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Investigation of methods to determine economic recoverability of timber inventories on a regional basis Cooney, Timothy Martin 1981

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INVESTIGATION OF METHODS TO DETERMINE ECONOMIC RECOVERABILITY OF TIMBER INVENTORIES ON A REGIONAL BASIS by TIMOTHY MARTIN COONEY B.Sc,  Michigan  State  University,  1976  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY in  THE (Faculty  FACULTY OF GRADUATE STUDIES  of F o r e s t r y ,  We a c c e p t to  THE  University  this  thesis  the required  as conforming standard  UNIVERSITY OF BRITISH COLUMBIA April  ©  Of B r i t i s h  1981  Timothy M a r t i n  Cooney, 1981  Columbia)  In  presenting  requirements  this thesis f o r an  of  British  it  freely available  agree for  that  understood for  Library  shall  for reference  and  study.  I  for extensive  that  h i s or copying  f i n a n c i a l gain  be  her or  shall  publication  not  be  DF-6  (2/791  of  Columbia  make  further this  thesis  head o f  this  my  It i s thesis  a l l o w e d w i t h o u t my  Forestry  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  the  representatives.  permission.  Department of  copying of  g r a n t e d by  the  University  the  p u r p o s e s may by  the  I agree that  permission  department or  f u l f i l m e n t of  advanced degree at  Columbia,  scholarly  in partial  written  ii  ABSTRACT Information inventories  on  the  becomes  harvesting  economic  recoverability  increasingly  approaches  the  important  extensive  margin.  Columbia, as elsewhere i n North America, concern temporal  a l l o c a t i o n of  understanding now  and  timber  supplies  of  timber  as  timber  In  British  for e f f i c i e n t  requires  a  greater  of the economic dimensions of timber i n v e n t o r i e s  in future years.  There  are two  when attempting inventory.  to estimate  First,  misunderstanding supply.  general c a t e g o r i e s of problems the  there  has  economic been  inventory  recoverability  action  resulted  developed In  recoverability  in  have fairly  associated either  with  measuring  discouraged  subjective  timber  further  measures  being  for large regions. this  study,  two  broad  concepts  of economic  timber  supply are d i s c u s s e d ; flow, or true economic, supply and supply. supply That  From t h i s d i s c u s s i o n i t i s shown measure  is  i s , periodic  adjusted  for  as a r e s u l t of Various estimates  of  general c o n f u s i o n or  of the meaning and measure of economic  Second, the d i f f i c u l t i e s  or  a  encountered  uses  most stocks  inflows and both of  suited of  outflows  stock-flow  a  stock-flow  to f o r e s t management needs.  recoverable  biological  that  stock  timber  which  are  that occur between p e r i o d s  and  supply  i n f o r e s t management are then  socio-economic modeling  and  presented.  forces. inventory  iii  Next, three a l t e r n a t i v e means timber  supplies  are  discussed,  of  estimating  with  reference  s t u d i e s using each a l t e r n a t i v e : (a) experienced engineering  s t u d i e s , and  enumerated  for  developing  characteristics  that  the  describes  site,  the  previous (b)  Reasons  the s t a t i s t i c a l  r e l a t i n g the o p e r a b i l i t y of l o g g i n g to tree  to  estimates,  (c) s t a t i s t i c a l models.  further  stock-flow  are  approach, stand  physical  and timber  inventory. Using British  data c o l l e c t e d  Columbia  that s i g n i f i c a n t  over  from l o g g i n g operations the  p e r i o d 1977  in  to 1979,  coastal  i t i s shown  r e l a t i o n s h i p s can be developed f o r p r e d i c t i n g  l o g g i n g o p e r a b i l i t y , using only those  c h a r a c t e r i s t i c s that are  or c o u l d be  records.  equations  included are  in  inventory  estimated  for  determining  roads r e q u i r e d for logging an area, productivity,  (c)  logs harvested, harvesting  and  falling  bucking  a specific  system. are then  for  recoverable  stock timber  stumpage  combined  with  appraisals  Log  inventory was  Market,  s u p p l i e s c o u l d be  an  estimate  others  to  of  estimated.  the  Trends in l o g g i n g c o s t s and  Columbia were developed, and  on the Research F o r e s t was  how Using  l o g p r i c e s on 1980  inventory  log  the  economic  developed for the U n i v e r s i t y of B r i t i s h  Research F o r e s t .  already  illustrate  f a c t o r c o s t s in B r i t i s h Columbia and  Vancouver  and  (e) the p r o b a b i l i t y of choosing  developed  British  (a) the length of  yarding p r o d u c t i v i t y , (d) s c a l e d volume of  These equations  current  (b)  Specifically,  Columbia  prices  in  recoverability  p r o j e c t e d through the year  2000  to  XV illustrate temporal  stock  estimates  been concluded and  collating  that new  province.  then  be  adjusted for  simlar  developments in  f a c i l i t i e s being  B r i t i s h Columbia Forest S e r v i c e following  can  flows.  It has recording  how  procedures  enhance on  inventory  implemented by  the  feasibility  the of  Timber' Supply Areas in the  V  TABLE OF CONTENTS  Title  Page  i  Abstract Table Of Contents  i i ....  v  L i s t Of Tables  ix  L i s t Of F i g u r e s  x  Acknowledgement  xi  Glossary  xiii  1 INTRODUCTION  -  1  1.1 TIMBER INVENTORIES AND ECONOMIC RECOVERABILITY ...  1  1.2 RESEARCH OBJECTIVE  4  1.3 SCOPE OF RESEARCH AND PROCEDURAL OUTLINE  5  1.4 ORGANIZATION  10  2 EONOMIC TIMBER SUPPLY -- CONCEPTS AND USES  12  2.1 CONCEPTS OF ECONOMIC TIMBER SUPPLY  12  2.11 Flow S u p p l i e s  12  2.12 Stock S u p p l i e s  23  2.2 APPLICATIONS OF STOCK-FLOW  SUPPLY MODELS  30  2.21 M u l t i p l e - u s e Planning  32  2.22 Access Planning  33  2.23 Logging  34  Planning  2.24 S i l v i c u l t u r a l 2.25 Determining  35  Optimum R o t a t i o n P e r i o d s  2.26 Y i e l d Planning 2.3 SUMMARY  Planning  ;  36 37 39  vi  3  ALTERNATIVE  METHODS  FOR  ESTIMATING  ECONOMIC TIMBER  SUPPLY  41  3.1 INTRODUCTION  41  3.2 EXPERIENCED ESTIMATES  42  3.3 ENGINEERING STUDIES  45  3.4 STATISTICAL STUDIES  47  3.5 STUDY APPROACH  53  4 RESOURCE CHARACTERISTICS  AND  LOGGING  OPERABILITY  COASTAL BRITISH COLUMBIA  IN  '  55  4.1 INTRODUCTION  55  4.2 PROCEDURAL CONCEPTS  56  4.21 Revenues And Costs  56  4.22 Cost v s . Time Studies  57  4.221  4.3  Cost Center Problems  58  4.222 Dual Vector Of Temporal Cost Changes  60  4.223 Industry Reluctance  60  4.224 Accounting D i f f e r e n c e s  60  4.23 E s t i m a t i o n by Phase of Logging  61  RESOURCE  FACTORS  AFFECTING  LOGGING  COSTS  -  DESCRIPTION  64  4.31 H a r v e s t i n g System Choice  64  4.32 Access Development  70  4.33 F a l l i n g And Bucking  72  4.34 Yarding  74  4.4 INPUT  DEMANDS  AND  PRODUCTIVITY  OF  LOGGING  IN  COASTAL BRITISH COLUMBIA  76  4.41 O b j e c t i v e  76  vii  4.42 Scope 4.43 V a r i a b l e s  78 Sampled And Measurement Procedures  4.44 Regression Hypotheses  .  And Procedures  80 82  4.45 Q u a l i t a t i v e A n a l y s i s  84  4.46 Regression A n a l y s i s  91  4.461  Road Length  (RL)  ;  4.462 F a l l i n g And Bucking P r o d u c t i v i t y 4.463 Yarding P r o d u c t i v i t y 4.464 Volume Harvested  (F&BP) ..  (YP)  93 97 101  (Q)  107  4.465 System P r o b a b i l i t i e s  109  4.5 SUMMARY  113  5 ECONOMIC TIMBER SUPPLY OF THE U.B.C. RESEARCH FOREST .. 117 5.1 INTRODUCTION  117  5.2 DESCRIPTION OF THE RESEARCH FOREST  119  5.3 PROCEDURES  124  5.31 Data C o l l e c t i o n , P r e p a r a t i o n And C o l l a t i n g ... 124 5.32 Logging Production S i m u l a t i o n  132  5.33 Costs  139  5.34 Revenues  143  5.35 P r o f i t And Risk  150  5.36 H a r v e s t i n g P r i o r i t i e s  152  5.37 Stand Growth  153  5.38 Cost And P r i c e Trends  156  5.4 RECOVERABLE TIMBER SUPPLIES ON THE U.B.C. RESEARCH FOREST: 1980-2000 5.41 M a r g i n a l Recovery 5.42 Comparative  164 Costs And Values  Inventory C h a r a c t e r i s t i c s  178 181  viii  6 CONCLUSIONS AND RECOMMENDATIONS  184  6.1 CURRENT APPLICABILITY  184  6 . 2 SUMMARY .  185  6.3 RECOMMENDATIONS  188  Bibliography Appendix  1.  192 Correlation  M a t r i c e s and  Histograms of  V a r i a b l e s used i n Logging P r o d u c t i v i t y , P r o d u c t i o n and • System P r o b a b i l i t y Regression Analyses Appendix  2.  L i s t i n g of  Developed f o r  Computer  Determining  202  Program  Recoverable  (ETS)  Timber Stocks  S u p p l i e s and Simulating P e r i o d i c Flow Adjustments Appendix  3.  U.B.C.  Research Forest  Economic  ....  Inventory  Data Appendix (DBH)  221  262 4.  C o e f f i c e n t s of  Height  (HGT),  Diameter  and Stand Density (SPH) Decadal Growth Equations 274  Appendix  5.  Annual  S u p p l i e s on the  Reports of University  Research F o r e s t : 1982-2000  Of  Economic British  Timber Columbia 276  ix  L I S T OF  TABLES  Table  1.  Page  Possible C o m b i n a t i o n s of Productivity in Determining L o g g i n g Cost Changes F a c t o r s and  Factor C o s t s and D i r e c t i o n of Unit  Identified Variables  2.  Resource  3.  Variable Statistics: Minimum and Maximum  4.  Beta Coefficients for Productivity Equation  5.  Beta Coefficients Equation '  6.  Beta Coefficients for P r o b a b i l i t y Equations  7.  L o g g i n g C o s t s By Component  141  8.  Log Prices U s e d i n R e v e n u e C a l c u l a t i o n s -- By S p e c i e s , D i a m e t e r L i m i t s And G r a d e C a t e g o r i e s  147?  9.  Real Wage Rates, Price Indices, P r o d u c t i o n , and F a c t o r C o s t s : 1 9 8 0 - 2 0 0 0  161  Mean, S t a n d a r d Falling  for  Supply of  Logging  Deviation,  and  Yarding „ .. ..  3ucking  Productivity  System  Economically  .  61  Linear  Annual  10.  1980 Stock Timber  11.  Report  12.  Summary R e p o r t Of E c o n o m i c Timber Supplies On The University Of British Columbia Research F o r e s t 1980 To 2000  of P r o j e c t e d Logging  Accessible  f o r 1981  81 86 99 102 109  167 172  174  X  LIST OF FIGURES  Figure  Page  la.  H y p o t h e t i c a l T o t a l Revenue and Cost Curves  14  lb.  H y p o t h e t i c a l Net Revenue Curve  14  lc.  H y p o t h e t i c a l Marginal Revenue  2.  and Cost Curves  14  Gross P h y s i c a l and Recoverable Stock Timber S u p p l i e s on a H y p o t h e t i c a l Management Unit  26  Change i n Recoverable Stock Over Time ( t ) , Under C o n d i t i o n s of I n c r e a s i n g P r o d u c t i v i t y ( a l l E l s e Constant)  29  Change i n Recoverable Stock Over Time ( t ) , Under C o n d i t i o n s of Increasing Factor C o s t s , Log P r i c e s and P r o d u c t i v i t y .  29  4.  Road Length  95  5.  Economic Timber  6.  U.B.C. Research Distribution  7.  Illustration  8.  Average Grade D i s t r i b u t i o n of Annual Harvests on the Research F o r e s t : 1968-1979  147  9.  P r o j e c t e d Real Log P r i c e s And Logging B r i t i s h Columbia: 1980 - 2000  163  3a.  3b.  10.  (A = lha) Supply Modeling Procedures Forest  Primary  118 Cover  Of Hauling D i s t a n c e Concept  Stocks Of Timber In P h y s i c a l And I n v e n t o r i e s On The University Of Columbia Research F o r e s t : 1980 - 2000  128  Costs  12.  In  Economic British  11a. 1980 ' T o t a l Cost and Revenue Curves Logging on the U.B.C. Research Forest lib.  121  175 180  1980 Marginal Cost and Revenue Curves Logging on the U.B.C. Research Forest  180  Recoverable v s . Non-recoverable Inventory C h a r a c t e r i s t i c s on the U.B.C. Research F o r e s t  183  XX  ACKNOWLEDGEMENT I would l i k e to provided  by  an area  of  direction  The  For  and  I  would  Limited),  Mr. B. D e v i t t  Dr. P. C o t t e l l  Mr. S. Chester  (Rayonier  Forest  and  Service)  appreciated.  cooperation during  (Pacific  (MacMillan  Logging  Company  Canada (B.C.) L i m i t e d ) , and, I  would  data  was  collected.  of Mr. G. Nagy ( B r i t i s h  data  Mr. P. Sanders  a s s i s t a n c e during  and  also  the a s s i s t a n c e of t h e i r management and  s t a f f a t the d i v i s i o n s from which assistance  this  (Canadian  Mr. H. K. W i l l i a m s  D. Thompson (Weldwood of Canada L i m i t e d ) . acknowledge  complete  (British  Limited),  and  of  to  l i k e to thank Mr. G. Boothroyd  Bloedel  to  provided  logging  Limited),  like  has  appreciated.  Products  Mr.  In a d d i t i o n  as well as the enthusiasm,  advice  Forest  Mr. D. Gyton  assistance  in o b t a i n i n g data on coast  Columbia F o r e s t Products  Limited),  the  Dr. Haley  necessary  was a l s o g r e a t l y  t h e i r cooperation  operations,  advice,  support  review  Dr. D. W i l l i a m s  research,  and  f r i e n d s h i p and f i n a n c i a l thesis.  acknowledge  my t h e s i s a d v i s o r , Dr. David Haley.  to suggesting continuous  gratefully  collection, provided  was  also  The  Columbia greatly  both h e l p f u l comments  the c o l l e c t i o n of inventory  data  on the  U n i v e r s i t y of B r i t i s h Columbia Research F o r e s t . Financial the  assistance  N a t i o n a l ' Sciences  Canada;  and  Assi stantships.  Canadian  f o r t h i s research was provided by  and  Engineering  Forestry  Service  Research Graduate  Council, Research  xix  Finally, Beverly,  the a s s i s t a n c e  made i t p o s s i b l e  and unending support of my  to c a r r y t h i s p r o j e c t  wife,  through to i t s  completion. Timothy M. Cooney Vancouver, B.C. A p r i l , 1981  xiii  GLOSSARY  General AAC AR ATC (AC) AVC cm c . u. cunit dbh DW G ha m MC MR m , cu.m. NR P Q Q 3  Q/t R SEE t TC TFC TVC TR  a l l o w a b l e annual cut average revenue average t o t a l c o s t average v a r i a b l e c o s t cent imeters Close u t i l i z a t i o n standards 100 cubic feet (CCF) diameter at breast height Durbin-Watson "d" s t a t i s t i c (autocorrelation test) gross p h y s i c a l stock of timber at a discrete point i n time hectare(s) meters marginal c o s t marginal revenue cubic meters net revenue product p r i c e t o t a l p r o d u c t i o n f o r a d i s c r e t e p o i n t i n time economically optimal rate of p r o d u c t i o n over a given p e r i o d (economic supply) p e r i o d i c r a t e of p r o d u c t i o n recoverable stock of timber at a d i s c r e t e point in time (economic inventory) standard e r r o r of the estimate time t o t a l cost t o t a l fixed cost t o t a l v a r i a b l e cost t o t a l revenue  O p e r a b i 1 i ty Study Regression V a r i a b l e s A ALV B C D E EX F&BP F&BT GY H HL LR 0  area i n hectares log volume ( a c t u a l ) f o r 10 m l o g , i n m brush d e n s i t y index c u l l (decay, waste and breakage %) diameter at breast height i n c e n t i m e t e r s e l e v a t i o n i n meters exposed bedrock index f a l l i n g and bucking p r o d u c t i v i t y (m /hour) f a l l i n g and bucking time i n man-hours grapple y a r d i n g stand average height (merchantable) i n meters highlead yarding long-reach y a r d i n g o b s t a c l e s index 3  3  xiv  Q RL S SD SM SPH ST T V VPH YP YT Z  volume harvested i n m (net) road l e n g t h i n meters ground slope i n % s o i l depth in meters s o i l moisture index stems per hectare s o i l type index t e r r a i n index t o t a l standing timber volume in m volume per hectare yarding p r o d u c t i v i t y (m /hour) yarding time in machine-hours dummy v a r i a b l e f o r y a r d i n g system i 3  3  3  Species A b b r e v i a t i o n s B C Cy D  F H Pw Ss  A Cot Mb  balsam f i r (Abies balsamea(L.)Mi11.) western red cedar (Thuja " p l i c a t a Donn) cypress (Chamaecypar i s n o o t k a t e n s i s (D-.Don) Spach) deciduous s p e c i e s ( i n t h i s s t u d y ) : red a l d e r (Alnus rubra Bong.) black cottonwood (Populus t r i c h o c a r p a T o r r . and Gray) broadleaf maple (Acer macrophyllum Pursh) Douglas f i r (Pseudotsuga m e n z i e s i i ( M i r b . ) F r a n c o ) western hemlock! (Tsuga h e t e r o p h y l l a (Raf . ) Sarg.) western white pine' (PTnus roonticola Dougl.) s i t k a spruce (Picea s i t c h e n s i s ( B o n g . ) C a r r )  1 CHAPTER 1  INTRODUCTION  1.1  TIMBER INVENTORIES AND Determination  and  future  of the '.economic r e c o v e r a b i 1 i t y  timber  i n v e n t o r i e s has been an  of f o r e s t managers. longstanding Jackson, terms  T h i s concern  is  e x p e c t a t i o n s of timber  products  will  similarly must  shortages  have  effect  on  world  recoverable  our  measures  supply estimates  physical  assets.  assessment of U.S.  mainly  (Clawson,  be  by 1978;  fulfilled  in  ( H a i r , 1978).  demands timber  for supply on r e l a t i v e p r i c e s ,  redefine  timber  the  current  i n c r e a s i n g concern  of economic rather than p h y s i c a l s c a r c i t y understand  of  precipitated  1980); e x p e c t a t i o n s which can only  To f u l l y  of  ECONOMIC RECOVERABILITY  for  timber  supplies,  i t is clear  that  and we  of resource s t o c k s .  Currently,  ( i n v e n t o r i e s ) are a simple  accounting  As  noted  by  Zivnuska  (1967) i n h i s  Timber Resources i n a World Economy:  "From the standpoint of economic and s o c i a l i n q u i r y . . . such a concept is inadequate, s i n c e i t f a i l s to c o n s i d e r the questions of why and to whom such a stock or flow is a resource. There must be . . . the a b i l i t y to use t h i s stock or flow to the s a t i s f a c t i o n of human wants and d e s i r e s . " (p. 8). Thus,  the  true,  or economic, stock supply of timber  is  the volume that can be s u p p l i e d to an economy at a given p o i n t in time, and (Stewart,  result  1975).  in a p o t e n t i a l The  accessible  increase in s o c i a l limit  of  welfare  t h i s supply i s  2 d e f i n e d by the p o i n t at  which  volumes  change  result  social  in  welfare  no  in  with  additional  in s o c i a l welfare.  pecuniary  r e c o v e r a b l e p o r t i o n of f o r e s t timber  harvesting  terms,  the  timber  Measuring  economically  resource  i n v e n t o r i e s c o n s i s t s of  market values s u f f i c i e n t  to provide a r e t u r n , at  l e a s t equal to o p p o r t u n i t y c o s t s , to a l l f a c t o r s of p r o d u c t i o n employed  in  harvesting,  transporting,  marketing the d e s i r e d products. market  ( i . e . no  manufacturing  and  T h i s assumes e i t h e r a p e r f e c t  externalities),  or,  that  c o n s i d e r e d earn t h e i r h i g h e s t use i n timber e x t e r n a l economies or diseconomies w i l l  the  lands  being  p r o d u c t i o n and any  be  included  in  the  a n a l y s i s of net value. Current  timber  inventories  r e d e f i n e d in terms of t h e i r  economic r e c o v e r a b i l i t y w i l l provide necessary  to  ". . . economic future  timber  forecast  the  'fall  the  occurrance  measure and/or  down'. . ." (Gayle,  supplies.  This  of  extent of an  1977. p. 44)  information  is  of  importance to the determination of harvest r a t e s on lands.  Inaccurate  harvest  rates,  supply  could  estimates, v i a t h e i r  adversely  affect  supply  in  primary regulated  i n f l u e n c e on  income  generation,  employment and the general economic development of c u r r e n t and future g e n e r a t i o n s , p a r t i c u l a r l y forest  in economies dependent on the  s e c t o r (Pearse, 1976).  Accurate measures of r e c o v e r a b l e timber important  in  British  1976. p. 26) of f o r e s t Consequently,  the  Columbia,  s u p p l i e s are very  where 94.1 percent  (Pearse,  lands are p u b l i c l y owned and r e g u l a t e d .  need  to  include  social  and  economic  3 variables  in  the  assessment  explicitly  recognized  Commission  on  in  of  the  current  1976  inventory data  Report  of  the  Forest Resources in B r i t i s h Columbia;  was  Royal in which  Commissioner Pearse recommended " . . . m o d i f i c a t i o n s to the inventory to recognize f o r e s t lands that w i l l probably not be operable, at least with present technology and under p r e v a i l i n g economic conditions, relative to recoverable v a l u e s , unacceptable environmental damage, or silvicultural difficulties." (Pearse, 1976. p. 236). T h i s recommendation was provincial  forest  planning  Columbia,' 1978a. s e c t . recently  completed  (Province  of  analysis,  however,  reflect  the  that  Columbia  will  economic  characteristics  and  necessary  step' due  ,  not,  is  recoverability.  that r e c o v e r a b l i t y estimates  recoverable  forces  timber  In  this  more that  supplies.  and  resource  approach  resource now  was  critically truly  alter  values. be  by  circumstances,  to the lack of i n f o r m a t i o n on  costs  a  Columbia  between  This  for  primarily  all  relationship  imperative  inventories  in B r i t i s h  into  British  basis  defined  under  harvesting  socio-economic  (Province of  1980a-1980d).  specific  timber  incorporated  1.01), which formed the  accessibility  true  'first  guidelines  a n a l y s i s of resources  British  physical c r i t e r i a  subsequently  siteIt  improved,  defined the  a  by status  is with the of  4  1.2  RESEARCH OBJECTIVE The  final  economic timber physical  result supply  supplies:  of  is  the  any  research  simply  a  volume  statement  of  raw  combined with other p r o d u c t i v e f a c t o r s , converted  into  o b j e c t i v e of my method  of  market  the  timber  is  to  location,  inventories.  necessary  stand  to  quality  supply  develop  and  site-specific  estimates.  in  Too  often  'supply' i s l o o s e l y timber.  This  economically the  of in  used  is  the the  to  clearly  demonstrate  operability  a  that  of p h y s i c a l it  will  be  r e l a t i o n s h i p s that d e f i n e in timber h a r v e s t i n g .  uses  be,  or  need  to c l a r i f y for  forestry  delineate not  primary  characteristics  of supply theory w i l l  terms  when  supply f o r a management  However, i t w i l l be necessary  theory  be  and  qualified  which,  In a c h i e v i n g t h i s o b j e c t i v e ,  concepts  developed.  can  tree  the p r o d u c t i v i t y of input f a c t o r s used No new  of  input  develop  and  quantifying  Therefore,  e s t i m a t i n g economic timber  u n i t , using the s i t e , define  products.  research  into  economic  timber  literature physical  be,  supply the  stocks  term of  a d e f i n i t i o n of supply in an  economic sense: which i s the q u a n t i t y s u p p l i e d to a market per unit  of  Therefore, the  need  time,  over  varying  prerequisite to  applicability  explicitly of  stock  management p l a n n i n g .  to  levels  of  meeting my identify  and  product  price.  outlined objective i s  the  differences  flow supply estimates  and  in f o r e s t  5  1.3  SCOPE OF RESEARCH AND  PROCEDURAL OUTLINE  There are three l e v e l s of timber i n v e n t o r i e d on a management technologically recoverable. stocks.  given  physical  c o n s i s t of the stocks  are  (a)  recoverable,  At any  The  unit:  the  total  and,  point  stocks  measurable  ' s u p p l i e s ' that c o u l d be  in are  (c) time  standing  synonymous  of  of  of  inventory timber"  The  is  commonly  economically  forest  referred  economic f e a s i b i l i t y , intensive  and  and  stocks.  with statements to  in  forestry  i s the volume and  Assuming, r e a l i s t i c a l l y ,  that  i n any  current  p r o d u c t i o n process  precede  t e c h n o l o g i c a l advances w i l l  increase  margins  w i l l decrease  recoverable  c a t e g o r i z e d i n t o two  of  recoverability,  from the  are  stocks  sub-levels.  recoverable  if  h a r v e s t i n g are c o n s i d e r e d .  The  physical  only The  intangible,  of  can  be  to  further  f i r s t comprises  market c o s t s and  second category  in a c c e s s i b l e stocks when a l l c o s t s and  volumes  revenue of  i s the  volume  b e n e f i t s , t a n g i b l e and  h a r v e s t i n g are c o n s i d e r e d  ( i . e . the  impact  h a r v e s t i n g on the p r o d u c t i o n of p u b l i c and q u a s i - p u b l i c and  of  level.  Economically  which  they  values  extensive  then, the stock of timber economic  fixed  these  r e c o v e r a b l e stock  resource use.  the f r o n t i e r s of technology  future  are  Technological  recovering  t e c h n o l o g i c a l stock as c o n s t r a i n e d by  costs  these  volumes of p h y s i c a l stocks as c o n s t r a i n e d by  This  literature.  economically  volumes.  in  "merchantable  (b)  the most obvious as  our c u r r e n t p h y s i c a l e f f i c i e n c y level  physical,  services  is  internalized  to  the  harvesting  of  goods  decision  6  process) . Given is  the s t a t e d o b j e c t i v e of my  focused  on  economically  the  supply  level  r e c o v e r a b l e volume.  market c o s t s and of  third  the  timber  analysis  stocks --  t h i s framework,  revenues w i l l be c o n s i d e r e d  perfect  strategies  conditions,  for  necessary  to  production  corrective first  are  economically  described  imperfections  can  common  of  be  to  analyzed.  economic  theory  in  to  which  terms  of  uses  will,  timber to  supplies  some  are  investment  (Berndt  and  in:  extent,  (a)  planning,  l e n g t h s , and  define  harvest  the  associated  The  relatively  o p p o r t u n i t i e s and  high, thus  to  with  (b)  two in  harvest  are part of the  f o r e s t management.  precision  ensure  efficient  first  that r e s u l t  these, the amount of i n f o r m a t i o n and be  Some of  scheduling,  , (e) r e g u l a t i o n of  o t h e r s , 1979).  activities  form,  (c) stumpage a p p r a i s a l , (d)  the t a c t i c a l or o p e r a t i o n a l p l a n n i n g year  of  c o u l d be a p p l i e d .  uses  rotation  timber  estimates  the  calculating  This  analysis,  r e q u i r e d p r e c i s i o n of such e s t i m a t e s .  silvicultural  be  alternative  c a l c u l a t i o n and primary  can  1980).  numerous  use  been  welfare  action  supply  recoverable  intended  market  step,  clarify  (Jackson,  There  to  only  in the d i s c u s s i o n  s u p p l i e s has  the impact on s o c i a l  approach i s the  rates  the  theory and development of the proposed methodology.  c o n s i d e r e d , and  The  of  Within  Once the a c c e s s i b i l i t y of timber under  research,  a  required  proper  allocation  ranking  year For will of  of  resources.  Stumpage a p p r a i s a l r e q u i r e s the g r e a t e s t amount of  information  7 and  precision  their  fair  Columbia The  due  to  implication  and  two  reflect  of N o r t h  Thus,  there  true  (or  rotation  require  A m e r i c a can  exists  to t h e i r  a  certain  b e n e f i t s o c i e t y the most.  and  approach taken  primary  reason  of t h e a f f e c t rate  as noted  earlier.  terms  stage  in this  Additionally, debated  yield  as  conditions  study  f o r use  more.  rate  in that  can  be  biological,  c h a n g e , and  i s to develop  in strategic  as  In f a c t ,  there are  hardship  estimates  thus  for  we  estimates  yield  for c o n c e n t r a t i n g i n t h i s area  d e t e r m i n a t i o n , and  economic  or  flexibility  estimates  of community s t a b i l i t y ,  in  century  The  forests  adjustments  where p a s t e r r o r s i n h a r v e s t  result  most  Continuous  that inaccurate supply  harvest  of  available.  of e c o n o m i c a c c e s s i b i l i t y The  terms  harvest  supply  1980).  nature.  in  of  whether  l e n g t h and  socio-economic  more i n f o r m a t i o n becomes The  amount  timber.  in  strategic  to a  for  determination  least  period  r a n g e up  t h e optimum r o t a t i o n  technological  the  British  (Haley,  length  earn  in  judging  market values  rotation)  made t o r e c o v e r a b l e t i m b e r  in  i s no means o f  p r e c i s i o n due  planning  true  l a c k of m a r k e t c o m p e t i t i o n  regulation,  typical  will  particularly  i s that there  i n f o r m a t i o n and  determining  is  uses mentioned,  harvest  long-term  that a l l productive resources  This the  prices  final  ensure  value.  appraised The  to  planning. i s because  can  t h e w e l f a r e of those  who  have  society,  believe  that,  have a l r e a d y reached  r a t e c a l c u l a t i o n s may some  regulation policies  are  areas  the soon  ( R e e d , 1979).  likely  i s s u e i n f o r e s t management a t p r e s e n t  on  the  (Pearse,  most 1976),  8  thus  i t i s urgent  that c u r r e n t r e s e a r c h  economics be d i r e c t e d towards improving regulation  y i e l d planning  the a n a l y s i s  will  recoverable  inventory  changes  forest  in  mortality), productive The first both  our a b i l i t y  r e q u i r e s estimates show  can  how  be  point  of s u p p l i e s over  and r e l a t i v e s c a r c i t y among  be c a r r i e d out i n three stages. of economic timber  are  reviewed.  of  These  first  supply economic  two stages are  p r i m a r i l y by the r e s u l t s of past s t u d i e s as reported  final  literature.  stage, and focus of t h i s a n a l y s i s , concerns the  development and a p p l i c a t i o n of a economically  narrowed  In the  supply are c l a r i f i e d ;  Second', a l t e r n a t i v e methods of determining  in the f o r e s t r y and economics  available  and  resources.  supplies  The  the  expected  growth  i n i s o l a t i o n and i n r e f e r e n c e to d e s i r e d uses  supported  of  to r e f l e c t  (i.e. biological  h a r v e s t i n g technology  stage, concepts  timber  and  to analyse  estimates  adjusted  structure  analysis w i l l  measures.  recoverable  inventory to  Here,  characteristics theoretically  data.  consider  e s t i m a t i o n process only.  policy  policies.  Since time,  in f o r e s t  and and  timber In  supplies  this  development  i n the context  the  methodology  stage,  and  estimating  from  currently  the  of c o a s t a l B r i t i s h  productivity  quantitatively defined.  o b j e c t i v e s of t h i s stage are as f o l l o w s :  scope  application  interrelationships logging  for  between will  of  is the  Columbia resource be  both  S p e c i f i c a l l y , the  9 (a)  I d e n t i f y s i t e , stand and t r e e characteristics which would seem a priori to have an i n f l u e n c e on p r o d u c t i v i t y of logging i n c o a s t a l B r i t i s h Columbia.  (b) Estimate the r e l a t i o n s h i p between logging development needs and the s i t e , stand and c h a r a c t e r i s t i c s i d e n t i f i e d above.  road tree  (c) Estimate the r e l a t i o n s h i p s between p r o d u c t i v i t y and the s i t e stand and t r e e c h a r a c t e r i s t i c s i d e n t i f i e d i n (a), f o r ; ( i ) labor i n f a l l i n g and bucking, and ( i i ) capital in yarding, of major logging system(s) c u r r e n t l y i n use. I f unique relationships can 'be identified f o r more than one system, i d e n t i f y the c r i t e r i a that determine the c h o i c e of system to be used on a logging o p e r a t i o n . (d) Estimate the r e l a t i o n s h i p s between logging output ( s c a l e d volume of logs) and timber input (cruised volume of timber) as i n f l u e n c e d by the p r o d u c t i v i t i e s experienced. (e)  I l l u s t r a t e how the r e l a t i o n s h i p s determined above, when combined with information on market prices, f a c t o r c o s t s and other p r o d u c t i v i t y r e l a t i o n s h i p s , can be a p p l i e d to inventory data on a c o a s t a l management unit i n B r i t i s h Columbia to estimate the r e c o v e r a b l e stock of timber. Objective  the  (a) i s completed p r i m a r i l y  available  literature  on  logging  objectives  (b)  to (d)  relationships  in  sample  collected  region  data  of B r i t i s h Columbia, from J u l y  University B.C.)  productivity. are  was  chosen  1979 to A p r i l  fulfilling  primarily  because  resource data  application.  the  consideration  model  The  Ridge,  for i l l u s t r a t i n g  of to  1980.  (Maple  objective  a v a i l a b i l i t y of s u f f i c i e n t Finally,  from  o p e r a t i o n s i n the coast  was used as the sample management u n i t of the model i n  of The  estimated  of B r i t i s h Columbia Research Forest  application area  on 64 logging  through a search  the  (e).  perceived  expedite  i s made  This  dynamic  sample with  given to the e f f e c t s of expected trends i n stand  growth, factor, c o s t s  and resource v a l u e s , on r e c o v e r a b i l i t y of  10  the i n v e n t o r y . the  final  Although  the s p e c i f i c  relationships  used  in  stage are a p p l i c a b l e only to other management u n i t s  in the c o a s t a l region, the b a s i c procedures similarly  developed  for  the  interior  followed region  can  of  be  British  Columbia, and i n g e n e r a l , f o r other r e g u l a t e d f o r e s t s  i n North  Amer i c a .  1.4 ORGANIZATION Chapter concepts (supply  Two begins with a d i s c u s s i o n of  of  supply.  in  the  (inventories)  true  is  management.  The  Some  difference  economic  developed  sense) in  applications  the  of  the  theoretical  between flow s u p p l i e s and  stock  framework  economic  supplies of  forest  timber  supply  estimates and r e l a t i o n s h i p s w i l l c l o s e the chapter. Chapter  Three  economic timber three  supplies.  