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

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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 THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ^ R £ $ r R y in THE FACULTY OF GRADUATE STUDIES FOREST SCIENCES We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA 1990 © John A.P. Neumann, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of ^""6>r£S^ SCJ&WULA The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT V a r i a b i l i t y i n the r e l a t i o n s h i p between t r e e l e a f area (TLA) and s e l e c t e d stem measurements was examined i n three D o u g l a s - f i r stands (Pseudotsuga menziesii (Mirb.) Franco, var. menziesii) t h a t were l e s s than 50 y e a r s - o l d , spaced to approximately 550 to 650 stems/ha, and d i f f e r e d i n s o i l moisture and n u t r i e n t s . A t t e n t i o n was giv e n to the e f f e c t of mean annual r i n g width (MARW), c r o s s - s e c t i o n a l area of the l i v e bark (ALB - a surr o g a t e measure of r e l a t i v e n u t r i e n t storage i n the stem), and c r o s s - s e c t i o n a l area of the most recent annual r i n g s equal i n number to the number of whorls i n the l i v e crown (ALC), on v a r i a b i l i t y i n the r e l a t i o n s h i p between TLA and c r o s s - s e c t i o n a l area of sapwood (ASW). At b r e a s t h e i g h t , b a s a l area, ASW, and c r o s s - s e c t i o n a l area of sapwood plus l i v e bark (ASWLB) were not l i n e a r l y r e l a t e d to TLA, and l i n e a r r e g r e s s i o n equations u s i n g l o g transformed v a r i a b l e s v a r i e d s i g n i f i c a n t l y between s i t e s . Nonlinear r e g r e s s i o n equation f o r ASW at br e a s t height was: TLA = 0.064ASW X- 3 3 ( I 2 = 0.856). I n c l u d i n g D (the d i s t a n c e between b r e a s t height and the center of the l i v e crown) i n the n o n l i n e a r equation, d i d not s i g n i f i c a n t l y improve the r e g r e s s i o n . Tree l e a f area p r e d i c t i o n models u s i n g stem measures from the base of l i v e crown ( b l c ) had higher adjusted R 2 v a l u e s than models u s i n g stem measures from b r e a s t h e i g h t . i i i At the b l c , b a s a l area, ASW, and ASWLB were l i n e a r l y r e l a t e d to TLA (adjusted R 2 = 0.926, 0.908, and 0.934, r e s p e c t i v e l y ) . M u l t i p l y i n g ASW by MARW d i d not improve the f i t of the r e g r e s s i o n models. M u l t i p l y i n g ASW by ALB improved the l i n e a r i t y of the r e l a t i o n s h i p of ASW at b r e a s t height to TLA. The best f i t t i n g TLA model o v e r a l l used the product of ASW at b l c and ALB at b l c as the independent v a r i a b l e (adjusted R 2 = 0.967). The r e s u l t s i n d i c a t e t h a t r e s e a r c h i n t o the a l l o m e t r i c r e l a t i o n s h i p of TLA to stem measures should g i v e c o n s i d e r a t i o n to more than h y d r a u l i c measures and i n c l u d e measures of bark f u n c t i o n . At b r e a s t height and the b l c , the independent v a r i a b l e ALC was l i n e a r l y r e l a t e d to t r e e l e a f area and had higher a d j u s t e d R 2 values than d i d ASW. In most t r e e s the ALC stem measure was found to i n c l u d e a p o r t i o n of heartwood area. The s t r o n g r e l a t i o n s h i p between TLA and ALC suggests t h a t a given t r a n s p i r i n g l e a f mass or area i s r e l a t e d to a p r o p o r t i o n a l amount of conducting stemwood and p h y s i c a l support stemwood. A quick a l t e r n a t i v e approach f o r e s t i m a t i n g i n d i v i d u a l t r e e l e a f area using photographs taken at f i x e d d i s t a n c e and angle from the t a r g e t t r e e d i d not r e s u l t i n a r e l i a b l e t r e e l e a f area p r e d i c t i o n technique. The d i f f i c u l t y of o b t a i n i n g views of the t r e e crown which were not o b s t r u c t e d by adjacent t r e e crowns was the major o b s t a c l e . Using a f i x e d d i s t a n c e and camera angle was a problem because of v a r i a b l e tree heights. However, a l t e r i n g these fixed positions introduced additional v a r i a t i o n into the tree leaf area estimation. Mean s p e c i f i c leaf area (SLA) varied s i g n i f i c a n t l y by s i t e , needle age cl a s s , and crown position. Mean SLA per needle age class per branch can be predicted with 95% confidence and a 10% allowable error using s i x 10-needle samples. V TABLE OF CONTENTS Page A b s t r a c t i i Table of Contents .v L i s t of F i g u r e s i x L i s t of Tables . x L i s t of A b b r e v i a t i o n s x i Acknowledgement x i i i 1. I n t r o d u c t i o n 1 1.1. Tree Leaf Area 1 1.2. A l l o m e t r i c R e l a t i o n s h i p s 2 1.3. S o l a r Transmittance and Photography 3 1.4. O b j e c t i v e •••• 3 2. L i t e r a t u r e Review 5 2.1. A l l o m e t r i c R e l a t i o n s h i p s 5 2.2. Photography 15 2.3. D e s t r u c t i v e Sampling.... 18 2.4. N u l l and A l t e r n a t i v e Hypotheses 20 3. M a t e r i a l s and Methods 23 3.1. L o c a t i o n 23 3.2. S i t e D e s c r i p t i o n 25 3.3. Tree S e l e c t i o n 26 3.4. Photography 29 3.5. F o l i a r Samples 31 3.5.1. D e s t r u c t i v e Sampling 31 3.5.2. Sample S i z e A n a l y s i s . . . . 34 3.6. Stem Samples 35 v i Page 3.7. Regression A n a l y s i s 36 4. Sampling A n a l y s i s 38 4.1. R e s u l t s 38 4.1.1. S p e c i f i c Leaf Area 38 4.1.2. Needle Dry 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 Leaf Area 45 4.2.2. Needle Dry Weight R a t i o 47 5. A l l o m e t r i c R e l a t i o n s h i p s 48 5.1. R e s u l t s 48 5.1.1. Tree Leaf Area ...48 5.1.2. Breast Height Stem Measurements and Tree Leaf Area 50 5.1.3. Base of L i v e Crown Stem Measurements and Tree Leaf Area 53 5.1.4. V a r i a t i o n Between S i t e s 54 5.1.4.1. Breast Height Versus Base of L i v e Crown 55 5.1.4.2. C r o s s - S e c t i o n a l Area of L i v e Bark 56 5.1.4.3. Mean Annual Ring Width 57 5.1.5. Nonlinear Regression 60 5.1.6. P r e d i c t i n g Base of L i v e Crown Stem Measures 62 5.1.6.1. C r o s s - S e c t i o n a l Area of Sapwood..62 5.1.6.2. C r o s s - S e c t i o n a l Area of Sapwood and L i v e Bark 64 5.1.6.3. C r o s s - S e c t i o n a l Area of Sapwood * L i v e Bark 65 v i i Page 5.1.6.4. C r o s s - S e c t i o n a l Area of Most Recent Annual Sapwood Rings Equal i n Number to the Number of Whorls i n L i v e Crown 66 5.2. D i s c u s s i o n 67 5.2.1. Base of L i v e Crown Versus Breast Height...67 5.2.2. C r o s s - S e c t i o n a l Area of Sapwood Versus Basal Area 68 5.2.3. In f l u e n c e 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 69 5.2.4. Mean Annual Ring Width 71 5.2.5. Number of L i v e Whorls 73 5.2.6. Nonlinear Models 74 5.2.7. C r o s s - S e c t i o n a l Area of L i v e Bark 76 5.2.8. P r e d i c t i o n of Base of L i v e Crown Stem Measures 76 5.2.9. P o r t a b i l i t y of Tree Leaf Area P r e d i c t i o n Models 77 5.2.10. Comparison With Other Work 78 6. Photography 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 85 7.1. Sampling A n a l y s i s 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. Photography Technique 88 8. Conclusions 89 8.1. Sampling A n a l y s i s 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. Photography Technique 91 v i i i Page 8.4. Research Recommendations ...92 L i t e r a t u r e C i t e d 93 Appendix I E x p l a n a t i o n of Symbols i n Box P l o t s 99 Appendix II Leaf Area Index Values 100 i x LIST OF FIGURES Page 1. R e l a t i o n s h i p of G versus probe angle 17 2. Stand l o c a t i o n s 23 3. Courtenay s i t e 24 4. Duncan s i t e 25 5. Haney s i t e 26 6. Examples of whole crown image and unobstructed crown image 30 7. SLA sample s i z e s by s i t e 40 8. SLA sample s i z e s by 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 by crown p o s i t i o n 43 11. NDW r a t i o by age c l a s s 43 12. NDW r a t i o by s i t e .44 13. Tree l e a f areas 50 14. TLA versus (ASW*ALB)bh 53 15. TLA versus (ASW*ALB)blc 54 16. The r e l a t i o n s h i p of MARW and TLA:ASWbh 58 17. The r e l a t i o n s h i p of MARW and TLA:ASWblc 59 18. TLA:ASWbh versus ASWbh..! 60 19. TLA versus ASWbh 61 20. ASWblc versus ASWbh 63 21. ASWLBblc versus ASWLBbh 64 22. (ASW*ALB)blc versus (ASW*ALB)bh 65 23. ALCblc versus ALCbh 67 24. TLA versus (ASW*MARW)bh 72 25. TLA versus s i l h o u e t t e area 81 X LIST OF TABLES Page 1. E x p l a i n e d v a r i a b i l i t y i n the TLA-ASW r e l a t i o n s h i p . . . 1 0 2. General c h a r a c t e r i s t i c s of the Duncan, Courtenay, and Haney s i t e s ..27 3. Sample t r e e d e s c r i p t i o n 28 4. 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 SLA by needle age c l a s s ( a l l s i t e s ) 39 5. 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 SLA by crown p o s i t i o n ( a l l s i t e s ) 39 6. 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 needle age c l a s s e s by s i t e 44 7. Ranking 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 each s i t e 45 8. Models f o r the r e g r e s s i o n of D o u g l a s - f i r one-s i d e d l e a f area on s e v e r a l stem measurements 51 9. Mean r a t i o s of TLA and s e l e c t e d stem measurements... 55 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 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 the r e l a t i o n s h i p between ASW and MARW at br e a s t height and the base of l i v e crown 58 12. C o e f f i c i e n t s f o r n o n l i n e a r models of the form TLA=a*ASWbht**Dt= 62 13. Comparison of sl o p e i n t e r c e p t s f o r TLA p r e d i c t i o n models which v a r i e d by s i t e 70 14. D e s c r i p t i o n of photographs s e l e c t e d f o r a n a l y s i s . . . . 8 0 LIST OF ABBREVIATIONS ACLA - needle age c l a s s area (cm 2). ADB - c r o s s - s e c t i o n a l area of dead bark (cm 2). AHW - c r o s s - s e c t i o n a l area of heartwood (cm 2). AHWSW - c r o s s - s e c t i o n a l area of heartwood and sapwood (cm 2). AHWSWLB - c r o s s - s e c t i o n a l area of heartwood, sapwood, and 1ive bark (cm 2). ALB - c r o s s - s e c t i o n a l area of l i v e bark (phloem) (cm 2). ALC - c r o s s - s e c t i o n a l area of most recent annual r i n g s equal i n number to the number of l i v e whorls on the main stem (cm 2). ALCLB - ALC plus ALB (cm 2). ASW - c r o s s - s e c t i o n a l area of sapwood (cm 2). ASWLB - ASW plus ALB (cm 2). ATOT - c r o s s - s e c t i o n a l area of stem measured o u t s i d e bark, same as basal area (cm 2). ASW*ALB - the product of ASW and ALB (cm 4). BLA - one-sided branch l e a f area (cm 2). CSA - c u r r e n t sapwood area (cm 2) (Rogers and Hi n k l e y 1979). D - d i s t a n c e (cm) between middle of l i v e crown and br e a s t height (1.3m) (Long and Smith 1988). DW - d r y weight ( g ) . FW - f r e s h weight ( g ) . G - mean p r o j e c t i o n of u n i t l e a f area i n the d i r e c t i o n of the beam on a plane normal to the beam (Lang 1987). K - l i g h t e x t i n c t i o n c o e f f i c i e n t . x i i LAI - l e a f area index (m 2/m 2). MARA - mean annual r i n g area i n the sapwood (cm 2). MARW - mean annual r i n g width i n the sapwood (cm). NDW - needle dry weight ( g ) . O p - probe angle. Q i - i r r a d i a n c e below the f o r e s t canopy. Q o - i r r a d i a n c e above the f o r e s t canopy. SLA - s p e c i f i c l e a f area (g/cm 2). T - s o l a r t r a n s m i t t a n c e . TLA - one-sided t r e e l e a f area (m 2). Stem l o c a t i o n a b b r e v i a t i o n s are i n lowercase and when attached to an uppercase a b b r e v i a t i o n i n d i c a t e the l o c a t i o n on the stem where the measurement was taken. bh - b r e a s t height (1.3 m). b l c - base of l i v e crown. ACKNOWLEDGEMENT I would l i k e to thank David New and my wife Heather f t h e i r a s s i s t a n c e i n c o l l e c t i n g and p r o c e s s i n g the samples. Both Dr. K a r e l K l i n k a and Reid C a r t e r gave many h e l p f u l comments and Reid provided i n v a l u a b l e advice r e g a r d i n g s t a t i s t i c a l a n a l y s i s . The use of F l e t c h e r Challenge of Canada's r e s e a r c h l a b o r a t o r y i n C r o f t o n , B.C. i s a l s o g r e a t l y a p p r e c i a t e d . T h i s work was funded by the N a t i o n a l Science and E n g i n e e r i n g Research C o u n c i l of Canada. 1 1. INTRODUCTION 1.1. TREE LEAF AREA Tree l e a f area measurements are used i n a wide v a r i e t y of a p p l i c a t i o n s . In f o r e s t p r o d u c t i v i t y s t u d i e s , a measure of l e a f area i s important f o r e s t i m a t i n g r a t e s of e v a p o t r a n s p i r a t i o n , exchange of p h o t o s y n t h e t i c gases, and r e c e i p t of s o l a r r a d i a t i o n . When the impact of stand treatments i s being analyzed, the response i n l e a f area i s o f t e n c o n s i d e r e d to be an important i n d i c a t o r of treatment impact. More r e c e n t l y , there has been i n c r e a s e d i n t e r e s t i n the r e l a t i o n s h i p between l e a f area and e c o l o g i c a l s i t e q u a l i t y ( C arter et al. 1990). Estimates of t r e e l e a f area (TLA) are commonly re p o r t e d i n the l i t e r a t u r e i n two ways: as a u n i t l e s s r a t i o on a stand b a s i s as l e a f area index (LAI - p r o j e c t e d l e a f area i n m2 to land s u r f a c e area i n m2) or on an i n d i v i d u a l t r e e b a s i s as p r o j e c t e d l e a f area (m2). In some s t u d i e s , TLA on a s i n g l e t r e e b a s i s i s of more use to the f o r e s t r e s e a r c h e r than TLA on a whole stand b a s i s . T h i s may be the case when treatments are a p p l i e d to a s m a l l number of t r e e s and i n d i v i d u a l t r e e response i s of i n t e r e s t . Or when l o o k i n g at c o m p e t i t i o n i n a f o r e s t ecosystem, a comparison of TLA between dominant t r e e s and codominants or intermediate t r e e s may be u s e f u l . However, the use of s i n g l e TLA estimates i s d e t e r r e d by the d i f f i c u l t y with which accurate TLA estimates are obtained. I t i s the estimate of s i n g l e TLA with which t h i s study i s concerned. 2 1.2. ALLOMETRIC RELATIONSHIPS S e v e r a l methods are used to estimate TLA. The most accurate but l a b o r i o u s method i s d e s t r u c t i v e sampling. Recently, as an a l t e r n a t i v e to d e s t r u c t i v e sampling, much a t t e n t i o n has been given to the p o t e n t i a l of t r e e bole or stem measures f o r p r e d i c t i n g TLA. Some of the stem measures used to p r e d i c t TLA have been diameter at stump height (Helgerson et al. 1988), diameter at b r e a s t height (dbh) (Gholz et al. 1979), c r o s s - s e c t i o n a l sapwood area at bre a s t height (ASWbh) (Kaufmann and Troendle 1981; Marchand 1984; Whitehead 1978) or a t the base of the l i v e crown (ASWblc) (Maguire and Hann 1989). The s e l e c t e d stem measurement i s used i n a p r e d i c t i v e a l l o m e t r i c equation as the independent v a r i a b l e . There has been much debate about the p o r t a b i l i t y of these a l l o m e t r i c equations over a range of s i t e c o n d i t i o n s (Long and Smith 1988) and stand s t r u c t u r e s and d e n s i t i e s (Espinosa B a n c a l a r i et al. 1987; Keane and Weetman 1987; Thompson 1989) and how they change as a r e s u l t of stand treatments ( B r i x and M i t c h e l l 1983; G r i e r et al. 1984; Whitehead et al. 1984). Many of these r e s e a r c h e r s have concluded t h a t one a l l o m e t r i c r a t i o should not be used over a range of s i t e s and stands. F u r t h e r work has been done to d i s c o v e r an independent v a r i a b l e , such as mean annual r i n g width, sapwood p e r m e a b i l i t y , or crown l e n g t h , which might enable the user to overcome these r e g i o n a l l i m i t a t i o n s to 3 the use of a l l o m e t r i c equations (Albrekson 1984; Whitehead et al. 1984; Maguire and Hann 1989). 1.3. SOLAR TRANSMITTANCE AND PHOTOGRAPHY Another approach to e s t i m a t i n g l e a f area u t i l i z e s measurements of s o l a r t r a n s m i t t a n c e through the canopy and r e l i e s on an i n v e r s i o n of the Beer-Lambert equation f o r the c a l c u l a t i o n of l e a f area index: (1) LAI = -Ln(Q1/Qc.)cos8'K where LAI i s l e a f area index, Q i i s s o l a r i r r a d i a n c e below the canopy, Q 0 i s s o l a r i r r a d i a n c e above the canopy, 0 i s the s o l a r i n c i d e n t angle, and K i s the l i g h t e x t i n c t i o n c o e f f i c i e n t . The e x t i n c t i o n c o e f f i c i e n t of 0.48 f o r D o u g l a s - f i r has been c a l c u l a t e d by Ungs (1981). The u n d e r l y i n g assumption of the equation i s t h a t the f o l i a g e i s randomly d i s t r i b u t e d i n space and the l e a f i n c l i n a t i o n angles are s p h e r i c a l l y d i s t r i b u t e d ( J a r v i s and Leverenz 1983). Cameras and radiometers have been used e x t e n s i v e l y to estimate s o l a r t r a n s m i t t a n c e through a f o r e s t canopy to p r e d i c t LAI. However, l i t t l e work has been p u b l i s h e d d e s c r i b i n g attempts to estimate s i n g l e TLA with e i t h e r approach. 1.4. OBJECTIVE The o b j e c t i v e of t h i s study i s t h r e e f o l d : (1) to examine v a r i a t i o n i n a l l o m e t r i c r e l a t i o n s h i p s between TLA and s e v e r a l stem measurements i n c o a s t a l D o u g l a s - f i r (Pseudotsuga menziesii (Mirb.) Franco, v a r . menziesii) over a range i n s o i l moisture and n u t r i e n t s ; (2) to t e s t a photographic technique f o r i t s u s e f u l n e s s at p r e d i c t i n g s i n g l e TLA estimates; and (3) to make recommendations r e g a r d i n g optimal sampling s t r a t e g i e s f o r e s t i m a t i n g i n d i v i d u a l TLA from d e s t r u c t i v e sampling. 