-
Notifications
You must be signed in to change notification settings - Fork 3
/
Chron1.0Radiocarbon.jl
173 lines (145 loc) · 9.43 KB
/
Chron1.0Radiocarbon.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
## --- Load required pacages, install Chron if required
using Chron
using Plots
## --- Define sample properties
# # # # # # # # # # # Enter sample information here! # # # # # # # # # # # #
# Input the number of samples we wish to model (must match below)
nSamples = 4
# Make an instance of a ChronSection object for nSamples
smpl = ChronAgeData(nSamples)
smpl.Name = ("Sample 1", "Sample 2", "Sample 3", "Sample 4") # Et cetera
smpl.Age_14C .= [ 6991, 7088, 7230, 7540,] # Measured ages
smpl.Age_14C_sigma .= [ 30, 70, 50, 50,] # Measured 1-σ uncertainties
smpl.Height .= [ -355, -380,-397.0,-411.5,] # Depths below surface should be negative
smpl.Height_sigma .= fill(0.01, nSamples) # Usually assume little or no sample height uncertainty
smpl.Age_Sidedness .= zeros(nSamples) # Sidedness (zeros by default: geochron constraints are two-sided). Use -1 for a maximum age and +1 for a minimum age, 0 for two-sided
smpl.Age_Unit = "Years BP" # Unit of measurement for ages
smpl.Height_Unit = "m" # Unit of measurement for Height and Height_sigma
# IMPORTANT: smpl.Height must increase with increasing stratigraphic height
# -- i.e., stratigraphically younger samples must be more positive. For this
# reason, it is convenient to represent depths below surface as negative
# numbers.
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
## --- Calculate and plot calendar age PDFs for each sample
# Choice of radiocarbon calibration
# Options include: intcal13, intcal20, shcal20
calibration = intcal20
smpl.Params = fill(NaN, length(calibration.Age_Calendar), nSamples)
for i = 1:nSamples
# The likelihood that a measured 14C age could result from a sample of
# a given calendar age is proportional to the intergral of the product
# of the two respective distributions
likelihood = normproduct.(smpl.Age_14C[i], smpl.Age_14C_sigma[i], calibration.Age_14C, calibration.Age_sigma)
likelihood ./= sum(likelihood) * calibration.dt # Normalize
# Estimate mean and standard deviation by drawing samples from distribution
samples = draw_from_distribution(likelihood, 10^6) .* maximum(calibration.Age_Calendar)
smpl.Age[i] = nanmean(samples)
smpl.Age_sigma[i] = nanstd(samples)
smpl.Age_025CI[i] = nanpctile(samples,2.5)
smpl.Age_975CI[i] = nanpctile(samples,97.5)
# Populate smpl.Params with log likelihood for each sample
smpl.Params[:,i] = normproduct_ll.(smpl.Age_14C[i], smpl.Age_14C_sigma[i], calibration.Age_14C, calibration.Age_sigma)
# Plot likelihood vector for each sample
t = (calibration.Age_Calendar .> smpl.Age[i] - 5*smpl.Age_sigma[i]) .& (calibration.Age_Calendar .< smpl.Age[i] + 5*smpl.Age_sigma[i])
plot(calibration.Age_Calendar[t], likelihood[t], label=smpl.Name[i], xlabel="Calendar Age", ylabel="Likelihood")
savefig("$(smpl.Name[i])_CalendarAge.pdf")
end
## --- Run stratigraphic model
# # # # # # # # # # Configure stratigraphic model here! # # # # # # # # # #
# Configure the stratigraphic Monte Carlo model
config = StratAgeModelConfiguration()
# If you in doubt, you can probably leave these parameters as-is
config.resolution = 0.2 # Same units as sample height. Smaller is slower!
config.bounding = 0.5 # how far away do we place runaway bounds, as a fraction of total section height
(bottom, top) = extrema(smpl.Height)
npoints_approx = round(Int,length(bottom:config.resolution:top) * (1 + 2*config.bounding))
config.nsteps = 15000 # Number of steps to run in distribution MCMC
config.burnin = 10000*npoints_approx # Number to discard
config.sieve = round(Int,npoints_approx) # Record one out of every nsieve steps
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# Run the stratigraphic MCMC model
@time (mdl, agedist, lldist) = StratMetropolis14C(smpl, config)
# Plot results (mean and 95% confidence interval for both model and data)
hdl = plot([mdl.Age_025CI; reverse(mdl.Age_975CI)],[mdl.Height; reverse(mdl.Height)], fill=(minimum(mdl.Height),0.5,:blue), label="model")
plot!(hdl, mdl.Age, mdl.Height, linecolor=:blue, label="")
plot!(hdl, smpl.Age, smpl.Height, xerror=(smpl.Age-smpl.Age_025CI,smpl.Age_975CI-smpl.Age),label="data",seriestype=:scatter,color=:black)
plot!(hdl, xlabel="Age ($(smpl.Age_Unit))", ylabel="Height ($(smpl.Height_Unit))")
savefig(hdl,"AgeDepthModel.pdf");
display(hdl)
## --- Interpolate results at a specific height
# Stratigraphic height at which to interpolate
height = -404
