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Analysis of measurement errors associated with variable-radius plot forest sampling Omule, Stephen Agnew Yen’Emurwon 1978

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ANALYSIS OF MEASUREMENT ERRORS ASSOCIATED VARIABLE-RADIUS  WITH  PLOT FOREST SAMPLING  by  STEPHEN AGNEW VWEMURWON OMULE B.Sc.  F o r . (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  accept to  this  thesis  the required  THE UNTVERSlTy  Sttphtn  standard  OF B R I T I S H COLUMBIA  kptill,  ©  as c o n f o r m i n g  Agnzw  1978  Vtn'Emuiwon  Omult  >  J  9  7  s  In p r e s e n t i n g t h i s  thesis  an advanced degree at the  Library shall  in p a r t i a l  make i t  freely available  for  I agree  that  r e f e r e n c e and s t u d y .  f o r e x t e n s i v e copying o f t h i s  thesis  s c h o l a r l y purposes may be granted by the Head of my D e p a r t m e n t o r  by h i s of  the r e q u i r e m e n t s f o r  the U n i v e r s i t y of B r i t i s h C o l u m b i a ,  I f u r t h e r agree t h a t p e r m i s s i o n for  fulfilment of  this  representatives. thesis  It  is understood that c o p y i n g o r p u b l i c a t i o n  f o r f i n a n c i a l gain s h a l l  written permission.  Department of The  f  € y Iv v f  University of B r i t i s h  2075 Wesbrook Place Vancouver, Canada V6T 1W5  f Date  Columbia  not be allowed without my  - i i -  ABSTRACT Forest  inventories  form a b a s i s  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 therefore,  of decision-making management.  i n v e n t o r i e s must be c o n d u c t e d  Implicitly,  efficiently  and w i t h a  minimum o f e r r o r . This  thesis analyses  a variable-radius  t h e e r r o r s o f measurement  p l o t forest inventory  c r u i s e , with the  objective  o f d e t e r m i n i n g crew v a r i a t i o n a n d b i a s  diameter,  and t o t a l  Data British  in  i n tree  count,  measurements.  f o r t h e s t u d y 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  Columbia  Columbia,  height  during  during  Research Forest, the t h i r d  Maple R i d g e ,  British  year f o r e s t r y students  field  school  mensuration. In  three  each o f the s i x l o t s  o f 10 p r e - s e t  sample p l o t  t o s i x 3~man s t u d e n t c r e w s e a c h e s t a b l i s h e d  relascope  p l o t s , took  m e t e r s a t breast heights  and  t h e t r e e c o u n t , and m e a s u r e d t h e d i a -  height  o f the f i r s t  prism  centers,  o f a l l the " i n " t r e e s  " i n " trees.  and t h e t o t a l  The c r e w s t o o k  their  measurements i n d e p e n d e n t l y o f each o t h e r ,  and had t o complete  the  The  exercise  within  a period  of 8 hours.  m e a s u r e m e n t s and o b s e r v a t i o n s the  author's  i n t h e same p l o t c e n t e r s  formed  c o n t r o l t o the study. The  c r e w v a r i a t i o n i n t r e e c o u n t was c a l c u l a t e d b y t h e  method o f A n a l y s i s  of Variance,  and i n d i a m e t e r and  height  measurement by p o o l i n g obtain  the v a r i a t i o n f o r each t r e e  a weighted average v a r i a t i o n per t r e e .  e v a l u a t e d by c o m p a r i n g t h e erew r e s u l t s w i t h  to  Bias  was  those of the  control. The f o l l o w i n g The a v e r a g e t r e e factor  c o u n t was 9.5  (BAF) - 6 p r i s m p l o t s  relasoope p l o t s . tree  r e s u l t s were o b t a i n e d  basal  and 7.4  area per hectare  error.  i n t h e BAF = 9  level.  the  i n the determination of  f r o m 2 5 p r i s m p l o t s was a s much a s  ± 4.09%. and f r o m 25 r e l a s c o p e p l o t s  lascope p l o t s  trees  area  t h e p r i s m and 4.93% w i t h  The p e r c e n t a g e e r r o r  probability  i n the basal  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  c o u n t v/as 10.445 w i t h  relascope.  trees  from the study:  ± 1.93% a t t h e a =  A b o u t 37% o f t h e t r e e  counts i n the r e -  and 2 5% i n t h e p r i s m p l o t s w e r e m e a s u r e d w i t h o u t  The maximum t r e e  count error  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, a n d t h e m e a s u r e r  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%.  O n l y 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  larger and  tree diameters.  m e a s u r e m e n t s was significant bias. with  h e i g h t was  21.86%.  Crews measured t r e e  31.38  m,  height  heights with  a  O n l y a b o u t 2% o f t h e m.onr."romontf? w e r e  o v e r 15% o f t h e measurements b e i n g  + 6.0 m o r more. and  The a v e r a g e t r e e  lower a t  the measurer c o e f f i c i e n t of v a r i a t i o n of the t r e e  correct,  .05  H e i g h t m e a s u r e m e n t was s u b j e c t  more s o u r c e s o f e r r o r ,  i n error to larger  by  -iv-  The r e s u l t s should  suggest  be more c a r e f u l  i n v e n t o r y work. training  that  forest  i n using  They should  resouce  untrained  crews i n f o r e s t  establish rigorous  p r o g r a m s , and o u t l i n e and i m p l e m e n t  guidelines.  managers  field  checkcruising  -  A C -  TABLE OF CONTENTS Page T I T L E PAGE  i  ABSTRACT  i i  L I S T OF TABLES  v  L I S T OF FIGURES  v i  ACKNOWLEDGEMENTS  v i i  INTRODUCTION  1  LITERATURE  4  REVIEW  10  SOURCE OF DATA METHOD OF ANALYSIS  AND RESULTS  13  Tree Count Diameter  13 24  Height  30  DISCUSSION  36  CONCLUSIONS  41  LITERATURE CITED  42  APPENDICES: I. II. III. IV. V. VI.  Maps o f t h e S t u d y A r e a Tree Counts i n t h e Relascope (BAF = 9) P l o t s Tree counts i n the Prism (BAF = 6) P l o t s T r e e D i a m e t e r M e a s u r e m e n t s ... Tree T o t a l Height Measurements Sample Q u e s t i o n n a i r e o f t h e Instrument User P r e f e r e n c e Survey  45 47 48 49 57  59  -vi-  L I S T OF TABLES  Table I II  Page ANOVA Table f o r Tree Count Important  .  S t a t i s t i c s from the Tree Count  ANOVA  17  ANOVA Table f o r the Prism P l o t s  17  IV  ANOVA T a b l e f o r the Relascope P l o t s  18  V  ' T r e e Count Accuracy i n the Prism P l o t s  19  III  VI VII  Tree Count Accuracy i n the Relascope P l o t s Tree Diameter Measurements Accuracy  III  The D i s t r i b u t i o n o f Diameter  r  15  E r r o r s by Diameter  19' 26  Measurement  Classes  29  IX  T r e e T o t a l H e i g h t Measurement A c c u r a c y  3.1  X  The D i s t r i b u t i o n o f Height Measurement E r r o r s by H e i g h t C l a s s e s  32  -vii-  LIST OF FIGURES  Figure la  lb  2a  2b  3 4  5  6  „ A P l o t o f the Residuals against True with the Relascope  Counts  A P l o t o f t h e R e s i d u a l s a g a i n s t True with the Prism  Counts  2G  21  R e l a t i o n s h i p between True Count and t h e Crew (Estimated) C o u n t i n t h e R e l a s c o p e P l o t s  22  R e l a t i o n s h i p b e t w e e n T r u e C o u n t a n d t h e Crew (Estimated) C o u n t i n t h e P r i s m P l o t s  23  A P l o t o f the Residuals a g a i n s t True Measurement  27  Diameter  R e l a t i o n s h i p between True Diameter and t h e Crew (Estimated) D i a m e t e r M e a s u r e m e n t A P l o t o f t h e R e s i d u a l s a g a i n s t True Measurement  Total  23 Height  R e l a t i o n s h i p b e t w e e n T r u e H e i g h t a n d t h e Crew (Estimated) T o t a l H e i g h t M e a s u r e m e n t  33  3<1  -viii-  ACKNOWLEDGEMENTS I am the  p r o b l e m and  o f my D.D.  most g r a t e f u l t o Dr.  committee  the  Analysis  the  to the the of  - Drs.  D e m a e r s c h a l k , A.  greatly  financial Ford  study,  t h e s i s , and  Model used  indebted support  Foundation  fellowship. the  the  the  suggesting to  the  Kozak  t o Dr.  members and S.W.  Department o f Mathematics f o r recommending  of Variance  I am for  me  J.P.  on  Munro f o r  supervising  Munro - f o r r e v i e w i n g  Nash o f  D.D.  For  D o n a l d S.  U n i v e r s i t y of  herein.  to Makerere U n i v e r s i t y , i n form of  f o r Eastern  the  a study  Africa  for  additional financial  McPhee F o r e s t r y  British  the  Award,  C o l u m b i a and  Uganda,  fellowship,  and  administering support  in  I acknowledge  a l l t h o s e who  form  The  made i t  possible. I Spring for  the  Faculty t o The the  am  also  g r a t e f u l to the  School Class study, of  to  U n i v e r s i t y of  of  Forestry  1977  o f whom I t o o k a d v a n t a g e t o c o l l e c t  a l l the  Forestry,  Faculty  members o f  for their British  p r o v i s i o n of computing  the  invaluable  Biometrics  Group,  suggestions,  Columbia Computing C e n t r e facilities.  data  and for  -1-  INTRODUCTION Forest aspects of necessary  inventories  to  conduct  inventories  u n b i a s e d , and significant  plot  valid  (VRP)  forest  variations  instruments.  thesis  a VRP  height.  The  a  sources of possible  or  errors  i n a VRP height  the  select  tree  measurement measurer.  are  the  count e r r o r s ,  are: and  the  total are  t o make e x a c t l y  d)  failure  to  a l i g n instrument w i t h the  e)  failure  to  correct  f)  moving  estimate  "doubtful"  con-  trees,  for  a  3 6 0 ° sweep,  away f r o m t h e  of basal  tree,  slope,  count r e s u l t s i n a  b a s e d on  a  trees,  instrument  i n tree  as  following:  failure  plot.  of  faulty  measurement e r r o r s  c)  per  of  of  (dbh),  missing hidden  samples are  use  cruise  b)  VRP  results  a result  the  failure  error  however,  parameter.  observer bias, to  efficient,  are  a t t r i b u t a b l e to  diameter at breast  common c a u s e s o f  i n the  with  among t h e  a)  small  error  the  f o r each  sequence of  A  examines the  forest cruise,  The  different  and  technique;  measurer b i a s  main p a r a m e t e r s measured  count,  therefore  i s an  These v a r i a t i o n s  c a u s e d by  This  sampling  inventory  measurement e r r o r s  tree  efficiently  have b e e n o b s e r v e d  independent c r u i s e r s .  The  It is  error.  Variable-radius  during  r e q u i r e m e n t i n most  f o r e s t r e s o u r c e s management.  minimum o f  of  form a b a s i c  area per  a relatively  plot  center.  large unit  small  percentage  area,  because  number o f  trees  In B r i t i s h measuring  t r e e dbh  systematic caused  the  the  instrument  i s the diameter  errors  by  a)  Columbia,  used  tape.  for  During  o f random m a g n i t u d e , o c c u r .  