Age-depth models

Given a known depths and known (or modelled) ages, it is often convenient to approximate age as a continuous function of depth in an archive. This package provides tools to flexibly create age-depth relationships with various rules for interpolating age within known age-depth values, and extrapolating above and below these values. Typically, this is interpolation between known values and extrapolating using average sedimentation rates based on ages known at discrete points in a core.

Example

Using the built-in dataset alta_lake_210Pb_ages, which contains a Lead-210 (CRS) age-depth relationship for a core from Alta Lake, Whistler, British Columbia, we can create an age-depth model (note that age and depth are evaluated within .data, if it is provided, and support tidy evaluation):

library(tidypaleo)
alta_lake_adm <- age_depth_model(
  alta_lake_210Pb_ages,
  depth = depth_cm, age = age_year_ad,
  age_max = age_year_ad + age_error_yr, 
  age_min = age_year_ad - age_error_yr
)
alta_lake_adm
#> <age_depth_model>
#> Call: 
#> age_depth_model(
#>   .data = alta_lake_210Pb_ages, depth = depth_cm,
#>   age = age_year_ad, age_min = age_year_ad - age_error_yr,
#>   age_max = age_year_ad + age_error_yr
#> )

Then, we can plot the relationship:

plot(alta_lake_adm)

…Or predict raw data:

predict(alta_lake_adm, depth = seq(-1, 10, 0.5))

depth	age	age_min	age_max	method
-1.0	2031.701	NA	NA	extrapolate_above
-0.5	2023.150	NA	NA	extrapolate_above
0.0	2014.600	2014.60	2014.60	interpolate
0.5	2011.300	NA	NA	interpolate
1.0	2008.000	2007.66	2008.34	interpolate
1.5	2003.400	2002.84	2003.96	interpolate
2.0	1998.100	1997.24	1998.96	interpolate
2.5	1989.950	NA	NA	interpolate
3.0	1981.800	1979.55	1984.05	interpolate
3.5	1973.700	NA	NA	interpolate
4.0	1965.600	1960.87	1970.33	interpolate
4.5	1956.400	NA	NA	interpolate
5.0	1947.200	1938.99	1955.41	interpolate
5.5	1934.750	NA	NA	interpolate
6.0	1922.300	1895.28	1949.32	interpolate
6.5	1909.150	NA	NA	interpolate
7.0	1896.000	1838.81	1953.19	interpolate
7.5	1887.450	NA	NA	extrapolate_below
8.0	1878.899	NA	NA	extrapolate_below
8.5	1870.349	NA	NA	extrapolate_below
9.0	1861.798	NA	NA	extrapolate_below
9.5	1853.248	NA	NA	extrapolate_below
10.0	1844.697	NA	NA	extrapolate_below

The default behaviour is to interpolate within known ages/depths, and extrapolate using a linear fit of ages/depths. These can be specified using transform functions, which take XY data and produce forward and inverse predictions based on them. The default call is:

age_depth_model(
  ...,
  interpolate_age = age_depth_interpolate,
  extrapolate_age_below = ~age_depth_extrapolate(.x, .y, x0 = last, y0 = last),
  extrapolate_age_above = ~age_depth_extrapolate(.x, .y, x0 = first, y0 = first),
  interpolate_age_limits = trans_exact,
  extrapolate_age_limits_below = trans_na,
  extrapolate_age_limits_above = trans_na
)

To customize the behaviour of the predictions (e.g., disable extrapolating above or below), specify a transform function in the appropriate category. One-sided formulas are turned into functions using the rlang::as_function(). A more advanced way might be to only use the first/last few observations to extrapolate above and below, which one could do like this:

alta_lake_adm2 <- age_depth_model(
  alta_lake_210Pb_ages,
  depth = depth_cm, age = age_year_ad,
  age_max = age_year_ad + age_error_yr, 
  age_min = age_year_ad - age_error_yr,
  extrapolate_age_below = ~age_depth_extrapolate(
    tail(.x, 3), tail(.y, 3), x0 = dplyr::last, y0 = dplyr::last
  ),
  extrapolate_age_above = ~age_depth_extrapolate(
    head(.x, 3), head(.y, 3), x0 = dplyr::first, y0 = dplyr::first
  )
)

plot(alta_lake_adm2)

Age-depth models

Dewey Dunnington

2023-01-17

Example