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| A '''paleothermometer''' is a methodology for determining past [[temperature]]s using a [[Proxy (climate)|proxy]] found in a natural record such as a [[sediment]], [[ice core]], [[tree ring]]s or [[TEX86|TEX<sub>86</sub>]].
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| ==Common paleothermometers==
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| ==={{delta|18|O|}}===
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| The ratio of <sup>18</sup>O to <sup>16</sup>O, usually in foram tests or ice cores. High values mean low temperatures. Confounded by ice volume - more ice means higher {{delta|18|O|}} values.
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| Ocean water is mostly H<sub>2</sub><sup>16</sup>O, with small amounts of HD<sup>16</sup>O and H<sub>2</sub><sup>18</sup>O. In [[Standard Mean Ocean Water]] (SMOW) the ratio of D to H is <math>155.8*10^{-6}</math> and <sup>18</sup>O/<sup>16</sup>O is <math>2005*10^{-6}</math>. [[Fractionation]] occurs during changes between condensed and vapour phases: the vapour pressure of heavier isotopes is lower, so vapour contains relatively more of the lighter isotopes and when the vapour condenses the precipitation preferentially contains heavier isotopes. The difference from SMOW is expressed as δ<sup>18</sup><math>O = 1000 * ( (^{18}O/^{16}O)/(^{18}O/^{16}O)_{SMOW} - 1)</math>; and a similar formula for δD. {{delta|18|O|}} values for precipitation are always negative. The major influence on {{delta|18|O|}} is the difference between ocean temperatures where the moisture evaporated and the place where the final precipitation occurred; since ocean temperatures are relatively stable the {{delta|18|O|}} value mostly reflects the temperature where precipitation occurs. Taking into account that the precipitation forms above the [[Inversion (meteorology)|inversion layer]], we are left with a linear relation:
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| : δ<sup>18</sup>O = aT + b | |
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| which is empirically calibrated from measurements of temperature and {{delta|18|O|}} as a = 0.67 ‰/<sup>o</sup>C for [[Greenland]] and 0.76 ‰/<sup>o</sup>C for East [[Antarctica]]. The calibration was initially done on the basis of ''spatial'' variations in temperature and it was assumed that this corresponded to ''temporal'' variations (Jouzel and Merlivat, 1984). More recently, [[borehole thermometry]] has shown that for glacial-interglacial variations, a = 0.33 ‰/<sup>o</sup>C (Cuffey et al., 1995), implying that glacial-interglacial temperature changes were twice as large as previously believed.
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| ===Mg/Ca and Sr/Ca===
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| Magnesium (Mg) is incorporated into the calcite shells (tests) of planktic and benthic [[foraminifera]] as a trace element.