5 2. LITERATURE REVIEW 2.1. ALLOMETRIC RELATIONSHIPS The study of the r e l a t i o n s h i p between growth r a t e s of p l a n t organs w i t h i n one organism i s known as allometry. The o b s e r v a t i o n of a l l o m e t r y i n t r e e s was made long ago by Leonardo da V i n c i . He observed, " A l l the branches of a t r e e at every stage of i t s height when put together are equal i n t h i c k n e s s to the trunk (below them)" (as quoted by Zimmermann 1983). I t was Huber (1928) t h a t began to speak s p e c i f i c a l l y about r a t i o s of c r o s s - s e c t i o n a l xylem areas and f r e s h weight of l e a v e s . Since t h a t time a l l o m e t r i c equations have been developed f o r many t r e e s p e c i e s f o r p r e d i c t i n g TLA or f o l i a r biomass u s i n g a stem measurement as the independent v a r i a b l e . Waring (1983) p u b l i s h e d a l i s t of r a t i o s of p r o j e c t e d l e a f area to sapwood c r o s s - s e c t i o n a l area at b r e a s t h e i g h t (ASWbh) f o r f o u r t e e n North American c o n i f e r s p e c i e s . As a r e s u l t of f u r t h e r r e s e a r c h , many more s p e c i e s c o u l d be added to t h i s l i s t today. An example of the r e l a t i o n s being observed f o r c o n i f e r t r e e s i s provided by Whitehead (1978) f o r Scots pine {Pinus sylvestris L . ) . The r e l a t i o n between TLA and ASWbh f o r eleven t r e e s from four spacing treatments was l i n e a r and s t r o n g : (2) TLA = 0.137(ASWbh) - 7.004 R 2 = 0.97; n = 11 6 A t h e o r e t i c a l e x p l a n a t i o n f o r the c l o s e r e l a t i o n between the growth of TLA and the stem has been provided by Shinozaki et al. (1964a,b). They presented the "pipe model theory" which contends t h a t a given t r a n s p i r i n g l e a f mass r e q u i r e s a p r o p o r t i o n a l amount of conducting stemwood. Researchers have examined the r e l a t i o n s h i p s of v a r i o u s stem measurements to TLA f o r many s p e c i e s to v e r i f y the v a l i d i t y of the pipe model theory. Much a t t e n t i o n has been given to r e l a t i o n s h i p s between TLA and stem parameters f o r D o u g l a s - f i r and the r e s u l t s have been v a r i a b l e . One focus i n the work has been to determine i f dbh i s as a c c u r a t e a p r e d i c t o r of TLA as ASW. I t has been found i n some in s t a n c e s f o r D o u g l a s - f i r t h a t dbh, b a s a l area, and ASWbh are e q u a l l y accurate as p r e d i c t o r s of TLA (Espinosa B a n c a l a r i et al. 1987; B r i x and M i t c h e l l 1983; G r i e r et al. 1984). In each of these s t u d i e s the sample t r e e s were l e s s than 30 years o l d . Gower et al. (1987), examining 65 to 70 y e a r - o l d D o u g l a s - f i r t r e e s found ASW to improve l e a f area p r e d i c t i o n over dbh. S n e l l and Brown (1978) found ASWbh to be more h i g h l y c o r r e l a t e d than dbh with f o l i a g e mass. In t h e i r study, sample t r e e s were l e s s than 20 cm dbh but the authors d i d n o t . I n d i c a t e the age of t h e i r D o u g l a s - f i r sample t r e e s . Basal area and dbh provide a measure which i n c l u d e both the conducting p o r t i o n of the stem, the sapwood, and the nonconducting, p h y s i c a l support p o r t i o n of the stem, the heartwood. If the pipe model theo r y holds t r u e , one would expect the conducting p o r t i o n 7 of the stem, r a t h e r than dbh or b a s a l area, to be more c l o s e l y r e l a t e d to TLA. The d i s t i n c t i o n between the two measures would l i k e l y be c l e a r e r i n ol d e r t r e e s where heartwood area makes up a l a r g e r p o r t i o n of t o t a l b a s a l area. A second focus i n D o u g l a s - f i r a l l o m e t r y s t u d i e s has been on the p r e d i c t i v e u s e f u l n e s s of ASW at the base of the l i v e crown ( b l c ) over the ASWbh. Shinozaki et al. (1964b) s t a t e t h a t the amount of leaves per t r e e should be most c l o s e l y c o r r e l a t e d with the sum of c r o s s - s e c t i o n a l areas of l i v i n g pipes s u p p o r t i n g them, which i n tu r n c o u l d be approximated by the c r o s s - s e c t i o n a l area of the stem at b l c . Geron and Ruark (1988) comment th a t even though measuring dbh or ASWbh may be convenient, i t i s p h y s i o l o g i c a l l y an a r b i t r a r y p o s i t i o n to take such measurements and i t s r e l a t i v e p o s i t i o n changes with height growth. They note t h a t diameter at b l c i s an " a c t u a l organ dimension of a t r e e " and t h e r e f o r e a more p h y s i o l o g i c a l l y s i g n i f i c a n t measure than dbh f o r p r e d i c t i n g TLA. In other words, measuring ASW at bh r e s u l t s i n the measure being taken at the same height on a l l sample t r e e s but p h y s i o l o g i c a l l y -speaking not n e c e s s a r i l y the same l o c a t i o n . T h e r e f o r e , measuring ASW at b l c ensures t h a t d e s p i t e v a r i a t i o n s i n crown l e n g t h , the measurement i s taken at the same p h y s i o l o g i c a l p o s i t i o n i n a l l sample t r e e s . The concern i s v a l i d only i f there i s a d i f f e r e n c e i n ASW between bh and b l c . Long et al. (1981) found t h a t ASW v a r i e d only s l i g h t l y 8 between bh and b l c i n a stand of 45 y e a r - o l d D o u g l a s - f i r t r e e s . E s p i nosa B a n c a l a r i et al. (1987) found ASW to decrease with i n c r e a s i n g height i n the t r e e i n thr e e adjacent 22 y e a r - o l d D o u g l a s - f i r stands with d i f f e r e n t e a r l y growth r a t e s (see a l s o B r i x and M i t c h e l l (1983) and Waring et al. (1982) f o r s i m i l a r r e s u l t s ) . A review of a v a i l a b l e l i t e r a t u r e suggests ASWblc i s a s l i g h t l y b e t t e r p r e d i c t o r of TLA than ASWbh; u n f o r t u n a t e l y , l i t t l e i n f o r m a t i o n i s a v a i l a b l e i n t h i s regard f o r Douglas-f i r . E s p i n o sa B a n c a l a r i et al. (1987) r e p o r t t h a t ASWblc was b e t t e r than ASWbh f o r p r e d i c t i n g TLA only f o r t h e i r f a s t growing stand of D o u g l a s - f i r , while i n t h e i r medium and slow growing stands ASWbh was as good as ASWblc. Gower et al. (1987) found ASWbh to be m a r g i n a l l y b e t t e r than ASWblc f o r p r e d i c t i n g TLA (R 2 = 0.971 and 0.968, r e s p e c t i v e l y ) . For lodgepole pine, Hungerford (1987) found ASWblc onl y m a r g i n a l l y b e t t e r than ASWbh f o r p r e d i c t i n g TLA (R 2 i n c r e a s e d from 0.89 to 0.90; n = 54). Marchand (1984) found ASWblc a b e t t e r TLA p r e d i c t o r than ASWbh f o r balsam f i r (Abies ba Is ante a (L.) M i l l ) and red spruce (Picea rubens Sarg) and Blanche et al. (1985) found the same f o r l o b l o l l y pine (Pinus taeda L . ) . Geron and Ruark (1988) were able to remove much of the v a r i a b i l i t y i n p r e d i c t i n g TLA f o r s i x t r e e s p e c i e s by us i n g ASWblc r a t h e r than ASWbh. Research i s i n d i c a t i n g t h at i n most s i t u a t i o n s , p a r t i c u l a r l y when the p r o p o r t i o n of crown t o bole i s v a r i a b l e w i t h i n or between stands, ASWblc i s the p r e f e r r e d v a r i a b l e over ASWbh f o r 9 p r e d i c t i n g TLA. In very uniform stands with low crown to bole r a t i o v a r i a b i l i t y w i t h i n or between stands ASWbh may be an adequate p r e d i c t o r of TLA. Despite the decrease i n v a r i a b i l i t y gained through using ASWblc, r e s e a r c h e r s have favored bh measurements because of the ease with which they can be gathered. E x p l o r i n g the p o s s i b i l i t y of p r e d i c t i n g ASWblc from ASWbh, some workers have found the r e l a t i o n s h i p between ASWbh and ASWblc to be l i n e a r (Blanche et al. 1985 f o r l o b l o l l y pine) while others have found i t to be n o n l i n e a r (Dean and Long 1986 f o r lodgepole p i n e ) . The f i n d i n g s of Long et al. (1981), B r i x and M i t c h e l l (1983), and Espinosa B a n c a l a r i et al. (1987) suggest t h a t ASWblc p r e d i c t i o n models with ASWbh as the independent v a r i a b l e would have to be s i t e - s p e c i f i c f o r D o u g l a s - f i r . While the l i t e r a t u r e i n d i c a t e s ASWblc prov i d e s a p r e c i s e and accurate estimate of TLA, sources of 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 the ASW-TLA r e l a t i o n s h i p which need to be c o n s i d e r e d . The r e l a t i o n s h i p v a r i e s between s p e c i e s (Kaufmann and Troendle 1981; Whitehead et al. 1984) and w i t h i n s p e c i e s (Geron and Ruark 1988). Table 1 presents s e v e r a l sources of w i t h i n s p e c i e s v a r i a t i o n i n the ASW-TLA r e l a t i o n s h i p . Independent v a r i a b l e s have been in t r o d u c e d i n t o a l l o m e t i c equations i n attempts to e x p l a i n 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 s . Dean and Long (1986) in t r o d u c e d a second independent v a r i a b l e , D, the d i s t a n c e between the 10 middle of the l i v e crown and bh, i n t o the TLA p r e d i c t i o n model. T h i s measure takes i n t o account v a r i a t i o n s r e s u l t i n g Table 1. Explained v a t i a b i l i t y i n the TLA-ASH r e l a t i o n s h i p for s e v e r a l c o n i f e r s p e c i e s . Source of Species Source of v a r i a t i o n i n f o r n a t i o n stand d e n s i t y Pious contoita Reane and Beetman (1987) s i t e q u a l i t y Pseadotsuga aenziesii Binkley (1984) B a n c a l a r i et a l . (1987) Pinus sylvestiis Whitehead (1978) Al b i e k t s o n (1984) d e n s i t y X s i t e index Pinas contoita Long and Su i t h (1988) Abies lasiocaipa Long and Smith (1989) stand treatment: f e r t i l i z a t i o n Pseadotsuga aenziesii B r i x and M i t c h e l l (1983) t h i n n i n g Pseudotsuga aenziesii Granier (1981) f e r t . I t h i n . Pseadotsuga aenziesii B i i x and M i t c h e l l (1983) crown c l a s s Pinas contoita Dean and Long (1986) Thonpson (1989) nean annual r i n g width Pinns sylvestiis Albrektson (1984) Pinus contoita Thonpson (1989) Pseadotsuga aenziesii B a n c a l a r i et al. (1987) t i n e of sampling Pious taeda Blanche et a l . (1985) d e n s i t y X age X s i t e Pious contoita Pearson et al. (1984) from crown c l a s s . At the time of Dean and Longs' r e s e a r c h i t had been shown t h a t f o r some s p e c i e s the r e l a t i o n s h i p between TLA and ASW may vary with s i t e q u a l i t y and stand d e n s i t y (Whitehead 1978; B r i x and M i t c h e l l 1983; A l b r e k t s o n 1984; Pearson et al. 1984). Dean and Long (1986) were the f i r s t to r e p o r t a c u r v i l i n e a r r e l a t i o n s h i p between ASWbh and TLA: (3) TLA = 0.028 * ASWbh 1- 1 5 6 * D~° - 7 4 R 2 = 0.99; n = 17 11 They found t h a t the r e l a t i o n s h i p between ASWblc and TLA was l i n e a r i f suppressed t r e e s were not i n c l u d e d i n the a n a l y s i s . T h e i r lodgepole pine data from Utah i n c l u d e d samples from s a p l i n g s and mature t r e e s . They suggested t h a t others have not found the r e l a t i o n s h i p to be no n l i n e a r because they may have 1) used on l y s h o r t t r e e s with high r a t i o s of crown to stem l e n g t h , thereby i n a d v e r t e n t l y t e s t i n g ASWblc, 2) used only average t r e e s w i t h i n a stand, 3) analyzed stands with low inherent v a r i a b i l i t y , such as p l a n t a t i o n s or thinned stands, 4) not i n c l u d e d suppressed t r e e s , or 5) not analyzed r e s i d u a l s from l i n e a r r e g r e s s i o n . Long and Smith (1988) t e s t e d the s u i t a b i l i t y of using two power terms to p r e d i c t TLA f o r lodgepole pine i n Wyoming. They found the r a t i o of TLA to ASWbh i n c r e a s e d across the range of ASWbh i n d i c a t i n g t h a t a l i n e a r model would in t r o d u c e b i a s i n t o TLA p r e d i c t i o n s . The two power term model was unbiased toward ASWbh, stand d e n s i t y , and s i t e index. However the models d i f f e r e d between the Wyoming and Utah s i t e s . Long and Smith (1988) suggest t h i s may be due t o d i f f e r e n c e s i n s i t e water balance. Thompson (1989) found the r e l a t i o n s h i p between TLA and ASW at the base of the t r e e to be n o n l i n e a r f o r lodgepole pine as w e l l . Long and Smith (1989) found there was a s i g n i f i c a n t n o n l i n e a r r e l a t i o n s h i p between TLA and ASWbh f o r su b a l p i n e f i r ( Abies lasiocarpa (Hook.) Nutt.) S p i t t l e h o u s e (1981) found the r e l a t i o n s h i p between TLA and dbh to be n o n l i n e a r i n a 30 y e a r - o l d thinned D o u g l a s - f i r stand l o c a t e d near Courtenay, 12 B.C. Research has not been p u b l i s h e d i n d i c a t i n g i f a non l i n e a r model u s i n g two power terms to p r e d i c t TLA i s u s e f u l i n regard to D o u g l a s - f i r . Another approach to e x p l a i n i n g v a r i a b i l i t y i n the ASW-TLA r e l a t i o n s h i p between s i t e s has focused on d i f f e r e n c e s i n sapwood p e r m e a b i l i t y . The assumption i s t h a t the c a p a c i t y of the conducting system i n the stem depends on ASW and the p e r m e a b i l i t y of the sapwood (Whitehead and J a r v i s 1981). Whitehead et al. (1984) found t h a t i n a p a r t i c u l a r c l i m a t e the TLA of lodgepole pine and S i t k a spruce (Picea sitchensis (Bong.) C a r r . was more c l o s e l y r e l a t e d to the product of ASWbh and a sapwood p e r m e a b i l i t y measure than i t was to ASWbh alone. Saturated p e r m e a b i l i t y was measured u s i n g the method d e s c r i b e d by Edwards and J a r v i s (1982). An e a s i l y measured sur r o g a t e of p e r m e a b i l i t y , mean annual r i n g width (MARW) i n the sapwood, has a l s o been examined f o r i t s c o n t r i b u t i o n to e x p l a i n i n g v a r i a b i l i t y i n the TLA-ASW r e l a t i o n s h i p . Wider growth r i n g s g e n e r a l l y have l a r g e r t r a c h e i d diameters (Bannan 1965) which should mean higher p e r m e a b i l i t y . P o t h i e r et al. (1989) found t h a t sapwood p e r m e a b i l i t y at the b l c was s t r o n g l y c o r r e l a t e d with mean diameter growth over the l a s t 10 years f o r 15 and 35 ye a r - o l d stands of jack pine {Pinus banksiana Lamb.). A l b r e k t s o n (1984) found t h a t the r a t i o of f o l i a g e mass to ASWbh i n Scots pine v a r i e d mith MARW. For D o u g l a s - f i r , Espinosa B a n c a l a r i et al. (1987) found t h a t the TLA:ASWbh r a t i o c o r r e l a t e d p o s i t i v e l y with MARW i n the sapwood but 13 i n c l u s i o n of MARW as an independent v a r i a b l e i n t o the TLA p r e d i c t i o n model was not u s e f u l because MARW i n the sapwood c o r r e l a t e d c l o s e l y with ASWbh. Thompson (1989) used mean r i n g area i n the sapwood (MARA) as an i n t e r a c t i o n term with ASW f o r lodgepole pine and found i t improved the f i t of the r e g r e s s i o n compared with u s i n g ASW alone. Espinosa B a n c a l a r i et al. (1987) suggest that i n s i t u a t i o n s where ASW i s not c l o s e l y c o r r e l a t e d with MARW, i n c l u s i o n of MARW may improve the p r e c i s i o n of TLA p r e d i c t i o n . The d i f f e r e n t i a t i o n of conducting versus nonconducting sapwood has a l s o been given a t t e n t i o n f o r i t s p o t e n t i a l as an e x p l a n a t i o n of v a r i a b i l i t y i n ASW-TLA r e l a t i o n s h i p . In oak, water t r a n s p o r t i n the stem i s r e s t r i c t e d to the most re c e n t one or two annual r i n g s (Rogers and H i n c k l e y 1979). T h i s band of conducting sapwood i s r e f e r r e d to as "c u r r e n t sapwood are a " (CSA). Rogers and H i n c k l e y found t h a t both CSAbh and ASWbh were l i n e a r l y r e l a t e d to TLA i n black oak (Quercus velutina Lam.) with c o r r e l a t i o n c o e f f i c i e n t s of 0.97 and 0.93 r e s p e c t i v e l y . In white oak (Quercus alba L.) CSAbh and ASWbh were a l s o l i n e a r l y r e l a t e d to TLA but with c o r r e l a t i o n c o e f f i c i e n t s of 0.94 and 0.73, r e s p e c t i v e l y . The i m p l i c a t i o n of these c o r r e l a t i o n s i s t h a t CSAbh i s the more c l o s e l y c o r r e l a t e d v a r i a b l e with TLA and th a t f o r some s p e c i e s there may be a f o r t u i t o u s c o r r e l a t i o n between n o n f u n c t i o n a l stem measures and conducting sapwood area. C o m p l i c a t i n g the matter i s t h a t the p o r t i o n of sapwood t h a t conducts water v a r i e s with s p e c i e s . Dixon (1971) r e p o r t s 14 that i n Tilia s p e c i e s the outermost r i n g accounts f o r o n l y nine percent of conducted water. I t seems t h a t most workers examining the ASW-TLA r e l a t i o n s h i p are working under the assumption t h a t i n c o n i f e r s a l l the earlywood i n sapwood i s conducting water with the outermost p o r t i o n of the sapwood conducting more than the innermost p o r t i o n . The b a s i s of t h i s assumption i s work done by Swanson (1975), Kozlowski et al. (1966, 1967), and Booker and Kininmonth (1978). However, Edwards and J a r v i s (1982) r e p o r t t h a t i n lodgepole pine and S i t k a spruce the number of conducting r i n g s approximated the number of l i v e whorls i n the crown. If t h i s i s the case f o r D o u g l a s - f i r , one would expect t h a t TLA i s c l o s e l y r e l a t e d to the c r o s s - s e c t i o n a l area of the most rec e n t annual r i n g s , the number of r i n g s being equal to the number of whorls i n the l i v e crown (ALC). Aside from h i g h l i g h t i n g the importance of d i f f e r e n t i a t i n g conducting and nonconducting sapwood, Rogers and H i n c k l e y s ' (1979) work a l s o suggests t h a t i n some t r e e s the ASW i s f o r t u i t o u s l y r e l a t e d to some other p h y s i o l o g i c a l c h a r a c t e r i s t i c t h a t i s c o r r e l a t e d with TLA. In response to t h i s , Waring and S c h l e s i n g e r (1985) propose t h a t storage of n u t r i e n t r e s e r v e s i n the stem may come i n t o p l a y with the ASW-TLA r e l a t i o n s h i p . Some of the photosynthates produced i n the growing season are t r a n s p o r t e d v i a the phloem to the stem and r o o t s of the t r e e . Sucrose t h a t accumulates i n the stem i s transformed i n t o s t a r c h and s t o r e d i n parenchyma c e l l s i n the phloem and xylem. At the outset of the growing 15 season the s t a r c h r e s e r v e s are u t i l i z e d i n new growth ( S a l i s b u r y and Ross 1978). That n u t r i e n t r e s e r v e s i n the stem are u t i l i z e d f o r shoot e l o n g a t i o n i n red pine (Pinus resinosa A i t . ) i s documented by Kramer and Kozlowski (1979). F l u c t u a t i o n s i n n u t r i e n t r e s e r v e s should r e s u l t i n a c o r r e s p o n d i n g f l u c t u a t i o n i n f o l i a g e and wood p r o d u c t i o n . Seeing that l i v i n g bark s t o r e s n u t r i e n t r e s e r v e s , i t s c r o s s -s e c t i o n a l area (ALB) at some p o i n t on the stem (or p o s s i b l y the sum of ASW and ALB (ASWLB)) may be more c l o s e l y c o r r e l a t e d with TLA than ASW alone (John W o r r a l l , p e r s o n a l comm.). If ALB i s c l o s e l y c o r r e l a t e d with ASW then i t s c o n t r i b u t i o n to TLA p r e d i c t i o n may be l i m i t e d . Brack et al. (1985) found t h a t bark area was c o r r e l a t e d with TLA and ASW f o r three s p e c i e s of Eucalyptus. They recommend t h a t t h e o r i e s r e l a t i n g TLA and ASW through h y d r o l o g i c f u n c t i o n s need to be expanded to i n c l u d e bark f u n c t i o n s as w e l l . The r e l a t i o n s h i p between ASW, ALB, and TLA i n D o u g l a s - f i r needs to be e x p l o r e d . 