# Corridor method

## The Besancon corridor method

All information I have on this method comes from Georges Lambert at the University of Franche-Comte, Besancon. Georges Lambert is the inventor of the Besancon variant of this method which is used by a number of dendro labs in France, see note 2 below!

Georges Lambert headed a short description of the method (a poster) as "Standardization by the curve corridor method (polynomial regressions)". Using the nomenclature of CDendro, I would name the method either a normalization method or a detrending method. Within the (development version of) CDendro the method is implemented in both ways, either as a mathematical transformation operating on pure ring width data with the resulting data - looking very much as the ring width curve - fed into a correlation calculus or as a detrending operation where detrended ring width data is used for viewing but can also be fed into another - second - transformation (like the Proportion of last two years growth), from which the data is fed into the correlation calculus.

**Ceiling** First the mean value (mean) and the standard deviation (stddev) are calculated from all ring widths. Then all ring width values above a "ceiling level" of mean + 1.5 * stddev are given that ceiling level value.

**The trend curve** Compute the curving trend from this "ceiled ring width curve" by a polynomial, normally of the degree 3. (An operator may decide to use another degree.)

**Roof trend** and **floor trend** Calculate a roof trend by a polynomial of the same degree as previous using the points above the trend curve. Do the same to get a floor trend out of the points below the trend. Send a message to the operator if the roof and floor curves cross each other.

**Prefiltering** Those ring width values which were "ceiled" above, are now taken into account again. When such a point has another too high point at either side, then it is marked as non-existent, so that it will not be considered for any more analysis (i.e. not take part in correlation analysis). However a sole point surrounded by not too high points, will be left with its "ceiled value".

**Standardize each point** Create a new index value at each point t as

- <math>index(t) = \frac{width(t)-trend(t)}{roof(t)-floor(t)}</math>

**Note 1:
A.** The formula above should not be applied to points which are taken out of consideration during prefiltering. The "width()" value refers to the "ceiled" width value where no value is above mean + 1.5 * stddev.

**B.**Please also note, that the formula above implies that corridor data is a mix of positive and negative numbers, though if shifted up above the zero line it can be plotted as a (green) ring width curve as shown below.

**C.**The original Besancon formula states that the index(t) could be optionally multiplied by any factor for convenience of drawing. This implies that if you get corridor data from e.g. Besancon, that is probably scaled in another way than the CDendro corridor data. Though by using the checkboxes for individual ring width and for norm. scaling that problem can easily be handled.

The two curves above represent the same corridor data, though the "missing points" are drawn differently. CDendro plots the lowest point of a "green corridor curve" at 10% of the distance between the highest and the lowest points of the curve. Then the "missing points" are placed at the zero level as shown above. Lars-Ake 21:10, 14 July 2009 (UTC)

**Note: 2:**

The Besancon corridor method: This computation was inspired from an idea of S. Shiyatov (Shiyatov & al. 1989) and the algorithm revisited by G. Lambert (Lambert 2006) :

Stepan G. Shiyatov, Harold C. Fritts, Robert G. Logfren 1989 - Comparative Analysis of the Standardization Methods of Tree-Ring Chronologies in: *Reginald D. Noble, Juri L. Martin Keith, F. Jensen eds : Proceedings of the second US-USSR Symposium on Air Pollution Effects on Vegetation including Forest Ecosystems*. International Conference of Corvallis, Oregon; Raleigh, North Carolina; Gatlinburg, Tennessee - September 13 - 25, 1988.

Georges Lambert 2006 - *Dendrochronologie, histoire et archéologie, modélisation du temps; le logiciel Dendron II et le projet Historic Oaks*. Research diploma. 2 vol. Besançon (F).