categories:  studies, Supported  and  effect  Four  basic  (a) experienced estimates, and  forestry  grouped  into  (b) e n g i n e e r i n g  statistical  models.  of each are d i s c u s s e d . begins  with  a  discussion  of  procedural  to the methodology I am proposing.  of resource c h a r a c t e r i s t i c s on logging  hypothesized the  The a l t e r n a t i v e s are  past s t u d i e s , the b a s i c methodology, advantages  and disadvantages  concepts  a l t e r n a t i v e means of e s t i m a t i n g  (c) mathematical  by  Chapter  presents  by phase of l o g g i n g , based literature.  The  Next, the  operability  is  upon i n f o r m a t i o n from  remainder  of  this  chapter  presents the r e s u l t s of r e g r e s s i o n analyses on l o g g i n g data  11 for  c o a s t a l B r i t i s h Columbia  quantitative estimated  description  i n c l u d i n g both a q u a l i t a t i v e  of  sample  Five  i l l u s t r a t e s a p p l i c a t i o n of the  r e l a t i o n s h i p s for e s t i m a t i n g inventories.  Using inventory  in B r i t i s h  Vancouver Log  Columbia  Market, an  productivity  economic r e c o v e r a b i l i t y of data a v a i l a b l e on  of B r i t i s h Columbia Research F o r e s t , and  current  current  the  prices  machine on  the  supply  Reviewing trends in log p r i c e s and  factor  i s derived.  costs,  recoverability  estimates are developed for the  - 2000, to i l l u s t r a t e adjustments for temporal  timber  University  labor and  log  timber  estimate of recoverable timber  in 1980  1981  and  equations.  Chapter  costs  characteristics  and  period  flows  in  supplies.  A brief  statement on  the c u r r e n t  a p p l i c a b i l i t y of s i m i l a r  procedures on timber supply areas in B r i t i s h Columbia i s given in  Chapter  Six.  recommendations  This for  is  followed  further  economic supply modeling in the  by  research province.  the  needed  conclusion to  and  implement  12 CHAPTER 2  EONOMIC TIMBER SUPPLY ~  CONCEPTS AND USES  2.1 CONCEPTS OF ECONOMIC TIMBER SUPPLY The  purpose of t h i s chapter  s e l e c t i n g the method of timber  supplies.  i s to set the foundation f o r  estimating  Although  economically  this  recoverable  s e c t i o n b r i e f l y covers w e l l  known n e o - c l a s s i c a l t h e o r i e s of p r o d u c t i o n and supply, necessary  to  set  these  production  i n order to c l a r i f y  for y i e l d p l a n n i n g .  It  definition  term  forth,  of  the  theories  evidenced  by  studies  a c t u a l l y statements  necessary  "supply"  of  the context of timber  the measure of supply  i s also  so as to a v o i d semantic  in  used  that  necessary the  basic  i n t h i s paper be set  confusion.  forest  i t is  This  confusion  is  resource "supply" that are  of i n v e n t o r i e s (Callahan, 1979).  2.11 Flow S u p p l i e s The sense  economic timber  is  the volume of timber  primary product a  given  level  between  supply  schedule)  supplied  i n a flow, or that w i l l  true  be made a v a i l a b l e to  of timber and  (stumpage) p r i c e .  stumpage  price  for  The r e l a t i o n s h i p  ( i . e . timber  supply  the volumes that w i l l be made a v a i l a b l e ,  time, over a range of p o s s i b l e p r i c e s .  supply  economic,  (log) markets over a given p e r i o d of time  expresses  per u n i t . o f timber  supply  schedule  and  periodic  estimates  i s , theoretically, quite straight  forward.  Deriving a of  volume  However,  13 i t w i l l be  shown l a t e r  that numerous  e m p i r i c a l a p p l i c a t i o n s of the The  following  condition factor it  receives  for  "price-takers"), sufficient run,  (Awh,  1976;  The  the  firms' i s the  the c u r r e n t of  firms  inputs.  In the  the  output  decision  are  short  production to  becomes to  and  total  ( i . e . where net (MC)  earned by  costs  firm.  the market over a  given  (TC)  of  production  revenue i s maximized).  of production the  the economic supply of the  shown in F i g u r e s  c o s t s and  2  total i s the  At t h i s  i s equal to the  l a s t u n i t of o u t p u t .  Graphically, hypothetical  given  f u n c t i o n of the  output l e v e l where the d i f f e r e n c e between  greatest  above are  (i.e. a l l  price  s i n g l e f i r m have input demands  products  (TR)  revenue (MR)  basic  o b j e c t i v e of a f i r m i s to maximize p r o f i t s ,  supply  the marginal cost  in  e x i s t s in both product . and  products  does any  revenue  output  presented under the  a problem of minimizing c o s t s with respect  p r i c e s and  period  its  nor  arise  s i n g l e producer c o n t r o l s the  I n t r i 1 i g a t o r ; 1971)  primarily input  is  t o , i n f l u e n c e market p r i c e s of  given  1  discussion  Thus, no  can  theory.  that p e r f e c t competition  markets.  problems  point  marginal  This l e v e l  of  firm. revenues as  described  productive  input  l a to l c .  1  P e r i o d of time over which at l e a s t f i x e d in q u a n t i t y .  one  is  2  Since product price (P) i s constant f o r the f i r m , p r i c e = marginal revenue = average revenue. Thus, the firm's economic supply i s that output where MC = P. It i s a l s o necessary to note that f o r p r o f i t maximization to be ensured using marginal a n a l y s i s , two " s u f f i c i e n t c o n d i t i o n s " must be met. The f i r s t order c o n d i t i o n i s f o r MC = P. The second order c o n d i t i o n i s for MC to be i n c r e a s i n g (Awh, 1976).  Figure l c . Hypothetical Marginal and Cost Curves  Revenue  15 The  f i r m ' s supply curve  p o r t i o n of i t s MC curve above  the  is clearly  represented  ( h e a v i l y shaded i n F i g .  by  that  l c ) that  lies  minimum average v a r i a b l e c o s t (AVC) of p r o d u c t i o n .  As long as p r i c e remains g r e a t e r than or equal to AVC the f i r m can continue to produce s i n c e i t can cover o p e r a t i o n a l Should  price  fall  costs.  below AVC the f i r m must c l o s e as continued  operation  i n c r e a s e s the  size  (average  total  the f i r m c o n t i n u e s o p e r a t i o n so as to  cost),  of  losses.  minimize the l o s s e s to f i x e d c o s t s incur  AVC < P < ATC  i t would  otherwise  (Awh, 1976). Assuming  not a f f e c t  industry-wide changes i n p r o d u c t i o n l e v e l s  f a c t o r p r i c e s , the i n d u s t r y supply curve  the summation of i n d i v i d u a l If  that  If  is  f i r m s u p p l i e s at a l l p r i c e  industry-wide changes i n p r o d u c t i o n r e s u l t  set  The i n d u s t r y supply curve  in factor  levels.  Analysis can be  freely  production, variable. concept sense.  of  Also, since  at the  (Awh, 1976).  main the  is  similar  difference long-run  a l l inputs  can  to being  is  that  for  that  essentially  short-run  a l l c o s t s are a  planning  be v a r i e d only i n a d i s c r e t e  Changing the q u a n t i t i e s of f i x e d  immediately  supply  production i n the long run, when a l l inputs  varied,  the  price  i s then the summation of the  of p o i n t s connecting each f i r m ' s new supply curve  higher output  simply levels.  i n c r e a s e s , each f i r m operates on a higher cost and thus curve.  will  i n t o a new short-run c o s t  inputs moves the f i r m  structure.  16 Jackson  (1980) has  p r o d u c t i o n and supply production  theory  investigated  of  theory  as  timber  d e s c r i b e d above. increment  Jackson's  production  (MAI, i . e . the flow  or  p r o d u c t i o n ) , to time and the l e v e l of inputs used to  e s t a b l i s h a growing conditions  of  stock  perfect  after  harvesting.  competition,  would maximize present wealth  Under  of  (profits).  Specifically,  h a r v e s t s ; that i s , revenue at harvest  p r i c e x vol./acre harvested), less establishment  stated  i t was assumed the firm  assumed that a f i r m w i l l attempt to maximize the value  of  i n the context of n e o - c l a s s i c a l economic  f u n c t i o n r e l a t e d mean annual rate  the  the  (unit cost of establishment  net  i t was present  (net stumpage  compounded  costs  of  inputs x q u a n t i t y of  inputs used), discounted to the p r e s e n t . Holding  the  supply of land, u n i t establishment  net stumpage p r i c e constant,  i t was shown that a f i r m ' s market  r a t e of harvest was a f u n c t i o n of both q u a n t i t y rotation 1980.  age  and  pp. 22-23).  determined  the  of  output  over  As  harvests.  price  a l l time p e r i o d s .  to  at  (Jackson,  increase  he  i n establishment to  higher  However, marginal  stand would approach marginal  p r o d u c t i o n at an e a r l i e r  frequency  available  ( y i e l d ) f u n c t i o n would s h i f t  value growth of the timber of  timber  of  t h a t , due to i n c r e a s e d investment  i n p u t s , the production levels  "frequency"  Allowing  cost and  r o t a t i o n age, thus  cost  i n c r e a s i n g the  but reducing the volume of h a r v e s t s . long  as  production  level  increase,  i t was  the  mean  annual  increment  at  the  new  i s g r e a t e r than the l e v e l p r i o r to the p r i c e shown  that  marginal  costs  of  timber  17 production  will  increase  Hence, supply w i l l timber  prices  demonstrate  with i n c r e a s i n g p r o d u c t i o n l e v e l s .  increase  (Jackson,  that  (as  1980.  the  analysis  with  pp. 24-25).  i n d u s t r y aggregate  by summing the supply of each with  expected)  increasing  He  went  supply c o u l d be  f i r m at v a r i o u s  determined  timber  a l s o c o n s i d e r i n g the impact  of  on to  prices,  increasing  u n i t establishment c o s t s and land supply on the e l a s t i c i t y aggregate  timber  Jackson's  supplies. work  is  a  significant  contribution  understanding of timber p r o d u c t i o n economics. to  point  supply  First,  Jackson's  growth  inventories,  determining appropriate  helps  a  assumed  neo-classical  the non-existence of o l d  ignoring  of  harvest.  the  problems  T h i s approach  the product of past p r o d u c t i o n . occurs  approach.  of  is quite  inventories  Depletion  of  at a r a t e dependent on present and  f u t u r e net timber p r i c e s , d u r a b i l i t y of the inventory decay  and  mortality),  and  o p p o r t u n i t y c o s t of c a p i t a l .  timber  inventories  recoverability cannot  determining  annual  the  private  However, i n an  analysis  be ignored where i t comprises  the bulk of  timber  stocks.  in  (or  old-growth  western  volume  North  supplies  know the r e c o v e r a b i l i t y of old-growth c u r r e n t growing  the  mature  harvested timber, as i n  of  also  i n a p r o d u c t i o n study s i n c e o l d growth  ( i . e . r a t e of  of  on  thereby rate  inventories  social)  based  analysis  their  are e s s e n t i a l l y  expected  It  to the  out some of the problems a s s o c i a t e d with e s t i m a t i n g  economic timber  these  of  America.  Hence,  in  i t w i l l be necessary to stocks, as w e l l as  that  18 A  second  applied  problem,  timber  determination production  possibly  production  function  t h e most p e r v a s i v e i n  economics,  and a p p l i c a b i l i t y  homogeneous o u t p u t  concerns  represents  the  maximum  Jackson  firm  each  productive  characteristics  and  would  capacity, homogeneous  be with  inputs  t h e impact of r i s i n g  limited  supplies  land  of  c o n s i d e r a t i o n was g i v e n  with respect species,  to  productive  aggregation estimate will  influence  within  capacities,  accessibility,  assumption that  no an  may  provide  since f a c t o r s other  than  and  aggregation  F o r e x a m p l e , i f s u p p l i e s were  recoverability.  and  that f o r e s t s are heterogeneous  a l l categories  of the t o t a l ,  establishment.  factor prices  by i d e n t i f i a b l e c a t e g o r i e s o f s i t e over  species-  aggregate i n d u s t r y supply,  i t w o u l d be a r e a l i s t i c  isolation  to  t o problems of a g g r e g a t i o n  Recognizing  problems would a r i s e . in  on  production,  homogeneous  he c o n s i d e r e d  firm.  of  o p e r a t i n g on l a n d s o f  Although  individual  quantity  A  t h a t c a n be p r o d u c e d u s i n g g i v e n q u a n t i t i e s In h i s a n a l y s i s of t i m b e r  assumed  the  of aggregate r e l a t i o n s h i p s .  of homogeneous i n p u t s .  homogeneous  3  and  estimated  productivity, a misleading site  quality  3  Although annual growth on s t a n d s f o r t h e same s i t e q u a l i t y (for a given specie) will be s i m i l a r once the stand i s e s t a b l i s h e d , the inputs r e q u i r e d f o r establishment w i l l d i f f e r according t o stand a c c e s s i b i l i t y . Thus, J a c k s o n s ' a n a l y s i s i s v a l i d o n l y under f u r t h e r a s s u m p t i o n s of homogeneity of l a n d i n t e r m s o f s l o p e , t e r r a i n , e l e v a t i o n , e t c . , as w e l l a s r e q u i r i n g t h a t p r o d u c t i o n i n p u t s be c e n t r a l l y l o c a t e d t o a l l s i t e s .  19  is  An  extension  the  problem  being  defined  substitutes.  of aggregation problems w i t h i n a s i n g l e f i r m of i n d u s t r i a l aggregation.  "...  . ."  as  a  (Awh,  1976.  that a l l firms enjoy the d i s t r i b u t i o n s , and  that  distributed  among  determining  industry  adjustments  for  set  of  With an  firms  p. 264),  same species  producing  it  types  industry  must be assumed  and  timber  i n c r e a s i n g stumpage p r i c e s are  all  species.  Without  supplies  relative  would  changes  close  size  equally  this  assumption,  require  additional  among  firms  within  the  i n d u s t r y over time. The cost  d i f f i c u l t i e s of a p p l i e d aggregation in production  s t u d i e s l e d Walters (1963) to conclude  and  that:  "The variety of competitive and t e c h n o l o g i c a l c o n d i t i o n s we f i n d in modern econonomies suggests that we can not approximate the basic requirements of s e n s i b l e aggregation except, perhaps, over firms in the same i n d u s t r y or for narrow sections of the economy." (p. 11; emphasis added). In the context may  be  of timber p r o d u c t i o n ,  smaller;  or, over narrow  I f e e l the  s e n s i b l e range  i n c l u d i n g only aggregation w i t h i n sections  of  the  industry  (e.g.  the  firm,  sawtimber,  pulpwood, e t c . ) . A t h i r d area accurately'  of d i f f i c u l t y  estimate  the  i s in our  coefficients  f u n c t i o n s over the range of production as  Jackson  (1980) has,  a measure of of  input  productive  our  current of  will  result  capacity.  timber  inputs.  in higher  At present  y i e l d s on we  define,  input  increasing lands  to  production  If we  l e v e l of establishment  "management i n t e n s i t y " , then,  inability  of any  to  be  levels given  have r e l i a b l e measures  of  20 natural  growth  usually  in  the  (production) form  of  functions.  These measures are  species-site-specific  volume/age  r e l a t i o n s h i p s developed  from inventory data on n a t u r a l  However,  information  stands  insufficient  to " b a s i c " (Province of  e x i s t s on the response of  British  "intensive" s i l v i c u l t u r a l p r a c t i c e s . exist,  particularly  old-growth  timber,  production  functions  in  areas  allows for  ranges of s i t e p r o d u c t i v i t y . and/or  4  Columbia,  Information  with  a  a  few  Projections  of  for  does of  managed-stand  other  species  o u t s i d e the range of sampled p r o d u c t i v i t y must r e l y of percentage i n c r e a s e s in y i e l d s ,  upon  . . 'best  ".  guesses'  Thus, attempts at determining context sound  . . ."  aggregate timber  of n e o - c l a s s i c a l p r o d u c t i o n basis  (Smith,  u n t i l accurate  of  the  generally 1977;  on  based p.  10).  s u p p l i e s in the  theory, cannot be made  responses to establishment  management input l e v e l s can be p r e d i c t e d , over portion  which  or  s p e c i e s w i t h i n narrow  estimates  a  1980c)  preponderance  development only  stands.  a  on and  substantial  range in p r o d u c t i o n p o s s i b i l i t i e s on a given  area.  4  Essentially, basic p r a c t i c e s represent those activities c a r r i e d out to ensure r e g e n e r a t i o n of lands denuded due to logging, w i l d f i r e , d i s e a s e s and p e s t s . T h i s can be a program of p l a n t i n g , seeding or planned natural reforestation, that include the necessary s i t e p r e p a r a t i o n , brushing or weeding activities. This a l s o i n c l u d e s b a s i c p r o t e c t i o n activities. Intensive silvicultural activities are b a s i c p r a c t i c e s plus j u s t i f i a b l e investments in such a c t i v i t i e s as fertilization, commercial t h i n n i n g , s p e c i e s c o n v e r s i o n , g e n e t i c improvement, shorter r o t a t i o n s , etc. (Province of B r i t i s h Columbia, 1980c; Smith, 1977).  21 F i n a l l y , assuming the r e l e v a n t production be  identified  individual  f o r a l l ownerships,  firms  and  across  that  harvest  could  would  still  be  desired  be estimated,  c a p a b i l i t i e s of a n e o - c l a s s i c a l supply  in  doubt,  inappropriateness  function  model  objective  of  (Marty,  a  supply  estimates  of  timber  1969).  of p r o f i t maximization as an o b j e c t i v e  downward from  bias  in  i s apparent  public  o b j e c t i v e s , some i n t a n g i b l e or with  ensure  rate  due to the assumption of  in f o r e s t management p r a c t i c e s and p o l i c i e s on  values,  "sensible"  then, the p r e d i c t i v e  i n the p u b l i c sector of timber production  Alternative  could within  market  production  p r o f i t maximization as the primary The  aggregation  i n d u s t r y would y i e l d  r e s u l t s , and the r e c o v e r a b i l i t y and old-growth  functions  lands.  non-pecuniary  neo-classical  economic  the true volume of recoverable  timber  supply. The forest  same c o n c l u s i o n s land  invested  5  of  corporate  r e t u r n s to c a p i t a l  that are lower than the minimum  objectives  1972).  private  provided  existence  large  rate  i n a l t e r n a t i v e p r i v a t e investments, suggests these  have  (Gregory, the  The  i n f o r e s t lands  achievable owners  owners.  could be drawn f o r  sector  As  that  override  profit  a r e s u l t , the true supply will  also  be  greater  through a n e o - c l a s s i c a l p r o d u c t i o n  maximization of timber i n  than  study.  estimates  5  The same could be s a i d of small p r i v a t e landowners, and non-corporate, although p r o f i t maximization may r e a l i s t i c i n these i n s t a n c e s .  corporate be more  22  Having  spent  considerable  time on the disadvantages of a  n e o - c l a s s i c a l approach to timber  supply  like  importance  to  briefly  restate  f o r e s t management. the v a l i d i t y is  an  The study  by Jackson  of  would  of such models to  (1980) has r e a s s e r t e d supply  f u n c t i o n of stumpage p r i c e s i n the p r i v a t e  T h i s tenet provides a strong  analysis  I  of the b a s i c economic premise that timber  increasing  sector.  the  estimation,  government p o l i c i e s  foundation  intended  for  rational  to s t i m u l a t e  timber  production. Neo-classical addition  to  models  providing  of  production  theoretical  analysis  in  f o r e s t management.  is  justified,  and  in  for  applied  In g e n e r a l ,  are u s e f u l where p a r t i a l a n a l y s i s of inputs  supply,  structure  p o l i c y a n a l y s i s , can be u s e f u l as t o o l s and  and  response  a l l variables  in  rational planning  such models  to  management  are / r e l a t i v e l y  homogeneous. Given that there are a number management,  i t i s evident  of  p. 91),  based  upon  concepts' and procedures." this  end,  recoverable current  costs  achieve  a n a l y s i s . . ."  " . . . new m u l t i r e s o u r c e (McClure,  1979. p. 67).  of  timber  information  should on  greatly  (Marty, inventory Towards  foregoing  any number of other  net  improve  the  the q u a l i t y of timber i n  T h i s information c o u l d then be used of  forest  development of stock measures of economically  s u p p l i e s of  status  inventories. the  the  in  that ". . . a new d e c i s i o n model i s  needed that i s adapted to m u l t i - g o a l 1969.  objectives  to  measure  value maximization i n order to  o b j e c t i v e s that  may  be  explicit  23 considerations  of the landowners.  and  procedures  the  basic  accessible presented 2.12  timber,  Concepts of stock s u p p l i e s  necessary  to  measure  as w e l l as a d j u s t for flows over  stocks  of  time,  are  i n the' f o l l o w i n g s e c t i o n .  Stock  Supplies  Stock  s u p p l i e s are an accounting  of  the  quantity  good.or s e r v i c e a v a i l a b l e at a s i n g l e point in time. no  i n t e r - t e m p o r a l dimension to stock estimates.  estimated  supply  periodic  is  a  production.  measure Stock  of  availability  determined by remeasuring the supply by a d j u s t i n g i n i t i a l the  good  reflect  is  in  periodic  (inflows).  Perishable  commonly  forest  management,  encountered  extensive  amount  to our a b i l i t i e s  in the f u t u r e p e r i o d , or,  must by  outflows.  and  also the  form  of  to estimate  be  rate  If  adjustments production  adjusted of  decay  for (or  and  relation  the  to  stock  supply  models.  The  f o r e s t mensuration a t t e s t s  stock s u p p l i e s .  However,  the  flow-adjustments are concerned only  with the p h y s i c a l a t t r i b u t e s is  i n v e n t o r i e s are the most  c u r r e n t stocks, as w e l l as a d j u s t  in resource  inventories  information  timber  of l i t e r a t u r e on  for temporal flows  services  in l a t e r p e r i o d s i s  (outflows)  as measured  not  loss).  In  current  That i s , the  p e r i s h a b l e then the flow  stocks  a  There i s  quantities,  f o r inflows and  consumption  a d d i t i o n a l outflows natural  estimates  no way  total  of  of  the  forest;  little  or  no  c o l l e c t e d that allow us to d e f i n e s u p p l i e s i n values  society  provided by the f o r e s t .  places Focusing  on  the  goods  on a subset  of  and the  24  goods a f o r e s t can produce, economic  stock  supply  manufactured  of timber  welfare.  exceed  That  is,  a l l costs incurred  Hence,  information  on  products,  the  i s the q u a n t i t y that can  converted to the d e s i r e d products and social  wood  result  product  i n a net gain  of manufacturing  equal or  in b r i n g i n g the products to  market.  the q u a n t i t y of goods p r o d u c i b l e from  from stump to product,  enable economic c l a s s i f i c a t i o n  of present  The process of producing f i n a l can  be  characterized  'sub-markets' (e.g.  known  l o g ) , secondary  etc.)  and  1978).  final  in  s a l e s revenues  the standing timber, market p r i c e s of the f i n a l products, costs  be  by  a  as  the  product  product  inventories.  of  four  stumpage,  (e.g. lumber,  markets  is  timber  interrelated  primary  (e.g. f u r n i t u r e )  Assuming each of these  i s necessary to  consumer goods from  chain  and  product  chips,  plywood,  markets  (Manthy,  characterized  by  p e r f e c t c o m p e t i t i o n , the economic stock supply of timber c o u l d be  estimated  supply i s the production  at  any p o i n t along the p r o d u c t i o n c h a i n .  volume  less  of  timber  with  cumulative  This  costs  of  .than or equal to the p r i c e of the product i n  the market to which s u p p l i e s are assessed.  The  product  price  in one market i s an input cost to the succeeding market, thus, p r o d u c t i o n c o s t s need only be assessed f o r the market in which supply  is  estimated.  recovery f a c t o r s  Because of the v a r i a b i l i t y  ( our t e c h n o l o g i c a l a b i l i t y  i n product  to f u l l y  utilize  raw m a t e r i a l i n p u t s ) , supply estimates d e r i v e d at the stumpage market  should  prove  to be the most r e l i a b l e .  are two  s i t u a t i o n s i n which t h i s w i l l  not h o l d  However, there true.  First,  25 if  the  owner  has  multiple-objectives,  producing a given volume of  timber  then  for  log  the  c o s t s of  production  understate the true value of the resource to the owner. these  c o s t s are i n t a n g i b l e and/or  stock supply w i l l be l e s s market  equilibria.  than  Second,  non-pecuniary,  the if  volume  the  non-competitive, there i s no assurance reflect  true  timber  values.  are  characteristic  Thus, r e l i a b l e production,  of  supply estimates  (lumber  If  the  from  market f o r stumpage i s that  stumpage  doubt.  Columbia's depend  prices  of economic  Both  situations  stumpage market.  on  the  f o r lack of a log  analysis  analysis  acceptable.  (log) markets  market,  secondary  i s to be c a r r i e d out i n a market other  Since  of p r o f i t  product  maximization  prices  may  (implicit  in  i n t e g r a t e d firm) are determined c o m p e t i t i v e l y , producers attempt  - to  minimize  production  costs  thereby  p r o f i t s to l o g g i n g , m i l l i n g or manufacturing. the  decision  to  harvest  o b j e c t i v e w i l l most l i k e l y as measured by p r o f i t s . supply  timber  That  be to maximize economic  Under t h i s assumption  in time, log  choose  of  proximity  to  those log  stands  markets,  an will  is,  once  has been made, the primary  market p r i c e s at a s i n g l e point log  be  maximizing  efficiency,  a stock  schedule can be developed as shown i n f i g u r e 2.  to  of  and c h i p ) markets i n the I n t e r i o r .  than stumpage, the assumption more  determined  c o s t s and p r i c e s at primary product  in the Coast Region, and product  British  Where  the economic  Thus,, the v a l i d i t y  timber supply estimates would be i n  may  producers  timber Given would  timber that f o r reasons of  slope,  terrain  and  timber  26 characteristics,  can  be  harvested  at  i n c r e a s e the volume of h a r v e s t , producers successively logging  higher c o s t stands.  of harvest  have  c o u l d be c o n t i n u o u s l y  to  log  i n c r e a s e d , at some l e v e l  the cost of l o g g i n g the next succeeding  F i g . 2)  economic stock is  will  To  Assuming t h a t a l l i n p u t s to  would exceed the a d d i t i o n a l revenue (MR) in  least cost.  ( l a b o r , c a p i t a l equipment, s u p p l i e s , e t c . ) , except f o r  l a n d or timber,  (R  the  relatively  earned.  i s then a measure of the gross supply small  of timber.  Unless  the  volume This  level  recoverable  management  with homogeneous s i t e ,  (MC)  stand and  or  unit timber  c h a r a c t e r i s t i c s r e p r e s e n t i n g the e a s i e s t o p e r a t i n g  conditions  and  volume can  highest  timber  q u a l i t y , then,  t h i s recoverable  be'expected to be l e s s than the gross p h y s i c a l stock of (G*in F i g . 2 ) .  R  *  G  *  Figure 2. Gross P h y s i c a l and Recoverable Stock Timber S u p p l i e s on a Hypothetical Management U n i t  timber  27 The include  costs  (temporary)  transport sorting, profit in  considered  in  road,  deriving  falling  the  and  MC  bucking,  primary  (yarding or s k i d d i n g ) , l o a d i n g , h a u l i n g , unloading, s c a l i n g , booming, t e r t i a r y t r a n s p o r t ( i f any), normal  allowance, and  figure  stumpage c o s t s .  6  Marginal  revenue  (MR)  2 has been i l l u s t r a t e d as a d e c r e a s i n g f u n c t i o n of  timber volume due increasing  to a presumed d e c l i n i n g  difficulty.  Although  the  tree  quality  function w i l l  s i g n i f i c a n t v a r i a n c e , the more i n a c c e s s i b l e s i t e s in  of l o g g i n g  with  exhibit  (especially  mountainous t e r r a i n ) are hypothesized, i n g e n e r a l , to have  poorer q u a l i t y and/or smaller timber  than the most  accessible  areas. It  must be emphasized at t h i s p o i n t that the r e c o v e r a b l e  stock as determined of  harvest.  producers (i.e.  above i s not a p e r i o d i c  Rather,  can  fulfill  select supply  it  is  timber  the to  total  c o s t curve i s n e i t h e r a  short  run  or  long-run  curves  ( i n the true microeconomic sense)  along  the  shown,  depending  remaining p h y s i c a l timber s u p p l i e s . much  more  rapidly  in  any  one  will  phenomenon, Producer c o s t  lie  somewhere  on the o p e r a b i l i t y of  Actual production  costs  will  period  d i m i n i s h i n g marginal r e t u r n s to a l l i n p u t s , i n c l u d i n g  6  quotas  The a s s o c i a t e d marginal  i t does not represent a p r o d u c t i o n r a t e .  curve  rate  from which  production  since  MC  annual)  volume  meet  requirements).  (or  due  rise to  timber.  I n B r i t i s h Columbia, although stumpage p r i c e s may not reflect true timber v a l u e s , they are an accurate measure of true timber input c o s t s to l o g producers.  28  It was volumes If an  assumed that  due  to logging  i n c r e a s i n g cost  determine define  what  costs  would  the e a s i e s t  function  is  factors influence  t h e i r impact on  the  costs  (lowest  to  exclude  criterion are  so  recoverable also  there  is  logging  as  timber.  a  to  l e v e l of d i f f i c u l t y  of  logging.  we  The  must and  general  f o r e s t s in the past  for  other  difficulty  has  The  criteria  s i g n i f i c a n t volumes of  "recoverable"  volumes  that  reasons  are  and  c h a r a c t e r i s t i c s of timber  1967).  exclude  need to q u a n t i f y  Assuming  justified  first.  the  S i m i l a r l y , the  significant  standard(s) but  sites  a l l timber that does not meet some p h y s i c a l  broad  include  cost)  increasing  be  of r e c o v e r a b i l i t y (Zivnuska,  often  over  to  approach taken for d e f i n i n g a c c e s s i b l e been  rise  timber  meet the  may  subjective  uneconomic.  Hence,  the a c t u a l r e l a t i o n s h i p between  the  site,  stand  and  tree  increase  future  inventories.  technological  advances  will  p r o d u c t i v i t i e s , while a l l e l s e remains constant, then marginal costs'of stock in  logging  (Rt) w i l l approach the  f i g u r e 3a.  real  w i l l d e c l i n e over time  total  growing  increasing real  stock  it  is  not  Also,  if  productivities,  the  logging  will  cost  costs  effects.  This  there  magnitude be  are and  recoverable (G*)  assumptions of log  prices  clear,  i n v e s t i g a t i o n , as to the d i r e c t i o n of stocks.  the  t o t a l growing stock  Under more r e a l i s t i c  factor costs,  and  real  in  increases  direction  unknown because of  increasing  and  without  change  as shown  of  changing empirical recoverable in  change  increasing  s i t u a t i o n i s shown in f i g u r e 3b,  factor in  factor  where  29  MC^  /r  t+1  /  /  7  /  /  /  i  f  Jt+n  /1  m  i .  R. ' t + l . . . t+n  F i g u r e 3a. Conditions  _  ———•  • (  Change i n R e c o v e r a b l e S t o c k O v e r Time (t), Under of I n c r e a s i n g P r o d u c t i v i t y ( a l l E l s e C o n s t a n t )  Fj___re 3b. Change i n R e c o v e r a b l e C o n d i t i o n s of Increasing Factor Productivity •  S t o c k O v e r Time ( t ) , Under Costs, Log P r i c e s and  30  Factor  cost  increases  are  expected  to  i n c r e a s e s in p r o d u c t i v i t y , y i e l d i n g net  more  annual  than  offset  increases  in  real logging costs. The  preceding  d i s c u s s i o n has  for d e r i v a t i o n of stock adjustment  process.  timber The  e s t i m a t i o n were to occur manufacturing). estimates  concentrated  supply  estimates  in a l a t e r  market  as one  moves along  p o s s i b l e market in  market  products.  To  the primary product or lumber and  which  the  flow  followed i f or  reliability  the market c h a i n .  competition  reiterate,  the  (i.e. milling  most d e s i r a b l e market for e s t i m a t i o n of timber first  log markets  and  same procedure c o u l d be  However, as noted e a r l i e r ,  declines  on  of The  s u p p l i e s i s the exists  for  the  i n B r i t i s h Columbia t h i s i s  or l o g market, and  the  secondary  product  Interior  regions,  c h i p market in the C o a s t a l and  respect i v e l y .  2.2  APPLICATIONS OF Economic  neglected supply  STOCK-FLOW SUPPLY MODELS  assessments  of  timber  for s e v e r a l reasons.  of a c c e s s i b l e timber  assessment.  Although  Initially,  obscured  this  inventories  belief  a seemingly  the is  need  reviews of inventory  statistics  impression  that  supplies exist  Second, there the  i s the b e l i e f  recoverability  shortages, equilibria  since  of market  that we  the  in f o r e s t products.  endless such  or  could  give  Although t h i s  the  (Reed, 1979).  