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A simulation of the tree component of the forest fuel complex to aid in planning for fire control and… McGreevy, Michael G. 1972

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A SIMULATION OF THE TREE COMPONENT OF THE FOREST FUEL COMPLEX TO A I D I N PLANNING FOR F I R E CONTROL AND USE BY MICHAEL G. MCGREEVY B. S c . , P u r d u e U n i v e r s i t y , 1969 A THESIS SUBMITTED IN PAR T I A L FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY i n t h e D e p a r t m e n t o f 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 o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA J a n u a r y , 1972 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 the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the 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 and study. I f u r t h e r agree t h a t permission f o r extensive copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t copying or 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 not be allowed without my w r i t t e n p e r m i s s i o n . Department o f F o r e s t r y The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, B. C. i i ABSTRACT A model was formulated t o estimate t r e e component weight by g e o m e t r i c a l l y d e s c r i b i n g the t r e e w i t h b a s i c t r e e parameters such as diameter, height, crown width, and crown l e n g t h and the shape equations that r e l a t e them. The stem i s d i v i d e d i n t o three s e c t i o n s w i t h shape equations t o describe the wood and bark i n each s e c t i o n . The crown i s d i v i d e d i n t o three s e c t i o n s w i t h three equations. The main branch stems are described i n three s e c t i o n s by s i x equations as i n the stem. The shapes and t h e i r d e f i n i n g parameters provide a volume estimate f o r the t r e e components. The d e n s i t y of the wood and bark i n each s e c t i o n of the stem and branches i s estimated as a random v a r i a b l e . The d e n s i t y of the crown i s defi n e d by estimates of i n t e r w h o r l d i s t a n c e s and numbers of branches per whorl, both of which are random v a r i a b l e s . The l e n g t h of the branches a l s o Influences the d e n s i t y of the crown because the weight of the needles and b r a n c h l e t s i s a f u n c t i o n of branch l e n g t h . The d e n s i t y and volume of the components combine t o give estimates of the weight of the components. In a d d i t i o n t o t h i s i n d i r e c t c a l c u l a t i o n of t r e e component weight, the model c a l c u l a t e s - t h e weight of i n d i v i d u a l i i i t r e e components w i t h equations having s p e c i f i c t r e e parameters as independent v a r i a b l e s . The estimates of weight are used to c a l c u l a t e the q u a n t i t y of s l a s h per t r e e and the center of mass of each major t r e e component. The weights of the stump and the unmerchantable top are a l s o c a l c u l a t e d i n conjunction w i t h the s l a s h c a l c u l a t i o n s . The weights and centers of mass are produced i n t a b u l a r form. The accuracy of the model i s l i m i t e d by the accuracy of the input data. The model was v e r i f i e d f o r D o u g l a s - f i r , western hemlock, and western redcedar. The v e r i f i c a t i o n procedure in c l u d e d manual c a l c u l a t i o n s and comparison wi t h other estimates of weight. The model i n i t s present form can a i d i n under-standing the q u a n t i t a t i v e e f f e c t s on the t r e e of v a r i a t i o n i n the parameters which describe the t r e e . Because the weight and volume of the t r e e components i n f l u e n c e t h e i r c o m b u s t i b i l i t y , the model can a i d i n d e s c r i b i n g the t r e e component of the f o r e s t f u e l complex. New data and f u r t h e r analyses would be needed t o determine the f u l l p o t e n t i a l and p r a c t i c a l u t i l i t y of the model described h e r e i n . i v T A BLE OF CONTENTS Page T I T L E I ABSTRACT ' i i TABLE OF CONTENTS i v L I S T OF TABLES ' v i L I S T OF FIGURES v i i ACKNOWLEDGEMENTS v l i i CHAPTER I . INTRODUCTION 1 CHAPTER I I . HISTORICAL'ATTEMPTS TO ESTIMATE FUEL QUANTITY 4 Volume 4 W e i g h t 5 CHAPTER m . FORMULATION OF THE MODEL 9 D e f i n i n g t h e s y s t e m 9 The s y s t e m i n r e l a t i o n t o i t s e n v i r o n m e n t 13 A n a l y s i s o f t h e r e a l s y s t e m 15 CHAPTER I V . THE MODEL 21 M e t h o d o l o g y 21 D e s c r i p t i o n 28 Use 4 l CHAPTER V. V E R I F I C A T I O N OF THE MODEL 44 V e r i f i c a t i o n p r o c e d u r e 44 P r e s e n t a t i o n o f r e s u l t s 45 D i s c u s s i o n 45 CHAPTER V I . CONCLUSIONS 56 BIBLIOGRAPHY ' 60 V APPENDIX I . PROGRAM L I S T I N G 63 APPENDIX I I . CONTROL CARD DESCRIPTION 96 APPENDIX HE. S T A T I S T I C A L TABLES TO A I D I N USING THE MODEL 104 APPENDIX I V . SAMPLE OUTPUT 116 v i L I S T OF TABLES Page 1. A summary o f t h e b e s t — t h o s e h a v i n g t h e l o w e s t r e s i d u a l v a r i a n c e — r e g r e s s i o n m o d e l s f r o m among t h o s e i n A p p e n d i x I I I , a l l o f w h i c h a r e b a s e d on d a t a c o l l e c t e d f r o m 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 R e s e a r c h F o r e s t b y K u r u c z (1969). 16 2. Wood a n d b a r k s p e c i f i c g r a v i t y o f f i n e , medium, a n d l a r g e b r a n c h c o m p o n e n t s o f D o u g l a s - f i r , w e s t e r n h e m l o c k , a n d w e s t e r n r e d c e d a r b a s e d on g r e e n v o l u m e a n d o v e n d r y w e i g h t . 18 3. An e s t i m a t e o f t h e o v e n d r y w e i g h t o f t h e c o m p o n e n t s o f D o u g l a s - f i r i n p o u n d s c o m p a r i n g t h e m e t h o d e m p l o y e d i n t h e m o d e l w i t h t w o o t h e r m e t h o d s . 46 4. An e s t i m a t e o f t h e o v e n d r y w e i g h t o f t h e c o m p o n e n t s o f w e s t e r n h e m l o c k i n p o u n d s c o m p a r i n g t h e m e t h o d e m p l o y e d i n t h e m o d e l w i t h t w o o t h e r m e t h o d s . 48 5. An e s t i m a t e o f t h e o v e n d r y w e i g h t o f t h e c o m p o n e n t s o f w e s t e r n r e d c e d a r i n p o u n d s c o m p a r i n g t h e m e t h o d e m p l o y e d i n t h e m o d e l w i t h two o t h e r m e t h o d s . 50 / v i i L I S T OF FIGURES Page 1. Components o f t h e t r e e w h i c h a r e c o n s i d e r e d i n t h e m o d e l , ( a d a p t e d f r o m Young, S t r a n d , a n d A l t e n b e r g e r , 1964). 10 2. An i l l u s t r a t i o n u s i n g K u r u c z ' s D o u g l a s - f i r d a t a t o p r o v i d e an a v e r a g e h e i g h t , d i a m e t e r , a n d c r o w n w i d t h s h o w i n g how t h e r e s u l t s w o u l d a p p e a r i f t h e o r i g i n o f m e a s u r e m e n t were t h e t i p o f t h e s t e m . 19 3. An e q u a t i o n o f t h e f o r m y = A x a + Bx + C t o i l l u s t r a t e t h e i n t e g r a t i o n o f r e g i o n t o f i n d i t s s o l i d o f r e v o l u t i o n a b o u t t h e y - a x i s u s i n g P a p p u s ' t h e o r e m ( P r o t t e r a n d M o r r e z , 1964). 24 4. An i l l u s t r a t i o n o f t h e s t e m a s d e s c r i b e d i n s u b r o u t i n e STEM3. 30 5. An i l l u s t r a t i o n o f t h e c r o w n s h a p e a s f o u n d i n s u b r o u t i n e B R C H 3 . 35 6. An i l l u s t r a t i o n o f a c o n i c a l b r a n c h h a v i n g a l e n g t h e q u a l t o o n e - h a l f t h e c r o w n w i d t h a n d a d i a m e t e r e q u a l t o BDIA. 37 7. An i l l u s t r a t i o n o f t h e c r o w n d i v i s i o n s u s e d f o r c a l c u l a t i n g t h e c e n t e r o f mass o f t h e c r o w n i n s u b r o u t i n e CSEC. v i i i ACKNOWLEDGEMENTS The w r i t e r w i s h e s t o t h a n k a l l t h o s e who a s s i s t e d h i m i e i t h e r d i r e c t l y o r i n d i r e c t l y i n t h i s u n d e r t a k i n g . Dr. J . H. G. S m i t h , Dr. A. K o z a k , Dr. D. D. Munro, a n d Mr. G. Young d e s e r v e s p e c i a l t h a n k s , a s d o e s M a n u e l B o n i t a , f o r t h e i r a d v i c e a n d r e v i e w o f t h i s t h e s i s . R e s e a r c h f u n d s f o r t h i s p r o j e c t were o b t a i n e d f r o m t h e Canada D e p a r t m e n t o f F i s h e r i e s a n d F o r e s t r y i n t h e f o r m o f an e x t r a m u r a l r e s e a r c h g r a n t t o Dr. S m i t h . A t t e n d a n c e a t t h e U n i v e r s i t y was f a c i l i t a t e d b y f i n a n c i a l a s s i s t a n c e f r o m t h e F a c u l t y o f F o r e s t r y , 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 , t h r o u g h t e a c h i n g a n d r e s e a r c h a s s i s t -a n t s h i p s a n d a U n i v e r s i t y F o r e s t F e l l o w s h i p . A s p e c i a l n o t e o f t h a n k s i s due Dr. S m i t h f o r h i s r o l e i n t h e c o n t i n u i n g f i n a n c i a l s u p p o r t r e c e i v e d . 1 I . INTRODUCTION F o r e s t f i r e i s one o f t h e most p o t e n t i a l l y d e s t r u c t i v e f o r c e s I n t h e f o r e s t c o m m u n i t y . C a t a -s t r o p h i c f i r e s d e s t r o y homes, p o l l u t e a i r a n d w a t e r , damage s o i l , t e m p o r a r i l y e l i m i n a t e a n i m a l l i f e , a n d g e n e r a l l y w a s t e t h e t i m b e r a n d f o r e s t l a n d r e s o u r c e s . P o t e n t i a l f i r e l o s s e s a r e g e n e r a l l y m e a s u r e d I n e c o n o m i c t e r m s ( L o c k m a n , 1969 a n d M a c T a v i s h , 1966)} h o w e v e r , t h e b a s i c l o s s o f h e a t e n e r g y due t o t h e c o m b u s t i o n o f f o r e s t f u e l s was s t u d i e d b y F a h n e s t o c k a n d D i e t r i c h (1962). O v i n g t o n (1962) a n d S m i t h (1968) p r o v i d e d a m e a s u r e o f l o s s i n t e r m s o f q u a n t i t y o f m a t e r i a l . S t u d y o f t h e l o s s o f a l l f o r m s o f e n e r g y d u r i n g t h e c o m b u s t i o n o f f o r e s t f u e l s h a s b e e n n e g l e c t e d , l e a v i n g t h e t o t a l l o s s due t o f o r e s t f i r e v i r t u a l l y unknown. E x t r e m e h e a t a n d t h e c h e m i c a l b r e a k d o w n o f wood d u r i n g a f i r e c a u s e p h y s i c a l and c h e m i c a l c h a n g e s i n t h e f o r e s t f l o o r . B u r n s (1962) r e p o r t e d r e d u c e d o r g a n i c m a t e r i a l , n i t r o g e n , a n d s o i l a n i m a l p o p u l a t i o n a l o n g w i t h i n c r e a s e d t e m p e r a t u r e , c o m p a c t i o n , a n d e r o s i o n i n t h e s o i l a f t e r a f i r e . He a l s o f o u n d t h a t f i r e s t i m -u l a t e d n i t r o g e n p r o d u c t i o n , i n c r e a s e d s o i l pH, and i n c r e a s e d t h e q u a n t i t y o f s o l u b l e n u t r i e n t s f o u n d i n t h e s o i l . B e a t o n . (1959) f o u n d t h a t f i r e r e d u c e d s o i l p o r o s i t y , i n c r e a s e d c a p i l l a r y s p a c e a n d b u l k d e n s i t y , a n d h e i g h t e n e d c h a r c o a l c o n t e n t a n d s o i l t e m p e r a t u r e a f t e r f i r e i n t h e i n t e r i o r o f B r i t i s h C o l u m b i a . D y e r (1967). R e n n i e (1955). and Young, S t r a n d , a n d A l t e n b e r g e r (1964) e s t i m a t e d t h e amount o f a v a i l a b l e n u t r i e n t s i n t h e c o m p o n e n t s o f t h e f u e l s y s t e m . T h e i r e s t i m a t e s a r e e q u i v a l e n t t o e s t i m a t e s o f t h e maximum p o s s i b l e a m o u n t s o f n u t r i e n t s r e l e a s e d d u r i n g t h e com-b u s t i o n o f f o r e s t f u e l s . B u r n i n g d e c o m p o s e s t h e wood f i b r e t o i o n f o r m m a k i n g i t more s u s e p t i b l e t o l e a c h i n g i n t h e s o i l . H owever, t h e i m p o r t a n c e o f l e a c h i n g i n t h e D o u g l a s - f i r r e g i o n was i n s i g n i f i c a n t a f t e r f i r e due t o t h e g e n t l e n a t u r e o f t h e r a i n f a l l ( D y r n e s s , Y o ung, a n d R u t h , 1967). Man h a s a l s o s u f f e r e d l o s s a t t h e h a n d s o f f o r e s t f i r e . I n Canada an a v e r a g e o f two p e o p l e p e r y e a r l o s t t h e i r l i v e s i n f o r e s t f i r e s f r o m 1957 t o 1966 w h i l e e i g h t p e o p l e d i e d i n 1967 ( L o c k m a n , 1969). The p r e s e n c e a n d t h e d e s t r u c t i v e c a p a b i l i t y o f f i r e m o t i v a t e a n e e d f o r a b e t t e r u n d e r s t a n d i n g o f i t . An a n a l y s i s o f t h e woody f u e l c o m p l e x , a b a s i c com-p o n e n t o f s l a s h f i r e s a n d w i l d f i r e s , i s t h e o b j e c t o f t h i s s t u d y . The s c o p e o f t h i s t h e s i s i s t o f u r n i s h a g e n e r a l m e t h o d o f d e s c r i b i n g c o n i f e r o u s t r e e s u s i n g 3 o n l y t h o s e f a c t o r s w h i c h a f f e c t t h e i r f u e l c h a r a c -t e r i s t i c s . To a c c o m p l i s h t h i s t h e t r e e i s d e s c r i b e d g e o m e t r i c a l l y i n t e r m s o f t h e s h a p e s o f i t s c o m p o n e n t s . V a r i a t i o n s w i t h i n t h e e x t e r n a l o u t l i n e d e f i n i n g t h e t r e e a r e r e g a r d e d a s f u n c t i o n a l r e l a t i o n s h i p s o r a s r a n d o m v a r i a b l e s . Wood a n d b a r k d e n s i t i e s , number o f b r a n c h e s , a n d b r a n c h l e n g t h s a r e u s e d i n c o n j u n c t i o n w i t h t h e t r e e ' s g e o m e t r i c s h a p e s t o d e s c r i b e t h e f u e l c o m p o s i t i o n o f t h e t r e e . A l t h o u g h t h e m e t h o d e m p l o y e d , a c o m p u t e r o r i e n t e d s i m u l a t i o n m o d e l , i s v e r i f i e d f o r t h r e e s p e c i e s s D o u g l a s - f i r ( P s e u d o t s u g a m e n z l e s l l ( M i r b . ) F r a n c o ) , w e s t e r n h e m l o c k (T.suga h e t e r o p h y l l a ( R a f ) S a r g . ), a n d w e s t e r n r e d c e d a r ( T h u j a p i 1 c a t a D o n n ) , an e x t e n s i v e a n a l y s i s o f t h e f a c t o r s w h i c h a r e most i m p o r t a n t i n d e -t e r m i n i n g t h e r e l a t i v e c o m b u s t a b i l i t y o f t h e s e a n d o t h e r c o n i f e r o u s f u e l s i s b e y o n d t h e s c o p e o f t h i s s t u d y . I t i s t h e o b j e c t i v e o f t h i s s t u d y t o p r o v i d e a m e t h o d t h a t c a n be u s e d t o a s s e s s t h e r e l a t i v e i m p a c t o f t h e v a r i o u s p a -r a m e t e r s w h i c h d e s c r i b e t h e t r e e . The a s s e s s m e n t o f t h e a c t u a l c h a n g e s i n t h e f u e l c h a r a c t e r i s t i c s o f t h e t r e e r e s u l t i n g f r o m v a r i a t i o n s i n t h e p a r a m e t e r s c h o s e n t o d e s c r i b e i t a r e b e y o n d t h e s c o p e o f t h i s s t u d y . 4 I I . HISTORICAL ATTEMPTS TO ESTIMATE FUEL QUANTITY A. Volume The v o l u m e o f m a t e r i a l c o n t a i n e d i n a t r e e i s e q u i v a l e n t t o t h e amount o f p o t e n t i a l f u e l i n t h a t t r e e * Any m e a s u r e m e n t o f a t r e e w h i c h e s t i m a t e s t h e v o l u m e o f a component o f t h a t t r e e must a l s o e s t i m a t e t h e maximum q u a n t i t y o f f u e l i n t h a t c o m p o n e n t . C l a s s i c a l m e a s u r e -m e n t s o f h e i g h t , d i a m e t e r , c r o w n l e n g t h , a n d c r o w n w i d t h , a n d s u b s e q u e n t c a l c u l a t i o n s o f s t e m a n d c r o w n v o l u m e s were p r o b a b l y t h e f i r s t a n d a r e s t i l l t h e most p r e v a l e n t means o f q u a n t i t a t i v e l y d e s c r i b i n g t h e amount o f f u e l i n t h e a e r i a l p o r t i o n s o f t h e s t e m . T h e s e v o l u m e s a l s o p r o v i d e a n e s t i m a t e o f t h e r e l a t i v e a m o u n t s o f f u e l i n d i f f e r e n t f o r e s t e d a r e a s . P r e s e n t c u b i c v o l u m e e s t i m a t i n g p r o c e d u r e s h a v e n o t e v o l v e d t o t h e a c c u r a c y i n d i c a t e d a s n e c e s s a r y b y t e c h n o l o g i c a l a d v a n c e m e n t s i n o t h e r a s p e c t s o f f o r e s t r y . H e g e r (1965), a s w e l l a s many o t h e r s , f o u n d t h a t t h e v o l u m e s o f t r e e s o f t h e same s p e c i e s h a v i n g e q u i v a l e n t d i a m e t e r s a n d h e i g h t s v a r i e d a s much a s 30 p e r c e n t ; t h i s v a r i a t i o n r e f l e c t s h e r e d i t a r y a n d e n v i r o n m e n t a l d i f f e r e n c e s w h i c h may be d i f f i c u l t t o m e a s u r e i n d e p e n d e n t l y o f t r e e v o l u m e . Numerous s t e m v o l u m e e q u a t i o n s a r e l i s t e d / 5 by H u s c h (1963); a r e a l i s t i c e q u a t i o n f o r d e s c r i b i n g i n d i v i d u a l s t e m v o l u m e i s B e h r e ' s a b s o l u t e f o r m f a c t o r w h ere t h e s t e m s h a p e i s d e s c r i b e d b y a n d e q u a t i o n h a v i n g h e i g h t a s a f u n c t i o n o f d i a m e t e r a n d t h e s t e m v o l u m e i s i s t h e s o l i d o f r e v o l u t i o n o f t h i s e q u a t i o n a b o u t t h e o r d i n a t e . K o z a k (19^9) s u g g e s t e d t h a t r e g r e s s i o n m o d e l s o f s t e m t a p e r be c o n d i t i o n e d a t t e n f e e t i n t e r v a l s t o p r o v i d e s p e c i f i c s t e m s h a p e e q u a t i o n s f o r p a r t i c u l a r d a t a s e t s . E a c h method m e n t i o n e d e s t i m a t e s t h e v o l u m e o f t h e s t e m b y a s s u m i n g t h a t i t i s s y m m e t r i c a l i n t h e h o r i z o n t a l p l a n e . The l a c k o f s y m m e t r y f o u n d i n l i v i n g t r e e s s h o u l d be r e c o g n i z e d a s a s o u r c e o f e r r o r i n a n y e s t i m a t e o f v o l u m e w h i c h i s d e p e n d e n t on m e a s u r e m e n t s o f t h e e x t e r n a l d i m e n s i o n s o f t h e t r e e , B. W e i g h t A r e c e n t t r e n d t o w a r d more p r e c i s e m e a s u r e m e n t o f p u l p w o o d ( D o b i e , 1965) h a s e n c o u r a g e d more e x t e n s i v e s t u d y o f w e i g h t s c a l i n g a n d b i o m a s s a n a l y s i s . Young (1965) a d v o c a t e d a c o m p l e t e t r e e u t i l i z a t i o n c o n c e p t w h i c h i m p l i e d a n e e d f o r w i d e r u s e o f mass e s t i m a t e s i n m e a s u r i n g wood q u a n t i t y . K u r u c z (1969) r e v i e w e d most o f t h e l i t e r a t u r e p u b l i s h e d p r i o r t o 1969 d e a l i n g w i t h b i o m a s s a n a l y s i s . K e a y s ( 1 9 7 1 a , b, c, d, a n d e ) 6 a n a l y z e d t h e l i t e r a t u r e d e a l i n g w i t h b i o m a s s a n d t h e c o m p l e t e - t r e e u t i l i z a t i o n c o n c e p t w h i c h i n c l u d e d many p u b l i c a t i o n s c o n c e r n e d w i t h b i o m a s s a n d w e i g h t s c a l i n g . The b u l k o f t h e t r e e h a s l e d t o many p r o b l e m s i n s e c u r i n g a c c u r a t e m e a s u r e m e n t s o f i t s w e i g h t . Many e a r l y i n v e s t i g a t o r s d e s i g n e d e x p e r i m e n t s w h i c h r e q u i r e d w e i g h i n g o f s p e c i f i c t r e e c o m p o n e n t s , o n l y t o h a v e t h e e x p e r i m e n t s d e t e r i o r a t e t o t h e w e i g h i n g o f s a m p l e s t o e s t i m a t e t h e t o t a l w e i g h t o f t h e c o m p o n e n t , s o m e t i m e s r e n d e r i n g t h e e x p e r i m e n t s s t a t i s t i c a l l y u n s o u n d a n d a l w a y s m a k i n g i t d i f f i c u l t t o compare r e s u l t s w i t h l a t e r a n a l y s e s . K u r u c z ( 1 9 6 9 ) e m p l o y e d s a m p l i n g a n d • s u b s a m p l i n g f r o m t h e b e g i n n i n g o f h i s a n a l y s i s , b u t t h e d i f f e r e n c e s b e t w e e n t h e s i z e c l a s s e s u s e d i n h i s wo r k a n d t h o s e u s e d b y o t h e r s make c o m p a r i s o n d i f f i c u l t . Y o u ng, S t r a n d , a n d A l t e n b e r g e r ( 1 9 6 4 ) d i s c o v e r e d t h a t l o s s e s o f m a t e r i a l o c c u r r e d i n t h e e x c a v a t i o n o f r o o t s a n d t h e c u t t i n g o f t h e s t e m i n t o m a n a g e a b l e p i e c e s . T h e s e l o s s e s when c o m b i n e d w i t h n a t u r a l l y o c c u r r i n g e x p e r i m e n t a l e r r o r a n d t h e i m p r e c i s i o n o f b o t h v o l u m e a n d w e i g h t m e a s u r e m e n t s i n d i c a t e t h e d i f f i c u l t y / o f o b t a i n i n g a c c u r a t e d a t a f o r b i o m a s s a n a l y s i s . The v a r i a t i o n i n e x p e r i m e n t a l t e c h n i q u e f r o m i n v e s t i g a t o r t o i n v e s t i g a t o r makes a n a s s e s s m e n t o f t h e r e s u l t s / . ? d i f f i c u l t regardless of the pr e c i s i o n achieved i n the measurements y i e l d i n g the data. The large number of samples required to obtain a precise estimate of biomass (Johnstone, 1967) and the d i f f i c u l t y i n measuring these samples a f t e r they have been selected i l l u s t r a t e s the i m p r a c t i c a b i l i t y of di r e c t biomass sampling f o r obtaining biomass estimates from p a r t i c u l a r forested areas. A stand table estimating procedure was favored over a mean tree approach f o r the estimating of biomass i n i n d i v i d u a l stands by Johnstone (1967). However, i f instead of a mean tree approach, a mean parameter approach were used most of the impreci-sion noted by Johnstone should be eliminated. Using t h i s method stand parameters such as stem diameter, crown width, height, crown length, basal area, crown width squared, or diameter times height, as well as any other parameters which may be included i n general re-gression models fo r predicting tree biomass, should be estimated from a sample of in d i v i d u a l s i n the stand. The measurements of the external dimensions of the tree constitute a description of the tree. Prom t h i s description, the volume of the tree and i t s component parts can be calculated by defining the external shape of each component measured. The volume calculated f o r 8 t h a t s o l i d m u l t i p l i e d "by t h e d e n s i t y o f m a t e r i a l c o n t a i n e d i n i t g i v e s a n e s t i m a t e o f i t s w e i g h t o r b i o m a s s . The q u a n t i t a t i v e e f f e c t o f c h a n g e s i n s h a p e a n d d e n s i t y on t r e e s o f v a r i o u s s i z e s w o u l d be v e r y d i f f i c u l t a n d e x p e n -s i v e t o o b t a i n f r o m e m p i r i c a l e x p e r i m e n t s . H owever, t h e i r e f f e c t on t r e e w e i g h t i s i m p o r t a n t f o r a more b a s i c u n d e r -s t a n d i n g o f t h e f a c t o r s w h i c h i n f l u e n c e t r e e w e i g h t . The r e l a t i v e i m p o r t a n c e o f t h e s e f a c t o r s s h o u l d a i d i n i m -p r o v i n g f u t u r e f o r e s t b i o m a s s e s t i m a t e s . The d i f f i c u l t i e s e n c o u n t e r e d i n d i r e c t b i o m a s s s a m p l i n g h a v e s t i m u l a t e d t h e c r e a t i o n o f a m o d e l w h i c h d e s c r i b e s t h e t r e e i n t e r m s o f s h a p e , h e n c e v o l u m e , a n d d e n s i t y . 