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Analysis of measurement errors associated with variable-radius plot forest sampling 1978

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ANALYSIS OF MEASUREMENT ERRORS ASSOCIATED WITH VARIABLE-RADIUS PLOT FOREST SAMPLING by STEPHEN AGNEW VWEMURWON OMULE B.Sc. F or. (Hons), Makerere U n i v e r s i t y , 1976 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN THE FACULTY OF GRADUATE STUDIES ( THE DEPARTMENT OF FORESTRY) We a c c e p t t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNTVERSlTy OF BRITISH COLUMBIA kptill, 1978 © Sttphtn Agnzw Vtn'Emuiwon Omult > J 9 7 s In presenting th i s thes is in pa r t i a l fu l f i lment of the r e q u i r e m e n t s f o r an advanced degree at the Univers i ty of B r i t i s h C o l u m b i a , I agree t h a t the L ibrary sha l l make it f ree ly ava i lab le for reference and s t u d y . I further agree that permission for extensive copying o f t h i s t h e s i s for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that c o p y i n g o r p u b l i c a t i o n o f th is thesis for f i nanc ia l gain sha l l not be allowed without my written permission. Department of f € y Iv v f The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 f Date - i i - ABSTRACT F o r e s t i n v e n t o r i e s form a b a s i s o f dec i s i o n - m a k i n g i n most a s p e c t s o f f o r e s t r e s o u r c e s management. I m p l i c i t l y , t h e r e f o r e , i n v e n t o r i e s must be conducted e f f i c i e n t l y and w i t h a minimum o f e r r o r . T h i s t h e s i s a n a l y s e s the e r r o r s o f measurement d u r i n g a v a r i a b l e - r a d i u s p l o t f o r e s t i n v e n t o r y c r u i s e , w i t h the o b j e c t i v e o f d e t e r m i n i n g crew v a r i a t i o n and b i a s i n t r e e count, diameter, and t o t a l h e i g h t measurements. Data f o r the study were c o l l e c t e d a t The U n i v e r s i t y o f B r i t i s h Columbia Research F o r e s t , Maple Ridge, B r i t i s h Columbia, d u r i n g the t h i r d year f o r e s t r y s t u d e n t s f i e l d s c h o o l i n mensuration. In each of the s i x l o t s of 10 p r e - s e t sample p l o t c e n t e r s , three t o s i x 3~man student crews each e s t a b l i s h e d p r i s m and r e l a s c o p e p l o t s , took the t r e e count, and measured the d i a - meters a t breast height o f a l l the " i n " t r e e s and the t o t a l h e i g h t s o f the f i r s t " i n " t r e e s . The crews took t h e i r measurements i n d e p e n d e n t l y o f each ot h e r , and had to complete the e x e r c i s e w i t h i n a p e r i o d of 8 hours. The author's measurements and o b s e r v a t i o n s i n the same p l o t c e n t e r s formed the c o n t r o l t o the study. The crew v a r i a t i o n i n t r e e count was c a l c u l a t e d by the method o f A n a l y s i s o f V a r i a n c e , and i n diameter and h e i g h t measurement by p o o l i n g the v a r i a t i o n f o r each t r e e t o o b t a i n a w e i g h t e d average v a r i a t i o n p e r t r e e . B i a s was e v a l u a t e d by comparing t h e erew r e s u l t s w i t h t h o s e o f the c o n t r o l . The f o l l o w i n g r e s u l t s were o b t a i n e d from the s t u d y : The average t r e e c o u n t was 9.5 t r e e s i n the b a s a l a r e a f a c t o r (BAF) - 6 p r i s m p l o t s and 7.4 t r e e s i n t h e BAF = 9 r e l a s o o p e p l o t s . The c o e f f i c i e n t o f v a r i a t i o n o f o b s e r v e r t r e e c o u n t v/as 10.445 w i t h the p r i s m and 4.93% w i t h the r e l a s c o p e . The p e r c e n t a g e e r r o r i n the d e t e r m i n a t i o n o f b a s a l a r e a p e r h e c t a r e from 2 5 p r i s m p l o t s was as much as ± 4.09%. and from 25 r e l a s c o p e p l o t s ± 1.93% a t the a = .05 p r o b a b i l i t y l e v e l . About 37% o f the t r e e c o u n t s i n the r e - l a s c o p e p l o t s and 2 5% i n the p r i s m p l o t s were measured w i t h o u t e r r o r . The maximum t r e e c o u n t e r r o r v/as ± 6 t r e e s per p l o t . The a v e r a g e t r e e d i a m e t e r v/as 52 .67 cm, and t h e measurer c o e f f i c i e n t o f v a r i a t i o n was 8.16%. Only 6% o f t h e t r e e d i a m e t e r measurements were c o r r e c t . A c c u r a c y was l o w e r a t l a r g e r t r e e d i a m e t e r s . The average t r e e h e i g h t was 31.38 m, and the measurer c o e f f i c i e n t o f v a r i a t i o n of t h e t r e e h e i g h t measurements was 21.86%. Crews measured t r e e h e i g h t s w i t h a s i g n i f i c a n t b i a s . Only about 2% o f t h e m.onr."romontf? were c o r r e c t , w i t h o v e r 15% o f the measurements b e i n g i n e r r o r by + 6.0 m o r more. H e i g h t measurement was s u b j e c t t o l a r g e r and more s o u r c e s o f e r r o r , - i v - The r e s u l t s suggest t h a t f o r e s t resouce managers should be more c a r e f u l i n u s i n g u n t r a i n e d crews i n f o r e s t i n v e n t o r y work. They should e s t a b l i s h r i g o r o u s f i e l d t r a i n i n g programs, and o u t l i n e and implement c h e c k c r u i s i n g g u i d e l i n e s . - A C - TABLE OF CONTENTS Page TITLE PAGE i ABSTRACT i i LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS v i i INTRODUCTION 1 LITERATURE REVIEW 4 SOURCE OF DATA 10 METHOD OF ANALYSIS AND RESULTS 13 Tree Count 13 Diameter 24 H e i g h t 30 DISCUSSION 36 CONCLUSIONS 41 LITERATURE CITED 42 APPENDICES: I . Maps o f the Study Area 45 I I . Tree Counts i n the Relascope (BAF = 9) P l o t s 47 I I I . Tree counts i n the Pr i s m (BAF = 6) P l o t s 48 IV. Tree Diameter Measurements ... 49 V. Tree T o t a l Height Measure- ments 57 V I . Sample Q u e s t i o n n a i r e o f the Instrument User P r e f e r e n c e Survey 59 - v i - LIST OF TABLES Table Page I ANOVA Table f o r Tree Count . 15 II Important S t a t i s t i c s from the Tree Count ANOVA 17 III ANOVA Table for the Prism Plots 17 IV ANOVA Table for the Relascope Plots 18 V ' Tree Count Accuracy i n the Prism Plots 19 VI Tree Count Accuracy i n the Relascope Plots 19' VII Tree Diameter Measurements Accuracy 26 rIII The D i s t r i b u t i o n of Diameter Measurement Errors by Diameter Classes 29 IX Tree Total Height Measurement Accuracy 3.1 X The D i s t r i b u t i o n of Height Measurement Errors by Height Classes 32 - v i i - LIST OF FIGURES F i g u r e „ l a A P l o t o f the R e s i d u a l s a g a i n s t True Counts w i t h the Relascope 2G l b A P l o t o f the R e s i d u a l s a g a i n s t True Counts w i t h the Prism 21 2a R e l a t i o n s h i p between True Count and the Crew (Estimated) Count i n the Relascope P l o t s 22 2b R e l a t i o n s h i p between True Count and the Crew (Estimated) Count i n the Prism P l o t s 23 3 A P l o t o f the R e s i d u a l s a g a i n s t True Diameter Measurement 2 7 4 R e l a t i o n s h i p between True Diameter and the Crew (Estimated) Diameter Measurement 2 3 5 A P l o t o f the R e s i d u a l s a g a i n s t True T o t a l H e i g h t Measurement 33 6 R e l a t i o n s h i p between True H e i g h t and the Crew (Estimated) T o t a l Height Measurement 3<1 - v i i i - ACKNOWLEDGEMENTS I am most g r a t e f u l to Dr. D.D. Munro f o r s u g g e s t i n g the problem and s u p e r v i s i n g me on the study, t o the members of my committee - Drs. J.P. Demaerschalk, A. Kozak and D.D. Munro - f o r r e v i e w i n g the t h e s i s , and to Dr. S.W. Nash of the Department o f Mathematics f o r recommending the A n a l y s i s o f V a r i a n c e Model used h e r e i n . I am g r e a t l y i n d e b t e d to Makerere U n i v e r s i t y , Uganda, f o r the f i n a n c i a l support i n form of a study f e l l o w s h i p , and to the F o r d Foundation f o r E a s t e r n A f r i c a f o r a d m i n i s t e r i n g the f e l l o w s h i p . F o r the a d d i t i o n a l f i n a n c i a l support i n form o f the Donald S. McPhee F o r e s t r y Award, I acknowledge The U n i v e r s i t y o f B r i t i s h Columbia and a l l those who made i t p o s s i b l e . I am a l s o g r a t e f u l to the F a c u l t y o f F o r e s t r y 1977 S p r i n g S c h o o l C l a s s o f whom I took advantage to c o l l e c t d a t a f o r the study, t o a l l the members o f the B i o m e t r i c s Group, F a c u l t y of F o r e s t r y , f o r t h e i r i n v a l u a b l e s u g g e s t i o n s , and t o The U n i v e r s i t y o f B r i t i s h Columbia Computing Centre f o r the p r o v i s i o n of computing f a c i l i t i e s . -1- INTRODUCTION F o r e s t i n v e n t o r i e s form a b a s i c requirement i n most aspects o f f o r e s t r e s o u r c e s management. I t i s t h e r e f o r e n e cessary to conduct i n v e n t o r i e s e f f i c i e n t l y and w i t h a minimum of e r r o r . V a r i a b l e - r a d i u s p l o t (VRP) sampling i s an e f f i c i e n t , unbiased, and v a l i d f o r e s t i n v e n t o r y technique; however, s i g n i f i c a n t v a r i a t i o n s have been observed among the r e s u l t s of independent c r u i s e r s . These v a r i a t i o n s are a r e s u l t o f measurement e r r o r s caused by measurer b i a s o r use o f faulty i n s t r u m e n t s . T h i s t h e s i s examines the e r r o r s o f measurement d u r i n g a VRP f o r e s t c r u i s e , a t t r i b u t a b l e to the measurer. The main parameters measured i n a VRP c r u i s e a r e : the t r e e count, the diameter a t b r e a s t h e i g h t (dbh), and t o t a l h e i g h t . The sources o f p o s s i b l e measurement e r r o r s a r e d i f f e r e n t f o r each parameter. The common causes o f the t r e e count e r r o r s , as a con- sequence of o b s e r v e r b i a s , are the f o l l o w i n g : a) f a i l u r e t o s e l e c t " d o u b t f u l " t r e e s , b) m i s s i n g hidden t r e e s , c) f a i l u r e t o make e x a c t l y a 360° sweep, d) f a i l u r e t o a l i g n instrument w i t h the t r e e , e) f a i l u r e t o c o r r e c t f o r s l o p e , f) moving ins t r u m e n t away from the p l o t c e n t e r . A small e r r o r i n t r e e count r e s u l t s i n a l a r g e percentage e r r o r i n the e s t i m a t e o f b a s a l area per u n i t a r e a , because VRP samples are based on a r e l a t i v e l y s m a l l number o f t r e e s per p l o t . In B r i t i s h Columbia, the