age_at_height = linterp1s(mdl.Height,mdl.Age,height)
age_at_height_min = linterp1s(mdl.Height,mdl.Age_025CI,height)
age_at_height_max = linterp1s(mdl.Height,mdl.Age_975CI,height)
print("Interpolated age at height=$height: $age_at_height +$(age_at_height_max-age_at_height)/-$(age_at_height-age_at_height_min) $(smpl.Age_Unit)")
# Optional: interpolate full age distribution
interpolated_distribution = Array{Float64}(undef,size(agedist,2))
for i=1:size(agedist,2)
interpolated_distribution[i] = linterp1s(mdl.Height,agedist[:,i],height)
end
hdl = histogram(interpolated_distribution, nbins=50, label="")
plot!(hdl, xlabel="Age ($(smpl.Age_Unit)) at height=$height", ylabel="Likelihood (unnormalized)")
savefig(hdl, "Interpolated age distribution.pdf")
display(hdl)
## --- Calculate deposition rate binned by age - - - - - - - - - - - - - - - -
# Set bin width and spacing
binwidth = round(nanrange(mdl.Age)/10,sigdigits=1) # Can also set manually, commented out below
# binwidth = 100 # Same units as smpl.Age
binoverlap = 10
ages = collect(minimum(mdl.Age):binwidth/binoverlap:maximum(mdl.Age))
bincenters = ages[1+Int(binoverlap/2):end-Int(binoverlap/2)]
spacing = binoverlap
# Calculate rates for the stratigraphy of each markov chain step
dhdt_dist = Array{Float64}(undef, length(ages)-binoverlap, config.nsteps)
@time for i=1:config.nsteps
heights = linterp1(reverse(agedist[:,i]), reverse(mdl.Height), ages)
dhdt_dist[:,i] .= abs.(heights[1:end-spacing] - heights[spacing+1:end]) ./ binwidth
end
# Find mean and 1-sigma (68%) CI
dhdt = nanmean(dhdt_dist,dim=2)
dhdt_50p = nanmedian(dhdt_dist,dim=2)
dhdt_16p = nanpctile(dhdt_dist,15.865,dim=2) # Minus 1-sigma (15.865th percentile)
dhdt_84p = nanpctile(dhdt_dist,84.135,dim=2) # Plus 1-sigma (84.135th percentile)
# Other confidence intervals (10:10:50)
dhdt_20p = nanpctile(dhdt_dist,20,dim=2)
dhdt_80p = nanpctile(dhdt_dist,80,dim=2)
dhdt_25p = nanpctile(dhdt_dist,25,dim=2)
dhdt_75p = nanpctile(dhdt_dist,75,dim=2)
dhdt_30p = nanpctile(dhdt_dist,30,dim=2)
dhdt_70p = nanpctile(dhdt_dist,70,dim=2)
dhdt_35p = nanpctile(dhdt_dist,35,dim=2)
dhdt_65p = nanpctile(dhdt_dist,65,dim=2)
dhdt_40p = nanpctile(dhdt_dist,40,dim=2)
dhdt_60p = nanpctile(dhdt_dist,60,dim=2)
dhdt_45p = nanpctile(dhdt_dist,45,dim=2)
dhdt_55p = nanpctile(dhdt_dist,55,dim=2)
# Plot results
hdl = plot(bincenters,dhdt, label="Mean", color=:black, linewidth=2)
plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_16p; reverse(dhdt_84p)], fill=(0,0.2,:darkblue), linealpha=0, label="68% CI")
plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_20p; reverse(dhdt_80p)], fill=(0,0.2,:darkblue), linealpha=0, label="")
plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_25p; reverse(dhdt_75p)], fill=(0,0.2,:darkblue), linealpha=0, label="")
plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_30p; reverse(dhdt_70p)], fill=(0,0.2,:darkblue), linealpha=0, label="")
plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_35p; reverse(dhdt_65p)], fill=(0,0.2,:darkblue), linealpha=0, label="")
plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_40p; reverse(dhdt_60p)], fill=(0,0.2,:darkblue), linealpha=0, label="")
plot!(hdl,[bincenters; reverse(bincenters)],[dhdt_45p; reverse(dhdt_55p)], fill=(0,0.2,:darkblue), linealpha=0, label="")
plot!(hdl,bincenters,dhdt_50p, label="Median", color=:grey, linewidth=1)
plot!(hdl, xlabel="Age ($(smpl.Age_Unit))", ylabel="Depositional Rate ($(smpl.Height_Unit) / $(smpl.Age_Unit) over $binwidth $(smpl.Age_Unit))", fg_color_legend=:white)
# savefig(hdl,"DepositionRateModelCI.pdf")
display(hdl)
## --- Optional: Stratigraphic model including hiatuses
# Data about hiatuses
nHiatuses = 2 # The number of hiatuses you have data for
hiatus = HiatusData(nHiatuses) # Struct to hold data
hiatus.Height = [-371.5, -405.0 ]
hiatus.Height_sigma = [ 0.0, 0.0 ]
hiatus.Duration = [ 100.0, 123.0]
hiatus.Duration_sigma = [ 30.5, 20.0]
# Run the model. Note the additional `hiatus` arguments
@time (mdl, agedist, hiatusdist, lldist) = StratMetropolis14C(smpl, hiatus, config)
# Plot results (mean and 95% confidence interval for both model and data)
hdl = plot([mdl.Age_025CI; reverse(mdl.Age_975CI)],[mdl.Height; reverse(mdl.Height)], fill=(minimum(mdl.Height),0.5,:blue), label="model")
plot!(hdl, mdl.Age, mdl.Height, linecolor=:blue, label="", fg_color_legend=:white)
plot!(hdl, smpl.Age, smpl.Height, xerror=(smpl.Age-smpl.Age_025CI,smpl.Age_975CI-smpl.Age),label="data",seriestype=:scatter,color=:black)
plot!(hdl, xlabel="Age ($(smpl.Age_Unit))", ylabel="Height ($(smpl.Height_Unit))")
## --- End of File