1. J.M. Abril Department of Applied Physics (I); University of Seville (Spain) IAEA Regional Training Course on Sediment Core Dating Techniques. RAF7/008 Project J.M. Abril, University of Seville Lecture 3:Clasical dating models using 210 Pb 210 Pb ex fluxes Radionuclide profiles and inventories Radiometric dating models CIC CF-CSR, CRS, CMZ-CSR, CD-CSR IMZ (*)-CSR 1

2. 2 J.M. Abril, University of Seville 2

3. z awaw 222 Rn 210 Pb 137 Cs J.M. Abril, University of Seville 3

4. Abril et al. (JENVRAD, 2009) 222 Rn exhalation depends, among other factors, on 226 Ra content in soil, soil texture and structure, water content, and the forcing factors… 4 J.M. Abril, University of Seville 4

5. Author: Israel López, Univ. Huelva (Spain) J.M. Abril, University of Seville 5

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7. Some global patterns for 210 Pb ex fallout Predominant west-east movement of air masses  210 Pb ex fallout is low in the western areas of the continents 210 Pb ex fallout is higher in the North hemisphere 210 Pb ex fallout is positively correlated with rainfall Figures from P.G. Appleby, STUK-A145 J.M. Abril, University of Seville 7

8. Some reference values for annual fallout of excess 210 Pb (Bq m -2 y -1 ) Global scale, F ~ 23-367 Bq m -2 y -1 (Robbins, 1978) Tropical Australia, F ~ 50 Bq m -2 y -1 (Brunskill and Pfitzner, 2000) Catchment concentration factor (normalization or focusing factor) : Z Input (*) = ZF Steady State Inventories Σ = ZF/λ For 210 Pb = ln2/T 1/2 with T 1/2 = 22.26 y. Inputs and Inventories (Bq m -2 ) in sediments J.M. Abril, University of Seville 8

9. Z [cm] 210 Pb [Bq/kg] 226 Ra total 210 Pb (unsupported) Radiometric dating with 210 Pb: Basic aspects If we assume that there is no Rn exhalation from the sediment, then the total activity of 210 Pb total will be 210 Pb total = 210 Pb supported + 210 Pb unsupported and 210 Pb supported = 226 Ra activity Supported fraction J.M. Abril, University of Seville 9

10. Basic Concepts and definitions z awaw J.M. Abril, University of Seville 10

11. Compaction and bulk density As depth increases in the sediment core, water pores are replaced by solids Saturated porous media Bulk density z VV mwmw msms J.M. Abril, University of Seville 11

12. Practical measurement of bulk densities ww ss mwmw msms mm Drying and gravimetric method J.M. Abril, University of Seville 12

13. Practical measurement of bulk densities. Refinement  mw mw  m s,o mm Drying and gravimetric method and loss by ignition ww  s,0  m s,i  s,i J.M. Abril, University of Seville 13

14. Bulk density versus depth profiles in sediment cores 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 05101520  (g/cm 3 ) Depth [cm] J.M. Abril, University of Seville 14

15. z Mass thickness, Δm, and mass depth :, m [ g dry weight cm -2 ] ΔzΔz J.M. Abril, University of Seville 15

16. (Mass) Sedimentation rate : w [ g dry weight cm -2 y -1 ] Time versus m for constant w (*) Z ≈ ZiZi A (Z i, t) A (Z i+1, t) A (Z i-1, t) w (Z i-1, t) w (Z i+1, t) J.M. Abril, University of Seville 16

17. Basic processes Z ≈ ZiZi A (Z i, t) A (Z i+1, t) A (Z i-1, t) w (Z i-1, t) w (Z i+1, t) J.M. Abril, University of Seville 17

18. In situations where the tracer is partially carried by pore water or in presence of selective and/or translocational bioturbation Eqs. has to be revisited Fundamental equations BOUNDARY CONDITIONS Mass conservation for a particle-associated radiotracer Mass conservation for solids J.M. Abril, University of Seville 18

19. [Bq L -2 T -1 ] Constant Flux and Constant Sedimentation rate (CF-CSR) Activity concentration at interface (non post-depositional mixing)  Constant A 0 w F incoming flux sedimentation rate J.M. Abril, University of Seville 19

20. (non post-depositional mixing) Layer at time t=0 The sediment-water interface displaces upwards Specific activity A 0 time = 0 z=z(t) time = t =m/w m=m(t) J.M. Abril, University of Seville 20

21. m Ln(A) Validation : Goldberg first validated the 210 Pb dating method in varved sediments Curve-fitting model, free parameters : A o, w Think about: Any implicit assumption concerning compaction? J.M. Abril, University of Seville 21

22. ZF = 172 Bq m -2 y -1 EXAMPLE from a case study J.M. Abril, University of Seville 22

23. Don't forget: Estimated sedimentation rates, ages and dates have to be provided with the corresponding uncertainties. Don't forget: Estimated sedimentation rates, ages and dates have to be provided with the corresponding uncertainties. Age : T(m) or T(z), from m(z)/w w, (mass) sedimentation rate Dates or chronology: Year of sampling – Age W = 0.115 ± 0.014 g cm -2 y -1 J.M. Abril, University of Seville 23

24. Associated uncertainties in 210 Pb chronology General formulae for error propagation G.F. mm J.M. Abril, University of Seville 24

25. a, b, R 2  easily produced with excel or other shifts Lest squares fitting ww tt Associated uncertainties in 210 Pb chronology J.M. Abril, University of Seville 25