9 III. FORMULATION OF THE MODEL A. Defining the system The formulation of a model requires a thorough analysis of the system to be modeled. The most important parameters in the system must be defined and studied and, where their relative importance is unknown, their hypo-thetical importance must be verified. A gross system description forms a basis for a more precise definition of each component. The system in question, the tree, can be divided into the divisions shown in Figure 1 . The crown includes the branch and needle components in Figure 1. Its exter-ior shape is defined by the locus of points formed by the longest horizontal distance from a vertical axis through the center of the stem to each branch and i t s respective vertical distance from the ground. When joined together by lines and surfaces these points form a surface which defines crown volume. The mean, variance, and frequency distribution of interwhorl distances provides part of a definition of crov/n density needed to calculate the weight of the material contained in the crown. Each whorl consists of a number of branches; the mean, variance, and frequency distribution of this number define i t . The branches within each whorl are defined in terms of length 10 U n m e r c h a n t a b l e s t e m F i n e b r a n c h e s Medium b r a n c h e s L a r g e b r a n c h e s N e e d l e s M e r c h a n t a b l e ,>st em Stump L a r g e r o o t s Medium r o o t s F i n e r o o t s F i g u r e 1. Components of. t h e t r e e w h i c h a r e c o n s i d e r e d i n t h e m o d e l , ( a d a p t e d f r o m Y o u n g , S t r a n d , a n d A l t e n b e r g e r , 1964). a n d s h a p e . The sh a p e o f t h e b r a n c h i s d e f i n e d b y a n e q u a t i o n h a v i n g b r a n c h l e n g t h a s a f u n c t i o n o f b r a n c h r a d i u s . The mean b r a n c h l e n g t h i n e a c h w h o r l i s d e t e r -m i n e d b y t h e d i s t a n c e t o a l i n e d e f i n i n g a g e n e r a l c r o w n s h a p e e q u a t i o n h a v i n g h e i g h t on t h e c r o w n s u r f a c e a f u n c t i o n o f c r o w n r a d i u s . The v a r i a n c e o f b r a n c h l e n g t h i s c o n s i d e r e d a p e r c e n t a g e o f t h i s mean. The mean a n d v a r i a n c e , when a s s o c i a t e d w i t h a d i s t r i b u t i o n , d e s c r i b e e a c h b r a n c h l e n g t h . The l e n g t h a n d s h a p e o f t h e b r a n c h d e f i n e i t s v o l u m e w h i c h i n d i r e c t l y d e f i n e s i t s w e i g h t b y u s i n g a mean, v a r i a n c e , a n d f r e q u e n c y d i s t r i b u t i o n of. t h e b r a n c h wood a n d b a r k d e n s i t i e s t o o b t a i n e a c h b r a n c h • w e i g h t . The n e e d l e s and b r a n c h l e t s , t h e wood a n d b a r k i n t h e c r o w n n o t c o n t a i n e d i n t h e m a i n b r a n c h s t e m s , a r e c o n -s i d e r e d a f u n c t i o n o f b r a n c h l e n g t h , t h u s c o m p l e t e l y d e s c r i b i n g t h e c r o w n o f t h e t r e e i n t e r m s o f i t s w e i g h t . The s t e m i s m e r e l y a l a r g e b r a n c h d e s c r i b e d b y a t h i n e x t e r i o r s h e l l o f b a r k c o v e r i n g a s o l i d c o r e o f wood. The d e f i n i t i o n o f t h e e x t e r i o r s u r f a c e o f b o t h t h e wood a n d b a r k p r o v i d e e n o u g h i n f o r m a t i o n t o c a l c u -l a t e t h e i r v o l u m e s . The d e f i n i t i o n o f t h e mean, v a r i a n c e , a n d f r e q u e n c y d i s t r i b u t i o n o f t h e wood a n d b a r k d e n s i t i e s i n t h e s t e m c o m p l e t e s i t d e f i n i t i o n . The stump i s a d e q u a t e l y d e s c r i b e d a s t h e l o w e r p o r t i o n o f t h e s t e m . I t c o n s i s t s o f wood a n d b a r k a n d i s d e f i n e d a s t h a t p a r t o f t h e s t e m b e t w e e n t h e g r o u n d a n d t h e h e i g h t a t w h i c h t h e t r e e i s c u t . The r o o t s a l s o c o n s i s t o f wood a n d b a r k . T h e i r w e i g h t a n d v o l u m e i s d i f f i c u l t t o e s t i m a t e b e c a u s e o f t h e i r s u b t e r r a n e a n p o s i t i o n . T h e y a r e d e s c r i b e d h e r e o n l y f o r c o m p l e t e n e s s , s i n c e t h e i r c o n t r i b u t i o n t o t h e r e a d i l y c o m b u s t i b l e p o r t i o n o f t h e f u e l c o m p l e x i s a l m o s t n e g l i g i b l e . The d i s t r i b u t i o n o f m o i s t u r e w i t h i n t h e c o m p o n e n t s a s w e l l a s t h e i r s i z e a n d q u a n t i t y i n f l u e n c e t h e i r f u e l c h a r a c t e r i s t i c s . I n s t a n d i n g t i m b e r t h e f r e q u e n t f l u c t u a t i o n o f m o i s t u r e i n t h e v a r i o u s p a r t s o f t h e t r e e makes i t d i f f i c u l t t o i n c l u d e i n t h e d e f i n i t i o n o f t h e t r e e . I n s l a s h , m o i s t u r e c o n t e n t i s i n f l u e n c e d more b y t h e s i z e a n d d i s t r i b u t i o n o f m a t e r i a l t h a n b y t h e m o r p h o l o g i c a l c h a r a c t e r o f t h e c o m p o n e n t s . A l t h o u g h t h e m o i s t u r e c o n t e n t o f f u e l d o e s a f f e c t i t s i g n i t i o n a n d c o m p l e t e n e s s o f c o m b u s t i o n a s w e l l a s t h e r a t e o f s p r e a d o f f i r e t h r o u g h i t , t h e d i f f i c u l t y o f e s t i m a t i n g f u e l m o i s t u r e c o n t e n t i n t e r m s o f i n d i v i d u a l t r e e p a r a m e t e r s e x c l u d e s i t f r o m f u r t h e r c o n s i d e r a t i o n I n t h e f o r m u l a t i o n o f t h e m o d e l . / 13 B. The s y s t e m i n r e l a t i o n t o i t s e n v i r o n m e n t A l t h o u g h t h e t r e e c a n be c o n s i d e r e d a s e l f c o n t a i n e d s y s t e m , i t c a n a l s o be c o n s i d e r e d p a r t o f t h e l a r g e r s y s t e m , t h e f o r e s t . The q u a n t i t y o f f u e l p e r a c r e i s l i m i t e d b y t h e d i a m e t e r , h e i g h t , s p e c i e s , a n d s p a t i a l d i s t r i b u t i o n o f t r e e s w i t h i n a s t a n d . The a v e r a g e t r e e h e i g h t a n d t h e a r e a o f a s t a n d d e f i n e a r e f e r e n c e s p a c e f o r c o m p a r i n g t h e r e l a t i v e q u a n t i t y o f f u e l p e r u n i t v o l u m e i n s t a n d s . A s u i t a b l e r e f e r e n c e s p a c e f o r s l a s h i s d e f i n e d b y t h e a r e a c o v e r e d b y s l a s h a n d t h e a v e r a g e s l a s h d e p t h . The q u a n -t i t y o f f u e l p e r u n i t v o l u m e i n t h i s s p a c e c o u l d be c o n s i d -e r e d a f u e l d e n s i t y i n d e x . S e p a r a t e i n d i c e s f o r s l a s h a n d s t a n d i n g t i m b e r s h o u l d e s t i m a t e t h e r e l a t i v e c o m b u s t i o n p o t e n t i a l f o r s l a s h a n d s t a n d i n g t i m b e r . The v e r t i c a l d i s t r i b u t i o n o f t h i s f u e l a s e s t i m a t e d b y t h e m o d e l c o n s t i t u t e s a f u r t h e r r e f i n e m e n t o f s u c h a n I n d e x f o r s t a n d i n g t i m b e r . T h i s e s t i m a t e c o n s i s t s o f a n e s t i m a t e o f t h e c e n t e r o f mass o f t h e t r e e . T o p o g r a p h i c a n d m e t e o r o l o g i c f a c t o r s a r e a l s o i m p o r t a n t f o r a s s e s s i n g f i r e i g n i t i o n a n d s p r e a d i n s l a s h a n d s t a n d i n g t i m b e r . T h e s e f a c t o r s s h o u l d be n o t e d a s p a r t o f t h e f o r e s t e n v i r o n m e n t i n f l u e n c i n g f i r e b e h a v -i o r , b u t t h e i r e f f e c t on f u e l a n d i t s c o m b u s t i o n i s b e y o n d t h e s c o p e o f t h i s s t u d y . 14 T h o s e f a c t o r s w h i c h i n f l u e n c e t h e q u a n t i t y o f f u e l p e r t r e e a l s o i n f l u e n c e t h e t o t a l q u a n t i t y o f f u e l i n t h e f o r e s t s i n c e t h e f o r e s t i s composed o f i n d i v i d u a l t r e e s . I f i t i s assumed t h a t b i o m a s s i s t h e most u s e f u l e s t i m a t e o f f u e l q u a n t i t y , t h e n b i o m a s s s h o u l d b e e s t i m a t e d on a s t a n d b a s i s . The o n l y p r a c t i c a l m e t hod o f d o i n g t h i s i s t o e s t i m a t e b i o m a s s u s i n g more e a s i l y m e a s u r e d t r e e p a r a m e t e r s t o e s t i m a t e s t a n d p a r a m e t e r s w h i c h i n t u r n a r e u s e d t o e s t i m a t e s t a n d b i o m a s s . K u r u c z ' s ( 1 9 6 9 ) a n a l y s i s p r o v i d e d g e n e r a l b i o m a s s e q u a t i o n s f o r D o u g l a s -f i r , w e s t e r n h e m l o c k , and w e s t e r n r e d c e d a r . However, h i s a n a l y s i s s t i m u l a t e d q u e s t i o n s a s t o t h e s e n s i t i v i t y o f t r e e b i o m a s s e s t i m a t e s t o c h a n g e s i n t h e s h a p e a nd d e n s i t y o f t h e c o m p o n e n t s o f t h e t r e e . The d i f f i c u l t y o f d i r e c t l y m e a s u r i n g t h e b i o m a s s , t h e s h a p e , a nd t h e d e n s i t y o f many s a m p l e s t o a s c e r t a i n t h e i r q u a n t i t a t i v e e f f e c t on t r e e w e i g h t i s c i r c u m v e n t e d t h r o u g h a n i n d i r e c t i n v e s t i g a t i o n on a m a t h e m a t i c a l m o d e l o f a t r e e w h i c h i s b a s e d on component s h a p e a n d d e n s i t y . The q u a n t i t y o f f u e l p e r t r e e c o n t a i n e d i n t h e s t e m , r o o t s , a n d t h e c r o w n c a n be e s t i m a t e d i n t e r m s o f w e i g h t a n d v o l u m e . E n v i r o n m e n t a l f a c t o r s w h i c h i n f l u e n c e t h i s q u a n t i t y a r e t o o nume r o u s t o be i n c l u d e d i n a m o d e l w h i c h d e s c r i b e s t h e t r e e a s a f u e l a t a p a r t i c u l a r moment i n t i m e . / 15 C. Analysis of the r e a l system The analysis used to study the system and to test the variables that are hypothetically important i n the system consisted of a re-analysis of data gathered by Kurucz (1969) from the U.B.C. Research Forest. The purpose of t h i s analysis was to determine whether or not s i g n i f i c a n t relationships among exterior measurements of the tree e x i s t . The r e s u l t s of t h i s analysis are found i n Tables 1 and 2 and Appendix I I I . The study i n which the data were gathered was not s p e c i f i c a l l y designed to provide information about i n t e r -tree r e l a t i o n s h i p s . Data consisted of a few measurements i n many trees rather than more measurements within each tree which would have provided data more suitable for t h i s study. Ideally the analysis which provides input data for the model would analyse tree shape with a l l measurements o r i g i n a t i n g at the apex of the stem; then i t would proceed downward producing data for each tree that would define an outline s i m i l a r to that i n Figure 2. This type of analysis would require the measurement of several lengths from the t i p of the component to appro-priate r a d i i on the component. D e f i n i t i o n of component shape rather than the p r e d i c t i o n of length would be emphasised by using t h i s method. An attempt to combine the measurements of branch butt-diameter and mid-diameter 16 T a b l e 1 . A summary o f t h e b e s t — t h o s e h a v i n g t h e l o w e s t r e s i d u a l v a r i a n c e — r e g r e s s i o n m o d e l s f r o m among t h o s e i n A p p e n d i x I , a l l o f w h i c h a r e b a s e d on d a t a c o l l e c t e d f r o m 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 R e s e a r c h F o r e s t b y K u r u c z ( 1 9 6 9 ) . D o u g l a s - f i r n = 112 Dependents-V a r i a b l e s R e g r e s s i o n m o d e l s 1 » z SEg R2 f t . % HT - 0 . 4 5 + 5 . H D B H - 0 . 0 1 D B H 2 1 5 . 7 0 94 L C L - 1 9 . 6 2 + 4 . 37CW - 0 . 0 3 C W 2 2 1 . 4 9 46 C L - 2 6 . 6 3 + 0 . 9 9 C W -0.05CW2 2 2 . 7 3 45 B L - 1 . 3 9 + 9 . 7 1 D O - 0 . 9 0 D O 2 2 . 0 7 89 B L - 1 . 4 5 + 1 4 . 5 0 D l - 3 . 9 3 D I 1 ' 5 2 . 0 7 89 B L - 2 . 8 2 + 2 0 . 0 4 M D 0 - 3 . 9 6 M D 0 1 « - 5 2 . 3 7 85 B L - 1 .48+ 2 1 . 46MDI -4 . 7 7 M D I 2 2 . 3 0 85 W e s t e r n h e m l o c k n = 89 H T 5 . 8 4 + 3 . 7 4 D B H - O . ^ D B H 1 ^ 6 . 9 6 98 L C L - 5 . 1 1 + 7 . 6 9 C W - 0 . 1 1 C W 2 1 2 , 8 7 71 C L - 5 8 . 3 7 + 8 . 27CW - 0 . 1 2 C W 2 1 5 . 8 5 68 B L - 0 . 0 8 + 1 1 . 5 3 D O - 3 . 3 2 D 0 1 * - 5 2 . 8 5 73 B L 0 . 3 1 + 1 2 . 8 9 D I - 3 . 9 3 D I 1 , 5 2 . 6 9 76 B L 0 . 2 6 + 2 1 . 6 6 M D O - S . O I M D O 1 * ^ 2.46 80 B L 0 .40+25 .65MDI-10.26MDI 1 , 5 2 . 2 9 83 17 Table 1 — continued Western redcedar n = 113 Dependent Variable Regression models SE E f t . R* % HT -7.94 +5.69DBH -0.05DBH2 15.37 90 LCL -35.54 +6.34CW -0.08CW2 21.48 53 CL -43.83 +7.17CW -0.09CW2 19.02 64 BL -6.71+14.26DO -1.96D02 2.23 84 BL -3.26+13.54DI -2.04DI2 2.06 86 BL -2.99+18.30MDO -3.84MD02 2.41 8i BL -1.89+19.62MDI -4.62MDI 2 2.31 83 1 HT = height in feet, LCL = live crown length in feet, CL = total crown length in feet, BL = total branch length in feet.DBH = diameter at breast height in inches, CW = crown width in feet, DO = branch diameter outside bark in inches, DI = branch diameter inside bark in inches, MDO = mid branch diameter outside bark in Inches, MDI = mid branch diameter inside bark in inches. 2 These regression models are a l l significant at the one per cent probability level using a test of R. T a b l e 2. Wood a n d b a r k s p e c i f i c g r a v i t y o f f i n e , medium, a n d l a r g e b r a n c h c o m p o n e n t s o f D o u g l a s - f i r , w e s t e r n h e m l o c k , a n d w e s t e r n r e d c e d a r b a s e d on g r e e n v o l u m e a n d o v e n d r y w e i g h t . S p e c i e s D o u g l a s - f i r W e s t e r n h e m l o c k S t a t i s t i c s 1 f o r s p e c i f i c g r a v i t y Number Mean S.D. CV% Number Mean S.D. cv% W e s t e r n r e d c e d a r Number Mean S.D. F i n e <.25" Wood B a r k 112 .436 .095 21.8 .552 .102 18.6 .545 .158 29.1 89 .648 .345 53.3 113 .530 .564 .090 .170 .170 30.1 Medium >.25"<.75" Wood B a r k .506 .068 13.4 .582 .061 10.6 .529 .058 10.9 112 .513 .174 33.9 88 .511 .118 23.0 112 .413 .058 14.0 L a r g e >.75" Wood B a r k 97 .526 .517 .042 .116 8.0 22.5 73 . 596 .505 .070 .164 11.8 32.5 100 .503 .374 .072 .070 14.3 18.7 1 D a t a f o r t h i s a n a l y s i s was c o l l e c t e d b y K u r u c z (1969). 120-100--P OJ (DBH/2,HT -4 .5) S c a l e j 1" -s 20' (CW/2,HT-HTC) 20-—p 2'0 4b F e e t F i g u r e 2., An i l l u s t r a t i o n u s i n g K u r u c z ' s D o u g l a s - f i r d a t a t o p r o v i d e a n a v e r a g e h e i g h t , d i a m e t e i a n d c r o w n w i d t h s h o w i n g how t h e r e s u l t s w o u l d a p p e a r i f t h e o r i g i n o f m e a s u r e m e n t w e r e t h e t i p o f t h e s t e m 0 20 into one analysis that describes branch shape is found in Appendix III in the equations having branch length as a function of branch diameter. These equations do not estimate branch length as well as do the regression models having branch length as a function of butt-diameter, however, they may describe branch shape more precisely than do those regression models having only one measurement of diameter and length per branch in the analysis. The results presented in Tables 1 and 2 and Appendix III consist of regression models based on data taken from the same trees as were the data for Kurucz (1969) biomass analysis. With only slight modification these results provide input data for validating the model, assuming the biomass equations proposed by Kurucz (I969) are valid. 21 I V . THE MODEL A. M e t h o d o l o g y The m e t h o d o l o g y u s e d i n t h e m o d e l f u r n i s h e s t h e b a s i s f o r a c o n c i s e d e f i n i t i o n o f i t . The m o d e l c a l c u -l a t e s t h e w e i g h t o f t h e a e r i a l p o r t i o n o f t h e t o t a l t r e e , t h e b o l e wood, t h e b o l e b a r k , t h e t o t a l c r o w n , t h e l a r g e b r a n c h e s , t h e medium b r a n c h e s , t h e f i n e b r a n c h e s , a n d t h e n e e d l e s d i r e c t l y f r o m e q u a t i o n s o f t h e f o r m : (1) W e i g h t = A ( B a s a l a r e a ) + B (2) W e i g h t - A ( D B H ) 2 ( H e i g h t ) + B ( D B H ) ( C r o w n l e n g t h ) + C ( D B H ) ( C r o w n w i d t h ) 2 + D((DBH) ( C r o w n l e n g t h ) ) 2 w h e r e A, B, C, a n d D a r e g e n e r a l e q u a t i o n c o e f f i c i e n t s s u p p l i e d t o t h e m o d e l . The c h o i c e o f t h e p a r a m e t e r s i n c l u d e d i n t h e a b o v e e q u a t i o n s i s t h e same a s t h o s e u s e d b y K u r u c z (196°) . The d i m e n s i o n s t h a t he u s e d were a l s o a d o p t e d . I n h i s s t u d y he d e f i n e d d i a m e t e r i n i n c h e s a n d a l l o t h e r p a r a m e t e r s i n f e e t . The m o d e l a l s o c a l c u l a t e s t r e e component w e i g h t i n d i r e c t l y u s i n g s h a p e e q u a t i o n s o f t h e fo r m s (3) y = A x a + Bx + C where y i s component h e i g h t o r l e n g t h i n f e e t a n d x i s component r a d i u s i n f e e t . When a component s h a p e i s 22 d e s c r i b e d i n more than one s e c t i o n u s i n g more than one e q u a t i o n of the form of equation (3), the i n t e r s e c t i o n o f the two equations must be f o r c e d through a c e r t a i n p o i n t on the l i n e d e s c r i b i n g t h e i r s u r f a c e . T h i s i s accomplished by changing C i n e q u a t i o n (3) i f one o f the p o i n t s through which the l i n e must pass has an x - c o o r d l n a t e equal t o zero, s i n c e C must equal the h e i g h t or l e n g t h of the component. For p o i n t s o f i n t e r -s e c t i o n where x i s not equal to zero, A i s changed i f i t i s not equal t o zero, o r B i s changed i f A i s equal to zero, thus f o r c i n g the equation to s a t i s f y the c o n d i t i o n s imposed by the p o i n t o f i n t e r s e c t i o n . The volume of each component i s c a l c u l a t e d u s i n g Pappus theorem ( P r o t t e r and Morrez, 1964): " I f a r e g i o n , R. l i e s on one s i d e of a l i n e , y, the volume o f the s o l i d generated by r e v o l v i n g R about Y i s equal t o the product of the area, A, o f R and the l e n g t h of the path d e s c r i b e d by the c e n t e r of mass of R. *• The e q u a t i o n of t h i s theorem f o r y equal t o the y - a x i s reduces t o : (4) Volume = J\f 2rrxdA where dA equals d y d x and x and y are d e f i n e d as above. Pappus' theorem i s used here i n s t e a d of d i r e c t l y c a l c u -l a t i n g the volume as a s o l i d of r e v o l u t i o n about the y - a x i s because i t i s not p o s s i b l e to f i n d a g e n e r a l 23 s o l u t i o n f o r x i n t e r m s o f y f o r e q u a t i o n (3). The t h e o r e m y i e l d s t h e same s o l u t i o n a s d o e s one w h i c h s o l v e s t h e e q u a t i o n a s d e f i n e d i n a t h r e e - d i m e n s i o n a l c o o r d i n a t e s y s t e m . However, i t h a s t h e a d v a n t a g e s o f h a v i n g f e w e r s t e p s i n t h e d e r i v a t i o n o f a v o l u m e e q u a t i o n f r o m i t a n d t h e v o l u m e e q u a t i o n d e r i v a t i o n i n c l u d e s p a r t o f t h e d e r i v a -t i o n n e c e s s a r y f o r t h e c a l c u l a t i o n o f t h e c e n t e r o f mass o f s o l i d s d e f i n e d b y e q u a t i o n (3). To f a c i l i t a t e t h e c a l c u l a t i o n o f t h e v o l u m e o f a n y i n t e r v a l a l o n g t h e x - a x i s o r t h e y - a x i s u s i n g t h i s t h e o r e m w i t h e q u a t i o n (3), t h e v o l u m e i s c a l c u l a t e d u s i n g t w o a r e a s i l l u s t r a t e d i n F i g u r e 3. The f i r s t a r e a i s d e -f i n e d b y ( O . Y U ) , ( X L . Y U ) , ( X L . Y L ) , a n d (O.YL) a n d t h e s e c o n d b y ( X L . Y U ) , ( X U . Y L ) , a n d ( X L , Y L ) . The v o l u m e s g e n e r a t e d b y r e v o l v i n g t h e s e t w o a r e a s a b o u t t h e y - a x i s i s b y P a p p u s ' t h e o r e m : x = XL y = YU (5) Volume = S S 2iTXdydx + x = 0 y = YL x = XU y = f ( x ) S S 2uxdydx x = XL y = YL w h ere f ( x ) i s o f t h e f o r m o f e q u a t i o n (3). The g e n e r a l e q u a t i o n f o r t h e v o l u m e o f t h e a r e a s i n F i g u r e 3 i s : y 24 F i g u r e 3. An e q u a t i o n o f t h e f o r m y = A x a + Bx + C t o i l l u s t r a t e t h e i n t e g r a t i o n o f a r e g i o n t o f i n d i t s s o l i d o f r e v o l u t i o n a b o u t t h e y - a x i s u s i n g P a p p u s ' t h e o r e m ( P r o t t e r a n d M o r r e z , 1964). 25 (6) Volume = TTX 2(YU-YL) + 2 n ( A x ^ a + 2 )/(a+2) x = 0 _ x = XU + BacV/3 + Cx 2/2 - Y L x 2 / 2 ) x = XL The b i o m a s s o f t h e s t e m o r b r a n c h i s t h e n c a l c u l a t e d b y m u l t i p l y i n g i t s v o l u m e b y i t s d e n s i t y . The sum o f a l l t h e i n d i v i d u a l b r a n c h w e i g h t s c o n s t i t u t e s a s e s t i m a t e o f t h e b i o m a s s o f t h e p r i m a r y b r a n c h e s i n t h e c r o w n . The d e f i n i t i o n o f c r o w n s h a p e b y e q u a t i o n s o f t h e f o r m o f e q u a t i o n (3) c o m b i n e d w i t h e s t i m a t e s o f c r o w n d e n s i t y c o m p r i s e d o f e s t i m a t e s o f i n t e r w h o r l d i s t a n c e s a n d number o f b r a n c h e s p e r w h o r l p r o v i d e a m e t h o d f o r . c a l c u l a t i n g c r o w n w e i g h t . The c r o w n s h a p e , c r o w n w i d t h , a n d c r o w n l e n g t h f u r n i s h t h e i n f o r m a t i o n n e c e s s a r y f o r e s t i m a t i n g i n d i v i d u a l b r a n c h l e n g t h s . T hus t h e number o f b r a n c h e s a n d t h e i r v o l u m e s a r e d e f i n e d l e a v i n g o n l y a d e f i n i t i o n o f t h e i r d e n s i t y n e e d e d t o c a l c u l a t e t h e w e i g h t o f t h e m a i n b r a n c h s t e m s i n t h e c r o w n . A c o m p l e t e e s t i m a t e o f c r o w n w e i g h t must i n c l u d e a n e s t i m a t e o f t h e w e i g h t o f t h e n e e d l e s a n d b r a n c h l e t s i n t h e c r o w n . T h e i r w e i g h t s a r e e s t i m a t e d b y a n e q u a t i o n o f t h e f o r m s (7) y = A x a where y i s t h e w e i g h t i n p o u n d s a n d x i s b r a n c h l e n g t h I n f e e t 2 6 w i t h 'A' a n d * a ' b e i n g p a r a m e t e r s d e f i n e d f o r t h e r e s p e c t i v e w e i g h t e q u a t i o n s . To c o m p l e t e t h e d e f i n i t i o n o f t h e t r e e , t h e w e i g h t o f t h e r o o t s must be d e f i n e d . B e c a u s e o f t h e d i f f i c u l t y o f m e a s u r i n g them d i r e c t l y a n ^ . i n d i r e c t a p p r o a c h must be u s e d . The p r o g r a m c a l c u l a t e s t h e t o t a l r o o t w e i g h t a s a p e r c e n t a g e o f t h e t o t a l t r e e w e i g h t a s i t i s c a l c -u l a t e d i n e q u a t i o n s " ( 1 ) a n d ( 2 ) . The v a l u e o b t a i n e d f o r t h e t o t a l r o o t w e i g h t i s t h e n m u l t i p l i e d b y t h e p e r c e n t o f b a r k e x p e c t e d i n t h e r o o t s t o o b t a i n a n e s t i m a t e o f t h e w e i g h t o f t h e b a r k i n t h e r o o t s . A n o t h e r m ethod o f d e s c r i b i n g t h e r o o t s i n t h e m o d e l i s b y a n e q u a t i o n o f t h e f o r m : (8) Root w e i g h t = A ( B a s a l a r e a ) + B(DBH) + C ( D B H ) 2 + D ( H e i g h t ) + E w h ere A, B, C, D, a n d E a r e p a r a m e t e r s s u p p l i e d t o t h e p r o g r a m b y t h e u s e r . E q u a t i o n s s i m i l a r t o e q u a t i o n (8) a r e s u p p l i e d f o r b o t h t h e r o o t wood a n d r o o t b a r k a l l o w i n g t h e u s e r t o c a l c u l a t e t h e t o t a l r o o t - w e i g h t , t h e r o o t wood w e i g h t , a n d t h e r o o t b a r k w e i g h t s e p a r a t e l y . O n l y v a r i a b l e s i n v o l v i n g d i a m e t e r a n d h e i g h t a r e u s e d i n t h e a b o v e e q u a t i o n s t o f a c i l i t a t e e s t i m a t e s o f r o o t w e i g h t f r o m e a s i l y m e a s u r e d a e r i a l d i m e n s i o n s . S h o u l d t h e s e e q u a t i o n s be u n s a t i s f a c t o r y , t h e y c a n be c h a n g e d 27 q u i t e e a s i l y i n the program. In a d d i t i o n t o c a l c u l a t i n g the weight of v a r i o u s components of the t r e e , the model c a l c u l a t e s the c e n t e r o f mass o f the v a r i o u s components of the t r e e d e f i n e d as (Meriam, 1959): (9) y = JydA/A o r y = J7ydydx/,f Jaydx where the l i m i t s of i n t e g r a t i o n are d e f i n e d as f o r equa-t i o n ( 5 ) . Equation (9.) d e s c r i b e s the c e n t e r o f mass of symmetrical s o l i d s (Adamovich, 1970) having u n i f o r m d e n s i t i e s . In the model i t i s p o s s i b l e f o r s e c t i o n s of components t o have d i f f e r e n t d e n s i t i e s , thus the equation f o r the c e n t e r of mass becomes: n _ -n (10) Center of mass = £ y^m*/ £ nu i = l i = l where y i s the moment of the volume of each s e c t i o n , m i s the weight of each s e c t i o n , and n i s the number of s e c t i o n s b e i n g c o n s i d e r e d . The methodology used i n the c a l c u l a t i o n of the v a r i o u s random v a r i a b l e s used i n the model i s e x p l a i n e d a dequately by Wagner (1969) o r any oth e r s u i t a b l e opera-t i o n s r e s e a r c h t e x t . I t i s s u f f i c i e n t t o s t a t e t h a t random v a r i a b l e s are used i n d e f i n i n g b r a n c h i n g c h a r a c t -e r i s t i c s and t r e e component d e n s i t i e s as a l l u d e d t o p r e v i o u s l y . 