possible  w i l l maintain  an  prevalent,  need not be concerned  inventory  forces  for  no longer  superficial  adequate timber  have been  with  timber  supply-demand  i s t r u e , we  must  31 ask o u r s e l v e s what degree of s c a r c i t y , increase  and  i n s t a b i l i t y are we  rate of r e l a t i v e  price  w i l l i n g to accept.  A l s o , the  very e x i s t e n c e of harvest r e g u l a t i o n s p o l i c i e s and,  in B r i t i s h  Columbia, stumpage r a t e s that do not r e f l e c t indicate  the  timber  market i s not o p e r a t i n g f r e e l y .  impending timber  shortages  scarcity,  The  s p e c t r e of  has prompted Reed (1979) to d e c l a r e  that "The issue f a c i n g us today i s one of stimulating supply, specifically. . . There i s a genuine urgency to intensify f o r e s t r y in Canada,. . ." (p. 219). There  is  no  question  management i s warranted  on most economically  lands  in  levels  in general w i l l not n e c e s s a r i l y  for  North  that some l e v e l of i n t e n s i f i e d  economic  responsibility  America  today.  shortages.  Marty  operable  forest forest  However, i n c r e a s i n g supply alter  the  conditions  (1969) has e l a b o r a t e d on  our  i n meeting s o c i a l demands for timber s u p p l i e s :  "More timber w i l l not in i t s e l f generate more wages, profits and wealth. A d d i t i o n a l s u p p l i e s of timber must f i n d a use and fill a need i n order to have economic v a l u e . Although f o r e s t e r s do not c o n t r o l the demand f o r f o r e s t products and services, they have a responsibility t o . . . determine (1) whether or not the c o n d i t i o n of the timber resource i s (or i s l i k e l y to be) a l i m i t i n g c o n d i t i o n and (2) the a c t i o n s that would be r e q u i r e d to remove or a m e l i o r a t e t h i s l i m i t a t i o n , and the economic cost of these actions." (p. 88). The the  stock-flow  previous  responsibility over  supply  section by  can  providing  time on a l o c a l ,  modeling procedures help  us  to  estimates  meet  d i s c u s s e d in our  first  of resource s u p p l i e s  r e g i o n a l and/or n a t i o n a l b a s i s .  If  the  32 associated temporal model  demands exceed  expected  s u p p l i e s , then  resource l i m i t a t i o n s to growth  also  provides  us  a  tool  c o r r e c t i v e s t r a t e g i e s can be efficient  course  d e s c r i p t i o n of estimates and One  of  the  has  difficulties.  been That  which  process  reason  supplies  is  changing  to  the  ignoring  the  difficulties, and 2.21  problem.  estimates,  The  technical  of  resource economic  used means  timber  and o t h e r s , 1979;  inaccurate  be  timber  to d e f i n e economic  from  longer  to  margin  Owing to the consequences of poor  no  of  the nature of the  v o l . 1 ; Berndt  supply  supply  can be a p p l i e d .  due  1979).  d i f f i c u l t i e s can  most  technology, e r r a t i c market  f r u s t r a t i n g attempts  (Pearse, 1976.  the  timber  assessment  neglected  impart an e l u s i v e q u a l i t y  recoverability,  determine  itself  demands, i n f l a t i o n a r y p r e s s u r e s and itself  which a l t e r n a t i v e  economic  economic  is,  The  This section presents a b r i e f  to  the modeling  final  inventories  uses  to  and  indicated.  through  tested  action.  are  spatial  as  planning these  Reed,  resulting analytical  justification  for  overcoming  in t h i s study, are d i s c u s s e d i n  chapters  for these 3,  4  5. M u l t i p l e - u s e Planning Stock-flow  analysis  estimates of r e g i o n a l and exclusive  of  multiple-use importance  the  value  of  timber  supplies  s u b - r e g i o n a l timber of  forests  f o r e s t management can  be  in  would provide recoverability,  other uses.  expected  to  Since  gain  with i n c r e a s i n g demands f o r non-timber uses,  in  forest  33  managers  must  become  increasingly  adept at p l a n n i n g  development so as to maximize the value of the f o r e s t its  uses.  Two  major  difficulties  of  market  values  insufficient timber 1976.  for  information  and vol.1).  One  alternative  1976.  analysis  provides  uses  possible is  vol.1).  approach.  the By  (a) the lack  uses,  to  (Kimmins,  and  1976;  (b)  Pearse,  approach f o r determining compare  opportunity  s t r a t e g i e s , as measured by foregone  (Pearse,  various  forest  explicit  on the t e c h n i c a l t r a d e - o f f s between  non-timber  development p r i o r i t i e s  this  non-timber  in a l l  preventing  c o n s i d e r a t i o n of other uses in supply models are:  forest  The  proposed  measure of timber  conducting  the  forest  costs  timber  values  stock-flow  supply  value necessary  supply  analysis  values  in each a l t e r n a t i v e development o p t i o n can be determined.  of  for  under  c o n s t r a i n t s (e.g. a v a i l a b l e land base), timber  most e f f i c i e n t  of  The  course of a c t i o n w i l l depend on the w i l l i n g n e s s  the decision-maker  to forego timber  value to achieve  other  objectives. 2.22  Access The  primary  Planning  costs  developed  for the supply a n a l y s i s are net of  t r a n s p o r t a t i o n network c o s t s .  assumes  the  That  is,  allow  analysis  t r a n s p o r t a t i o n i n f r a s t r u c t u r e necessary  other s e c t o r s of the economy a l r e a d y e x i s t s and to  the  full  development  of  sufficient  the f o r e s t resource.  strategic  level,  budget requirements  regional  b a s i s over time by comparing e x i s t i n g  with that needed to secure  is  a l s o for  c o u l d be  r e c o v e r a b l e timber  identified  At on  the a  infrastructure  supplies.  At  a  34 more t a c t i c a l l e v e l , such as i n Timber Supply Area planning British  Columbia, estimated  prepare access t h i s end as  stand values c o u l d be used to  development p r o p o s a l s .  One  i s through the a p p l i c a t i o n of  suggested  harvest  net  by  Kirby  in  (1972),  "integer  for  values of the v a r i o u s timber  method of a c h i e v i n g programming"  linking  stands  road c o s t s to  on  a  management  un i t . 2.23  Logging The  Planning  proposed  stock-flow on  the  supply  model  accessible  also  spatial  information  implied  through the c o n s i d e r a t i o n of h a u l i n g c o s t s  t r a n s p o r t phase; C o t t e l l , 1967b). transportation product  distance,  market.  logs d e s t i n e d (Province  a  timber  processing  not  Where more than one  c o u l d p o s s i b l y obtain the timber, timber,  as c o n s t r a i n e d by  be  as  product  would  provide  i n f o r m a t i o n on the f u t u r e timber  as w e l l as estimates  industrial  facility.  probable  be  assigned Log  facility  c l o s e s t to the  Hence,  locations  . ."  Vancouver  processing  log  true  i m p l i e s that  input requirements,  destination. the  the  that f a c i l i t y  assessed  the  to  the  to the a c t u a l  B r i t i s h Columbia, 1978b. p. 9) w i l l  Market on Howe Sound.  analysis  origin  as  (secondary  These c o s t s cover product  t r a n s p o r t cost to that f a c i l i t y ,  used  supply,  In C o a s t a l B r i t i s h Columbia t h i s  for " . . .  of  from  timber  provides  the  procurer of  could supply with  accessible  of t o t a l a v a i l a b l e s u p p l i e s .  35 This  information,  in  addition  stand and t r e e c h a r a c t e r i s t i c s of facilitate  the  development  plans) as r e q u i r e d by the  to the i d e n t i f i e d  recoverable  of o p e r a t i o n a l plans  B.C.  Forest  Service  B r i t i s h Columbia, 1978a. s e c t . 5.0-5.5). also to  provide  and  Silvicultural Stock-flow  labor  requirements,  (Province  supply  provided  by  financial  feasibility  such  analyses  analyses of  programs f o r investment (1968),  and  procedures First,  alternative  would  net  growth  be  (1969),  and  stand  investments.  and  yield  the  Computer  Goforth  calculated.  and  response,  These  Mills  externally. supply  investment  revenues can then  determine  by  feasibility  be of  investment. Second,  where  ownership  o b j e c t i v e s and numerous f e a s i b l e identified, the  values  f u n c t i o n s of the  treatment  compared with the i n i t i a l c o s t s to the  benefit  a n a l y s i s i n f o r e s t r y , such as those  Chappelle  the  could  in  are e s s e n t i a l , to determining  a n a l y s i s to r e f l e c t expected revenues  trends  f u t u r e cut b l o c k s .  (1975), a l l r e q u i r e f u t u r e revenue to be provided altering  of  Planning  s i l v i c u l t u r a l planning i n two ways.  By  (or working  In g e n e r a l , i t would  s p e c i e s and q u a l i t y of logs recovered from  Forster  would  l o g g i n g managers with the i n f o r m a t i o n necessary  project c a p i t a l  2.24  stands,  site,  relative  example,  ranking  of  is  characterized  investment  investments  profitabilities  plans  by m u l t i p l e have  been  w i l l depend on more than  between  alternatives.  For  f o r a f i r m r e q u i r i n g a minimum l e v e l of l o g input to  maintain continuous p r o d u c t i o n i n i t s  processing  facilities,  36 the  objective  may  be to maximize investment  to a minimum recoverable timber the p u b l i c s e c t o r , in order objective  may  providing  necessary  facilities, supplies.  be  via  supply  revenues subject  in any  to maintain  one  period.  In  employment l e v e l s ,  the  to maximize net s o c i a l b e n e f i t s subject to log  inputs  maintenance  all  manufacturing  or growth of r e c o v e r a b l e  Here the t o t a l estimated  the v a r i o u s investment  to  recoverable  a l t e r n a t i v e s becomes an  timber  s u p p l i e s under important  input  to the d e c i s i o n process. Supply  analyses,  investment of  under  assumed  silvicultural  l e v e l s , w i l l a l s o be u s e f u l in comparing the c o s t s  intensive  recoverable  vs. e x t e n s i v e timber  terrain  methods  supplies.  l o g g i n g an a d d i t i o n a l difficult  various  unit  of  of  Where  increasing  the  timber  on  future  "supply more  c o s t " of  remote  and  in the f u t u r e , exceeds the c o s t of supplying  that same volume through i n t e n s i v e s i l v i c u l t u r a l a c t i v i t i e s less  difficult  sites,  then a r e a l l o c a t i o n of funds from the  e x t e n s i v e to i n t e n s i v e economic 2.25  and  Optimum R o t a t i o n  is  necessary  to  ensure  Periods  On  ownerships  where the c a p i t a l c o s t s of h o l d i n g  land  ( i n timber  production)  i n f o r m a t i o n generated  The  investments  efficiency.  Determining  useful  on  for  generally net value  by a stock-flow  determining  optimum  rotation  are  considered,  the  in  value  supply a n a l y s i s would be  r o t a t i o n ages of f i n a n c i a l length,  timber  an  economic  maturity.  sense,  is  recognized as the p e r i o d of time that maximizes the (discounted)  of a stand.  If more than  one  rotation  37  is  to be c o n s i d e r e d ,  i t i s the r o t a t i o n l e n g t h that maximizes  the net present value of the stream successively Normally,  identical  stands of  characteristics  R e a l i z i n g that such values  rotations  similar  would  of c o s t s and  site  taken  revenues  into  perpetuity.  productivity  and  species  be assigned the same r o t a t i o n p e r i o d s .  stands  could  command  differing  market  due to l o c a t i o n and o p e r a b i l i t y c h a r a c t e r i s t i c s ,  evident that t h e i r  i t is •  r e s p e c t i v e growth i n value may a l s o d i f f e r .  Thus, the s t a n d - s p e c i f i c net values provided by  stock  cost  to  and  of  revenue  equations,  could  be  used  r o t a t i o n p e r i o d s that maximize f i n a n c i a l m a t u r i t y on  supply  calculate a  stand  by stand b a s i s i f d e s i r e d . 2.26  Yield One  Planning of the p r i n c i p a l  a c c e s s i b l e timber efforts  on  reasons  s u p p l i e s i s to  regulated  lands.  f o r developing estimates of improve  harvest  The importance of the economic  r e c o v e r a b i l i t y of i n v e n t o r i e s i n determining conceptually scheduled will  simple.  If  harvest  time  insufficient planned  are  in  the  future  that i s not,  resource s u p p l i e s , then,  (and  recoverable timber  optimized  over  will  be  is or or at  succeeding  periods)  available  to meet  harvests.  Harvest  scheduling models have a l l been developed  premise that users supply,  rates  harvest r a t e s  based on stocks which i n c l u d e timber  not become, a part of usable  some  scheduling  or,  the  will cost  know and  the revenue  recoverability relationships  of  on the their  defining  38  recoverable harvest  supplies.  scheduling  Timber RAM plans based ".  stands are c u r r e n t l y a c c e s s i b l e . " not  a c c e s s i b l e , then  percent  (Smith,  determines  a  optimizes  on  the a n a l y s i s timber.  and  term timber  . ."  "...  an  (Smith,  a n a l y s i s , using  Timber  from  Forest  rate  of  supply  are  of  the  to  be  Timber  Supply  levels.  inventory p. 77).  Areas  supply  In  the  to this  used in  accessible  accessibility  which  impact of  The  of  Service,  harvest  then p r o j e c t s the  1978. RAM,  expected  B.C.  year)  allocation  is  areas  c u r r e n t "Two-Phase Method"  the  • (20  facilities,  long  If a l l  percent  The  by  short-term  manufacturing rate  employed  timber  develops  the assumptions a l l  (p. 7).  and  in f u t u r e p e r i o d s .  1978),  . .on  1971)  the manager must supply estimates  of area a c c e s s i b l e now,  accessible  (Navon,  7  usable  long-term  constraints  are  r e l a x e d to i n c l u d e c u r r e n t l y i n a c c e s s i b l e areas. A  new  y i e l d p l a n n i n g model, FORPLAN (Johnson and  1980), being developed basic  user  input  on  in the U n i t e d  i n the p l a n n i n g u n i t .  (by  timber is  value  calculations  i n t e r n a l l y a d j u s t estimates  7  Although  type) i n f o r m a t i o n can be in  still  requires  the p e r i o d i c p r o p o r t i o n s of a c c e s s i b l e  area  purpose  States,  others,  s p e c i f i c harvesting  cost  input to the model, t h e i r that  are  of r e c o v e r a b l e timber  Acronym for Resources A l l o c a t i o n Method.  not  used  supplies.  to  39 As  discussed  earlier, accessible  are u s u a l l y d e f i n e d may  not  reflect  in terms of p h y s i c a l c r i t e r i a true  constraints  estimated s u p p l i e s w i l l economically for  likely  recoverable  future  d e c i s i o n s concerning on  the  stock  empirical  relationships  for  economic  Similarly, product  the  future  decision c r i t e r i a  2.3  the  true  rely  timber of  Hence,  on  judgemental  inaccessible supplies  costs  and  scheduling  factor  costs  changes  in  and  of  these estimates  and  supplies.  determined  from  revenues to p h y s i c a l  more r e l i a b l e estimates of true  harvest  can  or  volume  timber  models d i s c u s s e d  flow adjustments that e x p l i c i t l y consider  prices,  indicate  also  that may  operability.  Adjusting  remaining  Therefore,  supplies  must  supplies  i n f l u e n c e of future p r i c e s , c o s t s  the  s u p p l i e s would provide  on  overstate  timber.  accessibility  technology,  (recoverable)  above.  changing  productivity, will  accessibility  than  better  subjective  provide.  SUMMARY In  this  chapter  I have presented the b a s i c concepts of  n e o - c l a s s i c a l and  stock  timber s u p p l i e s .  Supply in the  quantity at a given Stock-flow  of  flow approaches to e s t i m a t i n g true  economic  goods or s e r v i c e s provided  price level, supplies  are  over  a  i n v e n t o r i e s of goods a v a i l a b l e under s p e c i f i c p r i c e , cost and  at  of  sense  is  to a s p e c i f i c  specified  measures  economic  period  total  discrete  technological  the  market,  of  time.  quantities points  in  conditions.  or time  40  The  neo-classical  stock-flow timber  approach  was  r e j e c t e d i n favor of a  supply model because: (a)  stumpage  markets  are c h a r a c t e r i z e d by resource owners with m u l t i p l e o b j e c t i v e s , (b)  insufficient  information  p r o d u c t i o n f u n c t i o n s , (c)  the  exists  on  heterogeneous  managed  timber  nature  of  resource and v a r i a b i l i t y among ownerships make i t d i f f i c u l t derive  "sensible"  neo-classical  aggregate  supply  estimates,  supply models p r o v i d e no means  the r e c o v e r a b i l i t y of old-growth  for  and  the to (d)  determining  timber i n v e n t o r i e s .  In c o n t r a s t , stock-flow s u p p l i e s do not provide a measure of  the  through  optimal  rate  of  harvest  (production)  n e o - c l a s s i c a l supply modeling.  recoverable  timber  stocks  derived  However, estimates from  modeling can be used in a v a i l a b l e harvest t e s t a l t e r n a t i v e harvest r a t e s . stock-flow  timber  The  in a p p l i c a t i o n s other than y i e l d  supply", inventory  "economic are  of  timber  exceeds c o s t ) at referring sense.  to  a  supply  this  timber  etc.,  defined  in  as  point the  supply  s c h e d u l i n g models to provided  by  a l s o shown to be u s e f u l  thesis  supply",  references  "accessible  describing  economically  single  of  planning.  Throughout the remainder of "supply",  stock-flow  information  supply a n a l y s i s was  as provided  the  recoverable in  time.  to  timber  stock  or  ( i . e . value  They  are  not  n e o - c l a s s i c a l or true economic  41 CHAPTER 3  ALTERNATIVE METHODS FOR  3.1  ESTIMATING ECONOMIC TIMBER SUPPLY  INTRODUCTION Determining  inventory  the  requires  economic an  recoverability  of  a  timber  assessment of the i n t e r a c t i o n between  net timber values and v a r i o u s p h y s i c a l c h a r a c t e r i s t i c s of  the  resource  interactions  may  recoverability  is  that  influence a c c e s s i b i l i t y .  be undefined as in supply based  upon  producers.  the  analyses  experienced  where  estimates  In such cases, expected  implicit  considerations  c o n t r a s t are o p e r a b i l i t y relationships  of  costs  the  The  of and  estimates  s t u d i e s that  supply  revenues  are  provided.  In  explicitly  between resource c h a r a c t e r i s t i c s and  revenues or net values of h a r v e s t i n g .  define  The  These i n t e r a c t i o n s  may  analyses  interactions.  following  sections  present  these three approaches to modeling The  the  the c o s t s ,  be modeled upon e n g i n e e r i n g p r i n c i p l e s or s t a t i s t i c a l of observed  region  descriptions  are  supported  s t u d i e s of a s i m i l a r nature. given f o r each  approach.  f u r t h e r d e s c r i p t i o n s of  inventory by  recoverability.  references  to previous  Advantages and disadvantages  are  42 3.2  EXPERIENCED ESTIMATES In g e n e r a l , s t u d i e s i n t h i s category determine  accessibility  using  broad  physical  inventory  criteria  based  on  judgements p r o v i d e d by timber owners, managers and p r o c e s s o r s . In  short,  estimates  observers.  Examples  include: Forests  are  the  best-guesses  of  informed  i n Canada over the p r e v i o u s two  Wood Products - the Supply of Timber from (Wilson, 1966),  1974) ,  decades Canadian  Canada's Reserve Timber Supply  (Reed,  T e r r a c e - H a z e l t o n Regional F o r e s t Resource  (Province  of  British  Canada (Reed,  1978.  1976  1978).  (Bowen,  vol.I),  economic supply modeling develop  accessibility  imposed by p h y s i c a l  Columbia,  Study  1976), F o r e s t Management in  and  Canada's F o r e s t Inventory -  Although  none  of  these  as a primary o b j e c t i v e , estimates  to  s t u d i e s had all  reduce the  had  inaccuracies  i n v e n t o r y data.  Such analyses u s u a l l y begin with a d i s a g g r e g a t i o n of study  area  into  regions,  zones  represent some broad measure of study  by  or  homogeneity.  for each supply area from  to  recoverability  p. 6 ) :  criteria.  the  i s then These  for i n a c c e s s i b l e  timber  estimates  s t u d i e s , they were a l l based on similar  u n i t s that  Excluding  Although the exact methods and s p e c i f i c  develop  the  inventory r e c o r d s .  estimates are then reduced to account volumes.  management  Bowen (1978), an a l l o w a b l e annual cut (AAC)  determined  to  differed  subjective  factors  used  among  these  judgements  using  In g e n e r a l , as noted by Reed (1978. v o l . 1 ,  43  "Economic a c c e s s i b i l i t y estimates are based upon c r i t e r i a such as l o c a t i o n r e l a t i v e to infrastructure, timber quality, terrain and d e l i v e r e d wood c o s t s . " . The  study  p r o v i n c i a l and  by Bowen (1978) was federal  forestry  respondent  was  responsible  accessible  and  inaccessible  inventory.  The  the  same  area,  agencies  for  in  separately  portions  estimates  subjective c r i t e r i a ,  completed by surveying a l l  were  during a s i m i l a r  by  their  likely Reed  (1978)  time p e r i o d and  Of  in each  covered  had  to r e l y  developing  province.  of B r i t i s h Columbia  (1976) went the  c o n c e p t u a l i z i n g r e l a t i o n s h i p s between resource and  timber  that  represented  accessibility.  shown how  expected  revenues of l o g g i n g c o u l d be p r o j e c t e d f o r  sub-units  operability  l e v e l s of r i s k or p r o f i t a b i l i t y  region  to  class.  system i t was  determine None  the  of  present  planning  acreages  the  procedures for a d j u s t i n g estimates  studies  analysis  in B r i t i s h Columbia f a l l s  timber  Regional  supply  level,  parallels  Generally, physical o p e r a b i l i t y  within addressed  each the  for flows over time.  system of inventory  At the P r o v i n c i a l and accessible  characteristics  logging.  w i t h i n the  The  in  O p e r a b i l i t y c l a s s e s were developed  the c l a s s i f i c a t i o n  c o s t s and  furthest  in  apply  yield  upon  the s t u d i e s mentioned above, the r e g i o n a l a n a l y s i s by  the Province  To  the  timber  based  upon such judgements as the only c u r r e n t means f o r a c c e s s i b i l i t y estimates  Each  identifying  of  most  s i n c e the study  Canada.  for  into this  strategic category.  calculations the  criteria  of  the  studies described. are  defined  which  44  constrain  the  inventoried  resource a n a l y s i s such  supply  (Province  In the  of B r i t i s h Columbia,  recent  1980a-1980d)  c o n s t r a i n t s were s p e c i f i e d by minimum c u t t i n g ages,  types,  minimum  types  and  harvestable general  r e g i o n a l assessments. but,  their  leaves  a  general margin  volumes  Hence, their  (per  judgements  C l e a r l y these  criteria  of  error  that . may future  may  be  provincial policies,  disadvantage impacts  of  c o s t s and modeled  are  by  relevant,  impose  rates  substantial  generations.  a  but  not  regional is  new  The  precision  of  s a t i s f a c t o r y f o r reviews of n a t i o n a l  their  or  for  inability  technology,  simulation  of  regulating  sub-regional to  the  basis.  readily  or  rate A  of  second  evaluate  the  changing product p r i c e s , f a c t o r  government p o l i c i e s . for  provided  the p r i n c i p a l disadvantage of these approaches i s  estimates  on  site  species  a p p l i c a t i o n in determining harvest  r e l i a n c e on broad p h y s i c a l c r i t e r i a .  harvest  hectare),  accessibility  unnecessary c o s t s on present and  the  of timber.  Flow  adjustments  cannot  assumed f u t u r e c o n d i t i o n s ,  be  thus,  updates r e q u i r e p e r i o d i c reassessment of the e n t i r e process. The of  p r i n c i p a l advantage of t h i s approach i s the  information,  estimates. the  This  supply region  minimum.  manpower  and  time  necessary  i s important when accuracy is  large  and  costs  must  low  level  to  develop  i s not  critical,  be  kept  to  a  45 3.3  ENGINEERING STUDIES To  my knowledge no major s t u d i e s have attempted to model  the economic a c c e s s i b i l i t y of engineering similar  approach.  to  a  timber  inventory  The b a s i c procedures,  those  used  in  using  an  however, would be  long-run  cost  analysis  manufacturing i n d u s t r i e s , and system c o s t comparisons  in  i n the  logging sector. Where  necessary,  the optimal timber  the  location  of  development.  a n a l y s i s would begin  transportation  Next,  by d e s i g n i n g  infrastructure for  proposed c u t t i n g b l o c k s would be  designated  based on inventory  For  each  block an optimal  l o g g i n g system would be determined  and  access  roads designed.  Base p r o d u c t i v i t i e s  logging could  (access be  development  developed  specifications.  and  from  These  landform  through local  characteristics.  final  by  phase  of  transportation)  averages  or  c o u l d then be adjusted  equipment  t o r e f l e c t the  i n f l u e n c e of p h y s i c a l f a c t o r s on p r o d u c t i v i t y , such as; slope, landing s i z e , t e r r a i n , supply  etc. .  Current  and  log  This  estimate  logging cost.  estimate  of  total  c o u l d be increased to r e f l e c t  a d m i n i s t r a t i v e c o s t s , and  total  capital  and  c o s t s could be a p p l i e d to phase input requirements and  p r o d u c t i v i t i e s , and summed f o r an costs.  labor,  thus  provide  an  overhead  estimate  of  Revenues c o u l d be determined using market  p r i c e s and information on s p e c i e s and l o g s i z e s ,  from inventory  phase  records.  value would be considered  obtained  Those blocks with a non-negative a part of the recoverable  o  net  inventory.  4 6  An example of a logging c o s t study Coast and  Logging: Nagy,  Highlead Versus Long-Reach A l t e r n a t i v e s (Sauder  1977).  In t h i s study,  f i v e a l t e r n a t i v e yarding methods, logging" British  a  using t h i s approach i s  map  the c o s t s of l o g g i n g , using were  developed  Columbia. an e n g i n e e r i n g approach c o u l d  substantially  improve the accuracy  of r e c o v e r a b i l i t y estimates.  approach  in  discussed  the previous  revenues would provide estimates  that  "paper  area of r e p r e s e n t a t i v e c o n d i t i o n s in c o a s t a l  If developed,  and  by  vary  more  Unlike  s e c t i o n , developed of  recoverable  r e a l i s t i c a l l y with resource  costs  supplies  characteristics.  Where the a n a l y s i s i s w e l l disaggregated,  productivities  be  and  more  localized  to  reflect  d i f f e r e n c e s i n c o s t s and Disadvantages optimality  of  intra  thus timber this  in system c h o i c e ,  the  could  inter-regional  accessibility.  approach are as f o l l o w s . cutting  block  First,  designation  and  road l a y o u t s are r e l a t i v e to the decision-maker.  That i s , the  variability  s k i l l s among  in  entrepreneurial  operators w i t h i n the supply harvest  design.  region i s  equipment  operate  timber supply  availability  sub-optimally.  estimate  the  in  Thus, an  least-cost  supply, which i s c o s t s experienced  of p r o d u c t i v i t i e s ,  management not  reflected  in  A l s o , given p e r f e c t knowledge of the  system or design, a manager may by  or  be c o n s t r a i n e d ,  for  a  example,  realistic  on the a r e a .  have to  approach  s o l u t i o n to h a r v e s t i n g the not  optimal  the short-run and may engineering  the  would  region's  representation  of  Second, the adjustment  input demands, e t c . , to  reflect  operating  47 conditions  that  vary  from  a  pre-defined  p r i n c i p a l l y on s u b j e c t i v e c r i t e r i a Third,  only  adjusting  a  few  developed by  variables will  production  norm,  estimates,  likely with  Finally,  this  approach  i n f o r m a t i o n , manpower, time and  3.4  the  rely  analyst.  be considered when omitted  p o s s i b l y c o n t r i b u t i n g to s i g n i f i c a n t v a r i a t i o n costs.  must  requires  variables  in true  a  high  logging  'level of  skill.  STATISTICAL STUDIES Models in t h i s category  statistical resource  are c h a r a c t e r i z e d by the  r e l a t i o n s h i p s to d e s c r i b e the  c h a r a c t e r i s t i c s and  (a) i t would  be  characteristics  extremely of  insignificantly  then,  timber  statistical  supply  d e t e r m i n i s t i c elements ( C o t t e l l , Basically, be s t a t i s t i c a l l y identified value  there are two modeled.  relationships  estimated  approach  directly  models  is  between  by  phase  Phase  costs  be  directly  chosen, total  permits  could  (b) some of  also include  ways in which r e c o v e r a b i l i t y can  be  can  separately  revenues, or, net  estimated.  If  the  relationships  can  be  l o g g i n g c o s t s and each  further  r e l a t i o n s h i p s d e f i n e phase p r o d u c t i v i t i e s costs.  random  accessibility,  will  l o g g i n g c o s t s and  can  the  1967a).  c h a r a c t e r i s t i c s , or, s e p a r a t e l y for Estimation  model  influence  Relationships  for c a l c u l a t i n g  cost-revenue  to  However, because  an e n t i r e logging system, and  the randomness w i l l  of  i n t e r a c t i o n s between  accessibility. difficult  use  phase  of  resource logging.  refinement rather  than  if  the  phase  then be c a l c u l a t e d using c u r r e n t  48 factor  costs.  For  the phase approach there  productivity  studies  in  yarding  s t u d i e s by Tennas and others  (1955),  and  yarding  c y c l e times by c y c l e elements against  variables  characteristics. single  cutting  each other,  (1975).  numerous  examples  and l o a d i n g .  (1965)  times  Dykstra  are  Each  Adams  These  (1965),  Binkley  describing  sampled  regressed  yarder  and/or  T h e i r samples c h a r a c t e r i s t i c a l l y block  include  of these s t u d i e s and  of  element resource  covered  a  or s e v e r a l u n i t s i n c l o s e p r o x i m i t y to  and were conducted f o r one type of  (e.g. h i g h l e a d ) .  yarding  systems  (1965)  also  units.  Nelson  yarding  and loading on s i x t e e n c u t t i n g blocks over a p e r i o d of  the  separately  analyzed  to  loading  five  s t u d i e d four  cutting  units.  productivity  on  Adams  the sampled  i n C o a s t a l B r i t i s h Columbia.  determine  (a)  whether block,  He  total  p r o d u c t i v i t y , and (b) the amount of block  v a r i a t i o n that  by resource  variation in  regressions  bucking, yarding road  (1966)  f o r phase times or c o s t s i n f a l l i n g and  ( h i g h l e a d ) , l o a d i n g , booming and towing,  c o n s t r u c t i o n , as a f u n c t i o n of l o g volume.  study were developed from the l i t e r a t u r e or based operator  could  variables.  For p r o d u c t i v i t i e s i n a l l phases of l o g g i n g , Dobie developed  used  s h i f t or machine  v a r i a t i o n s c o u l d account f o r the g r e a t e s t  be e x p l a i n e d  cable  (1980) sampled d a i l y p r o d u c t i v i t i e s i n h i g h l e a d  and one h a l f years data  on  (1975)  yarding  system  two  Dykstra  cable  information.  The  conducts logging p r o d u c t i v i t y  British studies  Data f o r the upon  Columbia F o r e s t f o r major  and  local Service  "stump  to  49 landing"  and  "log  loading"  appraisals  (Province of B r i t i s h Columbia, 1979).  i s r e l a t e d to v a r i o u s t r e e , which  are  sampled  cross-sectional not  undertaken  expected B.C.  stand  during  sampling in  a  systems  to  and  improve  site  operational  Productivity  characteristics  cruises.  of the r e g i o n a l l o g g i n g manner  productivities  or  that  will  costs.  As  stumpage  However,  industry  represent  is  average  described  by  the  Forest Service: "Productivity data used in an a p p r a i s a l i s not intended to represent the statistical averages of p r o d u c t i v i t y throughout the industry. Instead, they are intended to represent productivities that are reasonably attainable by an average e f f i c i e n t operator." (Province of B r i t i s h Columbia, 1979. p. 1 ) . An  example  of  the  total  cost (vs. phase) approach i s  p r o v i d e d by a recent study on the and Timber Supply and  Curves from F o r e s t Inventory Data  o t h e r s , 1979).  In t h i s study,  l o g g i n g on 26 c u t t i n g blocks (one related how  to  timber  forest noted  E s t i m a t i o n of Logging  resource  estimated  (Berndt  unit  costs  The  study  supply curves c o u l d then be developed  illustrated by  applying  inventory data to the estimated c o s t equation.  ". . . as collated  is in  a  often form  the  case,  amenable  (Berndt and o t h e r s , 1979.  p. 8).  input data these  to  of  f i r m , h i g h l e a d yarding) were  characteristics.  that although the necessary  Costs  this  sets kind  were  It  was  available,  of data are not of  analysis."  