powt function

Power Transformation of Tree-Ring Data

Power transformation of tree-ring width. UTF-8

powt(rwl, method = "universal", rescale = FALSE,
     return.power=FALSE)

Arguments

• rwl: a data.frame, typically of raw tree-ring widths series, such as that produced by read.rwl or read.fh
• method: a character vector to determine the transform method. See details below. Possible values are either "universal" or "cook." Pattern matching is used.
• rescale: logical flag. If TRUE then each transformed series is rescaled to have the orginal mean and standard deviation of the input data. See details.
• return.power: logical flag. If TRUE then the power estimate(s) is returned.

Returns

Either an object of class c("rwl", "data.frame") containing the power transformed ring width series with the series in columns and the years as rows or in the case of a single series, a possibly named vector of the same. With class rwl, the series ID s are the column names and the years are the row names.

If return.power=TRUE the returned object is a list containing the power transformed data and a numeric with the power estimate(s) used to transform the data.

Details

In dendrochronology, ring width series are sometimes power transformed to address heteroscedasticity.

The classic procedure used by method="cook"

is a variance stabilization technique implemented after Cook & Peters (1997): for each series a linear model is fitted on the logs of level and spread, where level is defined as the local mean $M_t = (R_t + R_(t-1))/2$ with ring widths R, and spread S is the local standard deviation defined as $S_t = |R_t - R_(t-1)|$. The regression coefficient b from a linear model $log S = k + b log M$ is then used for the power transform $R*_t = R_t^(1-b)$.

The procedure above is modified with method="universal" where all samples are used simultaneously in a linear mixed-effects model with time (year) as a random effect: lmer(log S ~ log M + (1|year). This "universal" or "signal free" approach accounts for the common year effect across all of the series in rwl and should address that not every year has the same change in environmental conditions to the previous year.

The rescale argument will return the series with a mean and standard deviation that matches the input data. While this is a common convention, users should note that this can produce negative values which can be confusing if thought of as "ring widths."

References

Cook, E. R. and Peters, K. (1997) Calculating unbiased tree-ring indices for the study of climatic and environmental change. The Holocene, 7 (3), 361 370.

Author(s)

Christian Zang implemented the Cook and Peters method. Stefan Klesse conceived and wrote the universal method. Patched and improved by Mikko Korpela and Andy Bunn.

Examples

library(utils)
data(zof.rwl)
powtUniversal <- powt(zof.rwl, method = "universal")
powtCook <- powt(zof.rwl, method = "cook")

op <- par(no.readonly = TRUE)
par(mfcol = c(1, 3))
hist(summary(zof.rwl)$skew,
     breaks = seq(-2.25,2.25,by=0.25),
     main="Raw Data",xlab="Skew")
hist(summary(powtUniversal)$skew,
     breaks = seq(-2.25,2.25,by=0.25),
     main="Universal POWT",xlab="Skew")
hist(summary(powtCook)$skew,
     breaks = seq(-2.25,2.25,by=0.25),
     main="Cook POWT",xlab="Skew")
par(op) # restore graphical parameters