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UBC Theses and Dissertations

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

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INFLUENCE OF CUTTING BLOCK S I Z E ON THE EFFICIENCY OF SEVERAL 3-P SAMPLING VARIATIONS AS COMPARED TO POINT SAMPLING by ERIC CARL TURNBLOM B . S c , The U n i v e r s i t y o f I l l i n o i s , 1983 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF FORESTRY We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t«j> .the r e q u i r e d / l s t a n d i r d THE UNIVERSITY OF BRITISH November 1986 © E r i c C a r l T u r n b l o m , COLUMBIA 1986 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f l~prest k?&Sdurces The U n i v e r s i t y o f B r i t i s h C o l u m b i a 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3 am D a t e DE-6 (3/81) 11 ABSTRACT F o r 3-P s a m p l i n g , an o c u l a r p r e d i c t i o n of volume must be made on e v e r y t r e e i n a c u t t i n g b l o c k , w h i c h c a s t s doubt on i t s e f f i c i e n c y i n l a r g e r b l o c k s . However, i t has t h r e e main a d v a n t a g e s o v e r t h e s t a n d a r d BCMF p r i s m c r u i s i n g p r o c e d u r e s . F i r s t , i n d i v i d u a l t r e e s a r e t h e s a m p l i n g u n i t s , n o t p l o t s o f t r e e s , so g r e a t e r p r e c i s i o n may r e s u l t f o r a g i v e n sample s i z e , s e c o n d , no h e i g h t / d b h r e g r e s s i o n s need be c a l c u l a t e d , t h i r d , i t p o t e n t i a l l y a v o i d s volume e q u a t i o n b i a s e s when i t i s u s e d i n c o n j u n c t i o n w i t h d e n d r o m e t r y . A s i m p l e r s a m p l i n g p r o c e d u r e , r a t i o e s t i m a t i o n , d i f f e r i n g from 3-P i n t h a t sample t r e e s a r e s e l e c t e d w i t h e q u a l p r o b a b i l i t y , may a l s o p r o v e a d v a n t a g e o u s . A s t u d y was c o n d u c t e d i n t h e UBC r e s e a r c h f o r e s t i n w h i c h s e v e r a l b l o c k s were c r u i s e d u s i n g a l l t h r e e of t h e s e methods. A volume e q u a t i o n , t h e w i d e - s c a l e r e l a s k o p , and t h e B a r r and S t r o u d d e n d r o m e t e r t y p e FP-12 were t e s t e d as t r e e measurement methods f o r use w i t h 3-P and r a t i o e s t i m a t i o n . R e s u l t s i n d i c a t e t h a t 3-P i s more e f f i c i e n t t h a n p o i n t s a m p l i n g i n b l o c k s r a n g i n g i n s i z e up t o between 5 and 14 h e c t a r e s , d e p e n d i n g on t h e t r e e measurement method c h o s e n and t h e h e i g h t / d b h r e g r e s s i o n s deemed n e c e s s a r y f o r use i n t h e s t a n d a r d c r u i s e . R a t i o e s t i m a t i o n i s more e f f i c i e n t t h a n p o i n t s a m p l i n g i n b l o c k s i z e s r a n g i n g up t o 14 h e c t a r e s d e p e n d i n g on t h e same f a c t o r s as 3-P. i i i TABLE OF CONTENTS Page T I T L E PAGE i ABSTRACT i ABSTRACT i i TABLE OF CONTENTS i i i L I S T OF TABLES i v L I S T OF FIGURES v ACKNOWLEDGEMENTS v i INTRODUCTION 1 SAMPLING TECHNIQUES USED 6 1 . 3-P SAMPLING 6 2. RATIO ESTIMATION 12 3. POINT SAMPLING 15 LITERATURE REVIEW 18 MATERIALS AND METHODS 28 RESULTS AND DISCUSSION 38 CONCLUSIONS 58 LITERATURE CITED 60 APPENDIX 63 I V L I S T OF TABLES T a b l e H e a d i n g Page 1. S t a n d C h a r a c t e r i s t i c s Summary 36 2. B l o c k HM Summary of a c t i v i t y t i m e s 39 3. B l o c k HW Summary of a c t i v i t y t i m e s 40 4. B l o c k M Summary of a c t i v i t y t i m e s 40 5. B l o c k W Summary of a c t i v i t y t i m e s 41 6. Summary o f c r u i s e r e s u l t s 42 V L I S T OF FIGURES F i g u r e H e a d i n g Page 1. T o t a l c r u i s e t i m e f o r p o i n t s a m p l i n g compared t o 3P u s i n g t h r e e t r e e measurement t e c h n i q u e s , g i v e n t h e o b s e r v e d v a r i a b i l i t y 49 2. T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g compared t o r a t i o e s t i m a t i o n u s i n g t h r e e t r e e measurement t e c h n i q u e s , g i v e n t h e o b s e r v e d v a r i a b i l i t y 50 3. T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g i n s t a n d s w i t h t h r e e s p e c i e s compared w i t h 3P u s i n g t h r e e t r e e measurement methods, g i v e n t h e o b s e r v e d v a r i a b i l i t y ...52 4. T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g i n s t a n d s w i t h t h r e e s p e c i e s compared w i t h r a t i o e s t i m a t i o n u s i n g t h r e e t r e e measurement methods, g i v e n t h e o b s e r v e d v a r i a b i l i t y 54 5. T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g i n s t a n d s w i t h t h r e e s p e c i e s compared w i t h 3P u s i n g t h e volume e q u a t i o n t r e e measurement method, a s s u m i n g t y p i c a l v a r i a b i l i t y 55 6. T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g i n s t a n d s w i t h t h r e e s p e c i e s compared w i t h 3P u s i n g t h e volume e q u a t i o n t r e e measurement method, a s s u m i n g t y p i c a l v a r i a b i l i t y , and a d j u s t e d t o normal p a c e 57 ACKNOWLEDGEMENTS The a u t h o r w i s h e s t o a c k n o w l e d g e t h e h e l p and a d v i c e of h i s p r i n c i p a l a d v i s o r , D r . J u l i e n P. D e m a e r s c h a l k , whose g u i d a n c e was i n v a l u a b l e and g r e a t l y a p p r e c i a t e d . The a d v i c e and o p i n i o n s o f Dr. Kim l i e s , b i o m e t r i c i a n a t M a c m i l l a n B l o e d e l L i m i t e d , were w e i g h t e d h e a v i l y , and a p p r e c i a t e d . C o n s u l t a t i o n s w i t h D r . A. Kozak were a l s o q u i t e v a l u a b l e . F i n a l l y , t h a n k s t o D r . P e t e r L. M a r s h a l l f o r t h e a d v i c e and f e e d b a c k . 1 INTRODUCTION In any f o r e s t i n v e n t o r y , t h e r e a r e t h r e e w i d e l y r e c o g n i z e d s o u r c e s o f e r r o r : 1) e r r o r due t o t h e c h a n c e l o c a t i o n of sample p l o t s , o r s a m p l i n g e r r o r , 2) e r r o r due t o t h e volume t a b l e s o r t h e method u s e d t o p r e d i c t o r o b t a i n i n d i v i d u a l t r e e v o lumes, and 3) measurement e r r o r ( C u n i a 1965). In c u t b l o c k volume d e t e r m i n a t i o n , p e r f o r m e d t o t h e s t a n d a r d s f o r p o i n t s a m p l i n g s e t f o r t h by t h e B r i t i s h C o l u m b i a M i n i s t r y o f F o r e s t s (BCMF), an a d d i t i o n a l s o u r c e o f e r r o r must be r e c o g n i z e d : 4) e r r o r due t o t h e h e i g h t / d b h r e g r e s s i o n c o n s t r u c t e d f o r e a c h i n d i v i d u a l s p e c i e s i n e a c h d i f f e r i n g s t a n d t y p e (BCMF 1982). The f i r s t s o u r c e of e r r o r can e a s i l y be d e t e r m i n e d . I t i s c h i e f l y a f u n c t i o n of s a m p l i n g d e s i g n and sample s i z e and i t i s a l w a y s c a l c u l a t e d . A c c o r d i n g t o t h e Manual of C r u i s i n g P r o c e d u r e s and C r u i s e C o m p i l a t i o n (BCMF 1982), when stumpage a s s e s s m e n t i s b a s e d on t h e s c a l e , t h e c r u i s e s h o u l d be d e s i g n e d t o y i e l d a s a m p l i n g e r r o r o f + o r - 15% t o t h e c l o s e u t i l i z a t i o n s t a n d a r d , 19 t i m e s o u t of 20. However, when p o i n t s a m p l i n g i s c o n s i d e r e d , and t h e c u t t i n g b l o c k i s l e s s t h a n or e q u a l t o 10 ha, t h e s t a t i s t i c a l f o r m u l a f o r e s t i m a t i n g t h e sample s i z e needed t o meet t h i s e r r o r o b j e c t i v e f r e q u e n t l y g i v e s a sample s i z e t h a t seems a b s u r d l y h i g h . The s a m p l i n g i n t e n s i t y i s e i t h e r much t o o g r e a t from a l o g i c a l , i n t u i t i v e s t a n d p o i n t , or i t w i l l c a u s e t h e s a m p l e r t o c o n s i d e r a 100% c r u i s e (a 100% c r u i s e i s c o n s i d e r e d , a c c o r d i n g t o t h e c r u i s e manual, when g r e a t e r t h a n 50% of t h e a r e a must be sampled t o a c h i e v e t h e e r r o r o b j e c t i v e ) . The s a m p l e r may c h o o s e t o " d e f a u l t " t o t h e minimum r e q u i r e m e n t , w h i c h i s one p l o t p e r ha, p r o v i d e d t h e r e a r e a t l e a s t 4 p l o t s p e r t y p e , but he may 2 r u n a g r e a t e r r i s k of n o t m e e t i n g t h e c r u i s e o b j e c t i v e . A s i m i l a r s i t u a t i o n e x i s t s when p l a n n i n g f o r c r u i s e - b a s e d stumpage a s s e s s m e n t , a l t h o u g h th e s a m p l i n g e r r o r r e q u i r e m e n t s a r e a l i t t l e d i f f e r e n t . T h i s c a n be a p r o b l e m i n t h a t a 100% c r u i s e may be p e r f o r m e d u n n e c e s s a r i l y , o r t h e r e q u i r e d e r r o r o b j e c t i v e may n o t be met. E r r o r component 3) i s o f t e n assumed t o be n e g l i g i b l e i f g r e a t c a r e i s t a k e n i n o b t a i n i n g t r e e measurements. As r e g a r d s s o u r c e 2 ) , B r i c k e l l (1976) a s s e r t e d t h a t p r o p e r use o f volume t a b l e s u s u a l l y r e q u i r e s c h e c k i n g them a g a i n s t a sample o f t r e e s measured by d i r e c t methods (volumes computed from a s e r i e s of stem measurements on s t a n d i n g t r e e s , or water d i s p l a c e m e n t t e c h n i q u e s ) and a d j u s t e d i f n e c e s s a r y . T h i s i s b e c a u s e most volume t a b l e s a r e not b a s e d on a sample drawn from t h e p o p u l a t i o n s t o w h i c h t h e y w i l l be a p p l i e d . T h e r e may be no r e a s o n , i n some c a s e s , t o suppose t h a t t h e p o p u l a t i o n s a r e g r e a t l y d i f f e r e n t , however, b i a s e d volumes may r e s u l t i f t h e a s s u m p t i o n of e q u a l i t y i s not t e s t e d . U s u a l l y , volume t a b l e s p r e d i c t volumes o n l y f o r u ndeformed, s i n g l e stemmed ( o r "normal") t r e e s , t h e r e f o r e , e s t i m a t e s may be r e l i a b l e f o r w e l l managed s t a n d s , where t h e r e a r e few a b n o r m a l t r e e s , but p e r h a p s not f o r more w i l d or u n t e n d e d s t a n d s . G r o s e n b a u g h (1964) i n t r o d u c e d 3-P ( P r o b a b i l i t y P r o p o r t i o n a l t o P r e d i c t i o n ) s a m p l i n g t o f o r e s t r y w h i c h e l i m i n a t e s t h e use o f volume t a b l e s and h e i g h t / d b h r e g r e s s i o n s , t h u s r e m o v i n g t h e s e s o u r c e s of e r r o r f r o m t h e t o t a l volume p e r h e c t a r e i n v e n t o r y e s t i m a t e . In a c t u a l p r a c t i c e , t h e e r r o r c o n t r i b u t i o n of t h e s e s o u r c e s i s s e l d o m c a l c u l a t e d , but knowing f o r c e r t a i n t h a t t h e y a r e n o t p r e s e n t w i l l g i v e more c r e d e n c e t o t h e s a m p l i n g e r r o r 3 t h a t i_s c a l c u l a t e d . A sample of d i r e c t t r e e measurements o v e r a f o r e s t a r e a i s r e q u i r e d by 3-P w i t h d e n d r o m e t r y . T h i s s a m p l i n g s y s t e m i s a l s o s t a t i s t i c a l l y v e r y e f f i c i e n t , i n t h a t i t can p r o d u c e e s t i m a t e s t h a t a r e e x t r e m e l y p r e c i s e (low v a r i a n c e ) . The i m p l i c a t i o n s o f t h i s f a c t a r e c l e a r . Fewer sa m p l e s a r e r e q u i r e d t o meet t h e c r u i s e o b j e c t i v e s , w h i c h e l i m i n a t e s t h e need f o r c o n s i d e r a t i o n o f 100% e n u m e r a t i o n i n s m a l l e r b l o c k s i z e s , and t h e e x e c u t i o n of much t o o i n t e n s i v e s u r v e y s . D i r e c t measurements o f t r e e volume a r e u s u a l l y o b t a i n e d by m e a s u r i n g f e l l e d t r e e s . However, t h e r e a r e many i n s t a n c e s when f e l l i n g t r e e s i s not p r a c t i c a l . F o r example, i f t h e f e l l e d t r e e s a r e a v a l u a b l e s p e c i e s and r e m a i n i n t h e woods t o o l o n g a f t e r t h e c r u i s e so t h a t p o t e n t i a l f o r d e c a y o r s t a i n i n c r e a s e s , or i f t h e y a r e c r o p t r e e s under r o t a t i o n age, t h e y m i g h t n o t be u t i l i z e d . In a d d i t i o n t o l o s s of v a l u e and g r o w i n g s t o c k , t h e f e l l e d t r e e s p r o v i d e b r e e d i n g p l a c e s f o r c e r t a i n i n s e c t s and p e s t s , and i n c r e a s e f o r e s t f i r e h a z a r d ( B r i c k e l l 1976). Sample t r e e s m i g h t no t be t h e p r o p e r t y of t h e p a r t y o r age n c y c o n d u c t i n g t h e s u r v e y , hence f e l l i n g them may be p r o h i b i t e d . In some c a s e s , t h e t r e e s may be l o c a t e d on permanent sample p l o t s and c a n n o t be d e s t r o y e d . C l i m b i n g t r e e s seems t o be an a l t e r n a t i v e t o f e l l i n g , b u t has d i s a d v a n t a g e s . F o r example, s p u r s may i n j u r e t r e e s and p r o v i d e pathways f o r d i s e a s e e n t r y . O f t e n , l o n g l a d d e r s a r e t o o u n w i e l d l y and heavy t o c a r r y t h r o u g h t h e woods ( B r i c k e l l 1976). A l s o , James and Kozak (1984) h y p o t h e s i z e d t h a t i t i s v e r y l i k e l y t h a t s t a n d i n g t r e e measurement w i t h i n s t r u m e n t s s u c h as t h e B a r r and S t r o u d o p t i c a l d e n d r o m e t e r w i l l be e f f i c i e n t and c o s t e f f e c t i v e when compared w i t h f e l l e d t r e e measurement. F o r t h e s e r e a s o n s , much a t t e n t i o n has t u r n e d t o t h e use of o p t i c a l d e n d r o m e t r y w h i c h 4 e n a b l e s t h e measurement of d i a m e t e r s a t v a r i o u s h e i g h t s on t h e s t a n d i n g t r e e w h i l e t h e o p e r a t o r r e m a i n s on t h e g r o u n d . Much l i t e r a t u r e e x i s t s on 3-P s a m p l i n g and d e n d r o m e t r y . The method i s known t o be a h i g h l y e f f i c i e n t t e c h n i q u e b e c a u s e i t e m ploys v a r i a b l e sample t r e e s e l e c t i o n p r o b a b i l i t i e s as does p o i n t s a m p l i n g . However, u n l i k e p o i n t s a m p l i n g , t o e f f e c t t h e 3-P method, an e s t i m a t e ( o c u l a r p r e d i c t i o n ) of volume must be made on e v e r y t r e e i n t h e s t a n d , w h i c h has l o g i c a l l y l e d t o t h e b e l i e f t h a t i t becomes i m p r a c t i c a l i n l a r g e r s t a n d s . A s t u d y w h i c h e s t a b l i s h e s a p r a c t i c a l upper l i m i t t o s t a n d s i z e has n e v e r been p u b l i s h e d . T h i s s t u d y was c o n d u c t e d t o d e t e r m i n e whether 3-P s a m p l i n g , o r r a t i o e s t i m a t i o n , w i t h any o f t h r e e d i f f e r i n g sample t r e e measurement t e c h n i q u e s , i s more e f f i c i e n t t h a n p o i n t s a m p l i n g i n F o r e s t I n v e n t o r y Zone C ( S o u t h C o a s t of B r i t i s h C o l u m b i a ) . T h r e e sample t r e e measurement methods were c o n s i d e r e d f o r use w i t h 3-P and r a t i o e s t i m a t i o n . They a r e : 1) measurement o f d i a m e t e r and h e i g h t f o r e n t r y i n t o an a p p r o p r i a t e volume t a b l e (volume e q u a t i o n , t a p e r e q u a t i o n ) , 2) measurement o f s e v e r a l d i a m e t e r s and a s s o c i a t e d h e i g h t s a l o n g t h e stem of the t r e e w i t h t h e w ide-s c a l e r e l a s k o p , and 3) measurement of s e v e r a l d i a m e t e r s and a s s o c i a t e d h e i g h t s w i t h t h e B a r r and S t r o u d o p t i c a l d e n d r o m e t e r . R a t i o e s t i m a t i o n has n o t w i d e l y been u s e d o r t e s t e d as an o n - t h e - g r o u n d method o f t i m b e r c r u i s i n g , where t h e a u x i l i a r y v a r i a b l e i s an o c u l a r p r e d i c t i o n , but has been p r e v i o u s l y d e s c r i b e d i n o t h e r f o r e s t r y a p p l i c a t i o n s ( e . g . , F r e e s e 1962). S p e c i f i c a l l y , t h e o b j e c t i v e s i n t h i s s t u d y a r e as f o l l o w s : 1) q u a n t i f y t h e e f f e c t s of c u t t i n g b l o c k s i z e on t h e c o s t ( m e a s u r e d as t o t a l c r u i s e t i m e ) t o o b t a i n a g i v e n p r e c i s i o n 5 ( p e r c e n t e r r o r o f t o t a l ) , 2) compare t h e c o s t of 3-P, r a t i o e s t i m a t i o n , and p o i n t s a m p l i n g , and 3) make recommendations as t o w h i c h method i s most e f f i c i e n t u n der c o n d i t i o n s l i k e l y t o be e n c o u n t e r e d i n F o r e s t I n v e n t o r y Zone C. SAMPLING TECHNIQUES USED 6 The t h r e e s a m p l i n g t e c h n i q u e s r e l e v a n t t o t h i s s t u d y a r e : 1) P o i n t s a m p l i n g 2) 3-P s a m p l i n g 3) R a t i o e s t i m a t i o n . A b r i e f d e s c r i p t i o n o f t h e f u n d a m e n t a l w o r k i n g c o n c e p t s of e a c h t e c h n i q u e w i l l be g i v e n a l o n g w i t h f o r m u l a s f o r sample s i z e e s t i m a t i o n , f o r T s , t h e sample b a s e d e s t i m a t o r of t h e p o p u l a t i o n t o t a l , f o r v ( T s ) , t h e sample b a s e d e s t i m a t o r of t h e v a r i a n c e o f T s , f o r E T s , t h e p r o b a b l e e r r o r o f t h e e s t i m a t e of t h e t o t a l , and f o r c o n f i d e n c e l i m i t s . F o r f u r t h e r i n f o r m a t i o n and r i g o r o u s m a t h e m a t i c a l p r o o f s o f t h e i r s t a t i s t i c a l v a l i d i t y , t h e r e a d e r i s r e f e r r e d t o t h e a p p r o p r i a t e l i t e r a t u r e . 