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A computer simulation of bluebunch wheatgrass (Agropyron spicatum) growth dynamics and implications to… Allaye-Chan, Ann 1984

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A COMPUTER SIMULATION OF BLUEBUNCH WHEATGRASS (AGROPYRON SP1CATUM) GROWTH DYNAMICS AND IMPLICATIONS TO  INTEGRATED  MANAGEMENT OF LIVESTOCK AND WILDLIFE  by ANN  C.(ALLAYE-CHAN  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  in THE FACULTY OF GRADUATE STUDIES Department of Plant  Science  We accept t h i s t h e s i s as conforming to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA October ©  1984  Ann C. Allaye-Chan,  1984  In  presenting  this  requirements  that  I agree that  available  permission  scholarly  for  partial  purposes or  understood  that gain  by  may his  be or  copying  shall  the  reference  for extensive  Department  financial  in  of  not  of Plant  of  this  granted  by  the  her  the  1984  make  allowed  Science  Head  i t  agree  thesis  representatives.  or p u b l i c a t i o n be  shall  copying  THE UNIVERSITY OF BRITISH COLUMBIA 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date: October  Library  and study. I f u r t h e r  permission.  Department  fulfilment  f o r an a d v a n c e d d e g r e e a t t h e THE UNIVERSITY OF  BRITISH COLUMBIA, freely  thesis  of It  for my is  of t h i s t h e s i s f o r  without  my  written  Abstract A c o m p u t e r model was {Agropyron  spicatum  developed  (Pursh)  f o r bluebunch  Scribn.  and  simulated  the growth dynamics of t h i s  species  presence  and  Growth  absence  mechanistically potential,  modeled  soil  photoperiod,  and  sampling.  discrepancies Sensitivity that  dry matter  moisture  on  research.  combination short  rate  of  low  photoperiods  low  fall.  ii  soil  in  some  values.  variables revealed sensitive  effect  by  from  between  observed  driving  absence  litterfall  and  to  soil  of s o i l  water  warrants that  low  availability  late  of  resulted  the  matter  obtained  rate  indicate  temperatures, in  dry  litterfall.  particularly  limited  moisture  low  and  highly  results  is primarily  spring,  is  consequently,  Simulation  accumulation early  of c l i m a t i c  water  maturity.  biomass,  relationship  growth  were  intensity,  plant  simulation  predicted  growth  rainfall  measurements  the  production  regimes;  potential  of  and  analysis  soil  of herbage p r o d u c t i o n i n the  However, e r r o n e o u s  between  dynamics  translocation  mortality,  with  the  carbohydrate  root  closely  potential  both  potential,  belowground  inaccurate portrayal  water  in  which  growth  and  predictions  Smith)  of  and  included  respiration,  and  g r a z i n g agreed  functions  nitrogen content,  dark  shoot  Model  field  as  a i r temperatures,  aboveground  production,  of  grazing.  processes  photosynthesis, between  and  foliar  Simulated  of  wheatgrass  dry  further matter  temperatures  in  i n mid-summer, and  foliar  nitrogen,  Simulated  a  and  carbohydrate  movement  from  initiation regrowth spring  the  of  i n one  matter  root  year  simulation,  of in  a  occurred  Simulated  field  two  values  of  following  of  crop  i n the  regimes;  production  was  strongly  defoliation  intensity  occurred  However,  the  storage c o i n c i d i n g  with  of  current  annual  the  support  Simulation  dry  from  matter  intensities  they  the  biological  results  also  61%.  