instrument used f o r measuring t r e e dbh i s the diameter tape. D u r i n g measurement sys t e m a t i c e r r o r s o f random magnitude, o c c u r . They are caused by the f o l l o w i n g : a) the t i l t i n g o f the tape such t h a t p a r t or whole of the c i r c u m f e r e n c e of the tape i s below or above the c o r r e c t measuring plane, o f t e n r e s u l t i n g i n an o v e r e s t i m a t e , b) the t a k i n g o f measurements a t h e i g h t s o t h e r than 1.3m above average ground l e v e l (or g e r m i n a t i o n p o i n t ) o f a t r e e , c) p e r s o n a l judgement i n regard to the i r r e g u l a r stem forms. These e r r o r s have a s i g n i f i c a n t i n f l u e n c e i n the e s t i m a t e o f t r e e volumes, e s p e c i a l l y i f the t r e e h e i g h t s are a l s o i n - a c c u r a t e l y determined* The common causes of e r r o r i n t r e e h e i g h t measurement based on t r i g o n o m e t r i c p r i n c i p l e s , are the f o l l o w i n g : a) m i s r e a d i n g i n s t r u m e n t s as a r e s u l t o f u n s t e a d i n e s s , b) d i f f i c u l t y i n l o c a t i n g s u i t a b l e p o i n t s from which t o observe the exact p o s i t i o n of the t r e e top and base, c) h o r i z o n t a l d i s t a n c e measurement e r r o r s - not p u l l i n g the tape t i g h t , i n c o r r e c t alignment of the tape, erroneous l o c a t i o n o f the zero p o i n t of tape, ommission of whole tape l e n g t h , and the use o f i n - c o r r e c t tape l e n g t h , d) b i a s e s o f i n d i v i d u a l persons as a r e s u l t of l e a n i n g t r e e s , -3- Measurement o f t r e e h e i g h t s r e q u i r e s s k i l l and c a r e , w i t h o u t which l a r g e e r r o r s may r e s u l t . Measurement e r r o r s i n f l u e n c e the r e l i a b i l i t y o f an i n v e n t o r y r e s u l t . T h i s i n f l u e n c e i s o f t e n underestimated, mainly because o f the d i f f i c u l t y i n o b t a i n i n g w e l l - f o u n d e d q u a n t i t a t i v e e s t i m a t e s o f the e r r o r s . The ob j e c t i v e o f t h i s study w i l l be to determine the b i a s e s and v a r i a t i o n among independent c r u i s e r s , o f t r e e count, dbh, and t o t a l h e i g h t measurement. T h i s w i l l be used as a b a s i s f o r the e s t a b l i s h m e n t o f g u i d e l i n e s f o r performance and c h e c k c r u i s i n g , and f o r r e v i s i n g the f o r e s t i n v e n t o r y measurement standards o f the B r i t i s h Columbia F o r e s t S e r v i c e i f d e s i r e d . -4- LITERATURE REVIEW A measurement e r r o r i s the d i f f e r e n c e between a true value of a u n i t and an in e x a c t measurement of the u n i t . I t may be due to the f o l l o w i n g , FAO (1973) : (a) a constant b i a s , (b) a v a r i a b l e component r e l a t i v e to the sampling u n i t being c o r r e l a t e d to the exact value of the measurement perameter i n the corresponding u n i t , (c) an a r b i t r a r y component w i t h mean zero. The sources, k i n d s , and i n f l u e n c e s of measurement e r r o r s have been d i s c u s s e d by Loetsch e t a l . (1973) . They emphasized the importance of measurement e r r o r s and c l a s s i f i e d the e r r o r sources as f o l l o w s : (a) p e c u l i a r i t i e s of the o b j e c t being measured, (b) u n c e r t a i n t i e s i n the measuring procedure, (c) inaccuracy of the measuring device, (d) t o p o g r a p h i c a l or p h y s i c a l i n f l u e n c e s , (e) defe c t s i n the observer senses. They f u r t h e r d i s t i n g u i s h e d between " t r u e " and "apparent" e r r o r s , and s t a t e d (p. 12) : " f o r comparative measurements used i n p r a c t i c e f o r e s t i m a t i n g the accuracy and e f f i c i e n c y of a measuring procedure and as a c o n f i r m a t i o n of the c o r r e c t n e s s of a statement i n ge n e r a l , o n l y "apparent" d e v i a t i o n s ( e r r o r s ) can be proven". Measurement e r r o r s have a l s o been discussed by Cochran (1973) and Carron (1968) . Ferguson (1975) pointed out tha t although the measurement e r r o r s a f f e c t i n g f o r e s t i n v e n t o r y estimates have long been known, there have been few e m p i r i c a l s t u d i e s on the magnitude of the e f f e c t of these e r r o r s . Some of these s t u d i e s w i l l be -5- mentioned below. K e n d a l l and S a y n - W i t t g e n s t e i n (1959) emphasized t h a t o f t h e s o u r c e s o f e r r o r i n VRP f o r e s t i n v e n t o r y , t h o s e a t t r i b u t a b l e t o the o b s e r v e r were most i m p o r t a n t and f r e q u e n t . K e r , e t a l _ . (19 57) r e p o r t e d b i a s e s o f u n t r a i n e d s t u d e n t s i n e s t i m a t i n g b a s a l a r e a per a c r e (ha.) w i t h a 3 - d i o p t e r (BAF = 2.2) p r i s m , t o be between -37% t o 1%. They found a t r e e c o u n t v a r i a t i o n among the s t u d e n t s t o be 1 t r e e p e r p l o t and an average n e g a t i v e b i a s o f 1.2% o f t h e a c t u a l t a l l y . They a l s o o b s e r v e d t h a t e r r o r s were not a s s o c i a t e d w i t h ground s l o p e , b u t r a t h e r w i t h t h e age o f t h e s t a n d . Carow (1958) o b s e r v e d t h a t t h e r e was a d e f i n i t e p e r s o n a l b i a s i n j u d g i n g l i n e t r e e s w i t h a r e l a s c o p e , and t h a t t h e c o e f f i c i e n t s o f v a r i a t i o n i n b a s a l a r e a d e t e r m i n a t i o n i n - c r e a s e d w i t h i n c r e a s e i n BAF. He o b s e r v e d a 38.7% c o e f f i c i e n t o f v a r i a t i o n w i t h a 49.0 minute (BAF = 2.17) and 69.0 m i n u t e (BAF = 4.35) a n g l e c o u n t , and 42.9% w i t h a 97.4 m i n u t e (BAF = 8.71) a n g l e . K e n d a l l and S a y n - W i t t g e n s t e i n (1959) compared t h e e r r o r s made by f o u r o p e r a t o r s t a k i n g i n d e p e n d e n t a c r e (ha ) t r e e c o u n t s a t 9 l o c a t i o n s (and u s i n g d i f f e r e n t BAFs) w i t h t r u e c o u n t s o b t a i n e d by c a r e f u l measurement. They o b t a i n e d an average e r r o r o f -6% w i t h BAF = 5 ( 1 . 1 4 ) , -3.5% w i t h BAF = 10 ( 2 . 2 9 ) , 1.5% w i t h BAF = 20 (4.59) and 4.5% w i t h BAF = 40 (9.18) . They a t t r i b u t e d the l a r g e e r r o r p e r c e n t by t h e o b s e r v e r s t o t h e f a c t t h a t o n l y a s m a l l number o f sample p o i n t s was used and t h a t the o b s e r v e r s d i d n o t check t h e -6- " d o u b t f u l " t r e e s . Stage (1962) reported on t e s t s of d o u b t f u l t r e e judgement made by f i e l d crews and f o r e s t r y students matching photographs. He deduced t h a t the assumption of t a l l y i n g one-half of marginal t r e e s could not be r e l i e d upon as not unbiased. He a l s o noted t h a t q u a l i f y i n g t r e e s were more l i k e l y to be missed w i t h smaller BAFs, and t h a t personal b i a s i n p r i s m sampling could be a r e s u l t of d i f f e r e n c e s i n response by d i f f e r e n t persons to t r e e bark and background c o l o u r . Willingham (196 2) on experiments w i t h p r i s m c a l i b r a t i o n r eported t h a t a g r e a t e r magnitude of e r r o r was l i k e l y to occur i n the e x c l u s i o n of t r e e s t h a t should be counted. He emphasized the importance of a personal c a l i b r a t i o n f o r each user of a given prism. Sayn-Wittgenstein (1963) reported t h a t there was one t r e e about which there was some doubt f o r every two t r e e s the observer was sure about. With the small BAFs, a s s o c i a t e d w i t h h i g h t r e e counts per p o i n t , the number of d o u b t f u l t r e e s was l a r g e . This provided an o p p o r t u n i t y f o r b i a s (mainly an underestimate). Sayn-Wittgenstein a l s o showed t h a t personal b i a s enters i n t o the e r r o r s a s s o c i a t e d w i t h l a r g e BAFs and low t r e e count per p o i n t . A p r o p e r l y executed re l a s c o p e c r u i s e y i e l d s r e s u l t s of o n l y a n e g l i g i b l e b i a s . K i r b y (1965) s t r e s s e d t h a t b i a s i n i n v e n t o r y estimates could be prevented by e l i m i n a t i n g as much as p o s s i b l e , human judgement i n the f i e l d . Munro (1966) reporte d a c o e f f i c i e n t of v a r i a t i o n of ± 11.15% among student crew estimates of i n d i v i d u a l p l o t s . A l l the c r u i s e r s had been i n s t r u c t e d to check d o u b t f u l t r e e s . The same study showed a negative, s t a t i s t i c a l l y i n s i g n i f i c a n t b i a s of 2.1% i n t r e e count. There was no c o n s i s t e n t r e l a t i o n - s h i p between pers o n a l e r r o r and the number of t r e e s per p l o t , slope of the p l o t , s i z e , species o r p o s i t i o n o f t r e e s w i t h i n the p l o t . 