28 B, D e s c r i p t i o n The model can be d i v i d e d i n t o s i x g e n e r a l s e c t i o n s : i n i t i a l i z a t i o n , d i r e c t c a l c u l a t i o n o f w e i g h t , i n d i r e c t c a l c u l a t i o n o f w e i g h t , c a l c u l a t i o n o f c e n t e r o f mass, c a l c u l a t i o n o f s l a s h , and o u t p u t . C o n t r o l o f t h e o r d e r o f e x e c u t i o n can be e x e r c i s e d by t h e u s e r . The p r o p e r e x e c u t i o n sequence f o r o b t a i n i n g s p e c i f i c r e s u l t s i s d i s c u s s e d i n c o n n e c t i o n w i t h t h e use o f t h e model. The i n i t i a l i z a t i o n phase o f t h e model, w h i c h i n c l u d e s t h e i n p u t o f pa r a m e t e r s i n t o t h e model, o c c u r s i n t h e BLOCK DATA s u b r o u t i n e and t h e MAIN program. The BLOCK DATA s u b r o u t i n e i n i t i a l i z e s a l l t h e pa r a m e t e r s c o n t a i n e d i n COMMON s t a t e m e n t s . The MAIN program i s r e s p o n s i b l e f o r r e a d i n g i n pa r a m e t e r s and f o r c a l l i n g t h e sequence o f s u b r o u t i n e s i n d i c a t e d by t h e u s e r . I t a l s o c a l c u l a t e s some o f t h e pa r a m e t e r s used l a t e r i n t h e program. The i n i t i a l i z a t i o n o f v a r i a b l e s and para m e t e r s i s n o t l i m i t e d t o t h e s e two a r e a s o f the program; an I n d i v i d u a l s u b r o u t i n e may i n i t i a l i z e t h o s e v a r i a b l e s i t u s e s e x c l u s i v e l y i t s e l f . I n t h e model t h e s u b r o u t i n e s : R00T1, R00T2, STEM1, STEM2, LEAF1, LEAF2, BRCHT, BRCH2, TREE1, and TREE2 use e q u a t i o n s o f t h e form o f e q u a t i o n (1) o r e q u a t i o n (2); t h e e q u a t i o n used i s i n d i c a t e d by t h e l a s t a l p h a n u m e r i c / 29 c h a r a c t e r i n t h e name. The s u b r o u t i n e s R00T1 a n d R00T2 e s t i m a t e t h e r o o t b i o m a s s a s a p e r c e n t a g e o f t h e t o t a l t r e e w e i g h t a s c a l c u l a t e d i n TREE1 a n d TREE2 r e s p e c t i v e l y . S u b r o u t i n e s STUMP1 a n d STUMP2 c a l c u l a t e t h e stump w e i g h t a s a p e r c e n t a g e o f t h e s t e m a s c a l c u l a t e d i n STEM1 a n d STEM2. The p e r c e n t u s e d i n c a l c u l a t i n g t h e stump w e i g h t s i s d e r i v e d f r o m c a l c u l a t i o n s i n STEM3. The i n d i r e c t " c a l c u l a t i o n o f component w e i g h t o c c u r s p r i m a r i l y i n s u b r o u t i n e s STEM3 a n d BRCH3. However, t h e s e t w o s u b r o u t i n e s a r e s u p p o r t e d b y nume r o u s s u b r o u t i n e s w h i c h p e r f o r m c a l c u l a t i o n s n e c e s s a r y t o t h e f u n c t i o n i n g o f t h e p r i m a r y s u b r o u t i n e s . S u b r o u t i n e ; STEM3 c a l c u l a t e s t h e v o l u m e , w e i g h t , a n d c e n t e r o f mass o f t h e wood a n d b a r k i n t h e s t e m . I t d i v i d e s t h e s t e m i n t o t h r e e s e c t i o n s d e s c r i b e d b y s i x -e q u a t i o n s a s i l l u s t r a t e d b y F i g u r e 4, The v a l u e s o f X I , X2, a n d Y3, a s w e l l a s t h e p o i n t s (0,HT), (DBHob/2,4.5), a n d (DBHib/2,4.5) i n f l u e n c e t h e e q u a t i o n o f t h e s e c t i o n o f t h e s t e m t h a t c o n t a i n s them. The s u b r o u t i n e f i r s t t e s t s t o d e t e r m i n e w h i c h s e c t i o n c o n t a i n s (DBHob/2,4.5) a n d (DBHib/2,4.5). I f t h e y a r e i n s e c t i o n I t h e e q u a t i o n s d e s c r i b i n g t h e wood a n d b a r k a r e c o n d i t i o n e d t o c o n t a i n t h e p o i n t s (O.HT) a n d (DBHib/2,4.5) a n d (DBHob/2,4.5) r e s p e c t i v e l y . The p o i n t s XI a n d Y l a r e t h e n c a l c u l a t e d F i g u r e 4 . An i l l u s t r a t i o n o f t h e s t e m a s d e s c r i b e d i n s u b r o u t i n e S T E M 3 . 31 using the modified equation. The Newton-Raphson method (McCracken, 1 9 6 ? ) is used in an algorithm, ALG2, to ca l -culate XII using the modified equation which describes the wood in the t i p of the stem. The equations describing section II are then modified to include (XI, Yl) or (XII, YI1). The points (X2,Y2) and (XI2, YI2) are calculated as described for the points (XI,Yl) and (XII, YI1). The equations which describe section III are conditioned to include the points (X2,Y2) or (XI2,YI2)j then X3 is found by finding the smallest positive root of the equation describing the exterior of the bottom section of the stem. XI3 is found similarly using the equation for the shape of the wood in section III. If (DBHob/2, 4 . 5 ) and (DBHib/2,4.5) occur in section II or III the same procedure is used as above except that points occurring at Y2 are used to condition the equation instead of the point (0,HT) as in section I. The subroutine used to implement the conditions imposed on the stem shape equations, as well as those on other equations, is subroutine PNC. The technique used in this subroutine is discussed under methodology. Using the modified stem shape equations, subroutine VOL calculates the volume generated by these equations as they are generated about the ordinate. These volumes 32 o b t a i n e d a r e m u l t i p l i e d b y t h e d e n s i t y o f t h e i r r e s p e c t i v e s e c t i o n s t h u s p r o v i d i n g a s e s t i m a t e o f t h e i r w e i g h t . The d e n s i t i e s u s e d i n t h e p r o g r a m a r e c o m p u t e d a s random v a r i a b l e s h a v i n g a mean, v a r i a n c e , a n d d i s t r i -b u t i o n number s u p p l i e d t o t h e p r o g r a m . The d i s t r i b u t i o n n umber i s a code n umber f r o m one t o s i x w h i c h i n d i c a t e s t o a s u b r o u t i n e , FCT, w h i c h random v a r i a b l e g e n e r a t o r t o c a l l . The d i s t r i b u t i o n s c o r r e s p o n d i n g t o t h e c o d e n u m b e r s one t o s i x a r e s t h e n o r m a l d i s t r i b u t i o n , t h e e x p o n e n t i a l d i s t r i b u t i o n , t h e l o g n o r m a l d i s t r i b u t i o n , t h e gamma d i s t r i b u t i o n , a d i s c r e t e d i s t r i b u t i o n w h i c h r e q u i r e s an i n p u t o f t e n p r o b a b i l i t i e s c o r r e s p o n d i n g t o t h e p r o b a b i l i t y mass f u n c t i o n o f i n t e g e r v a l u e f r o m one t o t e n , a n d a b i n a r y d i s t r i b u t i o n . I n a d d i t i o n t o t h e c a l c u l a t i o n o f s t e m v o l u m e a n d b i o m a s s , s u b r o u t i n e STEM3 a l s o c a l c u l a t e s t h e v o l u m e a n d w e i g h t o f t h e stump an d t h e u n m e r c h a n t a b l e t o p o f t h e s t e m . I t d o e s t h i s b y u s i n g t h e same p r o c e d u r e a s i n t h e c a l c u -l a t i o n o f e a c h i n d i v i d u a l s e c t i o n ' s w e i g h t a n d v o l u m e . The l i m i t s f o r t h e stump a r e e x p r e s s e d a s a stump h e i g h t i n f e e t a n d g r o u n d l e v e l w h i c h i s e q u a l t o z e r o . The l i m i t s f o r t h e u n m e r c h a n t a b l e t o p a r e g i v e n a s a t o p d i a m e t e r a n d t h e h e i g h t o f t h e t r e e . The x o r y c o o r d i -n a t e s n e e d e d t o c o m p l e t e t h e s e c a l c u l a t i o n s a r e d e r i v e d f r o m / 33 t h e v a l u e s s u p p l i e d a n d t h e m o d i f i e d s t e m s h a p e e q u a t i o n s . The d e n s i t y e s t i m a t e s u s e d t o c a l c u l a t e t h e stump a n d u n m e r c h a n t a b l e t o p w e i g h t s a r e t h e o n e s c a l c u l a t e d f o r t h e s t e m . U s i n g v a l u e s c a l c u l a t e d e a r l i e r i n t h e s u b r o u t i n e , STEM3 a l s o c a l c u l a t e s t h e c e n t e r o f mass o f t h e s t e m a l o n g t h e y - a x i s . The s t e m i s a s s u m e d t o be s y m m e t r i c a l a b o u t t h e x - a x i s ; t h u s t h e c e n t e r o f mass a l o n g t h e x - a x i s w o u l d be z e r o . I n t h e c a l c u l a t i o n o f c r o w n b i o m a s s , s u b r o u t i n e BRCH3 p l a y s a r o l e s i m i l a r t o t h a t o f STEM3 i n t h e c a l c u l a t i o n o f s t e m b i o m a s s , c r o w n s h a p e i s d e f i n e d b y t h r e e c r o w n s h a p e e q u a t i o n s o f t h e f o r m o f e q u a t i o n (3). I n i t i a l l y t h e e q u a t i o n d e s c r i b i n g t h e l o w e r s e c t i o n o f t h e c r o w n ( F i g u r e 5) i s c o n d i t i o n e d t o c o n t a i n t h e p o i n t (CD/2, ETC) w here CD i s c r o w n d i a m e t e r and HTC i s h e i g h t t o t h e c r o w n . The p o i n t (X2,Y2) i s f o u n d u s i n g t h e e q u a t i o n f o r t h e l o w e r s e c t i o n o f t h e c r o w n . I t i s t h e n u s e d t o c o n d i t i o n t h e e q u a t i o n w h i c h d e s c r i b e s t h e m i d d l e s e c t i o n o f t h e c r o w n . T h i s e q u a t i o n t h e n c a l c u l a t e s Y l f o r a g i v e n X I . The p o i n t s ( X I , Y l ) a n d (0,HT) a r e u s e d t o c o n d i t i o n t h e e q u a t i o n f o r t h e t o p o f t h e c r o w n . The l i n e t h u s f o r m e d p r o v i d e s a d e s c r i p t i o n o f t h e 34 e x t e r i o r c u r v a t u r e o f t h e c r o w n w h i c h u l t i m a t e l y p r o v i d e s a n e s t i m a t e o f mean b r a n c h l e n g t h a t a g i v e n h e i g h t i n t h e t r e e . A d e s c r i p t i o n o f t h e c r o w n s h a p e must be a c c o m p a n i e d b y an e s t i m a t e o f t h e d e n s i t y o f t h e m a t e r i a l w i t h i n t h a t s h a p e i f i t i s t o be u s e f u l f o r b i o m a s s c a l c u l a t i o n s . A d e n s i t y e s t i m a t e f o r t h e c r o w n i s f u r n i s h e d i n t h e f o r m o f a n e s t i m a t e o f i n t e r w h o r l d i s t a n c e s a n d n u m b e r s o f b r a n c h e s p e r w h o r l . T h e s e e s t i m a t e s a r e c a l c u l a t e d i n t h e p r o g r a m u s i n g a mean, v a r i a n c e , a n d d i s t r i b u t i o n g i v e n f o r t h e v a r i a b l e i n q u e s t i o n . C o n s e c u t i v e c a l c u -l a t i o n a n d s u m m a t i o n o f i n t e r w h o r l d i s t a n c e s a s a random v a r i a b l e g i v e s a y - c o o r d i n a t e t h a t c a n be u s e d w i t h t h e a p p r o p r i a t e c r o w n s e c t i o n e q u a t i o n t o g i v e a mean b r a n c h l e n g t h w h i c h c a n be u s e d t o c a l c u l a t e t h e random b r a n c h l e n g t h s i n t h e w h o r l a t " y " . The number o f b r a n c h e s p e r w h o r l i s a l s o a random v a r i a b l e w h i c h must be c a l c u l a t e d t o p r o v i d e t h e p r o p e r number o f b r a n c h l e n g t h s t o be c a l c u l a t e d f o r e a c h w h o r l . The v o l u m e a n d b i o m a s s c a l c u l a t e d f o r e a c h b r a n c h d e p e n d s on s i x b r a n c h e q u a t i o n s . The f i r s t e q u a t i o n d e s c r i b e s t h e b r a n c h t i p a n d i s c o n d i t i o n e d t o p a s s t h r o u g h t h e p o i n t (O.CD / 2 ) . The y - c o o r d l n a t e , F i g u r e 5. An i l l u s t r a t i o n o f c r o w n s h a p e a s f o u n d i n s u b r o u t i n e B R C H 3 . 36 BLTHF, i s c a l c u l a t e d f o r x = 0.01 t o p r o v i d e p o i n t (0.01,BLTHF) t h r o u g h w h i c h t h e e q u a t i o n d e s c r i b i n g s e c t i o n I I must f i t . The e q u a t i o n d e s c r i b i n g s e c t i o n I I i s u s e d t o c a l c u l a t e BLTHM u s i n g x = 0.03. t h u s f u r n i s h i n g p o i n t (0.03,BLTHM) f o r t h e c o n d i t i o n i n g o f t h e e q u a t i o n f o r s e c t i o n I I I . The t h r e e e q u a t i o n s w h i c h d e s c r i b e t h e wood i n t h e b r a n c h a r e m o d i f i e d i n t h e same way a s t h o s e a r e a b o v e , e x c e p t t h a t t h e I n i t i a l x v a l u e i s p r o v i d e d a s t h e d o u b l e b a r k t h i c k n e s s a t a d i a m e t e r o f 0.35 i n c h e s on t h e b r a n c h b y s u p p l y i n g i t d i r e c t l y o r b y s u p p l y i n g t h e c o e f f i c i e n t s f o r a n e q u a t i o n w h i c h c a l c u l a t e s i t . The v o l u m e s a n d w e i g h t s a r e c a l c u l a t e d a s d e s c r i b e d f o r t h e s t e m f o r e a c h b r a n c h . The t o t a l w e i g h t c a l c u l a t e d i n t h i s m anner i s a n e s t i m a t e o f t h e w e i g h t o f t h e m a t e r i a l c o n t a i n e d i n t h e m a i n b r a n c h s t e m s i n t h e c r o w n . The c r o w n c o n s i s t s o f n e e d l e s a n d b r a n c h l e t s i n a d d i t i o n t o t h e m a i n b r a n c h s t e m s . An e s t i m a t e o f t h e w e i g h t o f t h e n e e d l e s a n d t h e b r a n c h l e t s i s c o m p u t e d u s i n g a f u n c t i o n o f t h e f o r m o f e q u a t i o n (7) where t h e i n d e p e n d e n t v a r i a b l e i s l e n g t h a n d t h e d e p e n d e n t v a r i a b l e i s w e i g h t . T h u s t h e c r o w n i s c o m p l e t e l y d e s c r i b e d i n t e r m s o f w e i g h t . The d i s t r i b u t i o n o f t h e m a t e r i a l w i t h i n t h e c r o w n 37 S e c t i o n I ( X I I , B L T H F ) S e c t i o n I I (XI2,BLTHM) S e c t i o n I I I (BDIAl/2,0) - (0,BLTH) (0.01,BLTHF) F i g u r e 6. An i l l u s t r a t i o n o f a c o n i c a l b r a n c h h a v i n g a l e n g t h e q u a l t o o n e - h a l f t h e c r o w n w i d t h a n d a d i a m e t e r e q u a l t o BDIA. 38 i n f l u e n c e s t h e c e n t e r o f mass o f t h e c r o w n a l o n g t h e y - a x i s . The l o c a t i o n o f t h e c e n t e r o f mass p r o v i d e s a s i n g l e e s t i m a t e o f t h e h e i g h t o f t h e c r o w n component o f t h e f u e l c o m p l e x . S u b r o u t i n e s BRCH3 c a l c u l a t e s t h e c e n t e r o f mass u s i n g c a l c u l a t i o n s made p r e v i o u s l y i n BRCH3. S u b r o u t i n e CSEC c a l c u l a t e s t h e c e n t e r o f mass o f t h e c r o w n f i r s t a s s u m i n g t h a t t h e mass i n t h e c r o w n i s n o t u n i f o r m l y d i s t r i b u t e d , t h e n b y a s s u m i n g t h a t i t i s u n i f o r m l y d i s t r i b u t e d . The c r o w n i s d i v i d e d i n t o t h e s e c t i o n s a s shown i n F i g u r e 7. The mass o f t h e c r o w n i s t h e n d i v i d e d i n t o f o r t y f i v e p a r t s a l l o t t i n g 9,8,••«2, a n d 1 p a r t s t o s e c t i o n s I t h r o u g h I X r e s p e c -t i v e l y . The c e n t e r o f mass i s t h e n c a l c u l a t e d . T h i s m e t h o d a t t e m p t s t o a s s e s s t h e e f f e c t o f a h o r i z o n t a l a n d v e r t i c a l g r a d i e n t i n t h e c r o w n on i t s c e n t e r o f g r a v i t y . A more h o r i z o n t a l g r a d i e n t i s s i m u l a t e d b y g r o u p i n g s e c t i o n s I , I V , a n d V I I i n t o one s e c t i o n , s e c t i o n s I I , V, a n d V I I I i n t o a n o t h e r s e c t i o n , a n d s e c t i o n s I I I , V I , a n d I X i n t o a t h i r d s e c t i o n . T h e f i r s t s e c t i o n i s a s s i g n e d o n e - h a l f t h e t o t a l mass, t h e s e c o n d o n e - t h i r d t h e t o t a l m ass, a n d t h e t h i r d o n e - s i x t h t h e t o t a l mass; t h e c e n t e r o f mass i s t h e n c a l c u l a t e d . The c a l c u l a t i o n o f t h e c e n t e r o f mass, a s s u m i n g a u n i f o r m d i s t r i b u t i o n o f m a t e r i a l i n t h e c r o w n p r o v i d e s a s t a n d a r d F i g u r e 7. An i l l u s t r a t i o n o f t h e c r o w n d i v i s i o n s u s e d f o r . c a l c u l a t i n g t h e c e n t e r o f mass o f t h e c r o w n i n s u b r o u t i n e CSEC. / 40 o f c o m p a r i s o n f o r t h e m e t h o d s . The f i n a l c a l c u l a t i o n i n t h e m o d e l i s t h e c a l c u l a t i o n o f s l a s h . T h i s i s a s t r a i g h t f o r w a r d p r o c e d u r e i n w h i c h t h e amount o f m a t e r i a l r e m o v e d i n a l o g g i n g o p e r a t i o n i s s u b t r a c t e d f r o m t h e amount o f m a t e r i a l i n t h e t r e e . A p a r a m e t e r w h i c h i s t h e p e r c e n t o f t h e t o t a l c r o w n r e m a i n i n g a f t e r l o g g i n g i s p r o v i d e d t o e s t i m a t e t h e amount o f m a t e r i a l i n t h e c r o w n t h a t i s a c t u a l l y r e m a i n i n g on t h e g r o u n d a f t e r t h e l o g g i n g o p e r a t i o n . The o u t p u t s e c t i o n o f t h e p r o g r a m i s c o n t a i n e d i n f o u r s u b r o u t i n e s . S u b r o u t i n e WRITE1 p r i n t s t h e b a s i c t r e e p a r a m e t e r s a n d t h e w e i g h t c a l c u l a t i o n s f o r c o m p o n e n t s c o n s i d e r e d i n a p a r t i c u l a r r u n ; s u b r o u t i n e WRITE2 p r i n t s t h e e q u a t i o n s u s e d i n t h e m o d e l ; s u b r o u t i n e WCG p r i n t s t h e r e s u l t s o f t h e c e n t e r o f mass c a l c u l a t i o n s ; a n d s u b r o u t i n e SLASH p r i n t s t h e r e s u l t s o f i t s own c a l c u l a t i o n s T h u s t h e m o d e l i s d e s c r i b e d i n t e r m s o f b o t h i t s m e t h o d o l o g y a n d t h e i m p l e m e n t a t i o n o f t h i s m e t h o d o l o g y i n a c o m p u t e r m o d e l . T h i s d e s c r i p t i o n f o r m s t h e b a s i s f o r u n d e r s t a n d i n g , e x p a n d i n g , a n d u s i n g t h e m o d e l a s i t e x i s t s . 41 C. Use E f f e c t i v e u s e o f t h e m o d e l i s d e p e n d e n t on a k n o w l e d g e o f t h e a l t e r n a t i v e s a v a i l a b l e t o t h e u s e r . The i m p l e m e n t a t i o n o f t h e s e a l t e r n a t i v e s i s a c c o m p l i s h e d b y i n p u t t i n g t h e p r o p e r i n f o r m a t i o n i n t o t h e p r o g r a m . A t h o r o u g h d e s c r i p t i o n o f t h e c o n t r o l c a r d s i s g i v e n i n A p p e n d i x I I . T h i s d e s c r i p t i o n s h o u l d be s e l f e x p l a n a t o r y . P r o v i s i o n i s made i n t h e m o d e l f o r t h e e s t i m a t i o n o f c e r t a i n p a r a m e t e r s i f t h e y a r e i n c l u d e d on t h e c o n t r o l c a r d s a s z e r o . A summary o f t h e e q u a t i o n s w h i c h c a l c u l a t e t h e s e p a r a m e t e r s i s : (11) B a s a l a r e a = 3 . l 4 l 5 9 ( D B H / 2 4 ) 2 (12) H e i g h t = A(DBH) + B ( S t a n d b a s a l a r e a ) + C ( D B H ) 2 + D (13) H e i g h t t o c r o w n = A(DBH) + B ( H e i g h t ) + C ( A g e ) + D ( 1 4 ) Crown l e n g t h = H e i g h t - H e i g h t t o c r o w n (15) Crown w i d t h = A(DBH) + B ( D B H ) 2 + C (16) D o u b l e b a r k t h i c k n e s s * A ( D B H ) a + B(DBH) + C ( H t ) C + D (17) B r a n c h d o u b l e b a r k t h i c k n e s s = (16) w h e r e A, B, C, D, a, a n d c a r e p a r a m e t e r s s u p p l i e d t o t h e p r o g r a m i f t h e u s e r w i s h e s t o u s e t h e e q u a t i o n s . The p r o p e r s e q u e n c e f o r e n t e r i n g t h e p a r a m e t e r s i s g i v e n i n A p p e n d i x I I . Some k n o w l e d g e o f t h e s t e m , b r a n c h , a n d c r o w n s h a p e s i s e s s e n t i a l f o r u s i n g t h e m o d e l . Shape e q u a t i o n s n e c e s s a r y f o r t h e m o d e l c a n be f i t t e d t h r o u g h t h e c o o r d i -n a t e s o f t h e l e n g t h a n d r a d i u s o f t h e component u s i n g a l e a s t s q u a r e s m e t h o d o r some o t h e r t e c h n i q u e s u c h a s N e w t o n ' s m e t h o d . The t e c h n i q u e f o r f i t t i n g t h e c u r v e i s n o t i m p o r t a n t ; h o w e v e r , a l e a s t s q u a r e s a p p r o a c h e n a b l e s one t o c a r r y o u t a s t a t i s t i c a l a n a l y s i s c o n c u r r e n t w i t h t h e p r e l i m i n a r y a n a l y s i s f o r t h e m o d e l . I f t h e d a t a o r e q u a t i o n s a v a i l a b l e f o r u s e on t h e m o d e l a r e i n t e r m s o f d i a m e t e r i n s t e a d o f r a d i u s , t h e c o e f f i c i e n t ' s ; must be m o d i f i e d t o c o n f o r m t o e q u a t i o n s u s i n g r a d i u s a s t h e i n d p e n d e n t v a r i a b l e i n a f u n c t i o n h a v i n g l e n g t h a s t h e d e p e n d e n t v a r i a b l e . I f p a r t i c u l a r e q u a t i o n s a r e n o t a v a i l a b l e , t h e u s e r may u s e t h e o r e t i c a l e q u a t i o n s o f t h e f o r m o f e q u a t i o n (3). T h e s e e q u a t i o n s must h a v e l e n g t h i n f e e t a s a f u n c t i o n o f r a d i u s i n f e e t . The e q u a t i o n s u s e d f o r t h e p r o g r a m a r e e n t e r e d a s t h o u g h t h e l e n g t h m e a s u r e m e n t s o r i g i n a t e a t t h e a p e x o f t h e component ( F i g u r e 2 ) . The e q u a t i o n i s r e a d i n t o t h e m o d e l , t h e n i t i s s u b t r a c t e d f r o m a c o n s t a n t e q u a l t o t h e h e i g h t o f t h e t r e e i n t h e c a s e s o f c r o w n a n d s t e m s h a p e a n d f r o m o n e - h a l f t h e c r o w n w i d t h i n t h e c a s e o f 43 b r a n c h s h a p e . I f A i n t h e m o d i f i e d e q u a t i o n i s p o s i t i v e t h e e q u a t i o n c o n t a i n s a mimi'mum p o i n t . The p r o g r a m c a l c u l a t e s t h e y - c o o r d i n a t e o f t h i s p o i n t . I f t h i s c o o r d i n a t e i s l e s s t h a n z e r o t h e e q u a t i o n i s c o n d i t i o n e d t o c o n t a i n a p p r o p r i a t e p o i n t s a s s t a t e d p r e v i o u s l y . I f t h e y - c o o r d i n a t e i s p o s i t i v e , t h e e q u a t i o n i s a l t e r e d b y s e t t i n g A e q u a l t o z e r o a n d b y e q u a t i n g B t o t h e s l o p e o f t h e l i n e a t t h e c o n d i t i o n i n g p o i n t . To a v o i d t h e d i s t o r t i o n c a u s e d b y t h i s c h a n g e , t h e u s e r s h o u l d c h e c k t h e e q u a t i o n s b e f o r e e n t e r i n g t h e m i n t h e m o d e l t o make s u r e t h a t t h e minimum p o i n t i s l e s s t h a n z e r o . R e g a r d l e s s o f t h e p a r a m e t e r s u s e d t o c o n t r o l t h e c a l c u l a t i o n s i n t h e m o d e l , t h i s m o d e l s h o u l d n o t be t r e a t e d a s a " b l a c k b o x " where i n f o r m a t i o n i s f e d , d i g e s t e d , a n d r e g u r g i t a t e d i n a d i f f e r e n t f o r m . The m e t h o d o l o g y i n t h e p r o g r a m must be s t u d i e d i f r e a s o n a b l e e q u a t i o n s a r e t o be p r e s e n t e d t o t h e m o d e l f o r a n a l y s i s . The a c t u a l a n a l y s i s r e q u i r e s a b o u t t h i r t y s e c o n d s o f c o m p u t e r t i m e on t h e IBM 3 6 0 ( 6 7 ) f o r t h e mean t r e e p a r a -m e t e r s g i v e n b y K u r u c z ( 1 9 6 9 ) . Most o f t h i s t i m e i s u s e d f o r c a l c u l a t i n g t h e w e i g h t s o f i n d i v i d u a l b r a n c h e s i n t h e c r o w n . Any p a r a m e t e r w h i c h r e d u c e s t h e number o f b r a n c h e s i n t h e c r o w n s i g n i f i c a n t l y s h o u l d a l s o s i g n i f i c a n t l y r e d u c e t h e t i m e o f c a l c u l a t i o n f o r t h e p r o g r a m . 