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Influence of cutting block size on the efficiency of several 3-P sampling variations as compared to… Turnblom, Eric Carl 1986

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I N F L U E N C E OF OF  C U T T I N G BLOCK  SEVERAL  3-P  SIZE  SAMPLING  COMPARED TO  POINT  ON  THE  EFFICIENCY  VARIATIONS  AS  SAMPLING  by ERIC B.Sc,  A  THESIS  CARL  TURNBLOM  The U n i v e r s i t y  SUBMITTED  of I l l i n o i s ,  1983  I N P A R T I A L F U L F I L L M E N T OF  THE REQUIREMENTS MASTER  FOR  THE DEGREE  OF  OF S C I E N C E in  THE  We  accept  F A C U L T Y OF  this  FORESTRY  thesis  as  conforming  t«j> .the r e q u i r e d / l s t a n d i r d  T H E U N I V E R S I T Y OF  B R I T I S H COLUMBIA  November ©  Eric  Carl  1986  Turnblom,  1986  In  presenting  requirements of  British  it  freely  agree for  this for  an  available  that  I  by  understood  that  his  or  be  her or  shall  f u l f i l m e n t of at  of  l~prest  The U n i v e r s i t y o f B r i t i s h 1956 Main M a l l Vancouver, Canada V6T 1Y3  Date  DE-6  (3/81)  University  Library  shall  and  study.  I  copying  granted  by  the  of  publication  not  be  allowed  k?&Sdurces Columbia  am  of  this  It  this  without  make  further  head  representatives.  permission.  Department  the  the  the  extensive  may  copying  f i n a n c i a l gain  that  reference  for  purposes  or  degree  agree  for  permission  scholarly  in partial  advanced  Columbia,  department  for  thesis  thesis  of  my  is  thesis my  written  11  ABSTRACT  made  For  3-P  sampling,  on  every  tree  efficiency  in  advantages  over  an  in a  larger the  ocular cutting  prediction block,  blocks.  standard  which  However,  BCMF  individual  trees are  the  sampling  trees,  so  precision  may  result  second,  no  height/dbh  regressions  potentially  avoids  conjunction  with  estimation,  differing  with  probability,  equal  conducted cruised  in the  using  wide-scale FP-12 and than 14 the  UBC  from  A  3-P  may  a l l three  of  and  tree  sampling  hectares, height/dbh  standard  cruise.  sampling  in  the  factors  on  Ratio  block as  sizes 3-P.  in which  methods. and  indicate ranging  A  methods  in  estimation  3-P  size  up  ranging  necessary i s more  up  to  14  A  i t  used  in ratio  selected study  equation,  f o r use i s more  hectares  type 3-P  efficient 5  and  chosen  and  use  efficient  the  with  between  method for  was were  dendrometer  to  of  size,  several blocks  Stroud  that  main  third,  procedure,  trees are  t r e e measurement  deemed  i t is  volume  its  plots  sample  advantageous.  measurement  the  regressions  sample  Barr  in blocks  depending  in that prove  not  calculated, when  be  procedures.  given  sampling  these  estimation. Results  be  biases  forest  the  for a  on  three  cruising units,  must  doubt  has  simpler  also  research  t e s t e d as  point  same  equation  dendrometry.  relaskop,  were ratio  volume  need  volume  casts  i t  prism  First,  greater  of  in  than  the point  depending  on  iii  TABLE  OF  CONTENTS  Page TITLE  PAGE  i  ABSTRACT  i  ABSTRACT  ii  TABLE  OF  CONTENTS  LIST  OF  TABLES  LIST  OF  FIGURES  i i i iv v  ACKNOWLEDGEMENTS  v i 1  INTRODUCTION SAMPLING  TECHNIQUES  1 . 3-P  USED  SAMPLING  6 6  2. R A T I O E S T I M A T I O N  12  3.  15  POINT  LITERATURE MATERIALS RESULTS  SAMPLING  REVIEW AND  AND  METHODS  DISCUSSION  CONCLUSIONS LITERATURE APPENDIX  18 28 38 58  CITED  60 63  IV  LIST  Table  OF  TABLES  Heading  Page  1.  Stand  Characteristics  2.  Block  HM  Summary  of a c t i v i t y  times  39  3.  Block  HW  Summary  of a c t i v i t y  times  40  4.  Block  M  Summary  of a c t i v i t y  times  40  5.  Block  W  Summary  of a c t i v i t y  times  41  6.  Summary  of cruise  Summary  results  36  42  V  LIST  Figure 1.  2.  OF  FIGURES  Heading  Page  T o t a l c r u i s e t i m e f o r p o i n t s a m p l i n g c o m p a r e d t o 3P u s i n g t h r e e t r e e measurement t e c h n i q u e s , g i v e n t h e observed v a r i a b i l i t y  49  T o t a l c r u i s e times f o r p o i n t sampling compared r a t i o e s t i m a t i o n u s i n g t h r e e t r e e measurement techniques, given the observed v a r i a b i l i t y  50  to  3.  T o t a l c r u i s e times f o r p o i n t sampling i n stands w i t h t h r e e s p e c i e s c o m p a r e d w i t h 3P u s i n g t h r e e t r e e measurement methods, g i v e n t h e observed variability ...52  4.  T o t a l c r u i s e times f o r p o i n t sampling i n stands with three s p e c i e s compared with r a t i o e s t i m a t i o n u s i n g t h r e e t r e e measurement methods, g i v e n t h e o b s e r v e d variability 54  5.  T o t a l c r u i s e times f o r p o i n t sampling i n stands with t h r e e s p e c i e s c o m p a r e d w i t h 3P u s i n g t h e v o l u m e e q u a t i o n t r e e measurement method, a s s u m i n g t y p i c a l variability  55  T o t a l c r u i s e times f o r p o i n t sampling i n stands with t h r e e s p e c i e s c o m p a r e d w i t h 3P u s i n g t h e v o l u m e e q u a t i o n t r e e measurement method, a s s u m i n g t y p i c a l v a r i a b i l i t y , and a d j u s t e d t o normal pace  57  6.  ACKNOWLEDGEMENTS  The  author  principal  advisor,  invaluable Dr.  Kim  weighted Kozak  and  lies,  t o acknowledge  Dr. Julien  biometrician  also  f o r the advice  valuable. and  whose  Bloedel  Consultations  Finally,  feedback.  and advice  The a d v i c e  a t Macmillan  and appreciated. quite  the help  P. D e m a e r s c h a l k ,  greatly appreciated.  heavily,  were  Marshall  wishes  thanks  of  his  guidance  was  and opinions of Limited, with  were  Dr.  A.  t o Dr. Peter  L.  1  INTRODUCTION  In  any  sources plots,  forest  of  error:  or  method  3)  measurement  used  determination, by  the  additional the in  chiefly  and  based  due  or  to  stand  source  of  error  sampling 19  times  and  the  the  scale,  error  of  out  of  (BCMF  the  +  or  20.  cutting  -  However,  block  this  objective frequently  absurdly from  a  sampler  high. logical, to  according must  be  choose per  ha,  The  the  sampled to  sampling  a  cruise to  provided  there  the are  at  volume set  (BCMF),  an  e r r o r due  to  individual  species  (a  when  a  4  and  to  to  size  sample  is or 100%  is  i t  yield  the  to  meet  needed  that  seems  too  great  much  is  cause  of  objective).  The  sampler  which type,  the  considered,  50%  per  a  ha,  than  plots  is  standard,  10  will  cruise  i t is  considered,  size  either  is  Procedures  utilization  equal  It  assessment  designed  requirement,  least  size  stumpage  greater  error  determined.  Cruising  sample  gives  minimum  or and  sampling  4)  sampling  or  the  cruise  the  point  be  be  point  intensity  manual,  tables  block  sample  close  standpoint,  100%  achieve  " d e f a u l t " to  the  estimating  intuitive  consider to  for  sample  volumes,  Forests  of  when  than  formula  and  Manual  when  is less  for  easily  should  to  tree cut  for each  1982),  15%  In  of  volume  recognized:  can  cruise  location  the  of  recognized  1982).  the  statistical error  be  design  to  widely  individual  Ministry  sampling  Compilation  to  standards  (BCMF  calculated. According  chance  1965).  must  type  three  due  regression constructed  f u n c t i o n of  on  the  obtain  the  error  are  error  Columbia  of  to  (Cunia  performed  first  Cruise  there  2)  predict  source  a  error,  error  differing  The  always  to  error  British  height/dbh each  1)  sampling  the  forth  inventory,  the  i s one but  he  area may plot may  2  run  a  greater  situation  different. performed  This  not  meeting  when  although can  the  planning  the  sampling  be  a  unnecessarily,  for error  problem or  the  cruise  in  objective.  A  cruise-based requirements  that  required  a  100%  error  similar stumpage  are  a  little  cruise  objective  may  be  may  not  met. Error  great  care As  use  component i s taken  regards  of  sample a  of  exists  assessment,  be  risk  of  displacement because the  populations  to  reason,  in  greatly  different,  predict trees, stands, more  some  of  where or  there  volume sources  tables of  estimate. sources are  not  is  from  seldom  present  may  or  is  may  from be  populations  (or  for but  no are  if  volume  stemmed  trees,  water  drawn  result  a  from  This  There  may  reliable  to  the  3-P  the  tables  "normal")  well  managed  perhaps  forestry  (Probability  which  regressions,  total  volume  not  for  the  error  calculated,  but  knowing  give  more  credence  Proportional  eliminates thus  per  practice,  will  sample  Usually,  single  be  a  the  volumes  abnormal  height/dbh  actual  that  undeformed,  computed  necessary. on  proper  against  trees,  applied.  tested.  introduced  sampling and  be  biased  few  if  that  them  (volumes  based  will  not  asserted  standing  not  negligible if  stands.  (1964)  error In  are  untended  Prediction)  is  for  on  suppose  estimates  Grosenbaugh to  to  be  checking  adjusted  they  however,  only  (1976)  d i r e c t methods  are  to  measurements.  requires  and  which  cases,  therefore,  wild  by  tables  equality  volumes  tree  measurements  volume  assumed  Brickell  usually  techniques)  most  assumption  2),  measured  stem  is often  obtaining  tables  trees  series  in  source  volume of  3)  to  use  removing  hectare  contribution for  the  certain the  of  these  inventory of that  sampling  these they error  3  that  i_s  calculated.  forest  area  system  is  produce  also  of  that this  the c r u i s e of  the  o f much  Direct measuring felling are  are  trees  addition provide  to  not  under  loss  forest  of  felling  be l o c a t e d  Climbing  trees  disadvantages. pathways  places fire  seems For  to carry  and  Kozak  (1984)  optical  example, entry.  through  dendrometer  compared  with  felled  much  attention  has turned  will tree  The  are  the  block  required  need  for  sizes,  and  that  too long  stock,  and  trees  a f t e r the or i f they  Sample  trees  to  be  trees  ladders  are too  is  very  such  be e f f i c i e n t measurement.  t o the use of o p t i c a l  the  felling,  1976).  might  trees  destroyed.  injure  (Brickell  and  the survey,  cases,  and cannot  In  trees  pests,  conducting  instruments  when  the f e l l e d  I n some  i t  by  n o t be u t i l i z e d .  1976).  long  instances  i f the f e l l e d  insects  may  obtained  increases,  alternative  spurs  with  (low v a r i a n c e ) .  many  might  plots  t h e woods  measurement  are  or agency  Often,  that  are usually  or s t a i n  certain  hypothesized  when  volume  growing  be an  sampling  surveys.  be p r o h i b i t e d .  to  a  can  i n t h e woods  sample  over  i t  i n smaller  (Brickell  on p e r m a n e n t  heavy  Stroud  for  hazard  may  for disease  tree  and  in  eliminates  age, they  of t h e p a r t y  them  and  standing  value  This  samples  F o r example,  f o r decay  rotation  Fewer  there  and remain  potential  be t h e p r o p e r t y  hence may  species  precise  which  However,  measurements  dendrometry.  are clear.  of tree  tree  efficient,  too intensive  trees.  breeding  increase  fact  i s not p r a c t i c a l .  so t h a t  crop  very  100% e n u m e r a t i o n  felled  a valuable  with  are extremely  measurements  trees  cruise  b y 3-P  objectives,  consideration execution  of d i r e c t  statistically  estimates  meet  sample  i s required  implications to  A  but has  and  provide  unwieldly  Also,  James  likely  that  as the Barr  and cost For these  and  effective reasons,  dendrometry  which  4  enables  the  standing  tree  Much method  point  known  sampling.  every  an  in  be  a  sample  on  tree  3-P  on  which  upper  the  dendrometry.  The  of  to  volume  logically  stand  as  effect must  led  stands.  to  because  probabilities  larger  limit  on  technique  sampling,  has  heights  ground.  and  efficient  point  in  the  sampling  prediction)  impractical  practical  various  selection  unlike  stand,  at  remains  highly  (ocular  the  a  diameters  operator  However,  becomes  establishes  of  exists  estimate  tree it  the  to  variable  method,  that  while  literature  is  employs  measurement  to  A  size  does  the  be  it  3-P  made  on  the  belief  study  which  has  never  been  published. This or  ratio  study  Inventory  sample  tree  ratio  and  taper  and  heights  has  method  variable  is  an  described  in  Specifically, quantify as  the  2)  the  stem  of  Stroud  Barr  and  widely timber  been  cruising,  prediction,  objectives  cruise  of  in  cutting time)  several  but  to  block obtain  and  diameters the  wide-  the been  Freese  study  are  size  and  dendrometer.  