50  On  the  developing without  revenue s i d e , l i t t l e relationships  a priori  that  a t t e n t i o n has  can  knowledge  predict  of  d i s t r i b u t i o n s , beyond using average increase  the  necessary  of  An  revenue  of  inventory  economic  Columbia  log  the  complete  it  size  is Cottell's  on • the  Forest.  Costs  grade  (1967a) study  University  of  using a production road  and  landing  road  changing)  mathematical  equation  length  (1966).  inventory data Log  developed by  were  a  optimized  models obtained  other phase c o s t s were  local  by  average  r e s u l t s showed that few  stands  timber  was  under c o n d i t i o n s at the  were soil  stand  a  data  were and  series  calculated stand  negative  net  of  (d) a l l  developed  p r i c e s by s p e c i e s . had  (c)  yarding (including  using  using  on species d i s t r i b u t i o n  recoverability  firm,  from the l i t e r a t u r e , and  calculated  Revenues  Market  five  by  times (per c u n i t ) were c a l c u l a t e d  c o n s t r u c t i o n c o s t s , and  costs  British  by stand were estimated  for three land c l a s s e s , by four slope and  type c a t e g o r i e s , (b) y a r d i n g  Vancouver  be  approach to  phase: (a) road c o n s t r u c t i o n c o s t s per u n i t road  Dobie  To  will  and  cost-revenue  recoverability  accessibility  Research  developed  grade  species.  estimates of  values,  log  by  to  from f u t u r e h a r v e s t s .  example  estimating  stand  specific prices  to f u r t h e r develop models  distribution  of  accuracy  been given  area,  by from and  Cottell's  values,  thus  q u i t e high on the Research F o r e s t ,  time.  51 Jackson results  and  of  research  Specifically, equation  logging  (1979)  into  they estimated  that  logarithm  McQuillan  of  related tree  method,  recently  net the  to  Montana),  the  the  would  models of timber Dobie  of  (bid  value)  to the  selling  price  index,  r e g e n e r a t i o n method, average volume per acre  equation are s p e c i f i c  specification  prediction. linear  price  lumber  the  a  harvested, and haul d i s t a n c e to market.  Forest,  value  coefficients  stumpage  diameter,  stand  presented  be  area  sampled  authors useful  Although  noted  the data  (Lolo  that  elsewhere,  and  National  the  general  particularly  in  inventory v a l u a t i o n .  (1966)  combined  the cost equations and  d i s c u s s e d e a r l i e r with i n f o r m a t i o n  on  product  estimates  recovery  and  value to determine estimated c o n v e r s i o n r e t u r n (net value) per tree. tree  The and  estimated values were regressed a g a i n s t a number of stand v a r i a b l e s to develop a p r e d i c t i v e equation f o r  net v a l u e . The  p r i n c i p a l advantage of s t a t i s t i c a l  engineering  studies,  entirely  sampling  can  l e s s prone to b i a s than  s u b j e c t i v e assessments.  supply  the d e r i v e d estimates do rather,  recoverability  c h a r a c t e r i s t i c s of the would  be  valuable  with  those  provided  Likewise,  localized  improve the q u a l i t y of estimates  inter-regional  as  i s that estimates of r e c o v e r a b l e timber  are more accurate and through  models,  for  analysis. not  intra  and  Unlike engineering studies  represent  reflects logging  for  optimal  the  industry.  simulating  the  conditions;  current This effect  economic information of  various  52  policies  (e.g. t a x a t i o n )  impact on on  resource  fewer  included  sampling and  the  inventory  since the  estimates  specification Finally,  data o r g a n i z a t i o n  and  analysis  of  once  rely be  resource  the  have been  initial  completed,  r e q u i r e l e s s time than in an  approach.  There are three primary disadvantages to the modeling  subsequent  a n a l y s t , more v a r i a b l e s can  interactions.  updates  engineering  by  Also,  improve • model  accessibility  periodic  i n d u s t r y e f f i c i e n c y and  supplies.  judgements to  on  approach.  r e q u i r e s extensive  First,  operational  developing sampling  the  statistical • relationships  in each  supply  area.  Second, t e c h n o l o g i c a l changes over time reduce the v a l i d i t y  of  model  estimates.  be  strong  enough to support acceptable  The  first  Columbia  two  because  Third, s t a t i s t i c a l  through c o o p e r a t i v e Divisions been  of  reason  I  believe  r e l a t i o n s h i p s i s due In  the  Service.  noted  for  such  in  studies  and  British  results  others, have  studies discussed  other)  variables.  block  or s e t t i n g w i l l be  Engineering  t h i r d disadvantage of  1976). not  has  yarding  The  primary  shown  to the measure of production  (and  the  The the  ( C o t t e l l and  c y c l e times were regressed  to  in the r e s u l t s .  less c r i t i c a l  e f f o r t s of the V a l u a t i o n  studies  not  annual p r o d u c t i v i t y s t u d i e s c a r r i e d out  the Forest  specifically  productivity  confidence  disadvantages are of  r e l a t i o n s h i p s may  strong  used.  e a r l i e r , d a i l y p r o d u c t i v i t y or  against  block  or  setting  resource  Resource c h a r a c t e r i s t i c s on a s i n g l e r e l a t i v e l y homogeneous when  range of p o s s i b l e c o n d i t i o n s  that c o u l d  occur.  compared Hence,  53 production v a r i a b i l i t y  in yarding  stronger  to  correlation  the  can  day  be  to  of  shift  productivity  should  cover  conditions,  i s supported  productivity Mcintosh  widest  block  (1980)  to develop of  possible  averages  timber  range of of  both  variables.  by the f i n d i n g s of a study on s k i d d i n g  i n the I n t e r i o r Region  and Johnson  models  show  i n crew  Nelson's  T h e r e f o r e , sampling  the  using  p r o d u c t i v i t i e s and resource This  by  relationships for s t a t i s t i c a l  recoverability resource  variation.  to  day v a r i a t i o n  a t t i t u d e s , weather, e t c . , as i s suggested measure  expected  (1974).  of  British  Specifically,  Columbia  i t was  by  determined  that, "Average tree s i z e , stand and terrain characteristics were main f a c t o r s a f f e c t ing productivity between forest types, while degree of d i f f i c u l t y of i n d i v i d u a l logging chances and the skidder operators skill and m o t i v a t i o n were determining factors within forest types." (Mcintosh and Johnson, 1974. a b s t r a c t ) . Their  "forest  types  that  considered  maneuverability  " were based on a c l a s s i f i c a t i o n  species,  elevation,  terrain,  and a s u b j e c t i v e l o g g i n g chance  scheme ground  rating.  3.5 STUDY APPROACH In  this  study the s t a t i s t i c a l modeling approach w i l l be  f u r t h e r developed. increased estimates.  accuracy In  This approach was chosen p r i m a r i l y f o r the and  objectivity  specifying  in  developing  supply  and e s t i m a t i n g the r e l a t i o n s h i p s ,  and d e s i g n i n g the s i m u l a t i o n model, I w i l l attempt to  acheive  the f o l l o w i n g o b j e c t i v e s : (a) The estimates should r e f l e c t actual e f f i c i e n c i e s in the l o g g i n g i n d u s t r y . That i s , the model should not determine r e c o v e r a b i l i t y under optimum c o n d i t i o n s . (b) The model should c o n s i d e r the v a r i o u s l o g g i n g systems commonly used on the supply a r e a . (c) The v a r i a b l e s used for p r e d i c t i o n should be those available (or capable of being incorporated) i n inventory records; avoiding variables requiring o p e r a t o r , crew or machine s p e c i f i c data. (d) Samples should cover a wide range of resource, system and operator c h a r a c t e r i s t i c s , to develop r e l a t i o n s h i p s f u l l y r e p r e s e n t a t i v e of the supply area.  55  CHAPTER 4  RESOURCE CHARACTERISTICS AND  LOGGING OPERABILITY IN COASTAL  BRITISH COLUMBIA  4.1  INTRODUCTION There are four major f a c t o r s that together determine  portion  of  total  economically of  physical  timber  r e c o v e r a b l e : (a) the  the resource base,  biological  that  are  characteristics  (b) the t e c h n o l o g i c a l c a p a b i l i t y of the  logging  i n d u s t r y , (c) market demands for  supply  of  productive  factors  policies  towards  government  supplies  the  (other  resource than  resource  goods  timber), and development  and (d) and  allocation. At  any  point  in  time  we  can  c a l c u l a t e the economic  supply, under c u r r e n t c o n d i t i o n s of government p o l i c y and state  of  technology,  by  assessing  the i n t e r a c t i o n between  p h y s i c a l resources and market c o n d i t i o n s . measures  of  these two  factors  i n v e n t o r i e s , and p r i c e s factors.  This  for  chapter  Presently  we  this  the previous chapter  goods  details  and  costs  procedures  of  producing  f o r modeling  and  long-term  has been  chosen  for  the  process.  three a l t e r n a t i v e methods of modeling  i n t e r a c t i o n were presented.  accuracy  have  in the form of p h y s i c a l timber  i n t e r a c t i v e r e l a t i o n s h i p using these measures i n the In  the  For  reasons  of  short-term  f l e x i b i l i t y , the s t a t i s t i c a l  further  development  in  this  approach thesis.  56  Specifically, calculating between  I  will  present  operable  resource  a  volumes  method  by  for  statistically  developing  characteristics  and  the  relationships costs  of  timber  harvest i n g . In the next s e c t i o n I w i l l d i s c u s s some g e n e r a l for  procedural  assumed  effect  operability. statistical including  development.  Section  of  characteristics  The  resource final  two  in coastal  Revenues And  the r e s u l t i n g  detail  Columbia followed  for  testing,  equations.  determine  Costs  demand  productive  factors  for  forest  interact  economic timber  products  with  the  products,  determine  log q u a l i t y total  (specific prices  species-grade  logs.  sufficiently  the As  dispersed  resource  and  type).  timber  base  b a s i c ways. market  Thus,  by  categories),  gross the  the supply of  distribution  homogeneous combined  free  for  forest  from producer  for  by s p e c i e s  'products' with  market  value of c o n v e r t i n g f o r e s t s  markets and  the  to  First,  demand  value of standing timber  ( i . e . product  inventoried  provides  marketable  the  and  s u p p l i e s in two  e q u i l i b r i u m between market supply of  of  five,  PROCEDURAL CONCEPTS  Market  and  logging  British  the r e l a t i o n s h i p s hypothesized  sampled v a r i a b l e s t a t i s t i c s , and  4.21  on  d e s c r i p t i o n of the scope and procedures  d u r i n g sampling,  4.2  d e a l s with the  s e c t i o n s , four and  research c a r r i e d out a  three  concepts  products control,  into are the  57  p r i c e s are market determined point  in  time,  and are constant, at  for a l l producers  r e g a r d l e s s of resource l o c a t i o n .  a  discrete  supplying s i m i l a r  Second,  market  products  demand  and  supply e q u i l i b r i u m for the f a c t o r s of production determine the cost  of  employing  productive  (e.g. wages, i n t e r e s t , received  for  timber  assigned to product one  factors  etc.).  However,  produced,  is  directly  given  efficiency for  area  study  or  directly for any of  In t u r n , f a c t o r demand w i l l  i s h e l d constant, as the volume of timber  available  tree  even  s i z e , stand d e n s i t y , stand q u a l i t y  supply  logging  size',  vary  operator  timber  of  be  T h i s v a r i a n c e in the c o s t s  'plant  characteristics  economic  not  prices  though  harvesting,  terrain  can  the  r e l a t e d to the amount of each f a c t o r  employed in logging an area. for a  costs  unlike  production  groups, s i n c e they can vary widely  s p e c i e s or grade produced.  production  in timber  vary. for  costs  Therefore,  and  defining  the  an area becomes, e s s e n t i a l l y , a  and  the  factors  causing  their  var i a b i 1 i t y . 4.22  Cost vs. Time S t u d i e s There are two  logging  ways of measuring the r e l a t i o n s h i p s between  c o s t s and  resource v a r i a b l e s .  time method - i s to  measure  exist  time  between  the  the  it  The  direct  takes  to  first  relationships log  c h a r a c t e r i s t i c s that d e f i n e area o p e r a b i l i t y . machine  rates  can  the  Then  and  be a p p l i e d to time estimates A second, more i n d i r e c t  production  -  method  is  to estimate  that  an area and  the c o s t s of p r o d u c t i o n . cost  - production  the  wage  to c a l c u l a t e approach relationships  58 between the c o s t s of l o g g i n g an area and that  d e f i n e area o p e r a b i l i t y .  The  the  characteristics  f i r s t method i s c o n s i d e r e d  a d i r e c t approach, even though a two-stage procedure, resource  characteristics directly  i n f l u e n c e the times r e q u i r e d  to complete the e n t i r e h a r v e s t i n g process Costs, as  on the other hand, are  labor  and  capital availability, variability  in  Cottell  three,  by  (1979), are examples of the  for a c u t t i n g block. |  i n f l u e n c e d by other  not a f f e c t e d by resource chapter  because  f a c t o r s such  i n f l a t i o n , e t c . , that are .  Two  studies  (1967), and  production  discussed  Berndt and  time  and  others  production  cost methods r e s p e c t i v e l y . Primarily  for  between production time  study  analysis.  the  reason  times and  the  direct relationship  logging d i f f i c u l t y ,  approach f o r determining  favor  approach  the  supply are:  (b) dual vector of c o s t changes over  (c) i n d u s t r y r e l u c t a n c e , and  Each of these  I  logging c o s t s in a  Other reasons for a v o i d i n g the c o s t  (a) cost center problems, time,  of  problems with  (d) accounting d i f f e r e n c e s .  the cost approach are d i s c u s s e d in  turn below. 4.221 resource of unit  Cost  Center Problems.  To  analyze  the  c h a r a c t e r i s t i c s on logging c o s t s , over a  operating must  p ro du ct io n  conditions,  be  sampled  data  and  the  for  affect wide  of  range  smallest possible operational  which  measures  there of  are  identifiable  resource  variables.  O p e r a t i o n a l c r u i s e s conducted for c u t t i n g permit  applications  in  v a r i a b l e s on  B r i t i s h Columbia provide measures of resource  specific  c u t t i n g blocks  proposed  for  harvesting.  However,  59 estimates the  of production  divisional  range  from  loaders,  as  etc.). one of  level  as combined i n t o cost c e n t e r s  that can  small  as  yarders,  e t c . ) to  (e.g. f a l l i n g  and  These  c o s t s are most often a v a i l a b l e only at  a  entire  phases  bucking,  costs  single  administrative  thus,  It  should  time records  and  A  1  sampling  unit  the of  this  magnitude  samples that cover a wide  conditions.  be p o s s i b l e , however, to go back through d a i l y  and sum the t o t a l  to s p e c i f i c  time r e q u i r e d to l o g an area.  These times would thus be a r e a - s p e c i f i c and c o u l d be related  to  resource  c r u i s e s and/or s i t e the  range  in  effects  divisional  that a s s o c i a t e labor and machine data  c u t t i n g areas,  booming,  they i n c l u d e the  throughout  reduces the p r o b a b i l i t y of o b t a i n i n g range of operable  sorting  process  can not be d i r e c t l y a s s o c i a t e d with any  variability area.  (e.g.  i n the h a r v e s t i n g  scaling,  o p e r a t i o n a l c u t t i n g block, resource  machine  variables  inspection.  resource  estimated  from  T h i s approach  variability  operational  would  necessary  directly  to  provide identify  operability relationships.  *The need f o r o p e r a t i o n a l area accounting Wellburn (1976):  has  been  "... planning and accounting should be on the same b a s i s , cover the same area and t o t a l p e r i o d of l o g g i n g . We must c o n s i d e r each d e f i n a b l e logging area as a p r o j e c t and keep track of a l l c o s t s r e l a t i n g to the p r o j e c t or area." (pp. 115-116).  noted  by  60  4.222 Dual Vector changes  can  occur  f a c t o r c o s t s , or costs),  other  Of Temporal Cost Changes.  as  a  both.  cost  r e s u l t of changes i n p r o d u c t i v i t y , Increases  things being  in u n i t l o g g i n g c o s t s .  Unit  equal,  The  in  y i e l d decreases  opposite  costs).  productivity  (factor  (increases)  occurs with decreases  productivity  (factor  held constant  the d i r e c t i o n of change in u n i t logging c o s t s i s  directly  r e l a t e d to a c t i o n of  both act  in the  cost  on  p r o d u c t i v i t y and in  separately  the  of the  two  non-constant  vectors  vector.  same d i r e c t i o n then the e f f e c t on unit  depends  given  When one  in  the  relative  factor costs.  Table  1.  The  estimates of u n i t logging  of  logging  change  between  and  estimating  should  improve  the  final  costs.  Reluctance.  To  keep  i t s ' i n t e r n a l cost reluctant  to  its  Thus,  a  to  a n a l y s i s using obtaining operational the  supply  desired  external the cost  cooperation sampling. unit  investigators. study approach, from  the  T h i s can  problems  logging  be  and  in  open supply  arise  over  i n d u s t r y to conduct  extremely  s i z e i s extensive  important  the number of  when  samples  i s subsequently l a r g e .  4.224 Accounting D i f f e r e n c e s . that  is  each vector  s t r u c t u r e c o n f i d e n t i a l a company i s often books  If  range of p o s s i b i l i t i e s  Identifying  f o r future p r o j e c t i o n s  4.223 Industry  rate  is  are  representative  samples of logging  of  operations  the  To  develop  supply  relationships  u n i t being  analysed,  must n e c e s s a r i l y be drawn from a  number of d i f f e r e n t firms o p e r a t i n g  in the area.  This r a i s e s  61  Table 1. P o s s i b l e Combinations of Factor Costs and P r o d u c t i v i t y i n Determining D i r e c t i o n of Unit Logging Cost Changes Unit Logging  D i r e c t i o n of Chang e Factor Cost P r o d u c t i v i t y Factor  I ncreasing Tl TT  Increasing Constant Decreasing  TT TT  Decreasing  2  1  * *  > P  FC < P  Increasing Constant Decreasing  Increasing Constant Decreasing  FC = P * FC = P  Increas ing  Increasing Constant Decreasing  FC < P * * FC > P  Tl  Constant Decreasing  Tl  FC  II  Constant Decreas ing  TT Tl  Costs  Increasing  Tl  Tl  Constant  Relat ive Rate of Change  TT  FC = f a c t o r cost P = factor productivity * = irrelevant  Problems of a d j u s t i n g recorded c o s t s where  necessary,  to  ensure  between  comparability  the  companies,  between samples.  Time, on the other hand, i s a standard measure, thus, of  2  production  accounting supposed  times  between  discrepancies. to  represent  firms  Since  the  the expected  s t r u c t u r e s i s not  of  not  supply  suffer analysis  from is  p r o d u c t i o n c a p a b i l i t y on  the supply u n i t given c u r r e n t technology machine r a t e s , p r e c i s e knowledge  do  records  and standard wage and  individual  firms'  cost  important.  4.23 E s t i m a t i o n by Phase of Logging Developing  r e l a t i o n s h i p s between l o g g i n g o p e r a b i l i t y and  resource c o n d i t i o n s using a time  study approach i s not without  62 problems.  I f the cost study approach i s used, the c o s t of the  entire operation  from stump to dump c o u l d be d i r e c t l y  related  to resource f a c t o r s b e l i e v e d to cause cost v a r i a t i o n .  This i s  not p o s s i b l e , however, when p r o d u c t i o n times rather than c o s t s are  used as the independent v a r i a b l e .  in l o g g i n g i s not  homogeneous  with  production process must be d i v i d e d  Because a u n i t of time respect  to  value,  i n t o phases to which  the  single  wage and machine rates can be a p p l i e d . Commonly (a)  access development;  transport (e)  identified 2  phases  (b) f a l l i n g and bucking; (c) primary  (e.g. cable y a r d i n g  hauling;  i n c o a s t a l B.C.);  (f) unloading,  sorting  r e - h a u l i n g ; o r , some combination 1967b; Conway, 1976).  of the logging process a r e :  The s k i l l  of  (d)  loading;  and booming; and, (h)  these  phases  (Cottell,  and q u a n t i t y of labor  differs  between phases, thus, so w i l l  the average wage rate a p p l i c a b l e  to  applies  each  phase.  The  same  m a t e r i a l s used i n each phase.  to  the  equipment  Even w i t h i n phases the  wage and machine rates can d i f f e r , as the p a r t i c u l a r capital  to  labor  average  system or  combinations chosen to complete each phase  w i l l vary with operating c o n d i t i o n s . the  and  Therefore, to  calculate  c o s t s of l o g g i n g , a l l phases combined, i t i s necessary to  estimate  the  relationships  resource  variables  between  production  times  and  f o r each system commonly used w i t h i n each  phase of l o g g i n g .  2  I n c l u d e s c u t t i n g block l a y o u t , c r u i s i n g , engineering and construction.  road  63 Another reason for e s t i m a t i n g phase  is  due  production that are show  to  and  the  by  Estimates  embodied  total  times  Phases  unit w i l l  resource  not  specific  or c o s t s ,  s i t e c h a r a c t e r i s t i c s , are  Thus, by c o n c e n t r a t i n g  a f f e c t e d by operating developed.  of  between  i n some phases.  to  by  with  weakened  time or c o s t s which are e s s e n t i a l l y f r e e of  resource i n f l u e n c e .  be  association  from the operating  relationships  to t r e e , stand and  the  weak  variability  increasingly distant  characteristics. respect  indirect,  resource  strong  production r e l a t i o n s h i p s  conditions,  Costs  for  resource v a r i a b i l i t y can  on phases d i r e c t l y  stronger  phases  relationships  weakly  can  correlated  be c a l c u l a t e d based on  with  deterministic  equat ions. In the  logging,  first  bucking,  then, the v a r i a b i l i t y  three and  a f f e c t e d by  phases,  primary  productivity  volumes  to  be  productivity the  function most  can  is  determined and  be  the by  most  characteristics  Sauder and  1979b).  Nagy,  Hauling  importantly,  hauling  p r o d u c t i v i t y can  have  t r a i l e r s are  employed  not  operational the  1977;  loader  road  distance;  of  primarily  although when  Scaling,  and  British  conditions,  influence  (Conway, 1976).  yarder  Pearce  Province is  size,  productivity  1976;  productivity  considerable  and  unit.  landing  importantly,  (Conway,  of v e h i c l e load c a p a b i l i t i e s ,  falling  shown to be d i r e c t l y  , which i n d i r e c t l y a s s o c i a t e s  1972;  Columbia,  transport,  loaded,  resource  Stenzel,  development,  resource c h a r a c t e r i s t i c s on  Loading  to  access  of p r o d u c t i o n time i n  a and  loader pre-load  unloading,  64 sorting  and  booming  costs  are  p r i m a r i l y a f u n c t i o n of  volume of logs handled as r e l a t e d to the type of s c a l e , or  stick,  (Province  and  type  of  British  considerations  for  of  sorting  grounds,  Columbia,  developing  expected  productivities  in  Thus,  c o s t s in the l a s t area  earlier  weigh  d r y l a n d or water  1979b).  ( l o a d i n g to re-haul) are knowledge of  the  four phases  logging  phases  main  and  systems, estimated  production.  4.3  RESOURCE FACTORS AFFECTING LOGGING COSTS - DESCRIPTION In t h i s s e c t i o n I w i l l d e s c r i b e the p e r c e i v e d e f f e c t s  a  number  of  discussion as  resource  f a c t o r s on phase p r o d u c t i v i t i e s .  i s based upon hypothesized  reported by a number of sources  Pearce and  S t e n z e l , 1972;  B r i t i s h Columbia, 1976, purposes  1979b, and  choice and  (Dobie,  Harvesting  and  1966; 1978;  1980e).  bucking  stand  1969;  Province  of  For o r g a n i z a t i o n a l  and  sub-sections;  site  factors  on  development,  yarding.  general c a t e g o r i e s of systems a v a i l a b l e f o r  the  bucking,  operator  can  and choose  mechanized system or manual o p e r a t i o n . operator  Allan,  System Choice  the phases of f a l l i n g and  the  and  The  interactions  phase p r o d u c t i v i t i e s in access  bucking,  There are two  and  proven  t h i s s e c t i o n w i l l be d i v i d e d i n t o four  f a l l i n g and 4.31  or  Conway, 1976  d e s c r i b i n g the e f f e c t s of t r e e , system  of  yarding.  In  falling  between some form of In the  yarding  phase  has a choice of s e v e r a l ground s k i d d i n g or c a b l e  65 yarding  systems.  The site.  critical Skidding  slopes l e s s than  attached  35 percent  limiting  factor,  gullies,  ravines,  cutting  and  either,  ( S t u d i e r and  is  more  skidding  with  1974).  ( i . e . few and/or  operations  for  shallow  mechanized  A third  limiting  tree  diameter.  is  used  mechanized c u t t i n g d e v i c e , are l i m i t e d to t r e e diameters  of 61  or l e s s  the  A  the above, i s the  suitable  shears,  generally  commonly  centimeters  operated  Binkley,  operations.  f o r mechanized c u t t i n g  is  15 percent, and f a v o r a b l e  Uniform t e r r a i n  ground  Hydraulically  to  associated  etc.,)  the  or wheeled v e h i c l e s , or f a l l i n g  slopes l e s s than  terrain variability.  factor  track  cutters  t o adverse  second  i n each phase i s ground slope of  with  with mechanical limited  factor  ( A l l a n , 1969; Conway, 1976).  In c o a s t a l B r i t i s h Columbia the terrain  and l a r g e timber  the use of sizes  mechanized  of  uniform  future  even then unless  an  steep  sizes typical  cutting  second  slopes,  stands  limited  are  timber  on lower e l e v a t i o n ,  use  the high c a p i t a l c o s t s may l i m i t volumes  preclude  Smaller  of  such  i n t e g r a l part of i n t e r i o r o p e r a t i o n s .  sufficient  variable  of the region  operations.  growth  s i t e s may accommodate  presently  most  their  available  to  systems However,  coastal  use  justify  the  investment.  S i m i l a r l y , steep s l o p e s and v a r i a b l e t e r r a i n have  l i m i t e d the  extent  coastal  region.  of  ground  Ground  o c c a s i o n a l l y and o f t e n only commonly  used  skidding  skidders as  cable systems.  minor  operations are  used,  support  to  i n the but  only  the  more  Since t h i s t h e s i s i s concerned  66 with e s t i m a t i n g economic Columbia, the  the  effect  timber  remainder  of  resource  available  there  characteristics  necessary  to  know  coastal  British  on  manual  timber  a  number of d i f f e r e n t cable systems  the primary  the  effect  transport  phase,  i t is  of resource v a r i a b l e s on the  choice of a p a r t i c u l a r cable system to employ on a given The  c o n d i t i o n s which a f f e c t  d e s c r i b e d with r e f e r e n c e conditions  which  with  operations.  are  f o r completing  in  of t h i s s e c t i o n w i l l deal only  c u t t i n g and c a b l e yarding Because  supply  area.  the choice of c a b l e system w i l l be  to  'normal'  conditions;  are t y p i c a l of h i g h l e a d y a r d i n g  that i s , operations.  Resource c o n d i t i o n s c h a r a c t e r i s t i c of h i g h l e a d o p e r a t i o n s  can  be  used  considered  the  norm  because  i t i s the most widely  system i n c o a s t a l B r i t i s h Columbia, due o p e r a t i n g over an extensive Cottell  to  range of c o n d i t i o n s (Holmes, 1978;  yarding  direction  is uphill  yarders with a maximum slope of 70 percent of  capability, reduced Binkley,  for  1980).  Preferred  distance  capabilities  1000 thus,  feet. maximum  to 40 percent 1974).  Downhill slope  and maximum yarding  yarding and  for highlead  reduces  yarding  lift  d i s t a n c e are  and 600 f e e t , r e s p e c t i v e l y (Studier  Other  deterrents  to  and  d o w n h i l l yarding are  c o n c e n t r a t i o n of runoff v i a y a r d i n g roads, and i n c r e a s i n g the danger  to  yarder  (Holmes, 1978). not  extremely  single location.  operator  and landing crew from runaway logs  On g e n t l e slopes where difficult,  larger  downhill  yarding  areas can be yarded  On i n c r e a s i n g l y steep slopes  problems  is  from a with  67 downhill  yarding  yarder s e t t i n g s increases terrain  in  will and  road  become  prohibitive,  construction development  of  will  i s highly variable resulting  payload  capability,  distances  (both  compounded  if  which  uphill both  requiring  more  roads.  more  Similar  be necessary where the  i n poorer d e f l e c t i o n  and  must be o f f s e t by s h o r t e r y a r d i n g  and  downhill).  The  problem  is  steep slopes and broken t e r r a i n occur i n  combination. . Because of the higher road c o s t s and environmental  damage  resulting  from  increased  risk  of  h i g h l e a d o p e r a t i o n s on  steep, v a r i a b l e t e r r a i n with shallow s o i l s , a d i f f e r e n t  cable  yarding  these  system  conditions. coastal  is  To  meet  region  of  likely this  to  need  be  employed  operators  in  the  logs  travels.  y a r d i n g the s k y l i n e p r o v i d e s the l i f t provides  the  p r o v i d i n g both highlead  directional the  yarding.  pull,  vertical Depending  and on  to  a  stump or backspar,  one  or more intermediate supports.  over  and a separate  instead  of  horizontal the  the  percent or  to  l o g over  more  (Studier  a  mainline mainline  forces  as  in  ground p r o f i l e of the yarding  tower  and be supported along i t s length by  Because of these c h a r a c t e r i s t i c s long-reach designed  which  Thus, i n long-reach  s e t t i n g , the s k y l i n e can be suspended from the  be  western  These are c h a r a c t e r i z e d by  a " s k y l i n e " running the length of the s e t t i n g , suspending  the  North America have i n c r e a s i n g l y used some  form of long-reach y a r d i n g system.  carriage  under  f a v o r a b l e and adverse and  Binkley,  1974),  systems  can  slopes of 100 and  up  to  68 d i s t a n c e s of approximately  2800 meters (Conway, 1976).  the longer yarding d i s t a n c e s of these necessary  to  yarding  erosion.  This  on  aspect  distances,  operation not  slope,  more  of the  f u r t h e r reduces the r i s k of damage to However,  because  of  longer  higher c a p i t a l cost of yarders and l a r g e r  crew s i z e s , yarding c o s t s w i l l be greater than Subsequently,  the  suspended over the length  s o i l s and advance r e g e n e r a t i o n . yarding  Depending  d i s t a n c e and s e t t i n g l a y o u t , i t i s p o s s i b l e  to t r a n s p o r t the logs f u l l y skyline.  systems reduce the roads  l o g an area, which can lower l o g g i n g c o s t s and  reduce the r i s k of s o i l terrain,  Hence,  skill  i n planning  highlead.  and o p e r a t i n g a s k y l i n e  i s r e q u i r e d to ensure the r e d u c t i o n  l o s t to e x c e s s i v e  for  i n road c o s t s i s  i n c r e a s e s i n yarding and timber  cutting  costs.  3  Long-reach systems r e c e i v e should,  over  to a lack of relative yarding  less  only the more d i f f i c u l t experience  simplicity systems.  with  may  yarders,  experience  overstate  s k y l i n e c o s t s as noted by Waelti  than  they  or s e n s i t i v e s i t e s , due  long-reach  of and e x t e n s i v e  This  application  the  with  problem  and the highlead of  high  (1976):  "Operations should be planned on a drainage basis, so as to optimize the range and a p p l i c a t i o n of each system that w i l l be needed. So o f t e n the mistake i s made that common systems and equipment are used to the l i m i t (or even beyond the l i m i t ) of their capability, leaving only the toughest blocks for skylining. The  d e c r e a s i n g road d e n s i t i e s have been a s s o c i a t e d with d e c r e a s i n g productivity i n f a l l i n g and bucking due to i n c r e a s e d walking time (Sauder and Nagy, 1977).  69 consequence i s that the a p p l i c a t i o n s f o r the uncommon system become very limited and c o s t s abnormally h i g h . " (p. 173). In  summary then, we can conclude  that long-reach  be g e n e r a l l y used as a u x i l l i a r y  support  on steeper  variable  slopes  with  d e n s i t y has been reduced  more  to o f f s e t  systems w i l l  f o r high l e a d y a r d i n g , terrain  where  road  high c o s t s or environmental  damage. On the other end of the spectrum, running mechanical shorter  s k y l i n e s with a  or remote c o n t r o l l e d grapple are being used to yard distances  t y p i c a l of a distances  than  skyline  up  to  conventional  system  and  approximately  capable 365  150 meters or l e s s  s h o r t e r y a r d i n g d i s t a n c e s concern  of  meters  grapple yarders are p r e f e r a b l y used over approximately  highlead.  