Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Variability in the relationship between leaf area and selected stem measures in Douglas fir Neumann, John A. P. 1990

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1990_A6 N48.pdf [ 5.45MB ]
Metadata
JSON: 831-1.0098054.json
JSON-LD: 831-1.0098054-ld.json
RDF/XML (Pretty): 831-1.0098054-rdf.xml
RDF/JSON: 831-1.0098054-rdf.json
Turtle: 831-1.0098054-turtle.txt
N-Triples: 831-1.0098054-rdf-ntriples.txt
Original Record: 831-1.0098054-source.json
Full Text
831-1.0098054-fulltext.txt
Citation
831-1.0098054.ris

Full Text

VARIABILITY IN THE RELATIONSHIP BETWEEN LEAF AREA AND SELECTED STEM MEASURES IN DOUGLAS FIR by JOHN A. P. NEUMANN Bachelor of Science in Forestry  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF T H E REQUIREMENTS FOR T H E DEGREE OF MASTER OF  ^R£$rRy in  THE FACULTY OF GRADUATE STUDIES FOREST SCIENCES  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH COLUMBIA 1990 © John A.P. Neumann, 1990  In  presenting  degree freely  at  the  available  copying  of  department publication  this  of  in  partial  fulfilment  University  of  British  Columbia,  for  this or  thesis  reference  thesis by  this  for  his thesis  and  study.  scholarly  or for  her  of  ^""6>r£S^  financial  SCJ&WULA  The University of British Columbia Vancouver, Canada  DE-6 (2/88)  I  I further  purposes  gain  the  shall  requirements  agree  that  agree  may  representatives.  permission.  Department  of  be  It not  is be  that  the  for  Library  an shall  permission for  granted  by  understood allowed  advanced  the that  without  make  it  extensive  head  of  copying my  my or  written  ABSTRACT  Variability (TLA)  and s e l e c t e d s t e m measurements  Douglas-fir var.  i n the r e l a t i o n s h i p  stands  menziesii)  t h a t were  approximately moisture  (Pseudotsuga  and n u t r i e n t s .  live  bark  storage  the  recent  of w h o r l s  than  area  i n three  (Mirb.)  Franco,  50 y e a r s - o l d , s p a c e d t o  A t t e n t i o n was g i v e n  width  in soil  to the effect  (MARW), c r o s s - s e c t i o n a l a r e a o f measure  of r e l a t i v e  i n t h e s t e m ) , and c r o s s - s e c t i o n a l a r e a o f annual r i n g s equal  i n the l i v e  relationship  menziesii  (ALB - a s u r r o g a t e  nutrient most  was examined  550 t o 650 s t e m s / h a , and d i f f e r e d  of mean a n n u a l r i n g the  less  between t r e e l e a f  crown  (ALC),  i n number t o t h e number on v a r i a b i l i t y  i n the  between T L A and c r o s s - s e c t i o n a l a r e a  o f sapwood  (ASW). At area  breast  height,  o f sapwood  related  plus  live  bark  t o TLA, and l i n e a r  transformed Nonlinear  ASW,  and c r o s s - s e c t i o n a l  (ASWLB) were  regression equation X  between b r e a s t nonlinear  33  height  sites.  h e i g h t was:  I n c l u d i n g D (the d i s t a n c e  and t h e c e n t e r  equation,  using l o g  between  f o r ASW a t b r e a s t  ( I = 0.856). 2  not l i n e a r l y  r e g r e s s i o n equations  variables varied significantly  TLA = 0 . 0 6 4 A S W -  the  basal area,  of the l i v e  d i d not s i g n i f i c a n t l y  crown) i n  improve t h e  regression. Tree  leaf  area  p r e d i c t i o n models u s i n g s t e m measures  from t h e base of l i v e values  than  crown  ( b l c ) had h i g h e r  adjusted  models u s i n g s t e m measures f r o m b r e a s t  R  2  height.  i ii At  the  b l c , basal  t o TLA  (adjusted  area, R  ASW,  and  ASWLB were l i n e a r l y  = 0.926, 0.908, and  2  related  0.934,  respectively). Multiplying regression  of  TLA.  best  ASW  the  The  R  measures o f  area  a t b l c as  TLA  bark  function.  higher  I n most t r e e s  the  ALC  TLA  ALC  and  area  heartwood  A quick tree angle leaf  the  independent  research  At  was  linearly  adjusted  area.  The  R  area  product  of  target  t r e e crowns was  distance  and  camera a n g l e was  tree  than d i d to  ASW.  include  a  r e l a t i o n s h i p between or  conducting  for estimating  The  major  individual  fixed distance  result in a reliable difficulty  t r e e crown w h i c h were not the  r e l a t e d to  amount of  not  p r e d i c t i o n technique.  adjacent  blc,  found  and  include  stemwood.  tree did  the  give  the  values  photographs taken at  v i e w s of  allometric  t r a n s p i r i n g l e a f mass  a l t e r n a t i v e approach using  2  strong  a given  p h y s i c a l support  from the  to  variable  i n t o the  height  s t e m measure was  suggests that  l e a f area  the  the  the  height  measures and  breast  i s r e l a t e d to a p r o p o r t i o n a l  stemwood and  at breast  t o more t h a n h y d r a u l i c  had  of  improved  t o s t e m measures s h o u l d  and  portion  ALB  model o v e r a l l u s e d  i n d e p e n d e n t v a r i a b l e ALC  leaf  by  f i t of  0.967).  of  consideration  the  TLA  r e s u l t s indicate that  relationship  improve t h e  r e l a t i o n s h i p of ASW  ALB  =  2  MARW d i d n o t  M u l t i p l y i n g ASW  fitting  a t b l c and  (adjusted  by  models.  linearity The  ASW  of  obstructed  obstacle.  tree  obtaining by  Using  a p r o b l e m b e c a u s e of  and  a fixed variable  tree heights. introduced  However, a l t e r i n g these f i x e d  positions  a d d i t i o n a l v a r i a t i o n i n t o the t r e e l e a f area  estimation. Mean s p e c i f i c l e a f area (SLA) v a r i e d s i g n i f i c a n t l y by s i t e , needle age c l a s s , and crown p o s i t i o n .  Mean SLA per  needle age c l a s s per branch can be p r e d i c t e d  with 95%  confidence and a 10% a l l o w a b l e e r r o r using samples.  s i x 10-needle  V  TABLE OF CONTENTS Page Abstract  ii  Table  .v  of C o n t e n t s  List  of F i g u r e s  ix  List  of T a b l e s .  List  of A b b r e v i a t i o n s  x xi  Acknowledgement 1.  2.  3.  xiii  Introduction  1  1.1.  Tree Leaf  Area  1  1.2.  Allometric Relationships  2  1.3.  Solar  1.4.  Objective  T r a n s m i t t a n c e and  Photography  3 ••••  3  L i t e r a t u r e Review  5  2.1.  Allometric Relationships  5  2.2.  Photography  2.3.  Destructive  2.4.  N u l l and  Materials  and  15 Sampling....  18  A l t e r n a t i v e Hypotheses  20  Methods  23  3.1.  Location  23  3.2.  Site  25  3.3.  Tree S e l e c t i o n  26  3.4.  Photography  29  3.5.  Foliar  31  Description  Samples  3.5.1. D e s t r u c t i v e  3.6.  Sampling  31  3.5.2. Sample S i z e A n a l y s i s . . . .  34  Stem Samples  35  vi Page 3.7. R e g r e s s i o n A n a l y s i s 4. S a m p l i n g  36  Analysis  38  4.1. R e s u l t s  38  4.1.1. S p e c i f i c 4.1.2. N e e d l e  Leaf Area  38  D r y Weight R a t i o  42  4.2. D i s c u s s i o n  45  4.2.1. S p e c i f i c 4.2.2. N e e d l e 5. A l l o m e t r i c  Leaf Area  45  D r y Weight R a t i o  47  Relationships  48  5.1. R e s u l t s  48  5.1.1. T r e e L e a f A r e a  ...48  5.1.2. B r e a s t H e i g h t Stem Measurements and T r e e Leaf Area  50  5.1.3. Base o f L i v e Crown Stem Measurements and Tree Leaf Area  53  5.1.4. V a r i a t i o n  54  Between S i t e s  5.1.4.1. B r e a s t H e i g h t V e r s u s L i v e Crown  Base o f  5.1.4.2. C r o s s - S e c t i o n a l  of L i v e  Area  55  Bark 5.1.4.3. Mean A n n u a l  56 R i n g Width  5.1.5. N o n l i n e a r R e g r e s s i o n 5.1.6. P r e d i c t i n g Base o f L i v e Measures  57 60  Crown Stem 62  5.1.6.1. C r o s s - S e c t i o n a l  A r e a o f Sapwood..62  5.1.6.2. C r o s s - S e c t i o n a l and L i v e Bark  A r e a o f Sapwood  5.1.6.3. C r o s s - S e c t i o n a l * L i v e Bark  Area  64 o f Sapwood 65  vii Page 5.1.6.4. C r o s s - S e c t i o n a l A r e a o f Most R e c e n t A n n u a l Sapwood R i n g s E q u a l i n Number t o t h e Number o f W h o r l s i n L i v e Crown 5.2. D i s c u s s i o n  66 67  5.2.1. Base o f L i v e Crown V e r s u s B r e a s t 5.2.2. C r o s s - S e c t i o n a l Basal Area  A r e a o f Sapwood  Height...67 Versus 68  5.2.3. I n f l u e n c e o f E c o l o g i c a l S i t e Q u a l i t y on Allometric Equations  69  5.2.4. Mean A n n u a l  71  R i n g Width  5.2.5. Number o f L i v e W h o r l s  73  5.2.6. N o n l i n e a r  74  Models  5.2.7. C r o s s - S e c t i o n a l  A r e a o f L i v e Bark  5.2.8. P r e d i c t i o n o f Base o f L i v e Crown Stem Measures 5.2.9. P o r t a b i l i t y  of Tree Leaf  With  6. P h o t o g r a p h y  76  Area  P r e d i c t i o n Models 5.2.10. C o m p a r i s o n  76  77 Other  Work  78 80  6.1. R e s u l t s . . .  80  6.2. D i s c u s s i o n  82  7 . Summary 7.1. S a m p l i n g  85 Analysis  85  7.2. A l l o m e t r i c R e l a t i o n s h i p s  85  7.3. P h o t o g r a p h y  88  Technique  8. C o n c l u s i o n s 8.1. S a m p l i n g  89 Analysis  89  8.2. A l l o m e t r i c R e l a t i o n s h i p s  90  8.3. P h o t o g r a p h y  91  Technique  vi i i Page  8.4.  R e s e a r c h Recommendations  Literature Appendix  I  Appendix  II  ...92  Cited Explanation  93 o f Symbols  L e a f A r e a Index V a l u e s  i n Box P l o t s  99 100  ix  LIST OF FIGURES Page 1.  Relationship  of G versus  probe angle  2.  Stand  3.  Courtenay s i t e  24  4.  Duncan  25  5.  Haney  6.  Examples  locations  23  site site  crown  17  26  o f whole crown  image and u n o b s t r u c t e d  image  30  7.  SLA sample s i z e s  by s i t e  40  8.  SLA sample s i z e s  b y crown p o s i t i o n  41  9.  SLA sample s i z e s  by f o l i a g e c l a s s  41  10.  NDW r a t i o  b y crown p o s i t i o n  43  11.  NDW r a t i o  b y age c l a s s  43  12.  NDW r a t i o  by s i t e  13.  Tree  14.  TLA v e r s u s  15. 16.  T L A v e r s u s (ASW*ALB)blc The r e l a t i o n s h i p o f MARW and TLA:ASWbh  54 58  17.  The r e l a t i o n s h i p  59  18.  TLA:ASWbh v e r s u s ASWbh..!  60  19.  T L A v e r s u s ASWbh  61  20.  ASWblc  63  21.  ASWLBblc  22.  (ASW*ALB)blc v e r s u s  23.  ALCblc  24.  TLA v e r s u s  25.  TLA v e r s u s s i l h o u e t t e  .44  l e a f areas  50  (ASW*ALB)bh  versus  53  o f MARW and TLA:ASWblc  ASWbh  v e r s u s ASWLBbh (ASW*ALB)bh  v e r s u s ALCbh  64 65 67  (ASW*MARW)bh area  72 81  X  L I S T OF  TABLES Page  1.  Explained  2.  G e n e r a l c h a r a c t e r i s t i c s o f t h e Duncan, and  Haney  variability  i n t h e TLA-ASW  4.  Significant differences age c l a s s ( a l l s i t e s ) Significant differences position ( a l l sites)  7. 8.  tree  ..27  Sample  6.  Courtenay,  sites  3.  5.  relationship...10  description  28 i n mean SLA by n e e d l e 39 i n mean SLA by crown 39  S i g n i f i c a n t d i f f e r e n c e s i n mean NDW between n e e d l e age c l a s s e s b y s i t e  ratio 44  R a n k i n g and s i g n i f i c a n t d i f f e r e n c e s i n mean NDW r a t i o between age c l a s s e s f o r e a c h s i t e  45  M o d e l s f o r t h e r e g r e s s i o n o f D o u g l a s - f i r ones i d e d l e a f a r e a on s e v e r a l s t e m measurements  51  9.  Mean r a t i o s o f TLA and s e l e c t e d  10.  C o r r e l a t i o n c o e f f i c i e n t s f o r the r e l a t i o n s h i p between TLA and ASW, and TLA and (ASW*MARW)  57  Correlation c o e f f i c i e n t s f o r the r e l a t i o n s h i p between ASW and MARW a t b r e a s t h e i g h t and t h e b a s e o f l i v e crown  58  C o e f f i c i e n t s f o r nonlinear TLA=a*ASWbh **D =  62  11.  12.  t  13. 14.  models o f t h e f o r m  t  Comparison of s l o p e models w h i c h v a r i e d Description  s t e m measurements... 55  intercepts by s i t e  f o r TLA p r e d i c t i o n  of photographs s e l e c t e d  70 for analysis....80  L I S T OF ABBREVIATIONS  ACLA - n e e d l e age c l a s s  area  (cm ). 2  ADB - c r o s s - s e c t i o n a l  a r e a o f dead  bark  (cm ).  AHW  a r e a of heartwood  (cm ).  - cross-sectional  AHWSW - c r o s s - s e c t i o n a l  bark  2  a r e a of heartwood  AHWSWLB - c r o s s - s e c t i o n a l 1ive  2  and sapwood  a r e a of heartwood,  area of l i v e  ALC  - cross-sectional  a r e a o f most r e c e n t  bark  number t o t h e number o f l i v e  (phloem)  (cm ). 2  annual r i n g s  equal  w h o r l s on t h e main  (cm ). 2  ALCLB - ALC p l u s ALB  (cm ). 2  ASW - c r o s s - s e c t i o n a l  a r e a o f sapwood  ASWLB - ASW p l u s ALB  same a s basal  2  2  a r e a o f s t e m measured o u t s i d e  area  BLA  - one-sided branch l e a f  CSA  - current  bark,  (cm ). 2  ASW*ALB - t h e p r o d u c t o f ASW and ALB  D - distance  (cm ).  (cm ).  ATOT - c r o s s - s e c t i o n a l  height  sapwood, and  2  - cross-sectional  stem  2  (cm ).  ALB  in  (cm ).  area  (cm ). 4  (cm ). 2  sapwood a r e a ( c m ) ( R o g e r s and H i n k l e y 2  (cm) between m i d d l e o f l i v e  (1.3m) (Long and S m i t h  1979).  crown and b r e a s t  1988).  DW - d r y w e i g h t ( g ) . FW - f r e s h  weight ( g ) .  G - mean p r o j e c t i o n the  of unit  leaf  beam on a p l a n e n o r m a l  K - light  extinction  area i n the d i r e c t i o n of  t o t h e beam  coefficient.  (Lang  1987).  xi i LAI  - leaf  area  index  (m /m ). 2  2  MARA - mean a n n u a l  ring  area  MARW - mean a n n u a l  ring  width  NDW  - needle  i n t h e sapwood  d r y weight ( g ) .  - probe  Qi  - irradiance  below t h e f o r e s t  canopy.  Qo  - irradiance  above t h e f o r e s t  canopy.  TLA  angle.  - specific leaf  T - solar  area  (g/cm ). 2  transmittance.  - one-sided  Stem l o c a t i o n attached  tree leaf  area (m ). 2  a b b r e v i a t i o n s are i n lowercase  and when  t o an u p p e r c a s e a b b r e v i a t i o n i n d i c a t e  on  t h e s t e m where t h e measurement was  bh  - breast height  blc  2  i n t h e sapwood (cm).  Op  SLA  (cm ).  - base of l i v e  (1.3 m). crown.  taken.  the location  ACKNOWLEDGEMENT  I would their  like  t o t h a n k D a v i d New and my w i f e  assistance i n collecting  B o t h D r . K a r e l K l i n k a and R e i d comments and R e i d statistical  provided  analysis.  Canada's r e s e a r c h  Carter  t h e samples.  gave many h e l p f u l  invaluable advice  regarding  The u s e o f F l e t c h e r C h a l l e n g e o f  laboratory i n Crofton,  greatly appreciated. Science  and p r o c e s s i n g  Heather f  B.C. i s a l s o  T h i s work was f u n d e d  and E n g i n e e r i n g  by t h e N a t i o n a l  R e s e a r c h C o u n c i l o f Canada.  1 1. 1.1.  TREE LEAF  AREA  Tree  a r e a measurements a r e used  leaf  of a p p l i c a t i o n s . of  leaf  area  In f o r e s t  i s important  evapotranspiration, receipt  of s o l a r  treatments  i s being  impact.  analyzed, an  al.  i n two  leaf  to  land surface area  in m )  basis  as p r o j e c t e d l e a f  area  than  on  TLA  area  index  individual  t r e e response  deterred are this  by  study  is  (m2).  i s of  ecological  are  in  site  commonly ratio  an  individual  to the  forest  T h i s may  I t i s the concerned.  interest.  use  with  be  Or  a area  on  researcher  the  case  when  and  when l o o k i n g a t  TLA  which a c c u r a t e of s i n g l e  in  tree  of  TLA  intermediate  of s i n g l e  estimate  on  In some s t u d i e s , TLA  c o d o m i n a n t s or  However, t h e  reported  - projected leaf  ecosystem, a comparison  the d i f f i c u l t y  obtained.  is  interest  a p p l i e d t o a s m a l l number of t r e e s  in a forest  useful.  area  treatment  and  (LAI  basis.  between d o m i n a n t t r e e s and be  of  increased  or on  2  a whole s t a n d are  may  and  stand  in leaf  indicator  (TLA)  i s of more use  treatments  competition  gases,  of  ways: as a u n i t l e s s  m  tree basis  of  been  area  area  b a s i s as  a single  variety  1990).  of t r e e l e a f  literature  impact  response  important  stand 2  the  between l e a f  ( C a r t e r et  Estimates the  When t h e  More r e c e n t l y , t h e r e has  quality  in  for estimating rates  exchange of p h o t o s y n t h e t i c  t o be  relationship  i n a wide  p r o d u c t i v i t y s t u d i e s , a measure  radiation.  often considered  the  INTRODUCTION  TLA  trees  estimates TLA  is  estimates  with  which  2  1.2.  ALLOMETRIC  RELATIONSHIPS  S e v e r a l methods a r e u s e d accurate  b u t l a b o r i o u s method  t o e s t i m a t e TLA. i s destructive  Recently,  a s an a l t e r n a t i v e  to destructive  attention  has been g i v e n t o t h e p o t e n t i a l  stem measures f o r p r e d i c t i n g used  to predict  (Helgerson  et  1988), d i a m e t e r  et  height  (ASWbh) (Kaufmann and T r o e n d l e  (Maguire used  1979), c r o s s - s e c t i o n a l  in a predictive  of t r e e b o l e or  sapwood a r e a a t b r e a s t 1981; Marchand 1984;  The s e l e c t e d  allometric  much  a t stump h e i g h t  1978) o r a t t h e b a s e o f t h e l i v e and Hann 1 9 8 9 ) .  sampling,  a t b r e a s t h e i g h t (dbh)  (Gholz  Whitehead  sampling.  Some o f t h e s t e m measures  TLA have been d i a m e t e r  al.  al.  TLA.  The most  crown  (ASWblc)  s t e m measurement i s  e q u a t i o n as t h e  independent  variable. There  has been much d e b a t e  these  allometric  (Long  and S m i t h  equations  over  about  the p o r t a b i l i t y of  a range  of s i t e c o n d i t i o n s  1988) and s t a n d s t r u c t u r e s  ( E s p i n o s a B a n c a l a r i et  al.  and d e n s i t i e s  1987; Keane and Weetman 1987;  Thompson 1989) and how t h e y change as a r e s u l t treatments  ( B r i x and M i t c h e l l  Whitehead  et  concluded  that  a range  al.  1984).  discover  Many o f t h e s e  one a l l o m e t r i c  of s i t e s  and s t a n d s .  an i n d e p e n d e n t  1983; G r i e r  ratio  et  al.  of stand 1984;  r e s e a r c h e r s have  s h o u l d n o t be u s e d  over  F u r t h e r work has been done t o  variable,  such  as mean a n n u a l  width,  sapwood p e r m e a b i l i t y , or crown l e n g t h , w h i c h  enable  the user  t o overcome t h e s e  regional  ring  might  l i m i t a t i o n s to  3 t h e use et  1.3.  al.  of a l l o m e t r i c 1984;  equations  M a g u i r e and  approach  1989).  to estimating l e a f area  measurements of s o l a r relies  on an  calculation  (1)  t r a n s m i t t a n c e through  inversion  of t h e B e e r - L a m b e r t  of l e a f a r e a  utilizes  the canopy  and  equation  f o r the  irradiance  below  index:  LAI = -Ln(Q /Q .)cos8'K 1  where LAI  the s o l a r  index, Q i i s s o l a r  is solar  0  incident  coefficient. Douglas-fir underlying  The has  irradiance  a n g l e , and extinction  assumption  by Ungs  of the e q u a t i o n i n space  Cameras and  estimate solar  predict  LAI.  describing  light  and  the  radiometers  attempts  (1981).  ( J a r v i s and  work has  Leverenz  a f o r e s t canopy t o been p u b l i s h e d  t o e s t i m a t e s i n g l e TLA  of t h i s s t u d y  foliage is  have been used e x t e n s i v e l y  with  OBJECTIVE objective  The  leaf inclination  approach.  The  for  i s t h a t the  transmittance through  However, l i t t l e  0 is  extinction  c o e f f i c i e n t of 0.48  are s p h e r i c a l l y d i s t r i b u t e d  1983).  above t h e c a n o p y ,  K i s the  been c a l c u l a t e d  randomly d i s t r i b u t e d angles  c  i s leaf area  the canopy, Q  1.4.  Whitehead  SOLAR TRANSMITTANCE AND PHOTOGRAPHY Another  to  Hann  ( A l b r e k s o n 1984;  is threefold:  either  (1)  t o examine v a r i a t i o n TLA and s e v e r a l  in allometric  s t e m measurements  (Pseudotsuga  menziesii  over a range  in soil  single  i n coastal  (Mirb.) Franco, moisture  (2) t o t e s t a p h o t o g r a p h i c predicting  relationships  var.  destructive  Douglas-fir menziesii)  and n u t r i e n t s ;  technique  f o r i t s usefulness at  TLA e s t i m a t e s ; and  (3) t o make r e c o m m e n d a t i o n s r e g a r d i n g o p t i m a l strategies  between  f o r estimating sampling.  sampling  i n d i v i d u a l TLA f r o m  5  2. LITERATURE REVIEW 2.1.  ALLOMETRIC The  plant  study  RELATIONSHIPS o f t h e r e l a t i o n s h i p between g r o w t h r a t e s o f  organs w i t h i n  observation  of a l l o m e t r y  L e o n a r d o da V i n c i . at  every  stage  thickness  of i t s height  1983).  I t was Huber  about r a t i o s  fresh  of leaves.  equations  TLA or f o l i a r  area  of p r o j e c t e d  at breast  species.  