measurement  They  are  following:  the t i l t i n g  of the  the circumference  tape  such  of the tape  c o r r e c t measuring plane,  t h a t p a r t or whole  of  i s below o r above  often resulting  the  i n an  overestimate, 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  above average of c)  a  ground  level  (or g e r m i n a t i o n  than  1.3m  point)  tree,  personal  judgement i n r e g a r d t o t h e  irregular  stem  forms. These e r r o r s have a s i g n i f i c a n t t r e e volumes, accurately The based  on  especially  i n f l u e n c e i n the  estimate  of  i f the t r e e heights are a l s o i n -  determined*  common c a u s e s  of  error  i n tree height  trigonometric principles,  are the  a)  misreading  instruments  as  a result  b)  difficulty  in locating  suitable  to observe  the  exact  position  measurement  following: of  unsteadiness,  p o i n t s from  of the  which  t r e e top  and  base, c)  horizontal the  tape  tight,  incorrect  erroneous  location  ommission  o f whole tape  correct d)  d i s t a n c e measurement e r r o r s  tape  biases of trees,  of the  alignment  of  - not the  zero point of  l e n g t h , and  pulling  tape,  tape,  the use  of i n -  length,  individual  persons  as a r e s u l t  of leaning  -3-  Measurement o f t r e e which l a r g e  e r r o r s may  Measurement inventory  heights  requires  influence  the r e l i a b i l i t y  This  influence  i s often  a basis  and t o t a l  i n obtaining  study w i l l  desired.  height  well-founded  be t o d e t e r m i n e t h e  measurement.  f o r the establishment  checkcruising,  measurement if  underestimated,  a n d v a r i a t i o n among i n d e p e n d e n t c r u i s e r s , o f t r e e  c o u n t , dbh,  and  o f an  estimates o f the e r r o r s .  The o b j e c t i v e o f t h i s  as  without  result.  mainly because o f the d i f f i c u l t y  biases  and c a r e ,  errors  result.  quantitative  skill  This  of guidelines  and f o r r e v i s i n g the f o r e s t  standards of the B r i t i s h  will  be  used  f o r performance inventory  Columbia F o r e s t  Service  -4-  LITERATURE  REVIEW  A measurement e r r o r i s t h e d i f f e r e n c e between a t r u e v a l u e o f a u n i t and an i n e x a c t measurement o f t h e u n i t .  It  may be due t o t h e f o l l o w i n g , FAO (1973) : (a) a c o n s t a n t b i a s , (b) a v a r i a b l e component r e l a t i v e t o t h e s a m p l i n g u n i t b e i n g c o r r e l a t e d t o t h e e x a c t v a l u e o f t h e measurement perameter i n the c o r r e s p o n d i n g u n i t , (c) an a r b i t r a r y component w i t h mean zero. The s o u r c e s , k i n d s , and i n f l u e n c e s o f measurement have been d i s c u s s e d  by L o e t s c h e t a l . (1973) .  errors  They emphasized  the i m p o r t a n c e o f measurement e r r o r s and c l a s s i f i e d t h e e r r o r s o u r c e s as f o l l o w s : (a) p e c u l i a r i t i e s o f t h e o b j e c t  being  measured, (b) u n c e r t a i n t i e s i n t h e m e a s u r i n g p r o c e d u r e , (c) i n a c c u r a c y  o f t h e measuring device,  physical influences,  (d) t o p o g r a p h i c a l o r  (e) d e f e c t s i n t h e o b s e r v e r s e n s e s .  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 " a p p a r e n t " e r r o r s , and  stated  ( p . 12) :  " f o r c o m p a r a t i v e 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 t h e a c c u r a c y and e f f i c i e n c y o f a m e a s u r i n g p r o c e d u r e and as a c o n f i r m a t i o n o f the c o r r e c t n e s s o f a s t a t e m e n t i n g e n e r a l , o n l y " a p p a r e n t " d e v i a t i o n s ( e r r o r s ) c a n be proven". Measurement e r r o r s have a l s o been d i s c u s s e d  by C o c h r a n (1973)  and C a r r o n (1968) . Ferguson (1975) p o i n t e d  o u t t h a t a l t h o u g h t h e measurement  errors a f f e c t i n g f o r e s t inventory  e s t i m a t e s have l o n g been  known, t h e r e have been few e m p i r i c a l s t u d i e s on t h e magnitude of the e f f e c t of these  errors.  Some o f t h e s e s t u d i e s w i l l be  -5-  mentioned  below.  K e n d a l l and the  sources  o f e r r o r i n VRP  t o the o b s e r v e r Ker,  Sayn-Wittgenstein  (1959) e m p h a s i z e d t h a t  forest inventory,  were most i m p o r t a n t  e t a l _ . (19 57)  and  per  (BAF  b e t w e e n -37%  = 2.2)  prism,  count v a r i a t i o n  t o be  among t h e  an a v e r a g e n e g a t i v e  acre  students  b i a s o f 1.2%  r a t h e r w i t h t h e age Carow  frequent.  (ha.)  of the  with a  t o 1%.  t o be  They found a plot  They  a s s o c i a t e d w i t h ground  slope,  stand. a definite  trees with a relascope,  c o e f f i c i e n t s of v a r i a t i o n i n basal area determination  in-  w i t h i n c r e a s e i n BAF.  (BAF  = 4.35)  8.71)  angle  He  minute  c o u n t , and  and  personal the  o f v a r i a t i o n w i t h a 49.0  tree  and  that  creased  line  3-diopter  1 t r e e per  (1958) o b s e r v e d t h a t t h e r e was  bias i n judging  students  of the a c t u a l t a l l y .  a l s o o b s e r v e d t h a t e r r o r s were not but  those a t t r i b u t a b l e  reported biases of untrained  i n estimating basal area  of  o b s e r v e d a 38.7%  (BAF  42.9%  = 2.17)  and  w i t h a 97.4  coefficient 69.0  minute  minute  (BAF  =  angle. K e n d a l l and  made by  Sayn-Wittgenstein  four operators  t a k i n g independent acre  c o u n t s a t 9 l o c a t i o n s (and counts obtained  by  1.5%  (9.18) .  w i t h BAF  w i t h BAF  = 20  p o i n t s was  to the  = 5  4.5%  -3.5%  ) tree  w i t h BAF  large error percent  t h a t the o b s e r v e r s  true  d i d not  an  w i t h BAF  f a c t t h a t o n l y a s m a l l number o f  u s e d and  errors  They o b t a i n e d  (1.14),  (4.59) and  They a t t r i b u t e d the  observers  (ha  u s i n g d i f f e r e n t BAFs) w i t h  c a r e f u l measurement.  a v e r a g e e r r o r o f -6% (2.29),  (1959) c o m p a r e d t h e  =  by  40  the  sample  check  the  =  10  -6-  "doubtful"  trees.  Stage (1962) r e p o r t e d on t e s t s o f d o u b t f u l made by f i e l d crews and  t r e e judgement  f o r e s t r y students matching photographs.  He deduced t h a t t h e a s s u m p t i o n o f t a l l y i n g o n e - h a l f t r e e s c o u l d not be r e l i e d upon as not u n b i a s e d .  of marginal  He a l s o n o t e d  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 t o be m i s s e d w i t h s m a l l e r BAFs, and  that personal bias i n prism  sampling  could  be a r e s u l t o f d i f f e r e n c e s i n response by d i f f e r e n t p e r s o n s t o t r e e b a r k and background c o l o u r . W i l l i n g h a m (196 2) on e x p e r i m e n t s w i t h p r i s m reported  t h a t a g r e a t e r magnitude o f e r r o r was  calibration  l i k e l y to occur  i n the e x c l u s i o n o f t r e e s t h a t s h o u l d be c o u n t e d . the i m p o r t a n c e o f a p e r s o n a l given  He  emphasized  c a l i b r a t i o n f o r each u s e r o f a  prism. S a y n - W i t t g e n s t e i n (1963) r e p o r t e d  about w h i c h t h e r e was o b s e r v e r was  t h a t t h e r e was  some doubt f o r e v e r y two  sure a b o u t .  trees  one the  W i t h the s m a l l BAFs, a s s o c i a t e d  h i g h t r e e c o u n t s p e r p o i n t , t h e number o f d o u b t f u l t r e e s large.  This provided  underestimate).  an o p p o r t u n i t y  for bias  (mainly  S a y n - W i t t g e n s t e i n a l s o showed t h a t  tree  with was  an personal  b i a s e n t e r s i n t o t h e 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 t r e e count per p o i n t .  A p r o p e r l y executed relascope  low  cruise  y i e l d s r e s u l t s of only a n e g l i g i b l e b i a s . Kirby  (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  c o u l d be p r e v e n t e d 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  field.  Munro (1966) r e p o r t e d a c o e f f i c i e n t o f v a r i a t i o n o f ± 11.15%  among  student  crew e s t i m a t e s  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 t o check d o u b t f u l t r e e s . The same study  showed a n e g a t i v e ,  b i a s o f 2.1% i n t r e e c o u n t . s h i p between p e r s o n a l  statistically  insignificant  There was no c o n s i s t e n t  relation-  e r r o r and the number o f t r e e s p e r 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 . or l e s s .  92% o f t h e p l o t s measured had e r r o r s o f ± 1 t r e e A BAF = 30 (6.88) p r i s m was used.  H o l g a t e (1967) showed m a t h e m a t i c a l l y  that small  critical  a n g l e s were a s s o c i a t e d w i t h s m a l l e r v a r i a n c e s o f t r e e c o u n t . He c o n f i r m e d  h i s r e s u l t s w i t h t h e f i n d i n g s o f Husch  Carow and R i c k e r d  (1969) r e p o r t e d t h e r e s u l t s o f a  study o f p e r s o n a l b i a s i n p o i n t s a m p l i n g . estimated  basal area per acre  A c r u i s e r over-  (ha ) by 6% w i t h the BAF = 10  (2.29) and BAF = 20 (4.59) p r i s m s , -40  (1955) .  came c l o s e w i t h t h e BAF =  (9.18) wedge, and made a s l i g h t u n d e r e s t i m a t e w i t h t h e  BAF = 75 (17.21) a n g l e gauge.  They r e p o r t e d t h a t t h e between  p e o p l e 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 t h e 5%  i n an e x p e r i m e n t t o measure the c r i t i c a l BAF = 10.25  (2.35) p r i s m .  level,  distance of a  However, i n d i v i d u a l p e r s o n a l  bias  tended t o 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 t h e BAF u s e d , 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 t o have a p o s i t i v e b i a s w i t h one BAF and a n e g a t i v e one w i t h a n o t h e r .  They r e -  commend c h e c k c r u i s i n g t o be done i n terms o f b a s a l r a t h e r than t r e e count.  area,  -8Laar obtained (BAF  (1970) c o m p a r e d e s t i m a t e s with a relascope  of basal  (BAF = 8 . 7 ) a n d a wedge  = 10.25), and found t h a t the relascope  negative  a r e a p e r ha  b i a s o f 4.5% a n d t h e p r i s m  prism  showed a  was u n b i a s e d  (using the  f i x e d p l o t t r e e counts as t h e c o n t r o l ) .  