﻿equation. 
  The 
  early 
  work 
  of 
  Howell 
  and 
  Reveal 
  was 
  per- 
  

   haps 
  the 
  most 
  unique 
  in 
  that 
  the 
  number 
  of 
  4-foot 
  wood 
  

   segments 
  was 
  used 
  as 
  a 
  predictor 
  variable. 
  Some 
  form 
  of 
  

   diameter 
  measurement 
  of 
  the 
  main 
  stem 
  was 
  almost 
  a 
  

   unanimous 
  choice 
  for 
  a 
  predictor 
  variable, 
  but 
  the 
  exact 
  

   place 
  of 
  this 
  measurement 
  has 
  been 
  a 
  point 
  of 
  debate. 
  

   Unfortunately, 
  any 
  direct 
  comparison 
  of 
  all 
  the 
  P-J 
  vol- 
  

   ume 
  and 
  biomass 
  models 
  would 
  be 
  futile 
  unless 
  a 
  

   specific 
  study 
  were 
  designed 
  to 
  take 
  all 
  the 
  different 
  

   measurements 
  on 
  the 
  same 
  P-J 
  trees. 
  Also, 
  different 
  

   standards 
  were 
  used 
  for 
  the 
  minimum 
  diameter 
  of 
  

   branch 
  material 
  included 
  in 
  the 
  volume 
  and 
  biomass 
  

   equations. 
  

  

  This 
  study 
  resulted 
  from 
  efforts 
  in 
  multiagency 
  

   cooperation 
  required 
  by 
  1970's 
  "environmental 
  era" 
  

   legislation. 
  Its 
  design 
  mimicked 
  that 
  used 
  by 
  Clendenen 
  

   (1979) 
  in 
  New 
  Mexico. 
  Because 
  the 
  study 
  was 
  closely 
  

   linked 
  to 
  on-going 
  inventories, 
  it 
  was 
  not 
  possible 
  to 
  

   carefully 
  test 
  past 
  work 
  or 
  propose 
  new 
  ways 
  to 
  esti- 
  

   mate 
  pinyon-juniper 
  volume. 
  Instead, 
  a 
  few 
  simple 
  

   measurements— 
  basal 
  diameter, 
  crown 
  dimensions, 
  total 
  

   height, 
  and 
  number 
  of 
  stems— 
  important 
  in 
  past 
  work 
  

   were 
  made 
  on 
  a 
  random 
  subsample 
  of 
  aU 
  trees 
  inven- 
  

   toried. 
  This 
  paper 
  describes 
  the 
  search 
  for 
  the 
  best 
  vol- 
  

   ume 
  equations 
  from 
  the 
  data 
  provided 
  by 
  the 
  multi- 
  

   agency 
  pinyon-juniper 
  inventories. 
  

  

  DATA 
  COLLECTION 
  

  

  Data 
  were 
  collected 
  for 
  P-J 
  trees 
  in 
  Nevada, 
  Idaho, 
  

   Utah, 
  Colorado, 
  South 
  Dakota, 
  and 
  Wyoming 
  (figs. 
  8-11 
  

   in 
  appendix 
  A). 
  The 
  data 
  also 
  included 
  some 
  mountain- 
  

   mahogany, 
  oak, 
  and 
  other 
  hardwood 
  species 
  found 
  in 
  the 
  

   woodland 
  types. 
  Table 
  5 
  in 
  appendix 
  A 
  contains 
  a 
  sum- 
  

   mary 
  of 
  the 
  data 
  collected 
  by 
  species 
  and 
  area. 
  QuantUes 
  

   of 
  key 
  variables 
  and 
  percentage 
  of 
  single 
  stems 
  are 
  

   Hsted 
  to 
  illustrate 
  the 
  diversity 
  of 
  the 
  data 
  from 
  the 
  

   sample 
  areas. 
  

