Physics of Aquatic Systems II

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1 Physics of Aquatic Systems II 10. C-Dating Werner Aeschbach-Hertig Institute of Environmental Physics University of Heidelberg 1 Contents of Session 10 General principles of C dating Conventional C age, calibration of C age scale Reservoir effects in aquatic systems Complications of groundwater C dating The chemistry of carbon in water The isotopic signature of carbon sources Models for the initial C in groundwater Effect of mixing on C ages Literature: Mook: Vol. 1, ch. 8 9; Vol. 2, ch. 6; Vol. 4, ch. 5 Clark & Fritz, 1997: ch. 5; ch. 8 Kinzelbach et al., UNEP/DEWA Report RS 02, ch Origin and distribution of C in nature Basic principles of C dating I T 12 = 570 yr Problem: A 0 =? dn = λn dt () 0 N t = N e λt dn A = λn dt 1 ( ) t ln A t = λ A0 4 Basic principles of C dating II Atmospheric C: Anthropogenic effects Classical C dating on organic matter: Carbon in living organism in equilibrium with atmospheric CO 2 No further exchange after death of organism: pure radiodecay Initial activity A 0 = Activity of atmospheric CO 2 Production by N(n,p) C reaction with cosmic radiation Atmospheric activity / production not constant over time! Due to anthropogenic emissions (fossil 12 C, bomb C) Due to variations of geomagnetic field and solar activity Reconstruction of A 0 (t) needed (calibration of C age scale) Tree rings: Ring counting and C dating Varved lake sediments: Layer counting and C dating Corals: U/Th and C dating 5 Suess effect (fossil fuel) Bomb C 6

Natural variation of C for past 50 kyr Calibration of C age Tree rings Corals Cariaco Sediments Tree rings Corals Cariaco sediments Lake Suigetsu varves Bahamas speleothems N-Atlantic sediments from

C activity is measured and reported relative to a standard Standard activity chosen close to natural C content of living plants By definition: A st = 100 pmc (% modern carbon) = 0.95 A Ox1 (1950) = 0.

2 Natural variation of C for past 50 kyr Calibration of C age Tree rings Corals Cariaco Sediments Tree rings Corals Cariaco sediments Lake Suigetsu varves Bahamas speleothems N-Atlantic sediments from Hughen et al., 2004, Science 0: from Hughen et al., 2004, Science 0: Non-uniqueness of C age due to calibration What is a "conventional C age"? C activity is measured and reported relative to a standard Standard activity chosen close to natural C content of living plants By definition: A st = 100 pmc (% modern carbon) = 0.95 A Ox1 (1950) = A Ox2 (1950) = 1.56 dpm/gc = Bq/gC (Ox1, Ox2: International Oxalic Acid standards) Conventional age: 1. A 0 = Standard activity in C activity normalised for isotope fractionation to "biomass" δ 1 C = -25. Original (Libby) half-life of 5568 yr is used (current best value: 570 yr) 9 T 12 A sample τ = ln = age in C-yrs before present (BP) ln 2 A standard 1950 (present = 1950) 10 Reservoir Corrections Conventional C age assumes that C originates from atmosphere Other geochemical reservoirs (water!) may not be in equilibrium Correction needed for different initial activity of the reservoir! Marine reservoir correction: Marine organisms use the carbon dissolved in the ocean to form biomass (e.g. CaCO -shells, corals, fish bones, ) Total Dissolved Inorganic Carbon is present in several forms: TDIC = CO 2 (aq) + H 2 CO CO TDIC is not in immediate equilibrium with the atmosphere Large TDIC-reservoir, slow exchange, and upwelling of older carbon lead to a decreased activity: A surf < 100 pmc Typical (but variable!): A surf ~ 95 pmc τ surf ~ 400 yr 11 C-dating of the Deep Ocean from Broecker, 1995, The Glacial World according to Wally 12