2.2. PHOTOGRAPHY Cameras equipped with h e m i s p h e r i c a l lenses have been used s u c c e s s f u l l y as an i n d i r e c t method of p r e d i c t i n g whole stand l e a f area or LAI (Anderson 1971; Leong et al. 1982; Wang and M i l l e r 1987). The p o s s i b i l i t y of u s i n g photography to p r e d i c t s i n g l e t r e e l e a f area appears r e l a t i v e l y unexplored. A simple approach would be to photograph t r e e s at a f i x e d angle to the azimuth and a f i x e d d i s t a n c e from the t a r g e t t r e e . The view of the t a r g e t t r e e which provides 16 fewest o b s t r u c t i o n s to the e n t i r e crown would be s e l e c t e d as the d i r e c t i o n of the photograph. The photograph image of the t r e e c o u l d then be analyzed to determine t o t a l area of the image of the t r e e on the photograph. In t h i s study the area w i l l be c a l l e d silhouette area (the term comes from C a r t e r and Smith (1985), as c i t e d by D i e b o l t and Mudge (1988)). The s i l h o u e t t e area i s a su r r o g a t e of l e a f area d e n s i t y and there should be a s t r o n g c o r r e l a t i o n between TLA as determined by d e s t r u c t i v e sampling and s i l h o u e t t e area. There i s a s t r o n g t h e o r e t i c a l b a s i s f o r choosing 57.5° from the azimuth as the f i x e d camera angle. Lang et al. (1985) have developed the f o l l o w i n g equation to d e s c r i b e the r e l a t i o n s h i p between LAI ( L ) , canopy s t r u c t u r e , and s o l a r t r a n s m i t t a n c e ( T ) : (4) L * G< O E J) = -cosOp * l n T ( o p ) where Op i s the probe angle, or the angle between the sun's beam and the v e r t i c a l ( s o l a r z e n i t h angle) and G i s mean p r o j e c t i o n of u n i t l e a f area i n the d i r e c t i o n of the beam on a plane normal to the beam ( d e f i n i t i o n s from Lang (1987)). The s i z e of G depends on l e a f azimuth and z e n i t h angle d i s t r i b u t i o n s and the angle of the probe. I t has been found t h a t G r e l a t e s to l e a f i n c l i n a t i o n angle and probe angle as shown i n F i g u r e 1. 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 of mean p r o j e c t i o n of u n i t l e a f area (G) and probe angle (0°). The graph assumes random l e a f azimuth angle and <X i s constant at a given angle of e l e v a t i o n (Lang 1986). I t can be seen from F i g u r e 1 t h a t at probe angle 57.5°, the value of G i s independent of l e a f angle d i s t r i b u t i o n and can be assumed to equal 0.5. The r e f o r e , at probe angle 57.5°, equation (4) can be w r i t t e n as f o l l o w s : (5) L * 0.5 = -cos(57.5) * lnT« B 7.s>.. While t a k i n g a p i c t u r e of a t r e e at 57.5° i s not the same.as c o n s i d e r i n g a beam of the sun probing the canopy at 57.5°, choosing t h i s angle for the camera angle and ensuring the t r e e i s i n the center of the photo minimizes the impact of v a r i a t i o n s of l e a f z e n i t h angle w i t h i n and between t r e e s on the f i n a l exposure-of the t r e e . 18 2.3. DESTRUCTIVE SAMPLING As Geron and Ruark (1988) have noted, f o r many l e a f area s t u d i e s i t i s d i f f i c u l t to d i f f e r e n t i a t e between sampling v a r i a b i l i t y t h a t has r e s u l t e d from subsampling f o r crown l e a f area estimates and the random v a r i a b i l i t y a s s o c i a t e d with the TLA:ASW r a t i o . In most t r e e l e a f area s t u d i e s sampling r a t i o s are used to convert subsample values to whole t r e e v a l u e s . I t i s important to q u a n t i f y the v a r i a b i l i t y of these r a t i o s i n order to optimize sample s i z e s and minimize the e r r o r i n the TLA e s t i m a t e s . A common and convenient r a t i o used i n the e s t i m a t i o n of TLA i s s i n g l e - s i d e d s p e c i f i c l e a f area (SLA = r a t i o of p r o j e c t e d l e a f area of f r e s h needles (cm 3) to d r y weight (g) of those needles) (Gholz et al. 1976; E s p i n o s a B a n c a l a r i et al. 1987; Helgerson et al. 1988). The SLA r a t i o can be determined from a subsample and a p p l i e d a g a i n s t e a s i l y processed f o l i a r d r y weights. In order to minimize t e d i o u s subsampling i t i s necessary to determine the minimum s i z e and number of SLA subsamples needed to p r e d i c t branch l e a f area with a decided upon p r e c i s i o n . S p e c i f i c l e a f area has been found to vary i n lodgepole pine with needle age, crown p o s i t i o n , and stand treatment (Keane and Weetman 1987) and i n l o b l o l l y pine (Pinus taeda L.) with needle age (Johnson et al. 1985). D o u g l a s - f i r SLA v a r i e s between age c l a s s e s (Del Rio and Berg 1979; Smith et al. 1981; Gower et al. 1987) and crown p o s i t i o n s ( B o r g h e t t i et al. 1986) 19 n e c e s s i t a t i n g s t r a t i f i e d sampling of the crown i f accurate estimates of TLA are to be made from f o l i a r d r y weights. B o r g h e t t i et al. (1986)•divided the crown i n t o three l a y e r s and the needles i n t o four age c l a s s e s ( c u r r e n t through 3 y e a r - o l d p l u s ) . SLA decreased s i g n i f i c a n t l y with needle age and decreased w i t h i n every age c l a s s from base of l i v e crown to the apex. B o r g h e t t i et al. (1986) p o i n t out t h a t t h e i r data support the hypothesis t h a t l e a f morphology i s a f f e c t e d by l i g h t c o n d i t i o n s r e s u l t i n g i n the d i f f e r e n t i a t i o n between sun and shade l e a v e s . The o v e r a l l mean SLA f o r D o u g l a s - f i r found by B o r g h e t t i e t al. was 65.1 +0.9 cm 2/g compared to 70.8 to 82.4 cm 2/g (Gholz et al. 1976), 79.0 cm 2/g (Del Rio and Berg 1979) and 44.7 cm 2/g (Gower e t al. 1987). B o r g h e t t i et al. (1986) were s t u d y i n g 25 y e a r - o l d D o u g l a s - f i r t r e e s , Gholz et al. (1976) were examining o l d growth D o u g l a s - f i r f o r e s t s , Del Rio and Berg (1979) were examining 65 y e a r - o l d D o u g l a s - f i r r e g e n e r a t i o n growing under v a r y i n g d e n s i t i e s of thinned D o u g l a s - f i r f o r e s t s , and Gower e t al. (1987) were examining 65 to 70 y e a r - o l d D o u g l a s - f i r i n an even aged, mixed f o r e s t . When u s i n g SLA to p r e d i c t branch l e a f area, a second r a t i o of needle d r y weight to twig p l u s needle f r e s h weight i s u s e f u l i n order to avoid having to determine the f o l i a r dry weights of a l l needles i n each age c l a s s . The r a t i o may be denoted as NDW (needle d r y weight) r a t i o . C a l c u l a t i o n of the l e a f area of a s p e c i f i c age c l a s s of needles from one branch (ACLA) would be as f o l l o w s : 20 (6) ACLA (cm 2) = SLA (cm 2/g) * NDW (g/g) * FW (g) where FW i s f r e s h weight of twigs and needles of the age c l a s s of i n t e r e s t . As with SLA, i n order to a p p r o p r i a t e l y sample f o r NDW r a t i o , knowledge of i t s v a r i a b i l i t y i s e s s e n t i a l . Few s t u d i e s have provided adequate i n f o r m a t i o n on subsample s i z e requirements f o r p r e d i c t i o n of SLA. For the re s e a r c h e r f i r s t approaching the problem of d e s t r u c t i v e sampling f o r the purpose of p r e d i c t i n g TLA, the q u e s t i o n needs to be asked, what i s the v a r i a b i l i t y of SLA and what s i z e and how many subsamples are needed to estimate SLA with a g i v e n e r r o r and p r o b a b i l i t y ? Knowledge of the v a r i a b i l i t y of NDW r a t i o i s a l s o l a c k i n g . 2.4. NULL AND ALTERNATIVE HYPOTHESES The f o l l o w i n g n u l l and a l t e r n a t i v e hypotheses were t e s t e d on t h r e e s i t e s s u p p o r t i n g D o u g l a s - f i r stands. (1) Ho: bh stem measures are not l i n e a r l y r e l a t e d to b l c stem measures. H i : bh stem measures are l i n e a r l y r e l a t e d to b l c stem measures. (2) H 0: b l c stem measures are not more c l o s e l y c o r r e l a t e d with TLA than are bh stem measures. 21 Hi.: b l c stem measures are more c l o s e l y c o r r e l a t e d w i t h TLA than are bh stem measures . (3) H 0: ASW i s not 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 b a s a l a r e a . H x: ASW 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 b a s a l a r e a . (4) H 0: ALC i s not 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. H i : 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 or ASW*ALB a re not 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. H i : ASWLB or ASW*ALB a re 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. (6) H 0: the p r o d u c t of MARW and ASW i s not 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. H i : the p r o d u c t of MARW and ASW 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. (7) H«: i n c l u d i n g 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 not improve the f i t over t h a t o b t a i n e d u s i n g o n l y ASW. H i : i n c l u d i n g 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 improves the f i t over t h a t o b t a i n e d u s i n g o n l y ASW. (8) Ho : the r e l a t i o n s h i p s between TLA and c r o s s -s e c t i o n a l stem measures v a r y s i g n i f i c a n t l y (p=0.05) between s i t e s . 22 H i : the r e l a t i o n s h i p s between TLA and c r o s s -s e c t i o n a l stem measures do not v a r y s i g n i f i c a n t l y (p=0.05) between s i t e s . (9) H D: SLA does not v a r y s i g n i f i c a n t l y (p=0.05) between s i t e s , crown p o s i t i o n , or n e e d l e age c l a s s . H i : SLA v a r i e s s i g n i f i c a n t l y (p=0.05) between s i t e s , crown p o s i t i o n , or n e e d l e age c l a s s . (10) H 0: NDW r a t i o does not v a r y s i g n i f i c a n t l y (p=0.05) betweem s i t e s , crown p o s i t i o n , or n e e d l e age c l a s s . H Q: NDW r a t i o v a r i e s s i g n i f i c a n t l y (p=0.05) between s i t e s , crown p o s i t i o n , or n e e d l e age c l a s s . (11) H Q: t h e r e i s a poor c o r r e l a t i o n between TLA as determined by d e s t r u c t i v e s a m p l i n g and s i l h o u e t t e a r e a . H i : t h e r e i s a s t r o n g c o r r e l a t i o n between TLA as determined by d e s t r u c t i v e s a m p l i n g and s i l h o u e t t e a r e a . 23 3. MATERIALS AND METHODS 3.1. LOCATION T h r e e D o u g l a s - f i r s t a n d s , r e p r e s e n t i n g a r a n g e i n m o i s t u r e a n d n u t r i e n t c o n d i t i o n s , w e r e s e l e c t e d f o r s a m p l i n g i n t h e C o a s t a l W e s t e r n H e m l o c k (CWH) b i o g e o c l i m a t i c z o n e . F i g . 2 . M a p s h o w i n g l o c a t i o n o f s i t e s . C o u r t e n a y = A , D u n c a n = B , a n d H a n e y s i t e = C . . Two o f t h e s i t e s a r e l o c a t e d o n t h e e a s t s i d e o f V a n c o u v e r I s l a n d w i t h i n t h e V e r y D r y M a r i t i m e CWH s u b z o n e , o n e b e i n g 2 4 approximately 45 k i l o m e t e r s northwest of Courtenay on the Duncan Bay Main f o r e s t road i n the Western (CWHxm) v a r i a n t and the other approximately 22 k i l o m e t e r s west of Duncan along Cowichan Lake road i n the E a s t e r n (CWHmm) v a r i a n t . The t h i r d s i t e i s l o c a t e d at the Malcolm Knapp Research F o r e s t north of Haney, B.C. on G 2 0 road i n the Dry Maritime CWH subzone ( F i g u r e 2 ) . The s i t e s w i l l be r e f e r r e d to as the Courtenay s i t e ( F i gure 3 ) , the Duncan s i t e ( F i g u r e 4 ) , and the Haney s i t e ( F i gure 5 ) . F i g . 3 . Courtenay s i t e . 25 F i g . 4. Duncan s i t e . 3.2. SITE DESCRIPTION F o l l o w i n g the procedures o u t l i n e d by P o j a r et al. (1987) the s i t e s were examined and i n t e n s i v e l y sampled i n a previous study (Carter and K l i n k a 1988). S i t e i n f o r m a t i o n gathered by C a r t e r and K l i n k a (1988) as w e l l as a d d i t i o n a l i n f o r m a t i o n i s found i n Table 2. The s i t e s support even-aged, spaced D o u g l a s - f i r stands which are r e l a t i v e l y f r e e of d i s e a s e and i n s e c t damage and r e p r e s e n t a range of moisture and n u t r i e n t c o n d i t i o n s . As a r e s u l t of r e c e n t spacing there are no suppressed t r e e s i n the stands. F i g . 5. Haney s i t e . 3.3. TREE SELECTION Sample t r e e s were analyzed d u r i n g August and September 1988. Sample t r e e s were s e l e c t e d using the f o l l o w i n g c r i t e r i a : 1) to r e p r e s e n t the range of dbh s i z e s i n the stand; 2) f r e e of d i s e a s e or i n s e c t damage and growth a b n o r m a l i t i e s ; and 27 3) one view of the crown through which there was very l i t t l e o b s t r u c t i o n by adjacent t r e e s was a v a i l a b l e . Table 2. General c h a r a c t e r i s t i c s of the Duncan, Courtenay, and Haney s i t e s . Parameter Duncan Courtenay Haney Subzone CWHmm CWHxm CWHdm S o i l depth lm+ 1. 5m+ lm+ S o i l type O r t h i c D y s t r i c B r u n i s o l O r t h i c D y s t r i c B r u n i s o l Humo-F e r r i c Podzol Slope (%) 13 - 17 Slope p o s i t i o n middle f l a t middle E l e v a t i o n (m) 148 270 128 Mean annual ppt. (mm) 1304 1425 1827 A c t u a l e v a p o t r a n s p i r a t i o n (mm) 190 238 230 Growing season moisture d e f i c i t (mm) 138 77 0 Stand age (@ stump height 1988) 42 46 21 Stocking (stems/ha) 550 650 650 Year of sp a c i n g 1976 1982 19 83 S i t e index (m/50 y r s ) 16 21 37 S o i l moisture regime v. d r y mod. d r y f r e s h S o i l n u t r i e n t regime v. poor poor r i c h Dbh range estimates f o r each s i t e based on l a r g e f i x e d area p l o t s were a v a i l a b l e from C a r t e r and K l i n k a (1988). The dbh range estimate was d i v i d e d i n t o four equal dbh c a t e g o r i e s . At the Duncan and Haney s i t e s one t r e e f o r each 28 dbh group was s e l e c t e d , while at the Courtenay s i t e two t r e e s f o r each dbh group were s e l e c t e d . F i n d i n g sample t r e e s t h a t f u l f i l l e d c r i t e r i a three caused some d i f f i c u l t y . W i t h i n each dbh range, the t r e e s with the most unobstructed view of the crown and meeting c r i t e r i a two were s e l e c t e d as sample t r e e s . In many i n s t a n c e s o n l y one or two t r e e s w i t h i n the s i t e type were s u i t a b l e and t h e r e f o r e there was no o p p o r t u n i t y to make a random s e l e c t i o n and a b i a s was int r o d u c e d . The dbh range estimate of each s i t e and the dbh and height of each sample t r e e i s shown i n Table 3. Table 3. Sample t r e e d e s c r i p t i o n . S i t e Tree No. Dbh range estimate (cm) Duncan 10.7 - 20.7 1 2 3 4 Courtenay 13.8 - 24.7 1 2 3 4 5 6 7 8 Haney 15.0 - 24.0 1 2 3 4 Dbh Height Age SI (cm) (m) (stump (50 height) years) 16 10.7 8.54 47 15.1 11. 59 41 16.8 10.97 43 19 .9 14.35 43 13.8 13.32 47 14.9 16 . 33 47 18.1 15.86 46 17.5 18.56 48 20.2 17 .87 48 21. 3 19.59 46 24.0 21.09 44 23.0 20.69 46 16.9 19.80 22 18.5 17.89 21 21.5 19.18 21 23.2 20.91 21 29 3.4. PHOTOGRAPHY Before f e l l i n g the sample t r e e s each t r e e was photographed with a Canon AE-1 Program camera using Kodak black and white t e c h n i c a l pan f i l m (ESTAR-AH Base), and a AT-X 28-85 mm f/3.5-4.5 Tokina zoom lens with a B&W green f i l t e r . The view of the t r e e which o f f e r e d the fewest o b s t r u c t i o n s to a c l e a r view of the crown was chosen as the d i r e c t i o n of the photograph. Given the best d i r e c t i o n f o r viewing the f u l l crown, photographs were taken at 28, 50, and 85 mm f o c a l l e n g t h s , 12 meters d i s t a n c e from the t r e e at a camera angle of 57.5° from z e n i t h . I f at these s e t t i n g s the exposure d i d not i n c l u d e the e n t i r e l i v e crown more exposures were made at 14 meters d i s t a n c e from the t r e e at 57.5° from z e n i t h or other camera angles which provided f u l l crown exposures. P o s i t i v e s of the exposures to be analyzed were s e l e c t e d by the f o l l o w i n g p r i o r i z e d c r i t e r i a : 1) a c l e a r view of the e n t i r e l i v e crown without o b s t r u c t i o n of adjacent t r e e s i s presented i n the p o s i t i v e ; 2) camera angle equal to 57.5° from z e n i t h ; and 3) camera d i s t a n c e equal to 12 m. In cases where these c r i t e r i a c o u l d not be met, exposures t h a t came c l o s e s t to f u l f i l l i n g the c r i t e r i a were chosen. The f o r e s t canopy was so c l o s e to c l o s u r e at the Haney s i t e t h a t i t was d i f f i c u l t to meet c r i t e r i a 1, making none of the Haney photographs u s e f u l f o r f u r t h e r a n a l y s i s . 3 0 S e l e c t e d p o s i t i v e s were scanned with a LOGITECH SCANMAN PLUS hand-held scanner at a scanning r e s o l u t i o n of 200 dots per i n c h . The scanner has a l i n e a r t switch which was set at high c o n t r a s t . At high c o n t r a s t the image i s r e c e i v e d i n such a way that a l l the dark areas appear black and a l l the l i g h t areas appear white. The image f i l e was imported using LOGITECH PaintShow Plus v e r s i o n 2.2 program which allows you to e d i t , save, and p r i n t the image. The images were e d i t e d v i n order to c r e a t e two new images, one of the whole crown and one of the unobstructed p o r t i o n of the crown. In the whole crown image a l l p e r i p h e r a l t r e e s were erased l e a v i n g only the crown of i n t e r e s t i n the image. In the unobstructed crown image a l l p e r i p h e r a l t r e e s and any p o r t i o n of the crown of i n t e r e s t which was obstruc t e d by adjacent t r e e s were erased ( F i g u r e 6 ) . WHOLE UNOBSTRUCTED F i g . 6. Example of whole crown image and unobstructed crown image. 31 These two images were p r i n t e d and, using a dot g r i d , the crown p o r t i o n was determined, t h a t i s , the p o r t i o n of the whole crown remaining i n the unobstructed crown image. The unobstructed crown image was a l s o p r i n t e d onto t r a n s p a r e n c i e s and the area of unobstructed crown image determined u s i n g a L i C o r Model LI-3000 s u r f a c e area meter. The t r a n s p a r e n c i e s were run through the meter 10 times and the mean p a r t i a l s i l h o u e t t e area was c a l c u l a t e d f o r each image. The mean p a r t i a l s i l h o u e t t e area was d i v i d e d by the crown p o r t i o n to gi v e an estimate of the mean s i l h o u e t t e area of the e n t i r e crown. Scattergrams of TLA versus s i l h o u e t t e area were then v i s u a l l y examined to determine the s u i t a b i l i t y of r e g r e s s i o n a n a l y s i s . 