tested  where  a  (volume  diameters  or  (e.g.,  this  diameter  with  optical  has  Three 3-P  table  tree  in  with  several  used  forestry applications the  the  tree  sampling  use  of  volume of  sample  for  measurement  measurement  sampling,  Columbia).  considered  the  effects  total  1)  3-P  point  British  of  ocular  other  were  of  than  measurement  not of  Coast  whether  differing  appropriate  along  with  three  efficient  are:  an  3)  determine  of  methods  equation),  estimation  (measured  (South  into  on-the-ground  1)  any  They  heights  relaskop,  associated Ratio  C  estimation.  associated  scale  Zone  entry  to  i s more  measurement  for  equation,  with  techniques,  Forest  height  conducted  estimation,  measurement  and  was  on  given  as  an  auxiliary previously 1962). as  follows: the  cost  precision  5  (percent  error  estimation, which  method  encountered  of t o t a l ) ,  and  point  i s most in Forest  2)  compare  sampling, efficient Inventory  and  3) make  under Zone  the cost  C.  of  3-P,  ratio  recommendations as  conditions  likely  to  to be  6  SAMPLING  The  A  three  brief  sampling 1)  Point  2)  3-P  3)  Ratio  will  for T ,  total,  v(T ),  for  s  T ,  for E  for  confidence  T  s  ,  mathematical referred  1.  3-P  The  to this  study a r e :  estimation. the fundamental  the  along  limits.  based  error For  with based  sample  the probable  proofs  relevant  sampling  t h e sample  s  USED  sampling  be g i v e n  estimation,  s  techniques  d e s c r i p t i o n of  technique  TECHNIQUES  to the appropriate  concepts  of  each  formulas  for  estimator  of the p o p u l a t i o n  estimator  of the estimate  further  of t h e i r  working  size  of the variance of the t o t a l ,  information  statistical  sample  validity,  and  of and  rigorous  the reader  is  literature.  SAMPLING  first  step  survey,  i s deciding  usually  done  appropriate  with formula  in what  conducting size  a  sample,  statistical  3-P c r u i s e , n, s h o u l d  considerations  f o r sample  size  when  as  with  be d r a w n . in  sampling  mind from  This i s and a  population i s : t n  2  * C  2  2  2  * N  =  (1 ) t C  +  ND  2  any  the  finite  7  where, N  = number  of i n d i v i d u a l s  D  = desired  sampling  fraction error t  type C  error  o f t h e mean,  o f t h e mean,  = a value  i n population, limit m:  t*s /m,  deviation mean:  t statistic  of v a r i a t i o n  where  with  and degrees which  of observations  s/m,  as a s  m  decimal  i s standard  below,  I error probability  = coefficient  where  m  t as  of Student's  expressed  appropriate o f freedom, and  expresses  as a decimal  s i s the standard  the  standard  fraction  of the  d e v i a t i o n of  observat ions. Often, very  N  i s n o t known  i n advance  l a r g e , and the formula  The  only  the  consequence  possibility  corresponding sampling volumes plot  =  greater  increase  plans  refers  around  volumes  refers  the dispersion volume  So,  most  of  with  variation  exist.  This  .  N  tree  the  volume  average volume  conventional  variation  when  precision  i t really  isn't  i s  planned  with  a  than  per tree  volume  of the  sampling  t o t h e volume is  usually  C  i n most  individual  tree  or the dispersion of  plot  ratios trees  of  that  per plot,  o r mean  for individual  i s subject  large  (2)  dispersion  the  t o be  2  to  of  predicted  C  I t i s noteworthy  percentage to  mean  * -  in cost.  the average around  2  of assuming  of  o r i s assumed  becomes:  t n  of sampling,  of  around  expressed  volume. measured  With  3-P, C  volume  the average  techniques,  as a  to  ratio.  the c o e f f i c i e n t  d i s p e r s i o n as i t happens t o  large  even  with  stratification  8  by C  diameter depends  classes, on  the  with  consequence  whether  required  approximately result to  which  the  same  achieve  around  15  The sale  to  20%  cruiser's  25  step  denoted  select  one  totals  to  30%,  sample  tree  is  a  volumes.  in  actual  measured.  35%.  a  It or  3-P,  of  the  is  not.  manner  to predicted Beginners  trained  With  measure  "on-the-nose"  whereas  to  make  X,  of  than  may  of  no  A l l that  such  that  volume  will  be  expected  c r u i s e r s can  readily  1971).  by  predictions  of  tree  is  It  predict  ratio  to  lower  predict  predict he  sample  much  skill.  can  (Mesavage  second  volume,  he can  that  every  attain  he  is  for  not  predictor's  consistency  is  generally  a  rough  which  each  stands  tree's  for each  estimate  of  f o r the  volume.  accumulation  The of  the  sum  total  of  object  the i s to  predictions  that  X L  =  .  (3)  n  Third, will  be  writer to  from  as  are  numbers  f o r the has  greater  generated there  quantity  generated  The volumes  this  are  0.1 trees  cheap).  found  L list  that  largest i s taken  i t extremely  precision up  i s the  than  0.1  t o L.  As  many  expected  in  the  random into  difficult m^  so  numbers sale  number  the to  field. predict  numbers should  (extra,  that  be  tree  should  be  generated  unused  random  9  Fourth, a.  when  Predict using  If  in  gross a  b.  Record  the  c.  Draw  number  the  a  number  for  volume  and  random tree,  number  sampled.  probability  just  described,  chance  volume). have  20 A  15  the  actually different  may  to  turn  selection sample  out  or  indirectly  a  1  greater  the  it  sample  than  is  of be  volume being  or  probability  x^,  the  of  If  for  the that  and  with  the  to  accurately  tree.  not  greater  random  number  selection  system  1 would  only  one  c a r e f u l l y measured  for  of  15,  have  however,  selected,  equal  equal  "rejected"  trees  With  (to  predicted  sample  Suppose  20.  or  measured  a  larger  to  than  prediction,  i.e.,  of  be  as  prediction  twenty  list.  to  15  would  because  numbers  selection  its  appearing  is  clearly  prediction. statistics when  the  planned  selection the  sum  with  some  varies  calculated.  cruise the  is  3-P  predictions,  procedures).  that  are  probabilities of  probability  size  than  manner.  a a  is  "selected"  from  as  the  cruise  field  directly  should  selects  greater  Thus,  than  of  tree  greater  with  in  obtained  tree  estimate prior  tree  is  to  tree:  number  tree  required,  with  volume  Fifth,  is  qualify  tree  proportional  sample  to  list.  the  the  ranging  a  x^,  random  following  chances  predicted  for  is  the  integers  in  the  procedure  in  has  from  drawn,  more  list  volume,  is considered  This  each  table.  x^,  drawn  nothing  for  estimate.  prediction,  random  field,  total  volume  the  on  the  The  finished method are or  for  sample  may  be  two  approximate total  slightly  reasons.  The  (recall  the  volume,  necessary  So,  when  the  trees  may  have  received  a  or  slightly  reduced  probability.  a  randomly  due  to  the  cruise  nature  size  i s completed, slightly  of  the  it  greater Also,  selection  probabilities has  an  the  sample  extremely  sample in  a  themselves. low  size  size,  n .  Simply  after  a l l  the  sample  number  of  sample  estimated  total  given  inflate trees  (2)  have  is  given  versa.  can  this  even  For  be  the  though i t  this  the  reason,  "expected"  insured,  objective  what  been  in  occur  is called  size  over  E  still  vice  if  trees  volume  or  or  way n  may  sample  correct  important.  the  (1)  by  A  E  statistically  event  probability,  given  or  An  however,  is absolutely  formula  gives,  s e l e c t e d , randomly  excess by  of  what  the  elminate  desired  is called  and  n .  The  E  the  adjusted  est imator:  T  where,  x  Y. i  X = T  =  S  X *(£ l  , summing  the  cruiser's  (  T  over  y i  /xi)/n)  i=1,N  or  (4)  the  predictions after  total the  of a l l  cruise  is  completed,  This all  the  ocular  prediction  n  sample  size  =  be  is called  does  because  i t  appears  some a r g u m e n t  reliable  not  of  this  estimator  as  to  adjusted  tree  " i " .  because is  an  knowledge  of  the  estimator precise  Literature best  Review  sample.  use  sum  estimates.  of a l l used  A  very  in  Further  s e c t i o n . There for  of  unadjusted  i s always  approximation a  i t makes  there  more  from  on  " i "  obtained.  adjusted  the  tree  volume  require  estimate  i s :  on  Although  yields  i n the  of  actually  p r e d i c t i o n s , the  variance  volume  predictions.  which  ocular  discussion  the  x^=  ocular  practice  to  a c t u a l measured  estimator  estimator, the  y^=  seems  calculating  good,  stable,  11  X V  2 T  (1-n /N) p  (T ) =—i  *  S  {I n  n,  as above,  sampling theory (1968).  is  can  i  X  i  )  2  1/n<£ Y i A i )  -  i s the  found  actual  A  sample  detailed  sampling  size  discussion  i n Grosenbaugh  The p r o b a b l e  2  }  (5)  I  completed. be  y  /  I  n(n-1)  where  n (  (1965)  error  obtained of  statistical  or Schreuder,  f o r the estimate  after  et  a l .  Tg, i s given  by:  E  T  = t * s  s  T  (5A)  s  where: s  To  find  the upper  probability to  Ts  an  &  T  and lower  associated  the following  v  "^/ ( s)  =  with  t  confidence t  *  s  a  s  before.  limits  i n (5A), simply  with find  the  the  same  solution  equations: U  = T  s  +  E  T  s  L  = T  s  -  E  T  s  U  = upper  confidence  limit  L  = lower  confidence  limit.  where:  The  range  interval.  of values  from  L  to U  i s known  as  the  confidence  12  2.  RATIO  ESTIMATION  Ratio making being  estimators  use  of  is  the  tree  and  of  of  that  basal  volume  as  variable,  x^,  be  selected with  of  this  will  estimate Step  selected.  the  (1)  be  may  of  the  used  is used.  total  i t is  accurate  is  much c o n c e r n  direct As  but  This of  over  N/n  the  with  a  a  an  stand  and case,  the  improve  variability  of  small  residual  between  volume  prediction the  y^,  3-P,  to  the  the  3-P,  of  auxiliary  the  variable  trees  will  the  not  variance  estimator.  cruise  i n which  appropriate  in  of  increase  result,  3-P  trees how  measurement,  =  a  ocular  As  a  a  ratio  sample  size.  i s n a t u r a l l y preceded  easy  i n which  to  unlike  the  select  deciding most  the  c o r r e l a t e d with  than  number  k  There  a  will  by  population  help  relationship  in planning to  may  forest,  the  case),  larger  step  be  area  probabilities.  be  involves  Often  by  positively  first be  the  of  sample  information),  reducing  information.  varying  should  two  for  in  by  a  the  area  estimator  study,  in this  systematically,  selected  ratio  exist  about  basal  basal  estimate  this  (volume  estimator  Equation  trees  In  will  interest  an  volume  auxiliary  of  estimator  A  p r e c i s i o n of  supplementary  and  i s unexplained  the  Again,  volume  they  area.  is  i f the  (the  volume.  this  volumes  variance  known  the  information  example,  between  estimate  precision  For  exactly  relationship  increase  supplementary  studied.  timber  can  the  cruise,  sample  convenient every  1  trees to  1  k -*  by  making  N. should  select  tree  be the  will  be  where  (6)  .  reliability  of  estimates  from  a  13  single true, the  systematic however,  that  attribute  observed were  more  random. of  1977,  chpt.8).  long  there  i s no  random  sample  (or total)  will  be a  individuals  but  This  the  can  selecting  the  when  i n the  P r e d i c t gross indirectly  b.  record  the  tree  total  with  the  is  field,  unbiased,  one  t r e a t e d as  the  systematic  sample  i f multiple  random  at  the extreme  with  individuals  i fi t  and  individual  be  handled  f o r each  tree  the use  a  list  will  be  random case  of a  of  random  b i t more  tree:  volume of a  x^,  directly  volume  table.  the  next th individual,  measured sample  accurately  tree.  required,  volume  f o r volume  If i t  i s not  cruise  i s given  by  = X *(  variables are  estimator  is  £ l  T  defined  evident.  mean-of-ratios  estimator  based  of variance  estimate  are  will  not  tree,  should  as  be  " s e l e c t e d " as nothing  a  more i s  sampled. total  estimator:  (yi/xi)/n)  The be  1  k*-*  tree  c a l c u l a t e d . Estimated  the mean-of-ratios s  the  i s considered  the next  statistics  T  a l l  and  i . e . , i t i s " r e j e c t e d " and  Fourth,  or  estimate.  k  3-P  individual  be  one  that  consuming.  a.  where  first  A  i t is  pattern  be  would  be  general  can  random  selecting  In  cyclic  conservative. truly  For example, k  from  systematic  will  starts.  again,  as  displays,  approximates  group of  Third,  If  a  mean  variance  every  numbers time  last,  are used.  multiple  as  (Cochran  interest  The  closely  starts from  of  to the  estimate  sample  before.  (7)  Similarity  appropriateness  discussed  f o r the t o t a l i s :  shortly.  with  the  of  the  The  sample  14  X v(T )  2 T  (1-n/N)  =-  s  { t  n(n-1)  where  a l l v a r i a b l e s are The  probable  limits  are  Merely  substitute  v(Tg) L  wherever  The  x  these  i  2  ~  as  3-P  same  appear  of  y  )  i  2  (7)  >  in  as  for  in this the  and  the  confidence  the  3-P  estimator.  section  equations  for T  for  E,  s  and  U  and  section.  estimator  regression  x  y i /  estimate  given  sampling  t  n  / <  total  formulas  symbols  1  before.  the  following conditions  the  )  the  exactly  the  the  of  mean-of-ratios  the  i)  in  y i /  defined  error  computed  presented  where  (  is  appropriate  in  situations  hold:  on  x  is linear  and  through  the  origin ii)  An  the  variance  of  proportional  to  alternate  Conditions  ratio  most  y^  about  estimator  appropriate  is  for  variance  of  y^  about  proportional  to  x^  (  Carlo  ratio-of-means than for  the the  study  each  may  Ek  the are  ratio-of-means.  different  regression  be  not  of  from  the  more  robust  when  met.  line  is  2  x^ ).  (1971)  estimator are  the  instead  by  estimator  of  is  in  mean-of-ratios use  called  i t s use  ii)  Monte  line  2  only  A  regression  x^ .  mean-of-ratios  the  the  the  suggested and  contain  conditions  However,  as  that  the  less  bias  appropriate  Cochran  (1977,  15  chpt.6) of  x^  suggested,  a  is helpful  hold.  It  ocular  in  i s the  of  examining  sample  which,  of  to  volume,  x^  ,  the  making  values  i f any,  of  that,  when  writer's experience  estimate  proportional  plotting  variance  the  against  these x^  of  appropriate  conditions is a  y^  those  is  direct usually  estimator  the  mean-of-rat i o s .  3.  POINT  SAMPLING  This by  sampling  Grosenbaugh  with  numerous  been  described  technique  (1952).  Since  examples in  was  then,  (e.g.,  standard  first  described  i t has  Dilworth  mensuration  been  and  in North  America  described  further  Bell  texts  1967),  (e.g.  and  Husch,  has  et a l .  1972) . The formula to  first  ( 1 ) . Many  sampling  sampling has  followed  led  A  to  samples,  and of  are  s t i l l  the  cruise  tract  of  point  with  samples  chosen  to  locate  course  there  are  an  units  land. (n/N)  and  Cunia for a  or  there  (1959) given  or  is  gave  proof  which  "points"  as  of  in  can  points  not  number  that  angle  belief  center,  them,  finite  critical  This  this  number of  congruent  with  selects  groups  with  equivalently,  "plot"  infinite  is a  size  selected  the  technique  trees,  sampling  are  the  However,  sample  replacement.  that  sample  intensity  way  of  population,  population  the is  that  belief  land.  of  is estimation  infinite  finite  from  the  tract  any  an  point  any  in  a  again,  foresters feel  from  from  technique. has  step,  points, of  trees  the  expected  be  computed  16  from  3  things:  1) n u m b e r  o f sample  2) a v e r a g e 3)  This  total  can  be  following  basal  area  points,  area  t o be  f o r any c r i t i c a l  for estimating  t n  2  C  C  2  2  the  volume mean  2  +  at the  ,  (8)  2  of p l o t  expressed  (instead  individual  to arrive  size:  F — gt C  = the dispersion plot  sample  angle  A  = AFD  where  tree,  cruised.  generalized  formula  per  volumes  around  as a decimal  f r a c t i o n of  of the d i s p e r s i o n  ratios  around  factor  t o be  t h e mean  t h e mean  of  ratio  as  before),  all  other  F  = basal  area  A  = stand  (cruise)  g  = average  variables  Second, subtending the  n  lines lines  in  the  points.  measured recorded.  appear for  the f i e l d ,  a  center  Points  depending  diameters  as b e f o r e  plot  belonging  basal  t o an on  area  than  tree,  i n appendix horizontal  and r o t a t e d  imaginary desired  per  fixed  located grid  cruise this  sometimes  (m /ha),  i n ha,  (proof  are usually  larger  dbh, and  area  2  used  360 on  1).  angle  degrees,  on e a c h o f  the spacing  intensity.  height,  projected  the i n t e r s e c t i o n s of  pattern,  critical  is  angle  of the  Trees are tallied  and these  values  whose and are  17  Third, of  the  cruise  trees  estimated  statistics  selected  by  are  at each  appropriate  calculated.  plot  volume  i s  The a c t u a l  unknown  tables.  but  volume  i s usually  The e s t i m a t e  of  total  volume i s :  A F  T  n  =  S  1  = Number gjj=  with  other  basal  variables  I  {t n  where  m^  <>  D  of " i n " trees  area  9  <yij/9ij>J  of tree  as before.  The  on p l o t  j on p l o t  sample  " i " ,  and  i ,j =  based  1,...,mj  estimate  of  variance i s : 2  2  A F (1-gn/AF) V  ( T  S  ) n(n  Proofs  of  same the  way  -  the lack  estimators The  — 1)  c a n be  m:  n £  (£  i  confidence  l  of bias  found  limits.  and v a l i d i t y  in Palley  described  m;  yij/9ij) -l/n<Z: E  j  probable ' error a s was  n  yij/9ij> > 2  2  -  j  of these  and Horwitz  of the e s t i m a t e d in the section  sampling  (1961).  total on  point  3-P  i s calculated sampling,  the  as a r e  18  LITERATURE  Foresters sampling  by  objective  for  of  was  through down  was  ocular  within  stands  in  the  or  any  other  in  volume will  estimates  separate  conditions  a  conditions,  way  the  were  that  may  cause  This  individual  can  tree  hectare, the  stands  used.  Grosenbaugh  tended same  would to as  the a  sampling  but  has  fundamental  differences  sampling  no  population units  sampling  i s completed.  to  individual  probability interest  i f  must any  of  in  be gain  to  Second, the  list from  the  population  positively  differing strata  homogenous  stand  be  lower  than  that  so  if  very  coefficient  case  of  that  the  stratum  where  each  Grosenbaugh d i s c u s s e d and  each.  pps  First,  is available  sampling, with  until  probability  with  efficiency  the  i s to  3-P after  assigned  is purely arbitrary.  correlated  in sampling  broken  each  strata,  sampling  selection  was  composition,  have  the  special  theory  be  in p r o p o r t i o n to  stratum.  3-P  each  similar  be  for  contiguous  observed  for a l l  ocular  homogenous  strata,  stabilize  level  samples  i s regarded  to  how  list  to  will  the  can  species  as  make  valid  from  stands  can  errors  fairly  differing  3-P  efficiency  forest  estimate  of  extended  is  large  to  o l d days,  sampling  error  the  be  the  3-P  known  of  at  volume.  well  because  not  of  the  variability  variation  allocation  a  but  treating  time  that  exhibiting  per  stratification  optimum  In  one  example,  stems  intensive  about  claimed  improve  of  By  smaller  stratification  to  first  assessing probable  The  stands,  numbers  thus  but  themselves,  dispersions.  have  who  impossible.  For  the  judgement.  popular,  stratification.  into  for  (1964),  subjective  quite  technique using  introduced  Grosenbaugh  use  estimating this  were  REVIEW  This  variable be  of  expected,  19  though  the form  postulated.  Subjective  Grosenbaugh, geometric  of the r e l a t i o n s h i p  is  usually  be  Grosenbaugh  described  which  been  "Sampling  individuals, unadjusted  i f  estimates  formula  appropriate lieu  of  procedures technique Carlo  (1964)  o f t h e 3-P  sample  variation  for different  sample. over error  The  sampling  designs  to  a l l samples. estimates  mean  which  technique.  intervals  fell  Sharpnack  are reliable  in  these  considered using  i s most  also  and  as well  as  estimator.  sampling  of  the  unadjusted  simulation  i s  the  method, i n  confuse the  field  sampling  101  trials  in a  The  trials  included  different  around  than  one t h a t  performance of  population  variance  may  3-P  o f t h e sum o f  are given,  a new  titled  "adjusted"  a l l  of both  computer  simulate  sample  two  and  for  total  a total  3-P  described  p r e d i c t o r s of s e l e c t i o n  67% c o n f i d e n c e true  used  i tcan  population.  a  of the adjusted  tests and  Sharpnack  different  constructed  field  that  the  knowledge  Formulas  that  simple  i n the section  i s the  for testing  operation  itself.  study  point  in  smaller  i t  variance  claimed  consuming  with  a much  f o r the population  starting  time  work  requires  used.  o f some  height),  "unadjusted"  Consequently,  f o r the r e l a t i v e  Sharpnack  or  probabilities  not always,  stated  Grosenbaugh the  have  probabilities,  of selecting  this  estimate  should  n o t be  individual  Used". called  and need  measurement  diameter  in  arbitrary  but  than  the mechanics  he  estimate.  frequently,  a  every  The a d j u s t e d  predicted  adjusted  to  described  which  estimates. the  as  Techniques  estimators  cheaper  (such  applied  have  p r e d i c t i o n of these  s o much  dimension  i s immaterial  Monte 8  coefficients  of  probabilities.  He  t h e means  within  each  intervals  64% o f t h e t i m e  this  indication  t h e 3-P  a s an method.  that  20  Hartman conducted BLM  by  sells  land  of  BLM  is  form  class  The  intensity  precise using  admitted gained  was  in  eastern one  table.  this  the  They  species  and  total  the  the  just  is  a_l.  standard as  much  this  may  change.  3-P  Washington.  depending  on  from  desired  sample  trees  are  ocular  predictions table",  sales  every  cruise  taken made i.e., a  from in  the  on  5,  too  volume with  3-P  i s every  standard more  another  U.S.  standard  10,  20  or  using  the  bit  as  costs  of  technique.  He  experience  is  the  trial  of  3-P  method  national  forests  method  i s to  number  form  tables.  volume  each  sampling  other  volume  were  was  sampling  that  foot  local  a  it at  sale,  The  study  average  the  as  volume  anyway  but  aided  table  by  to  appropriate  i n t e n s i t y . Board  the  A  in  accepted  class  great  an  an  of  achieved  and  most  tree  variability  using  is visited  reported to  and  greater  the  entering  the  trial  Oregon  random  as  The  location  sampling.  technique,  one  (1967)  the  as  sale  trees  concluded  cut  at  volume  U.S.  intermingled  that  estimate  only  compared  and  tree  3,056  the  trial  sales. Traditionally,  through  quick  in  is generally  the  a  field  to  in  policy  in  selectively  tree  "crutch"  be  method, et  of  as  sum  cruise  each  due  expects  lump  tree  make  of  BLM  a  (BLM)  problems  accuracy,  Hartman  accurate to  The  Since  to  3.9%.  seemed  causes  each  of  mainly  Douglas-fir  any  for  4%  basis  100%  every  of  Johnson,  use  for  only  a  results  Management  through  to  error  that  sampling.  which  standard  with  sum  gain  effort  and  3-P  or  volume  method  lump  growth  class  extra  Land  facilities.  old  made  the  of  fostered  in  is  16-foot  tree.  patterns  economy,  little  a  i s committed  estimate  form  on  scaling  encountered effect  reported  Bureau  timber  utilization  3-P  the  ownership  numbers  the  (1966)  for  select  of  trees,  volumes  the  derived  in  The use  for quick of  from  a a  21  similar  type  may  sufficiently  be  instead a  of  on  blanket  that  sale.  endorsement,  local  on  of  particular  (1964) the  the  study to  and  they  be  estimate  a  sample  optimal the  and  lack  a  t o make and  as  felt  to  how  can a l l  techniques.  stated,  2) use  y  bias  the  there  is a  of  (the  reliable  of  will  Of  require  associated  bias,  they  with  there o r more  possible we x  ocular  v a r i a b l e of sample  was  are  (the  i t s  concerned a  was  b u t more  loss  efficiency  fortunate  of  (underlined  enough  auxilliary  estimate  three  precise  size  interest),  found  with  sample of  Carlo  possibility  costly  a  favored  a Monte  estimate  that  t o have  which  by  p r e d i c t i o n of  based  of  proved  likely  estimate,  is  3-P  Grosenbaugh's  also  supported  random  between  They  the  proofs  that  but  were  1)  information  an  was  length  simple  the adjusted  precise  of  at  showed  the unadjusted  3-P:  less  mentioned,  interest) of  of  relationship  previously  not  methods  costs  unbiased.  use. This  The  because  mine),  was  However,  observing  about  than  performed.  weaknesses  making  and  3-P  the c r u i s e  explanation  he  that  trial,  sampling  yet  proofs  contained  estimator's  negligable.  portion  single  discussed  rigorous,  Their  variance  planned,  on  cautious  sampling  design,  variances  estimate  potential  than  a  probability  optimal  gave  "unadjusted"  adjusted  only  "simplified"  (1968),  validity.  smaller  was  were  a  equal  al.  et  "adjusted"  much  they  selling  justified.  