Physics of Lakes Contents Introduction to Isotope Hydrology. Introduction to Isotope Hydrology 1. Tracers and Isotopes. Stable Isotopes. Radioisotopes and Dating Werner Aeschbach Hertig Bertram Boehrer Limnophysik UFZ Magdeburg For details, updates and lecture notes see http://www.iup.uni heidelberg.de/institut/studium/lehre/aquaphys/pol.html and http://www.iup.uni heidelberg.de/institut/studium/lehre/aquaphys/mvenv.html What is Isotope Hydrology? Application of environmental isotopes/tracers to study (parts of) the hydrological cycle and aquatic systems Scientific discipline that evolved since ~195 by application of nuclear techniques to hydrology / aquatic systems Mix between physics (analytical techniques) and earth / environmental sciences (problems) Classical part of environmental physics Problems studied in Isotope Hydrology Origin of water masses and formation conditions Identification and separation of water components Quantification of processes such as evaporation, mixing Delineation of recharge areas and flow paths Origin of contaminants Paleoclimate, paleotemperatures Residence time of water in the system Flow velocities, dispersion, (turbulent) diffusion Fluxes, recharge rates, exchange rates Transport and degradation rates of contaminants What is a tracer? Substance, which: is present only in trace concentrations ( Spurenstoff ) marks a trace in a natural system (marker) Tracers in aquatic systems Ideally mark the water or dissolved substances therein, and move passively with water or solutes Isotopes are often nearly ideal tracers, e.g.: isotopes of H and O mark the water molecule isotopes of C, N, S etc. mark dissolved substances Conservative solutes (e.g. noble gases) are good tracers Environmental Isotopes and Tracers Isotopes or other tracers that are widely distributed in the environment, especially the hydrosphere. They can be both of natural or anthropogenic origin. Transient tracers: Anthropogenic, variable input e.g. Tritium, CFCs, SF 6, 85 Kr Geochemical tracers: Natural origin, constant input e.g. stable isotopes, 14 C, noble gases Contrast: Artificial tracers are released deliberately, in local tracer experiments (dyes, chemicals, also isotopes) 1
Literature on Isotope Hydrology Mook, W.G. (ed.), 1: UNESCO/IAEA Series on Environmental Isotopes in the Hydrological Cycle Principles and Applications. Available online at http://www naweb.iaea.org/ napc/ih/ihs_resources_publication_en.html Clark, I. D, Fritz, P., 1997: Environmental Isotopes in Hydrogeology. Lewis Publishers, Boca Raton. IUP 1868 Cook, P. G., Herczeg, A. L. (eds.), : Environmental Tracers in Subsurface Hydrology. Kluwer Academic Press, Boston IUP 1869 Kendall, C., McDonnell, J. J., 1998: Isotope Tracers in Catchment Hydrology. Elsevier, Amsterdam Mazor, E., 1997: Chemical and Isotopic Groundwater Hydrology. Dekker, New York. IUP 1885 Moser, H., Rauert, W., 198: Isotopenmethoden in der Hydrogeologie. Lehrbuch der Hydrogeologie, Band 8. Bornträger, Berlin. IUP 188 Isotopes: Chart of the Nuclides stable radioactive Isotopes (const. Z) Isobars (const. A) Isotones (const. N) Fundamentals of Stable Isotope Geochemistry Stable isotope geochemistry of the light elements: Mainly: Hydrogen, carbon, nitrogen, oxygen Also used: Boron, sulfur, chloride and others The light elements have: One highly abundant light isotope ( 1 H, 1 C, 14 N, 16 O) One or two rare heavy isotopes ( H, 1 C, 15 N, 17 O, 18 O) Some radioactive heavy isotopes ( H, 14 C) Stable isotope geochemistry studies natural variations of the ratios between rare and abundant isotopes Isotope Ratios abundance of rare isotope abundance of heavy isotope R = abundance of common isotope abundance of light isotope Isotope "concentration" or mixing ratio: Fractional abundance of given isotope relative to all isotopes of the element (often in %) Element Isotope mixing ratio (%) Isotope ratio Hydrogen 1 H 99.985 H.15 H/ 1 H.15 Carbon 1 C 98.89 1 C 1.11 1 C/ 1 C.11 Nitrogen 14 N 99.6 15 N.7 15 N/ 14 N.7 Oxygen 16 O 99.758 18 O.4 18 O/ 16 O. Oxygen 16 O 99.758 17 O.8 17 O/ 16 O.8 δ Notation Stable isotope ratios are measured and reported relative to a reference material or standard. Definition of δ (relative deviation of sample from standard): Rsample Rstandard Rsample δ = 1 ( 1 ) R R standard ( ) standard 18 16 O O 18 e.g. δ O = ( ) sample 1 18 16 O O standard Note δ values are dimensionless, small numbers, usually reported in. We follow the convention of Mook (1), in which the factor of 1 (used to convert to ) does not occur in equations, i.e.: δ 18 O [ ] = is equivalent to δ 18 O =. Reference Materials Several international refererence standards are distributed by the IAEA in Vienna: VSMOW = Vienna Standard Mean Ocean Water VPDB = Vienna Pee Dee Belemnite (a carbonate rock) Element Ratio Standard Ref. value Hydrogen H/ 1 H VSMOW 1.5575. 