26. Time resolution. Each sectioned layer in the core corresponds to a time interval Δt = dm/w Remember: As the analytical method is homogenizing the material from each layer, it is not possible to solve other time marks within such an interval (e.g. two 137-Cs peaks). Note for advanced students: Apply lineal regression taking into account the associated uncertainties in measurements J.M. Abril, University of Seville 26

27. CAUTION ! Estimation of the supported fraction is not a trivial task ! 226 Ra may be non uniform in depth and being different from the 210 Pb baseline Settling particles can be depleted in 226 Ra in the water column while enriched in 210 Pb Data from Axelsson and El-Daoushy, 1989 J.M. Abril, University of Seville 27

28. 10 100 1000 10000 00.20.40.60.81 210 Pb (Bq/kg) Mass depth (g cm -2 ) Redó Gossenkollesee 1.- Many unsupported 210 Pb profiles do not follow a simple exponential decay pattern  More complex models are required PROBLEMS: J.M. Abril, University of Seville 28

29. CIC model (Constant Initial Concentration) w F incoming flux Activity concentration at interface (no post-depositional mixing) CIC model assumes constant A o; Thus, changes in F must be compensated with changes in w. Also, it assumes non post-depositional mixing -Reasonable when F is associated with inputs of solids sedimentation rate J.M. Abril, University of Seville 29

30. CIC model can equally be formulated in terms of actual depth (z) or mass depth (m) Chronology (one date per data point) Alternative estimation of sedimentation rates (one per data point) – only for cores with high spatial resolution- CAUTION ! Estimation of the initial concentration, A o, is not a trivial task ! A0A0 A (m) m A -Unknowns for CIC: A o and w i (N+1; N= number of sections in the core) - It is a “mapping” model J.M. Abril, University of Seville 30

31. EXAMPLE from a case study CF-CSR CIC J.M. Abril, University of Seville 31 ZF (recent) = 76 Bq m -2 y -1

32. CRS model (Constant Rate of Supply) w F incoming flux Initial concentration CRS model assumes constant F, independently of w. A o can vary. Also assumes non post-depositional mixing. - Reasonable when F is not coupled with inputs of matter J.M. Abril, University of Seville 32

33. CRS model Inventory under the horizon z After a time t, the horizon now at z=0 will be located at depth z(t), and because of the radioactive decay. At “geological” timescale the inventory is steady state; thus, Z z J.M. Abril, University of Seville 33

34. CRS Chronology: Once the chronology is established, sedimentation rates can be obtained for each two adjacent layers: z Alternatively, from the mass balance in the steady state inventory below depth z CRS model -Unknowns for CRS: F, w i (N+1; N= number of sections in the core) - It is a “mapping” model J.M. Abril, University of Seville 34

35. CAUTION Check for completeness of inventories (sometimes it will be necessary to estimate the “missing” part of the total inventory) J.M. Abril, University of Seville 35

36. EXAMPLE from a case study J.M. Abril, University of Seville 36

37. ZF = 170 Bq m -2 y -1 from CF-CSR w = 0.115 ± 0.014 g cm -2 y -1 J.M. Abril, University of Seville 37

38. Complete mixing zone model with constant sedimentation rate and constant flux. Mixing mama w F F A a m a Radioactive decay wAawAa Sediment growth Steady-state mass balance Curve-fitting model, free parameters : A a, w, m a J.M. Abril, University of Seville 38

39. Example CMZ-1 mixing m a =9.5 g cm -2 ; w=0,374 g cm -2 y -1 J.M. Abril, University of Seville 39

40. Acceleration or mixing? 10 100 1000 10000 00.20.40.60.81 210 Pb (Bq/kg) Mass depth (g cm -2 ) Redó Gossenkollesee 2.- Many times unsupported 210 Pb profiles can be equally explained by different models  210 Pb chronologies must be validated against an independent dating method PROBLEMS: J.M. Abril, University of Seville 40

41. J.M. Abril, University of Seville 41 Think about: What other hypothesis are implicitly assumed in all the previous models ?

42. Constant flux, CSR and constant difussion Model Demonstration will be provided within lecture 6 Curve-fitting model, free parameters : ZF, k m, w Data: CF-CS-C Diffusion Fit : CF-CSR Model w0,1 g cm^(-2) y^(-1) km6 g^2 cm^(-4) y^(-1) ZF200 Bq m^(-2) y^(-1) w0,49 g cm^(-2) y^(-1) ZF200,6 Bq m^(-2) y^(-1) J.M. Abril, University of Seville 42

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44. J. N. Smith proposed a protocol for research journals for the acceptance of papers that rely on 210 Pb dating to establish a sediment core geochronology: ‘‘The 210 Pb geochronology must be validated using at least one independent tracer which separately provides an unambiguous time-stratigraphic horizon’’. J.M. Abril, University of Seville 44

45. ZFo=10 mBq/(cm^2 y), w=0.1+0.1 t/150 g/(cm^2 y) D=0 Examples generated with numerical solutions Constat aceleration, constant diffusion or CF-CSR? J.M. Abril, University of Seville 45

46. Effect of “episodic” changes in sedimentation rates? J.M. Abril, University of Seville 46 Examples generated with numerical solutions

47. Numerical algorithm: MSOU T= - 50 y sgt= 5 y J.M. Abril, University of Seville 47 λ=0 Ts =150 y

48. J.M. Abril, University of Seville 48 T= - 20 y sgt= 2 y Ts =150 y λ=0 Numerical algorithm: MSOU

49. Periodic changes in w with T=7 y When data are smooth enough to apply CSR models? J.M. Abril, University of Seville 49 Examples generated with numerical solutions