal components of empirical orthogonal functions to a random measurement in an unknown fossil as was accused.

The Physics of Proxies: The Literature

There are plenty of articles in the literature that describe the physical basis of each proxy in great detail. Here I have provided a (few) links to articles in the literature as an example of the scientific scrutiny through which a proxy is put through before it is used for reconstructing geophysical parameters. Note: I have only included a few proxies off the top of my head. Feel free to include your favourites in the comments.

• Thermodynamics & Isotopes
• The Thermodynamic Properties of Isotopic Substances - H. Urey, Journal of the Chemical Society (1947)
• Oxygen isotopes in nature and in the laboratory - H. Urey, Science (1948)
• On the Isotopic Chemistry of Carbonates and a Paleotemperature Scale - J. M. McCrea, Journal of Chemical Physics (1950)
• Foraminiferal δ¹⁸O
• Experimental paleotemperature equation for planktonic foraminifera - Erez & Luz, Geochimica Cosmochimica Acta (1983)
• Reevaluation of the oxygen isotopic composition of planktonic foraminifera: Experimental results and revised paleotemperature equations - B. E. Bemis et al., Paleoceanography (1998)
• Foraminiferal Mg/Ca
• Magnesium in tests of Neogloboquadrina pachyderma sinistral from high northern and southern latitudes - D. Nürnberg, Journal of Foraminiferal Research (1995)
• Calibration of Mg/Ca thermometry in planktonic foraminifera from a sediment trap time series - Anand et al., Paleoceanography (2003)
• Coral δ¹⁸O
• Coral Skeletal Chemistry: Physiological & Environmental Regulation of Stable Isotopes and Trace Metals in Montastrea annularis - T. J. Goreau, Proceedings of the Royal Society (1977)
• Evaluating climate indices and their geochemical proxies measured in corals - R. G. Fairbanks et al., Coral Reefs (1997)
• Coral Sr/Ca
• Sea-Surface Temperature from Coral Skeletal Strontium/Calcium Ratios - J. W. Beck et al., Science (1992)
• Speleothems
• The isotopic geochemistry of speleothems—I. The calculation of the effects of different modes of formation on the isotopic composition of speleothems and their applicability as palaeoclimatic indicators - C. H. Hendy, Geochimica et Cosmochimica Acta (1971)
• Oxygen isotopes in meteoric calcite cements as indicators of continental paleoclimate - P. D. Hays et al., Geology (1991)
• Palaeo-climate reconstruction from stable isotope variations in speleothems: a review - F. McDermott, Quaternary Science Reviews (2004)

Take Home Message

Climatic proxies (including stable isotopes, trace metals, organic biomarkers) are based on sound, well-established, well understood thermodynamic, physical principles. With respect to isotopic reconstructions, whatever I have just explained in this post has been known for over 65 years! Stable isotopes play a huge role in the natural science world today. These principles are even used for oil exploration and in the petroleum industry! It is a shame that deniers cannot even perform a cursory google search before making non-scientific claims. Granted, there are proxies such as faunal assemblages where the mechanistic relationship of species diversity could be related to more than one parameter, thereby complicating transfer functions and there are (new) proxies such as Tex86 paleothermometry where biological constraints aren't fully understood. However, the real strength of proxies lies in how reproducible and repeatable the measurements are. So, you have reconstructed sub-annual sea surface temperatures from a coral head, what does another coral from another colony indicate? Ok, you have estimated paleotemperatures from isotopes in a marine core, how do Tex86 measurements from the same core correlate with those?

To state that paleoclimatologists don't understand the fidelity of proxies is to be in denial. In fact, paleoclimatologists themselves are most critical of proxy measurements and their transferral into reconstructed variables. With advancing scientific progress in terms of instrumentation and new analytical techniques, new proxies are being developed as we speak. Harry Elderfield has an amusing graph regarding the confidence of newly proposed proxies:

Nobody is more critical of new proxies than paleoclimatologists/paleoceanographers themselves.
Taken from Elderfield, GCA (2002)

We paleoclimatologists are well within our right as scientists to state that proxies do indeed show a 20th century warming and this is with sound physical reasoning and not mere 'statistical hokum'.