44 V. V E R I F I C A T I O N OF THE MODEL A. V e r i f i c a t i o n p r o c e d u r e To f u l f i l l t h e i n i t i a l o b j e c t i v e s o f t h i s s t u d y , i t i s n e c e s s a r y t o show t h a t t h e m o d e l c r e a t e d g i v e s p l a u s i b l e e s t i m a t e s o f t r e e component w e i g h t s . A s t a t i s -t i c a l a n a l y s i s o f t h e r e s u l t s g e n e r a t e d b y t h e m o d e l i s b e y o n d t h e s c o p e o f t h i s s t u d y . H owever, a. d i s c u s s i o n o f t h e p o s s i b l e u s e f u l n e s s o f t h e s e r e s u l t s i s i n c l u d e d i n t h e t e x t . The p l a u s i b i l i t y o f t h e m o d e l i s shown b y i l l u s t r a t -i n g t h a t t h e v a l u e s i t g e n e r a t e s a r e w i t h i n a n a c c e p t a b l e r a n g e o f t h e v a l u e s e s t i m a t e d i n e m p e r i c a l s t u d i e s . K u r u c z ( 1 9 6 9 ) p r o v i d e d t h e b a s i s f o r d e t e r m i n i n g t h e p l a u s i b i l i t y o f t h e m o d e l i n h i s a n a l y s i s o f d a t a f r o m 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 R e s e a r c h F o r e s t . I f t h e a s s u m p t i o n t h a t t h e v a l u e s c a l c u l a t e d w i t h h i s r e g r e s s i o n m o d e l s a r e " t r u e " i s t r u e , i t i s s u f f i c i e n t t o show t h a t t h e r e s u l t s f r o m t h e m o d e l a p p r o x i m a t e h i s r e s u l t s . T r u e v a l i d a t i o n o f t h e m o d e l c a n o c c u r o n l y a f t e r f u r t h e r e m p e r i c a l a n a -l y s i s c o n f i r m s t h e a s s u m p t i o n s made r e g a r d i n g : 1. The r a n d o m n e s s o f b r a n c h l e n g t h w i t h i n e a c h w h o r l . 2. The r a n d o m n e s s o f i n t e r w h o r l d i s t a n c e s . 3. The f u n c t i o n a l r e l a t i o n s h i p b e t w e e n i n d i v i d u a l b r a n c h l e n g t h a n d w e i g h t o f n e e d l e s on e a c h b r a n c h . / 1*5 k. The f u n c t i o n a l r e l a t i o n s h i p b e t w e e n i n d i v i d u a l b r a n c h l e n g t h a n d b r a n c h l e t w e i g h t o n e a c h b r a n c h . I f f u r t h e r a n a l y s i s c o n f i r m s t h e s e a s s u m p t i o n s , s i m u l a t i o n e x p e r i m e n t s w i t h t h e m o d e l c a n p r o c e e d . I f t h e a s s u m p t i o n s a r e n o t c o n f i r m e d , t h e m o d e l must be m o d i f i e d t o a c c o m o d a t e t h e new i n f o r m a t i o n . B. P r e s e n t a t i o n o f r e s u l t s T a b l e s 3 - 5 show t h e r e s u l t s g e n e r a t e d b y t h e m o d e l u s i n g t h e mean, maximum, a n d minimum t r e e d i m e n s i o n s o c c u r -r i n g i n t h e d a t a a n a l y s e d b y K u r u c z (19^9). The v a l u e s a s s o c i a t e d w i t h t h e c a l c u l a t i o n s p e r f o r m e d i n t h e s i m u l a t i o n s e c t i o n o f t h e p r o g r a m a r e o n l y a s r e l i a b l e a s t h e i n p u t i n f o r m a t i o n s u p p l i e d t o c o n t r o l them. The d i s c r e p a n c i e s among t h e s e e s t i m a t e s c a n be t r a c e d t o t h e i n f o r m a t i o n s u b m i t t e d on t h e c o n t r o l c a r d s f o r t h e m o d e l . C D i s c u s s i o n The a p p a r e n t l y l a r g e d i f f e r e n c e s i n t h e e s t i m a t e s shown i n T a b l e s 3 - 5 make a v e r b a l e x p l a n a t i o n o f t h e s e d i f f e r e n c e s n e c e s s a r y . The..most c o n v e n i e n t means f o r d i s c u s s i n g them i s t o d i s c u s s t h e i n d i v i d u a l c o m p o n e n t ' s d i f f e r e n c e s . . The. r e l a t i v e r v a r l a t i o n among t h e e s t i m a t e s o f s t e m w e i g h t i s due t o t h e d i f f e r e n c e i n t h e m e t h o d s 46 T a b l e 3 « An e s t i m a t e o f t h e o v e n d r y w e i g h t o f t h e c o m p o n e n t s o f D o u g l a s - f i r i n p o u n d s c o m p a r i n g t h e m e thod e m p l o y e d i n t h e m o d e l w i t h t w o o t h e r m e t h o d s . DBH = 25.1" H e i g h t = 117.3' Crown w i d t h = 27.1* Crown l e n g t h = 77.3' Component Methods-B a s a l area2»3 K u r u c z b e s t 2 M o d e l T o t a l t r e e 6994.48 B o l e 61OO.83 Wood 5170.73 B a r k 930.10 T o t a l c r o w n 959.70 B r a n c h 744.97 L a r g e 549.20. Wood B a r k Medium 89.78 Wood B a r k F i n e 105<99 Wood B a r k N e e d l e 214.60 B r a n c h l e t Wood B a r k DBH = 48.4" H e i g h t = 218.0' Crown w i d t h = 39.0' Crown l e n g t h = 157.0' T o t a l t r e e B o l e Wood B a r k T o t a l c r o w n B r a n c h L a r g e Wood B a r k Medium 26007.53 22684.70 19226.32 3458.39 2885.90 2301.37 1760.19 254.74 4379.68 3844.80 3260.40 584.40 1475.01 1174.33 899.12 127.76 147.45 300.65 30265.32 26569.03 22530.59 4038.44 5890.56 4689.80 3590.71 510.23 5879.50 4955.35 3935.04 1020.32 924.12 231.15 205.09 140.93 64.16 24.71 18.82 5.88 l i 3 6 1.14 0*22 692.99 274.48 219.08 55.40 38971.11 35927.52 29374.23 6553.28 3043.59 1339.39 1276.08 787.17 488.91 60.65 47 T a b l e 3 — c o n t i n u e d Component M e t h o d B a s a l a r e a K u r u c z b e s t M o d e l Wood 45.39 B a r k 15.26 F i n e 286.44 588.857 2.65 Wood 2.24 B a r k 0.4l N e e d l e 584.30 1200.68 1704.20 B r a n c h l e t 674.98 Wood 538.74 B a r k 136.24 DBH = 1.4" H e i g h t =12.0' Crown w i d t h =6.0' Crown l e n g t h = 11.1' T o t a l t r e e 21.76 1.39 41.22 B o l e 18.98 1.22 2.30 Wood 16.09 1.04 0.40 B a r k 2.89 0.19 1.90 T o t a l c r o w n 253.30 4.03 38.91 B r a n c h 174.18 3.21 0.39 L a r g e 105.09 2.46 0.00 Wood 0.00 B a r k 0.00 Medium 29.29 0.35 0.25 Wood 0.18 B a r k 0.06 F i n e 39.81 0.40 0.14 Wood 0.13 B a r k 0.01 N e e d l e 79.02 0.82 38.52 B r a n c h l e t 15.26 Wood 12.18 B a r k 3.08 1 B o t h t h e b a s a l a r e a m e t h o d a n d K u r u c z b e s t m e t h o d a r e b a s e d on e q u a t i o n s f o u n d b y K u r u c z (1969). 2 Component w e i g h t s n o t shown w e r e n o t c a l c u l a t e d b y K u r u c z . 3 N o n a d d i t i v i t y due t o u s e o f b o t h c o n d i t i o n e d a n d u n c o n -d i t i o n e d r e g r e s s i o n s . 48 T a b l e 4. An e s t i m a t e o f t h e o v e n d r y w e i g h t o f t h e c o m p o n e n t s o f w e s t e r n h e m l o c k i n p o u n d s c o m p a r i n g t h e m e t h o d s e m p l o y e d i n t h e m o d e l w i t h t w o o t h e r m e t h o d s . DBH = 19.1" H e i g h t _ 95.V Crown w i d t h = 24.3' Crown l e n g t h = 68,5' Component T o t a l t r e e B o l e Wood B a r k T o t a l c r o w n B r a n c h L a r g e Wood B a r k Medium Wood B a r k F i n e Wood B a r k N e e d l e B r a n c h l e t Wood B a r k DBH = 36.4" H e i g h t = 176.0-Crown w i d t h = 36.0' Crown l e n g t h = 128.0' T o t a l t r e e 14724.62 16779.38 16418.83 B o l e 13270.35 15144.23 15053.65 Wood 11566.99 13184.02 11750.84 B a r k 1703.36 1960.22 3302.81 T o t a l c r o w n 1483.32 6304.77 1365.18 B r a n c h 1142.42 6299.09 570.57 L a r g e 775.93 4159.98 516.66 Wood 478.42 B a r k 38.24 Medium 179.77 507.63 51.36 M e t h o d 1 B a s a l a r e a 2 » 3 K u r u c z b e s t 2 M o d e l 4054.22 2504.24 2685.34 3653.81 2260.20 2243.59 3184.81 1967.65 1675.41 469.00 292.55 568.17 372.54 652.50 441.76 289.98 449.01 132.01 168.57 278.20 113.83 70.35 43.48 70.58 76.79 16.90 13.10 3.80 50.83 94.03 1.28 1.16 0.12 109.61 203.49 309.75 21.06 16.73 4.34 49 Table 4— continued Component Wood Bark Fine Wood Bark Needle Branchlet Wood Bark Method Basal area Kurucz best 1.86.73 367.84 DBH = 1.6" Height = 14.0' Crown width = 8.0' Crown length = l4.0' Total tree Bole Wood Bark Total crown Branch Large Wood Bark Medium Wood Bark Fine Wood Bark Needle Branchlet Wood Bark 28.45 25.64 22.35 3.29 •46.54 •31.63 •60.58 29.40 -0.44 12.18 631.47 1005.69 2.58 2.33 2.03 0.30 3.83 0.86 -1.08 0.88 1.06 2,96 Model 47.95 3,41 2.55 2.31 0.24 794.61 54.03 42.91 11.12 46.71 3.28 0.68 2.60 43.43 1.35 0.00 0.00 0.00 1.08 0.87 0.21 0. 26 0.27 0.01 42.08 2.86 2.27 0.59 1 Both the basal area method and Kurucz best method are based on equations found by Kurucz (1969). 2 Component weights not shown were not calculated by Kurucz. 3 Nonadditivity due to use of both conditioned and uncon-ditioned regressions. 50 T a b l e 5. An e s t i m a t e o f t h e o v e n d r y w e i g h t o f t h e c o m p o n e n t s o f w e s t e r n r e d c e d a r i n p o u n d s c o m p a r i n g t h e method e m p l o y e d i n t h e m o d e l w i t h two o t h e r m e t h o d s . DBH = 25.4" H e i g h t •- 94.5' Crown w i d t h = 24.7' Crown l e n g t h = 74.7* Component T o t a l t r e e B o l e Wood B a r k T o t a l c r o w n B r a n c h L a r g e Wood B a r k Medium Wood B a r k F i n e Wood B a r k N e e d l e B r a n c h l e t Wood B a r k M e t h o d J B a s a l a r e a 2 * 3 K u r u c z best2 3290.36 2833.22 2487.99 325.23 462.66 294.99 219.72 48.21 27.07 167.67 DBH = 47.1" H e i g h t = 160.0' Crown w i d t h = 39.0' Crown l e n g t h = 153.0' T o t a l t r e e B o l e Wood B a r k T o t a l c r o w n B r a n c h L a r g e Wood B a r k Medium 11314.07 9742.17 8555.09 1187.08 1494.33 1011.91 775.75 153.58 2273.91 1964.37 1724.89 239.48 831.25 524.18 390.20 84.29 49.69 307.08 13238.39 11436.34 10042.11 1394.22 5911.68 4515.84 3624.41 626.21 M o d e l 4304.37 3624.85 2981.96 642.88 679.52 153.62 135.37 89.31 46.06 17.09 12.77 'i-4?32 1.16 1.04 0.12 525.90 11.66 9.41 2.26 24827.22 22138.93 18635.91 3503.03 2688.28 1049.91 994.66 574.87 419.79 52.56 51 T a b l e 5 — c o n t i n u e d Component Wood B a r k F i n e Wood B a r k N e e d l e B r a n c h l e t Wood B a r k B a s a l a r e a 82.58 482.41 DBH = 1.3" H e i g h t =12.0* Crown w i d t h = 6.0' Crown l e n g t h = 11.0' T o t a l t r e e B o l e Wood B a r k T o t a l c r o w n B r a n c h L a r g e Wood B a r k Medium Wood B a r k F i n e Wood B a r k N e e d l e B r a n c h l e t Wood B a r k 8.62 7.42 6.52 0.90 40.71 1.77 -7.70 5.11 4.36 38.94 M e t h o d K u r u c z b e s t 265.22 1395.94 0.76 0.65 0.57 0.08 4.33 2.17 1.43 0.42 0.32 2.15 M o d e l 39.23 13.34 2.69 2.36 0.33 1638.37 36.34 29.31 7.03 45.93 1.55 0.26 1.29 44.38 0.50 0.00 0.00 0.00 0.33 0.26 0.07 0.16 0.15 0.01 43.88 0.97 0.78 0.19 1 B o t h t h e b a s a l a r e a m e t h o d a n d K u r u c z b e s t m e t h o d a r e b a s e d on e q u a t i o n s f o u n d b y K u r u c z (1969). 2 Component w e i g h t s n o t shown were n o t c a l c u l a t e d b y K u r u c z . 3 N o n a d d i t i v i t y due t o t h e u s e o f b o t h c o n d i t i o n e d a n d u n -c o n d i t i o n e d r e g r e s s i o n s . 52 u s e d b y K u r u c z (1969) a n d b y t h e m o d e l t o c a l c u l a t e t h e s t e m w e i g h t . K u r u c z m e a s u r e d t h e d i a m e t e r o f t h e s t e m a t one f o o t , a t f o u r a n d o n e - h a l f f e e t , a n d a t t e n t h s o f t o t a l h e i g h t a b o v e f o u r a n d o n e - h a l f f e e t . The v o l u m e s o f t h e s e s e c t i o n s a s c a l c u l a t e d b y S m a l i a n ' s f o r m u l a were m u l t i p l i e d b y a s p e c i f i c g r a v i t y f o u n d b y K e n n e d y (1965) t o o b t a i n a n e s t i m a t e o f t h e s e c t i o n w e i g h t . The sum o f t h e s e c t i o n s ' w e i g h t s c o n s t i t u t e d a m e s t i r a a t e o f w e i g h t o f t h e s t e m . The m o d e l c a l c u l a t e d t h e w e i g h t o f t h e s t e m b y f i n d i n g a n e q u a t i o n o f h e i g h t a s a f u n c t i o n o f t h e r a d i u s s q u a r e d w h i c h c o n t a i n e d DBH a n d h e i g h t o f t h e t r e e , u s i n g t h i s e q u a t i o n t o c a l c u l a t e t h e v o l u m e o f t h e s t e m a s a g e o m e t r i c s o l i d o f r e v o l u t i o n , a n d m u l t i p l y i n g t h e c a l c u l a t e d v o l u m e b y a s p e c i f i c g r a v i t y e s t i m a t e w h i c h i s a n o r m a l l y d i s t r i b u t e d random v a r i a b l e h a v i n g a mean a n d v a r i a n c e e q u a l t o t h o s e f o u n d b y K e n n e d y (1965). The u s e o f a c o n t l n o u s p a r a b o l i c e q u a t i o n t o d e s c r i b e t h e s h a p e o f t h e s t e m i n t h e m o d e l c a u s e s c o n s i s t e n t o v e r e s t i m a t e s o f v o l u m e . A f t e r m a n u a l l y c h e c k i n g t h e r e s u l t s g e n e r a t e d b y t h e m o d e l , t h e v a r i a t i o n b e t w e e n t h e model's e s t i m a t e s a n d t h e r e g r e s s i o n s ' e s t i m a t e s must be a t t r i b u t e d t o t h e f a c t t h a t a s i n g l e p a r a b o l i c e q u a t i o n d o e s n o t a d e q u a t e l y d e s c r i b e t h e s h a p e o f t h e t r e e s t e m . 53 The d i f f e r e n c e s b e t w e e n t h e r e l a t i v e a m o u n t s o f s t e m wood a n d b a r k c a l c u l a t e d u s i n g t h e m o d e l a n d t h e o t h e r two m e t h o d s i s due t o t h e m e t h o d o f d e t e r m i n i n g b a r k t h i c k n e s s o f t h e s t e m i n t h e m o d e l . The b a r k t h i c k -n e s s i s c a l c u l a t e d f r o m a n e q u a t i o n b y S m i t h , K e r , a n d C s i z m a z i a ( l ° 6 l ) . T h e s e e q u a t i o n s a r e b a s e d on d a t a d i f f e r e n t f r o m t h o s e a n a l y s e d b y K u r u c z (19^9) a n d t h e i r r e s u l t s c a n o n l y be c o n s i d e r e d a s r o u g h e s t i m a t e s o f t h e t r u e b a r k t h i c k n e s s . The d i f f e r e n c e s f o u n d i n t h e e s t i m a t e s o f c r o w n component w e i g h t s a r e due t o a l a c k o f q u a n t i t a t i v e i n f o r m a t i o n r e g a r d i n g i n t e r w h o r l d i s t a n c e s , b r a n c h l e n g t h c h a r a c t e r i s t i c s , a n d b r a n c h s h a p e . G i v e n more r e l i a b l e i n f o r m a t i o n a b o u t t h e s e f a c t o r s a n d b e t t e r e s t i m a t e s o f c r o w n s h a p e , t h e m o d e l s h o u l d p r e d i c t t h e a c t u a l c r o w n t o a r e a s o n a b l e d e g r e e o f a c c u r a c y . I t s h o u l d be n o t e d t h a t t h e d i f f e r e n c e s i n e s t i m a t e s o f f i n e a n d medium b r a n c h m a t e r i a l i n t h e c r o w n b e t w e e n t h e r e g r e s s i o n m e t h o d s a n d t h e m o d e l a r e p a r t i a l l y b e c a u s e much o f t h e medium a n d f i n e b r a n c h m a t e r i a l i s i n c l u d e d i n t h e b r a n c h l e t s r a t h e r t h a n i n t h e m a i n b r a n c h s t e m . The d i f f e r e n c e s f o u n d i n t h e c a l c u l a t i o n s o f t h e l a r g e m a t e r i a l a r e due t o p o o r b r a n c h s h a p e e q u a t i o n s . / / 54 The c a l c u l a t i o n o f n e e d l e w e i g h t i n t h e m o d e l i s d e p e n d e n t on a n e q u a t i o n . N e e d l e w e i g h t = A ( B r a n c h l e n g t h ) where "A" a n d " a " a r e s u p p l i e d t o t h e p r o g r a m . The v a l u e o f " a " u s e d i n t h e c a l c u l a t i o n s shown was d e r i v e d by-a s s u m i n g t h a t n e e d l e w e i g h t i n p o u n d s was a f u n c t i o n o f t h e s q u a r e r o o t o f t h e b r a n c h l e n g t h i n f e e t . A v a l u e f o r "A" was d e t e r m i n e d b y s o l v i n g : i N e e d l e w e i g h t = A ( B r a n c h l e n g t h ) 2 f o r "A" i n t e r m s o f t h e mean n e e d l e w e i g h t p e r b r a n c h a n d t h e mean b r a n c h l e n g t h . As i n d i c a t e d b y t h e v a l u e s f o r n e e d l e w e i g h t a s c a l c u l a t e d b y t h e m o d e l a nd shown i n T a b l e s 3 - 5» t h i s e q u a t i o n g i v e s c o n s i s t e n t l y l a r g e r v a l u e s t h a n t h e b e s t r e g r e s s i o n e q u a t i o n s f o r t h e t h r e e s p e c i e s . The o v e r e s t i m a t e i n l a r g e c r o w n s i s p a r t i a l l y b e c a u s e no d i s t i n c t i o n i s made b e t w e e n t h e l i v e a n d d e a d p a r t s o f t h e c r o w n . However, a . r e v i s e d e s t i m a t e f o r "A" a n d " a " s h o u l d g i v e more p r e c i s e r e s u l t s . A l t h o u g h t h e v a l u e s i n T a b l e 3 - 5 seem t o g i v e v a l u e s f o r t h e m o d e l w h i c h a r e i n c o n s i s t e n t w i t h t h o s e f o u n d u s i n g r e g r e s s i o n a n a l y s i s , i t r e q u i r e s o n l y a m a n i p u l a t i o n o f t h e e q u a t i o n s c o n t r o l l i n g t h e m o d e l t o o b t a i n r e s u l t s w h i c h a r e s i m i l a r t o t h o s e f o u n d w i t h r e g r e s s i o n a n a l y s i s . I t i s c o n s i d e r e d s u f f i c i e n t t o 5 5 show t h a t t h e m o d e l d o e s p e r f o r m t h e c a l c u l a t i o n s t h a t a r e a l l u d e d t o i n t h e s e c t i o n s d e s c r i b i n g t h e m e t h o d o l o g y o f t h e m o d e l a n d t h e model i t s e l f . M a n i p u l a t i n g t h e e q u a t i o n c o e f f i c i e n t s s u p p l i e d t o t h e m o d e l m e r e l y t o o b t a i n r e s u l t s w h i c h a r e s i m i l a r e s t i m a t e s o f r e a l i t y w o u l d a c h i e v e l i t t l e more t h a n t o i l l u s t r a t e t h a t e q u a t i o n c a n be f o r c e d t o g i v e a n y d e s i r e d r e s u l t , a f a c t t h a t i s a l r e a d y o b v i o u s . A more r e a l i s t i c a p p r o a c h w o u l d be t o r e a n a l y s e p r e v i o u s l y o b t a i n e d d a t a o r g a t h e r new d a t a t o p r o v i d e i n p u t f o r a r e a l i s t i c a n a l y s i s w i t h t h e m o d e l . T h i s a n a l y s i s c o u l d t h e n be c o m p a r e d d i r e c t l y w i t h t h e v a l u e s f o r t h e r a w d a t a , o r i t c o u l d be c o m p a r e d w i t h o t h e r b i o m a s s s t u d i e s . 56 V I . CONCLUSIONS As i s a n y g e n e r a l model b a s e d on a m a t h e m a t i c a l a n a l o g u e o f a s y s t e m , t h i s one i s l i m i t e d b y t h e a v a i l a b i l i t y o f m a t h e m a t i c a l e q u a t i o n s w h i c h d e s c r i b e t h e c o m p o n e n t s o f t h e r e a l s y s t e m . The m o d e l i s l i m i t e d s p e c i f i c a l l y b y a l a c k o f p r e c i s e e q u a t i o n s w h i c h d e s c r i b e t h e s h a p e o f t h e c r o w n , s t e m , a n d b r a n c h e s . T h e r e i s l i t t l e e m p i r i c a l e v i d e n c e t o g u i d e t h e c h o i c e o f t h e p a r a m e t e r s w h i c h c o n t r o l t h e c a l c u l a t i o n o f f o l i a g e — m a t e r i a l , i n c l u d i n g wood, b a r k , a n d n e e d l e s , a s s o c i a t e d w i t h b u t n o t i n c l u d e d i n t h e c a l c u l a t i o n o f t h e m a i n b r a n c h s t e m . T h e y must be c h o s e n on t h e b a s i s o f t h e . u s e r ' s u n d e r s t a n d i n g o f t h e i r s i g n i f i c a n c e a n d b e h a v i o r i n t h e s y s t e m . Thus when t h e r e a r e two o r more unknown p a r a m e t e r s i n v o l v e d i n one c a l c u l a t i o n , n e i t h e r p a r a m e t e r c a n be c o n s i d e r e d t r u e r e g a r d l e s s o f how c l o s e l y t h e r e s u l t s o f t h e c a l c u l a t i o n m i m i c r e a l i t y . The r e s u l t s f r o m t h i s m o d e l s h o u l d be c o n s i d e r e d w i t h i n t h e f r a m e w o r k o f t h e m o d e l a n d a g e n e r a l u n d e r s t a n d i n g o f t h e s y s t e m . The m o d e l s h o u l d be c o n s i d e r e d i n t h r e e d i s t i n c t i v e s e c t i o n s ; r o o t s , s t e m , a n d c r o w n . The r o o t s a r e i n c l u d e d i n t h e m o d e l a t t h i s s t a g e o f d e v e l o p m e n t f o r c o m p l e t e n e s s o n l y , The e q u a t i o n s s u p p l i e d a r e g e n e r a l e n o u g h t o a l l o w t h e c a l c u l a t i o n o f t h e w e i g h t o f t h e r o o t s u s i n g - p a r a m e t e r s 57 f o u n d i n t h e a e r i a l p o r t i o n o f t h e t r e e . The g e o m e t r y o f t h e s t e m i s b e t t e r d e f i n e d t h a n t h e g e o m e t r y o f t h e r o o t s a n d c r o w n . However, t h e s h a p e o f t h e s t e m wood a n d b a r k c a n n o t be a d e q u a t e l y d e s c r i b e d u s i n g o n l y one c o n t i n u o u s e q u a t i o n . The d i v i s i o n o f t h e s t e m i n t o t h r e e s e p a r a t e s e c t i o n s p r o v i d e s a d e q u a t e f l e x -i b i l i t y f o r d e s c r i b i n g t h e s t e m . I t i s i m p o r t a n t t o n o t e t h a t t h e e q u a t i o n s w h i c h d e f i n e shape:'in t h e . m o d e l a r e d e f i n e d b y t h e u s e r a n d c a n be m a n i p u l a t e d t o g i v e w e i g h t s c o n s i s t e n t w i t h t h o s e f o u n d i n e m p i r i c a l s t u d i e s . The o b j e c t i v e o f t h e s t u d y was n o t t o m i m i c r e a l i t y e x c e p t a t t h e v e r i f i c a t i o n s t a g e , r a t h e r i t was t o f u r n i s h a means o f d e t e r m i n i n g t h e r e l a t i v e e f f e c t s o f c h a n g i n g t h e p a r a m e t e r s i n t h e m o d e l . Crown s h a p e a n d c r o w n w e i g h t a r e n o t a s w e l l d e f i n e d a s a r e s t e m s h a p e a n d w e i g h t . The m o d e l c a l c u l a t e s t h e w e i g h t o f t h e c r o w n s e q u e n t i a l l y u s i n g f i r s t t h e c r o w n s h a p e a n d c r o w n d i m e n s i o n s , t h e n t h e c r o w n d e n s i t y a s e x p r e s s e d b y i n t e r w h o r l d i s t a n c e s a n d numbers o f b r a n c h e s p e r w h o r l , a n d f i n a l l y b y u s i n g b r a n c h s h a p e a n d d e n s i t y . E a c h s u c c e s s i v e s t e p i n t h e c a l c u l a t i o n o f c r o w n w e i g h t a ssumes t h a t t h e p r e v i o u s c a l c u l a t i o n s a r e v a l i d . However, t h e v a l i d i t y o f a n y o f t h e c a l c u l a t i o n s i s s u b j e c t t o much u n c e r t a i n t y c a u s i n g a s u c c e s s i v e d e c r e a s e i n t h e / / 58 c e r t a i n t y o f t h e f i n a l c r o w n w e i g h t c a l c u l a t i o n . T h i s u n c e r t a i n t y d o e s n o t p r e v e n t t h e m o d e l f r o m b e i n g u s e f u l f o r a s s e s s i n g t h e e f f e c t o f v a r i a t i o n i n t h e p a r a m e t e r s c o n t r o l l i n g t h e c a l c u l a t i o n s o f t h e f i n a l w e i g h t o f t h e c r o w n c o m p o n e n t s . The m o d e l i s u s e f u l b e c a u s e i t p r o d u c e s r e l a t i v e e f f e c t s due t o p a r a m e t r i c c h a n g e s i n t h e s y s t e m , r a t h e r t h a n b e c a u s e I t e s t i m a t e s t h e q u a n t i t y o f m a t e r i a l i n t h e t r e e a c c u r a t e l y . The p a r a m e t e r s u s e d t o d e s c r i b e t h e t r e e i n t h e m o d e l a r e t h o s e p a r a m e t e r s w h i c h i n f l u e n c e t h e c o m b u s t i b i l i t y o f t h e t r e e c o m p o n e n t s . W i t h s l i g h t m o d i f i c a t i o n t h e m o d e l c o u l d be programmed t o g e n e r a t e v o l u m e : s u r f a c e a r e a r a t i o s f o r t h e s t e m and b r a n c h e s i n t h e t r e e . T h i s r e f i n e m e n t c o u l d a i d g r e a t l y i n t h e d e v e l -opment o f f u e l d e n s i t y i n d i c e s b a s e d on t h e t r e e component o f t h e f o r e s t f u e l c o m p l e x . The t e c h n i q u e s u s e d i n t h i s m o d e l c a n be u s e f u l f o r a n y s t u d y r e q u i r i n g a k n o w l e d g e o f t h e w e i g h t o f m a t e r i a l p r e s e n t on a f o r e s t e d a r e a . The r e l a t i o n b e t w e e n c r o w n d e n s i t y a n d t h e q u a n t i t y o f m a t e r i a l i n t h e c r o w n c o u l d be i m p o r t a n t i n s t u d i e s r e q u i r i n g e s t i m a t e s o f t h e amount o f n u t r i e n t s a v a i l a b l e i n t h e crown,, I t a l s o c o u l d a i d i n a s s e s s i n g t h e e f f e c t o f v a r i o u s s i l v i c u l t u r a l t e c h n i q u e s on t h e t o t a l w e i g h t p r o d u c t i o n o f s t a n d s . A k n o w l e d g e o f t h e w e i g h t / 59 / o f t h e t o t a l t r e e w o u l d be i m p o r t a n t i f t h e c o m p l e t e t r e e u t i l i z a t i o n c o n c e p t becomes p r a c t i c a l . The m o d e l ' s a b i l i t y t o e s t i m a t e t h e w e i g h t o f t h e t r e e u s i n g b a s i c p a r a m e t e r s makes i t u s e f u l f o r s t u d y i n g t h e r e l a t i o n s h i p s o f t h e s e p a r a m e t e r s i n s i m u l a t i o n e x p e r i m e n t s p r i o r t o t h e i r a n a l y s i s i n e m p i r i c a l e x p e r i -m e n t s . The i n c r e a s e d u n d e r s t a n d i n g o f t h e s y s t e m g a i n e d f r o m t h e s i m u l a t i o n a n a l y s i s s h o u l d g u i d e t h e e m p e r i c a l i n v e s t i g a t i o n . The f e a s i b i l i t y o f u s i n g t h e t e c h n i q u e s e m p l o y e d i n t h e m o d e l f o r s i m u l a t i n g t h e t o t a l f o r e s t f u e l c o m p l e x i s q u e s t i o n a b l e . However, t h e u s e o f t h e m o d e l i n c o n -j u n c t i o n w i t h e s t i m a t e s o f o t h e r f u e l s i n a g r o s s m o d e l o f t h e t o t a l f u e l c o m p l e x w o u l d seem t o be a more p r a c t i c a l a n d u s e f u l a p p r o a c h . The m o d e l c r e a t e d s h o u l d s e r v e a s a s o u r c e o f i n p u t i n f o r m a t i o n f o r t h e c o m p l e t e m o d e l . T h i s t y p e o f m o d e l w o u l d g i v e a n a s s e s s m e n t o f t h e r e l a -t i v e a m o u n t s o f a l l t h e f u e l s f o u n d i n t h e f o r e s t f u e l c o m p l e x . A l t h o u g h i t w o u l d have b e e n d e s i r a b l e , t i m e and r e s o u r c e s d i d n o t p e r m i t i n v e s t i g a t i o n o f f u r t h e r a s p e c t s o f t h e a p p l i c a t i o n o f t h i s m o d e l . New d a t a f o r t e s t i n g i t s h o u l d be c o l l e c t e d . The m o d e l s h o u l d be m a n i p u l a t e d a n d a n a l y s e d c o m p r e h e n s i v e l y i n o r d e r t o d e t e r m i n e i t s f u l l p o t e n t i a l a n d p r a c t i c a l u t i l i t y . 