1 . 3-P SAMPLING The f i r s t s t e p i n c o n d u c t i n g a 3-P c r u i s e , as w i t h any s u r v e y , i s d e c i d i n g what s i z e sample, n, s h o u l d be drawn. T h i s i s u s u a l l y done w i t h s t a t i s t i c a l c o n s i d e r a t i o n s i n mind and t h e a p p r o p r i a t e f o r m u l a f o r sample s i z e when s a m p l i n g from a f i n i t e p o p u l a t i o n i s : t 2 * C 2 * N n = (1 ) t 2 C 2 + ND 2 7 where, N = number o f i n d i v i d u a l s i n p o p u l a t i o n , D = d e s i r e d s a m p l i n g e r r o r l i m i t e x p r e s s e d as a d e c i m a l f r a c t i o n of t h e mean, m: t * s m / m , where s m i s s t a n d a r d e r r o r of t h e mean, t as below, t = a v a l u e of S t u d e n t ' s t s t a t i s t i c w i t h a p p r o p r i a t e t y p e I e r r o r p r o b a b i l i t y and d e g r e e s o f f r e e d o m , and C = c o e f f i c i e n t of v a r i a t i o n w h i c h e x p r e s s e s t h e s t a n d a r d d e v i a t i o n o f o b s e r v a t i o n s a s a d e c i m a l f r a c t i o n of t h e mean: s/m, where s i s t h e s t a n d a r d d e v i a t i o n of o b s e r v a t i o n s . O f t e n , N i s not known i n a d v a n c e of s a m p l i n g , o r i s assumed t o be v e r y l a r g e , and t h e f o r m u l a becomes: t 2 * C 2 n = - . (2) The o n l y c o n s e q u e n c e of a s s u m i n g N l a r g e when i t r e a l l y i s n ' t i s t h e p o s s i b i l i t y o f g r e a t e r p r e c i s i o n t h a n p l a n n e d w i t h a c o r r e s p o n d i n g i n c r e a s e i n c o s t . I t i s n o t e w o r t h y t h a t C i n most s a m p l i n g p l a n s r e f e r s t o t h e d i s p e r s i o n o f i n d i v i d u a l t r e e v o l u m e s a r o u n d t h e a v e r a g e volume p e r t r e e o r t h e d i s p e r s i o n o f p l o t v o l u m e s a r o u n d t h e a v e r a g e volume p e r p l o t , e x p r e s s e d a s a p e r c e n t a g e o f mean t r e e volume o r mean p l o t volume. W i t h 3-P, C r e f e r s t o t h e d i s p e r s i o n of t h e r a t i o s of measured volume t o p r e d i c t e d volume f o r i n d i v i d u a l t r e e s a r o u n d t h e a v e r a g e r a t i o . So, w i t h most c o n v e n t i o n a l s a m p l i n g t e c h n i q u e s , t h e c o e f f i c i e n t of v a r i a t i o n i s s u b j e c t t o t h e volume d i s p e r s i o n a s i t happens t o e x i s t . T h i s v a r i a t i o n i s u s u a l l y l a r g e even w i t h s t r a t i f i c a t i o n 8 by d i a m e t e r c l a s s e s , g e n e r a l l y n o t much l o w e r t h a n 35%. W i t h 3-P, C d e pends on t h e p r e d i c t o r ' s s k i l l . I t i s a measure of t h e c o n s i s t e n c y w i t h w h i c h he c a n p r e d i c t v o l u m e s . I t i s o f no c o n s e q u e n c e whether he can p r e d i c t " o n - t h e - n o s e " o r n o t . A l l t h a t i s r e q u i r e d i s t h a t he p r e d i c t i n a manner s u c h t h a t a p p r o x i m a t e l y t h e same r a t i o o f a c t u a l t o p r e d i c t e d volume w i l l r e s u l t f o r e v e r y sample t r e e m e a s u r e d . B e g i n n e r s may be e x p e c t e d t o a c h i e v e a r o u n d 25 t o 30%, whereas t r a i n e d c r u i s e r s c a n r e a d i l y a t t a i n 15 t o 20% (Mesavage 1971). The s e c o n d s t e p i s t o make a r o u g h e s t i m a t e o f t h e t o t a l s a l e volume, d e n o t e d by X, w h i c h s t a n d s f o r t h e sum of t h e c r u i s e r ' s p r e d i c t i o n s of e a c h t r e e ' s volume. The o b j e c t i s t o s e l e c t one sample t r e e f o r e a c h a c c u m u l a t i o n o f p r e d i c t i o n s t h a t t o t a l s t o X L = . (3) n T h i r d , t h i s q u a n t i t y L i s t h e l a r g e s t random number t h a t w i l l be g e n e r a t e d f o r t h e l i s t t h a t i s t a k e n i n t o t h e f i e l d . The w r i t e r has f o u n d i t e x t r e m e l y d i f f i c u l t t o p r e d i c t t r e e v olumes t o g r e a t e r p r e c i s i o n t h a n 0.1 m^ so numbers s h o u l d be g e n e r a t e d from 0.1 up t o L. As many numbers s h o u l d be g e n e r a t e d as t h e r e a r e t r e e s e x p e c t e d i n t h e s a l e ( e x t r a , u n u s e d random numbers a r e c h e a p ) . 9 F o u r t h , when i n t h e f i e l d , f o r e a c h t r e e : a. P r e d i c t g r o s s t o t a l volume, x^, d i r e c t l y or i n d i r e c t l y u s i n g a volume t a b l e . b. R e c o r d t h e e s t i m a t e . c . Draw a number from t h e random number l i s t . I f t h e p r e d i c t i o n , x^, f o r t h e t r e e i s g r e a t e r t h a n or e q u a l t o t h e random number drawn, t h e t r e e s h o u l d be m e asured a c c u r a t e l y f o r volume and i s c o n s i d e r e d " s e l e c t e d " as a sample t r e e . I f t h e random number drawn i s g r e a t e r t h a n t h e p r e d i c t i o n , x^, f o r t h a t t r e e , n o t h i n g more i s r e q u i r e d , i . e . , i t i s " r e j e c t e d " and n o t s a m p l e d . T h i s p r o c e d u r e s e l e c t s l a r g e r t r e e s w i t h g r e a t e r p r o b a b i l i t y i n t h e f o l l o w i n g manner. Suppose t h e random number l i s t has i n t e g e r s r a n g i n g f r o m 1 t o 2 0 . W i t h t h e s e l e c t i o n s y s t e m j u s t d e s c r i b e d , a t r e e w i t h a p r e d i c t i o n of 1 would have o n l y one c h a n c e i n 20 t o q u a l i f y as a sample ( t o be c a r e f u l l y measured f o r v o l u m e ) . A t r e e w i t h a p r e d i c t e d volume of 15, however, would have 15 c h a n c e s i n t w e n t y o f b e i n g s e l e c t e d , b e c a u s e i t s p r e d i c t e d volume i s g r e a t e r t h a n o r e q u a l t o 15 numbers a p p e a r i n g on t h e l i s t . Thus, t h e p r o b a b i l i t y o f s e l e c t i o n i s c l e a r l y p r o p o r t i o n a l t o p r e d i c t i o n . F i f t h , c r u i s e s t a t i s t i c s a r e c a l c u l a t e d . The sample s i z e a c t u a l l y o b t a i n e d when t h e c r u i s e i s f i n i s h e d may be s l i g h t l y d i f f e r e n t t h a n p l a n n e d w i t h t h e 3-P method f o r two r e a s o n s . The sample t r e e s e l e c t i o n p r o b a b i l i t i e s a r e a p p r o x i m a t e ( r e c a l l t h e e s t i m a t e of t h e sum of p r e d i c t i o n s , o r t o t a l volume, n e c e s s a r y p r i o r t o f i e l d p r o c e d u r e s ) . So, when t h e c r u i s e i s c o m p l e t e d , i t may t u r n o u t t h a t some t r e e s may have r e c e i v e d a s l i g h t l y g r e a t e r s e l e c t i o n p r o b a b i l i t y or a s l i g h t l y r e d u c e d p r o b a b i l i t y . A l s o , sample s i z e v a r i e s r a n d o m l y due t o t h e n a t u r e of t h e s e l e c t i o n p r o b a b i l i t i e s t h e m s e l v e s . An e v e n t may s t i l l o c c u r even t h o u g h i t has an e x t r e m e l y low p r o b a b i l i t y , o r v i c e v e r s a . F o r t h i s r e a s o n , t h e sample s i z e g i v e n by (1) o r ( 2 ) i s c a l l e d t h e " e x p e c t e d " sample s i z e , o r n E . A g i v e n sample s i z e can be i n s u r e d , however, i n a s t a t i s t i c a l l y c o r r e c t way i f t h i s o b j e c t i v e i s a b s o l u t e l y i m p o r t a n t . S i m p l y i n f l a t e n E o v e r what t h e f o r m u l a g i v e s , and a f t e r a l l t h e sample t r e e s have been s e l e c t e d , r a n d o m l y e l m i n a t e t h e number o f sample t r e e s i n e x c e s s of t h e d e s i r e d n E . The e s t i m a t e d t o t a l volume i s g i v e n by what i s c a l l e d t h e a d j u s t e d e s t i m a t o r : T S = X T * ( £ ( y i / x i ) / n ) (4) l where, X T= Y.xi , summing o v e r i = 1,N or t h e t o t a l o f a l l t h e c r u i s e r ' s p r e d i c t i o n s a f t e r t h e c r u i s e i s c o m p l e t e d , y^= a c t u a l m easured volume on t r e e " i " x^= o c u l a r p r e d i c t i o n of volume on t r e e " i " . n = sample s i z e a c t u a l l y o b t a i n e d . T h i s e s t i m a t o r i s c a l l e d a d j u s t e d b e c a u s e i t makes use of a l l t h e o c u l a r p r e d i c t i o n s . A l t h o u g h t h e r e i s an u n a d j u s t e d e s t i m a t o r , w h i c h does not r e q u i r e knowledge o f t h e sum of a l l t h e o c u l a r p r e d i c t i o n s , t h e a d j u s t e d e s t i m a t o r i s a l w a y s u s e d i n p r a c t i c e b e c a u s e i t y i e l d s more p r e c i s e e s t i m a t e s . F u r t h e r d i s c u s s i o n a p p e a r s i n t h e L i t e r a t u r e Review s e c t i o n . T h e r e seems t o be some argument as t o t h e b e s t a p p r o x i m a t i o n f o r c a l c u l a t i n g t h e v a r i a n c e of t h i s e s t i m a t e from a sample. A v e r y good, s t a b l e , r e l i a b l e e s t i m a t o r i s : 11 X T 2 ( 1 - n p / N ) n n V(T S) =—i * { I ( y i / X i ) 2 - 1/n<£ Y i A i ) 2 } (5) n ( n - 1 ) I I where n, as a b o v e , i s t h e a c t u a l sample s i z e o b t a i n e d a f t e r s a m p l i n g i s c o m p l e t e d . A d e t a i l e d d i s c u s s i o n of s t a t i s t i c a l t h e o r y c an be f o u n d i n G r o s e n b a u g h (1965) o r S c h r e u d e r , e t a l . ( 1 9 6 8 ) . The p r o b a b l e s a m p l i n g e r r o r f o r t h e e s t i m a t e Tg, i s g i v e n by: E T s = t * s T s (5A) where: s T s = "^/ v( Ts) an& t * s a s b e f o r e . To f i n d t h e upper and l o w e r c o n f i d e n c e l i m i t s w i t h t h e same p r o b a b i l i t y a s s o c i a t e d w i t h t i n ( 5 A ) , s i m p l y f i n d t h e s o l u t i o n t o t h e f o l l o w i n g e q u a t i o n s : U = T s + E T s L = T s - E T s where: U = upper c o n f i d e n c e l i m i t L = l o w e r c o n f i d e n c e l i m i t . The r a n g e o f v a l u e s from L t o U i s known a s t h e c o n f i d e n c e i n t e r v a l . 1 2 2 . RATIO ESTIMATION R a t i o e s t i m a t o r s c a n i n c r e a s e t h e p r e c i s i o n o f a sample by making use o f s u p p l e m e n t a r y i n f o r m a t i o n a b o u t t h e p o p u l a t i o n b e i n g s t u d i e d . F o r example, i f t h e b a s a l a r e a of a s t a n d of t i m b e r i s e x a c t l y known ( t h e s u p p l e m e n t a r y i n f o r m a t i o n ) , t h e r e l a t i o n s h i p between volume and b a s a l a r e a may h e l p t o improve t h e e s t i m a t e of volume. A r a t i o e s t i m a t o r w i l l i n c r e a s e t h e p r e c i s i o n of t h i s volume e s t i m a t e by r e d u c i n g t h e v a r i a b i l i t y of t r e e volumes as t h e y e x i s t i n t h e f o r e s t , t o a s m a l l r e s i d u a l v a r i a n c e t h a t i s u n e x p l a i n e d by t h e r e l a t i o n s h i p between volume and b a s a l a r e a . In t h i s s t u d y , a d i r e c t o c u l a r p r e d i c t i o n o f volume i s t h e a u x i l i a r y i n f o r m a t i o n . As w i t h 3-P, t h e a u x i l i a r y v a r i a b l e , x^, w i l l be p o s i t i v e l y c o r r e l a t e d w i t h y^, t h e v a r i a b l e o f i n t e r e s t (volume i n t h i s c a s e ) , but u n l i k e 3-P, t r e e s w i l l n o t be s e l e c t e d w i t h v a r y i n g p r o b a b i l i t i e s . As a r e s u l t , t h e v a r i a n c e o f t h i s e s t i m a t o r may be l a r g e r t h a n t h e 3-P e s t i m a t o r . A g a i n , t h e f i r s t s t e p i n p l a n n i n g a c r u i s e i n w h i c h a r a t i o e s t i m a t o r w i l l be u s e d i s t o s e l e c t an a p p r o p r i a t e sample s i z e . E q u a t i o n ( 1 ) s h o u l d be u s e d . T h i s i s n a t u r a l l y p r e c e d e d by making an e s t i m a t e o f t h e t o t a l number o f t r e e s i n t h e c r u i s e , N. S t e p two i n v o l v e s d e c i d i n g how t h e sample t r e e s s h o u l d be s e l e c t e d . O f t e n i t i s most e a s y and c o n v e n i e n t t o s e l e c t t h e t r e e s s y s t e m a t i c a l l y , i n w h i c h c a s e , e v e r y k1-*1 t r e e w i l l be s e l e c t e d f o r a c c u r a t e measurement, where k = N/n . (6) T h e r e i s much c o n c e r n o v e r t h e r e l i a b i l i t y o f e s t i m a t e s f r o m a 13 s i n g l e s y s t e m a t i c sample ( C o c h r a n 1977, c h p t . 8 ) . In g e n e r a l i t i s t r u e , however, t h a t as l o n g a s t h e r e i s no c y c l i c p a t t e r n t h a t t h e a t t r i b u t e of i n t e r e s t d i s p l a y s , f r o m t h e f i r s t i n d i v i d u a l o b s e r v e d t o t h e l a s t , a s y s t e m a t i c sample can be t r e a t e d as i f i t were random. The mean ( o r t o t a l ) w i l l be u n b i a s e d , and t h e e s t i m a t e of v a r i a n c e w i l l be c o n s e r v a t i v e . A s y s t e m a t i c sample more c l o s e l y a p p r o x i m a t e s a t r u l y random one i f m u l t i p l e random s t a r t s a r e u s e d . F o r example, s e l e c t i n g one i n d i v i d u a l a t random from e v e r y g r o u p o f k i n d i v i d u a l s w o u l d be t h e e x t r e m e c a s e of m u l t i p l e random s t a r t s . T h i s can be h a n d l e d w i t h a l i s t of random numbers a g a i n , but s e l e c t i n g t h e i n d i v i d u a l s w i l l be a b i t more t i m e c o n s u m i n g . T h i r d , when i n t h e f i e l d , f o r e a c h t r e e : a . P r e d i c t g r o s s t o t a l t r e e volume x^, d i r e c t l y o r i n d i r e c t l y w i t h t h e use of a volume t a b l e . b. r e c o r d t h e e s t i m a t e . I f t h e t r e e i s t h e n e x t k t h i n d i v i d u a l , t h e t r e e s h o u l d be measured a c c u r a t e l y f o r volume and i s c o n s i d e r e d " s e l e c t e d " as a sample t r e e . I f i t i s n o t t h e n e x t k*-*1 t r e e , n o t h i n g more i s r e q u i r e d , i . e . , i t i s " r e j e c t e d " and n o t s a m p l e d . F o u r t h , c r u i s e s t a t i s t i c s a r e c a l c u l a t e d . E s t i m a t e d t o t a l volume i s g i v e n by t h e m e a n - o f - r a t i o s e s t i m a t o r : T s = X T * ( £ ( y i / x i ) / n ) (7) l where a l l v a r i a b l e s a r e d e f i n e d as b e f o r e . S i m i l a r i t y w i t h t h e 3-P e s t i m a t o r i s e v i d e n t . The a p p r o p r i a t e n e s s of t h e m e a n - o f - r a t i o s e s t i m a t o r w i l l be d i s c u s s e d s h o r t l y . The sample b a s e d e s t i m a t e o f v a r i a n c e f o r t h e t o t a l i s : 14 v ( T s ) =-X T 2 ( 1 - n / N ) n ( n - 1 ) { t ( y i / x i ) 2 ~ 1/ n< t y i / x i ) 2 > (7) where a l l v a r i a b l e s a r e d e f i n e d a s b e f o r e . The p r o b a b l e e r r o r o f t h e t o t a l e s t i m a t e and t h e c o n f i d e n c e l i m i t s a r e computed e x a c t l y t h e same as f o r t h e 3-P e s t i m a t o r . M e r e l y s u b s t i t u t e t h e f o r m u l a s g i v e n i n t h i s s e c t i o n f o r T s and v ( T g ) w h e r e v e r t h e s e symbols a p p e a r i n t h e e q u a t i o n s f o r E, U and L p r e s e n t e d i n t h e 3-P s a m p l i n g s e c t i o n . The m e a n - o f - r a t i o s e s t i m a t o r i s a p p r o p r i a t e i n s i t u a t i o n s where t h e f o l l o w i n g c o n d i t i o n s h o l d : i ) t h e r e g r e s s i o n o f y on x i s l i n e a r and t h r o u g h t h e o r i g i n i i ) t h e v a r i a n c e o f y^ a b o u t th e r e g r e s s i o n l i n e i s p r o p o r t i o n a l t o x ^ 2 . An a l t e r n a t e r a t i o e s t i m a t o r i s c a l l e d t h e r a t i o - o f - m e a n s . C o n d i t i o n s most a p p r o p r i a t e f o r i t s use a r e d i f f e r e n t from t h e m e a n - o f - r a t i o s o n l y i n i i ) t h e v a r i a n c e o f y^ a b o u t t h e r e g r e s s i o n l i n e i s p r o p o r t i o n a l t o x^ ( i n s t e a d of x ^ 2 ) . A Monte C a r l o s t u d y by Ek (1971) s u g g e s t e d t h a t t h e r a t i o - o f - m e a n s e s t i m a t o r may be more r o b u s t and c o n t a i n l e s s b i a s t h a n t h e m e a n - o f - r a t i o s e s t i m a t o r when t h e c o n d i t i o n s a p p r o p r i a t e f o r t h e u s e o f e a c h a r e n o t met. However, as C o c h r a n (1977, 1 5 c h p t . 6 ) s u g g e s t e d , a p l o t t i n g of sample v a l u e s a g a i n s t t h o s e of x^ i s h e l p f u l i n e x a m i n i n g w h i c h , i f any, o f t h e s e c o n d i t i o n s h o l d . I t i s t h e w r i t e r ' s e x p e r i e n c e t h a t , when x^ i s a d i r e c t o c u l a r e s t i m a t e of volume, t h e v a r i a n c e o f y^ i s u s u a l l y p r o p o r t i o n a l t o x^ , making t h e a p p r o p r i a t e e s t i m a t o r t h e m e a n - o f - r a t i o s . 