After the normalization has been done, comparison of two curves are based on calculating correlation coefficient values out of all possible overlapping positions for the two curves. Such calculations can be quickly done with modern computers.

There are other methods for scoring how well two samples match at a certain overlapping position. One of them is the "Gleichläufigkeit".

The Gleichläufigkeit score is based on counting how well the two trees have followed each other in growth over the years when comparing at a certain overlapping position.
Both trees growing more than the previous year gives a plus point. Both trees growing less than the previous year also gives a plus point.
One tree growing more, the other growing less gives a minus point.
The sum of these points divided by the number of years compared, gives the "Gleichläufigkeit". For a small update of this algorithm, please see the note at the end of this section!

As a few CDendro users asked for this type of score, it has been made available in CDendro. Though you have to turn on a setting to make it displayed in tables. In the diagram below, please find an example.

As you can see in the example above an incorrect dating may easily have a higher Gleichläufigkeit value than the correct dating. Typically this occurs when comparing a log from one area to a reference curve from - not the same but - a neighbour area.

In discussions, I have met people who strongly defend the Gleichläufigkeit values and pretend they are a good complement to other values. Today I would partly agree - though only when "as a complement" is being stressed. Gleichläufigkeit values are available within CDendro so you can build your own opinion of its usefulness. You can turn on or off Gleichläufigkeit calculations in the panel "Options for normalization of ring widths and for matching".

Here is a citation from a paper by Douglas Keenan (see the section on Other sites):

Another statistical method used in tree-ring matching relies on what I will call "g-scores" 1). The g-score is the proportion (or percentage) of years in which the two trees ring widths increased or decreased together (i.e. increased or decreased from the prior year). This method thus ignores the size of the increase or decrease. Because it ignores so much information, the g-score method might be expected to be less reliable than the t-score method [TTEST in CDendro]. Experience at Hohenheim, Germany, where g-scores were previously used, seems to support this: matches were thrice found to be in error, each time after strong assertions of reliability [Baillie, 1995: ch.2; Spurk et al., 1998]. Early trials in Ireland also indicated problems, and the method was abandoned there [Baillie, 1982: p.81–82,95]. Other testing found very high g-scores for matches known to be incorrect [Schweingruber, 1989: p.77]. In the pre-computer age, though, g-scores had one advantage: being easy to calculate. They are still sometimes used, perhaps out of habit.

1) The g-score is commonly called "Gleichläufigkeit" [Schweingruber, 1989] or "trend".

An exact description on calculating Gleichläufigkeit is found in the reference "BECKER AND GERMAN DENDROCHONOLOGY", see the section on Other sites.

First, we will see how a group of 80 years long segments (blocks) taken out of samples (members) of the ITRDB collection swed308.rwl (Saltsjöbaden) crossdate to the rest of that collection. We will then first use the CDendro P2Yrs method for crossdating (proportion of last two years growth) and then we will use the GLK method.

After that we will do the same crossdating with the reference taken from an island some 20 miles East of Saltsjöbaden. For that we will use a mean value curve created from the ITRDB collection swed302.rwl.

To see a summary of this short investigation, scroll down to the end of this section!

That was using GLK to crossdate a tree towards a reference consisting of trees which had grown in the very same neighbourhood of the first tree. We will now continue by looking at how GLK works when we try to crossdate trees from one area towards the reference of a more distant but anyhow neighbour area.

This is what happens when we use GLK values to crossdate samples towards a reference which is not from the very same area as the samples to be crossdated!

The problem gets worse with a lower correlation coefficient value between references from the two areas. The correlation coefficient between the Saltsjöbaden and the Nämdö collection is at 0.63 measured with the standard methods of CDendro. When correlation coefficient like P2Yrs is at 0.7 for two references from nearby areas, the problem with the GLK values is not as worse as shown above. Longer blocks also lessens the problem.

To complete the comparisons, we will look at the result of the standard P2YrsL method in CDendro.

Note: If you try to reproduce the results above with your own software, you may get somewhat different percentage values. This easily occurs because the sorting order for best match is undefined when there are more than one best match with exactly the same GLK value. This often occurs because of the construction of the Gleichläufigkeit algorithm.

Allan Buras at the university of Greifswald has remarked that the common GLK value is erronously calculated when two successive ring widths in both curves have their ring width values repeated, i.e. when the width increment (or decrement) from one year to the next happens to be exactly zero in both series. In this case the tree growth is actually similar though that similarity does not give any "credit" to the mean GLK value. This problem is taken care of from CDendro version 7.8.1. For practical usage this update has little relevance.

A concoct example demonstrating the problem is a series measured in millimeters but written to a file with only one decimal. This easily results in many successive ring widths becoming the same. Crossdating that series towards itself will give correlation coefficients of 1.0 as expected but the corresponding Gleichläufigkeit value will be only 0.92 The updated GLK algorithm in CDendro 7.8.1 will produce GLK=1.00 as to be expected.

Reference:
Allan Buras, Martin Wilmking: "Correcting the calculation of Gleichläufigkeit", Dendrochronologia 34 (2015) 29–30.