species  could  the  The four  (2)  relation spacing  2  ( a s q u o t e d by  (1928) t h a t began t o speak  that  time a l l o m e t r i c  biomass u s i n g Waring  area  a s t e m measurement as  (1983) p u b l i s h e d  (ASWbh) f o r f o u r t e e n  (1978) f o r S c o t s  North  list  today.  for conifer trees pine  {Pinus  t r e a t m e n t s was l i n e a r  many more  An example o f i s provided  sylvestris  between T L A and ASWbh f o r e l e v e n  = 0.97; n = 11  of  American  of f u r t h e r r e s e a r c h ,  be added t o t h i s observed  a list  t o sapwood c r o s s - s e c t i o n a l  T L A = 0.137(ASWbh) - 7.004 R  are equal i n  f o r many t r e e s p e c i e s f o r  As a r e s u l t  r e l a t i o n s being Whitehead  leaf  height  conifer  by  Since  independent v a r i a b l e .  ratios  of a t r e e  o f c r o s s - s e c t i o n a l x y l e m a r e a s and  have been d e v e l o p e d  predicting the  when p u t t o g e t h e r  The  ago by  " A l l the branches  (below them)"  specifically weight  i n t r e e s was made l o n g  He o b s e r v e d ,  to the trunk  Zimmermann  i s known as allometry.  one o r g a n i s m  and s t r o n g :  trees  L.). from  6 A t h e o r e t i c a l explanation between t h e et  Shinozaki theory"  g r o w t h o f TLA al.  and  (1964a,b).  a proportional  of  the  pipe  model  amount of  and  if  dbh  i s as  been f o u n d area,  One  focus  accurate  i n the  equally  (Espinosa  Bancalari  et  Grier  et  trees  were l e s s t h a n  improve  1984).  to  70  l e a f area  (1978) f o u n d  f o l i a g e mass.  than  20  their  cm  dbh  a measure w h i c h  portion theory  but  Douglas-fir  stem, t h e of  al.  30  years  as  the  stem  validity  old.  both the the  stem, t h e one  It  predictors  Gower  et  the al.  trees  area  conducting  and  (1987),  would  expect  I f the  than  the  to  dbh  were the dbh  portion  pipe  ASW  Brown  nonconducting, p h y s i c a l  heartwood.  TLA  1983;  found  not.Indicate  basal  sample  S n e l l and  Basal  has  of  Mitchell  s t u d y , sample t r e e s  sample t r e e s .  determine  t h a t dbh,  more h i g h l y c o r r e l a t e d  authors did  r e s u l t s have  ASW.  these s t u d i e s  Douglas-fir  In t h e i r the  the  been t o as  B r i x and  p r e d i c t i o n o v e r dbh.  include  holds true,  1987;  year-old  and  of TLA  accurate  e a c h of  sapwood, and the  model  t o r e l a t i o n s h i p s between  for Douglas-fir  In  ASWbh t o be  with  by  stemwood.  to v e r i f y  work has  a predictor  ASWbh a r e  65  "pipe  r e l a t i o n s h i p s of v a r i o u s  for Douglas-fir  and  examining  the  conducting  been g i v e n  i n some i n s t a n c e s  al.  been p r o v i d e d  theory.  stem parameters  been v a r i a b l e .  relation  t r a n s p i r i n g l e a f mass  f o r many s p e c i e s  Much a t t e n t i o n has TLA  s t e m has  a given  R e s e a r c h e r s have examined t h e measurements t o TLA  the  close  They p r e s e n t e d  which contends t h a t  requires  f o r the  less  age  of  provide of  the  support  model  conducting  portion  7 of  t h e stem, r a t h e r  closely  related  measures would heartwood  t h a n dbh o r b a s a l  t o TLA. likely  area,  The d i s t i n c t i o n  be c l e a r e r  between t h e two  i n older  a r e a makes up a l a r g e r  portion  t o be more  trees  where  of t o t a l  basal  area. A second  focus  i n Douglas-fir  been on t h e p r e d i c t i v e live  crown  state  that  closely living  ( b l c ) over  t h e ASWbh.  t h e amount o f l e a v e s  correlated  relative that  be most  could  areas of be  a r e a of t h e stem a t b l c . even t h o u g h  growth.  measuring  TLA.  crown l e n g t h ,  t h e measurement  physiological  position  valid  only  i f there  blc.  Long  et  In other  despite  words, taken a t  Therefore,  variations i n  i s t a k e n a t t h e same  i n a l l sample t r e e s .  i s a difference  (1981) f o u n d  of a  but p h y s i o l o g i c a l l y -  t h e same l o c a t i o n .  m e a s u r i n g ASW a t b l c e n s u r e s t h a t  note  significant  i n t h e measure b e i n g  on a l l sample t r e e s  not n e c e s s a r i l y  They  organ dimension  a more p h y s i o l o g i c a l l y  m e a s u r i n g ASW a t bh r e s u l t s  al.  (1964b)  i t i s p h y s i o l o g i c a l l y an  a t b l c i s an " a c t u a l  and t h e r e f o r e  speaking  al.  should  i n turn  p o s i t i o n changes w i t h h e i g h t  same h e i g h t  et  t o t a k e s u c h measurements and i t s  measure t h a n dbh f o r p r e d i c t i n g  the  per t r e e  (1988) comment t h a t  position  diameter  tree"  Shinozaki  them, w h i c h  o r ASWbh may be c o n v e n i e n t ,  arbitrary  o f ASW a t t h e base o f t h e  by t h e c r o s s - s e c t i o n a l  G e r o n and Ruark  s t u d i e s has  w i t h t h e sum o f c r o s s - s e c t i o n a l  pipes supporting  approximated  dbh  usefulness  allometry  that  The c o n c e r n i s  i n ASW between bh and ASW v a r i e d  only  slightly  8 between bh and b l c i n a s t a n d trees.  Espinosa  decrease with adjacent  22 y e a r - o l d  growth r a t e s et  al.  et  Bancalari  increasing  o f 45 y e a r - o l d al.  height  (seea l s o  Brix  (1982) f o r s i m i l a r  (1987) f o u n d ASW t o i n the tree  Douglas-fir  little fir. was  better  and M i t c h e l l  Espinosa better  s u g g e s t s ASWblc  o f T L A t h a n ASWbh;  i s available in this  Bancalari  (1983) and W a r i n g  results).  predictor  information  et  al.  of Douglas-fir,  regard  (1987) r e p o r t  while  in their  g r o w i n g s t a n d s ASWbh was a s good a s ASWblc. (1987) f o u n d ASWbh t o be m a r g i n a l l y predicting  TLA ( R pine,  marginally increased  (Abies  ba Is  ante  (Pinus  a (L.) M i l l )  tree  taeda  et  al.  L.).  by u s i n g  fast  medium and s l o w et  Gower  al.  t h a n ASWblc f o r  only  that  proportion  o f crown t o b o l e  2  (1984)  found  (Picea  rubens  t h e same f o r l o b l o l l y  G e r o n and Ruark  ASWblc  i n most  Marchand  and r e d s p r u c e  (1985) f o u n d  indicating  s t a n d s , ASWblc  fortheir  t h a n ASWbh f o r b a l s a m f i r  much o f t h e v a r i a b i l i t y  species  ASWblc  t h a n ASWbh f o r p r e d i c t i n g T L A ( R  TLA p r e d i c t o r  S a r g ) and B l a n c h e  remove  that  (1987) f o u n d ASWblc  f r o m 0.89 t o 0.90; n = 5 4 ) .  a better  f o r Douglas-  = 0.971 and 0.968, r e s p e c t i v e l y ) . F o r  Hungerford  better  ASWblc  pine  2  better  isa  unfortunately,  t h a n ASWbh f o r p r e d i c t i n g T L A o n l y  growing stand  lodgepole  i n three  stands with d i f f e r e n t e a r l y  A review of a v a i l a b l e l i t e r a t u r e slightly  Douglas-fir  (1988) were  i n p r e d i c t i n g TLA f o r s i x  rather  t h a n ASWbh.  Research i s  situations, particularly i s variable within  i s the p r e f e r r e d  able to  when t h e  o r between  v a r i a b l e o v e r ASWbh f o r  9 predicting  TLA.  bole r a t i o  variability  within  predictor  o f TLA.  an a d e q u a t e  In v e r y uniform stands with  Despite the decrease using  of t h e ease  Exploring  the p o s s i b i l i t y  ASWblc t o be l i n e a r while  of p r e d i c t i n g  gained  through  and M i t c h e l l  (1987) s u g g e s t  as t h e i n d e p e n d e n t  that  et  al.  from  between ASWbh and  1985 f o r l o b l o l l y  pine)  The f i n d i n g s (1983),  of Long  al.  and E s p i n o s a B a n c a l a r i  ASWblc p r e d i c t i o n  variable  et  models w i t h  would have t o be  et  ASWbh  site-specific  Douglas-fir. While  precise  the literature  indicates  ASWblc p r o v i d e s a  and a c c u r a t e e s t i m a t e o f TLA, s o u r c e s o f v a r i a b i l i t y  have been d i s c o v e r e d i n t h e ASW-TLA r e l a t i o n s h i p to  ASWbh,  i t t o be n o n l i n e a r (Dean and Long  f o r lodgepole pine). Brix  ASWblc  the r e l a t i o n s h i p  (Blanche  o t h e r s have f o u n d  (1981),  for  in variability  w i t h w h i c h t h e y c a n be g a t h e r e d .  some w o r k e r s have f o u n d  al.  o r between s t a n d s ASWbh may be  ASWblc, r e s e a r c h e r s have f a v o r e d bh measurements  because  1986  low crown t o  be c o n s i d e r e d .  The r e l a t i o n s h i p  (Kaufmann and T r o e n d l e within several  s p e c i e s (Geron  varies  1981; W h i t e h e a d and Ruark  sources of w i t h i n  1988).  et  which  need  between s p e c i e s al.  1984) and  Table  species variation  1 presents  i n t h e ASW-TLA  relationship. Independent allometic  variables  equations  i n attempts  TLA-ASW r e l a t i o n s h i p s . second  independent  have been  to explain  Dean and L o n g  variable,  introduced  into  variability in  (1986) i n t r o d u c e d a  D, t h e d i s t a n c e between t h e  10 middle of the l i v e model.  crown and bh, i n t o  T h i s measure t a k e s  into  t h e TLA p r e d i c t i o n  account v a r i a t i o n s  resulting  Table 1. Explained v a t i a b i l i t y i n the TLA-ASH relationship for several conifer species. Species  Source of variation stand density site quality  Pious contoita Pseadotsuga aenziesii  density X s i t e index stand treatment: fertilization thinning fert. I thin. crown class  Pinus  sylvestiis  Pinas Abies  contoita lasiocaipa  Reane and Beetman (1987) Binkley (1984) Bancalari et a l . (1987) Whitehead (1978) Albiektson (1984) Long and Suith (1988) Long and Smith (1989)  Pseadotsuga aenziesii Pseudotsuga aenziesii Pseadotsuga aenziesii Pinas contoita  nean annual ring width  Brix and M i t c h e l l (1983) Granier (1981) B i i x and M i t c h e l l (1983) Dean and Long (1986) Thonpson (1989) Albrektson (1984) Thonpson (1989) Bancalari et al. (1987) Blanche et a l . (1985) Pearson et al. (1984)  Pinns sylvestiis Pinus contoita Pseadotsuga aenziesii Pious taeda Pious contoita  tine of sampling density X age X s i t e  f r o m crown c l a s s . it  Source of infornation  A t t h e t i m e o f Dean and L o n g s '  had been shown t h a t  f o r some s p e c i e s  between T L A and ASW may v a r y w i t h s i t e density  (Whitehead et  1984;  Pearson  first  to report  al.  quality  and M i t c h e l l  1984).  Dean and Long relationship  TLA:  (3)  TLA R  2  the relationship  1978; B r i x  a curvilinear  = 0.028 * A S W b h 1  = 0.99; n = 17  156  * D~° -  7 4  research  and s t a n d  1983; A l b r e k t s o n (1986) were t h e between ASWbh and  11 They f o u n d linear  that  t h e r e l a t i o n s h i p between ASWblc and T L A was  i f suppressed  analysis. samples others  Their  trees  lodgepole  from s a p l i n g s  were n o t i n c l u d e d pine  3)  o f crown t o s t e m l e n g t h , ASWblc,  analyzed  2) u s e d  or t h i n n e d  thereby  stands,  (1988) t e s t e d  across would  They found t h e r a t i o  t h e r a n g e o f ASWbh introduce  bias  site  index.  high  a  variability,  s u c h as  suppressed  from l i n e a r  regression.  the s u i t a b i l i t y lodgepole  of using  pine i n  o f T L A t o ASWbh  i n d i c a t i n g that  increased  a linear  t o w a r d ASWbh, s t a n d  stand,  model  The two power d e n s i t y , and  However t h e m o d e l s d i f f e r e d between t h e Wyoming  and  Utah s i t e s .  due  to differences  found  within  i n t o TLA p r e d i c t i o n s .  t e r m model was u n b i a s e d  with  inadvertently  4) n o t i n c l u d e d  residuals  that  nonlinear  trees  average t r e e s  power t e r m s t o p r e d i c t T L A f o r  Wyoming.  short  low i n h e r e n t  o r 5) n o t a n a l y z e d  Long and S m i t h two  only  stands with  plantations trees,  only  included  They s u g g e s t e d  t h e r e l a t i o n s h i p t o be  b e c a u s e t h e y may have 1) u s e d  testing  from Utah  and mature t r e e s .  have n o t f o u n d  ratios  data  i n the  Long and S m i t h in site  (1988) s u g g e s t  water b a l a n c e .  this  may be  Thompson  (1989)  t h e r e l a t i o n s h i p between T L A and ASW a t t h e base o f  the  tree  and  Smith  t o be n o n l i n e a r (1989) f o u n d  relationship lasiocarpa  year-old  there  pine  as w e l l .  was a s i g n i f i c a n t  between T L A and ASWbh f o r s u b a l p i n e  (Hook.) N u t t . )  relationship  f o r lodgepole  Spittlehouse  Douglas-fir  stand  nonlinear fir(  Abies  (1981) f o u n d t h e  between T L A and dbh t o be n o n l i n e a r  thinned  Long  located  near  i n a 30 Courtenay,  12 B.C.  R e s e a r c h h a s n o t been p u b l i s h e d  nonlinear useful  model u s i n g  i n regard  Another TLA  to Douglas-fir.  approach t o e x p l a i n i n g v a r i a b i l i t y  r e l a t i o n s h i p between s i t e s  the conducting  permeability  the  al.  system  (Bong.) C a r r .  on d i f f e r e n c e s i n  i s that  pine  that  in a particular  and S i t k a s p r u c e  was more c l o s e l y  Saturated  method d e s c r i b e d An  easily  annual r i n g examined the  climate  (Picea  sitchensis  r e l a t e d t o the product of i t was t o  p e r m e a b i l i t y was measured u s i n g t h e  b y Edwards and J a r v i s  measured s u r r o g a t e  width  the capacity  ( W h i t e h e a d and J a r v i s 1 9 8 1 ) .  ASWbh and a sapwood p e r m e a b i l i t y measure t h a n ASWbh a l o n e .  i n t h e ASW-  i n t h e s t e m d e p e n d s on ASW and t h e  (1984) f o u n d  TLA of l o d g e p o l e  has focused  The a s s u m p t i o n  o f t h e sapwood  et  Whitehead  i f a  two power t e r m s t o p r e d i c t T L A i s  sapwood p e r m e a b i l i t y . of  indicating  (1982).  of permeability,  (MARW) i n t h e sapwood, h a s a l s o  mean been  for i t s contribution to explaining v a r i a b i l i t y i n  TLA-ASW r e l a t i o n s h i p .  larger  t r a c h e i d diameters  higher  permeability.  Wider g r o w t h r i n g s g e n e r a l l y have (Bannan 1965) w h i c h s h o u l d  Pothier  et al.  (1989) f o u n d  mean  that  sapwood p e r m e a b i l i t y a t t h e b l c was s t r o n g l y c o r r e l a t e d mean d i a m e t e r year-old  pine  {Pinus  (1984) f o u n d  that  the r a t i o  ASWbh i n S c o t s  ratio  10 y e a r s  of jack  stands  Albrektson  Espinosa  growth over t h e l a s t  pine  Bancalari  banksiana  v a r i e d m i t h MARW. et al.  with  f o r 15 and 35 Lamb.).  of f o l i a g e  mass t o  For Douglas-fir,  (1987) f o u n d t h a t t h e TLA:ASWbh  correlated positively  with  MARW i n t h e sapwood b u t  13 inclusion  o f MARW a s an i n d e p e n d e n t  variable  into  t h e TLA  prediction  model was n o t u s e f u l  b e c a u s e MARW i n t h e sapwood  correlated  c l o s e l y w i t h ASWbh.  Thompson  ring ASW  area  i n t h e sapwood  compared w i t h u s i n g et al.  Bancalari is  not c l o s e l y c o r r e l a t e d  The  explanation water  recent This  attention  of v a r i a b i l i t y  of conducting (CSA).  velutina  Complicating  related  t o as " c u r r e n t  found  that  both  t o T L A i n b l a c k oak  I n w h i t e oak (Quercus  linearly  related  alba L . )  t o TLA but with  c o e f f i c i e n t s o f 0.94 and 0.73, r e s p e c t i v e l y . of these c o r r e l a t i o n s  more c l o s e l y c o r r e l a t e d  nonfunctional  i s referred  1979).  Lam.) w i t h c o r r e l a t i o n c o e f f i c i e n t s o f  implication  some s p e c i e s  In  i s r e s t r i c t e d t o t h e most  R o g e r s and H i n c k l e y  CSAbh and ASWbh were a l s o  the  f o r i t s p o t e n t i a l as  ( R o g e r s and H i n c k l e y  sapwood  0.97 and 0.93 r e s p e c t i v e l y .  correlation  nonconducting  i n ASW-TLA r e l a t i o n s h i p .  i n t h e stem  CSAbh and ASWbh were l i n e a r l y  The  i n s i t u a t i o n s where ASW  of TLA p r e d i c t i o n .  been g i v e n  transport  sapwood a r e a "  (Quercus  Espinosa  w i t h MARW, i n c l u s i o n o f MARW may  one o r two a n n u a l r i n g s  band  that  with  the f i t of the  d i f f e r e n t i a t i o n of conducting versus  sapwood h a s a l s o  oak,  i t improved  ASW a l o n e .  (1987) s u g g e s t  improve t h e p r e c i s i o n  an  (MARA) a s an i n t e r a c t i o n t e r m  f o r l o d g e p o l e p i n e and f o u n d  regression  (1989) used mean  variable  correlation  s t e m m e a s u r e s and c o n d u c t i n g  c o n d u c t s water v a r i e s  i s that  the portion  with species.  CSAbh i s  w i t h T L A and t h a t f o r  t h e r e may be a f o r t u i t o u s  the matter  i s that  Dixon  sapwood  between area.  o f sapwood (1971)  that  reports  14 i n Tilia  that  species  the outermost  n i n e p e r c e n t of conducted examining  that  in conifers  conducting  water  al.  assumption (1966,  1967),  Sitka  approximated this is  and  Booker Jarvis  and  related  of whorls  whorls  differentiating  the  ASW  this,  Waring  nutrient  i n the l i v e  the  (1979) work a l s o  that  and  that  would  et  i n lodgepole  related  Schlesinger  being equal to the  (ALC). of sapwood,  of the t r e e .  stem  i s transformed into  i n some  t o some o t h e r  physiological  w i t h TLA.  (1985) p r o p o s e  cells  i n t h e p h l o e m and  xylem.  trees  In response t o that  s t o r a g e of  come i n t o p l a y w i t h t h e  and  produced  v i a the phloem t o t h e  Sucrose that  starch  Rogers  suggests that  season are t r a n s p o r t e d  and  TLA  a r e a o f t h e most  Some o f t h e p h o t o s y n t h a t e s  stem  If  expect t h a t  nonconducting  is correlated  ASW-TLA r e l a t i o n s h i p .  roots  of  (1978).  importance  r e s e r v e s i n t h e s t e m may  the growing  one  crown  c o n d u c t i n g and  is fortuitously  characteristic  basis  i n t h e crown.  t h e number o f r i n g s  from h i g h l i g h t i n g  Hinckleys'  the  i n sapwood i s  The  Kininmonth  to the c r o s s - s e c t i o n a l  number  and  under  workers  (1975), Kozlowski  (1982) r e p o r t  t h e number o f l i v e  annual r i n g s ,  Aside  most  o f t h e sapwood  innermost p o r t i o n .  i s the case f o r D o u g l a s - f i r ,  closely  portion  for only  s p r u c e t h e number o f c o n d u c t i n g r i n g s  recent  in  a l l the earlywood  i s work done by Swanson  However, Edwards and p i n e and  are working  with the outermost  c o n d u c t i n g more t h a n t h e  accounts  I t seems t h a t  t h e ASW-TLA r e l a t i o n s h i p  assumption  this  water.  ring  stored  accumulates  i n the  i n parenchyma  At the o u t s e t  of the  growing  15 season the  starch  ( S a l i s b u r y and  utilized  resinosa  Ait.)  that  sectional the  sum  o f ASW  correlated comm.).  and  w i t h TLA  I f ALB  (1985) f o u n d  that  theories  species relating  need t o be  be  2.2.  t h a n ASW  bark a r e a of  and  ASW  reserves, stem  i t s cross-  (or  (John W o r r a l l ,  be  ALB,  possibly  more c l o s e l y personal  then i t s  limited.  They recommend  bark and  functions TLA  et  Brack  as  al.  and  ASW  that  through hydrologic  include  between ASW,  production.  c o r r e l a t e d w i t h TLA  Eucalyptus.  TLA  functions well.  in Douglas-fir  The needs  explored.  s u c c e s s f u l l y as  stand  l e a f area  Wang and  Miller  with hemispherical an  or LAI 1987).  A simple  The  tree.  The  a z i m u t h and the  be  of  have been  p r e d i c t i n g whole  Leong  appears  a p p r o a c h would  v i e w of  lenses  method of  possibility  l e a f area  a f i x e d angle to the target  indirect  ( A n d e r s o n 1971;  predict single tree  unexplored.  the  was  result in  PHOTOGRAPHY  used  at  alone  (Pinus  should wood  the  be  p r e d i c t i o n may  Cameras e q u i p p e d  to  on  (ASWLB)) may  expanded t o  relationship to  a t some p o i n t  the  Kozlowski  reserves  nutrient  in  pine  i s c l o s e l y c o r r e l a t e d w i t h ASW  t o TLA  three  Kramer and  in nutrient  ALB  contribution  for  by  bark s t o r e s  (ALB)  growth  i n red  f l u c t u a t i o n i n f o l i a g e and  living  area  i n new  elongation  i s documented  a corresponding  utilized  That n u t r i e n t r e s e r v e s  for shoot  Fluctuations  Seeing  are  Ross 1978).  stem are  (1979).  reserves  et  using  al.  photography  relatively to photograph  a fixed distance  target  1982;  t r e e which  trees from  provides  16 fewest  o b s t r u c t i o n s to the e n t i r e  the d i r e c t i o n the t r e e the  of the photograph.  The p h o t o g r a p h  c o u l d t h e n be a n a l y z e d t o d e t e r m i n e  image o f t h e t r e e  area w i l l Carter  crown would be s e l e c t e d as  be c a l l e d  and S m i t h  (1988)).  