92% of the p l o t s measured had e r r o r s of ± 1 t r e e or l e s s . A BAF = 30 (6.88) prism was used. Holgate (1967) showed mathematically t h a t small c r i t i c a l angles were a s s o c i a t e d w i t h smaller v a r i a n c e s of t r e e count. He confirmed h i s r e s u l t s w i t h the f i n d i n g s of Husch (1955) . Carow and R i c k e r d (1969) reported the r e s u l t s o f a study o f personal b i a s i n p o i n t sampling. A c r u i s e r over- estimated b a s a l area per acre (ha ) by 6% w i t h the BAF = 10 (2.29) and BAF = 20 (4.59) prisms, came c l o s e w i t h the BAF = -40 (9.18) wedge, and made a s l i g h t underestimate w i t h the BAF = 75 (17.21) angle gauge. They reported t h a t the between people v a r i a n c e was s t a t i s t i c a l l y s i g n i f i c a n t a t the 5% l e v e l , i n an experiment to measure the c r i t i c a l d i s t a n c e o f a BAF = 10.25 (2.35) prism. However, i n d i v i d u a l p e r s o n a l b i a s tended to be c o n s i s t e n t i r r e s p e c t i v e o f the BAF used, though i t was p o s s i b l e f o r an i n d i v i d u a l to have a p o s i t i v e b i a s w i t h one BAF and a negative one w i t h another. They r e - commend c h e c k c r u i s i n g to be done i n terms of b a s a l area, r a t h e r than t r e e count. -8- L a a r (1970) compared e s t i m a t e s o f b a s a l a r e a p e r ha o b t a i n e d w i t h a r e l a s c o p e (BAF =8.7) and a wedge p r i s m (BAF = 10.25), and found t h a t the r e l a s c o p e showed a n e g a t i v e b i a s o f 4.5% and t h e p r i s m was u n b i a s e d ( u s i n g the f i x e d p l o t t r e e c o u n t s as the c o n t r o l ) . B i a s i n r e l a s c o p e e s t i m a t e s was a t t r i b u t e d t o the p e r s o n a l e lement i n t h e e v a l u a t i o n o f " b o r d e r l i n e " t r e e s . He r e i t e r a t e d t h a t p r o - v i d i n g more c o n t r a s t between t r e e stems and t h e i r b a ckground d i d n o t improve t h e d e t e r m i n a t i o n o f the s t a t u s o f " b o r d e r - l i n e " t r e e s . T h i s c o n f l i c t s w i t h S t a g e s ' (1962) recommenda- t i o n s o f p r o v i d i n g c o n t r a s t between t r e e stems and t h e i r b a c k - ground. Few i n v e s t i g a t i o n s have been made on t h e v a r i a t i o n i n d i a m e t e r a t b r e a s t h e i g h t and i n t r e e t o t a l h e i g h t measure- ments. Some o f t h e s e i n v e s t i g a t i o n s a r e m e n t i o n e d i n t h e f o l l o w i n g p a r a g r a p h s . Myers (1961) f o u n d t h a t 94% o f t h e measurements, under- t a k e n by f o r e s t r y s t u d e n t s and f i e l d f o r e s t e r s on permanent sample p l o t s o f p o n d e r o s a p i n e , were w i t h i n 0.1 i n c h (0.254 cm) o f t h e t r u e d i a m e t e r . Modal d i a m e t e r was t a k e n t o be t h e " t r u e " d i a m e t e r o f a t r e e . He n o t e d no t r e n d o f v a r i a t i o n i n a c c u r a c y w i t h i n c r e a s e i n d i a m e t e r a t b r e a s t h e i g h t .Sixty-two percent of the measurements were c o r r e c t . There were more measurements t h a t were t o o l a r g e t h a n were too s m a l l , i n d i c a t i n g more s o u r c e s o f p o s i t i v e e r r o r s . Most o f the l a r g e e r r o r s were due t o i n c o r r e c t t a p e r e a d i n g s o r r e c o r d i n g s ; b u t t h e s e g r e a t l y i n c o r r e c t measurements were e q u a l l y l a r g e r and s m a l l e r -9- than th e t r u e dbh. K e r (1951) r e p o r t e d s t a n d a r d e r r o r s o f s i n g l e t r e e h e i g h t s o f 1.4% f o r immature Douglas f i r and 2.3% f o r w e s t e r n hemlock. Meyer (195 3) n o t e d t h a t r e p e a t e d measurements made w i t h the U n i t e d S t a t e s F o r e s t S e r v i c e hypsometer and t h e C h r i s t e n hypsometer o f s i x d i f f e r e n t t r e e s r e s u l t e d i n s t a n d a r d e r r o r s o f h e i g h t s v a r y i n g between 1.1% t o 3.5%. Ker and S m i t h (1957) found a s t a n d a r d e r r o r o f 2.4% f o r f o r e s t r y s t u d e n t s w o r k i n g under near optimum c o n d i t i o n s u s i n g a r e l e s c o p e , and 1.8% u s i n g a B j u m l e i s s hypsometer .They ex- p r e s s e d t h e view t h a t t r e e h e i g h t measurements were d i f f i c u l t and e x p e n s i v e t o o b t a i n and were s u b j e c t t o l a r g e r and more s o u r c e s o f e r r o r . Schmid e t a l . (1971) n o t e d t h a t i n t r e e h e i g h t measure- ment, t h e e r r o r s o f measurement i n c r e a s e d i n a l m o s t e x a c t p r o p o r t i o n t o t h e h e i g h t o f t h e t r e e , i r r e s p e c t i v e o f t h e i n s t r u m e n t t h e y u s e d . They a l s o o b s e r v e d t h a t s y s t e m a t i c e r r o r s r e s u l t e d when t h e t r e e s were n o t e x a c t l y v e r t i c a l o r when the t o p was f l a t t e n e d o f f (and the p e r s o n m e a s u r i n g d i d n o t s t a n d f a r enough away from th e t r e e base) . -10- SOURCE OF DATA Data f o r t h i s study w e r e c o l l e c t e d a t The U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t , Maple Ridge, B r i t i s h Columbia, d u r i n g the t h i r d year f o r e s t r y s t u d e n t s f i e l d s c h o o l i n mensuration. S i x t y p l o t c e n t e r s , numbered'1 through 60, were system- a t i c a l l y s e t a t about 80 m (paced) i n t e r v a l s a l o n g the S t . Jean's and Lakeshore t r a i l s of the r e s e a r c h f o r e s t . The t r a i l s a r e i n a second growth stand about 80 y e a r s o l d , c o n t a i n i n g mainly D o u g l a s - f i r (Pseudotsuga m e n z i e s i i (Mirb.) F r a n c o ) , western hemlock (Tsuga h e t e r o p h y l l a (Raf.) S a r g . ) , and western redcedar (Thuja p l i c a t a Donn.) i n i n t i m a t e mixture. S i t e index ranges from 15m to 50m a t 100 y e a r s . 3 Gross volume averaged 650 m /ha. Tree dbh ranged from 5 cm to 190 cm, the average diameter being 53 cm. Topography v a r i e d from steep (over 50% slope) to r e l a t i v e l y f l a t (see maps 1 and 2, i n the appendix I ) . Underbrush and the weather d i d not r e s t r i c t l i n e - o f - s i g h t v i s i b i l i t y . The p l o t c e n t e r s were d i v i d e d i n t o s i x l o t s o f t e n . Three to s i x 3-man student crews were a l l o c a t e d t o each l o t . Each crew e s t a b l i s h e d prism (BAF = 6) and r e l a s c o p e (BAF = 9) p l o t s a t the p r e - s e t p l o t c e n t e r s d e s i g n a t e d to them. The s t u d e n t s had had a t h e o r e t i c a l background o f VRP sampling, and many o f them had v a r i e d f i e l d e x p e r i e n c e s i n p r i s m and r e l a s c o p e c r u i s i n g . Furthermore, the students were g i v e n two hours f i e l d i n s t r u c t i o n i n p r i s m use and were made aware of the f o l l o w i n g p r e c a u t i o n s to be borne i n mind -11- d u r i n g p l o t e s t a b l i s h m e n t w i t h the prism and 1 the r e l a s c o p e : i ) the p r i s m always to be h e l d d i r e c t l y above the p l o t c e n t e r when s i g h t i n g a t any t r e e i n a 360° sweep about the p o i n t , i i ) the prism t o be h e l d so t h a t i t s base was p e r p e n d i - c u l a r t o the stem o f the t r e e b e i n g measured (except when the l i n e o f s i g h t t o the t r e e exceeded an angle o f 10% from the h o r i z o n a l when s l o p e c o r r e c t i o n would be needed), i i i ) the p r i s m to be h e l d so t h a t i t s f a c e was p e r p e n d i - c u l a r to the l i n e o f s i g h t , i v ) a l l hidden t r e e s to be examined by moving the o b s e r v a t i o n p o i n t p r o v i d e d the e x a c t d i s t a n c e from the p l o t p o i n t to the t r e e was m a i n t a i n e d , v) a l l " d o u b t f u l " t r e e s to be checked by a p p l y i n g the a p p r o p r i a t e p l o t r a d i u s f a c t o r , v i ) the r e l a s c o p e to be h e l d d i r e c t l y above the p l o t c e n t e r , v i i ) ensure t h a t the r e l a s c o p e i s c o r r e c t e d f o r s l o p e , v i i i ) observe the t r e e s a t 1.3 m above i t s average ground l e v e l (or germi n a t i o n p o i n t ) . In o r d e r t o make meaningful comparisons and to e s t a b l i s h l i m i t s o f p r e c i s i o n and accuracy, i t was n e c e s s a r y t h a t each crew adhere to the same procedures e x a c t l y . P l o t t a l l y was s t a r t e d from t r u e North and each " i n " t r e e ( i n - c l u d i n g stumps g r e a t e r than 2 m high) was t a l l i e d on a cl o c k w i s e 360° sweep. The dbh of every " i n " t r e e was measured t o the n e a r e s t 0.1 cm with a l i n e n diameter tape, and r e c o r d e d i n st a n d a r d forms. The t r e e s p e c i e s name was -12- noted. The t o t a l h e i g h t of the f i r s t " i n " t r e e on each p l o t was measured to the n e a r e s t 0.1 mf. by t r i g o n o m e t r i c p r i n c i p l e s u s i n g a suunto or r e l a s c o p e and a ny l o n c h a i n . A prism was used on the even-numbered p l o t s , and a r e l a s c o p e on the odd-numbered p l o t s . The crews made t h e i r measurements and r e c o r d i n g s i n d e p e n d e n t l y o f each o t h e r , and had to complete t h e i r study w i t h i n a p e r i o d of e i g h t hours. As a c o n t r o l t o the study, I made independent o b s e r v a t i o n s and measurements, by c a r e f u l l y e s t a b l i s h i n g p r i s m and r e - lascope p l o t s i n a l l the p r e - s e t sample p l o t c e n t e r s and a b i d i n g by the same procedures the student crews had been i n s t r u c t e d t o f o l l o w . There was no time l i m i t . The t r e e count, dbh, and t o t a l h e i g h t measurements by the d i f f e r e n t crews and the c o n t r o l are g i v e n i n the appendices I I , I I I , IV and V. -13- METHOD OF ANALYSIS AND RESULTS L o t number 2 o f the sample p l o t s had o n l y one s e t of crew measurements, and so was d i s c a r d e d from the f i r s t p a r t of the a n a l y s i s . Each o f the remaining sample p l o t s had 3 to 6 independent s e t s o f crew measurement o f ( i ) t r e e count, ( i i ) t r e e dbh, and ( i i i ) t r e e t o t a l h e i g h t . P r i s m p l o t measurements were separate from those of the r e l a s c o p e . As mentioned i n the i n t r o d u c t i o n , the aim o f t h i s a n a l y s i s i s to o b t a i n a q u a n t i t a t i v e e s t i m a t e o f crew v a r i a t i o n and b i a s i n e s t i m a t i n g the t r e e count per p l o t , and dbh and t o t a l h e i g h t per t r e e . F i r s t l y , the crew v a r i a t i o n i n t r e e count e s t i m a t e s was asse s s e d by the method o f a n a l y s i s o f v a r i a n c e (ANOVA). Secondly, the crew v a r i a t i o n i n measuring t r e e dbh and t o t a l h e i g h t was assessed by c a l c u l a t i n g the v a r i a t i o n f o r each t r e e and p o o l i n g these t o o b t a i n a weighted average v a r i a t i o n per t r e e . In e i t h e r case, b i a s was determined by comparing crew measurements w i t h the c o n t r o l v a l u e s . TREE COUNT The c o n t r o l s e t o f data was t r e a t e d t o g e t h e r w i t h the student crew data, so t h a t f o r each l o t th e r e were up to 7 se t s o f measurement per p l o t . There was, t h e r e f o r e , a 25 x 7 t r e e count m a t r i x , w i t h some o b s e r v a t i o n s m i s s i n g , f o r each o f the pr i s m p l o t s and the r e l a s c o p e p l o t s . F i r s t , the crew and p l o t v a r i a t i o n a t each p l o t was determined by the method o f ANOVA. -14- The d e s i g n used was repeated subsampling w i t h unequal numbers i n the s u b c l a s s e s . The p l o t s and crews were nested w i t h i n the l o t s . L o t s v a r i e d from i = 1 t o p = 5, p l o t s from j = 1 to q = 5, and crews from k = 1 to s ( v a r y i n g between 4 and 7). The l o t s were c o n s i d e r e d f i x e d and the p l o t s and crews random. The model was: X ± j k = y + g. + V j ( i ) + 6 k ( i ) + l j k ( i ) (1) where: X. ., = t r e e count o f the k crew on the i 3 th p l o t i n the i l o t u = o v e r a l l t r e e count mean Der o l o t t h = e f f e c t of the i l o t v j ( i ) = e f f e c t o f the j ^ 1 1 p l o t w i t h i n the l o t 6 k ( i ) = e ^ ^ e c t °^ t n e crew w i t h i n the i t h l o t $ t h th j k ( i ) = the i n t e r a c t i o n o f the j p l o t and k crew w i t h i n the i t h l o t (ERROR). Reference t o t h i s model i s made to G a n g u l i (1941) and to Drs. A. Kozak and S.W. Nash ( p e r s o n a l communication) . The g e n e r a l p l a n o f the ANOVA i s shown i n Table I . TABLE I ANOVA T a b l e For Tfee Count Source of Variation Degrees of Freedom (d..:f.) Between lots P - 1 Sum of Squares SS. = p - - 2 qs. I n (x. - x ) 1 = 1 1.. Expected JMean Squares S? = a2 + qa 2 + s a 2 + qsa^ l ^ 5 V P Between plots- witain-lots p(q - 1) SS., = p q _ 2 s i I (x.. - x. ) i=l j=l ID. l . S 2 v= a 2 + s c 2 j ( i ) Between crews- wi thin-lots .T. n. - p i=l l ^ P s - - 2 S S = q I I (x. - x. ) C i=l k=l 1 , J C X " i Error Total (q-1) (.1, n.