.:. b- .% i * B R I T I S H C O L U M B i A F O R E S T S E R V I C E . .. .. ~. .. .. .,_ ,.. . : * ... ... No. 21 VICTORIA, B.C. 1952

An Analysis of the Difference in Gross Merchantable Cubic-foot Volumes of the

Upper Fraser Uneven-aged Spruce-Balsam Type When Computed by 2-, 4-, 6-, and 8-inch

DJ3.H. Classes

PART I BY

R. M. Malcolm

PART II BY

J. L. Alexander

RESEARCH DIVISION R. I% Spihhy, F o r e

FOREWORD

P a r t I of the following research note is a condensation by R. M. Malcolm of a thesis he submitted in partial fulfi l lment of the re - qu i rements for registration in the Association of Br i t i sh Columbia Fores- ters and is reproduced with their kind permission.

P a r t I1 of the note, by J. L. Alexander, is a further development from the same basic data of some important considerations in problems of application which were beyond the scope of Mr. Malcolm's original thesis. Owing to the untimely death* of M r . Alexander an anticipated, co-author publication was impossible. In fa i rness to the author no a t tempt was made to revise his draf t manuscr ipt and the reader is requested to overlook occasional repet i t ion in Par ts I and 11.

R. H. Spilsbury.

*April 3, 1951.

Spruce-Balsam Type in the Bowron River Valley

PART 1

W

by R. M. MALCOLM r_,.-.. ."

VICTOR*, B.C. vsw 3E7

INTRODUCTION

At a time when a forest inventory of Brit ish Columbia is urgently required for considerat ion of long-term management and sustained yield, i t is essential that the detail and degree of accuracy in f ield work shall not exceed that required in the answer of volume estimation.

For decades some commerc ia l c ru isers on the Coas t of Br i t i sh Columbia have been using the equivalent of 5 - to 10-inch diameter classes, and thus reducing time in field work and compilation compared with the use of 2- inch c lasses ,

N o reference to an analysis of the difference in volumes result- ing from the use of different ranges in diameter classes could be found for the Spruce, Picea glauca (Moench.) Voss, - -Balsam, Abies las iocarpa (Hook.) Nutt, type.

While cruising in the uneven-aged Spruce-Balsam type of the Prince George Region, it was felt that it would be possible to increase the speed of field work by cruis ing in larger diameter-groupings than the con- ventional 2,-inch classes. Larger d. b. h. classes would result in fewer classes and there would be fewer borderline trees between the classes. Th i s would achieve savings in time, both in cruising and in the compiling of volumes and checking.

These savings in time would lower the cost of forest inventory.

OBJECT

The object of this study is to determine the difference in volume es t imates in c ru i se s of the unevert-aged Spruce-Balsam type, when com- pi led in 4- , 6 - , and 8-inch d.b.h. classes as compared with 2- inch c lasses .

It is hoped to justify the u s e of a larger diameter-grouping than 2-inch d. b. h. c l a s ses in tallying.

METHOD OF STUDY

N o select ion or re ject ion of basic data was made. All the one- acre ta l l ies made by the author in two large areas of the Spruce-Balsam type in the 1948 field season were used. These areas are shown on the Location Map.

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Eleven ta l l ies f rom the area west of the Bowron River between the Fraser River and Bowron Lake, and thir ty- three ta l l ies f rom the area between Eaglet Lake and the Fraser River were used. These ta l l ies gave considerable variation in volume per acre and diameter spread.

LOCATION M A P \ O F

SAMPLED AREAS USED IN T H E STUDY

Fig. 1.

The init ial cruise and volume compilation was by 2-inch dia- meter c lasses . For the purposes of this study the trees above 7. 0 inches a t d.b.h. in each ta l ly were re-al located f rom 2- inch c lasses to 4- , 6-, and 8- inch c lasses .

W

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TABLE I - -TALLY VOLUMES BY 2-, 4-, 6- , and 8-INCH D.B.H. CLASSES _.

StriF No.