3. POINT SAMPLING T h i s s a m p l i n g t e c h n i q u e was f i r s t d e s c r i b e d i n N o r t h A m e r i c a by G r o s e n b a u g h ( 1 9 5 2 ) . S i n c e t h e n , i t has been d e s c r i b e d f u r t h e r w i t h numerous examples ( e . g . , D i l w o r t h and B e l l 1967), and has been d e s c r i b e d i n s t a n d a r d m e n s u r a t i o n t e x t s ( e . g . Husch, e t a l . 1972) . The f i r s t s t e p , a g a i n , i s e s t i m a t i o n o f sample s i z e w i t h f o r m u l a ( 1 ) . Many f o r e s t e r s f e e l t h a t p o i n t s a m p l i n g i s c o n g r u e n t t o s a m p l i n g from an i n f i n i t e p o p u l a t i o n , o r e q u i v a l e n t l y , s a m p l i n g from a f i n i t e p o p u l a t i o n w i t h r e p l a c e m e n t . T h i s b e l i e f has f o l l o w e d from t h e way s a m p l e s a r e s e l e c t e d w i t h t h i s t e c h n i q u e . A p o i n t i s c h o s e n t o l o c a t e t h e " p l o t " c e n t e r , w h i c h has l e d t o t h e b e l i e f t h a t t h e t e c h n i q u e s e l e c t s " p o i n t s " a s s a m p l e s , and of c o u r s e t h e r e a r e an i n f i n i t e number o f p o i n t s i n any t r a c t o f l a n d . However, t r e e s , or g r o u p s o f them, n o t p o i n t s , a r e s t i l l t h e sample u n i t s and t h e r e i s a f i n i t e number o f t r e e s i n any t r a c t of l a n d . C u n i a (1959) gave p r o o f t h a t t h e e x p e c t e d c r u i s e i n t e n s i t y (n/N) f o r a g i v e n c r i t i c a l a n g l e c a n be computed 16 from 3 t h i n g s : 1) number o f sample p o i n t s , 2) a v e r a g e b a s a l a r e a p e r t r e e , 3) t o t a l a r e a t o be c r u i s e d . T h i s c a n be g e n e r a l i z e d f o r any c r i t i c a l a n g l e t o a r r i v e a t t h e f o l l o w i n g f o r m u l a f o r e s t i m a t i n g sample s i z e : t 2 C 2 A F n = — - , (8) A F D 2 + g t 2 C 2 where C = t h e d i s p e r s i o n of p l o t volumes a r o u n d t h e mean p l o t volume e x p r e s s e d a s a d e c i m a l f r a c t i o n of t h e mean ( i n s t e a d of t h e d i s p e r s i o n o f i n d i v i d u a l r a t i o s a r o u n d t h e mean r a t i o a s b e f o r e ) , F = b a s a l a r e a f a c t o r t o be u s e d ( m 2 / h a ) , A = s t a n d ( c r u i s e ) a r e a i n ha, g = a v e r a g e b a s a l a r e a p e r t r e e , a l l o t h e r v a r i a b l e s as b e f o r e ( p r o o f i n a p p e n d i x 1 ) . Second, i n t h e f i e l d , a f i x e d h o r i z o n t a l a n g l e i s p r o j e c t e d s u b t e n d i n g t h e p l o t c e n t e r and r o t a t e d 360 d e g r e e s , on e a c h of th e n p o i n t s . P o i n t s a r e u s u a l l y l o c a t e d on t h e i n t e r s e c t i o n s of l i n e s b e l o n g i n g t o an i m a g i n a r y g r i d p a t t e r n , t h e s p a c i n g of t h e l i n e s d e p e n d i n g on d e s i r e d c r u i s e i n t e n s i t y . T r e e s whose d i a m e t e r s a p p e a r l a r g e r t h a n t h i s c r i t i c a l a n g l e a r e t a l l i e d and measured f o r dbh, and sometimes h e i g h t , and t h e s e v a l u e s a r e r e c o r d e d . 17 T h i r d , c r u i s e s t a t i s t i c s a r e c a l c u l a t e d . The a c t u a l volume of t h e t r e e s s e l e c t e d a t e a c h p l o t i s unknown but i s u s u a l l y e s t i m a t e d by a p p r o p r i a t e volume t a b l e s . The e s t i m a t e of t o t a l volume i s : A F n m^  T S = {t I < y i j / 9 i j > J <9> n 1 D where = Number o f " i n " t r e e s on p l o t " i " , and g j j = b a s a l a r e a o f t r e e j on p l o t i , j = 1,...,mj w i t h o t h e r v a r i a b l e s a s b e f o r e . The sample b a s e d e s t i m a t e o f v a r i a n c e i s : A 2 F 2 ( 1 - g n / A F ) n m: n m; V ( T S ) - — £ ( £ y i j / 9 i j ) 2 - l / n < Z : E y i j / 9 i j > 2 > n(n - 1 ) i j l - j P r o o f s of t h e l a c k of b i a s and v a l i d i t y of t h e s e p o i n t s a m p l i n g e s t i m a t o r s c an be f o u n d i n P a l l e y and H o r w i t z ( 1 9 6 1 ) . The p r o b a b l e ' e r r o r of t h e e s t i m a t e d t o t a l i s c a l c u l a t e d t h e same way as was d e s c r i b e d i n t h e s e c t i o n on 3-P s a m p l i n g , as a r e th e c o n f i d e n c e l i m i t s . 18 LITERATURE REVIEW F o r e s t e r s were i n t r o d u c e d f o r t h e f i r s t t i m e t o 3-P s a m p l i n g by G r o s e n b a u g h ( 1 9 6 4 ) , who c l a i m e d t h a t 3-P can make o b j e c t i v e use of s u b j e c t i v e j udgement. In t h e o l d d a y s , o c u l a r e s t i m a t i n g was q u i t e p o p u l a r , but a s s e s s i n g p r o b a b l e e r r o r s f o r t h i s t e c h n i q u e was i m p o s s i b l e . The one w e l l known v a l i d t h e o r y f o r u s i n g o c u l a r e s t i m a t e s t o improve s a m p l i n g e f f i c i e n c y was t h r o u g h s t r a t i f i c a t i o n . F o r example, a l a r g e f o r e s t c a n be b r o k e n down i n t o s e p a r a t e s t a n d s , e x h i b i t i n g f a i r l y homogenous c o n d i t i o n s w i t h i n t h e m s e l v e s , but d i f f e r i n g from c o n t i g u o u s s t a n d s i n t h e numbers o f stems p e r h e c t a r e , s p e c i e s c o m p o s i t i o n , or i n any o t h e r way t h a t may c a u s e t h e s t a n d s t o have d i f f e r i n g volume d i s p e r s i o n s . By t r e a t i n g t h e s t a n d s as s t r a t a , e a c h s t r a t a w i l l have a s m a l l e r v a r i a b i l i t y b e c a u s e of homogenous s t a n d c o n d i t i o n s , t h u s t h e e r r o r of t h e e s t i m a t e w i l l be l o w e r t h a n i f s t r a t i f i c a t i o n were n o t u s e d . G r o s e n b a u g h o b s e r v e d t h a t v e r y i n t e n s i v e s t r a t i f i c a t i o n t e n d e d t o s t a b i l i z e t h e c o e f f i c i e n t of v a r i a t i o n a t a b o u t t h e same l e v e l f o r a l l s t r a t a , so t h a t t h e optimum a l l o c a t i o n of s a m p l e s would be i n p r o p o r t i o n t o s t r a t u m v olume. T h i s can be e x t e n d e d t o t h e s p e c i a l c a s e where e a c h i n d i v i d u a l t r e e i s r e g a r d e d a s a s t r a t u m . G r o s e n b a u g h d i s c u s s e d how 3-P s a m p l i n g i s s i m i l a r t o l i s t s a m p l i n g a n d pps s a m p l i n g , but has f u n d a m e n t a l d i f f e r e n c e s f r o m e a c h . F i r s t , w i t h 3-P s a m p l i n g no l i s t o f p o p u l a t i o n u n i t s i s a v a i l a b l e u n t i l a f t e r s a m p l i n g i s c o m p l e t e d . S e c o n d , t h e s e l e c t i o n p r o b a b i l i t y a s s i g n e d t o e a c h i n d i v i d u a l i n t h e p o p u l a t i o n i s p u r e l y a r b i t r a r y . T h i s p r o b a b i l i t y must be p o s i t i v e l y c o r r e l a t e d w i t h t h e v a r i a b l e of i n t e r e s t i f any g a i n i n s a m p l i n g e f f i c i e n c y i s t o be e x p e c t e d , 19 t h o u g h t h e f o r m of t h e r e l a t i o n s h i p i s i m m a t e r i a l and need n o t be p o s t u l a t e d . S u b j e c t i v e p r e d i c t i o n o f t h e s e p r o b a b i l i t i e s , s t a t e d G r o s e n b a u g h , i s so much c h e a p e r t h a n measurement of some s i m p l e g e o m e t r i c d i m e n s i o n ( s u c h as d i a m e t e r or h e i g h t ) , t h a t i t c a n u s u a l l y be a p p l i e d t o e v e r y i n d i v i d u a l i n t h e p o p u l a t i o n . G r o s e n b a u g h d e s c r i b e d t h e m e c h a n i c s o f s e l e c t i n g a 3-P sample w h i c h have been d e s c r i b e d i n t h i s work i n t h e s e c t i o n t i t l e d " S a m p l i n g T e c h n i q u e s U s e d " . G r o s e n b a u g h d e s c r i b e d two 3-P e s t i m a t o r s w h i c h he c a l l e d t h e " u n a d j u s t e d " and " a d j u s t e d " e s t i m a t e s . The a d j u s t e d e s t i m a t e r e q u i r e s knowledge o f t h e sum of t h e p r e d i c t e d a r b i t r a r y p r o b a b i l i t i e s f o r a l l p o p u l a t i o n i n d i v i d u a l s , b u t s h o u l d have a much s m a l l e r v a r i a n c e t h a n t h e u n a d j u s t e d e s t i m a t e . C o n s e q u e n t l y , i t i s t h e one t h a t i s most f r e q u e n t l y , i f not a l w a y s , u s e d . F o r m u l a s o f b o t h u n a d j u s t e d and a d j u s t e d e s t i m a t e s f o r t h e p o p u l a t i o n t o t a l a r e g i v e n , a s w e l l a s a f o r m u l a f o r t h e r e l a t i v e v a r i a n c e o f t h e a d j u s t e d e s t i m a t o r . S h a r p n a c k (1964) c l a i m e d t h a t computer s i m u l a t i o n i s t h e a p p r o p r i a t e s t a r t i n g p o i n t f o r t e s t i n g a new s a m p l i n g method, i n l i e u of t i m e c o n s u m i n g f i e l d t e s t s w h i c h may a l s o c o n f u s e f i e l d p r o c e d u r e s w i t h o p e r a t i o n and p e r f o r m a n c e o f t h e s a m p l i n g t e c h n i q u e i t s e l f . S h a r p n a c k u s e d a t o t a l of 101 t r i a l s i n a Monte C a r l o s t u d y o f t h e 3-P s a m p l i n g t e c h n i q u e . The t r i a l s i n c l u d e d 8 d i f f e r e n t sample d e s i g n s t o s i m u l a t e d i f f e r e n t c o e f f i c i e n t s o f v a r i a t i o n f o r d i f f e r e n t p r e d i c t o r s o f s e l e c t i o n p r o b a b i l i t i e s . He c o n s t r u c t e d 67% c o n f i d e n c e i n t e r v a l s a r o u n d t h e means w i t h i n e a c h s ample. The t r u e mean f e l l i n t h e s e i n t e r v a l s 64% of t h e t i m e o v e r a l l s a m p l e s . S h a r p n a c k c o n s i d e r e d t h i s a s an i n d i c a t i o n t h a t e r r o r e s t i m a t e s a r e r e l i a b l e u s i n g t h e 3-P method. 20 Hartman (1966) r e p o r t e d t h e r e s u l t s o f a f i e l d t r i a l c o n d u c t e d by t h e B u r e a u o f Land Management (BLM) i n t h e U.S. The BLM s e l l s t i m b e r on a lump sum b a s i s m a i n l y due t o i n t e r m i n g l e d l a n d o w n e r s h i p p a t t e r n s w h i c h c a u s e s p r o b l e m s i n t h e l o c a t i o n and numbers of s c a l i n g f a c i l i t i e s . The BLM e x p e c t s t h a t g r e a t e r t r e e u t i l i z a t i o n i s f o s t e r e d t h r o u g h lump sum s a l e s . T r a d i t i o n a l l y , t h e BLM i s c o m m i t t e d t o a 100% c r u i s e p o l i c y as t h e v a r i a b i l i t y e n c o u n t e r e d i n o l d g r o w t h D o u g l a s - f i r i s g e n e r a l l y t o o g r e a t t o e f f e c t economy, o r g a i n any a c c u r a c y , t h r o u g h s a m p l i n g . A volume e s t i m a t e i s made f o r e v e r y t r e e i n t h e s a l e u s i n g an a v e r a g e 1 6 - f o o t f o r m c l a s s f o r e a c h s p e c i e s and e n t e r i n g an a p p r o p r i a t e form c l a s s volume t a b l e . S i n c e e a c h t r e e i s v i s i t e d anyway i t was l i t t l e e x t r a e f f o r t t o make a q u i c k e s t i m a t e of volume a t e a c h t r e e . The s t a n d a r d e r r o r o f t o t a l volume a c h i e v e d w i t h a s a m p l i n g i n t e n s i t y of o n l y 4% o f t h e 3,056 t r e e s i n t h e s a l e , u s i n g t h e 3-P method was 3.9%. Hartman c o n c l u d e d t h a t 3-P i s e v e r y b i t as p r e c i s e and a c c u r a t e a s t h e s t a n d a r d t e c h n i q u e , but the c o s t s of u s i n g 3-P seemed t o be j u s t as much as t h e s t a n d a r d t e c h n i q u e . He a d m i t t e d t h a t t h i s i s o n l y one t r i a l and as more e x p e r i e n c e i s g a i n e d w i t h t h e method, t h i s may c h a n g e . J o h n s o n , e t a _ l . (1967) r e p o r t e d a n o t h e r t r i a l of 3-P s a m p l i n g . They compared 3-P t o t h e a c c e p t e d s a m p l i n g method f o r use i n s e l e c t i v e l y c u t s a l e s on most U.S. n a t i o n a l f o r e s t s i n e a s t e r n O r e g o n and W a s h i n g t o n . The s t a n d a r d method i s t o s e l e c t one t r e e a t random from e v e r y 5, 10, 20 o r o t h e r number of t r e e s , d e p e n d i n g on d e s i r e d c r u i s e i n t e n s i t y . B o a r d f o o t volumes f o r sample t r e e s a r e t a k e n from form c l a s s volume t a b l e s . The q u i c k o c u l a r p r e d i c t i o n s made i n t h e s t u d y were a i d e d by t h e use of a " c r u t c h " t a b l e " , i . e . , a l o c a l volume t a b l e d e r i v e d from a 21 s i m i l a r t y p e s a l e . The r e s u l t s l e d them t o h y p o t h e s i z e t h a t 3-P may be s u f f i c i e n t l y a c c u r a t e t o j u s t i f y s e l l i n g on t h e c r u i s e i n s t e a d o f on t h e s c a l e . However, t h e y were c a u t i o u s n o t t o make a b l a n k e t e n d o r s e m e n t , as t h i s was o n l y a s i n g l e t r i a l , a nd f e l t t h a t a d d i t i o n a l f i e l d t e s t s a r e j u s t i f i e d . G r o s e n b a u g h (1967) gave a " s i m p l i f i e d " e x p l a n a t i o n as t o how s e v e r a l d i f f e r e n t v a r i a b l e p r o b a b i l i t y s a m p l i n g methods can a l l be more e f f i c i e n t t h a n e q u a l p r o b a b i l i t y s a m p l i n g t e c h n i q u e s . Of c o u r s e , d e c i d i n g on t h e o p t i m a l d e s i g n , he s t a t e d , w i l l r e q u i r e l o c a l s t u d i e s of e m p i r i c a l v a r i a n c e s and c o s t s a s s o c i a t e d w i t h t h e p a r t i c u l a r t e c h n i q u e s . S c h r e u d e r , e t a l . ( 1 9 6 8 ) , d i s c u s s e d a t l e n g t h t h e 3-P s a m p l i n g t h e o r y , and gave r i g o r o u s , y e t s i m p l e p r o o f s of i t s s t a t i s t i c a l v a l i d i t y . T h e i r p r o o f s showed t h a t G r o s e n b a u g h ' s (1964) " u n a d j u s t e d " e s t i m a t e was u n b i a s e d . They a l s o p r o v e d t h a t t h e " a d j u s t e d " e s t i m a t e c o n t a i n e d b i a s , b ut was l i k e l y t o have a much s m a l l e r v a r i a n c e t h a n t h e u n a d j u s t e d e s t i m a t e , w h i c h f a v o r e d t h e a d j u s t e d e s t i m a t o r ' s u s e . T h i s was s u p p o r t e d by a Monte C a r l o s t u d y t h e y p e r f o r m e d . The b i a s o f t h e a d j u s t e d e s t i m a t e was f o u n d t o be n e g l i g a b l e . However, t h e y were c o n c e r n e d w i t h t h r e e p o t e n t i a l w e aknesses of 3-P: 1) t h e r e i s a p o s s i b i l i t y of o b s e r v i n g a sample l e s s p r e c i s e or more c o s t l y but more p r e c i s e t h a n p l a n n e d , b e c a u s e of t h e random sample s i z e ( u n d e r l i n e d p o r t i o n m i n e ) , 2) t h e r e i s a p o s s i b l e l o s s o f e f f i c i e n c y by not making o p t i m a l use o f i n f o r m a t i o n we a r e f o r t u n a t e enough t o have a b o u t t h e r e l a t i o n s h i p between x ( t h e a u x i l l i a r y v a r i a b l e , as p r e v i o u s l y m e n t i o n e d , an o c u l a r p r e d i c t i o n of t h e v a r i a b l e of i n t e r e s t ) and y ( t h e v a r i a b l e o f i n t e r e s t ) , and 3) t h e a p p a r e n t l a c k o f a r e l i a b l e sample b a s e d e s t i m a t e of t h e a d j u s t e d 22 e s t i m a t o r ' s v a r i a n c e . S c h r e u d e r e_t a l . t h o u g h t t h e i r Monte C a r l o s t u d y i n d i c a t e d t h a t t h e sample b a s e d e s t i m a t e of t h e u n c o n d i t i o n a l v a r i a n c e o r i g i n a l l y s u g g e s t e d by G r o s e n b a u g h (1965) was somewhat u n s t a b l e , but t h e i r r e s u l t s were s l i g h t l y ambiguous. S c h r e u d e r , e t a l . (1968) went on t o d i s c u s s t h e c o n d i t i o n a l p r o p e r t i e s o f t h e s e e s t i m a t o r s , i . e . , t h e p r o p e r t i e s a f t e r n o b s e r v a t i o n s have been s e l e c t e d . T h e s e c o n d i t i o n a l p r o p e r t i e s , t h e y s t a t e d , a r e t h e most r e l e v a n t , f o r t h e y a r e r e l a t e d t o t h e a c t u a l sample o b s e r v e d . F o r example, i f t h e e x p e c t e d v a l u e of t h e t o t a l e s t i m a t e and i t s v a r i a n c e v a r y s i g n i f i c a n t l y w i t h n, doubt would be c a s t on t h e s a m p l i n g p r o c e d u r e . T h i s was examined a l s o i n t h e i r Monte C a r l o s t u d y . I t was f o u n d t h a t t h e sample b a s e d e s t i m a t e of v a r i a n c e p r o v i d e d r e a s o n a b l e e s t i m a t e s of t r u e c o n d i t i o n a l v a r i a n c e . However, s u b s e q u e n t s t u d i e s ( S c h r e u d e r , e_t a l . 