60 BIBLIOGRAPHY A d a m o v i c h , L. L. 1970. C e n t r e o f g r a v i t y o f o p e n - a n d s t a n d - g r o w n s e c o n d g r o w t h w e s t e r n c o n i f e r s . P a p e r p r e s e n t e d a t w i n t e r m e e t i n g o f A m e r i c a l S o c i e t y o f A g r i c u l t u r a l E n g i n e e r s . P a p e r No. 70-617. 30p. B e a t o n , J . D. 1959. The i n f l u e n c e . o f b u r n i n g on t h e s o i l i n t h e t i m b e r r a n g e a r e a o f L a c l e J e u n e , B r i t i s h , C o l u m b i a . I . P h y s i c a l p r o p e r t i e s . I I . C h e m i c a l p r o p e r t i e s . Can. J o u r . S o i l . S c i . 39:1-11 . B u r n s , P. J . 1952. E f f e c t o f f i r e on f o r e s t s o i l s i n t h e p i n e b a r r e n s o f New j e r s y . Y a l e U n i v . S c h o o l o f F o r . B u l l . 57:32p. D o b i e , J . 1965. F a c t o r s i n f l u e n c i n g t h e w e i g h t o f l o g s . R e p r i n t . B. C. Lumberman. S e p t . 1965. 4p. D y r n e s s , C. T., C. T. Y o u n g b e r g , a n d R. H. R u t h . 1957. Some e f f e c t s o f l o g g i n g a n d s l a s h b u r n i n g on p h y s i c a l s o i l p r o p e r t i e s i n t h e C o r v a l l i s W a t e r s h e d . U. S. D. A. P a c . N. W. F o r . a nd Range Exp. S t a . , Res. P a p e r 19:15p. D y e r , R. A. 1967. F r e s h a n d d r y w e i g h t , n u t r i e n t e l e m e n t s , a n d p u l p i n g c h a r a c t e r i s t i c s o f n o r t h e r n w h i t e c e d a r . M a i n e A g r . Exp. S t a . , T e c h . B u l l . 27:40p. F a h n e s t o c k , G. R.and. J . H. D i e t r i c h . 1962. L o g g i n g s l a s h f l a m m a b i l i t y a f t e r f i v e y e a r s . I n t e r m t n . F o r . a n d Range E x p . S t a . , Res. P a p e r . 7 0 : l 5 p . H e g e r , L. 1965. A . t r i a l o f H o h e n a d l ' s m e t h o d o f s t e m f o r m a n d s t e m v o l u m e e q u a t i o n . F o r . C h r o n . 4 l s 466-75. J o h n s t o n e , w. D. 1967. A n a l y s i s o f b i o m a s s , b i o m a s s s a m p l i n g m e t h o d s , a n d w e i g h t s c a l i n g o f l o d g e p o l e p i n e . U n i v . o f B. C., F a c . o f F o r . , MF t h e s i s , I53p. K e a y s , J . L. 1971a. C o m p l e t e t r e e u t i l i z a t i o n — An a n a l y s i s o f t h e l i t e r a t u r e . P a r I J U n m e r c h a n t a b l e t o p o f b o l e . Can. D e p t . F i s h . F o r e s t . , F o r e s t P r o d . L a b . I n f o r m . Rep. VP-x - 6 9 . V a n c o u v e r , B. C., 98p. / 61 1971b. Complete tree u t i l i z a t i o n — An analysis of the literature. Part l i s Foliage. Can. Dept. Fish. Forest., Forest Prod. Lab. Inform. Rep. VP-X-70, Vancouver, B. C. , 9%). . 1971c. Complete tree u t i l i z a t i o n — An analysis of the literature. Part I l l s Branches. Can. Dept. Fish. Forest., Forest Prod. Lab. Inform Rep. VP-X-71, Vancouver, B. C., 67p. 1971d. Complete tree u t i l i z a t i o n — An analysis of the literature. Part IV; Crown and slash. Can. Dept. Fish. Forest., Forest Prod. Lab. Inform. Rep. VP-X-77, Vancouver, B. C., 79p. ' 1971e» Complete tree u t i l i z a t i o n — An analysis of the literature. Part Vs Stump, roots, and stump-root system. Can. Dept. Fish. Forest., .Forest Prod. Lab. Inform. Rep. VP-X-79» Vancouver, B. C, 62p. Kennedy, E. J. 1965. Strength and related properties of woods grown in Canada. Dept. of For. Pub. No. 1104., 51P. Kozak, A. 1969. Personal communication. Kurucz, J. 1969. Component weights of Douglas-fir» western hemlock, and western redcedar biomass for simulation of amount and distribution of forest fuels. Univ. of B. C. Fac. of For. M. F. thesis, Mimeo. Il6p. Lockman, M. R. 1969. Forest f i r e losses in Canada— 1967. For. Fire Res. Inst., Dept. Fish. Forest. Ottawa, 0DC435.2(71), 13p. Meriam, J". L. 1959. Mechanics. J. Wiley and Sons, N.Y. , N.Y. 746p. McCracken, D. D. 1967. FORTRAN with Engineering Applications. J . Wiley and Sons, N.Y.,N.Y., 227p. MacTavish, J. S. 1966. Appraising fi r e damage to mature , forest stands. Can. Dept. For. and Rural Dev., For. Branch Dept. Pub. No. 1162, 31p. 62 Ovington, J. D. 1962. Quantitative ecology and the woodland ecosystem concept. Adv. in Ecol. Res. Vol. (1)»103-92. Protter, M. H.. and C. B. Morrez. 1964. College Calculus  with Analytic Geometry. Addison-Wesley Pub. Comp. Inc. Reading, Mass, b'97p. Rennie, P. J. 1955. The uptake of nutrients by mature forest growth. Plant and Soil Vol. VII:49-95. Smith, J. H. G. 1971. Bases for sampling and simulation v . , - in.studies of tree and stand weights. Forest Biomass Studies, XVth IUFR0 Congress. Univ. of Flor., Gainsville, Flor., U. S. A. ppl39-49. 1968. Some estimates of amounts of forest fuels for the B. C. coast. Univ. of B. C. Fac. of For., Mlmeo, 8p. Smith, J. H. G., J. W. Ker, and J. Csizmazia. 1961. Economics of reforestation of Douglas-fir, western hemlock, and western redcedar in the Vancouver forest d i s t r i c t . Univ. of B. C. Fac. of For., For. Bull. No. 3, l44p. Wagner, H. M. 1969. Principles of Operations Research with Applications to Managerial Decisions. Prentice-Hall Inc. Englewood C l i f f s , N.J., 937p. Young, H. E. 1965. Pound wise, and penny foolish. Paper presented at Amer. Pulpwood Assoc. , 8p. Young, H. E., L. Strand, and R. Altenberger. 1964. Preliminary fresh and dry weight tables for seven tree species in Maine. Maine Agr. Exp. Sta., Tech. Bull. 12., 76p. APPENDIX I PROGRAM L I S T I N G APPENDIX I I CONTROL CARD DESCRIPTION 97 Table I I - l A l i s t i n g of the input variables by-control card. Card Number Variable TITLE **DBH * HT * CLTH * CD * SPHT' **TDIA PCCR *BAC(1,1 ) *BAC(l ,2) *BAC(2,1) *BAC(2,2) *BAC(3,1) *BAC(3,2) *BAC(4,1) *BAC(4,2) *BAC (5,1) *BAC(5,2) *BAC(6,1) *BAC(6,2) Description 1 Space for information about a p a r t i c u l a r run of the model Diameter at breast height Height Crown length Crown diameter Stump height Top merchantable diameter Percent of crown removed i n logging B for t o t a l tree weight as per equation (1) A for t o t a l tree weight as per equation (1) B for stem wood weight as per equation (1) A for stem wood weight as per equation (1) B for stem bark weight as per equation (1) A for stem bark weight as per equation (1) B for t o t a l crown weight as per equation (1) A for t o t a l crown weight as per equation (1) B for large branch weight as per equation (1) A for large branch weight as per equation (1) B for medium branch weight as per equation (1) A for medium branch weight as per equation (1) 98 1 0 1 1 1 2 14 1 5 1 6 1 7 18 *BAC(7,U *BAC (7 ,2) *BAC(8,1) *BAC(8,2) ***RUCZ RUCZ RUCZ RUCZ RUCZ 1 3 ***RUCZ RUCZ ***RUCZ RUCZ ***RUCZ RUCZ ***RUCZ RUCZ ***RUCZ RUCZ ***RUCZ RUCZ l.D 1 , 2 ) 1.3) 1 , 4 ) 1.5) 2 , 1 ) 2 , 5 ) 3 , 1 ) 3 , 5 ) 4 , 1 ) 4 , 5 ) 5 , 1 ) 5 , 5 ) 6 , 1 ) 6 , 5 ) 7 , 1 ) 7 , 5 ) B for fi n e branch weight as per equation (1) A for fine branch weight as per equation (1) B for needle weight as per equation (1) A for needle weight as per equation (1) E for t o t a l tree weight as per equation (2) A for t o t a l tree weight as per equation (2) B for t o t a l tree weight as per equation (2) C for t o t a l tree weight as per equation (2) D for t o t a l tree weight as per equation (2) The variables on card 1 3 correspond to those of card 12 for stem wood weight as per equation (2) The variables on card 14 correspond to those on card 12 for stem bark weight as per equation (2) The variables on card 15 correspond to those on card 12 for t o t a l crown weight as per equation (2) The variables on card 1 6 correspond to those on card 12 for large branch weight as per equation (2) The variables on card 17 correspond to those on card 12 for medium branch weight as per equation (2) The variables on card 18 correspond to those on card 12 for fine branch weight as per equation (2) 99 19 ***RUCZ(8,1) RUCZ(8,5) 20 * SSEQUA(l.l) SSEQUA(1,2) SSEQUA(1,3) SSEQUA(l,4) SSEQUA(1,5) 21 * SSEQUA(2,1) SSEQUA(2,5) 22 * SSEQUA(3,l) SSEQUA(3.5) 23 * SSEQUA(4,1) SSEQUA(4,5) 24 * SSEQUA(5 .D SSEQUA(5,5) 25 * SSEQUA(6,1) SSEQUA(6,5) 26 * BS'(l.l) BS(1,2) BS(1,3) BS(1,4) The variables on card 19 correspond to those on card 12 for needle weight as per equation (2) A for top outside stem shape equation, equation (3) a for top outside stem shape equation, equation (3) B for top outside stem shape equation, equation (3) C for the top outside stem shape equation, equation (3) Radius i n feet which forms the lower l i m i t of the top stem section Card 21 variable descriptions correspond to card 20*s except that they describe the outside of the middle section of the tree Card 22 variable descriptions correspond to those of card 20 but describe bottom section of the stem The variables on t h i s card correspond to those on card 20 except that they describe the top inside bark equation These variable descriptions correspond to those on card 20 except they describe the middle inside bark section of the stem These variable descriptions correspond to those on card 20 except they describe the bottom inside section of the stem A for outside branch t i p equation, equation (3) a for the outside branch t i p equation, equation (3) B for the outside branch t i p equation, equation (3) C for the outside branch t i p equation, equation (3) 100 BS (2 , i BS (2 ,4 BS (3 , i BS (3 ,4 BS (k P i BS (4 .4 BS (5 , i BS (5 BS [6 l BS (6, CS [1 1 cs (1 2 CS [1 3 CS [ l i CS 5 CS [i. 6 CS(2,1 CS(2,7 CS(3,1 CS(3,7 *STEMd ,1) STEM(1 ,2) STEM(1 ,3) STEM(1 STEM(1 ,5) STEM(1 ,6) Middle branch shape equation as described for card 26 Large outside branch shape equation as described for card 26 Inside branch tip equation as described for card 26 Inside medium branch shape equation as described for card 26 Inside large branch shape equation as described for card 26 A for the top crown section equation, equation (3) a for the top crown section equation, equation (3) B for the top crown section equation, equation (3) C for the top crown section equation, equation (3) The lower limiting radius for the top crown section The percentage used to calculate the variance for the mean branch length in this section The distribution number which controls the selection of a distribution in the calculation of random variables Middle crown section as described for card 32 Lov/er crown section equation as described for card 32 A for the stem double bark thickness equation, equation (16) a for the stem double bark thickness equation, equation (16) B for the double bark thickness equation, equation (16) C for the stem double bark thickness equation, equation (16) c for the double bark thickness equation, equation (16) D for the stem double bark thickness equation, equation (16) 101 36 * * S T E M(2,1) STEM(2,6) 37 * HTA(1 HTA(2 HTA(3 H T A ( 4 ; 38 * CDA(1 CDA(2 CDA(3 Branch double b a r k t h i c k n e s s e q u a t i o n s as d e s c r i b e d f o r c a r d 35. D f o r h e i g h t e q u a t i o n , e q u a t i o n (12) A f o r h e i g h t e q u a t i o n , e q u a t i o n (12) B f o r h e i g h t e q u a t i o n , e q u a t i o n (12) C f o r h e i g h t e q u a t i o n , e q u a t i o n (12) C f o r crown w i d t h e q u a t i o n , e q u a t i o n (15) A f o r crown w i d t h e q u a t i o n , e q u a t i o n (15) B f o r crown w i d t h e q u a t i o n , e q u a t i o n (25) 39 * C L T H A (1) C f o r h e i g h t t o crown e q u a t i o n , [2) e q u a t i o n (13) C L T H A A f o r h e i g h t t o crown e q u a t i o n , 13) e q u a t i o n (13) C L T H A B f o r h e i g h t t o crown e q u a t i o n , e q u a t i o n (13) 4 0 2 S G A ( 1 , 1) Mean l a r g e stem wood d e n s i t y S G A ( I , 2) V a r i a n c e o f l a r g e stem wood d e n s i t i e s S G A ( I , 3) D i s t r i b u t i o n number w h i c h c o n t r o l s t h e d i s t r i b u t i o n f o r random number g e n e r a t i o n i n s u b r o u t i n e FCT. 4 1 S G A ( 2 , ) Large stem b a r k d e n s i t y p arameters 4 2 S G A(3, "\ Medium stem wood d e n s i t y parameters 43 S G A ( 4 , ) Medium stem b a r k d e n s i t y p arameters 44 SGA(5. ) F i n e stem wood d e n s i t y parameters 45 S G A ( 6 , ) F i n e stem b a r k d e n s i t y parameters 4 6 S G A ( 7 , ) Branch wood d e n s i t y parameters 4 7 SGA(8, ) Branch b a r k d e n s i t y parameters 4 8 SGA(9, ) Large b r a n c h wood d e n s i t y parameters 102 49 SGA(10,. 50 SGA(11, 51 SGA(12, 52 SGA(13, 53 SGA(l4, 54 * WHORL ( 1 , 1 ) WHORL ( 1 , 2 ) WHORL (1 ,3) 55 WH0RL ( 2 , ) 56 WHORL(3, ) 57 ***REQ(1 ,1 )• REQ(1,2) REQ(1,3) REQ(1,4) REQ(1,5) 58 ***REQ(2, ) 59 ***REQ(3, ) 60 AGE * SBA * XLEAF(l) XLEAF(2) 61 PROB(I) Large branch bark density parameters Medium branch wood density parameters Medium branch bark density parameters Fine branch wood density parameters Fine Branch bark density parameters Mean, interwhorl distance Variance of interwhorl distances Distribution number for interwhorl distances Number of whorls per tree parameters Number of branches per whorl parameters E for root weight equation, equation ( 8 ) . A for root v/eight equation, equation (8) 3 for root weight equation, equation (8 ) C for root weight equation, equation (8) D for root weight equation, equation (8) Coefficients for root bark weight equation as described for card 56 Coefficients for root wood weight equation, equation Age Stand basal area A for needle weight equation equation (7) a for needle weight equation, equation (7) The probability of getting I in the random number generator IDIS for 1=1,8 103 62 63 65 66 PROB(I) RPC RBPC 64 * SHT(l) SHT(2) SHT(3) SHT(4) **DBT **BDBT SEQ(I) The p r o b a b i l i t y of getting I i n IDIS for i=9,10 The percent of t o t a l tree weight contained i n the roots The percent of the t o t a l root weight contained i n root bark A for an equation of the form of equation (?) where branchlet bark weight i s a function of main branch length i n feet a for equation (7) as described for SHT(l) A for an equation of the form of equation (7) where branchlet wood weight i s a function of branch length i n feet a for an equation of the form of equation (7) as described for SHT(3) Double bark thickness Branch double bark thickness at 0.25 inches diameter The series of numbers which controls the c a l l i n g sequence i n the program The equations referred to are found i n the text. 2 Density input i n terms of grams per cubic centimeter. * Input i n terms of feet. ** Input in terms of inches. *** Refer to text for input information. APPENDIX I I I S T A T I S T I C A L TABLES TO A I D I N USING THE MODEL 105 T a b l e I I I - l B a s i c s t a t i s t i c s f o r b r a n c h d a t a c o l l e c t e d b y K u r u c z (1969) a n d r e a n a l y s e d t o s u p p l y s h a p e e q u a t i o n s f o r t h e v a l i d a t i o n o f t h e m o d e l . D o u g l a s - f i r I t e m s 1 2 n Mean Minimum Maximum 3 SD 4 CV TL ( f t . ) 112 14.07 2.60 26.80 6.07 43.19 BDO ( i n . ) 2.09 0.46 4.61 1.00 47.19 BDI ( i n . ) 1.76 0.32 3.75 0.85 48.60 MDO ( i n . ) 1.18 0.21 2.70 0.57 48.08 MDI ( i n . ) 1.01 0.18 2.34 0.51 50.35 L ( f t . ) 224 10.54 1.30 26.90 5.95 56.50 DO ( i n . ) ! 1.63 0.21 4.61 0.93 57.06 D l ( i n . ) 1.38 0.18 3.75 0.79 57.58 W e s t e r n h e m l o c k T L ( f t . ) 89 12.13 2.50 27.10 5.45 44.94 BDO ( i n . ) 1.92 0.33 5.20 1.14 59.36 BDI ( i n . ) 1.64 0.25 4.71 1.01 61.17 MDO ( i n . ) 0.90 0.15 2.18 0.50 56.03 L ( f t . ) 178 9.09 1.25 27.10 5.27 58.03 DO ( i n . ) 1.41 0.15 5.16 1,02 72.36 D l ( i n . ) 1.20 0.09 4.71 0.89 74.78 W e s t e r n r e d c e d a r T L ( f t . ) 113 11.13 0.80 24.40 5.55 49.84 BDO ( i n . ) 1.75 0.39 3.97 0.76 43.54 BDI ( i n . ) 1.48 0.19 3.65 0.76 51.65 MDO ( i n . ) 1.09 0.19 2.92 0.58 52.87 MDI ( i n . ) 0.94 0.14 2.70 0.54 57.76 L ( f t . ) 226 8.34 0.40 24.40 5.19 62.31 DO ( i n . ) 1.42 0.19 3.97 0.75 53.16 D l ( i n . ) 1.21 0.14 3.65 0.71 59.02 1 TL = t o t a l b r a n c h l e n g t h , BDO = b u t t d i a m e t e r o u t s i d e b a r k , BDI = b u t t d i a m e t e r i n s i d e b a r k , MDO = m i d - d i a m e t e r o u t s i d e b a r k , MDI = m i d - d i a m e t e r i n s i d e b a r k , L = a com-b i n a t i o n o f t o t a l b r a n c h l e n g t h a n d o n e - h a l f t o t a l b r a n c h l e n g t h , DO 3 a c o m b i n a t i o n o f m i d - d i a m e t e r a n d b u t t d i a m e t e r o u t s i d e b a r k , D l = a c o m b i n a t i o n o f m i d - d i a m e t e r a n d b u t t d i a m e t e r I n s i d e b a r k . 2 The number o f o b s e r v a t i o n s ( n ) i s d o u b l e d f o r e a c h s p e c i e s when t h e d i a m e t e r a n d t h e m i d - d i a m e t e r a r e c o m b i n e d i n one a n a l y s i s w i t h t h e l e n g t h a n d o n e - h a l f t h e l e n g t h . 3 The s t a n d a r d d e v i a t i o n (SD) i s e x p r e s s e d i n t h e u n i t s a s i s t h e i t e m w h i c h i t d e s c r i b e s . 4 The c o e f f i c i e n t o f v a r i a t i o n (CV) i s e x p r e s s e d a s a p e r c e n t a g e . 0= TABLE I I I - 2 B r a n c h s h a p e r e g r e s s i o n m o d e l c o e f f i c i e n t s h a v i n g b r a n c h l e n g t h a s t h e d e p e n d e n t v a r i a b l e a n d h a v i n g i n d e p e n d e n t v a r i a b l e s a s d e f i n e d i n T a b l e I I I - l . D o u g l a s - f i r n a 112 I n d e p e n d e n t V a r i a b l e s I n t e r c e p t 1 a BDO BDO 1' 5 BDO 2 BDI ( f t . ) ( i n . ) ( i n . ) ( i n . ) ( i n . ) 2.31 5.63 -2.52 13.55 -3.58 -1.39 9.71 -0.90 0.0 6.53 -2.06 0.0 10.02 0.0 8.46 -0.66 ~> 2.44 6.62 -1.45 14.50 -0.58 10.72 0.0 7.74 0.0 0.12 0.0 10.08 W e s t e r n h e m l o c k n = 89 4.57 3.93 -0.08 11.53 -3.32 1.08 7.79 -0.79 0.0 5.70 0.0 11.43 -3.28 0.0 8.73 -0.95 BDI 1 , - 5 B D I 2 S E F RV^ R 2 ( i n . ) ( i n . ) ( f t . ) ( f t ? ) (%) 2.27 5.23 86** 2.07 4.27 89** 2.07 4.27 89** 2.49 6.18 83!* 2.11 4.45 89?: 2.08 4.34 88** 2.24 5.02 87?* -3.93 2.07 4.30 89*1 -1.10 2.08 4.31 89** 2.47 6.12 83** 0.00 1.49 2.23 94** -0.95 2.07 4.29 88 3.11 9.70 68** 2.85 8.14 73?* 2.87 8.26 73?? 3.89 15.05 49 2.84 8.05 73** 2.88 8.27 72** > TABLE I I I - 2 — c o n t i n u e d I n t e r c e p t BDO ( i n . ) BDO 1 .5 BDO' ( i n . ) ( i n . ) 4.64 0 . 3 1 1 .36 0 . 0 0 . 0 0 . 0 W e s t e r n r e d c e d a r n = 113 -0.11' -8.17 •6 .71 0 . 0 0 . 0 0 . 0 1 .52 • 4.24 • 3 . 2 6 0 . 0 0 . 0 0 . 0 6.41 2 0 . 6 9 14 .26 6 . 3 6 7 . 7 6 7 . 3 3 -6.84 -0.92 -1.96 -0.40 BDI ( i n . ) 4.54 12.89 8.80 6 . 6 0 13 .37 10.17 6 . 5 0 19 .16 1 3 . 5 4 7 . 3 1 11 .26 9 . 6 2 B D I 1 ' 5 B D I 2 ( i n . ) ((in.>) -3.93 -4.14 - 6 . 5 7 -2.71 - 1 . 0 1 -1.28 -2.04 - 1 . 0 5 SEV RV ( f t ? ) ( f t 2 ) 2.97 2.69 2.71 3.82 2.68 2.73 2 . 6 3 2 . 2 7 2 . 2 3 2 . 6 1 2 . 5 8 2 . 5 5 2 . 4 9 2 .11 2 . 0 6 2 . 5 7 2 . 2 8 2 . 2 1 8.84 7 . 2 5 7 . 3 7 14 .63 7.18 7.46 6.90 5 .17 4.98 6.84 6.68 6.52 6.19 4.45 4.26 6 . 6 2 5.18 4.87 71 75 7 8 * * 84** 84** 7 8 * * 7 8 * * 7 0 * * 80** 85** 86** 78** 8 3 * * 84** * I n d i c a t e s a s i g n i f i c a n t c o r r e l a t i o n b e t w e e n t h e m o d e l a n d t h e d e p e n d e n t v a r i a b l e a t a p r o b a b i l i t y l e v e l o f f i v e p e r c e n t u s i n g R. ** I n d i c a t e s a s i g n i f i c a n t c o r r e l a t i o n b e t w e e n t h e m o d e l a n d t h e d e p e n d e n t v a r i a b l e a t a p r o b a b i l i t y l e v e l o f one p e r c e n t u s i n g R. a A z e r o i n t e r c e p t I m p l i e s a c o n d i t i o n e d r e g r e s s i o n b RV r e f e r s t o t h e r e s i d u a l v a r i a n c e TABLE I I I - 3 B r a n c h s h a p e r e g r e s s i o n m o d e l c o e f f i c i e n t s h a v i n g b r a n c h l e n g t h a s t h e d e p e n d e n t v a r i a b l e a n d h a v i n g i n d e p e n d e n t v a r i a b l e s a s d e f i n e d i n T a b l e I I I - l . D o u g l a s - f i r n = 112 I n d e p e n d e n t I n t e r c e p t a MDO MDO 1'^ MDO 2 ( f t . ) ( i n . ) ( i n . ) (m.) 2.85 9.48 -4.28 29.28 -11.67 -2.82 20.04 -3.96 0.0 11.44 0.0 5.27 -0.96 0.0 15.70 -2.54 3.32 -2.71 -1.48 0.0 0.0 0.0 W e s t e r n h e m l o c k n = 89 MDI MDI 1'5 M D I 2 SE-p R V b R2 ( i n . ) ( i n . ) (m. ) (ft. ) (ft 2 ) {%) 2.81 7.70 79?? 2.39 5.70 85** 2.37 5.61 85** 3.06 9.36 75** 3.04 9.23 75 2.44 5.98 84** 10.69 2.77 7.68 79** 30.90 -12.96 2.38 5.69 85** 21.46 -4.77 2.37 5.62 85** 13.33 3.14 9.84 73** 23.32 -8.40 2.44 5.96 84** 18.80 -3.75 2.39 5.71 85** 3.55 9.54 2.59 6 70 78** 0.26 21.66 -8.01 2.46 6.'o5 80** 1.16 15.48 -2.79 2.48 6.13 80** 0*0 W'll 8 *i 3'F 9'65 68** u « u 22.47 -0.51 2 4^ < oft fin** °-° 17.76 -3.71 l:l86 °09** TABLE I I I - 3 — c o n t i n u e d I n t e r c e p t MDO MDO 1'^ MDO 2 MDI M D I 1 * ^ M D I 2 S E r , RV R 2 ( f t . ) ( i n . ) ( i n . ) ( i n . ) t i n . ) ( i n . ) ( i n . ) ( f t ? ) ( f t 2 ) {%) 3.57 11.50 2.44 5.93 80** 0.40 25.65 -10.26 2.29 5.24 83? 1.21 18.59 -3.99 2.30 5.30 83 0.0 15.13 3.00 8.99 70 0.0 27.13 -11.26 2.28 5.18 83 0.0 2.14 -5.36 2.33 5.36 82 W e s t e r n r e d c e d a r n = 113 2.85 8.12 74** 2.41 5.83 81** 2.11 8.28 -4.46 27.46 -2.99 18.30 0.0 9.80 0.0 10.39 0.0 13.51 2.84 -3.31 -1.89 0.0 0.0 -3.84 2.4l 5.81 8 1 ^ 3.00 9.02 71! -5.21 2.58 6.64 79** -2.24 2.51 6.33 80 8.81 2.81 7.90 75 29.64 -13.16 2.30 5.28 83** 19.62 - -4.62 2.31 5.33 83** 20.29 -7.62 2.42 5.84 81** 16.19 -3.36 2.36 5.57 82** * I n d i c a t e s a s i g n i f i c a n t c o r r e l a t i o n b e t w e e n t h e m o d e l a n d t h e d e p e n d e n t v a r i a b l e a t a p r o b a b i l i t y l e v e l o f f i v e p e r c e n t u s i n g R. ** I n d i c a t e s a s i g n i f i c a n t c o r r e l a t i o n b e t w e e n t h e m o d e l a n d t h e d e p e n d e n t , v a r i a b l e a t a p r o b a b i l i t y l e v e l o f one p e r c e n t u s i n g R. a A z e r o I n t e r c e p t i n d i c a t e s a c o n d i t i o n e d r e g r e s s i o n . b RV r e f e r s t o r e s i d u a l v a r i a n c e . TABLE III-4 Branch shape regression models having'branch length as the independent variable and independent variables as defined in Table III-2. These model combine measurements of branch mid-diameter and butt-diameter in one analysis. Douglas-fir n m 224 Intercept 3 DO DO1'$ (ft.) (in.) (in.) 0.81 5.97 -0.62 8.80 -1.35 -0.49 7.69 0.0 6.33 0.0 7.82 -0.94 0.0 7.17 -0.89 -0.32 -0.07 0.00 0.00 0.00 Western hemlock n = I78 Independent Variables 2 DO' (in.) -0.42 -0.32 DI (in.) 6.98 9.88 8.53 7.47 9.28 8.46 DI 1'* (in.) DI (in.) -1.53 -1.24 -0.46 -0.44 SE 2.16 2.13 2.12 2.16 2.09 2.08 2.16 2.13 2.13 2.20 2.23 2.12 RVC ( f f . ) ( f t . 