Bias  estimates  element i n the  was a t t r i b u t e d t o t h e p e r s o n a l  evaluation  of "borderline" trees.  i n relascope  He r e i t e r a t e d t h a t  pro-  v i d i n g more c o n t r a s t b e t w e e n t r e e s t e m s a n d t h e i r b a c k g r o u n d d i d n o t improve t h e determination  o f the status o f "border-  line"  Stages'  trees.  This  c o n f l i c t s with  (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 a n d 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 h a v e b e e n made o n t h e v a r i a t i o n i n diameter a t breast ments. following  height  and i n t r e e t o t a l h e i g h t  measure-  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 paragraphs.  M y e r s (1961) f o u n d t h a t 9 4 % o f t h e m e a s u r e m e n t s , u n d e r taken by f o r e s t r y s t u d e n t s and f i e l d sample p l o t s o f p o n d e r o s a p i n e , cm) o f t h e t r u e  diameter.  "true" diameter o f a tree. accuracy with  increase  were w i t h i n 0.1 i n c h  (0.254  M o d a l d i a m e t e r was t a k e n t o b e t h 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  i n diameter a t breast  the measurements were c o r r e c t . t h a t were t o o l a r g e  f o r e s t e r s on permanent  h e i g h t . S i x t y - t w o p e r c e n t of  T h e r e w e r e more  measurements  t h a n w e r e t o o s m a l l , i n d i c a t i n g more  sources o f p o s i t i v e e r r o r s .  Most o f t h e l a r g e e r r o r s  due t o i n c o r r e c t t a p e r e a d i n g s  or recordings;  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  were  b u t these  l a r g e r and s m a l l e r  -9than the  true  Ker heights  dbh.  (1951) r e p o r t e d o f 1.4%  standard  e r r o r s of  single tree  f o r i m m a t u r e D o u g l a s f i r and  2.3%  for  western hemlock. Meyer  (195 3) n o t e d t h a t r e p e a t e d  the U n i t e d  States  Forest  m e a s u r e m e n t s made w i t h  S e r v i c e h y p s o m e t e r and  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 errors of heights Ker  and  v a r y i n g b e t w e e n 1.1%  Smith  (1957) f o u n d a s t a n d a r d  for f o r e s t r y students using a relescope, pressed and  the  and  1.8%  3.5%. e r r o r of  using a Bjumleiss  view t h a t t r e e height  hypsometer .They ex-  measurements were  w e r e s u b j e c t t o l a r g e r and  e r r o r s o f measurement i n c r e a s e d to the  instrument  they used.  height  stand  t o p was  of the  i n almost  more  t r e e s were not  flattened off  measureexact  tree, i r r e s p e c t i v e of  They a l s o o b s e r v e d t h a t  e r r o r s r e s u l t e d when t h e  not  difficult  error.  proportion  when t h e  2.4%  conditions  S c h m i d 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 ment, t h e  Christen  standard  w o r k i n g under near optimum  e x p e n s i v e t o o b t a i n and  sources of  to  the  (and  the  systematic  exactly vertical  the person measuring  f a r e n o u g h away f r o m t h e t r e e b a s e ) .  or did  -10-  SOURCE OF Data of  for this  British  Columbia, school  collected  were  Research F o r e s t ,  the t h i r d  year  a t The  University  Maple Ridge,  forestry  students  British field  i n mensuration.  atically  plot  centers,  s e t a t about  Jean's  trails  Columbia during  Sixty  St.  study  DATA  and  numbered'1 t h r o u g h 60,  80 m  (paced)  Lakeshore t r a i l s  a r e i n a second  w e s t e r n hemlock  and w e s t e r n redcedar mixture.  Site  system-  a l o n g the  of the r e s e a r c h  growth stand about  containing mainly Douglas-fir Franco),  intervals  were  forest.  80 y e a r s o l d ,  (Pseudotsuga m e n z i e s i i  (Tsuga h e t e r o p h y l l a  (Thuja p l i c a t a  i n d e x r a n g e s f r o m 15m  The  (Raf.)  (Mirb.) Sarg.),  Donn.) i n i n t i m a t e t o 50m  a t 100  years.  3 Gross volume a v e r a g e d to  190  varied  cm,  did  2,  (over  50%  T r e e dbh  ranged  plot  line-of-sight  I).  from 5  cm  Topography  slope) to r e l a t i v e l y  i n the appendix  not r e s t r i c t The  m /ha.  t h e a v e r a g e d i a m e t e r b e i n g 53 cm.  from steep  maps 1 and  650  Underbrush  flat  and  (see  the weather  visibility.  c e n t e r s were d i v i d e d  into  six lots  of ten.  T h r e e t o s i x 3-man s t u d e n t c r e w s were a l l o c a t e d  to  lot.  relascope  Each crew e s t a b l i s h e d  (BAF = 9) p l o t s them. VRP in  The  s a m p l i n g , and  were g i v e n  had  many o f them had  hours  field  made aware o f t h e f o l l o w i n g  and  centers designated to  a theoretical  relascope cruising.  two  (BAF = 6)  a t the p r e - s e t p l o t  s t u d e n t s had  p r i s m and  prism  each  varied  background field  Furthermore,  instruction precautions  of  experiences the students  i n p r i s m u s e and t o be b o r n e  were  i n mind  -11-  during  p l o t establishment  i)  the prism plot  a l w a y s t o be h e l d  center  sweep a b o u t ii)  the prism cular  and t h e r e l a s c o p e : 1  directly  above t h e  when s i g h t i n g a t any t r e e  i n a 360°  the point,  t o be h e l d  so t h a t  i t s b a s e was  t o t h e stem o f t h e t r e e b e i n g  (except an  with the prism  when t h e l i n e  perpendi-  measured  o f s i g h t to the tree  a n g l e o f 10% f r o m t h e h o r i z o n a l  when  exceeded  slope  c o r r e c t i o n w o u l d be n e e d e d ) , iii)  the prism cular  iv)  t o be h e l d  to the l i n e  a l l hidden  trees  observation the v)  vi) vii)  ensure  viii)  observe level  In limits  that  order  provided  trees  the exact  t o be h e l d  directly  the relascope  the trees  above  i s corrected  center,  f o r slope, ground  point).  t o make m e a n i n g f u l c o m p a r i s o n s a n d t o e s t a b l i s h  from t r u e  North  stumps g r e a t e r 3 6 0 ° sweep.  measured  to the nearest  recorded  the p l o t  a t 1.3 m a b o v e i t s a v e r a g e  (or germination  clockwise  and  from  factor,  i t was n e c e s s a r y t h a t  crew a d h e r e t o t h e same p r o c e d u r e s e x a c t l y .  cluding  distance  t o be c h e c k e d b y a p p l y i n g t h e  o f p r e c i s i o n and a c c u r a c y ,  was s t a r t e d  perpendi-  t o be e x a m i n e d b y m o v i n g t h e  plot radius  the relascope  was  t o t h e t r e e was m a i n t a i n e d ,  a l l "doubtful" appropriate  i t s face  of sight,  point  plot point  so t h a t  than  and e a c h  " i n " tree  2 m h i g h ) was t a l l i e d  The dbh o f e v e r y  i n standard  Plot  0.1 cm w i t h forms.  " i n " tree  tally (inon a was  a l i n e n diameter  The t r e e  species  each  tape,  name was  -12-  noted.  The t o t a l  height  o f the f i r s t  was m e a s u r e d t o t h e n e a r e s t principles A prism on and  using  f  recordings their  independently study  o f each o t h e r ,  e s t a b l i s h i n g prism  p l o t s i n a l l the pre-set  abiding  b y t h e same p r o c e d u r e s to follow.  The t r e e c o u n t , the  different  II,  I I I , I V a n d V.  hours.  I made i n d e p e n d e n t  lascope  instructed  measurements  and had t o  within a period of eight  measurements, by c a r e f u l l y  sample p l o t  the student  T h e r e was no t i m e dbh, a n d t o t a l  chain.  and a r e l a s c o p e  The c r e w s made t h e i r  As a c o n t r o l t o t h e study, and  and a n y l o n  was u s e d on t h e even-numbered p l o t s , plots.  plot  0.1 m . by t r i g o n o m e t r i c  a suunto o r r e l a s c o p e  t h e odd-numbered  complete  " i n " t r e e on e a c h  observations and r e -  c e n t e r s and  crews had been  limit.  h e i g h t measurements by  c r e w s and t h e c o n t r o l a r e g i v e n  i n the appendices  -13-  METHOD OF ANALYSIS AND RESULTS Lot  number 2 o f t h e sample p l o t s h a d o n l y  one s e t o f  crew m e a s u r e m e n t s , a n d so was d i s c a r d e d  from t h e f i r s t  of  sample p l o t s h a d  the a n a l y s i s .  Each o f the remaining  3 t o 6 independent count,  ( i i ) tree  s e t s o f c r e w measurement o f ( i ) t r e e  dbh, a n d ( i i i ) t r e e  p l o t m e a s u r e m e n t s were As m e n t i o n e d analysis  and b i a s  dbh  and t o t a l  in  tree count  of variance tree  Prism  the aim o f t h i s  a q u a n t i t a t i v e e s t i m a t e o f crew  per tree.  t h e t r e e c o u n t p e r p l o t , and Firstly,  t h e crew v a r i a t i o n  e s t i m a t e s was a s s e s s e d by t h e m e t h o d o f a n a l y s i s  (ANOVA).  Secondly,  height  f o r each t r e e  t h e crew v a r i a t i o n i n measuring  was a s s e s s e d b y c a l c u l a t i n g t h e  and p o o l i n g  weighted average v a r i a t i o n per t r e e . was  height.  from t h o s e o f t h e r e l a s c o p e .  i n estimating  height  dbh a n d t o t a l  variation  separate  total  i n the i n t r o d u c t i o n ,  i s to obtain  variation  part  determined by comparing  these  to obtain  a  In e i t h e r case,  crew measurements w i t h  bias  the c o n t r o l  values.  TREE COUNT The c o n t r o l  s e t o f d a t a was t r e a t e d  student crew data,  so t h a t  together  f o r each l o t t h e r e  with the  w e r e up t o 7  s e t s o f measurement p e r p l o t .  T h e r e was, t h e r e f o r e , a  25 x 7 t r e e  some o b s e r v a t i o n s  count matrix,  f o r each o f t h e prism  with  p l o t s and t h e r e l a s c o p e  missing,  plots.  First,  the  c r e w a n d p l o t v a r i a t i o n a t e a c h p l o t was d e t e r m i n e d b y  the  method o f ANOVA.  -14-  The d e s i g n u s e d was r e p e a t e d numbers within  i n the subclasses. the lots.  subsampling w i t h  The p l o t s  Lots varied  unequal  a n d c r e w s were  f r o m i = 1 t o p = 5, p l o t s  j = 1 t o q = 5, a n d c r e w s f r o m k = 1 t o s ( v a r y i n g 4 and 7 ) . crews  The l o t s  were  nested  considered  fixed  from  between  and t h e p l o t s and  random.  The m o d e l was: X  ± j k  =  y + g. +  V  j  (  i  + 6  )  k ( i )  + l  j  k  (  i  (1)  )  where: X. ., = t r e e 3  plot  count o f the k th i n the i l o t  u = overall  $  v  j(i)  6  k(i)  jk(i)  =  c o u n t mean Der o l o t  = effect  th o f the i l o t  = effect  o f the j ^  e  ^^  e  c  t  °^  t  n  t o t h i s model  the i  1 1  plot  within  crew w i t h i n  e  = the interaction within  Reference  tree  crew on t h e i  t  h  o f the j  th  the  the i plot  t  lot h  lot  th and k crew  l o t (ERROR).  