Physics of Aquatic Systems of - Institut für · PDF fileNt N e= ⋅−λt...

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Physics of Aquatic Systems

Werner Aeschbach‐HertigInstitut für UmweltphysikUniversität Heidelberg

13. Dating Old Waters

Physics of Aquatic Systems, 13. Dating old Groundwater Universität HeidelbergInstitut für Umweltphysik2

Contents of Session 13

13.1 Basic principles of 14C dating– Conventional 14C age, calibration of 14C age scale

13.2 Complications of 14C dating of (ground)water– Reservoir effects and carbonate dissolution

13.3 Models for the initial 14C in groundwater– Corrections based on chemistry and stable isotopes

13.4 Other dating methods for old groundwater– Noble gas radioisotopes

Literature (14C): – Mook: Vol. 1, ch. 8 – 9, 12; Vol. 2, ch. 6; Vol. 4, ch. 5– Clark & Fritz, 1997: ch. 5; ch. 8– Kinzelbach et al., 2002. UNEP/DEWA Report RS 02‐2, ch. 7.


Origin and Distribution of 14C in Nature

from Mook, 2001


13.1 Basic Principles of 14C Dating I

dN Ndt

λ= −

0

1 ( )ln A ttAλ

⎛ ⎞= − ⎜ ⎟

⎝ ⎠

1 2 5730 yrT =

NdtdNA λ−=≡

( ) 0tN t N e λ−= ⋅

Problem:A0 = ?


Basic Principles of 14C Dating II

Classical 14C dating on organicmatter:• Carbon in living organism in equilibrium with atmospheric CO2

• No further exchange after death of organism: pure radiodecay• Initial activity A0 = Activity of atmospheric CO2

Complications:

• Atmospheric activity is not constant over time!– Reconstruction of A0(t), i.e., calibration of the 14C age scale, is achieved by 14C measurements on samples of known age

• Organic carbon is isotopically fractionated with respect to air – Corrected based on measurement of stable isotope 13C

• Reservoir effects: Aquatic organisms use dissolved carbon pool in the water (reservoir), whose A0(t) may differ from that of air


Atmospheric 14C: Anthropogenic effects

from Mook, 2001Suess effect(fossil fuel)

Bomb 14C

2


Natural variation of 14C for past 50 ka

Tree ringsCoralsCariaco Sediments

Origin of 14C variations: Changes in shielding of cosmic ray flux

Geomagnetic field (long‐term)

Solar activity (short term9

from Hughen et al., 2004, Science 303: 202-207


Calibration of 14C age

Tree ringsCoralsCariaco sedimentsLake Suigetsu varvesBahamas speleothemsN-Atlantic sediments

from Hughen et al., 2004, Science 303: 202-207


Non‐uniqueness of 14C age due to calibration

from Mook, 2001


What is a "conventional 14C age"?

• 14C activity is measured and reported relative to a standard• Standard activity chosen close to natural 14C content of living plants• By definition: 14Ast = 100 pmC (% modern carbon) = 0.95∙14AOx1

(1950) = 0.7459∙14AOx2 (1950) = 13.56 dpm/gC = 0.226 Bq/gC(Ox1, Ox2: International Oxalic Acid standards)

Conventional age:1. A0 = Standard activity in 19502. 14C normalised for isotope fractionation to "biomass" δ13C = ‐25‰3. Original (Libby) half‐life of 5568 a is used (current value: 5730 a)

1 2 14

1950

ln age in C-years before present (BP)ln2

sample

standard

T AA

τ⎛ ⎞

= − =⎜ ⎟⎜ ⎟⎝ ⎠ (present = 1950)


13.2 Complications of 14C Dating of Water

How can water be dated by 14C?• Only dissolved carbon can be dated!• Usually dissolved inorganic carbon (DIC) is used, rarely DOC• Total Dissolved Inorganic Carbon is present in several forms:

TDIC = CO2(aq) + H2CO3 + HCO3‐ + CO3

2‐

• TDIC is not in immediate equilibrium with the atmosphere and influenced by the complex carbonate chemistry