270

272

273 276

279

300

30 2

306

307

337 336

364 365 440 441 442 443

445 444

'o ta l - - lean ' e r c e -

- Tall! No.

2 1

3 4 1 2 1

2 1

4 3

5 1 2 3 4 5 6

2 1

3 4 1 3 4 5 1 2 3

5 4

6 3 1

1 1

1 1 1 1 1

4 2

1 -

__ Volum 2-inch

l iamete Classe l

465C 550(

834C 506C 550C 501C 203C 400C 653C 530C 544c 864C 60lC 5730 6070

6220 5250

6060 4440

6660 3510

4740 5290 4650 3940 4090 29 20

4440 5 340

4840 3880 6580 5690 6020 7010 1520

4080 3950

3460

4670 5370

4150 4710

220660 3370

5015 : rence __

n o n e a c 4-inch

l iamete. C l a s s e s

5600 4690 8380 5090 5630 5090 2160 3980

5560 6640

5600 8720 61 20 5920 6160 5250 6250

4390 6250

3660

48 40 6690

5370 4740 3940 4240 2960 5430 4510 5100 4070 6850 5750 6070 7190

40 30 1560

41 70

5400 35 10

4730

48 70 4240

3450 224850

5110 m 2-inc

- -Gross 6-inch

J iamete Classes

5640 4600 8430 5090 5500 5010 2090 40 10 6530 5030 5810 8870 6190 5570 5960

6220 5240

4370 6030

3440

4720 6430

5250 4730 3970 4160 2920 5410 4410 5020 3990 6810 5720 6220 7210 1650 4100 4110 3540 5420 4900 4260 4850 3480

222910 5066

-

lbic F e e t

l iameter 8- inch

C l a s s e s

5970 49 30 8500 5310 5890 5190 2380 3920

5690 6540

5570 8730 61 70 6120 6460 5380 6210 6520 5010

6760 4050

4880 5540 4750 3900 4540 2990 5840 4610 5270 4390

5960 7420

6050 7430

4250 1770

4380 3640 5630 4840 4560 5380 3450

232770 5290

c l a s s

t100 t 40 t 40 t 30 t130 t 80 t130 - 20 t110 t260 t160 t 80 t110 t190 t 90

0 t 30 t190

t150 - 50

t 30 t100 t 80 t 90

t150 0

t 40 t 90 t 70 t260 t190

t 60 t2 70

t 50 t180 t 40 t 80 t 90

t 30 t 50

t 60 t 90 t l60

14190 t 80

+9 5 t1 .9

- - - - -

t 140

t 90 t 30

0

t 60 0

t 10 0

t 3 7 0 - 270

t 2 3 0 t180 - 160 -110 - 10

0 - 30 - 70

-230 - 70

- 20 - 40

t 30 t 80

t 70 0

t 70 - 30 t180

, t 1 1 0

t 30 t 2 3 0

t 2 0 0 t 2 0 0 t 1 3 0 t 1 5 0 t 30 t 80 + 50

t 1 1 0 t230

t140 t110

t2250 t 5 1

t 1 . 0

- 50

- - - -

t 2 8 0 $470

t 160 t 2 5 0 t 3 9 0 t 1 8 0 t 3 5 0 - 80

t 3 9 0 t 10

t 1 3 0 t 90 t160 t 3 9 0 t 390 t 1 3 0 - 10 t 4 6 0 t 5 7 0 t 5 4 0 $100 t140 t 2 5 0 t 1 0 0 - 40 t 4 5 0 t 70

t 1 7 0 t 5 0 0

t 4 3 0 t 5 1 0 t840

t 30 t270

t 4 2 0 t 2 5 0 t300 t300

t260 t180

t170 t410 t670 t 80 E t 2 7 5 t5 .5 -

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The gross cublc-foot volume of each tally was compiled, using the volume of the mid-diameter and number of trees in the d. b. h. class, for the 2 - , 4- , 6-, and 8-inch classes.