vision  (d) slower pull  (Oakley,  1976).  due  of  (c) one l o g per t u r n , increased  the  shorter  distances,  grapple  steeper,  smaller  times  and  crew costs  variable terrain  the  sizes.  Since  would  become  yarding  yarding  increased  road  prohibitive  on  s i t e s , grapple y a r d i n g w i l l  tend to  uniform • areas. ' Another  factor  be used on the g e n t l e r more affecting  line  increasing  These higher c o s t s can be o f f s e t by lower to  development  over  (b) r e s t r i c t e d  r e q u i r e s a higher road d e n s i t y than h i g h l e a d , thus  costs  Reasons f o r  a loss in p r o d u c t i v i t y  i n p l a c i n g the grapple,  of  1976).  Because  road c o s t s .  over  shorter distances  speeds of grapple y a r d e r s , and (e)  (Oakley,  yarding  (Conway, 1976),  longer d i s t a n c e s due to (a) l o s s of d e f l e c t i o n , operator  Although  productivity  of  grapple y a r d i n g i s l o g s i z e .  70  Since only one will  log i s yarded  change in log  proportionately alter productivity.  can o f f s e t decreases of  per t u r n , any  chokers,  long-reach most  i n log volumes by  to some extent  (Oakley,  systems, grapple y a r d i n g  commonly  used  as  highlead.  Efficiently  grapple  yarder  l o c a t e d on  can  Other c a b l e methods  increasing  1976).  a  the  number  Thus, as with  in c o a s t a l  an a u x i l l i a r y  size  B.C.  has  the been  system to c o n v e n t i o n a l  highlead  substantially  operation  increase  the  yarding  productivity. 4.32  Access Development Categories  cruising, road  (b)  in the development phase i n c l u d e :  (a)  engineering  boundaries,  locations,  setting  and  planning of area  layout,  etc.,  and  timber  (c)  road  construct ion. The  time  required  to  cruise  f u n c t i o n of area s i z e , timber  an  area  d e n s i t y , and  is primarily a  skill  of the  crew.  T h i s time w i l l a l s o be a f f e c t e d by c h a r a c t e r i s t i c s of the that may  impede crew m o b i l i t y , such as dense brush, w i n d f a l l s ,  rockbluffs,  variable  terrain,  given crew, over a f a i r l y wide correlations should develop  between  and  others.  range  area, timber  of  However, for a  conditions,  d e n s i t y and  strong  cruising  times  (Province of B r i t i s h Columbia, 1980e).  Engineering size..  area  times w i l l a l s o be p r i m a r i l y a f f e c t e d by  area  However, in a d d i t i o n to f a c t o r s that hamper f i e l d work,  the l o g g i n g system to be used on the area w i l l required  for  requirements  operational and  skill  design.  Thus,  in planning w i l l  a f f e c t the time increased  increase  road  engineering  71  times  (costs). Road c o n s t r u c t i o n times and c o s t s  size,  yarding  distance,  soil characteristics. increasing  area.  road  are  related  area  c l a s s , and s l o p e , t e r r a i n  T o t a l road requirements  Yarding  to  distance  is  increase  determined  and -with  by  the  yarding system employed, which i s i n f l u e n c e d by s l o p e , t e r r a i n and  timber  distances  size  characteristics  decrease,,  road  as  discussed  development  earlier.  As  (per u n i t area and in  total) increases. For a given area and development  costs  constructed. heavy  use  designed  will  involve  road  costs.  produce l o g s or from one  other  road  depending on the type of  roads  roads designed more  and/or  time and cost more than  permanent  roads  Thus, areas with a high branchlines  However, as these roads w i l l  have  be used to  to any  logging timber  (e.g. r e c r e a t i o n ,  will  areas, the f u l l cost should not be charged  roads,  expected  f o r long-term  etc.)  f a i r l y constant. be  or  services  road c o s t s w i l l  access  combination,  forestry,  specific  identifying of  system  f o r a s i n g l e short-term use.  p r o p o r t i o n of mainline higher  vary  On average, will  yarding  operation.  For  the  purposes  of  supply c o s t s on a s p e c i f i c area, a n a l y s i s be  thus,  concerned the  primarily  relevant  with  short-term  standard of road w i l l  However, f u r t h e r v a r i a n c e i n road c o s t s  f o r a s p e c i f i c area-system-road  as s l o p e , t e r r a i n and  class  soil characteristics alter  m a t e r i a l s r e q u i r e d to b u i l d a u n i t of  road.  be can  combination  the time  and  72  Calculation essentially  a  requirements yarding  of  road  two-stage are  costs  for  process.  determined  system  used  (or  characteristics  that  affect  as  a  supply  First,  analysis is  the  total  road  a f u n c t i o n of area s i z e  the  site,  system  stand  choice).  and  and tree  Second, f o r a  given road c l a s s the cost per u n i t of road must be a d j u s t e d to account and  for v a r i a b i l i t y  stems  per  c a l c u l a t i o n s as  in s o i l depth,  hectare,  to  determined  name  by  the  type, a  slope,  few  terrain  (e.g. road  B.C.F.S.  cost  (Province  of  B r i t i s h Columbia, 1980e) for stumpage a p p r a i s a l s ) . 4.33  F a l l i n g And  Bucking  There  two  are  b a s i c ways i n which t r e e , stand and  c h a r a c t e r i s t i c s of an area a f f e c t and  buck  standing  timber.  the time  First,  required  there are those  which hamper crew m o b i l i t y over an area, and those  to  site fall  factors  second, there are  f a c t o r s which i n c r e a s e the a c t u a l time c u t t i n g  a  given  t r e e or a r e a . In  the  windfalls, ability any  first  slope  category  and  terrain  same  factors  In dense brush  from  around  when  falling  breakage.  may  For  the  spent  also  same  the  increase in  moving,  increase  the f a l l e r must f i r s t  around  An  affect  rather  productivity  the t r e e to be f e l l e d . trees  will  an area.  f a c t o r s i n c r e a s e s the time  than c u t t i n g , thus decreasing These  f a c t o r s as brush d e n s i t y ,  variability  of a crew to move throughout  of these  times.  such  actual cutting  clear  the  E x t r a care must be  windfalls  to  avoid  brush taken  excessive  reason e x t r a time must be taken  on  73  h i g h l y v a r i a b l e or broken t e r r a i n . s l i d e or r o l l d o w n h i l l ,  thus,  time to complete bucking and Other  factors  per  increases volumes  so at  will  productivity. correlated,  imply Since  felling  when  falling  trees  of  tree  taller  increase  to  and  productive  falling  between f a l l i n g other  An  rather  unit  increase other  than  costs  log  are  times and is  in a l l stand  not  increased positively  excessive diameter  be  factors.  with taken  breakage. trees,  and  which r e q u i r e more  t h i n g s being  number  of  equal, r e s u l t s  However, more time i s spent walking,  thus, Best  conditions  (thus log and  densities,  productivity  the  high  and An  will  be  for  volume  stem volume) relationship  stems or volume per h e c t a r e , clear  stem  also associated  in e i t h e r the  decrease.  stem  or  but  are stands with many stems of  increasing  variables,  variations  is  larger  However, since diameter  decreases with  time thus  times  avoid  in c u t t i n g times.  increases  stem.  increased  greater merchantable height  on c u t t i n g timber  per  increased  diameter  height  diameter  greatly  greater  cutting  trees  stems or volume per hectare, an  the  tree  defect,  As  A d d i t i o n a l l y , more care must  cuts to d e s i r e d l e n g t h .  in  but,  Subsequently,  and  volume,  hectare.  offset  Bucking times a l s o increase with for  stem  per  t r e e height  times.  walking  c u t t i n g times are  or  times,  longer  increased  longer  log  diameters  increases.  also  timber  volume  falling  larger  productivity volumes  and  additional  will  limbing.  affecting  hectare  steep s l o p e s t r e e s  requiring  diameter, merchantable h e i g h t , stems  On  as  affected  with by  i n c r e a s i n g amount of t r e e  74  or stand d e f e c t buck  will  increase  the time necessary to  fall  an area, as well as decrease the net p r o d u c t i o n  site.  As a r e s u l t , defect  by i n c r e a s i n g  factor costs  Considering factors (e.g.  has a double impact on per u n i t and lowering  a l l variables  increasing  i t can  production  times  be  from the  unit  costs  productivity.  seen that  for  and  a  those  given area  tree diameter and h e i g h t , stems per h e c t a r e , e t c . , ) w i l l  increase factors (e.g.  productivity increasing  brush,  productivity 4.34  and  decrease  production  slope,  times  terrain,  and increase  unit  unit costs, for  area,  a  while those given volume  etc.) w i l l  decrease  costs.  Yarding Many of the  falling  same  variables  and bucking have an i n f l u e n c e  also.  However,  in an  indirect  position,  influence through  manner.  few  Once  production  resource  yarder  studies  This  y a r d i n g method v a r i a t i o n s  will  should  characteristics.  It  has  have  has been  felt been  strong  discovered  will  managers I have c o n t a c t e d .  have  greater  in productivity  be  traceable  is  these  influence  However, will  under s i m i l a r c o n d i t i o n s  experience, that  are mostly  as d i s c u s s e d e a r l i e r and has been  v a r i a t i o n at t h i s stage.  blocks,  productivity  setting  variables  by statements of logging  productivity  on y a r d i n g  in  system, and the yarder has been p l a c e d  Weather and crew e f f e c t s  cutting  a  over yarder p r o d u c t i v i t y .  reinforced  productivity  the e f f e c t s of these v a r i a b l e s  designed f o r a s p e c i f i c into  affecting  to  over  f o r any given occur  between  of weather and crew specific  variations  that  resource must  be  75 accounted for in a study  of timber  given area, temporal v a r i a t i o n mainly  affected  by  the  these  s i n c e over a  in l o g g i n g p r o d u c t i v i t y w i l l interaction  c h a r a c t e r i s t i c s and p r o d u c t i o n With  accessibility,  between  technology  considerations  be  resource  in each time p e r i o d .  in  mind  then,  yarding  p r o d u c t i v i t y w i l l a l s o be a f f e c t e d by such v a r i a b l e s as  brush  density,  other  slope,  terrain  variability,  windfalls  (and  o b s t a c l e s ) , l o g volume, volume per h e c t a r e , stems per t o t a l volume, area s i z e  and  bucking  with  falling  and  brush  slope,  terrain  and  decrease  in  hampering movement of the crew, in t h i s  case  productivity,  windfalls  (non-recoverable)  productivity the choker  by  setters.  may  conditions.  4  yarding times  As  density, will  However,  p o r t i o n of t o t a l y a r d i n g time, variables  defect.  effect  because  a  choking  per  is  only  the n o t i c e a b l e e f f e c t s of  a  these  be r e l a t i v e l y minor over a f a i r l y wide range of Increases  in log volumes r e s u l t  in i n c r e a s e s in  s i n c e : (a) i t takes longer to choke l a r g e r l o g s ,  (b) depending on equipment c a p a b i l i t y , the number used  hectare,  turn must be  turns,  other  larger  logs may  reduced, thus,  things being e q u a l ,  5  chokers  i n c r e a s i n g the number of  and,  i n c r e a s e inhaul times.  of  (c) h e a v i e r weight of In  general,  however,  4  With regard to slope e f f e c t on the ground crew, Conway (1976, p. 216) f e e l s that maximum production i s p o s s i b l e up to slopes of 50 percent, with a loss of ". . . 1 0 to 12 percent of normal p r o d u c t i o n . . . for each 10 percent i n c r e a s e in slope. . . ".  5  An i n c r e a s i n g number of turns may not be realistic, since, increases in log volumes are generally associated with d e c r e a s i n g number of stems per hectare and thus fewer pieces to be yarded on an a r e a .  76  the  increased  per  turn,  times  thus,  productivity. production decrease, greater  costs  times as the  increase  an  in  d e f e c t , as with  unit  unit volume  costs  of  production  recovered  should  be  time. to be yarded  increase  However, the  with  in and  production costs  times.  differ  a l l e l s e constant  i n c r e a s e s and cost decreases. when  greater  i n c r e a s e s i n t o t a l volume or area  increases  increases  through  i n c r e a s e d volume per u n i t area, but  increases  e f f e c t on p r o d u c t i v i t y  net  reduced  than increases i n yarding  in  Volume  are  S i m i l a r l y , with  Therefore, result  are o f f s e t by the g r e a t e r volume yarded  a l l other  The reverse  between  the  imply p r o d u c t i v i t y i s true  with  f a c t o r s remain c o n s t a n t .  f a l l i n g and bucking  two.  area  Finally,  p r o d u c t i v i t y , reduces  the  s c a l e yarded and thus decreases p r o d u c t i v i t y and i n c r e a s e s costs.  weights  This may be o f f s e t  thereby  productivity.  decreasing  somewhat i f decay reduces l o g  inhaul  net s c a l e reductions  increasing  by  decreasing  productivity  through  i n volumes yarded.  4.4  INPUT DEMANDS AND BRITISH COLUMBIA  4.41  Objective  PRODUCTIVITY  The o b j e c t i v e in t h i s stage  characteristics,  for  OF  LOGGING IN COASTAL  of the a n a l y s i s i s to develop  r e l a t i o n s h i p s between input demands,  directly  and  However, the l o s s of 'sound' wood i s l i k e l y to  have i t s g r e a t e s t e f f e c t  resource  times  logging p r o d u c t i v i t y  phases of the l o g g i n g  i n f l u e n c e d by v a r i a b i l i t y  in  operating  and  process  conditions.  77  Because of d i f f i c u l t i e s data the  encountered i n o b t a i n i n g  on road c o n s t r u c t i o n phases of  (yarding).  falling  times, the a n a l y s i s concentrated on  and  bucking,  Additionally,  yarding  operational The  system,  and  and  primary  relationships  provide estimates of the length of  area-specific  of roads  were  transport  analysed  constructed,  characteristics.  purposes.  be p r o j e c t e d  based on  costs  be  can  inventory  estimated.  production.  omitted v a r i a b l e s  used  characteristics,  The  preclude  equations  are  and not  among  development  the of  true  useful  and thus should be u s e f u l  in predicting  predictive  f o r i d e n t i f y i n g the most s i g n i f i c a n t  relevant modeling.  v a r i a b l e s which w i l l a i d future For  these  be  and  But,  it  timber  i t s economic  equations as  in  structural  on resource c h a r a c t e r i s t i c s .  Additionally,  to  included  i s these very c h a r a c t e r i s t i c s that q u a l i f y the p h y s i c a l  recoverability.  phase  of f u n c t i o n a l r e l a t i o n s h i p s  Interactions  r e l a t i o n s h i p s based only  inventory  for  Using the equations, p r o d u c t i v i t i e s can  misconstrued as r e p r e s e n t a t i v e logging  choice  a c t u a l volume cut, as determined by  r e l a t i o n s h i p s developed are intended to be  predictive  to  well  can be as a l l  e f f o r t s at p r o d u c t i o n  purposes the p r e d i c t i v e approach seems  most s u i t e d , as noted by Draper and Smith  (1966):  "... p r e d i c t i v e models are very useful and under c e r t a i n c o n d i t i o n s can lead to real insight into the process or problem. . . (which) are u s u a l l y r e f e r r e d to as 'problems with messy data' - that i s , data i n which much i n t e r c o r r e l a t i o n e x i s t s . . . " (p. 235).  78  4.42  Scope Sampling  was  c a r r i e d out  in the coast region of  Columbia, which i n c l u d e s the combined areas of and  Prince  Rupert "Forest A n a l y s i s Regions"  the  British  Vancouver  as designated  by  the M i n i s t r y of F o r e s t s (Province of B r i t i s h Columbia, 1980b). Although  this  is  an  extensive  c h a r a c t e r i s t i c s are s i m i l a r The  sampling  o p e r a t i o n s had All  samples  area,  throughout.  u n i t s were c u t t i n g blocks on which logging  been completed for a l l or part were  of  area  specific  resource data are a v a i l a b l e on these tenures. operations  may  take  completion,  the p e r i o d sampled ranged from 1977  several  years  were s t i l l  for the area completed. yarder  settings,  On  block.  (TFL), since and  Because logging initiation to 1979. cutting  and Most  blocks  in progress, data were c o l l e c t e d  Block s i z e ranged from  governed  the  production  between  blocks had been completed p r i o r to 1979. operations  of  l o c a t e d on Tree Farm L i c e n c e s  the best combined records  where  operational  mainly  one  by landform  to  many  and/or•timber  type. The m a j o r i t y of samples were l o c a t e d on Vancouver I s l a n d . Of a t o t a l 48 located  on  mainland, and the  samples Vancouver  taken Island,  along 7  coastal on  B.C.,  the southwestern  4 on the Queen C h a r l o t t e I s l a n d s .  distribution  37  6  Even  were lower though  of samples on a r e g i o n a l b a s i s i s narrow, I  'The exact l o c a t i o n of samples w i l l not be shown so as to conform with requests by cooperating firms to conceal the source of p r o d u c t i o n d a t a .  79 b e l i e v e the sample data are r e p r e s e n t a t i v e  of  the  range  in  l o g g i n g c o n d i t i o n s on the c o a s t ; e x h i b i t i n g c h a r a c t e r i s t i c s of the  easiest  timber of  to  most  quality.  the  major  Columbia These  d i f f i c u l t topography, and  A l s o , I b e l i e v e the companies sampled integrated  are  forest  indicative  companies  of  industrial  coastal  c o n t r o l l e d approximately  c o a s t a l a l l o w a b l e annual cut Each  (AAC)  logging 71.9  percent  employed.  on  the  yarding method was  classified  area.  yarding methods  minor.  As  system, t o t a l of  two  used  Since t h i s s i t u a t i o n occurred on only 3 of logged  cable  h i g h l e a d , grapple,  a  result  sample yarding  tension the  of  size were skidder systems  the  by the l e s s e r systems were  s m a l l , the e f f e c t on the dominant system be  of  If not,  by the system most e x t e n s i v e l y  the area  of  If the  were formed from the s i n g l e b l o c k .  sampled b l o c k s , and  will  one-third  i d e n t i f i e d s e p a r a t e l y f o r each method, then  samples  the sample was  the  i d e n t i f i e d by the type  the  more  of  7  On  or  six  management.  cable y a r d i n g method used to log the area. blocks more than- one  -  firms in B r i t i s h  on TFL's in 1978.  sampled c u t t i n g block was  data c o u l d be  7  poor to good  and  final  analysis  t h i s sample s p l i t t i n g increased encountered: and is  to  64.  among  36,  respectively.  Because of small sample s i z e s and  Four  conventional  slackline.  distribution  by  15,  Sample 6  and  7  similarities  I n t u r n , the AAC on c o a s t a l TFL's was about 55% of combined c o a s t a l AAC f o r PSYU's and TFL's. The most recent estimate of total control (Pearse, 1976. v o l . 1 , p. 39) show these same companies to c o n t r o l approximately 65% of t o t a l committed AAC in 1974.  80  between  t e n s i o n skidder and  were combined i n t o one  s l a c k l i n e systems the two  sample group c l a s s i f i e d  as  methods  long-reach  systems 4.43  V a r i a b l e s Sampled And  Measurement Procedures  For  I  each  constructed  (meters),  yarding  times  meters),  and  and  site  review  sample  f a l l i n g and  (machine  the  bucking  hours),  length  times  of  (man  hours),,  net volume harvested  (cubic  the  of  literature,  the as  area  logged.  discussed  in  were measured and Variables and  operational Site  recorded  defining stand  size  tree  size,  were  c r u i s e s that had  accessibility  measured  as shown i n Table  the  previous  variables  studies  from  records  (excluding  elevation)  were  o n - s i t e during t r i p s to the sampled o p e r a t i o n s .  Forest  Service  developed by  maps  of  times for f a l l i n g and  the  The  British  for stumpage a p p r a i s a l p r o d u c t i v i t y  (Province of B r i t i s h Columbia, 1979a).  engineering  of -  as w e l l as length of roads c o n s t r u c t e d  daily  d e n s i t y , volume,  been completed p r i o r to logging .  i n d i c e s are d i r e c t l y based on those Columbia  factors  2.  stand  determined  stand  Based on a  s e c t i o n , seventeen v a r i a b l e s d e s c r i b i n g seven resource  quality  roads  a number of v a r i a b l e s d e s c r i b i n g the t r e e ,  characteristics  of  recorded  were  Mean e l e v a t i o n calculated  the sampled c u t t i n g b l o c k s . bucking,  and  from  Production  yarding were developed from  time cards or monthly p r o d u c t i o n  summaries.  s c a l e d were a l s o determined from company  records.  Net  volumes  «•  81 Table  2.  Resource F a c t o r s and  Factor  Identified Variables  Notation  Tree S i z e  D H  Definition Stand average diameter at breast height (1.37m) i n c e n t i m e t e r s . Stand average height to c l o s e u t i l i z a t i o n standards i n meters. Stand average log volume f o r a 10 meter l o g , i n c u b i c meters, based on actual number of logs harvested and net harvested volume. Average volume per hectare to close u t i l i z a t i o n standards, i n c u b i c meters Average number of stems per hectare to c l o s e u t i l i z a t i o n standards. Total cruised timber volume to c l o s e u t i l i z a t i o n standards i n c u b i c meters. Estimated decay, waste and breakage, as a percent of t o t a l volume Area in h e c t a r e s . Ground slope across contours i n percent. Terrain variability index; measure of variability along contours: l=even, 2 = r o l l i n g , 3 = g u l l i e d , 4=broken. Brush d e n s i t y index: l = l i g h t , 2=medium, 3=heavy, 4=v. heavy. Exposed bedrock index; measure of percent of area with exposed bedrock: 0=none, 1=1-10%, 2=11-30%, 3=31%+, 4=rock b l u f f s or c l i f f s . O b s t a c l e s index; measure of the s i z e and extent of boulders, windfalls (<50% r e c o v e r a b l e ) , stumps, e t c . : sum of the number in each size category (0.25-0.5,0.51-1.0,1.1+ meters in height) times the low-end height value for the category. Mean stand e l e v a t i o n i n meters. S o i l type index: 10=organic, 2 0 = s i l t , 30=clay, 40=loam, 50=sand, 60=gravel, 70=cobble. Record major and minor types (e.g. 56=gravel/sand). Soil moisture index: l=dry, 2=moist, 3=wet, 4=swampy. S o i l depth to hardpan i n meters. :  ALV  Stand  Density  VPH SPH  Stand Volume  V  Stand Q u a l i t y  •c  Stand S i z e Site Accessibility  A S T  2  B  EX  0  Soil Characteristics  E ST  SM SD  ^lose utilization standards on the British Columbia coast consist of utilization of a l l volumes i n t r e e s with 22.5 cm+ DBH, between a 30 cm stump and 10 cm top d . i . b . "Site Accessibility" and "Soil Characteristics" indices and variables are d i r e c t l y based upon those developed f o r stumpage a p p r a i s a l p r o d u c t i v i t y s t u d i e s (Province of British Columbia, 1979a).  2  82 4.44 Regression Hypotheses And Procedures Based  on the presumed i n f l u e n c e of resource v a r i a b l e s on  p r o d u c t i o n times a set of hypotheses response  was formed  v a r i a b l e with an unknown l i n e a r  variables.  Seven  hypotheses  were  equating  the  f u n c t i o n of p r e d i c t o r set  up  to  determine  p r e d i c t i v e equations f o r : l e n g t h of roads c o n s t r u c t e d , f a l l i n g and  bucking  harvested  productivity, and  yarding  yarding system  productivity,  choice.  The  volume  hypothesized  r e g r e s s i o n s were as f o l l o w s : (4.1)  RL = F(D,H,ALV,SPH,VPH,A,E,S,T,B,EX,0,ST,SM,SD,Z)  (4.2) F&BP = F(D,H,ALV,SPH,VPH,C,A,S,T,B,EX,0,RPH) (4.3)  YP = F(D,H,ALV,SPH,VPH,C,A,S,T,B,EX,0,Z)  (4.4)  Q = F(Vnet,F&BT,YT,Z)  (4.5)  P i = F(D,H,ALV,SPH,VPH,V,C,A,E,S,T,B,EX,0,RPH)  Where:  RL = road length i n meters. F&BP = f a l l i n g and bucking productivity in cubic meters per man hour. YP = y a r d i n g productivity i n c u b i c meters per machine hour. Q = harvest volume, net s c a l e in c u b i c meters. Pi = p r o b a b i l i t y of choosing logging system i ; i=1,highlead; 2,grapple; 3,longreach. Z = v e c t o r of l o g g i n g system dummy v a r i a b l e s . RPH = road d e n s i t y i n meters per h e c t a r e . F&BT = f a l l i n g and bucking phase time i n manhours. YT = y a r d i n g phase time i n machine hours. Vnet = t o t a l cruised timber volume net of estimated decay, waste and breakage (C), i n c u b i c meters. (Other v a r i a b l e s as given i n Table 2)  Equations programs  were  compiled  calculated at  the  using  University  stepwise of  regression  British  Columbia  Computing Centre by White and G r i e g (1979), and Le and T e n i s c i (1978).  In a d d i t i o n to the o r i g i n a l v a r i a b l e s l i s t e d  i n Table  83 2, polynomial and independent A  of  factors  equation.  it  was  were  Because  interrelationships comprising  transformations  in  the  of  the  biotic  taken  that  would  present  and  attempt  specification,  (4.5).  most o f t e n , important  or  strongly,  initial  regression  of  variation  added  at  explanatory  correct  model  included).  To  estimations considered a i n each of the  indicated  each  to,  in  in  Through the use of " p a r t i a l F - t e s t s " were  in  the  obtained,  equations  V a r i a b l e s i n c l u d e d i n t h i s stage were those  sources  variables  in  of  communities  small sample  variables  subset of the v a r i a b l e s hypothesized to  edaphic  problems  ( i . e . a l l relevant  proper  extensiveness  multicollinearity  specification  (4.1)  potential  c o n s i d e r e d i n s e l e c t i n g the  f o r e s t s , and the r e l a t i v e l y  variables  of  v a r i a b l e s were t e s t e d .  number  "best"  logarithmic  retained  the  the  literature  response  variable.  (Draper and Smith, or  excluded  as  1966),  from  the  stage, i f t h e i r a s s o c i a t e d "F" value was  s i g n i f i c a n t at the 95 percent confidence l e v e l .  If  at  least  60 percent of t o t a l v a r i a t i o n c o u l d not be e x p l a i n e d , then the remaining  hypothesized v a r i a b l e s were c o n s i d e r e d f o r p o t e n t i a l  inclusion.  After  tests  of  relevant  transformations,  e x p l a i n e d v a r i a t i o n s remained l e s s than .60 percent, probability  level  was  reduced  to  10  percent  then  if the  (90 percent  c o n f i d e n c e l e v e l ) and r e g r e s s i o n s were r e c a l c u l a t e d . Equations analysed,  selected  using  (Johnston, 1972;  f o r hypotheses  dummy Cunia,  variable 1973),  to  (4.1)  to  (4.4)  covariance determine  were  techniques if  a  single  84 equation an  across a l l y a r d i n g systems was  individual  Finally,  equation  residuals  and t e s t e d  was  sufficient  necessary  for  f o r h e t e r o s c e d a s t i c i t y and  examined  autocorrelation. predicting  c h o i c e , the above procedures were c a r r i e d out f o r each  identified  From the s e l e c t e d  equations  that proved,to be s i g n i f i c a n t  of the e q u a t i o n s .  Regressions  were  necessary to ensure that the sum (Pindyc.k  and  Rubinfeld,  variables  in at l e a s t  recalculated  same independent v a r i a b l e s f o r each system.  one  system.  of the s e l e c t e d r e g r e s s i o n s were  system independently. were  whether  each  In d e v e l o p i n g the l i n e a r p r o b a b l i t y model f o r system  or  using  T h i s approach  two the was  of system p r o b a b i l i t i e s equal 1976),  guarantying  a  unique  solution. 4.45  Qualitative  Analysis  V a r i a b l e means, c o e f f i c i e n t s of maximum  values,  variation,  minimum  by i n d i v i d u a l y a r d i n g systems and a c r o s s a l l  systems, are given i n Table 3.  Simple c o r r e l a t i o n s by  and  given  across  a l l systems  .are  v a r i a b l e histograms f o r a l l systems Because of i t s wide use operating  This  can  maximums f o r each system  be  Appendix  1, as are  combined. relative  to  That  by  between  i n Table 3.  explain is,  range  seen  variable  (ALL) s t a t i s t i c s  be d i f f i c u l t choice.  and  in  system  insensitivity  to  c o n d i t i o n s , h i g h l e a d y a r d i n g o p e r a t i o n s occurred on  areas r e p r e s e n t i n g the f u l l sampled.  and  since  much  of  in  nearly  comparing  all  variables  the minimums and  highlead  (HL)  and  all  For t h i s reason, i t w i l l the  variation  h i g h l e a d y a r d i n g was  in  system  used over the  85  same c o n d i t i o n s as were  grapple  and  long-reach  systems  appears that equipment a v a i l a b i l i t y and management the  major  resource where  factors  in determining  variability. highlead  not  between systems, i t should  resource  characteristics  management  choice,  system c h o i c e , rather than  represent  comparing the r e l a t i v e d i s p e r s i o n means  s k i l l s were  However, by l o o k i n g at those  did  that  given  the  it  the  of  variables  extremes,  variables  and  about  by  their  be p o s s i b l e to i d e n t i f y some are  likely  to  influence  option of a l t e r n a t i v e  yarding  systems The was,  lowest  as  observed and lowest  expected,  were used.  of  the  density  (RPH)  yarding  systems  longer  yarding  Although the d i f f e r e n c e i s i n s i g n i f i c a n t , minimum  and mean road d e n s i t y was g r e a t e r operations.  This  supports  on  grapple  than  the assumption of s h o r t e r  d i s t a n c e s on average f o r grapple  expected  road  on areas where long-reach  This i s a natural result  distances.  The  mean  highlead yarding  yarding.  i n s i g n i f i c a n t d i f f e r e n c e between the two systems since  "splitting" operations.  the  13  of  sampled  the  16 a d d i t i o n a l samples d e r i v e d by  blocks,  were  For the samples obtained  grapple  (1976):  on  i t appears that  y a r d i n g was used to complement h i g h l e a d yarding d e s c r i b e d by Oakley  was  highlead grapple  i n a manner as  Table  3. V a r i a b l e S t a t i s t i c s : Mean, Standard D e v i a t i o n , Minimum and Maximum. ( B r i t i s h Columbia — Coast Region)  Means Variable ALL RL (M) RPH (RL/A) F&BT (Man Hours) F&BP (Q/F&BT) YT (Mach. Hrs.) YP (Q/YT) Q (Cu. M.) E (H) S tt) T B EX 0 SD (M) ST SM H (M) D (CM) C (7.) ALV (Cu. M.) SPH VPH (V/A) V (Cu.M., C.U.) A (HA) VNET  l  1  1003.4 37.52 1457.0 12.93 765.54 25.07 18511.0 454.04 30.31 2.47 1.84 0.98 1.01 0.52 45.84 2.29 30.60 54.85 17.70 1.71 206.25 982.15 27610.0 28.38 22230.0  HL  2  1268.9 41.67 1607.4 13.76 879.4 24.73 21389.0 484.5 32.91 2.60 1.79 0.96 1.20 0.57 45.19 2.37 31.36 55.45 19.74 1.52 231.02 989.7 33751.0 34.16 26628.0  C o e f f i c i e n t of •a  Minimum  Variation  Maximum  • A  GV  LR  ALL  875.4 42.39 1376.0 11.18 689.9 24.20 15172.0 362.5 21.84 2.26 1.73 0.71 0.87 0.60 42.0 2.32 29.05 52.17 16.39 1.71 .172.8 938.7 21085.0 23.34 17401.0  540.7 25.55 1134.0 12.66 537.4 27.0 14393.0 475.45 32.89 2.35 2.09 1.34 0.65 0.29 52.08 2.00 30.30 56.29 13.54 2.23 176.3 1011.3 18135.0 18.19 15622.0  95.9 60.5 68.9 39.3 79.2 27.4 83.4 46.6 45.6 27.1 41.3 95.9 87.1 105.8 36.3 17.9 11.4 11.8 33.6 36.2 34.5 21.5 83.0 76.1 80.7  HL 83.8 63.5 69.0 46.8 78.6 28.5 86.1 48.3 38.2 23.0 37.4 101.0 85.0 119.3 40.4 18.6 12.0 12.5 31.8 35.5 31.4 21.8 79.2 71.0 78.3  GY 105.7 31.5 68.2 14.7 77.5 32.7 68.3 42.6 41.8 28.8 48.0 104.2 51.7 66.7 36.8 19.0 10.7 13.5 31.4 24.6 20.5 23.4 69.4 71.2 69.2  LR 103.4 57.0 60.9 18.4 59.8 18.8 61.6 38.7 55.2 35.3 44.0 73.1 110.8 41.4 22.7 0.0 8.2 6.7 18.3 30.9 42.3 19.1 89.9 70.6 69.8  ALL 29.4 2.1 127.4 6.52 48.0 14.48 1276.0 91.4 0.0 1.0 1.0 0.0 0.0 0.11 13.0 2.0 26.2 43.2 11.4 0.55 108.2 539.9 1531.2 1.5 1286.2  HL  GY  148.6 205.0 16.8 24.1 163.6 127.4 6.52 6.87 130.6 48.0 14.48 14.98 2124.4 1276.0 91.4 121.9 0i0 7.3 1.0 1.0 1.0 1.0 0.0 0.0 0.0 . 0.19 0.12 0.11 13.0 13.0 2.0 2.0 26.2 26.2 43.2 43.2 11.7 11.9 0.55 0.99 114.70 114.70 539.9 556.8 2737.4 1531.2 2.4 1.5 2376.1 1286.2  LR  ALL  29.4 2.1 310.8 10.69 142.0 16.32 3822.8 182.9 10.0 1.0 1.0 0.0 0.0 0.12 13.0 2.0 27.0 49.7 11.4 0.81 108.2 573.1 5914.4 6.0 5163.3  3988.6 153.3 4101.5 44.47 2972.0 45.46 82206.0 1005.8 85.0 4.0 3.0 4.0 5.75 4.10 75.0 3.0 40.7 72.8 32.2 2.97 391.6 1336.8 103380.0 89.0 82396.0  Statistics  f o r A l l Systems Combined. N (Number o f O b s e r v a t i o n s ) = 64 f o r A l l V a r i a b l e s E x c l u d i n g RL and RPH Where N = 49.  Statistics  f o r H i g h l e a d Yarding. N " 36 f o r A l l V a r i a b l e s E x c l u d i n g RL and RPH Where N = 27.  HL 3988.6 153.3 4101.5 44.47 2972.0 44.36 82206.0 1005.8 60.0 4.0 3.0 4.0 5.75 • 4.10 75.0 3.0 40.7 72.8 32.2 2.77 391.6 1336.8 103380.0 89.0 82396.0  GY  LR  3044.7 61.9 3234.4 13.20 1868.9 45.46 39454.0 701.0 36.2 3.53 3.0 2.11 1.81 1.00 56.0 3.0 37.0 72.8 25.0 2.74 231.6 1186.6 42602.0 51.0 37532.0  1884.9 44.0 2830.8 20.23 1282.2 36.95 34530.0 792.5 85.0 4.0 3.0 3.0 2.25 0.50 56.0 3.0 36.1 61.8 20.2 2.97 335.5 1301.4 48136.0 53.7 42504.0  S t a t i s t i c s f o r Grapple Y a r d i n g . N - 15 f o r A l l V a r i a b l e s E x c l u d i n g RL and RPH Where N » 9. S t a t i s t i c s f o r Long-Reach Y a r d i n g . N • 13 f o r A l l V a r i a b l e s .  