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Age-depth modelling part 1

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Age-depth modelling part 1

0 random walk proxy simulations

1 Calibration of 14C dates

2 Basic 14C age-depth modelling

- Schedule flexible and interactive!
- Focus on uncertainty

Stats and graphing software

Many user-provided modules

Free, open-source

Open R and type:

plot(1:10, 11:20)

x <- 1:10 ; y <- 11:20 ; plot(x, y, type='l')

Case sensitive

Previous commands: use up cursor

Random walk simulations

Checkhttp://chrono.qub.ac.uk/blaauw/Random.R in browser

Open R and load the link:

Source ( url( 'http://chrono.qub.ac.uk/blaauw/Random.R' ) )

RandomEnv()

RandomEnv(nforc=2, nprox=5)

RandomProx()

Introduction – 14C decay

- Atm. 12C (99%), 13C (1%), 14C (10-12)
- 14C decays exponentially with time
- Cease metabolism -> clock starts ticking
- Measure ratio 14C/C to estimate age fossil

Calibrate – 14C age errors

- Counting uncertainty AMS
- Counting time (normal vs high-precision dates)
- Sample size (larger = more 14C atoms)
- Drift machine (need to correct, standards)

- Preparation samples
- Pretreatment, chemical & graphitisation
- Material-dependent (e.g. trees, bone, coral)
- Lab-specific

- Every measurement will be bit different
- Errors assumed to have Normal distribution

14C dating

Bull’s Eye- Precise and Accurate

Precise but inaccurate

Accurate (on average) but imprecise

An alternative to the normal model

- Christen and Perez 2009, Radiocarbon
- Spread of dates often beyond expected
- Reported errors are estimates
- Propose an error multiplier, gamma
- Results in t student distribution
- No need for outlier modelling?

http:///www.chrono.qub.ac.uk/blaauw/

14C calibration

Calibrate - methods

- Probability preferred over intercept
- Less sensible to small changes in mean
- Resulting cal.ranges make more sense

- Procedure probability method:
- What is prob. of cal.year x, given the date?
- Calculate this prob. for all cal.ages
Combine errors date and cal.curve √(2+sd2)

Calibrate - methods

- Multimodal distributions
- Which of the peaks most likely (Calib %)?
- How report date?
- 1 or 2 sd
- sd range
- mean±sd
- mode
- weighted mean (Telford et al. ‘05 Holocene)
- why not plot the entire distribution!

Calibration, the equations

- Calibration curve provides 14C ages µ for calendar years θ, µ(θ)
- 14C measurement y ~ N(mean, sd)
- Calibrate: find probability of y for θ
N( µ(θ) , σ ), where σ2 = sd2 + σ(θ)2

for sufficiently wide range of θ

Calibrate - DIY

- A) Using eyes/hands on handout paper
- Imagine invisible arbitrary second axes for probs
- Try to avoid using intercept
- Try “cosmic schwung”, not mm precision
- Don’t go from C14 to calBP! What is prob x cal BP?
- Calibrated ranges?

1. clam ... R

- R works in “workspace”
- Remember where you work(ed)!
- Change working dir via File > Change Dir
- Or permanently using Desktop Icon (right-click, properties, start in)

- Change R to your Clam workspace

1. Calibrating DIY

- Define years: yr <- 1:1000
- A date: y <- 230; sdev <- 70
- Prob. for each yr: prob < - dnorm(yr, y, sdev)
- plot(yr, prob, type=‘l’)
- But we should calibrate: cc <- read.table(“IntCal09.14C”, header=TRUE)
- cc[1:10,]
- prob <- dnorm(cc[,2], y, sqrt(sdev^2+cc[,3]^2))
- plot(cc[,1], prob, type='l', xlim=c(0, 1000) )

Calibrate - DIY

- clam (Blaauw, in press Quat Geochr)
- Open R (via desktop icon or Start menu)
- Change working directory to clam dir
- Type: source(''clam.R'') [enter]
- Type: calibrate(130, 35)

2. clam, calibrating

- Type calibrate()
- This calibrated 14C date of 2450 +- 50 BP
- Type calibrate(130, 30)
- Type calibrate(130, 30, sdev=1)
- Try calibrating other dates, e.g., old ones
- All clam code is open source, you can read the code to see/follow what it does

Feedback please

- What was for you the best way to understand 14C calibration? Why?
- Dedicated software (OxCal, Calib, clam)
- Draw by hand
- Animations
- Equations