i s made t o G a n g u l i  A. Kozak a n d S.W.  Nash  p l a n o f t h e ANOVA  i s shown i n T a b l e I .  (1941) a n d t o D r s .  ( p e r s o n a l communication) .  The g e n e r a l  TABLE I ANOVA T a b l e F o r T f e e C o u n t  Source o f V a r i a t i o n  Degrees o f Freedom (d..:f.)  -  p  Between l o t s  q  Total  I  =  S? = a l  SS  a.  E  SS  T  -  1 , J C  =  + qa  v= a j(i) 2  2  2  + s a + qsa^ 2  ^ 5  +sc  V  P  2  2  X  i  S o  S S --SS - SS - SS, L P C  2  m  p  n. - 1 - m  -  s  S  2  q I I (x. - x. ) i = l k=l "  C  i-i X  P  SS=  .T. n. - p i=l l ^  1—X  2  p q _ 2 SS., = s i I (x.. - x. ) i = l j = l ID. l .  (q-1) (.1, n.- p ) - m  Error  )  n  p(q - 1)  Between crewswi t h i n - l o t s  -  (x. - x SS. = qs. I 1 = 1 1..  P-1  Between plotswitain-lots  Expected JMean Squares  Sum o f Squares  q  s  _ I I I (x. ., - x...) i = l j = l k=l 2  1  3  tree count mean per p l o t o f a l l the crews i n a l l the p l o t s i n a l l the l o t s , tree count mean per p l o t o f a l l the crews i n a l l the p l o t s i n the i^ l o t .  crev; v a r i a t i o n -  1  ^i.. x. . = _i.k x. . = ID-  m  =  *l  =  c  z  V  =  tree count mean per p l o t o f the k ^ crew i n a l l the p l o t s i n the i l e t . 1  tree count mean per p l o t o f a l l the crews i n the j ^ p l o t i n the i th the number o f crews i n the i l o t . the t o t a l number o f missing observations i n a tree count m a t r i x . the l o t v a r i a t i o n * plot variation. 1  ^ lot.  ( l / n . ) - ( l / I n.) i=l ~ 1  I  i=l  Cn?  p-1  (2  -16-  The sums o f s q u a r e s  SS , SS , SS , SS , SS L  p  were computed u s i n g t h e g e n e r a l GENLIN  - a general  least  C  E  T  i n Table  r e g r e s s i o n method.  I  The UBC  squares a n a l y s i s o f v a r i a n c e computer  program o f t h e 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 u s e d .  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 r e f e r e n c e t o Anderson and B a n c r o f t  with  (1952) .  B y u s i n g t h e a p p r o p r i a t e mean s q u a r e s f r o m t h e ANOVA table, the estimates a  2  v  o f crew v a r i a n c e ,  and p l o t  variance,  , w e r e made a s f o l l o w s : S  52  _MiL  =  6  2  o  ( 3 )  q S  a2 v  - S  2  S o  2  2  =  ( 4 )  s  The c r e w 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 t h e 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 a n d w i t h t h e r e l a s c o p e was 2.080 t r e e s . o f t h e more i m p o r t a n t  Table  statistics  I I g i v e s a summary o f some i n t h e a n a l y s i s , and t a b l e s  I I I a n d 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  plots, respectively. Secondly, i r order  e a c h p l o t m e a s u r e m e n t was t r e a t e d  to evaluate  the t r e e count accuracy.  independently  Using  the t o t a l  number o f p l o t m e a s u r e m e n t s t h e v a r i a t i o n o f t h e p l o t m e a s u r e m e n t s was c a l c u l a t e d b y v a r i a t i o n  f r o m 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 w e r e u s e d 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 c o u n t e r r o r p e r p l o t was ± 6 t r e e s a n d  -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 T r e e C o u n t ANOVA-  Instrument  O v e r a l l Mean W i t h 95% Conf. L i m i t s (trees/plot)  Prism  9.509 (8.880 7.432 (7.400  Relascope  Note:  7.280 6.257) 5.420 4.801  Stand Coeff. of V a r i a t i o n (%)  10.44  32.96 (34.08) 28 .04 (26.82)  4.93  The v a l u e s i n b r a c k e t s a r e t h e r e s u l t s o f t h e C o n t r o l measurements.  TABLE I I I .  ANOVA T a b l e f o r t h e P r i s m  Source o f Variation Between l o t s Between p l o t s wi t h i n - l o t s Between c r e w s wi t h i n - l o t s Error Total @  ± ± ± ±  Coeff. of Variation of C r e w s (%)  d.f.  Sum o f Squares  Plots  Mean Square  Notes  4  408 .43  102.11  1. 513  20  1250.90  62.54  28 .820  @  26 100 150  184.74 217.01 2061.08  7.10 2.17  3. 27 2  @  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. N o t s i g n i f i c a n t  F-ratio  N.S.  TABLE I V :  ANOVA  Table f o r the Relascope  Plots  Mean square  d.f.  Sura o f squares  4  3 38.15  84.53  Between P l o t s within-lots  20  566 . 45  28 . 32  Between c r e w s within-lots  26  59.92  2. 30  Error  97  158.47  1.63  Source of Variation Between  lots  Notes  2. 915  C  *7  17.374  @ N.S .  1.411  1122.99  147  Total  Fratio  @ 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 .  it  occurred  i n 2 o u t o f 130 p r i s m p l o t  of  124 r e l a s c o p e  p l o t measurements.  i n the B r i t i s h Columbia Forest Club  (1971).  measurements and i n 2 o u t  The a l l o w a b l e  Service  tree count  i s ± 1 t r e e , UBC  plots, respectively.  w e r e 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 o n e s  were  (Fig. l a ,  p l o t s , 4 2% o f t h e t r e e  counts  overestimated. The  a c c u r a c y o f t h e crew t r e e counts a g a i n s t  was t e s t e d b y f i t t i n g counts  a l i n e a r regression  (X-.,) o n t h e c o n t r o l t r e e c o u n t s  student t - t e s t ,  f r o m unity , t h e i n t e r c c p i was s t a t i s t i c a l l y  o f  I f the  the control  o f t h e crew  (X ) , a n d t h e n  t o t e s t whether the  t i c a l l y d i f f e r e n t from u n i t y .  it  There  I n t h e p r i s m p l o t s , 56% o f t h e t r e e c o u n t s w e r e 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  the  Forest  T a b l e s V a n d VI s u m m a r i z e 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  b).  error  s l o p e  s l o p e  t lie r e g r e s s i o n  d i f f e r e n t f r o m */.oro  was  tree using statis-  was n o t d i f f e r e n t  l i n o was t e s t e d  whether  -19-  TABLE V-  VFC (Trees)  Tree  Count Accuracy  No. o f P l o t •Measurements  ±0 ±1 ±2 ±3 ±4 ±5 ±6 Total  24.62 29 .23 20.77 12.30 4.62 6.92 1.54  130  100.00  Tree  VFC (trees)  No. o f p l o t Measurements  0 1 2 3 4 5 6  Total  Percent of t o t a l (%).  32 38 27 16 6 9 2  Table VI.  + * + + + + ±  i n the Prism  Count Accuracy  Plots  Percent of t o t a l (cumulative) (%) 24.62 53.85 74.62 86.92 91.54 98.46 100.00  -  i n the Relascope  Percent of t o t a l (%)  46 45 13 10 4 4 2  37.10 36.29 10.48 8 .06 3.23 3.23 1.61  124  100.00  Plots  Percent of t o t a l ( c u m u l a t i v e ) (%) 37 .10 73.39 83.87 91.93 95.16 98.39 100.00  -  -20-  03  I  +  ID  I  +  to LU  I  4  +  +  +  +  UJ  OC COnM —J CC  a  »—i  +  +  I  |  4-  +  +  +  +  +  +  4-  4.  4.  4.  4.  4.  4.  4.  CO  o^-l  +  4. 4.  4.  4-44-  4-  44-  4-  4-  ,  0.0  2.0  ,  A.a  ,  G.O  ,  ,  ,  0.0  m.o 12.0 TRUE COUNT (TREES)  R  14.0  Figure l a A Plot  of  the R e s i d u a l s A g a i n s t With the Relascope  True  Counts  R  —  ie.o  4-  + + +  +  +  +  4-  +  +  4-  +  4-  +  -f  +  •f  + +  -  +  + +  +  4-  +  +  +  +  +  +  +  -r  +  + +  +  i  i  B.O  5.0  I  7.0  '  i  of  the  I  1  8.0  g.o  1D.0  TRUECOUNT [TREES} Figure  A Plot  +  Residuals Against  i 11.0  i 12.  lb True Counts w i t h  the  Prism  -2 2-  a  -23-  The Fig.  f o l lowing  r e l a t i o n s h i p s wore o b t a i n e d  (sec?  also  2a, b ) : Relascope _ p l o t s :  1.006 + 0.8 97 X 0.58 7,  Prism  plots:  1.065  C  SEE = 1.829 + 0.998  X'  (6)  c  0.693, SEE - 2.117 where: r  2  SEE At  =  the c o e f f i c i e n t  =  the standard error  t h e a = 0.05 p r o b a b i l i t y  regression l i n e and This  CO  of determination of t h e e s t i m a t e  l e v e l , the i n t e r c e p t  were n o t s t a t i s t i c a l l y  u n i t y , r e s p e c t i v e l y ; but the  slope  and s l o p e o f the  different of  from z e r o  the line  () was. 6  i n d i c a t e d t h a t , on a v e r a g e , crews c o u n t e d t r e e s w i t h  a negligible bias with  the relascope,  a significant bias with  and c o u n t e d t r e e s  only  with  the prism.  DIAMETER In t o t a l  398 t r e e s w e r e r e p e a t e d l y  the d i f f e r e n t crews.  The s p e c i e s  measured f o r d i a m e t e r by  measured were  w e s t e r n h e m l o c k a n d w e s t e r n redicdar  „  Firstly,  Douglas-fir, the bias of the  c r e w s i n m e a s u r i n g d b h was a s s e s s e d . In order  to evaluate  the accuracy i n measuring the d i a -  m e t e r s , e a c h t r e e m e a s u r e m e n t was t r e a t e d i n d e p e n d e n t l y . was a t o t a l  There  o f 1701 m e a s u r e m e n t s , grouper) i n t o 5 cm d b h c l a s s e s .  The  c o n t r o l d b h m e a s u r e m e n t s o f e a c h t r e e was a c c e p t e d a s  the  " t r u e " dbh o f the t r e e .  The d e v i a t i o n s  from 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  -25-  f o r m u l a was used f o r c a l c u l a t i n g t h e b i a s e s :  where th  Dg = dbh measurement b i a s on t h e i k. crew.  t r e e by t h e  tn  th  D  = t r u e dbh o f t h e i th ik *~ =  d t ) n  o f  t h e  t  r  e  e  a s  tree. measured by t h e k  th crew.  The b i a s e s were t h e n grouped i n t o v a r i a t i o n f r o m 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 . VFC Class 0 1 2 3  4 5 6 7 8 9 10  The f o l l o w i n g VFC c l a s s e s were used: Limits (cm)  + + + + + + + + + +  0.0-0.09 0.1-1.0 1.1-2.0 2.1-3.0 3.1-4.0 4.1-5.0 5.1-6.0 6.1-7.0 7.1-8.0 8.1-9.0 > 9.0  The v a r i a t i o n i n a c c u r a c y (bias) w i t h i n c r e a s e also investigated. biases  T h i s was done by s e p a r a t i n g  by 5 cm d i a m e t e r c l a s s e s , on a r e l a t i v e  i n dbh was  t h e measurement basis.  The a v e r a g e s t a n d d i a m e t e r was 52.67 cm from t h e c r e w e s t i m a t e s , and 52.72 cm by t h e c o n t r o l .  O n l y about 6% o f t h e  measurements were c o r r e c t , and 95% were w i t h i n 5.0 cm o f t h e t r u e v a l u e . Fourty-cight  small. fig.  %  • Or  t h e measurements were t o o l a r g e and 46% t o o  T h i s i n d i c a t e d more n e g a t i v e s o u r c e s o f e r r o r  (see a l s o  3 ) . A summary o f t h e a c c u r a c y o f d i a m e t e r measurements  i s aiven  i n Table V I I .  B r i t i s h Columbia F o r e s t  The a l l o w a b l e Service  dbh measurement e r r o r i n the  i s ±1%, U.B.C. F o r e s t  Club  (1971).  -26There seems t o be a 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 increase trees.  