The assessment of the accuracy in increment borings

The assessment of the accuracy in increment borings

V. J. Chacko

Forest Research Institute, New Forest, Dehra Dun (Indien)

Summary

The paper discusses the method, sources of error, and reviews some of the results obtained on the precision and accuracy of the estimates of diameter increments and basal area increments, based on increment borings. The results of a recent study on the precision and accuracy for 4 tree species are presented. lt was found that the actual errors made, measured by the relative mean square error, are of higher magni- tude than indicated by the estimates of precision.

With a view to utilize the results for practical use, the need for adopting a macroscopic approach in evaluating the performance of the increment core method is stressed. That is, we should attempt to assess the overall accuracy of the method by simultaneously considering all the factors together rather than confine to m1cro- scopic studies taking separately each factor or a subset of the factors.

1. lntroduction

lncrement boring is one of the most useful and quick methods commonly for determining the current increment or total volume growth of a tree or a crop in species of trees showing annual growth rings. The borings are normally taken at breast height or just above the buttress for a species showing buttress formation. Two borings per tree, one at each end of a normally developed diameter, are usually con- sidered adequate. The method gives all the information which can be normally obtained through stem analysis. Moreover, the fieid and office work could be organ- ised and conducted expeditiously and there is greater control over the data, as the borings can be taken on standing trees.

In normal forestry practice, the method of estimation of volume increment in a stand could be summarised as follows. Based on diameter increment estimates from increment cores and the corresponding average diameter of trees a periodic increment curve could be drawn which could later be converted into a growth curve showing the development of diameter for an average tree in the stand. However, relevant stand

tables and volume tables are necessary to der,ive estimates of volume increment. The stand table showing the number of trees in the stand by diameter classes and species could be compiled on the basis of sample enumerations in the stand. As for volume tables for a species, one may use a local volume table, if available or construct one, after collecting data on volume, diameter and height from sample trees in the stand and obtaining the regression re1ationship between the volume and diameter/height.

lt is well known that the estimate of volume increment by the above method based on increment borings is liable to errors due to a number of factors. The various sources of errors could be broadly grouped under the following heads:

( 1) Diameter growth determination

Selection of trees Ior increment borings, height at which the borings are made, the location and direction of boring on the circumference, the difference between the core and the actual radial growth in the tree, measurement of the core, and compilation of the data.

( 2) V olume growth determination

Conversion of diameter increments to cross-seclional or basal area increments and volume, volume tables and stand tables.

The contributions of some of the above sources of errors may be systematic and for the others it may be random. The effect of some of the sources may be negligible and may not be of much practical significance. However, the contribution to the error due to at least a few of the factors, appears to be of !arge magnitude and of serious consequence. lt seems that no systematic investigations have been conducted to study the magnitude of the contributions due to the various factors.

In general, the above study could be made by two different approaches: (1) By examining the contributions of each factor or some of the factors separately and attempting to combine the various contributions or (2) by an overall study fur- nishing estimates of the precision and accuracy of the method as a whole. In other words, it could either be a microscopic study or a macroscopic study. The former approach appears to have received some attention from various research workers.

However, these investigations were mainly confined to a study of the precision of the estimates, after taking account of some of the factors. The later approach is likely to be of more practical utility in assessing the usefulness of the method as a whole, but this wauld require careful planning -and large volume of dara and thus could perhaps be taken u,p only 'hy a group of research woJikers. For t!his reason, the propo- sal by Prof. K u r t h to include this study in the research programme of Section 25 of IUFRO should receive the cooperation and support from all quarters.

2. The need for assessment of the accuracy

The immediate reaction of an extension forester to the question whether there is a real need for assessing the accuracy of the method was a firm negative answer.

However, after some discussion he did agree that it may be necessary.

Estimates of increment are needed for various purposes. In forest management, it is felt that particularly in prediction and regulation of yield, great accuracy in the estimates may not be warranted. However, it is also conceded that accurate esti- mates are needed for diameter, basal area and volume in many investigations, especially, when the individual tree is the unit of study. Recentiy, this aspect has become increasingly important with the application of multivariate statistical analysis and the availahility of electronic computers. The use of multivariate analysis for esti- mating stand increments based on individual tree measurements in conjunction with a large number of other variables like size, crown, shading, density, etc. is becoming popular. In such studies, accurate estimation of increment is considered essential.