empirical  theory,  statistical  justify  are  gave  the  to hypothesize  techniques.  Schreuder, sampling  to  this  tests  than  deciding  studies  l e d them  variable probability  efficient  course,  as  (1967)  different  more  the  accurate  additional field  several  results  t h e s c a l e . However,  Grosenbaugh  be  The  by to  not have  variable,  as  the v a r i a b l e  of  and of  3)  the the  apparent adjusted  22  estimator's study  variance.  indicated  unconditional was  somewhat  Schreuder  that  the  but  Schreuder,  et  a l . (1968)  properties  of  these  they  have  stated,  actual  sample estimate  would  be  Monte  estimate  of  conditional al.  1971)  But, of  (which the  This  also  the  is a  behaves  crude for  as  (1968)  (5)  concluded  potential possible  experience  of  found  a  be  of  to  sample  does  saying  of  a l l the  of  under  Monte  previous that  3-P  to  sampling  alternatives sampling  fully  will  theory,  alternatives.  are  based true  It  variance  is  formula  replacement)  of  (l-n /N). E  the  determine  true  but i t  simulation.  require  e_t  estimate  Schreuder,  an  also  estimators.  exist.  important  and  doubt  of  replacement  section.  the  sample  (fpc) or  Carlo  of  (Schreuder,  estimate  without  the  examined  i s with  unbiased  to  n,  reliable  conditional  sampling  i n the  by  an  value  these  stable,  population correction  expected  given  of  n  properties,  the  studies  i f sampling  used  after  estimates  utility  that  ambiguous.  with  was  that  formula  existing  with  This  (1965)  related  significantly  reasonable  single  are  the  conditional  expected  the  type  weaknesses  i f the  the  the  Carlo  of  properties  multiplying  difficulties  extension  a  approximation  this  on  slightly  conditional  subsequent  Monte  Grosenbaugh  f o r they  I t was  showed on  finite  would  formula  doubt  (1976)  expected  variance  is  further  were  procedure.  However,  by  discuss  These  example,  their  estimate  i . e . , the  provided  v a r i a n c e based  is  For  study.  variance.  by  to  relevant,  sampling  Carlo  simply  on  i t s variance vary the  Grosenbaugh  the  most  variance  cast  obtained  by  on  went  results  selected.  observed.  cast  their  the  and  their  based  suggested  estimators,  been  are  total  in  sample  variance originally unstable,  observations  e_t a l . t h o u g h t  This  et a l . whether  relative  to  refinement  and  accumulation  of  23  In  Finland,,  variable study  selection  was  stands.  Optimum  efficient.  on  The  and  of  were  that  when  p o p u l a t i o n has  or  scaling  and  3-P  standing  dbh.  data  between  estimator for  i n which A Monte  from  2.1 was  6  and found  found  to  be  statistically  been  previously  the  Carlo  different  2.4  expected  is a  more  that  volume  b i a s e d . The  expensive  inventory first  detail. the  in  (0.9  was  for  to  be  and  the most  actual  small.  Seppala  efficient  enumerated  were  trees  plot  A  spruce  the  sampled and  into  sample,  to  and  Hartman  the  method (listed,  or  and  three  For  the  tenth-acre  point  effort and  facilitate  3-P  were  was  in  proposed  according  their  in  northern not  stage,  was  locating  sampling  samples  comparisons.  fixed  two select  as The  The  described in some  them. G r o u n d  method,  to  forest  B.C.  was  made  with  method  two-stage  which  plot  be  trees.  a  methods:  can  concerned as  and  dendrometry  dendrometers  however,  subplots,  was  to  i n magnitude  type  field  bucking,  This  standing  plots,  ground,  3-P.  9  vary  sampling  photo  from  may  forest  using  deliberate i n the  3-P  stage,  on  alternative  estimates  errors  tested  falling,  opportunity exists.  measuring  sampling  sampling,  sampled.  than  second  divided  logical  its practicality,  white  plots  ac)  point  a was  The  photo  on  (1972)  stage  proposed  o p e r a t o r . Johnson  i t s cost  Bonnor  a  found  instrument  was  as  the  and/or  of  trees when  erratic  of  were  (1972)  trees  they  effects  Hartman  sample  because  to  on  collected  were  not  sampling  based  calculated  sampling  3-P  framed). Johnson  of  3-P  were  3-P  differences  concluded the  dbh  adjusted  Variances  sizes  tested  previously  powers  stands.  (1971)  probabilities  performed  different  sample  Seppala  were 3-P  of  plots  area  plots,  each  ground  plot  of  which  were  the  same  selected  method  was  number in  the  judged  24  to  be  the  vastly  superior  sampling  that  3-P  plan  would  populations. practical  and  be  efficient  on  field  timber  Mexico,  (1974)  3-P  described  application lies  to  ignored  tables  several  estimates  of  several  skill  p r e d i c t i n g . Though  is  often  convenient  prediction diameters that  i t  local  at  estimation integers)  that The  tables  volume,  cruise  in  is  For  may  complicated  i t  real of  to y i e l d  i s this  list  the  office  by  computer.  i t s  real  may  be  very  the  combined  i s taken  a r e then  be  degrees  of  employed, i t  thus  standard to predict  lies  powers  functions  and  that been  volume.  the diameter  This  Deloya  largely  easier  random  volume,  which  selection probabilities  1974).  crews  differing  tree  o r much more  i s inverted  use  I t i s much  incorporate  terms  has  data,  to  an  instances  field  could  raw  as  discussed  crews  possess  total  Briefly,  technique  in  (Tariq  to  often  the  than  in  more  country.  one,  stratification  matter  until  recognized  and  preferable  cruises who  height  generated  and  3-P  in that  necessary.  efficiency. are  I t was  suggestion  combine  are  simple  equation  actual  to  breast  is a  Two,  forest  attention. Caballero of  work  the  people  procedures  volume  volume  this.  in  indicated  3-P  especially  gained  reasons.  at  used  most  the  are not a v a i l a b l e  principles  directly  this  deferred  described  in Pakistan.  that  when  sampling  were  technique,  inexperienced  at  (1974)  inventory  noted  volumes  for  Tariq  the  methods  accumulated.  sampling  forest  (1978)  predicting  be  trials  volume  in  conclusions  cruising  applicable In  could and  plot  to Bonnor,  efficient  definite  (1974)  and  According  more  experience  reported  where  tested.  More  Hussain  to the point  to  showed of  improve  numbers the  computed technique  (vs.  appropriate  which into  dbh,  generated the  field.  after  the  seems  to  25  eliminate  the  suffer  loss  a  information Pelz method.  In  (1980) stand  needed  sampling A used out  The  (Pelz  multiplied precision  by and  manner  sampling  are  aerial  photography  error  in  1982b)  performed  which  slow  dbh  of  of error  i t  trial  to assign  down t h e m e t h o d  t h e 3-P  because  may  i s being  shaped  efficiency  the  related.  eliminated  stands  be b i a s e d .  of  x and y.  regarding  determined  o f 3-P s a m p l i n g  which  1982a). The  in  Further  compared  (or  these  which  research to other  available, file.  Hetherington  o f 3-P,  should  be  a l l the  the p r o b a b i l i t i e s considerably.  achieve  stressed that  3-P  trees  where  volume  i s difficult later  though, were  but  found  an  (Hetherington  two m e t h o d s  noted  that the  access  the  i s  in  was p u b l i s h e d  that  by t h e  total  computed  e t c . Hetherington  i s concluded  seemed t o  efficiency".  the  particularly  where  An e r r a t u m  It  of  to  are  system  compared  of  takes  efficiencies  not a v a i l a b l e ,  were  an " i n d e x  i t  world-wide,  the tarif  T h e 3-P m e t h o d  i n percent  cost)  indexes.  with  methods  provides  the total  relative  comparably.  Hetherington's for  or  a computer  in  source  system.  applications  tables  between  use  t r e e s and a r e not area  estimates  t h e time then  be  3-P may  optimal  benefit  in irregularly  procedure  poor  not  (Hetherington  using  has  the relationship  need  was made  error  making  that  1980).  the tarif  common  not  3-P's r e l a t i v e  t h e U.K.  standard  usual  based  e t a l . (1968)  additional  additional  to test methods  by  are individual  area  perform  fairly  area  comparison  in  an  be i m p o r t a n t  conventional is  about  cited  s o , an  may  Schreuder  efficiency have  elements  doing  which  of  we may  The  sampling  o b j e c t i o n by  actually that  actually  of s e l e c t i o n ,  which  in  taped would  26  One forests and  example where  method  methods  'stockmapping' the  Another  and  stands the  a  with and  value  (1982).  3-P  stage  Data  total  stands.  Only  were  sampled  on-the-ground  earlier. method the  same  Steber scheme  the  and  then  first  phase  using  the  million  of  using  have  taken  of  a  the  method).  by  Takata  3-P  point,  four  natural 2  using  d h  as  precise. and  reported  sampling forest  only  in  901  ha,  was  by  angle  inventory the  three  3-P, count  7  years  angle  times  by  units  selected  conventional  i . e . , using  would  from  were  an  the  volume e s t i m a t i n g  method  the  from  cases  application.  came  stands  count  as  long  precision. Space  (1972)  described  g a i n i n g wide  popularity  i s the  plot  3-P  acres  forest  expensive  primary  area  came  efficiency  i n Germany,  the  221  sampling,  whole  7.8%  the  predictions  Conventional  for  of  select  of  proposed  sampling,  and  conducted  i n many  (1981)  four  accurate  stories,  application  conducted  3-P  was  15  was  straight  test  The  in this  study  most  to  and  The  221  3-P  the  tropical  inventorying  the  probabilty"  from  used  for  among  the  inventory.  The  made  in  and  Omule  study  was  was  Crude  crude  tested  "equal  easy  improve  such  was  plantations.  field  sampling.  for  sampling,  four  not  Comparison  Another  two  (one  to  simulation  predicted  Suss  forests.  computer  method".  and  these  was  3-P  "Beers  developed  technique  in Japan.  methods:  schemes.  is  multi-layered  prevent  been  sampling  technique  difficult  undergrowth,  sampling  in  3-P  is  trees  have  volume  employing  (1982)  heavy  inventory  stock  However,  access  buttressed  conventional  growing  where  generally  heavily  expensive  of  prism  technique  and  (second  in cooperation  in the  phase).  with  the  a  two  the  phase  Southern  " i n " trees They St.  Joe  sampling U.S.  are  sampled  inventoried Paper  The  Co.  one in  27  Northern  Florida.  inventory out  of  based  three.  combined  dollars". dollars,  not  that  estimation  sale  out  size  black  times  more  stands.  optimize  the  than  3-P  other The  classification  proven  3-P  limited  also  the  with  of  be  or  of -  were  the  entire  7.1%,  two  saved  using  of  times the  prism  objective.  method  of  a  the of  there  be  has  great  region  seven  Therefore, in value an  an  by  the  more  found  dollar  by  dbh  a  in  on  class.  class,  U.S.  in  a  where elm  and  alone  would  these  mixed  method  the  class  of  priori  than  interesting  by  using  goal  dollar  volume  based  for  advantages  of  times  sold  major  requires trees  scheme,  and  the  of  hardwood  trees  sampling  i s bought  method  trees  "3-P  should  described  a  priori  which  volume  to  seems  class  or  scheme. show  that  statisically  trials  testing that  dollars  maple.  citations  field  view  further  to  timber  differences  frequency  preceding  favorable  is  calls  sampling  for  also  compares  he  i s worth  Kasile  valid  evident  what  frequency  hard  distribution  for  +  money  His  the  walnut  probability  The  was  and  this  in  reflect  hardwood  have  error  time  of  of  that  stand  adequately  any  volume  since  inventory.  distribution  hardwood  three  proposed  believed  pointed  sawlog  sampling  foot  Considerable  direct  probability  mixed  cubic  (1983)  He  timber  Kasile  on  combined  techniques.  Kasile  any  The  that  the is a  cruising  been  overall,  method dearth in  efficient  have  technique  many M o n t e  under of  larger  Carlo  studies  estimation  system.  published, but  local  point  the  conditions.  information stands  to  give  where  as  to  clear  how  a  need It  is 3-P  felling  MATERIALS  Pfeiffer defines  work  study.  examination of  of  a  favored study  was,  o f many  B.C.  Work  Study  timber,  designed so  and  the operational  to effect  important  continuous  time  compare  the continuous  efficiency  work  study  study  i s  The  various  time  Pfeiffer  study  of a l t e r n a t i v e s . to  School critical  improvement.  