Ocean• Large TDIC‐reservoir, slow exchange, and upwelling of older carbon lead to a decreased activity: Asurf < 100 pmC

• Typical (but variable!): Asurf ~ 95 pmC ↔ τsurf ~ 400 yr


14C‐Dating of the Deep Ocean

from Broecker, 1995, The Glacial World according to Wally

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Lakes and Groundwater: "Hardwater" Effects

Fresh water may dissolve old calcite (Ca12CO3) Hard (carbonate‐rich) water can have ATDIC << 100 pmCEffect depends on geological setting (presence of carbonate)Correction can be many ka for "hardwater" lakes and groundwater

14C ages of groundwater are not conventional ages:– 14C activity of TDIC is not normalised for isotope fractionation– The more precise half‐life of 5730 a is used

Why is groundwater 14C dating special?– Main problem is the origin of TDIC to determine A0

– δ13C is used to estimate A0 (mixing of different carbon sources)– High resolution ages are useless because of mixing

05730 a lnln2

AA

τ ⎛ ⎞= ⎜ ⎟⎝ ⎠


Carbonate Geochemistry

( )2CO g

3CaCO

-3HCO

2 3H CO

( )2CO aq

2-3CO

Soil CO2

Dissolved CO2

Carbonic acid

Bicarbonate

Carbonate

Calcite

soil

air

grou

ndw

ater

rock

( ) ( )2 2CO g CO aq↔

( )2 2 2 3CO aq H O H CO+ ↔

+ -2 3 3H CO H + HCO↔

- + 2-3 3HCO H + CO↔

2+ 2-3 3CaCO Ca + CO↔


Reaction Constants in the Carbonate System

( )2CO g

3CaCO

-3HCO

2 3H CO

( )2CO aq

2-3CO

[ ]2

2 3 1.470

CO

H COK = 10

P−=

Note 1: [x] denotes the molar (mol/l) activity of compound xNote 2: Dissolved CO2 is denoted as H2CO3, although in reality [CO2 (aq)] >> [H2CO3]Note 3: All reaction constants depend on T, values given at 25°C

Solubility, Henry's law

[ ]

+3 6.35

12 3

H HCOK = 10

H CO

−−

⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦ = First dissociation const.

+ 23 10.33

23

H COK = 10

HCO

−−

−

⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦ =⎡ ⎤⎣ ⎦

Second dissociation const.

3

+ 2 8.48CaCO 3K = Ca CO 10− −⎡ ⎤ ⎡ ⎤ =⎣ ⎦ ⎣ ⎦ Solubility product


Distribution of Carbonate Species in Water

Carbonate speciation depends on pH = ‐log[H+]

from Clark & Fritz, 1997


Description of the Carbonate SystemCarbonate system is defined by pH and concentration of 1 species.In practice, often well‐measurable sum parameters are used:– TDIC = ΣCO2 = mCO2 + mHCO3

‐ + mCO32‐

– Alk = mHCO3‐ + 2mCO3

2‐ (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 = mHCO3‐ + 2mCO3

2‐ + mB(OH)4‐ + mH3SiO4‐ +…

– Usually: Total Alk ≈ mHCO3‐ + 2mCO3

2‐ = Carbonate Alk

Alkalinity can be measured by titration in the fieldAt given T, all species can be calculated from pH and Alk or TDIC


Calcite Dissolution

Calcite dissolution is enhanced by CO2 (H2CO3):

( ) 2+ -2 2 3 3CO g + H O + CaCO Ca + 2HCO→

Asoil gas = 100 pmC Acalcite = 0 pmC

Calcite dissolution produces 50:50 mixture of young and old carbon!