CO  87  "To gain a l l the advantages of y a r d i n g d i s t a n c e , l o g s i z e and d e f l e c t i o n , c a r e f u l engineering layout i s e s s e n t i a l . . . so that the maximum acres are logged with grapple y a r d i n g cranes without l e a v i n g an impossible situation for conventional yarding equipment. . . the usual p r a c t i c e i s to yard f i r s t with the crane so that doubtful areas are t r i e d and maximum p r a c t i c a l volumes are yarded." (p. 30) Thus, c u t t i n g blocks engineered road d e n s i t i e s appear to auxilliary Many  provide  logging with grapple of  the  grapple y a r d i n g For  f o r h i g h l e a d yarding with  example,  greater  opportunities for  yarders.  s i t e v a r i a b l e s support  i s g e n e r a l l y used on measures  of  the assumption that  more  accessible  i n exposed bedrock had t h e i r  maximum  on  variables  were  grapple  measured  areas.  slope, t e r r a i n v a r i a b i l i t y ,  d e n s i t y and area values  high  lowest  yarding o p e r a t i o n s .  separately  on  mean  Since  blocks  brush and these  with  both  h i g h l e a d and grapple y a r d i n g , the values are i n d i c a t i v e of the type  of  conditions  were the primary clear  a  grapple yarder would operate  system used.  The d i s t i n c t i o n  between h i g h l e a d and long-reach  on i f  i s not  it  equally  logging operations.  In  c o n t r a s t t o assumed r e l a t i o n s h i p s , slope and t e r r a i n v a r i a b l e s had  their  highest  mean  long-reach  cutting  blocks.  nearly  identical  blocks observed  had  the  value  on  the  two  highest  minimum, likely  systems, maximum  that  further  r e v e a l a g r e a t e r mean slope on long-reach statistics  may  equipment are being  also used  rather  than  However, s i n c e slope means were  between  values, i t i s  highlead  indicate beyond  that  and  long-reach  and v a r i a t i o n i n sampling  cutting blocks. conventional  efficient  limits  will The  yarding on  some  88  areas.  Another  possibility  samples were obtained appears  to  quality,  have  on  It  one  that most of the  company  over  an  is  than  did  probably  areas  sample  for  blocks.  o p e r a t i o n s over a wider  t h i s same reason  Increased  range  of  volumes  were  net  decay values as expressed It  height,  is difficult diameter,  could  not  cull,  inference  stems  per  located  on  long-reach  and  companies  to  take  summary,  about  The  all  probability  volume per  since  greater  advantage  since  of  log  size  log  in  the  variables,  for choosing  analysis  sampling  of  occurred volumes  maintaining  sampled values f o r v a r i a b l e s on  little  of  the  the  of  individual  range  variation  in  for the  a system can be p o s s i b l y e x p l a i n e d by  resource c h a r a c t e r i s t i c s as w i l l be seen i n the next However,  cruise  earlier.  h i g h l e a d c u t t i n g b l o c k s are r e p r e s e n t a t i v e of nearly  (C). comparative  and  samples,  to  s e t t i n g s i n d i c a t e that grapple yarders are  p r o d u c t i v i t y , as proposed In  Since sample  be s e p a r a t e l y i d e n t i f i e d where they  grapple  on  of  a l s o be due  hectare  highlead  together on a s i n g l e c u t t i n g b l o c k . yarded  that mean  by the v a r i a b l e c u l l  to draw any  hectare between grapple and data  other  of decay, p a r t of the e x p l a n a t i o n for  higher l o g volumes on long-reach cut blocks may lower  timber  greatest  sampling  conditions  that  from  would be needed to f u r t h e r t e s t t h i s assumption. log  area  sampled  log volume and volume per hectare were  long-reach  long-reach  e a s i e r logging c o n d i t i o n s and b e t t e r  average,  companies. diameter,  from  is  the  variables  grapple  and  shows  that  long-reach  section. increased logging  89 operations  should  strengthen  some  underlying  trends  in  resource c h a r a c t e r i s t i c s and system c h o i c e . Simple c o r r e l a t i o n s in  falling  site, a.  and  (Appendix  1)  between  productivities  bucking, y a r d i n g , and v a r i a b l e s r e p r e s e n t i n g  stand and t r e e c h a r a c t e r i s t i c s are as hypothesized, with  few  exceptions.  productivity  is  As  expected,  negatively  falling  correlated  and  bucking  with s l o p e , t e r r a i n ,  brush and exposed rock, and p o s i t i v e l y c o r r e l a t e d with height, diameter,  volume per  density.  hectare,  Similarly,  stems  yarding  per  hectare  productivity  and  i s negatively  c o r r e l a t e d with slope, t e r r a i n , exposed rock and road (because  of  positively  an  implicit  correlated  increase  with  road  density  i n s e t t i n g changes), and  height,  diameter,  volume  per  hectare and l o g volume. Discrepancies correlation  with  breakage), Since  in  and  values  positively  falling  obstacles (b)  for  and  negative  both  correlated  and bucking a r e ; (a) p o s i t i v e  obstacle with  increased  caused  i n c r e a s i n g decay percentages. essentially  and  height  in  times  the  waste  with  cull  old-growth  variables  offset  the  of  mobility  and  Hence, these two  measures  are  by  relationship  stands  That  i s , as  c u t t i n g time w i l l  tree  increase,  are  i t appears  loss  size.  between  falling  and bucking  p r o d u c t i v i t y and log volume i s d i s c u s s e d i n terms of a tree.  and  l o g volume.  and diameter,  i n d i c e s of r e l a t i v e timber  Usually,  (decay,  correlation  that g r e a t e r tree volumes cutting  cull  diameter but,  the  single  ( l o g volume) i n c r e a s e s change  in  volume  is  90 greater  than  increases  the  change i n time, thus p r o d u c t i v i t y  (Conway, 1978).  When measured on  b a s i s , as done here, log volumes w i l l with  stand height and  height  stand  m) 3  average  be n e g a t i v e l y c o r r e l a t e d  stems per hectare  ( i . e . as merchantable  i n c r e a s e s more logs are recovered per t r e e (per b l o c k ) ,  reducing the t r e e (block) average increasing  log  non-productive Apparent  volumes  more  volume).  time  Hence,  will  be  with  spent  are:  stems per h e c t a r e .  (a)  positive and  correlations  and  with  brush  (b) negative c o r r e l a t i o n  As with f a l l i n g  ( i . e . height  productivity  and bucking  diameter),  recovered  which i s p o s i t i v e l y  volumes at a g r e a t e r r a t e than  time by i n c r e a s e d d i f f i c u l t y .  with  productivity,  c o r r e l a t e d with brush, o b s t a c l e and c u l l v a r i a b l e s , appear increase  on  moving between t r e e s .  d e n s i t y , o b s t a c l e s and c u l l ;  size  log  exceptions to hypothesized yarding  relationships  tree  a  (per  Since the number of  to  i s yarding stems  per  hectare i s n e g a t i v e l y c o r r e l a t e d with l o g volume, turn volumes will  decrease  with i n c r e a s i n g stems per hectare, with smaller  r e l a t i v e changes in y a r d i n g time; which j u s t i f i e s negative hectare.  correlation In  resource and British  general  the  occur  coast  samples  Therefore,  long-term  planning w i l l operations.  region.  increasingly  stands.  logging  productivity  logging c h a r a c t e r i s t i c s  Columbia's  logging w i l l  between  to  improve require  Further,  obtained  observed  stems  per  are t y p i c a l of  i n o l d growth f o r e s t s In  in  and  the  the f u t u r e , however,  younger,  accessibility sampling  of  of  the v a r i a t i o n s  second-growth modeling second  for  growth  i n sample data  91 presented here can be reduced samples  of  resource  throughout sampling  their  by  i n c r e a s e d sampling,  variables  range  more  (Demaerschalk  and  their  range  and Kozak, 1974);  f o r each  across  measurement of  logging system  (c)  resource  considered.  Regression A n a l y s i s The  (4.12).  s e l e c t e d r e g r e s s i o n s are given i n Equations A l l c o e f f i c i e n t s are s i g n i f i c a n t at  confidence length  (0(=O.O5),  level  (Eq. 4.6),  for  the  equations  (Eq. 4.8)  and  (4.6)  95  volume harvested  road  (Eq.  4.7),  (Eq.  4.9).  Because of the r e s t r i c t i o n  that a l l f i n a l p r o b a b l i t y  have  some of t h e i r c o e f f i c i e n t s w i l l  the  same•variables,  significant  (OC=0.20),  which  the o r i g i n a l  the  explanatory two  will  probability  coefficient, identified  probability  of the system due  to  percent  individual  coefficients  in the  80  the minimum c r i t e r i o n  r e s p e c t i v e standard e r r o r s  can be seen  least  was  at  equations by  insignificant their  even  equations, the  manner  will  any  , +  '  to 4.12). one  of  which  f o r f i n a l e s t i m a t i o n (see s e c t i o n  the  to As the  i n at  intercept  variables 4.44).  in The  next  be s i g n i f i c a n t  excluding in  level  systems.  (Equations 4.10  variables  not  f o r acceptance  be noted with a  equations,  equations  confidence  logging  to  percent  expressing  f a l l i n g and bucking p r o d u c t i v i t y  yarding p r o d u c t i v i t y  be  (b)  of o p e r a t i n g c o n d i t i o n s ; and  s e l e c t i o n of samples to enable unique characteristics  (a)  distributed  by l o g g i n g systems more u n i f o r m l y d i s t r i b u t e d  companies  4.46  uniformly  with:  were  92 (4.6)  RL = 0.1164 A*SPH + 6.070 A*ALV {  R (4.7)  0.0  1 6 7 )  (  = 0.8198  2  2.1  6 8 )  SEE = 546.15 DW = 2.305 (54.4% of mean)  F&BP = 35.58 T - 4.566 0 - 0.1866 D - 0.052 VPH (  3.9  2 6 )  {  1.6  0 )  (  0.0  7 9 1 )  (  0.0  1 0 3 )  + 1.762 T*0 - 0.9688 T*H - 0.00796 T*VPH (  0.4 9 1 4 )  (  0.1  4 5 1 )  (  0.0  0 1 8 6 )  + 0.0026 H*VPH (  R (4.8)  0.0  0 0 2  7)  = 0.9683  2  SEE = 2.64 DW = 1.829 (20.4% of mean)  YP = -0.1131 S + 1.501 0 + 0.6732 H - 1.118 B*EX (  0.0  4 4 7 )  ( 0 .7 4 8 )  (  0.0  6 9 6)  (  0.3  2 4 )  + 0.0565 B*H*(z +z ) + 0.1461 B*H*z (  0.0  2 8 5 )  (  + 0.1354 C*ALV*z (  R  (4.9)  0.0  3 3 5 )  + 0.3072 C*ALV*z  6 2 4)  (  = 0 .9763  2  0.0  0,0  7 5 7 )  SEE = 4.277 DW = 1.561 (17.1% of mean)  Q = 11.273 YT + 0.4358 Vnet (  R  1.7  3 8 )  ( 0.0  = 0.9623  2  6 2 6 1 )  SEE = 4804.1 DW = 1.713 (26.0% of mean)  (4.10) P{HL} = -0.20044 - 0.000069 E + 0.0099 S - 0.1146 H (  0, 5 6 8 4 ) +  (0.0  0 0 3 0 ) +  (0.0  0 4 6 )  (  0,0  2 1 6 ) +  • + 0.03375 C + 0.00314 RPH + 0.000006 Vnet (  R  0.0  12  8)  (  = 0.2778  2  0.0  0 2 8 )  (  0.0  0 0 0 0 3 4 )  SEE = 0.4467  (4.11) P{GY} = 1.5198 - 0.000290 E - 0.0093 S + 0.0306 H (  0.5  0 7)  (  0.0 0 0 2 7 )  ( 0.0  0 4 1 )  (  0,0  1 9 )  + 0.00218 C + 0.00201 RPH - 0.000002 Vnet (  R  0.0 1 1 4 ) +  (  = 0.2119  2  0. 0 0 2 5 ) +  (  0.0  0 0 0 0 3 ) +  SEE = 0.3985  (4.12) P{LR] = -0.31936 + 0.000359 E - 0.0006 S + 0.0421 H (  0.4 5 9 4 ) +  (  0.0  0 0 2 5 )  (  0.0  0 3 7 )+  (  0. 0 1 7 5 )  - 0.03593 C - 0.00515 RPH - 0.000004 Vnet (  R Where:  2  0.0  10  3)  = 0.2827  (  0.0  0 2 3 )  I 0.0  0 0 0 0 3 )  SEE = 0.3610  A l l variables as d e f i n e d i n Table 3, and i n Equations (4.1) t o (4.5). Two adjacent v a r i a b l e s with '*' between indicate a cross-product term. C o e f f i c i e n t standard e r r o r s i n parantheses. P{xx} = p r o b a b i l i t y of system "xx"; HL=highlead, GY=grapple yard, LR=long-reach. Z] = dummy v a r i a b l e f o r system i ; i = l , h i g h l e a d ;  93 2,grapple; 3,long-reach. = standard e r r o r of the estimate. = Durbin-Watson "d-statistic" autocorrelation test. R based on uncorrected sums of squares for Equations (4.6) to (4.9). SEE DW  2  4.461 block  Road Length (RL).  or area  (hectares) accounted  variation  i n the t o t a l  None  the  of  account  As expected,  other  in  in roads retain  for the g r e a t e s t amount of  independent v a r i a b l e s c o u l d  the model.  in any  To account  b u i l t between blocks of area  same  size,  final  log  s e l e c t e d (Eq. 4.6)  correlations  volume  variables  (ALV),  Interpretation  variable  negative  with  requires  interpretation  correlation  a  and in  one  must be  analysed  per  hectare  other  resource  Appendix  SPH  and  in one can not be observed  opposite)  variation of  the  change  Since area i s i n c l u d e d  i s no longer v a l i d .  between  in  unit  the assumption that  variation  relationship  other  cross-products  stems  length  matrices  v a r i a b l e s are held constant. this  still  1).  of r e g r e s s i o n c o e f f i c i e n t s as measuring change  in the dependent v a r i a b l e  terms  between  road  (correlation  independent  and  independent v a r i a b l e s .  equation  with regard to the  area  variation  i n the model, i n t e r a c t i o n s between area and  of area and a l l other  (SPH),  significantly  for some of the  the  area.  form, as long as  resource c h a r a c t e r i s t i c s were t e s t e d using the  The  cutting  l e n g t h of roads needed to log an  for additional variation  remained  s i z e of the  other.  stand d e n s i t y and  ALV  without To  in  the  remaining in  both  A l s o , a strong implies  that  significant  (and  illustrate  the  l o g volume on road l e n g t h ,  94  r e p r e s e n t a t i v e log volumes for v a r i o u s extrapolated  from the sample data.  c a l c u l a t e the expected (Figure 4 ) .  stand  densities  These values were used  road lengths f o r an area of one  It i s readily  were to  hectare  seen that road l e n g t h (and  density  s i n c e area i s one h e c t a r e ) i n c r e a s e s with i n c r e a s i n g number of stems  per  hectare  (decreasing  l o g volume).  i n c r e a s i n g stand d e n s i t y (as measured by does  not  "cause"  more  roads  However, stems per hectare measure  of  area  slope,  terrain,  and  proxy  measures  of  It  Thus, SPH  which and  hectare)  provide by  a  positive  such  as  will  i n f l u e n c e road  ALV  elevation,  are  essentially  in a c c e s s i b i l i t y  i n road c o n s t r u c t i o n f o r a c u t t i n g  block  size. must  be  noted  that  v a l i d on mature old-growth sampled  variables  obstacles,  to  indicated  the u n d e r l y i n g v a r i a t i o n  that cause v a r i a t i o n of given  as  per  f o r a given area.  (log volume) appears  with  layout and c o n s t r u c t i o n .  stems  to be b u i l t  accessibility  (negative) c o r r e l a t i o n s  Realistically,  logging  the developed  stands s i m i l a r to  operations occurred.  the number of stems  per  hectare  will  equation those  on  i s only which  On young second-growth decline  (log  volume  i n c r e a s e s ) as the stand ages, thus p r e d i c t e d road l e n g t h would decrease  with i n c r e a s i n g stand age.  independent relative  variables  accessibility.  is  a  Here the v a r i a t i o n  function  i n the  of both stand age  and  Figure  4.  Road L e n g t h  (A = l h a )  96 Examination non-constant area.  of the r e s i d u a l s r e v e a l e d the p o s s i b i l i t y  variance  Using  Rubinfeld,  the  ( h e t e r o s c e d a s t i c i t y ) with  "Goldfeld-Quandt  1976) i t was found  test"  by  least-square  Johnston  (Pindyck  and  (1972),  the  block  area.  As  r e s i d u a l s from o r d i n a r y  (OLS) e s t i m a t i o n of road length were regressed on  s e v e r a l f u n c t i o n s of explanation selected  respect to  that the v a r i a n c e of r e g r e s s i o n  e r r o r s i n c r e a s e d s i g n i f i c a n t l y with c u t t i n g suggested  of  area  to  determine  variance  in  the  function  was  8  the  best  regression  possible  errors.  The  then used to weight a l l v a r i a b l e s at  each o b s e r v a t i o n , and c o e f f i c i e n t s were reestimated using regression  (Draper  and  and R u b i n f e l d , 1976).  Initially the  equation. observed  are those given i n Equation 4.6.  coefficient  different  from  was  zero  not  i s zero  and ALV are z e r o .  9  found  will  be  equation  was  to  zero  ( o b v i o u s l y ) , or, where both observed  Since bare  land c o u l d have  existing  i t would appear that an i n t e r c e p t term i s j u s t i f i e d . the  term.  specified  to  be  i t was dropped from the  T h i s i m p l i e s that road l e n g t h area  1972; Pindyck  the model was s p e c i f i e d with an i n t e r c e p t  estimated  significantly  Smith, 1966; Johnston,  OLS  C o e f f i c i e n t s estimated by the "weighted  l e a s t - s q u a r e s " procedures  Since  of  measure  when SPH roads  However,  the l e n g t h of road  8  |RESIDUALi| = 17.98Ai-0.1344Ai , uncorrected sums of squares)  9  A zero value f o r SPH i s s u f f i c i e n t to guarantee a zero value for ALV. However, merchantable l o g volume c o u l d be zero under c o n d i t i o n s of p o s i t i v e SPH. Since such a stand would have no marketable value under these c o n d i t i o n s the c a l c u l a t i o n of RL. is i r r e l e v a n t .  2  R =0.459 2  (based  on  97  necessary  to l o g a given area.  solution  of  contribute  RL  to the  recoverable has  is  the  physical  without  an  timber  the  variation  R  not  from  which  Because the e q u a t i o n term  the  For t h i s  i n observed  are  here w i l l  sum  Any  model  without  an i n t e r c e p t ,  values can  proportion  of  use  2  be  total  reason the of  a p p e a r t o be h i g h e r for a similar  corrected  to  explain  comparisons  be  than model  f o r the  that approximates  expected  variation.  interpreted.  mean.  the s e t of  a  significant  T h i s does n o t i n v a l i d a t e t h e  a s a measure o f t h e 'goodness o f f i t ' ;  that  of  RL e x p l a i n e d by  normally  be g r e a t e r t h a n  i n t e r c e p t and sums o f s q u a r e s  requires  does  v a r i a t i o n a b o u t t h e mean e x p l a i n e d  given  2  and i n f a c t . w i l l  of the R  the  2  with  observed  stock  intercept  the r e g r e s s i o n , as "r-squares"  expected,  area  then  o f m u l t i p l e d e t e r m i n a t i o n , o r R , i s a measure  p r o p o r t i o n of t o t a l  Therefore,  exists  the  n o t c o r r e c t e d f o r t h e mean.  the r e g r e s s i o n , r a t h e r than by  since  stocks are being estimated.  are  coefficient  unnecessary  total  been e s t i m a t e d  squares  I f no t i m b e r  made t o m o d e l s w i t h R  i t 2  only  values  c o m p u t e d i n t h e same manner. 4.462 F a l l i n g time with in  in falling total  and b u c k i n g  standing timber  Productivity  i s as expected volume.  each  and b u c k i n g  block.  bucking  This  to  measure  of  Although  a l l  Total  strongly correlated for variations  block  t i m e s were d i v i d e d by t o t a l productivity  was r e g r e s s e d a g a i n s t a l l o t h e r  untransformed.  (F&BP).  To a c c o u n t  t i m e c a u s e d by f a c t o r s n o t r e l a t e d  falling  and  And B u c k i n g  size,  production f o r i n f a l l i n g and  variables,  coefficients  total  in  transformed the  final  98  equation  (Eq. 4.7)  confidence l e v e l by  each  are  significant  90  independent  percent  variable,  confidence  significance level variations  to  the  reduced  result,  (O(=0.10).  level  by  approximately  possibly  between  masking  50  where  independent Rubinfeld  significant variables  at  explained  (R  of  adjusted)  2  the  estimate  However,  variables  the true i n f l u e n c e of (Johnston, dependence  as a  will  be  independent  1972).  In  exists  between  (multicollinearity),  (1976) suggest  already  By reducing the  percent.  included  linear  explained  total  while the standard e r r o r  v a r i a b l e s on the dependent v a r i a b l e cases  percent  i s only s i g n i f i c a n t  for entry i n t o the model,  correlations  greater,  95  variation  adjusted for the number of v a r i a b l e s  more than doubled, was  the  (<X = 0.05), the a d d i t i o n a l v a r i a t i o n  e x p l a i n e d by other i n c l u d e d v a r i a b l e s , the  at  such  Pindyck  and  that  "... The model can be utilized with a l l i t s v a r i a b l e s , i f s u f f i c i e n t care i s given to the interpretation of the r e g r e s s i o n results." (p. 6 7 ) . With  this  i n . mind,  and  upon  a  quick  review  c o r r e l a t i o n s among sample data, i t can be seen included  terms can be v a r i e d without  the o t h e r s . influence  Hence, each  each  of the  concurrent v a r i a t i o n s i n  magnitude  and  direction  l i n e a r dependence that  may  of  assessed  affect  its  A d d i t i o n a l l y , with the c o e f f i c i e n t s expressed i n  the s c a l e - f r e e manner Rubinfeld,  the  simple  that few  v a r i a b l e has on p r o d u c t i v i t y must be  with r e f e r e n c e to any estimation.  both  of  1976)  independent  of  "Beta  comparisons variable  can  Coefficients" of  the r e l a t i v e be  directly  (Pindyck  and  importance made.  of  These  99 coefficients  for  variables  i n the F&BP equation are given i n  Table 4.  Table 4. Beta C o e f f i c i e n t s for F a l l i n g and Bucking P r o d u c t i v i t y E q u a t i o n 1  Var i a b l e  Coefficient  T T*H H*VPH VPH T*VPH T*0 0 D 1  4.7114 -4.5599 4.4099 -2.1598 -1.4078 1.1282 -0.7911 -0.2400  /§; = (dx, / O V , ), where: /Jj = Beta c o e f f i c i e n t ; fi\ = estimated c o e f f i c i e n t of variable i ; = estimated standard d e v i a t i o n of independent v a r i a b l e i , and; ff = estimated standard d e v i a t i o n of the dependent v a r i a b l e . y  The  simple  relationships with  the  correlations  between  possible  (0.37027)  with  constant  at  productivity  not  show  any  t e r r a i n and other dependent  exception  obstacles. their  do  1 0  sample  w i l l decline  of  a  Holding means  positive a l l other i t can  with i n c r e a s i n g  be  terrain  strong  variables, association variables shown  that  difficulty,  even though the beta c o e f f i c i e n t i s strongest and p o s i t i v e f o r  1 0  This does not preclude the p o s s i b i l i t y of other r e l a t i o n s h i p s s i n c e , as noted by Pindyck and R u b i n f e l d (1976), simple correlations alone may not give adequate i n d i c a t i o n of the degree of m u l t i c o l l i n e a r i t y , p a r t i c u l a r l y with more than two independent variables, because of more complex linear dependencies among v a r i a b l e s .  100 terrain on  by i t s e l f .  productivity  I t appears  1 1  of  other  cross-product  t e r r a i n have a stronger j o i n t If  that the net  influence  negative  effect  terms that i n c l u d e  than  terrain  alone.  the measure of o b s t a c l e s does c o n s i s t e n t l y move i n p o s i t i v e  association  with  terrain  difficulty,  p r o d u c t i v i t y of i n c r e a s i n g d i f f i c u l t y from  the  results.  correlation  the  is  net  hard  affect  to  interpret  T h i s i s p a r t i c u l a r l y true i f the  (0.27337) between o b s t a c l e and  on  positive  t r e e height i s a l s o  cons i s t e n t . If a l l v a r i a b l e s other than volume per hectare constant  at  their  will  height  most  likely  association  of VPH  similarly either  with  volume  or  to  increase, associated greater  the with  assess  diameter  estimated c o e f f i c i e n t s . constant  (0.45221),  and  which  while  by  a  obscures  Because of  the their  the strong p o s i t i v e  diameter the  in  p o s i t i v e changes in t r e e  per hectare and  height  difficult  height  with  However, changes  on p r e d i c t e d p r o d u c t i v i t y .  c o r r e l a t i o n between  held  occur  (0.39862) and diameter  net a f f e c t  held  sample means, p r o d u c t i v i t y and volume per  hectare w i l l move i n the same d i r e c t i o n . VPH  are  (0.78025),  individual simple  it  is  i n f l u e n c e of  review  of  their  However, i f t e r r a i n and o b s t a c l e s are diameter,  relatively  height and volume per  minor  the diameter  reduction  coefficient  in  hectare  productivity  should be o f f s e t  by  i n c r e a s e s in p r o d u c t i v i t y a s s o c i a t e d with i n c r e a s e s in  height and volume per  hectare.  A  review  of  the  equation  The decreased e f f i c i e n c y of the Beta c o e f f i c i e n t s as measures of r e l a t i v e importance i s a f u r t h e r i n d i c a t i o n that the F&BP equation s u f f e r s from m u l t i c o l l i n e a r i t y , which i s not r e a d i l y d i s c e r n a b l e from an i n s p e c t i o n of simple c o r r e l a t i o n s .  11  101 statistics variation  r e v e a l s t h a t a s u b s t a n t i a l p r o p o r t i o n of the t o t a l i n observed  productivities  relatively  small standard  and  no  with  indication  observations. supported  Further the  coefficients  are  intercorrelations, observed  consistency  of  autocorrelated  examination  and a t e s t of  Hence,.  to  the s e l e c t e d equation  productivities.  with  a  productivity), errors  between  of the r e s i d u a l s  constant  although  difficult  of the e q u a t i o n  explained,  (±20.4% o f mean  assumption  (homoscedasticity).  fit  error  is  the  variance  variables  interpret  due  and to  appears t o acceptably  Rigorous  testing  of  d e p e n d s on e n h a n c i n g c u r r e n t  the data  w i t h a d d i t i o n a l samples. 4.463 Y a r d i n g bucking,  total  block  size  Again,  to  as  a  measure  variable. given  yarding  of  times  measured  account  accessibility,  Productivity (YP).  for  by some  were area  As  with  strongly  correlated  or standing  variation  falling  caused  and with  timber  volume.  by  relative  production  was d i v i d e d by p h a s e t i m e t o p r o v i d e  yarding  p r o d u c t i v i t y f o r use a s t h e d e p e n d e n t  Beta c o e f f i c i e n t s  i n Table 5 below.  f o r the independent v a r i a b l e s are  102  Table  5.  Beta C o e f f i c i e n t s f o r Yarding P r o d u c t i v i t y  Highlead  Grapple  Variable  Coefficient  H B*EX C*ALV B*H S 0  0.34075 -0.34005 0.31653 0.27.317 -0.22732 0.19185 Initially  Using  dummy  grapple; 3,  Variable  variables  long-reach), allowed  a  1972; Cunia, 1973). between  to e x p l a i n  differences any  of  C*ALV H B*EX B*H S 0  0.56281 0.34075 -0.34005 0. 27317 -0.22732 0.19185  the  testing  the  across  ( Z i ; i = l , h i g h l e a d ; 2, linear  regression  differences  I f there i s  estimated  was  between systems  an  the v a r i a b l e s ' sampled  across  insignificant  a l l systems  influence  yarding  indicate i t s influence  is  on p r o d u c t i v i t y  systems.  between two or a l l three of the  one v a r i a b l e  a l l systems.  c o e f f i c i e n t s f o r any given v a r i a b l e ,  then a s i n g l e c o e f f i c i e n t  all  0.52852 0.34075 -0.34005 -0.22732 0.19185  general  (Johnston,  for  Coefficient  f o r each system  that  sufficient  Variable  estimated  estimated  difference  Long-Reach  Coefficient  B*H H B*EX S 0  the model was  Equation  Significant  coefficients for  on yarder  productivity  i s dependent on the system, and thus separate c o e f f i c i e n t s are justified.  The  general  equation  for  (Eq. 4.8) shows that, based  on sample data  some  do  of  influence  the  variables  have  on p r o d u c t i v i t y , depending  yarding p r o d u c t i v i t y for  this  thesis,  significantly different on  the  yarding  method  used.  D i s a g g r e g a t i n g the equation by y a r d i n g system i t can be  seen,  through  that  the  use  of the Beta c o e f f i c i e n t s i n Table 5,  the r e l a t i v e importance  of  a  given  variable  may  also  103 differ  between systems.  Across to other  a l l systems, slope has  v a r i a b l e s ) impact on yarder  else constant.  This w i l l  grapple  yarding  i f the  exposed  rock  and  are c o n s i s t e n t . correlation log by  a negative  likely  be  positive  negative  volume w i l l  exposed  relative  p r o d u c t i v i t y , holding a l l r e i n f o r c e d in h i g h l e a d  correlation  'of  slope  c o r r e l a t i o n s with height  In long reach y a r d i n g ,  with  (minor  rock and  although  negative  r e i n f o r c e the r e d u c t i o n  with  and  a  will  offset  importance of the yarding,  it  is  the  height  correlation  likely  slope w i l l be a r e d u c t i o n Since  the  and  obstacles  old  1979a. p. 33)  index  stumps. . ."  the  lower  the  that  index may  caused  crew.  Hence, the  while  holding  by  else  includes  a  measure  and  productivity increasing  height is  unclear.  slope  remain constant  for  (Province of B r i t i s h  and  Columbia,  additional  variation rather than  a l o s s of m o b i l i t y f o r the impact  on  constant.  all If  exposed  of  sound wood content) uprooted  yarder  productivity,  slope, brush,  systems,  the  obstacles rock  yarding  However, s i n c e o b s t a c l e s  have p o s i t i v e c o r r e l a t i o n s (>0.20) with rock  long-reach  i n f l u e n c e of i n c r e a s i n g  account f o r  positive  all  relative  in  in the model as caused by l a r g e old-growth timber, strictly  and  in y a r d i n g p r o d u c t i v i t y .  ". . . . w i n d f a l l s ( l e s s than 50% trees  Since  is  that the net  with  in p r o d u c t i v i t y caused  reduction. variable  cull  positive  i n c r e a s i n g slope, a p o s i t i v e c o r r e l a t i o n between slope  height  and  while  net  exposed  impact  on  increase  with  brush and  height  (or even d e c l i n e ) , p r o d u c t i v i t y w i l l  decrease  104  because  of  the  greater  relative  importance  accounting f o r p r o d u c t i v i t y v a r i a t i o n s . actually  be  index  may  r e p r e s e n t a t i v e of d e c r e a s i n g a c c e s s i b i l i t y .  If,  however, slope and exposed rock remain density,  tree  height  Here  of S and EX i n the  constant  while  brush  (and diameter), and o b s t a c l e s i n c r e a s e ,  yarder p r o d u c t i v i t y w i l l a l s o  increase.  In  such  o b s t a c l e s index may be more a measure of timber  cases  the  s i z e than area  accessibility. As  hypothesized,  tree  height w i l l p o s i t i v e l y i n f l u e n c e  yarder p r o d u c t i v i t y due to i n c r e a s i n g the number of logs can  be  yarded  constant). if  per  setting  ( a l l other v a r i a b l e s  Increases i n p r o d u c t i v i t y may be  i n c r e a s e s i n brush d e n s i t y occur over  indicated  by  the  positive  that  remaining  offset  somewhat  i n c r e a s i n g height as  correlation  between  the  two  density  will  var i a b l e s . Contrary decrease crew  to  the  hypothesis  yarder p r o d u c t i v i t y through  mobility,  the  equation  p r o d u c t i v i t y and brush support impact.  that  Since  brush  i t s adverse  the c o n c l u s i o n  density  of  a  positive  i s positively correlated negatively  yarder  other  productivity.  choker  If  a  with  correlated  positively  with  variables  which  The reason  f o r the d i s c r e p a n c y with the  hypothesized e f f e c t - l i e s with the l e v e l at which measured.  on  between  exposed rock, movements i n brush d e n s i t y w i l l occur  changes i n the  is  effect  and simple c o r r e l a t i o n  o b s t a c l e s , height and l o g volumes, and with  brush  time  study  influence  productivity  i s c a r r i e d out f o r a s i n g l e  s e t t e r over v a r y i n g brush d e n s i t i e s ,  i t is likely  that  105  increased  difficulty  reduce p r o d u c t i v i t y However,  if  l e v e l as  done  associated  volume  movement  (all  other  productivity here,  with  diameter and  in  will  then  stands  log  is  measured  greater  having  volume.  higher d e n s i t i e s w i l l  variables  being  constant).  at the c u t t i n g block  brush  density  will  be  g r e a t e r average t r e e h e i g h t s ,  Thus,  the  be greater than the  time caused by  at  (positive)  change  in  ( p o s i t i v e ) change in yarding  increased d i f f i c u l t y  ,  and  productivity  will  increase. The  sample  data  p r o d u c t i v i t y and with  cull  is  cull  includes  positive log  The  correlation  component  and  decrease  appears  hence,  that an  in a  measures  the  log  waste  proportion  concentration  volume  of  are  breakage  i n c r e a s e in the c u l l v a r i a b l e  higher q u a l i t y p r o p o r t i o n of the actual  volume.  However, since  implies  and  c o r r e l a t i o n between  c o n t r a r y to that hypothesized.  it  harvested,  a  both c u l l and  estimates, a  show  of  of  total  yarding  time on  f e l l e d volumes.  negatively  Since  developed  timber  equation  is  u n c e r t a i n , f o r stands  s i z e , s i n c e changes in one  opposite  changes  of d i f f e r e n t  in the other.  timber  will  increase  cull  and  s i z e s i t can  with  actual  log  increases volume  v a r i a b l e of the  the cull  c o r r e l a t e d , the  i n f l u e n c e on p r o d u c t i v i t y of the C*ALV c r o s s product the  volume  term  net in  of a given term  imply  However, in comparing  stands  be  shown  that  productivity  in the C*ALV term, s i n c e both will  old-growth than smaller second growth  be  greater  stands.  