1 4 Carbon 1 C/ 1 C VPDB 1.17. 1 Nitrogen 15 N/ 14 N atmospheric N.677. 1 Oxygen 18 O/ 16 O VSMOW VPDB.5. 1.67. 1 Laboratories use internal standards that are calibrated against the international standards
Isotope Fractionation The physical and chemical properties of different isotopes (or compounds containing different isotopes) are slightly different: Slight variations of the isotope ratios in natural materials Mobility Heavy isotopes are slightly less mobile than the light isotopes Reason: / kt = 1/ mv v ~ m ½ at given T Binding Energy Molecules containing the rare heavier isotope generally have higher binding energies than molecules of the light isotopes Reason: lower zero point energy Heavy isotopes (compounds) diffuse and react slower (usually) Fractionation decreases with increasing temperature Energy Levels of Isotopic Molecules (Isotopomers) Diatomic molecule: m1 m Reduced mass: μ = m1+ m Rotation: E = B J( J+1) rot B = Θ Θ= μr Vibration: Evib = ( v + 1) ω ω = D μ Heavy Isotopomer (higher µ): Lower E and E vib, E rot Higher dissociation energy Processes Leading to Fractionation Isotope fractionation occurs in physical, chemical, or biological transitions/reactions between two phases or compounds A and B. Equilibrium fractionation: reversible equilibrium reaction A B at equilibrium: forward and backward reaction rates equal E.g. chemical equilibrium, phase equilibrium Kinetic fractionation: irreversible, unidirectional kinetic reaction A B E.g. isolated reaction products, phase separation, diffusion Mathematical description analogous Kinetic effects usually stronger than equilibrium fractionation Mathematical Description of Fractionation The isotopic effect of a transition/reaction A B or A B is described by the fractionation factor α: R( B) RB α B/ A= = R( A) RA α B/A expresses the isotope ratio in B relative to that in A Often only α used, sometimes α k for kinetic fractionation factors Fractionation effects are usually small: α 1. Often, the deviation of α from 1 is used, the fractionation or enrichment ε : RB εb/ A= αb/ A 1= 1 RA As the δ values, the ε's are usually given in. Sometimes 1. lnα is tabulated, because: lnα = ln (1 + ε) ε Rules of Thumb on Fractionation Light elements fractionate stronger than heavy elements H/ 1 H: Δm/m l = 1, 18 O/ 16 O: Δm/m l = 1/8 ε ( H) ~ 8ε( 18 O) Multiple isotopes: Fractionation scales with mass difference ε ( 18 O) ~ ε( 17 O), ε ( 14 C) ~ ε( 1 C) Fractionation decreases with temperature Heavy isotopes generally enriched in the denser phase (δ solid > δ liquid > δ gas ) chemically more strongly bound form compound with higher molecular weight Fractionation: The Rayleigh Process Change of isotope ratio in a diminishing reservoir (substrate) - - R R α 1 N α 1 ε = f or δ = ( 1+ δ ) f 1 N
Rayleigh Fractionation during Evaporation δ 18 O [ ] 4 1 remaining water instantaneously formed vapour accumulated vapour δ = α v/w =.99 ε v/w = -1 ( δ ) δ = 1+ f ε 1 ε δ P = δ + ε Stable Isotopes of Water in the Hydrological Cycle The Global Meteoric Water Line (GMWL) Empirical Finding (Craig, 1961): Isotopic composition of precipitation from all over the world, plotted in δ H versus δ 18 O graphs, is strongly correlated according to the equation: δ H= 8 δ 18 O+ 1 (in ) -1 1.8.6 α 1 f δσ P = ( 1+ δ ) 1 1 f.4. The slope of 8 is similar to the ratio of the equilibrium fractionations The intercept of 1 is called deuterium excess (d excess) f = N/N The Global Meteoric Water Line (GMWL) Origin of the GWML Rayleigh type condensation in clouds Approximately equilibrium fractionation: slope ~ 8 from Clark & Fritz, 1997 Progressive Rainout of Atmospheric Vapour Temperature Effect T, N(T), R = R f(t) ε = R(T) T, N, R 4 1 Vapour pressure [mbar] f = N/N = e(t)/e(t ) Temperature [ C] 5 1 15 5 Relationships between temperature T (in C) and δ 18 O (in ): Dansgaard (1964): δ 18 O =.695T 1.6 Yurtsever (1975): δ 18 O =.51T 15. Slope ~.6 C 1 from Dansgaard, 1964, Tellus 16: 46-468 4