RESULTS

The table on page 3 shows details of tally volumes, differences in volume, and the means of these values for each diameter-class group- ing, for the 44 tallies. totalling 44.0 a c r e s .

The s tandard e r ror of t.he mean differences in volume caused by the various compilation cla+ses was calculated by "Students" method and are summarized in Table XJ.

TABLE lI--TEST O F VOLUME DIFFERENCES BY 2-, 4-, 6- , AND 8 - INCH D.B.H. CLASSES

D.B.H.

44 samples inch Grouping ;ofDiffer- cubic iper acre ta l l ies Di f fe rence o f acre f rom 2 - Deviation Volume, Volume one-acre Grouping S.E. of Mean Standard Difference per Average Total No. of

feet ~ cubic cubic feet chbic ~ ence p e r ,

feet. fee t i cubic feet cpnt

Y

"

p e r a c r e I

2-inch 1 I 'I I W 5015 220660

~ 44 I I I I I I L

4-inch ~ 44 t95j f 72.6 1 f 10.9 t1 .9 5110 224850 **

I I I I I I I I **

6-inch

+199. 1 i -130.0 t275 t5 .5 5290 232770 44 8-inch

t123.9 I t ~ 1 8 . 7 ' t 5 1 t l . O 5066 222910 44

**

** Highly significant differences.

These results show that the mean differences in estimate caused by the three new methods of diameter grouping are all highly significant.

From the table it can be seen that the mean difference €or the 6-inch grouping is less than for those of the 4-inch and %-inch groupings. Th i s is accounted for by the fact that, in the 6-inch grouping, the ratio standard deviation to mean difference is higher than in the 4- or 8-inch groupings. In other words, there is a comparatively wide spread of dif- ferences between the tally volumes by 6 - and 2-inch d. b. h. classes, while the mean difference is small .

.

W

Y

No I

GRAPH o f VOLUMf PER ACRE br 2" and 4 DIAMETER CLASSES

3 4

W

v No 3

GRAPH of VOLUME PER A C R E by 2" And 8" DIAMETER CLASSES

"

+- M cubic f ee t

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Although they are highly significant, the absolute differences in volume due to grouping by the 4- and 6- inch diameter c lasses are only 1.9 and 1 .0 per cent, respect. ively, and unimportant. The difference in volume due to grouping by the 8- inch diameter c lasses is 5. 5 per cent , which is an important difference.

Graphs 1, 2 , and 3 show volumes by 4-, 6 - , and 6-inch diameter c lasses plot ted over vo lumes by 2-inch classes. Graphs 1 and 2 show that in tallies compiled by 4- and 6- inch diameter c lasses there is a con- sistently high difference in volume estimates over the range of volumes found in the Spruce-Balsam type. The difference is small in magnitude in both cases.

F r o m G r a p h 3 , i t is evident that computing volumes by 6-inch diameter c lasses gives a consistently high difference which is la rge enough to be important,

The reason for the consistently high difference is unknown, but i t may be associated with distributions and weighting which is beyond the scope of this study. The possibility of calculating a correct ion factor for volume estimates, computed from 8-inch diameter classes, will , there- fore, not be discussed.

SUMMARY

The conclusions of this study apply only to the uneven-aged Spruce-Bzlsam type of the Prince George Region, volumes compiled in cubic feet.

The sample of 44 one-acre tallies, computed by 2 - , 4- , 6 - , and 6-inch d. b. h. classes> gives the following differences in volume from the computations by 2-inch classes.

D. B.H. Per Cent Di f fe rence in Class--Inches Volume from 2-inch

C las s

I I 6 t5 .5 I These differences apply to the mean of 44 tall ies only.

- 6 - W

1.

2 .

3.

In the case of the es t imates by 4- and 6-inch d.b.h. classes the dif- ferences are highly s ignif icant for an unknown reason; but their magnitude is consistently small over the range in volumes normally encountered in the type, and they are, therefore, considered unim- portant.