3.5. FOLIAR SAMPLES 3.5.1. D e s t r u c t i v e Sampling A f t e r a t r e e was photographed i n the f i e l d the dbh was measured, b r e a s t height marked, and the t r e e c a r e f u l l y f e l l e d . A l l sample t r e e s were f e l l e d between J u l y 10 and August 11, 1988. F e l l i n g was c a r r i e d out at t h i s time because i t has been shown t h a t expansion of c u r r e n t needles normally terminates w i t h i n the f i r s t h a l f of J u l y ( B o r g h e t t i et al. 1986). I f branches were broken o f f , t h e i r o r i g i n was determined. Length of stem, le n g t h of l i v e crown, stump h e i g h t , and age at stump h e i g h t were measured and recorded. The l e n g t h of l i v e crown was d i v i d e d i n t o f i f t h s and marked. Two and a h a l f centimeter d i s c s were cut at bh, b l c , and at 32 each of the one f i f t h crown marks ( s i x d i s c s / t r e e ) . Beginning at the top of the crown, each branch was cut o f f and i t s l e n g t h (cm), diameter j u s t beyond the butt s w e l l (mm), and f r e s h weight (g) were measured and recorded. Nodal branches were i n c l u d e d with the whorl immediately below. A r e p r e s e n t a t i v e branch from the lowest whorl i n each crown l a y e r was s u b j e c t i v e l y chosen, l a b e l l e d , and brought to the l a b along with the stem d i s c s f o r f u r t h e r analys i s . Branches were s t o r e d i n a dark c o o l room and processed i n two to four days. Tree l e a f area estimates may be s l i g h t l y low as a r e s u l t of needle shrinkage d u r i n g t h i s time. The twigs from the r e p r e s e n t a t i v e branches were c l i p p e d i n t o age c l a s s e s and each age c l a s s sample weighed to the nearest 0.01 g. Only 8 age c l a s s e s were used and any needles o l d e r than 8 years were i n c l u d e d i n the 8 age c l a s s sample (needle r e t e n t i o n reached a maximum of 12 y e a r s ) . I n i t i a l l y approximate 25 g subsamples of twigs were randomly s e l e c t e d from the sample and weighed to the nearest 0.01 g, however, to improve e f f i c i e n c y , t h i s was adjus t e d to approximate 10 g subsamples f o r the l a s t nine t r e e s . T h i s change was made because the p r o c e s s i n g time f o r 25 g subsamples was too lengthy. The needles were then s t r i p p e d o f f the twigs of the subsamples, put i n t o s m a l l paper bags, and d r i e d at 105°C f o r 8 hours. F o l l o w i n g d r y i n g , the needles were weighed and recorded to the nearest 0.01 g. 33 Before d r y i n g the s t r i p p e d needles, 15 samples of ten needles each were randomly s e l e c t e d from each age c l a s s subsample. Sample s i z e of 15 was chosen on the b a s i s of a p r e l i m i n a r y study of SLA v a r i a b i l i t y on a branch from a D o u g l a s - f i r t r e e on the U n i v e r s i t y of B r i t i s h Columbia campus. For the sample branch, standard e r r o r of the mean of SLA of ten needle samples s t a b i l i z e d a t n=15. The one-s i d e d l e a f area of the ten needle samples was measured u s i n g a L i C o r Model LI-3000 s u r f a c e area meter. The needle samples were d r i e d at 105°C f o r 8 hours, weighed and recorded to the nearest 0.01 g. The 15 samples of ten needles were used to determine 15 s p e c i f i c l e a f areas f o r each age c l a s s f o r the r e p r e s e n t a t i v e branch. The 15 SLA's were averaged to gi v e an estimated SLA f o r each age c l a s s f o r the r e p r e s e n t a t i v e branch. T h i r t y repeated measures of the same ten needle sample had a c o e f f i c i e n t of v a r i a t i o n equal to 6.4%. The f o l l o w i n g example of the l e a f area per branch d e t e r m i n a t i o n , using age c l a s s 1 needles from a branch on t r e e #1 i n the Haney s i t e , o u t l i n e s the c a l c u l a t i o n s i n v o l v e d : T o t a l f r e s h weight of age c l a s s 1 twigs and needles (TFW) = 85.88 g. Fresh weight of twig subsample (FWSS) = 25.30 g. Dry weight of subsample needles (DW) = 9.71 g. S p e c i f i c l e a f area f o r age c l a s s 1 needles (SLA) = 56.255 cm 2/g or one-sided l e a f area/dry weight. 34 NDW r a t i o = DW/FWSS = 9.71g/25.30g = 0.384 Estimate of needle dry weight f o r the e n t i r e sample: NDW * TFW = 0.384 * 85.88g = 32.978g Estimate of the p r o j e c t e d l e a f area of age c l a s s 1 needles of the branch: 32.960g * SLA = 32.978g * 56.25cm 2/g = 1855.01cm 2 A p p l y i n g t h i s procedure to each age c l a s s and adding up the p r o j e c t e d l e a f areas f o r the branch g i v e s the estimated t o t a l branch l e a f area. In order to determine p r o j e c t e d l e a f areas f o r branches which d i d not have l e a f area measurements, a l i n e a r r e g r e s s i o n model was developed by p o o l i n g the branch l e a f area estimates from a l l t r e e s and s i t e s and u s i n g branch l e n g t h , f r e s h weight, and diameter at the base of the stem as independent v a r i a b l e s . Adding up the branch l e a f area estimates f o r each t r e e gave an estimate of the p r o j e c t e d l e a f area f o r each t r e e . 3.5.2. Sample S i z e A n a l y s i s The sample branch data provided the o p p o r t u n i t y to c a r r y out optimum sample s i z e a n a l y s i s f o r SLA. The number 35 of samples (n) necessary to estimate SLA with a confidence i n t e r v a l of 0.05 and two a l l o w a b l e e r r o r s (5 and 10%) was determined through the use of the f o l l o w i n g equation: (7) n > (sd/d) 2t« 2 df = n - 1 where sd i s the standard d e v i a t i o n , d i s the h a l f - w i d t h of the c o n f i d e n c e i n t e r v a l r e q u i r e d f o r the mean, and t« i s the Student's t value with the a p p r o p r i a t e degrees of freedom. Equation (7) was i t e r a t i v e l y s o l v e d to c o r r e c t f o r r a p i d changes i n t v a l u e s o c c u r r i n g when the c a l c u l a t e d sample s i z e was s m a l l (Cochran and Cox 1966). A n a l y s i s of v a r i a n c e and Tukey's HSD m u l t i p l e comparison method were c a r r i e d out on the data to d e t e c t 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 SLA and mean NDW r a t i o s between i n s t a l l a t i o n , crown p o s i t i o n , and needle age c l a s s e s . SYSTAT computer software was used f o r a l l s t a t i s t i c a l analyses (Wilkinson 1988). 3.6. STEM SAMPLES Six measurements, to the nearest 0.01 cm, were taken along each of four e q u i d i s t a n t r a d i i on each stem d i s c (24 measurements/disc). The q u a d r a t i c mean of the measurements along the four r a d i i was used to c a l c u l a t e the c r o s s -s e c t i o n a l area of heartwood (AHW), area of sapwood (ASW), area of l i v e bark (ALB), area of dead bark (ADB), area of heartwood and sapwood (AHWSW), area of heartwood, sapwood, and l i v e bark (AHWSWLB), area of sapwood and l i v e bark 36 (ASWLB), t o t a l d i s c b a s a l area (ATOT), area of most rec e n t r i n g s equal i n number to the number of whorls on the stem i n the l i v e crown (ALC), and ALC plus ALB (ALCLB). At b l c , ALC and ALCLB equal AHWSW and AHWSWLB, r e s p e c t i v e l y . Mean annual r i n g width i n the sapwood (MARW) and mean annual r i n g area i n the sapwood (MARA) were a l s o determined. Sapwood was d i s t i n g u i s h e d by soaking the d i s c s i n water f o r a sh o r t p e r i o d before measuring. I f moistening the d i s c was not s u f f i c i e n t , h o l d i n g the d i s c up to the sun e a s i l y d i s t i n g u i s h e d the sapwood. 3.7. REGRESSION ANALYSIS Scattergrams were produced f o r the bh and b l c stem measurements a g a i n s t TLA. Regression a n a l y s i s was c a r r i e d out f o r those stem measurements which were l i n e a r l y r e l a t e d to TLA. Re s i d u a l s were examined f o r each l i n e a r r e g r e s s i o n . In cases where stem measurements were not l i n e a r l y r e l a t e d 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 out on the dependent and/or independent v a r i a b l e i n order to make the 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 r e g r e s s i o n a n a l y s i s and examination of r e s i d u a l s . F u r t h e r a n a l y s i s was c a r r i e d out to determine i f the r e l a t i o n s h i p s between stem parameters and TLA v a r i e d between the three s i t e s . T h i s was done us i n g an a n a l y s i s of co v a r i a n c e technique d e s c r i b e d by Zar (1984) which t e s t s the homogeneity of r e g r e s s i o n c o e f f i c i e n t s f o r more than two r e g r e s s i o n l i n e s . 37 Non-linear r e g r e s s i o n a n a l y s i s u sing the Quasi-Newton m i n i m i z a t i o n method was c a r r i e d out with TLA as the dependent v a r i a b l e and ASW and D as the independent v a r i a b l e s . Scattergrams and r e g r e s s i o n a n a l y s i s were used to examine the r e l a t i o n s h i p between the TLA:ASW r a t i o and MARW and between stem measures at bh and the b l c . 38 4. SAMPLING ANALYSIS 4.1 RESULTS 4.1.1. S p e c i f i c Leaf Area O v e r a l l mean SLA was 42.8 cm 2/g with a 95% conf i d e n c e i n t e r v a l of + 0.7 cm 2/g (SE = 0.375, n = 556, range = 25.4 -99.4). The number of r e p l i c a t i o n s i n each s i t e (4 or 8), crown p o s i t i o n ( 5), and needle age c l a s s c a t e g o r y (8) d i d not 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 as there were more f a c t o r s than r e p l i c a t i o n s i n some m a t r i c e s . T h e r e f o r e , 2-way a n a l y s i s of v a r i a n c e was c a r r i e d out on the e f f e c t of s i t e and needle age c l a s s on mean SLA pooled by crown p o s i t i o n , the e f f e c t of s i t e and crown p o s i t i o n on mean SLA pooled by needle age c l a s s , and the e f f e c t of crown p o s i t i o n and needle age c l a s s on mean SLA pooled by s i t e . For each a n a l y s i s the two f a c t o r s had a s i g n i f i c a n t e f f e c t on mean SLA. There was a l s o a s i g n i f i c a n t i n t e r a c t i o n of crown p o s i t i o n and s i t e on mean SLA pooled by needle age c l a s s . In each s i t e mean SLA tended to decrease with i n c r e a s i n g needle age and he i g h t i n crown. Tukey's m u l t i p l e comparison t e s t was used to i d e n t i f y d i f f e r e n c e s i n mean SLA between needle age c l a s s e s and crown p o s i t i o n s f o r each s i t e . Tables 4 and 5 g i v e the r e s u l t s of a m u l t i p l e comparison on the data pooled by s i t e . A s i m i l a r a n a l y s i s of data f o r each s i t e showed the same trends with a few refinements r e g a r d i n g g e n e r a l i z a t i o n s t h a t can be made from the pooled d a t a . 39 Table 4. S i g n i f i c a n t d i f f e r e n c e s 1 in mean s p e c i f i c l e a f area (cn'/g) by needle age ( a l l s i t e s ) . Crown p o s i t i o n 1 2 3 Needle < 4 ige 5 6 7 8+ top 43.2a 40.lab 36.1abc 34.9bc 34.2c 32.2c 34.7* -2 48.3a 40.8b 39.8bc 37.7bcd 36.0cde 34.8de 35.4de 32.8e 3 51.2a 44.Sab 43.0DC 40.7bcd 38.9cde 37.6de 37.Ode 35.5e 4 57.1a 48.6b 45.1bc 44.3bc . 41.led 39.9cd 37.8d 37.7d bottom 64.8a 53.5b 50.2bc 47.0bcd 44.3bcd 42.5cd 39.3d 38.3d 1. Means separated i n columns and not sh a r i n g 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 m u l t i p l e comparison t e s t . 2. Crown p o s i t i o n 1, needle age 7 has only one sanple. Table 5. S i g n i f i c a n t d i f f e r e n c e s 1 i n mean s p e c i f i c l e a f area (cm 2/g) by crown p o s i t i o n ( a l l s i t e s ) . Crown p o s i t i o n 1 2 3 Needle age 4 5 6 7 8+ top 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 bottom 64.8d 53.5c 50.2c 47.Od 44.3d 42.5c 39.3a 38.3a 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, osin g the Tukey BSD m u l t i p l e comparison t e s t . 2. Crown p o s i t i o n 1, needle age 7 has only one sample. In a l l three s i t e s the mean SLA i n each crown p o s i t i o n d i d not vary s i g n i f i c a n t l y between needle age c l a s s e s 6-8 ( i n Duncan and Haney the mean d i d not vary between needle 40 age c l a s s e s 4-8) and i n age c l a s s e s 7 and 8 the mean SLA d i d not vary s i g n i f i c a n t l y between crown p o s i t i o n s . T h i s suggests that i t was unnecessary to d i f f e r e n t i a t e between age c l a s s e s 6-8 i n the sampling procedure and ra t h e r than 8+ being the o l d e s t needle age c l a s s , 6+ would have been s u f f i c i e n t . The comparison of mean SLA between crown p o s i t i o n s showed no common trends between s i t e s i n d i c a t i n g t h a t l e s s than 5 , p o s i t i o n s would have obscured s i g n i f i c a n t d i f f e r e n c e s . F i g u r e s 7, 8, and 9 i l l u s t r a t e the number of ten needle samples needed to estimate mean SLA per needle age c l a s s per branch 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. 2 0 i , , , , . 15 -Q . C D H Site F i g . 7. Number of 10-needle samples needed to p r e d i c t s p e c i f i c l e a f area with 95% conf i d e n c e and 5% allowable e r r o r (empty bars) or 10% a l l o w a b l e e r r o r ( f i l l e d bars) by s i t e . 1 2 3 4 5 Crown Position F i g . 8. Number of 10-needle samples needed to p r e d i c t s p e c i f i c l e a f area with 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 bars) or 10% a l l o w a b l e e r r o r ( f i l l e d bars) by crown p o s i t i o n . 15 -D. Foliage Age F i g . 9. Number of 10-needle samples needed to p r e d i c t s p e c i f i c l e a f area with 95% co n f i d e n c e and 5% all o w a b l e e r r o r (empty bars) or 10% a l l o w a b l e e r r o r ( f i l l e d bars) by f o l i a g e age. 42 Six ten needle samples were r e q u i r e d to estimate the mean SLA per needle age c l a s s per branch with 95% confidence and a 10% a l l o w a b l e e r r o r and 19 or 20 ten needle samples to estimate the mean with 95% confidence and a 5% a l l o w a b l e e r r o r . T h i s suggests t h a t i n t h i s study mean SLA values for each needle age c l a s s and crown p o s i t i o n had an e r r o r of somewhere between 5 and 10% as 15 ten needle sample were used. F i g u r e 8 i n d i c a t e s t h a t SLA was most v a r i a b l e i n crown p o s i t i o n 5 which l i k e l y r e f l e c t s t r e e t o t r e e v a r i a b i l i t y i n co m p e t i t i o n f o r l i g h t i n the lower crowns. If the a l l o w a b l e e r r o r was 10%, mean n v a r i e d l i t t l e with s i t e , crown p o s i t i o n or f o l i a g e age. S e t t i n g the a l l o w a b l e e r r o r at 5% r e s u l t e d i n s i t e and crown p o s i t i o n having some impact on mean n, the d i f f e r e n c e s i n mean n w i t h i n the v a r i a b l e c a t e g o r i e s was not s i g n i f i c a n t . 4.1.2. NEEDLE DRY WEIGHT RATIO O v e r a l l mean NDW r a t i o was 0.421 with a 95% confidence i n t e r v a l of + 0.008 (SE = 0.004, n = 557, range = 0.023 -0.773). The NDW r a t i o was examined f o r v a r i a t i o n between s i t e , crown p o s i t i o n , and needle age c l a s s ( F i g u r e s 10, 11, and 12 (see Appendix I f o r e x p l a n a t i o n of symbols)). With one e x c e p t i o n , the mean NDW r a t i o f o r each needle age c l a s s d i d not vary s i g n i f i c a n t l y between crown p o s i t i o n s a c r o s s the t r e e s i t e s . In the Duncan s i t e the mean NDW r a t i o f o r age c l a s s 4 needles i n crown p o s i t i o n 1 was 4 3 CO cr CD Q a> "D CD CD 0.8 0.6 0.4 0.2 0.0 D C Site F i g . 10. V a r i a b i l i t y i n needle dry weight r a t i o by s i t e 0.8 CD 0 6 2> Q) >-6 O 0.4 -0.2 * o o 0.0 o i F i g . 11. pos i t i o n . Crown Position V a r i a b i l i t y i n needle dry weight r a t i o by crown 44 CO o c >-Q 0 CD 0.8 0.6 0.4 0 2 0.0 Foliage Age F i g . 12. V a r i a b i l i t y i n needle dry weight r a t i o by f o l i a g e age. s i g n i f i c a n t l y d i f f e r e n t than crown p o s i t i o n s 2-5. This e x c e p t i o n was ignored i n the a n a l y s i s with a l l NDW r a t i o data pooled and s o r t e d by age c l a s s and s i t e (Table 6). Table 6. Significant differences in Bean HOH ratio between needle age classes for each s i t e . Site Needle age class 1 2 3 4 5 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 in rows and not sharing a common letter are s i g n i f i c a n t l y different at p < 0.05, using the Tukey HSD multiple comparison test. 45 Mean NDW r a t i o s at the Duncan and Courtenay s i t e s were not s i g n i f i c a n t l y d i f f e r e n t except i n age c l a s s 7 and d i f f e r e d s i g n i f i c a n t l y from Haney i n a l l age c l a s s e s (Table 6). The ranki n g of mean NDW r a t i o by age c l a s s f o r each s i t e i s shown i n Table 7. Table 7. Ranking 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 each s i t e . S i t e Needle age c l a s s e s ranked by NDW r a t i o Small Large 8 1 6 7 4 2 5 3 7 8 6 1 2 3 5 4 8 7 6 5 1 3 2 4 Note: needle age c l a s s e s u n d e r l i n e d by the same l i n e are not 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, u s i n g the Tukey HSD m u l t i p l e comparison t e s t . 4.2. DISCUSSION 4.2.1. S p e c i f i c Leaf Area Mean SLA (42.8 cm 2/g) was lower than most e a r l i e r r e p o r t e d values f o r D o u g l a s - f i r ; B o r g h e t t i et al. (1986) r e p o r t 65.1, Del Rio and Berg (1979), 79.0, Gower et al. (1987), 44.7, and Tan et al. (1978; see S p i t t l e h o u s e (1981)), 47 and 54. P r i c e (1987) r e p o r t s a range of 40 to 60 cm 2/g f o r unthinned D o u g l a s - f i r near Nanaimo. The low mean SLA i n t h i s study may be due i n pa r t to needle shrinkage d u r i n g the sampling p r o c e s s . I t may a l s o be a r e s u l t of seasonal v a r i a t i o n i n SLA. Smith et al. (1981) Duncan Courtenay Haney 46 found t h a t seasonal changes i n SLA i n D o u g l a s - f i r were l e s s pronounced i n a more humid Coast Range s i t e than i n a Cascade Mountains s i t e i n Oregon. At the Cascade Mountain s i t e , where the SLA was found to be g e n e r a l l y higher than on the Coast, the SLA was h i g h e s t d u r i n g November to March. Based on e l e v a t i o n and mean annual p r e c i p i t a t i o n of the two s i t e s , i t appears t h a t B o r g h e t t i ' s sample t r e e s were taken from a s i t e more s i m i l a r to the Cascade Mountain s i t e of Smith et al. (1981) than the Coast Range s i t e . F u r t h e r to t h a t , B o r g h e t t i et al. (1986) sampled d u r i n g November, the time of h i g h e s t SLA. Del Rio and Berg (1979) sampled i n September and Gower et al. (1987) i n November and February. The SLA data of B o r g h e t t i et al. (1986), P r i c e (1987), and Tan et al. (1978; see S p i t t l e h o u s e (1981)) show s i m i l a r trends as found i n t h i s study with SLA d e c r e a s i n g with i n c r e a s i n g age and from bottom to top of the crown. The f i n d i n g of B o r g h e t t i et al. (1986) t h a t needle age c l a s s d i d not e f f e c t mean SLA i n the top t h i r d crown p o s i t i o n was not supported i n t h i s study. In t h i s upper crown p o s i t i o n i t i s suggested t h a t needle age c l a s s e s experience near f u l l l i g h t c o n d i t i o n s r e s u l t i n g i n l e s s d i f f e r e n t i a t i o n between sun and shade leaves than found i n lower l a y e r s ( B o r g h e t t i et al. 1986). C o n s i d e r i n g t h a t the crowns i n t h i s study were d i v i d e d i n t o f i v e s e c t i o n s r a t h e r than t h r e e , the needle age c l a s s e s i n the top l a y e r should experience equal l i g h t c o n d i t i o n s even more so than the top l a y e r i n the B o r g h e t t i et al. (1986) study. Yet, 47 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 SLA between age c l a s s e s were found i n the top l a y e r , s u g g e s t i n g t h a t something more than sun and shade l e a f d i f f e r e n t i a t i o n accounts f o r v a r i a t i o n i n SLA across needle age c l a s s e s , p o s s i b l y r e l a t e d to the e f f e c t s of aging on needle p h y s i o l o g y . As B o r g h e t t i et al. (1986) note, v e r t i c a l changes i n SLA may r e s u l t from sun and shade l e a f d i f f e r e n t i a t i o n , with a s m a l l e r p o r t i o n of shade leaves i n the lower crown p o r t i o n s as a r e s u l t of l e a f shedding. 