Then, it is also necessary to assess the accuracy of the method of estimating the increments.

3. Microscopic study of the errors

Estimates of the precision likely to be obtained taking into consideration one or more factors have been obtained by various research workers. A typical study is the one by Matern [3] who based on 37 discs investigated, essentially, the precision of observed diameter growth due to random changes in the direction of increment borings on a stem. He found that for a 5 year growth, the relative standard errors were 19.0

%

for one core, 12.5

%

for two cores at right angles and 10

%

for two in opposite directions. The results also confirmed the common belief that l,ater growth rings were more irregular than earlier rings and thus are reliatively more variable.

Due to the limited number of observations, the study of variations according to species, ages or diameter classes could not be made.

The precision of the diameter measurements and the accuracy in estimation of the basal area was studied by the present author and the results published in 1961, [l].

A total of 112 discs from four species (Shorea robusta, Albizzia lebbek, Pinus roxburghi•i and Salmal:ia malabarica) were used in t!he study. Four met!hods of estimat- ing the cross-sectional area were tried: M1 - One diameter in a random direction, M2 - the average of a random diameter and the diameter at right angles to it, Ma - the geometric means of two diameters and M4 - the average of the maximum diameter and the diameter at right angles to it. The precision was studied based on the measurements from the two independent random directions. With a view to study the accuracy of the estimates, for each of the four methods, the area of the section was estimated assuming, as usual, that the section is a circle. The estimated area was expressed as a percentage of the true area of the section obtained by planimeter and

the mean and standard error computed. The ahove study demonstrated that all the four methods give overestimates of the sectional area. Method M-1 gave maximum overestimates (6 to 14 percent) foUowed hy M1• Method M2 gave least over estimates.

lt may he pointed out that overestimation is more likely due to the assumption that the cross section is a circle. The relative standard errors differed considerahly hetween the various species.

4,. A recent study of the precision and accuracy

The volume increments, using increment horings, are usually estimated hy initially ohtaining estimates of radius or diameter increments ( depending on whether the core is taken up to the pith or the whole diameter), converting them to cross sectional area increments and finally, using height measurements, to volume increments. The ohject of the present study was to .assess the magnitude of the errors up to the stage of ohtaining estimates of sectional area increments. The study was hased on discs ohtained from 4 species of trees and instead of taking increment cores, the measure- ments on increment cores were simulated hy actual measurements on the discs. lt was assumed that cores up to the pith are taken. Thus, radius increments were studied rather than diameter increments. The details regarding the species and the numher of discs used in the study are shown in Tahle 1.

Table 1 Material used

f

or the study

Spccics

1

Number of discs.

Tectona grandis 19

Pinus roxburghii 10

Michelia champaca 13

C edrela toona 6

The following measurements were accurately made on each disc.

(1) The radius in two independent random directions ,and the radius increments ( omitting the hark and final years growth) during the last 5 years as also the previous 5 years.

(2) Identical measurements as m (1) ahove for the two directions at right angles to them.

( 3) The area of the cross section and the increments in area ( omitting the hark and last years growth) during the last 5 years and for the previous 5 years. These ohservations were ohtained accurately using a planimeter.

Based on the radius incr-ements, estimates for the cross-sectional area increments were obtained assuming that the sections are circles. The precision of the estimates was determined from the estimates computed from independent random directions and the accuracy of the estimates was determined by comparing the estimates with the correct area increments obtained by a planimeter.

With a view to examine the precision of the estimates of area increments during a 5 year period the relative standard error percentages were computed as the square root of the sum of squares of the differences between the two estimates from the pair of random directions and divided by 4 times the number of pairs and average area increment. The accuracy of the method was assessed by comparing the estimates based on radius increments with the true area increments obtained by pianimeter.

The ratio of the square root of the average sum of squares of deviations of the esti- mates from the true value to the average area increment was taken as a measure of the rel,ative mean square error of increment borings. The above measures of preci- sion and accuracy were expressed as percentages.