on  larger  106 As that  with f a l l i n g and  a  bucking, the  substantial „ proportion  observed p r o d u c t i v i t y standard  error  of  productivity).  "d"  for  statistic  range, thus we  can  hypothesis  autocorrelated  of  possible  that  variables  rather  the  are  1972).  the  patterns possible any  that  that that  one  omitted  equation  depending on  the  distinct  disprove  but,  that  For  this  1976).  indicate  equation  that  that  are  (Johnston,  equation  will  have  system used, i t  follow  systems.  different Thus  i t is  e x i s t s for the p r e d i c t i o n the  reason,  the  independent  Rubinfeld,  yarding  between  the  indeterminate  among  the  productivity  yarding  In t h i s range i t i s  is  from  small  mean  or  (Pindyck and  o b s e r v a t i o n s i s c o r r e l a t e d with the  supported  prove  the p r e d i c t i o n e r r o r s w i l l  system,  Finally,  of  in the  residuals.  no a u t o c o r r e l a t i o n  without f u r t h e r  falls  positively  yarding  are  observation.  relatively  e r r o r term in a continuous p a t t e r n  variables  is possible  (DW)  v a r i a t i o n in  among independant v a r i a b l e s may  Since the  different  a  yarding  autocorrelation  variables  influencing  total  (±17.1%  the  than r e s i d u a l s  Autocorrelation there  not  the with  estimate  However,  Durbin-Watson  of  i s explained, the  equation s t a t i s t i c s show  error logging  the  term  across  system  equation  was  on  on all each  accepted  adjustment. examination  the  (homoscedasticity).  hypothesis  and  testing of  of  constant  the error  residuals variance  107  4.464 Volume Harvested harvested  should  equal  waste and breakage. waste  and  (Q).  can be estimated be  in e r r o r , the volume i n  different  estimated volume s t a t e d i n  than  estimated  close  utilization  terms  be g r e a t e r than harvested volume. Knowledge  of  actual  volume  harvested  determine how much of standing timber to  decay,  U s u a l l y , as can be seen i n the v a r i a b l e means given  earlier, will  volume  s i n c e estimated volumes,  logs harvested w i l l most l i k e l y volumes.  the  standing timber volume net of decay,  However,  breakage  Hypothetically  harvest  unregulated supply  volumes  equal  to  stocks must  allowable  lands, how much timber must be  requirements.  Also,  in  i s necessary to be  removed  cuts;  cut  determining  or, f o r  to  meet  stand  log  values,  a p p l y i n g l o g p r i c e s to standing volumes would overestimate the total  stand v a l u e . Estimates of harvest volume  estimated  timber  volume  converted  of  course  depend  on  volume and the amounts of labor and c a p i t a l  employed to harvest the timber  will  are  timber.  increased,  As more  i n t o marketable products  the  constant  timber  ( i . e . logs).  will  However,  increase.  To  and  unit  time, y a r d i n g time and net volume. in  costs  than  will  estimate t h i s r e l a t i o n s h i p f o r my sample data,  p r o d u c t i o n was s p e c i f i e d as a f u n c t i o n of f a l l i n g  given  other  the  d e c l i n e thus the p r o d u c t i v i t y or recovery per u n i t decline  inputs  be  timber w i l l  also  increasing  a  volume  labor or c a p i t a l w i l l  by  of  to  additional  of  gained  inputs  Equation  4.9.  and  bucking  The r e g r e s s i o n r e s u l t s are  Since y a r d i n g time, and f a l l i n g and  108 bucking  time  maintained  were  as  highly  correlated,  explanatory  variables.  both  The  could  higher  the  falling  production w i l l time the  and  of  Yarding  logging  equation  weighted l e a s t original  squares  As  volume  entry  expected,  or  yarding  since  it  is  positively  phases.  given  for  production  regression,  unweighted  v a r i a n c e with  variable.  the  time can be considered a measure of  operation  c o r r e l a t e d with a l l other The  time  increase as e i t h e r timber  increases. size  bucking  be  correlation  between production and y a r d i n g time thus prevented of  not  OLS  is  since  regression  i n c r e a s i n g net volume.  the  residuals revealed  result  of  of  the  increasing  Procedures were the same  as followed in the road length r e g r e s s i o n .  That i s , r e s i d u a l s  were regressed on s e v e r a l f u n c t i o n s of net volume to determine an  equation  function  for  used  changing to  weight  p r o d u c t i o n equation variables As variation  in an OLS  to  was  each  with  observation. using  1 2  the  the Then,  best the  transformed  regression.  in observed  approximately  variance,  reestimated  shown in Equation  s e l e c t e d equation,  error  4.9,  a high p r o p o r t i o n of the  production has  with a standard one-fourth  Durbin-Watson s t a t i s t i c  allows  been  explained  by  e r r o r of the estimate of  mean  rejection  production. of  the  total the equal The  hypothesis  that e r r o r s in e s t i m a t i o n are c o r r e l a t e d between o b s e r v a t i o n s .  12  |RESIDUALi| = 1511.8 + 0.00000181 V n e t , R = 0 .4431 2  2  109 4.465  System P r o b a b i l i t i e s .  Because  forced by s p e c i f i c a t i o n to have the same system will  be  statistically  significant,  as  separately  presented,  and  will  determining v a r i a t i o n s coefficients  given  o r i g i n a l equation Table 6. Probability  +  +  Most  be  relatively  Table  6.  the  more  equations  important  +  C  +  the  Logging  Grapple Variable Coefficient S H E RPH Vnet  earlier.  their  , +  Linear  Long-Reach Variable Coefficient  -0.30016 -0 . 2 4 4 9 7 -0.14369 0.09457 -0.09231 0.03032  C  -0.52611 0.36146 -0.25547 0.18726 -0.16601 -0.02163  H RPH E Vnet S +  o r i e n t e d as  would be hypothesized.  I n c r e a s i n g road d e n s i t y and c u l l  general  size)  highlead  and  grapple  long-reach y a r d i n g . yarding  increases  yarding  while  Because of the  the  probability  decreasing  common  (as a  use  of  that  of of  highlead  systems and more s p e c i a l i z e d c o n d i t i o n s necessary f o r  grapple or expressed  Beta  '.  System  c o e f f i c i e n t s are d i r e c t i o n a l l y  index of timber  in  Those v a r i a b l e s not i n the  Beta C o e f f i c i e n t s for Equations  of  in  other  in p r e d i c t i n g  for each system are i n d i c a t e d by a  0.40079 0.27385 0.21346 0.12644 -0.07987 -0.02918  RPH H E  significant  was  equation  discussed  in p r o b a b i l i t y as shown by  in  Highlead Var i a b l e Coef f ic ient  c s Vnet  are  as  i n any  those v a r i a b l e s which were s i g n i f i c a n t  system  system  variables  equations, not a l l of the c o e f f i c i e n t s  However, each  each  long-reach by  net  systems,  volume),  characteristics, will  increase  larger  with the  y a r d i n g , with subsequent decreases  a  cutting  blocks  (as  wide range i n o p e r a t i n g probability  f o r grapple and  of  highlead  long-reach.  110  Considering  that  increasingly  between  and  o b s t a c l e s ) , and/or more  that  Similarly, height  higher  elevation  p r o b a b i l i t y of long-reach while  at  elevations  i n a c c e s s i b l e (sample c o r r e l a t i o n s  relationships rock and  stands  for  highlead  and  and  elevation,  then  to  grapple  long-reach  yarding yarding.  probability  of  increasing  slope i s  probability  is  contrary  the  to  discrepancy  samples that are operations observed), operations  or  (b)  were  The the  because  lower  some  undertaken  to  not c r i t i c a l  of  in  of the  yarding  increasing  slope  hypothesized.  The  factors,  such as:  (a)  typical  long-reach  end  of  range  the  sampled  the  was  long-reach  a v o i d stream damage, average to  the  choice  importance of slope i s minor in the  highlead  long-reach  with  of  heights  a s s o c i a t e d with  equation  was  of  system.  determining  accepted  with  the  based  on  coefficient.  R-squares of the p r o b a b i l i t y equations  corrected  intercept  representative  probability  slope  several  of  with  probability  yarding  relationship  the  decreases.  (decrease)  However,  decrease  to  ( i . e . only  Since the r e l a t i v e  negative  to  due  not  slopes were low and  long-reach  (grapple)  positive be  the  increase  expected.  shown  may  increasing  The  highlead  increase  i n c r e a s i n g average stand  while  the  correlated  ( d e c r e a s i n g log volumes) reduces the p r o b a b i l i t y and  exposed  logging,  yarding  negatively  be  positive  understandably  grapple  s i n c e l o g volumes are  show  slope, t e r r a i n ,  sensitive  yarding w i l l  will  sums  of  squares  term) and are unadjusted  are  (due to s p e c i f i c a t i o n of an for the degrees of  freedom  Ill  (since  all  equations  variables). the  equation  will  grapple  Normally, R  number of  provide  values w i l l  2  indicating  a  the other  less  than  r e l a t i v e to 1976).  the  thus  maximum  Intuitively,  most  fit.  a  low  possible  because  R  likely  it  can  can  2  the  indicates  with  variance Pindyck  as  1971;  weighted  least-squares  estimation  However,  it  suggested  samples  weighted  has  been  and  or  may  for  2  be  that  heteroscedastic  1976). seem  Therefore, appropriate.  lead  to  may  to  retain  (Pindyck long-reach  and and  respectively)  Rubinfeld, grapple are  1976). yarding  relatively  least-squares Because  sample  operations small,  and  (13 to  small  greater  l i n e a r p r o b a b i l i t y e s t i m a t i o n , and ordinary  0.50  for r e l a t i v e l y  may  of  model,  approaches  would  of  long-reach.  in  better  high  highlead  inefficiencies be  be  Rubinfeld,  probability  Rubinfeld,  least-squares  linear  a lower e x p l a n a t i o n  probability  (Kmenta,  a  distribution  the R  shown that the e r r o r term w i l l  increasing  in  higher  a c t u a l l y be  wide  be  equation.  with  and  for  can  assume  may  2  to the s p e c i f i c a t i o n of a l i n e a r be  one  (Pindyck  of  that  equations  However,  observed v a r i a t i o n s than that for grapple Due  seen  conclusion  sampled v a r i a b l e s on h i g h l e a d o p e r a t i o n s , probabilities  two  range from zero to better  one,  be  "goodness of f i t " of each  p r o b a b i l i t y model the maximum value an R much  explanatory  b e t t e r p r e d i c t i o n s of  yarding, no d e f i n i t e  about the i n d i v i d u a l  values  same  p r o b a b i l i t i e s than w i l l  h i g h l e a d and made  the  Although in r e l a t i v e terms i t can  long-reach  long-reach  have  thus i t estimates  s i z e s for and  ensure  15 that  112 predicted  probabilities  equations  were  procedures.  across  estimated  using  Durbin-Watson s t a t i s t i c  statistics can are  sum  unweighted  were not given  can  in Equation  4.9,  using  weighted  and  d i s t r i b u t e d and  a u t o c o r r e l a t i o n could be  tested.  System  probability  a  also  (Cottell,  regression  single  be  and  no  using  for  conclusion  equations  are  hypothesis  are  various  the for  improved by  commonly  Therefore,  the  DW  If sample s i z e s  the  the  methods  operation.  developed  1980).  normally  Thus, the  p r e d i c t i o n c o u l d a l s o be  r e c o g n i z i n g that v a r i o u s y a r d i n g on  the  l e a s t - s q u a r e s e s t i m a t i o n , then  e r r o r s would be normally  should  OLS  not be a p p l i e d .  i n c r e a s e d through f u r t h e r study,  together  one,  t e s t s for a u t o c o r r e l a t i o n  be drawn about p o s s i b l e a u t o c o r r e l a t i o n .  developed  to  Furthermore, s i n c e the e r r o r term i s not  d i s t r i b u t e d , the c o n v e n t i o n a l the  systems  used  probabilities combinations  T h i s suggests that even g r e a t e r sampling i s  r e q u i r e d , s i n c e for the  four  yarding  methods  sampled  (separating  into  tension  skidder  and  long-reach  y a r d i n g ) , there are 15 d i f f e r e n t combinations.  here  slackline  If the  logging  systems on each sample are ranked by the p r o p o r t i o n of  volume  logged,  the  number  of p o s s i b l e permutations would equal  If a d d i t i o n a l systems are sampled, the permutations greater.  Even  if  it  are  120  permutations for p r e d i c t i n g system p r o b a b i l i t y .  The  implication be  be  i s assumed only three systems, of s i x  p o s s i b l e , w i l l be used on a s i n g l e o p e r a t i o n , possible  would  64.  i s that an extremely l a r g e sampling  required.  For  this  reason  it  may  there  effort  b e t t e r to  would  continue  113  modeling p r o b a b i l i t y for s i n g l e systems, and systems  have  combination  nearly could  equal  be  weighting provided  probability  identified  by the  as the  where two  of  or more  occurring,  a  system chosen, with  i n d i v i d u a l system p r o b a b i l i t i e s .  4 . 5 SUMMARY To develop stock  estimates of a c c e s s i b l e timber  requires  some  physical  stocks.  In  values  the  determine  means  of  p r e d i c t i n g net values  choosing analyst  (a) d i r e c t l y develop net value net value  from  separate  revenue.  The  chapter,  since  specific  forces  latter it  timber s u p p l i e s . estimation can  be a p p l i e d  approach  to  i s l e f t with two a l t e r n a t i v e s : r e l a t i o n s h i p s , or  approach was  of  (b) c a l c u l a t e  logging  cost,  and  f u r t h e r developed in t h i s  more  detailed  analysis  influence  economic  r e c o v e r a b i l i t y of  S i m i l a r l y , in developing  i s favored  because  logging  of  the  costs  the  (or  definition variations  over d i r e c t u n i t cost r e l a t i o n s h i p s ,  i t permits separate a n a l y s i s of the  influencing unit costs. time  harvesting  of p r o d u c t i v i t y r e l a t i o n s h i p s to which f a c t o r c o s t s  primarily  a  statistical  predictions  allows  that  a  of  supplies  Other reasons e l a b o r a t e d  productivity)  of cost centers in  resource  i n d u s t r y to provide  may  analysis  of  for choosing were:  pose problems i n o b t a i n i n g  characteristics;  samples  problems of c o m p a r a b i l i t y  vs. cost  forces  operational  (b)  wide  reluctance  costs;  in i n t e r - f i r m accounting  (a)  and  data.  of (c)  114  In timber  developing  productivity  s u p p l i e s for y i e l d planning  relationships  to determine  on p u b l i c lands, only  v a r i a b l e s that are or c o u l d be a part of inventory can  be  used  for  explanatory  v a r i a b l e s , which are of  productivity  satisfactorily  will  not  That  to a more p r e c i s e  be  known  and  statistics is,  their  etc.,.  characteristics,  could  These  variables  crew  must  some  determination not  p r o j e c t e d , such as; season of l o g g i n g ,  l o c a t i o n s and weather,  important  purposes.  those  be  landing  characteristics,  be omitted  from the  productivity analysis. With t h i s logging to  in mind, a  operations  determine  developed  if  The  homogeneous predicting  engineered  may  logging  of  and  was  equations  yarding  system  could  and  and for  total which  be  resource into  hypothesized  falling  on  completed,  disaggregated were  productivity  data  and  for  bucking  production. an  area  is  i n f l u e n c e the p r e d i c t i o n in each phase, s i n g l e  'systems'  were  (b) grapple,  slackline)  of  relationships  characteristics  process  were hypothesized  highlead,  for each system by l o g g i n g  represented and  by  the  (c) long-reach  phase.  sample data:  (a)  ( t e n s i o n skidder  and  yarding.  Analyses  the  logging  yarding  type  resource  significant  length of roads c o n s t r u c t e d ,  Since the  Three  any  phases"  productivity,  equations  analysis  in c o a s t a l B r i t i s h Columbia was  between  variables.  preliminary  of the sample data  c h a r a c t e r i s t i c s was  sampling  was  show that a wide v a r i a t i o n in  obtained  distributed  over  as d e s i r e d . six  major  Also, since companies  115 operating  in  the c o a s t a l region i t i s f e l t  r e p r e s e n t a t i v e of c u r r e n t efficiency. grapple  However,  and  logging  characteristics  on  operations  relatively  long-reach  small  operations,  highlead  that the data are and  sample  extensive  operations,  close  long-reach  likely  observations  reduced  between  sampled  of  sizes  for  range  in  association  between grapple and h i g h l e a d samples, and narrow of  level  distribution logging firms,  c u r r e n t data c a p a b i l i t i e s f o r determining  true  d i f f e r e n c e s between systems. Results  of  that s i g n i f i c a n t resource  the  regression  a n a l y s i s are encouraging i n  r e l a t i o n s h i p s can be  variables.  As a r e s u l t  identified  the estimated  using  only  equations  were  able to e x p l a i n a s u b s t a n t i a l p r o p o r t i o n of  total  in  errors.  However,  among  resource  each  phase with r e l a t i v e l y  there i s a f a i r variables. some  amount  Hence,  degree  of  interpretation  be  intercorrelation  the accepted  equations  multicollinearity,  of  the  i n f l u e n c e of a s i n g l e not  of  low standard  which  likely  suffer  requires  results.  Specifically,  independent on  dependant  d i r e c t l y concluded  variations  from the estimated  careful  the r e l a t i v e variable  I t i s a l s o necessary  i n t e r p r e t i n g the reason  some v a r i a b l e s were s i g n i f i c a n t ,  may  variables  represent (i.e.  instrumental In  to be c a r e f u l  in  since  combined v a r i a t i o n s caused by other  i n essence these c o u l d be c o n s i d e r e d proxy or  variables.).  predicting  productivity,  the  can  c o e f f i c i e n t s in  some of the equations.  they  from  and  road volume  length, harvested,  falling the  and  hypothesis  bucking of  a  116  separate equation f o r each system was s i n g l e equation across a l l systems. productivities utilize  the  rejected  i n favor  of  The p r e d i c t i o n of y a r d i n g  i s , however, dependent on the system used. present  equation  a  for  prediction  To  purposes,  therefore,  r e q u i r e s knowledge of the yarding method that w i l l  most l i k e l y  be used on f u t u r e o p e r a t i o n s .  linear The  probability  Given  resource the  data,  of expected  e a r l i e r , the samples  the p r o b a b i l i t y a method w i l l  c h a r a c t e r i s t i c s on the proposed  current  explanation  this  the  equations  probabilities.  distinction  available  purpose,  equations were estimated f o r each system.  equations p r e d i c t  given  For  may  between  p r e d i c t i o n s of system p r o b a b i l i t i e s  chosen  c u t t i n g area.  provide  acceptable  However, as mentioned  systems  be r e l a t i v e l y  be  provided  narrow, and  will  depend  by  the  thus b e t t e r on  greater  sampling. In  general,  the  sample  size  i s small r e l a t i v e to the  number of v a r i a b l e s r e l e v a n t f o r p r e d i c t i o n to  the v a r i a t i o n  suggested  i n observable v a l u e s f o r most v a r i a b l e s .  i n t h i s chapter,  improved r e l a t i o n s h i p s w i l l  on i n c r e a s i n g the sample s i z e distribution variable.  of  i n each phase, and  samples  and  across  ensuring possible  a  more  values  As  depend uniform  for  each  Further improvement can be acheived by reducing the  p o s s i b i l i t y of s i g n i f i c a n t m u l t i c o l l i n e a r i t y .  One  means  of  approaching  t h i s problem i s to e l i m i n a t e i n t e r c o r r e l a t i o n s of  independent  variables  variables, principal  or,  by  components.  through  identifying  the and  identification running  of  new  r e g r e s s i o n s on  117 CHAPTER 5  ECONOMIC TIMBER SUPPLY OF THE U.B.C. RESEARCH FOREST  5.1 INTRODUCTION The purpose stock timber as  those  of t h i s chapter i s to i l l u s t r a t e how economic  s u p p l i e s c o u l d be estimated using equations  developed  in  the  p r e v i o u s chapter, and how c o s t ,  p r i c e and p r o d u c t i v i t y trends could be in  adjusting  stock  estimates  over  explicitly time.  considered  To acheive  o b j e c t i v e , the U n i v e r s i t y of B r i t i s h Columbia was  such  Research  Forest  s e l e c t e d as a r e p r e s e n t a t i v e f o r e s t management u n i t .  procedures  outlined  here  could  be  followed,  this  with  The some  m o d i f i c a t i o n s , f o r supply e s t i m a t i o n on any management u n i t i n coastal  British  Columbia  License, e t c . , ) . costs  (e.g. Timber Supply Area, Tree Farm  Augmented  with  a  The modeling  region c o u l d be s i m i l a r l y  basic  components  process  are  of  shown  an in  manufacturing  the  calculation  current period.  of  economic  timber  timber  However, these adjustments  planning.  long-term  development,  harvest  not  lines  necessary  stocks  i n the  are necessary  estimation in future periods; a c r i t i c a l  short or  supply  The dashed  which are  recoverable  forests  estimated.  F i g u r e 5.  represent temporal- flow adjustments,  stock  of  and lumber recovery, stock timber s u p p l i e s from  of the i n t e r i o r  for  model  and  for  requirement of silvicultural  118  Figure  5.  Economic Timber Supply Modeling Procedures  Physical Inventory  Site  Data  Records  Collection  Ownership, Product Market and Infrastructure  T  Stochastic Processes  Deterministic] Processes  Data Preparation and Collating  I  Growth and Depletion  Production Simulation Input Factor  Subjective Constraints  Costs Cost and Revenue Calculation  By Type Product Prices By Type  Economic j Stock I Timber Suppl}  Technological Change and Productivity  Cost & Price Trends  uJ  119 5.2 DESCRIPTION OF THE RESEARCH FOREST Prior  to  completing  detailing  the  the supply modeling  specific  data  on the Research  and  means  Forest, a brief  review of i t s ' management h i s t o r y and c u r r e n t s t a t u s presented. rather, timber  1  of  will  T h i s i s not meant to be a comprehensive  be  analysis,  i t i s presented to provide a general understanding of r e c o v e r a b i l i t y on the f o r e s t .  The distant highways. Columbia  Research  Forest  is  approximately  35  kilometers  from Vancouver, and i s a c c e s s i b l e year-round The area Research  (5157 h e c t a r e s ; the U n i v e r s i t y of Forest,  educational forest  by paved  undated)  was  British  established  as an  i n 1947 and i s r e p r e s e n t a t i v e of  " . . . typical lower coast topography mountain l a k e s , steep slopes and rock outcrops i n the north, and more g e n t l e slopes of g l a c i a l till i n the south. E l e v a t i o n s i n the f o r e s t range from sea level at P i t t Lake to 1025 metres on the slopes of Mount Blanchard. . ." (the University of B r i t i s h Columbia Research F o r e s t , undated). E x c l u d i n g the steep slopes on the n o r t h e a s t e r n boundary, of  the  eastern  years) second have  (greater  of  F o r e s t i s young ( l e s s than 50 deciduous  regenerated f o l l o w i n g r a i l r o a d  Most of the western than  the  growth mixed-conifer and  naturally  1920's.  half  100  years)  much  half  of  the  types  that  l o g g i n g i n the  Forest  i s older  second growth mixed c o n i f e r  types  i n f o r m a t i o n i n t h i s s e c t i o n , i f not e x p l i c i t l y r e f e r e n c e d , i s based upon Annual Reports of the Research F o r e s t (1961-1980), and d r a f t appendices to the F o r e s t Management Plan which i s i n preparat i o n .  120 that regenerated the  old  f o l l o w i n g a major f i r e  growth  (Mirb.)Franco),  Douglas-fir  western  (Raf.)Sarg.),  in 1868.  and  (Tsuga h e t e r o p h y l l a  redcedar  f o r e s t s that dominated the area, can be slopes  of  boundary,  Pitt and  Lake, around  (Gwendoline, Eunice Prior designed  Mount  to  the  and  1967,  solely  for  road  for timber  considered  planned  found  on  the  across the  elevation  steep  northern  northern  lakes  Katherine). construction  on  the  Forest  h a r v e s t i n g ; no d i s t i n c t  plan had been formulated. need  (Thuja p i i c a t a Donn)  Blanchard,  high  of  (Pseudotsuga menz i e s i i  hemlock  western  Remnants  In the 1967-1968  access  to  the  in the f o r m u l a t i o n of a proposal  development  fiscal  Forest  was  was  year  the  explicitly  for a  " . . . general road development plan for the whole Forest. . . in which a l l aspects of our management (research, demonstration, crop-growing, p r o t e c t i o n and h a r v e s t i n g ) . . . (are) taken into consideration." (the University of B r i t i s h Columbia Research F o r e s t , August 1968). . Construction culminated roads  based  in an  this  integrated  that provide  From  upon  plan  network  general access  (Adamovich, of  main  1967)  and  secondary  to a l l p a r t s of the  this  base,  spur  and  temporary)  roads  have  been c o n s t r u c t e d as needed to  timber  four-wheel  drive  has  Forest.  access  (or  recover  values.  Logging on the Research F o r e s t has southwest l i m i t e d , as  to  northeast  (Figure  6)  progressed and  has  from  g e n e r a l l y been  i s t y p i c a l of c o a s t a l l o g g i n g development, to  lower c o s t , most a c c e s s i b l e areas.  the  the  121  Figure  6.  U.B.C. R e s e a r c h F o r e s t P r i m a r y Cover D i s t r i b u t i o n  N  I  LEGEND  Major reserves and/or Protection Immature, Second-Growth Mixed Conifer and Deciduous Logging Since Forest Established Main Entrance Map Source: Univ. of B. C. Res. For. Brochure  122 Logging  a c t i v i t y was most intense  the 1960's. increased  from the mid 1950's through  Concern over the r a t e of h a r v e s t i n g  i n the l a t e 1960's, and as a  result  on the Forest of  a  revised  y i e l d a n a l y s i s which showed that ". . . o n the b a s i s of the AAC c a l c u l a t i o n s of 1966. . ., by 1981 a l l mature stands (except those excluded from production as reserves, p r o t e c t i o n . . .) w i l l have been logged. . ." (Walters, 1970), The  annual harvest  cunits  rate was reduced from approximately  to 6000 c u n i t s .  reductions immature  Following  to p r o d u c t i v e stands,  the  c o n s i d e r a t i o n of a d d i t i o n a l  areas and expected calculated  December of 1971 t o 4600 c u n i t s . l e d to the c u r r e n t harvest  11,000  AAC  was  growth  rates  on  reduced again i n  Continued reassessments have  rate of  approximatly  4000  cunits  (11,300 c u . m.). Over  the  past  two decades management o b j e c t i v e s of the  F o r e s t have become i n c r e a s i n g l y non-timber o r i e n t e d . the concept of "best-use f o r e s t r y " , Forestry  proposed  designated  a  sections  management  for  resource of  the  the  management plan  Forest  to  " . . . wood p r o d u c t i o n ,  management, game management, education, and  forestry  Forest,  of  i n 1971, that  single  or  combined  r e c r e a t i o n , watershed community development,  Under  the  proposed  plan,  wood  w i l l be the primary o b j e c t i v e only on the southern  t h i r d of the  protection  Faculty  ( U n i v e r s i t y of B r i t i s h Columbia Research  1972. p. 11).  production one  . . ."  U.B.C.  Based on  Forest  areas),  (excluding  education  reserves  and a minor o b j e c t i v e subject  management c o n s t r a i n t s on the  northcentral  and  and  to w i l d l i f e northwestern  123 areas  of  the F o r e s t .  excluded from education,  a  Throughout the F o r e s t l o g g i n g has been  number  of  areas  designated  as  research,  e c o l o g i c a l or p r o t e c t i o n r e s e r v e s .  The  l a r g e s t of  2  these r e s e r v e s are the Loon Lake Camp Education Pitt  Lake  and Golden  reserves,  of  418  acres).  102,  233  and  169  hectares  10 percent of t o t a l F o r e s t area In  total,  m a j o r i t y of remaining old-growth  all-  reserves  (251,  account  in a manner t y p i c a l of f o r e s t  and management in c o a s t a l B r i t i s h Columbia. progressing  from  some  would (Perrin,  decisions  the  based of  the  Logging has  1979)  it  must  F o r e s t , as elsewhere  increasing  forest  unforeseen  withdrawals  Because  awareness  values by s o c i e t y  p r o d u c t i o n throughout Forest.  been  inaccessible  areas.  the h i s t o r i c a l l y be  remembered  high that  in the p r o v i n c e , were capacity  F o r e s t , given c u r r e n t understanding of the i n v e n t o r y .  non-timber in  Research  development  upon the best estimates of the s u s t a i n e d y i e l d  Additionally,  2  readily c r i t i c i z e  harvest r a t e s on  f o r the  the low e l e v a t i o n , most a c c e s s i b l e s i t e s to  high e l e v a t i o n , steep s l o p e , i n c r e a s i n g l y Although  576  timber on the F o r e s t .  In r e t r o s p e c t , development and management of the Forest has proceeded  and  (northwestern boundary) p r o t e c t i o n  approximately  r e s p e c t i v e l y , almost and  Ears  Reserve,  of  and  demand  i n g e n e r a l , has  forest  resulted timber  the p r o v i n c e , as w e l l as i n the  Research  unique  lands  for  from  the  of  of  o r i e n t a t i o n of the  Research  I n a d d i t i o n to the major p r o t e c t i o n r e s e r v e s , p r o t e c t i o n areas are a l s o designated by leave s t r i p s around lakes and each side of main creeks (approximately 30.5 m wide; 121.9 m around Loon Lake), (appendix 13(2), p. 14).  124 F o r e s t as an  educational  facility,  the  magnitude  of  area  withdrawn and thus the impact on timber h a r v e s t i n g c a p a c i t y of the  Forest  province  has  been  proportionately  than f o r the  as a whole.  Because the balance reserves,  of  the  Forest  i s young second-growth timber,  (Sanders,  1980)  that  harvest  t h i s decade, given c u r r e n t prices  greater  l e v e l s of  acheive  begin  to r i s e  harvestable  course d i f f e r  i n the  size  logging  declining in  costs,  I t i s expected that 1990's  and v a l u e .  as  immature  product harvest stands  This s c e n a r i o c o u l d of log  values,  r e a l decreases i n h a r v e s t i n g c o s t s , development of new  logging  technology, reserve  i f substantial real  not i n  i t has been p r o j e c t e d  l e v e l s w i l l begin  and management i n t e n s i t y .  levels will  inventory,  increased management  restrictions  increases  in  i n t e n s i t y and/or an easing of  occur.  5.3 PROCEDURES In  this  completing  section,  the s p e c i f i c a c t i o n s are d e t a i l e d f o r  each step of the general  estimate  recoverable  Excluding  most of the i n i t i a l  all were  t h i s study  out  to  data  preparation  and  collating,  c o s t s , revenues, growth, e t c . ,  using a computer program (ETS) w r i t t e n f o r  (program l i s t i n g  i n Appendix 2).  5.31 Data C o l l e c t i o n , P r e p a r a t i o n Fortunately,  5)  timber s u p p l i e s on the Research F o r e s t .  c a l c u l a t i o n s of p r o d u c t i o n , carried  procedures (Figure  And C o l l a t i n g  timber type boundaries are  overlayed  on  a  125 topographic of  the  site,  straight timber  map  stand  forward.  type and  occurred  of the Research and  F o r e s t so that c o l l a t i n g much  tree  characteristics  was  I n d i v i d u a l stands were i d e n t i f i e d  second  by l o c a t i o n .  i n more than one d i s t i n c t was  fairly first  Thus, where a timber l o c a t i o n on the  indentified  Forest,  individual  stands were l e s s than one hectare in area they were  age,  stock t a b l e s , and  weighted  site  average  distribution  by  1:5000), t o t a l reserve  planimeter.  summary  total  diameter  at  breast  average  be  the  r e c o r d for each  height,  and  stem  topographic map  (scale  in  a  As areas of exposed bedrock  could  of  stems per hectare,  area  with  protection  compensating  or  polar  (rock outcrops)  were  these areas were a l s o measured with the  planimeter so that percent of area index  the  stand  measured  i d e n t i f i e d on the map,  and  height,  From  stand area and were  statistics  to determine  index,  species.  forests  If  stand.  1964-1966 inventory were used stand:  location.  a  stand  Stand and  each  type  separate  combined with an adjacent  for  by  determined.  i n exposed rock and  Finally,  ground slope were determined  thus an  median e l e v a t i o n  from the topographic  and map  for each stand. In  the  way  i n f o r m a t i o n was density,  of  still  inventory needed  obstacles,  cull  on  and  site  terrain  (decay,  characteristics,  variability,  waste  and  merchantable h e i g h t , l o g volume and volume per determining  the l a t t e r  program designed  by  three i t was  Province  of  brush  breakage),  hectare.  For  decided to use a computer British  Columbia  (1977),  126 which, at  given  input on t r e e s p e c i e s , inventory zone, diameter  breast h e i g h t , maturity  and  utilzation  standards,  logs per t r e e , volume per stem  volume  class, total  to  log  w i l l provide values  log f o r each l o g  utilization  c a l c u l a t i o n s had  height,  standards,  of  length,  f o r number of the  tree  and  to name a few.  