o f t h e most  f o r comparison  of course,  cruising  governing  explained that  technique  the  i n order  review  and  how  METHODS  I t i s the systematic, o b j e c t i v e ,  activity  thorough  techniques,  related  a l l factors  any s p e c i f i c  gave  for  (1967)  AND  the  present  alternatives technique  was  adopted. With activity begins, is,  this  and stopped  naturally  "rating"  at  this  without  resulting  1967),  and  multiplied  i s  by  i s started  and end t o  that  hand  i n hand  Organization  could  sustain  in buildup a  the rating  with  "Normal  Elapsed  over  long  of cumulative  rating  of  as a decimal  I t should  rate  of  working  periods  The  fraction  be  i s d e f i n e d by  of  fatigue"  100%.  time  t i m i n g goes the  pace"  as "the  each  as the a c t i v i t y  t o do t h e a c t i v i t y .  performance.  Labor  given  watch  necessary  point,  operator  defined beginning  the d e f i n e d end i s reached.  of the workers'  the  well  The s t o p  when  the time  International  which  a  are necessary.  mentioned  the  method,  time  (Pfeiffer  observed  results  in  time normal  time. This estimate or  fact a  companies  their  crews  parties  i s mentioned  normal may  time already  display  can "rate"  when  because  f o r each have angle  the times  no  activity.  established count  attempt  made  to  Various organizations normal  sampling.  r e p o r t e d here  was  So,  times  which  interested  for a specific  two  man  29  crew  (same  their  for  a l l times)  organization's  from  a  case  angle  may  crew  time  be  study  count  used  "normal are  the  3-P  same  adjust  pace".  applicable  sampling,  for  and  Also,  to  the  sampling,  job  at  any  of  each  them the  accordingly  resultant  particular or  ratio  other  times  (in  this  estimation)  but  place  job  to  under  similar  condit ions. To  facilitate  technique The shall The  was 3-P  be  broken  The  called  bounded  by  against  numbers,  included  both  men  ended  traversed  or in  the  the and  selection  criteria  it  took  to  measuring,  was  This  selected  under  trees  may  cruising the tree  time  be  for  were each  the  tree  recorded  method. i t took  measurement  The to  in  and  locate  phase.  Last,  the  volumes.  testing  the  criteria,  namely,  the  the  Timing to  had  the  1  k*-*  tree,  were  started be  with  cruised  been  and  ocularly  sample.  Since  two  simultaneously,  the  time  later  for  could  be  under  located the  different  because  marked  activity trees  differing  cruises  activity each  strips  and  and  tree  different  locating  block  were  tract  in  because  criteria  selected  it  separately  is necessary each  last  the  which  i t was  the  employed so  m  which  dendrometry.  individual tree  activity. of  activities,  through  10-12  if  inclusion  being  4  Recording  see  edge  for  checked  mark  marking.  the  volume  predicted  to  predicting at  of  each  activities.  into  selection  checking  positioned  when  two  technique,  l o c a t i n g , and  successive string.  the  or  walking  estimates  in a  down  marking,  included  ocular  cruising  components  broken  predicting,  trailing  also  into  were  activity  was  predictions random  down  predicting  stand  timing  variations  predicting  directly  the  tree  dendrometry  could  be  numbers  of  using  consisted  called  of  during activity  the  same  just  that,  the  sample  consisted  30  of  finding  the  a suitable  dendrometer  or  take  actually  setting  necessary  information  application then  location  up  locations  heights  and  with  using  decay,  the instruments  i n which  clinometer  the  on p a t h o l o g y  of appropriate  taking  or  down  and  instruments,  and q u a l i t y  waste  t o s e t up  and s t o r i n g  recording  needed  and breakage  chain,  f o r the  f a c t o r s , and  them  properly for  transit. Three the  d i f f e r e n t methods  sample  trees.  clinometer, for  and  entry  into  (1976).  This  because  i t  accurate  three  nylon  method  i f and  may  applied  to  a new which  the  relationship  the  two  volume error When  stands, table  error (based  on  was  table  1) a n d  Behre's  volume  differences  dendrometer  estimates.  "acceptable"  index  or  tree  Hazard  and  the  volume  small  They  found  for  Berger table i s  portion  tree  the  in  the table.  volume,  that  volume  taper)  set  the  measurement  into  volumes  between  of the  characteristicsfor  tree  Berger  local  a r e : 1) c h a n g e s i n  f o r input total  be  However,  of u t i l i z a t i o n  I t was  from  will  and  3) s y s t e m a t i c  gross  expression  of v a r i a t i o n  Hazard  and the t r e e  and  appealing  objectives.  to a  the trees  3) a p p l y .  represents  height  b y t h e BCMF  i s quite  an e x i s t i n g  tape,  dbh and  i s quick,  by  standards  predicts  substantial  when  desired,  (1927)  truly  developed.  different those  volumes  measure"  diameter  published  for certain  trees  i n measuring  volume  sources  of  the table  2)  table  tree  a  t o measure  identified  problems  between  used  table  Were  stand  method,  volume  be a d e q u a t e  cause  than  incurred the  were  to "accurately  few m e a s u r e m e n t s ,  volume  of error  that  for  very  may  (1972)  stand  chain  tested  first  for obtaining  the  sources  the  the appropriate  requires  conditions,  In  were  only tables  produce  derived an  volume  from  arbitrary table  and  31  dendrometer  at  10%  Freese  (1960)  failed  resoundingly  estimates  ,  could  so be  the  Chi-Square  used.  at  the  acceptably  In  their  95%  test study  probability  similar  to  expostulated  those  the  volume  level  to  obtained  by  tables produce  from  the  dendrometer. The using  second  the  method  wide-scale  described  in  individual  "logs"  tree  volume,  the  measurement  with  problems  encountered  branches  large  amount  of  down,  so  the  over  that  several an  of  stem.  All  distance  tree  It  new  particularly  easy  to  in  while  proportional comparison  to  with  is a  that  spot  diameter  itself,  and  wind.  to  offers  for  time the  to  use  with  in so  the  these  readings  field.  readings at  the  same  die  and  forth  be  spent  ideal  view one for  horizontal  relaskop that  be  to  a  measurements.  are  Relaskop can  be  other  than  seem  the  the  a  real  possible  stem of  of  also  more  may  lower  observation Also,  can  The  wind  back  best  location for  pose  Sometimes  the  travel  one,  can  branches  one  another  not  and  waiting  of  total  this  calipers.  "suspicious" readings  still  as  trunks  however,  location.  other  mechanical  as  mentioned  diameters  Considerable  new  errors  such  here,  obtain  lower  appears  example, and  table  to  and  or  longer  bands.  them  was  volumes  does  spent  no  aim  woods  can  be  The  the  tree  For  each  volume  brush,  location  is required  error,  tape high  summing  subject  measurements  at  dbh  tested  calculating  instrument  is possible,  location.  stem  that  time  instrument  instrument upper  the  relaskop  finding the  are  is  in  because  measurement  dendrometer.  the  any  diameter  of  a  and  underbrush  problem, a  tree  using  low  as  eliminating  measured  trees,  Relaskop  tree  introduction,  When  encountering  sample  i n the  thus  previously.  of  is  probably  units  spotted  instrument  i t  are  through  location.  32  Relaskop the  units  stem.  optical  When  gave  based  the  on The  Barr  relaskop,  because  because  the  with  available, related  to  the  Barr  and  no  expect  the  in  hypothesized Stage  (1962)  prism  and  Ross  prism.  Brickell  it  very  is  when  carrying setting  the  case the  also  found  that  tree  volume,  +  that  average,  up  Stroud the  than  those  vision  Barr  to and  be  use  unwieldly  random  may  are error  than  10  tree  this the  precise also  in  stands  newer  FP-12  model  are  found  area  that  one +5.4%  would bias  He  cause.  He  caused  this  error.  with  the  wedge  the  Wheeler  instrument  instrument  i n volume %  in  could  penta  writer corroborates, two  not  estimates  volume.  and  consuming.  15  of  and  specific  i t with  times,  time  the  using  (1976)  phenomenon  The  -  the  However,  have  than  at  is a  in basal  any  the  more  Stroud.  instrument  less  and  from  felled  demonstrated  found,  There  bias.  itself  as  Consequently,  to  this  Use  viewing  Brickell  bias  over  t r e e s was  accurate  aids  changes  i n volume  sample  m a g n i f i c a t i o n , and  weather.  2.39%  found  has  (1976)  much  &  found  FP-12.  more  5.5x  1969).  demonstrated  the  progress  Barr  advantages  which  discrepancy  (1968)  type  measurements.  was  human  can  up  has  design  exhibits  cumbersome  using  the  the  even  light  but  this  has  give  (Mesavage  volume  that  on  same  in cloudy  height  attribute  the  may  same m a g n i t u d e  dendrometered not  or  FP-15,  Stroud  bias  dendrometer  "gathers"  accuracy  and  the  (1975)  measure  instrument  canopies the  readings  to  Bower  higher,  to  gives  the  lens  dense  used  in addition  results  and  1.6%  optical  certainly but  relaskop  as  Stroud.  method  Stroud  instrument  &  the  Yocom  estimates  third  and  g e n e r a l l y decrease  comparing  dendrometer,  relaskop  Barr  should  plus  locations tripod  and  dismantling Brickell  measurements usually  that  and  (1976)  was  associated  3%  of  with  33  volume  tables  equations 16.8%  give  forest.  rotated that  bulkiness carried. tripod  The  and  weight time  either  by  measuring  sample  The  necessary  clinometer, simply  by  sample  tree  the  they  measurement was  not  "true" bias,  number  are  technique  volumes, or  However,  to  of  were  start.  space  t h e stem f o r  I t was  f o r dendrometry  that  t r e e s when  the  Barr  and  trees tape  three  measurements 2)  (number  any of  statements  methods 1)  desired,  relative  of  the  Stroud  be a  was  actually  i n the  estimated  two t h i n g s :  and  must  carrying  t o walk  on t h e  field.  only  a  separately,  t o each  marked  instruments.  these  fell  was  were  carrying  spent  spent  when  necessary  those  on  time  in  recognized  extent  or  was  applied  to a certain  the t o t a l  time  consequently  accuracy strong  of  to  a s i t was v i s i t e d  for locating  locating  only  taken,  possible  random  and diameter  depend  6.3% t o  techniques  t h e sum o f a l l t h e t i m e s  among  will  tree  depended  from  for  carrying  choice  measurement  which  subtracting  chain,  5m a l o n g  t h e methods  relaskop  trees  from  made  measurement  of instruments  recording the  The  desired,  forest  the  was  than  sample  a  necessary  estimated  time  after  i n the  and  these  i n which  systematically  mobility  of  t o each  The o r d e r  ranging  attempt  greater  l o g a r i t h m i c volume  and the r e l a s k o p .  each  consecutively  An  no  (1976)  of estimate  species.  intervals  field,  T h e BCMF  errors  and Stroud  the  applied  on  at  the Barr In  the  standard  depending  measurements both  or equations.  of  level  trees  no s t a t e m e n t s these  c a n b e made  tree  of  tree  accuracy  or t h e purpose f o r  productivity  t r e e s per hour  sample  sample  of  or per day). I t  or otherwise c a n b e made  obtain  about  measurement  regarding  the  criteria  the  methods. 2 ) , and  34  will  be  discussed  more  fully  in  the  Results  and  Discussion  section. The are  referred  sweeping is  prism  species,  included  dbh,  spent  establishment, Before  plot,  actual  for  each  the  necessary Finally,  the  a l l  total  block,  park is  photos  volume  figure".  It  volumes  was  a  from  be  may  be  needed  for  is generally  preferable  Aproximately  can  type  to day  used  an spent  to  the  necessary  estimates  block  or  the 3-P  practicing an  idea  of  required  meet  of  20.  In  size  the  this  the  included  a  was  center  started,  with of  may  slight  be  executed in  this in  the  estimate only  a  of  "ball  overestimation 1965).  prediction  predictor's  of  tree  (crewman's)  showed  objective  i t was  per  estimation  (Grosenbaugh  formula  the  trees  experience The  on  a l l  quickly  judge.  cruise  study  for  performed  ocular  the  activity  ratio  perhaps  that  the  were  to  two be  underestimation  obtain  and  estimation  sample  out  number  better  agreed  a l l  performed  members  or  used,  and  "plot"  were  3-P  not  sample  times  or  prism  activites.  and  need  appropriate  19  point  crew  one  The  15%  activity  for  variability. trees  trees  chaining  The  measured  etc.,  heights  methods  volume  These  total  the  familiarize of  forest  class,  cruising techniques  of  the  marked,  timing  prism  particular  which  of  points,  which  chaining.  