on t h e p h o t o g r a p h .  silhouette  (1985),  The s i l h o u e t t e  area  as c i t e d area  image o f  total  In t h i s  (the term  by D i e b o l t  There from  by d e s t r u c t i v e  sampling  as t h e f i x e d  (1985) have d e v e l o p e d relationship  from  and Mudge  i s a surrogate of l e a f  i s a strong theoretical  the azimuth  study the  comes  d e n s i t y and t h e r e s h o u l d be a s t r o n g c o r r e l a t i o n as d e t e r m i n e d  area of  area.  f o r choosing  camera a n g l e .  the following  between TLA  and s i l h o u e t t e  basis  area  et  Lang  57.5° al.  equation to describe the  between LAI ( L ) , c a n o p y s t r u c t u r e ,  and s o l a r  transmittance ( T ) :  (4)  L * G<  OEJ  lnT(op)  ) = -cosOp *  where Op i s t h e p r o b e  a n g l e , or t h e a n g l e between t h e sun's  beam and t h e v e r t i c a l  (solar  projection  of u n i t  a p l a n e normal The  size  area  t o t h e beam  G relates  and t h e a n g l e to leaf  shown i n F i g u r e 1.  a n g l e ) and G i s mean  i n the d i r e c t i o n  (definitions  o f G d e p e n d s on l e a f  distributions that  leaf  zenith  azimuth  f r o m Lang  and z e n i t h  of the probe.  inclination  o f t h e beam on (1987)). angle  I t has been  a n g l e and p r o b e  found  a n g l e as  17 1.0  0.8  0.6  G  0.4  0.2 0 0  20  40  60  80  Angle of probe to vertical. 6°  F i g . l . R e l a t i o n s h i p o f mean p r o j e c t i o n o f u n i t l e a f a r e a (G) and p r o b e a n g l e (0°). The g r a p h assumes random l e a f a z i m u t h a n g l e and <X i s c o n s t a n t a t a g i v e n a n g l e o f e l e v a t i o n (Lang 1986).  It  c a n be s e e n  value be  of G i s independent  assumed t o e q u a l  equation  (5)  taking  choosing  a picture  angle d i s t r i b u t i o n angle  and c a n 57.5°,  as f o l l o w s :  * lnT« .s>..  of a t r e e  B 7  a t 5 7 . 5 ° i s n o t t h e same.as  angle  f o r t h e camera a n g l e  i s i n t h e c e n t e r of t h e photo  final  57.5°, the  a beam o f t h e sun p r o b i n g t h e c a n o p y a t 5 7 . 5 ° ,  this  variations  angle  T h e r e f o r e , a t probe  (4) c a n be w r i t t e n  considering  tree  0.5.  a t probe  of l e a f  L * 0.5 = - c o s ( 5 7 . 5 )  While  the  from F i g u r e 1 t h a t  of l e a f  zenith  exposure-of  minimizes  angle w i t h i n  the t r e e .  and e n s u r i n g t h e t h e impact o f  and between t r e e s on  18  2.3.  DESTRUCTIVE As  SAMPLING  G e r o n and  Ruark  (1988) have n o t e d ,  area s t u d i e s i t i s d i f f i c u l t sampling crown  variability area  estimates  associated  with  the  studies  sampling  sizes  and  ratios  of t h e s e  minimize  TLA  of those al.  leaf  area  needles)  1987;  from  processed  foliar  subsampling and  position,  loblolly  et  al.  1987)  and  et  al.  al.  and  1988).  (SLA  (cm ) 3  The  = ratio  SLA  In o r d e r  treatment  (Pinus taeda  1979;  Smith  crown p o s i t i o n s  L.)  et  al.  easily  leaf  size leaf  area  age,  age  al.  Gower 1986)  has  crown  Weetman 1987)  between age  ( B o r g h e t t i et  tedious  branch  needle  1981;  et  be  t h e minimum  with needle  varies  can  to minimize  pine with  (g)  Bancalari  ratio  Specific  (Keane and  of  to d r y weight  applied against  upon p r e c i s i o n .  sample  e s t i m a t i o n of  Espinosa  to determine  D o u g l a s - f i r SLA Berg  i n the  area  1976;  i n lodgepole  stand  pine  1985).  (Del Rio  needles  values  estimates.  s u b s a m p l e s needed t o p r e d i c t  to vary  in  of  for  area  subsample  to optimize  used  leaf  et  subsampling  to q u a n t i f y the  TLA  specific  i t i s necessary  and  ratio  fresh  between  variability  to convert  i n the  dry weights.  a decided  been f o u n d  error  leaf  In most t r e e l e a f  i n order  a s u b s a m p l e and  number o f SLA  area with  t h e random  used  ratios  (Gholz  Helgerson  determined  are  convenient  is single-sided  projected  and  from  I t i s important  the  A common and  resulted  TLA:ASW r a t i o .  t o whole t r e e v a l u e s . variability  to d i f f e r e n t i a t e  t h a t has  leaf  f o r many  and  (Johnson classes et  al.  19 necessitating estimates  stratified  et  al.  (1986)•divided  and t h e n e e d l e s  through  o f t h e crown  o f TLA a r e t o be made f r o m f o l i a r  Borghetti layers  sampling  3 year-old  into four  plus).  live  crown t o t h e apex.  Borghetti  that  their  is  support  a f f e c t e d by l i g h t  differentiation  conditions  2  1 9 7 6 ) , 79.0 cm /g 2  e t al.  25  year-old  examining  found  et  significantly  al.  (1986) p o i n t o u t  that  2  Borghetti  et  al.  year-old  Douglas-fir  ratio is dry be the  useful  weights denoted leaf  branch  t o twig  to avoid  a s NDW  (needle  regeneration  having  leaf  plus  65 t o 70  forest. area,  needle  d r y weight) r a t i o .  fresh  weight  The r a t i o  may  C a l c u l a t i o n of  age c l a s s o f n e e d l e s  (ACLA) would be a s f o l l o w s :  a second  to determine the f o l i a r  i n e a c h age c l a s s .  of a s p e c i f i c  studying  Douglas-fir  i n an even aged, mixed  of a l l needles  area  Douglas-fir  SLA t o p r e d i c t b r a n c h  i n order  al.  (1976) were  (1987) were e x a m i n i n g  of needle d r y weight  et  f o r e s t s , D e l R i o and B e r g  d e n s i t i e s of thinned  e t al.  was 65.1  (Gholz  e t al.  growing  and Gower  e t al.  (1986) were  65 y e a r - o l d  forests,  The o v e r a l l  2  (1979) were e x a m i n i n g under v a r y i n g  morphology  1979) and 44.7 cm /g  t r e e s , Gholz  o l d growth D o u g l a s - f i r  When u s i n g  leaf  by B o r g h e t t i  t o 70.8 t o 82.4 cm /g  Douglas-fir  with  r e s u l t i n g i n the  ( D e l R i o and B e r g  1987).  three  (current  between s u n and s h a d e l e a v e s .  cm /g compared  (Gower  into  e v e r y age c l a s s f r o m b a s e o f  the hypothesis  mean SLA f o r D o u g l a s - f i r +0.9  t h e crown  SLA d e c r e a s e d within  data  d r y weights.  age c l a s s e s  n e e d l e age and d e c r e a s e d  i f accurate  f r o m one  20  (6)  ACLA  where FW class  (cm )  = SLA  2  i s fresh  f o r NDW  2  (g/g) * FW  (g)  w e i g h t o f t w i g s and n e e d l e s o f t h e  of i n t e r e s t .  sample  ( c m / g ) * NDW  As w i t h  SLA,  r a t i o , knowledge  i n order  to  age  appropriately  of i t s v a r i a b i l i t y i s  essential. Few  studies  subsample  size  researcher sampling needs size  2.4.  provided  and  NDW  first  how  ratio  many s u b s a m p l e s and  (1)  following  Ho:  (2)  H : 0  For the  the  question  o f SLA and  to estimate  what  SLA  with  variability  lacking.  HYPOTHESES  n u l l and a l t e r n a t i v e  bh s t e m measures stem  h y p o t h e s e s were  Douglas-fir  stands.  are not l i n e a r l y r e l a t e d  are l i n e a r l y r e l a t e d  measures.  b l c s t e m measures correlated measures.  to  measures.  bh s t e m measures stem  on  destructive  Knowledge o f t h e  s i t e s supporting  blc Hi:  a r e needed  probability?  i s also  on t h r e e  o f SLA.  TLA,  i s the v a r i a b i l i t y  NULL AND ALTERNATIVE  tested  information  a p p r o a c h i n g t h e p r o b l e m of  f o r the purpose of p r e d i c t i n g  error  The  adequate  requirements for p r e d i c t i o n  t o be a s k e d , what  a given of  have  a r e n o t more  w i t h TLA t h a n a r e bh  closely stem  to b l c  21 Hi.:  b l c s t e m measures  a r e more c l o s e l y  w i t h T L A t h a n a r e bh s t e m (3)  H : 0  x  H : 0  basal  with TLA  area. w i t h TLA than  area.  ALC i s n o t more c l o s e l y c o r r e l a t e d than  Hi:  i s basal  ASW i s more c l o s e l y c o r r e l a t e d is  (4)  measures.  ASW i s n o t more c l o s e l y c o r r e l a t e d than  H :  correlated  with TLA  i s ASW.  ALC i s more c l o s e l y c o r r e l a t e d  w i t h TLA than  i s ASW. (5)  H : Q  ASWLB o r ASW*ALB a r e n o t more correlated  Hi:  w i t h TLA than  H : 0  the product  the product correlated  (7)  H«: including  o f MARW and ASW i s n o t more  Hi:  (8)  Ho:  including  with TLA than  o f MARW and ASW i s more w i t h TLA than  n o t improve t h e f i t o v e r  that  u s i n g o n l y ASW. D i n a n o n l i n e a r TLA p r e d i c t i o n  improves t h e f i t over  using  o n l y ASW.  the r e l a t i o n s h i p s  (p=0.05)  closely  i s ASW.  model  sectional  i s ASW.  D i n a n o n l i n e a r TLA p r e d i c t i o n  model does obtained  correlated  i s ASW.  closely correlated Hi:  i s ASW.  ASWLB o r ASW*ALB a r e more c l o s e l y with TLA than  (6)  closely  between  s t e m measures between  sites.  that  obtained  T L A and c r o s s -  vary s i g n i f i c a n t l y  22 Hi:  t h e r e l a t i o n s h i p s between T L A and c r o s s sectional  s t e m measures  significantly (9)  H : D  SLA d o e s between  (p=0.05)  do n o t v a r y between  sites.  not vary s i g n i f i c a n t l y sites,  (p=0.05)  crown p o s i t i o n , o r n e e d l e age  class. Hi:  SLA v a r i e s sites,  (10)  H : 0  (p=0.05)  H : Q  between  crown p o s i t i o n , o r n e e d l e age  NDW r a t i o  needle  s i g n i f i c a n t l y (p=0.05)  does  not vary s i g n i f i c a n t l y  betweem s i t e s ,  age  NDW r a t i o  class.  crown p o s i t i o n , o r  class. varies  between s i t e s ,  significantly  (p=0.05)  crown p o s i t i o n , o r n e e d l e age  class. (11)  H : Q  Hi:  there  i s a poor c o r r e l a t i o n  determined  by d e s t r u c t i v e  silhouette  area.  there  is a strong  area.  s a m p l i n g and  correlation  d e t e r m i n e d by d e s t r u c t i v e silhouette  between T L A as  between T L A as  s a m p l i n g and  23  3. MATERIALS AND METHODS 3.1.  LOCATION Three  moisture in  the  Fig.  and n u t r i e n t  Coastal  2. =  Two  the  Island  B,  Western  and Haney  sites  within  the  are  stands,  representing  conditions,  Map s h o w i n g  Duncan  of  Douglas-fir  Hemlock  location site  =  located  Very  were  a  range  selected  for  (CWH) b i o g e o c l i m a t i c  of  s i t e s .  Courtenay  C.  on t h e  Dry Maritime  in sampling zone.  = A,  .  east  side  of  CWH s u b z o n e ,  Vancouver one  being  24  45 k i l o m e t e r s northwest  approximately Duncan Bay and  the  along The  Main  other  forest  road  approximately  Cowichan Lake road  third  Forest  site  north  i n the 22  i n the E a s t e r n  o f Haney, B.C.  subzone  the  Courtenay s i t e  (Figure 3 ) ,  and  the  (Figure  Fig.  3.  Courtenay  The  on  CWH  Haney s i t e  Western  site.  sites  5).  the  will  Duncan  (CWHmm) v a r i a n t .  M a l c o l m Knapp  G20 road  the  (CWHxm) v a r i a n t  k i l o m e t e r s west o f  i s l o c a t e d at the  (Figure 2 ) .  of C o u r t e n a y on  i n the be  Research Dry  referred  Duncan s i t e  Maritime to  (Figure  as 4),  25  Fig.  3.2.  4.  Duncan  SITE  DESCRIPTION  Following (1987) t h e  study  gathered  by  information aged, s p a c e d  and  the  sites  previous  disease  site.  and  p r o c e d u r e s o u t l i n e d by P o j a r  were examined and  ( C a r t e r and  Carter  and  i s found  i n Table  D o u g l a s - f i r stands i n s e c t damage and  nutrient conditions.  there  are  no  (1988) as 2.  suppressed  al.  i n t e n s i v e l y sampled  K l i n k a 1988).  Klinka  et  The  Site well  sites  which are  represent  As  a result  trees  i n the  in a  information  as a d d i t i o n a l support  even-  relatively  free  a range  of r e c e n t stands.  of  of  moisture  spacing  Fig.  3.3.  5.  TREE  Haney  site.  SELECTION  Sample t r e e s were a n a l y z e d 1988.  Sample  during  t r e e s were s e l e c t e d  using  A u g u s t and September the f o l l o w i n g  criteria: 1) t o r e p r e s e n t  t h e r a n g e o f dbh s i z e s i n t h e  2) f r e e o f d i s e a s e abnormalities;  or i n s e c t damage and g r o w t h and  stand;  27 3) one v i e w o f t h e crown t h r o u g h w h i c h t h e r e little  obstruction  by a d j a c e n t  trees  was v e r y  was a v a i l a b l e .  T a b l e 2. G e n e r a l c h a r a c t e r i s t i c s o f t h e Duncan, C o u r t e n a y , and Haney s i t e s . Parameter  Duncan  Subzone Soil  depth  Soil  type  Slope  (%)  Slope  position  Elevation  Haney  CWHmm  CWHxm  CWHdm  lm+  1. 5m+  lm+  Orthic Dystric Brunisol  Orthic Dystric Brunisol  13  -  middle  (m)  Mean a n n u a l Actual  Courtenay  p p t . (mm)  evapotranspiration  Growing season d e f i c i t (mm)  (mm)  moisture  S t a n d age (@ stump h e i g h t 1988) Stocking  (stems/ha)  Year  of spacing  Site  index  Soil  moisture  regime  Soil  nutrient  regime  area plots The  were a v a i l a b l e  flat  middle  148  270  128  1304  1425  1827  190  238  230  138  77  0  42  46  21  650  650  1976  1982  19 83  16  21  v. d r y  mod. d r y  v.  poor  from C a r t e r  37 fresh r ich  poor  f o r each s i t e  dbh r a n g e e s t i m a t e was d i v i d e d  categories.  17  550  (m/50 y r s )  Dbh r a n g e e s t i m a t e s  HumoFerr i c Podzol  based  on l a r g e  and K l i n k a  into  four  A t t h e Duncan and Haney s i t e s  fixed  (1988).  e q u a l dbh  one t r e e  f o r each  28 dbh  g r o u p was s e l e c t e d ,  while at the Courtenay s i t e  trees  f o r e a c h dbh g r o u p were s e l e c t e d .  trees  that  Within  fulfilled  criteria  three  e a c h dbh r a n g e , t h e t r e e s  caused  within no  I n many i n s t a n c e s  the s i t e  opportunity  introduced. and  height  Table Site  3.  some  w i t h t h e most  v i e w o f t h e crown and m e e t i n g c r i t e r i a sample t r e e s .  Finding  only  sample difficulty.  unobstructed  two were s e l e c t e d as one o r two t r e e s  t y p e were s u i t a b l e and t h e r e f o r e  there  t o make a random s e l e c t i o n and a b i a s  The dbh r a n g e e s t i m a t e o f e a c h sample t r e e  two  of each s i t e  i s shown i n T a b l e  was  was  and t h e dbh 3.  Sample t r e e d e s c r i p t i o n .  T r e e No. Dbh r a n g e estimate (cm)  Duncan  Dbh (cm)  Height (m)  Age SI (stump (50 height) years)  10.7 15.1 16.8 19 .9  8.54 11. 59 10.97 14.35  47 41 43 43  13.8 14.9 18.1 17.5 20.2 21. 3 24.0 23.0  13.32 16 . 33 15.86 18.56 17 .87 19.59 21.09 20.69  47 47 46 48 48 46 44 46  16.9 18.5 21.5 23.2  19.80 17.89 19.18 20.91  22 21 21 21  10.7 - 20.7 1 2 3 4  Courtenay  16  13.8 - 24.7 1 2 3 4 5 6 7 8  Haney  15.0 - 24.0 1 2 3 4  29 3.4.  PHOTOGRAPHY Before  felling  photographed black AT-X  28-85 mm The  obstructions direction viewing  f/3.5-4.5  to a c l e a r  the f u l l focal  film  exposure d i d not  from z e n i t h  crown  exposures. Positives  offered  a clear  the  v i e w o f t h e crown was  12 m e t e r s  fewest  chosen  distance  as  the  I f at these  include the e n t i r e  live  distance  50,  from the t r e e  at  settings  crown more  from the t r e e  or o t h e r camera a n g l e s w h i c h  provided  a n a l y z e d were  at full  selected  criteria:  view of the e n t i r e  obstruction  a  green  were t a k e n a t 28,  from z e n i t h .  priorized  Kodak  Given the best d i r e c t i o n f o r  o f t h e e x p o s u r e s t o be  by t h e f o l l o w i n g 1)  camera u s i n g  T o k i n a zoom l e n s w i t h a B&W  e x p o s u r e s were made a t 14 m e t e r s 57.5°  was  (ESTAR-AH B a s e ) , and  crown, p h o t o g r a p h s lengths,  each t r e e  Program  view of the t r e e which  a camera a n g l e o f 5 7 . 5 ° the  pan  of the photograph.  85 mm  trees  w i t h a Canon AE-1  and w h i t e t e c h n i c a l  filter.  and  t h e sample  live  of a d j a c e n t t r e e s  crown w i t h o u t  i s presented i n the  positive;  In  2)  camera a n g l e e q u a l t o 5 7 . 5 °  from z e n i t h ;  3)  camera d i s t a n c e  m.  e q u a l t o 12  c a s e s where t h e s e c r i t e r i a  that The that  came c l o s e s t forest i t was  canopy  to f u l f i l l i n g was  difficult  Haney p h o t o g r a p h s  could  so c l o s e  n o t be met,  the c r i t e r i a to closure  t o meet c r i t e r i a  useful  for further  and  exposures  were  chosen.  a t t h e Haney  site  1, making none o f t h e  analysis.  30  Selected  p o s i t i v e s were  PLUS h a n d - h e l d per  inch.  at high  The s c a n n e r  contrast.  s u c h a way t h a t light  scanner  areas  has a  At high  v  edit,  i n order and  s a v e , and p r i n t to create  only  t h e image.  portion adjacent  portion  image a l l p e r i p h e r a l  crown  were  The images were  o f t h e crown.  trees  of i n t e r e s t erased  were  i n t h e image.  using  erased  edited crown  In the leaving  In t h e trees  and a n y  w h i c h was o b s t r u c t e d  (Figure  WHOLE F i g . 6. Example crown image.  was i m p o r t e d  program which a l l o w s you  image a l l p e r i p h e r a l  o f t h e crown trees  and a l l t h e  two new images, one o f t h e whole  t h e crown o f i n t e r e s t  unobstructed  file  dots  i s received i n  appear black  2.2  SCANMAN  w h i c h was s e t  t h e image  The image  one o f t h e u n o b s t r u c t e d  whole crown  areas  version  switch  art  contrast  a l l t h e dark  appear white.  line  a LOGITECH  r e s o l u t i o n o f 200  at a scanning  LOGITECH P a i n t S h o w P l u s to  scanned with  by  6).  UNOBSTRUCTED  o f whole crown  image and u n o b s t r u c t e d  31 T h e s e two images were  printed  and, u s i n g  crown p o r t i o n was d e t e r m i n e d , t h a t whole crown r e m a i n i n g unobstructed  crown  transparencies determined  image was a l s o p r i n t e d  a LiCor  The t r a n s p a r e n c i e s the  mean p a r t i a l  image.  area  were  suitability  3.5.  FOLIAR  area  were  August because  height, The  Scattergrams  then v i s u a l l y  height  11, 1988.  marked, were  Felling  was d i v i d e d  by t h e  of TLA v e r s u s  examined t o d e t e r m i n e t h e  1986).  within  o f stem,  and age a t stump of l i v e  t h e dbh was  and t h e t r e e c a r e f u l l y felled  between J u l y 10 and  expansion  the f i r s t  I f b r a n c h e s were Length  i n the f i e l d  was c a r r i e d o u t a t t h i s  i t has been shown t h a t  length  10 t i m e s and  analysis.  A l l sample t r e e s  determined.  meter.  Sampling  normally terminates al.  area  o f t h e mean s i l h o u e t t e  a t r e e was p h o t o g r a p h e d  measured, b r e a s t felled.  image  SAMPLES  3.5.1. D e s t r u c t i v e After  The  was c a l c u l a t e d f o r e a c h  an e s t i m a t e  of r e g r e s s i o n  image.  crown  t h e meter  s i l h o u e t t e area  of t h e e n t i r e crown.  silhouette  et  run through  of the  onto  of unobstructed  s i l h o u e t t e area  to give  crown  Model LI-3000 s u r f a c e  The mean p a r t i a l  crown p o r t i o n  i s , the p o r t i o n  i n the unobstructed  and t h e a r e a  using  a dot g r i d , the  of c u r r e n t  needles  of J u l y  (Borghetti  broken o f f , t h e i r  length  height  half  time  of l i v e  crown,  were measured  crown was d i v i d e d  Two and a h a l f c e n t i m e t e r d i s c s were  origin  was  stump  and r e c o r d e d .  into f i f t h s  and marked.  c u t a t bh, b l c , and a t  32 each  o f t h e one f i f t h  Beginning and  (cm), d i a m e t e r  and f r e s h  weight  A representative  e a c h crown  layer  just  beyond  the butt  swell  (g) were measured and r e c o r d e d .  N o d a l b r a n c h e s were i n c l u d e d below.  (six discs/tree).  a t t h e t o p o f t h e crown, e a c h b r a n c h was c u t o f f  i t s length  (mm),  crown marks  with the whorl  immediately  branch from t h e lowest whorl i n  was s u b j e c t i v e l y  chosen,  l a b e l l e d , and  brought t o t h e l a b a l o n g w i t h t h e stem d i s c s  f o r further  analys i s . Branches in  two t o f o u r d a y s .  slightly time.  Tree l e a f  low as a r e s u l t  into  age c l a s s e s  the nearest  needles older sample  i n a dark c o o l  0.01 g .  of needle shrinkage d u r i n g  selected  however, t o improve  and weighed  10 g s u b s a m p l e s  sample  weighed  were used  and a n y  i n t h e 8 age c l a s s  , this  0.01 g,  was a d j u s t e d t o  f o r the l a s t  nine trees.  This  t i m e f o r 25 g  The n e e d l e s were t h e n  t h e twigs of the subsamples,  put into  and  dried  Following  f o r 8 hours.  