4.2.2. Needle Dry Weight R a t i o Reports of mean NDW r a t i o values f o r D o u g l a s - f i r were not a v a i l a b l e . Two p a t t e r n s emerge out of the NDW r a t i o data i n t h i s study: 1) on these s i t e s twigs began dropping needles at approximately year 6; and 2) w i t h i n each s i t e mean NDW r a t i o s d i d not vary s i g n i f i c a n t l y between age c l a s s e s 6-8. Th i s suggests t h a t i t was unnecessary to d i f f e r e n t i a t e between needle age c l a s s e s 6 through 8 i n the sampling procedure to determine mean NDW by age c l a s s . 48 5. ALLOMETRIC RELATIONSHIPS 5.1. RESULTS 5.1.1. Tree Leaf Area The f o l l o w i n g model was developed to p r e d i c t BLA (cm 2): (8) In(BLA) = 3.976 + 1.366(In(fw) ) - 0.673(In(d i a ) ) - 0.428(ln( l e n g t h ) ) - 0.092( i n s t l ) + 0.047( inst2) - 0.05(crpol) + 0.115(crpo2) + 0.164(crpo3) + 0.131 {crpo4) Adjusted R 2 = 0.975, n = 87, F r a t i o = 380, S.E.E. = 0.162. where fw i s f r e s h weight of branch ( g ) , dia i s diameter of the branch j u s t beyond the b u t t s w e l l (mm), length i s branch l e n g t h (cm), and instl, inst2, crpol, crpo2, crpo3, and crpo4 are dummy v a r i a b l e s f o r i n s t a l l a t i o n and crown p o s i t i o n . Continuous v a r i a b l e s were transformed to n a t u r a l l o g values i n order to improve l i n e a r i t y between the dependent and independent v a r i a b l e s . A l l p o s s i b l e subset equations with the three continuous transformed v a r i a b l e s were f i t to the data, and the model with the lowest r e s i d u a l mean square value was s e l e c t e d as the most promising model. Each v a r i a b l e improved the ad j u s t e d R 2 and was s i g n i f i c a n t at p = 0.05. C o l l i n e a r i t y between diameter and length v a r i a b l e s was ignored on the grounds t h a t the model would not be used to p r e d i c t branch l e a f area f a r beyond the reach of the data used to develop the model. A s c a t t e r g r a m of the 49 r e s i d u a l s of t h i s model was analyzed f o r o u t l i e r s and each o u t l i e r was i n v e s t i g a t e d f o r p o s s i b l e r e c o r d i n g e r r o r . When the model was run with the o u t l i e r s removed from the data s e t , the model c o e f f i c i e n t s d i d not change s i g n i f i c a n t l y (p = 0.05) and i t was concluded the o u t l i e r s were not a f f e c t i n g the model i n any s i g n i f i c a n t manner. The main cause of the o u t l i e r s appeared to be the e x i s t e n c e of lower crown branches which had l a r g e b a s a l diameters and lengths but, as a r e s u l t of needle drop, low f r e s h weight. The sc a t t e r g r a m of the r e s i d u a l s a g a i n s t the estimates and each of the transformed v a r i a b l e s showed no b i a s . However, model r e s i d u a l s p l o t t e d a g a i n s t crown p o s i t i o n and i n s t a l l a t i o n showed d e f i n i t e trends s u p p o r t i n g the i n c l u s i o n of dummy v a r i a b l e s i n the model f o r each of these f a c t o r s . F o l l o w i n g the i n c l u s i o n of dummy v a r i a b l e s the model was run again without o u t l i e r s and as before i t was decided to leave the o u t l i e r s i n the data s e t se e i n g they had no s i g n i f i c a n t e f f e c t (p = 0.05) on the model c o e f f i c i e n t s . The BLA model was used to p r e d i c t the l e a f area of a l l branches on each t r e e . The branch l e a f areas were summed to giv e TLA f o r each t r e e ( F i g u r e 13; see Appendix II f o r c a l c u l a t i o n of LAI f o r each s i t e ) . B r i x (1981) r e p o r t e d TLA values of 25.19 to 92.92 m2 f o r 25 y e a r - o l d D o u g l a s - f i r t r e e s under t h i n n i n g and f e r t i l i z e r regimes on Vancouver I s l a n d . Tan et al. (1978) r e p o r t a range of 16 to 55 m2 f o r t r e e s i n a 22 y e a r - o l d thinned D o u g l a s - f i r stand near Courtenay B.C. (840 stems/ha). Three years l a t e r , S p i t t l e h o u s e (1981) r e p o r t e d a range of 27 to 92 m2 f o r the same stand. The TLA values f o r the 16 sample t r e e s i n t h i s study ranged from 15.72 to 96.05 m2. F i g . 13. One-sided t r e e l e a f area (m 2) f o r sample t r e e s . Sample t r e e s denoted as Dl - D4 are from Duncan, CI - C8' are from Courtenay, and HI - H4 are from Haney. 5.1.2. Breast Height Stem Measures and Tree Leaf Area C r o s s - s e c t i o n a l sapwood area at b r e a s t h e i g h t , ASWLBbh, and ATOTbh were not l i n e a r l y r e l a t e d to TLA i n t h i s data s e t . 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 the dependent v a r i a b l e , TLA, was necessary to develop l i n e a r r e g r e s s i o n models with ASWbh, ATOTbh, and ASWLBbh (Table 8). Table 8. Models f o i the r e g r e s s i o n of D o u g l a s - f i r one-sided l e a f area on s e l e c t e d stem measurements (n = 16). BREAST HEIGHT STEM MEASUREMENTS [11 TLA ( i i 2 ) ~- 10.015 + 0.012(AS»*ALB)bh (cm 4) Adjusted R 2 = 0.887 P = 119.3 S.E.E. = 7.41 ( a 2 ) 121 TLA ( a 2 ) = -0.383 + 0.266(ALCbh) ( c a 2 ) Adjusted R 2 = 0.910 P = 153.1 S.E.E. = 6.64 ( a 2 ) [31 TLA [ a 2 ) = -2.550 + 0.249(ALCLBbh) ( c a 2 ) Adjusted R 2 = 0.911 P = 155.2 S.E.E. = 6.60 ( a 2 ) [4] LnTLA ( a 2 ) = 2.364 t O.OlO(ASWbh) ( c a 2 ) 1 Adjusted R 2 = 0.894 P = 127.1 S.E.E. = 0.17 ( a 2 ) [51 LnTLA ( a 2 ) = 2.314 t 0.009(ASHLBbh) ( c a 2 ) 1 Adjusted R 2 = 0.897 P = 131.8 S.E.E. = 0.17 ( a 2 ) [61 LnTLA ( a 2 ) = 2.447 + 0.005(ATOTbh) ( c a 2 ) 1 Adjusted R 2 = 0.790 P = 57.4 S.E.E. = 0.24 (m 2) BASE OP LIVE CROWD STEM MEASUREMENTS 171 TLA ( a 2 ) = -7.458 t 0.515(ASBblc) ( c a 2 ) Adjusted R 2 = 0.908 P = 149.0 S.E.E. = 6.72 ( a 2 ) 18] TLA ( a 2 ) = -10.402 t 0.450(ASBLBblc) ( c a 2 ) Adjusted R 2 = 0.934 P = 215.0 S.E.E. = 5.67 ( a 2 ) [91 TLA (•») = 12.493 t 0.013(AS»*ALB)blc ( c a 4 ) Adjusted R 2 - 0.967 P = 440.0 S.E.E. = 4.03 ( a 2 ) 1101 TLA ( a 2 ) = -1.621 t 0.330(ALCblc) ( c a 2 ) Adjusted R 2 = 0.920 P = 174.0 S.E.E. = 6.26 ( a 2 ) [111 TLA ( a 2 ) - -4.171 t 0.302(ALCLBblc) ( c a 2 ) Adjusted R 2 = 0.939 P = 230.5 S.E.E. = 5.49 ( a 2 ) 52 Table 8 cone. 1121 TLA Ul) = -4.078 » 0.296(ATOTblc) (en') 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 Table 8 the models with l o g transformed (base e) v a r i a b l e s were not c o r r e c t e d f o r b i a s introduced by the t r a n s f o r m a t i o n . I t i s s a f e to assume the e r r o r i n t r o d u c e d by the t r a n s f o r m a t i o n was l e s s than 10% (Sprugel 1983). When comparing the models u s i n g InTLA the a d j u s t e d R 2 v a l u e s i n d i c a t e d t h a t model [5] was the best p r e d i c t o r of InTLA, fo l l o w e d by model [41, and model [61. Models [2] and [31 a t t r a c t a t t e n t i o n because they were l i n e a r l y r e l a t e d to TLA and had the h i g h e s t adjusted R 2 values of a l l the bh measurements (adjusted R 2 = 0.910 and 0.911, r e s p e c t i v e l y ) . The ALC v a r i a b l e may be determined i n such a way as to i n c l u d e heartwood area when the number of whorls i n the l i v e crown i s g r e a t e r than the number of annual r i n g s i n the sapwood or to d e l i b e r a t e l y not i n c l u d e heartwood and r e s t r i c t ALC to be l e s s than or equal to but never g r e a t e r than ASW. In t h i s study i t was found there were onl y two bh samples i n which ALC was not g r e a t e r than ASW, and i n one of the exceptions the ALC e q u a l l e d ASW. I f ALC was r e s t r i c t e d to be l e s s than or equal to ASW, there was very l i t t l e d i f f e r e n c e between ALC and ASW as p r e d i c t i v e v a r i a b l e s . I t was decided to i n c l u d e heartwood area i n ALC 53 when the number of whorls i n the l i v e crown exceeded the number of annual r i n g s i n the sapwood. The product of ASWbh and ALBbh was l i n e a r l y r e l a t e d to TLA (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 one-sided t r e e l e a f area (m 2) and the product of c r o s s - s e c t i o n a l area of sapwood (ASW) and l i v e bark (ALB) at bh. 5.1.3. Base of L i v e Crown Stem Measurements and Tree Leaf Area A l l s e l e c t e d stem measurements at the b l c were l i n e a r l y r e l a t e d to TLA.. E x c l u d i n g the product v a r i a b l e (ASW*ALB)blc / the best f i t t i n g model ac c o r d i n g to the adjusted R 2 values was model [11] (adjusted R 2 =' 0.939), followed by model [8] (adjusted R 2 = 0.934), model [12] (adjusted R 2 = 0.926), model [10] (adjusted R2 = 0.920), and 54 model [7] (adjusted R 2 = 0.908). Model [ 9 ] was the best f i t t i n g model o v e r a l l ( F i g u r e 15). 0 I i i i i i i i 0 1000 2000 3000 4000 5000 6000 7000 ' (ASW • ALB)blc (cm2'cm2) Fig.15. R e l a t i o n s h i p between one-sided t r e e l e a f area (m 2) and the product of c r o s s - s e c t i o n a l area of sapwood (ASW) and l i v e bark (ALB) at b l c . 5.1.4. V a r i a t i o n Between S i t e s Each of the models i n Table 8 were examined by a n a l y s i s of c o v a r i a n c e f o r v a r i a b i l i t y i n the model c o e f f i c i e n t s between s i t e s . The y - i n t e r c e p t f o r models [ 4 ] , [5] and [6] v a r i e d s i g n i f i c a n t l y by s i t e (p = 0.05). As a f u r t h e r check of v a r i a t i o n between s i t e s the mean TLA:stem measurement r a t i o was examined for s i g n i f i c a n t d i f f e r e n c e s between s i t e s using ANOVA (Table 9 ) . Mean TLA:ASWbh r a t i o was 0.32 (+ 0.03 at p = 0.05) and mean TLA:ASWblc r a t i o was 0.43 (+ 0.03 at p = 0.05). Gower et al. (1987) r e p o r t the mean TLA:ASWbh r a t i o to be 0.34 and the mean TLA:ASWblc r a t i o to be 0.58 f o r 65 to 70 y e a r - o l d D o u g l a s - f i r t r e e s (n = 5) on the e a s t e r n s l o p e s of the Washington Cascades. The r a t i o s of TLA:stem measurement were not s i g n i f i c a n t l y d i f f e r e n t between s i t e s i n the case of ALCbh, ALCLBbh, (ASW*ALB)bh, ALBSWblc, and (ASW*ALB)blc (p < 0.05). Table 9. Mean r a t i o s of one-sided t r e e l e a f area (m 2) and s e l e c t e d stem measurements. SITE STEM HEASUREHERTS BREAST HEIGHT BASE OF LIVE CROHN ASS ASWLB ATOT ALC ALCLB ASH ASH ASWLB ATOT ALC ALCLB ASH *ALB *ALB (cm 2) (cm*) (cm 1) (cm 2) (cm 2) (cm*) (cm 2) (cm 2) (cm 2) (cm 2) (cm 2) (cm 4) Duncan (n-4) 0.30a 0.26a 0.17ab 0.26a 0.22a 0.020a 0.36a 0.31a 0.24a 0.28a 0.25a 0.026a Courtenay (n=8) 0.30a 0.26a 0.14a 0.27a 0.24a 0.016a 0.46b 0.36a 0.28b 0.34b 0.29b 0.023a Haney (n=4) 0.39b 0.34b 0.21b 0.28a 0.24a 0.017a 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 m u l t i p l e comparison t e s t . 5.1.4.1. Breast Height Versus Base of Live Crown Three of the TLA p r e d i c t i o n models using bh stem measures as independent v a r i a b l e s had c o e f f i c i e n t s which v a r i e d s i g n i f i c a n t l y by s i t e (p = 0.05). None of the c o e f f i c i e n t s of the TLA p r e d i c t i o n models u s i n g b l c stem measures v a r i e d s i g n i f i c a n t l y by s i t e or had adjus t e d R 2 v a l u e s l e s s than 0.90. The mean r a t i o s of TLA:stem measurements d i d not, i n g e n e r a l , become l e s s v a r i a b l e 56 between s i t e s by us i n g b l c measures r a t h e r than bh measures as independent v a r i a b l e s . The one ex c e p t i o n was TLA:ASWLBbh and TLA:ASWLBblc, with the l a t t e r not s i g n i f i c a n t l y d i f f e r e n t between s i t e s . 5.1.4.2. Cross-Sectional Area of Live Bark I n c l u d i n g a measure of l i v e bark improved the TLA p r e d i c t i o n models f o r both b l c and bh measurements. Adding ALBbh to ASWbh d i d not improve l i n e a r i t y with TLA but ASWLBbh had a higher a d j u s t e d R 2 than ASWbh when used to p r e d i c t InTLA (models [4] and [ 5 ] ) . M u l t i p l y i n g ASWbh by ALBbh r e s u l t e d i n l i n e a r i t y with TLA. At the b l c , adding ALB t o ASW i n c r e a s e d the ad j u s t e d R 2 and m u l t i p l y i n g ASW by ALB i n c r e a s e d the adjus t e d R 2 f u r t h e r , r e s u l t i n g i n the best o v e r a l l p r e d i c t i v e v a r i a b l e . The p r e d i c t i v e value of ALC was a l s o improved by i n c l u d i n g ALB (ALCLB), i n c r e a s i n g the adjust e d R 2 from 0.910 to 0.911 at bh and from 0.920 to 0.939 at b l c . At bh i n c l u d i n g ALB i n the ASWbh model d i d not remove v a r i a b i l i t y i n the model c o e f f i c i e n t s between s i t e s . However, model [ 1 ] , which used (ASW*ALB)bh as the independent v a r i a b l e , d i d not vary between s i t e s . C r o s s -s e c t i o n a l area of l i v e bark had the same i n f l u e n c e on the mean r a t i o of TLA:ASWbh. The mean r a t i o s of TLA:ASWbh and TLA:ASWLBbh v a r i e d between s i t e s while TLA:(ASW*ALB) d i d not. At the b l c the model c o e f f i c i e n t s d i d not vary-s i g n i f i c a n t l y by s i t e (p = 0.05). The mean r a t i o of TLAiASWblc v a r i e d s i g n i f i c a n t l y by s i t e while TLA:ASWLBblc and TLA:(ASW*ALB)blc d i d not (p = 0.05). 5.1.4.3. Mean Annual Ring Width At the b l c , m u l t i p l y i n g ASW by MARW r e s u l t e d i n a higher a d j u s t e d R 2 than when using ASW alone at the Haney s i t e but decreased the adjus t e d R 2 at the Duncan and Courtenay s i t e s (Table 10). Table 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 between TLA and (ASW * MARW). S i t e BH BLC ASW (ASW * MARW) ASW (ASW * MARW) Duncan 0.831 0.762 0.996 0.987 (n = 4) Courtenay 0.913 0.953 0.867 0.806 (n = 8) Haney 0.662 0.695 0.917 0.929 (n = 4)  At bh, the adjus t e d R 2 value was in c r e a s e d by m u l t i p l y i n g ASW by MARW i n the cases of Haney and Courtenay but the oppos i t e occurred i n the case of Duncan (Table 10). In ge n e r a l , these r e s u l t s do not support Espinosa B a n c a l a r i et aJ.'s (1987) s u g g e s t i o n , t h a t i f the c o r r e l a t i o n between the v a r i a b l e s MARW and ASW i s not s t r o n g then MARW should be of value along with ASW as a p r e d i c t i v e v a r i a b l e of TLA. Mean annual sapwoood r i n g width was more c l o s e l y c o r r e l a t e d with 58 ASW at bh than at b l c i n t h i s study (Table 11). And yet at bh, p r e d i c t i o n of TLA was improved by m u l t i p l y i n g ASW by Table 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 the r e l a t i o n s h i p between ASW and MARW at br e a s t height and base of l i v e crown. S i t e Breast height Base of l i v e crown Duncan (n = 4) Courtenay (n = 8) Haney (n = 4) 0.884 0.961 0.979 0.635 0.627 0 .823 MARW f o r two s i t e s while at b l c m u l t i p l y i n g ASW by MARW improved TLA p r e d i c t i o n f o r o n l y one s i t e . 0.5 CM E CJ \ C M E CD < < 0.4 0.3 0.2 1 1 1 1 1 H H c H D c C H D D c c C c c 1 D I 1 1 1 0.0 0.1 0.2 0.3 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 the r e l a t i o n s h i p between the t r e e l e a f area to sapwood area r a t i o (TLA:ASWbh) and mean annual r i n g width. 59 If the sample t r e e s were not s t r a t i f i e d by s i t e the adjus t e d R 2 f o r TLA and (ASW * MARW)bh was 0.705 compared to 0.845 for TLA and ASWbh. I n c l u d i n g MARW i n the TLA p r e d i c t i o n model (combined s i t e s ) d i d not improve the f i t because (MARW * ASW) had a v a r i a b l e e f f e c t between s i t e s - F u r t h e r to t h a t , the r e l a t i o n s h i p of MARW with the TLA:ASW r a t i o at bh and b l c v a r i e d by s i t e ( F i g u r e s 16 and 17). i 1 1 1 -c H c c c c H H C H ^ DD C C D D I I 1 I 0.1 0 2 0.3 0.4 0.5 0.6 MARWbic (cm) F i g . 17. V a r i a b i l i t y i n the r e l a t i o n s h i p between the t r e e l e a f area to sapwood area r a t i o (TLA:ASWblc) and mean annual r i n g width. Mean MARW v a r i e d s i g n i f i c a n t l y between Haney and the other s i t e s (F = 34.0 for bh measurements and F = 37.8 for b l c measurements) and the r e was l i t t l e v a r i a t i o n of MARW w i t h i n C M E u N C M E C O < < 0.5 0.4 the Duncan and Courtenay s i t e s . Mean annual sapwood r i n g area was more v a r i a b l e than MARW but only m a r g i n a l l y so. 5.1.5. Nonlinear Regression C r o s s - s e c t i o n a l sapwood area at bh was not l i n e a r l y r e l a t e d to TLA i n t h i s study. The r a t i o of TLA:ASWbh inc r e a s e d with ASWbh (Fi g u r e 18). 0.5 C M E o \ C M J O $ C O 3 0.4 0.3 0.2 0 100 200 300 ASWbh (cm2) F i g . 18. The r a t i o of t r e e l e a f area to sapwood area at brea s t height (TLA:ASWbh) i n c r e a s e d with sapwood area at brea s t h e i g h t (ASWbh). The f o l l o w i n g n o n l i n e a r model was f i t to the data u s i n g the Quasi-Newton m i n i m i z a t i o n method (F i g u r e 19): 61 (9) TLA = 0.064 * ASWbh 1• 3 3 1 2 = 0 .975, n = 16, 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 area and sapwood area at bre a s t height i s n o n l i n e a r . Long and Smith (1988, 1989) found s i m i l a r r e l a t i o n s between the TLA:ASWbh r a t i o and ASWbh for lodgepole pine and s u b a l p i n e f i r . Using the same independent v a r i a b l e s suggested by Long and Smith (1988), D, the d i s t a n c e between bh and the center of the l i v e crown, and ASWbh, the f o l l o w i n g n o n l i n e a r model was developed: (10) TLA = 0.063 * ASWbh1- 4 2 5 * D - o - x 9 S 1 2 = 0.976, n = 16, S.E.E. = 8.40. 62 Equation (10), with an 1 2 of 0.976, f i t the data m a r g i n a l l y b e t t e r than equation ( 9 ) . For comparison Table 12 g i v e s the c o e f f i c i e n t s f o r s i m i l a r models developed f o r lodgepole pine and s u b a l p i n e f i r . Table 12. C o e f f i c i e n t s f o r n o n l i n e a r models of the form TLA = a * ASWbh'3 * D=. Species Source s u b a l p i n e f i r 0 .280 1 .27 -0. 50 Long & Smith (1989) lodgepole pine (mature) 0 .028 1 .56 -0. 74 Dean & Long (1986) ( s a p l i n g ) 0 .021 1 . 47 -0. 14 Dean & Long (1986) 0 .064 1 . 43 -0. 73 Long & Smith (1988) Douglas-f i r 0 .063 1 .42 -0. 20 ( t h i s study) 5.1.6. P r e d i c t i n g Base of L i v e Crown Stem Measures Since TLA was found t o be more c l o s e l y c o r r e l a t e d to b l c stem measures than bh stem measures and bh stem measures are much e a s i e r to determine than b l c stem measures, i t was decided to examine whether bh stem measures c o u l d be used to p r e d i c t b l c stem measures. Four stem measures were examined: ASW, ASWLB, ASW*ALB, and ALC. 5.1.6.1. Cross-Sectional Area of Sapwood P l o t t i n g ASWblc versus ASWbh i n d i c a t e d t h a t the r e l a t i o n was p o s i t i v e l y c u r v i l i n e a r ( F igure 20). S e v e r a l t r a n s f o r m a t i o n s were c a r r i e d out on the dependent and independent v a r i a b l e s . The most s u c c e s s f u l t r a n s f o r m a t i o n ( l o g base e of the independent v a r i a b l e 200 150 c3 E o 100 BS CO < 50 0 0 100 200 300 ASWbh (cm2) F i g . 20. Sapwood area at bh (ASWbh) versus sapwood area at b l c (ASWblc). ASWblc) y i e l d e d the f o l l o w i n g equation: (11) LnASWblc = 3.431 + 0.008(ASWbh) adj u s t e d R 2 = 0.850, n = 16, F = 85.928. • P l o t t i n g the r e s i d u a l s by s i t e i n d i c a t e d the model underestimated the ASWblc i n Haney and Duncan si'tes and overestimated the ASWblc i n the Courtenay s i t e . 64 5 . 1 . 6 . 