- p)- m 1—X a. q I n. - 1 - m i - i SS = SS m --SS - SS - SS, E SS T L P C p q s _ 2 I I I (x. ., - x...) i=l j=l k=l 1 3 S 2 o X = ^ i . . x. . = _i . k x. . = ID- m = *l = c z = V tree count mean per plot of a l l the crews i n a l l the plots i n a l l the lots, tree count mean per plot of a l l the crews i n a l l the plots i n the i^1 l o t . tree count mean per plot of the k^ 1 crew i n a l l the plots i n the i l e t . tree count mean per plot of a l l the crews i n the j ^ 1 plot i n the i ^ l o t . th the number of crews i n the i l o t . the t o t a l number of missing observations i n a tree count matrix. the l o t variation* plot variation. crev; variation - I Cn? i=l ( l / n . ) - ( l / I n.) 1 i=l ~ p-1 (2 -16- The sums o f s q u a r e s S S L , S S p , S S C , S S E , S S T i n T a b l e I were computed u s i n g t h e g e n e r a l r e g r e s s i o n method. The UBC GENLIN - a g e n e r a l l e a s t squares a n a l y s i s o f v a r i a n c e computer program o f the U n i v e r s i t y o f B r i t i s h . C o l u m b i a -was used. The components o f v a r i a n c e and t h e i r c o e f f i c i e n t s were d e r i v e d w i t h r e f e r e n c e t o Anderson and B a n c r o f t (1952) . By u s i n g t h e a p p r o p r i a t e mean sq u a r e s from t h e ANOVA t a b l e , t h e e s t i m a t e s o f crew v a r i a n c e , and p l o t v a r i a n c e , a 2 , were made as f o l l o w s : v S 2 - S 2 52 = _ M i L o ( 3 ) 6 q S 2 S 2 a2 = o ( 4 ) v s The crew d e v i a t i o n e s t i m a t e w i t h t h e p r i s m was 0.993 t r e e s p e r p l o t and w i t h the r e l a s c o p e 0.366 t r e e s p e r p l o t . P l o t d e v i a t i o n w i t h t h e p r i s m was 3.134 t r e e s and w i t h t h e r e l a s c o p e was 2.080 t r e e s . T a b l e I I g i v e s a summary o f some o f the more i m p o r t a n t s t a t i s t i c s i n the a n a l y s i s , and t a b l e s I I I and I V g i v e t h e ANOVA r e s u l t s o f t h e p r i s m and r e l a s c o p e p l o t s , r e s p e c t i v e l y . S e c o n d l y , each p l o t measurement was t r e a t e d i n d e p e n d e n t l y i r o r d e r t o e v a l u a t e the t r e e count a c c u r a c y . U s i n g t h e t o t a l number o f p l o t measurements the v a r i a t i o n o f t h e p l o t measure- ments was c a l c u l a t e d by v a r i a t i o n from c o n t r o l (VFC) c l a s s e s . The f o l l o w i n g VFC c l a s s e s were used i n t h e a n a l y s i s : 0, ± l , i 2> + 3, ± 4, ± 5, ± 6 t r e e s . The maximum t r e e count e r r o r p e r p l o t was ± 6 t r e e s and -17- TABLE I I . I m p o r t a n t S t a t i s t i c s From The Tree Count ANOVA- I n s t r u m e n t O v e r a l l Mean W i t h 95% Conf. L i m i t s ( t r e e s / p l o t ) C o e f f . o f V a r i a t i o n o f Crews (%) Stand C o e f f . o f V a r i a t i o n (%) P r i s m 9.509 ± 7.280 10.44 32.96 (8.880 ± 6.257) (34.08) R e l a s c o p e 7.432 ± 5.420 4.93 28 .04 (7.400 ± 4.801 (26.82) Note: The v a l u e s i n b r a c k e t s a r e the r e s u l t s o f the C o n t r o l measurements. TABLE I I I . ANOVA T a b l e f o r the P r i s m P l o t s Source o f Sum o f Mean V a r i a t i o n d.f. Squares Square F - r a t i o Notes Between l o t s 4 408 .43 102.11 1. 513 N.S. Between p l o t s - wi t h i n - l o t s 20 1250.90 62.54 28 .820 @ Between c r e w s - wi t h i n - l o t s 26 184.74 7.10 3. 27 2 @ E r r o r 100 217.01 2.17 T o t a l 150 2061.08 @ S i g n i f i c a n t a t ct = 0.05 p r o b a b i l i t y l e v e l N.S. Not s i g n i f i c a n t TABLE IV: ANOVA T a b l e f o r the R e l a s c o p e P l o t s Source of V a r i a t i o n d . f . Sura o f squares Mean square F- r a t i o Notes Between l o t s 4 3 38.15 84.53 2. 915 *7 C Between P l o t s - w i t h i n - l o t s 20 566 . 45 28 . 32 17.374 @ Between c r e w s - w i t h i n - l o t s 26 59.92 2. 30 1.411 N.S . E r r o r 97 158.47 1.63 T o t a l 147 1122.99 @ S i g n i f i c a n t a t a = o.05 p r o b a b i l i t y l e v e l N.S. Not s i g n i f i c a n t . i t o c c u r r e d i n 2 o u t o f 130 p r i s m p l o t measurements and i n 2 o u t o f 124 r e l a s c o p e p l o t measurements. The a l l o w a b l e t r e e c o u n t e r r o r i n t h e 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 i s ± 1 t r e e , UBC F o r e s t C l u b (1971). T a b l e s V and VI summarize t h e a c c u r a c y i n t r e e c o u n t , i n t h e p r i s m and r e l a s c o p e p l o t s , r e s p e c t i v e l y . There were more n e g a t i v e s o u r c e s o f e r r o r t h a n p o s i t i v e ones ( F i g . l a , b ) . I n t h e p r i s m p l o t s , 56% o f the t r e e c o u n t s were o v e r - e s t i m a t e d , and i n t h e r e l a s c o p e p l o t s , 4 2% o f t h e t r e e c o u n t s were o v e r e s t i m a t e d . The a c c u r a c y o f t h e crew t r e e c o u n t s a g a i n s t t h e c o n t r o l was t e s t e d by f i t t i n g a l i n e a r r e g r e s s i o n o f t h e crew t r e e c o u n t s (X-.,) on t h e c o n t r o l t r e e c o u n t s (X ) , and then u s i n g t h e s t u d e n t t - t e s t , t o t e s t whether the s l o p e was s t a t i s - t i c a l l y d i f f e r e n t from u n i t y . I f t h e s l o p e was n o t d i f f e r e n t from unity , t h e i n t e r c c p i o f t lie r e g r e s s i o n l i n o was t e s t e d whether i t was s t a t i s t i c a l l y d i f f e r e n t from */.oro -19- TABLE V- Tree Count Accuracy i n the Prism P l o t s VFC (Trees) No. of P l o t •Measurements Percent of t o t a l (%). Pe r c e n t of t o t a l (cumulative) (%) ±0 32 24.62 24.62 ±1 38 29 .23 53.85 ±2 27 20.77 74.62 ±3 16 12.30 86.92 ±4 6 4.62 91.54 ±5 9 6.92 98.46 ±6 2 1.54 100.00 T o t a l 130 100.00 - Table VI. Tree Count Accuracy i n the Relascope P l o t s VFC (trees) No. of p l o t Measurements Percent of t o t a l (%) P e r c e n t of t o t a l (cumulative) (%) + 0 46 37.10 37 .10 * 1 45 36.29 73.39 + 2 13 10.48 83.87 + 3 10 8 .06 91.93 + 4 4 3.23 95.16 + 5 4 3.23 98.39 ± 6 2 1.61 100.00 T o t a l 124 100.00 - -20- 03 I I D I to I LU UJ OC + + 4 + + COnM + + + + — J I CC a | 4- + + + + + »—i CO o ^ - l + + 4- 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4 - 4 - 4- 4- 4- 4- 4- 4- , , , , , , R R — 0.0 2.0 A.a G.O 0.0 m.o 12.0 14.0 ie.o TRUE COUNT (TREES) F i g u r e l a A P l o t of the R e s i d u a l s A g a i n s t True Counts With the Relascope 4- + + + + + + + •f 4- + + 4 - + + + 4 - + + + + -f + + + 4 - + + + + + -r + - + + + + i 5 . 0 i B.O I 7 . 0 ' i 8 . 0 1 g.o I 1 D . 0 i 1 1 . 0 i 1 2 . TRUE COUNT [TREES} F i g u r e l b A P l o t o f the R e s i d u a l s A g a i n s t True Counts wi t h the Prism -2 2- a - 2 3 - The f o l l o w i n g r e l a t i o n s h i p s wore o b t a i n e d (sec? a l s o F i g . 2a, b ) : R e l a s c o p e _ p l o t s : 1.006 + 0.8 97 X C 0.58 7, SEE = 1.829 P r i s m p l o t s : 1.065 + 0.998 X' c (6) 0.693, SEE - 2.117 where: 2 r = the c o e f f i c i e n t of determination SEE = the standard e r r o r of the estimate A t the a = 0.05 p r o b a b i l i t y l e v e l , the i n t e r c e p t and slope of the r e g r e s s i o n l i n e CO were not s t a t i s t i c a l l y d i f f e r e n t from zero T h i s i n d i c a t e d t h a t , on average , crews c o u n t e d t r e e s w i t h o n l y a n e g l i g i b l e b i a s w i t h t h e r e l a s c o p e , and c o u n t e d t r e e s w i t h a s i g n i f i c a n t b i a s w i t h the p r i s m . DIAMETER In t o t a l 398 t r e e s were r e p e a t e d l y measured f o r d i a m e t e r by the d i f f e r e n t c r ews. The s p e c i e s measured were D o u g l a s - f i r , w e s t e r n hemlock and w e s t e r n redicdar „ F i r s t l y , t h e b i a s o f t h e crews i n m e a s u r i n g dbh was a s s e s s e d . I n o r d e r t o e v a l u a t e t h e a c c u r a c y i n m e a s u r i n g t h e d i a - m e t e r s , each t r e e measurement was t r e a t e d i n d e p e n d e n t l y . There was a t o t a l o f 1701 measurements, grouper) i n t o 5 cm dbh c l a s s e s . The c o n t r o l dbh measurements of each t r e e was a c c e p t e d as the " t r u e " dbh o f t h e t r e e . The d e v i a t i o n s f r om t r u e dbh of t h e crew measurements were c a l c u l a t e d f o r each t r e e . The f o l l o w i n g and u n i t y , r e s p e c t i v e l y ; b u t the slope o f t h e l i n e ( 6) was. -25- formula was used f o r c a l c u l a t i n g the b i a s e s : where t h Dg = dbh measurement b i a s on the i t r e e by the k.tn crew. t h = t r u e dbh of the i t r e e . t h t h D i k = d t ) n o f t h e *~ t r e e a s measured by the k crew. The biases were then grouped i n t o v a r i a t i o n from c o n t r o l (VFC) c l a s s e s f o r each dbh c l a s s . The f o l l o w i n g VFC c l a s s e s were used: VFC L i m i t s C l a s s (cm) 0 0.0-0.09 1 + 0.1-1.0 2 + 1.1-2.0 3 + 2.1-3.0 4 + 3.1-4.0 5 + 4.1-5.0 6 + 5.1-6.0 7 + 6.1-7.0 8 + 7.1-8.0 9 + 8.1-9.0 10 + > 9.0 The v a r i a t i o n i n accuracy (bias) w i t h i n c r e a s e i n dbh was a l s o i n v e s t i g a t e d . This was done by s e p a r a t i n g the measurement biases by 5 cm diameter c l a s s e s , on a r e l a t i v e b a s i s . The average stand diameter was 52.67 cm from the crew estimates, and 52.72 cm by the c o n t r o l . Only about 6% of the measurements were c o r r e c t , and 95% were w i t h i n 5.0 cm o f the true value. Fourty-cight % • Or the measurements were too l a r g e and 46% too sm a l l . This i n d i c a t e d more negative sources of e r r o r (see a l s o f i g . 