Form determination and volume estimation of standing trees: with special reference to permanent sample plots - Anderson, Mark Louden (The University of Edinburgh, 1924)
The purpose of the investigation was to test a method of measuring standing sample trees for Permanent Sample Plot work. Up to date the sample trees have had to be felled before measure- gent, which has many disadvantages.

Form -quotient principles and the assumption of the general applicability of a mathematical formula representing t.o stem-curve or taper of coniferous trees, form the basis of the method.

The Basal area of the tree is found in the usual way. The height is taken with a hypsometer and the Form is arrived at from girth measurements taken with the aid of a ladder up to 25 feet from the ground. These girth measurements are expressed as Form- quotients and they not only give the curve at the base of the stem, but, used as indicators of the Form -class of the stem in conjunctior, with the stem -curve formula, they show the trend of the whole stem curve of the tree. Once this is known, the volume of t're tree can be accurately obtained.

The data were collected from a half -acre plot of 100 stems of European Larch, 60 years old, of Quality Class II, in a fully- stocked wood near Tintern, Monmouthshire. These trees were felled and accurately measured in 10 foot sections and the total volume arrived at in this way is taken to be the true volume.

Thirty sample trees were measured Standing inside the plot by the proposed method.

The plot was also measured in the usual way by felling 8 sample trees outside the plot area. These 8 trees were also treated as if they had been measured standing.

The heights were taken with the Abney Level. In the case of the 30 sample trees within the plot, the systematic error came to, -1.47% with a Standard Deviation of 2.65% For the 8 trees out- side the error was -2.35iß. These results are sufficiently exact for the purposes in view.

Rootswelling was found to be present in a11= items. It was found that this could be satisfactorily eliminated graphically from the standing tree Form- quotient measurements. The average rootswelling for the 30 sample trees was 2.04 inches of the breast -height girth 1 1.079 S. Dev. From the same trees felled, the rootswelling worked out at 2.21 inches with a S. Dev. of .91 inches. Similar satisfactory results were found in the ease of the 8 outside trees.

From an examination of rootswelling over the plot area there seemed good reason for assuming that the degree of rootswelling is closely dependent upon local ground variations.

An examination of the percentage of Bark in the girth up the stem, showed that this remains very uniform up to the 70% height - quotient at least, so that the use of the over -bark girth measure - meats for finding the stem curve was justified in this case, no bark -measuring instrument being available.

The.Form-class was arrived at graphically from the standing tree measurements. For the 30 sample trees a value of .693 with a S. Dev. of 1 .037 was found. For the 8 sample trees the mean Form -class was .721. The true average for the whole plot from the felled stems came to .703 with a S. Dev. of .032. The positive error in the case of the 8 trees was clearly due to the negative error in the height determination.

The average difference in the over -bark volume of individual trees between standing tree measurements and felled tree sectional measurements amounted to - 1.365¡ with a S. Dev. of 1 3.413 %. This corresponds to a maximum variation for a single stem of x.10,2¡, which is highly satisfactory. The negative error is almost certainly due to the under -estimation of Form -class from graphs based on a limited number of Form -quotients obtained up to 25 feet only. Greater accuracy can be secured if one or more additional Form -quotients are measured. The type of wood and size and type of tree were against the method, so that as a rule better results may be expected.

Various methods of arriving at the total volume of the plot were applied, based on data from both sets of sample trees measured standing. Better results were obtained from the data from the 8 outside trees and in no case was the error larger than 1 %0. Errors up to - 3.19% were obtained with the data from the 30 inside trees which were partly due to the unrepresentative character of these trees and partly to the error involved in obtaining the Form -class and volume by the new method.

The difference between the actual volume and that found by the usual sample plot method was only -0.73% which is extremely. good, but not better, in this case, than the result from the same trees measured standing.

It thus appears that the proposed method is quite as accurate as the one in use, even for a single volume measurement. For recurring measurements, it would undoubtedly, therefore, be much more valuable, since the error involved in the use of different sets of sample stems would be eliminated.

The graphical method could therefore be retained but the data for constructing the graphs would be obtained from standing sample trees.

Further investigation is, however, necessary to see whether the method is completely applicable to other species and types of wood. If this, as seems likely, proves to be so, then a wide field for accurate research into tree -form is opened up.