Example: Lake groundwater interaction Delay and damping of seasonal variations in groundwater from Stichler & Moser, In: Isotope Hydrology 1979, IAEA Law of Radioactive Decay Radioactive decay: Statistical process, constant decay probability λ dn = λn dt Activity A Units for A: Becquerel (Bq) = s 1 or: Curie (Ci): 1 Ci =.7. 1 1 Bq (activity of 1 g Ra) Use for dating: N(t) (or A(t)) can be measured, the problem is to know N! Integration with N() = N yields N N / N /e N /4 N Radioactive Decay T 1/ ( ) = N t half-life: T 1/ = ln/λ mean life: τ = 1/λ τ N e T 1/ λt t Basic Properties of Tritium Tritium in the Hydrological Cycle Tritium in the table of nuclides: β - 14 1 ( H) C N n, Tritium decay: β decay, half life 1. a, λ = ln/t 1/ =.566 a 1 = 1.78. 1 9 s 1 Energy: 18.6 kev (very low) Origin and Abundance of Tritium Bomb Tritium in Precipitation Natural tritium production: Cosmic rays in atmosphere: Rapid reaction to HTO precipitation water cycle Subsurface production: ( ) Nn,H 14 1 ( α ) Li n, 6 H C Production very low concentration very small Activity concentrations in water ~ 1 Bq/l ~ 1 11 Ci/l ~ 1 15 mol/l Tritium units: 1 tritium unit (TU) H/ 1 H = 1 18 (also called tritium ratio, TR) 1 TU =.118 Bq/kg =.19 pci/kg = 1.11. 1 16 mol/kg = 6.68. 1 7 at/kg 5
Tritium in Oceanography: NADW Formation Tritium Dating 1 Input Decay Tritium at large depth in region of North Atlantic Deep Water (NADW) production Tritium [TU] 1 1 from Östlund & Fine, 1979, In: Behaviour of tritium in the environment, IAEA. 195 196 197 198 199 Year 1 Tritium Dating Basics of the H He Method The product of H decay is a stable, conservative isotope: He Closed system: Sum of H + He is conserved ("stable H") Initial H known: Dating possible independent of input function Tritium [TU] 1 concentration mother - daughter pair He tri ( t) () 1 He t= ln1+ λ Ht H 1975 198 1985 199 1995 Year time H He Method in Lakes H He ages in Lake Baikal Tritium R = He/ 4 He Air-Standard: R a = 1.84 1-6 Time R = R a Gas exchange Temperature R = R eq.98r a H He Epilimnion Thermocline Hypolimnion R > R eq Hohmann et al. 1998, J. Geophys. Res., 1: 18-188. 6
H He ages in Lake Baikal Principles of Transient Trace Gas Dating Methods air water atmospheric input dissolved input 6.5 atmospheric mixing ratio [pptv] 5 4 1 SF 6 solubility equilibrium concentration [fmol/kg] 1.5 1.5 SF 6 197 198 199 Year 197 198 199 Year solubility sample c air c diss Hohmann et al. 1998, J. Geophys. Res., 1: 18-188. Multitracer Studies I: Ocean Age of Denmark Strait Overflow Water E.g.: CFCs and H He along S N section through N Atlantic. Labrador Sea Denmark Strait aus Smethie et al.,, JGR 15(C6):1497-14 Multitracer Studies II: Caspian Sea Origin and Distribution of 14 C in Nature 7
Basic Principles of 14 C Dating I 14 C Dating of Water Problem: A =? T 1 = 57 yr dn = λn dt () N t = N e λt dn A = λn dt 1 ( ) t ln A t = λ A How can water be dated by 14 C? 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 = CO (aq) + H CO + HCO + CO 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: A surf < 1 pmc Typical (but variable!): A surf ~ 95 pmc τ surf ~ 4 yr 14 C Dating of the Deep Ocean Transport: Advection and Diffusion Pulse Advection: Translation Fad = vc Front Diffusion: Broadening Fdif = K gradc from Broecker, 1995, The Glacial World according to Wally 1 D Vertical Diffusive Transport in a Stratified Lake Summary From: Von Rohden und Ilmberger, 1, Aquat. Sci. 6:417-41 Tracer experiment to determine K z c F = Kz z c = K t Variance/width: σ = σ= z (, ) C z t Kt z c z e Kt z ( z z ) σ Isotope Hydrology: Use of environmental isotopes or tracers to study origin and flow of water Stable isotopes: Fractionation, Rayleigh process lead to variations in R Indicators of origin, mixing, fractionating processes Stable isotopes of water: GMWL, T effect Radioisotopes: Often of cosmogenic origin, main use for dating Tritium dating problematic, H He, CFCs, etc. better 14 C dating of water via DIC (ocean, groundwater) Tracers can be used to determine transport parameters Advective velocity (v), turbulent diffusivity (K) 8