necessary  obtained  aerial  in  sampling  number  the  and  are  crown  The  between  were  manner,  "sweep",  pathology,  respectively, plots.  trees,  activities  miscellaneous  to  Estimates  three  a l l " i n " trees  checked.  using  areas  into  prism  are  chaining and  down  sampling  the  quality,  cruises  contiguous  hectare  the  regression.  time  broken  included  measuring  practice  was  sweeping,  trees  height/dbh  methods.  as  around  borderline  the  to  activity  rotated  for  cruise  found  of  that  18  +  -  that  or  the  35  auxiliary  variable,  correlated  with  correlation volume  while  "actual"  coefficient,  table  volumes  and  obtained  volumes  predicted  ocular  by  the  gave  correlations  actually  from  to  difficulty size  for  the  analysis, each  was  actually  the  one  prism time  volumes  obtained  the  set  As  be in  at  was in  arriving  to  the  was  in  chosen  because  i t represents  Forest  Inventory  time,  and  yellow  two  and  Extreme  accuracy method  comparisons these  two  a  are  blocks  near  (FIZ)  and  0.9214.  The  ranged  introduction, sample  in the  final  precision  using  of  the  precision  sample  blocks  size  and  each  Suunto  C.  The  was  eight  was  one  using  a  for  block  Care  similar  two  hectare  to  areas  was  in  sizes,  held  1/2  in and  to  the  and  one  a  with nylon  corrections.  necessary,  identical  i n d e n s i t y as  funds  compass,  however,  was  found  delineated  slope  i s not  taken,  area  study  were  make  the  of  the  block  hand  British  conditions  limited  Silva  executed  valid. were  of  the  of  This  availibility  of  clinometer  the  University B.C.  well  constraints  flagging  in  the  Haney,  replications  blocks  chain,  cruising  Zone  logistical  plastic  hectare  0.9073,  block  since  the  the  between  appropriate  given  regardless trials,  conducted  Forest  Two  an  a  from  was  of  the  that  achieve  half  Research  hectare.  at  simple  dendrometer  separate in  decided  field  for  each  outlined  I t was  the  Stroud  coefficient  in  compared,  six  and  The  correlation  p r e d i c t e d volume  Barr  Columbia  of  and  The  highly  blocks.  study  examination  0.9370.  experienced  required  would  hectare  The  between  cruise.  achieved  arbitrarily  r,  experienced  the  method  overall.  correlation  0.9895.  was  volume,  by a  volume,  measured  relaskop  obtained  of  or  p r e d i c t i o n s was  volume  0.8151  prediction  to  measured  as  each  block  and  ensure  that  i n number  of  36  trees  per  hectare,  dimensions, cruise  time.  compass, the  meters  second about  which growth  hectare,  Douglas-fir,  m, 431  low  about stems  salal  740 per  ground  summarized  dominant  and  meters  gross  cubic  hectare,  cover,  in table  35%  making  slope, travel  1.  STAND C H A R A C T E R I S T I C S  BLOCK  SLOPE  A S P E C T NO./HA  BA/HA V O L / H A  M W  40% 35  270 225  68m 55  enabled for  data  any  carefully  given  predictions detail  392 431  prediction  will  in the  Each  of  hypothesized  each and  2  985m 739  obtained  the  time  3  from  W  985  ha,  40%  of  western  consisted  total  fairly  were  per  codominant  south  Height  height  volume  west  of of per  aspect  and  easy.  The  HEIGHT DIAM  %F  %C  %H  50.5m 51.1  32 70  32 23  36 7  be  outlined  briefly  47.0cm 40.3  sampling  i t takes  The  areas  to  methods  these  cruise used  here  but  to  block  sizes  larger  blocks  make  these  discussed  i n more  chapter.  separate  relationship  there  M,  SUMMARY.  precision.  next  Block  1.  TABLE  The  Block  these  cedar.  stems  the  Nesting  that  understory  somewhat.  had  50.5m, 390  overall  blocks.  and  tree  using  constant.  about ha,  affect  ensured  Douglas-fir,  significant  work  to  hectare  fairly  per  individual  divided  further  t r e e s was  a  inhibited  0.5  fashion  volume  and  further  into  hemlock,  total  in  hypothesized  remain  codominant  aspect  51.1  this  possible  were  clinometer  would  as  were  blocks  in  gross  west  hemlock  very  and  similar  factors  o l d growth  dominant  slope,  and  blocks  of  as  two  factors  consisted  are  These  smaller  cubic  these  chain,  important  of  as  and  cruising has  with  developed  on  activity  was  increasing strong  analyzed area  and  sampled  the was  theoretical considerations.  37  Then, (+  to  or  arrive  -15%  activity's A  from  19  relaskop  available  cones,  in  this  total each  and  shown for  and  volume,  obtained inside  as  table  bark  affect  sampling  error  used  to  estimate  this  has  effect  on  No  each  may  It  of  under  not  cruising  the  bark  equations  sizes,  were  and  the  formulas  the time  gross  sampling  point  gross of  were volume are  measurement  total  volume However,  that error  estimate  necessary  in  volume  for tree  to  made  total  total  gross  not  was  volumes  estimates,  the  are  estimate  dendrometers.  the  Martin  assumed  output  whose  predicts  i s only  volumes  as  f o r bark  are  was  algorithm using  i n c r e a s e the  trees  of  tree  adopted  volumes  volumes  which  language  when m e a s u r e m e n t s  top  tree  precision  the  for  mathematical  correction  involving  obtained. sample  tree  Tree  was  best  estimates  volume  the  the  the  volume  f o r methods  not  objective.  point  the  precision  times  standing  r e a d i n g s . An  which  volume  outside  no  bark,  so  the  involving  will  stem.  total  given  programming  calculate  the  over  methods  this  on  algorithm,  gross  i n BASIC  cylinders.  the  a  predicted  l o g volumes  volume  So,  the  Stroud  total  bark.  20),  i t i s among  the  outside  from  reported  and  logs  stumps  to achieve  to  compute  that  time  summed.  IBM-PC  Barr to  of  written  an  along  computer  tree's  were  middle  spaced  be  on  cruise out  program  formula  (1984) has  equally  times  f o r use  Smalian's  total  completion  computer  developed  at  i s , the that  is  itself,  so  f o r any  cruise  RESULTS  The blocks from  total  (HM  By  see  these  of  and  16.90  W).  time  to  HW)  cruise  remaining  block.  Column  make  each  up  volume  coefficient  hours 5  times,  and  cruising of  total  of  time.  the  total.  eight  of  the  cruises,  measurement the  relaskop  using than  the  the  cruise  volume  examining  that  overlap  is  whether  these  biases  or  to  actually  to  this  used  to  present  chance.  fell  question.  these  In  total  by  in  their  was  one  the  used. of  tree  case,  the  a  Thus, point  trees  can  for  each  times  that  the  total  of  along  In  with  and  is  percent  that as  the  in a l l  the  tree  greater  than  when  a l l but  one  estimates  case,  greater  r e l a s k o p was less  volumes.  presented  reader  variations  volumes  total  and  each  Stroud  the  (M  for  limits,  volume  took  times  summary  and  When  the  addition,  sample  a  i t  blocks  component  trees.  total  them. in  the  hectare  and  the  cruise  development  cruise  gave  5,  method,  Barr  limits  between  differences  just  the  obtain  a l l but  hectare  confidence  estimate  confidence in  block  half  hours,  through  6 gives  measure  table  the  and  the  15.35  tables gives  95%  Stroud  an  the  interesting  to  volume  the  seen  and  was  tables 2  resulted  gave  table  in  also  sample  to  cruise  using  i s used  Barr  when  every  be  method  An  12.15  Table  variation,  of  point  to  each  error  to  methods  these  for  DISCUSSION  from  column  4  estimates  took  ranged  26.82  examining  the  i t  AND  than  used,  when  However,  in this  table  considerable i t is difficult estimates  upon  i t  amount to  opportunity  was  to  determine  better  a  will of  assess  represent  no  the  real  available answer  TABLE  2. BLOCK  METHOD  HM  SAMP.  PRISM  SIZE 6  3-P  SUMMARY  18  OF  ACTIVITY  TIMES  ACTIVITY SWEEPING SAMPLING CHAINING  TIME(HRS)  TREES(33)  PREDICTING MARKING LOCATING" 3  DENDROMETRY  EST.  d  MARKING LOCATING  0  a. b. c.  d.  7.7808 6.9025 .6667  15.3500  1.9000 .7633 .8260 1.9162 4.0967 8.7684 14.5434  7.5860 13.3479 19.1229  .2867 .6397 1 ) 2) 2.1014 6.5097 DENDROMETRY 3.6833 1 ) 2) 7.2628 11.5509 17.1514 3) 12.8633 T h i s t i m e i n c l u d e s 12 t r e e s t h a t w e r e r a n d o m l y d i s c a r d e d to achieve the d e s i r e d c r u i s e i n t e n s i t y . 1) g i v e s t i m e when c a r r y i n g o n l y a c l i n o m e t e r a n d c h a i n 2) g i v e s t i m e when c a r r y i n g t r i p o d p l u s d e n d r o m e t e r a n d c h a i n . 1) when m e a s u r e d v o l u m e i s f r o m a t a b l e . 2) when m e a s u r e d v o l u m e i s f r o m w i d e - s c a l e relaskop readings. 3) when m e a s u r e d v o l u m e i s f r o m B a r r & S t r o u d readings P r e d i c t i o n t i m e i s t h e same a s f o r 3-P s o i s n o t l i s t e d twice.  RATIO  17  0  1 ) 2) 1 ) 2) 3)  TOTAL(HRS)  40  TABLE  3. BLOCK  METHOD  HW  SUMMARY  SAMP. S I Z E  PRISM  6  3-P  OF A C T I V I T Y  ACTIVITY  TIME (HRS)  SWEEPING SAMPLING T R E E S ( 4 1 ) CHAINING  1 3  PREDICTING MARKING LOCATING DENDROMETRY  RATIO  d  EST.  12  TABLE  f o rexplanation  SAMPLE  PRISM  SIZE 8  3-P  25  OF  EST.  d  18  ACTIVITY  as  5.5833 5.0333 1 .5333  12.1499  1.3017 .3942 .4758 1 ) 2) 1.4083 2.3075 1) 2) 7.4894 3) 10.5481  4.4792 10.5936 13.6523  .2542 .3032 .91 97 1 .8994 3.6256 6.4350  3.8075 6.1502 8.9596  TIMES(HRS)  TOTAL(HRS)  1) 2) 1) 2) 3) t a b l e 2.  SWEEPING SAMPLING T R E E S ( 6 7 ) CHAINING  11.5167 12 . 1 8 3 3 3.1167  26.8167  PREDICTING MARKING LOCATING"  1 ) 2) 1 ) 2) 3)  3.4350 .621 7 1 .2500 3.6271 4.6111 10.7917 17.5347  9.9178 18.4755 25.2185  1 ) 2) 1 ) 2) 3)  .41 00 .9300 3.0550 4.2200 9.9300 14.7850  8.9950 16.8300 21.6850  0  MARKING LOCATING DENDROMETRY  b, c , d -  TOTAL (HRS)  A C T I V I T Y TIMES  DENDROMETRY  RATIO  0  see foot of  4. BLOCK M SUMMARY  METHOD  0  MARKING LOCATING" DENDROMETRY  b, c , d -  TIMES  d e s c r i b e d under  table  0  2.  TABLE  5. BLOCK  METHOD  W ACTIVITY  SAMPLE  PRISM  SIZE 8  3-P  24  TIMES  SUMMARY  ACTIVITY SWEEPING SAMPLING CHAINING  TIME(HRS)  TREES(41)  PREDICTING MARKING LOCATING DENDROMETRY  RATIO  EST.  d  18  MARKING LOCATING" DENDROMETRY  b,c,d  - same  as i n  0  table  2.  0  7.8667 7.7000 1.3333  TOTAL(HRS)  16.9000 >  1) 2) 1 ) 2) 3)  2.8100 .5552 1.0000 2.9785 3.4150 11.4933 18.2567  7.7802 17.8370 24.6004  1 ) 2) 1 ) 2) 3)  .3550 .8400 2.2750 2.9067 7.3100 11.6367  6.9117 10.4750 14.8017  TABLE  6. SUMMARY  BLOCK  METHOD  HW  PRISM 3-P  R.EST  W  PRISM 3-P  R.EST  HM  PRISM 3-P  R.EST  M  a~!  3  OF C R U I S E  sizes made  can  varied of  VOL(m ) C  C. L I M I T S UPPER 499. 457. 432. 481 . 489. 367. 497.  1 ) 2) 3) 1) 2) 3)  404. 412. 374. 431 . 403. 322. 400.  36 19 27 20 31 23 40  1 ) 2) 3) 1) 2) 3)  739. 835. 797. 930. 806. 784. 976.  33 25 34 30 31 38 42  556. 749. 686. 815. 686. 640. 775.  921 . 919. 908. 1 044. 925. 927. 1 176.  24.7 10.2 13.9 12.4 14.8 18.3 20. 0  1 ) 2) 3) 1) 2) 3)  389. 559. 476. 539. 434. 387. 461 .  38 31 29 26 41 45 37  256. 476. 410. 473. 348. 302. 377.  522. 642. 542. 605. 517. 472. 544.  34. 1 14.8 13.8 12.3 19.4 22. 0 18.1  31 985. 752. 1218. 23. 6 1 231 . 34 13.8 1061. 1 401 . 1 1 50. 36 984. 1315. 14.4 1 304. 33 1 1 29. 1 479. 13.4 1 1 68. 34 976. 1 359. 16.4 1 087. 33 16.2 91 1 . 1 263. 15.2 1 266. 31 1 074. 1 459. t h e volume t a b l e t r e e measurement procedure. t h e r e l a s k o p t r e e measurement procedure. t h e B a r r & S t r o u d t r e e measurement procedure.  be s e e n  from  between  actual  sample  cannot  be  Again,  however,  later,  i t  size  column  cruising  the variation  methods.  i n t h e sample  obtained  controlled  2 of tables  rigidly  i f the block  sizes  at the  i n the field,  minute  eliminate  extra  sample  trees  a s was d o n e  2,  marking  It  office  i s  note  sample  should  of  the  as mentioned  i s t o be r e t u r n e d  five  5,  o f t h e 3-P c r u i s e .  termination  simple  activity).  2 through  Particular  i s a  the  ERROR (%) 23.5 10.9 15.4 11.7 21 .6 14.0 24.2  95% LOWER 309. 367. 316. 380. 316. 277. 303.  1 ) 2) 3) R . E S T 1) 2) 3) represents represents represents As  3  TOT  PRISM 3-P  n 2) 3)  RESULTS  be The  cruise earlier.  t o f o r dendrometry  procedure  f o rblock  difficult  HM  to  t o randomly (see table assess  the  43  probability expected and  of  obtaining a  from  this  study,  the  study  was  possibility  of  because  information.  The  implications  if  concurrently  with  field  the  method  sample in  obviously discover given A  also  prohibits  block  should  study.  which  because  designed  to  this  happening  has  be  activity  the  E r r o r s range  sampling  technique  practical  method  to  time)  i t  takes  achieve  given  three  basic  to  first  step  method  i s to  i n each  C,  for  sampling)  ratio  e s t i m a t i o n ) . For volume  measurement, ratio  C  and  block,  the  given given  point  table was  small  yield  such  much to  such  to  raw  most  greater be  done in  3-P  cases.  