The principles of growth and isotopic fractionation of stalagmites [Elektronische Ressource] : a numerical model to reconstruct temperature and precipitation records from stalagmites grown under disequilibrium conditions / presented by: Christian Mühlinghaus

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AbstractSpeleothems and stalagmites in particular are frequently used as archives of paleocli mate.Theirgrowth,isotopiccarbonandoxygenprofilesandthepossibilityofanexactdating provide time series in a high temporal resolution. However, the interpretationoftheseprofilesisdifficultsincetheisotopicsignalinstalagmitesunderliesseveralin fluencesoutsideandinsidethecave.In this study the basic principles of stalagmite growth and isotopic enrichment underequilibrium and disequilibrium conditions in dependence on climate related parame ters are described quantitatively using numerical models. In a final step these basicsare used to develop a combined model, which enables the reconstruction of tempera ture and drip interval records from isotopic profiles of kinetically grown stalagmites.In contrast to former models, which have been limited in their application to samp lesdevelopedunderequilibriumconditions,thismodelisabletocopewithkineticallygrown samples and hence extends the number of stalagmites, which might be inves tigated. Furthermore the model exceeds the results of former models by yielding dripintervals in addition to temperature records. The model is applied to two stalagmitesfrom Southern Chile and reveals first temperature and drip interval records obtainedbystalagmitesfromextremelylowlatitudes.The study was carried out in the framework of the daphne Forschergruppe in Heidel berg.

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Published 01 January 2008
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Abstract
Speleothems and stalagmites in particular are frequently used as archives of paleocli
mate.Theirgrowth,isotopiccarbonandoxygenprofilesandthepossibilityofanexact
dating provide time series in a high temporal resolution. However, the interpretation
oftheseprofilesisdifficultsincetheisotopicsignalinstalagmitesunderliesseveralin
fluencesoutsideandinsidethecave.
In this study the basic principles of stalagmite growth and isotopic enrichment under
equilibrium and disequilibrium conditions in dependence on climate related parame
ters are described quantitatively using numerical models. In a final step these basics
are used to develop a combined model, which enables the reconstruction of tempera
ture and drip interval records from isotopic profiles of kinetically grown stalagmites.
In contrast to former models, which have been limited in their application to samp
lesdevelopedunderequilibriumconditions,thismodelisabletocopewithkinetically
grown samples and hence extends the number of stalagmites, which might be inves
tigated. Furthermore the model exceeds the results of former models by yielding drip
intervals in addition to temperature records. The model is applied to two stalagmites
from Southern Chile and reveals first temperature and drip interval records obtained
bystalagmitesfromextremelylowlatitudes.
The study was carried out in the framework of the daphne Forschergruppe in Heidel
berg.
Speläotheme, und speziell Stalagmiten, werden aufgrund ihrer genauen Datierbarkeit
sowie der hochaufgelösten Kohlen und Sauerstoff Isotopenprofile häufig als Archive
des Paläoklimas genutzt. Die Interpretation dieser Profile ist jedoch schwierig, da das
SignaldiversenEinflüssensowohlaußerhalbalsauchinnerhalbderHöhleunterliegt.
IndieserArbeitwerdendieGrundlagendesStalagmitenwachstumssowiederisotopi
schenAnreicherungunterGleichgewichts undUngleichgewichtsbedingungeninAb
hängigkeit von klimarelevanten Parametern mit Hilfe numerischer Modelle beschrie
ben. Basierend darauf wird ein kombiniertes Modell entwickelt, welches die Rekon
struktion von Temperatur und Tropfabständen anhand kinetisch gebildeten Stalagmi
ten ermöglicht. Im Gegensatz zu früheren Modellen, welche auf die Verwendung von
unterGleichgewichtsbedingungenentstandenenProbenbeschränktwaren,ermöglicht
dieses Modell auch die Interpretation kinetisch gebildeter Stalagmiten. Neben einer
Temperaturbestimmmung ist so zusätzlich die Bestimmung des Tropfabstands mög
lich. Das Modell wurde auf zwei Stalagmiten aus Süd Chile angewendet und liefert
dieerstenTemperatur-undTropfabstands ZeitreihenausStalagmitenextremsüdlicher
Breiten.
