dplR (version 1.8.0)

rcs: Regional Curve Standardization

Description

Detrend multiple ring-width series simultaneously using a regional curve.

Usage

rcs(rwl, po = NULL, nyrs = NULL, f = 0.5, biweight = TRUE, ratios = TRUE,
    rc.out = FALSE, make.plot = TRUE, method = c("caps", "ads"),
    min.n = NULL, pos.slope = TRUE, ...)

Value

An object of class c("rwi", "data.frame") (see

as.rwi) containing the dimensionless and detrended ring-width indices with column names, row names and dimensions of

rwl. If rc.out is TRUE then a

list will be returned with a data.frame containing the detrended ring widths as above and a vector containing the regional curve.

Arguments

rwl

a data.frame with series as columns and years as rows such as that produced by read.rwl

po

a data.frame containing two variables. Variable one (series in the example below) gives the series ID as either characters or factors. These must exactly match colnames(rwl). Variable two (pith.offset in the example below) must be integral values and give the years from the beginning of the core to the pith (or center) of the tree. The minimum value is 1. If NULL (the default) a pith offset of 1 is assumed for all series, meaning each series is treated as beginning at cambial age 1. This is almost certainly unrealistic for most datasets but is provided as a convenience when pith offset data are unavailable.

nyrs

a number giving the rigidity of the smoothing spline. For method = "caps" this defaults to 0.1 of the length of the regional curve if NULL. For method = "ads" this sets the starting stiffness (nyrs0) and defaults to 50 if NULL.

f

a number between 0 and 1 giving the frequency response or wavelength cutoff. Defaults to 0.5.

biweight

logical flag. If TRUE then a robust mean is calculated using tbrm.

ratios

logical flag. If TRUE (the default) then indices are calculated by division, if FALSE indices are calculated by subtraction.

rc.out

logical flag. Returns the regional curve along with the ring-width indices if TRUE.

make.plot

logical flag. Makes a plot of the raw ring-width series by cambial age, the biweight mean, and the regional curve if TRUE.

method

a character string giving the smoothing method to apply to the mean regional curve. Either "caps" (the default, a cubic smoothing spline via caps) or "ads" (an age-dependent spline via ads).

min.n

an optional integer giving the minimum sample depth required at a given cambial age for that age to be included when fitting the regional curve. Ages where fewer than min.n series contribute are excluded from the tail of the curve, and indices for rings falling beyond the truncated curve are returned as NA. If NULL (the default) the full curve is used.

pos.slope

a logical flag passed to ads. If TRUE (the default) a positive slope is allowed at the end of the fitted curve. Ignored when method = "caps".

...

other arguments passed to plot.

Author

Code provided by DendroLab based on programming by F. Qeadan and F. Biondi, University of Nevada Reno, USA and adapted for dplR by Andy Bunn. Patched and improved by Mikko Korpela. Extended with method, min.n, and pos.slope arguments by Andy Bunn.

Details

This method detrends and standardizes tree-ring series by calculating an age-related growth curve specific to the rwl. The detrending is the estimation and removal of the tree’s natural biological growth trend. The standardization is done by either dividing each series by the growth trend or subtracting the growth trend from each series to produce units in the dimensionless ring-width index (RWI). The option to produce indices by subtraction is intended to be used on series that have been subject to variance stabilization (e.g., using powt).

Two smoothers are available for fitting the regional curve. The default (method = "caps") uses a cubic smoothing spline where the frequency response is 0.50 at a wavelength of 10 percent of the maximum cambial age unless specified differently via nyrs and f (see caps). The alternative (method = "ads") uses an age-dependent spline whose stiffness increases with cambial age, which may better preserve low-frequency variability in the biological trend (see ads).

The min.n argument can be used to truncate the regional curve where sample depth becomes thin, preventing poorly replicated tail ages from influencing the fit.

This attempts to remove the low frequency variability that is due to biological or stand effects. See the references below for further details on detrending in general, and Biondi and Qeadan (2008) for an explanation of RCS.

A series with no values at all is dropped, with a message naming it, and the rest are standardized as if it had never been there.

References

Biondi, F. and Qeadan, F. (2008) A theory-driven approach to tree-ring standardization: Defining the biological trend from expected basal area increment. Tree-Ring Research, 64(2), 81–96.

Cook, E. R. and Kairiukstis, L. A., editors (1990) Methods of Dendrochronology: Applications in the Environmental Sciences. Springer. ISBN-13: 978-0-7923-0586-6.

Fritts, H. C. (2001) Tree Rings and Climate. Blackburn. ISBN-13: 978-1-930665-39-2.

See Also

detrend, chron, cms, caps, ads

Examples

library(utils)
data(gp.rwl)
data(gp.po)

## Basic use: caps smoother (default), return indices only
gp.rwi <- rcs(rwl = gp.rwl, po = gp.po, biweight = TRUE,
              make.plot = FALSE)
str(gp.rwi)

## Return the regional curve alongside the indices
gp.out <- rcs(rwl = gp.rwl, po = gp.po, biweight = TRUE,
              rc.out = TRUE, make.plot = FALSE)
str(gp.out)

## Plot the regional curve with a title
rcs(rwl = gp.rwl, po = gp.po, biweight = TRUE,
    rc.out = FALSE, make.plot = TRUE, main = "Regional Curve")

## Use the age-dependent spline smoother instead of caps
gp.rwi.ads <- rcs(rwl = gp.rwl, po = gp.po, biweight = TRUE,
                  method = "ads", rc.out = FALSE, make.plot = FALSE)

## Truncate the regional curve where fewer than 5 series contribute.
## Indices for rings beyond the truncated curve are returned as NA.
gp.out.trunc <- rcs(rwl = gp.rwl, po = gp.po, biweight = TRUE,
                    method = "ads", min.n = 5,
                    rc.out = TRUE, make.plot = FALSE)

## Compare the two smoothers visually
op <- par(no.readonly = TRUE)
par(mfrow = c(1, 2))
rcs(rwl = gp.rwl, po = gp.po, biweight = TRUE,
    method = "caps", make.plot = TRUE, main = "caps")
rcs(rwl = gp.rwl, po = gp.po, biweight = TRUE,
    method = "ads", make.plot = TRUE, main = "ads")
par(op)

## Compare caps and ads indices for one series
gp.caps <- rcs(rwl = gp.rwl, po = gp.po, biweight = TRUE,
               method = "caps", rc.out = FALSE, make.plot = FALSE)
gp.ads  <- rcs(rwl = gp.rwl, po = gp.po, biweight = TRUE,
               method = "ads",  rc.out = FALSE, make.plot = FALSE)
cor(gp.caps[[1]], gp.ads[[1]], use = "complete.obs")

## Use subtraction rather than division (e.g. after variance stabilization)
gp.rwi.sub <- rcs(rwl = gp.rwl, po = gp.po, biweight = TRUE,
                  ratios = FALSE, make.plot = FALSE)