3). A summary of the accuracy of diameter measurements i s aiven i n Table V I I . The al l o w a b l e dbh measurement e r r o r i n the B r i t i s h Columbia F o r e s t Service i s ±1%, U.B.C. F o r e s t Club (1971). -26- There seems to be a trend of v a r i a t i o n i n accuracy w i t h increase i n dbh. Accuracy tends to decrease a t higher dbh t r e e s . Examination of t a b l e V I I I which shows measurement d i s t r i b u t i o n by diameter c l a s s e s and d e v i a t i o n s from c o n t r o l may r e v e a l t h i s . TABLE V I I . Tree Diameter Measurements Accuracy VFC (cm) Number of measurements Percent of t o t a l (%) Percent of t o t a l ! (cumulative) (%) 0 96 5.64 5 .64 1 943 55.44 61.08 2 271 15.94 77.02 3 142 8.35 85. 37 4 68 4.00 89.37 5 57 3.35 92.72 6 39 2.29 95. 01 7 13 0.76 95.77 8 23 1.35 97 .12 9 14 0.82 97.94 10 35 2.06 100.00 T o t a l 1701 100.00 - Large e r r o r s were as much as 30 cm and were e q u a l l y l a r g e r and smaller than the t r u e dbh values. The accuracy of crews i n measuring diameters was t e s t e d by comparing the crew measurements w i t h the c o n t r o l values using the r e g r e s s i o n method adopted w i t h the t r e e count. The f o l l o w i n g r e l a t i o n s h i p was obtained (see a l s o f i g . 4 ) . D_ = -0.527 + 1 .002 D„ (8) r 2 = 0.979, SEE = 4.387 where: D,-, = estimated dbh i n cm E Dp = c o n t r o l (true) dbh i n cm to F i g u r e 3 A P l o t of the R e s i d u a l s A g a i n s t True Diameter Measurement TRUE DISMETER (CM) F i g u r e 4 R e l a t i o n s h i p Between True Diameter and the Crew (Estimated) Diameter Measurement -29- TABLE V I I I . The D i s t r i b u t i o n o f Diameter Measurement E r r o r s &y Diameter C l a s s e s Diameter Class Midpoint 0 1 2 ERROR (VFC) 3 4 5 6 CLASS 7 8 9 10 TOTAL (cm) NUMBER OF MEASUREMENTS 7 3 24 1 1 29 12 8 24 5 5 1 43 17 2 76 3 2 1 1 85 22 6 44 8 3 1 1 63 27 10 86 11 6 4 115 32 1 122 26 16 5 7 2 2 194 37 16 98 21 5 3 4 3 5 1 1 157 42 11 6 7 18 7 2 1 1 107 47 5 76 25 11 8 1 1 3 1 131 52 6 81 24 10 6 5 5 2 139 57 2 67 31 11 4 5 2 1 1 1 123 62 2 56 15 10 8 2 1 5 5 104 67 12 11 10 1 7 6 3 4 1 5 60 72 4 22 9 10 5 4 5 1 1 61 77 22 17 10 1 3 2 1 2 58 82 20 6 5 1 1 .1 1 1 36 87 1 14 7 3 1 1 1 28 92 5 9 4 1 3 1 2 25 97 1 1 2 3 1 2 10 102 1 7 5 1 4 3 1 1 26 107 1 5 2 2 10 112 2 1 3 1 1 8 117 1 1 2 12 2 5 1 1 1 1 1 10 127 1 1 3 2 4 2 13 132 1 6 4 1 3 1 1 1 18 137 1 2 1 2 2 2 10 142 1 4 1 2 8 . 152 1 3 2 6 162 1 1 1 1 1 1 3 9 167 1 1 1 1 2 6 170 1 1 1 4 7 TOTAL 96 94 3 271 14 2 68 57 59 13 23 14 35 1701 - 3 0 - The i n t e r c e p t and slope of the r e g r e s s i o n l i n e ( 8 ) were not s t a t i s t i c a l l y d i f f e r e n t from zero and u n i t y , r e s p e c t i v e l y , a t the a = 0.05 p r o b a b i l i t y . This i n d i c a t e d t h a t on average, crews measured t r e e diameters w i t h only a n e g l i g i b l e b i a s . Secondly, v a r i a t i o n i n dbh measurement from crew to crew was c a l c u l a t e d by p o o l i n g the squared d e v i a t i o n s of the crew measurements on a l l the t r e e s and d i v i d i n g the r e s u l t by the pooled degrees of freedom of a l l the measured t r e e s . Model 9 was used. n k _ 9 Z Z (D„. .- D^.K Op = 1 = 1 3=1 J n I d.f.. i = l (9) where: = diameter measurement crew v a r i a t i o n estimate j = crew j measurement on the l t r e e D_. = mean of the k measurements on the i ^ t r e e £ i 1 d.f.. = the degrees of freedom f o r the i " 1 " * 1 t r e e (=k.- 1) The average crew d e v i a t i o n i n diameter measurement was 4.3 cm per t r e e . The c o e f f i c i e n t of v a r i a t i o n = 8.16% (the average tr e e dbh was 52.67 cm). The v a r i a t i o n of p r e c i s i o n w i t h i n c r e a s e i n dbh was, i n gen e r a l , uniform (see F i g . 4 ) . TOTAL HEIGHT In 31 p l o t s the crews measured the same t r e e s f o r height. In the r e s t of the p l o t s the crews d i d not measure corresponding t r e e s . The data f o r the 31 tre e s were analysed to determine the -31- a c c u r a c y and p r e c i s i o n o f crew measurement. The r e s t o f t h e da t a were d i s c a r d e d . The p r o c e d u r e o f a n a l y s i s was s i m i l a r t o t h a t used f o r d i a m e t e r . Only seven VFC c l a s s e s , and 1 m h e i g h t c l a s s e s were used. L e s s t h a n 2% o f t h e t o t a l measurements were c o r r e c t , i f c o n t r o l v a l u e s a r e a c c e p t e d as the " t r u e " h e i g h t . About 60% o f t h e measurements were l e s s than and 4 0% more t h a n , t h e t r u e v a l u e s . D e t a i l s o f b i a s e s i n h e i g h t e s t i m a t i o n a r e shown i n T a b l e I X . Tree T o t a l H e i g h t Measurement A c c u r a c y VFC C l a s s L i m i t s (ro) Number o f measurements P e r c e n t o f t o t a l (%) P e r c e n t o f t o t a l ( c u m u lative) (%) 0 ±0.0-0.09 2 1.82 1.82 1 ±0.1-1.0 19 17.27 19.09 2 ±1.1-2.0 17 15.46 34. 55 3 ±2.1-3.0 19 17.27 51.82 4 ±3.1-4.0 18 16.36 68 .18 '5 ±4.1-5.0 11 10. 00 78 .18 6 ±5.1-6.0 6 5.46 83.64 7 >± 6.0 18 16.36 100.00 T o t a l 110 100.00 - The a l l o w a b l e t r e e h e i g h t measurement e r r o r i s ± 3% i n t h e 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 , UBC F o r e s t C l u b (1971) There was no t r e n d o f v a r i a t i o n i n b i a s e s o f t h e crews as h e i g h t i n c r e a s e d (see t a b l e X ) . V a r i a b i l i t y o f t h e r e s i d u a l s around z e r o was q u i t e h i g h (see F i g . 5) . The t r e e h e i g h t s ranged from about 8 m t o ab o u t 51 m, t h e crew a v a e r a g e b e i n g 31.38 m. The c o n t r o l a v e r a g e was 32.33 m. -32- TABLE X. The D i s t r i b u t i o n of H e i g h t Measurement E r r o r s By H e i g h t C l a s s e s HEIGHT CLASS E R R 0 R (VFC) C L A S S MID-POINT(m) 0 1 2 3 4 5 6 7 TOTAL NUMBER OF EASUREMENTS 10. 5 1 1 1 1 4 11.5 4 1 4 18.5 2 3 2 2 1 J 10 21.5 1 i •; 2 22. 5 2 1 I 4 24.5 1 1 2 26.5 2 2 3 i j 8 27.5 1 1 2 2 6 29.5 1 1 3 i 5 30. 5 1 1 3 5 31.5 1 1 1 1 i 4 32.5 1 1 2 1 3 ! 8 34.5 1 2 3 35. 5 2 1 1 2 6 37.5 2 4 6 38.5 1 1 1 3 39.5 1 2 3 40. 5 1 1 2 4 42. 5 1 1 3 1 1 7 47.5 1 2 1 1 5 48.5 1 1 2 4 50.5 1 1 2 1 1 1 ! ^ TOTAL: 2 19 17 19 18 11 6 18 110 ..,.„.» -33- + 4- + •f 4- 4= + + 4- + 4- + 4- + 4- + + + 4- 4- 4= 4- t 4- V 4- 4- + t- 4- + 4- + 4- 4- 4- + + + + + 4- 4- , , , f 1 , , 1 , — 10.D 1U.Q 20.0 25.0 53.0 Ifi.O 40.0 4r>.0 r.O 0 TRUE HEIGHT IM) F i g u r e 5 P l o t o f the R e s i d u a l s a g a i n s t True T o t a l H e i o h t M e a s u r e s A n t -24- F i g u r c 6 R e l a t i o n s h i p between True Height. and_thc Crew ( E s t i m a t e d ) T o t a l 11 e i q h t Me a s u r em e n t -35- A l i n e a r r e g r e s s i o n of the crew measurements (H ) on the c o n t r o l (true) values (H^) gave the f o l l o w i n g r e l a t i o n s h i p : H„ - 3.358 + 0.8668 1i_ (10) r 2 = 0.729, SEE - 5.62 The i n t e r c e p t of the r e g r e s s i o n l i n e (9) was s t a t i s t i c a l l y d i f f e r e n t from zero a t the a = 0.05 p r o b a b i l i t y l e v e l . This i n d i c a t e d t h a t on average, crews measured t r e e h e ights w i t h a s i g n i f i c a n t b i a s . The crew d e v i a t i o n i n measuring height was 6.86 m the c o e f f i c i e n t of v a r i a t i o n being 21.86%. There was no trend of v a r i a t i o n i n p r e c i s i o n of height measurements w i t h increase i n height (see f i g . 6). - 3 6 - DISCUSSION I t i s only u n t i l r e c e n t l y that there has been more emphasis on the accuracy of i n d i v i d u a l t r e e measurement than on, say, the t o t a l number of tr e e s measured per p l o t or the t o t a l number of p l o t s measured per day. The a n a l y s i s of e r r o r s a s s o c i a t e d w i t h basal area per ha , diameter, and height measurements was, t h e r e f o r e , a p p r o p r i a t e . The average t r e e count per p l o t i s 9.5 t r e e s w i t h a BAF = 6 prism and 7.4 t r e e s w i t h a BAF = 9 r e l a s c o p e . The c o e f f i c i e n t of v a r i a t i o n of observer t r e e count i s 10.44% w i t h the prism and 4.93% wi t h the rel a s c o p e . This means t h a t 68% of the t r e e counts f a l l w Tithin 10.44% of the average prism p l o t s count, or w i t h i n 4.9 3% o f the average r e l a s c o p e p l o t s count. Since b a s a l area per ha i s a f u n c t i o n of t r e e count per p l o t , c o n c l u s i o n s reached regarding v a r i a b i l i t y i n t r e e count can be assumed to apply w i t h reasonable c o n s i s t e n c y to b a s a l area per ha. Therefore, the percentage e r r o r i n the determination of b a s a l area per ha from the 25 prism p l o t s i s ± 4.09% and from the 25 relascope p l o t s i s ± 1.93%, a t the a = o.05 p r o b a b i l i t y l e v e l . Percentage e r r o r i s h a l f the confidence i n t e r v a l o f an estimate expressed as a percentage of the estimate. When the number of sample p l o t s i s 1, then c o e f f i c i e n t of v a r i a t i o n = percentage e r r o r . I n t h i s case, percentage e r r o r means tha t one i s 55% sure t h a t the average b a s a l area per ha i s w i t h i n 4.09% of the t r u e b a s a l area per ha. estimate w i t h the prism, or 1.93% of the t r u e b a s a l area per ha estimate w i t h the relascope. -37- The prism crew c o e f f i c i e n t of v a r i a t i o n r e s u l t i s lower than, but c l o s e to the ± .11.15% wi t h a BAF = 6.8 orism i n s i m i l a r stands found bv Munro (1966), and s l i a h t l v bigger than ± 6% w i t h a BAF = 4.6 prism found by Carow and R i c k e r d (1969). E r r o r s of t h i s magnitude warrant c h e c k c r u i s i n g programs, e s p e c i a l l y i f the number of sample p l o t s e s t a b l i s h e d i s low. The standard d e v i a t i o n i n the crew t r e e count of 0.99 3 t r e e s per p l o t using the prism i s c l o s e to t h a t of 0.805 t r e e s per p o i n t obtained by Munro (1966), t h a t of 1 t r e e per p