1971) c a s t f u r t h e r doubt on t h e u t i l i t y o f t h e s e e s t i m a t o r s . B u t , G r o s e n b a u g h (1976) showed t h a t a s t a b l e , r e l i a b l e e s t i m a t e of t h e v a r i a n c e b a s e d on a s i n g l e sample does e x i s t . I t i s o b t a i n e d s i m p l y by m u l t i p l y i n g t h e c o n d i t i o n a l v a r i a n c e f o r m u l a ( w h i c h i s a l s o t h e f o r m u l a u s e d i f s a m p l i n g i s w i t h r e p l a c e m e n t ) by t h e e x p e c t e d f i n i t e p o p u l a t i o n c o r r e c t i o n ( f p c ) o r ( l - n E / N ) . T h i s i s a c r u d e a p p r o x i m a t i o n t o an u n b i a s e d e s t i m a t e o f t h e t r u e v a r i a n c e f o r t h i s t y p e o f s a m p l i n g w i t h o u t r e p l a c e m e n t but i t b e h a v e s a s would be e x p e c t e d under Monte C a r l o s i m u l a t i o n . T h i s i s f o r m u l a (5) g i v e n i n t h e p r e v i o u s s e c t i o n . S c h r e u d e r , e t a l . (1968) c o n c l u d e d by s a y i n g t h a t t o f u l l y d e t e r m i n e whether p o t e n t i a l d i f f i c u l t i e s of 3-P s a m p l i n g a r e i m p o r t a n t r e l a t i v e t o p o s s i b l e w e aknesses of a l t e r n a t i v e s w i l l r e q u i r e r e f i n e m e n t and e x t e n s i o n of e x i s t i n g s a m p l i n g t h e o r y , and an a c c u m u l a t i o n o f e x p e r i e n c e w i t h a l l t h e a l t e r n a t i v e s . 23 In F i n l a n d , , S e p p a l a (1971) t e s t e d 3-P s a m p l i n g i n w h i c h t h e v a r i a b l e s e l e c t i o n p r o b a b i l i t i e s were b a s e d on dbh. A Monte C a r l o s t u d y was p e r f o r m e d on p r e v i o u s l y c o l l e c t e d d a t a from 6 d i f f e r e n t s t a n d s . Optimum powers o f dbh were between 2.1 and 2.4 f o r t h e d i f f e r e n t s t a n d s . The a d j u s t e d 3-P e s t i m a t o r was f o u n d t o be most e f f i c i e n t . V a r i a n c e s were c a l c u l a t e d f o r e x p e c t e d and a c t u a l sample s i z e s and d i f f e r e n c e s were f o u n d t o be s m a l l . S e p p a l a c o n c l u d e d t h a t 3-P s a m p l i n g i s a s t a t i s t i c a l l y e f f i c i e n t method when t h e p o p u l a t i o n has n o t been p r e v i o u s l y e n u m e r a t e d ( l i s t e d , or f r a m e d ) . J o h n s o n and Hartman (1972) p r o p o s e d f a l l i n g , b u c k i n g , and s c a l i n g 3-P sample t r e e s as a l o g i c a l a l t e r n a t i v e t o d e n d r o m e t r y of s t a n d i n g t r e e s when t h e o p p o r t u n i t y e x i s t s . T h i s was p r o p o s e d b e c a u s e t h e y f o u n d t h a t volume e s t i m a t e s from d e n d r o m e t e r s can be e r r a t i c a n d / o r b i a s e d . The e r r o r s may v a r y i n m a g n i t u d e a c c o r d i n g t o i n s t r u m e n t o p e r a t o r . J o h n s o n and Hartman were c o n c e r n e d w i t h e f f e c t s of i t s c o s t on i t s p r a c t i c a l i t y , however, as t h e i r method was more e x p e n s i v e t h a n m e a s u r i n g t h e s t a n d i n g t r e e s . Bonnor (1972) t e s t e d 3-P s a m p l i n g i n a t w o - s t a g e f o r e s t i n v e n t o r y i n a w h i t e s p r u c e f o r e s t t y p e i n n o r t h e r n B.C. The f i r s t s t a g e was s a m p l i n g p h o t o p l o t s , w h i c h was n o t d e s c r i b e d i n d e t a i l . The s e c o n d s t a g e , o r f i e l d s t a g e , was l o c a t i n g some of t h e p h o t o p l o t s on t h e g r o u n d , and s a m p l i n g them. Ground p l o t s (0.9 a c ) were sampled u s i n g t h r e e methods: f i x e d a r e a p l o t s , p o i n t s a m p l i n g , and 3-P. F o r t h e p l o t method, e a c h g r o u n d p l o t was d i v i d e d i n t o 9 t e n t h - a c r e s u b p l o t s , two of w h i c h were s a m p l e d . A d e l i b e r a t e e f f o r t was made t o s e l e c t t h e same number of t r e e s i n t h e p o i n t and 3-P samples as were s e l e c t e d i n t h e p l o t sample, t o f a c i l i t a t e c o m p a r i s o n s . The 3-P method was j u d g e d 24 t o be v a s t l y s u p e r i o r t o t h e p o i n t and p l o t methods when us e d i n t h e s a m p l i n g p l a n t e s t e d . A c c o r d i n g t o Bonnor, t h i s i n d i c a t e d t h a t 3-P w o u l d be more e f f i c i e n t i n s a m p l i n g most f o r e s t p o p u l a t i o n s . More d e f i n i t e c o n c l u s i o n s were d e f e r r e d u n t i l more p r a c t i c a l e x p e r i e n c e c o u l d be a c c u m u l a t e d . H u s s a i n (1974) and T a r i q (1974) d e s c r i b e d t h e 3-P t e c h n i q u e and r e p o r t e d on f i e l d t r i a l s i n P a k i s t a n . I t was r e c o g n i z e d as an e f f i c i e n t t i m b e r c r u i s i n g t e c h n i q u e , e s p e c i a l l y i n i n s t a n c e s where a p p l i c a b l e volume t a b l e s a r e n o t a v a i l a b l e ( T a r i q 1974). In M e x i c o , 3-P s a m p l i n g g a i n e d a t t e n t i o n . C a b a l l e r o D e l o y a (1974) d e s c r i b e d t h e p r i n c i p l e s of 3-P and d i s c u s s e d i t s a p p l i c a t i o n t o f o r e s t i n v e n t o r y work i n t h a t c o u n t r y . l i e s (1978) n o t e d t h a t t h e s u g g e s t i o n t o f i e l d crews t h a t p r e d i c t i n g v olumes d i r e c t l y i s p r e f e r a b l e has l a r g e l y been i g n o r e d f o r s e v e r a l r e a s o n s . F o r one, c r e w s may be v e r y i n e x p e r i e n c e d a t t h i s . Two, c r u i s e s o f t e n use t h e combined e s t i m a t e s of s e v e r a l p e o p l e who may p o s s e s s d i f f e r i n g d e g r e e s of s k i l l a t p r e d i c t i n g . Though s t r a t i f i c a t i o n c o u l d be employed, i t i s o f t e n c o n v e n i e n t t o combine t h e raw d a t a , t h u s s t a n d a r d p r e d i c t i o n p r o c e d u r e s a r e n e c e s s a r y . I t i s much e a s i e r t o p r e d i c t d i a m e t e r s a t b r e a s t h e i g h t t h a n t o t a l t r e e volume. l i e s showed t h a t i t i s a s i m p l e m a t t e r t o i n c o r p o r a t e r e a l powers of dbh, l o c a l volume t a b l e s or much more c o m p l i c a t e d f u n c t i o n s t o improve e s t i m a t i o n e f f i c i e n c y . B r i e f l y , r e a l random numbers ( v s . i n t e g e r s ) a r e g e n e r a t e d i n terms o f volume, and t h e a p p r o p r i a t e volume e q u a t i o n i s i n v e r t e d t o y i e l d t h e d i a m e t e r w h i c h g e n e r a t e d t h a t volume, and i t i s t h i s l i s t w h i c h i s t a k e n i n t o t h e f i e l d . The a c t u a l s e l e c t i o n p r o b a b i l i t i e s a r e th e n computed a f t e r t h e c r u i s e i n t h e o f f i c e by c o m p u t e r . T h i s t e c h n i q u e seems t o 25 e l i m i n a t e t h e o b j e c t i o n by S c h r e u d e r e t a l . (1968) t h a t 3-P may s u f f e r a l o s s of e f f i c i e n c y by n o t making o p t i m a l use of i n f o r m a t i o n we may have a b o u t t h e r e l a t i o n s h i p between x and y. P e l z (1980) c i t e d an a d d i t i o n a l b e n e f i t r e g a r d i n g t h e 3-P method. The s t a n d a r e a need not be d e t e r m i n e d b e c a u s e t h e s a m p l i n g e l e m e n t s a r e i n d i v i d u a l t r e e s and a r e n o t a r e a r e l a t e d . In d o i n g s o , an a d d i t i o n a l s o u r c e of e r r o r i s b e i n g e l i m i n a t e d w h i c h may be i m p o r t a n t i n i r r e g u l a r l y s h a p e d s t a n d s i n w h i c h c o n v e n t i o n a l a r e a b a s e d e s t i m a t e s may be b i a s e d . F u r t h e r r e s e a r c h i s needed t o t e s t 3-P's r e l a t i v e e f f i c i e n c y compared t o o t h e r s a m p l i n g methods ( P e l z 1980). A c o m p a r i s o n was made of 3-P s a m p l i n g w i t h t h e t a r i f s y s t e m u s e d i n t h e U.K. ( H e t h e r i n g t o n 1982a). The 3-P method seemed t o out p e r f o r m t h e t a r i f s y s t e m . The methods were compared by t h e f a i r l y common p r o c e d u r e w h i c h p r o v i d e s an " i n d e x o f e f f i c i e n c y " . The s t a n d a r d e r r o r of t h e t o t a l i n p e r c e n t o f t h e t o t a l i s m u l t i p l i e d by t h e t i m e ( o r c o s t ) i t t a k e s t o a c h i e v e t h a t p r e c i s i o n and t h e n r e l a t i v e e f f i c i e n c i e s a r e computed i n t h e u s u a l manner u s i n g t h e s e i n d e x e s . H e t h e r i n g t o n s t r e s s e d t h a t 3-P s a m p l i n g has a p p l i c a t i o n s w o r l d - w i d e , p a r t i c u l a r l y where volume t a b l e s a r e p o o r or n o t a v a i l a b l e , where a c c e s s i s d i f f i c u l t b u t a e r i a l p h o t o g r a p h y a v a i l a b l e , e t c . H e t h e r i n g t o n l a t e r f o u n d an e r r o r i n a computer f i l e . An e r r a t u m was p u b l i s h e d ( H e t h e r i n g t o n 1982b) i n w h i c h i t i s c o n c l u d e d t h a t t h e two methods a c t u a l l y p e r f o r m e d c o m p a r a b l y . I t s h o u l d be n o t e d t h o u g h , t h a t i n H e t h e r i n g t o n ' s t r i a l of 3-P, a l l t h e t r e e s were a c t u a l l y t a p e d f o r dbh t o a s s i g n t h e p r o b a b i l i t i e s of s e l e c t i o n , w h i c h would slow down t h e method c o n s i d e r a b l y . 26 One example o f where a c c e s s i s d i f f i c u l t i s i n t r o p i c a l f o r e s t s where g e n e r a l l y heavy u n d e r g r o w t h , m u l t i - l a y e r e d s t o r i e s , and h e a v i l y b u t t r e s s e d t r e e s p r e v e n t e a s y a p p l i c a t i o n of c o n v e n t i o n a l i n v e n t o r y s a m p l i n g schemes. Crude and i n many c a s e s e x p e n s i v e methods have been d e v e l o p e d f o r i n v e n t o r y i n g t h e g r o w i n g s t o c k volume i n t h e s e f o r e s t s . Omule (1981) p r o p o s e d a method e m p l o y i n g 3-P s a m p l i n g t o improve t h e e f f i c i e n c y of t h e ' s t o c k m a p p i n g ' t e c h n i q u e (one s u c h c r u d e and e x p e n s i v e m e thod). However, t h e t e c h n i q u e was n o t t e s t e d i n t h i s a p p l i c a t i o n . A n o t h e r computer s i m u l a t i o n s t u d y was c o n d u c t e d by T a k a t a (1982) i n J a p a n . C o m p a r i s o n was made among f o u r volume e s t i m a t i n g methods: 3-P s a m p l i n g , " e q u a l p r o b a b i l t y " s a m p l i n g , 3-P p o i n t , and " B e e r s method". D a t a from t h e s t u d y came f r o m f o u r n a t u r a l s t a n d s and f o u r p l a n t a t i o n s . The s t r a i g h t 3-P method u s i n g d 2 h as t h e p r e d i c t e d v a l u e was t h e most a c c u r a t e and p r e c i s e . A n o t h e r f i e l d t e s t was c o n d u c t e d i n Germany, and r e p o r t e d by S u s s ( 1 9 8 2 ) . 3-P was u s e d t o s e l e c t t h e p r i m a r y s a m p l i n g u n i t s i n a two s t a g e i n v e n t o r y . The t o t a l a r e a of t h e f o r e s t was 901 ha, w i t h 221 s t a n d s . O n l y 15 of t h e 221 s t a n d s were s e l e c t e d by 3-P, and were s a m p l e d o n - t h e - g r o u n d u s i n g c o n v e n t i o n a l a n g l e c o u n t s a m p l i n g . The 3-P p r e d i c t i o n s came from an i n v e n t o r y 7 y e a r s e a r l i e r . C o n v e n t i o n a l s a m p l i n g , i . e . , u s i n g o n l y t h e a n g l e c o u n t method f o r t h e whole f o r e s t w o u l d have t a k e n t h r e e t i m e s as l o n g f o r t h e same 7.8% p r e c i s i o n . S t e b e r and Space (1972) d e s c r i b e d a two phase s a m p l i n g scheme t h e n g a i n i n g wide p o p u l a r i t y i n t h e S o u t h e r n U.S. The f i r s t p h a s e i s t h e p r i s m p l o t and t h e " i n " t r e e s a r e sampled u s i n g t h e 3-P t e c h n i q u e ( s e c o n d p h a s e ) . They i n v e n t o r i e d one m i l l i o n a c r e s i n c o o p e r a t i o n w i t h t h e S t . J o e Paper Co. i n 27 N o r t h e r n F l o r i d a . The combined s a m p l i n g e r r o r o f t h e e n t i r e i n v e n t o r y b a s e d on c u b i c f o o t volume was + or - 7.1%, two t i m e s o u t o f t h r e e . C o n s i d e r a b l e t i m e and money were s a v e d u s i n g t h e c ombined t e c h n i q u e s . K a s i l e (1983) p r o p o s e d what he c a l l s "3-P s a m p l i n g f o r d o l l a r s " . He b e l i e v e d t h a t s i n c e t i m b e r i s bought and s o l d u s i n g d o l l a r s , d i r e c t e s t i m a t i o n of d o l l a r s s h o u l d be t h e m a j o r g o a l of any t i m b e r s a l e i n v e n t o r y . H i s method r e q u i r e s an a p r i o r i p r o b a b i l i t y d i s t r i b u t i o n o f f r e q u e n c y of t r e e s by d o l l a r c l a s s . K a s i l e p o i n t e d o u t t h a t t h i s method has g r e a t a d v a n t a g e s i n a m ixed hardwood s t a n d i n t h e hardwood r e g i o n of t h e U.S. where s a w l o g s i z e b l a c k w a l n u t i s w o r t h s e v e n t i m e s more t h a n elm and t h r e e t i m e s more t h a n h a r d maple. T h e r e f o r e , volume a l o n e would not a d e q u a t e l y r e f l e c t d i f f e r e n c e s i n v a l u e f o u n d i n t h e s e mixed hardwood s t a n d s . K a s i l e d e s c r i b e d an i n t e r e s t i n g method t o o p t i m i z e t h e 3-P s a m p l i n g scheme, b a s e d on t h e a p r i o r i p r o b a b i l i t y d i s t r i b u t i o n o f t r e e s by d o l l a r c l a s s w h i c h seems v a l i d a l s o f o r f r e q u e n c y of t r e e s by dbh c l a s s , volume c l a s s or any o t h e r c l a s s i f i c a t i o n scheme. The p r e c e d i n g c i t a t i o n s show t h a t many Monte C a r l o s t u d i e s have p r o v e n 3-P t o be a s t a t i s i c a l l y e f f i c i e n t e s t i m a t i o n s y s t e m . The l i m i t e d f i e l d t r i a l s t h a t have been p u b l i s h e d , g i v e a f a v o r a b l e v i e w of t h e t e c h n i q u e o v e r a l l , b ut p o i n t t o t h e need f o r f u r t h e r t e s t i n g of t h e method under l o c a l c o n d i t i o n s . I t i s e v i d e n t a l s o t h a t t h e r e i s a d e a r t h o f i n f o r m a t i o n as t o how 3-P compares w i t h p r i s m c r u i s i n g i n l a r g e r s t a n d s where c l e a r f e l l i n g i s t h e o b j e c t i v e . MATERIALS AND METHODS P f e i f f e r (1967) r e l a t e d how t h e B.C. Work S t u d y S c h o o l d e f i n e s work s t u d y . I t i s t h e s y s t e m a t i c , o b j e c t i v e , and c r i t i c a l e x a m i n a t i o n of a l l f a c t o r s g o v e r n i n g t h e o p e r a t i o n a l e f f i c i e n c y o f any s p e c i f i c a c t i v i t y i n o r d e r t o e f f e c t improvement. P f e i f f e r gave a t h o r o u g h r e v i e w of many o f t h e most i m p o r t a n t work s t u d y t e c h n i q u e s , and e x p l a i n e d t h a t c o n t i n u o u s t i m e s t u d y i s t h e f a v o r e d t e c h n i q u e f o r c o m p a r i s o n o f a l t e r n a t i v e s . The p r e s e n t s t u d y was, of c o u r s e , d e s i g n e d t o compare v a r i o u s a l t e r n a t i v e s f o r c r u i s i n g t i m b e r , so the c o n t i n u o u s t i m e s t u d y t e c h n i q u e was a d o p t e d . W i t h t h i s method, a w e l l d e f i n e d b e g i n n i n g and end t o e a c h a c t i v i t y a r e n e c e s s a r y . The s t o p watch i s s t a r t e d as t h e a c t i v i t y b e g i n s , and s t o p p e d when t h e d e f i n e d end i s r e a c h e d . E l a p s e d t i m e i s , n a t u r a l l y t h e t i m e n e c e s s a r y t o do t h e a c t i v i t y . I t s h o u l d be m e n t i o n e d a t t h i s p o i n t , t h a t hand i n hand w i t h t i m i n g goes t h e " r a t i n g " o f t h e w o r k e r s ' p e r f o r m a n c e . "Normal p a c e " i s d e f i n e d by t h e I n t e r n a t i o n a l L a b o r O r g a n i z a t i o n as " t h e r a t e o f w o r k i n g w h i c h t h e o p e r a t o r c o u l d s u s t a i n o v e r l o n g p e r i o d s of t i m e w i t h o u t r e s u l t i n g i n b u i l d u p o f c u m u l a t i v e f a t i g u e " ( P f e i f f e r 1967), and i s g i v e n a r a t i n g o f 100%. The o b s e r v e d t i m e m u l t i p l i e d by t h e r a t i n g as a d e c i m a l f r a c t i o n r e s u l t s i n n o r m a l t i m e . T h i s f a c t i s m e n t i o n e d b e c a u s e no a t t e m p t was made t o e s t i m a t e a n o r m a l t i m e f o r e a c h a c t i v i t y . V a r i o u s o r g a n i z a t i o n s o r c o m p a n i e s may a l r e a d y have e s t a b l i s h e d n o r m a l t i m e s w h i c h t h e i r crews d i s p l a y when a n g l e c o u n t s a m p l i n g . So, i n t e r e s t e d p a r t i e s can " r a t e " t h e t i m e s r e p o r t e d h e r e f o r a s p e c i f i c two man 29 crew (same crew f o r a l l t i m e s ) and a d j u s t them a c c o r d i n g l y t o t h e i r o r g a n i z a t i o n ' s "normal p a c e " . A l s o , t h e r e s u l t a n t t i m e s from a t i m e s t u d y a r e a p p l i c a b l e t o t h e p a r t i c u l a r j o b ( i n t h i s c a s e a n g l e c o u n t s a m p l i n g , 3-P s a m p l i n g , or r a t i o e s t i m a t i o n ) but may be u s e d f o r t h e same j o b a t any o t h e r p l a c e u n d e r s i m i l a r c o n d i t i o n s . To f a c i l i t a t e t h e t i m i n g of e a c h c r u i s i n g t e c h n i q u e , e a c h t e c h n i q u e was b r o k e n down i n t o components o r a c t i v i t i e s . The 3-P v a r i a t i o n s