Six- inch diameter c lasses appear to be the largest grouping giving volume estimates .of suff ic ient accuracy for extensive forest survey purposes, without the application of a correct ion factor .

Tallying by 6- inch diameter c lasses in the Spruce-Balsam type should cause savings in time and cost of both field and subsequent office work.

A t e s t was ca r r i ed out to determine the approximate saving in t ime of compiling tallies by 6- inch diameter c lasses , ins tead of by 2-inch classes. The author was the compiler throughout this test .

The results were as follows.

U

Diamete r C la s s

C las ses - -minutes inches t ime f rom 2- inch Compile ta l l ies Grouping

Per Cent Saving in Time to Number of

2 56 15

6 41 3 3 15

This saving in t ime of office compiling is indicative of the faster compiling and tallying which may be expected in the field.

It would be of great value to carry out a field study to determine the saving in time and cost of tallying by 6- inch d iameter c lasses ins tead of by 2-inch classes.

PART I1

by J. L. ALEXANDER

INTRODUCTION

r*

C r u i s e r s in Eastern Canada and the United States, where the d iameter - range of s tands is relatively small, have used 2-inch diameter classes for tal lying from the early days. On most areas in the softwood forests six classes would cover the bulk of the trees even cruising down to 4 inches d. b. h. A s the forests in the West became more important,

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necessitating stock-taking, government agencies and some commercial cruisers adhered to the 2-inch classes even though, for Coast t imber, there might be 30 o r more d i ame te r c l a s ses i n a stand. Some commer- c ia l c ru isers jumped to 5 - inch c lasses in the ear ly days , and some o ld- t i m e c r u i s e r s who recorded the volume of individual trees directly, used the equivalent of 1 0 - to 12-inch classes in old-growth Douglas Fir and Sitka Spruce stands.

The 2-inch diameter classes will give the most accurate esti- mate but the difference between using 2-inch classes and larger classes may be unimportantly small, i f based on a sufficient number of tall ies.

The re la t ive e r ror is more c losely re la ted to the number of dia- meter c lasses recognized in a stand than the range in diameters from the smallest to the largest trees.

The range covered by each d iameter c lass for a given precision in the volume wil l depend on the total range of d iameters in a stand and the number of tal l ies making up each average. The larger the diameter classes, the greater the saving in f ield work and computation and for a given area ta l l ied the less precis ion in the resul ts . This necessi ta tes balancing costs against accuracy.

OBJECT

The object of this study is to determine the maximum sizes of diameter classes which may be used in the uneven-aged Spruce-Balsam type of the Upper Fraser a t a predetermined sacr i f ice of precis ion for a given number of acres ta l l ied.

DATA

M r . R. M. Malcolm, while cruising in the uneven-aged Spruce- Balsam type of the Upper Fraser tal l ied one-acre units, compiled the volumes by 2- , 4- , 6- , and 8-inch classes and made them available for this study. (See Part I . )

ANALYSIS AND RESULTS

The results from this analysis apply only to this type or similar types covering the same range in diameters, The gross merchantable volume averaged 5 , 0 0 0 cubic feet per acre . The loss f rom defect is pro- bably about one-seventh of the gross volume. This lat ter factor was not taken into consideration in the analysis. The diameters ranged from 7 t o 30 inches with a few larger t rees , g iving about 12, 6, 4, and 3 c la s ses when compiled by 2- , 4-, 6 - , and 8-inch classes, respectively.

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-V

W

i

There is high correlation between the volume of individual tallies calculated by 2- inch c lasses and the larger diameter c lasses; a low volume per acre for one c lass wi l l mean a low volume per acre for each of the other classes. "Students" method which is especially adapted to this kind of data was used in the analysis of differences.