o i n t obtained by Ker et_ a l . (1957), and i s w i t h i n the ± 1 stem al l o w a b l e e r r o r of the B r i t i s h Columbia F o r e s t S e r v i c e . The standard d e v i a t i o n obtained w i t h the r e l a s c o p e i s much lower, 0.366 t r e e s per p l o t . This may be because the BAF used was lower, or because the relascope i s a b e t t e r c r u i s i n g instrument, or both. I t i s d i f f i c u l t t o p i n p o i n t the exact reason f o r the low e r r o r s obtained using the r e l a s c o p e . The average stand c o e f f i c i e n t of v a r i a t i o n i s 32.9% using the prism and 28.04% us i n g the relascope. The c o e f f i c i e n t s of v a r i a t i o n obtained by the c o n t r o l were 34.08% and 26.82% w i t h the prism and r e l a s c o p e , r e s p e c t i v e l y . This i m p l i e s t h a t lower t r e e counts per p l o t g i v e a lower stand c o e f f i c i e n t of v a r i a - t i o n . T h i s i s c o n t r a r y to the f i n d i n g s of Sayn-Wittgenstein (1963). He i n d i c a t e d t h a t the average c o e f f i c i e n t of v a r i a - t i o n decreased w i t h an i n c r e a s e i n the average number of t r e e s per p l o t . No p l a u s i b l e e x p l a n a t i o n can be o f f e r e d f o r t h i s d i f f e r e n c e . -38- The t o t a l average t r e e count per crew o f 237.72 t r e e s w i t h the p r i s m i s h i g h e r than the t r u e count o f 222.0 t r e e s . T h i s means t h a t the crews had an o v e r a l l n e g a t i v e b i a s o f 7.08%. Us i n g the r e l a s c o p e , the t o t a l average t r e e count per crew was 185.8 t r e e s . T h i s i s s l i g h t l y h i g h e r than, but c l o s e to the t r u e t r e e count o f 185.0 t r e e s . No reason f o r the h i g h n e g a t i v e b i a s i n prism count i s apparent. There was no c o n s i s t e n t r e l a t i o n s h i p between the e r r o r committed and the number of t r e e s per p l o t i n e i t h e r o f the p r i s m or r e l a s c o p e p l o t s . The v a r i a b i l i t y o f the t r e e counts was due to some o f the e r r o r sources l i s t e d i n the i n t r o d u c t i o n . However, one of the more r e c o g n i s a b l e sources of e r r o r i s the s u b j e c t i v i t y i n l o c a t i n g the t r e e count c e n t e r when che c k i n g the " d o u b t f u l " t r e e s . The s u g g e s t i o n by Beers and M i l l e r (1964) t h a t an a d j u s t i n g f a c t o r ( r e l a t e d to t r e e diameter) be made such t h a t d i s t a n c e s are measured to the near face of the t r e e i n q u e s t i o n , reduces t h i s s u b j e c t i v i t y of l o c a t i n g t r e e h e a r t c e n t e r s . Another important e r r o r o c c u r s when one i s c r u i s i n g f o r stand t a b l e c o n s t r u c t i o n or f o r t h i n n i n g purposes. Although the t r e e count per p l o t of a crew i s i d e n t i c a l t o the t r u e v a l u e , i t does not n e c e s s a r i l y f o l l o w t h a t the crews i d e n t i f i e d the same t r e e s ( i n terms of dbh). Slope c o r r e c t i o n w i t h a prism by swinging the p r i s m about a p e r p e n d i c u l a r a x i s c o n t r i b u t e s many p e r s o n a l e r r o r s . I t i s d i f f i c u l t to m a i n t a i n the angle of i n c i d e n c e w i t h i n 2 degrees of the c o r r e c t angle when hand h o l d i n g an unmounted pris m ( M i l l e r and Beers 19 75) . A l s o , slope c o r r e c t i o n w i t h the r e l a s c o p e i s not a u t o m a t i c ; i t i s o n l y done when t h e b r a k e knob i s r e l e a s e d . A s u r v e y o f t h e s t u d e n t i n s t r u m e n t p r e f e r e n c e s i n d i c a t e s t h a t 17 o u t o f the 32 s t u d e n t s asked p r e f e r r e d t o use a p r i s m f o r c r u i s i n g . The main r e a s o n was t h a t t h e y had used a p r i s m p r e v i o u s l y , b u t n o t a r e l a s c o p e . However, 13 o u t o f t h e 32 s t u d e n t s asked p r e f e r r e d t h e r e l a s c o p e , more because i t i s e a s i e r t o c o r r e c t f o r s l o p e , and t o a l i g n w i t h t h e t r e e (see a l s o a sample q u e s t i o n n a i r e i n the appendix V I ) . E f f e c t i v e l y , the r e l a s c o p e i s a much b e t t e r c r u i s i n g i n s t r u m e n t . T h i s may i n p a r t e x p l a i n the f a c t t h a t s m a l l e r v a r i a b i l i t i e s i n crew t r e e c o u n t s were o b t a i n e d w i t h t h e r e l a s c o p e . The a v e r a g e t r e e d i a m e t e r was 52.67 cm, and t h e c o e f f i c i e n t o f v a r i a t i o n i n crew d i a m e t e r measurements was 8.16%. T h i s e r r o r i s much b i g g e r t h a n t h e B r i t i s h Columbia F o r e s t S e r v i c e a l l o w a b l e e r r o r o f ± 1%. I t i s a l s o h i g h e r t h a n t h e e r r o r found by Myers (1961); b u t t h i s i s m a i n l y because Myers' r e s u l t s were based on measurements on p e r m a n e n t l y l a b e l l e d dbh p o i n t s , and p r o b a b l y on s m a l l e r t r e e s . There were more n e g a t i v e s o u r c e s o f e r r o r , i n d i c a t e d by a h i g h e r p e r c e n t a g e o f t h e measurements b e i n g t o o l a r g e . Other s o u r c e s o f such e r r o r s , o t h e r t h a n t h o s e l i s t e d i n t h e i n t r o d u c t i o n were the f o l l o w i n g : i ) n o t p u l l i n g t h e measuring tape t i g h t i i ) f o r l a r g e t r e e s , t h e r e i s the tendency t o t a k e r e a d i n g s t o t h e n e a r e s t 10 cm (or a t most, t o t h e n e a r e s t 1 cm), and t o a p p r o x i m a t e t h e d i a m e t e r s when t h e t r e e dbh exceeds th e measuring tape l e n g t h . E r r o r s o u r c e ( i i ) e x p l a i n s why a c c u r a c y i s low a t l a r g e r t r e e d i a m e t e r s . The a v e r a g e t r e e t o t a l h e i g h t was '31.38 m, and t h e c o e f f i c i e n t o f v a r i a t i o n i n crew t r e e h e i g h t measurements was 21.86%. T h i s e r r o r i s much h i g h e r than t h e 2.3% e r r o r found by Ker (1951), t h a t o f 3.5% r e p o r t e d by Meyer (1953), t h a t o f 2.4% found by K e r and S m i t h (1957), t h a t o f ± 5,10% noted by Young (1967), and t h e + 3% a l l o w a b l e e r r o r of the B r i t i s h C olumbia F o r e s t S e r v i c e . D i s t a n c e measurement e r r o r s c o n - t r i b u t e d q u i t e s i g n i f i c a n t l y t o t h e h i g h e r r o r i n t r e e h e i g h t measurement. The p r o b a b l e r e a s o n f o r t h e u n r e a s o n a b l y h i g h e r r o r i n h e i g h t e s t i m a t i o n i s t h a t t h e s t u d e n t s had n o t had enough e x p e r i e n c e i n h e i g h t measurement. F u r t h e r m o r e , t h e s t u d e n t s c o u l d not v i s u a l i s e w e l l i n t h e m e t r i c u n i t terms. A c c u r a t e t r e e h e i g h t measurement r e q u i r e s more e x p e r i e n c e and g r e a t e r p a t i e n c e . F o r e s t r y s t u d e n t s a r e o f t e n employed t o u n d e r t a k e f o r e s t c r u i s i n g f o r v a r i o u s a g e n c i e s . I f t h e s t u d e n t i n v e n t o r y r e s u l t s a r e t o be r e l i e d upon, e r r o r s o f t h i s magnitude must be watched o u t f o r , and r e d u c e d . On t h e o t h e r hand, i t i s p r o b a b l e t h a t the c u r r e n t m e a s u r i n g p r o c e d u r e s a r e n o t a dequate, as h i n t e d by t h e f o l l o w i n g q u o t a t i o n from Young (1967, p. 18) : " I f wood were as v a l u a b l e as g o l d , we would measure i t w i t h the same, a c c u r a c y , b u t as m a t t e r s s t a n d our methods r e f l e c t t h e q u a n t i t y and v a l u e o f s t a n d i n g t r e e s and t h e p r i m a r y c u t p r o d u c t s " . -4 1- CONCLUSIOMS The f o l l o w i n g c o n c l u s i o n s were made from the study. The average t r e e count was 9.5 trees i n the prism p l o t s and 7.4 t r e e s i n the relascope p l o t s . The c o e f f i c i e n t of v a r i a t i o n of observer tree count i s 10.44% w i t h the prism and 4.93% with the r e l a s c o p e . E r r o r s decrease w i t h i n c r e a s e i n BAF. A s i g n i f i c a n t negative b i a s of 7.08% i n t r e e count w i t h a prism, and an i n s i g n i f i c a n t negative b i a s o f 0.43% w i t h a relascope was observed. About 37% of the t r e e counts i n the relascope p l o t s , and 29% i n the prism p l o t s were c o r r e c t . N i n e t y - f i v e % of the relascope p l o t s and 91% of the prism p l o t s had e r r o r s of ± 4 t r e e s or l e s s . The maximum t r e e count e r r o r per p l o t was ± 6 t r e e s . The percentage e r r o r i n the d e t e r - mination of bas a l area per ha from 25 prism p l o t s was ± 4.09%, and from 25 relascope p l o t s , ± 1.93%, at the a = 0.05 pro- b a b i l i t y l e v e l . These e r r o r s show t h a t accuracy of a relascope or prism survey depends on the care w i t h which the work i s done, and t h a t the rel a s c o p e y i e l d s more p r e c i s e r e s u l t s . The average c o e f f i c i e n t o f v a r i a t i o n o f the measurer i n dbh measurement was 8.16% (the average dbh = 52. 6 7 cm) . About 95% o f a l l the measurements of dbh were i n e r r o r by ±5 cm or l e s s . There were e r r o r s as l a r g e as ± 30 cm. Only 6% of the measurements were c o r r e c t . V a r i a b i l i t y of the measurements about t h e i r mean was uniform i r r e s p e c t i v e of the dbh, but accuracy was lower a t l a r g e r t r e e diameters. There were more negative sources of e r r o r than p o s i t i v e ones. -42- A c o e f f i c i e n t of v a r i a t i o n of 21.86% of the measurer i n h e i ght measurement was obtained (average t o t a l t r e e height = 31.38 m). Over 15% of the height measurements were i n e r r o r by ± 6.0 m. or more. Only 1.8% of the measurements were c o r r e c t . Height measurements were su b j e c t to l a r g e r and more sources of e r r o r s . E r r o r s of t h i s magnitude i n VRP tr e e counts, dbh and height measurement, c l e a r l y demonstrate the need f o r c a u t i o n i n u sing untrained crews i n f o r e s t i n v e n t o r y work. Thex~e i s ob v i o u s l y a need f o r r i g o r o u s f i e l d t r a i n i n g programs and the establishment and implementation of c h e c k c r u i s i n g guide- l i n e s . -43- LITERATURE CITED Anderson, R.L. and T.A. B a n c r o f t . 