when h e r b a g e effects  may  Total by  indicate  of  minor  Simulation  indicate  annual  dry  that  herbage  results  matter date  occurred  defoliation when  by  increase standing  defoliation  removal  is  qualitative  i s c o n s i d e r a b l y depressed  affected  mid-July.  of  However,  intensity  became  ground-level  values obtained  data.  fall  a s much a s  intensity  after  to  of  following  results  a t 25%  by  defoliation  accounted  aboveground  the  defoliation  however,  fall  July.  annual  validation  suitable  defoliations  i n the  system  onset  with  lighter  simulation  standing crop  spring  simulation.  translocation  thirds  favorably  Quantitative  by want o f  most g r a z i n g  of  before  regrowth  soundness of p r o j e c t e d y i e l d s . that  fall  occurred only during  root  Photosynthate  primarily  compared  accumulation  validation  the  of  both  completed.  sampling.  precluded  but  w i t h peak c a r b o h y d r a t e  been  defoliation  commencement  year  from  s t a g e when a p p r o x i m a t e l y  g r o w t h had  occurred during  6 t o 7 p e r c e n t of t o t a l  production.  system  and  second  translocated  aestivation, the  growth  approximately  dry  shoots  spring  inititation  Carbohydrates for  r o o t s to the  and  before  date  and  removal  suggest  that  improvements  in crude p r o t e i n y i e l d  regimes surpass grazing  improvements  treatments,  yield  are  promoted  well  as  occur  at a h i g h e r  stimulated  improvement in  in  biomass  effect  following herbage  removal  damaging  at  Simulation removal  on  dry  comparable  crude  Thus, d e f o l i a t i o n  may  later  than  date  f o r an  for  indicate  parallels  accumulation  mid-season g r a z i n g  at  the during  fall  that  the  the  year  effect  of  the  of  grazing  comparable  an  improvement  matter production  e a r l y s p r i n g or  protein as  results  closely root  In g e n e r a l , than  on  grazing  concentrations  a  crude p r o t e i n y i e l d  defoliation  treatment.  or  for  in  nitrogen  production.  intensity  herbage  yield  improvements  enhanced  foliar  yield.  of  in forage  since  by  following select  year are  less  defoliation  intensities. Simulation  results  judicious  grazing  bluebunch  wheatgrass  to w i n t e r i n g predicated in  the  regrowth w i l l  spring  growth.  defoliation  management forage  wildlife. on  on  support  not  may and  However,  assumption exceed  that  the  yield.  Currently,  tenuously  m o d e l e d b e c a u s e of  the  used  to  r a t e of  the  l a c k of  nitrogen  simulated in  tillering  data.  improve  quality  nitrogen  is critical  that  availability  forage  of  simulated  i v  contention  crude p r o t e i n  rate  behavior  regrowth  be  improved  Additionally,  tillering  the  is loss  loss  in  effect  of  determining behavior  is  Table  of Contents  Abstract  i i  List  of Tables  List  of F i g u r e s  v i i viii  Acknowledgements  x i i  1.  INTRODUCTION  1  2.  LITERATURE REVIEW  4  2.1  GENERATION OF ASSIMILATES  2.2  PARTITIONING  2.3  (PHOTOSYNTHESIS)  AND TRANSLOCATION  2.2.1  Effects  of A b i o t i c  2.2.2  Effects  of B i o t i c  OF ASSIMILATES ...5  Factors  5  Factors  6  DRY MATTER PRODUCTION 2.3.1  3.  METHODS  4.  