The resul ts of the ana lys i s a re p resented in Table I1 of P a r t I. The standard deviation of the differences in cubic feet per acre from the volume by 2-inch d. b. h. c l a s ses is the real meat in this ' table . The res i - dual error af ter a l lowing for the s ignif icant dif ferences is direct ly propor- t ional to the s tandard error of the differences shown in Table 11. F o r example, the res idual error when 6- inch c lasses are used is 5 = 1.71

t imes the e r ror for 4 - inch c lasses and when 8- inch c lasses a re used - 191.1 = 2. 74 t imes the error for the 4- inch c lasses . 72.6

72. 6

The significant differences of 95, 51, and 275 cubic feet were subtracted f rom the acre volumes for each ta l ly computed by 4-, 6-, and 8-inch classes, respectively. Then the differences between the residual volumes computed by 4-, 6-, and 8-inch classes and by 2- inch c lasses were determined and, together with the uncorrected differences (see Table I) , a re summar ized in Table I11 on page 9.

The average difference in per cent in Table 111 w a s calcu- lated from the total volumes. Although the average difference based on 44 ta l l ies for 4- and 6- inch c lasses are low, individual tallies had differ- . ences up to 5.5 and 6.8 per cent, respectively. The maximum difference for one acre calculated by 6- inch c lasses is 7 t imes the average for the 44 acres . Therefore , averages without reference to the number o f ta l l ies on which they are based may lead to erroneous conclusions.

Since the error to be expected when different diameter c lasses are used depends on the number of acre- ta l l ies making up each average , Table IV has been prepared. It is based on the s tandard errors of the differences in Table I1 and indicates the maximum difference in cubic feet due to sampling that may be expected at a probability of 0.05 between volumes compiled by 4-, 6-, and 8-inch classes compared with volume compiled with 2-inch classes.

Table IV shows that the sampling error for the same number of ta l l ies is greater the larger the diameter class used in compilation and that the sampling error also depends on the number of t a l l i e s . Fo r ex - ample , the e r ror for 20 ta l l ies by 8 - inch c lasses wi l l be l ess than the e r r o r for 5 ta l l ies by 4- inch c lasses . The number of tall ies making up a type should be considered in deciding the diameter class to be used.

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TABLE 111--DISTRIBUTION OF ACRE TALLIES ACCORDING TO DIFFER- ENCES IN CUBIC FEET PER ACRE FROM VOLUMES COM- PUTED BY 2-INCH D.B.H. CLASSES

W

Difference in Not Correc ted Correc ted Cubic Fee t per Acre D. B. H. C l a s s s e s

4-inch 6-inch 8-inch 4-inch 6-inch 8-inch Number of Acre Ta l l i e s

0 - 50 14 16 4 51-100 15 9 6

101-150 6 8 3 151-200 6 5 6 201-250 0 4 3 25 1-300 3 1 5 301-350 1 1 35 1-400 4 401 -450 4 45 1-500 3 501-550 2 551-600 1 601-650 0 651-700 1 701-750 0 751-800 0 801 -850 1

Total 44 44 44 Maximum Difference 260 370 840 Cubic Fee t per Acre

Maximum Difference per cent 5.5 6.8 12.8

Average Difference per Acre (1) Cubic Fee t 95 51 275 ( 2 ) P e r c e n t 1.9 1.0 5 .6

20 12 8 19 17 3 2 7 13 3 4 8

0 4 2 4 2 1

2 0 0 0 I

44 44 44

175 321 565

3 .3 6. 1 8.9

Note: Numbers corresponding to average difference per acre based on 44 tall ies are underlined.

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TABLE IV--MAXIMUM DIFFERENCES DUE TO SAMPLING FOR VARIOUS D. B. H. CLASSES AND NUMBERS O F TALLIES.