3 Freshwater Reservoir or "Hardwater" Effects Fresh water may dissolve old calcite (Ca 12 CO ) Hard (carbonate-rich) water may have A TDIC << 100 pmc Effect depends on geological setting (presence of carbonate) Correction can be many kyr for "hardwater" lakes Tricks for C-dating of lake sediments in carbonate-rich areas: Use macrofossils (wood, leaves, ) of terrestrial plants or (if sufficient) terrestrial microfossils (pollen) Avoid aquatic organisms (may appear too old) Else, use Dissolved Organic Carbon (DOC) rather than DIC 1 Groundwater C ages How can groundwater be dated by C? No micro- or macrofossils present Only dissolved carbon (DIC or DOC) can be dated! Usually total dissolved inorganic carbon is used C ages of groundwater are not conventional ages: C activity of TDIC is not normalised for isotope fractionation The more precise half-life of 570 yr is used Why is groundwater C dating special? Main problem is the origin of TDIC to determine A 0 δ 1 C is used to estimate A 0 (mixing of different carbon sources) High resolution ages are useless because of mixing soil air groundwater rock ( g) ( aq) 2 - CO CaCO Carbonate geochemistry Soil CO 2 Dissolved CO 2 Carbonic acid Bicarbonate Carbonate Calcite ( ) ( ) CO g CO aq 2 2 ( ) CO aq + H O H CO H H + CO - + CaCO Ca + CO Reaction constants in the carbonate system ( g) ( aq) 2 - CO CaCO Note 1: [x] denotes the molar (mol/l) activity of compound x Note 2: The dissolved CO 2 is usually denoted as H 2 CO, although in reality [CO 2 (aq)] >> [H 2 CO ] Note : All reaction constants depend on T, values given at 25 C [ ] K= 0 = 10 P H 6.5 [ 2 ] Solubility, Henry's law K= 1 = 10 First dissociation const. H CO K= 2 = K = Ca CO = CaCO Second dissociation const. Solubility product 16 Distribution of carbonate species in water Carbonate speciation depends on ph = -log[h + ] Description of the carbonate system Carbonate system is defined by ph and concentration of 1 species. In practice, often well-measurable sum parameters are used: TDIC = ΣCO 2 = mco 2 + m - + mco Alk = m - + 2mCO (carbonate alkalinity) with: mx = molal concentration (mol/kg) of compound X Alkalinity is a measure of the buffering capacity of water, formally the equivalent sum of bases titratable with strong acids: Total Alk = m - + 2mCO + mb(oh) 4- + mh SiO 4- + Usually: Total Alk m - + 2mCO = Carbonate Alk from Clark & Fritz, Alkalinity can be measured by titration in the field At given T, all species can be calculated from ph and Alk or TDIC 18

4 Calcite dissolution The calcite solubility constant K CaCO is low Calcite dissolution is enhanced by CO 2 (H 2 CO ): 2+ - ( ) CO g + H O + CaCO Ca + 2 A soil gas = 100 pmc 2 2 A calcite = 0 pmc 1) Vogel model: empirical value Constant A 0 of 85 ± 5 pmc Based on young groundwater samples from NW Europe No physical basis, not universally applicable Calcite dissolution produces 50:50 mixture of young and old carbon! Open system: Constant supply of soil CO 2 (unsaturated zone) C-active soil CO 2 is dominant reservoir Closed system: Closed off from soil CO 2 (saturated zone) C-dead CaCO is dominant reservoir ) Tamers model: Chemical balance (chemical dilution) Idea: TDIC = CO 2 + -, half of - from dead calcite ( ) ( ) mco aq m A= A g m aq + m with: mx = molal concentration (mol/kg) of compound X A g = activity of soil gas CO 2, usually 100 pmc Assumes stoichiometric dissolution, no other reactions Yields A 0 50 pmc for most natural groundwaters Oversimplified δ 1 C of natural carbon compounds/reservoirs Idea: Use δ 1 C to distinguish contributions from soil gas and calcite 21 from Clark & Fritz, ) Pearson model: Isotopic mixing balance Idea: A 0 and δ 1 C result from mixing of soil gas and calcite with: δ - δ A= ( A- A ) + A δ - δ t s 0 g s s g s A s = activity of solid calcite, usually taken as 0 pmc δ t = measured δ 1 C of TDIC δ g = δ 1 C of soil gas CO 2, usually taken as -25 δ s = δ 1 C of solid calcite, usually taken as 0 Pure isotope mixing, no reference to chemistry Does not include isotope fractionation effects! Isotopic composition of carbon components δ - δ A= A δ - δ t s 0 g g s 2 24