  

  The 
  trees 
  were 
  selected 
  as 
  a 
  subsample 
  of 
  an 
  inventory 
  

   using 
  0.1-acre 
  plots 
  located 
  on 
  a 
  5 
  000 
  m 
  grid 
  (some- 
  

   times 
  2 
  500 
  or 
  10 
  000 
  m). 
  Individual 
  trees 
  were 
  sampled 
  

   by 
  diameter 
  size 
  class 
  and 
  species 
  on 
  each 
  plot. 
  At 
  most, 
  

   three 
  trees 
  of 
  each 
  species 
  were 
  selected 
  in 
  the 
  diameter 
  

   classes 
  of 
  3 
  to 
  9.9 
  inches, 
  10 
  to 
  17.9 
  inches, 
  and 
  greater 
  

   than 
  18 
  inches. 
  Measurements 
  recorded 
  for 
  each 
  tree 
  

   were 
  diameter 
  at 
  root 
  collar 
  (DRC), 
  total 
  height 
  (HT), 
  

   maximum 
  (CRMX) 
  and 
  minimum 
  (CRMN) 
  crovra 
  di- 
  

   ameter, 
  and 
  number 
  of 
  stems 
  (STEMS) 
  3 
  inches 
  and 
  

   larger 
  within 
  the 
  first 
  foot 
  above 
  DRC. 
  If 
  a 
  tree 
  forked 
  

   at 
  the 
  ground 
  line, 
  an 
  equivalent 
  DRC 
  (EDRC) 
  was 
  com- 
  

   puted 
  from 
  the 
  DRC 
  of 
  each 
  fork: 
  

  

  EDRC 
  = 
  VDRC2+DRC2+DRC|+. 
  . 
  . 
  

  

  A 
  gross 
  volume 
  that 
  included 
  bark, 
  wood, 
  and 
  dead 
  

   branches 
  (from 
  ground 
  line 
  to 
  1.5-inch 
  nunimiim 
  branch 
  

   diameters) 
  was 
  estimated 
  for 
  each 
  tree 
  by 
  a 
  visual 
  tech- 
  

   nique. 
  This 
  volume 
  estimate 
  was 
  obtained 
  by 
  visually 
  

   classifying 
  each 
  stem 
  and 
  branch 
  segment 
  into 
  a 
  2-inch 
  

   by 
  2-foot 
  class. 
  Ruber's 
  formula 
  was 
  used 
  to 
  compute 
  

   the 
  volume 
  of 
  each 
  segment. 
  Segment 
  volumes 
  were 
  then 
  

   summed 
  to 
  obtain 
  the 
  volume 
  of 
  each 
  tree. 
  

  

  The 
  technique, 
  called 
  visual 
  segmentation, 
  has 
  proved 
  

   an 
  adequate 
  base 
  for 
  constructing 
  volume 
  equations. 
  

   Born 
  and 
  Chojnacky 
  (in 
  preparation) 
  compared 
  volume 
  

   equations 
  built 
  from 
  visual 
  estimates 
  to 
  actual 
  volume 
  

   measurements 
  of 
  destructively 
  sampled 
  trees. 
  The 
  equa- 
  

   tions 
  using 
  visual 
  estimates 
  predicted 
  mean 
  volume 
  per 
  

   acre 
  within 
  to 
  —9 
  percent 
  of 
  the 
  actual 
  measurements. 
  

  

  In 
  theory, 
  visual 
  volume 
  estimation 
  should 
  only 
  result 
  

   in 
  random 
  error 
  among 
  aU 
  the 
  volume 
  estimates. 
  Ran- 
  

   dom 
  error 
  measurements 
  for 
  a 
  dependent 
  variable 
  (in 
  

   this 
  case 
  the 
  visual 
  volume) 
  present 
  no 
  difficulties 
  when 
  

   developing 
  volume 
  equations 
  by 
  regression 
  (Neter 
  and 
  

   Wasserman 
  1974, 
  p. 
  167). 
  The 
  consistent 
  negative 
  error 
  

   found 
  in 
  the 
  field 
  test 
  of 
  visual 
  volume 
  estimation 
  indi- 
  

   cated 
  a 
  discrepancy 
  between 
  theory 
  and 
  practice, 
  but 
  

   not 
  enough 
  to 
  justify 
  increasing 
  field 
  sampling 
  costs 
  10 
  

   to 
  20 
  times 
  by 
  felling 
  trees 
  to 
  measure 
  actual 
  dimen- 
  

   sions 
  of 
  each 
  volume 
  segment. 
  

