Volume tables for small trees of larch (Larix sp.) in the southern part of

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Volume tables for small trees of larch (Larix sp.) in the southern part of Belgium J. RONDEUX AND D. PAUWELS Unit of Forest Management and Economy, Gembloux Agricultural University, Passage des Déportés 2, B-5030 Gembloux, Belgium

Introduction Volume tables have been constructed for European larch (Larix decidua Mill.), Japanese larch (Larix kaempferi (Lamb.) Carr.) and hybrid larch (Larix 3 eurolepis Henry) trees in the Ardenne (southern part of Belgium), which is a natural region located at elevations ranging from 340 to 550 m on mainly siliceous rocks. The application of the proposed tables is only for trees whose diameters (d.b.h.) are less than 22 cm over bark at 1.3 m above ground level. They are particularly useful for estimating total tree volume of trees (excluding branches) of early thinnings and volume increment of small-sized trees in genetic improvement experiments. The volume equations are based on data collected over a wide range of site conditions. In these regional volume tables, the volumes (total volume of the stem and volume to an upper diameter limit of 7 cm) are correlated with both d.b.h. and total height.

Material and methods The data used in the construction of these tables came from 242 felled sample trees (67 per cent Japanese larch, 14 per cent European larch and 19 per cent hybrid larch) in 15 even-aged stands located in the Ardenne. The site index of the stands © Institute of Chartered Foresters, 2000

varied from 1 to 5 (22–34 m dominant height at 50 years) according to Pauwels et al. (1999) and ages ranged from 12 to 46 years. Due to their small size, the trees come from thinnings. To avoid bias effects, the sample comprises trees representative of the different observed social classes in the following proportions: 4 per cent dominant trees, 23 per cent co-dominant trees, 35 per cent intermediate and 38 per cent dominated trees. For each tree the following basic measurements were recorded: • diameter over bark at breast height (1.3 m) in cm; • diameter over bark in cm at different points up the stem (stump level, 0.5 m and every metre); • total height in cm. Total volume and volume to 7 cm top diameter have been estimated by summing the volumes of successive logs (form being assumed to be a frustum of a cone). vv = pL (d2 + d2 + d d ) = ––– f 0 f v = 12 0 where: L = log length, d0 = small end diameter, df = large end diameter. Table 1 shows some statistical parameters of the sample trees. Forestry, Vol. 73, No. 1, 2000

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Table 1: Mean and dispersion parameters of independent and dependent variables

Variable d.b.h. (cm) Total height (m) Total volume (m3) Bole volume (m3) (to the limit of 7 cm)

Mean

Coefficient of variation (%)

Minimum

Maximum

14.7 15.5 0.1583 0.1516

26.6 27.0 65.4 69.2

5 5.3 0.0079 0.0005

22 23.1 0.4549 0.4514

Table 2: Regression equations of the volumes over diameter and total height Equations v = 4.01782e – 5 * d2 * h v7 = –0.008677 + 4.06987e – 5 * d2 * h

It has been assumed that the general form of the larch species did not affect the tree volume significantly.

Results Relationships have been established between diameter, total height and volumes using nonweighted regression analysis because the use of transformed variables is not required by the heterogeneity of the variance of volume. The most suitable functions with regard to the residual standard coefficient (CRV, which is the residual standard deviation divided by the mean volume) and determination coefficient (R2) for expressing these relationships are shown in Table 2. In these equations v is the volume of the stem (in m3), v7 is the volume to an upper limit of 7 cm in diameter (in m3), d is the diameter at 1.3 m above the ground level (in centimetres) and h is the total height from the ground level to the apical bud (in centimetres). Table 3 gives the results for diameters ranging from 6 cm to 21 cm (3 cm class interval) and total heights ranging from 6 m to 22 m (2 m class interval). It predicts both total and bole volumes. The accuracy of the volume tables has been tested on an independent data set of 45 felled larch trees observed in 14 stands located in the same region to which the equations refer. The relative

R2 (%)

CRV (%)

98.3 98.2

8.6 9.4

means error (difference between measured and estimated volumes divided by measured volumes) is 0.35 per cent for total volume and 2.2 per cent for bole volume. The volume tables give unbiased estimation of the volumes. In comparison, the use of the general volume table (that only concerns the bole volume) of Dagnelie et al. (1999) constructed for diameters ranging from 8 cm to 75 cm and total heights ranging from 10 m to 36 m gives over-estimations (relative mean error of 24.5 per cent). Acknowledgements This research was financially supported by the Région Wallonne, Ministère de l’Environnement, des Ressources Naturelles et de l’Agriculture. We are grateful to E. Lorent and S. Marenne for valuable help in collecting data and to forest owners and the Forest Service for the gift of the sampled trees.

References Dagnelie, P., Palm, R., Rondeux, J. and Thill, A. 1999 Tables de Cubage des Arbres et des Peuplements Forestiers. Les Presses Agronomiques, Gembloux, 128pp. Pauwels, D., Thibaut, A., Lejeune, P. and Rondeux, J. 1999 Elaboration de courbes de croissance en hauteur dominante pour les mélèzes (Larix decidua Mill, et Larix kaempferi (Lamb.) Carr.) en Belgique méridionale. Ann. Sci. For. 56, 27–34.

Received 14 May 1999

0.0060 0.0243 0.0499 0.0829 0.1232 0.1708

0.0145 0.0325 0.0579 0.0904 0.1302 0.1772

Bold values correspond to tree sizes outside the data range.

0.0116 0.0260 0.0463 0.0723 0.1041 0.1417

0.0089 0.0309 0.0617 0.1012 0.1496 0.2067

0.0174 0.0391 0.0694 0.1085 0.1562 0.2126

0.0118 0.0375 0.0734 0.1195 0.1759 0.2426

0.0202 0.0456 0.0810 0.1266 0.1822 0.2481

0.0148 0.0441 0.0851 0.1378 0.2023 0.2785

0.0231 0.0521 0.0926 0.1446 0.2083 0.2835

0.0177 0.0507 0.0968 0.1562 0.2287 0.3144

0.0260 0.0586 0.1041 0.1627 0.2343 0.3189

0.0206 0.0573 0.1085 0.1745 0.2551 0.3503

0.0289 0.0651 0.1157 0.1808 0.2604 0.3544

0.0236 0.0638 0.1203 0.1928 0.2814 0.3862

0.0318 0.0716 0.1273 0.1989 0.2864 0.3898

6 9 12 15 18 21

0.0030 0.0177 0.0382 0.0646 0.0968 0.1349

0.0001 0.0111 0.0265 0.0463 0.0704 0.0990

d.b.h. 0.0087 0.0195 0.0347 0.0542 0.0781 0.1063

6 8 10 12 14 16 18 20 22 —————––— ——–——–—— —–————–— ——–—–——— —–———–—— ——–——–—— ——–——–—— ——–——–—— —–———–—— v v7 v v7 v v7 v v7 v v7 v v7 v v7 v v7 v v7

Height (m)

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Table 3: Tree and bole volume tables for small trees of larch (d.b.h. ≤ 22 cm)

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