$Isotope fractionations in the carbonate system 4) Fontes & Garnier model: Chemical & isotopic balance Idea: Partial isotope exchange between soil CO 2 and carbonate Open system: soil CO 2 solid$

5 Isotope fractionations in the carbonate system 4) Fontes & Garnier model: Chemical & isotopic balance Idea: Partial isotope exchange between soil CO 2 and carbonate Open system: soil CO 2 solid carbonate from Clark & Fritz, C t -C s q C s -q δ g δ s δ g - ε ( - ) ( - ) ( - ) Cδ = C q δ + C C δ + q δ ε t t s s t s g g with: C t, C s = molal concentrations of total and solid-derived C q = fraction of solid-derived C at equilibrium with soil CO 2 ε = δ 1 C fractionation between CO 2 gas and solid carbonate 26 Fontes & Garnier model Isotope mass balance equations for 1 C and C: ( ) ( ) ( ) ( ε ) Cδ = Cδ + C C δ + q δ ε δ t t s s t s g g s CA t 0 = CA s s + Ct Cs Ag + q Ag 0.2 As assuming ε C(%) = 0.2ε 1 C( ) Eliminating q from the above equations yields the final model equation: C s Cs A0 = 1 Ag + As + Ct Ct t ( Cs Ct) s ( 1 Cs Ct) g ( Ag 0.2ε As) δ δ + + δ δ ε δ g s 27 Fontes & Garnier model: Closed system Model also describes carbonate dissolution in closed system Closed system: soil CO 2 C t C s -q' δ g q' δ s + ε solid carbonate C s δ s ( ) ( ) Cδ = Cδ + C C q δ + q δ + ε t t s s t s g s Mathematically equivalent to open system with q -q' 28 Effect of carbonate dissolution along the flow path Fontes & Garnier model Includes chemical and isotopic balance Applies for both open and closed conditions: Calcite dissolution in unsaturated zone during recharge Calcite dissolution in confined part of aquifer Combination of both processes Widely used, probably best of the "simple" models Does not include more complex chemical reactions Incongruent dissolution (dissolution and re-precipitation) Addition of C from other sources (e.g. oxidation of organic C by sulphate reduction, geogenic CO 2 ) 29 from Kendall & McDonnell,

6 5) NETPATH: Complete chemical and isotopic modeling USGS developed software to model geochemical and isotopic evolution along a flow path in groundwater Plummer, L. N. et al An interactive code (netpath) for modeling net geochemical reactions along a flow path, Version 2.0. Water-Resources Investigations Report , U.S. Geological Survey, Reston, Virginia. available at: Allows modeling of geochemically complex systems Any possible reactions can be implemented Requires some knowledge of aquatic geochemistry and experience in use of the program Does not always yield unequivocal results 1 The effect of mixing on C ages of groundwater Usually only piston-flow C ages are calculated and reported! Useful first approximation for confined aquifers Dispersion model would probably be more appropriate C age true age The piston flow C-age underestimates the true mean age of a mixed water parcel 2 Summary C dating requires knowledge of atmospheric C history In aquatic systems: DIC-reservoir not in equilibrium, A 0 < A atm Groundwater C dating is special: Carbon from calcite dissolution: A 0 << A atm Mixing: no single exact age, no high resolution C correction models (estimation of A 0 ): Different models based on chemical and isotopic balances Fontes & Garnier (1979) model: most flexible, often used Detailed geochemical modeling: NETPATH Mixing: C piston flow ages underestimate true mean age Puts differences between correction models into perspective

Dating of ground water

PART 16 Dating of ground water Introduction Why date? - to determine when recharge occurred - to determine groundwater velocities - to reconstruct regional flow patterns How to do this? - decay of radioactive