Accuracy of Estimates of Diameter Growth

On the Accuracy of Estimates of Diameter Growth and Basal Area Growth from Repeated

Caliperings and from lncrement Borings

]Ör[Jn Fries

Skogshögskolan, Stockholm (Schweden)

1 lntroduction

In this study a comparison is made between the two standard methods of determining the diameter and basal area increment of individual trees, by means of repeated calipering and boring. The true increment has not been determined. However other studies can be used to investigate the question whether calipering and boring can be taken for unbiased estimates of the true increment.

1.1 Calipering

Matern (1956) reports estimates of basal area by calipering made on a number of convex regions. He finds (pp. 15-16) that calipering, in two directions at right angles as done in his study, results in an overestimation of the basal area of 1.8-3.2 per cent and a relative standard error between zero and 9.1 per cent. If the calipering is done in the same direction at the beginning and at the end of the period, these errors in the determination of the increment will probably be of relatively little significance.

1.2 Boring

Siostrzonek (1958) has studied the mean value and standard error of basal area increment over a ten-year period. He finds (p. 249) that the mean measurement of growth of an increment core is 2.5 per cent too high for increment periods between 25 and 55 years and 7 .0 per cent too low for increment periods between 60 and 100 years.

2 Data

The material for the study has been taken from the Royal College of Forestry's permanent sample plots. All the trees in these plots are numbered and taged with a coloured cross at breast height. All tht; crosses in any one plot have the same

exposure. During rev1s10ns, which are made at intervals of five years, each tree is caiipernd in itwo dirnctions, the caliper heing app1ied first 1:hat the handle touches the cross at hreast height, and second 'llhat one of the jaws touches the cross. At each measurement the diameter is rounded to the nearest full millimeter. The diameter of the tree at hreast height is calculated as the arithmetic mean of the two measure- ments rounded to full millimeters. Certain additional ohservations are made with respect to a numher of standing sample trees, including the 5-10 largest (G trees).

Thus in the case oI pines the thickness of hark is measured with the Swedish hark gauge, fi11stly at a poinL diametrioally opposire the cross at ¹hreast height and secondly at a point on a radius al right angles to the radius passing through the cross. The hark thickness is expressed as the sum of the two measurements in millimeters. No hark measurements are made on spruce.

For this study ahout ten of the representative standing sample trees, as well as five of the G trees, were ,selec'l:ed hy stratifü.ed sampling from each plot. The selected sampLe trees wer-e horied alternately 10 cm ahove and 10 cm helow hreast height, the diirnction of horing being v,aried from one tree to another. The numhers of plots and sample trees invoived-are indicated 1in the tahle below:

No. of plots No. of trees

Pine

16 221

Spruce

16 224

The plots are situated in 60- to 170-year-old stands of timher distributed all over the country.

3 Calculations

3.1 Calipering

For the pe11iod between two revisions the diameter increment over bark of each tree has been determined as diameter-diifference hetween two revisions. The study covers the last five revisions, i. e. four periods of increment. Where hark measurements have been made simultaneously with the calipering at the begin- ning and at the end of the incr·ement period, the diameter increment under bark also has been calcu1ated.

The basal area increment over bar/, has been calculated as the difference in basal area measured at two consecutive revisions. The basal area increment under bark has been calculated from the diameters under hark in those cases where records of hark thickness were available.

3.2 Boring

The radial increment of the cores has been measured by means of the Swedish tree ring measuring machine (Eklund 1949) and recorded in hundredths of a milli-

meter. The diameter increment under bark of each tree during the period between two revisions has been determined as twice the radial increment for the 'same period.

The basal area at the end of the period has been determined from the calipered diameter under hark at the end of the period. The basal area at the beginning of the period has been calculated from the same diameter less the diameter increment during the period as measured by boring. The basal area increment under bark has been determined as the difference between these two basal areas.

The calculations described above have been made i) for a periiod of approximately five years and ii) for two such periods i. e. a period of approximately ten years.