i n dbh.  Accuracy tends t o decrease a t higher  with dbh  E x a m i n a t i o n o f 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 d i a m e t e r 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 TABLE V I I .  VFC (cm)  this. Tree D i a m e t e r Measurements A c c u r a c y  Number o f measurements  0 1 2 3 4  96 943 271 142 68 57 39 13 23 14 35 1701  5  6 7 8 9 10 Total  Percent of t o t a l (%)  Percent of t o t a l ! ( c u m u l a t i v e ) (%)  5.64 55.44 15.94 8.35 4.00 3.35 2.29 0.76 1.35 0.82 2.06 100.00  5 .64 61.08 77.02 85. 37 89.37 92.72 95. 01 95.77 97 .12 97.94 100.00  -  Large e r r o r s were as much as 30 cm and were e q u a l l y and  larger  s m a l l e r t h a n the t r u e dbh v a l u e s . The a c c u r a c y o f crews i n measuring d i a m e t e r s was t e s t e d  by comparing t h e crew measurements w i t h t h e c o n t r o l v a l u e s the r e g r e s s i o n method adopted w i t h t h e t r e e c o u n t . r e l a t i o n s h i p was o b t a i n e d  2  =  0.979, SEE = 4.387  where: D,-E, = e s t i m a t e d dbh i n cm Dp = c o n t r o l  The f o l l o w i n g  (see a l s o f i g . 4 ) .  D_ = -0.527 + 1 .002 D„ r  using  ( t r u e ) dbh i n cm  (8)  to  Figure A Plot  of the Residuals  Against  3 True Diameter  Measurement  TRUE DISMETER (CM) Figure Relationship  4  Between T r u e D i a m e t e r a n d t h e Crew Diameter Measurement  (Estimated)  -29-  TABLE V I I I .  The D i s t r i b u t i o n o f D i a m e t e r M e a s u r e m e n t E r r o r s &y Diameter Classes  Diameter C l a s s Midpoint (cm)  0  7 12 17 22 27 32 37 42 47 52 57 62 67 72 77 82 87 92 97 102 107 112 117 12 2 127 132 137 142 152 162 167 170  TOTAL  ERROR 2  1  3  4  (VFC) 5  6  CLASS 7  8  9  10  TOTAL  NUMBER OF MEASUREMENTS 3 8 2 6 10 1 16 11 5 6 2 2 4  1  1  1 1 1  24 24 76 44 86 122 98 67 76 81 67 56 12 22 22 20 14 5 1 7 1 2 5 1 6 2  1 5 3 8 11 26 21 18 25 24 31 15 11 9 17 6 7 9 1 5 5 1 1 1 3 4 1  1 5 2 6 16 5 7 11 10 11 10 10 10 10 5 3 4 2 1 2 3 1 1 2 1 2  1 1 3 5 3 2 8 6 4 8 1 5 1 1 1 1 3 4 2 1  4 3  1 1 1  96  1 1  1 1  94 3 271 14 2  68  1 1 7 4 1 5 5 2 7 4 3  3 1 3  2 3 1 5 2 6 5 2 1 1  1  1 3 1 1 .1  1  5  1  3 2 1  1  4  1 5 1 1  2 1  4 2 1 1  1 5 5  1 1  1  2  2 1  1  1  1  1  2 1 2 1 3 1 1 1 57  1 2 4 2 1  1 1  2  1  3 2 4  1 1  59  1  13  23  14  35  29 43 85 63 115 194 157 107 131 139 123 104 60 61 58 36 28 25 10 26 10 8 2 10 13 18 10 8. 6 9 6 7 1701  -30-  The i n t e r c e p t and s l o p e o f t h e r e g r e s s i o n  line  ( 8 ) were n o t  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 .  T h i s i n d i c a t e d t h a t on a v e r a g e ,  crews measured t r e e d i a m e t e r s w i t h o n l y a n e g l i g i b l e b i a s . S e c o n d l y , v a r i a t i o n i n dbh measurement was c a l c u l a t e d by p o o l i n g  from crew t o crew  t h e squared d e v i a t i o n s o f t h e crew  measurements on a l l t h e t r e e s and d i v i d i n g t h e r e s u l t by t h e p o o l e d d e g r e e s o f freedom o f a l l t h e measured t r e e s .  Model  9 was used. n Z Op  1=1  =  k Z  3=1  _  (D„. .-  9  D^.K  J  (9)  n  I d.f.. i=l where: =  d i a m e t e r measurement crew v a r i a t i o n e s t i m a t e  j  =  crew j  D_.  =  mean o f t h e k measurements on t h e i  =  t h e d e g r e e s o f freedom f o r t h e i " " *  £i  d.f..  measurement on t h e l  tree ^ tree  1 1  1  tree  (=k.- 1)  The a v e r a g e crew d e v i a t i o n i n d i a m e t e r measurement was 4.3 cm p e r t r e e .  The c o e f f i c i e n t o f v a r i a t i o n = 8.16% ( t h e average  t r e e dbh was 52.67 cm). i n dbh was, i n g e n e r a l ,  The v a r i a t i o n o f p r e c i s i o n w i t h  increase  u n i f o r m (see F i g . 4 ) .  TOTAL HEIGHT I n 31 p l o t s t h e crews measured t h e same t r e e s f o r h e i g h t . I n t h e r e s t o f t h e p l o t s t h e crews d i d n o t measure c o r r e s p o n d i n g trees.  The d a t a f o r t h e 31 t r e e s were a n a l y s e d t o d e t e r m i n e t h e  -31-  accuracy  and p r e c i s i o n o f crew measurement.  The r e s t o f t h e  d a 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 diameter.  t o t h a t used f o r  O n l y s e v e n VFC c l a s s e s , a n d 1 m h e i g h t  classes  were used. Less than control values  2% o f t h e t o t a l m e a s u r e m e n t s w e r e c o r r e c t , i f are accepted  as the " t r u e " h e i g h t .  o f t h e measurements were l e s s than values.  A b o u t 60%  a n d 4 0% more t h a n ,  the true  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  Table IX.  Tree T o t a l Height  VFC Class  Limits (ro)  0  ±0.0-0.09 ±0.1-1.0 ±1.1-2.0 ±2.1-3.0 ±3.1-4.0 ±4.1-5.0 ±5.1-6.0 >± 6.0  1 2 3  4  '5 6 7  Total  Measurement  Number o f measurements  Accuracy  Percent o f t o t a l (%)  2 19 17 19 18 11 6 18  1.82 17.27 15.46 17.27 16.36 10. 00 5.46 16.36  110  100.00  Percent of t o t a l ( c u m u l a t i v e ) (%) 1.82 19.09 34. 55 51.82 68 .18 78 .18 83.64 100.00  -  The a l l o w a b l e t r e e h e i g h t m e a s u r e m e n t 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)  T h e r e 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 c r e w s a s height increased  (see t a b l e X ) . V a r i a b i l i t y  a r o u n d z e r o was q u i t e h i g h  of the residuals  ( s e e F i g . 5) .  The t r e e h e i g h t s r a n g e d f r o m a b o u t 8 m t o a b o u t 51 m, the crew avaerage being  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 o f H e i g h t M e a s u r e m e n t By H e i g h t C l a s s e s  HEIGHT CLASS MID-POINT(m)  0  1  E R R 0 R (VFC) 2 3 4 5 NUMBER  10. 5 11.5 18.5 21.5 22. 5 24.5 26.5 27.5 29.5 30. 5 31.5 32.5 34.5 35. 5 37.5 38.5 39.5 40. 5 42. 5 47.5 48.5 50.5 TOTAL:  1 4 2 2 2  1  1 1 1 2 1 1  1  1 1 1  3 1 1 3 1  1  1  1 1 1 2  2  19  17  1 3  TOTAL  EASUREMENTS 1 2  4 1  C L A S S 7 6  1  3 1 2 1  OF  Errors  1 2 3 2 2 1 2 2  1  1  19  18  2  1 i  1  J  •;  I  1 i  2  j i  1 1 1  1  i  1 1  3 2 2  !  1 1 1  11  1 1 1 6  2 1 1 2 !  18  4 4 10 2 4 2 8 6 5 5 4 8 3 6 6 3 3 4 7 5 4 ^  110 ..,.„.»  -33-  +  4-  +  +  4-  4-  4-  •f  +  4=  +  4-  + 4-  4-  +  4-  + + 4-  4-  4+  4-  +  t  4=  +  4-  t-  V  + + + +  4-  44-  4-  +  +  4-  4-  ,  10.D  ,  1U.Q  ,  20.0  f  1  25.0  TRUE Plot of theResiduals  53.0  ,  Ifi.O  ,  40.0  1  4 >.0 r  , —  r.O 0  HEIGHT IM)  Figure 5 a g a i n s t True T o t a l H e i o h t  MeasuresAnt  -24-  Figurc 6 R e l a t i o n s h i p between T r u e H e i g h t . a n d _ t h c C r e w 11 e i q h t Me a s u r em e n t  (Estimated)  Total  -35A l i n e a r r e g r e s s i o n o f the crew measurements the c o n t r o l  ( t r u e ) v a l u e s (H^) gave t h e f o l l o w i n g  (H ) on relationship:  H„ - 3.358 + 0.8668 1i_ r The i n t e r c e p t  2  = 0.729, SEE -  of t h e r e g r e s s i o n l i n e  (10)  5.62 (9) was  statistically  d i f f e r e n t from z e r o a t t h e a = 0.05 p r o b a b i l i t y indicated  level.  This  t h a t on a v e r a g e , crews measured t r e e h e i g h t s w i t h  a significant  bias.  The crew d e v i a t i o n  i n measuring h e i g h t was 6.86  the c o e f f i c i e n t o f v a r i a t i o n b e i n g 21.86%. trend of v a r i a t i o n i n p r e c i s i o n i n c r e a s e i n h e i g h t (see f i g . 6 ) .  m  There was no  o f h e i g h t measurements  with  -36-  DISCUSSION  I t i s o n l y u n t i l r e c e n t l y t h a t t h e r e has been more emphasis on t h e a c c u r a c y  o f i n d i v i d u a l t r e e measurement  than  on, say, t h e t o t a l number o f t r e e s measured p e r p l o t o r t h e t o t a l number o f p l o t s measured p e r day.  The a n a l y s i s o f  e r r o r s a s s o c i a t e d w i t h b a s a l area p e r ha , d i a m e t e r ,  and  h e i g h t measurements was, t h e r e f o r e , a p p r o p r i a t e . The a v e r a g e t r e e c o u n t p e r p l o t i s 9.5 t r e e s w i t h a BAF = 6 p r i s m and 7.4 t r e e s w i t h a BAF = 9 r e l a s c o p e . c o e f f i c i e n t of v a r i a t i o n of observer  The  t r e e c o u n t i s 10.44%  w i t h t h e p r i s m and 4.93% w i t h the r e l a s c o p e .  T h i s means t h a t  68% o f t h e t r e e c o u n t s f a l l w i t h i n 10.44% o f t h e average p r i s m T  p l o t s c o u n t , o r w i t h i n 4.9 3% o f t h e average r e l a s c o p e p l o t s count.  S i n c e b a s a l a r e a p e r 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 r e a c h e d r e g a r d i n g v a r i a b i l i t y c o u n t can be assumed t o a p p l y w i t h r e a s o n a b l e t o b a s a l a r e a per ha. determination  Therefore,  i n tree  consistency  the percentage e r r o r i n the  o f b a s a l a r e a p e r ha  from t h e 25 p r i s m p l o t s i s  ± 4.09% and from t h e 25 r e l a s c o p e 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 . confidence  Percentage e r r o r i s h a l f the  i n t e r v a l o f an e s t i m a t e expressed  of the estimate.  When t h e number o f sample p l o t s i s 1, t h e n  c o e f f i c i e n t o f v a r i a t i o n = percentage e r r o r . p e r c e n t a g e e r r o r means t h a t one i s 55% sure t h a t b a s a l a r e a p e r ha  as a p e r c e n t a g e  In this  case,  t h e average  i s w i t h i n 4.09% o f t h e t r u e b a s a l a r e a p e r  ha. e s t i m a t e w i t h t h e p r i s m , o r 1.93% o f t h e t r u e b a s a l per ha  estimate w i t h the relascope.  area  -37The p r i s m 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 t o the ± .11.15% w i t h a BAF  = 6.8  s i m i l a r s t a n d s found bv Munro (1966), and  sliahtlv  t h a n ± 6% w i t h a BAF  = 4.6  orism i n bigger  p r i s m found by Carow and R i c k e r d  (1969). E r r o r s o f t h i s magnitude w a r r a n t 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 o f sample p l o t s e s t a b l i s h e d i s low. The  s t a n d a r d d e v i a t i o n i n the crew t r e e c o u n t o f 0.99 3  t r e e s p e r p l o t u s i n g t h e p r i s m i s c l o s e t o t h a t o f 0.805 t r e e s per p o i n t o b t a i n e d by Munro (1966), t h a t o f 1 t r e e per p o i n t o b t a i n e d by Ker et_ a l .  (1957), and i s w i t h i n t h e ± 1 stem  a l l o w a b l e e r r o r o f the B r i t i s h Columbia F o r e s t S e r v i c e . The s t a n d a r d d e v i a t i o n o b t a i n e d w i t h the r e l a s c o p e i s much l o w e r , 0.366 t r e e s p e r p l o t . used was  T h i s may  be because the  BAF  l o w e r , o r because the r e l a s c o p e 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 to p i n p o i n t the  exact  reason f o r the low e r r o r s o b t a i n e d u s i n g t h e r e l a s c o p e . The a v e r a g e s t a n d c o e f f i c i e n t o f v a r i a t i o n i s 32.9% the p r i s m and 28.04% u s i n g the r e l a s c o p e .  The c o e f f i c i e n t s of  v a r i a t i o n o b t a i n e d by the c o n t r o l were 34.08% and the p r i s m and r e l a s c o p e , r e s p e c t i v e l y .  using  26.82% w i t h  T h i s i m p l i e s t h a t lower  t r e e c o u n t s per p l o t g i v e a lower s t a n d c o e f f i c i e n t o f v a r i a tion.  T h i s i s c o n t r a r y t o the f i n d i n g s o f  (1963).  Sayn-Wittgenstein  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 o f v a r i a -  t i o n decreased per p l o t . difference.  w i t h an i n c r e a s e i n the average number o f t r e e s  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  -38The  total  average t r e e count per  with  the  prism  i s higher  This  means t h a t  7.08%.  Using  the  the  per  crew was  185.8  but  close  the  for  the  was  no  and  the  to  high  The error  relascope, trees.  negative  number o f  relascope  c r e w s had  true  consistent  the The  o v e r a l l negative total  distances  are  reduces t h i s  than,  bias  count  i s apparent.  of  i n prism  No  error  per  p l o t i n either of  the  t r e e c o u n t s was  i n the  stand  by  true value, identified  error  reason There  committed  the  ( r e l a t e d to  measured  prism  or  i t does not  or  the  by  ( M i l l e r and  Beers  be the  19 75) .  Also,  an  made s u c h tree  in  that  question,  centers.  purposes.  that  the  crews  the  prism  to  the  dbh). swinging  incidence  slope  the  is cruising  many p e r s o n a l  c o r r e c t a n g l e when hand h o l d i n g  the  "doubtful"  a crew i s i d e n t i c a l  ( i n terms of  angle of  of  (1964) t h a t  for thinning  p l o t of  axis contributes  to maintain  the  locating tree heart  Slope c o r r e c t i o n with a prism  difficult  of  necessarily follow  same t r e e s  a perpendicular  Miller  face  some o f  subjectivity in  e r r o r o c c u r s when one  t r e e c o u n t per  the  near  to  However, one  tree diameter)  to the  s u b j e c t i v i t y of  i s the  due  when c h e c k i n g  B e e r s and  table construction the  introduction.  sources of  Another important  the  higher  of  count  trees.  suggestion  factor  of  bias  average t r e e  is slightly  trees.  185.0  t r e e count center  adjusting  Although  This  222.0  plots.  more r e c o g n i s a b l e  for  the  trees  tree count of  trees  sources l i s t e d  trees.  an  237.72  true count of  r e l a t i o n s h i p between t h e  variability  locating  than the  crew o f  an  errors.  within  unmounted  2  about It is  degrees  prism  correction with  the  relascope i s not automatic;  i t i s o n l y done when t h e  brake  knob i s r e l e a s e d . A survey of the student instrument p r e f e r e n c e s t h a t 17 o u t o f t h e  32  for  m a i n r e a s o n was  cruising.  The  students asked  p r e v i o u s l y , but not a relascope. students asked  indicates  p r e f e r r e d t o use  t h a t t h e y had  a  prism  used a  prism  H o w e v e r , 13 o u t o f t h e  32  p r e f e r r e d t h e r e l a s c o p e , more b e c a u s e 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  to a l i g n w i t h the t r e e  a l s o a sample q u e s t i o n n a i r e i n the appendix  VI).  (see  Effectively,  t h e 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 .  This  i n p a r t e x p l a i n the  i n crew t r e e  fact that smaller v a r i a b i l i t i e s  may  c o u n t s were o b t a i n e d w i t h the r e l a s c o p e . The of  average t r e e diameter  v a r i a t i o n i n crew diameter  was  Other  labelled  ii)  f o u n d by  dbh  p o i n t s , and  error  Myers  error,  of the measurements b e i n g  sources o f such e r r o r s , o t h e r than those  not p u l l i n g  too  listed  following:  the measuring  tape  tight  f o r l a r g e t r e e s , t h e r e i s the tendency to take r e a d i n g s t o t h e n e a r e s t 10 cm ( o r a t m o s t , t o t h e n e a r e s t 1 c m ) , 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 e x c e e d s t h e m e a s u r i n g t a p e l e n g t h .  E r r o r source diameters.  ( i i ) e x p l a i n s why  accuracy  on  probably  T h e r e w e r e more n e g a t i v e s o u r c e s o f  i n the i n t r o d u c t i o n were the i)  This  Columbia F o r e s t S e r v i c e a l l o w a b l e  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 large.  coefficient  i s m a i n l y because Myers' r e s u l t s were based  m e a s u r e m e n t s on p e r m a n e n t l y smaller trees.  the  8.16%.  I t i s a l s o higher than the e r r o r  (1961); but t h i s  on  and  m e a s u r e m e n t s was  i s much b i g g e r t h a n t h e B r i t i s h e r r o r o f ± 1%.  52.67 cm,  i s low a t l a r g e r  tree  The  a v e r a g e t r e e t o t a l h e i g h t was  c o e f f i c i e n t of v a r i a t i o n 21.86%. by K e r  (1951), t h a t o f found  by K e r  by Y o u n g  3.5%  and  tributed  The  error  (1953),  greater  found that  D i s t a n c e measurement e r r o r s con-  probable  to the high e r r o r i n t r e e h e i g h t reason  f o r the unreasonably s t u d e n t s had  i n h e i g h t measurement.  high  not  Furthermore,  had the  terms.  t r e e h e i g h t m e a s u r e m e n t r e q u i r e s more e x p e r i e n c e  and  patience.  Forestry cruising a r e t o be out  was  5,10%  students c o u l d not v i s u a l i s e w e l l i n the m e t r i c u n i t Accurate  the  a l l o w a b l e e r r o r o f the B r i t i s 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 the enough e x p e r i e n c e  2.3%  (1957), t h a t o f ±  t h e + 3%  quite significantly  measurement.  the  r e p o r t e d by M e y e r  Smith  ( 1 9 6 7 ) , and  Columbia F o r e s t S e r v i c e .  and  i n crew t r e e h e i g h t measurements  T h i s e r r o r i s much h i g h e r t h a n  o f 2.4% noted  '31.38 m,  s t u d e n t s are o f t e n employed t o undertake  f o r various agencies. relied  f o r , and  I f the  student  inventory  u p o n , e r r o r s o f t h i s m a g n i t u d e m u s t be  reduced.  On  the o t h e r hand, i t i s p r o b a b l e  the c u r r e n t measuring procedures  forest results watched that  a r e not adequate, as h i n t e d  t h e f o l l o w i n g q u o t a t i o n f r o m Young  (1967, p.  18) :  " I f wood w e r e a s v a l u a b l e a s g o l d , we w o u l d m e a s u r e i t w i t h t h e same, a c c u r a c y , b u t a s 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 the primary cut products".  by  -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 t h e 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 t h e p r i s m p l o t s and 7.4 t r e e s i n t h e r e l a s c 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 i s 10.44% w i t h t h e p r i s m and 4.93% w i t h 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 B A F .  A  s i g n i f i c a n t n e g a t i v e b i a s o f 7.08% i n t r e e c o u n t w i t h a p r i s m , and an i n s i g n i f i c a n t n e g a t i v e b i a s o f 0.43% w i t h a r e l a s c o p e was o b s e r v e d .  About 37% o f t h e t r e e c o u n t s i n t h e  r e l a s c o p e p l o t s , and 29% i n t h e p r i s m p l o t s were c o r r e c t . N i n e t y - f i v e %  o f t h e r e l a s c o p e p l o t s and 91% o f t h e p r i s m p l o t s had  errors of ± 4 trees or less. per p l o t was ± 6 t r e e s .  The maximum t r e e c o u n t e r r o r  The p e r c e n t a g e  m i n a t i o n o f b a s a l a r e a p e r ha  e r r o r i n the deter-  from 25 p r i s m p l o t s was ± 4.09%,  and from 25 r e l a s c o p e p l o t s , ± 1.93%, a t t h e a = 0.05 p r o bability level.  These e r r o r s show t h a t a c c u r a c y o f a r e l a s c o p e  o r p r i s m s u r v e y depends on t h e c a r e w i t h w h i c h t h e work i s done, and t h a t t h e r e l 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 t h e measurer i n dbh measurement was 8.16% ( t h e average dbh = 52. 6 7 cm) . About 95% o f a l l t h e measurements o f 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.  measurements were c o r r e c t .  Only 6% o f t h e  V a r i a b i l i t y o f t h e measurements  about t h e i r mean was u n i f o r m i r r e s p e c t i v e o f t h e dbh, b u t a c c u r a c y was lower a t l a r g e r t r e e d i a m e t e r s . n e g a t i v e s o u r c e s o f e r r o r than p o s i t i v e ones.  There were more  -42A c o e f f i c i e n t o f v a r i a t i o n o f 21.86% o f t h e measurer i n h e i g h t measurement was o b t a i n e d h e i g h t = 31.38 m).  t o t a l tree  Over 15% o f t h e h e i g h t measurements were  i n e r r o r by ± 6.0 m. o r more. were c o r r e c t .  (average  Only 1.8% o f t h e measurements  H e i g h t measurements 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 s . E r r o r s o f t h i s magnitude i n VRP t r e e c o u n t s , dbh and h e i g h t measurement, c l e a r l y demonstrate t h e need f o r c a u t i o n 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. Thex~e i s o b 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 e s t a b l i s h m e n t and i m p l e m e n t a t i o n lines .  of c h e c k c r u i s i n g guide-  -43-  LITERATURE CITED  A n d e r s o n , R.L. a n d 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 Research. M c G r a w - H i l l Book Company, I n c . , New Y o r k . p . 3 1 3 - 3 3 0 . B e e r s , T.W. and C . I . M i l l e r . 1964. Point sampling: Research 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. C r u i s i n g P o l e T i m b e r by B i t t e r l i c h ' s Angle-Count M e t h o d . P a p e r s o f t h e M i c h i g a n Academy o f S c i e n c e , A r t s , and L e t t e r s , V o l . X L I I I : 151-156". Carow, J . a n d R. R i c k e r d . 196 9. Studies of Personal Bias i n Bitterlich Cruising. M i c h i g a n A c a d e m i c i a n ; 2 ( 2 ) : 67-71. C a r r o n , L.T. 1968. An o u t l i n e o f F o r e s t M e n s u r a t i o n w i t h S p e c i a l References to A u s t r a l i a . A u s t r a l i a n National Univ. Press C a n b e r r a , p. 1-4. C o c h r a n , W.G. 196 3. Sampling Techniques. New Y o r k . p. 3 5 5 - 3 9 3 .  