Age-depth modelling part 1

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# Age-depth modelling part 1 - PowerPoint PPT Presentation

Age-depth modelling part 1. 0 random walk proxy simulations 1 Calibration of 14 C dates 2 Basic 14 C age-depth modelling Schedule flexible and interactive! Focus on uncertainty. R. Stats and graphing software Many user-provided modules Free, open-source Open R and type:

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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
R

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

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
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?
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’)
• 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