2 ) 4.67 4.54 4.49 4.67 4.38 4.34 4.65 4.55 4.55 4.82 4.52 4.51 R 2.69 4.55 2.53 6.41 77 0.07 10.04 -2.59 2.33 5.43 81 0.61 7.50 -0.69 2.33 5.42 81 0.0 5.80 2.98 8.86 68 0.0 10.16 -2.14 2.32 5.40 81 0.0 8.13 -0.81 2.33 5.44 81 87 87 * 87** 87** 88** 88** 87** 87** 87** 86** 87** 87** TABLE III-4 - continued Intercept DO DO 1* 5 DO2 Dl D l 1 * 5 D l 2 SET? R V R 2 ( f t . ) (in.) (in.) (in.) (in.) (in.) (in.) (f£.) (ft?) (%) 2.81 5.24 2.42 5.84 79** 0.13 11.85 -3.35 2.17 4.71 83** 0.73 8.72 -0.94 2.18 4.73 83** 0.0 6.75 2.94 8.65 69** 0.0 12.01 -3.46 2.16 4.68 83** 0.0 20.60 -0.18 1.92 3.67 87 * Western red cedar n = 26 -O.32 6.12 -1.69 -9.19 -1.60 -1.75 8.26 -0.62 0.0 5.94 0.0 6.06 -0.08 0.0 6.17 -0.10 0.53 6.45 -I.65 12.18 -3.18 -1.24 9.58 -1.02 0.0 6.78 0.0 8.67 -1.36 0.0 3.02 0.15 2.41 5.80 79 ** 2.39 5.70 79 *«• 2.37 5.61 79 ## 2.41 5.80 78 #* 2.41 5.83 78 *# 2.41 5.81 79 *# 2.41 5.80 79 2.33 5.42 80 ** 2.32 5.38 80 2.42 5.84 78 2.36 5.57 79 1.25 1.57 94 * I n d i c a t e s a s i g n i f i c a n t c o r r e l a t i o n b e t w e e n t h e m o d e l a n d t h e d e p e n d e n t v a r i a b l e a t a p r o b a b i l i t y l e v e l o f f i v e p e r c e n t u s i n g R. ** I n d i c a t e s a s i g n i f i c a n t c o r r e l a t i o n b e t w e e n t h e m o d e l a n d t h e d e p e n d e n t v a r i a b l e a t a p r o b a b i l i t y l e v e l o f one p e r c e n t u s i n g R. a A z e r o i n t e r c e p t I n d i c a t e s a c o n d i t i o n e d r e g r e s s i o n . b RV r e f e r s t o r e s i d u a l v a r i a n c e . TABLE III-5 Douglas-fir Dependent* Variable HT (ft.) LCL (ft.) CL (ft.) Crown and stem shape regression models having l i v e crown length (LCL), crown length (CL), and height (HT) as dependent variables with crown width (CW) and diameter at breast height (DBH) as independent variables. n = 112 (ft.) (in-) 5.39 4.46 0.68 5.24 -0.45 5.11 0.0 4.62 - 0.0 5.33 0.0 5.07 -0.74 24.05 -19.62 0.0 0.0 0.0 2.28 -33.37 -26.63 0.0 0.0 0.0 Independent Variables •5 DBH2 CW CW1*' (in.) (in.) (ft.) (ft.) (ft.) (ftD (ft.^) (%) Intercept a DBH DBH1, CW1 ^ CW2 SE E RVb R2 15.70 246.51 94** -0.11 15.70 246.64 94** -0.01 15.62 243.85 94 .84 15.84 250 94** -0.12 15.63 244.43 94** -0.01 15.55 241.65 94** 2.66 21.50 462.15 46** 5.85 -0.43 21.44 459.85 46** 4.37 -0.03 21.44 459.69 46** 2.64 21.40 458.02 46** 2.94 -0.05 21.48 461.52 46** 2.84 -0.01 21.47 461.12 46** 2.74 22.96 527.31 44** 7.62 -0.66 22.73 516.85 45** 5.36 -0.05 22.73 516.45 45?? 2.82 22.87 522.90 44 3.57 -0.14 22.89 523.41 44** 3.28 -0.01 22.85 522.07 44** TABLE I I I - 5 - continued Intercept DBH DBH1*-(ft.) (in.) (in.! Western hemlock n = 8 9 HT (ft.) 0 . 2 9 4.98 5.84 3.74 -0.19 4.41 4 . 3 6 0 . 0 4 . 9 9 0 . 0 4.74 - 0 . 0 5 0 . 0 4.84 LCL (ft.) -0.16 - 6 . 2 3 - 5 . 1 1 0 . 0 0 . 0 0 . 0 CL (ft.) -5.96 - 6 8 . 5 6 -58.37 0 . 0 0 . 0 0 . 0 Western redcedar HT 13.49 3.18 17.35 301.10 8 7 * * -9.81 7.24 -0.56 15.78 248 . 92 8 9 DBH2 CW CW1#5 CW2 SEp R2 (in.) (ft.) (ft.) (ft.) (ft?) (ft. 2) W 7 . 1 3 50.84 9 8 6 . 9 6 48 . 4 7 9 8 0 . 0 2 7 . 0 0 4 9 . 0 2 9 8 4 . 0 9 5 0 . 2 9 9 8 7 . 0 9 5 0 . 2 2 9 8 - 0 . 0 1 7 . 0 8 50.17 9 8 2 . 5 9 14 . 7 0 216.24 6 1 1 1 . 9 4 - 1 . 3 3 1 3 . 0 6 170.64 6 9 7 . 6 9 - 0 . 1 1 1 2 . 8 7 1 6 5.64 7 1 2 . 5 8 14 . 6 2 2 1 3 . 7 8 6 1 3 . 5 1 -0.18 14 . 4 9 2 1 0 . 0 3 6 3 3 . 3 2 - 0 . 0 2 14 . 3 4 2 0 5 . 7 8 6 3 3 . 0 3 17 . 4 3 3 0 3 . 9 6 6 1 1 2 . 4 5 - 1 . 3 4 1 6 . 0 8 2 5 8 . 6 6 6 7 8 . 2 7 - 0 . 1 2 1 5 . 8 5 2 5 1 . 2 3 6 8 2.80 17.41 3 0 3 . 2 7 6 0 3 .18 - 0 . 0 7 17.48 3 0 5 . 7 6 61 3.18 - 0 . 0 1 17.41 3 0 3 . 2 3 6 1 - 7 . 9 4 5 . 6 9 - 0 . 0 5 1 5 . 3 7 2 3 6.14 9 0 * * 0 . 0 3 . 6 9 18 . 4 4 340 . 05 8 5 * * 0 . 0 5 . 9 6 - 0 . 3 9 1 5 . 9 2 253.40 8 9 * * 0 . 0 5 . 0 3 - 0 . 0 4 15.48 2 3 9 . 6 5 9 0 TABLE 111-5 - continued. Intercept DBH DBH1'5 DBH2 CW CW1,5 CW2 SE E RV R (ft.) (in.) (in.) (in.) (ft.) (ft.) (ft.) (ft.) (ft?) {%) LCL 2.27 2.74 22.15 490.64 49** -43.62 9.31 '-0.91 21.53 463.63 52** -35.54 6.34 -0.08 21.48 461.58 53 0.0 2.82 22.06 486.73 49** 0.0 3.71 0.17 21.99 483.72 50** 0.0 1.38 -0.02 21.93 48Q.86 50** -1.14 3.10 20.03 401.02 60** -52.21 10.41 -1.01 19.12 365.70 64** -43.83 7.17 -0.09 19.02 361.93 64** 0.0 3.06 19.94 397.55 60** 0.0 3.71 -0.12 19.93 397.17 6 l * * 0.0 3.51 -0.02 19.86 394.32 61** CL 1 Basic statistics for these variables are given by Kurucz (1969). * Indicates a significant correlation between the model and the dependent variable at a probability level of five per cent using R. Indicates a significant correlation between the model and the dependent variable at a probability level of one per cent using R. a A zero intercept indicates a conditioned,regression. b RV refers to residual variance. 115 TABLE I I I - 6 Species Douglas-fir Western Hemlock Western redcedar Height to l i v e crown regression models (Smith, Ker, and Cizmazia, 1961). Independent Variables Intercept ( f t . ) - 7 . 3 2 -13.42 -0.81 DBH (in.) HT ( f t . ) AGE (yr.) SE« (ft?) R 2 <* + 0 . 3 4 3 +0.288 + 0 . 4 1 3 1 5 . 5 7 6 - 6 . . 3 7 + 0 . 6 2 2 +0.188 1 3 . 6 7 0 - 1 . 9 4 3 + 0 . 5 4 9 + 0 . 2 5 1 14.2 48 TABLE I I I - 7 Crown width regression models (Smith, Ker, and Cizmazia, 1 9 6 1 ) . Independent Variables Intercept DBH HT , S E E * R2 Species (in.) ( f t . ) ( f t . ) w Douglas-fir ( 0 ) 1 6 . 3 1.71 - 0 . 0 5 4 2 . 2 9 1 Douglas-fir 14.2 1 . 1 1 - 0 . 1 2 6 4 . 3 6 5 Western hemlock 8 . 8 0.81 - 0 . 0 3 3 4 . 9 48 Western redcedar 7 . 5 0 . 5 4 - 0 . 0 2 5 4 . 6 5 0 Douglas-fir ( 0 ) 5 . 8 1 . 5 0 . - — 2 . 2 9 0 Douglas-fir 1 0 . 7 . 5 7 4 . 8 5 6 Western-hemlock 7 . 8 0 . 6 8 5 . 0 46 Western redcedar 8 . 1 O . 6 3 4 . 6 4 9 Open grown APPENDIX I V SAMPLE OUTPUT f :  THIS IS THE FIRST KUN USING FIR CATA DBH = 25.0*7999 HT = 117.29997 CD = 27.09999 . CL TH = 77. 29999 s BASAL AREA KUKUCZ BEST MODEL 9A-MCDEL TOTAL TREE 6994.477 _ 4379.684 . .5198.621 1795.855 BOLE 6100.832 3844.798 4955.355 1145.477 WOOD 5170.734 3260.396 3935.038 1235.697 BARK 930.100 584.401 1020.319 -90 .219 TOTAL CROWN 959.7C5 14 75.CC6 243.268 716.43 7 BRANCH 744.967 1174.335 64.271 680.696 LARGE 549.198 899. 120 57.768 491.430 " " WOOD 0.0 39.595 -39.595 BARK 0.0 0.0 18.173 -18.173 MEDIUM 89.783 127.764 6.106 83.676 WOOD 0.0 0.0 4.603 - 4 . 6 0 3 BARK 0.0 0.0 1.50 3 -1 .503 FINE 105.987 147.451 0.397 105. 589 WOOD 0.0 0.0 0.342 -0 .342 _ BARK _ _o.o_.._ . 0.0 0.056 - C . 0 5 6 NEEDLE 214.603 3 0 0 . £ 5 3 178.996 35.607 ROOT 3497.238 2189.842 0.0 0.0 WOOD 3497.238 2189.842 0.0 0.-0 BARK -0.000 -0 .000 0.0 0.0 BRANCHLET 70.896 WCOD 56.587 BARK 14.3C9 STUMP _ 0.0 0.0 95.921 -95.921 WOOD 0.0 0.0 76.363 -76 .363 BARK 0.0 0. 0 19.558 -19.558 y SLASH CALCULATIONS BASAL AREA OTHER MODEL TOTAL SLASH STUMP WOOO BARK STEM WOOD 1 9 5 . 5 2 5 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 2 9 8 . 5 8 4 0 . 0 0 . 0 0 . 0 0-. 0 0 . 0 146 . 158 9 5 . 9 2 1 7 6 . 3 6 3 1 9 . 5 5 8 3 . 5 * 4 2. 675 ' BARK CROWN BRANCHES WOOD BAP K F INE 0 .0 1 9 1 . 9 4 1 1 4 8 . 9 9 3 0 . 0 0 . 0 1 0 9 . 8 4 0 0 .0 295.CO 1 2 3 4 . 8 6 7 0 .0 C O 1 7 9 . 8 2 4 0 . 9 0 8 4 8 . 6 5 4 1 2 . 8 5 4 . 8 . 908 3 . 9 4 6 1 1 . 5 5 4 MFDIUM LARGE NEEDLES 1 7 . 9 5 6 2 1 . 1 9 7 4 2 , 9 2 1 2 5 . 5 5 3 2 9 . 4 9 0 6 0 . 1 3 1 1.221 0 . C 7 9 3 5 . 7 9 9 -• - —- - : -- — - : - - • • — -"- -- '• -- : .. v -•-1 •1 , --' - --• : ' • : —' - ...... 119 / • " ' COMPONENT METHOD OF C A L C U L A T I N G CENTER CF GRAVITY WEIGHT CROWN STEM TREE BA 4 8 . 07668 T R E E OTHER 5 8 . 7 4 3 0 4 s • TREE GECMETRIC 5 2 . 3 8 9 3 1 ? TREE BA NUI 44.^ 5630 TREE OTHER NU1 5 0 . 1 0 2 2 0 TREE GEOMETRIC NUI 51 18871 TREE BA : NU2 4 7 . 4 5 6 6 5 TREE OTHER NU2 5 7 . 2 2 1 1 6 TREE GECMETRIC NU ? : » 5 2 . 1 7 7 8 4 STEM BA + OTHER 4 6 . 9 1 9 9 7 STEM GECMETRIC 5 2 . 4 C 2 5 0 STEM GEOMETRIC NUI 5 1 . 3 9 5 6 8 HOOD GEOMETRIC NUI 51.59e66 BARK GEOMETRIC NUI 5 1 . 3 4 3 0 5 CROWN BA + OTHER 5 2 . 1 2 0 6 5 CRCWN BA t OTHER NUI 2 6 . 4 6 3 6 8 CROWN BA + OTHER _ . _ NU2 . 4 7 . 6 0 1 7 9 BRANCHES GEOMETRIC 6 9 . 2 6 8 3 4 - - •• - • - - - - • - - - - - - -; ; •' - -.. - •- — - • -• - • • - -~ ' ..... : - 4 -1 • • - -•' --- ...... / 120 THE FOLLOWING EQUATIONS ARE BO • OF THF FORM R l —BICMASS=B0+B1(BASAL AREA) TOTAL TPEE . ROLE-WOOD 0 . 0 0 .0 2 0 3 5 . 5 5 0 1 5 C 4 . 8 0 0 ? ROLE-BARK TOTAL CP OWN LARGE MEDIUM F INE NEFDLE 0 . 0 2 51 . ICO 1 0 3 . 7 0 0 2 9 . I C C J 9 . 6 C C 73 .600 2 7 0 . 6 8 0 2 0 6 . 2 2 0 1 2 9 . 6 5 0 1 7 . 6 6 0 1 9 . 3 2 0 39 .5 90 • - • • - - • - - - - -THE FOLLOWING TOTAL TREE EQUATIONS ARE BO 0 . 0 OF THE F CS M B l 0 . 0 5 9 —BICMASS=R0+B1<D2H)+B2(DXCL 82 R3 0 . 0 0 . 0 )+33<DXCW2)+R4((DXCL); B4 0 . 0 BCLE-WOOD 0 . 0 0 . 0 4 4 0 . 0 0 . 0 0 . 0 B O L E - B A R K 0 . 0 0 . 0 0 8 0 . 0 0 . 0 0 . 0 TOTAL CRCWN 0 .0 0 . 0 0 . 0 0 .080 0 . 0 LARGE 0 . 0 0 , 0 0 . 0 0 . 0 * 9 0 . 0 MEDIUM 0 .0 0 . 0 0 . 0 0 . 0 0 7 0 . 0 F INE 0 . 0 0 . 0 0 . 0 0 .008 0 . 0 NFEDLF 0 . 0 0 . 0 0 . 0 0 . 0 1 6 0 . 0 THE FOLLOWING C O E F F I C I E N T S ARE USEC IN EOLATIONS O F : HElGHT = B0+Bl(DBH)+i32(SEA) +B3 ( C B H * * 2 ) CD=E0+B1(DBH)+3 210BH**2 ) CLTH=HT-{PO + 31 (EBK) + F 2 ( C B h * * 2 ) ) BDIB=BDOB-(aO+r51(L)3H)+B2{HT) ) BO 31 B2 B3 R4 5 . 1 1 0 0 0 0 .0 - 0 . 0 1 0 0 C - 0 . 4 5 0 C 0 0 . 0 . C O C . 5 7 C 0 0 0 . 0 10 .70000 0 . 0 0 . 0 0 . 0 C O 1 .00000 0 . C 9 6 3 0 0 . 0 1.OOCOO C .71000 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 V " 0 . 3 4 3 0 0 0 .28800 0 . 4 1 3 0 0 - 7 . 3 2 C P 0 C O 0 . 0 THE FOLLOWING C G F F F I C I E N T S ARE FOR EOUATIONS O F : Y = A * X * * E A « - B * X + C A EA B C BSL 2 4 2 . 0 4 9 9 9 1 . 5 0 0 C 0 - 2 4 0 . 4 8 0 0 0 BSM 2 4 2 . 0 5 C 0 5 1 . 5 C C 0 C - 2 4 0 . 4 8 0 0 0 BSF 2 4 2 . O 5 C 0 2 1 . 5 C C C C - 2 4 0 . 4 8 0 C 0 BSL 6 0 . 6 8 6 5 2 l . 5 0 0 0 0 - 2 4 0 . 4 R 0 C 0 BSC 6 C . 6 6 6 5 2 1 . 5 C 0 C 0 - 2 4 C . 4 8 0 0 0 BSF 6 0 . 6 8 0 2 6 1 .5000 0- 2 4 0 . 4 8 C 0 0 SSEQUA - 1 0 3 . 1 3 2 . 0 0 - 0 . 0 117 .30 0 . 1 7 SSEOUA - 1 0 3 . 13 2 . 0 C ' - 0 . C 1 1 7 . 3 0 0 . 5 0 SSEQUA - 10 3 . 13 2 . 0 0 \ - 0 . 0 , 1 1 7 . 3 0 1 .05 SSEOUA - 1 3 4 . 7 2 2 .00 1 - o . c 117 .30 0 . 1 7 SSEOUA - 1 3 4 . 7 2 2 . C C - 0 . 0 1 1 7 . 3 0 0 . 5 0 SSEOUA - 1 3 4 . 7 3 2 . 0 0 - 0 . 0 117 .30 0. 0 CS 0 .0631 1 2 . C C C 0 C - 6 . 5 6 0 0 0 CS 0 . 0 6 3 1 1 2 . C C C O C - 6 . 5 6 0 C 0 CS 0 . 0 6 3 1 1 2 . 00000 - 6 . 5 6 0 C 0 121 THE FOLLOWING REPRESENT THE KE AN, VARIANCE AND DISTRIBUTION OF A PARAMETER MEAN VARIANCE DISTRIBUTION SMWSGL 0 . 4 5 0 0 0 0 . 0 0 2 5 0 l . C C C C O SMBSGL C . 4 3 0 0 0 0 . 0 0 4 9 0 l . C C O C O SMWSGM C . 4 5 0 0 0 0 . C 0 2 5 0 1 .00000 SMBSGM SMWSGF SMBSGF BWSG BBSG BWSGL 0 . 4 3 0 0 0 0 . 4 5 0 0 0 0 . 4 3 0 C 0 0 . 0 0 .0 0 . 5 2 6 0 0 0 . C 0 4 9 C 0.00250 0 .CC49G 0. 0 0.0 o.CQ2ro 1.CC000 1 .ccooo 1 .00000 0.0 0.0 1.00000 BBSGL BWSGM BBSGM BWSGF BBSGF NW 0 . 51700 C . 5 0 6 0 0 0 . 5 1 3 C 0 C . 4 3 6 0 0 0 . 5 4 5 0 0 0 . 0 0 . C 1 3 0 C 0 .00500 0 . C 3 C C 0 0 . C 0 9 0 0 0 . 0 2 5 0 0 0 . 0 l . O C O C O 1 .00000 l . O O O C O l . C G C O O 1 .00000 0 . 0 CBW NPW 1 . 5 0 0 0 0 5.20000 0 . 5 0 0 0 C 1 . S 6 C 0 C 1 .oooco 5 .00000 STOP 0 EXECUTION TERMINATED $COPY $ S I G -B * P U N C H * . i ! / $LI5T -MODEL 1 BLOCK DATA 2 C BLOCK DATA I N I T I A L I Z E S HOST OF THE A EBAYS IB THE PROGRAM TO 0 3 C0MM0M/BLK1/TITLE(20) ,SEQ (40) 4 C0MM0N/BLK2/BAC (8,2) ,BUCZ(8,5) 5 C0MM0N/BLK3/HTA (6) ,CDA (6) , CLTHA (6) 6 COMMON/BLK4/D BH,BA,HT,CD,CLTH,D2H,DXCL,DXCW2,DX CL 2,CNPC 7 C0MM0N/BLK5/DBT,BDBT 8 COMMON/BLK10/XLEAF (2) 9 CQMM0N/BLK28/BLTHLT,BLTHMT,BLTHFT,BLTHT 10 COMMON/BLK29/BWSGMA (3) ,BBSGLA (3) ,BWSGLA(3) 11 COMMON/BLK30/WHORL(3,3) 12 C0MM0H/BLK31/STEM(2,6),BS(6,4) 13 C0MM0N/BLK32/CS (3,7) 14 COMM0N/BLK33/SSIQUA(6,5) 15 C0MM0N/BLK35/SGA (14,3) 16 C0MM0N/BLK36/SUMR X (40 ,4) 17 COMMON/BLK3 7/T W BM,TBBM,TBM 18 COMMON/BLK38/CG (18) 19 COMMON/BLK40/SPHT,TDIA,PCCR,SPPC,SPBPC 20 C0MM0S/BLK43/REQ (3,5) ,RPC,RBPC 21 C0MMON/BLK44/CSS (6,6) 22 COMM0H/BL K45/T BH,UMTWBM,UMTBBK,UMTBM 23 COMMON/BLK4 6/PROB(10) 24 C0MM0N/BLK47/SHT (4) 25 DATA TITLE,SEQ /60*0./ 26 DATA BAC,RUCZ /56*0./ 27 DATA HTA , CD A, CLTH A /18*0./ 28 DATA DBH,BA,HT,CD,CLTH,D2H,DXCL,DXC82,DXCL2,CNPC /10*0./ 29 DATA DBT,BDBT /2*0./ 30 DATA XLEAF /2*0./ 31 DATA BLTHLT,BLTHMT,BLTHFT,BLTHT /4 * 0 . / 32 DATA BWSGMA,BBSGLA,BSSGLA / 9 * 0 . / 33 DATA WHORL /9*0./ 34 DATA STEM,BS /36*0./ 35 DATA CS /21*0./ 36 DATA SSEQUA /30*0./ 37 DATA SGA /42*0./ 38 DATA SUMRY /160*0./ 39 DATA TWBM , TB BM, T BM /3 * 0 . / 40 DATA CG /18*0./ 41 DATA SPHT,TDIA,PCCR,SPPC,SPBPC/5*0./ 42 DATA REQ,RPC,RBPC /17*0./ 4 3 DATA CSS /36*0./ 44 DATA TMH,UHTWBM,UMTBBM,UMTEM /4* 0 . / 45 DATA PROB /10*0./ 46 DATA SHT /4*0./ 47 END 48 C THIS IS THE MAIN PROGRAM 49 C THE MAIN PROGRAM SERVES MAINLY AS A CALLING PROGRAM AND FOR THE INPUT 50 C OF DATA 51 C0MM0N/BLK1/TITLE(20) ,SEQ (40) 52 COMMON/BLK2/EAC (8,2) ,RUCZ (8,5) 53 C0MM0N/BLK3/HTA (6) ,CDA (6) , CLTH A (6) 54 COMMON/BLK4/DBH,BA,HT,CD,CLTH,B2H,DXCL,DXCW2,DXCL2,CNPC 55 C0MM0N/BLK5/DBT,BDBT 56 COMMON/BLK10/XLEAF(2) 57 C0MMON/BLK28/BLTHLT,BLTHMT,BLTBFT,BL THT 56 COMMON/BL K29/BWSGMA (3) ,BBSGLA (3) ,BHSGLA (3) 59 COMHON/BLK3Q/WHORL(3,3) 60 COMMON/BLK31/STEM(2,6),BS(6,4) 61 C0MM0N/BLK32/CS (3,7) 62 COMMON/BLK33/SSEQUA (6,5) 63 COMMON/BLK35/SGA (14 , 3) 64 CGMMON/BLK36/SUMRY(40 ,4) 65 C0MM0N/BLK3 7/TWBM,TBBM,TBM 66 COM MON/BLK3 8/CG (18) 67 COMMON/BLK40/SPHT,TDIA,PCCR, SPPC,SPBPC 68 C0MM0N/BLK43/REQ(3,5),BPC,RBPC 69 C0MM0N/BLK44/CSS (6,6) 70 COMMON/BLK45/T MH ,UMTWBM , UMTBBfl,UMTBM 71 COMMON/BLK46/PROB(10) 72 COMMON/BLK47/SHT (4) 73 EXTERNAL FCT 74 EXTERNAL GAMMA,EXPO,XLOGN,X80RM 75 EXTERNAL ALG2 76 INTEGER SEQ 77 HTLC=0. 78 T=RAN0 (.7) 79 S = RANDN (. 7) 80 • C INPUT AREA OF THE PROGRAM 81 READ (5, 1007) (TITLE (J) , 3=1, 20) 82 R HAD (5 , 1000) DBH , HT ,CLTB ,CD 83 READ (5 , 1000) SPHT,TDIA,PCCR 84 DO 101 1=1,8 85 101 READ{5, 1000) (BAC (1,3) ,3=1, 2) 86 DO 102 1=1,8 87 102 READ(5, 1000) (RUCZ ( I , J) ,J=1,5) 88 DO 103 K=1,6 89 103 READ (5, 1000) (SSEQUA (K ,L) , L= 1, 5) 90 DO 104 1=1,6 91 104 READ(5,1000) (BS (1,3) ,3=1,4) 92 c : STEM IS USED FOR THE COEFFICIENTS OF EBT EQ. 93 DO 106 1=1,3 94 106 READ(5,1000) (CS (I,K) ,K=1 ,7) 95 DO 107 1=1,2 96 107 READ(5,1000) (STEM (1,3) ,3=1 ,6) 97 READ(5,1000) (HTA (3) ,3=1,6) 98 READ(5,1000) (CDA (3) ,J=1 ,6) 99 READ(5,1000) (CLTHA (3) ,3=1, 6) 100 DO 108 K=1,14 101 108 READ(5,1000) (SGA (K,L) ,L=1, 3) 102 DO 109 1=1,3 103 109 READ (5,1000) (WHORL (1,3) ,3=1, 3) 104 DO 110 1=1,3 105 110 READ(5, 1000) (REQ (1,3) ,3=1, 5) 106 READ (5, 1000) AGE,SBA , (XLEAF (I) ,1=1,2) 107 READ(5,1000) (PROB (I) ,1=1, 10) 108 READ(5,1000) RPC,RBPC 109 READ (5, 1000) DBT, BDBT 110 READ(5,1000) (SHT (I) ,1=1 ,4) 111 READ(5,1010) (SEQ (I) ,1=1, 40) 112 TBIA=TDIA/24. 113 IF (BA.LT..00001)BA = 3.14159*(DBH/24.)**2 114 IF (HT.LT..00001)HT=HTA (1) +HTA (2) * CB H+BT A (3 ) *S BA + HTA ( 4) *DBH**2 1 15 IF (CD.LT..00001)CD=CDA(1) +CDA (2) *DBH+CDA (3) *DBH *D8H 116 IF (CLTH.LT. .00001) HTLC=CLTHA (1) + CLTBA(2) *DBH+CLTHA (3) *BT 117 1+CLTHA (4) *AGE 118 IF (HTLC.GT.1.)CLTH = HT-BTLC 119 D2H=DBH**2*HT 120 D X C L = D B H * C L T H 121 DXCH2= D B H * C D**2 122 DXCL2=(DBH*CITH)**2 123 DO 75 1=1,3 124 CS ( I , 1) = - C S ( I , 1) 125 CS (I,3)=-CS (1,3) 126 CS (1,4) = HT-CS (1,4) 127 75 CS (1,5) =CS (1,5)/2. 128 DO 76 1=1,6 129 SSEQOA (I, 1) =-SSEQUA (I, 1) 130 SSEQUA (1,3) =-SSEQUA (1,3) 131 SSEQUA (I, 4) = HT-SSEQUA (I, 4) 132 BS (1,1) =-BS ( I , 1) 133 BS (I,3)=-BS (1,3) 134 BS (1,4) =CD/2.-BS (1,4) 135 76 SSEQOA (I, 5)=SSEQUA (1,5)/24. 136 BS (1,4)=CD/2. 137 IF (SEQ{1) .EQ. 77) GO TO 77 138 C PROGRAM COSTROXLED CALLING SEQUENCE 139 CALL STEM 1 140 CALL BRCH1 14 1 CALL LEAF1 142 CALL CRW81 143 CALL TSEE1 144 CALL STEM2 145 CALL BRCH2 146 CALL LEAF2 147 CALL CRWS2 148 CALL TREE2 149 CALL STEM3 150 CALL BRCH3 151 CALL TREE3 152 CALL STUMP1 153 CALL STUMP2 154 CALL R00T1 155 CALL R00T2 156 CALL R00T3 157 CALL SLASH 158 CALL CSEC 159 CALL WBITE1 16 0 CALL WRITE2 161 GO TO 113 162 77 DO 112 1=2,40 163 C USER CONTROLLED CALLING SEQUENCE 164 NNN=SEQ (I) 165 IF (NNN.EQ.O.)GO TO 113 166 GOTO (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18 167 1,19,20,21,22),ANN 168 1 CALL R00T1 169 GO TO 111 170 2 CALL RO0T2 171 GO TO 111 172 3 CALL ROOT3 173 GO TO 111 174 4 CALL STUMP 1 175 GO TO 111 176 5 CALL STUHP2 177 GO TO 111 178 6 CALL STEM 179 GO TO 111 180 7 CALL STEM2 181 GO TO 111 182 8 CALL STEM3 183 GO TO 111 184 9 CALL LEAF 1 185 GO TO 111 186 10 CALL LEAF2 187 GO TO 111 188 11 CALL B.RCH1 189 GO TO 111 190 12 CALL BRCH2 191 GO TO 111 192 13 CALL BRCH3 193 GO TO 111 194 14 CALL CRWN1 195 GO TO 111 196 15 CALL CHIH2 197 GO TO 111 198 16 CALL TREE1 199 GO TO 111 2 00 17 CALL TREE2 201 GO TO 111 202 18 CALL TREE3 203 GO TO 111 204 19 CALL SLASH 205 GO TO 111 2 06 20 CALL WRITE1 207 GC TO 111 208 21 CALL WRITE2 209 GO TO 111 210 22 CALL CSEC 211 111 CONTINUE 212 112 CONTINUE 213 113 CONTINUE 214 1000 FORMAT(8E10.5) 215 1007 FORMAT (20 A4) 216 1010 FORMAT(40I2) 217 1011 FORMAT (1X, 13FJEBR0R IN MAIN) 218 9999 STOP 219 END 220 SUBROUTINE SICALC 221 C CALLING SEQUENCE WHEN SLASH IS USED ALONE 222 CALL STEM 1 223 CALL BRCH1 2 24 CALL LEAF1 225 CALL CRWN1 226 CALL TREE1 227 CALL STEM2 228 CALL BRCH2 229 CALL LEAF2 230 CALL CRWN2 231 CALL TREE2 232 CALL STEM3 233 CALL BRCH3 234 CALL TREE3 235 CALL STUMP1 236 CALL STUMP2 237 CALL ROOT1 238 CALL ROOT2 239 CALL R00T3 240 RETURN 241 END 242 FUNCTION FCT (XMN,VAR,NNX) 243 t~ AN INTERMEDIATE CALLING PROGRAM FOR CALLING RANDOM VARIABLES 244 C 1=NORMAL, 2=EXPONENTIAL, 3= LOG NORMAL, 4= GAMMA, 5 = DISCRETE, 6=BINARY 245 WRITE{3,7) 246 7 FORMAT(3HFCT) 247 GO TO(1,2,3,4,5,6) ,NNX 248 1 FCT=XNORM(XMN,VAR) 249 GO TO 10 250 2 FCT=EXPO(XMN,VAR) 251 GO TO 10 252 3 FCT=XLOGN(XMN,VAS) 253 GO TO 10 254 4 FCT=GAMMX(XMN,VAR) 255 GO TO 10 256 5 FCT=IDIS(XMN,VAR) 257 GO TO 10 258 6 FCT=IBIN(XMN,VAR) 259 10 CONTINUE 260 RETURN 26 1 END 262 FUNCTION XNORM (XMN,VAR) 263 C NORMAL RANDOM VARIABLE 264 WRITE (3,1) 265 1 FORMAT(5HXNORM) 266 7 T = RANDN (0.) 267 XNORM=XMN+ (SQRT (VAR) *T) 268 RETURN 269 END 270 FUNCTION EXPO (XHN,VAR) 271 C EXPONENTIAL RANDOM VARIABLE 272 SRITE(3,1) 273 1 FORMAT(4HEXPO) 274 7 U=RAND(0.) 275 IF (U)7,7,2 276 2 EXPO=(-ALOG(U) )*XMN 27 7 RETURN 278 END 279 FUNCTION X LOG N (XMN , V AR) 280 C LOGNORMAL RANDOM VARIABLE 281 WRITE(3,1) 282 1 FORMAT(5HXLOGN) 283 V = LN (VAR/XMN/XMN+ 1. ) 284 XM=LN(XMN) -.5*V 285 XLOGN=EXP (XM+SQRT (V) * ( RANDN (0. ) ) 286 RETURN 287 END 288 FUNCTION GAMMX (XMN,VAR) 289 c GAMMA RANDOM VARIABLE 290 WRITE (3,1) 291 1 FORMAT(5HGAMMX) 292 A = 0. 293 R=XMN**2/VAR 294 XLAM=XMN/VAR 295 I NT = R 296 fi1=INT 297 R2=R-R1 298 DO 10 J=1,INT 299 7 X=RAND(0.) 300 IF (X) 7 ,7, 10 301 10 A=A-ALOG(X)/X LAM 3 02 IF (R-FLOAT(INI).GT.1.E-4) GO TO 2 303 Y=0. 304 GO TO 4 3 05 2 C=RAND (0.) 306 IF (C) 2,2,5 3 07 5 C1 = RAND(0.) 3 08 IF (C1) 5,5,6 309 6 C2=RAND(0.) 310 IF (C2) 6,6,11 3 11 11 IF (C-2.718/(2. 718+R2) .GT.O.) GOTO 3 3 12 C3=C2**(1./R2) 313 IF (AL0G(C1) +C3.GT.0.) GO TO 2 3 14 Y=C3/XLAfl 315 GO TO 4 3 16 3 IF(C1-(-ALOG(C2/2.718))** (R2-1.).GT .0 3 17 Y=-ALOG(C2/2. 71 8) /XLAM 3 18 4 GAMMX=A+Y 3 19 RETURN 320 END 321 FUNCTION IDIS (XMN,VAR) 3 22 C DISCRETE RANDOM VARIABLE 323 COMMON/BLK4 6/PROB(10) 324 WRITE (3,1) 325 1 FORMAT(1X,4HIDIS) 326 DO 20 1=2,10 3 27 20 PROB (I) =PROB (I) + PROB (1-1) 328 R=RAND (0.) 329 DO 30 1=1,10 330 IF (R.GT.PROB (I) ) GO TO 30 331 GO TO 35 3 32 30 CONTINUE 333 35 IDIS=I 334 HETURN 335 END 336 FUNCTION IBIS (XMN,VAR) 337 C BINARY RANDOM VARIABLE 338 COMMON/BL K4 6/PROB(10) 339 WRITE (3,1) 340 1 FORMAT(1X,4HIBIW) 34 1 P=XMN/10. 34 2 Q=1.-P 343 PROB (1) =10. *P*Q**9 344 PROB (2) =45.*P**2*Q**8 345 PROB (3)=120.*P**3*Q**7 346 PROB (4) =210. *P**4 *Q**6 347 PROB(5)=252. *p**5*Q**6 348 PROB (6) =210.*P**6*Q**4 349 PROB (7)=120.*P**7*Q**3 350 PROB(8)=45.*P**8*Q**2 35 1 PROB (9) =10. *p**9*Q 352 PROB(10)=P**10 353 DO 10 1=2,10 354 10 PROB (I) =PR0B (I) +PROB (1-1) 355 R=RAND (0.) 356 DO 20 1=1,10 357 IF (R.GT.PROB (I) ) GO TO 20 358 I8IN=I 359 20 CONTINUE 36 0 2 5 RETURN 36 1 END 362 SUBROUTINE PNC (A, EA ,B ,C ,XV, YV, XF, YF) 363 C HODIFIS THE EQUATION THAT IS SUPPLIED AS EXPLAINED IN THE TEXT 364 COMMON/BLK3 6/SUMR Y (40,4) 365 WRITE(3,1) 366 1 FORMAT(1X,3HPNC) 367 IF (ABS (A) .LT. . 000001) GO TO 100 368 IF (XV.LT..000001)GO TO 20 369 A= (YF-B*XF-C)/XF**EA 370 19 GO TO 21 371 20 C=YV 372 A=(YF-B*XF-C)/XF**EA 373 21 YV=A*XV**EA+B*XV+C 374 GO TO 200 375 100 IF (XV.LT..000001)GO TO 120 3 76 B=(YF-C)/XF 377 GO TO 121 378 120 C=YV 3 79 B=(YF-C)/XF 380 121 YV=B*XV+C 381 C TEST TO DETERMINE THE MINIUMUM. IF THE MINIMUM EXISTS IT MUST BE LESS 382 C THAN A SPECIFIED Y VALUE WHICH IS ZERO FOR THE STEM SHAPES AND MINUS 2 383 C STARDARD DEVIATIONS OF A BRANCH OF LENGTH EQUAL TO ONE-HALF THE CROWN 3 84 C WIDTH 385 200 IF (A.LE.O.. AND. EA.GE.O.) GO TO 300 386 IF (A.EQ.O. .OR.EA.EQ.O.) GO TO 300 3 87 XT=-B/(A*EA) 388 IF (XT.LE.O.) GO TO 250 389 XT = ALOG(XT) 390 XT = XT/(EA-1.) 391 XT=EXP(XT) 392 YT=A*XT**EA+B*XT+C 393 IF (YT.LT. -SUMRY (8,3) ) GO TO 300 3 94 250 B=(YF-C)/XF 395 A=0. 396 IF (B.GT.O.) B=-B 397 300 CONTINUE 3 98 RETURN 3 99 END 400 FUNCTION ALG2 (A,EA,B ,C ,Y) 4 01 C NEWTON—APHSON ALGORITHM TO SOLVE THE GIVEN EQUATION AT Y 4 02 WRITE { 3, 100) 403 100 FORMAT (IX,4HALG2) 4 04 XT=.005 405 YT=A*XT**EA+B*XT+C-Y 406 IF (YT.LT.0.) GO TO 49 4 07 X=.005 408 1 XNEW=X-(A*X**EA+B*X4-C-Y)/(A*EA*X** (EA-1 . ) +B) 409 IF (ABS (X-XNEW) . LT. .00001) GO TO 50 4 10 X=XNEW 411 GO TO 1 4 12 49 ALG2=0. 413 GO TO 52 4 14 50 ALG2=X 4 15 52 CONTINUE co rt CO S 3 H EH CJ CO to B S O H 0 3 H rt 3 w O) Fx X3 pa EX rt CO a E H IE W HE .