John W i l e y and  Sons,  F.A.O. 1 9 7 3 . Manual o f F o r e s t I n v e n t o r y w i t h S p e c i a l Reference to Mixed T r o p i c a l F o r e s t s . FAO, Rome, I t a l y , p. 2 4 - 2 5 . F e r g u s o n , I . S . 1975. Measurement B i a s i n P l a n t a t i o n I n v e n t o r y . A u s t r a l i a n F o r e s t e r , 3 8 ( 2 ) : 81-86. G a n g u l i , M.  1941.  H o l g a t e , P. 1967. 615-623.  A N o t e on N e s t e d S a m p l i n g . The A n g l e - C o u n t  Method.  Sankhya,  5:  449-452.  Biometrika, 54(3):  H u s c h , B. 1 9 5 5 . R e s u l t s o f an I n v e s t i g a t i o n o f t h e P l o t M e t h o d o f C r u i s i n g . J . F o r . , 53: 5 7 0 - 5 7 4 .  Variable  K e n d a l l , R.H. a n d L. S a y n - W i t t g e n s t e i n 1959. An E v a l u a t i o n o f t h e Relascope. Canada Department o f F o r e s t r y . T e c h n i c a l Note No. 77 O t t a w a . 26p. K e r , J.W. 1951. A T e s t o f A c c u r a c y o f Tree H e i g h t Measurement T a k e n by A b n e y L e v e l and C h a i n . B r i t i s h C o l u m b i a Lumberman, 35 (1) : 58 . K e r , J.W. a n d J.H.G. S m i t h . 19 57. Sampling R e l a t i o n s h i p . J . F o r . , 55: 2 0 5 - 2 0 7 .  f o r Height-Diameter  K e r , J.W.; J.H.G. S m i t h ; a n d J . W a l t e r s . 1 9 5 7 . 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 . Lumberman, November I s s u e : 32-36.  O b s e r v a t i o n s on t h e B r i t i s h Columbia  -4 4K 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 Aspen Stands o f Saskatchewan. J . F o r . , 6 3 : 924-92 L a a r , A. V a n . 1 9 6 2 . The A n g l e - C o u n t S. A f r . F o r . J . , 72: 1-6.  Spruce-  Method.  L o e t s c h , F . j . Zohrer/nnd K.K. Hallet. , 1973. Forest Inventory, 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 . W i e n . 469 p. 1?  M e y e r , H.A. 1 9 5 3 . F o r e s t M e n s u r a t i o n . I n c . , P e n n s y l v a n i a , p. 1 0 1 - 1 0 3 .  Penns V a l l e y  Publishers,  M i l l e r , C . I . a n d B e e r s , T.W. 1 9 7 5 . T h i n P r i s m s a s A n g l e Gauge i n F o r e s t I n v e n t o r y . Purdue Univ. A g r . Exp. S t a . Research B u l l . No. 929 L a f a y e t t e , I n d i a n a . 8 p . M u n r o , D.D. 196 6 . Some P e r s o n a l E r r o r s i n P o i n t S a m p l i n g F o r e s t r y C h r o n i c l e , 4 2 ( 4 ) : 407-413. M y e r s , C.A. 1 9 6 1 . V a r i a t i o n i n M e a s u r i n g D i a m e t e r a t B r e a s t H e i g h t o f M a t u r e P o n d e r o s a P i n e . U.S. F o r . S e r . R o c k y M t . F o r . a n d Range E x p . S t a . R e s e a r c h N o t e , No. 6 7 3p. Sayn-Wittgenstein,  L . 196 3.  An A t t e m p t t o f i n d  Area Factor f o r Point-Sampling. I n s e r v i c e R e p o r t , O t t a w a . 17p.  the  Best B a s a l  Canada Department o f F o r e s t r y ,  S c h m i d , P.; R o i k o - J o k e l a , P.; M i n g a r d , P.; a n d M. Z o b e i r y . 1 9 7 1 . The O p t i m a l D e t e r m i n a t i o n o f t h e V o l u m e o f S t a n d i n g T r e e s . M i t t e i l u n g e n Der F o r s t l i c h e n Bundes-Versuchsanstalt. Osterreichs, 91: 33-48. S t a g e , A.R. 1 9 6 2 . A F i e l d T e s t o f P o i n t - S a m p l e C r u i s i n g . U.S. F o r . S e r v . I n t e r m t . F o r . Range E x p . S t a . R e s e a r c h P a p e r No. 6 7 . Ogden, U t a h , 1 7 p . U.B.C. F o r e s t C l u b . 1 9 7 1 . F o r e s t r y Handbook f o r B r i t i s h 3rd E d i t i o n . 815p. W i l l i n g h a m , J.W. 1 9 6 2 . E r r o r i n Wedge P r i s m J . F o r . F e b r u a r y : 123-127.  Columbia  Calibration.  Y o u n g , H.E. 1 9 6 7 . F o r e s t M e a s u r e m e n t A c c u r a c y . I N 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 N o t e Mo. 7: 1 7 - 2 3 .  -45APPENDIX  I : MAP 1.  U . B . C Research Fore Pllt Loko  AAaple Ridge, B.C.  .  I  S\  /Eunice loko / \  legend: •'X'X?'- I'! <• i :  V'l^S-'v''/' //Gwendoline!  « .:• vK-'.V.,  , X' )  conlours al 50' intorvols ( ( ( main road branch  v  rood  '  trail building powerlinc*  ^ ~~*  study a r e c j ^ ^jl-  nor  -47APPENDIX  LOT NC .  PLOT NO.  II:  TREE  COUNTS  IN . THE  RELA SCOPE  CREW  1  CONTROL  2  PLOTS  NO.  3 TREE  ( B A F = 9)  4  5  6  COUNT  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  2  3  6  6  6  6  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  5  1  6  5  2  6  5  3  5 5  a  9  8  10  9  5  6  8  9  5  5  5  5  4  5  5  6  6  6  5  3  6  4  5  6  6  5  5  8  5  5  3  4  4  4  4  4  4  -4 8A P P END TX  LOT NC.  PLOT NO.  ITT:  TREE  CONTROL  COUNTS  1  I N THE  PRISM  CRFW NOo 3 4 ' T R E E COUNT  2  1  1  5  4  4  5  1  2  4  3  3  5  16  16 12  1  3  11  13  1  *  11  11  1  5  5  . (RAF=6)  3  6  PLOTS  6  5  5  4  4  5 4  4  12  16  16  12  12  12  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  9  12  5  1  5  5  5  8  5  5  2  8  l i  11  11  11  6  11  5  3  14  14  13  14  12  12  15  3  4  5  4  4  9  4  4  4  5  5  4  6  6  3  5  3  4  - 4'9APPENDIX  TREE  IV:  NO. CONTROL  1 2 3 4 5 6  7 8 9 10 11 12 13 14 15 16 17 18 19 2C 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50  5.9 6.1 7.5 8.3 9.3 9.7 9.8 10. 1 10.5 10.6 10. 8 11.4 13.0 13.5 14.2 14.5 14.8 15.2 15.4 15.7 16.0 16.8 17.1 17.8 18. 1 18.2 18.4 18 o & 18.8 18.9 19.2 19.2 19.6 19.9 20.4 20.5 20.8 20.9 21.2 21.5 21.7 22.0 22.1 22,5 22.5 22.5 23.8 24.3 24.4 24.6  TREE  DIAMETER  1 12.9 5.6  7.5 8.6  9.2 9.6 10.8 9.9 io.e  10.8 10.8 15.3 13.9 14.9 14.5 14.7 12.2 19.5 15.9 16.1 15.7 16.9 16 o 9 18.5 17.9 18*7 21.0 18.1 18.3 19.0 22.0 19.1 19.7 20.4 20.1 20.3 21.0 20.5 21.8 20.7 22.6 21.8 23. 1 21.1 23.9 20.8 27.4 27.9 23.7 24.8  MEASUREMENTS  CREW NC. 2 3 4 MEA S U R E M E N T S ( C M ) 6.0 6.0 5.9 5.0 7.6 8.7 8.6 9.0 9.2 9.4 9.2 9.9 9. 8 9.7 10.8 10.0 10. 1 9.9 1C.5 10.6 10.5 10.9 11.4 13.5 14.9 14.1 14.7 12.4 18.5 15.8 15.8 15.8 16.6 17.2 18.3 18.0 19.2 18.0 18.1 18.4 19.0 19.0 19.1 19.4 19.2 19.7 20.5 21.0 20.8 .21.1  20.6 20.5 19.4 21. 1 21.5 20. 5 21.2  21.8 20.5 21.9  21.5 20.5 22. 1  23.0 21.C 32.0 24.5 23.2 25.2  23.0 21. 1 27. 1  22.0 22.0  24. 0 24.0  23.9 24.0  5  6  6.3  6.0  8.8 9. 1 9.8  8.7 9.2  10.0 10.7  9.9  10.7 11.2 13.5 14. 8 14.2  10.9 11.0 13«5 14.7 14.2  13.3 15.0 14.1  12.2  12.0  12.1  15. 8 15.6 15.8 16.6 17.2 18.4 £8.0 19.2 18.3 18.5 18.3 19.0 19.2  15.7  15.2  15.7  15.4 17.0 16.8 17.3 17.9 18.6 18.3 17.9 18«4 19.0 18.0  15.2 16.6  15.7 16.5  17.7 17.9 • 17.0 17.8 18.5 18.3 18.8 17.9  18.2 18.1  19.8 19.8 20o3 20.8 20.8  19.3 19.7 20.0 20.5  19.4 20.6 20.7 20.6  21.0  21.0  21.1 22.1  22.2  32.3  14.2  18-9  -50APPENDIX  IV:  CI A METER  TREE  TREE NO. CONTROL 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100  24.9 25.0 25.2 25.4 25.6 26.0 26.0 26. 5 26.7 26.7 27.1 27.2 27.5 27.6 28.0 28.1 28.4 28.5 28.6 28.7 29.0 29.0 29. 1 29.2 29.4 29.6 29«,6 30. 0 30.0 30. 1 30.1 30. 1 30.3 30.4 30.4 30.5 30.7 30.7 31.2 31.2 31.3 31.4 31.4 31.5 31.5 31.5 31.5 31.5 31.5 31.5  1 24.6 25.0 24.8 26.3 24.9 26.2 26.3 26.5 26.5 24.4 28.3 27.8 27.6 27.5 28.2 27.6 27.0 28.0 28.2 31.7 29.0 27.6 29.6 31.9 30.7 29.7 28.8 28.6 30.0 34.0 29.2 26. 1 30.9 30.5 30.3 30.1 30.8 28. 1 31*3 31.2 31.a 31.7 31.7 33.3 32.S 30.9 32.9 31.2 31.8 31.5  MEASUREMENTS  CREW NG. 2 3 4 ME4SUREMENTSCCM) 24.8 24.6 24.8 24.9 24.0 24.8 25. 1 25.5 26.4 26.3 25.4 25. 1 24.9 25.0 27.5 26.0 25.4 27.4 26.1 26.0 27.5 27.0 26.2 26.4 27.0 26.2 24.2 24.8 25.0 26.8 27.2 26.9 27.8 27.6 27.7 27.4 27.6 27.7 27.3 27.1 27.8 28.4 27.9 26 28.8 29.0 31.5 29.1 28.3 29.0 30.0 29.1 29.5 26.6 30 = 3 31.7 35.3 29.1 32.7 30.5 31.2 31.4 31.2 30.0 29.0 30.8 31.5 31.8 31.8 32.4 32.0 31.3 32.9 31.5 31.5  5  6  25.0 25.0 25.9  25.1 24.8  27.1  26. C  26.5  26.2  27.7 27.3  27.6  2 7.8  28 .3  28.5  28.4  28.6  21.6 29.5 29. 1 30.1  29.1 29.9 29.1  29.7  29.5 30c0  28o8 29.6  30-.!  34.7 29.4  30.0  22.4 29.2 30.7 29.5 28.2 30.0 29.9 29.1 29.6 28.6 30.4 32.2 35.2 29.6  29.5 30.0 31.3 30.5 32.7 35.9 31.9 31.8 31. 8 33.6 32. 1 31.5 31.8 30. 3 31.4  -  30.8  31.3 31.0 31.0 33.3 32.8 31.5  31.7 31.7 31.3 32.0  31.3 34.2 32.7  APPENDIX I V : TREE N O . 101 102 103 104 105 106 107 1C8 109  no  111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 14 5 146 147 148 149 150  CCNTRCl 32.0 32o0 32o0 32* 1 32. 1 32o2 3.2 © 2 32.3 32.5 32. 5 32.7 33.2 33.2 33.2 33.2 33.3 33.4 33.7 33. 8 33.9 34.0 34.0 34.3 34.5 34.8 35.0 35.3 35.9 36.0 36.0 36.0 36.0 36.2 36.2 36.2 . 36.2 36.3 36.5 36„5 37. 1 37.1 37. 1 37.2 37.2 37.3 37.3 37.3 37.4 37.5 37.5  -5 1CI AM ET ER  TREE  1 27.8 32.3 29.9 32.9 31.4 32.8 31.1 32.2 32.9 32. 5 33.2 32.5 32.5 32.8 36.2 32.3 32.5 34.1 33. a 35.0 34.0 37.3 36.7 35.4 32.7 34. 8 35.5 36.8 35.4 35.4 36.2 36.4 36.3 36.0 44.2 35.1 37.5 36.G 34.4 37. 2 32.8 42.9 38.0 36.8 36.8 37.7 37.3 38.8 35.8 37. 1  MEASUREMENTS  CREW N O . 2 3 ME A SLREMENTS( 27.9 31.6 33.2 30.4 33.5 33.0 31.2 29.4 3 1 .9 32. 1 31.4 31. 3 20.7 32.5 32.8 32.8 32.3 33.3 33.1 32.7 33.3 31.8 32.0 32.0 32.2 34.2 34.0 32.8 33.6 32.2 32.0 34.5 32.6 33.5 33.2 31.0 34.0 34.4 34.3 36.4 33.5 34.2 34.2 34.5 35.3 33.8 35.4 34.6 34.9 35.5 35.9 35.9 35.5 36.6 35.1 35.2 36.4 37.4 35.5 36.0 35.9 36c3 36.2 36. 3 44.1 35.8 36.2 35.1 36.8 36.4 33.0 35.9 37.7 34.5 36.8 36.9 32.1 31.8 42.3 37.2 37.5 37.6 37.2 38.8 3 8.7 39.7 38.0 37.5 39*0 37.0 37.0 37.0 37.0 38.8 37.5 37.2  4 CM) 27.6 31.5 31.6 32.3 34.0 32.8 32.7 32.2 34.0  5  6  27.8  31.3 31.8 35.9 33.2  32 .2 34 . 7 33 .0  32.3  32 . 2  33.6 32.7  32.0  33.0  33.2  33.2  33.9 36.4 37.5 34.2 33.9 35.0  34.0 38.7 34.2 35.0 34.0 34.6  35ol 35.4  35.5 36.0  36.4 36.6 35.0  36.7 35.7 35.1  36 . 2  36.9  36.4  36 o 8  37.7 37.2  37.1 37.9  35 . 3 34 . 7 35 . 2  35.9 36„8  37.1 38.5 37.0  37.2 37.0  APPENDIX I V :  TREE  CIAMETER  TREE NO. CCNTROL 151 152 153 154 155 156 157 158 159 160 161 162 163 164 16 5 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 19 8 199 200  37.5 37.6 37.7 37.7 37.7 37.9 38. 1 38.2 38.2 38. 3 38.4 38o7 38.9 39.0 39.2 39.9 40.0 40.0 40.0 40.2 40.3 40.8 41.0 41.0 41.1 41. 2 41.2 41.3 41.5 42.0 42. 1 42.6 43.6 43.7 43. 8 43.9 44.1 44.2 44.3 44.5 44.8 44o9 45.0 45.1 45.7 45.7 45.8 45.9 46.0 46.2  1 42.3 38.8 37.6 38.0 41„5 40.0 46.G 38.2 38.1 39. 1 38.5 37.0 37o9 38.1 31.2 38.5 42.0 40.3 40.1 38.2 40.5 42.8 41.2 38.7 40.7 41.5 43.7 41.4 41.7 38.7 42.4 43.3 43.7 43.3 46.5 42.9 44.0 44.3 43.9 44.6 44.5 43.6 A4.5 45.0 50.7 44.6 45.5 47.7 46.3 45.0  MEASUREMENTS  CREW NC. 2 3 MEASUREMENTS(CM 1 37.5 47. 