The  by  each  34.1%.  cruise  This  times  efficient  the  examine  to  for  efficiency  the  precision.  33%,  for  relaskop  tree  measurement Second,  the  precision  given  the  are  C  to  the  a  To  of  total  cost  do  requires  obtain  stand  and  so  Barr  volume  sample the  (or  and  table 35%,  was  case  case  3-P  and  was  34%.  For  for  relaskop  tree and  C  28%,  Stroud  coefficient  ( i n the  average  C  variation  of  measurement  measurement for Barr  and  of  29%. C  was  Stroud  37%. sizes  needed  variability  estimated  ( i n the  the  of  expected  conditions  sampling  for  an  predictor  t r e e measurement, was  coefficients  t r e e mesurement  estimation with  34%,  field  a  to  average  the  point  For  so  obtained  10.2 the  was  than  steps.  variation,  with  of  larger  variation in  compare  is  3-P  from  i s the  techniques  of  common  precision  comparison  sampling  each  is  considered  affected  direct  size  not  different  for  sample  or  size.  very  The  smaller  the  dendrometry  and  sizes  this  size  p r e d i c t i o n s (another  procedures),  varying  sample  separately  to  (measured f o r each  obtain as  C)  method.  the  desired  encountered  in  44  Third, separate the  average  values  activities  activities  must  will  for  be  be  a  the  time  modeled. function  to  complete  The  time  to  of  sample  each  complete size,  of  the  some  others  of  will  not. In  point  described "in" of  with  trees  for  will  measured  for  the  each  average  block,  and  plots  study  a  that  distance  to to  the  number  that  sample  square,  so  sizes. the  cut  a  this  plots  p r o v i d e good  shape  essence, are  cruise  The  coverage  of  is calculated  and  to  the  arranged  on a  types  which manual  points  for  i t  will  type  is  extrapolate  i n meters  in a  of  of  used  necessary  a  the  points in  this  times  sample  to  size  systematic  b l o c k . The and  The  largely  shape  shapes  square  the  hours.  number  paper,  is  encountered.  the  the  be  species  for  i s 0.1655  block  after  of  species displays  of  i s used  must  forest  activity  size)  trees  cruising  i n one  forest  function  that  the  one  1.1105  sampling  trees  of  number  was  simplicity,  chaining  block  the  number  for height  installed.  In  chained  the  degree,  be  For  this  plot  The  number  average  height/dbh  species  that  tree  complete  lesser  one  30  i n a l l the  a  (or  in  adequately  the  developed.  type.  only  relationship to  be  forest  per  of  on  recommends  equivalently,  must  be  must  Service  each  to  estimated,  fashion  types  distance  block  of  time  the  to complete  encountered  or  to  time  is  same mean  study  average  forest  time  were  larger  The  function  assumed  of  the  this  i s dependent  necessary  function  a  In  height. This  height/dbh  time  is  activity.  in  encountered,  The  and  activity  p r o v i d e d the  is obtained.  Forest  be  sweeping  average,  eight,  be  species  same  the  relationships  B.C.  initially  or  was  differing  height/dbh  simple  plot  this  activity  of  a  per  " i n " trees  hours  in  sampling,  total  multiplied  by  45  the  average  meter  chaining  obtained The  in this  components  essentially complete size  the  the  constant  per meter.  study,  same  so  The  to predict  relationship  strong  theoretical  grounds.  strips  of  more  a given,  predictions increasing  go the  block  increase  in  the e f f e c t i v e  increase  in  t h e amount  fitted  regression  volumes The  time  number The  of t r e e s  time  largely of  a  to  made,  relationship  so  is  of r e l o c a t i n g  marked  while  block also the  strip  selected  3-P  may  thus,  linearly.  because  occur  in  clumps,  linear The  estimate  sample  size.  chaining, i s  size. the  along  i s missed.  By  strip  which  easiest strips  way  of the  when t h e length i s  t o walk  be n o t e d might  The  the  activity,  i t takes  should  to  block  the e f f e c t i v e  It  a  a n d n o t t h e number  i s t o walk  the time  linear  f u n c t i o n of the  with  with  linear  tree  linearly  observations.  as with  f o r the p r e d i c t i n g  linearly,  linearly,  directly  traveled,  trees no  is a  in  and the  strip.  necessary  trees,  be  the  four  on  traversed  producing  upon  with  linear  ( t o o wide  along  chiefly  to  so t h a t  earlier  i s increased with  vary  t h e sample  i s increased  increased  sample  fairly  a corresponding  activity vary  is  to  block  directly  t o be  thus  are  time  kept  inefficient),  the time  i s based  was  vary  width  t o walk  the distance  predicting,  presented  size  locate  is  length,  and w i l l  hypothesized  method  argument  strip  i t will  Density will  The  f u n c t i o n of  block  produce  the marking  f u n c t i o n of  stops  will  a block  t o mark,  necessary  narrow  predicting  on  to complete  the  constant  of time  line  for a l l trees  Since  too  size  a  i s hypothesized  or less  wild,  volumes  per  estimation  together.  i s largely  time  used.  ratio  be d e s c r i b e d  activity  chaining  was  and  of t r e e s per h e c t a r e .  the time  size.  average  hours,  sampling  and w i l l  predicting  An  0.0074  f o r 3-P  a n d t h e number  block  time  that  along trees  affect  the  46  location  time.  average,  the  However, sample  fashion  as  with  fitted  regressions  differing  observations,  dendrometry  trees  that  Stroud, to  14,  than  varied  with  the  relate  relationship  This  is  time  the  on  Brickell per when  was  using  samples trees  with  tree  to  of  used  3-P  accounted of  of  measure  a  each  to  one  measurement  effect  on  the  amount  The  of  per  and  per  tree.  simply  less to  than  1986).  was  and  of  etc.  The  average  that  in  by time  general,  because than to  the much  selected  appear the  high  is  simple  probability  measuring  this  Indeed,  reported  this  spent  5  variation.  also  found  did  from  topography,  expect  this  and  height.  the  We  method  Barr  made  were  greater  of  complete  dendrometer  a  number  were  trees  would  the  complete  Attempts  smaller  with  time  It  to  four  more  trees,  Thus,  eight  ranged  to  dbh  phenomenon  the  much  for  a  for  height)  50%  account  with  (a  to  the  and  the  tree  dbh  method.  3-P.  selected  and  (i.e.,  tree  a_l  time  relaskop  neighboring  estimation,  compared are  et  the  time  for  branches  3-P,  of  the  Thus,  upon  from  the  tree  failing  In  ratio  per  based  that  measurements  trees.  for  found size  spent  for  the  times  function  measurements  was  Gregoire,  ratio  when  in  stem It  are  on  distributed  estimation.  Finally,  For  that  well  locating  largely a  i t s surroundings  1976;  tree  is  8.7.  and  required  estimation.  of  a  observations  measured.  result  boles  dependent  be  time  best  brush,  methods  ratio  in  ratio  measurement  number  the  for  predict  four  assumed  occur  to  number  averaging  further  will  used  activity  must  the  activity  to  from  is  selected  i.e.,  observations the  trees  trees  tree  i t  large small  have  trees  as  an  selected  estimation. pertinent  estimation  are  as  r e l a t i o n s h i p s developed follows:  for  3-P  and  ratio  47  LT  =  .11735  + .88765 A  r  2  C  =  .6184  p-value  = . 02  LT  = 0.1889  + 2.7950 A  r  2  D  =  .6879  p-value  = . 01  = 0.0792  + 3.0433 A  r  2  -  .8608  p-value  = . 10  PT MT  3 p  =  .02589  hours/tree  MT  =  .02094  VT  3  p  = .1782  VT  R  =  . 1 906  RT  3 p  = .4175  RT  =  .4615  1!  R  BT  3 p  = .7619  BT  =  .7395  1!  R  R  hours/tree I!  where, LT  C  A  = block  r  =  2  time n e c e s s a r y to locate a l l sample trees on a given size block, A i n h a , when carrying only clinometer and chain. size  = c o e f f i c i e n t o f d e t e r m i n a t i o n w h i c h c a n be i n t e r p r e t e d as t h e decimal f r a c t i o n of the total variation that i s e x p l a i n e d by t h e r e l a t i o n s h i p .  p-value = value LT  the p r o b a b i l i t y of observing a o f r , under t h e h y p o t h e s i s o f no  more extreme correlation.  = t i m e n e c e s s a r y t o l o c a t e a l l s a m p l e t r e e s on a g i v e n block size A , i n h a , when carrying a tripod and either of the relaskop o r Barr & Stroud.  D  PT  = t h e time n e c e s s a r y t o o c u l a r l y p r e d i c t a l l t h e t r e e s on a b l o c k o f A h e c t a r e s  t h e volumes of in size.  MT  3 p  ,  MT = the average time n e c e s s a r y t o mark a s a m p l e tree during a 3-P c r u i s e , o r d u r i n g r a t i o e s t i m a t i o n r e s p e c t i v e l y , f o reasy l o c a t i o n later  VT  3 p  ,  V T = The average time n e c e s s a r y d u r i n g 3-P or ratio estimation e n t r y i n t o a volume t a b l e  RT  3 p  ,  RT = t h e time n e c e s s a r y t o measure a t r e e d u r i n g 3-P o r r a t i o e s t i m a t i o n r e s p e c t i v e l y , w i t h t h e widescale relaskop  BT  3 p  ,  B T = t h e time n e c e s s a r y t o measure a t r e e Barr and Stroud dendrometer during 3-P estimation, respectively,  R  R  activity  R  estimate  given  total  t o "measure" a respectively,  tree for  R  Fourth,  the  i n hectares  the  t h e sample  cruise  time  time  size by  necessary  to  with the or ratio  complete  each  p r e v i o u s l y c a l c u l a t e d , and d e r i v e summing  a l l the  times  f o r the  48  activities.  This  complete  cruise  a  twenty, method in  on  complete  below its  for  a  five  efficient  than  variations  i t  sizes  ratio  results  a  objectives,  technique hectare block than  using is  block  sizes, that.  to  of  slightly sizes, then  less but  less  more  when  a size  efficient becomes more  efficient  again  less  only  its  up  to  that  it  small  trees  equal  probability  trees  than  It  is  for  meet  ratio This cruise  interesting  tree  efficient  a  3-P.  i s used. to  point  When  with  employing  the  than  point  a l l  found  2  with  estimator  as  with  of  necessary  Stroud  Figure  trees.  its efficiency.  and  of  large  smaller  3-P  any  of  p r e d i c t i o n s when  sample  Barr  selected  time sizes  with  with  i t was  volumes  the  block  sampling  volumes  to  slightly  that  study  each  takes  sizes.  be  point  this  are of  decreasing the  In  for  block  seen  than  predict  trees  than  larger  thus  is  i t  sampling  to  of  graphically  estimation  found  out for  representing  these  to  3P.  cruise  ocularly predict  selection  greater  in  that  hectares.  variability is  in  was  efficient  hectares  time  3P  time  times  displayed  curve  ratio  i t  12  the  indicates that  efficient  i t is  the  are  sampling  because  to  to  19  v a r i a t i o n s of  the  comparing  estimation,  the  estimator  note  three  than  in  point  estimation 3-P  0.5  results and  required  precision  from  below  This  i s more  of  consistently  Hence,  a  graph  difficult  resulting  -15%  the  representing  are  i s more  Ratio  using  curves  hectares.  similar  more  or  estimate  sampling  complete  sampling.  is  to  ranging  cruise  variations  block  +  sizes  the  3-P to  shows a  for  point  that  takes  done  i t s v a r i a t i o n s . The 1  Note  it  block  and  figure  was  measurement  sampling for  block  to  two  sizes  in  one  hectare greater  Figure 1. T o t a l c r u i s e t i m e f o r p o i n t s a m p l i n g u s i n g t h r e e t r e e measurement t e c h n i q u e s , given variability.  c o m p a r e d t o 3P the observed  50  Figure 2. T o t a l c r u i s e estimation using three observed variability.  times f o r p o i n t sampling compared t o r a t i o t r e e measurement t e c h n i q u e s , given the  o  o i 0"08  i  1  O'OZ.  0 09  (SJI|  1 O'OS  'uaiu  1  00*  1  O'Of  z) 3kNll 3Sind3  1  003  1  O'Ol  1V101  r O'O  51  This  is  making the  the a  smaller  smallest  displaying because  be  is  more  block  cut  to  used)  estimation  using  considered,  then  Kozak  there  times  is  only  height/dbh  of  been or  measured  in  for  necessary  to  3  measurement  far  field,  a  comparison  techniques. •  quickly,  If  using  3-P  sampling  equations  hectares. tree  as  If  well 3-P ratio  volumes than  of  under  just  a  and  is  point eight  equations  accurate by  an  then  efficient  those  for  point  encountered be  trees  When  then  may  be  precise  Demaerschalk  with  of  sampling 3-P  assume  the  for  for  two  this  sampling  This  or  logically  impact point  in  developed.  30  curve.  