were b r o k e n down i n t o 4 a c t i v i t i e s , w h i c h s h a l l be c a l l e d p r e d i c t i n g , m a r k i n g , l o c a t i n g , and d e n d r o m e t r y . The p r e d i c t i n g a c t i v i t y i n c l u d e d w a l k i n g t h r o u g h t h e b l o c k and d i r e c t l y p r e d i c t i n g o c u l a r e s t i m a t e s of i n d i v i d u a l t r e e v o l u m e s . The s t a n d was t r a v e r s e d i n s u c c e s s i v e 10-12 m s t r i p s w h i c h were bounded by t r a i l i n g a s t r i n g . R e c o r d i n g and t e s t i n g t h e p r e d i c t i o n s a g a i n s t t h e two s e l e c t i o n c r i t e r i a , namely, t h e random numbers, o r c h e c k i n g t o see i f i t was t h e k*-*1 t r e e , were a l s o i n c l u d e d i n t h e p r e d i c t i n g a c t i v i t y . T i m i n g s t a r t e d w i t h b o t h men p o s i t i o n e d a t t h e edge of t h e t r a c t t o be c r u i s e d and ended when t h e volume f o r t h e l a s t t r e e had been o c u l a r l y p r e d i c t e d and c h e c k e d f o r i n c l u s i o n i n t h e s a mple. S i n c e two s e l e c t i o n c r i t e r i a were b e i n g employed s i m u l t a n e o u s l y , t h e t i m e i t t o o k t o mark e a c h t r e e so i t c o u l d be l o c a t e d l a t e r f o r m e a s u r i n g , was r e c o r d e d s e p a r a t e l y u nder t h e a c t i v i t y c a l l e d m a r k i n g . T h i s i s n e c e s s a r y b e c a u s e d i f f e r e n t t r e e s c o u l d be s e l e c t e d under e a c h c r i t e r i a and b e c a u s e d i f f e r i n g numbers of t r e e s may be s e l e c t e d i n d i f f e r e n t c r u i s e s u s i n g t h e same c r u i s i n g method. The l o c a t i n g a c t i v i t y c o n s i s t e d o f j u s t t h a t , t h e t i m e i t t o o k t o l o c a t e e a c h marked t r e e d u r i n g t h e sample t r e e measurement p h a s e . L a s t , t h e d e n d r o m e t r y a c t i v i t y c o n s i s t e d 30 of f i n d i n g a s u i t a b l e l o c a t i o n o r l o c a t i o n s i n w h i c h t o s e t up th e d e n d r o m e t e r o r t a k e h e i g h t s w i t h c l i n o m e t e r and c h a i n , a c t u a l l y s e t t i n g up and u s i n g t h e i n s t r u m e n t s , r e c o r d i n g n e c e s s a r y i n f o r m a t i o n on p a t h o l o g y and q u a l i t y needed f o r t h e a p p l i c a t i o n of a p p r o p r i a t e d e c a y , waste and b r e a k a g e f a c t o r s , and t h e n t a k i n g t h e i n s t r u m e n t s down and s t o r i n g them p r o p e r l y f o r t r a n s i t . T h r e e d i f f e r e n t methods were t e s t e d t o " a c c u r a t e l y measure" t h e sample t r e e s . In t h e f i r s t method, a d i a m e t e r t a p e , c l i n o m e t e r , and n y l o n c h a i n were u s e d t o measure dbh and h e i g h t f o r e n t r y i n t o t h e a p p r o p r i a t e volume t a b l e p u b l i s h e d by t h e BCMF ( 1 9 7 6 ) . T h i s method f o r o b t a i n i n g t r e e v o l u m e s i s q u i t e a p p e a l i n g b e c a u s e i t r e q u i r e s v e r y few measurements, i s q u i c k , w i l l be a c c u r a t e i f t h e volume t a b l e t r u l y r e p r e s e n t s t h e l o c a l c o n d i t i o n s , and may be a d e q u a t e f o r c e r t a i n o b j e c t i v e s . However, t h r e e s o u r c e s of e r r o r Were i d e n t i f i e d by H a z a r d and B e r g e r (1972) t h a t may c a u s e p r o b l e m s when an e x i s t i n g volume t a b l e i s a p p l i e d t o a new s t a n d o f t r e e s or t o a s m a l l p o r t i o n o f t h e s t a n d f o r w h i c h t h e t a b l e was d e v e l o p e d . They a r e : 1) c h a n g e s i n t h e r e l a t i o n s h i p between volume and t h e t r e e c h a r a c t e r i s t i c s f o r th e two s t a n d s , 2) d i f f e r e n t s t a n d a r d s o f u t i l i z a t i o n i n t h e volume t a b l e t h a n t h o s e d e s i r e d , and 3) s y s t e m a t i c measurement e r r o r i n c u r r e d i n m e a s u r i n g t h e t r e e s f o r i n p u t i n t o t h e t a b l e . When t h e volume t a b l e p r e d i c t s g r o s s t o t a l t r e e volume, o n l y e r r o r s o u r c e s 1) and 3) a p p l y . I t was f o u n d t h a t volume t a b l e s ( b a s e d on B e h r e ' s (1927) e x p r e s s i o n f o r t r e e t a p e r ) p r o d u c e s u b s t a n t i a l d i f f e r e n c e s from t r e e v o l u m e s d e r i v e d from d e n d r o m e t e r e s t i m a t e s . H a z a r d and B e r g e r s e t an a r b i t r a r y " a c c e p t a b l e " i n d e x of v a r i a t i o n between t h e volume t a b l e and 31 d e n d r o m e t e r a t 10% , so t h e C h i - S q u a r e t e s t e x p o s t u l a t e d by F r e e s e (1960) c o u l d be u s e d . In t h e i r s t u d y t h e volume t a b l e s f a i l e d r e s o u n d i n g l y a t t h e 95% p r o b a b i l i t y l e v e l t o p r o d u c e e s t i m a t e s a c c e p t a b l y s i m i l a r t o t h o s e o b t a i n e d from t h e d e n d r o m e t e r . The s e c o n d method of sample t r e e measurement t e s t e d was u s i n g t h e w i d e - s c a l e R e l a s k o p as a d e n d r o m e t e r . The aim h e r e , a s d e s c r i b e d i n t h e i n t r o d u c t i o n , i s c a l c u l a t i n g volumes o f i n d i v i d u a l " l o g s " i n t h e t r e e and summing them t o o b t a i n t o t a l t r e e volume, t h u s e l i m i n a t i n g t h e volume t a b l e e r r o r s m e n t i o n e d p r e v i o u s l y . When u s i n g any i n s t r u m e n t s u c h a s t h i s one, e n c o u n t e r i n g low u n d e r b r u s h i n t h e woods d o e s not pose a measurement p r o b l e m , b e c a u s e dbh and l o w e r d i a m e t e r s can be m e a s u r e d w i t h a d i a m e t e r t a p e o r m e c h a n i c a l c a l i p e r s . The r e a l p r o b l e m s e n c o u n t e r e d a r e h i g h b r u s h , t r u n k s and b r a n c h e s of o t h e r t r e e s , b r a n c h e s o f t h e s u b j e c t t r e e i t s e l f , and w i n d . Sometimes a l a r g e amount of t i m e c a n be s p e n t w a i t i n g f o r t h e wind t o d i e down, so t h a t t h e t r e e no l o n g e r a p p e a r s t o t r a v e l back and f o r t h o v e r s e v e r a l r e l a s k o p b a n d s . C o n s i d e r a b l e t i m e c a n a l s o be s p e n t f i n d i n g an i n s t r u m e n t l o c a t i o n t h a t o f f e r s t h e b e s t p o s s i b l e v i e w of t h e stem. I t i s p o s s i b l e , however, t o use more t h a n one i n s t r u m e n t l o c a t i o n . F o r example, one l o c a t i o n may seem i d e a l f o r u p p e r stem measurements and a n o t h e r f o r l o w e r stem measurements. A l l t h a t i s r e q u i r e d i s a new o b s e r v a t i o n of t h e h o r i z o n t a l d i s t a n c e a t e a c h new l o c a t i o n . A l s o , w i t h t h e r e l a s k o p i t i s p a r t i c u l a r l y e a s y t o s p o t " s u s p i c i o u s " r e a d i n g s t h a t a r e p r o b a b l y i n e r r o r , w h i l e s t i l l i n t h e f i e l d . R e l a s k o p u n i t s a r e p r o p o r t i o n a l t o d i a m e t e r so t h e s e r e a d i n g s can be s p o t t e d t h r o u g h c o m p a r i s o n w i t h o t h e r r e a d i n g s a t t h e same i n s t r u m e n t l o c a t i o n . 32 R e l a s k o p u n i t s s h o u l d g e n e r a l l y d e c r e a s e as r e a d i n g s p r o g r e s s up t h e stem. When c o m p a r i n g t h e r e l a s k o p t o t h e B a r r & S t r o u d o p t i c a l d e n d r o m e t e r , Yocom and Bower (1975) f o u n d t h a t t h e r e l a s k o p gave e s t i m a t e s 1.6% h i g h e r , on t h e a v e r a g e , t h a n t h o s e b a s e d on t h e B a r r & S t r o u d . The t h i r d method u s e d t o measure t h e sample t r e e s was t h e B a r r and S t r o u d o p t i c a l d e n d r o m e t e r t y p e FP-12. Use of t h i s i n s t r u m e n t c e r t a i n l y g i v e s t h e same a d v a n t a g e s as u s i n g t h e r e l a s k o p , but i n a d d i t i o n may g i v e even more a c c u r a t e and p r e c i s e r e s u l t s b e c a u s e t h e i n s t r u m e n t has 5.5x m a g n i f i c a t i o n , and a l s o b e c a u s e th e l e n s " g a t h e r s " l i g h t w h i c h a i d s v i e w i n g i n s t a n d s w i t h dense c a n o p i e s or i n c l o u d y w e a t h e r . T h e r e i s a newer model a v a i l a b l e , t h e FP-15, but d e s i g n c h a n g e s from t h e FP-12 a r e not r e l a t e d t o a c c u r a c y (Mesavage 1969). B r i c k e l l (1976) f o u n d t h a t t h e B a r r and S t r o u d e x h i b i t s + 2.39% b i a s i n b a s a l a r e a e s t i m a t e s and no b i a s i n h e i g h t measurements. C o n s e q u e n t l y , one would e x p e c t t h e same m a g n i t u d e i n volume b i a s . However, +5.4% b i a s i n d e n d r o m e t e r e d volume was f o u n d o v e r f e l l e d t r e e volume. He c o u l d n o t a t t r i b u t e t h i s d i s c r e p a n c y t o any s p e c i f i c c a u s e . He h y p o t h e s i z e d t h a t human v i s i o n i t s e l f may have c a u s e d t h i s e r r o r . S t a g e (1962) has d e m o n s t r a t e d t h i s phenomenon w i t h t h e wedge p r i s m and Ross (1968) has d e m o n s t r a t e d i t w i t h t h e Wheeler p e n t a p r i s m . B r i c k e l l (1976) f o u n d , and t h e w r i t e r c o r r o b o r a t e s , t h a t i t i s v e r y cumbersome t o use more t h a n two i n s t r u m e n t l o c a t i o n s when u s i n g t h e B a r r and S t r o u d . The i n s t r u m e n t p l u s t r i p o d and c a r r y i n g c a s e c a n be u n w i e l d l y a t t i m e s , and d i s m a n t l i n g and s e t t i n g up t h e i n s t r u m e n t a r e t i m e c o n s u m i n g . B r i c k e l l (1976) a l s o f o u n d t h a t t h e random e r r o r i n volume measurements was 3% of t r e e volume, much l e s s t h a n 10 - 15 % u s u a l l y a s s o c i a t e d w i t h 33 volume t a b l e s o r e q u a t i o n s . The BCMF (1976) l o g a r i t h m i c volume e q u a t i o n s g i v e s t a n d a r d e r r o r s o f e s t i m a t e r a n g i n g from 6.3% t o 16.8% d e p e n d i n g on s p e c i e s . An a t t e m p t was made t o s p a c e measurements a t i n t e r v a l s no g r e a t e r t h a n 5m a l o n g t h e stem f o r b o t h t h e B a r r and S t r o u d and t h e r e l a s k o p . In t h e f i e l d , e a c h o f t h e s e measurement t e c h n i q u e s was a p p l i e d c o n s e c u t i v e l y t o e a c h sample t r e e a s i t was v i s i t e d i n t h e f o r e s t . The o r d e r i n w h i c h t h e methods were a p p l i e d were r o t a t e d s y s t e m a t i c a l l y a f t e r a random s t a r t . I t was r e c o g n i z e d t h a t m o b i l i t y i n t h e f o r e s t d e pended t o a c e r t a i n e x t e n t on t h e b u l k i n e s s and w e i g h t of i n s t r u m e n t s f o r d e n d r o m e t r y t h a t must be c a r r i e d . The time n e c e s s a r y f o r l o c a t i n g t r e e s when c a r r y i n g a t r i p o d and e i t h e r t h e r e l a s k o p o r t h e B a r r a n d S t r o u d was e s t i m a t e d by s u b t r a c t i n g t h e sum o f a l l t h e t i m e s s p e n t a c t u a l l y m e a s u r i n g sample t r e e s from t h e t o t a l t i m e s p e n t i n t h e f i e l d . The t i m e n e c e s s a r y f o r l o c a t i n g t r e e s when c a r r y i n g o n l y a c l i n o m e t e r , c h a i n , and d i a m e t e r t a p e was e s t i m a t e d s e p a r a t e l y , s i m p l y by r e c o r d i n g t h e t i m e n e c e s s a r y t o walk t o e a c h marked sample t r e e c a r r y i n g o n l y t h o s e i n s t r u m e n t s . The c h o i c e among t h e s e t h r e e methods o f sample t r e e measurement w i l l d epend on two t h i n g s : 1) l e v e l o f a c c u r a c y d e s i r e d , t h e number o f measurements d e s i r e d , o r t h e p u r p o s e f o r w h i c h t h e y a r e t a k e n , and 2) r e l a t i v e p r o d u c t i v i t y o f t h e measurement t e c h n i q u e (number of t r e e s p e r hour o r p e r d a y ) . I t was not p o s s i b l e t o f e l l t h e sample t r e e s o r o t h e r w i s e o b t a i n " t r u e " v o l u m e s , c o n s e q u e n t l y no s t a t e m e n t s c a n be made abo u t t h e b i a s , o r a c c u r a c y of any of t h e s e t r e e measurement methods. However, s t r o n g s t a t e m e n t s c an be made r e g a r d i n g c r i t e r i a 2 ) , and 34 w i l l be d i s c u s s e d more f u l l y i n t h e R e s u l t s and D i s c u s s i o n s e c t i o n . The p r i s m c r u i s e was b r o k e n down i n t o t h r e e a c t i v i t i e s w h ich a r e r e f e r r e d t o as s w e e p i n g , s a m p l i n g t r e e s , and c h a i n i n g . The s w e e p i n g a c t i v i t y i n c l u d e d t h e p r i s m "sweep", i n w h i c h t h e p r i s m i s r o t a t e d a r o u n d t h e p l o t , a l l " i n " t r e e s a r e marked, measured f o r s p e c i e s , dbh, q u a l i t y , p a t h o l o g y , crown c l a s s , e t c . , and a l l b o r d e r l i n e t r e e s a r e c h e c k e d . The s a m p l i n g t r e e s a c t i v i t y i n c l u d e d m e a s u r i n g t h e n e c e s s a r y number of h e i g h t s f o r t h e h e i g h t / d b h r e g r e s s i o n . F i n a l l y , t h e c h a i n i n g a c t i v i t y i n c l u d e d t h e t i m e s p e n t c h a i n i n g between p o i n t s , p o i n t o r " p l o t " c e n t e r e s t a b l i s h m e n t , and m i s c e l l a n e o u s n e c e s s a r y a c t i v i t e s . B e f o r e a c t u a l t i m i n g o f t h e c r u i s i n g t e c h n i q u e s was s t a r t e d , p r a c t i c e c r u i s e s u s i n g a l l t h e methods were p e r f o r m e d on c o n t i g u o u s a r e a s t o f a m i l i a r i z e t h e crew members w i t h a l l t h e methods. E s t i m a t e s o f t o t a l volume and number of t r e e s p e r h e c t a r e f o r e a c h b l o c k , n e c e s s a r y f o r 3-P and r a t i o e s t i m a t i o n r e s p e c t i v e l y , were o b t a i n e d f r o m one or two q u i c k l y e x e c u t e d p r i s m p l o t s . T h e s e e s t i m a t e s need n o t be p e r f o r m e d i n t h i s manner, a e r i a l p h o t o s c a n be u s e d , o r p e r h a p s e x p e r i e n c e i n t h e p a r t i c u l a r f o r e s t t y p e may be t h e b e t t e r j u d g e . The e s t i m a t e of t o t a l b l o c k volume needed f o r 3-P e s t i m a t i o n may be o n l y a " b a l l p a r k f i g u r e " . I t i s g e n e r a l l y a g r e e d t h a t a s l i g h t o v e r e s t i m a t i o n i s p r e f e r a b l e t o an u n d e r e s t i m a t i o n ( G r o s e n b a u g h 1965). A p r o x i m a t e l y a day s p e n t p r a c t i c i n g t h e o c u l a r p r e d i c t i o n of t r e e v o l u m e s was u s e d t o o b t a i n an i d e a o f t h e p r e d i c t o r ' s (crewman's) v a r i a b i l i t y . The a p p r o p r i a t e sample s i z e f o r m u l a showed t h a t 18 sample t r e e s were r e q u i r e d t o meet t h e c r u i s e o b j e c t i v e of + o r -15% 19 t i m e s out of 20. In t h i s s t u d y i t was f o u n d t h a t t h e 35 a u x i l i a r y v a r i a b l e , o c u l a r p r e d i c t i o n of volume, was h i g h l y c o r r e l a t e d w i t h " a c t u a l " o r m e a s u r e d volume, o v e r a l l . The s i m p l e c o r r e l a t i o n c o e f f i c i e n t , r , between volumes o b t a i n e d from t h e volume t a b l e and p r e d i c t i o n s was 0.9370. The c o r r e l a t i o n between volu m e s o b t a i n e d by t h e r e l a s k o p and p r e d i c t e d volume was 0.9073, w h i l e volumes o b t a i n e d by t h e B a r r and S t r o u d d e n d r o m e t e r and p r e d i c t e d volume gave a c o r r e l a t i o n c o e f f i c i e n t o f 0.9214. The c o r r e l a t i o n s a c t u a l l y e x p e r i e n c e d i n each s e p a r a t e b l o c k r a n g e d from 0.8151 t o 0.9895. As was o u t l i n e d i n t h e i n t r o d u c t i o n , d i f f i c u l t y was e x p e r i e n c e d i n a r r i v i n g a t an a p p r o p r i a t e sample s i z e f o r t h e p r i s m c r u i s e . I t was d e c i d e d t h a t s i n c e i n t h e f i n a l a n a l y s i s , t h e t i m e r e q u i r e d t o a c h i e v e a g i v e n p r e c i s i o n u s i n g e a c h method would be compared, r e g a r d l e s s o f t h e p r e c i s i o n a c t u a l l y a c h i e v e d i n t h e f i e l d t r i a l s , t h e sample s i z e was a r b i t r a r i l y s e t a t s i x f o r t h e h a l f h e c t a r e b l o c k s and e i g h t f o r t h e one h e c t a r e b l o c k s . The s t u d y was c o n d u c t e d i n t h e U n i v e r s i t y of B r i t i s h C o l u m b i a R e s e a r c h F o r e s t n e a r Haney, B.C. T h i s a r e a was c h o s e n b e c a u s e i t r e p r e s e n t s w e l l t h e c o n d i t i o n s f o u n d i n F o r e s t I n v e n t o r y Zone ( F I Z ) C. The a v a i l i b i l i t y of f u n d s and t i m e , and l o g i s t i c a l c o n s t r a i n t s l i m i t e d t h e s t u d y t o t h e e x a m i n a t i o n of two r e p l i c a t i o n s o f