1952. S t a t i s t i c a l Theory i n R e s e a r c h . M c G r a w - H i l l Book Company, I n c . , New Y o r k . p.313-330. B e e r s , T.W. and C . I . M i l l e r . 1964. P o i n t s a m p l i n g : R e s e a r c h R e s u l t s , Theory and A p p l i c a t i o n s . Purdue U n i v . A g r . Exp. S t a . R e s e a r c h B u l l . , No. 786. L a f a y e t t e , I n d i a n a . 56 p. Carow, J . 1958. 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O b s e r v a t i o n s on t h e A c c u r a c y and U t i l i t y o f P l o t l e s s C r u i s i n g . B r i t i s h Columbia Lumberman, November I s s u e : 32-36. -4 4- K i r b y , C L . 1965. A c c u r a c y o f P o i n t S a m p l i n g i n VJhite S p r u c e - Aspen Stands o f Saskatchewan. J . F o r . , 63: 924-92 L a a r , A. Van. 1962. The Angle-Count Method. S. A f r . F o r . J . , 72: 1-6. L o e t s c h , F . j 1?. Zohrer/nnd K.K. Hallet. , 1973. F o r e s t I n v e n t o r y , V o l . 11. BLV V e r i a g s z e s e l l s c h a f t Munchem B e r n . Wien. 469 p. Meyer, H.A. 1953. F o r e s t M e n s u r a t i o n . Penns V a l l e y P u b l i s h e r s , I n c . , P e n n s y l v a n i a , p. 101-103. M i l l e r , C . I . and B e e r s , T.W. 1975. T h i n P r i s m s as A n g l e Gauge i n F o r e s t I n v e n t o r y . Purdue U n i v . A g r . Exp. S t a . R e s e a r c h B u l l . No. 929 L a f a y e t t e , I n d i a n a . 8p. Munro, D.D. 196 6 . 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I n t e r m t . F o r . Range Exp. S t a . R e s e a r c h Paper No. 67. Ogden, Utah, 17p. U.B.C. F o r e s t C l u b . 1971. F o r e s t r y Handbook f o r B r i t i s h Columbia 3r d E d i t i o n . 815p. W i l l i n g h a m , J.W. 1962. E r r o r i n Wedge P r i s m C a l i b r a t i o n . J . F o r . F e b r u a r y : 123-127. Young, H.E. 1967. F o r e s t Measurement A c c u r a c y . IN Wood Measurement C o n f e r e n c e P r o c e e d i n g s , e d i t e d by F . Buckingham ' U n i v e r s i t y o f Toronto T e c h n i c a l Note Mo. 7: 17-23. -45- APPENDIX I : MAP 1. U . B . C Research Fore Pllt Loko AAaple Ridge, B.C. l e g e n d : conlours al 50' intorvols ( ( ( main road v branch rood ' trail building ^ powerlinc* ~~* study a r e c j ^ ^jl- . I S\ /Eunice loko / \ « .:• vK-'.V., •'X'X?'-:I'! <• i V'l^S-'v''/' //Gwendoline! , X' ) n o r  - 4 7 - A P P E N D I X I I : T R E E C O U N T S I N . T H E R E L A S C O P E ( B A F = 9 ) P L O T S L O T P L O T C R E W N O . NC . N O . C O N T R O L 1 2 3 4 5 6 T R E E C O U N T 1 1 6 6 7 7 7 7 7 1 2 1 I 1 I 1 1 I I 3 7 7 8 8 8 8 8 1 4 8 6 7 7 7 8 7 1 5 9 9 9 9 9 9 9 2 1 10 11 11 13 12 14 2 2 7 8 8 7 8 a 2 3 6 6 6 6 9 2 4 9 12 11 9 12 2 «; 8 8 . a 9 9 3 I 11 10 6 11 11 11 11 3 2 7 7 4 7 7 7 7 3 3 6 6 a 6 6 6 8 3 4 9 8. 6 7 7 9 3 3 5 8 9 9 8 S 8 s 4 i 9 9 7 6 4 2 10 6 6 5 A 3 12 17 6 11 4 4 9 14 13 15 4 5 8 10 8 10 5 1 6 9 5 6 8 9 5 2 6 5 5 5 5 4 5 5 3 5 6 6 6 5 3 6 5 4 5 6 6 5 5 8 5 5 5 3 4 4 4 4 4 4 APP END TX -4 8- I T T : TREE COUNTS IN THE P R I S M . (RAF = 6 ) PLOTS LOT PLOT CRFW NOo NC. NO. CONTROL 1 2 3 4 5 6 ' T R E E COUNT 1 1 5 4 4 5 5 4 5 1 2 4 3 3 5 4 4 4 1 3 11 13 16 16 12 16 16 1 * 11 11 12 12 12 12 1 5 5 3 6 6 4 5 5 2 1 12 8 8 13 13 13 2 2 12 10 11 12 13 14 2 3 8 10 9 12 11 10 2 4 11 12 11 15 11 12 2 5 10 6 6 11 13 9 3 1 9 13 9 9 12 11 3 2 8 11 7 7 10 10 7 3 3 8 8 8 13 11 8 14 3 4 12 12 11 14 14 12 13 3 5 8 12 7 11 . 10 11 11 4 1 9 10 11 11 4 2 6 6 10 9 4 3 14 12 15 16 4 4 12 14 13 17 4 5 12 14 14 15 5 1 5 9 12 5 5 8 5 5 2 8 l i 11 11 11 6 11 5 3 14 14 13 14 12 12 15 5 4 4 9 4 4 4 3 4 5 5 4 6 6 3 5 3 4 - 4'9- APPENDIX I V : TREE DIAMETER MEASUREMENTS TREE NO. CREW NC. CONTROL 1 2 3 4 5 6 MEA SUREMENTS(CM) 1 5.9 12.9 6 .0 6.0 5 .9 6.3 6 .0 2 6.1 5 . 6 5.0 3 7.5 7.5 7.6 4 8.3 8 . 6 8.7 8 .6 9 .0 8.8 8.7 5 9 .3 9 .2 9 .2 9.4 9.2 9. 1 9.2 6 9.7 9 .6 9.9 9. 8 9 .7 9.8 7 9 .8 10.8 10.8 8 10. 1 9 .9 10.0 10. 1 9 .9 10.0 9 .9 9 10.5 i o . e 1C.5 10.6 10.5 10.7 10 10 . 6 10.8 11 10. 8 10.8 10.9 10.7 10.9 12 11 .4 15.3 11.4 11.2 11 .0 13 13.0 13.9 13.5 13.5 13«5 13.3 14 13.5 14.9 14.9 14. 8 14.7 15.0 15 14.2 14.5 14.1 14.2 14.2 14.1 14.2 16 14.5 14.7 14.7 17 14.8 12.2 12.4 12.2 12.0 12.1 18 15.2 19.5 18.5 19 15.4 15.9 15.8 15 . 8 15.7 15.2 15.7 2C 15.7 16.1 15.8 15.6 21 16.0 15 .7 15.8 15.8 15.4 15.2 15.7 22 16.8 16.9 16 .6 16.6 17.0 16.6 16.5 23 17.1 16 o 9 17.2 17.2 16.8 24 17.8 18.5 18.3 18.4 17.3 17.7 25 18. 1 17.9 18.0 £ 8 . 0 17.9 17.9 26 18.2 18*7 19.2 19.2 18.6 • 17.0 27 18.4 21.0 18.0 18.3 18.3 17.8 18.2 28 18 o & 18.1 18.1 18.5 17.9 18.5 18.1 29 18.8 18.3 18.4 18.3 18«4 18.3 30 18.9 19.0 19.0 19.0 19.0 18.8 18-9 31 19.2 22 .0 19.0 19.2 18.0 17.9 32 19.2 19.1 19.1 33 19 . 6 19.7 19.4 20 .6 19.8 19.3 19.4 34 19.9 20 .4 19.2 20 .5 19.8 19.7 20.6 35 20.4 20.1 19.7 19.4 20o3 20.0 20.7 36 20 .5 20 .3 20.5 2 1 . 1 20.8 20 .5 20.6 37 20 .8 21 .0 21.0 21 .5 20.8 38 20 .9 20 .5 20.8 20. 5 39 21.2 21 .8 .21.1 21.2 21.0 21 .0 40 21 .5 20 .7 41 21 .7 22.6 21 .8 21 .5 42 22 .0 21.8 20 .5 20 .5 21.1 43 22.1 2 3 . 1 21.9 22 . 1 22.1 22.2 44 22,5 21.1 45 22 .5 23 .9 23 .0 23.0 22.0 46 22 .5 20.8 21 .C 21 . 1 22.0 47 23 .8 27 .4 32 .0 2 7 . 1 48 24.3 27 .9 24.5 49 24.4 23 .7 23.2 24 . 0 23.9 32.3 50 24 .6 24.8 25.2 24.0 24.0 -50- APPENDIX IV: TREE CI A METER MEASUREMENTS TREE NO. CREW NG. CONTROL 1 2 3 4 5 6 ME4SUREMENTSCCM) 51 24.9 24.6 24.8 24.6 52 25.0 25.0 24.8 24.9 24.0 25.0 25.1 53 25.2 24.8 24.8 25. 1 25.5 25.0 24.8 54 25.4 26.3 26.4 26.3 25.4 25.9 55 25.6 24.9 25. 1 24.9 25.0 56 26.0 26.2 27.5 26.0 25.4 57 26.0 26.3 27.4 26.1 26.0 27.1 26. C 58 26. 5 26.5 27.5 27.0 26.2 59 26.7 26.5 26.4 27.0 26.2 26.5 26.2 60 26.7 24.4 24.2 24.8 25.0 61 27.1 28 .3 26.8 27.2 26.9 27.7 62 27.2 27.8 27.8 27.6 27.7 63 27.5 27.6 27.4 27.6 27.7 27.3 27.6 64 27.6 27.5 27.3 27 .1 65 28.0 28.2 27.8 28.4 27.9 2 7.8 28 .3 66 28 .1 27.6 67 28.4 27.0 26 22.4 68 28.5 28.0 28.8 69 28.6 28.2 29.0 29.2 28.5 28.4 28.6 70 28.7 31.7 31.5 30.7 71 29.0 29.0 29.1 29.5 72 29.0 27.6 28.3 28.2 21.6 29.1 73 29. 1 29.6 29.0 30.0 29.5 74 29.2 31.9 30.0 29.9 29. 1 29.9 75 29.4 30.7 29.1 29 .1 30.1 29.1 29.7 76 29.6 29.7 29.5 29.6 77 29«,6 28.8 26.6 28.6 29.5 28o8 78 30. 0 28.6 30 = 3 30.4 30c0 29.6 30-.! 79 30.0 30.0 31.7 32.2 80 30. 1 34.0 35.3 35.2 34.7 81 30.1 29.2 29.1 29.6 29.4 30.0 82 30. 1 26. 1 32.7 83 30.3 30.9 84 30.4 30.5 30.5 29.5 - 85 30.4 30.3 31.2 30.0 86 30.5 30 .1 31.4 31.3 87 30.7 30.8 31.2 30.5 30.8 88 30.7 28. 1 30.0 89 31.2 31*3 29.0 32.7 90 31.2 31.2 30.8 35.9 31.3 91 31.3 31.a 31.5 31.9 92 31.4 31.7 31.8 31.8 31.0 31.7 93 31.4 31.7 31.8 31. 8 31.0 31.7 31.3 94 31.5 33.3 32.4 33.6 33.3 31.3 34.2 95 31.5 32.S 32.0 32. 1 32.8 32.0 32.7 96 31.5 30.9 31.3 31.5 31.5 97 31.5 32.9 32.9 31.8 98 31.5 31.2 31.5 30. 3 99 31.5 31.8 31.5 31.4 100 31.5 31.5 APPENDIX I V : TREE NO. CCNTRCl 101 32.0 102 32o0 103 32o0 104 32* 1 105 32. 1 106 32o2 107 3.2 © 2 1C8 32 .3 109 32.5 n o 32. 5 111 32 .7 112 33.2 113 33 .2 114 33.2 115 33 .2 116 33 .3 117 33.4 118 33 .7 119 33 . 8 120 33 .9 121 34 .0 122 34 .0 123 34 .3 124 34 .5 125 34.8 126 35.0 127 35.3 128 35 .9 129 36 .0 130 36 .0 131 36 .0 132 36 .0 133 36.2 134 36.2 135 36 .2 . 136 36.2 137 36.3 138 3 6 . 5 139 3 6 „ 5 140 37 . 1 141 37.1 142 37. 1 143 37.2 144 37.2 14 5 37 .3 146 37.3 147 37 .3 148 37.4 149 37.5 150 37.5 -5 1- TREE CI AM ET ER MEASUREMENTS CREW NO. 1 2 3 4 5 6 ME A S LREMENTS( CM) 27.8 27.9 31 .6 27.6 27.8 32.3 33.2 29 .9 30 .4 32 .9 33.5 33.0 31.5 31 .4 31 .2 29.4 31.6 31 .3 32 .8 3 1 .9 32 . 1 32.3 31.8 32 .2 31.1 31 .4 31. 3 34.0 35.9 34 . 7 3 2 . 2 20.7 32 .5 32.8 33 .2 33 .0 32 .9 32.8 32.8 32.7 32. 5 32 .3 33 .3 32 .2 32.3 32 .2 33.2 33 .1 32.7 34.0 32 .5 33.3 32 .5 31.8 32 .0 33.6 32 .8 32 .0 32.2 32 .7 32 .0 3 3 . 0 36.2 34 .2 34 .0 32 .3 32 .8 33 .6 33.2 33.2 32 .5 32 .2 32 .0 34 .1 34 .5 3 2 . 6 3 3 . a 3 3 . 5 33 .2 35 .0 31.0 34 .0 34 .0 34 .4 34 .3 33 .9 34 .0 37 .3 36 .4 33 .5 36.4 38.7 36 .7 34.2 34.2 37.5 34.2 35 .4 34 .5 35 .3 34.2 35 .0 35 .3 3 2 . 7 33.8 35 .4 33.9 34 .0 34. 8 34 .6 34 .9 35 .0 34 .6 34 . 7 35 .5 35 .5 35 .9 36 .8 35.9 35 .5 35ol 35.5 35 .2 35 .4 36 .6 3 5 . 1 35.4 36 .0 35 .4 35.2 36.2 36 .4 37 .4 36.4 36 .7 36 .4 35.5 36 .0 36.6 35 .7 36 .2 36 .3 35 .9 36c3 35.0 35.1 36.0 36.2 36. 3 44 .2 44 .1 35 .8 35.9 35 .1 36.2 35 .1 37.5 36.8 36 .4 3 6 . G 3 3 . 0 35 .9 3 6 „ 8 34 .4 37 .7 34.5 37. 2 36.8 36 .9 36.9 36 .4 36 o 8 32 .8 32 .1 31.8 42 .9 42.3 37.2 38 .0 37 .5 37 .6 37.7 37.1 36 .8 37.2 38.8 37.2 37 .9 36.8 3 8.7 39.7 37 .7 38 .0 37 .5 37.1 37.3 39*0 37.0 38 .8 37 .0 37 .0 35 .8 37 .0 38.8 38.5 37 .2 37 . 1 37.5 37.2 37.0 37 .0 APPENDIX I V : TREE CIAMETER MEASUREMENTS TREE NO. CREW NC. CCNTROL 1 2 3 5 6 MEASUREMENTS(CM 1 151 37.5 42.3 37.5 47. 0 152 37.6 38.8 37.1 37.7 153 37.7 37.6 30.0 37.7 154 37.7 38.0 37.7 38.6 37.7 155 37.7 41„5 38.1 37.4 156 37.9 40.0 38.2 40. C 38.7 157 38. 1 46.G 4>5<,8 45.5 38.5 158 38.2 38.2 38.0 38.4 38.6 3 8.4 159 38.2 38.1 38.8 39„9 38.1 35.0 38ol 160 38. 3 39. 1 38o3 37. C 161 38.4 38.5 38.5 39.3 162 38o7 37.0 36.9 36.4 163 38.9 37o9 39.6 164 39.0 38.1 38.2 38.1 16 5 39.2 31.2 27.4 166 39.9 38.5 4Q.0 38.4 167 40.0 42.0 42.2 44.2 39.0 39.5 168 40.0 40.3 169 40.0 40.1 40.0 40.2 40.0 40.4 170 40.2 38.2 41.8 38.0 40o2 42.2 38.7 171 40.3 40.5 40.4 43.5 172 40.8 42.8 42o2 40.8 40.8 173 41.0 41.2 174 41.0 38.7 38.9 39.0 40.8 175 41.1 40.7 40.9 39.3 176 41. 2 41.5 41.2 40. 8 41.7. 41.0 41.1 177 41.2 43.7 41.0 41.9 42.2 41.9 41.9 178 41.3 41.4 41 • 6 4-0.5 179 41.5 41.7 42.5 42.5 41.2 41.3 44.2 180 42.0 38.7 42«5 42.0 181 42. 1 42.4 42.8 42*6 42*9 43.0 42.0 182 42.6 43.3 43.8 42.6 43.0 42.0 42.9 183 43.6 43.7 43.8 43.7 43„2 45.0 184 43.7 43.3 44.1 42.4 185 43. 8 46 .5 43.0 44.0 56. 1 44.0 186 43.9 42.9 187 44.1 44.0 42.5 42.3 188 44.2 44.3 44.0 44 . 3 44.2 44.0 44.0 189 44.3 43.9 44.1 45. 1 44.3 44.3 45«8 190 44.5 44.6 191 44.8 44.5 44.6 45.4 192 44o9 43.6 44.0 43.0 46.8 193 45.0 A4.5 45.2 45.0 45.0 45.4 45.5 194 45.1 45.0 45.3 45.3 195 45.7 50.7 51.0 53. 2 48. i 5 0.7 48.1 196 45 .7 44.6 44.3 44.3 45.1 44.3 45.2 197 45.8 45.5 19 8 45.9 47.7 46.0 46.7 45.2 46.5 46.4 199 46.0 46.3 46.5 46.1 200 46.2 45.0 45.7 47.6 47.2 47.2 49.9 -53- APPENDIX IV: TREE DIAMETER MEASUREMENTS TREE NO CREW NC. CCNTRCL 1 2 3 4 C 6 MEA SUREMENTS(CM> 201 46,4 46.2 45.0 46.0 k 202 46.9 46.7 48.9 49.0 48.3 203 46o9 46.6 47.2 46.8 204 47.1 48.2 45.5 46. 5 47.8 46.3 46 .9 205 47.1 47. 1 47.5 47.5 46.6 47.0 206 47.8 47.9 48.3 48.2 48.0 4 7.9 207 47.9 48. 