The summary of the preliminary results obtained are presented in Table 2 and Table 3. The relative standard error percentages are given in Table 2 and the relative mean square error percentages are shown in Table 3.

Precision of area increment estimates Table 2

Relative standard error percentage Species

Last 5 years

1 Previous 5 years

T ectona grandis 43.9 37.2

Pinus roxburghii 14.4 11.6

Michelia champaca 8.9 11.7

Cedrela toona 19.2 19.8

Accuracy of area increment estimates Table 3

Relative Mean Square error percentages Species

Last 5 years

1 Previous 5 years

Tectona grandis 73.5 63.l

Pinus roxburghii 18.5 17.9

Michelia champaca 16.7 15.9

Cedrela toona 23.6 26.3

The results presented in Tables 2 and 3 demonstrate that the prec1s10n and ac- curacy of the estimates based on increment borings differ considerabl,y with species of trees. The relative standard errors are f.airly high, suggesting that the annual

growths are highly variable in behaviour. Partly, this variation is due to the shape of cross sections and the pattern of growth in the viarious species of trees studied. lt may be of some significance to note that the values in Table 3 are consistently 1arger than the corresponding values in Table 2. This appears to indicate that wi1h a view t!o judge the performance of the method of estimating increment using the increment borer, ,any study on the precision alone can be very misleading.

lt may be stressed at this point that in the above study, only the estimates of growth in sectional area were considel'ed. The errors in estimating the volume incre- ment is 1ikely to be very much !arger in magnitude.

5. Macroscopic study on the accuracy of the method

The microscopic studies on the precision of the estimates indicated in the pirevious sections, essentially fumishes estimates of the relative standard errors attributable to some of the factors. Likewise, the studies on the accuracy of the estimates give an assessment of the actual ,errors attributable to these factors. However, no study reported so far, appears to have taken ,account of all the factors and furnished an indication of the accumcy of the method as a whole in estimating volume increments.

lt is clear, that the results of this type of research work can be utilized for practical use in forestry work only on the basis of overall assessment of the errors of the esti- mates.

In

other words, the performance of the method as a whole should be assessed and its reliabilüy should be known. This can only be accomplished on the hasis of macroscopic studies.

There are, obviously, difficulties for such a study. The main difficulty is the existence of a large number of experimental :factors which have to be accounted for.

If we think in terms of the classical method of experimentation by studying the contribution of one factor at a time, since the number of factors is large, it will Iead to a very elaborate factorial experiment. Such a complex experiment mises difficult problems of interpretation. To obtain acceptable results by attempting to combine the effect of different factors in the appropriate proportions consistent with actual condi- tions is ,a serious problem.

Thus, it is fairly obvious that by taking individual factors separately is not likely to lead us very far. What is probably desired is that all factors should be considered simultaneously under normal forest conditions and normal use of the increment borer and an overall assessment of the accuracy of the method should be made. A macroscopic study of this nature would require very careful planning and a huge amount of data. This could not, perhaps, be taken up by one ;research worker or even one institution. With a view to obtaiin r,esults of pl.'lactfoal use, the planning of such an investigation would involve the principles of sampling and design of experi- ments. lt is desirable that a working group should standardise the method of collec- tion of tlie relevant data, the method of analysis of the data and the mode of presen- ting the results.

References

[l]. Ch a c k o, V. J., "A study of the shape of cross section of stems and the accuracy of calliper measurements". Indian Forester, Vol. 87, No.12 (1961).

[2]. Kurt h , A., and Schmid , P., "The determination of volume increment by increment borings". IUFRO, 13. Kongreß, Wien 1961, 2. Teil: Proceedings, Bd. 2, Sect. 25/8.

[3]. Matern , B., "On the precision of estimates of diameter growth from increment borings".

IUFRO, 13. Kongreß, Wien 1961, 2. Teil: Proceedings, Bd. 2, Sect. 25/8-S/2.

[ 4]. Set h , S. K., "Rapid determination of increment in Indian Forestry". IUFRO, 12th Congress, Oxford 1956, Papers, vol. 3, sect. 25, p. 76-80.