Thinning programme

Thinning has been carried out on t h e sample plots against t h e background of t h e condition of t h e existing stand, t h e quality and position of t h e individual trees a n d an assessment of their development potential. For t h e purpose of constructing yield tables, i t is, however, necessary t o schematise t h e informa- tion about t h e thinning of t h e sample plots. This has been done b y defining the thinning grade, thinning method and thinning interval.

The thinning grade has been characterised b y means of t h e basal area of t h e stand after thinning. The relationship between t h e basal area after thinning a n d top height according t o Fig. 5.1 has been used for regulating t h e thinning grade in all quality classes.

The ratio between t h e mean diameter of t h e thinnings a n d t h e mean dia- meter of t h e stand before thinning defines simply t h e thinning method. The relationship between this ratio a n d t h e mean diameter before thinning is given b y function 5.1.

The thinning interval has been regulated b y making i t dependent on t h e development of t h e top height of t h e stand. Standard programme A assumes a n increase in t o p height of ca 1.5 m between each thinning. This leads t o a thinning interval which mainly lies within t h e limits of t h e material. Programme B has been obtained b y approximately doubling both t h e interval a n d t h e thinning yield. For ease of comparison, t h e same average basal area has been sought after as t h a t in Programme A. Both programmes are illustrated sche- matically in Fig. 5.3.

I t should be emphasised t h a t yield tables constructed in accordance with Programme B are t o be considered as worked examples only. Since t h e limits of t h e material have been greatly exceeded in several respects, t h e calculated stand development involves a considerable degree of uncertainty. In addition, t h e likelihood of poorer timber quality must also be taken into account. The heavy thinning reduces, in other words, t h e opportunities for future choice a n d increases t h e risk of adventitious branching.

14.6. Estimate of basal area increment

The stand's development, up t o t h e point a t which merchantable timber begins t o be produced, is determined both b y quality class, b y t h e method of establishment and b y t h e opening-up of t h e young stand b y cleanings. After this, stand development is regulated b y t h e alternating changes brought about b y thinning a n d growth.

Functions have been derived for calculating basal area increment. The task consists in forecasting increment during t h e period between two successive thinnings. In principle, this m a y be done b y discovering t h e relationship be- tween increment during this period a n d t h e factors which determine increment.

As an expression for these factors variables have been used which express t h e stand's condition a t t h e beginning of t h e growth period.

The calculations have been performed as a stepwise regression analysis, implying t h a t one independent variable a t a time was introduced into t h e regression function, in t h e order in which i t contributed t o decreasing t h e error sum of squares significantly. A correlation coefficient matrix ( h p p d x V) served in t h e derivation of t h e choice of t h e order in which t h e variables should be introduced into t h e analysis. The calculations have been carried o u t according t o a standard programme, on an I B M 1401 a t t h e College's Computer Centre. The results of t h e regression analysis are shown in Appendix VI. Of t h e combination of variables tested, function 14, given below, gave t h e least standard deviation.

T o investigate how closely t h e selected function estimates t h e percentage increment in stands of various types, t h e material was assorted into classes in respect of separate variables. In each class a comparison was made between t h e observed a n d t h e calculated increment. Figures 6.1-6.3 show examples of such comparisons.

14.7. Calculation of top diameter, mean height a n d stand f o r m factor The construction of yield tables implies, t h a t in addition t o t h e relationships discussed above, t o p diameter, mean height a n d t h e stand form factor can be calculated a t various stages of stand development. The necessary relationships have been obtained b y regression analysis of t h e material, a n d t h e functions t h u s obtained are shown in Appendix VII.

14.8. T h e construction and applicability of the yield tables

W i t h regard t o t h e limitations of t h e material, only two treatment options were calculated. These have been tested on four different quality classes, which means t h a t in all, eight yield tables have been prepared. I t was con- sidered t h a t t h e amount of calculation was too small t o justify t h e considerable effort involved in programming t h e calculations for t h e computer. The com- putation was therefore performed manually, using standard calculators.

The beginning of all yield tables has been selected so t h a t t h e t o p height is about 1 5 m and t h e number of stems per hectare before thinning about 1 800.

After adjustment of t h e age t o t h e nearest five years, t h e initial age in t h e various quality classes is as follows:

With t h e aid of t h e sequences of figures in Tab. IV:1, t h e t o p height for t h e quality classes given above could be calculated. The mean diameter of t h e initial stand was then obtained b y substituting t h e values for stem number a n d t o p height in function 4.1.

