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))
#> # A tibble: 23 × 5
#>    depth   age age_min age_max method           
#>    <dbl> <dbl>   <dbl>   <dbl> <chr>            
#>  1  -1   2032.     NA      NA  extrapolate_above
#>  2  -0.5 2023.     NA      NA  extrapolate_above
#>  3   0   2015.   2015.   2015. interpolate      
#>  4   0.5 2011.     NA      NA  interpolate      
#>  5   1   2008    2008.   2008. interpolate      
#>  6   1.5 2003.   2003.   2004. interpolate      
#>  7   2   1998.   1997.   1999. interpolate      
#>  8   2.5 1990.     NA      NA  interpolate      
#>  9   3   1982.   1980.   1984. interpolate      
#> 10   3.5 1974.     NA      NA  interpolate      
#> # ℹ 13 more rows

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)

- Example