-3 33 E H P Q E H Q Ou CD % C i S 3 rt cn M M a CO » fa O rs tt) to E H S B ta H an 3 ft rt E H O • J % ft CD 3 E H X 55 X w H •> ca CO O 1-1 s CD £3 O X 0 rt s W E H u w a CO a s rt CO S B 3 cv % rt • J CO «5 0 W < > u «« W rt Q rt 03 w — rt rn CO ss rt E H S3 O pa ia O H 03 EC OS M to rt E H 0 E H H ft, rt CJ ca CO H4 t» 2s W Q OS M E-i W U ft H rt CO i-5 O •J 3 rt pa OS O O CJ 3 CC u w CQ H a C Q . J OS 3 ( H SB 3 rt (El X O w W CO CJ 3 : E H Q m CN —« o • rt E H O W II OS O t-5 rt CD X X ^ ^ . » o o on w EH W rt EH SS H OS OS O 3 E H E H • * 3 »J X X ft ft H H CJ II a (H . IX O I • 3 pa >•« • # w II X CM Ol II M CO CO 3 IX # 5H I 3 X *• u • CN \ 3 x ti-cs x # CQ w rt * B X * •3! II u a » H I 3 # 0 1 < C 0 CN + \ u • a r-II II a E H a co C N rt ca \ C N • X CN # + X rt fl-ea u * CD * * x # * CN OJ '—• * + rt —> * t • T— CN + w rt + ca ~ \ + —, rt . * + . rt CN ca + rt ca * • CN X * rt * rt X # I m a • x 1  II a x a + u . — a ro x \ \ # — . a a + CO # E H CO u ~— Q II # > H I X # U C O <C + + a a r - CN E H X ca E H ^ pa > rn - E H CH S= •• H x a % ca O sa X M % rt X CM » X u ca CQ CO » rt rt ca ss » o rt M H ^ rt O > ca S 3 ca H b EH 35 55 C • • H 03 O O O & H 3 CB |l || S5 FH O CO fa rt o ca S3 3 Q Q CJ as ca co ca as o ca E H CO 3 Qa Cu rt ft CD S3 H CO ft 3 » O W S 30 3 O HJ H o co > M u co ca ca os E H 0 4 rt t-j ca a J U CQ •4 3 rt O U Q >4 11 O t» X ro T . *o X . • E H >J ' E H • rt >J E X 03 O Cn PH H CN o U E H II 3 O S H CD O O • • ca ca • • • J 3 X x I 3 > H — • CN >-3 X * 4-3 X in CN \ X » X # + ro \ X * X X « P Q CN + rt ca CN + rt W * X # rt O EH O CD o a-> H ro ll — ' tsS II Pu Cn H H X Ol !X H X CL, ro CN \ • x <— ro * •» X O O • # +• E H • CN ft O X II O I! I > CD > II ft u ca ca co CJ ft CQ 03 U ft — 03 3 " ^ O ro >^  " 03 0> S ca 3 03 CO \ \ ro a- ro « « . CQ CQ \ \ SS S3 o o S SE El £ o o u u E H O o PS x in T ~ X ro EH ca A ; 03 O ca ca 03 EH • J rt E H O EH ft O ca CD rt E H S3 ca u QS pa , ft — *— 03 «-rt — CQ pH S3 03 CQ H E £3 O 3 # O CO CQ OS •»• U U ft || Oi 03 03 II II 53 ft 2 CQ CQ PQ til 03 03 03 CJ u u u CN in CN ro CN Or CN L) CJ CN ro r- co 0 r— CN ro =r m vo cocr>or - (Nrostmvor*» CO 0 t— CN ro a m vO r*» CO cn O r- CN ro a tn vo 00 cn 0 «— CN ro a in vO CO cn 0 T- CN ro a m T— r- «— CN CN CN CN CN CN CN CN CNCNrorororororororo ro ro a a a a a a a a a-a in in in in in in in in ui in vO vO vO vO vO VO VO vO vO VO r- r-S t =* a-=t S t =t =r a-a a a-a a a-a a a a a a a a a- a a a a a a a a a a a a a a a-a a a a a a 476 RWBM=RBM-RBBM 477 SOBS* (20, 1) =RBM 478 SUMRY(25,1)=RWBM 479 SUMRY (26,1) =RBBM 480 RETURN 481 END 482 SUBROUTINE ROOT2 483 COMMON/BLK43/REQ(3,5) ,RPC,RBPC 4 84 COMMON/BLK36/SUMRY (40 ,4) 4 85 WRITE (3, 1) 4 86 1 FORMAT(1X,5HROOT2) 487 C ROOT1 488 RBM = RPC*SUHRY (1,2) 489 RBBM=RPCB*RBM 490 R WBM = RBM-RB BM 491 SUMRY (20,2) = RBM 4 92 SUMRY(25,2) = R WBM 493 SUMRY (26, 2) = RBBM 494 RETURN 495 END 496 SUBROUTINE ROOT3 497 COMMON/BLK3 6/S D MR Y (40,4) 498 COMMON/BLK43/REQ(3,5),RPC,RBPC 499 WRITE (3, 1) 500 1 FORMAT(1X,5HROOT3) 501 c REFER TO TEXT 502 RBM=REQ (1,1) +REQ (1 ,2) *BA+REQ (1 , 3 ) * EBH + REQ (1,4 ) *B8H*DB B+REQ (1,5) *HT 503 REBM=REQ (2,1) + REQ (2, 2) *BA+REQ (2,3) *DB H+REQ (2,4) *DBH*DBH+REQ (2,5)*H 504 1T 5 05 RWBM=REQ(3,1) + REQ (3, 2) *BA+REQ (3,3) *DB H+REQ (3,4) *DB H*DBH+REQ (3,5)*H 506 1T 5 07 SUMRY (20 , 3) = RBM 5 08 SUMRY (25,3) = RWBM 509 SUMRY (26,3)=RBBM 510 RETURN 5 11 END 512 SUBROUTINE STUMP1 513 COM MON/BLK3 6/S UMRY (40,4) 514 COMMON/BLK40/SPHT,TDIA,PCCR,SPPC,S EBPC 5 15 1 FORMAT (1X, 6HSTUMP1) 516 c SPPC = STUMP PERCENTAGE OF THE STEM 517 c SPBPC = STUMP BARK PERCENTAGE 518 SPBM=SPPC*SUMRY (2,1) 519 SPBBM=SPBPC*SPBM 520 SPWBM=SPBM-SPBBM 521 SUMRY (36,1) =SPBM 522 SUMRY(37,1)=SPWBH 5 23 SUMRY (38, 1) = SPBBM 524 RETURN 5 25 END 526 SUBROUTINE STUMP2 527 COM MON/BLK3 6/SU MRY (40, 4) 528 COMMON/BLK40/SPHT,TDIA,PCCR,SPPC,S EBPC 529 WRITE (3, 1) 530 1 FORMAT(1X,6HSTUHP2) 531 c SEE STUMP1 532 SPBM=SPPC*SUMRY(2,2) 533 SPBBM=SPBPC*SPBM 534 SPWBM=SPBM-SPBBH 535 SUMRY (36,2) = SPBM E S ca PP 3! CP PJ OI to to il II CMCM r - o o o n r n w ' B5 >* >4 03 03 03 » » a E-i s a w to in as H 33 o 03 a CP w JO u DJ BB U CN CJ X « CM ES CJ X P % I-H CJ X % 33 CM Q « * U"! 33 » EH C O H — CJ IS! "* C J Q S3 U ca •» * e-t ^ 3 3 CN » * «a! 00 CO U EC «S CP OP Q \ \ CM =t US S»5 t-3. >-J C P C O \ \ o o S E E S3 o o u cj o at M 03 s to vO m CQ «• \<T> ES ^ O P3 a H E H O 03 cj is CP CP # * CN <N (N rn u u PP CP E !H W X E-i W co et m o •—EH EH «i 03 E M 03 CM o m PM 0 3 (N rn + u u II II s a C P C P ss CP E S io cn E S a o C Q 3 S c o CO CO II II E C P E 35 C O S S3 CO CO II SE -~ —. 03 v «— *— C Q " * » E fN m d-CO — ' >-II s C O s 03 £3 o co cn S3 P CO CO 25 33 S3 \ o \ • o # CN CN . CO 3E * \ U CJ CO E X X \CQ o Q f-1 CP u # # CJ E E P J 0J to JO a- a- S2S CO * CJ u a a «» CN ro CO CQ CM *~» CM P N N! •J a a u U U u E JO X D X > % a a CQ 1-3 + * a a CN CN CO PP \ E* U L> 3 * ce o CJ X X u CM a 9 X Q Q X a to # a # a > •« vO co a \ m cn u3 CJ a a a u U CO CP CP X CN m X CQ E * 28 PJ a *~" •~— Q OJ CO lA E CO * N - CO EH E CO 32 U U 33 » S3 to » a (N » CM U 35 S = CM CO Q 03 03 O PJ * a a cu + + » Cu E CO » Ot in sc CP 33 33 a CO CP » SS to m % EH CM CM EH % CP E E a 00 P Q Q VO 03 EH a co a • «• # u — o £3 > - » CP CM N » co u © S HH O C* vO U Q ^ CN CN Q CP — . DJ E E # D J \ D U » % CJ » in a- » a CO CQ rn CO • . — , oq » » CM CN m CN % —» k —, » «6 CO «• CP \ - o X - EH O w •~* EH VD VO CO O H 3= (*j s a a # iz ~ 33 = T tSJ u tsi o 33 EH » W » a Q EH a to to to CM to CN - ~— u x u X * c p c M < * a ' ~ ' — . e-i E to •> a CP \ ss * «. *J tx o n < D « 3 r- fH 00 fc SD CM 3 E to P J a o 03 co cq ce Q3 * 03 cqca a cv w « r- M * * E E C0 to H <J CN » E + + Si ss 23 cn .» i.m w «: s - B 33 vo JO CP E » ts to SE* u x a . . cn CO CP OQ S ^ R W C S D O f t E "*"** . . * CO to E g-i «* «c cq JO CN *— « — CO CO CO w c n o a c o c o t o t o u c o EH QJ m t-? E CQ to a Hi EH PQ a \ e CN m 3= s S3 f H Q Q \ W W W E E o to a CS D 35 a CO \ \ v O X m CN — ' m ^—• CO CO CO CO CO \ \ « — c n m v o o o o c n p p W to CO PJ » U X A ^  CN m p EH —' N + II II II a m m c r , m c n m a a EH E H CQ CM CO E H3 r— CM rn *— W « *s « CO tS) U tsi CJ 53 w ^& a & 3 ^ ^ ^ & 3 ^ < 3 ta3 CO a s » to «S % H % a P P P K3 u o CJ CP CM CN CN !35 CP *J CQ to a CP CJ »— «•"• CJ CM H CO C P CQ o LD C3 03 o 03 Se I-l CQCQCQCQCQCQCQCQ CO o cn O CP 3S CP EH ' — ' ,—^ CM H X \ \<"0 03 03 + & CN m C3- EH \ W W W W H r n — ' to a a E a i«J «a! II < a z 2 a —* EH II II CO —* »-» 53 33 a co EH BB CO CO C0 S3 EH o C5 o *4 o o o o w 03 «6 SS S3 II SH tH 03 O o o o o o o o o O 25 W H CO CO to O CO 03 S3 ZJ S3 EH M S CQ CP S3 03 03 05 35 03 E E E S E E E E E ( W EH E < BU et, CO II II II to II pa S3 S3 S3 1-4 CM P3 » CP CP s sa EH Q C Q E E E E E E E E E E H 03 EH EH EH EH EH 35 as 03 X PS SB o o o o 03 w O 83 E3 s S3 C3 ca SB S3 O O O O O O O O O H OS O < «c < •« W a «: S3 a a CO u u u 3t 03 CM CO CO CO to- co CO 03 w CO uuuuuuuo CJ Q 3E CM Q P Q P P Q X to 35 CO X r- U U vor^ooc^o*—cMcnain'vor^coc^o*—cMrnatjnvop^ooc^ c n c n c n r n a a a a a a a a a a i n L n u n i n L n i n c n i n i n i r i v o v ^ i n i n c n c n u n i n u ^ t n i n i n u n i r i u i t n ' r ) ^ 596 VAR=SGA(2,2) 597 NNX=SGA(2,3) 5 98 SM3SGL=FCT(XMN,VAR,NNX)*62.43 599 XMN=SGA(3,1) 600 VAR=SGA(3,2) 601 NNX=SGA(3,3) 6 02 SMWSGM=FCT(XMN,VAR,NNX)*62.43 603 XMN=SGA(4,1) 604 VAR=S GA(4/2) 605 NNX=SGA (4, 3) 6 06 SMBSGM=FCT(XMN,VAR,NNX)*62.43 607 XMN=SGA(5,1) 608 VAR=SGA(5,2) 6 09 NNX=SGA(5,3) 610 SMWSGF=FCT(XMN,VAR,NNX)*62.43 611 XMN=SGA(6,1) 612 VAR=SGA(6,2) 6 13 NNX=SGA(6,3) 614 SMBSGF=FCT(XMN,VAR,NNX)*62.43 615 C BARK THICKNESS CALCULATIONS FOLLOWED BY MODIFICATION OF SHAPE EQUATIONS 616 BH=4.5 617 R=BBH/24. 6 18 IF (DBT.LT. .00001) DBT=STEM (1,1) *DBH**STEM (1,2) + 6 19 1ST EM (1,3) *D BH+STEM (1,4) *HT**STEM (1,5) + STEM (1,6) 620 RW=R-DBT/24. 621 XL=0. 6 22 YU=HT 623 YL=4.5 6 24 XU=R 625 IF (R.LE. SSEQUA (1,5) ) GO TO 200 626 IF (R.LE.SSEQUA (2,5) ) GO TO 100 6 27 CALL PNC (SSEQUA (3,1) , SSEQUA (3,2) ,SSEQUA(3,3) , SSEQUA ( 3, 4) , 1. , 2. , R , 628 14.5) 629 X3=ALG2 (SSEQUA (3, 1) , SSEQUA (3, 2) , SS EQU A (3, 3) ,SSEQUA (3,4) ,0.) 630 X2=SSEQUA (2,5) 631 13=0. 63 2 Y2=SSEQUA (3,1) *X2**SSEQUA (3,2) +SSEQUA (3,3) *X2+SSEQUA (3,4) 633 CALL PNC(SSEQUA (6, 1) ,SSEQUA(6,2) ,SSEQUA(6,3) ,SSEQUA (6,4) ,1.,2.,RW 634 1,4.5) 6 35 XI3=ALG2 (SSEQUA (6, 1) , SSEQUA (6, 2) ,SSEQUA (6, 3) , SSEQUA (6,4) ,0. ) 636 YI3=0. 6 37 XI2=ALG2 (SSEQUA (6, 1) ,SSEQUA (6,2) ,SSEQUA (6,3) , SSEQUA (6,4) ,Y2) 638 YI2=Y2 639 YL=Y2 640 XU=X2 6 4 1 CALL PNC (SSEQUA (2, 1) , SSEQUA (2,2) ,S SEQUA (2, 3) , SS EQUA (2,4) , 642 1 1. ,2. ,X2,Y2) 643 CALL PNC (SSEQUA (5, 1) ,SSEQUA (5, 2) ,SSEQUA (5, 3) ,SSEQUA (5,4) , 644 1 1. ,2. ,XI2,YI2) 645 XL=SSEQUA(1,5) 64 6 YU=SSEQUA (2,1) *XL**SSEQUA (2,2) +SSEQUA (2,3) *XL+SSEQUA (2,4) 647 X1=XL 648 Y1=YU 64 9 CALL PNC (SSEQUA (1,1) , SSEQUA (1, 2) ,SSEQUA (1,3) , SSEQUA (1 ,4) ,0. ,HT, 650 1X1 ,11 ) 65 1 XL= ALG2 (SSEQUA (5, 1) ,SSEQUA (5, 2) ,SSEQUA (5, 3) ,SSEQUA (5,4) ,Y1) 65 2 XU=XI2 653 YL=YI2 654 YU=Y1 655 XI1=XL 656 YI1=Y1 657 CALL PNC(SSEQUA (4, 1) , SSEQUA (4,2) ,SSEQUA(4,3) ,SSEQUA (4,4) , 658 1X11, YI1) 659 GO TO 300 660 100 A=SSEQUA(2,1) 661 EA=SS EQUA(2,2) 662 B=SSEQUA(2,3) 663 C=SSEQUA (2,4) 664 CALL PNC(A,EA,B,C,1.,2.,XU,YL) 665 SSEQUA(2,1)=A 666 SSEQUA (2,3) =B 667 SSEQUA (2,4) =C 668 X1=SSEQUA(1,5) 669 X2=SSEQUA(2, 5) 670 Y1=A*XU**EA+E*X1+C 671 Y2=A*X2**EA+E*X2+C 672 A=SSEQUA(5,1) 673 EA=SS EQUA(5,2) 674 B=SSEQUA(5,3) 675 C=SSEQUA (5, 4) 676 XU=RW 677 CALL PNC(A,EA, B,C, 1. ,2.,XU,YL) 678 SSEQUA (5,1) =A 679 SSEQUA (5,3) =B 680 SSEQUA (5,4) =C 681 XI1=ALG2(A,EA, B,C,Y1) 682 XI2=ALG2(A,EA,B,C,Y2) 6 83 YI1=Y1 684 YI2=Y2 685 A=SSEQUA (1, 1) 686 EA=SSEQUA (1 ,2) 687 B=SSEQUA (1, 3) 688 C=SSEQUA(1,4) 689 CALL PNC(A,EA, B,C,0. ,HT,X1,Y1) 690 SSEQUA (1 ,1) = A 691 SSEQUA (1 , 3) = E 692 SSEQUA (1 ,4) =C 693 A=SSEQUA (4, 1) 694 EA=SSEQUA(4,2) 695 B=SSEQUA (4, 3) 696 C=SSEQUA(4,4) 697 XU=XI1 6 98 YL=YI1 699 CALL PNC(A,EA, B,C,0. ,HT,XU,YL) 700 SSEQUA(4,1)= A 701 SSEQUA (4, 3) = E 702 SSEQUA (4,4) =C 703 A=SSEQUA (6, 1) 704 EA=SSEQUA(6,2) 705 B=SSEQUA (6,3) 706 C=SSEQUA(6,4) 707 CALL PNC(A,EA, B,C, 1. ,2.,XI2, YI2) 708 SSEQUA(6,1)=A 709 SSEQUA (6,3) = E 710 SSEQUA (6,4) =C 711 XU=ALG2 (A,EA, B, C, 0.) 712 SSEQUA (6,5) =XU 7 13 YL=0. 714 YI3=0. 715 XI3=XU 716 A=SSEQUA (3,1) 717 EA=SS EQUA (3,2) 718 B=SSEQOA (3,3) 719 C=SSEQUA (3,4) 720 CALL PNC(A,EA,B,C,1.,2.,X2,Y2) 721 SSEQOA (3, 1) = A 722 SSEQUA (3,3) =E 723 SSEQOA (3,4) =C 724 XU=ALG2(A,EA,B,C,0.) 725 YL=0. 7 26 XL=X2 727 ¥0=12 728 X3=XU 729 SSEQUA (3, 5) =X3 73 0 Y3 = 0. 731 GO TO 300 732 200 A = SSEQUA (1 , 1) 733 EA=SSEQUA(1,2) 734 B=SSEQUA(1,3) 735 C=SSEQUA (1,4) 736 CALL PNC(A,Efl,B,C,XL,YU,XU,YL) 737 SSEQUA (1, 1) = A 738 SSEQOA (1 ,3) =B 739 SSEQOA (1,4) =C 740 X1=SSEQ0A(1,5) 741 Y1=A*X1**EA+B*X1+C 742 A=SSEQUA(4,1) 743 EA=SSEQUA(4,2) 744 B=SSEQUA(4,3) 745 C=SSEQUA (4,4) 746 XU=RW 747 CALL PNC(A,EA, B,C,XL,YU,XU,YL) 748 SSEQUA (4, 1) = A 749 SSEQUA (4,3) = E 75 0 SSEQUA (4,4) =C 751 XI 1 = ALG2 (A,EA, B,C,Y1) 752 YI1=Y1 75 3 XL=X1 754 YU=Y1 755 CALL PNC (SSEQUA (2, 1) ,SSEQUA (2,2) ,SSEQUA(2,3) , SSEQUA (2,4) , 756 11.,2. ,X1 ,Y1) 757 CALL PNC (SSEQUA (5, 1) ,SSEQUA (5,2) ,SSEQUA (5,3) ,SSEQUA (5,4) , 758 1 1.,2. ,XI1,YI1) 759 XU=SSEQUA (2, 5) 760 YL=SSEQUA (2,1) *XU**SSEQUA (2,2) +SSEQUA (2,3) *XU+SS EQUA (2, 4) 761 X2=X0 762 Y2=YL 763 A=SSEQUA(5,1) 764 EA=SSEQUA(5,2) 765 B=SSEQUA (5,3) 766 C=SSEQUA(5,4) 767 XL=XI1 768 YU=YI1 769 YL=Y2 770 XU=ALG2(A,EA,B,C,Y2) 77 1 XI2=XU 772 CALL PNC (SSEQUA (3, 1) ,SSEQUA (3,2) ,SSEQUA (3,3) ,SSEQUA (3, 4) , 773 1 1. ,2. ,X2,Y2) 774 CALL PNC (SSEQUA (6,1) ,SSEQUA (6,2) ,SSEQUA (6,3) ,SSEQUA (6,4) , 775 11.,2.,XI2,Y2) 776 YI2=Y2 777 A=SSEQOA (3,1) 778 EA=SSEQUA(3,2) 779 B=SSEQUA (3, 3) 780 C=SSEQUA(3,4) 781 XL=X2 782 YU=Y2 783 XU=ALG2 (A,ES, B, C,0.) 784 SSEQUA (3, 5) = XU 785 YL=0. 786 X3 = X0 787 Y3=0. 788 A=SSEQUA(6,1) 789 EA=SS EQUA(6,2) 790 B=SSEQUA(6,3) 791 C=SSEQUA(6,4) 7 92 XL=XI2 793 YU=YI2 794 XU=ALG2 (A,EA, B,C,0.) 795 SSEQUA (6, 5) = XU 796 YL=0. 797 XI3=XU 798 YI3=0. 799 300 CONTINUE 800 C CALCULATION OF THE VOLUME WEIGHT AND CENTER CF MASS OF THE STEM SECTIONS 801 A=SSEQUA (1, 1) 802 EA=SSEQUA(1,2) 803 B=SSEQUA (1 ,3) 804 C=SSEQUA(1,4) 805 XL=0. 806 YL=Y 1 8 07 XU=X1 8 08 YU=HT 809 IF(YL.LT.O.)YL=0. 810 IF (YL.LT.O.) XU=ALG2 (A , EA , B, C, 0. ) 811 CALL AREA(A,EA,B, C, XL ,YU, XU,YL,DA,DB) 812 TEMP (1,2) =DB 813 TEMPO,1)=DA 814 CALL VOL(A,E&,B,C,XL ,XU,YL,YU,V) 815 SMBVMF=V 816 BVOL=BVOL+V 817 IF (Y1.LT.0.) GO TO 898 818 A=SSEQUA(2,1) 819 EA=SS EQUA(2,2) 820 B=SSEQUA(2,3) 821 C=SSEQUA (2,4) 822 XU=X2 823 YL=Y2 824 XL=X1 825 YU=Y1 826 IF (YL .LT.O.) YL=0. 827 IF (YL.LT.O.) XU = ALG2 (A , EA, B, C, 0.) 828 CALL AREA(A, E A, B, C, XL ,YU , XU, Y.L,DA,DB) 829 TEMP(2,2)=DB 830 TEMP(2,1)=DA 831 CALL VOL(A,EA,B,C,XL,XU,YL,YU,V) 832 SMBVMM=V 833 BVOL=BVOL+V 834 IF (Y2.LT.O.) GO TO 898 835 A=SSEQUA(3,1) 836 EA=SSEQUA(3,2) 837 B=SSEQUA (3,3) 838 C=SSEQUA(3,4) 839 XL=X2 840 XU=X3 84 1 YU=Y2 842 YL = 0. 843 CALL AREA (A,EA, B,C,XL,YD,XU, YL, DA,DB) 84 4 TEMP (3,2) =DB 845 TEMP(3,1)=DA 846 CALL VOL(A,EA,B,C,XL,XU,YL,YU,V) 847 SMBVML=V 848 BVOL=BVOL+V 849 898 A=SSEQUA(4,1) 850 EA=SSEQUA(4,2) 851 B=SSEQUA (4,3) 852 C=SSEQUA(4,4) 85 3 XL=0. 854 XU=XI1 855 YU=UT 856 YL=YI1 857 IF (YL.LT.O.) YL=0. 858 IF (YL.LT.O.) XU=ALG2 (A,EA,B,C,0. ) 859 CALL AREA (A, E A, B, C,XL , YU, XU, YL,DA,DB) 860 TEMP (4,2) =DB 861 TEMP(4,1)=DA 862 CALL VOL(A,EA,B,C,XL,XU,YL,YU,V) 863 SMWVMF=V 864 WV0L=WV0L+V 865 IF (Y1.LT.O.)GO TO 899 866 A=SSEQUA(5,1) 867 EA=SSEQUA(5,2) 868 B=SSEQUA(5,3) 869 C=SSEQUA (5,4) 870 XL = XI1 871 XU=XI2 872 YU=YI1 873 YL=YI2 874 IF (YL .LT.O.) YL=0. 875 IF (YL.LT.O.)XU=ALG2(A,EA, B, C, 0.) 876 CALL AREA(A,EA,B,C,XL,YU,XU,YL,DA,DB) 877 TEMP(5,2)=DB 878 TEMP(5,1)=DA 879 CALL VOL (A,EA, B, C, XL ,XU , Y L, Y U , V) 880 SMWVMM=V 881 WV0L=WV0L*V 882 IF (Y2.LT.O.)GO TO 899 883 A=SSEQUA(6,1) 884 EA=SSEQUA(6,2) 885 B=SSEQUA(6,3) 886 C=SSEQUA(6,4) 887 XL=XI2 888 XU=XI3 889 YU=YI2 890 YL=0. 891 CALL AREA (A, E A, B, C, XL , Y U, X U, YL, DA,DB) 892 TEMP(6,2)=DB 893 TEMP(6,1)=DA 894 CALL VOL(A,EA,B,C,XL,XU,YL,YU,V) 895 SMWVML=V + • J O > 3 t! >-3 O > CB CM a: S E > > rs ts a so cn to t i CM E E SB ca co E E to to II II s s > > > CQ CQ pp S S 2 cn to cn t-a O s=> 3 ! I t-J O > CO II E to to I » t-1 CM E CO > CO CQ CQ E E CO CO II II >J PM E E t> CO CQ CQ a E CO CO PM S 15 CD to J/1 3! CQ E S co to * * PM E s sa e> > 3 CQ to co II ll PM E a E CQ CQ a m UI CO E E CS s> co 3 CQ E E CO CO * # E >-l CD E CO > CS CQ 53 E CO to II II a i j E E CQ CQ £5 CQ E E CO CO CM E CQ CC CO <-A + CD E CO E rz ca E BB CO s # s t> 3 E to II hJ II E E CQ CQ CS 3 S E CO to \ P —« W t— •» u -—. Ol r -S «, ca ic * a. — E CN W Qj CN E % W « H —' | CM —, E <- W % EH M + CM —^ ^_ E Qj r - CB CQ E » CO CQ W H + E EH — — CO # ^ C u r -+ «-» —» SB * E CN «- pa « S «• * EH -~ CQ H tv: # QJ CO+ 1-4 E CQ 3 se CO ca ss E CQ CO CQ • E I-J. cn E + CQ E CQ CQ E 3 CO E ll cn E II CQ E CQ CQ E E CO CO E E CQ CQ 3 E E co to II II rn co CN ro >J SH 03 03 E S a 3 co cn rn E CQ CQ E CO II ro" *— o SH • O OS O Ol E |l D 03 O CO CO Q E pa EH CN M m + On H E CM CN E « ca M EH ~-I Qj E r - oa « en HI II cvi »-E *~ ca — H CD -- U E ca EH - O M • — E H CM CD E • ca as E H CO II 03 PM CO H S CQ CQ SO cn # CN ro OJ E ca EH + E S CO CQ E co # CN * CN CM E ca EH + PM E CQ CQ E CO • 03 CN CO — s \ . «~ — o — <- • OJ CD pa CD • EH u s — ll cc II so »- s ro «~ co <-CD CM CD U H U H3 E CQ 3 E CO # CN \o CM E ca E H + E S CQ 3 CO • CN tn ft S ca EH + CM E CQ 3 E CO * CN t a o *— • CM H S CD ca . EH E ~-CQ II E is CQ E a CQ CO s w — • cn PM CD \ H U rt 3 a pa co cn * . , ro ro «. rt Ol pa co co E cq E CO \ sT CQ ts E CO * CD u + E CQ CQ E CO . ro o «-EH CD CD U SS II S CQ ^ CQ S CN 3 I T " 5£J * *"* CO CM C5 \ H U o o o o vo m o CO EH o o H CD E H — . «; CN •4 H D . u ca j •a rt • U EH 33 PM OJ S CO O •— EH CM CO H O E H O O CD II i - Sw > H t • pa o . E H EH 33 • > On «~ cn >• CM PM H H rt o CO cn rt 3 O ca to CO CN CD .-a rt E H • J «— • M <~ || > H r— • H PM SH H rt 3 o> ca CO CO — CN CN » rt 3 o> pa co co rt 3 a pa to to CN «-CD » •a — rt II ^ r t T - . 3 H O Ol - p a CO EH EH EH PC 3 33 CM OM CM CO CO CO ,—^  » a- a a > zt a * T~ H a % CN —• *— a >—» rt - - rt rt 3 rt 3 rt 3 O* 3 Ol 3 o» ca o ca tn ca cn ca t-J HH CO CO CO CO CO S E cn » cn •> CO CQ CQ tz tu ro ~- ro E E ro » ro » ro CO CO i — % a % + • CN *~" r— w a E E rt ^  rt ~— E S rt 3 rt 3 rt 03 CQ 3 O 3 O 3 3 CQ Ol pa cv pa o> S E ca co ca cn ca CO CO cn to CO to CO + + CO » CO - cn PM PM «. —^^  % —^. % CD CS CN CN — . CO to CN » CN - CN 3 CU % *- » a » E E CN r— — a CO CO *-* rt rt —- * * rt 3 rt 3 rt 3 0> 3 CS 3 o> ca oi ca a E E ca to ca to ca > > CO to CO to CO 3 CQ to - CO - CO S E • a CN EH — CD • J rt t-5 • 3 rt - s ' - O II • CH pa CQ o — cn ca » PM cn ft —. H »cn *- > » —» CQ > E — * CO rt H + 3 33 s Ol CM E ca to > co » CQ CO T- E 5H tn o *- > t=» X II * E • J CQ t> i-J 03 CQ rt CJ CM U CO CO a •> » ^ a - EH rt ~33 3 rt pj O) 3 tO pa o » to ca CN C l CO M '—tO >i CN » CD J CN i-J O H rt > X II » 3 J 3 03 H» 03 OJ rt PJ CO U co •-3 E > 3 E CO + E S P» P> I 3 E S > CO CQ + CM CO CO I I S E S S 3 CQ CM CM cn co £> > 3 CQ S E to co I i E E > > 3 CQ CM QJ to CO II II S E CQ CQ 3 CQ OJ OJ CO CO E CQ CQ CM CO + E CQ O 3 O PJ co CO II o S H CQ Oj O CO CD CN rt o 3 || Ol CN ca SH co —. CO • CN E H i-J • CN CN X * M 03 — ' CN CM PM H CO H X CO o o cn o o tn v o r ^ c o o ^ o r - c N r o 3 L n v o r ^ c o c n o r - r N i r o a i n u 3 c n c n c n c n o o o o o o o o o o r - ^ r - r - T - ^ r - r ^ o o a D O T o o c T i c n c n c n c n o>cncncncnc7^ 956 IF (Y2.LT.0.) X2 = ALG2 (SSEQOA (2,1) , SS EQUA (2,2) ,SS EQUA (2,3) 957 1,SSEQUA (2,4) ,0. ) 95 8 IF (¥2.LT.O .) XI2=ALG2 (SSEQUA (5,1) ,SSEQUA (5, 2 ) , SS EQU A (5, 3) 959 1 ,SSEQUA (5,4) ,0. ) 960 CALL V0L(SSEQUA (2,1) ,SSEQUA (2,2) ,SSEQUA{2,3) ,SSEQUA (2,4) , 96 1 1SPRB,X2,Y2,SPHT,V) 962 SPBVM^V+SMBVML 963 SPHW=ALG2 (SSEQUA (5, 1) ,SSEQUA (5,2) ,SSEQUA (5,3) ,SSEQUA (5,4) ,SPHT) 964 CALL VOL (SSEQUA (5,1) , SSEQUA (5,2) ,S S EQUA (5,3) , SS EQUA (5,4), 965 1SPRW,X2,Y2,SPBT,V) 966 SPWVM=V+SMWVML 967 SPBBM= (SPBVM-SMBVML) *SMBSGM+SHBBML 968 SPWBM=(SPWVM-SMHVML)*SMWSGM+SMWBML 969 SPBM=SPWBM+SPBSM 970 GO TO 800 971 600 SPRB=ALG2 (SSEQUA (3, 1) ,SSEQUA (3,2) ,SSEQUA (3,3) ,SSEQUA (3,4) ,SPHT) 972 CALL VOL (SSEQUA (3,1) ,SSEQUA (3,2) ,SSEQUA (3,3) ,SSEQUA (3,4) , 973 1SPRB,X3,0.,SPHT,V) 974 SPBVM=V 975 SPRW = ALG2 (SSEQUA (6, 1) , SSEQUA (6,2) , SSEQUA (6, 3) , SSEQUA (6,4) ,SPHT) 976 CALL VOL (SSEQUA (6, 1) ,SSEQUA (6,2) ,SSEQUA (6,3) ,SSEQUA (6, 4) , 977 1SPRW,XI3,0.,SPHT,V) 978 SPWVW=V 979 SPBVM=SPBVM-V 980 SPBBM=SPBVM*SMBSGL 981 SPWBM=SPWVM*SMWSGL 982 SPBM=SPHBM+SPEBM 983 800 CONTINUE 984 SUM BY (36,3) = SPBM 985 S U MRY (37 , 3) =SP¥BM 986 SUMRY ( 38 , 3) =SPEBM 987 SPPC=SPBM/SMBM 988 SPBPC=SPBBM/SPBM 989 C UNMERCHANTABLE TOP CALCULATIONS 990 IF(TDIA.GE.X2)GO TO 850 99 1 IF {TDIA. GE.X1) GO TO 830 992 TMH=SSEQUA (1,1) *TDIA**SSEQUA (1,2) + SSEQUA (1 ,3) *T DIA+SSEQUA (1,4) 993 CALL VOL (SSEQUA (1, 1) ,SSEQUA(1,2) ,SSEQUA(1,3) ,SSEQUA (1,4) , 994 10.,TDIA,TMH,HI,V) 995 UMTBVM=V 996 T DIAI=ALG2 (SSEQUA (4 ,1) ,SSEQUA (4,2) ,SSEQUA (4,3) ,SSEQUA (4,4) ,TMH) 997 CALL VOL (SSEQUA (4, 1) , SSEQUA (4,2) ,SSEQUA (4, 3) , SSEQUA (4,4) , 998 10.,TDIAI,TMH,HT,V) 999 UMTWVM=V 1000 UMTBVM = UM TB VM-V 1001 U MTBBM=UMTBVM#S MBSGF 1002 UMTWBM=UMTMVM*SMWSGF 1003 U MTBM=UMTWBM+U MT BBM 1004 GO TO 860 1005 830 TMH=SSEQUA (2, 1) *T DIA**SSEQUA (2, 2) +SSEQUA (2, 3 ) *TDIA+SSEQUA (2,4) 10 06 CALL VOL (SSEQUA (2,1) ,SSEQUA (2,2) ,SSEQUA (2,3) ,SSEQUA (2,4), 1007 1X1,TDIA,TMH,Y1,V) 1008 UMTBVM=V+SMBVMF 1009 TDIAI=ALG2 (SSEQUA (5, 1) , SSEQUA (5,2) ,SSEQUA (5,3) ,SSEQUA (5,4) ,TMH ) 1010 CALL VOL (SSEQUA (5, 1) ,SSEQUA (5,2) ,SSEQUA (5,3) ,SSEQUA (5, 4) , 1011 1XI1,TDIAI,TMH,YI1,V) 1012 DMTWVM=V+SMWVMF 1013 U MT BVM= UMTBVM-V 1014 UMTBBM= (UMTBVM-SKBVMF)*SMBSGM+SMBBMF 1015 U MTWBM= (UMTHVM-SMWVMF) *SMBSGM+SMWBMF 1016 UMTBM=UMTUBM+UMTBBM 1017 GO TO 860 1018 850 TMH=SSEQUA (3,1) *T DIA** SSEQU A (3, 2) +SSEQUA (3,3) *T CIA + SSEQUA (3,4) 1019 CALL VOL(SSEQDA (3, 1) ,SSEQUA(3,2) ,SSEQUA(3,3) , SSEQUA (3,4) , 1020 1X2,TDIA,TMH,YI2,V) 1021 UMT BVM=V+SMBVMM+SMBVMF 1022 TDIAI=ALG2 (SSEQUA (6 ,1) , SSEQUA (6,2) ,SSEQUA (6,3) ,SSEQUA (6,4) , T MH) 1023 CALL VOL (SSEQUA (6, 1) ,SSEQUA (6,2) ,SSEQUA(6, 3) ,SSEQUA (6,4) , 1024 1SPRW,XI2,YI2,SPHT,V) 1025 UMTWVM=V+SMWVMM+SMWVMF 1026 UMTBVM=UMTBVM-V 1027 UMTBBM= (UMTBVM-SMBVMF-SMBVMM) *SMBSGL + SMBBHF +SHBBMM 1028 UMTWBM=(UMTWVM-SMWVMF-SMWVM8) *S MWS GL + SMWBMF+S MSBKH 1029 U MT BM = UMTBBM + U MTW BM 1030 860 CONTINUE 1031 RETURN 1032 END 1033 SUBROUTINE BRCH1 1034 COM MON/BLK2/BAC (8,2) ,RUCZ (8,5) 1035 COMMON/BLK4/DBH,EA,HT,CD, CLTH,D2H , DXCL,DXCW2,DXCL2,CNPC 1036 COMMON/BL K3 6/SUMR Y (40,4) 1037 WRITE(3,1) 1038 1 FORMAT(5HBRCH1) 1039 C REFER TO TEXT 1040 BBHL=BAC (5,1) +BAC (5,2) *BA 1041 BBMM=BAC (6,1) +BAC (6,2) *BA 1042 BBMF=BAC (7,1) +BAC (7,2) *BA 1043 BBM=BBML+BBMM+BBMF 1044 SUMRY(6,1)=EEM 1045 SUMRY (7, 1) =BBML 1046 SUMRY (10,1) = BBMM 1047 SUMRY (13, 1) = BBMF 104 8 RETURN 1049 END 1050 SUBROUTINE BRCH2 1051 COM MON/BL K2/ B AC (8,2) , RUCZ (8, 5) 1052 COM MON/BLK4/DBH,BA,HT,CD,CLTH,D2H,DXCL,DXCW2,BXCL2,CNPC 105 3 COMMON/BLK3 6/S 0 MR Y (40,4) 1054 WRITE(3,1) 1055 1 FORMAT(5HBRCB2) 1056 c REFER TO TEXT 1057 BBML = RUCZ (5, 1) +RUCZ (5,2) *D2 H+RUCZ (5 , 3) *DXCL+RUCZ (5,4) *DXCW2 1058 1 +RUCZ(5,5)*DXCL2 1059 BBMM = RDCZ (6, 1) +RUCZ (6 , 2) *D2H+RUCZ (6 , 3) *DXCL+RUCZ (6 ,4) *DXCW2 1060 1 +RUCZ(6,5)*DXCL2 1061 BBMF=RUCZ (7, 1) +RUCZ (7,2) *D2H+RUCZ (7 , 3) *DXCL+RUCZ (7,4) *DXCW2 1062 1 +RUCZ(7,5)*DXCL2 1063 BBM=BBM F+BBMM + BBML 1064 SUMRY (6,2) =BBM 1065 SUMRY (7,2) =BBML 1066 SUMRY (10,2) =BBBM 1067 SUMRY (13,2) = EBMF 1068 RETURN 1069 END 1070 SUBROUTINE BRCH3 1071 COMMON/BLK4/D BB,BA,HT,CD,CLTH,D2H,DXCL,DXCW2,DXCL2,CNPC 1072 C0MM0N/BLK5/DBT,B DBT 1073 C0MM0N/BLK10/XLEAF(2) 1074 COMMON/BLK2 8/BLTHLT,BLT HMT,BLTHFT,BLT HT 1075 COMMON/BLK30/WHORL(3,3) 1076 COMMON/BLK31/STEM(2,6) ,BS (6,4) 1077 COMMON/BLK32/CS (3,7) 1078 COMMON/BLK34/HK,BK,BWK 1079 COMMON/BLK3 5/SG A(14,3) 1080 COMMON/BLK36/SUMRY (40,4) 1081 COMMON/BLK38/CG (18) 1082 COMMON/B.LK4 7/SHT (4) 1083 WRITE (3,1) 1084 1 FORMAT (5HBRCH3) 1085 DATA BBVOLF,BBVOLM,BBVOLL,BWVOLF,B»VOLM,BWVOLL,BBVMF,BBVMM/8*.0/ 1086 DATA BBVOL,BWVOL,BVOL/3*0./ 1 087 DATA BBVML,BWVMF,BWVMM,BWVML,BWVM,BBVM,BVM,BBBML/8*.0/ 1088 DATA BBBMM,BBBMF,BWBML,BWBMM,EWBMF,BBBM,BWBM,EBM/8*.0/ 1089 CG (18)=0. 1090 HTLC=HT-CLTH 1091 XX=1. 1092 SD=CS (3,6) *CD/2. 1093 SD=SQRT(SD) 1094 SUMRY (8,3) =2. *SD 1095 A=CS (3,1) 1096 EA=CS (3,2) 1097 B=CS (3,3) 1098 C=CS (3,4) 1099 YL=HTLC 1100 YU = HT 1101 XL=0. 1 102 XU=CD/2. 11 03 CALL PNC (A, E A, B, C,XX ,XXX , XU, YL) 1104 CS (3,1) =A 1105 CS (3,3) =B 1 106 CS(3,4)=C 1107 YC3=HTLC 1108 YC2=A*CS(2,5) **EA + B*CS (2,5) +C 1109 A=CS (2, 1) 11 10 EA=CS(2,2) 1111 B=CS (2,3) 1112 C=CS (2,4) 1113 XL=CS (1,5) 1114 YU=A*XL**EA+B*XL+C 1 1 15 XU=CS (2,5) 1 116 YL=YC2 11 17 CALL PNC(A,EA, B, C , XL , YU ,X U, YL) 1118 CS (2,1) = A 1119 CS (2,3)=B 1120 CS(2,4)=C 1121 YC1=A*XL**EA+B*XL+C 1 122 XC1=XL 11 23 YL=YC1 1124 XU=XC1 1125 XL=0. 1126 YU=HT 1127 A = CS (1,1) 1128 EA=CS(1,2) 1129 B=CS (1,3) 1130 C=CS (1 ,4) 1131 CALL PNC (A,EA, B, C, XL ,YU,XU,YL) 1 132 CS (1, 1) =A 1133 CS (1 ,3) =B 1 134 CS (1,4)=C 1135 C SOLVE FOR MEAN BLTH AND NNX AND VAR HERE 1136 C DESIGNATE BS EQUATIONS FINE MED AND LARGE 1137 C TES IF CW IS GREATER THAN FINE AND MEDIUM BRANCH LENGTHS 1138 P=.25/24. 1139 Q=.75/24. 1140 BLTH=CD/2. 1141 BLT BL=BLT H 1142 BLT HF=B S (1 , 1) *P**BS (1 ,2) +BS(1,3)*P+BLTH 1143 CALL PNC (BS (2, 1) , BS { 2, 2) , BS (2, 3) ,BS ( 2, 4) , XX, X XX, P ,BLTHF) 1 144 BLTHM=BS(2,1) *Q**BS (2,2) +BS (2,3) *Q+BS (2,4) 1 145 CALL PNC (BS (3,1), BS (3,2) , BS (3,3) ,BS (3,4) , XX, XXX,Q,BLTHM) 1 146 IF (BDBT.LT..00000001)BDBT=STEM (2,1) *BLTHF**ST EM (2,2) + 1 147 1ST EM (2, 3) *BLTHF+STEM (2, 4) 1148 BWRF=P-BDBT/24. 1149 CALL PNC (BS (4, 1) , BS (4 , 2) , BS (4 , 3) , BS (4 , 4) , 0 . , BLTH,BWRF,BLTHF) 1150 CALL PNC(BS(5,1) ,BS (5 ,2) ,BS (5,3),BS (5,4) ,XX,XXX,BWRF,BLTHF) 1151 BWRM=ALG2 (BS (5, 1) ,BS (5,2) , BS (5,3) ,BS(5,4) ,BLTHM) 1152 CALL PNC(BS(6,1) , BS (6,2) ,BS(6,3) ,BS(6,4) ,XX,XXX,BWRM,BLTHM) 1153 CALL VOL (BS (1, 1) , BS ( 1, 2) , BS (1, 3) ,BS (1, 4) , 0. , P, BLTHF ,BLTHL, V) 1154 BBVOLF=V 1155 CALL VOL(BS(4, 1) , BS (4,2) , BS (4,3) ,BS(4,4) , 0., B WRF, BLTHF, BLTH L, V) 1156 BWVOLF=V 1157 EBVOLF=BBVQLF-V 1158 CALL VOL(BS(2,1) ,BS (2,2) ,BS (2,3) ,BS (2,4) , P, Q, ELTHM ,BLTHF, V) 1159 BBVOLM=V 1160 CALL VOL(BS (5, 1) , BS (5 ,2) , BS (5 , 3 ) ,BS (5 , 4) , BWRF, BWRM ,BLTHM, BLTHF, V) 1161 BWVOLM=V 1162 BBVOLM=BBVOLM-V 1163 XMN=W HORL(2, 1) 1164 VAR=WHORL(2,2) 1165 NNX=W HORL(2,3) 1166 NCALC=FCT(XMN,VAR,NNX) 1167 XC=HTLC 1168 XMN^WHORL(3,1) 1169 VAR=WHORL (3, 2) 1170 89 NNX=WHORL(3,3) 1171 NPW=FCT (WHORL (3, 1) ,WHORL (3, 2) , NNX) 1172 IF (XC.GT.HT-1.5) GO TO 500 1173 IF (XC.LT.IC2) GO TO 91 1174 IF (XC.LT.YC1) GO TO 93 1175 IF (XC.LT. HT) GO TO 94 1 176 91 XMN=ALG2(CS(3, 1) , CS (3,2) ,CS (3,3) ,CS (3,4) ,XC) 1177 VAR=XMN*CS(3,6) 1178 NNX=CS(3,7) 1179 GO TO 101 1180 93 XMN=ALG2 (CS (2, 1) , CS (2,2) ,CS (2,3) ,CS (2,4) ,XC) 1181 VAR=XMN*CS(2, 6) 1182 NNX=CS(2,7) 1 183 GO TO 101 1 184 94 XMN=ALG2 (CS (1 , 1) ,CS (1 ,2) ,CS (1 ,3) ,CS (1 ,4) ,XC) 1185 VAR = XMN*CS (1 r 6) 1186 NNX=CS(1,7) 1187 101 CONTINUE 1188 DO 150 1=1,NPW 1189 IF (XMN.LE.O. ) GO TO 500 1190 IF (VAR.LE.O.)GO TO 500 1191 102 BLTH=FCT(XMN,VAR,NNX) 1192 IF(BLTH.GT.CD/2.+SD)GO TO 102 1193 IF (BLTH.LE.O. )GO TO 500 1 194 CNV=XLEAF (1) *BLTH**XLEAF (2) 1195 SUMRY (16, 3) =SDMRY (16 , 3) +CNV 1 196 WK=SHT (1) *BLTH**SHT (2) 1197 BK=SHT (3) *BLTH**SHT (4) 1 198 SUMRY (22,3) =WK+BK+SUMRY (22,3) 1199 SUMRY (23, 3) = WK+SUMRY (23, 3) 1200 SUMRY (24,3) =BK+SUMRY (24,3) 1201 BWSGF=FCT (SGA (13,1) , SGA (13, 2) , S GA ( 13 , 3) ) * 62. 4 3 1202 BBS GF=FCT (SG A (14,1) ,SGA (14,2) ,SGA (14,3) ) *62.4 3 1203 BWSGM = FCT (SGA (11,1) , SGA (11, 2) ,SGA( 11,3)) *62. 43 1204 BBSGM=FCT (SGA (12,1) ,SGA (12,2) ,SGA (12,3))*62.43 1205 BWSGL= FCT (SGA (9, 1) ,SGA (9,2) , SGA (9, 3) ) *62.43 1206 BBSGL=FCT (SGA (10,1) ,SGA (10,2) ,SGA (10 ,3) )*62. 