After  been completed for each s p e c i e s in the  stand,  weighted stand average merchantable  height,  log  volume  and  volume per hectare were c a l c u l a t e d , using stem d i s t r i b u t i o n s p e c i e s for Stand  weighting. average  cull  average of s p e c i e s c u l l determined  as  a  was  also  determined as a weighted  estimates.  function  Species  of stand age  estimates  Volume ( l o s s ) F a c t o r s " ( B r i t i s h  S e r v i c e , 1966)  for inventory zone 2.  Regression  5.2),  equations  variability  and  the extent  were estimated  (Equation  5.1),  of o b s t a c l e s  information  productivities and  (4.8)  (5.1)  brush  density  (Equation  T = 1.692 2  5.3),  + 1.423 R (5.3)  2  for  using  of  phase  Equations  (4.7)  + 0.2628 EX + 0.01711 S SEE  T - 1.393 EX  2  = 0.265  = 0.5485 T  2  - 0.2216 SEE  + 0 .1865 EX  T  3  - 2.126  EX  3  = 0.665  0 = 0.3818 T + 0.00352 E - 0.0000034 E  2  the  in Chapter Four.  prediction  y a r d i n g , using  stand  (Equation  in Chapter Four.  = 0 . 356  B = 3 . 207  necessary  in f a l l i n g and  estimated  R (5.2)  is  Columbia Forest  for p r e d i c t i n g  sample data on coast l o g g i n g o p e r a t i o n s given This  were  and average diameter  u s i n g the "Net  terrain  by  - 0.2014 EX  127 - 0.3983 EX  + 0.1654 EX  2  -• 0.000022 S R All  = 0.583  2  coefficients  - 0.07865 S + 0.0027 S  3  3  SEE = 0.5922 (polynomials  s i g n i f i c a n t at or  2  greater  than  in the  orthogonal 95  form)  percent  are  confidence  l e v e l , with 64 o b s e r v a t i o n s on each equation. The  final  category  of  data  collected  .on the F o r e s t ,  concerning the t r a n s p o r t a t i o n network, i n c l u d e d  two  separate  measurements on each stand f o r which road access e x i s t e d as of 1979,  and  a  length of measured  t h i r d measurement f o r a l l stands.  existing with  road c l a s s  roads  (kilometers)  on  (main,  secondary,  spur  and  main gate  (access c o n t r o l p o i n t ) of the Forest  Forest  the  the  approximate  be  map measurer.  straight-line stand  Finally,  distance  four-wheel  was  measured,  f o r a l l stands on the (kilometers)  between  center and the main gate was measured. stands  with  In  access  r e l a t e d to s t r a i g h t - l i n e d i s t a n c e (Equation 5.4) so  that a c t u a l h a u l i n g d i s t a n c e s c o u l d stands  were  a c t u a l h a u l i n g d i s t a n c e ( k i l o m e t e r s ) to the  t h i s way, the a c t u a l h a u l i n g d i s t a n c e of could  stand  the  " c a t " or  Second,  with  total  a "map measurer", i n c l u d i n g boundary roads, by  drive).  also  First,  presently  without a c c e s s .  be  predicted  The concept  for  those  is illustrated  in F i g u r e 7. (5.4)  AHDi = ^QSLDi + £i  where:  AHDi = a c t u a l hauling distance in kilometers from stand i to the main gate. SLDi = s t r a i g h t - l i n e distance in kilometers from stand i to the main gate. - c o e f f i c i e n t to be estimated through r e g r e s s i o n € i = p r e d i c t i o n e r r o r of AHD f o r stand i  7.-  I l l u s t r a t i o n Of H a u l i n g D i s t a n c e Concept  i  LEGEND  H y p o t h e t i c a l Stand "Best"  Existing H a u l i n g Route — — Chord Between Stand and Main Gate V A c t u a l Haul D i s t a n c e o f Stand t SLD-—> S t r a i g h t L i n e D i s t a n c e of Stand t  129 Where more than one route route  was  determined  by  constrained  by  substantial  difference  selected. most  road  the  class. in  be  chosen  the  i s , i f - there  distance,  the  was  a  the s h o r t e s t route was  I f h a u l i n g d i s t a n c e s were s i m i l a r , the  distance  "best"  s h o r t e s t h a u l i n g d i s t a n c e , as That  route  with  t r a v e l e d on higher q u a l i t y roads was s e l e c t e d .  If d i s t a n c e by road c l a s s and again  could  total  distance  s h o r t e s t route was s e l e c t e d .  were  similar,  Assuming the c u r r e n t  road network p r o v i d e s equal access to a l l areas on the F o r e s t , then a s i n g l e most  of  r e l a t i o n s h i p should  the  observed  however, the " f i t " then  it  is  relatively  be  variations  sufficient,  explaining  in hauling distance. I f ,  of a s i n g l e equation model i s f a i r l y  likely  that  l e s s developed  some  sections  of  poor,  the F o r e s t are  than o t h e r s , and separate  equations  estimated by s e c t i o n would improve o v e r a l l f i t . An equation was estimated the  data  in Equation  c o l l e c t e d on stands with access, and i s given below 5.5.  estimation,  An i n t e r c e p t  since  actual  standard  error  s i n g l e equation (5.5)  of  the  included  i n the  d i s t a n c e should be zero when Given  the high R  2  value  0.0 0 8  9 )  2  and  estimate, i t was decided that a  f o r the F o r e s t would be s u f f i c i e n t .  AHD = 1 . 220 SLD, R (  term was not  haul  s t r a i g h t - l i n e distance i s zero. low  f o r a c t u a l haul d i s t a n c e , using  = 0.940 SEE = 0.837 N = 258  130 T h i s approach r e s u l t s i n a c t u a l haul not  related  to  road  class.  c o s t s a s i n g l e t r a v e l speed used,  rather  than  more  detailed  a  reported by Bradley quality  f o r the e n t i r e  to haul  distance  will  distance  estimation  on  estimation,  a  consideration  and u l t i m a t e l y ,  in a  of  A  was  i n c o r p o r a t e d road  i n an a n a l y s i s of t r a n s p o r t a t i o n d i s t a n c e s . is justified,  be  f o r each road c l a s s .  (1972), which e x p l i c i t l y  the added p r e c i s i o n depends  estimates  Thus, when c a l c u l a t i n g h a u l i n g  separate speed  approach  distance  planning  the i n c r e a s e d  the d i f f e r e n c e  in  Whether context, cost  of  projected  h a u l i n g c o s t s estimated by the two approaches. For  timber  types number 107 and g r e a t e r , no stand t a b l e s  were a v a i l a b l e from which average per  hectare  calculated.  (SPH)  or  Equations  3  stand diameter  species  were  (DBH),  distribution  estimated  stems  could  for predicting  be DBH  (Equation 5.6) and SPH (Equation 5.7), using data c o l l e c t e d on stands of timber (5.6)  types l e s s than 107.  DBH = 12.054 - 0.1189 SI - 0.1557 AGE + 0.0015 AGE (  3.9  4 8 )  (  0.0  4 2 1 )  - 0.000003 AGE (  R (5.7)  2  (  0. 0 0 4 1 )  (  + 1.295 H - 0.0132 H  0 . 0 0 0 0 0 0 6 )  ( 0 . 0 3 4 4 )  = 0.701 SEE = 4.60  ( 0 .0  0.0  0 0 0 t)  2  0 2 1 4 )  N = 340  InSPH = 10.119 - 1.1651 InDBH (  R Where:  3  2  2  0.0  5 8 6 )  (  = 0.697  0.2  0 7 2 )  SEE = 0.143 N = 340  DBH = average stand diameter i n centimeters SPH = stems per hectare ( a l l s p e c i e s ) . SI = stand s i t e index; height i n meters at 100 y e a r s .  'Types number 107 - 120 are a mix of mature old-growth and older second-growth stands. Types number 121+ are young immature second growth c o v e r i n g the area logged i n the 1920's - 1930's on the eastern h a l f of the F o r e s t .  131 AGE = stand age in years. H = average stand height ln = n a t u r a l l o g a r i t h m . C o e f f i c i e n t s of the DBH g r e a t e r than the  SPH  are  all  the 99 percent confidence  equation  confidence  equation  ( t o t a l ) i n meters,  are  all  significant  level.  significant  at  or  C o e f f i c i e n t s of  at the 99.9  percent  level.  Although  exact  species  distribution  could  not  be  i d e n t i f i e d , approximate s p e c i e s d i s t r i b u t i o n s were a r b i t r a r i l y assigned  according  to  the  number  and  order of a l p h a b e t i c  s p e c i e s codes a s s o c i a t e d with each type. was  indicated  then  100  assigned to that s p e c i e . major  species  of  i n d i c a t e d , 50, assigned If  equally timber  the stem  an  or  20  type was  stem  FC  minor  percent second and  the  types l e s s than 107:  or  assigned  species  was  assigned  three s p e c i e s were distribution  was  t h i r d species respectively.  three  Alder  first  was  stem  i n d i c a t e d , the  between  the  was  code)  Where of  species  distribution  species,  distribution.  30 and  divided  of  two  given  second  to the f i r s t ,  a deciduous  Given  (e.g. f i r  t w o - t h i r d s , and one-third  percent  If only one  percent species  assigned  was  c a t e g o r i z e d on  (Alnus rubra Bong.),  Maple  (Acer macrophyllum Pursh) and Cottonwood (Populus t r i c h o c a r p a T o r r . and  Gray).  For  lack  of  b e t t e r i n f o r m a t i o n , i t was  assumed that species d i s t r i b u t i o n would remain  constant  over  time. In t o t a l , stands  are  557  stands were i d e n t i f i e d .  of  second-growth timber  mature  old-growth,  f o r which a l l data  Of  this total,  immature described  or  445  mature  above  was  132 collated. through  The  remaining  1979.  On  112  these  stands are areas that were logged stands  i n f o r m a t i o n was  a v a i l a b l e on c u r r e n t s p e c i e s d i s t r i b u t i o n , diameter these  or stems per h e c t a r e .  Because  site  even  not  readily  index, h e i g h t , the  oldest  of  stands w i l l not l i k e l y be recoverable by the end of the  supply e s t i m a t i o n p e r i o d in t h i s limitations, further  i t was  decided to  calculations.  A  i l l u s t r a t i o n , and due eliminate  these  stands  stand by stand l i s t i n g  assumed-to be constant over time  (area, s i t e  to time from  of the data  index,  elevation,  line  distance,  slope, exposed rock, haul d i s t a n c e ,  straight  species  of area i n p r o t e c t i o n ) i s  given 5.32  distribution  i n Appendix Logging This  and  percent  3.  Production S i m u l a t i o n  section  details  the  methodology  in  length of roads c o n s t r u c t e d , f a l l i n g and bucking yarding  productivity,  loading  Forest.  In Chapter for  predicting  area. likely  Four an equation the  required  However, i t was provide  each  The methods i n v o l v e a combination  and d e t e r m i n i s t i c processes, and,  of  (Equation 4.6) l e n g t h of roads this  was  on  stochastic  estimated  f o r l o g g i n g an equation  would  r e s u l t s on immature stands where  growth ( v i s - a - v i s annual change i n stems per hectare volume)  stand  subjective c r i t e r i a .  p o i n t e d out that  inconsistent  productivity,  productivity, ' hauling  p r o d u c t i v i t y and a c t u a l volume harvested, f o r the  determining  and  log  would have a g r e a t e r e f f e c t on road requirements  than  site accessibility.  Since many of the stands on the  Research  133  Forest  are  immature, an equation was estimated which  road l e n g t h to area o n l y . 5.8)  (Equation equation  when  The  compared  shows that only  a  related  results  of  this  estimation  to  original  road length  the  slightly  poorer  explanation  527.61  N  is  obtained. (5.8)  RL  =  37.128  A,  R  2  =  0.794  SEE  =  49  =  ( 2.7 3 3 )  However, variations has  no  the  implies  that  i n s i t e a c c e s s i b i l i t y between stands of equal  area  impact  equation  unrealistically  on the r e q u i r e d length of roads.  to t h i s dilemma, as d i s c u s s e d i n Chapter development components. equations;  of  new  explanatory  For t h i s i l l u s t r a t i o n the  the  or  i n the principal  i t was decided to use  both  l e s s than 8 0 y e a r s .  c a l c u l a t e d road requirements  length  variables  lies  o r i g i n a l on stands g r e a t e r than 8 0 years, and  the above equation on stands The  Four,  The s o l u t i o n  were  then  compared  of roads a l r e a d y e x i s t i n g on the stand.  roads p r e v i o u s l y e x i s t e d , t o t a l  to  Where no  stand roads were set equal  to  c a l c u l a t e d road length, f o r which road c o n s t r u c t i o n c o s t s were calculated.  If  the e x i s t i n g  roads on a stand were l e s s  the c a l c u l a t e d road requirements, the  difference.  calculated  only  Hence,  road l e n g t h was i n c r e a s e d by  construction  f o r the d i f f e r e n c e .  roads exceeded c a l c u l a t e d  than  requirements  were c o n s t r u c t e d or c o s t s c a l c u l a t e d .  costs  were  also  F i n a l l y , where e x i s t i n g no  additional  roads  134 Falling calculated  and  bucking  using  (Equation  the  4.7),  productivity  equation  and  the  on  developed  recorded  or  probability  equations  system  with the  productivity  of  be  the  system  were  and necessary  used.  yarding  stand  falling  estimated  to  calculations  be  or  chosen.  price  per  Using  estimated  Given  the  stand  for  the  on  hectare  the  linear  each  system.  system,  was estimated  using the  (Equation  4.8),  data. yarding  negative,  productivity no  further  of  a  production  were completed f o r the c u r r e n t p e r i o d .  was not economically assumptions.  the most  yarding  f o r each system  a negative p r o d u c t i v i t y was taken as an stand  data  g r e a t e s t p r o b a b i l i t y of o c c u r r i n g was  r e l a v e n t c o e f f i e n t s estimated  If  Four  (Equations 4.10 to 4.12), and necessary  stand data, p r o b a b i l i t i e s  as  Chapter  yarding p r o d u c t i v i t y c o u l d be estimated,  l i k e l y y a r d i n g system had to  chosen  volume  was  at breast h e i g h t .  Before  That  in  stand  calculated  t e r r a i n , o b s t a c l e s , merchantable h e i g h t , and diameter  each  indication  stand or  was cost  That i s , that  the  r e c o v e r a b l e , r e g a r d l e s s of cost or  4  R e a l i s t i c a l l y , a negative p r o d u c t i v i t y c o u l d be i n d i c a t i v e of other peculiarities. First, a negative productivity may i n d i c a t e that a method of f a l l i n g or y a r d i n g other than those represented by the equations, would a c t u a l l y be used. Second, i t may a l s o i n d i c a t e that the equations are being used o u t s i d e their r e l e v a n t range, resulting i n a negative p r o d u c t i v i t y even though the p r e d i c t e d l o g g i n g system i s the 'true' system.  135 C a l c u l a t i o n s of based  loading  and  hauling  productivity  are  upon procedures followed by the B r i t i s h Columbia Forest  Service,  Valuation  appraisals  Division  (Province  of  in  of  projected  yarding  productivity  i s i n c r e a s e d by one  that  slope  stand  slope of 26%,  out  stumpage  B r i t i s h Columbia, 1979b and  In l o a d i n g , a base p r o d u c t i v i t y i s percent  carrying  first  calculated  productivity. percent  1980e). as  Second,  for each one  i s l e s s than 40 percent  120 base  percent  (e.g. given a stand  base loader p r o d u c t i v i t y i s i n c r e a s e d by 40 - 26  = 14%) . Hauling  productivity  First,  total  the sum  of l o a d i n g time per  and  unloading  40 cubic loading  time.  time  Using  per  from  the  c a l c u l a t e d as  coast  (trip)  logging  and  unloaded  The  method  data,  (m /load) 3  5  d r i v i n g time i t i s necessary  speed).  load  c a l c u l a t e d as load s i z e 3  loaded  steps.  to know t o t a l  driving of  speeds  estimating  Since  bulk of a l l timber Lumber  (or  hauling  d i s t a n c e on the F o r e s t has a l r e a d y been d i s c u s s e d .  Whonnock  the  (logs) harvested  from the F o r e s t  i s s o l d to  Company, the m i l l  in Whonnock was  assumed to  be the d e l i v e r y point  5  load was  loader p r o d u c t i v i t y (m /hour).  return  three  an approximate average l o a d s i z e of  load was  calculate  in  load, d r i v i n g time per  determined  hauling distance, average  calculated  r e t u r n t r i p time per  meters  d i v i d e d by To  or  is  for  all  loads,  and  a  one-way  haul  S i n c e the g r e a t e s t haul d i s t a n c e from the F o r e s t to d e l i v e r y point will involve highway h a u l i n g , load average was e x t r a p o l a t e d from those sampled operations with p r i m a r i l y highway h a u l i n g and no intermediate dump and r e h a u l .  136 distance  of  16.25  gate to Whonnock, was the  design  per  72  the  speed  speed  Forest per  operations would  was  (25mph).  kilometers  coastal logging travel  travel hour  highways between average  estimated from area  be  assumed  Unloaded  loaded t r a v e l  to  average  t r a v e l speed on the was  hour  (45mph).  From the data on  it  was  determined  assumed  that  kilometers  loaded  per  hour  D r i v i n g t i m e . i s then equal  of Forest and highway haul d i s t a n c e s d i v i d e d by the  time was  speeds.  assumed to be 10 minutes  as i n d i c a t e d by c o a s t a l l o g g i n g o p e r a t i o n s and in  stumpage  appraisals  (0.17  the  (Province of B r i t i s h  hours)  allowance Columbia,  Equation (5.9) below summarizes the c a l c u l a t i o n s  return time per l o a d . = Loading Time + D r i v i n g Time + Unloading Time = ALS + HDF + HDH + HDH + HDF + UT LP LTSF LTSH UTSH UTSF = 40m /load + HDF +16.25+ HDF +16.. 25 + LP 27kph 48kph 40kph 72kph 3  = 40mVload + HDF ( 0 . 062037 ) + LP where:  to  were used f o r Forest and highway  speeds r e s p e c t i v e l y .  Unloading  (5.9) RPL  40  Whonnock  r e s p e c t i v e loaded and unloaded t r a v e l  1979b).  upon  approximately two-thirds of unloaded  (approximately 17 and 30 mph)  given  Based  and  t r a v e l speed; thus, values of 27 and 48  to the sum  maps.  speed of main and secondary roads on the Research  F o r e s t , unloaded kilometers  k i l o m e t e r s , from the Research Forest main  RPL ALS LP HDF HDH  = = = = =  0.17hrs.  0.73hrs.  r e t u r n time per load (hours) average load s i z e (cubic meters) loader p r o d u c t i v i t y (cubic meters/hour) haul d i s t a n c e on the f o r e s t , one way (km) haul d i s t a n c e on the highway, one way (km)  for  137 LTSF LTSH UTSF UTSH UT  = = = = =  Because and be are  ultimately  highway haul  constant that  dependent  second  requires  shift  5.9)  ( i . e . stand  The  load,  size,  times are  (Equation  distance  step  in  as  estimated  (Equation as  multiplied (Equation  by  volume  assumed  (5.10)  LPS  (5.11)  HP  where:  LPS SL RPL HP ALS  for  = _SL RPL  For  this  travel  illustration,  in return  p r o d u c t i v i t y and  on  Forest.  the  calculating shift  hauling  length  the  the  shift divided  illustration,  a  return  can load  hauling  time  per  loads  per  productivity  is  (loads by 9 hour  per  shift shift  hauling.  = 9  it  productivity  number of  hauling  per  size)  by  speeds  time per  loader  Finally,  load  hrs./shift RPL  = LPS*ALS = SL = = = = =  on  hauled  average  5.11).  in t h i s  above, t o d e t e r m i n e 5.10).  distance,  variations  location)  d i v i d i n g hauling  calculated  was  load  unloading seen  l o a d e d t r a v e l s p e e d on t h e f o r e s t (km/hour) l o a d e d t r a v e l s p e e d on the highway (km/hour) u n l o a d e d t r a v e l s p e e d on the f o r e s t (km/hour) u n l o a d e d t r a v e l s p e e d on t h e highway (km/hour) unloading time (hours)  LPS*40m /load 9 hrs./shift 3  l o a d s per s h i f t s h i f t length (hours/shift) r e t u r n time per l o a d ( h o u r s / l o a d ) hauling p r o d u c t i v i t y (cubic meters/hour) average.load size (cubic meters/load)  shift length length  138 Two p r o b l e m s a r i s e harvested  (Q)  using  (Equation 4.9). (5.12) where:  the  equation  Recalling  Q = ^YT  +  to predict actual estimated  volume  i n Chapter Four  the s t r u c t u r e of the equation a s ;  faVnet  YT = y a r d i n g t i m e ( m a c h i n e h o u r s ) Vnet = s t a n d i n g t i m b e r volume ( n e t of c u l l ) /3 ,/3 = estimated c o e f f i c i e n t s 1  it  i n attempting  2  i s clear  standing  that  first,  timber  specification;  predicted  volume  and a  due  second,  to  as  (YT), thus  no v a l u e s a r e a v a i l a b l e  realizing  the  yarding  estimated  productivity  of h a r v e s t volume.  harvest  can  exceed  unconstrained input  the  linear  demands  were  (YP i n m / h o u r ) n o t t o t a l 3  time  to complete the c a l c u l a t i o n  The l a t t e r  p r o b l e m c a n be  (5.14)  into the harvest  dealt  with  by  that  ( 5 . 1 3 ) YP =  Q/YT,  or, ( 5 . 1 4 ) YT = Q/YP Hence,  substituting  a n d r e a r r a n g i n g , an e q u a t i o n  equation  (5.12)  i s obtained;  ( 5 . 1 5 ) Q = ( / 3 * V n e t * Y P ) / ( Y P - fa) z  which uses the estimate  of  yarding  productivity  calculated  earlier. The order. certain harvest  first That  problem  still  i s , i n equation  limit,  for  a  equation  YT  limit,  yield  the  i n reverse  ( 5 . 1 2 ) i n c r e a s e s i n YT . b e y o n d  standing timber  ( 5 . 1 5 ) decrea.ses will  although  g i v e n Vnet, would r e s u l t  volumes g r e a t e r than  in  remains,  a  in predicted  volume;  whereas,  i n YP, b e l o w t h e i n v e r s e o f t h e same  results.  Since  Vnet  is  139 calculated  .on  predicted  harvest  Therefore,  . to  incorporated timber  5.33  a close-utilization  use  to  volume  will  exceed  i t i s u n l i k e l y that  estimated  equation  set harvest  basis,  timber  (5.15)  volume  (Q)  a  equal  volume.  constraint to  net  ( V n e t ) whenever p r e d i c t e d Q e x c e e d e d  was  standing  Vnet.  Costs In  addition  productivities estimates  to  treatment  out'  c a l c u l a t e d i n the  a l s o had  engineering,  'costing  to  be  maintenance,  following  logging,  estimates  production  derived  road  the  f o r timber crew  of  phase  simulation,  cost  cruising,  logging  transportation,  s c a l i n g , and  stand  adminstration  and  overhead. Road c o n s t r u c t i o n from  historic  costs  made t o a s s e s s of  roads  and  costs  built  is  on by  real  constructed  i n each year  kilometer,  cost  of  of  Annual depending  years  and in  the  class,  the  independent. per  attempt  estimated  For  length  the  kilometer  was  period of  roads  an  average  cost  entire period,  was  calculated.  This  the  estimated  applied  against  stand  on  maintenance of  the  Forest.  costs  will  special  reditching,  snow r e m o v a l .  since  No  developed  and  occurrance  and/or  were  were d e t e r m i n e d  log each  road  on  resurfacing  to  costs  Research F o r e s t .  (1976=100)  the  $28173.62/km was  roads b u i l t  grading  road  costs  over  the  class  1962-1976,  per  maintenance  'Rather  which major maintenance  etc.) than  vary  projects  projects  greatly,  (e.g.  in addition attempt  length  to  major  regular  to p r o j e c t  will  occur,  a  the real  140 average maintenance c o s t per total  maintenance  costs  F o r e s t , over the p e r i o d of  $257.62/km,  total  harvesting meter The  an  timber  on  estimate  of the  logging  cost.  (5.16)  UMC  annually  UMC RMC TARDSi TVi  =' = = =  from  appraisals Columbia, yarding Nagy  (1977),  hourly  costs,  and are  which  shown i n E q u a t i o n  (5.16).  the  i n the c u r r e n t  cubic  timber  period  component  of  for  total  Warren  (Table  transportation, costs  and/or  ( 1 9 7 7 ) and  1980e).  costs  7).  of  those  Province  timber are  of  be  of  in  (Province  Procedures  terms  Hourly  used  Columbia  Most c o s t s c o u l d in  i  (m ) 3  e x c l u d i n g y a r d i n g , were d e v e l o p e d  a combination  u n i t c o s t s by d i v i d i n g  treatment  on  the  3  1980e).  r a t e or d i r e c t l y  harvested  areas  c o s t ($/m ) c o s t (s/km) i n p e r i o d i (km) the F o r e s t i n p e r i o d  coastal British  1979b  and  as  maintenance c o s t  procedures  for  costs  (1979b  of  the  value  charged against  i s then charged a g a i n s t  u n i t maintenance road maintenance t o t a l area roads t i m b e r v o l u m e on  remaining  directly  r o a d s on  maintenance c o s t s per  i n the F o r e s t  road  of  using  the e s t i m a t e d  were  (net)  developed  = RMC*TARDS i TVi  where:  All  Using  costs  Therefore,  developed  each stand  length  volume  u n i t maintenance cost  volume  total  1S62-1976.  i s allowed.  were  was  and  maintenance  standing  kilometer  of  for u s e d by  Sauder  British  per  British  calculating  expressed  cost  stumpage  and  Columbia  as a  single  cubic  meter  p h a s e c o s t s were c o n v e r t e d  i n t o phase p r o d u c t i v i t y . cruising,  engineering  not. e x p r e s s a b l e  Loading, and  as a u n i q u e v a l u e  to  crew stand since  .141 .-they d e p e n d  on c h a r a c t e r i s t i c s  Table  7.  that vary  Logging Costs  by  stand.  By Component  Component  Cost  T a i l i n g & Bucking -Yarding Highlead Grapple Long-reach :Hauling Unloading, S o r t i n g & Booming Scaling lAdministration & Overhead 1  33.75/hr  2  3  4  5  168.91/hr ,160.73/hr 241.49/hr 44.59/hr 3.08/m 0.17/m 5.64/m 3  3  6  3  .180 s h i f t s / y e a r , 6.5 h o u r s / s h i f t * .200 s h i f t s / y e a r , 8.0 h o u r s / s h i f t 9 hours/shift * : d r y l a n d s o r t , no r e h a u l ..stick s c a l e * " a l l o t h e r s " tenure c a t e g o r y ( P r o v i n c e of B r i t i s h Columbia,1980e) 1  3  s  L o a d i n g c o s t p e r c u b i c meter the  sum  ($/m ). .Service  has  British  base  cost  an e q u a t i o n developed  as  a  third  200 8-hour  $10.42  per  that the  s h i f t s per year,  to  productivity  a  cost  (Equation  was  given  Columbia  Forest  a p p r a i s a l s (Province of  i s calculated  degree polynomial  d e p r e c i a t i o n allowance converted  British  to  allowance  3  f o r stumpage  hour  5.19) i s e q u a l  ($/m ) and d e p r e c i a t i o n  C o l u m b i a , 1980e), base c o s t  Assuming of  a  Using  3  5.17)  of  (Equation  (Equation  of loader p r o d u c t i v i t y .  a depreciation  calculated  using  for appraisals.  allowance the  This  annual  is  then  p e r c u b i c m e t e r when d i v i d e d by l o a d e r 5.18).  (5.17)  BLC = 6 . 5 0 4 5 - 0 . 0 2 6 8 2 8 L P + 0 . 0 0 0 0 4 8 8 2 L P - 0 . 0 0 0 0 0 0 0 3 L P  (5.18)  LDA = HDA = $10.42 LP LP  2  3  142 (5.19)  LC = BLC + LDA  •where:  BLC LP LDA •-HDA LC  = = = = =  b a s e l o a d e r c o s t a l l o w a n c e ($/m ) loader p r o d u c t i v i t y per s h i f t (m /shift) l o a d e r d e p r e c i a t i o n a l l o w a n c e ($/m ) hourly d e p r e c i a t i o n allowance f o r loading u n i t l o a d i n g c o s t ($/m ) 3  3  3  3  ^Round-trip t r a n s p o r t a t i o n travel  between  point)  and s t a n d  coast  stumpage  .cubic  meter  crew c o s t s .given  ...population (5.20) (5.21) -C5.22) (5.23)  (5.24)  VC  a  using  main g a t e  procedures  (marshalling detailed  meter.  The d e t a i l s  run" since  for per  o f v e h i c l e , d r i v e r and o f e a c h component  (5.20) t o (5.23) b e l o w .  "town  crew  B a s i c a l l y , transportation cost  c a l c u l a t e d a s t h e sum  per cubic  for  logged,  appraisals. was  were c a l c u l a t e d f o r  Research Forest's  being  i n Equations  •given  where:  the  costs  the area  No  allowance  i s located  near  are was main  centers. = VFC+[2*TD*FC] VF  = $31. 64 +[TP*0 .19/km] 32m 3  TT = TD*120 TS  = TD*120 40kph  DC  = $0 .87/min. *TT LP*8 h r s .  = DCPM*TT LPS  CC = = = =  (FBC + OCC)*TT ($0.72/min.+$3.30/min.)*TT, ($0.72/min.+$4.95/min.)*TT, ($1.08/min.+$4.95/min.)*TT,  TC = VC + DC VC VFC TD FC VF  = = = = =  TT TS DC DCPM LPS  = = = =  i f TT<90min. i f 90<TT<250min. i f TT>250min.  + CC  v e h i c l e c o s t ($/m ) v e h i c l e f i x e d c o s t ($) travel distance (km) f u e l c o s t ($/km) vehicle factor; volume of daily s e r v i c e d by one v e h i c l e ( P r o v i n c e of Columbia', 1980e) t r a v e l time ( m i n u t e s ) t r a v e l s p e e d (kph) d r i v e r ' s c o s t ($/m ) d r i v e r ' s c o s t per minute ($/min.) loader productivity per shift, 8 3  production British  3  nr.  shift  143  CC FBC OCC TC  =' = = =  (-•/shift) crew c o s t ($/m ) f a l l i n g and b u c k i n g c r e w c o s t ( $ / m i n . ) o t h e r crew c o s t ($/min.) t o t a l crew t r a n s p o r t a t i o n c o s t 3  T i m b e r c r u i s i n g c o s t s were d e t e r m i n e d cubic  meter  dependent  allowed  on  in  volume  stumpage  small as  stands  of  low  5 percent  of the  loading  costs  and  Columbia,  meter, again were  sum  cubic  the  ($15.20/ha).  as  logging process, t h e sum  5.34  costs  of  spot  estimated  and  3  last by  area  of  British  appraisal  and  cubic costs,  burning  residual  component was  stand  yarding  c o s t s per  slash  on  costs falling  converted  to a  dividing  by  the c o s t total  f o r each phase or component  logging cost  ( $ / m ) was 3  of  determined  of a l l phase c o s t s .  Revenues Determining  knowledge their  stumpage  and  (net).  After calculating the  .(Province  ($0.01/m )  The  v o l u m e b a s i s by m u l t i p l y i n g volume  (higher  stand treatment  sum  3  timber  meter  from c o a s t  ($0.02/m ), r e s i d u e surveys allowance  meter  are  of each s t a n d ,  Engineering costs are  Finally,  as  area  per  which  of r o a d c o n s t r u c t i o n , f a l l i n g ,  per  developed  calculated  cubic  volume).  1980e).  appraisals,  p e r h e c t a r e and  r a n g e f r o m 3 t o 52 c e n t s p e r  using the c o s t s  of  the  value  t h e t y p e and  of  quality  c u r r e n t market p r i c e s .  information T h i s has  is  not  harvested  commonly  often l e d to harvest  b a s i s of s p e c i e s d i s t r i b u t i o n  timber  of p r o d u c t s  requires  recovered,  Unfortunately, product available  and  recovery  from i n v e n t o r y  revenues being c a l c u l a t e d  and  data. on  a v e r a g e market p r i c e of  the logs  144 by  species,  which  .distribution  of  distribution producers  the  .being  future  supplying  previous fairly  assumption  a  be s i m i l a r  the  and  in  in  •-necessary -suggested  of  would p a r a l l e l analysis  of  of  market  stand  harvest  revenues,  that must be to e x p l i c i t l y  the that  the  product  the t r u e v a r i a t i o n than  harvest of  historic  the  product  market  product  to  in  recovery  logging inventory  information  i n timber values as  automatically by  on a given  As elsewhere,  lack  of  depending  (or q u a l i t y ) of the timber  Rather  this  the d i s t r i b u t i o n  It i s this variation  Forest  analyse  above.  distribution  since,  recoverability.  Research to  for a l l  on the  (or p o s s i b l y g r e a t e r ) importance  limiting  -data on the  total,  However,  vary from stand to  determining  stand i s of equal  In  to product  i n an a n a l y s i s of the l i m i t s to  recoverability,  .recognize that the value  costs  market.  predictable.  type and q u a l i t y .  .considered  be s i m i l a r  product  year, with temporal changes i n d i s t r i b u t i o n  products recoverable w i l l on timber  will  that  to product d i s t r i b u t i o n  gradual  timber  assumption  given market, product d i s t r i b u t i o n  i s h i g h l y untenable  economic  the  harvests  c u r r e n t l y on  .harvests may in  requires  assume  that  type on the F o r e s t general,  a  simple  from the F o r e s t  was  undertaken. P r o d u c t s recovered from past timber included;  sawlogs  and b l a n k s . cedar  snags  important  generally  and pulpwood, p o l e s , p i l i n g s , cedar  P r o d u c t i o n of shakes from  s a l e s have  the  area  source of revenues  and  killed  blanks, by f i r e  by  shakes  salvaging  in 1S68,  was  an  on the F o r e s t d u r i n g the f i r s t  10  145 to 15 years .of o p e r a t i o n s .  As noted  Report,  m a t e r i a l had  the  and,.  last  usable  .  i n the  1968-1969  Annual  been s a l v a g e d by  1967  •.  " . . . a 20-year p e r i o d of manufacture of shakes and blanks from cedar. . , was brought to a c l o s e . Although suitable material w i l l be salvaged o c c a s i o n a l l y i n the f u t u r e the volume w i l l be minimal." (University of B r i t i s h Columbia Research F o r e s t , 1970. p. 1 ) . An a n a l y s i s of r e c o v e r a b l e timber the recovery of primary which  initial  c u r r e n t and fires  in  forest products,  logging  operations  f u t u r e shake and old-growth  supplies is  cedar)  were  will  with  that i s , products undertaken.  blank p r o d u c t i o n  regular logging operations, t h e i r excluded  concerned  for  Since  (barring  major  occur as salvage f o l l o w i n g recovered  from the a n a l y s i s (as w i l l  values  will  be  t h e i r a d d i t i o n a l c o s t s of  recovery). Sawlogs have, h i s t o r i c a l l y , volumes recovered and  of  the  total  recovered  through  recovery  have  logging.  The  products  can  been  the  be expected  forthcoming and  integrated primary  p r o p o r t i o n of annual  i n t o predominantly  Forest,  harvest.  Pulpwood,  s m a l l , though i n c r e a s i n g ,  Pulpwood has  with  sawlog  product  g e n e r a l l y been piling  operations  in  harvests in  second-growth stands.  f o r new  poles  or  second-growth "small-timber"  to i n c r e a s e as f u t u r e l o g g i n g moves  change i n product  need  product