R: Calculate Gleichläufigkeit

glk {dplR} | R Documentation

## Calculate Gleichläufigkeit

### Description

This function calculates the Gleichläufigkeit and related measures for a given set of tree-ring records.

### Usage

      glk(x, overlap = 50, prob = TRUE)
      glk.legacy(x)

### Arguments

`x` | a `data.frame` of tree-ring data with records in columns, and years as rows.
`overlap` | integer value with minimal length of overlapping growth changes (compared number of tree rings - 1). Comparisons with less overlap are not compared.
`prob` | if `TRUE` then the probability of exceedence of the Gleichläufigkeit will be calculated

### Details

Gleichläufigkeit is a classical agreement test based on sign tests (Eckstein and Bauch, 1969). This function implements Gleichläufigkeit as the pairwise comparison of all records in data set. This vectorized implementation is faster than the previous version and follows the original definition (Huber 1942), instead of the incorrect interpretation that has been used in the past (Schweingruber 1988, see Buras/Wilmking 2015 for the correction).

The probability of exceedence (p) for the Gleichläufigkeit expresses the chance that the Gleichläufigkeit is incorrect. The observed value of the Gleichläufigkeit is converted to a z-score and based on the standard normal curve the probability of exceedence is calculated. The result is a matrix of all p-values (Jansma 1995, 60-61, see also Visser 2020).

Note that prior to dplR version 1.7.2, `glk` did not have the `overlap` or `prob` and returned a `matrix` with just the Gleichläufigkeit for all possible combinations of records. That function can still be accessed via `glk.legacy`.

### Value

The funtions returns a named `list` of two or three matrices (p_mat is optional if `prob = TRUE`):

1. glk_mat: `matrix` with Gleichläufigkeit

2. overlap: `matrix` with number of overlapping growth changes.This is the number of overlapping years minus one.

3. p_mat: `matrix` of all probabilities of exceedence for all observed Gleichläufigkeit values.

The matrices can be extracted from the list by selecting the name or index number. If two curves have less than 3 years of overlap, Gleichläufigkeit cannot be computed, and `NA` is returned. To calculate the global glk of the dataset `mean(x$glk_mat, na.rm = TRUE)`.

### Author(s)

Christian Zang. Patched and improved by Mikko Korpela. Improved by Allan Buras. Further improved and expanded by Ronald Visser and Andy Bunn

### References

Buras, A. and Wilmking, M. (2015) Correcting the calculation of Gleichläufigkeit, Dendrochronologia 34, 29-30. DOI: https://doi.org/10.1016/j.dendro.2015.03.003

Eckstein, D. and Bauch, J. (1969) Beitrag zur Rationalisierung eines dendrochronologischen Verfahrens und zur Analyse seiner Aussagesicherheit. Forstwissenschaftliches Centralblatt, 88(1), 230-250.

Huber, B. (1943) Über die Sicherheit jahrringchronologischer Datierung. Holz als Roh- und Werkstoff 6, 263-268. DOI: https://doi.org/10.1007/BF02603303

Jansma, E., 1995. RemembeRINGs; The development and application of local and regional tree-ring chronologies of oak for the purposes of archaeological and historical research in the Netherlands, Nederlandse Archeologische Rapporten 19, Rijksdienst voor het Oudheidkundig Bodemonderzoek, Amersfoort

Schweingruber, F. H. (1988) Tree rings: basics and applications of dendrochronology, Kluwer Academic Publishers, Dordrecht, Netherlands, 276 p.

Visser, R.M. (2020) On the similarity of tree-ring patterns: Assessing the influence of semi-synchronous growth changes on the Gleichläufigkeit for big tree-ring data sets,Archaeometry, 63, 204-215 DOI: https://doi.org/10.1111/arcm.12600

### See Also

`sgc` `sgc` is an alternative for `glk`)

### Examples

    library(utils)
      data(ca533)
      ca533.glklist <- glk(ca533)
      mean(ca533.glklist$glk_mat, na.rm = TRUE)

[Package dplR version 1.7.2 Index]