Diese Arbeit wurde im Rahmen der daphne Forschergruppe in Heidelberg durchge
führt.Contents
1 Introduction 9
1.1 Motivationandintention . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2 Stalagmitedevelopment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Preliminarymodelremarks . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4 Modeltypes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.4.1 Forwardmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.4.2 Reverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 Basics 25
2.1 Speciesinthesystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 ThekineticsoftheCO –H O–CaCO reaction . . . . . . . . . . . . . . 302 2 3
2.3 Mixingprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4 Fractionationprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.1 Fractionationandstandards . . . . . . . . . . . . . . . . . . . . . . 37
2.4.2factorsofcarbonandoxygen . . . . . . . . . . . . . 38
2.4.3usedinthemodels . . . . . . . . . . . . . . . 43
3 ForwardModels 47
3.1 Growthmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1.1 Exponentialapproximation . . . . . . . . . . . . . . . . . . . . . . 55
3.1.2 Gaussianappr . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2 Carbonisotopemodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.2.1 Fractionationunderequilibriumconditions . . . . . . . . . . . . . 62
3.2.2underdisequilibrium . . . . . . . . . . . 62
3.2.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3 Oxygenisotopemodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.3.1 Fractionationunderequilibriumconditions . . . . . . . . . . . . . 68
3.3.2disequilibrium . . . . . . . . . . . 68
3.3.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.4 Multi box model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.4.1 Calibrationofthemultiboxmodel . . . . . . . . . . . . . . . . . . 77
3.5 Isotopicprofilesalongindividualgrowthlayers . . . . . . . . . . . . . . 82
73.5.1 Carbonprofile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.5.2 Oxygenprofile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.5.3 Hendy Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4 ReverseModels 89
4.1 Stalagmites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.1.1 Age depthrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1.2 Isotopicprofiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2 AGEmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2.1 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.3 AXISmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.3.1 Carbonprofilealongthegrowthaxis. . . . . . . . . . . . . . . . . 100
4.3.2 Oxygenprofilealongthegrowthaxis . . . . . . . . . . . . . . . . 100
4.4 LAYERmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.4.1 Carbonprofilealongindividualgrowthlayers . . . . . . . . . . . 105
4.4.2 Oxygenprofilealonggrowth . . . . . . . . . . . 107
4.5 BUFFERmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.6 CombinedStalagmiteModel–CSM . . . . . . . . . . . . . . . . . . . . . 112
4.6.1 Detaileddescription . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.6.2 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . 121
5 Summaryandfutureprospects 131
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.2 Futureprospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A Stalagmitedatasets 147
A.1 StalagmitesMA 1andMA 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 148
B Mathematicalproofs 155
B.1 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
B.1.1 Proofofthemixingprocessofbicarbonateconcentrations . . . . 156
B.1.2 Proofoftheprocessofratios . . . . . . . . . . 156
B.1.3 Proofofthelimitofλ . . . . . . . . . . . . . . . . . . . . . . . . . 158
B.1.4 Proofofthelimitofdisequilibriumfractionation . . . . . . . . . . 158
C Databases 161
C.1 Calibratedmixingparameters . . . . . . . . . . . . . . . . . . . . . . . . . 162
C.1.1 Exponentialcalibration . . . . . . . . . . . . . . . . . . . . . . . . 162
C.1.2 Gaussian . . . . . . . . . . . . . . . . . . . . . . . . . . 171Chapter1
Introduction
9CHAPTER1. INTRODUCTION
1.1 Motivationandintention
Climate. An issue which nowadays is more present than ever. But do we understand
climate, its mechanisms and the driving forces behind? An idea of the answer of this
question might be found in the past, which reveals information on climate in order
to understand what is happening now and in the future. Two important climate pa
rametersaretemperatureandprecipitation,whichareessentialforlifeandculture. To
investigate these two parameters archives are needed, which are able to preserve cli
mate information of the past over a long period and last long enough to be used by
scientists today. The Earth offers many possibilities like ice cores, tree rings, pollen
records, sediments or speleothems. All these archives have their advantages and dis
advantages regarding the global distribution, climate information storage, easy access
andtransportofsamples,precisedatingtechniquesortheunderstandingofthemech
anismsoccurringinthesearchivesandaccordingtotheirinteractionwithclimate.
Inthisworkthefocusliesonspeleothemsandstalagmitesinparticular. Thesearchives
are found in many caves all over the world providing a good coverage of the Earth’s
land masses. Stalagmites grow very slowly with growth rates ranging around 80 μm
peryearandareabletooutlastperiodsofseveralthousandyearsduetotheirprotected
location, which is not exposed to environmental stresses like erosion for instance. A
stalagmiteisfedbydripwater,fromwhichcalciteisprecipitatedinannuallayerscom
parable to tree rings. This calcite saves information in form of carbon and oxygen iso
topeproxiesandtraceelementslikeuranium,magnesiumandothers. Thelonglasting
growth and storage of climate related proxies predestine stalagmites as an archive for
climate.
Themostimportantdatasets,whichcanbeobtainedfromstalagmitesareinformation
on the growth rate and the isotopic profiles of rare carbon and oxygen isotopes con
tained in the precipitated calcite. Profiles of the isotopes can be found both along the
verticalgrowthaxisofthestalagmiteandalongindividualgrowthlayers.
In general stalagmites can develop under two kind of conditions: (i) the development
under equilibrium conditions and (ii) the development under disequilibrium condi
tions. Therebytheterms"equilibrium"and"disequilibrium"refertotheconditionpre
vailing during the fractionation and precipitation of calcite. In the early years of sta
lagmiteresearchmainlysampleswhichdevelopedunderequilibriumconditionswere
used for analysis and interpretation, since the extraction of temperature records from
theoxygenisotopeprofileisbasedonthewellknowntemperaturedependenceoffrac
tionation under equilibrium. However, these samples do not provide any information
aboutrainfall. Bycontraststalagmites,whichshowfractionationunderdisequilibrium
contain both, the information about temperature and about precipitation. Thus, these
samples came into focus of research during the last years. However, the extraction of
temperature and precipitation from these stalagmites is complicated and can not be
performed in the same manner as for growing under equilibrium condi
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