(umber of Maximum Difference due to Sampling. icre Tal l ies Cubic Feet per Acre

1 0.: 4-inch

5 10 15

20 30 50

100 1000

10 1 54 42

35 28 21

15 5

H. C l a s s e s 6-inch 1 8-inch

I

172 91

276

114 71 148

59 96 47 76 36 57

25 12 8 40

The error due to the use of larger than 2-inch classes is a com- promise against reduced costs and s ince the total error of a c ru ise is the sum of a l l the e r rors some maximum must be established. Let u s a s - sume that the saving in labour justified a one per cent a l lowable error due to diameter grouping. Since this type averages 5 , 000 gross merchantable cubic feet per acre the a l lowable error will be 50 cubic feet . Referring to Table IV this tolerance requires 13, 26, and 60 tallies when computed by 4-, 6 - , and 8-inch classes respectively. Where 4-, 6-, and 8-inch are used in computing, the volume 91, 51, and 275 cubic feet, respective- ly, should be deducted from the average volume per acre to obtain the best estimate of the average type volume. This i l lustrates the use of Table IV.

-

In high-intensity surveys for the planning of logging coast t imber -where the logging costs $ 1 , 0 0 0 per acre , the saving in using larger dia- m e t e r c l a s s e s will be a very small percentage of this operating cost. However, where the logging chance is broken down only into broad volume c lasses such as 3,000-5,000, 6,000-10,000, and over 10,000 cubic feet per acre , large c lasses may f requent ly be used a t considerable actual saving without m u c h loss in precision.

The loss in precis ion in using diamkter c lasses larger than 2-inch will depend on the range in diameters in the type and the number of tall ies making up each average and these are the factors that should be considered in determining the diameter classes to be used. No one diameter class can be expected to be acceptable for all types in Bri t ish -

Litj i \ '+i \ I MINISTR'f OF FORESTS PARLIAMENT BUILDINGS

VICTORIA, 0.c. V8W 3E7

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Columbia varying f rom the small-diameter range of Lodgepole Pine to the large range in mature coast forests on good si tes. Under tertain condi t ions large-diameter c lasses may be used with re la t ively l i t t le loss in precision and at considerable saving in labour costs.

SUMMARY

This analysis is based on 44 one-acre tal l ies made by R. Malcolm in the uneven-aged Spruce-Balsam type of the Upper Fraser and compiled by him in 2-, 4- , 6 - , and 8-inch d. b. h. c lasses .

The gross merchantable cubic-foot volume per acre without allow- ance for defect averaged 5, 000 cubic feet per acre with individual ta l l ies varying f rom 1, 520 to 8 , 640 cubic f re t . The range in diameters was f rom 7 inches to 30 inches with a few la rger t rees .

The resul ts of this study apply only to this type or similar types having about the same average volume and diameter distribution.

The aggregate difference per acre for the 44 ta l l ies compiled by 4-, 6 - , and 8-inch classes compared with 2-inch d. b. h. c lasses was 95, 51, and 275 cubic feet , respectively. This amounted to 1.9, 1.0, and 5. 6 per cent of the gross cubic feet volume. Al l these differences were posit ive and significant.

The maximum differences for individual tal l ies were 260, 370, and 840 cubic feet per acre for 4-, 6 - , and 8- inch c lasses respect ively. These amounted to 5.5, 6.8, and 12.8 per cent of the average volume.

The standard deviation of the differences based on individual one- acre tal l ies were 72.6, 123.9, and 199.1 cubic feet per acre for 4- , 6 - , and 8- inch c lasses . The e r ror a f te r cor rec t ion for the significant differences of 95, 51, and 275 cubic feet is proportional to the standard deviations when various classes are used.

The sampling error depends on the diameter class used and the number of ta l l ied acres making up the average for the type.

Assuming a max imum e r ro r o f 1 per cent for the use of d iameter c lasses l a rger than 2 inches, a minimum of 13, 26, and 60 ta l l ies a r e r equ i r ed when 4-, 6 - , and 8- inch c lasses are used.

When tall ies are computed by 4- , 6 - , and 8-inch classes the signi- ficant differences of 95, 51, and 275, respectively, should be deducted from the average volume per acre for the type.

W

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(10) The range in diameters and the number of tall ies making up each average determine the diameter c lasses to be used for a given pre- cision. Therefore, no one diameter class can be expected to be suitable for all of the types in British Columbia.

(11) The larger the diameter c lass the less the precis ion but the greater the saving in labour and costs.

. *

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