3.3 Calculation of relative standard errors

The relative standard error ( v) has been calculated for each plot and increment period according to the formula

where

v= l0Q V(i- i)2/(n- l)/i

1 = increment of the individual tree

1 = corresponding mean figure for the plot n = number of trees observed

(1)

A mean value of v for all the period and plots concerned (v) has been calculated according to the formula

where

v1, v2 ... VN = relative standard errors for each period N = number of relative standard errors counted.

(2)

In order to be able to compare the two methods, i. e. calipering and boring, the same ttees have always been included in the calculation of v.

4 Results

Tables la-lc show the mean relative standard errors, and in Figures la-ld the relative standard errors have been plotted against the increment.

As expected, Tables la-lc show that the increment over hark is greater than the increment under hark. The ratio between the mean increment figures under hark as measured by boring and over hark as measured by calipering is 0.82 for pine and 0.95 for spruce. These figures are in fairly good agreement with the prevalent ratJio in Sweden between hark t!hickness and ,dri.ameter over hark (Öst1in 1963).

In the case of pine ( op. cit., p. 8), the thickness of the hark at breast height is 14-23

Means and mean Standard errors of increment determined by means of calipering and boring

Table 1 a. Scots pine, o.b.

Calipering

Length of pcriod etc. No.

1

periods relative

mcan standard error, 0/o

Ca 5 years' diameter increment, mm 64 15.7 35.3

· Ca 10 years' diameter increment, mm 32 31.4 28.7

Ca 5 years' basal area increment, sq. cm 64 67.4 44.5

1 increment u.b. from boring for all calipered trees.

b. Scots pine, u.b.

Length of pcriod etc.

Ca 5 years' diameter increment, mm Ca 10 years' diameter increment, mm Ca 5 years' basal area increment, sq. cm

No.

periods

25 10 25

Culipering

mean

13.6 28.7 54.1

1 relative standard error, 0/o

49.6 33.6 57.5

c. Norway spruce, o.b.

Calipering

Length ol period etc. No.

1

periods relative

mcan standard error, ⁸/o

Ca 5 years' diameter increment, mm 64 19.9 44.5 Ca 10 years' diameter increment, mm 32 39.7 42.3 Ca 5 years' basal area increment, sq. cm 64 94.0 54.5

1 increment u.b. from boring for all calipered trees.

mcan

12.9 25.7

-

mcan

12.8 26.4 50.4

mean

18.9 37.9

-

Boring 1

1 relative standard error, 0/o

33.8 32.0

-

Daring

relative standard error, ⁰/o

32.9 29.2 42.4

Boring 1

1

relative standard error, 0/o

43.7 41.4

-

per cent of the diameter over hark, and in that of spruce (ibid., p. 142), the average thickness of hark is 5 mm plus 5 per cent of the diameter over hark.

A comparison hetween the calipering and horing methods with respect to the increment under hark in pine (Tahle lh) shows that calipering gave a mean f,igure 6 per cent higher than horing. Comparisons hetween the two methods for each separate five-year period show that calipering gave a greater increment in 15 cases out of 25, while horing showed a higher increment in the remaining 10 cases. This suggests that the difference is not significant. However it is possihle, that horing results in a slight underestimation of increment ( cf. 1.2).

Figure 1

Relative standard error of ca 5 years' diameter increment, v, plotted over the increment of the period. Values for the same plot are connected with straight lines.

a. Calipered increment of Scots pine o.b.

b. Bored increment of Scots pine u.b.

V

100 a

80 + -- - + - - - - + - - - - + - - - + -

V

100

80

60

40

20

0 0

0

0

10

10 20 30mm

20 30 40

c. Calipered increment of Norway spruce o.b.

d. Bored increment of Norway spruce u.b.

b

0

10 20 30mm

d

0

10 20 30 mm

The relative standard errors for increment over bark measured by calipering are only insignificantly greater than those for increment under bark measured by boring for the same trees. Thus calipering gives the same relative standard error in measure- ment of increment over hark as does horing in measurement of increment under hark.