• Open system: Constant supply of soil CO2 (unsaturated zone)– 14C‐active soil CO2 is dominant reservoir

• Closed system: Closed off from soil CO2 (saturated zone)– 14C‐dead CaCO3 is dominant reservoir

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13.3 Models for A0 in Groundwater

Components or "endmembers" used in the models:t: Total carbon (TDIC) with measured conc., activity, isotope ratiog: Gaseous CO2 (soil air),usually with Ag = 100 pmC, δ13Cg = ‐25 ‰s: Solid calcite, usually with As = 0 pmC, δs = δ13Cs = 0 ‰

1) Vogel model: empirical value– Constant A0 of 85 ± 5 pmC– Based on young groundwater samples from NW Europe– No physical basis, not universally applicable


Models for A0 in Groundwater

2) Tamers model: Chemical balance (chemical dilution)– Idea: TDIC = CO2 + HCO3

‐, half of HCO3‐ from dead calcite

with: mX = molal concentration (mol/kg) of compound XAg = activity of soil gas CO2, usually 100 pmC

– Assumes stoichiometric dissolution, no other reactions – Yields A0 ≈ 50 pmC for most natural groundwaters– Oversimplified

( )( )

-2 3

0 g-2 3

CO aq + 0.5 HCOA = A

CO aq HCOm m

m m⋅

+


δ13C of Natural Carbon Compounds/Reservoirs


Idea: Use δ13C to distinguish contributions from soil gas and calcite



3) Pearson model: Isotopic mixing balance– Idea: 14A0 and δ13C result from mixing of soil gas and calcite

with: As = activity of solid calcite, usually taken as 0 pmCδt = measured δ13C of TDICδg = δ13C of soil gas CO2, usually taken as ‐25 ‰δs = δ13C of solid calcite, usually taken as 0 ‰

– Pure isotope mixing, no reference to chemistry– Does not include isotope fractionation effects!

( )t s0 g s s

g s

δ - δA = A - A + Aδ - δ

⋅


Isotopic Composition of Carbon Components

from Mook, 2001

t s0 g

g s

δ - δA = Aδ - δ

⋅


Isotope Fractionation in the Carbonate System


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4) Fontes & Garnier model: Chemical & isotopic balance– Idea: Partial isotope exchange between soil CO2 and carbonate

( )t g s g sC C C C C q q= + = + − +

with: Ct , Cs = molal concentrations of total and solid‐derived Cq = fraction of solid‐derived C at equilibrium with soil CO2ε = δ13C fractionation between CO2 gas and solid carbonate

Open system:

Cg

δg

Cs - qq

δsδg - ε

soil CO2 solid carbonate


This part is identical to Tamers with


Fontes & Garnier modelIsotope mass balance equations for 13C and 14C:

( ) ( ) t t s s t s g g sC C C C qδ δ δ δ ε δ= + − + − −

( ) ( )0 0.2t s s t s g g sC A C A C C A q A Aε= + − + − −

assuming ε14C(%) = 0.2ε13C(‰)

( ) ( ) ( )

0 1

1 0.2

δ δ δ

εδ ε δ

⎛ ⎞= − + +⎜ ⎟⎝ ⎠

− − −+ − − ⋅

− −

s sg s

t t

t s t s s t gg s

g s

C CA A AC C

C C C CA A

Eliminating q from the above equations yields the final model equation:

-S 3C = 0.5 HCO⋅m



Fontes & Garnier model: Closed system– Model also describes carbonate dissolution in closed system

Mathematically equivalent to open system with q' = ‐q

Closed system:

Cg- q'

δg

Csq'

δsδs + ε

soil CO2 solid carbonate

( )t g s g sC C C C q q C′ ′= + = − + +



Fontes & Garnier model– Widely used, probably best of the "simple" models– 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

– 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 CO2)


Effect of Carbonate Dissolution along Flow Path

from Kendall & McDonnell, 1998


Models for A0 in Groundwater5) 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. 1994. An interactive code (netpath) for modeling net geochemical reactions along a flow path, Version 2.0. Water‐Resources Investigations Report 94‐4169, U.S. Geological Survey, Reston, Virginia.

– available at: http://water.usgs.gov/software/netpath.html

– 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

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The Effect of Mixing on 14C Ages

Usually only piston‐flow 14C ages are calculated and reported!– Useful first approximation for confined aquifers– Dispersion model would probably be more appropriate

true age

14C age

The piston flow 14C‐ageunderestimates the true meanage of a mixed water parcel


13.4 Other Dating Methods for old Groundwater

10-3 10-1 101 103 105 107

age [yr]

222RnSF6CFCs

4He

39Ar

3H-3He

3H

85Kr

40Ar36Cl81Kr

14C

Here: NG radio‐isotopes 39Ar & 81Kr

Old: 36Cl and 81KrIntermediate: 39Ar39Ar closes gap from 50 – 1000 yr !