complete  in  so  must  The  out  curve  and  (1986).  species  height.  the  of  (taper)  where as  2  in  characteristics  obtain  volume  sampling  i s considered,  sizes  such  levels  taper  i s more  cases  approximately  the  or  figure  eight  to  block  in  Ormerod  one  rapidly.  approximately  tables  reported  the  measurements  developed,  height/dbh  encountered  figure  volume  from  or  correction)  for point  sample  equations  to  relationship  measurement reliable  up  satisfactory  (1977), The  to  seen  increases,  tree  population  needed  point  estimator  Use  have  a  be  ratio  a  hectares.  equations  can  equations  estimator  completely  As  volume  sampling  of  samples  (volume  up  (finite  approached  obtain  efficient  of  size  are  only  to  fpc  complete  block  table  the  size.  population  volume  may  of  number  times  as  infinite a  result  60  block  to  three 90  trees  using  the  is  on  form  be  time  illustrated different  a are  must the  a  the  species  development cruise  which  necessitates  height  or  that  in  tree  F i g u r e 3. T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g t h r e e s p e c i e s c o m p a r e d w i t h 3P u s i n g t h r e e t r e e methods, g i v e n the observed variability.  i n stands with measurement  53  It  will  is  now  4  be  seen  more  that  different  tree  efficient  than  this  coefficients each  considered (Mesavage  to  coefficients coefficient 32  percent.  percent  be  somewhat  or  variation  and  their  effect  for  point  sampling  procedure. efficient as  compared  ratio  3-P  The  a  required  actually  slightly  because  less The  of  cruise  total  tree  virtually  size  sampling  has  figure  3).  There  is  to  is  time  than spent is  for  technique  coincide.  a  complete  less  volumes  given  in  using  the  drawn  on  the  around  in  figure  is 14  choose  for  that 3-P  5  measurement  3-P  of  50  facts  more  hectares  variability  sample  and  the  these  seen  ratio  however,  estimation  Also,  nearly  to  achieve  approximately  which to  is  beginner  can  equation  needed  employing  a  of  variability  time  slight  be  little  the  were  can  by  This  variation  observed  cruise  ratio  of  volume  a  so  of  was  to  achieved  percent.  increased the  different  percent.  cruisers  block  when  for  necessary  30  time  the  of  of  implications  11,  difference  measurement  The  more  of  time  the  hectares.  variation  coefficients  now  effects  20  plot  a l l  six  of  as  is  Figure  of  indicative  only  time  criteria.  prism  using  the  estimator  time  amount  cruising  3-P  sizes  the  low  uncommon.  and  that  to  (see  of  total  point  considered or  not  on  Note than  as  with  estimation  experienced  typically,  are  block  methods  hectares.  estimation  Ratio  and  measurement  eight  around  high,  variation  more  to  was  Typically,  More  ratio  the  study  tree to  coefficient  this  of  up  on  The  in  of  up  consider  variation  1970).  the  methods.  may  cruise.  predictor  for  sampling  one  of  sizes  situation  point  of  any  block  measurement  Additionally,  the  with  e f f i c i e n t in  illustrates  complete  3-P  is  between  a  predictions. estimation a  3-P  tree if  cruise, selection  the  using  same a x e s  is  curves  the  they  same would  F i g u r e 4. T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g i n stands with t h r e e s p e c i e s compared w i t h r a t i o e s t i m a t i o n u s i n g t h r e e t r e e measurement methods, g i v e n t h e observed variablity.  o  o i  0"08  i  0 0L  i  i  0'09 0 09, (SJI| «U9LU  i  O'OV  i  00£  i  003  1  O'Ol  z) 3WI1 3Sind0 1 V 1 0 1  r  O'O  F i g u r e 5. T o t a l c r u i s e times f o r point sampling i n stands with t h r e e s p e c i e s c o m p a r e d w i t h 3P u s i n g t h e v o l u m e e q u a t i o n t r e e measurement method, a s s u m i n g t y p i c a l variability.  o i  O'OOt  1 0 08 ( S J L J  1 0*09 'U8LU  1  0 0V  h  1  00Z  z) IkNIi 3Sind0 1 V 1 0 1  O'O  6  56  Therefore,  a  estimation,  given  not  these  hypothetical  sampling  coefficients  the  times  and  not  r e p r e s e n t what  some  absolute value,  i t must  may  in  terms  relative valid  for  no  matter time.  point long  given  the  block  Note  that  in figure  amount  with of  ratio  variation  to  normal  expressed  as  rate  cut  although  the  s l o p e s of  up  3-P to  have  block  same  is  size  foregoing discussion sampling  when  compared  to  lose  their  superiority  been  known  before  size  is  around be  12  point  is to  in that 15  encountered  as  is  the this  5 are  more  3-P  as  as  block  practical  field.  in  the  judged  When a l l by  0.5  figure  changed  and  differences than  6. the  have point  5.  certainly  does  twice  relationship  efficient  figure  be  a  times  cruise  them  the  have  at  be  pace.  appears  relative  However,  larger  to  multiplying  curves  in  to  the  remain  cruise  would  normal  that  arrive  judged  study  of  hectares, given i n the  to  man  realistic  will  estimated  i s as  that  technique,  sampling.  given  by  the  still  shows  is  fraction),  the  block  methods  50%  size  changed,  estimator  the  of  a decimal  and  the  in this  two  reiterated  i s necessary  pace  time  efficient  to  work  corrected  the  likely  the  specific  consider  be  the  that  are  not  an  time  a  differences  The  of  Then,  absolute  sampling  appear  at  that  work  suppose  performed  cruise  and  the  for a  would  illustrate,  sizes.  rating  between  rating  are  between  been  times  (the  To  reported here  existing  what  sampling as  have  the  of  differences  "normal"  be  point  Although  times  to  comparing  given.  crew  as  graph  ratio was  appears  estimation,  suspected,  sizes.  upper typical  to  What  limit  they  has to  not  block  variabilities  57  F i g u r e 6. T o t a l c r i u s e t i m e s f o r p o i n t s a m p l i n g in stands with t h r e e s p e c i e s c o m p a r e d w i t h 3P u s i n g t h e v o l u m e e q u a t i o n m e t h o d , a s s u m i n g t y p i c a l v a r i a b i l i t y , and a j u s t e d t o n o r m a l p a c e .  CONCLUSIONS  From sampling cutting  the  block  means  block  this  up  up t o  by  means  3-P  more  slightly  be  than  hectares  said  point  for  that  of  a l l the  than  equation  point  general,  precise  in  tree  I f one c o n s i d e r s t r e e measurement  r e l a s k o p , then  a volume  3-P  sampling  i t i s more  efficient  s i x h e c t a r e s . I f one c o n s i d e r s o b t a i n i n g  In  more  i t can  efficient  five  tested.  efficient  hectares.  study,  more  to  of the wide-scale  volumes  eight  sizes  techniques  sizes  i s  of  i s unconditionally  measurement by  results  sampling  i t  than  (or taper  was  ratio  tree  equation),  in block  discovered  sizes  that  in  then up t o  3-P  is  estimation  (mean-of-ratios  Barr  Stroud  estimator). Ratio  estimation  dendrometer than If  point  one  ratio  to obtain tree sampling,  estimation  volume  up  When height/dbh  tree  was  was  3-P  one  method more  estimation  eight  i s also  six  more  point  efficient  of  variation.  measurement  technique,  efficient  hectares.  possibility  f o r more  six  than  efficient  than  point  Considering  tree  volumes,  sampling  efficient  Under than  of  the ratio  i n block  having  one s p e c i e s  than  and e l e v e n  method chosen. more  less  coefficient  obtaining than  t o be  optical  sizes  hectares.  i s more  between  measurement  of  efficient  relationships  to  be  of  considers the  sampling up  sizes  to  and  found  the observed  found  to block  to approximately  sizes  volumes  given  was  equation  estimation  then  the  considers the relaskop as the tree  sampling  up  using  point  to  develop  i n the  sampling  cruise, in block  hectares, depending this point  on t h e  hypothesis, sampling  i n the  ratio same  59  block  sizes  method  likely  to  estimation 14  3-P,  depending  again,  on  the  tree  measurement  chosen.  Under  of  as  the be  hypothesis encountered  can  be more  of  typical  in  the  efficient  coefficients  field, in block  of  then  3-P  sizes  up  variation and  to a  ratio maximum  hectares. These  similar  conclusions  stand  conditions  apply  broadly  to those  where  to  any  area  t h e methods  exhibiting  were  <  tested.  60  LITERATURE  CITED  BCMF.  1976. Whole stem c u b i c m e t r e v o l u m e e q u a t i o n s a n d t a b l e s centimetre diameter c l a s s merchantable volume f a c t o r s . F o r . Inv. D i v . B r i t i s h Columbia M i n i s t r y of F o r e s t s . Dept. of F o r e s t s . 4 p . , 64 t a b l e s , 13 f i g s .  BCMF.  1982. Forest service cruising compilation. Province of British F o r e s t s . 117 p . , a p p e n d i c e s .  Behre, C.E. 1927. Form their application.  procedures Columbia  and cruise Ministry of  c l a s s t a p e r c u r v e s and volume J . A g r i c . Res. 35:673-744.  B o n n o r , G.M. 1 9 7 2 . 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F o r . 70(4):216-219.  1 9 8 2 a . 3-P sampling F o r e s t r y . 36(0:25-35.  J.C. 1982b. E r r a t u m . F o r e s t r y . 36(3):219.  H u s c h , B., C . I . M i l l e r , 2nd e d . J o h n W i l e y lies,  Berger. surveys.  Better  J a m e s , C.A., standing  the d e v i l  you  don't  the  you  know!  devil  a n d T.W. B e e r s . 1 9 7 2 . F o r e s t & S o n s , New Y o r k , 210 p .  1978. I n c r e a s i n g estimation Chron. 54(0:42-43.  vs.  efficiency  a n d A. K o z a k . 1984. F i t t i n g t a p e r t r e e s . F o r . Chron. 60(6):157-161.  Mensuration,  i n 3-P  cruises.  equations  from  J e f f e r s , J.N.R. 1956. B a r r a n d S t r o u d d e n d r o m e t e r t y p e F P - 7 . F o r . Comm. R e p . on F o r e s t Research f o r the year ended March, 1955:127-136. IN B r i c k e l l , J . E . 1976. ( s e e a b o v e ) . J o h n s o n , F.A., W.G. Dahms, a n d P . E . H i g h t r e e . o f 3-P c r u i s i n g . J . F o r . 6 5 : 7 2 2 - 7 2 6 .  1967. 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Bulletin, Nigata Universtiy Forests, No. 15., 99-103. IN For. Abs. Y o c o m , H.A., a n d D.A. Bower. 1975. E s t i m a t i n g i n d i v i d u a l tree volumes with Spiegel Relaskop and Barr and Stroud dendrometer. J . F o r . 73(9):581-582,605.  APPENDIX  Let,  A = total G = total  cruising basal area  r = r a d i u s of tree N = total R = plot  area  i n ha,  of a l l t r e e s i n stand  2  (m ),  ( i n m),  number o f t r e e s i n s t a n d , r a d i u s f o r t r e e of r a d i u s r i n meters.  Then  fjT i  r 2  G = 1  It  i s known  (Husch, M i l l e r ,  where F = b a s a l a r e a "gauge c o n s t a n t " Solving  Beers  1972, p.263)  that  2  F  = 2500k  factor  of p r i s m  in m  2  p e r ha a n d k i s t h e  (k = 2 r / R ) .  f o r R i n terms o f F: F = 2500k  2  •^F/50 = k  y/f/50  = 2r/R  )00rAjF  Now,  = R  l e t us d e f i n e Q as t h e sum o f t h e a r e a s  generated  a r o u n d e a c h t r e e by any F f a c t o r  o v e r l a p 50 e a c h p o i n t i n t h e f o r e s t these  .  circles,  sometimes  of the c i r c l e s  prism  i s covered  (these  areas  by one o r more  none).  nR 2  Q 1  f. i  = J^riOOOOriVF = 10000G/F. To p u t t h i s  on a h e c t a r e b a s i s :  2  1 ha/10000m *10000G/F  = G/F.  And, any  l e t us  define  m  as  the  number  of  circles  falling  c  point, m  So, If  average  as we  i s known, call  q  the  = Q/A  basal  area  per  total  area  of  E(q)  = E(  =  G/FA.  hectare tree  ° £  K  (G/A)  circles  =  Fm.  i n the  sample,  j  i  Q_  E(nK ) M  N Q  ', E(K )  n  N  where  E  number per  denotes of  expectation,  trees  point  on  i n the  expressed  as  a  n  j , and  sample.  Let p  K  Qnm N  i s the  point  decimal.  =  M  w  sample  i s the  M  = q/Q  , or  size,  mean  Kj  number  cruise  i s the of  trees  intensity  Then,  E(p)  = E(q/Q) =  =  E(q)/Q  nm/N nG NFA  Now,  call  sampling  error  of  t h e mean, E  where  t  = an  S = M  appropriate  Standard  error  value of  where But,  S n/N  =  standard  = p  w  ng/FA  S  of  M  Student's  t-statistic  volume/ha  estimate  S ^ ( 1-n/N)  =  deviation or  t  average t  E  =  E.  the  of  plot  average  volume/ha  cruise  estimates.  intensity.  Substituting  this  into  the previous  t S E  expression  gives  -yJil-nq/Fh)  =  t  1-ng/FA)  S E  t S (1-ng/FA) 2  2  =  n  2  E  2  -t S n  2  2  = E  2  2  E FA  2  2  2  t S g  t S  (1 +  n  2  t S ng  2  ) = E  2  t S  2  E  2  2  ~1T n  = (1  2  +  E  t  2  t S g)  2  S  2  2  A  F  n 2  2  AFE +gt S  Finally,  multiply  2  where  V  which  gives  M  by  = t h e mean  M  i/v  M  volume  2  2  per hectare  : t n  completes  the  C  A  F  = AF  which  i/v  D  2  proof.  2  +  2  gt C  2  squared,  


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