randomly  to the nearest  off  n e e d l e s were weighed  were  o f t w i g s were  the processing  was t o o l e n g t h y .  a t 105°C  this  r e a c h e d a maximum o f 12 y e a r s ) .  efficiency  change was made b e c a u s e subsamples  included  25 g s u b s a m p l e s  f r o m t h e sample  approximate  and e a c h age c l a s s  t h a n 8 y e a r s were  approximate  branches  O n l y 8 age c l a s s e s  (needle r e t e n t i o n  Initially  room and p r o c e s s e d  a r e a e s t i m a t e s may be  The t w i g s f r o m t h e r e p r e s e n t a t i v e  clipped to  were s t o r e d  small  stripped  paper  bags,  drying, the  and r e c o r d e d t o t h e n e a r e s t  0.01 g.  33 Before drying  the s t r i p p e d  n e e d l e s e a c h were r a n d o m l y subsample.  Sample s i z e  n e e d l e s , 15 s a m p l e s  selected  f r o m e a c h age c l a s s  o f 15 was c h o s e n  p r e l i m i n a r y s t u d y o f SLA v a r i a b i l i t y Douglas-fir campus. of  tree  on t h e U n i v e r s i t y  F o r t h e sample  sided  leaf  Model  LI-3000  samples  were d r i e d  a t 105°C  to the nearest  n e e d l e s were u s e d e a c h age c l a s s  0.01 g.  was measured  using  The n e e d l e  The 15 s a m p l e s 15 s p e c i f i c  The one-  of t e n  leaf  branch.  and  areas f o r The 15 SLA's  an e s t i m a t e d SLA f o r e a c h age c l a s s branch.  t h e same t e n n e e d l e sample  Thirty  r e p e a t e d measures o f  had a c o e f f i c i e n t  of v a r i a t i o n  t o 6.4%. The  following  determination, tree  o f t h e mean  f o r 8 h o u r s , weighed  f o r the r e p r e s e n t a t i v e  the representative  equal  Columbia  a t n=15.  a r e a meter.  t o determine  were a v e r a g e d t o g i v e for  of B r i t i s h  stabilized  surface  of a  on a b r a n c h f r o m a  a r e a o f t h e t e n n e e d l e samples  a LiCor  recorded  on t h e b a s i s  branch, standard error  SLA o f t e n n e e d l e s a m p l e s  of t e n  example o f t h e l e a f  using  age c l a s s  #1 i n t h e Haney s i t e ,  area per branch  1 n e e d l e s f r o m a b r a n c h on  outlines  the c a l c u l a t i o n s  involved: Total  f r e s h weight  o f age c l a s s  1 t w i g s and n e e d l e s  85.88 g. F r e s h weight Dry w e i g h t Specific  o f subsample  leaf  56.255 cm /g 2  o f t w i g subsample  (FWSS) = 25.30 g.  n e e d l e s (DW) = 9.71 g.  a r e a f o r age c l a s s or o n e - s i d e d l e a f  1 needles  (SLA) =  area/dry weight.  (TFW) =  34  NDW  ratio  Estimate  of needle d r y weight  NDW  * TFW  Estimate of  the  = DW/FWSS = 9.71g/25.30g = 0.384  of the p r o j e c t e d  leaf  this  projected  branch  leaf  f r e s h weight,  d e v e l o p e d by p o o l i n g  The  and  f o r each t r e e  a r e a f o r each  leaf  a d d i n g up  the  areas f o r branches  a r e a measurements, a  and  sites  linear  the branch  and  using  a t the base  of the  Adding  up t h e b r a n c h  leaf  gave an e s t i m a t e o f t h e  leaf  branch  diameter  variables.  3.5.2. Sample S i z e  carry  projected  e s t i m a t e s from a l l t r e e s  estimates  and  area.  model was  independent  class  2  areas f o r the branch gives the estimated  d i d n o t have l e a f  length,  leaf  1 needles  2  p r o c e d u r e t o e a c h age  leaf  regression  as  class  = 32.978g * 56.25cm /g = 1855.01cm  In o r d e r t o d e t e r m i n e  area  a r e a o f age  branch:  Applying  which  sample:  = 0.384 * 85.88g = 32.978g  32.960g * SLA  total  f o r the e n t i r e  stem area  projected  tree.  Analysis  sample b r a n c h d a t a p r o v i d e d t h e o p p o r t u n i t y t o  o u t optimum sample s i z e  analysis  f o r SLA.  The  number  35 (n)  of s a m p l e s interval  to estimate  o f 0.05 and two a l l o w a b l e  determined (7)  necessary  through  n > df  (sd/d) t« 2  Equation changes size  with  d e v i a t i o n , d i s t h e h a l f - w i d t h of r e q u i r e d f o r t h e mean, and t« i s t h e  t h e a p p r o p r i a t e degrees of freedom.  (7) was i t e r a t i v e l y i n t values  Analysis  solved to correct for rapid  o c c u r r i n g when t h e c a l c u l a t e d  (Cochran  significant  o f v a r i a n c e and T u k e y ' s HSD m u l t i p l e  3.6.  o u t on t h e d a t a  to detect  d i f f e r e n c e s i n mean SLA and mean NDW  installation,  crown p o s i t i o n ,  SYSTAT computer  statistical  sample  and Cox 1 9 6 6 ) .  c o m p a r i s o n method were c a r r i e d  classes.  e r r o r s (5 and 10%) was  2  interval  t value  was s m a l l  between  confidence  = n - 1  confidence  Student's  a  t h e use of t h e f o l l o w i n g e q u a t i o n :  where sd i s t h e s t a n d a r d the  SLA w i t h  analyses  software  (Wilkinson  ratios  and n e e d l e age  was u s e d  for a l l  1988).  STEM SAMPLES S i x measurements, t o t h e n e a r e s t  along  each o f four e q u i d i s t a n t r a d i i  0.01 cm, were  taken  on e a c h s t e m d i s c  (24  measurements/disc).  The q u a d r a t i c mean o f t h e measurements  along  was u s e d  the four r a d i i  sectional area  of l i v e  heartwood and  area  live  of heartwood  bark  (ALB),  and sapwood bark  to c a l c u l a t e  (AHW), a r e a  area  (AHWSWLB), a r e a  o f sapwood  o f dead b a r k  (AHWSW), a r e a  the c r o s s (ASW),  (ADB), a r e a o f  of heartwood,  o f sapwood and l i v e  sapwood, bark  36 (ASWLB), t o t a l rings  equal  disc  basal  i n number  (ATOT), a r e a  t o t h e number  and  ALCLB e q u a l AHWSW and AHWSWLB, r e s p e c t i v e l y . r i n g width  i n t h e sapwood  was d i s t i n g u i s h e d period  by s o a k i n g  holding  distinguished  At b l c ,  i n water  Sapwood for a  I f m o i s t e n i n g t h e d i s c was n o t  the disc  up t o t h e s u n e a s i l y  TLA.  f o r t h e bh and b l c s t e m  Regression analysis  was c a r r i e d  f o r t h o s e s t e m measurements w h i c h were l i n e a r l y  to  TLA.  R e s i d u a l s were examined f o r e a c h  In  c a s e s where s t e m measurements were n o t l i n e a r l y  to  TLA, t r a n s f o r m a t i o n s were c a r r i e d independent v a r i a b l e  i n order  r e l a t i o n s h i p more l i n e a r , p r i o r  to determine and an  of r e s i d u a l s .  which t e s t s  Further  between t h e t h r e e  of covariance  regression. related  t o make t h e  analysis  a n a l y s i s and  was c a r r i e d o u t  between s t e m  sites.  This  technique described  lines.  related  o u t on t h e d e p e n d e n t  t h e homogeneity of r e g r e s s i o n  more t h a n two r e g r e s s i o n  linear  to regression  i f the relationships  TLA v a r i e d analysis  short  ANALYSIS  measurements a g a i n s t  examination  ring  t h e sapwood.  REGRESSION  and/or  ALC  Mean  (MARW) and mean a n n u a l  the d i s c s  S c a t t e r g r a m s were p r o d u c e d  out  ALB ( A L C L B ) .  (MARA) were a l s o d e t e r m i n e d .  before measuring.  sufficient,  3.7.  i n t h e sapwood  recent  o f w h o r l s on t h e s t e m i n  live  area  ( A L C ) , and ALC p l u s  o f most  the  annual  crown  area  parameters  was done  using  by Z a r (1984)  coefficients for  37 Non-linear  regression  m i n i m i z a t i o n method dependent v a r i a b l e  was  analysis  carried  and ASW  using  the Quasi-Newton  o u t w i t h TLA as t h e  and D as t h e i n d e p e n d e n t  variables. S c a t t e r g r a m s and r e g r e s s i o n examine t h e r e l a t i o n s h i p and  analysis  were u s e d t o  between t h e TLA:ASW r a t i o  between s t e m measures a t bh and t h e b l c .  and MARW  38  4. SAMPLING ANALYSIS 4.1  RESULTS  4.1.1. S p e c i f i c L e a f Overall interval 99.4).  mean SLA was 42.8 cm /g w i t h a 9 5 % c o n f i d e n c e 2  o f + 0.7 cm /g The number  of r e p l i c a t i o n s  ( 5 ) , and n e e d l e  i n each s i t e  age c l a s s  a l l o w f o r a 3-way f a c t o r i a l a n a l y s i s  factors  than  replications  way a n a l y s i s site  pooled and  the effect  by n e e d l e  needle  analysis SLA.  age c l a s s  T h e r e was a l s o  position In  needle  comparison t e s t between n e e d l e site.  Tables  comparison data  on mean SLA p o o l e d  by crown  o f crown  by s i t e .  a significant interaction  age and h e i g h t  was used  by n e e d l e  to decrease i n crown.  pooled  by s i t e .  of a  the pooled  regarding generalizations  Tukey's  data.  multiple  i n mean SLA  f o r each  multiple  A similar  that  on mean  age c l a s s .  f o r e a c h s i t e showed t h e same t r e n d s w i t h  refinements  F o r each  with  and crown p o s i t i o n s  4 and 5 g i v e t h e r e s u l t s  position  o f crown  to identify differences  age c l a s s e s  on t h e d a t a  on mean SLA  had a s i g n i f i c a n t e f f e c t  e a c h s i t e mean SLA t e n d e d  2-  o u t on t h e e f f e c t o f  and t h e e f f e c t  and s i t e on mean SLA p o o l e d  increasing  Therefore,  o f s i t e and crown p o s i t i o n  t h e two f a c t o r s  (8) d i d  a s t h e r e were more  on mean SLA p o o l e d  age c l a s s ,  age c l a s s  (4 o r 8 ) ,  category  i n some m a t r i c e s .  o f v a r i a n c e was c a r r i e d  and n e e d l e  position,  of  (SE = 0.375, n = 556, r a n g e = 25.4 -  2  crown p o s i t i o n not  Area  analysis a few  c a n be made  from  39  Table 4. Significant d i f f e r e n c e s in mean s p e c i f i c leaf area (cn'/g) by needle age ( a l l s i t e s ) . 1  Crown position  Needle <ige 4  5  6  7  8+  36.1abc  34.9bc  34.2c  32.2c  34.7*  -  40.8b  39.8bc  37.7bcd  36.0cde  34.8de  35.4de  32.8e  51.2a  44.Sab  43.0DC  40.7bcd  38.9cde  37.6de  37.Ode  35.5e  57.1a  48.6b  45.1bc  44.3bc . 41.led  39.9cd  37.8d  37.7d  1  2  43.2a  40.lab  2  48.3a  3 4  top  3  64.8a 53.5b 50.2bc 39.3d 38.3d 47.0bcd 44.3bcd 42.5cd bottom 1. Means separated i n columns and not sharing a common l e t t e r are s i g n i f i c a n t l y d i f f e r e n t at p < 0.001, using the Tukey BSD multiple comparison t e s t . 2. Crown position 1, needle age 7 has only one sanple. Table 5. Significant d i f f e r e n c e s in mean s p e c i f i c leaf area (cm /g) by crown position ( a l l s i t e s ) . 1  Crown position  2  Needle age 1  2  3  4  5  6  7  8+  43.2a  40.1a  36.1a  34.9a  34.2a  32.2a  34.7*  -  2  48.3ab  40.8a  39.8ab  37.7ab  36.0ab  34.8a  35.4a  32.8a  3  51.2bc  44.Sab  43.0b  40.7bc  38.9bc  37.6ab  37.0a  35.5a  4  57.led  48.6bc  45.1bc  44.3cd  41.led  39.9bc  37.8a  37.7a  top  38.3a 64.8d 53.5c 50.2c 47.Od 44.3d 42.5c 39.3a bottom 1. Means separated i n rows and not sharing a common l e t t e r are s i g n i f i c a n t l y d i f f e r e n t at p < 0.001, osing the Tukey BSD multiple comparison test. 2. Crown position 1, needle age 7 has only one sample.  In a l l t h r e e  sites  t h e mean SLA i n e a c h crown  did  not vary  significantly  between n e e d l e  (in  Duncan and Haney t h e mean d i d n o t v a r y  position  age c l a s s e s between  6-8  needle  40 age c l a s s e s not  4-8) and i n age c l a s s e s  v a r y s i g n i f i c a n t l y between crown p o s i t i o n s .  suggests  that  age c l a s s e s being  i t was u n n e c e s s a r y  6-8  i n the sampling  the o l d e s t  sufficient. positions that  7 and 8 t h e mean SLA d i d  t o d i f f e r e n t i a t e between procedure  n e e d l e age c l a s s ,  The c o m p a r i s o n  and r a t h e r  5 ,positions  t h a n 8+  6+ would have been  o f mean SLA between  showed no common t r e n d s between s i t e s  l e s s than  This  crown indicating  w o u l d have o b s c u r e d s i g n i f i c a n t  differences. Figures samples branch  7, 8, and 9 i l l u s t r a t e  t h e number  of t e n needle  needed t o e s t i m a t e mean SLA p e r n e e d l e age c l a s s p e r and how n i s a f f e c t e d  by s i t e ,  crown p o s i t i o n and  f o l i a g e age. 20  i  15  -  ,  ,  ,  C  D  H  ,.  Q.  Site  F i g . 7. Number o f 1 0 - n e e d l e s a m p l e s needed t o p r e d i c t s p e c i f i c l e a f a r e a w i t h 9 5 % c o n f i d e n c e and 5% a l l o w a b l e e r r o r (empty b a r s ) or 10% a l l o w a b l e e r r o r ( f i l l e d b a r s ) by site.  1  2  3  4  5  Crown Position  F i g . 8. Number o f 1 0 - n e e d l e s a m p l e s needed t o p r e d i c t s p e c i f i c l e a f a r e a w i t h 95% c o n f i d e n c e and 5% a l l o w a b l e e r r o r (empty b a r s ) o r 10% a l l o w a b l e e r r o r ( f i l l e d b a r s ) by crown p o s i t i o n .  15  -  D.  Foliage Age  F i g . 9. Number o f 1 0 - n e e d l e s a m p l e s needed t o p r e d i c t s p e c i f i c l e a f a r e a w i t h 95% c o n f i d e n c e and 5% a l l o w a b l e e r r o r (empty b a r s ) o r 10% a l l o w a b l e e r r o r ( f i l l e d b a r s ) by f o l i a g e age.  42 Six  t e n n e e d l e s a m p l e s were r e q u i r e d  SLA  p e r n e e d l e age c l a s s  a  10% a l l o w a b l e  error  to estimate  per branch with  error.  This  95% c o n f i d e n c e and  and 19 o r 20 t e n n e e d l e  e s t i m a t e t h e mean w i t h 95% c o n f i d e n c e suggests that  e a c h n e e d l e age c l a s s  in this  t h e mean  samples t o  and a 5% a l l o w a b l e  s t u d y mean SLA v a l u e s f o r  and crown p o s i t i o n  had an e r r o r o f  somewhere between 5 and 10% a s 15 t e n n e e d l e sample used.  Figure  8 indicates  crown p o s i t i o n variability If  5 which  that  likely  i n competition  the allowable  error  SLA was most v a r i a b l e i n reflects  for light  or f o l i a g e age.  error  a t 5% r e s u l t e d  in site  variable  4.1.2.  Setting  crowns.  little  with  the allowable  and crown p o s i t i o n  the differences  categories  to tree  was 10%, mean n v a r i e d  crown p o s i t i o n  on mean n,  tree  i n t h e lower  site,  impact  were  having  some  i n mean n w i t h i n t h e  was n o t s i g n i f i c a n t .  NEEDLE DRY WEIGHT RATIO  Overall  mean NDW  ratio  was 0.421 w i t h a 95% c o n f i d e n c e  interval  o f + 0.008 (SE = 0.004, n = 557, r a n g e = 0.023 -  0.773).  The NDW  site, and  ratio  crown p o s i t i o n ,  12 ( s e e A p p e n d i x  was examined  and n e e d l e age c l a s s I for explanation  W i t h one e x c e p t i o n , age  class  across ratio  t h e mean NDW  d i d not vary s i g n i f i c a n t l y  the tree  sites.  f o r age c l a s s  for variation  (Figures  10, 11,  of symbols)). ratio  f o r each  between crown  I n t h e Duncan s i t e  4 needles  between  t h e mean  i n crown p o s i t i o n  needle  positions NDW  1 was  43  0.8  0.6 CO  cr  CD  0.4 Q  a>  "D CD CD  0.2  0.0 D  C  Site  Fig.  10.  Variability  i n needle d r y weight  ratio  by  site  ratio  by crown  0.8  06 CD  2> Q)  >6  0.4  -  O  0.2  *  o  o  o 0.0  i  Crown Position  F i g . 11. pos i t i o n .  Variability  i n needle d r y weight  44  0.8  0.6 CO oc  0.4  >Q  0  CD  02  0.0  Foliage Age  F i g . 12. Variability f o l i a g e age.  i n needle  significantly  different  than  exception  ignored  data  was  pooled  Table 6.  d r y weight  ratio  crown p o s i t i o n s 2-5.  i n the a n a l y s i s with  and s o r t e d by age c l a s s  a l l NDW  and s i t e  by This ratio  (Table 6).  S i g n i f i c a n t differences in Bean HOH ratio between needle age classes for each s i t e .  Site 1  2  3  Needle age class 5 4  6  7  8+  Duncan  0.403a  0.470a  0.491a  0.466a  0.483a  0.431a  0.447a  0.402a  Courtenay  0.416a  0.459a  0.463a  0.474a  0.471a  0.390a  0.359b  0.377a  Haney  0.358b  4.390b  0.383b  0.395b  0.351b  0.267b  0.219c  0.216b  Note:  Means separated i n rows and not sharing a common l e t t e r are s i g n i f i c a n t l y d i f f e r e n t at p <  0.05, using the Tukey HSD multiple comparison test.  45 Mean NDW not  significantly  differed (Table for  ratios  a t t h e Duncan and C o u r t e n a y  different  significantly  6).  each  site  except  f r o m Haney  i n age c l a s s i n a l l age  The r a n k i n g o f mean NDW i s shown  i n Table  Needle Small  were  7 and  classes  ratio  by age  class  7.  T a b l e 7. R a n k i n g and s i g n i f i c a n t d i f f e r e n c e s r a t i o between age c l a s s e s f o r e a c h s i t e . Site  sites  age c l a s s e s  ranked  i n mean  by NDW  NDW  ratio Large  Duncan  8  1  6  7  4  2  5  3  Courtenay  7  8  6  1  2  3  5  4  Haney  8  7  6  5  1  3  2  4  Note: n e e d l e age c l a s s e s u n d e r l i n e d by t h e same l i n e a r e not s i g n i f i c a n t l y d i f f e r e n t a t p < 0.001, u s i n g t h e T u k e y HSD m u l t i p l e c o m p a r i s o n t e s t .  4.2.  DISCUSSION  4.2.1. S p e c i f i c Mean SLA reported report  Leaf  Area  (42.8 cm /g) was 2  values for Douglas-fir;  65.1, D e l R i o and B e r g 44.7, and Tan et  (1987), (1981)),  47 and 54.  60 c m / g  f o r unthinned  2  mean SLA i n t h i s  al.  Price  (1979),  be due  of s e a s o n a l v a r i a t i o n  et  earlier al.  79.0, Gower  (1986) et  al.  see S p i t t l e h o u s e  (1987) r e p o r t s  Douglas-fir  s t u d y may  t h a n most  Borghetti  (1978;  shrinkage d u r i n g the sampling result  lower  a range  n e a r Nanaimo. i n part  process. i n SLA.  o f 40 t o The low  to needle  I t may Smith  et  also al.  be a (1981)  46 found  that  s e a s o n a l changes  pronounced  site  where t h e SLA  the Coast, Based  was  and  mean a n n u a l  i t appears  that  al.  that,  B o r g h e t t i et  The  SLA et  Tan  t r e n d s as  The  al.  in this and  finding  d i d not  position  was  layers  crowns than  layer  o f B o r g h e t t i et mean SLA  full  and al.  t h r e e , the needle light  age  needle  similar  crown. needle  In t h i s age  classes  upper  classes in less found  Considering that five  sections  i n the top  layer  al.  (1986) s t u d y .  Yet,  in the  rather should  c o n d i t i o n s e v e n more so t h a n t h e  i n t h e B o r g h e t t i et  age  crown  shade l e a v e s t h a n  into  February.  show  (1986) t h a t  1986).  in  decreasing with  study.  that  the  (1987),  i n the top t h i r d  s t u d y were d i v i d e d  equal  of  Price  conditions resulting  between sun et  al.  in this  light  (Borghetti  in this  experience  s t u d y w i t h SLA  i t i s suggested  differentiation  (1986),  two  Further to  S p i t t l e h o u s e (1981))  not supported  near  site  (1987) i n November and al.  on  taken  (1979) sampled  from bottom t o top of the  effect  crown p o s i t i o n experience  al.  (1978; s e e  age  of the were  Range s i t e .  Berg  d a t a o f B o r g h e t t i et  found  increasing  D e l R i o and  Gower et  and  the Coast  Mountain  (1986) s a m p l e d d u r i n g November,  o f h i g h e s t SLA.  September  precipitation  t o the Cascade Mountain  (1981) t h a n al.  in a  t o March.  B o r g h e t t i ' s sample t r e e s  more s i m i l a r  less  g e n e r a l l y higher than  on e l e v a t i o n  et  lower  t o be  h i g h e s t d u r i n g November  Smith  class  found  were  At t h e C a s c a d e  was  from a s i t e  and  i n Oregon.  than  t h e SLA  sites,  time  in Douglas-fir  i n a more humid C o a s t Range s i t e  Cascade Mountains site,  i n SLA  top  47 significant found  differences  i n mean SLA between age c l a s s e s  i n the top layer,  sun  and s h a d e  SLA  a c r o s s n e e d l e age c l a s s e s ,  effects  leaf  suggesting that  differentiation  shade  leaf  leaves  accounts  differentiation,  i n t h e lower  more  than  for variation in  possibly related  to the  As B o r g h e t t i et  o f a g i n g on n e e d l e p h y s i o l o g y .  (1986) n o t e , v e r t i c a l c h a n g e s  something  were  i n SLA may r e s u l t  f r o m s u n and  with a smaller p o r t i o n  crown p o r t i o n s as a r e s u l t  al.  o f shade  of l e a f  shedding.  4.2.2. N e e d l e Reports not  D r y Weight R a t i o o f mean NDW  ratio  values f o r Douglas-fir  available. Two p a t t e r n s emerge o u t o f t h e NDW  study:  1) on t h e s e s i t e s  approximately year ratios This  were  6; and  ratio  t w i g s began d r o p p i n g 2) w i t h i n  each  data  in this  needles at  s i t e mean  NDW  d i d n o t v a r y s i g n i f i c a n t l y between age c l a s s e s  suggests  between n e e d l e procedure  that  i t was u n n e c e s s a r y  age c l a s s e s  t o determine  6 through  mean NDW  to differentiate 8 i n the sampling  b y age c l a s s .  6-8.  48 5. ALLOMETRIC RELATIONSHIPS 5.1.  RESULTS  5.1.1. T r e e L e a f The  Area  following  model was d e v e l o p e d  to predict  BLA  2  I n ( B L A ) = 3.976 + 1.366(In(fw) ) - 0 . 