two b l o c k s i z e s , 1/2 and one h e c t a r e . Two b l o c k s e a c h of one h e c t a r e were d e l i n e a t e d w i t h y e l l o w p l a s t i c f l a g g i n g u s i n g a S i l v a hand h e l d compass, a n y l o n c h a i n , and a S u u n t o c l i n o m e t e r t o make s l o p e c o r r e c t i o n s . E x t r e m e a c c u r a c y i n t h e b l o c k a r e a s i s not n e c e s s a r y , as e a c h c r u i s i n g method was e x e c u t e d i n t h e i d e n t i c a l b l o c k and c o m p a r i s o n s a r e v a l i d . C a r e was t a k e n , however, t o e n s u r e t h a t t h e s e two b l o c k s were s i m i l a r i n d e n s i t y as m e a s u r e d i n number of 36 t r e e s p e r h e c t a r e , and as s i m i l a r as p o s s i b l e i n i n d i v i d u a l t r e e d i m e n s i o n s , as t h e s e f a c t o r s were h y p o t h e s i z e d t o a f f e c t o v e r a l l c r u i s e t i m e . T h e s e two b l o c k s were f u r t h e r d i v i d e d u s i n g t h e compass, c h a i n , and c l i n o m e t e r i n t o 0.5 h e c t a r e b l o c k s . N e s t i n g t h e s m a l l e r b l o c k s i n t h i s f a s h i o n f u r t h e r e n s u r e d t h a t t h e s e i m p o r t a n t f a c t o r s would r e m a i n f a i r l y c o n s t a n t . B l o c k M, c o n s i s t e d o f o l d growth hemlock, D o u g l a s - f i r , and c e d a r . H e i g h t of dominant and c o d o m i n a n t t r e e s was a b o u t 50.5m, t h e r e were 985 c u b i c m e t e r s g r o s s t o t a l volume p e r ha, 390 stems p e r ha, 40% s l o p e , west a s p e c t and a s i g n i f i c a n t u n d e r s t o r y o f w e s t e r n hemlock w h i c h i n h i b i t e d work somewhat. B l o c k W c o n s i s t e d o f s e c o n d g r o w t h D o u g l a s - f i r , had dominant and c o d o m i n a n t h e i g h t o f about 51.1 m, a b o u t 740 c u b i c m e t e r s g r o s s t o t a l volume p e r h e c t a r e , 431 stems p e r h e c t a r e , 35% s l o p e , s o u t h west a s p e c t and v e r y low s a l a l g r o u n d c o v e r , making t r a v e l f a i r l y e a s y . The a r e a s a r e summarized i n t a b l e 1. TABLE 1. STAND CHARACTERISTICS SUMMARY. BLOCK SLOPE ASPECT NO./HA BA/HA VOL/HA HEIGHT DIAM %F %C %H M 40% 270 392 68m 2 985m 3 50.5m 47.0cm 32 32 36 W 35 225 431 55 739 51.1 40.3 70 23 7 The d a t a c a r e f u l l y o b t a i n e d f r o m s a m p l i n g t h e s e b l o c k s i z e s e n a b l e d p r e d i c t i o n of t h e t i m e i t t a k e s t o c r u i s e l a r g e r b l o c k s f o r any g i v e n p r e c i s i o n . The methods u s e d t o make t h e s e p r e d i c t i o n s w i l l be b r i e f l y o u t l i n e d h e r e but d i s c u s s e d i n more d e t a i l i n t h e n e x t c h a p t e r . E a c h s e p a r a t e c r u i s i n g a c t i v i t y was a n a l y z e d and t h e r e l a t i o n s h i p e a c h has w i t h i n c r e a s i n g a r e a s a m p l e d was h y p o t h e s i z e d and d e v e l o p e d on s t r o n g t h e o r e t i c a l c o n s i d e r a t i o n s . 37 Then, t o a r r i v e a t t o t a l c r u i s e t i m e t o a c h i e v e a g i v e n p r e c i s i o n (+ o r - 1 5 % 19 t i m e s out o f 2 0 ) , t h e p r e d i c t e d t i m e s f o r e a c h a c t i v i t y ' s c o m p l e t i o n were summed. A computer p r o g r a m w r i t t e n i n BASIC programming l a n g u a g e was d e v e l o p e d f o r use on an IBM-PC t o c a l c u l a t e s t a n d i n g t r e e volumes from r e l a s k o p and B a r r and S t r o u d r e a d i n g s . An a l g o r i t h m u s i n g S m a l i a n ' s f o r m u l a t o compute l o g volumes was a d o p t e d as M a r t i n (1984) has shown t h a t i t i s among t h e b e s t m a t h e m a t i c a l f o r m u l a s a v a i l a b l e f o r m i d d l e l o g s on t h e t r e e when measurements a r e not e q u a l l y s p a c e d a l o n g t h e stem. T r e e t o p v o l u m e s were assumed t o be c o n e s , and stumps c y l i n d e r s . No c o r r e c t i o n f o r b a r k was made i n t h i s computer a l g o r i t h m , so t r e e volumes a r e o u t p u t i n g r o s s t o t a l volume, o u t s i d e b a r k , w h i c h may i n c r e a s e t h e e s t i m a t e o f e a c h t r e e ' s t o t a l volume o v e r t h e t r e e s whose volumes were o b t a i n e d from t h e volume t a b l e w h i c h p r e d i c t s g r o s s t o t a l volume i n s i d e b a r k . So, t h e p o i n t e s t i m a t e s o f t h e t o t a l volume a r e r e p o r t e d as g r o s s t o t a l volume under b a r k f o r t r e e measurement methods i n v o l v i n g t h e volume e q u a t i o n s and g r o s s t o t a l volume o u t s i d e b a r k f o r methods i n v o l v i n g t h e d e n d r o m e t e r s . However, t h i s w i l l n o t a f f e c t t h e p r e c i s i o n of t h e e s t i m a t e s , t h a t i s , t h e s a m p l i n g e r r o r o b t a i n e d . I t i s o n l y t h e s a m p l i n g e r r o r t h a t i s u s e d t o e s t i m a t e sample s i z e s , n o t t h e p o i n t e s t i m a t e i t s e l f , so t h i s has no e f f e c t on t h e c r u i s i n g time n e c e s s a r y f o r any c r u i s e o b j e c t i v e . RESULTS AND DISCUSSION The t o t a l t i m e i t t o o k t o p o i n t sample t h e h a l f h e c t a r e b l o c k s (HM and HW) r a n g e d f r o m 12.15 t o 15.35 h o u r s , and i t t o o k from 16.90 t o 26.82 h o u r s t o c r u i s e t h e h e c t a r e b l o c k s (M and W). By e x a m i n i n g column 5 i n t a b l e s 2 t h r o u g h 5, t h e r e a d e r c a n see t h e s e c r u i s e t i m e s , and a l s o t h e t o t a l c r u i s e t i m e s f o r e a c h of t h e r e m a i n i n g c r u i s i n g methods and t h e i r v a r i a t i o n s f o r e a c h b l o c k . Column 4 of t h e s e t a b l e s g i v e s t h e component t i m e s t h a t make up e a c h t o t a l t i m e . T a b l e 6 g i v e s a summary of t h e t o t a l volume e s t i m a t e s f o r e a c h b l o c k by method, a l o n g w i t h t h e c o e f f i c i e n t o f v a r i a t i o n , 95% c o n f i d e n c e l i m i t s , and p e r c e n t e r r o r o f t h e t o t a l . An i n t e r e s t i n g d e v e l o p m e n t i s t h a t i n a l l e i g h t o f t h e c r u i s e s , u s i n g t h e B a r r and S t r o u d as t h e t r e e measurement method r e s u l t e d i n c r u i s e volumes g r e a t e r t h a n when th e r e l a s k o p i s u s e d t o measure t h e t r e e s . In a l l but one c a s e , u s i n g t h e B a r r and S t r o u d gave t o t a l volume e s t i m a t e s g r e a t e r t h a n when t h e volume t a b l e was u s e d . When t h e r e l a s k o p was u s e d , e v e r y c r u i s e gave an e s t i m a t e o f t h e t o t a l l e s s t h a n when t h e volume t a b l e was u s e d t o o b t a i n t r e e v o l u m e s . However, upon e x a m i n i n g t h e c o n f i d e n c e l i m i t s p r e s e n t e d i n t h i s t a b l e i t w i l l be s e e n t h a t i n a l l but one c a s e , a c o n s i d e r a b l e amount o f o v e r l a p i s p r e s e n t between them. T h u s , i t i s d i f f i c u l t t o a s s e s s whether t h e s e d i f f e r e n c e s i n t h e p o i n t e s t i m a t e s r e p r e s e n t r e a l b i a s e s o r j u s t c h a n c e . In a d d i t i o n , no o p p o r t u n i t y was a v a i l a b l e t o a c t u a l l y f e l l t h e s e sample t r e e s t o d e t e r m i n e a b e t t e r answer t o t h i s q u e s t i o n . TABLE 2. BLOCK HM SUMMARY OF ACTIVITY TIMES METHOD SAMP. SIZE ACTIVITY TIME(HRS) TOTAL(HRS) PRISM 6 SWEEPING 7.7808 SAMPLING TREES(33) 6.9025 CHAINING .6667 15.3500 3-P 18 PREDICTING 1.9000 MARKING 3 .7633 LOCATING" 1 ) .8260 2) 1.9162 DENDROMETRY 0 1 ) 4.0967 7.5860 2) 8.7684 13.3479 3) 14.5434 19.1229 RATIO E S T . d 17 MARKING .2867 LOCATING 1 ) .6397 2) 2.1014 DENDROMETRY 0 1 ) 3.6833 6.5097 2) 7.2628 11.5509 3) 12.8633 17.1514 a. T h i s t i m e i n c l u d e s 12 t r e e s t h a t were ra n d o m l y d i s c a r d e d t o a c h i e v e t h e d e s i r e d c r u i s e i n t e n s i t y . b. 1) g i v e s t i m e when c a r r y i n g o n l y a c l i n o m e t e r and c h a i n 2) g i v e s t i m e when c a r r y i n g t r i p o d p l u s d e n d r o m e t e r and c h a i n . c . 1) when m e a s u r e d volume i s from a t a b l e . 2) when m e a s u r e d volume i s from w i d e - s c a l e r e l a s k o p r e a d i n g s . 3) when m e a s u r e d volume i s from B a r r & S t r o u d r e a d i n g s d. P r e d i c t i o n t i m e i s t h e same as f o r 3-P so i s not l i s t e d t w i c e . 40 TABLE 3. BLOCK HW SUMMARY OF ACTIVITY TIMES METHOD SAMP. S I Z E ACTIVITY TIME (HRS) TOTAL (HRS) PRISM 6 SWEEPING 5.5833 SAMPLING TREES(41) 5.0333 CHAINING 1 .5333 12.1499 3-P 1 3 PREDICTING 1.3017 MARKING .3942 LOCATING 1 ) .4758 2) 1.4083 DENDROMETRY 0 1) 2.3075 4.4792 2) 7.4894 10.5936 3) 10.5481 13.6523 RATIO E S T . d 12 MARKING .2542 LOCATING" 1) .3032 2) .91 97 DENDROMETRY 0 1) 1 .8994 3.8075 2) 3.6256 6.1502 3) 6.4350 8.9596 b, c , d - f o r e x p l a n a t i o n see f o o t of t a b l e 2. TABLE 4. BLOCK M SUMMARY OF ACTIVITY TIMES METHOD SAMPLE S I Z E ACTIVITY TIMES(HRS) TOTAL(HRS) PRISM 8 SWEEPING 11.5167 SAMPLING TREES(67) 12 . 1833 CHAINING 3.1167 26.8167 3-P 25 PREDICTING 3.4350 MARKING .621 7 LOCATING" 1 ) 1 .2500 2) 3.6271 DENDROMETRY 0 1 ) 4.6111 9.9178 2) 10.7917 18.4755 3) 17.5347 25.2185 RATIO E S T . d 18 MARKING .41 00 LOCATING 1 ) .9300 2) 3.0550 DENDROMETRY 0 1 ) 4.2200 8.9950 2) 9.9300 16.8300 3) 14.7850 21.6850 b, c , d - as d e s c r i b e d u n d e r t a b l e 2. TABLE 5. BLOCK W ACTIVITY TIMES SUMMARY METHOD SAMPLE SIZE A C T I V I T Y TIME(HRS) TOTAL(HRS) PRISM 8 SWEEPING 7.8667 SAMPLING TREES(41) 7.7000 CHAINING 1.3333 16.9000 > 3-P 24 PREDICTING 2.8100 MARKING .5552 LOCATING 1) 1.0000 2) 2.9785 DENDROMETRY 0 1 ) 3.4150 7.7802 2) 11.4933 17.8370 3) 18.2567 24.6004 RATIO E S T . d 18 MARKING .3550 LOCATING" 1 ) .8400 2) 2.2750 DENDROMETRY 0 1 ) 2.9067 6.9117 2) 7.3100 10.4750 3) 11.6367 14.8017 b , c , d - same as i n t a b l e 2. TABLE 6. SUMMARY OF CRUISE RESULTS BLOCK METHOD 3 TOT VOL(m 3 ) C 95% C. LIMITS ERROR LOWER UPPER (%) HW PRISM 404. 36 309. 499. 23.5 3-P 1 ) 412. 19 367. 457. 10.9 2) 374. 27 316. 432. 15.4 3) 431 . 20 380. 481 . 11.7 R.EST 1) 403. 31 316. 489. 21 .6 2) 322. 23 277. 367. 14.0 3) 400. 40 303. 497. 24.2 W PRISM 739. 33 556. 921 . 24.7 3-P 1 ) 835. 25 749. 919. 10.2 2) 797. 34 686. 908. 13.9 3) 930. 30 815. 1 044. 12.4 R.EST 1) 806. 31 686. 925. 14.8 2) 784. 38 640. 927. 18.3 3) 976. 42 775. 1 176. 20. 0 HM PRISM 389. 38 256. 522. 34. 1 3-P 1 ) 559. 31 476. 642. 14.8 2) 476. 29 410. 542. 13.8 3) 539. 26 473. 605. 12.3 R.EST 1) 434. 41 348. 517. 19.4 2) 387. 45 302. 472. 22. 0 3) 461 . 37 377. 544. 18.1 M PRISM 985. 31 752. 1218. 23. 6 3-P 1 ) 1 231 . 34 1061. 1 401 . 13.8 2) 1 1 50. 36 984. 1315. 14.4 3) 1 304. 33 1 1 29. 1 479. 13.4 R.EST 1) 1 1 68. 34 976. 1 359. 16.4 2) 1 087. 33 91 1 . 1 263. 16.2 3) 1 266. 31 1 074. 1 459. 15.2 a~! n r e p r e s e n t s t h e volume t a b l e t r e e measurement p r o c e d u r e . 2) r e p r e s e n t s t h e r e l a s k o p t r e e measurement p r o c e d u r e . 3) r e p r e s e n t s t h e B a r r & S t r o u d t r e e measurement p r o c e d u r e . As c a n be seen from column 2 of t a b l e s 2 t h r o u g h 5, sample s i z e s v a r i e d between c r u i s i n g methods. P a r t i c u l a r n o t e s h o u l d be made o f t h e v a r i a t i o n i n t h e sample s i z e s of t h e 3-P c r u i s e . The a c t u a l sample s i z e o b t a i n e d a t t h e t e r m i n a t i o n of t h e c r u i s e c a n n o t be c o n t r o l l e d r i g i d l y i n t h e f i e l d , a s m e n t i o n e d e a r l i e r . A g a i n , however, i f t h e b l o c k i s t o be r e t u r n e d t o f o r d e n d r o m e t r y l a t e r , i t i s a s i m p l e f i v e m i n u t e o f f i c e p r o c e d u r e t o ran d o m l y e l i m i n a t e e x t r a sample t r e e s as was done f o r b l o c k HM ( s e e t a b l e 2, t h e m a r k i n g a c t i v i t y ) . I t i s d i f f i c u l t t o a s s e s s t h e 43 p r o b a b i l i t y o f o b t a i n i n g a sample s i z e s m a l l e r o r l a r g e r t h a n e x p e c t e d f r o m t h i s s t u d y , b e c a u s e t h e sample s i z e was so s m a l l and b e c a u s e t h e s t u d y was not d e s i g n e d t o y i e l d s u c h i n f o r m a t i o n . The p o s s i b i l i t y of t h i s h a p p e n i n g has much g r e a t e r i m p l i c a t i o n s i f t h e d e n d r o m e t r y a c t i v i t y i s t o be done c o n c u r r e n t l y w i t h p r e d i c t i o n s ( a n o t h e r common v a r i a t i o n i n 3-P f i e l d p r o c e d u r e s ) , and s h o u l d be c o n s i d e r e d i n s u c h c a s e s . The v a r y i n g sample s i z e s a l s o a f f e c t e d t h e p r e c i s i o n o b t a i n e d by e a c h method i n t h i s s t u d y . E r r o r s r a n g e from 10.2 t o 34.1%. T h i s o b v i o u s l y p r o h i b i t s d i r e c t c o m p a r i s o n of t h e raw c r u i s e t i m e s t o d i s c o v e r w h i c h s a m p l i n g t e c h n i q u e i s t h e most e f f i c i e n t f o r a g i v e n b l o c k s i z e . A v e r y p r a c t i c a l method t o compare t h e e f f i c i e n c y of d i f f e r e n t s a m p l i n g t e c h n i q u e s i s t o examine t h e t o t a l c o s t ( o r t i m e ) i t t a k e s t o a c h i e v e a g i v e n p r e c i s i o n . To do so r e q u i r e s t h r e e b a s i c s t e p s . The f i r s t s t e p i s t o a v e r a g e t h e c o e f f i c i e n t s of v a r i a t i o n f o r e a c h method i n e a c h b l o c k , t o o b t a i n an e x p e c t e d c o e f f i c i e n t of v a r i a t i o n , C, f o r t h e g i v e n s t a n d c o n d i t i o n s ( i n t h e c a s e o f p o i n t s a m p l i n g ) and t h e g i v e n p r e d i c t o r ( i n t h e c a s e of 3-P and r a t i o e s t i m a t i o n ) . F o r p o i n t s a m p l i n g t h e a v e r a g e C was 34%. F o r 3-P w i t h volume t a b l e t r e e mesurement C was 28%, f o r r e l a s k o p measurement, C was 33%, and f o r B a r r and S t r o u d measurement 29%. F o r r a t i o e s t i m a t i o n w i t h volume t a b l e t r e e measurement C was 34%, f o r r e l a s k o p t r e e measurement, 35%, and f o r B a r r and S t r o u d t r e e measurement C was 37%. S e c o n d , t h e sample s i z e s needed t o o b t a i n t h e d e s i r e d p r e c i s i o n g i v e n t h e v a r i a b i l i t y (measured a s C) e n c o u n t e r e d i n t h e f i e l d a r e e s t i m a t e d s e p a r a t e l y f o r e a c h method. 