1. Radiocarbon age-depth modelling II – Bayesian age-depth models
Dr. Maarten Blaauw
School of Geography, Archaeology and Palaeoecology
Queen’s University Belfast
Northern Ireland

2. This lecture A biased introduction to tuning
Bayesian age-depth modelling

3. Tuning -- intro Advocated by famous scientists such as Shackleton
Major (climate) events must have been synchronous
e.g. tephra, sediment layers separated by valley/ocean
Use events to tune/tie between proxy sites
Produces 'rope&rubber-band' age-models

4. Oman stalagmite vs solar forcing, tuned
U/Th dated
Oman stalagmite vs solar forcing, tuned
Neff et al. Nature Oman d18O & d14C

5. 14C dated
Bond et al Science

6. “Millennial-scale pollen changes are synchronous
No dates
“Millennial-scale pollen changes are synchronous
with Greenland events”
Sanchez Goñi et al. Climate Dynamics 2002 Alboran Sea

7. “Millennial-scale dust fluxes are synchronous with North Atlantic
No dates
“Millennial-scale dust fluxes are synchronous
with North Atlantic
Heinrich stadials”
Itambi et al. Paleoceanography Senegal

8. Age model based on calibrated 14C ages (circles), astronomical calibration (squares), and tuning to GISP2 chronology (diamonds)
Tzedakis et al. Geology Greece

9. Cariaco Basin (Venezuela) tuned against Hulu Cave (China)
No dates (for this part)
Hughen et al. 2006
Cariaco Basin (Venezuela) tuned against Hulu Cave (China)

10. Blaauw, submitted (Quat. Sci. Rev.)

11. Tuning Based on “model”: Events happened simultaneously
Major local event must be expressed on large scale
So should also be found back in other sites
Event shapes can be used as ID (saw, tephra)
Events happened simultaneously
So provide very precise tie-points for age-models!
Use events to glue to famous well-dated archives
Especially handy where 14C has problems (old, ocean)
Between tie-points, assume linear accumulation

12. Now hold on... Isn't this circular reasoning?
How precise are tie-points for age-models?
Do independent data support tuning?

13. 1) Circular reasoning premise 1) God is not a liar (Hebrews 6:18)
premise 2) God wrote the Bible (Lk. 16:1, etc.)
premise 3) The Bible says that God exists (2 Cor. 1)
→ therefore, God exists

14. Circular reasoning in palaeoclimate
Before dating, no robust time frames and thus much freedom to speculate about chronologies and correlations. Few could resist the urge to fit their results into existing framework, e.g. pollen zones. Thus arose 'coherent myths' or 'reinforcement syndrome' (Oldfield 2001 The Holocene)
von Post (1946) warned us about this
Problems still exists, suck-in smear effect (Baillie 1991), 'precisely dated known event becomes associated with more poorly dated events' (Bennett 2002 JQS)

15. “Millennial-scale pollen changes synchronous with Greenland events”
Of course, because they were tuned (via SST)!!!
Sanchez Goñi et al. Climate Dynamics 2002 Alboran Sea

16. Courtillot et al. (EPSL '07, ‘08) show Mangini et al's (EPSL '05) d18O record with d14C. "The match can of course not be perfect because of the uncertainties. If solar variability played only a minor role in the past two millennia, tuning could not improve the correlation. The correlation coefficient is only 0.6, and other forcing factors have to be taken into account. It is therefore not surprising that the tuned curve should reveal the link between solar activity and δ18O."
Bard and Delaygue (EPSL '08) comment: "To prove correlations and make inferences about solar forcing, only untuned records [...] with their respective and independent time scales, should be used.
???

17. 2) How precise are tie-points?
Depends on reliable event-IDing (order, shape, tephra)
Resolution/noise: did we catch the event (start)?
Multiple/different proxies: do they agree? (ice, ocean)
How precisely dated is 'mother archive'? (rubber band)
NGRIP: uncertainty thousands of years
SPECMAP: c. 5,000 yr uncertainties
Radiocarbon: errors stated more explicitly
Linear accumulation between tie-points reasonable?

18. Are all climate events global?

19. Barber and Langdon 2007, Quat. Sci. Rev.
Charman et al. 2009, Quat. Sci. Rev.

20. Independent support for tuning?
WARNING
ILLEGAL CURVES
Blaauw et al 2010, JQS

21. Blaauw et al 2010, JQS

22. Blaauw et al 2010, JQS

23. Blaauw et al 2010, JQS

24. Know your resolution

25. Tuning With tuning dates become 'nuisance'
Approach inherited from pre-dating period?
Cannot use tuning for spatio-temporal patterns
Keep time-scales independent+errors
Assume non-synchroneity until proven false
Stick with appropriate resolution (millennial/decadal)
Our eyes/minds are eager to interpret patterns
Use quantitative, objective methods (e.g. for tuning)

26. Bayesian age-modelling
Bayes: combine data with prior information
express everything in probabilities, not “black/white”
MexCal: Christen, PhD thesis Nottingham
BCal: Buck et al., Internet Archaeology 7
OxCal: Bronk Ramsey, QSR 27:42-60
Bpeat: Blaauw & Christen, Appl Stat 54:
Prior information:
chronological ordering dates in stratigraphy
accumulation rate, ranges and variation; hiatuses
outlying dates

27. Stratigraphic order dates
Christen, Appl Stat 43:
Only accept iterations with correct order
Reduces error ranges
Removes outliers
Hard to question
Easy in Bcal / OxCal

28. Stratigraphic order dates
Blaauw and Heegaard, in press

29. Stratigraphic order dates
Example: Marshall et al Quat Res 68
Large calibrated range of C14 dates
Many ranges unlikely given other dates and acc.rate

30. Stratigraphic order dates
Example: Marshall et al Quat Res 68
Large calibrated range of C14 dates
Many ranges unlikely given other dates and acc.rate

31. Outlier analysis Why outliers?
chance? About 1 in 20 dates are off...
contamination?
errors in labelling?
real?
Outlier analysis: assign prior outlier probabilities
e.g. 5% for good dates, 50% for unreliable material
base on prior knowledge, NOT after seeing the dates!
available in BCal, Bpeat, mexcal, not in OxCal

32. Wiggle-match dating Assume linear accumulation (Bpeat)‏
age = a*depth + b

33. Wiggle-match dating Assume linear accumulation (Bpeat)‏
age = a*depth + b

34. Wiggle-match dating

35. Include additional information
prior outlier
probabilities
hiatus, size
prior outlier
probabilities
other dates:
tephra, pollen,
210Pb, U/Th, ...

36. Include additional information
p(date1)*p(date2)*p(date3)*p(date4)*p(date5) *
p(acc.rate1)*p(hiatus1)*p(acc.rate2)*p(acc.rate2)‏

37. MCMC process Many parameters Get initial point estimate all parameters
acc.rate, division depth and hiatus per section
outlier probability every date
Get initial point estimate all parameters
Change values parameters one by one
within prior limits
repeat millions of times
Simulates true distribution parameters

38. Grey-scale ghost graphs

39. Age-depth modelling
Wohlfarth et al. JQS 2006

40. Order of events between archives

41. Timing between events
Buck and Bard 2007, Quat. Sci. Rev.

42. Meta-analysis Europe
Blaauw et al. in prep.