6 7 3 ( I n ( d i a ) )  (8)  - 0.428(ln(length))  Adjusted F ratio where  -  + 0.115(crpo2)  + 0.164(crpo3)  crpo4  2  {crpo4)  = 0.975, n = 87,  just  weight  beyond  ( c m ) , and instl,  of branch  position.  Continuous  log values  i n order  inst2,  crpo2,  for installation  t o improve  i s diameter of  (mm), length  crpol,  variables  d e p e n d e n t and i n d e p e n d e n t with  ( g ) , dia  the butt swell  a r e dummy v a r i a b l e s  equations  0.05(crpol)  = 380, S.E.E. = 0.162.  fw i s f r e s h  the branch length  R  - 0.092(instl)  + 0.047(inst2)  + 0.131  crpo3,  variables.  the three continuous  and  and crown  were t r a n s f o r m e d linearity  i s branch  to natural  between t h e  A l l possible transformed  subset  variables  were f i t t o t h e d a t a , and t h e model w i t h t h e l o w e s t mean s q u a r e  v a l u e was s e l e c t e d  Each v a r i a b l e  improved  at  Collinearity  p = 0.05.  variables not  (cm ):  as t h e most p r o m i s i n g  the adjusted R  2  to predict  between d i a m e t e r  of t h e d a t a used  branch  t o develop  leaf  area  t h e model.  model.  and was s i g n i f i c a n t  was i g n o r e d on t h e g r o u n d s t h a t  be used  residual  and l e n g t h  t h e model would  f a r beyond t h e r e a c h A s c a t t e r g r a m of the  49 residuals outlier the  of t h i s  model was a n a l y z e d f o r o u t l i e r s  was i n v e s t i g a t e d  for possible  model was r u n w i t h t h e o u t l i e r s  set,  t h e model c o e f f i c i e n t s  recording  removed  model  outliers  i n any s i g n i f i c a n t appeared  branches which a result of  transformed residuals  plotted  showed d e f i n i t e variables the  effect  branches  against  BLA model was used on e a c h t r e e .  Island. trees  weight.  crown  The s c a t t e r g r a m  However, model and i n s t a l l a t i o n  the inclusion  o f dummy  t h e y had no s i g n i f i c a n t coefficients.  to predict  (Figure  thinning al.  2  thinned  C o u r t e n a y B.C. (840 s t e m s / h a ) .  II  for  (1981) r e p o r t e d T L A  f o r 25 y e a r - o l d  (1978) r e p o r t  area of a l l  a r e a s were summed t o  Brix  and f e r t i l i z e r  i n a 22 y e a r - o l d  the leaf  13; s e e A p p e n d i x  o f LAI f o r each s i t e ) .  T a n et  Following  t h e model was r u n a g a i n  The b r a n c h l e a f  o f 25.19 t o 92.92 m under  of the  and as b e f o r e i t was d e c i d e d t o l e a v e t h e  i n the data s e tseeing  calculation  trees  of lower  crown p o s i t i o n  trends supporting  g i v e TLA f o r each t r e e  values  The main c a u s e  showed no b i a s .  (p = 0.05) on t h e model  The  were n o t a f f e c t i n g  t h e e s t i m a t e s and e a c h o f t h e  o f dummy v a r i a b l e s  outliers  outliers  from t h e d a t a  i n t h e model f o r e a c h o f t h e s e f a c t o r s .  inclusion  without  low f r e s h  against  variables  When  b a s a l d i a m e t e r s and l e n g t h s b u t , a s  of needle drop,  the residuals  manner.  t o be t h e e x i s t e n c e  had l a r g e  error.  d i d n o t change s i g n i f i c a n t l y (p  = 0.05) and i t was c o n c l u d e d t h e o u t l i e r s the  and e a c h  regimes  a range  Douglas-fir on V a n c o u v e r  o f 16 t o 55 m f o r  Douglas-fir Three years  2  s t a n d near later,  Spittlehouse  (1981) r e p o r t e d a r a n g e of  same s t a n d .  The  study  from  ranged  TLA  values  15.72  f o r the  t o 96.05  16  27  t o 92  m  2  for  sample t r e e s i n  the this  m. 2  F i g . 13. O n e - s i d e d t r e e l e a f a r e a (m ) f o r sample t r e e s . Sample t r e e s d e n o t e d as D l - D4 a r e f r o m Duncan, CI - C8' a r e f r o m C o u r t e n a y , and HI - H4 a r e f r o m Haney. 2  5.1.2. B r e a s t  Height  Cross-sectional and set.  ATOTbh were not  Stem Measures and  TLA,  models w i t h  was  Leaf  Area  sapwood a r e a a t b r e a s t h e i g h t , ASWLBbh, linearly  related  t o TLA  A n a t u r a l l o g t r a n s f o r m a t i o n on  variable,  Tree  necessary  the  to develop  ASWbh, ATOTbh, and  ASWLBbh  in this  data  dependent  linear (Table  regression 8).  Table 8. Models f o i the regression of Douglas-fir one-sided leaf area on selected stem measurements (n = 16). BREAST HEIGHT STEM MEASUREMENTS [11 TLA (ii ) ~- 10.015 + 0.012(AS»*ALB)bh (cm ) 2  4  Adjusted R = 0.887 2  P = 119.3  S.E.E. = 7.41 ( a )  P = 153.1  S.E.E. = 6.64 ( a )  P = 155.2  S.E.E. = 6.60 ( a )  P = 127.1  S.E.E. = 0.17 ( a )  P = 131.8  S.E.E. = 0.17 ( a )  P = 57.4  S.E.E. = 0.24 (m )  P = 149.0  S.E.E. = 6.72 ( a )  P = 215.0  S.E.E. = 5.67 ( a )  P = 440.0  S.E.E. = 4.03 ( a )  P = 174.0  S.E.E. = 6.26 ( a )  P = 230.5  S.E.E. = 5.49 ( a )  2  121 TLA ( a ) = -0.383 + 0.266(ALCbh) ( c a ) 2  2  Adjusted R = 0.910 2  2  [31 TLA [ a ) = -2.550 + 0.249(ALCLBbh) ( c a ) 2  2  Adjusted R = 0.911 2  [4] LnTLA ( a ) = 2.364 t O.OlO(ASWbh) ( c a ) 2  2  1  Adjusted R = 0.894 2  [51 LnTLA ( a ) = 2.314 t 0.009(ASHLBbh) ( c a ) 2  2  2  [61 LnTLA ( a ) = 2.447 + 0.005(ATOTbh) ( c a ) 2  2  1  Adjusted R = 0.897 2  2  2  1  Adjusted R = 0.790 2  2  BASE OP LIVE CROWD STEM MEASUREMENTS 171 TLA ( a ) = -7.458 t 0.515(ASBblc) ( c a ) 2  2  Adjusted R = 0.908 2  2  18] TLA ( a ) = -10.402 t 0.450(ASBLBblc) ( c a ) 2  2  Adjusted R = 0.934 2  2  [91 TLA (•») = 12.493 t 0.013(AS»*ALB)blc ( c a ) 4  Adjusted R - 0.967 2  2  1101 TLA ( a ) = -1.621 t 0.330(ALCblc) ( c a ) 2  2  Adjusted R = 0.920 2  2  [111 TLA ( a ) - -4.171 t 0.302(ALCLBblc) ( c a ) 2  2  Adjusted R = 0.939 2  2  52 Table 8 cone. 1121 TLA U ) = -4.078 » 0.296(ATOTblc) (en') l  Adjusted V -- 0.926  F = 187.9  S.E.E. = 6.04 (•»)  1. Analysis of covatiance (p - 0.05) indicated the model slope oi model elevation vaiied significantly between sites.  In T a b l e variables  8 the  were n o t  transformation. by  the  corrected  transformation  indicated followed  by model  linearly  was  [31  bh  whorls  i n the  annual r i n g s heartwood  to  live  never g r e a t e r  than  were o n l y two  bh  ASW,  and  ALC  was  was  very  i n one  variables.  model  [61.  ASW.  of t h e  (Sprugel  1983).  adjusted  p r e d i c t o r of  R  values  2  InTLA,  the  had  ALC  highest  v a r i a b l e may area  i s greater  less study  i n w h i c h ALC  exceptions  decided  to  be  the  than  the or  than  i t was  and  not  of  include  equal  to  found  there  not  ALC  e q u a l l e d ASW.  and  in  of  was  equal  2  number  number  or  R  determined  when t h e  than  were  = 0.910  2  to d e l i b e r a t e l y  t o be  less  adjusted  (adjusted R  d i f f e r e n c e between ALC  I t was  introduced  and  In t h i s  t o be  the  a t t e n t i o n because they  ALC  samples  restricted little  best  sapwood or  restrict  error  by  e)  attract  The  crown  10%  the  (base  introduced  InTLA the  i n c l u d e heartwood  i n the  and  than  measurements  0.911, r e s p e c t i v e l y ) . as  and  t o TLA  of a l l t h e  less  [5] was  [41,  [2] and  related  s u c h a way  for bias  models u s i n g  t h a t model  Models  log transformed  I t i s s a f e t o assume t h e  When c o m p a r i n g t h e  values  models w i t h  greater  t o ASW, ASW  i n c l u d e heartwood  but  than If  there  as p r e d i c t i v e area  in  ALC  53 when t h e number o f w h o r l s number o f a n n u a l r i n g s The p r o d u c t TLA  i n the l i v e  crown e x c e e d e d t h e  i n t h e sapwood.  o f ASWbh and ALBbh  was l i n e a r l y  related to  (Figure 14).  100  r  (ASW • ALB)bh (cm2'cm2)  F i g . 14. R e l a t i o n s h i p between o n e - s i d e d t r e e l e a f a r e a (m ) and t h e p r o d u c t o f c r o s s - s e c t i o n a l a r e a o f sapwood (ASW) and l i v e b a r k (ALB) a t b h . 2  5.1.3. Base o f L i v e Crown Stem Measurements and T r e e  Leaf  Area All related  selected  s t e m measurements  t o TLA.. E x c l u d i n g  (ASW*ALB)blc  /  the best  adjusted  R  followed  b y model  (adjusted  values  2  R  2  a t t h e b l c were  the product  fitting  was model  = 0.926), model  variable  model a c c o r d i n g  [11] ( a d j u s t e d  [8] ( a d j u s t e d  R  2  linearly  R  2  to the =' 0.939),  = 0.934), model [ 1 2 ]  [10] ( a d j u s t e d  R2 = 0.920), and  54 model  [7] ( a d j u s t e d  fitting  R  model o v e r a l l  0 I 0  = 0.908).  2  Model  [ 9 ] was t h e b e s t  (Figure 15).  i i i i i i 1000 2000 3000 4000 5000 6000 '  i 7000  (ASW • ALB)blc (cm2'cm2)  Fig.15. R e l a t i o n s h i p between o n e - s i d e d t r e e l e a f a r e a (m ) and t h e p r o d u c t o f c r o s s - s e c t i o n a l a r e a o f sapwood (ASW) and l i v e bark (ALB) a t b l c . 2  5.1.4. V a r i a t i o n  Between  Each o f t h e models of  covariance  between s i t e s . varied  Sites i n Table  for variability  As a f u r t h e r  f o r models  [ 4 ] , [5] and [ 6 ]  (p = 0.05).  c h e c k o f v a r i a t i o n between s i t e s t h e mean  T L A : s t e m measurement differences  i n t h e model c o e f f i c i e n t s  The y - i n t e r c e p t  s i g n i f i c a n t l y by s i t e  8 were examined by a n a l y s i s  r a t i o was examined f o r s i g n i f i c a n t  between s i t e s u s i n g  ANOVA  (Table  9).  Mean  TLA:ASWbh r a t i o was 0.32 (+ 0.03 a t p = 0.05) and mean  TLA:ASWblc  r a t i o was 0.43 (+ 0.03 a t p = 0 . 0 5 ) .  al.  (1987) r e p o r t  the  mean TLA:ASWblc  Douglas-fir  t h e mean TLA:ASWbh r a t i o  trees  ratio  were of  The r a t i o s  ALCLBbh,  slopes  of TLA:stem  not s i g n i f i c a n t l y d i f f e r e n t  ALCbh,  t o be 0.34 and  t o be 0.58 f o r 65 t o 70 y e a r - o l d  (n = 5) on t h e e a s t e r n  Washington Cascades.  et  Gower  measurement  between s i t e s  (ASW*ALB)bh, ALBSWblc,  of the  i n the case  and (ASW*ALB)blc  (p < 0.05).  Table 9. Mean ratios of one-sided tree leaf area (m ) and selected stem measurements. 2  SITE ASS  BREAST HEIGHT ASWLB ATOT ALC ALCLB  STEM HEASUREHERTS  BASE OF LIVE CROHN ASH ASWLB ATOT ALC ALCLB ASH *ALB (cm ) (cm ) (cm ) (cm ) (cm ) (cm )  ASH *ALB (cm ) (cm*) (cm ) (cm ) (cm ) (cm*) 2  1  2  2  2  Duncan (n-4) 0.30a 0.26a 0.17ab 0.26a 0.22a 0.020a Courtenay (n=8) 0.30a 0.26a 0.14a 0.27a 0.24a 0.016a Haney (n=4) 0.39b 0.34b 0.21b 0.28a 0.24a 0.017a  2  2  2  2  4  0.36a 0.31a 0.24a 0.28a 0.25a 0.026a 0.46b 0.36a 0.28b 0.34b 0.29b 0.023a 0.44b 0.38a 0.26ab 0.30ab 0.27ab 0.018a  Note: Means separated i n rows and not sharing a common l e t t e r are s i g n i f i c a n t l y d i f f e r e n t at p ( 0.05, using the Tukey BSD multiple comparison test.  5.1.4.1.  Breast  Height  Versus  Base  T h r e e o f t h e TLA p r e d i c t i o n measures varied  coefficients  values  less  measurements  than  which  None o f t h e b l c stem  o r had a d j u s t e d  The mean r a t i o s  d i d not, i n general,  bh s t e m  models u s i n g  s i g n i f i c a n t l y by s i t e 0.90.  Crown  had c o e f f i c i e n t s  (p = 0 . 0 5 ) .  o f t h e TLA p r e d i c t i o n  measures v a r i e d  Live  models u s i n g  as i n d e p e n d e n t v a r i a b l e s  s i g n i f i c a n t l y by s i t e  of  of TLA:stem  become l e s s  variable  R  2  56 between s i t e s b y u s i n g as  b l c measures r a t h e r  independent v a r i a b l e s .  and  TLA:ASWLBblc,  different  5.1.4.2.  with  The one e x c e p t i o n was TLA:ASWLBbh  the l a t t e r  Cross-Sectional  prediction  Area  a measure  models  of  of l i v e  ASWLBbh had a h i g h e r  ALB t o ASW  was a l s o  improved  adjusted  R  2  bark  improved  linearity R  2  t h e TLA  R  2  variable.  w i t h TLA b u t  R  2  ASWbh by  At the b l c , adding  and m u l t i p l y i n g  further,  resulting  The p r e d i c t i v e  by i n c l u d i n g  Adding  t h a n ASWbh when u s e d t o  w i t h TLA.  the adjusted  the adjusted  predictive  Bark  [4] and [ 5 ] ) . M u l t i p l y i n g  in linearity  increased  increased  overall  adjusted  I n T L A (models  ALBbh r e s u l t e d  Live  f o r b o t h b l c and bh measurements.  ALBbh t o ASWbh d i d n o t improve  ALB  not s i g n i f i c a n t l y  between s i t e s .  Including  predict  t h a n bh m e a s u r e s  ALB ( A L C L B ) ,  ASW by  i n the best  value  o f ALC  increasing the  f r o m 0.910 t o 0.911 a t bh and f r o m 0.920 t o  0.939 a t b l c . At  bh i n c l u d i n g  variability  i n t h e model c o e f f i c i e n t s between s i t e s .  However, model independent sectional  ALB i n t h e ASWbh model d i d n o t remove  [ 1 ] , which used  variable,  area of l i v e  d i d n o t v a r y between s i t e s . bark  mean r a t i o o f TLA:ASWbh. TLA:ASWLBbh v a r i e d not.  (ASW*ALB)bh a s t h e  had t h e same i n f l u e n c e  The mean r a t i o s  Crosson t h e  o f TLA:ASWbh and  between s i t e s w h i l e TLA:(ASW*ALB) d i d  At  t h e b l c t h e model c o e f f i c i e n t s  significantly TLAiASWblc and  by s i t e  (p = 0 . 0 5 ) .  varied significantly  d i d n o t vary-  The mean r a t i o o f  by s i t e  while  TLA:ASWLBblc  T L A : ( A S W * A L B ) b l c d i d n o t (p = 0 . 0 5 ) .  5.1.4.3.  Mean Annual  Ring  Width  A t t h e b l c , m u l t i p l y i n g ASW b y MARW r e s u l t e d higher site  adjusted  R  than  2  but decreased  Courtenay s i t e s  when u s i n g ASW a l o n e  the adjusted R  2  in a  a t t h e Haney  a t t h e Duncan and  (Table 10).  T a b l e 10. C o r r e l a t i o n c o e f f i c i e n t s f o r t h e r e l a t i o n s h i p between T L A and ASW and between T L A and (ASW * MARW). Site  BH (ASW * MARW)  ASW Duncan (n = 4) Courtenay (n = 8) Haney (n = 4)  At ASW  0.762  0.996  0.987  0.913  0.953  0.867  0.806  0.662  0.695  0.917  0.929  R  2  value  b y MARW i n t h e c a s e s occurred  general,  these  aJ.'s  value annual  results  was i n c r e a s e d b y m u l t i p l y i n g  o f Haney and C o u r t e n a y b u t t h e  i n the case  o f Duncan  do n o t s u p p o r t  (1987) s u g g e s t i o n ,  variables  that  (Table  Espinosa  with  sapwoood  ASW a s a p r e d i c t i v e ring  width  10). In Bancalari  i f the c o r r e l a t i o n  MARW and ASW i s n o t s t r o n g t h e n  along  BLC (ASW * MARW)  0.831  bh, t h e a d j u s t e d  opposite  ASW  between t h e  MARW s h o u l d  v a r i a b l e o f TLA.  was more c l o s e l y  et  correlated  be o f Mean with  58 ASW  a t bh t h a n  a t b l c i n t h i s study  bh,  prediction  o f T L A was i m p r o v e d  (Table  11).  by m u l t i p l y i n g  And y e t a t ASW by  T a b l e 11. C o r r e l a t i o n c o e f f i c i e n t s f o r t h e r e l a t i o n s h i p between ASW and MARW a t b r e a s t h e i g h t and base o f l i v e crown. Site  Breast  Duncan (n = 4) Courtenay (n = 8) Haney (n = 4)  0.635  0.961  0.627  0.979  0 .823  at b l c multiplying  TLA p r e d i c t i o n 0.5  Base o f l i v e  0.884  MARW f o r two s i t e s w h i l e improved  height  crown  ASW by MARW  f o r o n l y one s i t e .  1  1  1  1  1  H  CM  E  H  0.4  CJ  \  c  CM  H  E D  CD  c  <  <  H  C D  0.3  c c c  1  0.2 0.0  0.1  D  c C  D 1  I  0.2  0.3  1  1  0.4  0.5  0.6  MARWbh (cm)  F i g . 16. V a r i a b i l i t y i n t h e r e l a t i o n s h i p between t h e t r e e l e a f a r e a t o sapwood a r e a r a t i o (TLA:ASWbh) and mean a n n u a l r i n g width.  59 If  t h e sample t r e e s were n o t s t r a t i f i e d by s i t e  R  f o r T L A and (ASW * MARW)bh was 0.705 compared t o 0.845  2  for  the adjusted  T L A and ASWbh. Including  sites)  d i d n o t improve  variable  effect  relationship varied  MARW i n t h e T L A p r e d i c t i o n the f i t because  between s i t e s -  o f MARW w i t h  by s i t e  (Figures  i  (combined  (MARW * ASW) had a  Further  t h e TLA:ASW  model  to that, the  ratio  a t bh and b l c  16 and 1 7 ) .  1  1  1  -  c  CM  E u N  0.5  H  c c c c  CM  E  H  CO  < <  0.4  H  H  C  ^  D C D  C  D D  0.1  I  I  02  0.3  1  0.4  I  0.5  0.6  MARWbic (cm)  F i g . 17. V a r i a b i l i t y i n t h e r e l a t i o n s h i p between t h e t r e e l e a f a r e a t o sapwood a r e a r a t i o (TLA:ASWblc) and mean a n n u a l r i n g width. Mean MARW v a r i e d sites  significantly  between Haney and t h e o t h e r  (F = 34.0 f o r bh measurements  measurements) and t h e r e was l i t t l e  and F = 37.8 f o r b l c variation  o f MARW w i t h i n  the  Duncan and C o u r t e n a y s i t e s .  a r e a was  more v a r i a b l e t h a n  5.1.5. N o n l i n e a r  with  ring  MARW b u t o n l y m a r g i n a l l y s o .  sapwood a r e a  t o TLA i n t h i s  increased  sapwood  Regression  Cross-sectional related  Mean a n n u a l  ASWbh  study.  a t bh was  The r a t i o  not l i n e a r l y  o f TLA:ASWbh  (Figure 18).  0.5  CM  E o \  0.4  CM  JO $ CO  3  0.3  0.2 0  100  200  300  ASWbh (cm2)  Fig. breast breast The  18. The r a t i o o f t r e e l e a f a r e a t o sapwood a r e a a t h e i g h t (TLA:ASWbh) i n c r e a s e d w i t h sapwood a r e a a t h e i g h t (ASWbh).  f o l l o w i n g n o n l i n e a r model was  Quasi-Newton m i n i m i z a t i o n  method  f i t to the data (Figure 19):  using the  61 (9)  TLA = 0.064 * A S W b h • 1  1  3 3  = 0 .975, n = 16,  2  S.E.E.  =  8.29.  300  Sapwood Area at Breast Height  (cm2)  F i g . 19. The r e l a t i o n s h i p between t r e e l e a f sapwood a r e a a t b r e a s t h e i g h t i s n o n l i n e a r . Long the  and S m i t h  (1988, 1989)  TLA:ASWbh r a t i o fir.  suggested  by Long and S m i t h  following  Using  (10)  = 0.976,  S.E.E. =  pine  between  and  n = 16,  8.40.  the d i s t a n c e  crown, and ASWbh, t h e  model was  1  2  D,  (1988),  TLA = 0.063 * ASWbh 1  relations  and  t h e same i n d e p e n d e n t v a r i a b l e s  of the l i v e  nonlinear  similar  and ASWbh f o r l o d g e p o l e  subalpine  bh and t h e c e n t e r  found  area  developed:  4  2  5  *  D  - o - x  9  S  between  62  Equation better  ( 1 0 ) , w i t h an 1  than equation  coefficients  (9).  for similar  and s u b a l p i n e  o f 0.976, f i t  2  the data  marginally  For comparison Table  models d e v e l o p e d  12 g i v e s t h e  for lodgepole  pine  fir.  T a b l e 12. Coefficients TLA = a * ASWbh' * D=.  for nonlinear  models o f t h e f o r m  3  Species  Source  subalpine f i r lodgepole  pine  0 .280  1 .27  -0. 50  (mature)  0 .028  1 .56  -0. 74  (sapling)  0 .021  1 . 47  -0. 14  0 .064  1 . 43  -0. 73  0 .063  1 .42  -0. 20  Douglas-f i r  5.1.6. P r e d i c t i n g S i n c e TLA was blc  Base o f L i v e Crown Stem  Long & S m i t h (1989) Dean & Long (1986) Dean & Long (1986) Long & S m i t h (1988) ( t h i s study)  Measures  f o u n d t o be more c l o s e l y  correlated  to  s t e m measures t h a n bh s t e m measures and bh s t e m measures  a r e much e a s i e r  t o d e t e r m i n e t h a n b l c s t e m m e a s u r e s , i t was  decided  t o examine whether bh s t e m measures c o u l d  predict  b l c stem measures.  e x a m i n e d : ASW,  5.1.6.1.  relation  ASWLB, ASW*ALB, and  Cross-Sectional  Plotting was  Four stem measures  Area  of  were  ALC.  Sapwood  ASWblc v e r s u s ASWbh i n d i c a t e d positively  be u s e d t o  curvilinear  that  (Figure 20).  the  Several and  t r a n s f o r m a t i o n s were c a r r i e d  independent v a r i a b l e s .  transformation  The most  o u t on t h e successful  e of t h e i n d e p e n d e n t  ( l o g base  dependent  variable  200  150 c3 E  100  o  BS CO  <  50  0  0  100  200  ASWbh  300  (cm2)  F i g . 20. Sapwood a r e a a t bh (ASWbh) v e r s u s at b l c (ASWblc). ASWblc) y i e l d e d t h e f o l l o w i n g e q u a t i o n : (11)  LnASWblc  = 3.431  adjusted  R  F  Plotting  2  sapwood  area  + 0.008(ASWbh)  = 0.850, n = 16,  = 85.928. •  the r e s i d u a l s  underestimated overestimated  by s i t e  t h e ASWblc t h e ASWblc  indicated  t h e model  i n Haney and Duncan s i ' t e s and i n the Courtenay  site.  64 5.1.6.2.  Cross-Sectional  As w i t h ASW, indicated  that  Area  of  Sapwood  and  Live  p l o t t i n g ASWLBblc a g a i n s t  Bark  ASWLBbh  t h e r e l a t i o n s h i p was s l i g h t l y  curvilinear  (Figure 21).  300  r  200  CSJ  E  _o SD  CO CO <  100  0 100  0  200  300  ASWLBbh (cm2)  F i g . 21. C r o s s - s e c t i o n a l a r e a of sapwood p l u s l i v e b a r k a t bh (ASWLBbh) v e r s u s c r o s s - s e c t i o n a l a r e a o f sapwood p l u s l i v e bark a t b l c . A log transformation  (base  e) of t h e d e p e n d e n t  ASWLBblc was most s u c c e s s f u l (12)  LnASWLBblc = 3.617 adjusted F  R=  = 106.994.  