<ref>{{cite journal|last=Branson|first=Oscar|coauthors=Redfern, Simon A.T.; Tyliszczak, Tolek; Sadekov, Aleksey; Langer, Gerald; Kimoto, Katsunori; Elderfield, Henry|title=The coordination of Mg in foraminiferal calcite|journal=Earth and Planetary Science Letters|date=1 December 2013|volume=383|pages=134–141|doi=10.1016/j.epsl.2013.09.037|url=http://www.sciencedirect.com/science/article/pii/S0012821X13005487}}</ref> Because the incorporation of Mg as an impurity in calcite is endothermic,<ref>{{cite journal|last=Katz|first=Amitai|title=The interaction of magnesium with calcite during crystal growth at 25–90°C and one atmosphere|journal=Geochimica et Cosmochimica Acta|date=June 1973|volume=37|issue=6|pages=1563–1586|doi=10.1016/0016-7037(73)90091-4}}</ref> more is incorporated into the growing crystal at higher temperatures. Therefore a high Mg/Ca ratio implies a high temperature, although ecological factors may confound the signal. Mg has a long [[residence time]] in the ocean, and so it is possible to largely ignore the effect of changes in seawater Mg/Ca on the signal.<ref>{{cite journal | title = Benthic foraminiferal Mg/Ca-paleothermometry: A revised core-top calibration | journal = [[Geochimica et Cosmochimica Acta]] | first = C.H. | last = Lear | coauthors = Rosenthal, Y. and Slowey, N. | volume = 66 | issue = 19 | pages = 3375–3387| id = | url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V66-46VRYT4-4&_user=1495569&_coverDate=10%2F01%2F2002&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1338301001&_rerunOrigin=scholar.google&_acct=C000053194&_version=1&_urlVersion=0&_userid=1495569&md5=f507b6904410ba5a7502bc5f7dd82229 | accessdate = 2010-05-17 | doi = 10.1016/S0016-7037(02)00941-9 | year = 2002 | bibcode=2002GeCoA..66.3375L}}</ref>
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| Strontium (Sr) incorporates in coral aragonite,<ref>{{cite journal|last=Casey|first=W. H.|coauthors=Rock P. A., Chung J. B., Walling E. M. and McBeath|title=Gibbs energies of formation of metal carbonate solid solutions - 2|journal=Am. J. Sci.|year=1996|volume=296|issue=1|pages=1–22|doi=10.2475/ajs.296.1.1}}</ref><ref>{{cite journal | title = Thermochemistry of strontium incorporation in aragonite from atomistic simulations | journal = Geochimica et Cosmochimica Acta | first = S.E. | last = Ruiz-Hernandez | coauthors = Grau-Crespo, R., Ruiz-Salvador, A.R. and De Leeuw, N.H. | volume = 74 | issue = 4 | pages = 1320–1328| url = http://www.sciencedirect.com/science/article/pii/S0016703709006978| doi = 10.1016/j.gca.2009.10.049 | year = 2010|bibcode = 2010GeCoA..74.1320R }}</ref> and it is well established that the precise Sr/Ca ratio in the coral skeleton shows an inverse correlation with the seawater temperature during its biomineralization.<ref>{{cite journal|last=Weber|first=J.N.|title=Incorporation of strontium into reef coral skeletal carbonate|journal=Geochim. Cosmochim. Acta|volume=37|issue=9|pages=2173–2190| doi =10.1016/0016-7037(73)90015-X|year=1973|bibcode = 1973GeCoA..37.2173W }}</ref><ref>{{cite journal|last=De Villiers|first=S.|coauthors=Shen, G. T. and Nelson, B. K|title=The Sr/Ca temperature relationship in coralline aragonite—influence of variability in (Sr/Ca) seawater and skeletal growth-parameters|journal=Geochim. Cosmochim. Acta|year=1994|pages=197–208| doi = 10.1016/0016-7037(94)90457-X|volume=58|bibcode = 1994GeCoA..58..197D }}</ref>
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| ===Alkenones===
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| {{further2|[[alkenone]], [[alkenone unsaturation index]], and [[TEX86|TEX<sub>86</sub>]]}}
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| Distributions of organic molecules in marine sediments reflect temperature.
