R: Detrend a Ring-Width Series

detrend.series {dplR} | R Documentation

## Detrend a Ring-Width Series

### Description

Detrend a tree-ring series by one of two methods, a smoothing spline or a statistical model. The series and fits are plotted by default.

### Usage

    detrend.series(y, y.name = "", make.plot = TRUE,
                   method = c("Spline", "ModNegExp",
                   "Mean", "Ar", "Friedman", "ModHugershoff"),
                   nyrs = NULL, f = 0.5, pos.slope = FALSE,
                   constrain.nls = c("never", "when.fail", "always"),
                   verbose = FALSE, return.info = FALSE,
                   wt, span = "cv", bass = 0, difference = FALSE)

### Arguments

`y` | a `numeric` vector. Usually a tree-ring series.
`y.name` | an optional `character` vector to name the series for plotting purposes.
`make.plot` | a `logical` flag. Makes plots of the raw data and detrended data if `TRUE`.
`method` | a `character` vector to determine the detrending methods. See details below. Possible values are all subsets of `c("Spline", "ModNegExp", "Mean", "Ar", "Friedman", "ModHugershoff")`. Defaults to using all the available methods.
`nyrs` | a number controlling the smoothness of the fitted curve in method `"Spline"`, defaults to 0.67 of series length if `nyrs` is `NULL`. See `ffcsaps`.
`f` | a number between 0 and 1 giving the frequency response or wavelength cutoff in method `"Spline"`. Defaults to 0.5. See `ffcsaps`.
`pos.slope` | a `logical` flag. Will allow for a positive slope to be used in method `"ModNegExp"`. If `FALSE` the line will be horizontal.
`constrain.nls` | a `character` string which controls the constraints of the `"ModNegExp"` model and and the `"ModHugershoff"` model which are fit using nonlinear least-squares via `nls`. The value is an answer to the question: When should the parameters of the `nls` function be constrained? The options are `"never"`: do not constrain (the default), `"when.fail"`: only compute the constrained solution if the unconstrained fit contains other than positive values, and `"always"`: return the constrained solution, even if the unconstrained one would have been valid. See ‘Details’.
`verbose` | a `logical` flag. Write out details to the screen?
`return.info` | a `logical` flag. If `TRUE`, details about models and data will be added to the return value. See ‘Value’.
`wt` | a `numeric` vector of case weights for method `"Friedman"`. The default means equals weights.
`span` | a `numeric` value controlling method `"Friedman"`, or `"cv"` (default) for automatic choice by cross-validation. See `supsmu`.
`bass` | a `numeric` value controlling the smoothness of the fitted curve in method `"Friedman"`. See `supsmu`.
`difference` | a `logical` flag. Compute residuals by substraction if TRUE, otherwise use division.

### Details

This detrends and standardizes a tree-ring series. The detrending is the estimation and removal of the tree’s natural biological growth trend. The standardization is done by dividing each series by the growth trend to produce units in the dimensionless ring-width index (RWI). There are currently six methods available for detrending although more are certainly possible. The methods implemented are a smoothing spline via `ffcsaps` (`method = "Spline"`), a modified negative exponential curve (`method = "ModNegExp"`), a simple horizontal line (`method = "Mean"`), the residuals of an AR model (`method = "Ar"`), Friedman's Super Smoother (`method = "Friedman"`), or a modified Hugershoff curve (`method = "ModHugershoff"`).

The `"Spline"` approach uses an 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 `ffcsaps`.

The `"ModNegExp"` approach attempts to fit a classic nonlinear model of biological growth of the form f(t) = a exp(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 >= 0, b <= 0 and k >= 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 `"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 `"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 `"ModHugershoff"` approach attempts to fit a Hugershoff model of biological growth of the form f(t) = a t^b exp(-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 >= 0, b >= 0 and d >= 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.

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 exp(b t) + k) for detrending. It is, of course, up to the user to determine the best detrending method for their data.

See the references below for further details on detrending.

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`.

### Value

If several methods are used, returns a `data.frame` containing the detrended series (`y`) according to the methods used. The columns are named and ordered to match `method`. If only one method is selected, returns a vector.

If `return.info` is `TRUE`, the return value is a `list` with four parts:

`series` | the main result described above (`data.frame` or vector)
`curves` | the curve or line used to detrend `series`. Either a `data.frame` or vector.
`model.info` | Information about the models corresponding to each output series. Whereas `series` may return a vector, `model.info` is always a list where each top level element corresponds to one selected method. Also these elements are named and arranged according to the methods selected. Each element is a list with some of the following sub-elements, depending on which detrending method was actually used: n.zeros See `"data.info"` below. Always present. zero.years See `"data.info"`. Always present. method The method actually used for detrending. One of `"Mean"`, `"Line"`, `"ModNegExp"`, `"Spline"` or `"Ar"`. Always present. mean Mean of the input series, missing values removed. Only for method `"Mean"`. coefs Coefficients of the model. Methods `"Line"` and `"ModNegExp"`. formula The `"ModNegExp"` `formula`. is.constrained A `logical` flag indicating whether the parameters of the `"ModNegExp"` model were constrained. Only interesting when argument `constrain.nls` is set to `"when.fail"`. nyrs The value of `nyrs` used for `ffcsaps`. Only for method `"Spline"`. order The order of the autoregressive model, selected by AIC (Akaike information criterion). Only for method `"Ar"`. ar The autoregressive coefficients used by method `"Ar"`. A `numeric` vector ordered by increasing lag.
`data.info` | Information about the input series: number (`"n.zeros"`) and location (`"zero.years"`) of zero values. If the locations are in a `character` vector, they are years. Otherwise they are indices to the input series.

### Author(s)

Andy Bunn. Patched and improved by Mikko Korpela. A bug fix related to negative output values is based on work by Jacob Cecile.

### References

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`

### Examples

    library(stats)
    library(utils)
    ## Use series CAM011 from the Campito data set
    data(ca533)
    series <- ca533[, "CAM011"]
    names(series) <- rownames(ca533)
    # defaults to all six methods
    series.rwi <- detrend.series(y = series, y.name = "CAM011", verbose=TRUE)
    # see plot with three methods
    series.rwi <- detrend.series(y = series, y.name = "CAM011",
                                 method=c("Spline", "ModNegExp","Friedman"),
                                 difference=TRUE)
    # see plot with two methods
    # interesting to note difference from ~200 to 250 years
    # in terms of what happens to low frequency growth
    series.rwi <- detrend.series(y = series, y.name = "CAM011",
                                 method=c("Spline", "ModNegExp"))
    # see plot with just one method and change the spline
    # stiffness to 50 years (which is not neccesarily a good choice!)
    series.rwi <- detrend.series(y = series, y.name = "CAM011",
                                 method="Spline",nyrs=50)

    # note that method "Ar" doesn't get plotted in first panel
    # since this approach doesn't approximate a growth curve.
    series.rwi <- detrend.series(y = series, y.name = "CAM011",
                                 method="Ar")

    # note the difference between ModNegExp and ModHugershoff at the
    # start of the series. Also notice how curves, etc. are returned
    # via return.info
    data(co021)
    series <- co021[, 4]
    names(series) <- rownames(co021)
    series.rwi <- detrend.series(y = series, y.name = names(co021)[4],
                                 method=c("ModNegExp", "ModHugershoff"),
                                 verbose = TRUE, return.info = TRUE,
                                 make.plot = TRUE)

[Package dplR version 1.7.2 Index]