44 T h i r d , a v e r a g e v a l u e s f o r t h e t i m e t o c o m p l e t e e a c h o f t h e s e p a r a t e a c t i v i t i e s must be m o d e l e d . The t i m e t o c o m p l e t e some of t h e a c t i v i t i e s w i l l be a f u n c t i o n of sample s i z e , o t h e r s w i l l n o t . In p o i n t s a m p l i n g , t h e s w e e p i n g a c t i v i t y i s a d e q u a t e l y d e s c r i b e d w i t h a s i m p l e a v e r a g e , p r o v i d e d t h e same mean number o f " i n " t r e e s p e r p l o t i s o b t a i n e d . In t h i s s t u d y t h e a v e r a g e number of " i n " t r e e s was e i g h t , and t h e a v e r a g e t i m e p e r p l o t was 1.1105 h o u r s f o r t h i s a c t i v i t y . The t i m e t o c o m p l e t e t h e s a m p l i n g t r e e s a c t i v i t y w i l l be a f u n c t i o n o f t h e number of t r e e s t h a t must be m e asured f o r h e i g h t . T h i s i s d e p e n d e n t on t h e number of s p e c i e s i n d i f f e r i n g f o r e s t t y p e s e n c o u n t e r e d i n t h e c r u i s e f o r w h i c h h e i g h t / d b h r e l a t i o n s h i p s must be d e v e l o p e d . The c r u i s i n g manual of t h e B.C. F o r e s t S e r v i c e recommends 30 h e i g h t / d b h p o i n t s f o r e a c h s p e c i e s i n e a c h f o r e s t t y p e . F o r s i m p l i c i t y , i t w i l l i n i t i a l l y be assumed t h a t o n l y one s p e c i e s i n one f o r e s t t y p e i s e n c o u n t e r e d , o r e q u i v a l e n t l y , t h a t t h i s one s p e c i e s d i s p l a y s t h e same h e i g h t / d b h r e l a t i o n s h i p i n a l l t h e f o r e s t t y p e s e n c o u n t e r e d . The a v e r a g e t i m e t o sample a t r e e f o r h e i g h t i s 0.1655 h o u r s . The t i m e n e c e s s a r y t o c o m p l e t e t h e c h a i n i n g a c t i v i t y i s l a r g e l y a f u n c t i o n of d i s t a n c e ( o r c u t b l o c k s i z e ) and t h e shape o f t h e b l o c k , and t o a l e s s e r d e g r e e , a f u n c t i o n o f t h e number o f p o i n t s or p l o t s t h a t must be i n s t a l l e d . The b l o c k s h a p e s used i n t h i s s t u d y were s q u a r e , so t h i s shape i s u s e d t o e x t r a p o l a t e t i m e s t o l a r g e r b l o c k s i z e s . In e s s e n c e , a f t e r t h e n e c e s s a r y sample s i z e i s e s t i m a t e d , t h e p l o t s a r e a r r a n g e d on p a p e r , i n a s y s t e m a t i c f a s h i o n t o p r o v i d e good c o v e r a g e o f a s q u a r e b l o c k . The t o t a l d i s t a n c e t o be c h a i n e d i s c a l c u l a t e d i n m e t e r s and m u l t i p l i e d by 45 t h e a v e r a g e c h a i n i n g t i m e p e r m e t e r . An a v e r a g e c h a i n i n g t i m e p e r meter o b t a i n e d i n t h i s s t u d y , 0.0074 h o u r s , was u s e d . The components f o r 3-P s a m p l i n g and r a t i o e s t i m a t i o n a r e e s s e n t i a l l y t h e same and w i l l be d e s c r i b e d t o g e t h e r . The time t o c o m p l e t e t h e p r e d i c t i n g a c t i v i t y i s l a r g e l y a f u n c t i o n of b l o c k s i z e and t h e number of t r e e s p e r h e c t a r e . D e n s i t y was kept f a i r l y c o n s t a n t so t h e t i m e t o p r e d i c t v o l u m e s w i l l v a r y d i r e c t l y w i t h b l o c k s i z e . The r e l a t i o n s h i p i s h y p o t h e s i z e d t o be l i n e a r on s t r o n g t h e o r e t i c a l g r o u n d s . S i n c e t h e b l o c k i s t r a v e r s e d i n s t r i p s o f a g i v e n , more o r l e s s c o n s t a n t w i d t h ( t o o wide and t h e p r e d i c t i o n s go w i l d , t o o narrow i s i n e f f i c i e n t ) , l i n e a r l y i n c r e a s i n g t h e b l o c k s i z e w i l l p r o d u c e a c o r r e s p o n d i n g l i n e a r i n c r e a s e i n t h e e f f e c t i v e s t r i p l e n g t h , t h u s p r o d u c i n g a l i n e a r i n c r e a s e i n t h e amount of t i m e t o walk a l o n g t h e s t r i p . The f i t t e d r e g r e s s i o n l i n e p r e d i c t i n g t h e t i m e n e c e s s a r y t o e s t i m a t e volumes f o r a l l t r e e s on a b l o c k i s b a s e d upon f o u r o b s e r v a t i o n s . The t i m e t o c o m p l e t e t h e m a r k i n g a c t i v i t y i s a f u n c t i o n o f t h e number of t r e e s t o mark, and w i l l v a r y d i r e c t l y w i t h sample s i z e . The t i m e n e c e s s a r y t o l o c a t e sample t r e e s , as w i t h c h a i n i n g , i s l a r g e l y a f u n c t i o n of t h e d i s t a n c e t r a v e l e d , and not t h e number of s t o p s made, so i t w i l l v a r y c h i e f l y w i t h b l o c k s i z e . The r e l a t i o n s h i p i s h y p o t h e s i z e d t o be l i n e a r b e c a u s e t h e e a s i e s t method o f r e l o c a t i n g t h e sample t r e e s i s t o walk a l o n g t h e s t r i p s marked w h i l e p r e d i c t i n g , so t h a t no t r e e i s m i s s e d . By way of t h e argument p r e s e n t e d e a r l i e r f o r t h e p r e d i c t i n g a c t i v i t y , when t h e b l o c k s i z e i s i n c r e a s e d l i n e a r l y , t h e e f f e c t i v e s t r i p l e n g t h i s a l s o i n c r e a s e d l i n e a r l y , t h u s , t h e t i m e i t t a k e s t o walk a l o n g t h e s t r i p i s i n c r e a s e d l i n e a r l y . I t s h o u l d be n o t e d t h a t t r e e s s e l e c t e d w i t h 3-P may o c c u r i n c l u m p s , w h i c h might a f f e c t t h e 46 l o c a t i o n t i m e . However, i t i s f u r t h e r assumed t h a t on t h e a v e r a g e , t h e sample t r e e s w i l l o c c u r i n a w e l l d i s t r i b u t e d f a s h i o n as w i t h t r e e s s e l e c t e d f o r r a t i o e s t i m a t i o n . Thus, t h e f i t t e d r e g r e s s i o n s u s e d t o p r e d i c t l o c a t i n g t i m e s f o r t h e d i f f e r i n g t r e e measurement methods a r e b a s e d upon e i g h t o b s e r v a t i o n s , i . e . , f o u r o b s e r v a t i o n s f r o m 3-P, and f o u r o b s e r v a t i o n s f r o m r a t i o e s t i m a t i o n . F i n a l l y , t h e t i m e t o c o m p l e t e t h e d e n d r o m e t r y a c t i v i t y i s l a r g e l y a f u n c t i o n of t h e number of t r e e s t h a t must be m easured. F o r t h e r e l a s k o p and t h e B a r r and S t r o u d , th e number of stem measurements p e r t r e e r a n g e d f r o m 5 t o 14, a v e r a g i n g 8.7. I t was f o u n d t h a t t h e t i m e t o c o m p l e t e t h i s a c t i v i t y v a r i e d w i t h t r e e s i z e ( i . e . , dbh and h e i g h t ) much more t h a n w i t h t h e number of measurements p e r t r e e . A t t e m p t s were made t o r e l a t e t h e t i m e s p e n t p e r t r e e s i m p l y t o dbh and h e i g h t . The b e s t r e l a t i o n s h i p a c c o u n t e d f o r l e s s t h a n 50% o f t h e v a r i a t i o n . T h i s i s t h e r e s u l t of f a i l i n g t o a c c o u n t f o r t o p o g r a p h y , h i g h b r u s h , b o l e s and b r a n c h e s o f n e i g h b o r i n g t r e e s , e t c . I n d e e d , t h e t i m e r e q u i r e d t o measure a t r e e w i t h a d e n d r o m e t e r i s much d e p e n d e n t on i t s s u r r o u n d i n g s (a phenomenon a l s o r e p o r t e d by B r i c k e l l 1976; G r e g o i r e , e t a_l 1986). Thus, a s i m p l e a v e r a g e t i m e p e r t r e e was u s e d f o r e a c h method. I t was f o u n d t h a t i n g e n e r a l , when u s i n g r a t i o e s t i m a t i o n , s m a l l e r t r e e s were s e l e c t e d as s a m p l e s when compared t o 3-P. We would e x p e c t t h i s b e c a u s e l a r g e t r e e s i n 3-P a r e s e l e c t e d w i t h g r e a t e r p r o b a b i l i t y t h a n s m a l l t r e e s . In one measurement method t h i s d i d a p p e a r t o have an e f f e c t on t h e amount of t i m e s p e n t m e a s u r i n g t h e t r e e s s e l e c t e d f o r r a t i o e s t i m a t i o n . The p e r t i n e n t r e l a t i o n s h i p s d e v e l o p e d f o r 3-P and r a t i o e s t i m a t i o n a r e as f o l l o w s : 47 L T C = .11735 + .88765 A L T D = 0.1889 + 2.7950 A PT = 0.0792 + 3.0433 A M T 3 p = .02589 h o u r s / t r e e V T 3 p = .1782 R T 3 p = .4175 B T 3 p = .7619 where, L T C = ti m e n e c e s s a r y t o l o c a t e a l l sample t r e e s on a g i v e n s i z e b l o c k , A i n ha, when c a r r y i n g o n l y c l i n o m e t e r and c h a i n . A = b l o c k s i z e i n h e c t a r e s r 2 = c o e f f i c i e n t o f d e t e r m i n a t i o n w h i c h c a n be i n t e r p r e t e d a s t h e d e c i m a l f r a c t i o n o f t h e t o t a l v a r i a t i o n t h a t i s e x p l a i n e d by t h e r e l a t i o n s h i p . p - v a l u e = t h e p r o b a b i l i t y o f o b s e r v i n g a more extreme v a l u e of r , under t h e h y p o t h e s i s of no c o r r e l a t i o n . L T D = ti m e n e c e s s a r y t o l o c a t e a l l sample t r e e s on a g i v e n b l o c k s i z e A, i n ha, when c a r r y i n g a t r i p o d and e i t h e r of t h e r e l a s k o p o r B a r r & S t r o u d . PT = t h e time n e c e s s a r y t o o c u l a r l y p r e d i c t t h e volumes of a l l t h e t r e e s on a b l o c k of A h e c t a r e s i n s i z e . M T 3 p , MT R = t h e a v e r a g e t i m e n e c e s s a r y t o mark a sample t r e e d u r i n g a 3-P c r u i s e , or d u r i n g r a t i o e s t i m a t i o n r e s p e c t i v e l y , f o r e a s y l o c a t i o n l a t e r V T 3 p , V T R = The a v e r a g e t i m e n e c e s s a r y t o "measure" a t r e e d u r i n g 3-P o r r a t i o e s t i m a t i o n r e s p e c t i v e l y , f o r e n t r y i n t o a volume t a b l e R T 3 p , R T R = t h e t i m e n e c e s s a r y t o measure a t r e e d u r i n g 3-P or r a t i o e s t i m a t i o n r e s p e c t i v e l y , w i t h t h e wide-s c a l e r e l a s k o p B T 3 p , B T R = t h e ti m e n e c e s s a r y t o measure a t r e e w i t h t h e B a r r and S t r o u d d e n d r o m e t e r d u r i n g 3-P o r r a t i o e s t i m a t i o n , r e s p e c t i v e l y , F o u r t h , e s t i m a t e t h e t i m e n e c e s s a r y t o c o m p l e t e e a c h a c t i v i t y g i v e n t h e sample s i z e p r e v i o u s l y c a l c u l a t e d , and d e r i v e t h e t o t a l c r u i s e t i m e by summing a l l t h e t i m e s f o r t h e r 2 = .6184 p - v a l u e = . 02 r 2 = .6879 p - v a l u e = . 01 r 2 - .8608 p - v a l u e = . 10 MT R = .02094 h o u r s / t r e e V T R = . 1 906 I ! R T R = .4615 1! B T R = .7395 1! 48 a c t i v i t i e s . T h i s was done t o e s t i m a t e t h e r e q u i r e d t i m e t o c o m p l e t e a c r u i s e f o r + o r - 1 5 % p r e c i s i o n 19 t i m e s o u t of t w e n t y , on b l o c k s i z e s r a n g i n g from 0.5 t o 12 h e c t a r e s f o r e a c h method and i t s v a r i a t i o n s . The r e s u l t s a r e d i s p l a y e d g r a p h i c a l l y i n f i g u r e 1 f o r p o i n t s a m p l i n g and v a r i a t i o n s o f 3P. Note t h a t t h e c u r v e s r e p r e s e n t i n g t h e t i m e i t t a k e s t o c o m p l e t e a 3-P c r u i s e a r e below t h e c u r v e r e p r e s e n t i n g t h e t i m e i t t a k e s t o c o m p l e t e a p o i n t s a m p l i n g c r u i s e f o r b l o c k s i z e s below f i v e h e c t a r e s . T h i s i n d i c a t e s t h a t 3P s a m p l i n g w i t h any of i t s v a r i a t i o n s i s more e f f i c i e n t i n t h e s e b l o c k s i z e s . F i g u r e 2 shows a s i m i l a r g r a p h c o m p a r i n g r a t i o e s t i m a t i o n w i t h p o i n t s a m p l i n g . R a t i o e s t i m a t i o n was f o u n d t o be s l i g h t l y l e s s e f f i c i e n t t h a n 3-P b e c a u s e i t i s seen t h a t w i t h a l l i t s v a r i a t i o n s i t i s more e f f i c i e n t t h a n p o i n t s a m p l i n g o n l y up t o b l o c k s i z e s o f t h r e e h e c t a r e s . In t h i s s t u d y i t was f o u n d t h a t i t i s more d i f f i c u l t t o o c u l a r l y p r e d i c t v o l u m e s o f s m a l l t r e e s c o n s i s t e n t l y t h a n i t i s t o p r e d i c t volumes of l a r g e t r e e s . When u s i n g r a t i o e s t i m a t i o n , t r e e s a r e s e l e c t e d w i t h e q u a l p r o b a b i l i t y r e s u l t i n g i n t h e s e l e c t i o n o f more s m a l l e r t r e e s than w i t h 3-P. Hence, t h e v a r i a b i l i t y of p r e d i c t i o n s when e m p l o y i n g a r a t i o e s t i m a t o r i s g r e a t e r t h a n when a 3-P e s t i m a t o r i s u s e d . T h i s r e s u l t s i n a l a r g e r sample s i z e n e c e s s a r y t o meet c r u i s e o b j e c t i v e s , t h u s d e c r e a s i n g i t s e f f i c i e n c y . I t i s i n t e r e s t i n g t o n o t e t h a t u s i n g t h e B a r r and S t r o u d as t h e t r e e measurement t e c h n i q u e i s s l i g h t l y l e s s e f f i c i e n t t h a n p o i n t s a m p l i n g i n one h e c t a r e b l o c k s i z e s , but becomes more e f f i c i e n t f o r two h e c t a r e b l o c k s i z e s , t h e n l e s s e f f i c i e n t a g a i n f o r b l o c k s i z e s g r e a t e r t h a n t h a t . F i g u r e 1. T o t a l c r u i s e t i m e f o r p o i n t s a m p l i n g compared t o 3P u s i n g t h r e e t r e e measurement t e c h n i q u e s , g i v e n t h e o b s e r v e d v a r i a b i l i t y . 50 F i g u r e 2 . T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g compared t o r a t i o e s t i m a t i o n u s i n g t h r e e t r e e measurement t e c h n i q u e s , g i v e n t h e o b s e r v e d v a r i a b i l i t y . o o i i 1 1 1 1 1 1 r 0"08 O'OZ. 0 09 O'OS 0 0 * O'Of 003 O'Ol O'O (SJI | 'uaiu z) 3kNll 3Sind3 1 V 1 0 1 51 T h i s i s t h e r e s u l t o f t h e f p c ( f i n i t e p o p u l a t i o n c o r r e c t i o n ) making a s m a l l e r number o f s a m p l e s needed f o r p o i n t s a m p l i n g i n t h e s m a l l e s t b l o c k s i z e . As c a n be s e e n f r o m f i g u r e 2 t h e c u r v e d i s p l a y i n g t i m e s t o c o m p l e t e a p o i n t sample l e v e l s o u t q u i c k l y , b e c a u s e a s c u t b l o c k s i z e i n c r e a s e s , t h e c h a r a c t e r i s t i c s of an i n f i n i t e p o p u l a t i o n a r e a p p r o a c h e d r a p i d l y . I f 3-P s a m p l i n g u s i n g a volume t a b l e o n l y (volume e q u a t i o n s o r t a p e r e q u a t i o n s as w e l l may be used) t o o b t a i n t r e e measurements i s c o n s i d e r e d , t h e n 3-P i s more e f f i c i e n t up t o a p p r o x i m a t e l y e i g h t h e c t a r e s . I f r a t i o e s t i m a t i o n u s i n g volume e q u a t i o n s t o o b t a i n t r e e volumes i s c o n s i d e r e d , t h e n a r a t i o e s t i m a t o r i s more e f f i c i e n t t h a n a p o i n t s a m p l i n g e s t i m a t o r up t o b l o c k s i z e s of j u s t under e i g h t h e c t a r e s . Use o f volume t a b l e s o r volume ( t a p e r ) e q u a t i o n s may be c o m p l e t e l y s a t i s f a c t o r y i n c a s e s where a c c u r a t e and p r e c i s e e q u a t i o n s have been d e v e l o p e d , s u c h a s t h o s e by D e m a e r s c h a l k and Kozak ( 1 9 7 7 ) , o r Ormerod ( 1 9 8 6 ) . The t i m e s r e p o r t e d so f a r f o r p o i n t s a m p l i n g assume t h a t t h e r e i s o n l y one s p e c i e s e n c o u n t e r e d i n t h e b l o c k f o r w h i c h a h e i g h t / d b h r e l a t i o n s h i p must be d e v e l o p e d . T h i s n e c e s s i t a t e s t h e measurement of a p p r o x i m a t e l y 30 t r e e s f o r h e i g h t t o form a r e l i a b l e h e i g h t / d b h c u r v e . When two o r t h r e e s p e c i e s a r e e n c o u n t e r e d i n t h e f i e l d , t h e n l o g i c a l l y 60 or 90 t r e e s must be m e asured f o r h e i g h t . The impact o f t h i s d e v e l o p m e n t on t h e t i m e n e c e s s a r y t o c o m p l e t e a p o i n t s a m p l i n g c r u i s e i s i l l u s t r a t e d i n f i g u r e 3 i n c o m p a r i s o n w i t h 3-P u s i n g t h e d i f f e r e n t t r e e measurement t e c h n i q u e s . • F i g u r e 3. T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g i n s t a n d s w i t h t h r e e s p e c i e s compared w i t h 3P u s i n g t h r e e t r e e measurement methods, g i v e n t h e o b s e r v e d v a r i a b i l i t y . 53 I t w i l l be s e e n t h a t 3-P w i t h any of t h e t r e e measurement methods i s now more e f f i c i e n t i n b l o c k s i z e s up t o e i g h t h e c t a r e s . F i g u r e 4 i l l u s t r a t e s t h i s s i t u a t i o n f o r r a t i o e s t i m a t i o n w i t h a l l t h e d i f f e r e n t t r e e measurement methods. R a t i o e s t i m a t i o n i s now more e f f i c i e n t t h a n p o i n t s a m p l i n g up t o b l o c k s i z e s o f s i x h e c t a r e s . A d d i t i o n a l l y , one may c o n s i d e r t h e e f f e c t s of d i f f e r e n t c o e f f i c i e n t s o f v a r i a t i o n on t h e amount of t i m e n e c e s s a r y t o c o m p l e t e e a c h c r u i s e . The c o e f f i c i e n t of v a r i a t i o n a c h i e v e d by t h e p r e d i c t o r i n t h i s s t u d y was a r o u n d 30 p e r c e n t . T h i s i s c o n s i d e r e d t o be somewhat h i g h , and i n d i c a t i v e o f a b e g i n n e r (Mesavage 1970). T y p i c a l l y , e x p e r i e n c e d c r u i s e r s can a c h i e v e c o e f f i c i e n t s o f v a r i a t i o n as low as 20 p e r c e n t . A l s o , t h e c o e f f i c i e n t o f v a r i a t i o n of p r i s m p l o t volumes was a p p r o x i m a t e l y 32 p e r c e n t . More t y p i c a l l y , c o e f f i c i e n t s of v a r i a t i o n a r o u n d 50 p e r c e n t o r more a r e not uncommon. The i m p l i c a t i o n s of t h e s e f a c t s and t h e i r e f f e c t on t o t a l c r u i s i n g t i m e c a n be seen i n f i g u r e 5 f o r p o i n t s a m p l i n g and 3-P u s i n g t h e volume e q u a t i o n measurement p r o c e d u r e . Note t h a t t h e s i z e of b l o c k i n w h i c h 3-P i s more e f f i c i e n t t h a n p o i n t s a m p l i n g has i n c r e a s e d t o n e a r l y 14 h e c t a r e s as compared t o o n l y 11, when t h e o b s e r v e d v a r i a b i l i t y i s c o n s i d e r e d ( s e e f i g u r e 3 ) . T h e r e i s l i t t l e t o c h o o s e between a r a t i o or a 3-P e s t i m a t o r f o r a g i v e n v a r i a b i l i t y o f p r e d i c t i o n s . The t i m e r e q u i r e d t o c o m p l e t e a c r u i s e u s i n g r a t i o e s t i m a t i o n i s a c t u a l l y s l i g h t l y l e s s t h a n t h e t i m e needed f o r a 3-P c r u i s e , b e c a u s e l e s s t i m e i s s p e n t e m p l o y i n g t h e sample t r e e s e l e c t i o n c r i t e r i a . The d i f f e r e n c e i s so s l i g h t however, t h a t i f t h e c u r v e s of t o t a l c r u i s e t i m e f o r r a t i o e s t i m a t i o n and 3-P u s i n g t h e same t r e e measurement t e c h n i q u e were drawn on t h e same a x e s t h e y would v i r t u a l l y c o i n c i d e . F i g u r e 4. T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g i n s t a n d s w i t h t h r e e s p e c i e s compared w i t h r a t i o e s t i m a t i o n u s i n g t h r e e t r e e measurement methods, g i v e n t h e o b s e r v e d v a r i a b l i t y . o o i i i i i i i 1 r 0"08 0 0L 0 ' 09 0 09, O'OV 0 0 £ 0 0 3 O'Ol O'O (SJI| «U9LU z) 3WI1 3Sind0 1 V 1 0 1 F i g u r e 5. T o t a l c r u i s e t i m e s f o r p o i n t s a m p l i n g i n s t a n d s w i t h t h r e e s p e c i e s compared w i t h 3P u s i n g t h e volume e q u a t i o n t r e e measurement method, a s s u m i n g t y p i c a l v a r i a b i l i t y . o i 1 1 1 1 h 6 O'OOt 0 08 0*09 0 0V 00Z O'O ( S J L J 'U8LU z) IkNIi 3Sind0 1 V 1 0 1 56 T h e r e f o r e , a g r a p h c o m p a r i n g p o i n t s a m p l i n g w i t h r a t i o e s t i m a t i o n , g i v e n t h e s e h y p o t h e t i c a l c o e f f i c i e n t s o f v a r i a t i o n i s not g i v e n . A l t h o u g h t h e t i m e s r e p o r t e d h e r e a r e f o r a s p e c i f i c two man crew and may n o t r e p r e s e n t what some would c o n s i d e r r e a l i s t i c t i m e s i n t e r m s o f a b s o l u t e v a l u e , i t must be r e i t e r a t e d t h a t t h e r e l a t i v e d i f f e r e n c e s e x i s t i n g between t h e methods w i l l remain v a l i d no m a t t e r what r a t i n g t h e work i s g i v e n t o a r r i v e a t a " n o r m a l " t i m e . To i l l u s t r a t e , s u p p o s e t h e e s t i m a t e d c r u i s e t i m e s f o r p o i n t s a m p l i n g t h a t a p p e a r i n f i g u r e 5 a r e j u d g e d t o be t w i c e as l o n g as t h e amount o f t i m e t h a t i s n e c e s s a r y t o c r u i s e t h e g i v e n b l o c k s i z e s . Then, th e work i n t h i s s t u d y would be j u d g e d t o have been p e r f o r m e d a t a r a t e o f 50% of n o r m a l p a c e . When a l l t h e t i m e s a r e c o r r e c t e d t o normal p a c e by m u l t i p l y i n g them by 0.5 ( t h e r a t i n g e x p r e s s e d as a d e c i m a l f r a c t i o n ) , t h e r e l a t i o n s h i p between c r u i s e t i m e and c u t b l o c k s i z e i s as a p p e a r s i n f i g u r e 6. Note t h a t a l t h o u g h t h e s l o p e s o f t h e c u r v e s have c h a n g e d and t h e a b s o l u t e d i f f e r e n c e s have c h a n g e d , t h e r e l a t i v e d i f f e r e n c e s have not and t h e 3-P e s t i m a t o r i s s t i l l more e f f i c i e n t t h a n p o i n t s a m p l i n g up t o t h e same s i z e b l o c k as i n f i g u r e 5. The f o r e g o i n g d i s c u s s i o n shows t h a t 3-P c e r t a i n l y a p p e a r s t o be an e f f i c i e n t s a m p l i n g t e c h n i q u e , as does r a t i o e s t i m a t i o n , when compared t o p o i n t s a m p l i n g . However, as was s u s p e c t e d , t h e y l o s e t h e i r s u p e r i o r i t y i n t h e l a r g e r b l o c k s i z e s . What has not been known b e f o r e i s t h a t t h i s p r a c t i c a l u p p e r l i m i t t o b l o c k s i z e i s a r o u n d 12 t o 15 h e c t a r e s , g i v e n t y p i c a l v a r i a b i l i t i e s l i k e l y t o be e n c o u n t e r e d i n t h e f i e l d . 