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| ===Leaf physiognomy===
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| The characteristic leaf sizes, [[leaf shapes|shapes]] and prevalence of features such as drip tips (‘leaf or foliar physiognomy’) differs between [[tropical rainforests]] (many species with large leaves with smooth edges and drip tips) and temperate deciduous forests (smaller leaf size classes common, toothed edges common), and is often continuously variable between sites along climatic gradients, such as from hot to cold climates, or high to low precipitation.<ref>Bailey, I.W. & Sinnott, E.W. 1916. The climatic distribution of certain kinds of angiosperm leaves. ''American Journal of Botany'' 3, 24 - 39.</ref> This variation between sites along environmental gradients reflects adaptive compromises by the species present to balance the need to capture light energy, manage heat gain and loss, while maximising the efficiency of gas exchange, [[transpiration]] and [[photosynthesis]]. Quantitative analyses of modern vegetation leaf physiognomy and climate responses along environmental gradients have been largely [[univariate]], but [[multivariate analysis|multivariate]] approaches integrate multiple leaf characters and climatic parameters. Temperature has been estimated (to varying degrees of fidelity) using leaf physiognomy for [[Late Cretaceous]] and [[Cenozoic]] leaf floras, principally using two main approaches:<ref>Greenwood, D.R. 2007. North American Eocene Leaves and Climates: From Wolfe and Dilcher to Burnham and Wilf. In: Jarzen, D., Retallack, G., Jarzen, S. & Manchester, S. (Eds.) Advances in Mesozoic and Cenozoic Paleobotany: studies in celebration of David L. Dilcher and Jack A. Wolfe. ''Courier Forschungsinstitut Senckenberg'' 258: 95 – 108.</ref>
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| ==== ''Leaf margin analysis'' ====
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| A [[univariate]] approach that is based on the observation that the proportion of woody [[dicot]] species with smooth (i.e. non-toothed) [[leaf margin]]s (0 ≥ ''P''<sub>margin</sub> ≥ 1) in vegetation varies proportionately with mean annual temperature (MAT<ref>often written as 'annual mean temperature'; the mean of the monthly mean daily air temperatures for a location.</ref>).<ref>Wolfe, J.A. 1979. Temperature parameters of Humid to Mesic Forests of Eastern Asia and relation to forests of other regions of the Northern Hemisphere and Australasia. ''United States Geological Survey Prof. Paper'' 1106, 1 - 37.</ref> Requires the fossil flora to be segregated into morphotypes (i.e. ‘species’), but does not require their identification. The original LMA regression equation was derived for East Asian forests,<ref>Wing, S.L. & Greenwood, D.R. 1993. Fossils and fossil climates: the case for equable Eocene continental interiors. ''Philosophical Transactions of the Royal Society, London B'' 341, 243-252.</ref> and is:
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| :(1) MAT = 1.141 +(0.306 * ''P''<sub>margin</sub>), standard error ± 2.0 °C
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| The error of the estimate for LMA is expressed as the binomial sampling error:<ref>Wilf, P. 1997. When are leaves good thermometers? A new case for Leaf Margin Analysis. ''Paleobiology'' 23, 373-90.</ref>
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| :(2) <math>\sigma\lbrack\text{LMA}\rbrack = c \sqrt{\frac{P_{margin} (1 - P_{margin})}{r}}</math>
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| where c is the slope from the LMA regression equation, ''P''<sub>margin</sub> as used in (1), and ''r'' is the number of species scored for leaf margin type for the individual fossil leaf flora.
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| Alternative LMA calibrations have been derived for major world regions, including North America,<ref>Miller, I.M., Brandon, M.T. & Hickey, L.J. 2006. Using leaf margin analysis to estimate the Mid-Cretaceous (Albian) paleolatitude of the Baja BC block. ''Earth & Planetary Science Letters'' 245: 95–114.</ref> Europe,<ref>Traiser, C., Klotz, S., Uhl, D., & Mosbrugger, V. 2005. Environmental signals from leaves – A physiognomic analysis of European vegetation. ''New Phytologist'' 166: 465–484.</ref> South America,<ref>Kowalski, E.A., 2002. Mean annual temperature estimation based on leaf morphology: a test from tropical South America. ''Palaeogeography, Palaeoclimatology, Palaeoecology'' 188: 141-165.</ref> and Australia.<ref>Greenwood, D.R., Wilf, P., Wing, S.L. & Christophel, D.C. 2004. Paleotemperature estimates using leaf margin analysis: Is Australia different? ''PALAIOS'' 19(2), 129-142.</ref>
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| ====''CLAMP (Climate leaf analysis multivariate program)''====
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| CLAMP is a multivariate approach largely based on a data set of primarily western hemisphere vegetation,<ref>Wolfe, J.A. 1993. A method of obtaining climatic parameters from leaf assemblages. ''U.S. Geological Survey Bulletin'', 2040, 73pp.</ref> subsequently added to with datasets from additional world regional vegetation.<ref>Spicer, R.A., 2008. CLAMP. In: V. Gornitz (Editor), ''Encyclopedia of Paleoclimatology and Ancient Environments''. Springer, Dordrecht, pp. 156-158.</ref><ref>CLAMP online. http://clamp.ibcas.ac.cn/Clampset2.html</ref> [[Canonical Correlation Analysis]] is used combining 31 leaf characters, but leaf margin type represented a significant component of the relationship between physiognomic states and temperature. Using CLAMP, MAT is estimated with small standard errors (e.g. CCA ± 0.7–1.0 °C). Additional temperature parameters can be estimated using CLAMP, such as the coldest month mean temperature (CMMT) and the warmest month mean temperature (WMMT) which provide estimates for winter and summer mean conditions respectively.