y i e l d i n g the  equation:  + 0.007(ASWLBbh)  = 0.876,  n = 16,  variable  Plotting  the  residuals  underestimated overestimated  5.1.6.3. Area  the the  by s i t e  ASWblc ASWblc  in  Cross-Sectional  of  Live  The  the the  Area  Haney  the  site  Courtenay  of  Sapwood  model and  s i t e .  *  Cross-Sectional  Bark  r e l a t i o n  s l i g h t l y  in  indicated  between  c u r v i l i n e a r  8000  (ASW*ALB)blc  (Figure  and  (ASW*ALB)bh  was  22).  r  6000 CM  E  4000  CD  CO  <  2000  2000  0  4000  6000  8000  (ASW'ALB)bh (cm2)  F i g . 22. The product of c r o s s - s e c t i o n a l a r e a of sapwood and l i v e b a r k a t bh ((ASW*ALB)bh) v e r s u s the product of c r o s s - s e c t i o n a l , a r e a of sapwood and l i v e bark a t b l c .  Attempts  to  improve  unsuccessful. data  produced  l i n e a r i t y  Regression the  using  analysis  following  model:  transformations on the  were  nontransformed  66  (13)  (ASW*ALB)blc = -99.371 adjusted  R  2  +  0.837(ASW*ALB)bh  = 0.853, n = 16,  F = 88.010.  Plotting  the r e s i d u a l s  indicated variable plot  variability i n the case  a g a i n s t the independent increases with the  variable  independent  o f t h e Duncan and C o u r t e n a y  sites.  of the e s t i m a t e s a g a i n s t the dependent v a r i a b l e  a wide s c a t t e r  around  the l e a s t  squares  linear  A  showed  regression  1 ine.  5.1.6.4. Rings  Cross-Sectional Equal  The  in  Area  Number  relation  to  the  of  Most  Number of  between A L C b l c  Recent  Annual  Whorls  and ALCbh was  in  Sapwood  Live  Crown  linear  (Figure 23): (14)  ALCblc  = 5.795  adjusted F  The  =  R  2  + 0.795(ALCbh)  = 0.958,  n = 16,  339.225  s c a t t e r g r a m of the r e s i d u a l s  unbiased  and t h e g r a p h  a good f i t . Courtenay  against the estimates  of estimates a g a i n s t the a c t u a l s  However, t h e model o v e r e s t i m a t e d A L C b l c  site  was  and u n d e r e s t i m a t e d  ALCblc  i n t h e Haney  was  i n the site.  300  200 CNJ  £ o  • ••  u  O  <  100  1  0  1  100  i  200  i  300  400  ALCbh (cm2)  23.  Fig.  5.2.  ALCbh v e r s u s  DISCUSSION  5.2.1.  Base o f L i v e  According the bh.  Waring  to adjusted R  et  al.  Bancal-ari  found  et  (1987)  fast  stand of 22 y e a r - o l d  b l c was a b e t t e r  measures t a k e n a t  o f T L A t h a n stem  (1982) al.  Breast Height  v a l u e s , stem  2  predictors  s t a n d was r e l a t i v e l y  growing the  Crown V e r s u s  b l c were b e t t e r  Espinosa the  ALCblc.  t h e same f o r D o u g l a s - f i r . found  that  i t mattered i f  or slow growing. Douglas-fir  predictor  measures a t  trees  In t h e f a s t diameter a t  o f T L A t h a n a t bh.  measures a t t h e b l c c o n s i d e r e d i n t h i s  Stem  s t u d y were a l l  68  linearly  related  t o TLA and had a d j u s t e d  R  A t bh two models had a d j u s t e d  values  2  than  0.90.  than  0.90 and t h r e e o f t h e models were n o n l i n e a r .  coefficients sites.  based  R  values  2  support  bh s t e m m e a s u r e s .  T L A : s t e m measure using  ratios  b l c r a t h e r than  Cross-sectional  the adjusted  for  t h e ATOT model  for  the r e l a t i o n s h i p  with  R  o f Sapwood V e r s u s  sapwood  value  2  was b a s a l a r e a  (ATOT).  At the  f o r t h e ASW model was lower 0.926).  than  The a d j u s t e d  R  2  d i f f e r e n c e (p = 0.05) i n t h e r a t i o o f  than  That  the adjusted  R  2  value f o r  i t was f o r A T O T b l c i n a TLA p r e d i c t i o n  model c o n t r a d i c t s t h e p i p e model t h e o r y either  Area  between ASWblc and A T O T b l c was 0.969  ASW:ATOT by i n s t a l l a t i o n . ASWblc was lower  Basal  a r e a was n o t c o n s i s t e n t l y a  (0.908 v e r s u s  no s i g n i f i c a n t  was n o t d e c r e a s e d  bh m e a s u r e s .  p r e d i c t o r o f TLA t h a n  blc  less  The v a r i a b i l i t y i n  between s i t e s  5.2.2. C r o s s - S e c t i o n a l A r e a  better  No model  t h e comment by G e r o n and Ruark  (1988) t h a t b l c s t e m m e a s u r e s a r e p h y s i o l o g i c a l l y than  greater  on b l c s t e m measures v a r i e d between  These r e s u l t s  arbitrary  greater  and s u g g e s t s  that  a v a r i a b l e e x p l a i n i n g d i f f e r e n c e s i n sapwood  permeability  between  individuals  needs t o be i n c l u d e d i n t h e  model o r f u r t h e r c o n s i d e r a t i o n s t h a t move beyond t h e t h e o r y need  t o be e x p l o r e d .  t h e ASW model h a v i n g (0.894 v e r s u s  0.790).  significantly  between  A t bh t h e s i t u a t i o n a higher  R  2  value  was r e v e r s e d  than  t h e ATOT model  B o t h models a t bh v a r i e d installations.  with  The r e l a t i o n s h i p  69 between ASWbh and ATOTbh was n o t a s s t r o n g adjusted  R  o f 0.882 and t h e r a t i o  2  a s a t b l c w i t h an  o f ASW:ATOT  being  s i g n i f i c a n t l y d i f f e r e n t between t h e C o u r t e n a y and Duncan installations considerable report  (p = 0.05).  strong  stand  linear  a r e s u l t of the  B r i x and M i t c h e l l  i n Douglas-fir.  between  A T O T b l c was a b e t t e r  However, t h e u n i f o r m i t y v a r i a t i o n i n the  i n d i v i d u a l s , does n o t e x p l a i n  f i t w i t h TLA t h a n was ASWblc.  highly  uniform stands, with  ratio,  the pipe  should  p r e d i c t TLA e q u a l l y  ATOT i n c l u d e s  (1983)  r e l a t i o n s h i p s between ASWbh and  s t r u c t u r e , which r e s u l t s i n l i t t l e  ASW:ATOT r a t i o  little  model t h e o r y  For  v a r i a t i o n i n t h e ASW:ATOT  suggests that  well.  why  This  ATOT and ASW  study suggests  that  a measure o f t h e s t e m w h i c h r e l a t e s t o crown  dimensions which ALC  is likely  v a r i a t i o n i n ADBbh.  ATOTbh(under b a r k ) in  This  i s not included  i n ASW.  The r e s u l t s f o r  and ALCLB s u g g e s t what t h o s e m e a s u r e s m i g h t be and a r e  discussed  in section  5.2.3. I n f l u e n c e  5.2.5.  of E c o l o g i c a l S i t e Q u a l i t y  on A l l o m e t r i c  Equations In t h i s [6]) al.  varied  study several significantly  (1987) f o u n d  that  fora fast  slopes  ( [ 4 ] , [ 5 ] , and et  Espinosa  Bancalari  slopes  u s i n g dbh,  i n T L A p r e d i c t i o n models were  growing stand  slow growing stands regression  by s i t e .  the regression  ASWbh, and (ASW * MARW)bh higher  o f t h e bh models  than  of D o u g l a s - f i r .  f o r intermediate Their  study  f o r ASWblc and d i a m e t e r ( b l c )  and  found t h e increased  70 from  f a s t to slow to intermediate  a u t h o r s do n o t i n d i c a t e slopes  growth s t a n d s .  i f the differences  The  i n regression  between s t a n d s were s i g n i f i c a n t l y d i f f e r e n t .  study the regression  slopes  d i d not vary s i g n i f i c a n t l y  between s i t e s whereas t h e s l o p e  T a b l e 13. prediction  Comparison of s l o p e models w h i c h v a r i e d  Independent variable  intercepts  d i d (Table 13).  i n t e r c e p t s f o r InTLA s i g n i f i c a n t l y by s i t e .  Site  a  b  ASWbh  Duncan Courtenay Haney  2.204 2.362 3.029  0.011 0.009 0.007  ASWLBbh  Duncan Courtenay Haney  2.194 2.296 2.995  0.010 0.008 0.006  ATOTbh  Duncan Courtenay Haney  2.288 2.328 3 . 023  0.006 0.005 0.004  N o t e : The f o r m o f t h e l i n e a r model X i s the independent v a r i a b l e  In T a b l e of  Binkley that  with s i t e  quality.  intercepts  Brix  ( 1 9 8 4 ) , and E s p i n o s a  t h e TLA:ASW v a r i e d  suggests the r a t i o  and M i t c h e l l  Bancalari  with s i t e  listed  et  quality.  al.  there  (1983),  (1987) In t h i s  found study  b l c model c o e f f i c i e n t s d i d n o t v a r y s i g n i f i c a n t l y  between s i t e s , coefficients an  i n slope  i s InTLA = a + b X, where  InTLA t o any of t h e independent v a r i a b l e s  increases  the  13 t h e t r e n d  In t h i s  additional  would  account  suggesting  the d i f f e r e n c e s  between s i t e s a t bh r e s u l t e d physiological  variable  for differences  i n model from t h e lack of  i n t h e bh m o d e l s  between bh and b l c ASW.  that  71  5.2.4. Mean A n n u a l R i n g It  Width  was h y p o t h e s i z e d  that  improve t h e TLA p r e d i c t i o n  mean a n n u a l r i n g w i d t h  model and a c c o u n t  would  for differences  i n model c o e f f i c i e n t s between s i t e s b e c a u s e MARW s h o u l d partially  account  between t r e e s variable,  for differences  and s i t e s .  i n sapwood  The r e s u l t s  permeability  i n t h i s study are  o f f e r i n g no f i r m c o n c l u s i o n s .  At  the b l c the  models d i d n o t v a r y between s i t e s and t h e r e f o r e of MARW was l e s s  important  (1984) t r a n s f o r m e d  t h e ASWbh v a r i a b l e  sapwood p e r m e a b i l i t y differences  than a t bh.  and by so d o i n g  between T L A p r e d i c t i o n  the e f f e c t  Whitehead  et  al.  by m u l t i p l y i n g removed  models  i t by  slope  for Sitka  and  lodgepole pine.  Thompson  TLA  prediction  f o r l o d g e p o l e p i n e b y m u l t i p l y i n g ASW  by  MARA.  model  (1989) i m p r o v e d  spruce  I n t h i s s t u d y MARA v a r i e d  Multiplying  little  the f i t of h i s  f r o m MARW.  ASWbh b y MARW d i d n o t improve t h e r e l a t i o n s h i p  with TLA ( F i g u r e  24).  A natural  log transformation  o f TLA  and  (ASW * MARW) d i d improve t h e r e l a t i o n s h i p between t h e  two  variables.  intercept Therefore,  An a n a l y s i s  of covariance  coefficient varied including intercepts  indicated  s i g n i f i c a n t l y between  MARW d i d n o t a c c o u n t  the  slope  nor  d i d i t improve t h e m o d e l ' s  that the sites.  for variability i n  between s i t e s i n t h e TLA-ASWbh linearity.  model  MARW d i d n o t  improve t h e r e l a t i o n s h i p o f T L A t o ASW i n D o u g l a s - f i r (Espinosa Bancalari  et  al.  1987).  Espinosa  Bancalari  et  al.  72 (1987 ) a l s o  found  significantly  the r a t i o  o f TLA-.ASW a t b l c v a r i e d  and MARW d i d n o t .  I t may be t h a t  a more  100  80 CM  E  60  CD CD  < CO CD  40  CD CD  20  0 0  100  50  150  (ASW • MARWObh (cm2 • cm2)  F i g . 24. The r e l a t i o n s h i p between t r e e l e a f a r e a and t h e p r o d u c t o f sapwood a r e a and mean a n n u a l r i n g w i d t h a t b r e a s t h e i g h t ((ASW*MARW)bh) i s n o t l i n e a r . precise  measure o f sapwood  n e c e s s a r y t o improve Mean a n n u a l variability stratified this in  ring  the TLA p r e d i c t i o n width  by s i t e .  t h e Haney s i t e  expect  was f o u n d  Crown  sites.  more l i g h t  closure  some  when t h e d a t a was  than  that  crown  c o m p e t i t i o n between  closure  i n t h e Duncan and  T h e r e f o r e , i n t h e Haney s i t e  c o n c u r r e n t l y more v a r i a b i l i t y  /  was n o t q u a n t i f i e d i n  i t was o b s e r v e d  was more a d v a n c e d  model.  to explain  i n t h e ASW-TLA r e l a t i o n s h i p  s t u d y but v i s u a l l y  Courtenay  p e r m e a b i l i t y t h a n MARW i s  one would  individual  i n MARW between  t r e e s and  individuals  73  than  a t t h e two o t h e r  Figures the  sites.  i s shown i n  16 a n d 17 where MARW v a r i e d n o t i c e a b l y more amongst  Haney sample t r e e s t h a n  T h i s was s u p p o r t e d effect  This effect  by the f a c t  i n improving effect  little  the  m o d e l s were i m p r o v e d  f r o m 0.917  R  t h a t MARW had a p o s i t i v e  on t h e o t h e r  t o 0.929  sites.  site  I n Haney t h e f i t o f  a t bh and b l c b y m u l t i p l y i n g ASW b y  increased  2  sample t r e e s .  t h e f i t o f t h e model on t h e Haney  and  MARW; a d j u s t e d  amongst t h e o t h e r  f r o m 0.662 t o 0.695  at blc.  At the other  a t bh and  two s i t e s  the f i t  of t h e m o d e l s a t bh and b l c were p o o r e r  when ASW was  multiplied  a t C o u r t e n a y where  the  b y MARW, t h e e x c e p t i o n  being  f i t o f t h e model a t bh was i m p r o v e d .  stands the  f o r w h i c h Thompson  TLA p r e d i c t i o n  greatly  i n stand  density  f r o m 550 t o 650 s t e m s / h a . advanced  component  i n improving  (3,853 t o 12,597 s t e m s / h a ) . in this  with  in variation  Stands with  between t r e e s would  o f MARW on t h e p r e d i c t i o n  study  density  Stand ranging  However, crown c l o s u r e i n Haney  enough t o r e s u l t  o f t h e model.  competition  (1989) had s u c c e s s  pine  model b y m u l t i p l y i n g ASW b y MARA v a r i e d  d e n s i t y was n o t a f a c t o r  was  The l o d g e p o l e  i n MARW, a u s e f u l  a high degree of  likely  show a marked  effect  models.  5.2.5. Number o f L i v e W h o r l s At from R  2  bh, ALC and ALCLB were t h e o n l y v a r i a b l e s ,  (ASW*ALB), w h i c h were l i n e a r l y  = 0.910  and 0.911, r e s p e c t i v e l y ) ,  coefficients  d i d not vary  related  aside  t o TLA ( a d j u s t e d  whose r e g r e s s i o n  between s i t e s ,  and, i n r a t i o  with  74 TLA,  d i d n o t v a r y between s i t e s .  higher  adjusted R  ALCLBblc  was  2  t h a n ASW  A t t h e b l c , ALC  and,  a s i d e from  the best p r e d i c t i v e  variable  ALCLB d i f f e r e d  f r o m ASWLB i n t h a t  i n a l l but  samples.  two  i t included  in ALCblc  was  linearly  heartwood  i n ALCbh  central given  concept  proportional physical  related  (adjusted R  These r e s u l t s  leaf  The  2  f o r ALC  and  appears  (heartwood).  bh,  some h e a r t w o o d  AHW  from  included a r e a of  = 0.888; F = 120.0;  and  ALCLB s t r e t c h  and  amount o f c o n d u c t i n g stemwood  and  At  to c r o s s - s e c t i o n a l  mass o r a r e a r e q u i r e s  s u p p o r t stemwood  i n c l u d e s ASW  i t included  o f t h e P i p e Model T h e o r y  transpiring  o f TLA.  a l l heartwood.  a  (ASW*ALB)blc,  A t t h e b l c , ALCLB d i f f e r e d  ASWLB i n t h a t  S.E.E. = 1 1 . 4 ) .  had  suggest both  that  ALC  a  a  (sapwood)  The  the  and  variable  t o p r o v i d e a measure o f t h e a r e a o f  h e a r t w o o d w h i c h t h e crown d e p e n d s on  for physical  support.  5.2.6. N o n l i n e a r M o d e l s F o r m o d e l s u s i n g ASWbh, ASWLBbh, and be  log transformed  linearity  variable.  variables  ASWblc, d i a m e t e r  et  relationship  used  in their  Brix  al.  and  The  Mitchell TLA  ( e . g . , dbh,  three s i t e s  linear  used  also  and ASWbh,  natural  (1983) f o u n d  t o be  to  and  (1987)  (ASWbh * MARW)) w i t h  between ASWbh and  of D o u g l a s - f i r .  study  had  the  between t h e d e p e n d e n t  Espinosa Bancalari  a t b l c , and  transformations.  stand  i n o r d e r t o improve  i t n e c e s s a r y t o t r a n s f o r m both the dependent  independent  log  e)  of the r e l a t i o n s h i p  independent found  (base  ATOTbh, TLA  the  in a thinned  in this  study  75 had  been t h i n n e d , r e m o v i n g  earlier  date.  relationship suppressed the  a l l suppressed  Dean and L o n g  (1986) f o u n d  between TLA and ASWblc  t r e e s were e x c l u d e d  inclusion  nonlinear.  of suppressed  This suggests  n o t been removed  from  have had a s i m i l a r  trees  that  f o r l o d g e p o l e p i n e when However, w i t h  the r e l a t i o n s h i p  i f suppressed in this  became  i n d i v i d u a l s had  study they  on t h e r e l a t i o n s h i p  would  between TLA  and  ASWblc.  and  1989) f o u n d  for  s u b a l p i n e f i r and l o d g e p o l e p i n e were enhanced b y  introducing  Dean and Long  a t an  a linear  from t h e d a t a .  the s i t e s  impact  trees,  their  a second  (1986) and Long and S m i t h (1988  n o n l i n e a r models f o r TLA p r e d i c t i o n  power t e r m ,  D (where D i s t h e d i s t a n c e  between bh and t h e c e n t e r o f t h e l i v e D i n the nonlinear p r e d i c t i o n impact  on t h e m o d e l .  varied  significantly  crown).  model o f t h i s  T h i s was s u r p r i s i n g by s i t e .  I n c l u s i o n of  s t u d y had l i t t l e  a s t h e mean D  The mean v a l u e f o r D a t  Duncan was 6.55 m (n = 4; S.E.M. = 0.87) w h i c h was significantly  different  (p = 0.05) f r o m  11.18 m (n = 4;  S.E.M. = 0.43) f o r Haney and 12.74 m (n = 8; S.E.M. = 0.60) for  Courtenay.  include  I n t h e s i m p l e n o n l i n e a r model w h i c h d i d n o t  D as a second  when p l o t t e d differences marginal resulting  variable  residuals  a g a i n s t D or s i t e .  I t appears  i n D d i d not influence  improvement from  were n o t b i a s e d that  significant  t h e TLA-ASW m o d e l .  The  i n t h e f i t o f t h e n o n l i n e a r model  D d i d not warrant  i t s inclusion  i n t h e model.  76 5.2.7. C r o s s - S e c t i o n a l The g e n e r a l l y  Area of L i v e  Bark  p o s i t i v e r e s u l t s o f i n c l u d i n g ALB  TLA p r e d i c t i o n models e i t h e r by a d d i n g using  the product  o f ASW  and ALB  equations.  correlated  w i t h TLA a t bh and b l c w i t h a d j u s t e d  also  found  species  strong  suggest  et  that  consideration  to live  only  bark  1978).  store  with  transporting  and s t o r i n g  The r e s u l t s o f t h i s  provide  (1987) who  of the  measures  An  and  important of  f o l i a g e and t h e use Phloem  ( S a l i s b u r y and  study suggest  a proportional  who  of water t r a n s p o r t  excess carbohydrates  that  Ross  t h e crown  amount o f p h l o e m c a p a b l e o f  carbohydrates.  Crown Stem  s t u d y complemented  found  that  Measures the f i n d i n g of  s t e m measures t a k e n a t b l c  better  predictions  o f TLA t h a n bh s t e m m e a s u r e s .  However, s i n c e  bh m e a s u r e s  are easy t o o b t a i n  desirable  i f b l c stem measures c o u l d  stem measures.  This  of  and TLA f o r t h r e e  functions.  5.2.8. P r e d i c t i o n o f Base o f L i v e  Hungerford  (1985),  by t h e g r o w i n g s t e m .  The r e s u l t s o f t h i s  interacts  values  2  between crown and s t e m i s t h e p r o d u c t i o n  those carbohydrates  parenchyma  R  our u n d e r s t a n d i n g  c a r b o h y d r a t e s by t h e p h o t o s y n t h e s i z i n g of  al.  strongly  between TLA and c r o s s - s e c t i o n a l s t e m  n e e d s t o move beyond t h i n k i n g  interchange  Brack  ALB was  c o r r e l a t i o n s between ALB  o f Eucalyptus,  relationship  give  study,  0.783, r e s p e c t i v e l y .  and ALC or  e n c o u r a g e s i t s use i n  allometric  0.799 and  In t h i s  i t t o ASW  i n the  study  i t would  be p r e d i c t e d  i n d i c a t e d one c a n n o t  be  using  assume a  bh  77 linear blc.  r e l a t i o n s h i p between a g i v e n Three of the v a r i a b l e s  (ASW*ALB)) were n o n l i n e a r and  the b l c .  variable  examined  i n their  The ALC v a r i a b l e  w h i c h was c l e a r l y  (ASW, ASWLB and  r e l a t i o n s h i p between bh  s t a n d s out as t h e o n l y  linear  between t h e b l c and b h .  This  include  i n future  t h e ALC v a r i a b l e  s t e m measure a t bh and  in its relationship  i s another  good r e a s o n t o  allometric  studies.  I n t h e models f o r e a c h o f t h e f o u r  residuals  were b i a s e d  to  towards s i t e .  be u s e d t o p r e d i c t  variables the  I f bh s t e m m e a s u r e s a r e  b l c s t e m measures a much l a r g e r  t h a n n = 4, a s t h e c a s e  f o r t h e Duncan and Haney  w o u l d need t o be g a t h e r e d each  relationship  sample  sites,  and s e p a r a t e m o d e l s d e v e l o p e d f o r  site. Using  predicted  t h e models  i n Table  by t h e i n d e p e n d e n t  8 and s e c t i o n  variables  5.1.6., T L A was  ASW, ASWLB,  (ASW*ALB), ALC a t bh and t h e b l c and t h e s e same b l c variables  as p r e d i c t e d  measurements. destructive  m o d e l s was s t r o n g e s t  equally  as w e l l  equations stands  and t h e p r e d i c t e d  TLAs b a s e d  f o r t h e models b a s e d  Breast  on t h e  on b l c s t e m  height  s t e m measurements p r e d i c t e d  as p r e d i c t e d  b l c s t e m measurements d i d .  