2 . Cross-Sectional Area of Sapwood and L i v e Bark As with ASW, p l o t t i n g ASWLBblc a g a i n s t ASWLBbh i n d i c a t e d t h a t the r e l a t i o n s h i p was s l i g h t l y c u r v i l i n e a r ( F i g u r e 21). 300 r C S J E _o SD CO CO < 200 100 0 0 100 200 300 ASWLBbh (cm2) F i g . 21. C r o s s - s e c t i o n a l area of sapwood plus l i v e bark at bh (ASWLBbh) versus c r o s s - s e c t i o n a l area of sapwood plus l i v e bark at b l c . A l o g t r a n s f o r m a t i o n (base e) of the dependent v a r i a b l e ASWLBblc was most s u c c e s s f u l y i e l d i n g the equation: (12) LnASWLBblc = 3.617 + 0.007(ASWLBbh) adjusted R= = 0.876, n = 16, F = 106.994. P l o t t i n g t h e r e s i d u a l s b y s i t e i n d i c a t e d t h e m o d e l u n d e r e s t i m a t e d t h e A S W b l c i n t h e H a n e y s i t e a n d o v e r e s t i m a t e d t h e A S W b l c i n t h e C o u r t e n a y s i t e . 5 . 1 . 6 . 3 . Cross-Sectional Area of Sapwood * Cross-Sectional Area of L i v e Bark T h e r e l a t i o n b e t w e e n ( A S W * A L B ) b l c a n d ( A S W * A L B ) b h w a s s l i g h t l y c u r v i l i n e a r ( F i g u r e 2 2 ) . 8000 r 6000 C M E C D 4000 C O < 2000 0 2000 4000 6000 8000 (ASW'ALB)bh (cm2) F i g . 2 2 . 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 s a p w o o d a n d l i v e b a r k a t b h ( ( A S W * A L B ) b h ) v e r s u s 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 s a p w o o d a n d l i v e b a r k a t b l c . A t t e m p t s t o i m p r o v e l i n e a r i t y u s i n g t r a n s f o r m a t i o n s w e r e u n s u c c e s s f u l . R e g r e s s i o n a n a l y s i s o n t h e n o n t r a n s f o r m e d d a t a p r o d u c e d t h e f o l l o w i n g m o d e l : 66 (13) (ASW*ALB)blc = -99.371 + 0.837(ASW*ALB)bh adjus t e d R 2 = 0.853, n = 16, F = 88.010. P l o t t i n g the r e s i d u a l s a g a i n s t the independent v a r i a b l e i n d i c a t e d v a r i a b i l i t y i n c r e a s e s with the independent v a r i a b l e i n the case of the Duncan and Courtenay s i t e s . A p l o t of the estimates a g a i n s t the dependent v a r i a b l e showed a wide s c a t t e r around the l e a s t squares l i n e a r r e g r e s s i o n 1 i n e . 5.1.6.4. Cross-Sectional Area of Most Recent Annual Sapwood Rings Equal in Number to the Number of Whorls in Live Crown The r e l a t i o n between ALCblc and ALCbh was l i n e a r ( F i g u r e 23): (14) ALCblc = 5.795 + 0.795(ALCbh) adjus t e d R 2 = 0.958, n = 16, F = 339.225 The s c a t t e r g r a m of the r e s i d u a l s a g a i n s t the estimates was unbiased and the graph of estimates a g a i n s t the a c t u a l s was a good f i t . However, the model overestimated ALCblc i n the Courtenay s i t e and underestimated ALCblc i n the Haney s i t e . 300 • • • 1 1 i i 0 100 200 300 400 ALCbh (cm2) F i g . 2 3 . ALCbh versus ALCblc. 5.2. DISCUSSION 5 . 2 . 1 . Base of L i v e Crown Versus Breast Height According to adjusted R 2 v a l u e s , stem measures taken at the b l c were b e t t e r p r e d i c t o r s of TLA than stem measures at bh. Waring et a l . ( 1 9 8 2 ) found the same f o r D o u g l a s - f i r . E s p i nosa Bancal-ari et a l . ( 1 9 8 7 ) found t h a t i t mattered i f the stand was r e l a t i v e l y f a s t or slow growing. In the f a s t growing stand of 22 y e a r - o l d D o u g l a s - f i r t r e e s diameter at the b l c was a b e t t e r p r e d i c t o r of TLA than at bh. Stem measures at the b l c considered i n t h i s study were a l l 200 CNJ £ o u O < 100 68 l i n e a r l y r e l a t e d to TLA and had adjus t e d R 2 values g r e a t e r than 0.90. At bh two models had adjus t e d R 2 values g r e a t e r than 0.90 and three of the models were n o n l i n e a r . No model c o e f f i c i e n t s based on b l c stem measures v a r i e d between s i t e s . These r e s u l t s support the comment by Geron and Ruark (1988) t h a t b l c stem measures are p h y s i o l o g i c a l l y l e s s a r b i t r a r y than bh stem measures. The v a r i a b i l i t y i n TLA:stem measure r a t i o s between s i t e s was not decreased using b l c r a t h e r than bh measures. 5.2.2. C r o s s - S e c t i o n a l Area of Sapwood Versus Basal Area C r o s s - s e c t i o n a l sapwood area was not c o n s i s t e n t l y a b e t t e r p r e d i c t o r of TLA than was b a s a l area (ATOT). At the b l c the adjus t e d R 2 value f o r the ASW model was lower than f o r the ATOT model (0.908 versus 0.926). The adjus t e d R 2 f o r the r e l a t i o n s h i p between ASWblc and ATOTblc was 0.969 with no s i g n i f i c a n t d i f f e r e n c e (p = 0.05) i n the r a t i o of ASW:ATOT by i n s t a l l a t i o n . That the adjus t e d R 2 value f o r ASWblc was lower than i t was f o r ATOTblc 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 the pipe model theory and suggests t h a t e i t h e r 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 p e r m e a b i l i t y between i n d i v i d u a l s needs to be i n c l u d e d i n the model or 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 the the o r y need to be ex p l o r e d . At bh the s i t u a t i o n was re v e r s e d with the ASW model having a higher R 2 value than the ATOT model (0.894 versus 0.790). Both models at bh v a r i e d s i g n i f i c a n t l y between i n s t a l l a t i o n s . The r e l a t i o n s h i p 69 between ASWbh and ATOTbh was not as s t r o n g as at b l c with an adjuste d R 2 of 0.882 and the r a t i o of 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 the Courtenay and Duncan i n s t a l l a t i o n s (p = 0.05). T h i s i s l i k e l y a r e s u l t of the c o n s i d e r a b l e v a r i a t i o n i n ADBbh. B r i x and M i t c h e l l (1983) r e p o r t s t r o n g l i n e a r r e l a t i o n s h i p s between ASWbh and ATOTbh(under bark) i n D o u g l a s - f i r . However, the u n i f o r m i t y i n stand 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 v a r i a t i o n i n the ASW:ATOT r a t i o between i n d i v i d u a l s , does not e x p l a i n why ATOTblc was a b e t t e r f i t with TLA than was ASWblc. For h i g h l y uniform stands, with l i t t l e v a r i a t i o n i n the ASW:ATOT r a t i o , the pipe model the o r y suggests t h a t ATOT and ASW should p r e d i c t TLA e q u a l l y w e l l . T h i s study suggests t h a t ATOT i n c l u d e s a measure of the stem which r e l a t e s to crown dimensions which i s not i n c l u d e d i n ASW. The r e s u l t s f o r ALC and ALCLB suggest what those measures might be and are d i s c u s s e d i n s e c t i o n 5.2.5. 5.2.3. I n f l u e n c e 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 study s e v e r a l of the bh models ( [ 4 ] , [ 5 ] , and [6]) v a r i e d s i g n i f i c a n t l y by s i t e . E spinosa B a n c a l a r i et al. (1987) found t h a t the r e g r e s s i o n s l o p e s u s i n g dbh, ASWbh, and (ASW * MARW)bh i n TLA p r e d i c t i o n models were higher f o r a f a s t growing stand than f o r in t e r m e d i a t e and slow growing stands of D o u g l a s - f i r . T h e i r study found the r e g r e s s i o n s l o p e s f o r ASWblc and d i a m e t e r ( b l c ) i n c r e a s e d 70 from f a s t to slow to int e r m e d i a t e growth stands. The authors do not i n d i c a t e i f the d i f f e r e n c e s i n r e g r e s s i o n s l o p e s between stands were s i g n i f i c a n t l y d i f f e r e n t . In t h i s study the r e g r e s s i o n s l o p e s 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 the s l o p e i n t e r c e p t s d i d (Table 13). Table 13. Comparison of sl o p e i n t e r c e p t s f o r InTLA p r e d i c t i o n models which v a r i e d s i g n i f i c a n t l y by s i t e . Independent v a r i a b l e S i t e a b ASWbh Duncan 2.204 0.011 Courtenay 2.362 0.009 Haney 3.029 0.007 ASWLBbh Duncan 2.194 0.010 Courtenay 2.296 0.008 Haney 2.995 0.006 ATOTbh Duncan 2.288 0.006 Courtenay 2.328 0.005 Haney 3 . 023 0.004 Note: The form of the l i n e a r X i s the independent v a r i a b l e model i s InTLA = a + b X, where In Table 13 the trend i n sl o p e i n t e r c e p t s suggests the r a t i o of InTLA to any of the independent v a r i a b l e s l i s t e d there i n c r e a s e s with s i t e q u a l i t y . B r i x and M i t c h e l l (1983), B i n k l e y (1984), and Espinosa B a n c a l a r i et al. (1987) found t h a t the TLA:ASW v a r i e d with s i t e q u a l i t y . In t h i s study the b l c model c o e f f i c i e n t s d i d not vary s i g n i f i c a n t l y between s i t e s , s u g g e s t i n g the d i f f e r e n c e s i n model c o e f f i c i e n t s between s i t e s at bh r e s u l t e d from the lack of an a d d i t i o n a l p h y s i o l o g i c a l v a r i a b l e i n the bh models t h a t would account f o r d i f f e r e n c e s between bh and b l c ASW. 71 5.2.4. Mean Annual Ring Width I t was hypothesized t h a t mean annual r i n g width would improve the TLA p r e d i c t i o n model and account f o r d i f f e r e n c e s i n model c o e f f i c i e n t s between s i t e s because MARW should p a r t i a l l y account f o r d i f f e r e n c e s i n sapwood p e r m e a b i l i t y between t r e e s and s i t e s . The r e s u l t s i n t h i s study are v a r i a b l e , 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 not vary between s i t e s and t h e r e f o r e the e f f e c t of MARW was l e s s important than at bh. Whitehead et al. (1984) transformed the ASWbh v a r i a b l e by m u l t i p l y i n g i t by sapwood p e r m e a b i l i t y and by so doing removed sl o p e d i f f e r e n c e s between TLA p r e d i c t i o n models f o r S i t k a spruce and lodgepole pi n e . Thompson (1989) improved the f i t of h i s TLA p r e d i c t i o n model f o r lodgepole pine by m u l t i p l y i n g ASW by MARA. In t h i s study MARA v a r i e d l i t t l e from MARW. M u l t i p l y i n g ASWbh by MARW d i d not improve the r e l a t i o n s h i p with TLA (Fi g u r e 24). 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 of TLA and (ASW * MARW) d i d improve the r e l a t i o n s h i p between the two v a r i a b l e s . An a n a l y s i s of co v a r i a n c e i n d i c a t e d t h a t the i n t e r c e p t c o e f f i c i e n t v a r i e d s i g n i f i c a n t l y between s i t e s . T h e r e f o r e , i n c l u d i n g MARW d i d not account f o r v a r i a b i l i t y i n the s l o p e i n t e r c e p t s between s i t e s i n the TLA-ASWbh model nor d i d i t improve the model's l i n e a r i t y . MARW d i d not improve the r e l a t i o n s h i p of TLA to ASW i n D o u g l a s - f i r (Espinosa B a n c a l a r i et al. 1987). Espinosa B a n c a l a r i et al. 72 (1987 ) a l s o found the r a t i o of TLA-.ASW at b l c v a r i e d s i g n i f i c a n t l y and MARW d i d not. I t may be th a t a more C M E CD CD < CO CD CD CD 100 80 60 40 20 0 0 50 100 150 (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 area and the product of sapwood area and mean annual r i n g width at brea s t height ((ASW*MARW)bh) i s not l i n e a r . p r e c i s e measure of sapwood p e r m e a b i l i t y than MARW i s necessary to improve the TLA p r e d i c t i o n model. / Mean annual r i n g width was found to e x p l a i n some v a r i a b i l i t y i n the ASW-TLA r e l a t i o n s h i p when the data was s t r a t i f i e d by s i t e . Crown c l o s u r e was not q u a n t i f i e d i n t h i s study but v i s u a l l y i t was observed t h a t crown c l o s u r e i n the Haney s i t e was more advanced than i n the Duncan and Courtenay s i t e s . T h e r e f o r e , i n the Haney s i t e one would expect more l i g h t c o m p e t i t i o n between i n d i v i d u a l t r e e s and c o n c u r r e n t l y more v a r i a b i l i t y i n MARW between i n d i v i d u a l s 73 than at the two other s i t e s . T h i s e f f e c t i s shown i n Fi g u r e s 16 and 17 where MARW v a r i e d n o t i c e a b l y more amongst the Haney sample t r e e s than amongst the other sample t r e e s . T h i s was supported by the f a c t t h a t MARW had a p o s i t i v e e f f e c t i n improving the f i t of the model on the Haney s i t e and l i t t l e e f f e c t on the other s i t e s . In Haney the f i t of the models were improved at bh and b l c by m u l t i p l y i n g ASW by MARW; adj u s t e d R 2 i n c r e a s e d from 0.662 to 0.695 at bh and from 0.917 to 0.929 at b l c . At the other two s i t e s the f i t of the models at bh and b l c were poorer when ASW was m u l t i p l i e d by MARW, the exc e p t i o n being at Courtenay where the f i t of the model at bh was improved. The lodgepole pine stands f o r which Thompson (1989) had success i n improving the TLA p r e d i c t i o n model by m u l t i p l y i n g ASW by MARA v a r i e d g r e a t l y i n stand d e n s i t y (3,853 to 12,597 stems/ha). Stand d e n s i t y was not a f a c t o r i n t h i s study with d e n s i t y ranging from 550 to 650 stems/ha. However, crown c l o s u r e i n Haney was advanced enough to r e s u l t i n v a r i a t i o n i n MARW, a u s e f u l component of the model. Stands with a high degree of compe t i t i o n between t r e e s would l i k e l y show a marked e f f e c t of MARW on the p r e d i c t i o n models. 5.2.5. Number of L i v e Whorls At bh, ALC and ALCLB were the o n l y v a r i a b l e s , a s i d e from (ASW*ALB), which were l i n e a r l y r e l a t e d t o TLA (adjusted R 2 = 0.910 and 0.911, r e s p e c t i v e l y ) , whose r e g r e s s i o n c o e f f i c i e n t s d i d not vary between s i t e s , and, i n r a t i o with 74 TLA, d i d not vary between s i t e s . At the b l c , ALC had a higher a d j u s t e d R 2 than ASW and, a s i d e from (ASW*ALB)blc, ALCLBblc was the best p r e d i c t i v e v a r i a b l e of TLA. At bh, ALCLB d i f f e r e d from ASWLB i n t h a t i t i n c l u d e d some heartwood i n a l l but two samples. At the b l c , ALCLB d i f f e r e d from ASWLB i n t h a t i t i n c l u d e d a l l heartwood. The AHW i n c l u d e d i n ALCblc was l i n e a r l y r e l a t e d to c r o s s - s e c t i o n a l area of heartwood i n ALCbh (adjusted R 2 = 0.888; F = 120.0; and S.E.E. = 11.4). These r e s u l t s f o r ALC and ALCLB s t r e t c h the c e n t r a l concept of the Pipe Model Theory and suggest t h a t a given t r a n s p i r i n g l e a f mass or area r e q u i r e s both a p r o p o r t i o n a l amount of conducting stemwood (sapwood) and p h y s i c a l support stemwood (heartwood). The ALC v a r i a b l e i n c l u d e s ASW and appears to provide a measure of the area of heartwood which the crown depends on f o r p h y s i c a l support. 5.2.6. Nonlinear Models For models u s i n g ASWbh, ASWLBbh, and ATOTbh, TLA had to be l o g transformed (base e) i n order to improve the l i n e a r i t y of the r e l a t i o n s h i p between the dependent and independent v a r i a b l e . Espinosa B a n c a l a r i et al. (1987) a l s o found i t necessary to t r a n s f o r m both the dependent and independent v a r i a b l e s used i n t h e i r study (e.g., dbh, ASWbh, ASWblc, diameter at b l c , and (ASWbh * MARW)) with n a t u r a l l o g t r a n s f o r m a t i o n s . B r i x and M i t c h e l l (1983) found the r e l a t i o n s h i p between ASWbh and TLA to be l i n e a r i n a thinned stand of D o u g l a s - f i r . The three s i t e s used i n t h i s study 75 had been thinned, removing a l l suppressed t r e e s , at an e a r l i e r date. Dean and Long (1986) found a l i n e a r r e l a t i o n s h i p between TLA and ASWblc f o r lodgepole pine when suppressed t r e e s were excluded from the d a t a . However, with the i n c l u s i o n of suppressed t r e e s the r e l a t i o n s h i p became n o n l i n e a r . T h i s suggests t h a t i f suppressed i n d i v i d u a l s had not been removed from the s i t e s i n t h i s study they would have had a s i m i l a r impact on the r e l a t i o n s h i p between TLA and ASWblc. Dean and Long (1986) and Long and Smith (1988 and 1989) found t h e i r n o n l i n e a r models f o r TLA p r e d i c t i o n fo r s u b a l p i n e f i r and lodgepole pine were enhanced by i n t r o d u c i n g a second power term, D (where D i s the d i s t a n c e between bh and the center of the l i v e crown). I n c l u s i o n of D i n the n o n l i n e a r p r e d i c t i o n model of t h i s study had l i t t l e impact on the model. T h i s was s u r p r i s i n g as the mean D v a r i e d s i g n i f i c a n t l y by s i t e . The mean value f o r D at Duncan was 6.55 m (n = 4; S.E.M. = 0.87) which was s i g n i f i c a n t l y d i f f e r e n t (p = 0.05) from 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) fo r Courtenay. In the simple n o n l i n e a r model which d i d not i n c l u d e D as a second v a r i a b l e r e s i d u a l s were not biased when p l o t t e d a g a i n s t D or s i t e . I t appears t h a t s i g n i f i c a n t d i f f e r e n c e s i n D d i d not i n f l u e n c e the TLA-ASW model. The marginal improvement i n the f i t of the n o n l i n e a r model r e s u l t i n g from D d i d not warrant i t s i n c l u s i o n i n the model. 76 5.2.7. C r o s s - S e c t i o n a l Area of L i v e Bark The g e n e r a l l y p o s i t i v e r e s u l t s of i n c l u d i n g ALB i n the TLA p r e d i c t i o n models e i t h e r by adding i t to ASW and ALC or using the product of ASW and ALB encourages i t s use i n a l l o m e t r i c equations. In t h i s study, ALB was s t r o n g l y c o r r e l a t e d with TLA at bh and b l c with a d j u s t e d R 2 values of 0.799 and 0.783, r e s p e c t i v e l y . Brack et al. (1985), who a l s o found s t r o n g c o r r e l a t i o n s between ALB and TLA f o r three s p e c i e s of Eucalyptus, suggest that our understanding of the r e l a t i o n s h i p between TLA and c r o s s - s e c t i o n a l stem measures needs to move beyond t h i n k i n g o n l y of water t r a n s p o r t and gi v e c o n s i d e r a t i o n t o l i v e bark f u n c t i o n s . An important interchange between crown and stem i s the p r o d u c t i o n of carbohydrates by the p h o t o s y n t h e s i z i n g f o l i a g e and the use of those carbohydrates by the growing stem. Phloem parenchyma s t o r e excess carbohydrates ( S a l i s b u r y and Ross 1978). The r e s u l t s of t h i s study suggest t h a t the crown i n t e r a c t s with a p r o p o r t i o n a l amount of phloem capable of t r a n s p o r t i n g and s t o r i n g carbohydrates. 