AGGRO:  10  Abiotic Controls Production  2.3.2 D e f o l i a t i o n Product ion  4  of  Effects  Dry on  Dry  Matter ...10 Matter 13 15  SIMULATION  MODEL  OF  BLUEBUNCH  WHEATGRASS  GROWTH  18  4.1  GENERAL MODEL STRUCTURE  18  4.2  ABIOTIC DRIVING VARIABLES  18  4.2.1  Soil  22  4.2.2  A i r and S o i l  4.2.3  Precipitation  29  4.2.4  Daylength  29  Water P o t e n t i a l Temperatures  25  4.3  GROWTH POTENTIAL AND DRY MATTER PRODUCTION  30  4.4  GENERATION OF ASSIMILATES  40  4.5  RESPIRATION  42  4.6  CARBOHYDRATE PARTITIONING  44  v  5.  4.7  SHOOT AND  ROOT MORTALITY  4.8  LITTERFALL  48  4.9  FOLIAR NITROGEN  48  4.10  EFFECTS  49  OF DEFOLIATION  SIMULATION RESULTS, MODEL ANALYSIS, AND DISCUSSION 5.1  BLUEBUNCH WHEATGRASS OF GRAZING 5.1.1  5.2  47  Dry Matter Biomass  VALIDATION,  SENSITIVITY 53  DYNAMICS IN THE  ABSENCE 53  Production  of  Aboveground 53  5.1.2  Crude P r o t e i n Y i e l d  60  5.1.3  Carbohydrate P a r t i t i o n i n g and B e l o w g r o u n d B i o m a s s  Between  Above 63  BLUEBUNCH WHEATGRASS DYNAMICS IN THE  PRESENCE  OF GRAZING 5.2.1  Regrowth  5.2.2  Total  5.2.3  Crude P r o t e i n Y i e l d  74  5.2.4 5.2.5  B e l o w g r o u n d Dynamics Dry M a t t e r P r o d u c t i o n Herbage Removal  80  5.2.6 6.  70 Following  Defoliation  A n n u a l Dry M a t t e r  Production  the Year  Implications to Integrated C a t t l e and W i l d l i f e  GENERAL DISCUSSION  70 74  Following 83  Management o f 86 94  LITERATURE CITED  99  APPENDICES  108  vi  List  of Tables  Table  Page  I.  Summary  II.  Results  of v a r i a b l e of  names a n d l i t e r a t u r e  sensitivity  analysis  sources.  f o r t h e 1968 c o n t r o l  simulat ion III.  The e f f e c t  59 of  availability  The e f f e c t  grazing  of crude  concentration IV.  ...20  concentration  protein  o f 5% f o l i a r  of  availability  regime  grazing  of crude  on  regime  o f 5% f o l i a r  vi i  November  1st  w h i c h o c c u r s a t a minimum  content  protein  the  on  by w e i g h t the  December  89 1st  w h i c h o c c u r s a t a minimum  content  by w e i g h t  89  List  of  Figures  Figure  Page  1.  G e n e r a l model  2.  Soil  water  medium,  Broersma,  low  o f AGGRO  growth  19  t o e v a l u a t e the e f f e c t s  moisture  availability  dynamics  (From  on  van  of  Ryswyk  soil  water  and 23  curve  bluebunch wheatgrass  Seasonal  high,  bluebunch  unpublished data)  Moisture c h a r a c t e r i s t i c ( 1969)  4.  regimes used  and  wheatgrass  3.  structure  developed  mesic  potentials  (1969) b l u e b u n c h w h e a t g r a s s  mesic  for  Harper's  site.  24  generated f o r Harper's site  i n 1967  and  1968. 26  5.  6.  Simulated a i r temperatures wheatgrass  mesic  Simulated  effect  (Adapted 7.  8.  Simulated (Adapted  i n 1967  of  soil  of f o l i a r  1968  vi i i  on  on  28 growth )  growth  (1975) )  nitrogen  from d a t a by W i l s o n  (1969) b l u e b u n c h  e t a l . ( 1979)  water  f r o m d a t a by M a j e r u s effect  and  of a i r temperature  f r o m d a t a by d e V r i e s  Simulated e f f e c t (Adapted  site  f o r Harper's  on g r o w t h  (1975) )  potential 33 potential 35 potential 37  9.  Simulated  effect  of  hormonal a c t i v i t y 10.  Simulated (Adapted  11.  from  Simulated (Adapted  12.  effect  of a i r  data  temperature  by D e p u i t of  data  effect  from  by D e p u i t  water p o t e n t i a l  of temperature and C a l d w e l l  foliar  n i t r o g e n over  14.  Simulated  effect  of d e f o l i a t i o n  16.  