Properties of 39Ar and 81Kr

• Noble gas isotopes: conservative, except for radioact. decay• Small but ± constant cosmogenic source, simple behaviour

Property 39Ar 81Kr

Half‐life [yr] 269 229'000

Decay constant [s‐1] 8.17∙10‐11 9.59∙10‐14

Production (in atmosphere) 40Ar(n,2n)39Ar Spallat. 82‐86Kr80Kr(n,γ)81Kr

Isotope conc. in air [iX/X] 8.1∙10‐16 5.2∙10‐13

Absolute conc. in air [atoms m‐3] 2.0∙108 1.6∙107

Absolute conc. in water [atoms/L] ≈ 7000 ≈ 1000

⇒ Potentially very good dating tracers, but very low abundance


Analytical Methods for 39Ar and 81Kr

1. Low‐Level Counting (LLC): Count decaying atoms– best labs have background count rate ≈ 0.1 cpm– Required sample size for signal of 0.1 cpm (modern samples, 100 % efficiency!): Min. sample size 39Ar 81Kr

Air volume [L] 100 1∙106

Water volume [L] 3000 2∙107

2. Accelerator Masss Spectrometry (AMS): Count all atoms– Conventional MS impossible due to extremely low abundance– Conventional AMS impossible because negative NG ions unstable– Cyclotron‐AMS possible, but enormously complex and costly

Difficult for 39Ar, impossible for 81Kr!


New Detection Method for NG Radioisotopes

Atom Trap Trace Analysis (ATTA)Chen et al., 1999. Ultrasensitive Isotope Trace Analyses with a Magneto‐Optical Trap. Science 286, 1139‐1141.

• Idea – Isotopically selective laser cooling and trapping– Detection of single atoms in magneto‐optical trap (MOT)

• Advantage – extremely selective (no interferences)

• Problem – achieve sufficient trapping/counting efficiency


Principle of ATTAatoms laserlight

source Laser Cooling:Slowing (cooling) of atoms by multiple photon absorption

Isotopically selective due to resonance condition and very arge number of absorbed photons

hν, ħk

7


Principle of ATTA

1) Excitation to metastable state in source.

2) Cooling in Zeeman slower.

3) Trapping in magneto‐optical trap (MOT).

4) Detection of single atoms in MOT by fluorescence.


First Application of ATTA

6 (!) groundwater samples for 81Kr, Nubian Sandstone, Egypt

Sturchio et al., 2004. Geophys. Res. Lett. 31, doi:10.1029/2003GL019234

Sampling:Several m3 of water degasssed

Sample preparation:Separation of Kr by GC system

Measurement by ATTA:12 cph from 50 µl Kr (∼ 700 l water)Efficiency ∼ 10‐4

Results:Groundwater ages 0.2 – 1 Myr


ATTA in Heidelberg: StatusEnviron. physics: Gas extraction & Ar separation under developmentAtom physics: Dedicated atom trap system for ATTA constructedTrapping and detection in MOT demonstrated with 40Ar atoms

2 atoms1 atom0 atoms

• Spectroscopy of 39Ar conducted successfully

Welte et al., 2009. Rev. Sci. Instrum. 80, 113109, doi:10.1063/1.3257691


Summary

• 14C dating requires knowledge of atmospheric 14C history• In aquatic systems: DIC‐reservoir not in equilibrium, A0 < Aatm

• Groundwater 14C dating is special:– Carbon from calcite dissolution: A0 << Aatm

– Mixing: no single exact age, no high resolution• 14C correction models (estimation of A0):

– Different models based on chemical and isotopic balances– Fontes & Garnier (1979) model: most flexible, often used

• Mixing: 14C piston flow ages underestimate true mean age• Alternative Methods: Noble gas radioisotopes 39Ar and 81Kr

– Very promising tracers in principle, but hard to measure– Atom trap trace analysis (ATTA) offers an new chance

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