Press release 27.9.2006

A sample order statistic or a ”quantile tree” is a tree whose diameter and rank are visually measured. The quantile tree approach has been shown to improve the accuracy of forest inventory results. Quantile trees can be, for example, the smallest tree, the second largest tree or the tree closest to the plot centre. A collaborative study of the Finnish Forest Research Institute (Metla), the University of Helsinki and the University of Joensuu showed that using the smallest tree as the quantile tree was the best way to improve accuracy of inventories. Measuring the minimum tree diameter on just one plot reduced the standard error of the stand’s stem number by 8 % and the standard error of energy wood volume by 6 %.

The finding is interesting from the measuring technique point of view as well: visual assessment of the smallest tree is easier than selecting any other quantile tree; on relascope sample plots trees are counted at only a close distance from the measuring staff. Additionally, nearby trees are reached more quickly.

Another good technique is to measure the tree closest to the plot centre. These strategies produced better predictions than, for example, using the maximum diameter, one approaching the log-size limit or selecting a tree randomly. It is recommended that quantile tree measurements be performed on several plots: the results are better if one minimum quantile tree is measured on two plots rather than taking the two smallest trees on a single plot.

The data set comprised 512 stands and on each site, three plots were selected where the locations and diameters of trees were measured. Error-free quantile tree measurements were then simulated on the test plots. The standard error and bias calculated for volume, log-sized volume, energy wood volume and stem number were used as metrics for the accuracy of the inventory.

In particular, using the minimum trees reduced the standard error of stem number and energy wood volume. However, simultaneously, it also increased the bias for stem number, total volume and log-sized volume. Therefore, the quantile tree approach is justified when a small standard error overrides the effect in small bias. The results are dependent on the diameter distribution prediction model used, and they may change if another model is used.

The quantile tree approach seems to provide a relatively accurate prediction for any part of the diameter distribution.

The study was conducted in collaboration between the Finnish Forest Research Institute (Metla), the Universities of Joensuu and Helsinki and it was funded by the Academy of Finland.

**Publication:** Mehtätalo, L., Maltamo, M. and Kangas, A. 2006. The use of quantile trees in the prediction of the diameter distribution of a stand. Silva Fennica 40(3): 501-516.

**Additional information:**

- Lauri Mehtätalo, Yale School of Forestry and Environmental Studies, USA, lauri.mehtatalo @ metla.fi
- Matti Maltamo, Joensuun yliopisto, matti.maltamo @ joensuu.fi, tel. +358 13 251 3615
- Annika Kangas, Helsingin yliopisto, annika.kangas @ helsinki.fi, tel.+ 358 9 191 58177