5.2.8. P r e d i c t i o n of Base of L i v e Crown Stem Measures The r e s u l t s of t h i s study complemented the f i n d i n g of Hungerford (1987) who found t h a t stem measures taken at b l c pro v i d e b e t t e r p r e d i c t i o n s of TLA than bh stem measures. However, s i n c e bh measures are easy to o b t a i n i t would be d e s i r a b l e i f b l c stem measures co u l d be p r e d i c t e d using bh stem measures. T h i s study i n d i c a t e d one cannot assume a 77 l i n e a r r e l a t i o n s h i p between a given stem measure at bh and b l c . Three of the v a r i a b l e s examined (ASW, ASWLB and (ASW*ALB)) were n o n l i n e a r i n t h e i r r e l a t i o n s h i p between bh and the b l c . The ALC v a r i a b l e stands out as the only v a r i a b l e which was c l e a r l y l i n e a r i n i t s r e l a t i o n s h i p between the b l c and bh. Th i s i s another good reason to in c l u d e the ALC v a r i a b l e i n f u t u r e a l l o m e t r i c r e l a t i o n s h i p s t u d i e s . In the models f o r each of the four v a r i a b l e s the r e s i d u a l s were bia s e d towards s i t e . I f bh stem measures are to be used to p r e d i c t b l c stem measures a much l a r g e r sample than n = 4, as the case f o r the Duncan and Haney s i t e s , would need t o be gathered and separate models developed f o r each s i t e . Using the models i n Table 8 and s e c t i o n 5.1.6., TLA was p r e d i c t e d by the independent v a r i a b l e s ASW, ASWLB, (ASW*ALB), ALC at bh and the b l c and these same b l c v a r i a b l e s as p r e d i c t e d by the corresponding bh stem measurements. The c o r r e l a t i o n between TLA as determined by d e s t r u c t i v e sampling and the p r e d i c t e d TLAs based on the models was s t r o n g e s t f o r the models based on b l c stem measurements. Breast height stem measurements p r e d i c t e d TLA e q u a l l y as w e l l as p r e d i c t e d b l c stem measurements d i d . 5.2.9. P o r t a b i l i t y of Tree Leaf Area P r e d i c t i o n Model The f e a s i b i l i t y of us i n g the stronger a l l o m e t r i c equations of t h i s study to p r e d i c t TLA i n other D o u g l a s - f i r stands i n the CWH zone i s enhanced by the f a c t t h a t the 78 a d j u s t e d R a values were high f o r the best models and ranges of TLA values from the three i n s t a l l a t i o n s overlapped. S e v e r a l r e s t r i c t i o n s as to the types of D o u g l a s - f i r stands to which these a l l o m e t r i c equations should apply a re: 1) r e c e n t l y spaced stands i n the range of 500 to 700 stems/ha i n which crown c l o s u r e has yet or only r e c e n t l y o c c u r r e d . Dean and Long (1986) i n d i c a t e t h a t suppressed t r e e s have d i f f e r e n t l i n e a r r e l a t i o n s h i p s between TLA and ASWbh than other crown c l a s s e s . T h i s problem can be a l l e v i a t e d by usi n g n o n l i n e a r r e l a t i o n s h i p s , u sing b l c stem measurements, or not i n c l u d i n g suppressed i n d i v i d u a l s ; 2) stands which have not r e c e n t l y been f e r t i l i z e d . B r i x and M i t c h e l l (1983) found that f e r t i l i z a t i o n a f f e c t e d the l i n e a r r e l a t i o n s h i p s between TLA and ASWbh 5 to 9 years a f t e r treatment; and 3) stands l e s s than 60 years of age. The sample t r e e s i n t h i s study were below 50 y e a r s - o l d and i t should not be assumed the a l l o m e t r i c equations apply to ol d e r t r e e s . 5.2.10. Comparison With Other Work There i s l i t t l e D o u g l a s - f i r a l l o m e t r i c data to compare with the n o n l i n e a r (using ASWbh) or l i n e a r (using ASWblc) equations of t h i s study. Waring et al. (1982) and B r i x and M i t c h e l l (1983) found the r e l a t i o n s h i p between ASWbh and TLA 79 to be l i n e a r and G r i e r er al. (1984), Espinosa B a n c a l a r i et al. (1987) and Gower et al. (1987) transformed both the. dependent and independent v a r i a b l e s to improve the l i n e a r i t y of t h e i r a l l o m e t r i c equations f o r D o u g l a s - f i r . Waring et al. (1982) found a s l o p e c o e f f i c i e n t f o r the l i n e a r r e g r e s s i o n of TLA and ASWblc f o r c e d through the o r i g i n to be 0.54. In t h i s study the constant was i n s i g n i f i c a n t f o r the TLA-ASWblc r e g r e s s i o n model (p = 0.05) and the sl o p e c o e f f i c i e n t was 0.515. If the model was f o r c e d through the o r i g i n the s l o p e c o e f f i c i e n t became 0.451. Reports of n o n l i n e a r r e g r e s s i o n models f o r D o u g l a s - f i r TLA with ASWbh as the independent v a r i a b l e were not a v a i l a b l e . 80 6. PHOTOGRAPHY 6.1. RESULTS T a k i n g photographs from 12 m d i s t a n c e a t a camera a n g l e of 5 7 . 5 ° r e s u l t e d i n the image of some sample t r e e s not b e i n g s i t u a t e d i n the c e n t e r of the e x p o s u r e , r e q u i r i n g Table 14. D e s c r i p t i o n of photographs s e l e c t e d for a n a l y s i s . T r e e 1 - Zenith Zooa lens D i s l .ance P a r t i a l Crown P o r t i o n T o t a l angle s e t t i n g f i on s i l h o u e t t e p o r t i o n of t r e e s i l h o n e t t e (degrees) (Ml) tret ! (m) area (en 3) of t r e e i n photo area (CD2) 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-22- 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 1- 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 1 2 " 111.62 0.79 0.95 148.73 1. D-l through D-4 r e f e r t o sample tree s from Duncan and C - l through C-8 r e f e r to sample t r e e s f r o n Courtenay. 2. The second exposure of the same t r e e was taken at r i g h t angles from the f i r s t exposure. 81 adjustments i n d i s t a n c e or camera angle. As a r e s u l t of advanced crown c l o s u r e , none of the exposures from the Haney s i t e had r e l a t i v e l y unobstructed images of the t r e e crown. The photographs s e l e c t e d f o r f u r t h e r a n a l y s i s , exposure setup f o r each photograph, and the c a l c u l a t i o n of t o t a l s i l h o u e t t e area are g i v e n i n Table 14. F i g u r e 25 i l l u s t r a t e s the r e l a t i o n s h i p between TLA (estimated by d e s t r u c t i v e sampling) and s i l h o u e t t e a r e a . c c D C I I 0 50 100 150 Silhouette Area (cm2) CM E CO CD cd CD CD CD I W W 80 -60 40 20 C C D F i g . 25. Scattergram of t r e e l e a f area (m 2) and s i l h o u e t t e area (cm 2), where D i n d i c a t e s a sample t r e e from Duncan and C i n d i c a t e s a sample t r e e from Courtenay. 82 6.2. DISCUSSION F i g u r e 25 i n d i c a t e s t h a t the c o n s i d e r a b l e v a r i a t i o n i n the r e l a t i o n s h i p between the two v a r i a b l e s would have to be accounted f o r before accurate p r e d i c t i o n s of TLA c o u l d be made us i n g s i l h o u e t t e area. Important sources of v a r i a t i o n i n the a n a l y s i s were: 1) sun angle - the p o s i t i o n of the sun at the time of the photograph i n f l u e n c e d l i g h t r e f l e c t a n c e of the f o l i a g e i n the photograph. Areas with high r e f l e c t a n c e appeared white, sometimes as white as the sky. I f the photo was taken at mid-day, the m a j o r i t y of r e f l e c t a n c e was o f f the top of the crown. Later i n the day the r e f l e c t a n c e was spread deeper through the crown. T h i s complicated attempts at d e n s i t y measurement based on d i f f e r e n c e s i n exposure between sky and l e a v e s ; 2) weather c o n d i t i o n s - exposure of the crown v a r i e d between c l e a r days with d i r e c t s u n l i g h t and cloudy days with d i f f u s e l i g h t . On b r i g h t sunny days there was high l i g h t c o n t r a s t i n the crown making i t d i f f i c u l t to f i n d an a p p r o p r i a t e exposure s e t t i n g f o r the camera. Consequently, i n the sunny day photographs, i t was d i f f i c u l t to d i f f e r e n t i a t e between the top of the t r e e and the sky while the lower crown appeared c o n s i d e r a b l y darker even though the f o l i a g e may not have been r e l a t i v e l y denser. On days with c l o u d cover t h i s problem was l e s s s e r i o u s . 3) t r e e height - g i v e n a f i x e d d i s t a n c e and angle f o r t a k i n g the photos, d i f f e r e n c e s i n t r e e height r e s u l t e d i n 83 v a r i a t i o n i n the probe angle through the crown. T a l l e r t r e e s ended up being i n the upper p o r t i o n of the exposure. F u r t h e r a g g r a v a t i n g the problem was v a r i a b l e t e r r a i n which a l s o e f f e c t e d where the t r e e was on the exposure when the d i s t a n c e between the t r e e and camera and the camera angle were f i x e d . With t a l l t r e e s p o s i t i o n e d at the top of the photograph the exposure view was through the bottom of the t r e e . Shorter t r e e s were p o s i t i o n e d i n the middle of the photograph and the view was of the broadside of the t r e e ; 4) view options - i n most cases a c l e a r view of the t r e e with no o b s t r u c t i o n s i n the background was a v a i l a b l e from on l y one d i r e c t i o n , sometimes two. With more than one view of the t r e e , mean s i l h o u e t t e area c o u l d have been c a l c u l a t e d f o r each t r e e and some v a r i a b i l i t y taken i n t o account. 5) camera s e t t i n g s - with t a l l t r e e s or s l o p i n g t e r r a i n i t was sometimes necessary to use d i f f e r e n t camera s e t t i n g s than the usual 50 mm zoom, 12 m d i s t a n c e , and 57.5° camera angle. I t was a l s o d i f f i c u l t to l e v e l the camera and keep i t l e v e l d u r i n g the photograph s e s s i o n . I t was not known how much v a r i a b i l i t y was introduced as a r e s u l t of the camera not being l e v e l . The sources of v a r i a b i l i t y t h a t had the g r e a t e s t impact appeared to be 2), 3), and 5). V a r i a b i l i t y source 2) co u l d have been c o n t r o l l e d by t a k i n g photographs at the same time of day and under s i m i l a r weather c o n d i t i o n s ; i d e a l l y 84 o v e r c a s t c l o u d c o n d i t i o n s . Time c o n s i d e r a t i o n s i n the f i e l d made t h i s a d i f f i c u l t t a s k . C o n s i d e r i n g how few o p p o r t u n i t i e s there were to get an unobstructed view of a t r e e crown i n these stands, there was l i t t l e t h a t c o u l d be done i n the f i e l d to reduce v a r i a b i l i t y source 3). I t would be p o s s i b l e to mathematically d e r i v e a t r e e h e i g h t and s l o p e c o r r e c t i o n f a c t o r f o r each t r e e i n order to s t a n d a r d i z e the s i l h o u e t t e areas to a common base, but the prospect of adding another c o r r e c t i o n to the e n t i r e s i l h o u e t t e area d e r i v a t i o n process would seem to hold l i t t l e promise f o r p r e d i c t i o n improvement. For those photographs which were not taken at 12 m d i s t a n c e or at a zoom s e t t i n g of 50 mm, i t would be necessary to d e r i v e a second c o r r e c t i o n f a c t o r i n order to b r i n g a l l photo images to a common standard. T h i s was not attempted i n t h i s study. V a r i a b i l i t y i n t r e e s i z e , stand d e n s i t y , t e r r a i n , and l i g h t c o n d i t i o n s encourages a more f l e x i b l e approach which does not r e q u i r e f i x e d camera d i s t a n c e s and a n g l e s . A more f r u i t f u l approach might be one which u t i l i z e s video imaging of sample branches to determine branch l e a f a r ea. Adaption of the technique d e s c r i b e d by D i e b o l t and Mudge (1988), who determined l e a f s u r f a c e area of Scots pine u s i n g a v i d e o -imaging system, c o u l d be a p p l i e d to branches of o l d e r t r e e s . The approach would be o n l y p a r t i a l l y d e s t r u c t i v e , r e q u i r i n g branches from designated crown p o r t i o n s and an estimate of the number of branches f i t t i n g i n t o b a s a l area c a t e g o r i e s . 85 7. SUMMARY 7.1. SAMPLING ANALYSIS O v e r a l l mean SLA was 42.8 cm 2/g (S.E.M. = 0.38). Mean SLA was found to vary 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 (p = 0.05). O v e r a l l mean NDW r a t i o was 0.421 (S.E.M. = 0.004). Mean NDW r a t i o was found to v a r y 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 , but not crown p o s i t i o n (p = 0.05). Mean SLA f o r each needle age c l a s s - crown p o s i t i o n c a t e g o r y can be p r e d i c t e d with 95% confi d e n c e and a 10% a l l o w a b l e e r r o r u sing s i x 10-needle samples i n each category. A 5% a l l o w a b l e e r r o r and 95% confi d e n c e can be reached u s i n g 19 or 20 10-needle samples. 7.2. ALLOMETRIC RELATIONSHIPS Tree l e a f area p r e d i c t i o n models based on stem measures at the b l c d i d not va r y between s i t e s and had adjus t e d R 2 values g r e a t e r than 0.90. In g e n e r a l , b l c stem measures were b e t t e r p r e d i c t o r s of TLA than were bh stem measures. T h i s data s e t i n d i c a t e s one cannot assume a l i n e a r r e l a t i o n s h i p between a gi v e n stem measure at bh and the b l c . Models p r e d i c t i n g b l c stem measures using bh stem measures as independent v a r i a b l e s should be d e r i v e d on a s i t e - t o - s i t e b a s i s . C r o s s - s e c t i o n a l sapwood area d i d not c o n s i s t e n t l y prove to be a b e t t e r p r e d i c t o r of TLA than ATOT. At the b l c the adjust e d R 2 of the TLA model u s i n g ASW as the independent 86 v a r i a b l e was lower than the TLA model using ATOT as the independent v a r i a b l e . At bh the r e s u l t s were r e v e r s e d . C r o s s - s e c t i o n a l sapwood area at bh was not l i n e a r l y r e l a t e d to TLA across s i t e s . A l o g t r a n s f o r m a t i o n (base e) of TLA made the r e l a t i o n s h i p with ASW more l i n e a r , although the TLA model v a r i e d between s i t e s . The same r e s u l t s were found f o r the models u s i n g ASWLB and ATOT as independent v a r i a b l e s . The product of c r o s s - s e c t i o n a l area of sapwood and c r o s s - s e c t i o n a l area of l i v e bark was l i n e a r l y r e l a t e d to TLA, as was ALC and ALCLB. The ALCLB stem measure r e s u l t e d i n the best f i t t i n g TLA p r e d i c t i o n model at bh. At the b l c a l l independent v a r i a b l e s were l i n e a r l y r e l a t e d to TLA with none of the TLA p r e d i c t i o n models v a r y i n g s i g n i f i c a n t l y between s i t e s . The best f i t t i n g TLA p r e d i c t i o n model at the b l c used (ASW*ALB) as the independent v a r i a b l e . The best f i t t i n g model at the b l c was the best f i t t i n g model o v e r a l l . The n o n l i n e a r model developed f o r ASW was not improved by the i n c l u s i o n of the second v a r i a b l e D. T h i s was l i k e l y due to the low v a r i a b i l i t y i n stand d e n s i t y between s i t e s . Mean annual r i n g width d i d not improve the f i t of the bh models or account f o r v a r i a t i o n between s i t e s . T h i s was l i k e l y a r e s u l t of the high u n i f o r m i t y i n stand d e n s i t y between s i t e s . On the Haney s i t e , where crown c l o s u r e was most advanced, i n c l u s i o n of MARW i n the TLA model d i d improve the adjus t e d R 2. 87 A d d i t i o n of ALB to ASWbh d i d not i n c r e a s e e x p l a i n e d v a r i a t i o n i n the TLA models between s i t e s nor d i d i t improve the models l i n e a r i t y . M u l t i p l y i n g ASW by ALB, on the other hand, d i d improve the models l i n e a r i t y and the TLA p r e d i c t i o n model d i d not vary between s i t e s . Both at bh and the b l c the i n c l u s i o n of ALB e i t h e r through a d d i t i o n or m u l t i p l i c a t i o n with ASW i n c r e a s e d the a d j u s t e d R 2 f o r the TLA models. T h i s r e s u l t supports the hypothesis t h a t a l l o m e t r i c equations between TLA and stem measurements are improved by moving beyond water t r a n s p o r t c o n s i d e r a t i o n s to the i n c l u s i o n of measures of n u t r i e n t s t o r a g e . The r e l a t i o n s h i p between the independent v a r i a b l e ALC and ALCLB and TLA was l i n e a r at bh and the b l c . The TLA models at bh and the b l c u s i n g ALC and ALCLB as the independent v a r i a b l e s d i d not vary s i g n i f i c a n t l y between s i t e s . The ALC and ALCLB stem measures were found to i n c l u d e area of heartwood i n a l l but two stem d i s c s . The s t r o n g r e l a t i o n s h i p between TLA and the ALC v a r i a b l e s suggests t h a t a given t r a n s p i r i n g l e a f mass or area i s r e l a t e d to a p r o p o r t i o n a l amount of conducting stemwood and p h y s i c a l support stemwood. C o n s i d e r i n g the s m a l l number of sample t r e e s i n t h i s study i t may be best to speak of trends r a t h e r than hard and f a s t c o n c l u s i o n s . The " c o n c l u s i o n s " reached i n t h i s study should have a p p l i c a t i o n to other D o u g l a s - f i r stands i n the CWH zone which are l e s s than 60 y e a r s - o l d , spaced to between 500 - 700 stems/ha, and have not been f e r t i l i z e d i n the l a s t 88 10 y e a r s . In stands which do not meet these c r i t e r i a the a l l o m e t r i c equations d e r i v e d i n t h i s study should be a p p l i e d with c a u t i o n . The t r a n s f o r m a t i o n s needed to improve the l i n e a r i t y between the dependent and independent v a r i a b l e s i n the bh models were d i f f e r e n t than the t r a n s f o r m a t i o n s r e q u i r e d i n other s t u d i e s d e v e l o p i n g a l l o m e t r i c equations f o r D o u g l a s - f i r . T h i s suggests that a l l o m e t r i c equations f o r D o u g l a s - f i r may have l i m i t e d p o r t a b i l i t y , with s e v e r a l of the TLA models u s i n g bh measures v a r y i n g s i g n i f i c a n t l y between s i t e s . 7.3. PHOTOGRAPHY TECHNIQUE A poor c o r r e l a t i o n was found between TLA and s i l h o u e t t e area. The photography technique r e q u i r e s adjustments to reduce v a r i a b i l i t y r e s u l t i n g from l i g h t c o n d i t i o n s , t r e e h e i g h t , d i f f i c u l t i e s i n m a i n t a i n i n g a l e v e l camera, and l i m i t e d crown view o p p o r t u n i t i e s . In g e n e r a l , the a p p l i c a b i l i t y of the photography technique to a v a r i e t y of f o r e s t c o n d i t i o n s i s extremely l i m i t e d due to d i f f i c u l t i e s i n o b t a i n i n g r e l a t i v e l y c l e a r views of a g i v e n t r e e crown. Even i n f o r e s t s with low stand d e n s i t i e s , i t i s v e r y d i f f i c u l t to get even one view of a t r e e crown which i s not o b s t r u c t e d by adjacent t r e e s . A more f r u i t f u l approach should be one which u t i l i z e s video imaging of sample branches under c o n t r o l l e d l i g h t c o n d i t i o n s to determine branch l e a f area. 89 8. CONCLUSIONS 8.1. SAMPLING ANALYSIS When sampling to determine mean SLA i t i s necessary to s t r a t i f y by s i t e , crown p o s i t i o n , and needle age c l a s s , as SLA was found to va r y s i g n i f i c a n t l y a c c o r d i n g to these v a r i a b l e s . B a n c a l a r i et al. (1987) s t r a t i f i e d D o u g l a s - f i r crowns i n t o q u a r t e r s and B o r g h e t t i et al. (1986) i n t o t h i r d s . T h i s study suggests t h a t accuracy i s gained by s t r a t i f y i n g by f i f t h s . B o r g h e t t i et al. (1986) s t r a t i f i e d needles i n t o four age c l a s s e s . T h i s study suggests t h a t accuracy can be gained by s t r a t i f y i n g needles i n t o s i x age c l a s s e s with needles o l d e r than s i x years i n c l u d e d i n the o l d e s t needle age c l a s s . A decrease i n sampling time can be gained by determining the minimum number of samples needed to achieve a d e s i r e d a l l o w a b l e e r r o r and conf i d e n c e l e v e l . When sampling to determine mean SLA per needle age c l a s s per branch, a 5% a l l o w a b l e e r r o r and 95% co n f i d e n c e l e v e l can achieved u s i n g 19 or 20 10-needle samples per category. A 10% a l l o w a b l e e r r o r and 95% confidence l e v e l can be achieved u s i n g 6 10-needle samples per category. When sampling to determine mean NDW r a t i o i t i s necessary t o s t r a t i f y by s i t e and needle age c l a s s , as NDW r a t i o was found to vary s i g n i f i c a n t l y a c c o r d i n g to these v a r i a b l e s . Needle dry weight r a t i o d i d not var y by crown p o s i t i o n . 