This detrends and standardizes a tree-ring series. The detrending is the estimation and removal of the tree’s natural biological growth trend. The default standardization is done by dividing each series by the growth trend to produce units in the dimensionless ring-width index (RWI). If difference is TRUE, the index is calculated by subtraction. Values of zero (typically missing rings) in y are set to 0.001.
There are currently seven methods available for
detrending although more are certainly possible. The methods
implemented are an age-dependent spline via ads
(method = "AgeDepSpline"), the residuals of an AR model
(method = "Ar"), Friedman's Super Smoother
(method = "Friedman"), a simple horizontal line
(method = "Mean"), or a modified Hugershoff
curve (method = "ModHugershoff"), a modified negative exponential
curve (method = "ModNegExp"), and a smoothing spline via caps (method = "Spline").
The "AgeDepSpline" approach uses an age-dependent spline with an initial
stiffness of 50 (nyrs=50). See ads. If some of the fitted
values are not positive then method "Mean" is used. However, this is
extremely unlikely.
The "Ar" approach is also known as prewhitening where the detrended
series is the residuals of an ar model divided by the
mean of those residuals to yield a series with white noise and a mean of one.
This method removes all but the high frequency variation in the series
and should only be used as such.
The "Friedman" approach uses Friedman’s ‘super
smoother’ as implemented in supsmu. The parameters
wt, span and bass can be
adjusted, but periodic is always set to FALSE. If some of
the fitted values are not positive then method "Mean" is used.
The "Mean" approach fits a horizontal line using the mean of
the series. This method is the fallback solution in cases where the
"Spline" or the linear fit (also a fallback solution itself)
contains zeros or negative values, which would lead to invalid
ring-width indices.
The "ModHugershoff" approach attempts to fit a Hugershoff
model of biological growth of the form \(f(t) = a t^b e^{-g t} + d\), where the argument of the function is time, using
nls. See Fritts (2001) for details about the
parameters. Option constrain.nls gives a
possibility to constrain the parameters of the modified negative
exponential function. If the constraints are enabled, the nonlinear
optimization algorithm is instructed to keep the parameters in the
following ranges: \(a \ge 0\), \(b \ge 0\) and
\(d \ge 0\). The default is to not constrain the parameters
(constrain.nls = "never") for nls but
warn the user when the parameters go out of range.
If a suitable nonlinear model cannot be fit
(function is non-decreasing or some values are not positive) then a
linear model is fit. That linear model can have a positive slope
unless pos.slope is FALSE in which case method
"Mean" is used.
The "ModNegExp" approach attempts to fit a classic nonlinear
model of biological growth of the form \(f(t) = a e^{b t} + k\), where the argument of the function is time, using
nls. See Fritts (2001) for details about the
parameters. Option constrain.nls gives a
possibility to constrain the parameters of the modified negative
exponential function. If the constraints are enabled, the nonlinear
optimization algorithm is instructed to keep the parameters in the
following ranges: \(a \ge 0\), \(b \le 0\) and
\(k \ge 0\). The default is to not constrain the parameters
(constrain.nls = "never") for nls but
warn the user when the parameters go out of range.
If a suitable nonlinear model cannot be fit
(function is non-decreasing or some values are not positive) then a
linear model is fit. That linear model can have a positive slope
unless pos.slope is FALSE in which case method
"Mean" is used.
The "Spline" approach uses a spline where the frequency
response is 0.50 at a wavelength of 0.67 * “series length in
years”, unless specified differently using nyrs and
f in the function caps. If some of the fitted
values are not positive then method "Mean" is used.
These methods are chosen because they are commonly used in
dendrochronology. There is a rich literature on detrending
and many researchers are particularly skeptical of the use of the
classic nonlinear model of biological growth (\(f(t) = a e^{b t} + k\)) for detrending. It is, of course, up to the
user to determine the best detrending method for their data.
Note that the user receives a warning if a series has negative values in the
fitted curve. This happens fairly commonly with with the ‘Ar’ method
on high-order data. It happens less often with method ‘Spline’ but
isn't unheard of (see ‘Examples’). If this happens, users should look
carefully at their data before continuing. Automating detrending and not
evaluating each series individually is folly. Remember, frustration over
detrending is the number one cause of dendros going to live as hermits in
the tallgrass prairie, where there are no trees to worry about.
See the references below for further details on detrending. It's a dark art.