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| ===Nearest living relative analogy / coexistence analysis===
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| Certain plants prefer certain temperatures; if their pollen is found one can work out the approximate temperature.
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| ===<sup>13</sup>C-<sup>18</sup>O bonds in carbonates===
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| There is a slight thermodynamic tendency for heavy isotopes to form bonds with each other, in excess of what would be expected from a [[stochastic]] or random distribution of the same concentration of isotopes. The excess is greatest at low temperature (see [[Van 't Hoff equation]]), with the isotopic distribution becoming more randomized at higher temperature. Along with the closely related phenomenon of [[equilibrium fractionation|equilibrium isotope fractionation]], this effect arises from differences in [[zero point energy]] among [[isotopologues]]. Carbonate minerals like calcite contain CO<sub>3</sub><sup>2–</sup> groups that can be converted to CO<sub>2</sub> gas by reaction with concentrated phosphoric acid. The CO<sub>2</sub> gas is analyzed with a mass spectrometer, to determine the abundances of isotopologues. The parameter Δ<sub>47</sub> is the measured difference in concentration between [[isotopologue]]s with a mass of 47 [[atomic mass unit|u]] (as compared to 44) in a sample and a hypothetical sample with the same bulk isotopic composition, but a [[stochastic]] distribution of heavy isotopes. Lab experiments, quantum mechanical calculations, and natural samples (with known crystallization temperatures) all indicate that Δ<sub>47</sub> is correlated to the inverse square of [[temperature]]. Thus Δ<sub>47</sub> measurements provide an estimation of the temperature at which a carbonate formed. <sup>13</sup>C-<sup>18</sup>O paleothermometry does not require prior knowledge of the concentration of <sup>18</sup>O in the water (which the δ<sup>18</sup>O method does). This allows the <sup>13</sup>C-<sup>18</sup>O paleothermometer to be applied to some samples, including freshwater carbonates and very old rocks, with less ambiguity than other isotope-based methods. The method is presently limited by the very low concentration of isotopologues of mass 47 or higher in CO<sub>2</sub> produced from natural carbonates, and by the scarcity of instruments with appropriate detector arrays and sensitivities. The study of these types of isotopic ordering reactions in nature is often called [[Clumped isotope geochemistry|"clumped-isotope" geochemistry]].<ref name="Eiler2007">{{cite journal|title="Clumped-isotope" geochemistry – The study of naturally-occurring, multiply substituted isotopologues|author=Eiler JM|year=2007|journal=Earth and Planetary Letters|volume=262|pages=309–327|doi=10.1016/j.epsl.2007.08.020|bibcode=2007E&PSL.262..309E|issue=3–4}}</ref>
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| ==See also==
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| *[[Paleoclimatology]]
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| ==References==
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| <!--See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for an explanation of how to generate footnotes using the <ref(erences/)> tags-->
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| {{reflist|35em}}
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| [[Category:Paleoclimatology]]
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