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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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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

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

14C dating

• 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?

14C calibration

• 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)

• 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 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

• 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?

• 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

• 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) )

• 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)

• 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

• What was for you the best way to understand 14C calibration? Why?

• Dedicated software (OxCal, Calib, clam)

• Draw by hand

• Animations

• Equations