Radiocarbon age-depth modellingII – Bayesian age-depth models

Dr. Maarten BlaauwSchool of Geography, Archaeology and Palaeoecology

Queen’s University BelfastNorthern Ireland

This lecture

A biased introduction to tuning Bayesian age-depth modelling

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

Neff et al. Nature 2001 Oman d18O & d14C

Oman stalagmite vs solar forcing, tuned

U/Th dated

Bond et al. 2001 Science

14C dated

Sanchez Goñi et al. Climate Dynamics 2002 Alboran Sea

“Millennial-scale pollen changes are synchronous with Greenland events”

No dates

Itambi et al. Paleoceanography 2009 Senegal

“Millennial-scale dust fluxes are synchronous with North Atlantic Heinrich stadials”

No dates

Tzedakis et al. Geology 2004 Greece

Age model based on calibrated 14C ages (circles), astronomical calibration (squares), and tuning to GISP2 chronology (diamonds)

Hughen et al. 2006Cariaco Basin (Venezuela) tuned against Hulu Cave (China)

No dates (for this part)

Blaauw, submitted (Quat. Sci. Rev.)

Tuning

• Based on “model”:

– 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

Now hold on...

• Isn't this circular reasoning?

• How precise are tie-points for age-models?

• Do independent data support tuning?

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

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)

Sanchez Goñi et al. Climate Dynamics 2002Alboran Sea

“Millennial-scale pollen changes synchronous with Greenland events”

Of course, because they were tuned (via SST)!!!

Courtillot et al. (EPSL '07, ‘08) show Mangini et al's (EPSL '05) 18O record with 14C. "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.

???

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?

Are all climate events global?

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

Blaauw et al 2010, JQS

Independent support for tuning?

WARNINGILLEGAL CURVES

Blaauw et al 2010, JQS

Blaauw et al 2010, JQS

Blaauw et al 2010, JQS

Know your resolution

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)

Bayesian age-modelling

Bayes: combine data with prior information express everything in probabilities, not “black/white”

MexCal: Christen, 1994. PhD thesis Nottingham

BCal: Buck et al., 1999. Internet Archaeology 7

OxCal: Bronk Ramsey, 2008. QSR 27:42-60

Bpeat: Blaauw & Christen, 2005. Appl Stat 54: 805-816

Prior information: chronological ordering dates in stratigraphy accumulation rate, ranges and variation; hiatuses outlying dates

Stratigraphic order dates

Christen, 1994. Appl Stat 43:489-503 Only accept iterations with correct order Reduces error ranges Removes outliers Hard to question Easy in Bcal / OxCal

Stratigraphic order dates

Blaauw and Heegaard, in press

Stratigraphic order dates

Example: Marshall et al. 2007. Quat Res 68 Large calibrated range of C14 dates Many ranges unlikely given other dates and acc.rate

Stratigraphic order dates

Example: Marshall et al. 2007. Quat Res 68 Large calibrated range of C14 dates Many ranges unlikely given other dates and acc.rate

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

Wiggle-match dating

Assume linear accumulation (Bpeat) age = a*depth + b

Wiggle-match dating

Assume linear accumulation (Bpeat) age = a*depth + b

Wiggle-match dating

Include additional information

prior outlier probabilities

prior outlier probabilities

other dates:tephra, pollen,210Pb, U/Th, ...

hiatus, size

Include additional information

p(date1)*p(date2)*p(date3)*p(date4)*p(date5) * p(acc.rate1)*p(hiatus1)*p(acc.rate2)*p(acc.rate2)

MCMC process

• Many 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

Grey-scale ghost graphs

Age-depth modellingWohlfarth et al. JQS 2006

Order of events between archives

Timing between events

Buck and Bard 2007, Quat. Sci. Rev.

Meta-analysis Europe

Blaauw et al. in prep.