5.2.9. P o r t a b i l i t y The  bh s t e m  The c o r r e l a t i o n between T L A a s d e t e r m i n e d by  sampling  measurements.  by t h e c o r r e s p o n d i n g  of Tree Leaf  feasibility of t h i s  of using  Area P r e d i c t i o n  the stronger  study to predict  i n t h e CWH zone  i s enhanced  TLA  Model  allometric  TLA i n other by t h e f a c t  Douglas-fir that the  78 adjusted of  values  a  TLA v a l u e s  Several to  R  from  were h i g h  f o r t h e b e s t models and r a n g e s  the three  installations  restrictions  which these 1)  as t o t h e types  allometric  equations  of D o u g l a s - f i r stands should  apply a r e :  recently  spaced  stems/ha  i n w h i c h crown c l o s u r e h a s y e t o r o n l y  recently  occurred.  that  suppressed  relationships  i n t h e r a n g e o f 500 t o 700  Dean and L o n g  (1986)  t r e e s have d i f f e r e n t  indicate  linear  between T L A and ASWbh t h a n  crown c l a s s e s . using  stands  overlapped.  other  T h i s p r o b l e m c a n be a l l e v i a t e d by  nonlinear relationships,  measurements, o r n o t i n c l u d i n g  u s i n g b l c stem suppressed  individuals; 2)  stands Brix  w h i c h have n o t r e c e n t l y been  and M i t c h e l l  affected  (1983) found  the linear  ASWbh 5 t o 9 y e a r s 3)  stands in  less  this  not  than  study  relationships after  60 y e a r s  with  Mitchell  of age.  The sample t r e e s  equations  apply to  trees.  is little  the nonlinear  equations  between TLA and  were b e l o w 50 y e a r s - o l d and i t s h o u l d  5.2.10. C o m p a r i s o n W i t h O t h e r There  fertilization  t r e a t m e n t ; and  be assumed t h e a l l o m e t r i c  older  that  fertilized.  of t h i s  Work  Douglas-fir allometric  ( u s i n g ASWbh) o r l i n e a r study.  (1983) f o u n d  Waring  et  al.  the r e l a t i o n s h i p  data  t o compare  ( u s i n g ASWblc)  (1982) and B r i x and between ASWbh and TLA  79  t o be l i n e a r al.  (1987) and Gower  d e p e n d e n t and of al.  their  a slope  v a r i a b l e s t o improve  TLA-ASWblc  through  s t u d y t h e c o n s t a n t was  regression  coefficient  forced  f o r the  was  the slope  model  0.515.  as t h e i n d e p e n d e n t  models  Waring  the o r i g i n  forced  for Douglas-fir  et  linear  and t h e  became 0.451.  v a r i a b l e were n o t  linearity  insignificant  I f t h e model was  coefficient  regression  (p = 0.05)  both the. the  for Douglas-fir.  coefficient  et  Espinosa Bancalari  (1987) t r a n s f o r m e d  o f TLA and ASWblc  In t h i s  nonlinear  al.  (1984),  a l l o m e t r i c equations  regression  origin  et  independent  (1982) f o u n d  0.54.  e r al.  and G r i e r  t o be  f o r the  slope through the  Reports  of  TLA w i t h ASWbh  available.  80 6. PHOTOGRAPHY 6.1.  RESULTS Taking  of  57.5°  being  photographs  resulted  situated  f r o m 12 m d i s t a n c e  i n the  i n the  at  a camera  image of some s a m p l e t r e e s  center  of t h e  exposure,  angle  not  requiring  Table 14. Description of photographs selected for analysis. Tree -  Zenith angle (degrees)  Zooa lens setting  Disl .ance fi on tret ! (m)  Partial silhouette area (en )  Crown portion of tree  D-l  71  50  2  35.50  1.00  1.00  35.50  D-2  57.5  50  2  36.49  0.95  0.90  42.68  D-2 -  57.5  50  12'  37.82  0.95  0.95  41.91  D-3  57.5  50  2  40.50  0.60  1.00  67.50  D-4  57.5  50  12  31.88  0.76  1.00  41.95  C-l  57.5  85  4  56.90  0.67  0.98  86.66  C-2  57.5  50  12  15.21  0.88  1.00  17.28  C-3  57.5  50  12  40.99  0.98  1.00  41.83  C-3 -  57.5  50  L2  31.86  0.94  1.00  33.89  C-4  45.0  50  12  13.78  0.92  1.00  14.98  C-5  57.5  50  14  31.47  0.97  1.00  32.44  C-6  57.5  50  14  30.91  0.94  0.98  33.88  C-7  57.5  85  14  82.90  0.82  0.98  103.16  C-8  45  85  111.62  0.79  0.95  148.73  1  2  1  (Ml)  1 2  3  Portion of tree in photo  Total silhonette area (CD ) 2  "  1. D-l through D-4 refer to sample trees from Duncan and C - l through C-8 refer to sample trees fron Courtenay. 2. The second exposure of the same tree was taken at right angles from the f i r s t exposure.  81 adjustments  in distance  advanced  crown c l o s u r e ,  site  relatively  The  had  photographs  setup  or camera a n g l e .  Figure  u n o b s t r u c t e d images  selected  for further  (estimated  area are given 25  illustrates  by d e s t r u c t i v e  I  a r e s u l t of  none o f t h e e x p o s u r e s  f o r each photograph,  silhouette  As  and  from the  of the t r e e  analysis,  crown.  exposure  t h e c a l c u l a t i o n of  in Table  Haney  total  14.  t h e r e l a t i o n s h i p between s a m p l i n g ) and  silhouette  TLA area.  W W  80  c  -  CM  E CO CD  60  c  cd CD CD CD  40  D  C  C D  20  C  I  0  50  100  I  150  Silhouette Area (cm2)  F i g . 25. S c a t t e r g r a m o f t r e e l e a f a r e a (m ) and s i l h o u e t t e a r e a ( c m ) , where D i n d i c a t e s a sample t r e e Duncan and C i n d i c a t e s a sample t r e e f r o m C o u r t e n a y . 2  2  from  82 6.2.  DISCUSSION Figure  the  for before  made u s i n g the  in  sun  angle  photograph the  influenced  crown.  spread deeper at d e n s i t y between s k y 2)  variables  Important  p o s i t i o n of light  w h i t e as  the  majority  Later  through the  and  the  in  the  day  s u n n y day  the  bright  on  cloud  may  This  cover 3)  differences  taking  the  the  time  of  foliage  appeared  photo was  in  was  off  the was  attempts  exposure  was to  find  tree  and  darker denser.  with  light  an  Consequently,  of  less  to the  sky  while  even t h o u g h On  days  the  with  serious.  a fixed distance  photos, d i f f e r e n c e s  high  difficult  the  varied  c l o u d y days  camera.  considerably  - given  crown  i t was  have been r e l a t i v e l y  height  the  and  it difficult  top  t h i s p r o b l e m was  tree  of  the  complicated  sunny days t h e r e  photographs,  between t h e  not  be  variation  reflectance  - e x p o s u r e of  crown making  l o w e r crown a p p e a r e d  foliage  at  I f the  the  exposure s e t t i n g f o r the  differentiate  be  leaves;  On  i n the  sun  reflectance  sky.  crown.  measurement b a s e d  light.  appropriate  could  s o u r c e s of  between c l e a r d a y s w i t h d i r e c t s u n l i g h t  contrast  o f TLA  of r e f l e c t a n c e  i n the  weather c o n d i t i o n s  diffuse  variation in  would have t o  reflectance  Areas with high  t a k e n at mid-day, the the  two  considerable  accurate predictions  - the  photograph.  of  the  were:  w h i t e , sometimes as  top  that  s i l h o u e t t e area.  analysis  1) the  indicates  r e l a t i o n s h i p between t h e  accounted  in  25  in tree  height  and  angle  resulted  for in  83 variation trees  ended up b e i n g  Further also  i n the probe a n g l e  aggravating  through  t h e crown.  i n t h e upper p o r t i o n  Taller  of the exposure.  t h e p r o b l e m was v a r i a b l e t e r r a i n  which  e f f e c t e d where t h e t r e e was on t h e e x p o s u r e when t h e  distance  between t h e t r e e  were f i x e d .  With t a l l  and camera and t h e camera  trees  positioned  angle  a t the t o p of the  p h o t o g r a p h t h e e x p o s u r e v i e w was t h r o u g h t h e b o t t o m o f t h e tree.  Shorter  trees  were p o s i t i o n e d  i n the middle  p h o t o g r a p h and t h e v i e w was o f t h e b r o a d s i d e 4)  view options  i n the background  one d i r e c t i o n , sometimes two.  v i e w o f t h e t r e e , mean s i l h o u e t t e a r e a calculated  of the t r e e ;  - i n most c a s e s a c l e a r v i e w o f t h e  t r e e w i t h no o b s t r u c t i o n s from o n l y  of the  f o r each t r e e  was a v a i l a b l e  W i t h more t h a n one  could  have  and some v a r i a b i l i t y  been  taken  into  account. 5) terrain settings  camera s e t t i n g s  than the usual  i t level  50 mm  during  camera n o t b e i n g  appeared  or s l o p i n g  zoom, 12 m d i s t a n c e ,  I t was a l s o d i f f i c u l t  sources  to l e v e l  the photograph s e s s i o n .  known how much v a r i a b i l i t y  The  trees  i t was sometimes n e c e s s a r y t o u s e d i f f e r e n t camera  camera a n g l e . keep  - with t a l l  was i n t r o d u c e d  and 5 7 . 5 °  t h e camera and I t was n o t  as a r e s u l t o f t h e  level. of v a r i a b i l i t y  t o be 2 ) , 3 ) , and 5 ) .  have been c o n t r o l l e d by t a k i n g  that  had t h e g r e a t e s t  Variability  source  impact  2) c o u l d  p h o t o g r a p h s a t t h e same t i m e  of d a y and under s i m i l a r w e a t h e r c o n d i t i o n s ;  ideally  84 overcast  cloud  made t h i s  conditions.  a difficult  Considering unobstructed  how  that could  source  3).  but  and  prospect  silhouette promise  area  distance  those or  necessary  i n the  i n these field  to reduce  the  s i l h o u e t t e areas  of adding  another  an  there  was  variability derive  a  in  t o a common b a s e ,  c o r r e c t i o n to the  entire  would seem t o h o l d  p h o t o g r a p h s w h i c h were n o t  a t a zoom s e t t i n g  conditions  of  50  mm,  little  i t would  be to  T h i s was  not  stand  density,  terrain,  and  e n c o u r a g e s a more f l e x i b l e  approach  which  fixed  angles.  A more  fruitful  a p p r o a c h m i g h t be  camera d i s t a n c e s one  described surface  by  area  and  which u t i l i z e s  o f sample b r a n c h e s t o d e t e r m i n e b r a n c h  leaf  m  c o r r e c t i o n f a c t o r i n order  in tree size,  require  determined  12  study.  does not  technique  taken at  images t o a common s t a n d a r d .  in this  Variability  the  stands,  c o r r e c t i o n f a c t o r f o r each t r e e  to d e r i v e a second  attempted  of  were t o g e t  p o s s i b l e to mathematically  d e r i v a t i o n process  a l l photo  light  field  f o r p r e d i c t i o n improvement.  For  bring  opportunities there  done  slope  to standardize  the  few  I t would be  height  order  be  i n the  task.  v i e w of a t r e e crown  little  tree  Time c o n s i d e r a t i o n s  leaf  D i e b o l t and of  Scots  video  area.  Mudge  pine  a  who  video-  imaging system, c o u l d  be  The  only p a r t i a l l y destructive, requiring  a p p r o a c h would be  branches the  from d e s i g n a t e d  number o f b r a n c h e s  crown p o r t i o n s  fitting  and  into basal  of  Adaption  (1988),  using  a p p l i e d to branches  imaging  an  area  older  trees.  estimate  of  categories.  85 7. SUMMARY 7.1.  SAMPLING Overall  SLA  ANALYSIS mean SLA was 42.8 cm /g  was f o u n d t o v a r y s i g n i f i c a n t l y  class, ratio  and crown p o s i t i o n was 0.421  crown p o s i t i o n  by s i t e ,  (p = 0.05).  - crown p o s i t i o n  confidence samples  i n each c a t e g o r y .  Tree  leaf  greater  were b e t t e r  Models as  NDW  was  found  but not  error  using  A 5% a l l o w a b l e  w i t h 95%  s i x 10-needle error  and 95%  19 o r 20 1 0 - n e e d l e  samples.  RELATIONSHIPS area p r e d i c t i o n  t h a n 0.90.  predictors  models b a s e d  In g e n e r a l ,  b l c stem  R  2  measures measures.  linear  s t e m measure a t bh and t h e b l c .  b l c stem measures u s i n g  independent v a r i a b l e s  measures  and had a d j u s t e d  one c a n n o t assume a  between a g i v e n  predicting  on s t e m  o f TLA t h a n were bh s t e m  This data s e t indicates relationship  ratio  n e e d l e age c l a s s ,  a t t h e b l c d i d n o t v a r y between s i t e s values  mean  c a t e g o r y c a n be p r e d i c t e d  and a 10% a l l o w a b l e  ALLOMETRIC  n e e d l e age  Overall  Mean NDW  Mean  Mean SLA f o r e a c h n e e d l e age  c o n f i d e n c e c a n be r e a c h e d u s i n g  7.2.  by s i t e ,  (p = 0.05).  (S.E.M. = 0.004).  to vary s i g n i f i c a n t l y  class  (S.E.M. = 0.38).  2  s h o u l d be d e r i v e d  bh s t e m on a  measures  site-to-site  basis. Cross-sectional t o be a b e t t e r adjusted  R  2  sapwood a r e a d i d n o t c o n s i s t e n t l y  predictor  o f TLA t h a n ATOT.  o f t h e TLA model u s i n g  ASW  prove  At the b l c the  as t h e i n d e p e n d e n t  86 variable  was lower  than  independent v a r i a b l e . Cross-sectional related  t h e TLA model u s i n g ATOT as t h e A t bh t h e r e s u l t s  sapwood  t o TLA a c r o s s  area  sites.  with  ASW more l i n e a r ,  (base  The p r o d u c t  although  The same r e s u l t s  of c r o s s - s e c t i o n a l area  c r o s s - s e c t i o n a l area  of l i v e  t o TLA, as was ALC and ALCLB. resulted At  were  i n the best  fitting  o f sapwood  b a r k was l i n e a r l y  The ALCLB  stem  TLA p r e d i c t i o n  related  measure  model a t bh.  t h e b l c a l l i n d e p e n d e n t v a r i a b l e s were  linearly  related  t o TLA w i t h  models  varying  significantly  prediction  none o f t h e TLA p r e d i c t i o n between s i t e s .  model a t t h e b l c used  independent v a r i a b l e .  The b e s t  the  overall.  best  fitting  model  the i n c l u s i o n  fitting  ring  bh m o d e l s o r a c c o u n t likely  a result  between s i t e s . most a d v a n c e d ,  width  i n stand  f o r ASW was n o t improved T h i s was  d e n s i t y between  between s i t e s .  of the h i g h u n i f o r m i t y i n stand On t h e Haney s i t e ,  improve t h e a d j u s t e d  R . 2  TLA  likely sites.  d i d n o t improve t h e f i t o f t h e  for variation  inclusion  fitting  model a t t h e b l c was  o f t h e s e c o n d v a r i a b l e D.  due t o t h e low v a r i a b i l i t y Mean a n n u a l  The b e s t  (ASW*ALB) a s t h e  The n o n l i n e a r model d e v e l o p e d by  e)  f o r t h e models u s i n g ASWLB and ATOT a s i n d e p e n d e n t  variables. and  a t bh was n o t l i n e a r l y  TLA model v a r i e d between s i t e s .  found  reversed.  A log transformation  o f T L A made t h e r e l a t i o n s h i p the  were  T h i s was  density  where crown c l o s u r e was  o f MARW i n t h e TLA model d i d  87 Addition variation the  o f ALB t o ASWbh d i d n o t i n c r e a s e  i n t h e TLA models between  models  linearity.  M u l t i p l y i n g ASW  hand, d i d improve t h e m o d e l s prediction the  b l c the i n c l u s i o n  TLA m o d e l s . allometric improved the  with  This  o f ALB  ASW  ALCLB  of measures  and TLA was  independent  f o r the that are  storage.  a t bh and t h e b l c . ALC and ALCLB  TLA  as t h e  significantly  s t e m measures were  The  between  found t o  o f h e a r t w o o d i n a l l b u t two s t e m d i s c s .  The  r e l a t i o n s h i p between TLA and t h e ALC v a r i a b l e s  related  transpiring leaf  mass or a r e a i s  t o a p r o p o r t i o n a l amount o f c o n d u c t i n g  physical  support  stemwood.  Considering  the small  i t may  be b e s t  conclusions.  should  2  t h e i n d e p e n d e n t v a r i a b l e ALC  v a r i a b l e s d i d not vary  suggests that a given  fast  R  the hypothesis  of n u t r i e n t  linear  The ALC and ALCLB  include area  study  B o t h a t bh and  between TLA and s t e m measurements  models a t bh and t h e b l c u s i n g  strong  sites.  by moving beyond w a t e r t r a n s p o r t c o n s i d e r a t i o n s t o  inclusion  sites.  other  and t h e TLA  the adjusted  supports  The r e l a t i o n s h i p between and  on t h e  e i t h e r t h r o u g h a d d i t i o n or  increased  result  equations  between  n o r d i d i t improve  by ALB,  linearity  model d i d n o t v a r y  multiplication  sites  explained  number o f sample t r e e s  t o speak o f t r e n d s  The  stemwood  "conclusions"  have a p p l i c a t i o n t o o t h e r than  rather  reached  in this  than hard  in this  D o u g l a s - f i r stands  CWH  zone w h i c h a r e l e s s  60 y e a r s - o l d ,  spaced  500  - 700 s t e m s / h a , and have n o t been f e r t i l i z e d  and  and  study i n the  t o between i n the  last  88 10  years.  In s t a n d s w h i c h do  allometric  equations derived  with caution. linearity the  bh  The  i n other  Douglas-fir.  for  Douglas-fir  between  7.3.  in this  transformations  between t h e  for  the  TLA  study should  needed  d e p e n d e n t and  studies This  may  to  developing  be  applied  improve  the in  transformations allometric  equations  allometric  equations  have l i m i t e d p o r t a b i l i t y , bh  the  independent v a r i a b l e s  suggests that  models u s i n g  measures v a r y i n g  with  several  significantly  sites.  PHOTOGRAPHY TECHNIQUE A poor  area.  The  c o r r e l a t i o n was  found  r e s u l t i n g from l i g h t  height,  difficulties  limited  crown v i e w o p p o r t u n i t i e s .  applicability forest  of  conditions  obtaining  Even  the  should  be  by one  leaf  low  even one  adjacent  stand  trees.  camera,  to  i m a g i n g of  conditions  and  to  of  difficulties tree  crown.  very  crown w h i c h  A more f r u i t f u l video  tree  to a v a r i e t y  a given  a tree  to  the  densities, i t is  view of  which u t i l i z e s  area.  level  In g e n e r a l ,  c l e a r v i e w s of  b r a n c h e s under c o n t r o l l e d l i g h t branch  a  silhouette  conditions,  photography technique  relatively  to get  obstructed  in maintaining  and  adjustments  i s e x t r e m e l y l i m i t e d due  in forests with  difficult  between TLA  photography technique r e q u i r e s  reduce v a r i a b i l i t y  in  meet t h e s e c r i t e r i a  models were d i f f e r e n t t h a n t h e  required  of  not  is  approach sample determine  not  89  8. CONCLUSIONS 8.1.  SAMPLING  ANALYSIS  When s a m p l i n g stratify SLA  by s i t e ,  was f o u n d  t o determine  mean SLA i t i s n e c e s s a r y t o  crown p o s i t i o n ,  and n e e d l e  to vary s i g n i f i c a n t l y  according to these  variables.  B a n c a l a r i et  crowns  q u a r t e r s and B o r g h e t t i et  into  thirds.  This study  stratifying needles accuracy classes oldest  with  needles  needle  B o r g h e t t i et  10%  i n sampling  time  s i x age  included i nthe  c a n be g a i n e d  and c o n f i d e n c e  mean SLA p e r n e e d l e  a 5% a l l o w a b l e e r r o r  by  level.  When  age c l a s s p e r  and 95% c o n f i d e n c e  l e v e l can  u s i n g 19 o r 20 1 0 - n e e d l e s a m p l e s p e r c a t e g o r y . and 95% c o n f i d e n c e  level  A  c a n be a c h i e v e d  6 10-needle samples per c a t e g o r y . When s a m p l i n g  necessary ratio  into  that  t h e minimum number o f s a m p l e s needed t o a c h i e v e  allowable error  using  by  stratified  suggests  needles  s i x years  into  i s gained  (1986)  This study  o l d e r than  t o determine  achieved  al.  by s t r a t i f y i n g  a desired allowable error  branch,  (1986)  age c l a s s .  A decrease  sampling  al.  that accuracy  f o u r age c l a s s e s .  c a n be g a i n e d  determining  (1987) s t r a t i f i e d D o u g l a s - f i r  suggests  by f i f t h s .  into  al.  age c l a s s , a s  to stratify  was f o u n d  variables. position.  t o determine by s i t e  mean NDW  and n e e d l e  to vary s i g n i f i c a n t l y  Needle d r y weight  ratio  ratio  i t  age c l a s s ,  is a s NDW  according to these  d i d n o t v a r y by crown  90 8.2.  ALLOMETRIC Across  linearly  s t u d y TLA was n o t  by a n a t u r a l  log transformation  i n t e r c e p t c o e f f i c i e n t s f o r the three  varied  significantly  equations developed the  in this  above  three  by s i t e .  This  to predict Douglas-fir  height  v a r i a b l e s w h i c h were  o f TLA, b u t t h e  that  of  three  sites  and  independent  represented  Limitations  linearly  stand  age and d e n s i t y  related  t o TLA.  greater  than  with s i t e .  The a d j u s t e d  0.90 This  over  2  related to  o f t h e models r e l a t e t o subzone.  values  linearly  f o r t h e models  were  vary  b l c s t e m measurements a r e  better  predictors  o f TLA t h a n a r e bh s t e m measurements.  cannot  be assumed  that  s t e m measurements Several pipe  ATOT.  that  linear.  First, ASW  It  t h e r e l a t i o n s h i p between bh and b l c  of the r e s u l t s from t h i s  model t h e o r y .  conclusively  are  on  the range  and t h e model c o e f f i c i e n t s d i d n o t suggests that  sites  Douglas-fir  a t t h e b l c were R  The  The models b a s e d  and b i o g e o c l i m a t i c  t h e s t e m measurements  any o f  between  study to p r e d i c t  on t h e p o r t a b i l i t y  allometric  specific.  