0 37.1 37.7 30.0 37.7 37.7 38.6 37.7 38.1 37.4 38.2 40. C 38.7 4>5<,8 45.5 38.5 38.0 38.4 38.6 38.8 39„9 38.1 38o3 37. C 38.5 39.3 36.9 36.4 39.6 38.2 38.1 27.4 4Q.0 38.4 42.2 44.2 39.0 40.0 41.8 40.4 42o2  40.2 38.0 43.5 40.8  38.9 40.9 41.2 41.0 41 • 6 42.5 42«5 42.8 43.8 43.8 44.1 43.0  39.0 39.3 40. 8 41.9 4-0.5 42.5 42.0 42*6 42.6 43.7 42.4 44.0  42.5 44.0 44.1  42.3 44.3 45. 1  44.6 44.0 45.2 45.3 51.0 44.3  45.4 43.0 45.0 45.3 53. 2 44.3  46.0 46.5 45.7  46.7 46.1 47.6  40.0 40o2  5  3 8.4 35.0  6  38ol  39.5 40.4 42.2  38.7  41.7. 42.2  41.0 41.9  41.1 41.9  41.2  41.3  44.2  42*9 43.0 43„2  43.0 42.0 45.0  42.0 42.9  56. 1  44.0  44.2 44.3  44.0 44.3  44.0 45«8  46.8 45.0  45.4  45.5  48. i 45.1  5 0.7 44.3  48.1 45.2  45.2  46.5  46.4  47.2  47.2  49.9  40.8 40.8  -53APPENDIX  IV:  TREE  DIAMETER  TREE NO CCNTRCL 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 22 4 225 226 22 7 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 24 3 244 245 246 247 24 8 249 250  46,4 46.9 46o9 47.1 47.1 47.8 47.9 47.9 48.0 48.0 48.1 48.4 48.5 48.5 48.8 48.9 48.9 49. 1 49.3 49.9 49.9 49.9 50. 0 50.0 50.0 50.1 50.1 50.4 50.5 50.8 51.0 51.5 51.5 51.7 51.7 51.8 51.9 52.1 52.5 52.9 52.9 53. 1 53.1 53.1 53.1 53.4 53.6 54.0 54.0 54.2  1 46.2 46.7 46.6 48.2 47. 1 47.9 48. 1 55.2 48.0 47.7 44.8 48.8 48.0 50.2 45.7 50.8 49.8 49.0 49.5 52.5 50.1 53.7 48. 5 49.0 50.8 49.0 49,8 50.2 51.1 51.5 50.2 52.5 51.0 ' 45.9 44.0 52.3 50,3 46.3 52.0 53.5 53.4 52.5 53.7 53.5 50.9 53.4 53.5 52.7 54.5 53.0  MEASUREMENTS  CREW NC. 3 2 4 MEA SUREMENTS(CM> 45.0 46.0 48.9 49.0 48.3 47.2 46.8 45.5 46. 5 47.8 47.5 47.5 46.6 48.3 48.2 48.0 48.3 49. C 49.7 56.1 49.0 49.0 47.9 47.6 48-4 48.8 47.4 46.6  C  6  k  46.3 47.0 4 7.9  46 .9  51.0 48.7 . 47.8  50 .3 47 .6  47.9 48.2 48.7 46.3 50.4 49.5 48.0 46 .9 51.8 50.2 53.0 51.0 50.6  48.0 47.9 48.9 45.8 50.7 49.6  48.5 48.7 48.5  49.0  51 .0 49.6  42.0 44.2  49 .2  47.0 46. 0 51.1  48.5 49.7  46.0  49 .0  50. 0 51.0  50.7 50.7  50.8 50.0  50 .4 49 .7  49.0 46 .8 50.9 51.3 49.9 51.0 54.3 51.6 44.3 47.6 53.2 49.7 47.1 52.8 52.5 53.0 53.6 57 .I 53.1 51.6 53.3 53.7 52.7 53.0 50.1  49.6 51.0 52. 1 51.0 50.6 51. 3 53.4  50.4 50.9 51.0 50.3  50.9 51.0 51.3  52 .8 55 .5  50.4 53.4  50.8 52.5  51 .8  50.2 53.0  51.2 47.4  46 .5  52.8 53.6 52.6 54.5 53.5  52.7 54.1 54.5 54.0  54 .1  53.0  52.1  53 .3  53.7  50.9  54.3  50.3  50. 8 49.6 51.3 51.2 50 o 9 52.5 53.0 53.4 53.7 54.4 55. 2 49.4 57.2 55.8 55.2 52.2 52. I  51 .3  i6„5  -5 4APPENDIX TREE  IV:  DIAMETER  NO, CONTROL  251 252 253 254 255 256 257 258 259 260 261 262 263 264 26 5 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 235 286 287 288 289 290 291 292 293 294 295 296 29 7 298 299 300  TREE  54.5 54„6 54.8 55.0 55o4 55o4 55o5 55.5 55.6 55o6 56o0 56. 1 56.5 56.6 56.9 57.0 57.1 57o6 57o9 57.9 58. 0 58.2 58.6 58.8 59.0 59.0 59.9 59.9 60.0 60.0 60. 1 60.4 61.0 61.3 61.3 61.3 61.6 63.1 63.4 63*4 63.5 64.0 64.0 64. 1 64.3 64.4 64.4 64.5 64.5 64.6  1 52.2 54.8 54.0 54.3 55.2 56.5 64.5 54.3 55.5 55.7 58.5 52. 1 53.1 56.1 55.6 50.8 51.5 55.4 63.0 57.5 56*8 58.5 58.1 56.9 58.4 58.8 58.4 61.4 59.3 59.9 62.5 60.2 69.7 ' 61.G 61.3 58.0 60.6 62.8 63.5 64.0 59.1 67.7 66.2 65.9 63. 1 65.6 64.7 58.0 56.4 60.9  MEASUREMENTS  CREW NC 2 3 4 MEASUREMENTS(CM) 53.1 53.4 52.8 55.6 55.2 55.0 60.1 54.0 53.9 55.0 54.6 54.9 55..1 55.2 56.6 54. 3 56.1 54.9 54.5 55.5 55.7 56.7 56. 8 56.6 55.1 55.1 55.8 58.2 58.5 58.7 57.7 56. C 57.0 51.2 54.6 55,5 55.8 55.6 60.9 56.1 57.C 57.2 58.7 59.8 55.8 50.0 57.8 52.7 57.4 57 o 2 57.9 43.6 60.8 58.7 57.5 56.4 57.2 57.5 57.8 57.8 58.8 50.1 57.2 58.0 59.3 58.3 59.2 58.0 60.1 58.5 57.9 60.7 60.2 60.1 61.7 60.9 58.8 59.0 61.2 5^.2 60. 1 60.8 60.3 59.5 77.3 78.5 60.5 64.2 61.5 60.4 60.0 61.7 62.0 61.2 61.5 60.9 62.1 60.5 58.4 62.3 61.2 62.3 61.1 66.7 62.8 6 3.1 62. 0 64. 1 '63.5 59.6 62.0 60.8 63.9 64.2 63.8 66.5 66.7 64.5 60.2 64.8 63.5 64.0 64. 1 65.7 65.7 65.7 64.0 64. 5 64.9 64.5 64. 1 54.4 52.5 55.3 61.7 66. 6 64.5  . 5  6  53.0 54.8 55.3  55.2  54.2 56. 1 55.7 56.5 56.5  56.2 53.7  60.0 56.1 57.2 53 = 2 59.0 59.7  56.4 58.7  59.3 56.2 59.2  58.3 58.4  55.2  59.5 57.6 57.2  61.3 58.0  59.3  59.3 61.4 63.2 60.7 61,2  61.8  61.3  55.2  61.0 63.9  60.1 64.8  66.8 64.5 59.8  63.4 65.1  56.4 64.5  63.2  73.0  - 5 5APPENDIX  IV:  CIAMETER  TREE  TREE NO  301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 32? 328 329 33 0 331 332 333 334 335 336 337 338 339 340 341 342 34 3 344 345 346 347 34 8 349 350  CONTROL  I  65.0 65.6 65.8 67.0 67.2 67.6 67.7 67.9 68.0 68. 1 68.4 69.2 69.5 69.9 70.0 71.0 71.1 71.5 72.0 72. 1 72.6 72.6 72.7 73. 1 74.0 74. 1 74.5 75.1 75.5 75.8 76.0 76.1 77.0 77.1 77.1 77.1 77.4 77.4 77.7 79.3 79.5 82.1 82.2 82.6 83. 0 83.2 84.2 84. 7 85.2 85.5  57.3 72.2 60.5 65.6 65.0 68.7 67.8 64.2 72.3 75.0 67.4 66.2 72.0 75.4 67.8 73.3 66. 1 73.5 73.0 78.0 74.7  73.3 66.4 73.0 79.7 82.2 74.0 74.6 74.® 80.0 73.3 75.2 . 75.0 75.4 75.1  75.2 72.0  76.0 80.2 81.6 80.7 79.8 78*7 82.0  85.4 83.4 84.8 84. 5 84. 1 82. 1  MEASUREMENTS  CREW NG. 4 3 2 MEASUREMENTS(CM) 54.8 52.4 57.0 71.1 70.0 70. 1 53.5 58.1 60.3 76.3 68. 1 65.3 65.4 60.3 66.2 67.3 72.0 66. 5 67.0 68.2 65.0 69.9 62.5  66.9 68. 5 66.0  62.2 78.4 69.0 75.3 67.9 73.6 73.0 75. 1 76.5 72.9 66.7 73.5 77.5 77.0 76.2 76.1 72.3 75.3 78.5 75.1 75.0 69.5 76.0 75.0 77.8 76.2 78.5 81.7 81.5 89.6 80*7 83.2 84.3 84.2 84.0 85.0 84.8 82.5  71.9 80.8 70. 0 71.0 66.8 71.9 73.8 71.9 74. 1 73. 1 68.8 74,0 79.2 77.0 76.0 7 5. 5 72.5 80.4 74.2 76.0  5  6  61.0 61.3 64.3  62.7 65.S 67.2 65 .4  68.2  67.0  70.1  66.9 69.9 65 .9  66.1  69 = 2 69. 1 73.2 70.0  6 8.6  72.6  71.0 74.8 74.5 73.5 67.4 73.4 73.7 '74.1 74.5 75.3 82.7  72.5 72.5 76.2  76.7  70.0  75. 1 75.2 76.2 75.7 72.5 81.5 78.4 76.4 S2*-0  76.8 75.9 76.8  76.6 76.2 76.6  81.4 79.0 88.9  79.0 78.6 81.0  82*7  82.7 83.2 86.0 85.5 86.4 86.3 83.4  82.5  82*4  82.5 85.5 85.5 84.8  98.4  85.3 86.1  84. 1 85.2 86.0 86. C  72.8 77.0 76.0 76.1  72.5  72.9 73.0 74.5 70.5  85.1 86.6  73.9  85.6  -56APPENDIX I V :  TREE  CIAMETER  T R E E NO.  CREW NO. 2 3 4 MEASUREMENTS(CM >  1  CONTROL  MEASUREMENTS  3 5 1  8 7 , 0  8 5 . 2  8 5 . 2  3 5 2  8 9 . 0  9 0 . 6  88.0  3 5 3  8 9 . 4  9 0 . 5  8 9 . 2  8 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  3 5 6  9 0 . 1  9 1 . 0  9 2 . 9  9 2 .  8  8 8 . 4  9 0 .  8  9 6 . 2  5  9 2 . 0  8 6 . 7  1  8 9 . 9  9 0 . 6  9 2 .  3 5 8  9 2 . 4  3 5 9  9 2 . 7  9 1 . 1  9 1 . 0  9 1 .  3 6 0  9 3 . 5  9 3 . 0  92.7  9 5 . 6  9 8 . 2  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 0 . 0  9 0 .  3 6 3  9 7 .  9 8 . 7  9 1 . 0  9 3 . 5  9 3 . 5  9 2 . 1  6  9 4 . 0  9 8 . 0  9 3 . 2  9 6 . 8  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  3 6 7  1 0 0 . 1  9 6 . 5  1 0 5 . 0  1  9 3 . 3  107.8  1 0 3 . 2  1 0 0 . 2  9 6 .  9 6 . 6  9 2 . 3  9 6 . 7 0  0  3 6 8  1 0 0 . 7  1 0 0 . 7  1 0 1 . 0  1 0 3  1 0 2 . 9  1 1 2 . 2  1 0 4 . 5  1 1 3 . 9  3 7 0  1 0 3 . 0  1 0 7 . 3  1 0 7 . 7  1 0 1 . 8  1 0 5 . 6  3 7 1  103.1  101.7  1 0 0 . 0  1 0 3 . 5  1 0 2 . 5  3 7 2  1 0 3 . 3  1 0 4 . 5  3 7 3  1 0 5 .  3 7 4  1 0 6 . 9  1 0 4 . 0  1 1 0 . 0  1 0 8 .  5  92.1  9 4 . 5  3 6 9  3 7  9 5 . 0  9 7 . 3  3 6 4  0  6  8 7 . 0  3 5 7  1  5  1 0 3 .  1  8  .  1 0 1 . 1  1 0 1 , 0  1 0 1  . 1  1 0 4 . 0 1 0 2 . 0  1 0 6 . 5  1 0 5 . 3  1 0 3 . 8  1 0 2 . 0  1 0 1 . 7  1 0 8 . 0  1 0 5 . 5  1 0 6 . 8  1 1 0 . 2  105.1  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  103.0  1 2 2 . 0  121.0  3 7 9  1 2 1 . 8  1 2 1 . 5  120.8  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  1 2 5 . 0  1 2 9 . 0  1 2 4 . 5  1  1 2 7 . 0  1 3 2 . 0  1 3 1 . 0  1 2 9 . 3  1 2 4 , 2  1 3 4 . 7 1 2 7 . 0  1 3 1 . 1  1 3 2 . 0  1 3 3 . 3  1 2 8 . 7  1 3 2 . 0  1 3 0 . 5  1 3 2 . 8  1 3 7  1 4 1 . 0  1 3  3 8 2  1 2 8 . 2  3 8 3  1 3 0 .  3 8 4  1 3 0 . 9  3 8  5  1 3 1 .  1  1 3 1 . 5  3 8 6  1 3 2 . 5  1 3 1 .  1  3 8 7  1 3 5 . 0  134.7  1 3 0 . 3  3 8 8  1 3 5 . 2  141.0  1 3 7 . 4  3 8 9  1 3 5 . 3  1 3 5 . 3  1 3 5 . 0 1 5 0 . 0  P  4  3 9 0  1 4 0 . 1  1 3 5 . 2  3 9 1  1 4 0 . 2  1 5 0 . 0  1 4 6 . 2  1 4 6 . 2  3 9 2  1 5 4 . 4  1 5 0 . 0  1 5 0 . 0  1 5 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  3 9 5  1 6 0 . 5  159.0  1 6 3 . 0  3 9 6  1 6 7 . 7  1 3 5 . 6  1 4 0 . 0  3 9 7  1 7 0 . 0  1 3 1 . 5  1 9 5 . 0  1 9 0 . 0  1 8 0 . 0  179.0  3 9  8  1 3 2 o 0  7 . 2  1 2 6 . 0  131,0  1 4 9 . 0  1 4 6 . 2  1 3 4 . 5  1 5 9 . 2  1 5 1 . 0  1 5 4 . 2  1 6 9 . 0  1 6 8 . 7  1 6 5 . 0  1 6 3 . 0  3 0 2 . 0  2 0 7 . 0  2 1 4 . 0  1 2 6 .  •»> *r o  ii. J O v  8  0 n. V  7  - D /APPENDIX V: TR F E TOTAL HEIGHT TREE NO. CONTROL  1  8.1  1.  MEASUREMENTS  CREW NO. ? 3 4 MEASUREMENTS(IN M)  10.8  9.0  9.5  5  6  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  12  30.0  30.5  27.3  23.2  13  30 5  28.0  28.4  14  31.2  31.2  32.5  26.7  15  32.3  26.6  21.0  30.5  16  32.4  31.1  30.4  28.4  17  32.5  48.5  53.8  31.5  18  34.8  49.0  19  35.0  49.0  30.3  30.2  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  24  39.0  40.2  .35.0  25  40.0  35.0  37.5  o  35.G  33.3  28.7  28.5  26.2  41.0  40.5  -58APPENOIX  V: TR F E TOTAL H E I G H T  TREE NG. CONTROL  1  MEASUREMENTS  CREW NO 1 2 3 4 MEASUREMENTS ( I N M).  26  40.2  3 3.8  24.0  3 5.5  27  42.5  44.1  39.8  42.9  28  42.6  33.0  45.0  38.0  29  4 0.0  4 1.5  42.0  30  48.8  29.0  47.0  42.8  27.0  31  50.5  52.0  49.0  49.5  54.0  5L.5  5  6  40.2  44.0  49.5  56.0  50.5  APPENDIX V I : INSTRUMENT  USER  P R E F E R E NCE  SURVEY  Faced with a choice between a prism and a relascope f o r determining fhe basal area per hectare of a forest, c r u i s e r s (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 f o r e s t r y students, for the two instruments.  Please mark with a " V^" your choice: 1.  In the UBC Research Forest, which instrument would you rather use f o r determining the basal area per ha.?  2.  (  )  PRISM  (  )  RELASCOPE  (  )  BOTH.  What i s the reason f o r your choice i n (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  3.  OTHER  please  s t a t e :  For how many summers have you been cruising? (  )  ZERO  (  )  ONE  (  )  TWO  (  )  THREE  (  )  FOUR OR MORE  I f you checked other than zero i n (3) above, d i d you use: i  (  )  PRISM  (  )  RELASCOi'E  (  ') BOTH  PLEASE RETURN THE COMPLETED FORM TO:  THANK YOU. SO/DDM/mpl Sept 1977  STEPHEN OMULE, MacMillan Room 192.  

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