90 8.2. ALLOMETRIC RELATIONSHIPS Across the range of s i t e s i n t h i s study TLA was not l i n e a r l y r e l a t e d to ASWbh, ASWLBbh, or ATOTbh. The l i n e a r i t y of the r e l a t i o n s h i p of TLA with these v a r i a b l e s was improved by 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 of TLA, but the slo p e 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 th r e e l i n e a r models v a r i e d s i g n i f i c a n t l y by s i t e . T h i s suggests t h a t a l l o m e t r i c equations developed to p r e d i c t D o u g l a s - f i r TLA u s i n g any of the above independent v a r i a b l e s are s i t e s p e c i f i c . The three b r e a s t height v a r i a b l e s which were l i n e a r l y r e l a t e d to TLA and whose model c o e f f i c i e n t s d i d not vary between s i t e s were ALCbh, ALCLBbh, and (ASW*ALB)bh. The models based on these three independent v a r i a b l e s can be used over the range of s i t e s r e presented by t h i s study to p r e d i c t D o u g l a s - f i r TLA. L i m i t a t i o n s on the p o r t a b i l i t y of the models r e l a t e to stand age and d e n s i t y and b i o g e o c l i m a t i c subzone. A l l the stem measurements at the b l c were l i n e a r l y r e l a t e d to TLA. The adjus t e d R 2 values f o r the models were g r e a t e r than 0.90 and the model c o e f f i c i e n t s d i d not vary with s i t e . T h i s suggests t h a t b l c stem measurements are b e t t e r p r e d i c t o r s of TLA than are bh stem measurements. I t cannot be assumed t h a t the r e l a t i o n s h i p between bh and b l c stem measurements are l i n e a r . S e v e r a l of the r e s u l t s from t h i s study c h a l l e n g e the pipe model theory. F i r s t , i t co u l d not be shown c o n c l u s i v e l y t h a t ASW was a b e t t e r p r e d i c t o r of TLA than was ATOT. At the b l c , ATOT, a c r o s s - s e c t i o n a l stem measure that 91 i n c l u d e s more than the l i v i n g stem, was more closely-c o r r e l a t e d with TLA than was ASW. Secondly, i t was found t h a t when ALB was added to or m u l t i p l i e d by ASW the f i t of the TLA p r e d i c t i o n model was improved. The f i t of the model was f u r t h e r improved by i n c l u d i n g a measure of heartwood i n the independent v a r i a b l e . At the b l c , the best f i t t i n g TLA p r e d i c t i o n model, next to ASW*ALB, was ALCLB, which i n c l u d e s AHW. At bh, ALCLB, which i n c l u d e s a p o r t i o n of AHW i n 14 of the 16 sample t r e e s , was the best f i t t i n g model. In terms of p h y s i o l o g y , these r e s u l t s f o r ALB and ALC suggest t h a t t h a t crown dimensions r e l a t e to a p r o p o r t i o n a l amount of conducting stemwood, both sapwood and l i v e bark, and p h y s i c a l support stemwood. The ALCLB v a r i a b l e i n c l u d e s ASW and ALB and appears to p r o v i d e a measure of the area of heartwood which the crown depends on f o r p h y s i c a l support. T h i s study suggests t h a t a l l o m e t r i c equations developed to p r e d i c t D o u g l a s - f i r TLA may be improved by u s i n g ALCLB. The product of MARW and ASW was not more c l o s e l y c o r r e l a t e d with TLA than was ASW. T h i s was l i k e l y a r e s u l t of low v a r i a b i l i t y i n stand d e n s i t y between and w i t h i n s i t e s . 8.3. PHOTOGRAPHY TECHNIQUE S e v e r a l c o r r e c t i o n f a c t o r s must be d e r i v e d i n order to e x p l a i n v a r i a b i l i t y r e s u l t i n g from v a r y i n g t r e e h e i g h t s and camera p o s i t i o n s (angle and d i s t a n c e ) before a c c u r a t e TLA p r e d i c t i o n s can be made using s i d e - v i e w photography. I t was 9 2 d i f f i c u l t to f i n d unobstructed side-views of i n d i v i d u a l crowns even i n stands with d e n s i t i e s as low as 500 stems/ha. V a r i a b i l i t y i n l i g h t c o n d i t i o n s i n the n a t u r a l f o r e s t , along with the sources of v a r i a t i o n mentioned above, encourage the development of a photography technique u s i n g sample branches i n a c o n t r o l l e d l i g h t environment. 8.4. RESEARCH RECOMMENDATIONS T h i s study suggests two areas f o r f u r t h e r r e s e a r c h : examination of the r e l a t i o n s h i p between ALCLB and TLA i n a wider range of stand c o n d i t i o n s and the development of a photography technique using video or s i n g l e lense r e f l e x cameras i n a c o n t r o l l e d l i g h t environment to p r e d i c t branch l e a f a r ea. The development of such a photography technique would speed up TLA sampling and a l l o w f o r l a r g e r sample s i z e s . 93 LITERATURE CITED A l b r e k t s o n , A. 1984. Sapwood b a s a l area and needle mass of Scots pine (Pinus sylvestris L.) t r e e s i n C e n t r a l Sweden. F o r e s t r y 57: 35-43 Anderson, M. C. 1971. R a d i a t i o n and crop s t r u c t u r e . Pp. 412-466 in Z. Sestak, J . Catsky and P.G. J a r v i s ( E d i t o r s ) , P l a n t P h o t o s y n t h e t i c P r o d u c t i o n . Manual of Methods, W. Junk, The Hague. Bannan, M. W. 1965. The l e n g t h , t a n g e n t i a l diameter, and length/width r a t i o of c o n i f e r t r a c h e i d s . Can. J . Bot. 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 area 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 red a l d e r . For. S c i . 30: 259-263. Blanche, C. A. and J . D. Hodges. 1985. A l e a f area -sapwood area r a t i o developed to r a t e l o b l o l l y pine t r e e v i g o r . Can. J . For. Res. 15: 1181-1184. Booker, R. E. and J . A. Kininmonth. 1978. V a r i a t i o n i n l o n g i t u d i n a l p e r m e a b i l i t y of green r a d i a t a pine wood. N. Z. J . For. S c i . 8: 295-308. B o r g h e t t i , M., G. G. Vendramin, and R. G i a n n i n i . 1986. S p e c i f i c l e a f area and l e a f area index 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 . For. Res. 16: 1283-1288. Brack, C. L., M. P. Dawson, and A. M. G i l l . 1985. Bark, l e a f and sapwood dimensions i n Eucalyptus. Aust. For. Res. 15: 1-7. B r i x , H. 1981. E f f e c t s of t h i n n i n g and n i t r o g e n f e r t i l i z a t i o n on branch and f o l i a g e p r o d u c t i o n i n D o u g l a s - f i r . Can. J . For. Res. 11: 502-511. B r i x , H. and A. K. M i t c h e l l . 1983. Th i n n i n g and n i t r o g e n f e r t i l i z a t i o n e f f e c t s on sapwood development and r e l a t i o n s h i p s of f o l i a g e q u a n t i t y to sapwood area and b a s a l area i n D o u g l a s - f i r . Can. J . For. Res. 13: 384-389 . C a r t e r , G. A., and W. K. Smith. 1985. I n f l u e n c e 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 photosynthesis i n c o n i f e r s . 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. D o u g l a s - f i r f e r t i l i z a t i o n : d ecision-making 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 area 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 lodgepole 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. Regression A n a l y s i s by Example. W i l e y - I n t e r s c i e n c e , New York. Cochran, W. G., and G. M. Cox. 196G. Experimental Designs. 2nd ed. John Wiley and Sons, New York. Dean, T. J . , and J . N. Long. 1986. V a r i a t i o n i n sapwood area - l e a f area r e l a t i o n s w i t h i n two stands of lodgepole p i n e . F or. S c i . 32: 749-758. Del Rio, E., and A. Berg. 1979. S p e c i f i c l e a f area of 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 needle age. For. S c i . 25: 183-186. D i e b o l t , D. S., and K. W. Mudge. 1988. Use of 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 area of Pinus sylvestris s e e d l i n g s . Can. J . For. Res. 18: 377-380. Dixon, A. F. G. 1971. E f f e c t of aphids on wood formation. Appl. E c o l . 8: 165-179. 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 content, 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 of c o n i f e r s . P l a n t , C e l l and Environment 5: 271-277. Espinosa B a n c a l a r i , M. A. E., D. A. Pe r r y , and J . D. M a r s h a l l . 1987. Leaf area - sapwood area r e l a t i o n s h i p s i n adjacent young D o u g l a s - f i r stands with d i f f e r e n t e a r l y growth r a t e s . Can. J . For. Res. 17: 174-180. Geron, C. D., and G. A. Ruark. 1988. Comparision of constant 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 . For. Res. 18: 1298-1304. Gower, S. T., C. C. G r i e r , D. J . Vogt, and K. A. Vogt. 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 evergreen 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. Can. J . For. Res. 17: 630-634. G r a n i e r , A. 1981. Etude des r e l a t i o n s entre l a s e c t i o n du b o i s d'aubier et l a mass f o l i a i r e chez l e D o u g l a s - f i r (Pseudotsuga menziesii Mirb. F r a n c o ) . Ann. S c i . For. 38: 503-512. 95 G r i e r , C. C , K. M. Lee, and R. M. A r c h i b a l d . 1984. E f f e c t of urea 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 D o u g l a s - f i r t r e e s . Can. J . For. Res. 14: 900-904. Helgerson, 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. Equations 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 red 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 . For. Res. 18: 1082-1085. Huber, H. 1928. Weitere q u a n t i t a t i v e Untersuchungen uber das Wasserleitungssystem der P f l a n z e n . Jahrb. Wiss. Bot. 67: 877-959. Hungerford, R. D. 1987. E s t i m a t i o n of f o l i a g e area i n dense Montana lodgepole pine stands. Can. J . For. Res. 17: 320-324. J a r v i s , P. G., and J . W. Leverenz. 1983. P r o d u c t i v i t y of temperate, deciduous and evergreen f o r e s t s . In 0. L. Lange, P. S. Nobel, 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 Ecology IV, Ecosystem Processes: 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 . Johnson, J . D., S. M. Zedaker, 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 p i n e . For. S c i . 31: 891-898. Kaufmann, M. R. and C. A. Troendle. 1981. The r e l a t i o n s h i p of l e a f area and f o l i a g e biomass to sapwood conducting area i n four s u b a l p i n e f o r e s t t r e e s p e c i e s . For. S c i . 27: 477-482. Keane, M. G. and G. F. Weetman. 1987. Leaf 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 lodgepole p i n e . Can. J . For. Res. 17: 205-209. Kozlowski, T. T., J . F. Hughes, and L. Leyton. 1966. P a t t e r n s of water movement i n dormant gymnosperm s e e d l i n g s . B i o r h e o l o g y 3: 77-85. Kozlowski, T. T., J . F. Hughes, and L. Leyton. 1967. Dye movement i n gymnosperms i n r e l a t i o n to t r a c h e i d alignment. F o r e s t r y 40: 209-227. Kramer, P. J . , and T. T. Kozlowski. 1979. P h y s i o l o g y of Woody P l a n t s . 2nd e d i t i o n . Academic P r e s s , London New York. Lang, A. R. G. 1986. Leaf area and average l e a f angle from 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. J . Bot., 34: 349-355. 96 Lang, A. R. G. 1987. S i m p l i f i e d estimate of l e a f area index from t r a n s m i t t a n c e of the sun's beam. A g r i . and For. Meteorol. 41: 179-186. Lang, A. R. G., X. Yueqin, and J . M. Norman. 1985. Crop s t r u c t u r e and the 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 For. M e t e o r o l . 35: 83-101. Leong, 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 area index and canopy l i g h t p e n e t r a t i o n of Hevea brasiliensis M u e l l . Arg. 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. Long, J . N., and F. W. Smith. 1988. Leaf area - sapwood area r e l a t i o n s of lodgepole pine as i n f l u e n c e d by stand d e n s i t y and s i t e index. Can. J . For. Res. 18: 247-250. Long, J . N., and F. W. Smith. 1989. E s t i m a t i n g l e a f area of Abies lasiocarpa a c r o s s ranges of stand d e n s i t y and s i t e q u a l i t y . Can. J . For. Res. 19: 930-932. Long, J . N., F. W. Smith, 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 stem sapwood and heartwood i n the mechanical and p h y s i o l o g i c a l support of crowns and development of stem form. Can. J . For. Res. 11: 459-464 . Maguire, D. A., and D. W. Hann. 1989. The r e l a t i o n s h i p between gross crown dimensions and sapwood area at crown base i n D o u g l a s - f i r . Can. J . For. Res. 19: 557-565. Marchand, P. J . 1984. Sapwood area as an estimator of f o l i a g e biomass and p r o j e c t e d l e a f area f o r Abies balsamea and Picea rubens. Can. J . For. Res. 14: 85-87. Pearson, J . A., T. J . Fahey, and D. H. Knight. 1984. Biomass and l e a f area i n c o n t r a s t i n g lodgepole pine f o r e s t s . Can. J . For. Res. 14: 259-265. P o j a r , J . , K. K l i n k a , and D. V. Meidinger. 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. For. 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. Waring. 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 conductance with stand development. Can. J . For. Res. 19: 432-439. 97 P r i c e , D. 1987. Some e f f e c t s of v a r i a t i o n i n weather and s o i l water storage on canopy e v a p o t r a n s p i r a t i o n and net photosynthesis of a young D o u g l a s - f i r stand. PhD t h e s i s . 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. Rogers, R. and T. M. H i n c k l e y . 1979. F o l i a r weight and area r e l a t e d to c u r r e n t sapwood area i n oak. For. S c i . 25: 298-303. S a l i s b u r y , F. B., and C. W. Ross. 1978. P l a n t P h y s i o l o g y . 2nd ed. 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 of p l a n t form - the pipe model theory. I. B a s i c a n a l y s e s . Jpn. J . E c o l . 14: 97-105. S h i n o z a k i , K., K. Yoda, K. Hozumi, and T. K i r a . 1964b. A q u a n t i t a t i v e a n a l y s i s of p l a n t form - the pipe model theory. I I . F u r t h e r evidence of the theory and i t s a p p l i c a t i o n i n f o r e s t ecology. Jpn. J . E c o l . 14: 133-139. Smith, R. B., R. H. Waring, 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 nalyses from D o u g l a s - f i r as weight per u n i t of l e a f a r ea. Can. J . For. Res. 11: 593-598. S n e l l , J . K. A. and J . K. Brown. 1978. Comparison of t r e e e s t i m a t o r s - dbh and sapwood area. F or. S c i . 24: 455-457. S p i t t l e h o u s e , D. L. 1981. Measuring 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 stands. D o c t o r a l T h e s i s , Department of S o i l S cience, 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. Sprug e l , D. G. 1983. C o r r e c t i n g f o r b i a s i n l o g -transformed a l l o m e t r i c equations. Ecology 64: 209-210. Swanson, R. H. 1975. V e l o c i t y d i s t r i b u t i o n p a t t e r n s i n ascending xylem sap d u r i n g t r a n s p i r a t i o n . In R. B. Dowdell (ed.), F l o w — I t s Measurement and C o n t r o l i n Science and Industry, V o l . 1, pp. 1425-1430. I n s t r u . Soc. Am. Tan, C. S., T. A. Black, and J . U. Nnyamah. 1978. A simple d i f f u s i o n model of t r a n s p i r a t i o n a p p l i e d to a thinned D o u g l a s - f i r stand. Ecology 59: 1221-1229. Thompson, D. C. 1989. The e f f e c t of stand s t r u c t u r e and stand d e n s i t y on the l e a f area - sapwood area r e l a t i o n s h i p of lodgepole p i n e . Can. J . For. Res. 19: 392-396. 98 Ungs, M. J . 1981. D i s t r i b u t i o n of l i g h t w i t h i n the crown of an open-grown D o u g l a s - f i r . PhD T h e s i s . Oregon State 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 of the h e m i s p h e r i c a l photographic technique to measure l e a f area index 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. Waring, R. H. 1983. E s t i m a t i n g f o r e s t growth and e f f i c i e n c y i n r e l a t i o n to canopy l e a f a r ea. Adv. E c o l . Res. 13: 327-354. Waring, R. H. and W. H. S c h l e s i n g e r . 1985. F o r e s t Ecosystems: Concepts and Management. Academic P r e s s , Inc. Orlando, F l o r i d a . 340 p. Waring, R. H., P. E. Schroeder, and R. Oren. 1982. A p p l i c a t i o n of the pipe model theory to p r e d i c t canopy l e a f a r e a . Can. J . For. Res. 12:556-560. Whitehead, D. 1978. The e s t i m a t i o n of f o l i a g e area from sapwood b a s a l area i n Scots p i n e . F o r e s t r y 51: 137 -149. Whitehead, D., and P. G. J a r v i s . 1981. Co 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. Kozlowski (ed), Water D e f i c i t s and P l a n t Growth. Academic P r e s s , New York. Whitehead, D., W. R. N. Edwards, and P. G. J a r v i s . 1984. Conducting sapwood area, f o l i a g e area, and p e r m e a b i l i t y i n mature t r e e s of Picea sitchensis and Pinus contorta. Can. J . For. Res. 14: 940-947. W i l k i n s o n , L. 1988. SYSTAT: the System f o r S t a t i s t i c s . SYSTAT, Inc., Evanston, IL. 822 pp. Wi l k i n s o n , L. 1989. SYGRAPH: the system f o r Graphics f o r the PC. 2nd e d i t i o n . SYSTAT, Inc., Evanston, IL. 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 ed. P r e n t i c e - H a l l , Toronto. 718 pp. Zimmermann, M. H. 1983. Xylem s t r u c t u r e and the ascent of sap. Springer V e r l a g , 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 are produced u s i n g SYGRAPH (Wi l k i n s o n , 1989). The f o l l o w i n g e x p l a n a t i o n of the f i g u r e s i s taken d i r e c t l y from the SYGRAPH document: The inner fences are d e f i n e d as f o l l o w s : lower fence = lower hinge - (1.5Hspread)" upper fence = upper hinge + (1.5Hspread) The outer fences are d e f i n e d as f o l l o w s : lower fence = lower hinge - OHspread) upper fence = upper hinge + OHspread) Values o u t s i d e the inner fences are p l o t t e d with a s t e r i s k s . Values o u t s i d e the outer fences are p l o t t e d with empty c i r c l e s . * The Hspread i s comparable to the i n t e r q u a r t i l e range or 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 the values of the two hinges. 100 APPENDIX II LEAF AREA INDEX VALUES S i t e Dbh c l a s s ATOTbh Ho. of P r e d i c t e d Leaf Area LAI midpoint trees/ha Leaf Area* per ha (en) ( en 2) (B2) (n 2/ha) |B2/B2) Haney Duncan Courtenay 16.9 224.32 217.0 35.47 7696.2 18.5 268.80 153.0 44.30 6778.1 3.20 21.5 363.05 130.0 70.97 9226.0 19.9 311.03 152.0 54.71 8316.6 13.8 149.57 256.0 24.41 6249.0 16.0 201.06 64.0 31.57 2020.5 2.33 18.2 260.16 192.0 42.43 8146.6 19.8 307.91 128.0 53.87 6895.4 14.9 174.37 48.9 27.63 1351.1 11.5 240.53 114.2 38.46 4392.1 18.1 257.30 32.6 41.82 1363.3 20.2 320.47 114.0 57.36 6539.0 2.97 21.3 356.33 65.3 68.62 4480.9 23.0 415.48 65.0 92.24 5995.6 24.0 452.39 50.0 110.94 5547.0 * P r e d i c t e d l e a f area (one-sided) deterained by InTLA = 2.447+0.005(ATOTbh). 

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