v a r i a b l e s c a n be u s e d  by t h i s  TLA.  All  (ASW*ALB)bh.  models  TLA u s i n g  TLA and whose model c o e f f i c i e n t s d i d n o t v a r y were ALCbh, ALCLBbh,  variables  linear  suggests  independent v a r i a b l e s are s i t e  breast  these  The  o f t h e r e l a t i o n s h i p o f TLA w i t h t h e s e  improved  slope  the range of s i t e s  r e l a t e d t o ASWbh, ASWLBbh, or ATOTbh.  linearity was  RELATIONSHIPS  was  i t could a better  study challenge  the  n o t be shown predictor  o f TLA t h a n  At t h e b l c , ATOT, a c r o s s - s e c t i o n a l s t e m measure  was that  91 i n c l u d e s more t h a n correlated that  with  when ALB  t h e TLA  the  independent  prediction  of  than  by  model, next  and  ALB  and  the  the  f o r ALB  relate  The  product  correlated of  low  may  be  of MARW and  w i t h TLA  variability  best  ALC  than  fitting  live  In  bark,  was  improved  ASW.  TLA  of  terms that of  and  includes area  for physical equations  was  in  i n 14  suggest  ALCLB v a r i a b l e  ASW  model  ALCLB, w h i c h i n c l u d e s  and  sapwood and  that allometric  The  f i t of t h e  t o p r o v i d e a measure of t h e  D o u g l a s - f i r TLA  f i t of  t o a p r o p o r t i o n a l amount  This  predict  the  f i t t i n g model.  crown d e p e n d s on  suggests  The  b l c , the  heartwood which the study  by ASW  found  a measure of h e a r t w o o d  best  results  stemwood.  appears  improved.  i t was  i n c l u d e s a p o r t i o n of AHW  stemwood, b o t h  support  more c l o s e l y -  Secondly,  t o ASW*ALB, was  was  crown d i m e n s i o n s  physical  ASW.  At  ALCLB, w h i c h  sample t r e e s ,  conducting  stem, was  including  variable.  physiology, these  that  was  model was  improved  A t bh, 16  living  added t o or m u l t i p l i e d  prediction  further  the  TLA  was  was  AHW.  the  ASW  of  support.  developed  to  by u s i n g ALCLB.  n o t more  T h i s was  closely  likely a  i n s t a n d d e n s i t y between and  result  within  sites.  8.3.  PHOTOGRAPHY TECHNIQUE Several  correction  explain v a r i a b i l i t y camera p o s i t i o n s predictions  can  factors  resulting  ( a n g l e and be  must be  from  d e r i v e d i n order  varying tree heights  distance) before accurate  made u s i n g s i d e - v i e w p h o t o g r a p h y .  to and  TLA It  was  92  difficult  to find  u n o b s t r u c t e d s i d e - v i e w s of  crowns even  i n stands with d e n s i t i e s  Variability  in light  with  the s o u r c e s of v a r i a t i o n  development  of a photography  in a controlled  8.4.  conditions  RESEARCH This  light  individual  as low as 500  i n the n a t u r a l  mentioned  above,  technique using  forest,  encourage  sample  areas for f u r t h e r  between ALCLB and  wider  of s t a n d c o n d i t i o n s  and  leaf would  sizes.  technique using  in a controlled  area.  The  branches  research:  of the r e l a t i o n s h i p  cameras  the  RECOMMENDATIONS  examination  photography  along  environment.  s t u d y s u g g e s t s two  range  stems/ha.  development  s p e e d up TLA  the development  v i d e o or s i n g l e  light  TLA  environment  lense  in a  of a reflex  to predict  branch  of such a photography t e c h n i q u e  s a m p l i n g and  allow  for larger  sample  93 LITERATURE A l b r e k t s o n , A. 1984. S c o t s p i n e (Pinus Sweden. Forestry  CITED  Sapwood b a s a l a r e a and n e e d l e mass o f sylvestris L.) t r e e s i n C e n t r a l 57: 35-43  A n d e r s o n , M. C. 1971. R a d i a t i o n and c r o p s t r u c t u r e . Pp. 412-466 in Z. S e s t a k , J . C a t s k y and P.G. J a r v i s (Editors), Plant Photosynthetic Production. Manual o f Methods, W. J u n k , The Hague. Bannan, M. W. 1965. The l e n g t h , t a n g e n t i a l d i a m e t e r , and l e n g t h / w i d t h r a t i o of c o n i f e r t r a c h e i d s . Can. J . B o t . 43: 967-984. B i n k l e y , D. 1984. D o u g l a s - f i r stem growth per u n i t of l e a f a r e a i n c r e a s e d by i n t e r p l a n t e d s i t k a a l d e r and r e d alder. F o r . S c i . 30: 259-263. B l a n c h e , C. A. and J . D. Hodges. 1985. A l e a f area sapwood a r e a r a t i o d e v e l o p e d t o r a t e l o b l o l l y p i n e vigor. Can. J . F o r . R e s . 15: 1181-1184.  tree  B o o k e r , R. E . and J . A. K i n i n m o n t h . 1978. Variation in l o n g i t u d i n a l p e r m e a b i l i t y o f g r e e n r a d i a t a p i n e wood. N. Z. J . F o r . S c i . 8: 295-308. B o r g h e t t i , M., G. G. V e n d r a m i n , and R. G i a n n i n i . 1986. S p e c i f i c l e a f a r e a and l e a f a r e a i n d e x d i s t r i b u t i o n i n a young D o u g l a s - f i r p l a n t a t i o n . Can. J . F o r . Res. 16: 1283-1288. B r a c k , C. L . , M. P. Dawson, and A. M. G i l l . 1985. Bark, l e a f and sapwood d i m e n s i o n s i n Eucalyptus. Aust. F o r . Res. 15: 1-7. Brix,  Brix,  H. 1981. E f f e c t s o f t h i n n i n g and n i t r o g e n fertilization on b r a n c h and f o l i a g e p r o d u c t i o n Douglas-fir. Can. J . F o r . R e s . 11: 502-511. H. and A. K. fertilization relationships basal area i n 389 .  in  M i t c h e l l . 1983. T h i n n i n g and n i t r o g e n e f f e c t s on sapwood d e v e l o p m e n t and o f f o l i a g e q u a n t i t y t o sapwood a r e a and Douglas-fir. Can. J . F o r . R e s . 13: 384-  C a r t e r , G. A., and W. K. S m i t h . 1985. Influence of shoot s t r u c t u r e on l i g h t i n t e r c e p t i o n and p h o t o s y n t h e s i s i n conifers. P l a n t P h y s i o l . 79: 1038-1043. C a r t e r , R. and K. K l i n k a . 1988. Douglas-fir f e r t i l i z a t i o n : d e c i s i o n - m a k i n g f o r i n d u s t r i a l use. F a c u l t y of F o r e s t y , U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B.C.  94  C a r t e r , R., Q. Wang, J . A. P. Neumann, and K. K l i n k a . 1990. R e l a t i o n s h i p s between l e a f a r e a and e c o l o g i c a l s i t e q u a l i t y i n immature l o d g e p o l e p i n e . Submitted f o r p u b l i c a t i o n i n Ecology. C h a t t e r j e e , S., and B. P r i c e . 1977. R e g r e s s i o n Example. W i l e y - I n t e r s c i e n c e , New Y o r k .  A n a l y s i s by  C o c h r a n , W. G., and G. M. Cox. 196G. E x p e r i m e n t a l 2nd e d . J o h n W i l e y and Sons, New Y o r k .  Designs.  Dean, T. J . , and J . N. L o n g . 1986. V a r i a t i o n i n sapwood a r e a - l e a f a r e a r e l a t i o n s w i t h i n two s t a n d s o f lodgepole pine. F o r . S c i . 32: 749-758. D e l R i o , E . , and A. B e r g . 1979. S p e c i f i c l e a f a r e a o f D o u g l a s - f i r r e p r o d u c t i o n as a f f e c t e d by l i g h t and n e e d l e a g e . F o r . S c i . 25: 183-186. D i e b o l t , D. S., and K. W. Mudge. 1988. Use o f a v i d e o imaging system f o r e s t i m a t i n g l e a f s u r f a c e a r e a of Pinus sylvestris s e e d l i n g s . C a n . J . F o r . R e s . 18: 377-380. D i x o n , A. F . G. Appl. E c o l .  1971. E f f e c t 8: 165-179.  of aphids  on wood  formation.  Edwards, W. R. N., and P. G. J a r v i s . 1982. R e l a t i o n s between water c o n t e n t , p o t e n t i a l and p e r m e a b i l i t y i n stems o f c o n i f e r s . P l a n t , C e l l and E n v i r o n m e n t 5: 271-277. E s p i n o s a B a n c a l a r i , M. A. E . , D. A. P e r r y , and J . D. Marshall. 1987. L e a f a r e a - sapwood a r e a r e l a t i o n s h i p s i n a d j a c e n t young D o u g l a s - f i r s t a n d s d i f f e r e n t e a r l y growth r a t e s . Can. J . F o r . R e s . 17: 174-180.  with  G e r o n , C. D., and G. A. R u a r k . 1988. C o m p a r i s i o n o f c o n s t a n t and v a r i a b l e a l l o m e t r i c r a t i o s f o r p r e d i c t i n g f o l i a r biomass of v a r i o u s t r e e genera. Can. J . F o r . Res. 18: 1298-1304. Gower, S. T., C. C. G r i e r , D. J . V o g t , and K. A. V o g t . 1987. A l l o m e t r i c r e l a t i o n s of deciduous {Larix occidentalis) and e v e r g r e e n c o n i f e r s (Pinus contorta and Pseudotsuga menziesii) of the Cascade Mountains i n c e n t r a l Washington. C a n . J . F o r . R e s . 17: 630-634. G r a n i e r , A. 1981. E t u d e d e s r e l a t i o n s e n t r e l a s e c t i o n du b o i s d ' a u b i e r e t l a mass f o l i a i r e c h e z l e D o u g l a s - f i r (Pseudotsuga menziesii Mirb. Franco). Ann. S c i . F o r . 38: 503-512.  95  G r i e r , C. C , K. M. L e e , and R. M. A r c h i b a l d . 1984. Effect of u r e a f e r t i l i z a t i o n on a l l o m e t r i c r e l a t i o n s i n young Douglas-fir trees. Can. J . F o r . Res. 14: 900-904. H e l g e r s o n , 0. T., K. Cromack, S. S t a f f o r d , R. E . M i l l e r , and R. S l a g l e . 1988. E q u a t i o n s f o r e s t i m a t i n g aboveground components of young D o u g l a s - f i r and r e d a l d e r i n a c o a s t a l Oregon p l a n t a t i o n . Can. J . F o r . Res. 18: 1082-1085. Huber, H. 1928. W e i t e r e q u a n t i t a t i v e U n t e r s u c h u n g e n uber das W a s s e r l e i t u n g s s y s t e m d e r P f l a n z e n . Jahrb. Wiss. B o t . 67: 877-959. H u n g e r f o r d , R. D. 1987. E s t i m a t i o n of f o l i a g e d e n s e Montana l o d g e p o l e p i n e s t a n d s . Can. 17: 320-324.  area i n J. For.  Res.  J a r v i s , P. G., and J . W. L e v e r e n z . 1983. P r o d u c t i v i t y of t e m p e r a t e , d e c i d u o u s and e v e r g r e e n f o r e s t s . In 0. L. L a n g e , P. S. N o b e l , C. B. Osmond, and H. Z i e g l e r ( e d s ) . P h y s i o l o g i c a l P l a n t E c o l o g y IV, E c o s y s t e m P r o c e s s e s : M i n e r a l C y c l i n g , P r o d u c t i v i t y and Man's I n f l u e n c e . J o h n s o n , J . D., S. M. Z e d a k e r , and A. B. H a i r s t o n . 1985. F o l i a g e , stem, and r o o t i n t e r r e l a t i o n s i n young l o b l o l l y pine. F o r . S c i . 31: 891-898. Kaufmann, M. R. and C. A. T r o e n d l e . 1981. The r e l a t i o n s h i p of l e a f a r e a and f o l i a g e b i o m a s s t o sapwood c o n d u c t i n g area i n four subalpine f o r e s t tree s p e c i e s . For. S c i . 27: 477-482. Keane, M. G. and G. F. Weetman. 1987. L e a f area-sapwood c r o s s - s e c t i o n a l area r e l a t i o n s h i p s i n repressed stands of l o d g e p o l e p i n e . Can. J . F o r . Res. 17: 205-209. K o z l o w s k i , T. T., J . F. Hughes, and L. L e y t o n . 1966. P a t t e r n s o f w a t e r movement i n dormant gymnosperm seedlings. B i o r h e o l o g y 3: 77-85. K o z l o w s k i , T. T., J . F. Hughes, and L . L e y t o n . 1967. movement i n gymnosperms i n r e l a t i o n t o t r a c h e i d alignment. F o r e s t r y 40: 209-227. Kramer, P. J . , and Woody P l a n t s . York.  Dye  T. T. K o z l o w s k i . 1979. P h y s i o l o g y of 2nd e d i t i o n . A c a d e m i c P r e s s , London New  L a n g , A. R. G. 1986. L e a f a r e a and a v e r a g e l e a f f r o m t r a n s m i s s i o n of d i r e c t s u n l i g h t . Aust. 34: 349-355.  angle J . Bot.,  96 L a n g , A. R. G. 1987. S i m p l i f i e d e s t i m a t e of l e a f a r e a i n d e x f r o m t r a n s m i t t a n c e of t h e s u n ' s beam. Agri. F o r . M e t e o r o l . 41: 179-186.  and  L a n g , A. R. G., X. Y u e q i n , and J . M. Norman. 1985. Crop s t r u c t u r e and t h e p e n e t r a t i o n of d i r e c t s u n l i g h t . A g r i . and F o r . M e t e o r o l . 35: 83-101. L e o n g , W., R. Lemeur, and P. K. Yoon. 1982. C h a r a c t e r i s a t i o n of l e a f a r e a i n d e x and c a n o p y l i g h t p e n e t r a t i o n of Hevea brasiliensis M u e l l . A r g . by h e m i s p h e r i c a l photography. J . Rubb. Res. I n s t . M a l a y s i a 30: 80-90. L o n g , J . N., and F. W. S m i t h . 1988. L e a f a r e a - sapwood a r e a r e l a t i o n s of l o d g e p o l e p i n e as i n f l u e n c e d by s t a n d d e n s i t y and s i t e i n d e x . Can. J . F o r . Res. 18: 247-250. L o n g , J . N., and F. W. S m i t h . 1989. Estimating leaf area of Abies lasiocarpa a c r o s s r a n g e s of s t a n d d e n s i t y and site quality. Can. J . F o r . Res. 19: 930-932. L o n g , J . N., F. W. S m i t h , and D. R. M. S c o t t . 1981. The r o l e of D o u g l a s - f i r s t e m sapwood and h e a r t w o o d i n t h e m e c h a n i c a l and p h y s i o l o g i c a l s u p p o r t o f crowns and development of stem form. Can. J . F o r . Res. 11: 459-464 . M a g u i r e , D. A., and D. W. Hann. 1989. The r e l a t i o n s h i p between g r o s s crown d i m e n s i o n s and sapwood a r e a a t crown b a s e i n D o u g l a s - f i r . Can. J . F o r . Res. 19: 557-565. M a r c h a n d , P. J . 1984. Sapwood a r e a as an e s t i m a t o r o f f o l i a g e b i o m a s s and p r o j e c t e d l e a f a r e a f o r Abies balsamea and Picea rubens. Can. J . F o r . Res. 14: 8587. P e a r s o n , J . A., T. J . F a h e y , and D. H. K n i g h t . 1984. B i o m a s s and l e a f a r e a i n c o n t r a s t i n g l o d g e p o l e p i n e forests. Can. J . F o r . Res. 14: 259-265. P o j a r , J . , K. K l i n k a , and D. V. M e i d i n g e r . 1987. B i o g e o c l i m a t i c ecosystem c l a s s i f i c a t i o n i n B r i t i s h Columbia. F o r . E c o l . Manage. 22: 119-154. P o t h i e r , D., H. A. M a r g o l i s , and R. H. W a r i n g . 1989. P a t t e r n s of change of s a t u r a t e d sapwood p e r m e a b i l i t y and sapwood c o n d u c t a n c e w i t h s t a n d d e v e l o p m e n t . Can. J . F o r . Res. 19: 432-439.  97 P r i c e , D. 1987. Some e f f e c t s o f v a r i a t i o n i n w e a t h e r and s o i l w a t e r s t o r a g e on c a n o p y e v a p o t r a n s p i r a t i o n and n e t p h o t o s y n t h e s i s o f a young D o u g l a s - f i r s t a n d . PhD thesis. F a c u l t y of F o r e s t y , U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B r i t i s h Columbia, Canada. R o g e r s , R. and T. M. H i n c k l e y . 1979. F o l i a r w e i g h t and a r e a r e l a t e d t o c u r r e n t sapwood a r e a i n oak. For. S c i . 25: 298-303. S a l i s b u r y , F. B., and C. W. R o s s . 1978. Plant Physiology. 2nd e d . Wadsworth P u b l i s h i n g Co., C a l i f o r n i a . S h i n o z a k i , K., K. Yoda, K. Hozumi, and T. K i r a . 1964a. A q u a n t i t a t i v e a n a l y s i s o f p l a n t f o r m - t h e p i p e model theory. I. Basic analyses. J p n . J . E c o l . 14: 97-105. S h i n o z a k i , K., K. Yoda, K. quantitative analysis theory. I I . Further application in forest 139.  Hozumi, and T. K i r a . 1964b. A o f p l a n t f o r m - t h e p i p e model e v i d e n c e o f t h e t h e o r y and i t s ecology. J p n . J . E c o l . 14: 133-  S m i t h , R. B., R. H. W a r i n g , and D. A. P e r r y . 1981. I n t e r p r e t i n g f o l i a r a n a l y s e s f r o m D o u g l a s - f i r as w e i g h t per u n i t of l e a f a r e a . Can. J . F o r . R e s . 11: 593-598. S n e l l , J . K. A. and J . K. Brown. e s t i m a t o r s - dbh and sapwood 457.  1978. area.  Comparison of t r e e F o r . S c i . 24: 455-  S p i t t l e h o u s e , D. L . 1981. M e a s u r i n g and m o d e l l i n g e v a p o t r a n s p i r a t i o n from D o u g l a s - f i r s t a n d s . Doctoral T h e s i s , Department of S o i l S c i e n c e , U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B r i t i s h Columbia, Canada. S p r u g e l , D. G. 1983. Correcting for bias i nl o g transformed a l l o m e t r i c equations. E c o l o g y 64: 209210. Swanson, R. H. 1975. Velocity d i s t r i b u t i o n patterns i n a s c e n d i n g xylem sap d u r i n g t r a n s p i r a t i o n . In R. B. D o w d e l l ( e d . ) , F l o w — I t s Measurement and C o n t r o l i n S c i e n c e and I n d u s t r y , V o l . 1, pp. 1425-1430. Instru. S o c . Am. Tan,  C. S., T. A. B l a c k , and J . U. Nnyamah. 1978. d i f f u s i o n model o f t r a n s p i r a t i o n a p p l i e d t o a Douglas-fir stand. E c o l o g y 59: 1221-1229.  A simple thinned  Thompson, D. C. 1989. The e f f e c t o f s t a n d s t r u c t u r e and s t a n d d e n s i t y on t h e l e a f a r e a - sapwood a r e a r e l a t i o n s h i p of lodgepole pine. Can. J . F o r . R e s . 19: 392-396.  98  Ungs, M. J . 1981. D i s t r i b u t i o n o f l i g h t w i t h i n t h e crown o f an open-grown D o u g l a s - f i r . PhD T h e s i s . O r e g o n S t a t e U n i v e r s i t y , C o r v a l l i s , Oregon. Wang, Y. S. and D. R. M i l l e r . 1987. C a l i b r a t i o n o f t h e h e m i s p h e r i c a l p h o t o g r a p h i c t e c h n i q u e t o measure l e a f a r e a i n d e x d i s t r i b u t i o n s i n hardwood f o r e s t s . F o r . S c i . 33: 210-216. W a r i n g , R. H. 1983. E s t i m a t i n g f o r e s t g r o w t h and e f f i c i e n c y i n r e l a t i o n t o canopy l e a f a r e a . Adv. E c o l . Res. 13: 327-354. W a r i n g , R. H. and W. H. S c h l e s i n g e r . 1985. F o r e s t E c o s y s t e m s : C o n c e p t s and Management. Academic Inc. Orlando, F l o r i d a . 340 p. W a r i n g , R. H., P. E . S c h r o e d e r , and R. O r e n . 1982. A p p l i c a t i o n o f t h e p i p e model t h e o r y t o p r e d i c t leaf area. Can. J . F o r . R e s . 12:556-560.  Press,  canopy  W h i t e h e a d , D. 1978. The e s t i m a t i o n o f f o l i a g e a r e a f r o m sapwood b a s a l a r e a i n S c o t s p i n e . F o r e s t r y 51: 137 -149. W h i t e h e a d , D., and P. G. J a r v i s . 1981. C o n i f e r o u s f o r e s t s and p l a n t a t i o n s . In T. T. K o z l o w s k i ( e d ) , Water D e f i c i t s and P l a n t G r o w t h . A c a d e m i c P r e s s , New Y o r k . W h i t e h e a d , D., W. R. N. Edwards, and P. G. J a r v i s . 1984. C o n d u c t i n g sapwood a r e a , f o l i a g e a r e a , and p e r m e a b i l i t y i n m a t u r e t r e e s o f Picea sitchensis and Pinus contorta. Can. J . F o r . R e s . 14: 940-947. W i l k i n s o n , L . 1988. SYSTAT: t h e S y s t e m f o r S t a t i s t i c s . SYSTAT, I n c . , E v a n s t o n , I L . 822 pp. W i l k i n s o n , L . 1989. SYGRAPH: t h e s y s t e m f o r G r a p h i c s f o r t h e PC. 2nd e d i t i o n . SYSTAT, I n c . , E v a n s t o n , I L . 980 pp. Zar,  J . H. 1984. B i o s t a t i s t i c a l A n a l y s i s . 2nd e d . P r e n t i c e - H a l l , T o r o n t o . 718 pp.  Zimmermann, M. H. 1983. X y l e m s t r u c t u r e and t h e a s c e n t o f sap. Springer Verlag, B e r l i n .  99  APPENDIX I EXPLANATION OF SYMBOLS  IN BOX PLOTS  The box p l o t f i g u r e s i n t h i s t h e s i s a r e p r o d u c e d u s i n g SYGRAPH ( W i l k i n s o n , 1 9 8 9 ) . The f o l l o w i n g e x p l a n a t i o n o f t h e f i g u r e s i s t a k e n d i r e c t l y f r o m t h e SYGRAPH document: The  inner fences lower upper  The  outer lower upper  fence fence fences fence fence  a r e d e f i n e d as f o l l o w s : = lower hinge = upper hinge  - (1.5Hspread)" + (1.5Hspread)  a r e d e f i n e d as f o l l o w s : = lower h i n g e = upper hinge  Values outside the inner fences asterisks. Values outside the outer empty c i r c l e s .  +  OHspread) OHspread)  are p l o t t e d with fences are p l o t t e d  with  * The H s p r e a d i s c o m p a r a b l e t o t h e i n t e r q u a r t i l e r a n g e o r midrange. I t i s the a b s o l u t e value of the d i f f e r e n c e between t h e v a l u e s o f t h e two h i n g e s .  100  APPENDIX I I LEAF AREA  Site  Haney  Duncan  Courtenay  Dbh class midpoint (en)  ATOTbh (en )  Ho. of trees/ha  2  INDEX VALUES  Predicted Leaf Area* (B ) 2  Leaf Area LAI per ha (n /ha) |B /B ) 2  2  2  16.9 18.5 21.5 19.9  224.32 268.80 363.05 311.03  217.0 153.0 130.0 152.0  35.47 44.30 70.97 54.71  7696.2 6778.1 9226.0 8316.6  13.8 16.0 18.2 19.8  149.57 201.06 260.16 307.91  256.0 64.0 192.0 128.0  24.41 31.57 42.43 53.87  6249.0 2020.5 8146.6 6895.4  2.33  14.9 11.5 18.1 20.2 21.3 23.0 24.0  174.37 240.53 257.30 320.47 356.33 415.48 452.39  48.9 114.2 32.6 114.0 65.3 65.0 50.0  27.63 38.46 41.82 57.36 68.62 92.24 110.94  1351.1 4392.1 1363.3 6539.0 4480.9 5995.6 5547.0  2.97  * Predicted leaf area (one-sided) deterained by InTLA = 2.447+0.005(ATOTbh).  3.20  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0098054/manifest

Comment

Related Items