  

  AU 
  field 
  procedures 
  used 
  in 
  this 
  study 
  were 
  from 
  

   manuals 
  used 
  by 
  the 
  USDA 
  Forest 
  Service, 
  Forest 
  Sur- 
  

   vey 
  Unit 
  in 
  Ogden, 
  UT 
  (USDA 
  1983). 
  AU 
  field 
  personnel 
  

   involved 
  in 
  the 
  study 
  used 
  the 
  same 
  manuals, 
  but 
  it 
  was 
  

   not 
  possible 
  to 
  uniformly 
  monitor 
  quaUty 
  control 
  for 
  aU 
  

   agencies 
  and 
  aU 
  crews. 
  

  

  DATA 
  ANALYSIS 
  

  

  The 
  volimie 
  modeUng 
  process 
  involved 
  four 
  steps: 
  (1) 
  

   identifying 
  important 
  predictor 
  variables, 
  (2) 
  choosing 
  an 
  

   equation 
  form, 
  (3) 
  selecting 
  the 
  number 
  of 
  equations, 
  and 
  

   (4) 
  determining 
  the 
  reUabUity 
  of 
  the 
  equations. 
  Before 
  

   any 
  analysis 
  was 
  done, 
  data 
  were 
  grouped 
  by 
  species 
  

   into 
  two 
  large 
  geographic 
  areas. 
  This 
  was 
  done 
  at 
  the 
  

   request 
  of 
  the 
  study 
  designers. 
  Nevada, 
  Idaho, 
  and 
  Utah 
  

   (west 
  of 
  the 
  Wasatch, 
  Parvant, 
  and 
  Tushar 
  Mountains) 
  

   were 
  caUed 
  the 
  Great 
  Basin 
  States. 
  Colorado, 
  Wyoming, 
  

   and 
  the 
  remainder 
  of 
  Utah 
  were 
  caUed 
  the 
  Colorado 
  Pla- 
  

   teau 
  States. 
  These 
  two 
  areas 
  roughly 
  corresponded 
  to 
  

   the 
  geographic 
  ranges 
  of 
  the 
  two 
  species 
  of 
  pinyon 
  

   represented 
  in 
  the 
  data 
  (see 
  fig. 
  9, 
  appendix 
  A). 
  CoUec- 
  

   tively, 
  the 
  entire 
  area 
  was 
  referred 
  to 
  as 
  the 
  central 
  

   Rocky 
  Mountain 
  States. 
  AU 
  analyses 
  were 
  done 
  using 
  

   the 
  Statistical 
  Analysis 
  System 
  (SAS) 
  software 
  package 
  

   (SAS 
  1982). 
  

  

  Important 
  Predictor 
  Variables 
  

  

  Of 
  all 
  the 
  variables 
  available 
  to 
  predict 
  volume, 
  DRC 
  

   is 
  probably 
  most 
  important. 
  AU 
  previous 
  researchers 
  

   used 
  some 
  type 
  of 
  diameter 
  measurement 
  in 
  their 
  vol- 
  

   ume 
  and 
  biomass 
  equations. 
  Tausch 
  (1980) 
  and 
  Weaver 
  

   and 
  Lund 
  (1982) 
  also 
  gave 
  biological 
  support 
  to 
  the 
  

   hypothesis 
  that 
  a 
  function 
  of 
  DRC 
  is 
  proportional 
  to 
  

   stem 
  wood 
  (although 
  the 
  two 
  differ 
  on 
  the 
  exact 
  mean- 
  

   ing 
  of 
  the 
  proportionaUty 
  constant 
  in 
  this 
  relationship). 
  

   Figure 
  1 
  shows 
  the 
  relationship 
  between 
  DRC 
  and 
  vol- 
  

   ume. 
  This 
  figure 
  supported 
  findings 
  of 
  past 
  researchers 
  

   on 
  the 
  importance 
  of 
  DRC 
  and 
  was 
  characteristic 
  of 
  aU 
  

   P-J 
  data 
  avaUable 
  for 
  this 
  study. 
  

  

  An 
  attempt 
  was 
  made 
  to 
  explain 
  the 
  variabiUty 
  (ob- 
  

   served 
  in 
  fig. 
  1) 
  in 
  the 
  DRC-volume 
  relationship 
  for 
  aU 
  

   data 
  groups 
  Usted 
  in 
  table 
  5 
  in 
  appendix 
  A. 
  The 
  addi- 
  

   tional 
  variables, 
  HT, 
  CRMX, 
  CRMN, 
  and 
  STEMS, 
  were 
  

  

  2 
  

  

  