43 1207 T B=BLTHL-BLTH 1208 IF(BLTH.GE.BLTHL)GO TO 110 12 09 IF (BLTH. GE. (BLTHL-BLTHM) ) GO TO 110 1210 IF (BLTH.GE. (BLTHL-BLTHF) ) GO TO 105 1211 BDI A=ALG2 (BS (1,1) ,BS (1,2) , BS (1, 3) , BS ( 1, 4) , TB) 1212 CALL VOL (BS (1 , 1) , BS (1,2) ,BS (1 ,3) ,BS (1 ,4) ,0. , EDI A ,T B,BLTHL, V) 1213 BBVMF=V 1214 BBIAI=ALG2 (BS (4 , 1) ,BS (4 ,2) , BS (4 ,3) ,BS (4 ,4) , T E) 1215 CALL V0L(BS (4, 1) , BS (4,2) , BS (4,3) ,BS(4,4) ,0.,BDIAI ,TB,BLTHL,V) 1216 BWVM=V 1217 B BVM F=BBVM F-V 1218 BLTHFT=BLTHFI+ BLTH 1219 GO TO 120 1220 105 BDIA=ALG2 (BS (2, 1) ,BS (2,2) , BS (2,3) ,BS (2,4) , TE) 1221 CALL VOL(BS(2, 1) , BS (2,2) , BS (2,3) ,BS(2,4) , P, BDI A ,TB ,BL THF , V) 1222 BBVMM=V 1223 BDIAI=ALG2 (BS (5, 1) ,BS(5,2) , BS (5,3) ,BS(5,4) , TB) 1224 CALL V0L(BS(5,1) ,BS (5,2) , BS (5,3) ,BS (5,4) , BWRF, BDI A I , TB, BLT HF, V ) 1225 BWVMM=V 12 26 BBVMM=BBVMM-V 12 27 BWVMF=BWVOLF 1228 BBVM F=BBVOLF 1229 BLTHFT=BLTHL-BLTH F+BLTHFT 1230 BLTHMT=BLTHMT+BLTHF-BLTHM 1231 GO TO 120 123 2 110 B DIA=ALG2 (BS (3 , 1) , BS (3 ,2) , BS (3 , 3 ) , BS (3 ,4) , T B) 1233 xx=o. 1234 XXX=BS (3,4) -TB 1235 CALL VOL (BS (3, 1) , BS (3,2) , BS (3, 3) ,XXX,Q,BDIA, XX,BLTHM,V) 1236 BBVML=V 1237 BDIAI=ALG2 (BS (6,1) ,BS(6,2) , BS (6,3) ,BS(6,4) , TB) 1238 XXX=BS(6,4) -TB 1239 CALL VOL(BS (6, 1) , BS (6 , 2) , BS (6,3) ,XXX,BWRM, BDI Al , XX ,BLTHM, V) 1240 BWVML=V 124 1 BBVML=BBVML-V 1242 BBVMF=BBVOLF 124 3 BWVMF=BWVOLF 1244 BBVMM=BBVOLM 1245 BWVMM=BHVOLM 1246 BLTHFT=BLTHL-BLTH F+ BLT HFT 1247 BLTHMT=BLTHF-BLTHM+BLTHMT 1248 BLTHLT=BLTHH +BLTH-BLTHL +BLTHLT 1249 120 EBBMF=BBBMF + BBVMF *BBSGF 1250 BBBMM=BBBMM + BBVMM*BBSGM 1251 BBBML=BBBML+BBVML*BBSGL 1252 BWBMF=BHBMF+BHVMF*BWSGF 1253 BWBMM=BWBMM+BWVMM*BWSGM 1254 BWBML=BWBML+EWVML*BWSGL 1255 BWVF=BWVMF+BWVF 1256 BWVM=BWVMM+BSVM 1257 BWVL=BWVML+BWVL 1258 BBVF=BBVMF + B BVF 1259 BBVM=BBVMM +BBVM 1260 BBVL=BBVML+BB VI 1261 CG (18)=XC*(BBVMF*BBS GF+BBVMM*8BSGM + BBVML*BBSG L + B WVMF*BWSGF+BWVMM* 1262 1BWSGM+BWVML*BWSGL+CNV + BK+WK) +CG (18) 126 3 BLTHT=BLIHT+BLTH 1264 NPT=NPT+1 1265 150 CONTINUE 1266 XMN=WHORL (1 ,1) 1267 VAR=WHORL (1,2) 1268 NNX=WHORL (1,3) 1269 DIST=FCT(XMN,VAR,NNX) 1270 XC=DIST+XC 1271 GO TO 89 1272 500 CONTINUE 1273 EEBM=BBBM F+BBBMM+BBBML 1274 BWBM=BWBMF+BWBMH+BWBML 1275 B BM=BBBM +BWBM 1276 BWV=BWVF+BWVM+BWVL 1277 EBV=BBVF+BBVM + BBVL 1278 U=BBM+SUMRY(16,3)+SUMRY(22,3) 1279 IF(U.GT.O.) 1280 1CG (18) =CG (18) / (BBM+SUMRY (1 6, 3 ) +SUM RY (22 , 3) ) 1281 BBMF=BBBMF+BWBMF 1282 BBMM=BBBMM+BWBBM 1283 BBML=BBBML+BWBML 1284 SUMRY (6,3) =BBM 1285 SUMRY (7,3)=BBML 1286 SUMRY(10,3)=BBMH 1287 SUMRY (13,3) = B BMF 1288 SUMRY(8,3) =BWBML 1289 SUMRY (11, 3) = BWBMM 1290 SUMRY(14,3) = EWBMF 1291 SUMRY (9 , 3) = BBBHL 1292 SUMRY(12,3)=EBBMM 1293 SUMRY (15,3) = BBBMF 12 94 SUMRY (5,3) =SDMRY (16 ,3) + SUMRY (6,3) 1295 RETURN 1296 END 1297 SUBROUTINE LE AF1 1298 COMMON/BLK2/BAC(8,2) ,RUCZ (8,5) 1299 COMMON/BLK4/DBH,BA,HT,CD,CLTH, D2H,DXCL,DXCW2,DXCL2,CNPC 1300 COMMON/BLK36/SUMRY (40 ,4) 1301 WRITE (3,1) 13 02 1 FORMAT(5HLEAF1) 1303 C REFER TO TEXT 1304 CNBM=BAC (8,1) +BAC (8,2) *BA 1305 SUMRY (16, 1) =CNBM 1306 RETURN 13 07 END 1308 SUBROUTINE LEAF2 1309 COMMON/BLK2/BAC (8,2) ,RUCZ (8, 5) 1310 COM MON/BLK4/DBH,BA,HT,CD,CLTH,C2H,DXCL,DXCW2,EXCL2,CNPC 1311 COMMON/BLK3 6/S OMR Y (40, 4) 1312 WRITE(3,1) 13 13 1 FORMAT(5HLEAF2) 1314 C REFER TO TEXT 1315 CNBM=RUCZ (8, 1) +RUCZ(8,2) *D2 H+RUCZ (8 , 3) *DXCL+R UCZ (8 , 4) *DXCW2 1316 1 + RUCZ(8,5)*DXCL2 1317 SUMRY (16,2) = CNBM 1318 RETURN 1319 END 1320 SUBROUTINE CRHS1 13 21 COMMON/BLK2/B AC (8,2) , RUCZ (8, 5) 13 22. COMMON/BLK4/DBH , BA , HT ,CD , CITH , D2H , DXCL , DXCW2 , EXCL2,CNPC 13 23 COM MON/BLK3 6/S (J MR Y (40,4) 1324 WRITE (3,1) 1325 1 FORMAT(5HCRWN1) 1326 CBM=BAC (4,1) +BAC (4 ,2)*BA 1327 SUMRY (5,1) =CBM 1328 RETURN 1329 END 1330 SUBROUTINE CRWN2 1331 COMMON/BLK2/BAC (8,2) , RUCZ (8, 5) 1332 COMMON/BLK4/DBH,BA,HT,CD,CLTH,D2B,DXCL,DXCW2,DXCL2,CNPC 1333 COMMON/BLK36/SUMRY(4 0,4) 1334 WRITE(3,1) 1335 1 FORMAT(5HCRWN2) 1336 C REFER TO TEXT 1337 CBM=BUCZ(4,1) +RUCZ (4 , 2) *D2H+RUCZ (4 , 3) *DXCL+RUCZ (4 ,4) *DXCW2 1338 1 + RUCZ(4,5)*DXCL2 1339 SUMRY (5,2) =CBM 1340 RETURN 1341 END 1342 SUBROUTINE TREE1 134 3 COM MON/BL K2/ E AC (8,2) ,RUCZ (8, 5) 1344 C0MM0N/BLK4/D BH,BA,HT,CD,CITH,D2H,DXCL,DXCW2,DXCL2,CNPC 1345 COMMON/BLK36/SUMRY(40,4) 1346 WRITE(3,1) 1347 C REFER TO TEXT 1348 1 FORMAT(5HTREE1) 1349 T BM=BAC (1,1) +BAC(1,2)*BA 1350 SUMRY (1 ,1) =TBH 1351 RETURN 1352 END 1353 SUBROUTINE TREE2 1354 COMMON/BLK2/EAC(8,2) ,RUCZ (8,5) 1355 COMMON/BLK4/D BH,EA,HT,CD, CLTH,D2H,DXCL,DXCW2,DXCL2,CNPC 1356 COMMON/BLK3 6/SUMR Y (40,4) 1357 WRITE(3,1) 1358 1 FORMAT(5HTREE2) 1359 C REFER TO TEXT 1360 TBM = RBCZ (1 ,1) +RUCZ (1 ,2) *02H+RUCZ (1 ,3) *DXCL+RU CZ (1 ,4) *DXCW2 1361 1 +RUCZ (1,5) *DXCL2 1362 SUMRY(1,2)=TBM 1363 RETURN 1364 END 1365 SUBROUTINE TREE3 1366 COMMON/BLK36/SUMRY(40,4) 1367 WRITE(3,1) 1368 1 FORMAT(5HTREE3) 1369 C A SUMMATION OF PREVIOUSLY CALCULATED WEIGHTS 1370 SUMRY (1,3) =S0MRY (2,3) +SUMRY (5,3) 1371 RETURN 1372 END 1373 SUBROUTINE SLASH 1374 COMMON/BLK36/SUMRY (40 ,4) 13 75 COMMON/BLK40/SPHT,TDIA,PCCR,SPPC,SPBPC 1376 COM MON/BL K45/TNH,UMTWBM,UMTBBM,UMTBM 1377 IF (SUMRY (3,3) .LT. .000001) CALL SLCALC 1378 WRITE(6,98) 1379 WRITE(6,100) 1380 98 FORMAT(1H1,18HSLASH CALCULATIONS,//) 1381 100 FORMAT(15X,11HBASAL AREA ,8X,11HOTHER ,3X,11HMODEL ,//) 1382 C UMTBM = UNMERCHANTABLE TOP WEIGHT, PCCR = PER CENT REMAINING AFTER HARVEST 1383 C THE WRITE STATEMENTS IN WRITE1 DEFINE SUMRY 1384 T 1 = UMTBM + SUMR¥ (36,1) +SUMRY (5, 1) *PCCR 1385 T2=UMTBM + SUMRY (36,2) +SUMRY (5, 2) *PCCR 1386 T3=UMTBM + SUMRY (36,3) +SUMRY (5,3) *PCCR 1387 ¥RITE(6,102)T1,T2,T3 1388 102 FORMAT (1X,11 H TOTAL SLASH,3 (2X,F11.3)) 1389 T 1=SDM RY(3 6,1) 1390 T2=SUMRY(36,2) 1391 T3=SUMRY (36, 3) 1392 WRITE(6,104)T1,T2,T3 1393 104 FORMAT (1X , 11 H STUMP , 3 (2X, F 11. 3) ) 1394 T1=SUMRY(37,1) 1395 T2=SUMRY (37,2) 1396 T3=SUMRY(37,3) 1397 WRITE(6, 106) T1,T2,T3 1398 106 FORMAT (1X, 11 H WOOD , 3 (2 X,F 11. 3) ) 1399 T1=SDM RY(38,1) 1400 T2=SUMRY (38,2) 14 01 T3=SUMRY (38, 3) 1402 WRITE(6,108) T1 ,T2,T3 1403 108 FORMAT (1X, 11 H BARK , 3 (2X, F1 1. 3) ) 1404 T1=0. 1405 T2=0. 14 06 T3=UMTBM 1407 WRITE(6,110)T1,T2,T3 1408 110 FORMAT(1X,11H STEM , 3 (2 X, F11. 3) ) 1409 T3=UMTWBM 1410 WRITE(6 ,1 12) T1 ,T2,T3 14 11 112 FORMAT (1X , 11 H WOOD , 3 (2 X, F 1 1. 3) ) 1412 T 3 =U M TB B M 1413 WRITE(6, 114) T1,T2,T3 1414 114 FORMAT(1X,11H BARK , 3 (2 X, F11. 3) ) 14 15 T1=SUM RY(5,1)*PCCR 1416 T2=SUMRY(5,2)*PCCR 1417 T3=S0MRY(5,3)*PCCR 1418 WRITE(6,116) T1,T2,T3 1419 116 FORMAT (1X, 11 H CROWN , 3 (2X, F 1 1. 3) ) 14 20 T1=PCCR* (SUMRY (7, 1) + SUMRY (1 0 , 1)+SU M RY (13 , 1) ) 14 21 T2= PCCR* (SUMRY (7,2) + SUMRY (10,2) +SUMRY (13,2) ) 1422 T3 = PCCR* (SUMRY (7,3)+SUMRY (10,3)+SUMRY (13,3) ) 1423 WRITE(6,118) T1,T2,T3 1424 118 FORMAT(1X,11H BRANCHES , 3 (2 X, F11. 3) ) 1425 T 1 = PCCR* (SUMRY (8, 1) • SUMRY (11, 1) +SDM RY (14, 1) ) 14 26 T2=PCCR* (SUMRY (8, 2) + SUMRY (11 ,2) +SUMRY (14,2) ) 1427 T3 = PCCR* (SUMRY (8,3)+SUMRY (11, 3)+SUMRY ( 1 4, 3) ) 1428 WRITE(6,120) T1,T2,T3 1429 120 FORMAT (1X, 11 H WOOD , 3 (2X, F 1 1. 3) ) 14 30 T1 = PCCR* (SUMRY (9,1) + SDMRY (12, 1)+SUBRY (15, 1) ) 14 31 T2=PCCR* (SUMRY (9,2) + SUMRY (12,2) +SUMRY (15,2) ) 143 2 T3 = PCCR* (SUMRY (9,3)+SUMRY (12,3)+SUMRY (15,3) ) 1433 WRITE(6, 122) T1,T2,T3 1434 122 FORMAT(1X,11H BARK ,3(2X,F11.3)) 1435 T1=S0MRY(7,1)*PCCR 1436 T2=SUMBY (7,2) *PCCR 1437 T3=S0MRY(7,3)*PCCR 1438 WRITE (6 ,124) T1 ,T2,T3 1439 124 FORMAT (1X, 11 H FINE , 3 (2X, F 11 . 3) ) 1440 T1=SUMRY(10,1)*PCCR 1441 T2=SUMRY(10,2)*PCCR 1442 T3=SUMRY{10,3)*PCCB 1443 WRITE (6, 126) T1,T2,T3 1444 126 FORMAT(1X,11H MEDIUM , 3 (2 X, F11 .3) ) 1445 T1=SUMRY(13,1)*PCCR 1446 T2=SUMBY(13,2)*PCCB 1447 T3=SUMHY(13,3)*PCCR 1448 WRITE(6 , 128) T1 ,T2,T3 1449 128 FORMAT (1X,11 H LARGE , 3 (2 X, F 1 1 . 3) ) 1450 T1=SUMRY(16,1)*PCCR 1451 T2=SUMRY (1 6, 2) *PCCR 1452 T3=SUMRY(16,3)*PCCR 1453 WRITE(6,130) T1,T2,T3 1454 130 FORMAT (1X,11 H NEEDLES , 3 (2 X, F11 . 3) ) 1455 RETURN 1456 END 1457 SUBROUTINE CSEC 1458 COMMON/BLK4/DBH,EA,HT,CD,CLTH,D2H,DXCL,DXCW2,BXCL2,CNPC 1459 COMMON/BLK33/SSEQUA(6,5) 1460 COMMON/BLK31/STEM(2,6) ,BS (6,4) 1461 COMMON/BLK3 6/S UMRY (4 0,4) 1462 COMMON/BLK38/CG (18) 1463 COMMON/BLK32/CS (3,7) 1464 COMMON/BLK44/CSS (6,6) 1465 DIMENSION AR(9,2) 14 66 WRITE (3,1) 1467 1 FORMAT(1X,4HCSEC) 1468 C THIS CAN BE DONE BY FINDING THE ELEMENTS OF CG 1469 C CROWN DIVISION AND CALCULATION OF THE LINES THAT DIVIDE THESE SECTIONS 1470 C CSS IS OF THE FORM OF CS AS EXPLAINED IN APPENDIX I I 1471 XD=0. 1472 XX=1. 14 73 XXX=2. 1474 HTLC=HT-CLTH 1475 X1 = CS(1,5) 1476 X2=CS(2,5) 1477 X3 = CD/2. 14 78 Y1=CS (1 ,1) *X1 **CS (1,2) +CS (1,3) *X1+CS (1 ,4) 1479 Y2=CS (2,1) *X2**CS (2, 2) +CS (2, 3) *X2+CS (2, 4) 14 80 Y3=CS (3,1) *X3**CS (3,2) +CS (3,3) *X3*CS (3,4) 1481 T1=HT-.3* (HT-Y1) 1482 T2=HT-.6*(HT-Y1) 1483 T3=HT-.8*(HT-Y1) 1484 CSS(1,6)=Y1 1485 CSS (2,6)=Y1 1486 CSS(3,6)=Y2 14 87 CSS (4,6)=Y2 1488 CSS(5,6)=Y3 14 89 CSS(6,6) = Y3 1490 CSS (1,5) =.7*CS (1,5) 1491 CSS (2,5)=. 4*CS (1 ,5) 1492 CSS (3,5) =.7*CS (2,5) 1493 CSS (4 ,5) = . 4*CS (2,5) 1494 CSS (5 ,5) =. 7*CS (3 ,5) 1495 CSS (6 ,5) =. 4*CS (3 ,5) 1496 B1= (HT-Y1) / (0.-X1) 14 97 B2= (Y 1-Y2) / (X1-X2) 1498 B3= (Y2-Y3) / (X2-X3) 1499 C1=Y1-B1*X1 1500 C2=Y2-B2*X2 1501 C3=¥3-B3*X3 1502 CSS (1 ,3) = (T1-Y1)/ (0.-CSS(1 ,5) ) 1503 CSS (2,3)= (T2-Y1)/(0 .-CSS (2, 5) ) 1504 CSS (1,4)=CSS (1,6) - (CSS (1,3)*CSS (1,5) ) 15 05 CSS (2,4)=CSS (2,6)- (CSS (2, 3) *CSS (2,5) ) 1506 DO 5 1=3,6 15 07 K=I-2 15 08 CSS (1,3) = (CSS (K,6)-CSS (1,6) ) / (CSS (K,5) -CSS (1,5) ) 1509 5 CSS (I,4)=CSS (1,6)-(CSS ( I , 3) *CSS (1,5) ) 1510 C CALCULATION OF THE CENTER OF MASS GF THE CROWN SECTIONS 1511 CALL AREA(XD,CS (1,2) ,B 1, C1, XD, HT , X 1, ¥ 1 , D A, DB) 1512 AR(1,2)=DB 15 13 AR(1,1)=DA 1514 CALL AREA (CSS (1, 1) ,CSS (1 ,2) , CSS (1,3) ,CSS (1 ,4) , 0. ,T 1 ,CSS (1,5) 1515 1 , CSS (1,6) ,DA, DB) 1516 AR(2,2)=DB 15 17 AR(2,1)=DA 1518 CALL AREA (CSS (2,1) ,CSS (2,2) , CSS (2,3) ,CSS (2,4) , 0. ,T2,CSS (2,5), CSS 1519 1 (2,6) ,DA,DB) 1520 AR(3,2)=DB 1521 AS(3,1)=DA 1522 CALL AREA(XD,CS (2,2) ,B2 ,C2 , X1 , Y1 ,X2 ,Y2 , DA, DB) 1523 AR(4,2)=DB 1524 AR(4,1)=DA 15 25 CALL AREA (CSS (3 , 1) , CSS (3, 2) , CSS (3 , 3) , C SS (3, 4 ) , CSS (1 , 5) ,CSS (1 , 6 ) , 1526 1CSS (3,5) ,CSS (3,6) ,DA ,DB) 1527 AR(5,2)=DB 1528 AR(5,1)=DA 15 29 CALL AREA (CSS (4,1) ,CSS (4, 2) , CSS (4,3) ,CSS (4, 4) ,CSS (2,5) ,CSS (2,6) , 1530 1CSS (4 ,5) ,CSS (4 ,6) , DA ,DB) 1531 AR(6,2)=DB 1532 AR(6,1)=DA 1533 CALL A RE A (XD,CS (3,2) ,B3,C3, X2 ,Y2,X3,Y3,DA,DB) 1534 AR(7,2)=DB 1535 AR(7,1)=DA 1536 CALL AREA(CSS (5,1) ,CSS (5,2) , CSS (5,3) , CSS (5, 4 ) , CSS (3,5) ,CSS (3,6) , 1537 1CSS (5,5) ,CSS (5,6) , DA , DB) 1538 AR(8,2)=DB 1539 AR(8,1)=DA 154 0 CALL AREA (CSS (6,1) ,CSS (6,2) , CSS (6,3) ,CSS (6,4) , CSS (4,5) ,CSS (4,6) , 1541 1CSS (6 ,5) ,CSS (6,6) ,DA,DB) 1542 AR(9,2)=DB 1543 AR(9,1)=DA 1544 S=AR (7 ,1) +AR (4, 1)+AR (1 ,1) 1545 IF(S.GT.0.) 1546 1CG (15) = (AR (1 ,2) *AR (1 ,1) +AR (4,2) *AR (4,1) +AR (7, 2 ) *A R (7 , 1) ) 1547 1/(AR(7,1) +AR{4, 1)+AR(1,1)) 1548 DO 30 J=1,7,3 1549 DO 20 1=1,2 1550 L=J+I-1 1551 K=J+I 1552 IF (AR(L,1) .LE.0.)GO TO 30 1553 20 AR (L,2) = (AR (L, 1) *AR (L,2)-AR (K, 1) *AR (K, 2) )/AR (L, 1) 1554 30 CONTINUE 1555 DO 32 1=1,7,3 1556 DO 32 J=1,2 1557 K=J-1 1558 32 AR(I+K,1)=AR (I + K, 1) - A R ( 1 +J, 1) 3559 DO 50 1=1,9 lr>6 0 K=10-I 1561 XK=K 1562 50 CG (17) =CG (1 7) + AR (1,2)* (XK/45. ) 156 3 DO 6 0 N=1,3 1564 L=4-N 1565 XL=L 1566 DO 55 1=1,7,3 1567 K = N-1 1568 S = AR(N,1) +AR (N+3 , 1) + AR (H + 6,1 ) 1569 IF (S.LE.O.) GO TO 60 1570 55 CG (16) =CG(16) + (XL/6 .) * (AR (I+ K, 1) / (A R (N , 1) +AR (N + 3, 1) +AR (N+6, 1 ) ) ) 1571 1*AR(I + K,2) 1572 60 CONTINUE 1573 XX=-144. 1574 XXX=2. 1575 XD=0. 1576 XA=0. 15 77 XB=HT 1578 XC=0. 1579 IF (SSEQUA (3, 5) . LT..001) SSEQUA (3,5) =DBH/24. 1580 CALL PNC(XX,XXX,XD,XB,XA,XB,SSEQUA (3,5) ,XD) 1581 C CALCOLATION OF A PARABOLIC STEM SHAPE 1582 CALL A RE A (XX , XXX, XA , HT ,XC , XB, SSEQU A (3 , 5) , XD, DA, DB) 1583 CG(10)=DB 1584 IF (SUMRY (1 ,1) .GT.O.) 15 85 1CG (1) = (CG (10) *SUMRY (2, 1) +CG (1 5) *SUMR¥ ( 5, 1) ) /SUMRY (1 ,1) 1586 IF (SUMRY (1 ,2) .GT.O.) 15 87 1CG (2) = (CG(10) *SUMRY (2,2) +CG (15) *SUMRY (5,2) )/SUMRY (1 ,2) 1588 IF (SUMRY (1 ,3) .GT.O.) 15 89 1 CG (3) = (CG (11) *SUMRY (2,3) +CG (15) *SUMRY (5, 3) ) /SUMRY (1 ,3) 1590 IF (SUMRY (1,1) .GT.O.) 15 91 ICG (4) = (CG (10) *SUMRY (2, 1) +CG (16) *SU MRY ( 5, 1) ) /SUMRY (1 ,1) 1592 IF (SUMRY (1,2) .GT.O.) 15 93 1CG (5) = (CG (10) *SUMRY (2, 2) +CG (16) *SUMRY (5, 2) ) /SUMR Y (1 ,2) 1594 IF (SUMRY (1 ,3) .GT.O.) 1595 1 CG (6) = (CG (11) *SUMRY (2,3) +CG (16) *SUMRY (5, 3) ) /SUMR Y (1 ,3) 1596 IF (SUMRY(1,1).GT.0.) 15 97 1 CG (7) = (CG(10) *SUMRY (2, 1) +CG (17) *SUMRY (5,1) ) /SUI1R Y (1 ,1) 1598 IF(SUMRY(1,2).GT.O.) 15 99 1CG (8) = (CG (10) *SUMRY (2,2) +CG (17) *SUMRY (5, 2) ) /SUMR Y (1 ,2) 1600 IF (SUMRY (1 ,3) .GT.O.) 16 01 1 CG (9) = (CG (11) *SUMRY (2, 3) +CG (17) *SUMRY (5, 3) ) /SUMRY (1 ,3) 16 02 RETURN 1603 END 1604 SUBROUTINE WRITE1 1605 COMMON/BLK1/TITLE(20) ,SEQ(40) 1606 COMMON/BLK4/DBH,BA,HT,CD,CLTH,D2H,DXCL,DXCW2,DXCL2,CNPC 1607 COMMON/BLK36/SUMRY (40, 4) 1608 COMMON/BLK33/SSEQUA (6 ,5) 1609 COMMON/BLK38/CG(18) 16 10 COMMON/BLK28/ELTHLT,BLTHMT,BLTHFT,BLTHT 1611 HRITE(3,1) 1612 1 FORMAT(6HWRITE1) 16 13 WRITE(6, 1000) 1614 WRITE(6,1040) (TITLE (I) , 1=1 ,20) 1615 WRITE(6,1041) DBH 1616 WRITE(6,1042)HT 1617 WRITE (6, 1043) CD 1618 WRITE(6,1044)CLTH 1619 1000 FORMAT(1H1) 1620 1040 FORMAT(20A4) 1621 1041 FORMAT (7HDBH = ,F10.5) 1622 1042 FORMAT(7 BHT = ,F10.5) 1623 1043 FORMAT (7HCD = ,F10.5) 1624 1044 FORMAT(7 HCLTH = ,F10.5) 1625 1050 FORMAT(1 4X,1 1 H BASAL AREA,2X,1 1HKURUCZ BEST,2X, 1626 1 1 1H MODEL,2 X,11H BA-MODEL,/) 1627 WRITE(6,1050) 1628 SUMRY (1,4) =SUMRY (1,1) -SUMRY (1,3) 16 29 SUMRY (2,4) =SDMRY (2,1) -SUMRY (2,3) 163 0 SUMRY (3,4) =SUMRY (3,1) - SUMRY (3,3) 1631 SUMRY (4,4)=SUMRY (4,1) -SUMRY (4,3) 163 2 SUMRY (5 , 4) =S UMRY (5,1)-SUMRY (5,3) 163 3 SUMRY (6,4)=SUMRY (6,1) -SUMRY (6,3) 1634 SUMRY (7,4) =SUMRY (7,1) -SUMRY (7,3) 1635 SUMRY (8,4)=SUMRY (8, 1)-SUMRY (8,3) 1636 SUMRY (9,4) =SI!MRY (9,1) - SUMRY (9,3) 1637 SUMR¥(10,4)=SUHRY(10,1) -SUMRY (10,3) 1638 SUMRY (11 ,4) = SUMRY (11 ,1) -SUMRY (11,3) 1639 SUMRY (12,4) =SUMRY (12, 1) -SUMRY (12,3) 1640 SUMRY(13,4)=SUMRY (13,1) -SUMRY (13,3) 164 1 SUMRY (14,4) = SUMRY (14, 1) -SUMRY (14,3) 164 2 SUMRY (15,4) = SUMRY (15 ,1) -SUMRY (15,3) 1643 SUMRY (16,4) = SUMR¥ (16 , 1) -SUMRY (16,3) 1644 SUMRY (17,4) =SU MR Y (17 ,1) -SUMRY (17,3) 1645 SUMRY (18,4) =SUMRY (18, 1) -SUMRY (18,3) 1646 SUMRY (19,4) =S UMRY (19 ,1) -SUMRY (19,3) 1647 SUMRY (36,4) = S U MR Y (36 , 1) -SUMRY (36,3) 1648 SUMRY (37,4) =SU MR Y (37 ,1) -SUMRY (37,3) 164 9 SUMRY (38, 4) =S UMRY (38, 1) -SUMRY (38,3) 1650 WRITE (6 , 1051) (SUMRY (1,3) ,.3=1,4) 1651 WRITE(6,1052) {SUMRY (2,3) ,3= 1,4) 1652 WRITE(6 ,1053) (SUMRY(3,3) ,3=1,4) 1653 WRITE(6,1054) (SUMRY(4,3) ,3=1,4) 1654 WRITE (6 ,1055) (SUMRY (5 ,3) , 3=1 ,4 ) 1655 WRITE(6, 1056) (SDMRY(6,3) ,3=1,4) 1656 WRITE(6 , 1057) (SUMRY (7 ,3) , 3=1 ,4 ) 1657 WRITE(6,1058) (SUMRY(8,3) ,3=1,4) 1658 WRITE(6,1059) (SUMRY (9 ,3) , 3=1 ,4 ) 1659 WRITE(6, 1060) (SUMRY ( 10 , 3) , 3= 1 , 4) 1660 WRITE(6 ,1061) (S UMR Y (11 ,3) ,3= 1,4) 1661 WRITE (6, 1062) (SUMRY (12,3) ,3= 1,4) 1662 WRITE(6 ,1063) (SUMRY (13,3) ,3=1,4) 1663 WRITE(6,1064) (SUHRY (14,3) ,3=1,4) 1664 WRITE(6,1065) (SUMR Y (1 5 ,3) , 3= 1 ,4 ) 1665 WRITE(6, 1066) (S UMR Y (16 , 3) , 3= 1, 4) 1666 WRITE(6,1070) (SUMRY (20 , 3) , 3= 1 ,4 ) 1667 WRITE(6, 1064) (SUMRY ( 25, 3) , 3= 1, 4) 1668 WRITE (6 ,1065) (SUMRY (26 ,3) , 3= 1 ,4 ) 1669 WRITE (6 , 10 72) SUMRY (22, 3) 1670 WRITE (6,1073) SUMRY (23,3) 1671 WRITE{6,1074) SUMRY (24, 3) 1672 WRITE(6,1075) (SUMRY (36 ,3) , 3=1 ,4 ) 1673 WRITE(6, 1064) (SUMRY (37,3) ,3=1,4) 1674 WRITE(6 ,1065) (SUMRY (38 ,3) , 3=1 ,4 ) 1675 1051 FORMAT (1X, 11HTOTAL TREE , 3 (2X, F 11. 3) , 2X, F 11 . 3/) 1676 1677 1678 1679 1680 1681 16 82 1683 1684 16 85 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 17 03 1704 1705 17 06 1707 1708 1709 17 10 1711 1712 1713 17 14 1715 1716 17 17 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 17 31 1732 1733 1734 1735 10 52 FORMAT( 1053 FORMAT( 1054 FORMAT( 10 55 FORMAT( 1056 FORMAT( 10 57 FORMAT( 1058 FORMAT( 1059 FORMAT( 1060 F ORMAT{ 10 61 FORMAT ( 1062 FORMAT( 10 63 FORMAT ( 10 64 FORMAT( 10 65 FORMAT( 1066 F ORMAT( 1070 FORMAT( 10 72 FORMAT( 10 73 FORMAT( 10 74 FORMAT( 10 75 FORMAT( 1076 FORMAT (13HBRANCH LENGTH, F10. 5,/ 113HFINE ,F10.5,/ 213 HM EDIUM ,F10.5,/ 313HLARGE ,F10.5) CALL WCG RETURN END SUBROUTINE WRITE2 COMMON/BLK2/BAC (8,2) , RUCZ (8, 5) COHMON/BLK3/FJTA (6) ,CDA (6) ,CLTHA (6) COMMON/BLK4/D BH,EA,HT,CD,CLTH,D2H,DXCL,DXCW2,DXCL2,CNPC COM MON/BL K 30/WHORL (3,3) COMMON/BLK31/STEH(2,6) ,BS (6,4) COMMON/BLK32/CS (3,7) COMMON/BLK33/SS EQUA(6,5) COMMON/BL K3 5/SG A(14,3) COM MON/BLK3 6/SU MRY(40,4) 1X,11HB0LE ,3 (2X, F1 1 .3) ,2X,F11. 3/) 1X, 11 H WOOD , 3 (2X,F 1 1 • 3) ,2X,F1 1. 3) 1X,11H BARK ,3 (2X,F1 1 • 3) ,2X,F11. 3/) 1X,11HTOTAL CROWN ,3 (2X,F11 • 3) ,2X,F11. 3/) 1X,11H BRANCH ,3 (2X,F11 -3) ,2X,F11. 3/) 1X,11H LARGE ,3 (2X,F11 .3) ,2X,F1 1. 3/) IX,1IH WOOD ,3 (2X,F11 .3) , 2X , F1 1 . 3)1X,11H BARK ,3 (2X,F11 •3) ,2X,F11. 3/) 1X,11H MEDIUM ,3 (2X,F11 .3) ,2X,F11. 3/) 1X,11H WOOD ,3 (2X,F11 .3) ,2X,F11. 3) 1X , 11 B BARK , 3 (2X,F1 1 • 3) ,2X,F11. 3/) 1X,11H FINE ,3 (2X,F11 .3) ,2X,F11. 3/) 1X , 11 H WOOD , 3 (2X,F1 1 -3) ,2X,F1 1 . 3) 1X,11H BARK ,3 (2X,F11 .3) ,2X,F11. 3/) 1X, 11H NEEDLE , 3 (2X,F 1 1 .3) ,2X,F1 1. 3/) 1X,11HR00T ,3 (2X,F1 1 . 3) ,2X,F11. 3/) 1X , 11 HBR ANCHL ET ,2 8X,F11. 3) 1X,11H WOOD ,28X,F11. 3) IX, 1 1 H BARK ,28X,F 11. 3) 1X,11HSTUMP ,3 (2X,F1 1 .3) ,2X,F11. 3/) WRITE (6, ,99) WRIT E (6 , 100) WRITE (6 ,101) (BAC (1,K) , K=1,2) WRITE(6, 102) (BAC (2,K) , K=1,2) WRITE (6, ,103) (BAC (3,K) , K=1,2) WRITE(6, 104) (BAC (4 ,K) , K=1,2) WRITE (6 r105) (BAC (5 ,K) , K=1 ,2) WRITE (6 ( ,106) (BAC (6,K) , K=1,2) WRITE (6 r107) (BAC (7,K) , K=1,2) WRITE (6, 108) (BAC (8,K) , K=1,2) WRITE (6 ,110) WRITE (6, 101) (RUCZ (1,K) ,K=1, 5) WRITE (6 ,102) (RUCZ (2,K) ,K=1,5) WRITE (6, 103) (RUCZ (3,K) ,K=1, 5) WRITE (6 ,104) (RUCZ (4 ,K) ,K=1,5) WRITE (6, , 105) (RUCZ (5,K) ,K=1,5) WRITE (6 ,106) (RUCZ (6 ,K) ,K=1,5) WRITE (6, 107) (ROCZ (7,K) ,K=1, 5) WRITE (6 ,108) (RUCZ (8,K) /K=1,5) WRITE (6, 120) WRITE (6, ,121) (HTA (J) , J= 1 ,6) WRITE(6, 121) (CDA (J) , J= 1,6) WRITE (6 ,121) (STEM (1 ,J) ,6) 1736 WRITE(6,121) (STEM (2, J) , J= 1, 6) 1737 WRITE(6,121) (CLTHA (J) ,0=1 ,6) 1738 WRITE(6,130) 1739 WRITE (6, 132) (BS (1,J) ,J=1,3) 174 0 WRITE (6,133) (BS (2,3) , J=1,3) 1741 WRITE(6,134) (BS (3 ,J) ,J= 1 ,3) 1742 WRITE(6,132) (BS (4 ,J) , J= 1, 3) 1743 WRITE(6,133) (BS (5 ,J) ,J=1 ,3) 1744 WRITE(6,134) (BS (6 , J) , J= 1, 3) 1745 DO 200 1=1,6 1746 200 WRITE (6 , 1 35) (SS EQUA (I,K) , K= 1, 5) 1747 DO 300 1=1,3 1748 300 WRITE (6 ,1 36) (CS (I ,K) ,K= 1, 3) 1749 WRITE(6,99) 1750 WRITE(6,140) 1751 WRITE (6,141) (SGA (1,K) ,K=1 ,3) 1752 WRITE(6,142) (SGA (2,K) , K=1, 3) 1753 WRITE(6,143) (SGA (3 ,K) ,K=1 ,3) 1754 WRITE(6,144) (SG A (4 ,K) , K= 1, 3) 1755 WRITE(6,145) (SGA (5,K) ,K=1 ,3) 1756 WRITE(6,146) (SG A (6 ,K) , K= 1, 3) 1757 WRITE(6,147) (SGA (7 ,K) ,K=1 ,3) 1758 WRITE(6,148) (SGA (8 ,K) , K= 1, 3) 1759 WRITE(6,161) (SGA (9,K) ,8=1 ,3) 1760 WRITE(6,162) (SGA (10,K) ,K=1,3) 1761 WRITE (6,163) (SGA (11 ,K) ,K=1 ,3 ) 1762 WRITE(6,164) (SGA (12, K) , K= 1, 3) 1763 WRITE(6,165) (SGA (13 ,K) ,K=1 ,3) 176 4 WRITE (6, 16 6) (SGA (14,K) ,K=1,3) 1765 WRITE(6,151) (WHORL (2 , J) , 0=1,3 ) 1766 WRITE(6,152) (WHORL ( 1 , J) , J= 1, 3 ) 1767 WRITE(6,153) (WHORL (3 ,J) , J=1 ,3 ) 1768 99 FORMAT (1 Hi) 1769 100 FORMAT(67HTHE FOLLOWING EQUATIONS ARE OF THE FORM—BIOMASS=BO + B 1 (B 1770 1ASAL AREA) , / , 2 1X, 2HB0 , 10X, 2HB1/) 1771 101 FORMAT (1X , 11 HTOTAL TREE , 4 (2 X, F1 1. 3) ,2X , F1 1 . 3/) 1772 102 FORMAT(1X,11HBOLE-WOOD ,4 (2X,F 1 1.3) ,2X,F11.3/) 1773 103 FORMAT (1X , 11 H BOLE-BA RK , 4 (2 X, F11. 3) ,2X , F1 1. 3/) 1774 104 FORMAT (1X , 11 HTOT AL CROWN, 4 (2X, F 1 1. 3) , 2X, F1 1. 3 /) 1775 105 F0RMAT(1X,11H LARGE , 4 (2 X, F1 1. 3) , 2X , F11. 3/) 1776 106 FORMAT (1X, 11 H MEDIUM , 4 (2X, F 1 1. 3) , 2X , F11 . 3/) 1777 107 FORMAT (1X , 11 H FINE , 4 (2 X, F1 1. 3) ,2X , F1 1. 3/) 1778 108 FORMAT (1X, 11 H NEEDLE , 4 (2X, F 11. 3) , 2X , F1 1 . 3/) 1779 110 FORMAT(90HTHE FOLLOWING EQUATIONS ARE OF THE FORM—BIOMASS=BO+B1(D 1780 12H)+B2 (DXCL) *B3 (DXCW2) +B4( (DXCL) 2) ,/22X,2HB0, 10X, 1781 22HB1,11X,2HB2,11X,2HB3,11X,2HB4) 1782 120 FORMAT(52HTHE FOLLOWING COEFFICIENTS ARE USED IN EQUATIONS OF:,/ 1783 136HHEIGHT=B0 + B1 (DBH) +B2 (SBA) +E3 (DBH**2) ,/24 HCD=B0+B 1 (DBH) +B2 (DBH** 1784 22) ,/3lHCLTH=HT- (B0+B1 (DBH) +B2 (DBH**2) ) ,/29HBDIB=BDOB- (B0 + B1 (DBH) +B 1785 32 (HT))/, 8X, 2HB0, 8X , 2HB1 , 8X, 2 HB2 ,8 X ,2 HB3 , 8X, 2 HB4 ) 1786 121 FORMAT(4X,8F10.5) 1787 130 FORMAT(48HIHE FOLLOWING COEFFICIENTS ARE FOR EQUATIONS OF:,/ 1788 19X, 15HY = A*X**EA + B*X+C,/11X,1H A,9X,2HEA,8X,1H B,9X,1HC) 1789 131 FORMAT(2HBS,4X,6F10 . 5) 1790 132 FORMAT(3HBSL,3X, 6F10.5) 1791 133 FORMAT(3HBSM,3X,6F10 . 5) 1792 1 34 FORMAT (3HBSF, 3X, 6F10.5) 1793 135 FORMAT(6HSSEQUA,6F10.2) 1794 136 FORMAT (2HCS,4X,6F10.5,1H1) 1795 140 FORMAT(76HTHE FOLLOWING REPRESENT THE MEAN, VARIANCE AND DISTRIBUT 1796 2ION OF A PARAMETER , /11X , 4HME AN, 2X , 8HV AR IANCE, 1 X, 12HDISTRIBUTION) 1797 141 FORMAT(6HSMHSGL,3F10.5) 1798 142 FORMAT(6HSMBSGL,3F10.5) 1799 143 FORMAT(6HSHWSGM,3F10.5) 1800 144 FORMAT(6HSMBSGM,3F10.5) 1801 145 FORMAT(6HSMWSGF,3F10.5) 1802 146 FORMAT(6 HSMBSGF,3 F10.5) 1803 147 FORMAT(6HBWSG ,3F10.5) 1804 148 FORMAT (6BBBSG ,3F10.5) 1805 1 51 FORMAT(6HNW ,3F10.5) 1806 152 FORMAT (6HDBW ,3F10.5) 18 07 153 FORMAT(6HNPW ,3F10.5) 1808 1 54 FORMAT (6HNWPL ,3F10.5) 1809 1 55 FORMAT(6 HNPC ,3F10.5) 1810 161 FORMAT (6HBWSGL ,3F10.5) 1811 162 FORMAT(6HBBSGL ,3F10.5) 1812 1 63 FORMAT(6HBWSGM ,3F10.5) 1813 164 FORMAT(6HBBSGM ,3F10.5) 1814 1 65 FORMAT (6HBWSGF ,3F10.5) 1815 166 FORMAT(6HBBSGF ,3F10.5) 1816 RETURN 1817 END 1818 SUBROUTINE WCG 1819 COMMON/BLK3 6/SU MRY (40,4) 1820 COMMON/BLK38/CG (18) 1821 WRITE(3, 1) 1822 1 FORMAT(1X,3HWCG) 1823 WRITE (6, 1999) 1824 WRITE(6,2001) 1825 WRITE(6,2002) CG (1) 1826 WRITE(6,2003) CG (2) 1827 WRITE(6,2004) CG (3) 1828 WRITE(6,2005) CG (4) 1829 WRITE (6,2006) CG (5) 1830 WRITE(6,2007) CG (6) 1831 WRITE(6,2008) CG (7) 1832 WRITE (6,2009) CG (8) 1833 WRITE(6,2010) CG (9) 1834 WRITE (6, 20 11) CG (10) 1835 WRITE (6,2012) CG (1 1) 1836 WRIT E (6, 201 3) CG (12) 1837 WRITE(6,2014) CG (13) 1838 WRITE(6,2015) CG (14) 1839 WRITE (6,201 6) CG (15) 1840 WRITE(6,2017) CG (16) 1841 WRITE(6,2018) CG (17) 1842 WRITE(6,2019) CG (18) 184 3 1999 FORMAT (1H1) 1844 2001 FORMAT(1X,9 HCOMPONENT,2X,21H ,2X,21HHETHOD OF 1845 1CALCULATING,2X,17HCENTER OF GRAVITY/12X,6HWEIGHT,17X,5HCROWN,12X, 1846 24HSTEM) 1847 2002 FORMAT(1X,4HTREE,7X,2HBA,44X,F17.2) 184 8 2003 FORMAT (1X,4HTREE,7X,5HOTHER,41X,F17.2) 1849 2004 FORMAT(1X,4HTREE,7X,9HGEOaETRIC,37X,F17.2) 185 0 2005 FORMAT(1X,4HTREE,7X,2HBA,22X,3HNU1,19X,F17.2) 1851 2006 FORMAT(1X,4HTREE,7X,5 BOTHER,19X,3HNU1,19X,F17.2) 1852 2007 FORMAT(1X,4HTREE,7X,9HGE0METRIC,15X,3HNU1,19X,F17 .2) 1853 2008 FORMAT(1X,4HTREE,7X,2HBA,22X,3HNU2,19X,F17.2) 1854 2009 FORMAT(1X,4HTREE,7X,5HOTHER, 19X,3HNU2,19X,F17.2) 1855 2010 FORMAT(1X,4HTREE,7X,9 HGEOMETRIC,15X,3HNU2,19X,F17 .2) 1856 2011 FORMAT(1X,4HSTEM,7X,10BBA + OTHER,36X,F17.2) 1857 2012 FORMAT(1X,4HSTEM,7X,9HGEOMETRIC,37X,F17.2) 1858 2013 FORMAT(1X,4HSTEM,7X,9HGEOMETRIC,32X,3HNU1,2X,F17.2) 1859 2014 FORMAT(1X,5H HOOD,6 X ,9 EGEOMET RIC, 3 2X , 3 B8 01 , 2 X , F 17 . 2) 1860 2015 FORMAT(1X,5H BARK ,6 X ,9 HGEOMETR IC, 32X, 3HNU1,2X,F17.2) 1861 2016 FORMAT(1H0,5HCROWN,6X,10HBA + OTHEB,36X,F17.2) 1862 2017 FORMAT(1X,5HCROWN,6X,10HBA + OTHER,14X,3HNU1,19X,F17.2) 1863 2018 FORMAT(1X,5HCROWN,6X,10HBA + OTH ER , 1 4X , 3 HNU2 , 19X, F17 . 2) 1864 2019 FORMAT(1X,8HBRANCHES,3X,9HGEOMETRIC,37X,F17.2) 1865 RETURN 1866 END BBS OF FILE $SIG 

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