In the case of pine the relative standard error for increment under bark measured by calipering is considerahly greater than the corresponding figure measured hy boring. The reason for this is the margin of error in hark measurement ( cf. Östlin, 1963, p.12 ff.). Since the error in hark measurement is independent of the length of the increment period, it is natural that douhling of the increment period results in a considerahle reduction in the relative standard error with respect to increment under hark measured hy calipering.

For spruce according to Tahle 1 there is no equally marked reduction in the relative standard errors referring to the increments measured hy caiipering over hark. For pine and spruce holds the same for horing if the increment period is douhled. Figures la-ld show that there is a clear correlation hetweenrelativestandard error and increment during the period concerned. lt is apparent from the figures that this correlation shows a similar profile in hoth calipering and horing.

lt has heen stated ahove that measurement of increment over hark hy calipering gives the same relative error as measurement of increment under hark hy horing.

This conclusion also seems to apply where the increment rate varies within the intervals under study.

Means and standard errors in mm of differences between calipered and bored annual increment for Jour 5-year periods. Calipering is made 1.3 m above ground and boring 1 .2 m or 1.4 m

above groztnd.

a. Ovcr hark ^{Table 2}

Period No.

1 1

1 2 3

1 4

S.;ots pine, 1.2 m 0.59

±

±

±

±

±

±

±

±

±

±

±

±

±

±

±

±

b. Under hark

Period No.

1 1

1 2

Scots pine, 1.2 m 0.07

±

±

±

±

The relative standard errors for approximately Jive years' basal area increment are considerahly greater throughout than the corresponding figures for approxima- tely five years' diameter increment.

To investigate the influence of the height of boring on the recorded increment the trees were grouped according to height of boring. For each group the differerice between calipered and bored annual increment was calculated for each of the four 5-year periods. Table 2a and 2b show that the height of boring had no significant influence on the recorded increment of Scots pine. For Norway spruce, however, the difference between calipered and bored increment is significantly smaller at 1.2 m height than at 1.4 m height of boring. As the calipering is always made at 1.3 m, this means that boring at 1.2 m has given a greater increment than boring at 1.4 m. The difference is 0.22-0.32 mm or 6 to 8 per cent of the annual increment.

According to taper tables forspruce (Edgren & Nylinder 1949) the difference between diameters at 1.2 m and at 1.4 m should be 1-2 per cent. The differences in incre- ment are much bigger and can not be only explained by the taper. The results show that it is important to make the boring at proper height.

. References

E d g r e n, V., and Ny 1 in der, P. 1949: Funktioner och tabeller för bestämning av avsmalning och formkvot under hark. Tall och gran i norra och södra Sverige. (Summary: Funk- tions and tables for computing taper and form quotient inside hark for pine and spruce in Northern and Southern Sweden.) - Medd. Skogsforsknlnst., Stockh. 38 (7), 81 pp.

E k 1 und , B. 1949: Skogsforskningsinstitutets arsringsmätningsmaskiner. Deras tillkomst, konstruktion och användning. (Summary: The Swedish Forest Research lnstitute's machines for measuring annual rings. Their origin, construction and application.) - Medd. Skogsforsknlnst., Stockh. 38 (5), pp. 77.

M a t

e

Si o s t r z o n e k, E. 1958: Radialzuwachs und Flächenzuwachs. Genauere Bestimmung des Grundflächenzuwachses mit Bohrspänen und Stammscheiben. - Forstw. Cbl. Jg. 7/8, p. 237-253.

Ö s t 1 in , E. 1963: Barkuppgifter för tall, gran, björk m. fl. Del 1. Barkuppgifter för län, regioner. (Summary: Bark data for pine, spruce, birch, etc. Part 1. Bark data for provinces and regions.) - Rapp. Uppsats. Instn. Skogstaxering Skogshögsk., Stockh. No. 5, pp.146.