The increment function (function VI.14) should be employed with some caution. The reason for this is t h a t t h e t o p diameter ( d d o m ) included as variable in t h e increment function was calculated with t h e aid of a static function (VII.1) in t h e construction of t h e tables. The function has, as independent variables, only hdOm a n d h,,,. I t should give a good estimate of dd,, for stands which are near t h e mean for t h e material in respect of density. The thinning programme employed fulfils this requirement. If ddo, is influenced b y stand density, t h e function should provide a poorer estimate as soon as density deviates from t h e mean for t h e material. The negligible residual scatter about t h e function does not indicate, however, t h a t ddom in t h e present function has been much affected b y stand density. This notwithstanding, t h e problem deserves closer study. However, shortness of time has made this impossible.

The calculations have been carried o u t stepwise a t five-year intervals, even though t h e thinning interval comprised two or several five-year periods.

In t h e construction of t h e yield tables, t h e development of t o p height has been assumed t o follow t h e derived height development curves (see 3.2 a n d Appendix I\').

The yield tables given in Appendix V I I I show t h e development of t h e main stand and t h e yield from t h e first thinning. Previously removed cleanings a n d small trees are t h u s not shown in t h e tables. Cleanings are economically un-

interesting. Subsequent cleanings include, however, merchantable trees, b u t t o such a small extent t h a t i t is not profitable t o make use of them. In other contexts, however, as when i t is necessary t o compare t h e volume production in beech with t h a t of other tree species, i t is necessary t o know t h e total yield.

A summary calculation gives t h e following additional quantities:

Initial stand Calculated supplement for cleanings a n d age t o p height small trees

m m3 (stem volume

including bark)

6 0 1 4 , l 7 0

50 14,4 7 2

45 15,3 88

4 0 15,5 9 1

Yield tables of t h e t y p e presented here reproduce t h e average stand develop- ment and yield when quality class, t h e initial stand a n d t h e thinning programme are known. The yield in individual stands therefore deviates from t h e tables, as a rule. The deviations depend partly on experimental errors, e.g. errors in estimating t h e basal area increment, and partly on t h e influence of factors which are not taken into account b y t h e variables in t h e increment function.

The residual scatter in basal area increment m a y be seen from t h e standard deviation about t h e function. For t h e increment function employed, t h e standard deviation was 17.1 per cent of t h e mean of t h e percentage basal area increment for t h e material.

Naslund (1936) calculated t h a t t h e basal area increment for a growth period of five years can be estimated for pine stands with a standard error of about nine per cent. If a similar situation obtains in t h e case of beech stands, t h e other component in t h e standard deviation (S) could be calculated according t o t h e formula

The variation in yield which can be ascribed t o different conditions for basal area increment within t h e same height quality class can be brought out b y increasing or decreasing pg when forecasting yield b y means of t h e above standard deviation. As a n example i t was decided t o construct a table for Beech Height Quality Class 28 (Beech 28), for which purpose pg, calculated according t o t h e increment function, was multiplied b y t h e factor 1,15. The.

increase in basal area increment brought about a n increase in volume increment of about 1 5 per cent. For reasons discussed in 8.4, this calculation seems t o be unreliable. The constructed yield table has therefore not been published. I t is, however, clear t h a t t h e variation in increment t o be expected within t h e same height quality class, as a consequence of unexplained site differences, is con- siderably greater t h a n t h e yield difference between e.g. t h e two thinning programmes A a n d B. According t o t h e present yield tables, t h e difference in average increment between these two programmes is only one or two per cent.

I n using t h e tables, local deviations from them should be taken into account.

This is most reliably done b y observing development on sample plots in beech stands for a long period. The sample plots reported in t h e present paper seem in m a n y cases t o be capable of use for this purpose.

14.9. Distribution of volume by diameter classes

For calculating e.g. t h e outturn of various asortments, a n d their value, i t is necessary t o know t h e distribution of production b y diameter classes. Since t h e construction of t h e yield tables makes i t possible only t o express stand development in t h e form of averages, i t is necessary t o describe t h e stern distri- bution separately.

During t h e primary processing of t h e material, t h e volume of t h e stands was expressed in two-centimetre diameter classes. The distributions referring t o t h e stand after thinning were assorted into two-centimetre classes in respect of ddom In each such class, t h e average distribution of volume b y diameter classes was calculated. After graphical adjustment a n d redistribution into 2,5 a n d 5 cm classes, t h e distributions given in Appendix I X were obtained.

Corresponding calculations were made for thinnings. In these t h e distribu- tions were, however, assorted in respect of dg. The result of these calculations is given in Appendix X.

14.10. Comparison with other yield investigations

Comparison with other yield tables is made difficult b y t h e fact t h a t stand characteristics are often expressed in accordance with different definitions.

Attempts have been made t o compare these yield tables with British, Danish a n d German counterparts (Fig. 10.1-3). Figure 10.3 shows, for instance, t h a t t h e volume production according t o t h e Swedish tables near t h e centre of t h e diagram, t h a t is, for t h e average quality class, is ca 14 per cent lower t h a n t h a t given b y t h e Danish.