57 F i g u r e 6. T o t a l c r i u s e t i m e s f o r p o i n t s a m p l i n g i n s t a n d s w i t h t h r e e s p e c i e s compared w i t h 3P u s i n g t h e volume e q u a t i o n method, a s s u m i n g t y p i c a l v a r i a b i l i t y , and a j u s t e d t o n o r m a l p a c e . CONCLUSIONS From t h e r e s u l t s of t h i s s t u d y , i t c a n be s a i d t h a t 3-P s a m p l i n g i s u n c o n d i t i o n a l l y more e f f i c i e n t t h a n p o i n t s a m p l i n g i n c u t t i n g b l o c k s i z e s up t o f i v e h e c t a r e s f o r a l l t h e t r e e measurement t e c h n i q u e s t e s t e d . I f one c o n s i d e r s t r e e measurement by means o f t h e w i d e - s c a l e r e l a s k o p , t h e n i t i s more e f f i c i e n t i n b l o c k s i z e s up t o s i x h e c t a r e s . I f one c o n s i d e r s o b t a i n i n g t r e e volumes by means of a volume e q u a t i o n ( o r t a p e r e q u a t i o n ) , t h e n 3-P i s more e f f i c i e n t t h a n p o i n t s a m p l i n g i n b l o c k s i z e s up t o e i g h t h e c t a r e s . In g e n e r a l , i t was d i s c o v e r e d t h a t 3-P i s s l i g h t l y more p r e c i s e t h a n r a t i o e s t i m a t i o n ( m e a n - o f - r a t i o s e s t i m a t o r ) . R a t i o e s t i m a t i o n u s i n g t h e B a r r and S t r o u d o p t i c a l d e n d r o m e t e r t o o b t a i n t r e e v o l u m e s was f o u n d t o be l e s s e f f i c i e n t t h a n p o i n t s a m p l i n g , g i v e n t h e o b s e r v e d c o e f f i c i e n t o f v a r i a t i o n . I f one c o n s i d e r s t h e r e l a s k o p a s t h e t r e e measurement t e c h n i q u e , r a t i o e s t i m a t i o n was f o u n d t o be more e f f i c i e n t t h a n p o i n t s a m p l i n g up t o b l o c k s i z e s of s i x h e c t a r e s . C o n s i d e r i n g t h e volume e q u a t i o n method o f o b t a i n i n g t r e e v o l u m e s , r a t i o e s t i m a t i o n was more e f f i c i e n t t h a n p o i n t s a m p l i n g i n b l o c k s i z e s up t o a p p r o x i m a t e l y e i g h t h e c t a r e s . When one c o n s i d e r s t h e p o s s i b i l i t y of h a v i n g t o d e v e l o p h e i g h t / d b h r e l a t i o n s h i p s f o r more t h a n one s p e c i e s i n t h e c r u i s e , t h e n 3-P s a m p l i n g i s more e f f i c i e n t t h a n p o i n t s a m p l i n g i n b l o c k s i z e s up t o between s i x and e l e v e n h e c t a r e s , d e p e n d i n g on t h e t r e e measurement method c h o s e n . Under t h i s h y p o t h e s i s , r a t i o e s t i m a t i o n i s a l s o more e f f i c i e n t t h a n p o i n t s a m p l i n g i n t h e same 59 b l o c k s i z e s a s 3-P, d e p e n d i n g a g a i n , on t h e t r e e measurement method c h o s e n . Under t h e h y p o t h e s i s o f t y p i c a l c o e f f i c i e n t s o f v a r i a t i o n l i k e l y t o be e n c o u n t e r e d i n t h e f i e l d , t h e n 3-P and r a t i o e s t i m a t i o n c a n be more e f f i c i e n t i n b l o c k s i z e s up t o a maximum of 14 h e c t a r e s . T hese c o n c l u s i o n s a p p l y b r o a d l y t o any a r e a e x h i b i t i n g s i m i l a r s t a n d c o n d i t i o n s t o t h o s e where t h e methods were t e s t e d . < 60 LITERATURE CITED BCMF. 1976. Whole stem c u b i c metre volume e q u a t i o n s and t a b l e s -c e n t i m e t r e d i a m e t e r c l a s s m e r c h a n t a b l e volume f a c t o r s . F o r . I n v . D i v . B r i t i s h C o l u m b i a M i n i s t r y of F o r e s t s . D e p t . of F o r e s t s . 4 p., 64 t a b l e s , 13 f i g s . BCMF. 1982. F o r e s t s e r v i c e c r u i s i n g p r o c e d u r e s and c r u i s e c o m p i l a t i o n . P r o v i n c e o f B r i t i s h C o l u m b i a M i n i s t r y of F o r e s t s . 117 p., a p p e n d i c e s . B e h r e , C.E. 1927. Form c l a s s t a p e r c u r v e s and volume t a b l e s and t h e i r a p p l i c a t i o n . J . A g r i c . Res. 35:673-744. Bonnor, G.M. 1972. A t e s t of 3-P s a m p l i n g i n f o r e s t i n v e n t o r i e s . F o r . S c i . 18(3) : 198-202. B r i c k e l l , J . E . 1976. B i a s and p r e c i s i o n of t h e B a r r and S t r o u d d e n d r o m e t e r under f i e l d c o n d i t i o n s . USDA F o r . S e r v . I n t e r m o u n t a i n f o r e s t and Range Exp. S t a . Res. Pap. INT-186, 46 p. C o c h r a n , W.G. 1977. S a m p l i n g t e c h n i q u e s , 3 r d e d . John W i l e y & Sons, New Y o r k , 428 p. C u n i a , T. 1959. N o t e s on C r u i s i n g I n t e n s i t y by t h e B i t t e r l i c h method. J . F o r e s t r y . 57(11):849-850. C u n i a , T. 1965. Some T h e o r y on r e l i a b i l i t y o f volume e s t i m a t e s i n a f o r e s t i n v e n t o r y sample. F o r . S c i . 1 1 ( 1 ) : 1 1 5 - 1 2 8 . D e m a e r s c h a l k , J.P., and A. Kozak. 1977. The w h o l e - b o l e s y s t e m : a c o n d i t i o n e d d u a l e q u a t i o n s y s t e m f o r p r e c i s e p r e d i c t i o n of t r e e p r o f i l e s . Can. J . F o r . Res. 7:488-497. D i l w o r t h , J . R., and J . F . B e l l . 1967. V a r i a b l e p l o t c r u i s i n g . O.S.U. B o o k s t o r e s , I n c . C o r v a l l i s , OR. USA. 117 p. Ek, A.R. 1971. A c o m p a r i s o n of some e s t i m a t o r s i n f o r e s t s a m p l i n g . F o r . S c i . 1 7 ( 1 ) : 2 — 1 3 . F r e e s e , F. 1960. T e s t i n g a c c u r a c y . F o r . S c i . 6:139-145. F r e e s e , F. 1962. E l e m e n t a r y f o r e s t s a m p l i n g . USDA F o r . S e r v . Ag. Handbook No. 232, 91 p. G r e g o i r e , T.G., H.T. V a l e n t i n e , and G.M. F u r n i v a l . 1986. E s i m a t i o n of b o l e volume by i m p o r t a n c e s a m p l i n g . Can. J . F o r . Res. 16:554-557. G r o s e n b a u g h , L.R. 1952. P l o t l e s s t i m b e r e s t i m a t e s - New, f a s t , e a s y . J . F o r . 5 0 d ) : 3 2 - 3 7 G r o s e n b a u g h , L.R. 1963. O p t i c a l d e n d r o m e t e r s f o r o u t - o f - r e a c h d i a m e t e r s : a c o n s p e c t u s and some new t h e o r y . F o r . S c i . Mon. no. 4, 47 p. G r o s e n b a u g h , L.R. 1964. Some s u g g e s t i o n s f o r b e t t e r sample t r e e measurement. P r o c e e d i n g s . S o c. Am. F o r . M e e t i n g 1963. p36-42. G r o s e n b a u g h , L.R. 1965. 3-P s a m p l i n g t h e o r y and p r o g r a m THRP f o r computer g e n e r a t i o n o f s e l e c t i o n c r i t e r i a . USDA F o r . S e r v . Res. Pap. PSW-21, 53 p. G r o s e n b a u g h , L.R. 1967. The g a i n s from sample t r e e s e l e c t i o n w i t h u n e q u a l p r o b a b i l i t i e s . J . F o r . 65 ( 3 ) : 2 0 3 - 2 0 6 . G r o s e n b a u g h , L.R. 1976. A p p r o x i m a t e s a m p l i n g v a r i a n c e of a d j u s t e d 3-P e s t i m a t e s . F o r . S c i . 2 2 ( 2 ) : 1 7 3 - 1 7 6 . Hartman, G.B. 1966. Some p r a c t i c a l e x p e r i e n c e w i t h 3-P s a m p l i n g and t h e B a r r and S t r o u d d e n d r o m e t e r i n t i m b e r s a l e s . SAF P r o c e e d i n g s , 1965, p126-130. H a z a r d , J.W., and J.M. B e r g e r . 1972. Volume t a b l e s v s . d e n d r o m e t e r s f o r f o r e s t s u r v e y s . J . F o r . 7 0 ( 4 ) : 2 1 6 - 2 1 9 . H e t h e r i n g t o n , J . C . 1982a. 3-P s a m p l i n g - t h e d e v i l y ou do n ' t know. S c o t t i s h F o r e s t r y . 36 ( 0:25-35. H e t h e r i n g t o n , J . C . 1982b. E r r a t u m . B e t t e r t h e d e v i l you know! S c o t t i s h F o r e s t r y . 3 6 ( 3 ) : 2 1 9 . Husch, B., C . I . M i l l e r , and T.W. B e e r s . 1972. F o r e s t M e n s u r a t i o n , 2nd e d . John W i l e y & Sons, New Y o r k , 210 p. l i e s , K. 1978. I n c r e a s i n g e s t i m a t i o n e f f i c i e n c y i n 3-P c r u i s e s . F o r . C h r o n . 54 ( 0:42-43. James, C.A., and A. Kozak. 1984. F i t t i n g t a p e r e q u a t i o n s from s t a n d i n g t r e e s . F o r . C h r o n . 6 0 ( 6 ) : 1 5 7 - 1 6 1 . J e f f e r s , J.N.R. 1956. B a r r and S t r o u d d e n d r o m e t e r t y p e FP-7. F o r . Comm. Rep. on F o r e s t R e s e a r c h f o r t h e y e a r ended March, 1955:127-136. IN B r i c k e l l , J . E . 1976. ( s e e a b o v e ) . J o h n s o n , F.A., W.G. Dahms, and P.E. H i g h t r e e . 1967. A f i e l d t e s t o f 3-P c r u i s i n g . J . F o r . 65:722-726. K a s i l e , J.D. 1983. 3-P s a m p l i n g f o r d o l l a r s . IN Renewable r e s o u r c e i n v e n t o r i e s f o r m o n o t o r i n g c h a n g e s and t r e n d s . P r o c e e d i n g s o f an I n t e r n a t i o n a l c o n f e r e n c e . Aug. 15-19, 1983. C o r v a l i s , OR. USA. Eds John F. B e l l , Toby A t t e r b u r y , p703-706. M a r t i n , A . J . 1984. T e s t i n g volume e q u a t i o n a c c u r a c y w i t h water d i s p l a c e m e n t t e c h n i q u e s . F o r . S c i . 30 ( 0:41-50. 62 Mesavage, C. 1969. New B a r r and S t r o u d d e n d r o m e t e r Model FP-15. J . F o r . 6 7 ( 1 ) : 4 0 - 4 1 . Mesavage, C. 1971. STX t i m b e r e s t i m a t i n g w i t h 3-P s a m p l i n g and d e n d r o m e t r y . USDA F o r . S e r v . Ag. Handbook No. 415., 135 p. Omule, S.A.Y. 1981. Volume e s t i m a t e s i n t r o p i c a l f o r e s t s u s i n g 3-P s a m p l i n g . Commonw. F o r . Rev. 6 0 ( 3 ) : 2 0 7 - 2 0 9 . Ormerod, D.W. 1986. The d i a m e t e r - p o i n t method f o r t r e e t a p e r d e s c r i p t i o n . Can. J . F o r . Res. 16:484-490. P a l l e y , M.N., and H o r w i t z , L.G. 1961. P r o p e r t i e s o f some random and s y s t e m a t i c p o i n t s a m p l i n g e s t i m a t o r s . F o r . S c i . 7 ( 1 ) : 5 2 - 6 5 . P e l z , D.R. 1980. [ S a m p l i n g methods w i t h v a r i a b l e p r o b a b i l i t i e s o f s e l e c t i o n ] S t i c h p r o b e n m i t v a r i a b l e n a u s w a h l w a h r s c h w e i n l i c h k e i t e n . A l l g e m e i n e F o r s t - und J a g d z e i t u n g . 5 1 ( 2 ) : 3 7 - 4 1 . P f e i f f e r , K. 1967. A n a l y s i s of methods of s t u d y i n g o p e r a t i o n a l e f f i c i e n c y i n f o r e s t r y . MF t h e s i s , U n i v e r s i t y of B r i t i s h C o l u m b i a . , 93 p. R o s s , R.D. 1968. On t h e a c c u r a c y o f p e n t a - p r i s m c a l i p e r s . J . F o r . 66:932-933. IN B r i c k e l l , J . E . 1976. ( s e e a b o v e ) . S c h r e u d e r , H.T., J . S e d r a n s k , and K.D. Ware, 1968. 3-P s a m p l i n g and some a l t e r n a t i v e s , I . F o r . S c i . 1 4 ( 4 ) : 4 2 9 - 4 5 3 . S c h r e u d e r , H.T., J . S e d r a n s k , K.D. Ware, and D.A. H a m i l t o n . 1971. 3-P s a m p l i n g and some a l t e r n a t i v e s , I I . F o r . S c i . 17(1 ) : 1 0 3 - 1 1 8 . S e p p a l a , R. 1971. V a r i a b l e p r o b a b i l i t i e s i n s a m p l e - t r e e s e l e c t i o n . Commun. I n s t . F o r . F e n n . 7 4 ( 4 ) : 2 9 p. IN F o r . A bs. S h a r p n a c k , D.A. 1964. A computer t r i a l of 3-P s a m p l i n g . P r o c e e d i n g s , S o c . Am. F o r e s t e r s , D e n v e r , CO. USA, p225-226. S t a g e , A.R. 1962. A f i e l d t e s t o f p o i n t sample c r u i s i n g . USFS I n t e r m o u n t a i n F o r . and Range Exp. S t a . R e s . Pap. 67., I7p. IN B r i c k e l l , J . E . 1976. ( s e e a b o v e ) . S u s s , H. 1982. [ I n v e n t o r y o f a r a n g e r d i s t r i c t i n f o u r d a y s u s i n g d a t a f r o m a p r e v i o u s i n v e n t o r y and 3-P s a m p l i n g . ] A l l g e m e i n e F o r s t z e i t u n g . 3 ( 1 2 ) : 3 3 5 . IN F o r . Abs. T a k a t a , K. 1982. [A t e s t o f 3-P s a m p l i n g by co m p u t e r s i m u l a t i o n ] . B u l l e t i n , N i g a t a U n i v e r s t i y F o r e s t s , No. 15., 99-103. IN F o r . Abs. Yocom, H.A., and D.A. Bower. 1975. E s t i m a t i n g i n d i v i d u a l t r e e v o l u m e s w i t h S p i e g e l R e l a s k o p and B a r r and S t r o u d d e n d r o m e t e r . J . F o r . 73(9):581-582,605. APPENDIX Le t , A = t o t a l c r u i s i n g area i n ha, G = t o t a l b a s a l area of a l l t r e e s i n stand (m 2), r = r a d i u s of t r e e ( i n m), N = t o t a l number of t r e e s i n stand, R = p l o t r a d i u s f o r t r e e of r a d i u s r i n meters. Then G = fjTri2 1 I t i s known (Husch, M i l l e r , Beers 1972, p.263) that F = 2500k 2 where F = b a s a l area f a c t o r of prism i n m2 per ha and k i s the "gauge c o n s t a n t " (k = 2r/R). S o l v i n g f o r R i n terms of F: F = 2500k 2 •^F/50 = k y/f/50 = 2r/R )00rAjF = R . Now, l e t us d e f i n e Q as the sum of the areas of the c i r c l e s generated around each t r e e by any F f a c t o r prism (these areas o v e r l a p 50 each p o i n t i n the f o r e s t i s covered by one or more these c i r c l e s , sometimes none). Q - f.nRi2 1 = J ^ r i O O O O r i V F = 10000G/F. To put t h i s on a hectare b a s i s : 1 ha/10000m 2*10000G/F = G/F. And, l e t us d e f i n e m a s t h e a v e r a g e number of c i r c l e s f a l l i n g c any p o i n t , m = Q/A = G/FA. So, as i s known, b a s a l a r e a p e r h e c t a r e (G/A) = Fm. I f we c a l l q t h e t o t a l a r e a o f t r e e c i r c l e s i n t h e sample, E ( q ) = E( ° £ K j i Q_ N E ( n K M ) Q ', Qnm n E ( K M ) = N w N where E d e n o t e s e x p e c t a t i o n , n i s t h e sample s i z e , K j i s t h e number o f t r e e s on p o i n t j , and K M i s t h e mean number o f t r e e s p e r p o i n t i n t h e sample. L e t p = q/Q , o r c r u i s e i n t e n s i t y e x p r e s s e d a s a d e c i m a l . Then, E ( p ) = E(q/Q) = E ( q ) / Q = nm/N nG NFA Now, c a l l s a m p l i n g e r r o r o f t h e mean, E . E = t S M where t = an a p p r o p r i a t e v a l u e o f S t u d e n t ' s t - s t a t i s t i c S M= S t a n d a r d e r r o r o f a v e r a g e volume/ha e s t i m a t e t S ^ ( 1-n/N) E = where S = s t a n d a r d d e v i a t i o n o f p l o t volume/ha e s t i m a t e s . B u t , n/N = p w ng/FA o r t h e a v e r a g e c r u i s e i n t e n s i t y . S u b s t i t u t i n g t h i s i n t o t h e p r e v i o u s e x p r e s s i o n g i v e s t S -yJil-nq/Fh) E = t S 1-ng/FA) E t 2 S 2 ( 1 - n g / F A ) n = E 2 - t 2 S 2 t 2 S 2 n g n = E 2 E 2 F A t 2 S 2 g t 2 S 2 n (1 + ) = E 2 E 2 t 2 S 2 ~1T n = n F i n a l l y , m u l t i p l y by (1 + t 2 S 2 g ) E 2 t 2 S 2 A F A F E 2 + g t 2 S 2 i /v M 2 i /v M 2 where V M 2 = t h e mean volume p e r h e c t a r e s q u a r e d , w h i c h g i v e s : t C A F n = AF D 2 + g t 2 C 2 w h i c h c o m p l e t e s t h e p r o o f . 

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