1 48.3 49. C 49.7 208 47.9 55.2 56.1 49.0 49.0 51.0 50 .3 209 48.0 48.0 47.9 47.6 48-4 48.7 210 48.0 47.7 48.8 47.4 46.6 . 47.8 47 .6 211 48.1 44.8 212 48.4 48.8 47.9 48.0 48.5 213 48.5 48.0 48.2 47.9 48.7 49.0 214 48.5 50.2 48.7 48.9 48.5 215 48.8 45.7 46.3 45.8 216 48.9 50.8 50.4 50.7 51 .0 42.0 49 .2 217 48.9 49.8 49.5 49.6 49.6 44.2 218 49. 1 49.0 48.0 219 49.3 49.5 46 .9 47.0 48.5 46.0 49 .0 220 49.9 52.5 51.8 46. 0 49.7 221 49.9 50.1 50.2 51.1 222 49.9 53.7 53.0 223 50. 0 48. 5 51.0 50. 0 50.7 50.8 50 .4 22 4 50.0 49.0 50.6 51.0 50.7 50.0 49 .7 225 50.0 50.8 226 50.1 49.0 49.0 49.6 50.4 22 7 50.1 49,8 46 .8 51.0 50.9 50.9 228 50.4 50.2 50.9 52. 1 51.0 51.0 52 .8 229 50.5 51.1 51.3 51.0 50.3 51.3 55 .5 230 50.8 51.5 49.9 50.6 231 51.0 50.2 51.0 51. 3 50.4 50.8 232 51.5 52.5 54.3 53.4 53.4 52.5 51 .8 233 51.5 51.0 51.6 234 51.7 ' 45.9 44.3 50. 8 235 51.7 44.0 47.6 49.6 236 51.8 52.3 53.2 51.3 237 51.9 50,3 49.7 51.2 50.2 51.2 238 52.1 46.3 47.1 50 o 9 53.0 47.4 46 .5 239 52.5 52.0 52.8 52.5 240 52.9 53.5 52.5 53.0 52.8 52.7 241 52.9 53.4 53.0 53.4 53.6 242 53. 1 52.5 53.6 53.7 52.6 54.1 24 3 53.1 53.7 57 .I 54.4 54.5 54.5 244 53.1 53.5 53.1 55. 2 53.5 54.0 54 .1 245 53.1 50.9 51.6 49.4 246 53.4 53.4 53.3 57.2 53.0 52.1 53 .3 247 53.6 53.5 53.7 55.8 24 8 54.0 52.7 52.7 55.2 53.7 50.9 249 54.0 54.5 53.0 52.2 250 54.2 53.0 50.1 52. I 54.3 50.3 51 .3 i6„5 -5 4- A P P E N D I X IV: TREE DIAMETER MEASUREMENTS TREE NO, CREW NC CONTROL 1 2 3 4 . 5 6 MEASUREMENTS(CM) 251 5 4 . 5 5 2 . 2 53 . 1 5 3 . 4 5 2 . 8 5 3 . 0 252 5 4 „ 6 5 4 . 8 5 5 . 6 5 5 . 2 5 5 . 0 5 4 . 8 253 5 4 . 8 5 4 . 0 6 0 . 1 5 4 . 0 254 5 5 . 0 5 4 . 3 5 3 . 9 5 5 . 0 5 4 . 6 255 55o4 5 5 . 2 5 4 . 9 55..1 5 5 . 2 5 5 . 3 5 5 . 2 256 55o4 5 6 . 5 5 6 . 6 5 4 . 3 257 55o5 6 4 . 5 5 6 . 1 5 4 . 9 258 5 5 . 5 5 4 . 3 5 4 . 5 5 5 . 5 5 5 . 7 5 4 . 2 259 5 5 . 6 5 5 . 5 5 6 . 7 5 6 . 8 5 6 . 6 5 6 . 1 260 55o6 5 5 . 7 5 5 . 1 5 5 . 1 5 5 . 8 5 5 . 7 5 6 . 2 261 56o0 5 8 . 5 5 8 . 2 5 8 . 5 5 8 . 7 5 6 . 5 262 5 6 . 1 5 2 . 1 5 7 . 7 5 6 . C 5 7 . 0 5 6 . 5 5 3 . 7 263 5 6 . 5 5 3 . 1 5 1 . 2 5 4 . 6 5 5 , 5 264 5 6 . 6 5 6 . 1 5 5 . 8 5 5 . 6 6 0 . 9 6 0 . 0 5 9 . 5 26 5 5 6 . 9 5 5 . 6 56 . 1 5 7 . C 5 7 . 2 5 6 . 1 5 7 . 6 266 5 7 . 0 5 0 . 8 5 8 . 7 5 9 . 8 5 5 . 8 5 7 . 2 2 67 57 . 1 5 1 . 5 5 0 . 0 5 7 . 8 5 2 . 7 53 = 2 268 57o6 5 5 . 4 57 o 2 5 7 . 4 5 7 . 9 5 9 . 0 5 6 . 4 269 57o9 6 3 . 0 4 3 . 6 6 0 . 8 5 8 . 7 5 9 . 7 5 8 . 7 270 5 7 . 9 5 7 . 5 5 7 . 5 5 6 . 4 5 7 . 2 271 5 8 . 0 5 6 * 8 5 7 . 5 5 7 . 8 5 7 . 8 272 5 8 . 2 5 8 . 5 5 8 . 8 5 0 . 1 5 7 . 2 5 9 . 3 273 5 8 . 6 58 . 1 5 8 . 0 5 9 . 3 5 8 . 3 5 6 . 2 5 8 . 3 274 5 8 . 8 5 6 . 9 5 9 . 2 5 8 . 0 6 0 . 1 5 9 . 2 5 8 . 4 275 5 9 . 0 5 8 . 4 5 8 . 5 5 7 . 9 276 5 9 . 0 5 8 . 8 6 0 . 7 6 0 . 2 2 77 5 9 . 9 5 8 . 4 60 . 1 6 1 . 7 6 0 . 9 6 1 . 3 278 5 9 . 9 6 1 . 4 5 8 . 8 5 9 . 0 6 1 . 2 279 6 0 . 0 5 9 . 3 5^.2 6 0 . 1 6 0 . 8 5 8 . 0 5 9 . 3 280 6 0 . 0 5 9 . 9 6 0 . 3 5 9 . 5 281 6 0 . 1 6 2 . 5 7 7 . 3 7 8 . 5 282 6 0 . 4 6 0 . 2 6 0 . 5 6 4 . 2 6 1 . 5 5 9 . 3 6 1 . 8 283 6 1 . 0 6 9 . 7 6 0 . 4 6 0 . 0 6 1 . 7 6 1 . 4 284 6 1 . 3 ' 6 1 . G 6 2 . 0 6 1 . 2 6 1 . 5 6 3 . 2 2 3 5 6 1 . 3 6 1 . 3 6 0 . 9 6 2 . 1 6 0 . 5 6 0 . 7 286 6 1 . 3 5 8 . 0 5 8 . 4 6 2 . 3 6 1 . 2 6 1 , 2 2 87 6 1 . 6 6 0 . 6 6 2 . 3 61.1 288 6 3 . 1 6 2 . 8 6 6 . 7 6 2 . 8 289 6 3 . 4 6 3 . 5 6 3 .1 6 2 . 0 6 4 . 1 6 1 . 3 5 5 . 2 290 6 3 * 4 6 4 . 0 ' 6 3 . 5 291 6 3 . 5 5 9 . 1 5 9 . 6 6 2 . 0 6 0 . 8 6 1 . 0 60.1 292 6 4 . 0 6 7 . 7 6 3 . 9 6 4 . 2 6 3 . 8 6 3 . 9 6 4 . 8 293 6 4 . 0 6 6 . 2 6 6 . 5 6 6 . 7 6 4 . 5 294 6 4 . 1 6 5 . 9 6 0 . 2 6 4 . 8 6 3 . 5 6 6 . 8 295 6 4 . 3 6 3 . 1 6 4 . 0 6 4 . 1 296 6 4 . 4 6 5 . 6 6 5 . 7 6 5 . 7 6 5 . 7 6 4 . 5 6 3 . 4 29 7 6 4 . 4 6 4 . 7 6 4 . 0 6 4 . 5 6 4 . 9 5 9 . 8 6 5 . 1 298 6 4 . 5 5 8 . 0 6 4 . 5 6 4 . 1 299 6 4 . 5 5 6 . 4 5 4 . 4 5 2 . 5 5 5 . 3 5 6 . 4 300 6 4 . 6 6 0 . 9 6 1 . 7 6 6 . 6 6 4 . 5 6 4 . 5 6 3 . 2 5 5 . 2 5 7 . 2 7 3 . 0 - 5 5- APPENDIX IV: TREE CIAMETER MEASUREMENTS TREE NO CREW NG. CONTROL I 2 3 4 5 6 MEASUREMENTS(CM) 301 65.0 57.3 52.4 57.0 54.8 302 65.6 72.2 70. 1 70.0 71.1 70.1 62.7 303 65.8 60.5 60.3 58.1 53.5 61.0 65.S 304 67.0 65.6 65.3 68. 1 76.3 61.3 67.2 305 67.2 65.0 60.3 66.2 65.4 64.3 65 .4 306 67.6 68.7 67.3 72.0 307 67.7 67.8 68.2 67.0 66. 5 68.2 67.0 308 67.9 64.2 309 68.0 72.3 65.0 66.9 66.9 310 68. 1 75.0 69.9 68. 5 69.9 72.6 311 68.4 67.4 62.5 66.0 65 .9 66.1 312 69.2 66.2 313 69.5 72.0 62.2 71.9 314 69.9 75.4 78.4 80.8 69 = 2 315 70.0 67.8 69.0 70. 0 69. 1 316 71.0 73.3 75.3 71.0 73.2 317 71.1 66. 1 67.9 66.8 70.0 6 8.6 318 71.5 73.5 73.6 71.9 319 72.0 73.0 73.0 73.8 71.0 72.5 320 72. 1 78.0 75. 1 71.9 74.8 72.5 321 72.6 74.7 76.5 74. 1 74.5 76.2 322 72.6 73.3 72.9 73. 1 73.5 323 72.7 66.4 66.7 68.8 67.4 72.8 324 73. 1 73.0 73.5 74,0 73.4 325 74.0 79.7 77.5 79.2 73.7 326 74. 1 82.2 77.0 77.0 '74.1 77.0 72.9 32? 74.5 74.0 76.2 76.0 74.5 76.0 73.0 328 75.1 74.6 76.1 7 5. 5 75.3 76.1 74.5 329 75.5 74.® 72.3 72.5 82.7 72.5 70.5 33 0 75.8 80.0 75.3 80.4 331 76.0 73.3 78.5 74.2 332 76.1 75.2 75.1 76.0 76.7 70.0 333 77.0 . 75.0 75.0 334 77.1 75.4 69.5 335 77.1 75.1 76.0 75. 1 76.8 76.6 336 77.1 75.2 75.0 75.2 75.9 76.2 337 77.4 72.0 77.8 76.2 76.8 76.6 338 77.4 76.0 76.2 75.7 339 77.7 80.2 78.5 72.5 340 79.3 81.6 81.7 81.5 81.4 79.0 341 79.5 80.7 81.5 78.4 79.0 78.6 342 82.1 79.8 89.6 76.4 88.9 81.0 34 3 82.2 78*7 80*7 S2*-0 344 82.6 82.0 83.2 82*7 82.7 82.5 82*4 345 83. 0 85.4 84.3 85.3 83.2 346 83.2 83.4 84.2 86.1 86.0 82.5 98.4 347 84.2 84.8 84.0 84. 1 85.5 85.5 34 8 84. 7 84. 5 85.0 85.2 86.4 85.5 85.1 349 85.2 84. 1 84.8 86.0 86.3 84.8 86.6 350 85.5 82. 1 82.5 86. C 83.4 73.9 85.6 APPENDIX IV: - 5 6 - TREE CIAMETER MEASUREMENTS TREE NO. CREW NO. CONTROL 1 2 3 4 5 6 7 MEASUREMENTS(CM > 3 5 1 8 7 , 0 8 5 . 2 8 5 . 2 8 6 . 7 8 7 . 0 3 5 2 8 9 . 0 9 0 . 6 8 8 . 0 3 5 3 8 9 . 4 9 0 . 5 8 9 . 2 8 9 . 1 8 9 . 9 3 5 4 8 9 . 7 9 0 . 0 9 2 . 0 8 9 . 8 3 5 5 8 9 . 8 9 0 . 4 9 8 . 4 9 0 . 3 9 0 . 6 9 5 . 0 3 5 6 9 0 . 1 9 1 . 0 9 2 . 9 9 2 . 8 8 8 . 4 3 5 7 9 2 . 1 9 8 . 7 9 1 . 0 9 0 . 8 9 6 . 2 3 5 8 9 2 . 4 9 3 . 5 9 3 . 5 1 0 5 . 0 3 5 9 9 2 . 7 9 1 . 1 9 1 . 0 9 1 . 5 9 2 . 0 3 6 0 9 3 . 5 9 3 . 0 9 2 . 7 9 5 . 6 9 8 . 2 9 2 . 1 9 6 . 6 3 6 1 9 4 . 0 1 2 7 . 2 9 4 . 5 9 6 . 2 9 3 . 6 3 6 2 9 5 . 4 9 2 . 6 9 0 . 0 9 0 . 1 9 3 . 3 9 2 . 3 3 6 3 9 7 . 1 9 4 . 0 9 7 . 3 3 6 4 9 8 . 0 9 3 . 2 9 6 . 8 9 4 . 5 3 6 5 1 0 0 . 0 9 9 . 7 1 1 0 . 9 3 6 6 1 0 0 . 1 1 0 7 . 1 1 0 7 . 8 1 0 3 . 2 9 6 . 7 3 6 7 1 0 0 . 1 9 6 . 5 1 0 0 . 2 9 6 . 0 3 6 8 1 0 0 . 7 1 0 0 . 7 1 0 1 . 0 1 0 3 . 0 1 0 1 . 1 1 0 1 , 0 1 0 1 . 1 3 6 9 1 0 2 . 9 1 1 2 . 2 1 0 4 . 5 1 1 3 . 9 1 0 4 . 0 3 7 0 1 0 3 . 0 1 0 7 . 3 1 0 7 . 7 1 0 1 . 8 1 0 5 . 6 1 0 2 . 0 3 7 1 1 0 3 . 1 1 0 1 . 7 1 0 0 . 0 1 0 3 . 5 1 0 2 . 5 3 7 2 1 0 3 . 3 1 0 4 . 5 1 0 6 . 5 1 0 5 . 3 3 7 3 1 0 5 . 0 1 0 3 . 1 1 0 3 . 8 1 0 2 . 0 1 0 1 . 7 3 7 4 1 0 6 . 9 1 0 4 . 0 1 0 8 . 0 1 0 5 . 5 1 0 6 . 8 1 1 0 . 2 1 0 5 . 1 3 7 5 1 1 0 . 0 1 0 8 . 8 1 1 2 . 9 1 1 4 . 0 1 1 0 . 9 1 1 2 . 9 1 1 4 . 5 3 7 6 1 1 3 o 0 1 1 0 . 0 1 1 2 . 0 3 7 7 1 1 5 . 0 1 1 6 . 8 1 1 1 . 0 3 7 8 1 2 0 . 5 1 2 3 . 5 1 0 3 . 0 1 2 2 . 0 1 2 1 . 0 3 7 9 1 2 1 . 8 1 2 1 . 5 1 2 0 . 8 1 2 9 . 0 1 2 0 . 8 1 2 0 . 8 1 1 5 . 6 3 8 0 1 2 5 . 0 1 2 5 . 0 1 2 0 . 8 1 2 1 . 2 1 2 6 . 8 1 2 0 . 6 1 2 6 , 6 3 8 1 1 2 5 . 1 1 2 9 . 0 1 2 7 . 6 1 2 7 . 5 1 2 4 . 0 3 8 2 1 2 8 . 2 1 2 5 . 0 1 2 9 . 0 1 2 4 . 5 3 8 3 1 3 0 . 1 1 2 7 . 0 1 3 2 . 0 1 3 1 . 0 1 2 9 . 3 1 3 2 o 0 3 8 4 1 3 0 . 9 1 2 4 , 2 1 3 4 . 7 3 8 5 1 3 1 . 1 1 3 1 . 5 1 2 7 . 0 1 3 1 . 1 1 3 2 . 0 1 3 3 . 3 1 2 6 . 0 3 8 6 1 3 2 . 5 1 3 1 . 1 1 2 8 . 7 1 3 2 . 0 1 3 0 . 5 1 3 2 . 8 3 8 7 1 3 5 . 0 1 3 4 . 7 1 3 0 . 3 3 8 8 1 3 5 . 2 1 4 1 . 0 1 3 7 . 4 1 3 7 P 4 1 4 1 . 0 1 3 7 . 2 1 3 1 , 0 3 8 9 1 3 5 . 3 1 3 5 . 3 1 3 5 . 0 3 9 0 1 4 0 . 1 1 3 5 . 2 1 5 0 . 0 3 9 1 1 4 0 . 2 1 5 0 . 0 1 4 6 . 2 1 4 6 . 2 1 4 9 . 0 1 4 6 . 2 1 3 4 . 5 3 9 2 1 5 4 . 4 1 5 0 . 0 1 5 0 . 0 1 5 2 . 8 1 5 9 . 2 1 5 1 . 0 1 5 4 . 2 3 9 3 1 6 0 . 0 1 6 6 . 0 1 6 4 . 8 1 6 0 . 0 3 9 4 1 6 0 . 0 1 3 3 . 5 1 3 2 . 9 1 2 6 . 0 3 9 5 1 6 0 . 5 1 5 9 . 0 1 6 3 . 0 •»> *r o n. ii. J O v V 3 9 6 1 6 7 . 7 1 3 5 . 6 1 4 0 . 0 1 6 9 . 0 1 6 8 . 7 1 6 5 . 0 1 6 3 . 0 3 9 7 1 7 0 . 0 1 3 1 . 5 1 9 5 . 0 3 9 8 1 9 0 . 0 1 8 0 . 0 1 7 9 . 0 3 0 2 . 0 2 0 7 . 0 2 1 4 . 0 - D /- APPENDIX V: TR F E TOTAL HEIGHT MEASUREMENTS TREE NO. CREW NO. CONTROL 1. ? 3 4 5 6 MEASUREMENTS(IN M) 1 8.1 10.8 9.0 9.5 2 11.8 10.8 11.5 11.0 11.4 3 18.6 21.3 22.0 22.3 22.9 4 18.8 20.1 i8.2 17.9 17.5 17.6 28.0 5 21.5 13.2 19.9 6 22.1 22.0 27.0 22.2 7 24.6 30.3 32.1 21.0 8 26.5 23.8 28.0 24.2 26.3 24.0 28.4 9 27.4 26.0 24.2 25.0 30.7 10 27.7 34.8 23.6 32.4 11 29.8 29.4 26.8 33.0 33.3 12 30.0 30.5 27.3 23.2 13 30 o5 28.0 28.4 14 31.2 31.2 32.5 26.7 28.7 15 32.3 26.6 21.0 30.5 16 32.4 31.1 30.4 28.4 28.5 17 32.5 48.5 53.8 31.5 18 34.8 49.0 19 35.0 49.0 30.3 30.2 26.2 20 35.7 29.5 41.0 29.0 21 35.8 31.2 32-0 32.2 22 37.4 37.3 38.0 23 3S.0 33.6 35 .3 35.G 41.0 40.5 24 39.0 40.2 .35.0 25 40.0 35.0 37.5 - 5 8 - APPENOIX V: TR F E TOTAL HEIGHT MEASUREMENTS TREE NG. CREW NO 1 CONTROL 1 2 3 4 5 6 MEASUREMENTS ( I N M). 26 40.2 3 3.8 24.0 3 5.5 27 42.5 44.1 39.8 42.9 40.2 28 42.6 33.0 45.0 38.0 2 9 4 0.0 4 1.5 42.0 5L.5 44.0 49.5 30 48.8 29.0 47.0 42.8 27.0 31 50.5 52.0 49.0 49.5 54.0 56.0 50.5 APPENDIX VI: I N S T R U M E N T U S E R P R E F E R E N C E S U R V E Y Faced with a choice between a prism and a relascope for determining fhe basal area per hectare of a forest, cruisers (for some reason) usually prefer to use one more than the other. This survey aims at establishing the preference of the f i n a l year forestry students, for the two instruments. Please mark with a " V^" your choice: 1. In the UBC Research Forest, which instrument would you rather use for determining the basal area per ha.? ( ) PRISM ( ) RELASCOPE ( ) BOTH. 2. What is the reason for your choice in (1) above? ( ) I AM USED TO THE INSTRUMENT ( ) THE INSTRUMENT IS EASIER TO CORRECT FOR SLOPE ( ) THERE ARE FEWER CASES OF "BORDERLINE" TREES ( ) THE INSTRUMENT IS EASIER TO ALIGN WITH THE TREE ( ) OTHER If OTHER please s t a t e : 3. For how many summers have you been cruising? ( ) ZERO ( ) ONE ( ) TWO ( ) THREE ( ) FOUR OR MORE If you checked other than zero i n (3) above, did you use: i ( ) PRISM ( ) RELASCOi'E ( ') BOTH PLEASE RETURN THE COMPLETED FORM TO: STEPHEN OMULE, MacMillan Room 192. THANK YOU. SO/DDM/mpl Sept 1977

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