simulated  bluebunch  wheatgrass  Simulated  growth  temperature, nitrogen  17.  Simulated  growth  temperature, nitrogen  on  soil  and  43 (Adapted  )  45 50  shoot  biomass of  simulated  .....54 effects  of  d a y l e n g t h , and f o l i a r  f o r Harper's  i n 1967  potential  bluebunch 56  and  water p o t e n t i a l ,  site  (1977) )  f o r 1967 a n d 1968  maximum g r o w t h r a t e  wheatgrass mesic  (1975) ) . ..41  on p h o t o s y n t h e s i s . ...51  water p o t e n t i a l ,  site  photosynthesis  time  on maximum g r o w t h r a t e  wheatgrass mesic  39  on p h o t o s y n t h e s i s  ( 1975)  a n d measured  potential  soil  belowground  on r e s p i r a t i o n  Simulated  of  on  and C a l d w e l l  13.  15. C o m p a r i s o n  on  by Brown a n d T r l i c a  Simulated data  maturity  and i n c i d e n c e o f t i l l e r i n g  effect from  plant  simulated  e f f e c t s of  daylength,  and f o l i a r  f o r Harper's  i n 1968  bluebunch 57  18.  Simulated  crude  protein  yield  f o r 1 967  61  19.  Simulated  crude  protein  yield  f o r 1968  62  ix  20.  Simulated and  21.  fall  crude regrowth  Simulated and  belowground  bluebunch  bluebunch  25.  26.  site  biomass  and  65  between  cumulative  belowground site  aboveground movement  biomass  for  defoliation  67  on May  31, June  intensity  on November 1 s t f o r a g e a v a i l a b i l i t y  of  Simulated  effect  intensity  on t o t a l  Simulated  crude  four  crude  intensities crude  intensities  14, 71  effect  Simulated  regrowth  28, 1967  intensities  of  Harper's  i n 1968  Simulated  Simulated  Harper's  i n 1967  of c a r b o h y d r a t e s  wheatgrass mesic  for  ground-level  four 28.  movement o f  following  four 27.  cumulative  belowground  biomass, into  and  aboveground  o f s i m u l a t e d and m e a s u r e d v a l u e s o f  June  biomass  between  Comparison  and 24.  into  movement  carbohydrates  23.  biomass,  belowground  in foliar  64  of c a r b o h y d r a t e s  wheatgrass mesic  Simulated and  percentages  i n 1967 and 1968  movement  carbohydrates  22.  protein  defoliation  of  date  defoliation  annual  protein on May  date  dry matter  yields  following  1 a n d May  on J u n e  14 a n d June 28  on J u l y  following  following  15 a n d September  x  73 defoliation  defoliation  30  yields  yields  and  defoliation  production  protein  protein  and  75 at 76  defoliation at 77 defoliation 15  at 78  29.  30.  31.  Simulated  effect  intensity  on November  defoliation  at v a r i o u s dates  Simulated  effect on  dry  and  defoliation  following  ground-level 82  defoliation matter  81  date  and  defoliation  p r o d u c t i o n t h e year  following  removal  Forage  84  availability  availability livestock different Crude  accumulation  of  date  1st root biomass  root  herbage  33.  defoliation  Simulated  intensity  32.  of  for  grazing  for  wildlife on  six  cattle on  versus  November  different  1st f o l l o w i n g  dates  intensities  protein  at  four 91  availability  foliar  content  by  wildlife  following  livestock  d a t e s and f o u r d i f f e r e n t  forage  (minimum c o n c e n t r a t i o n o f 5%  weight)  for  grazing  intensities  xi  cattle on  versus  six different 92  Acknowledgements I  wish  t o thank my s u p e r v i s o r , Dr. M.D. P i t t ,  assistance, counsel, Constructive  and  support  throughout  for h i s  this  study.  c r i t i c i s m s and guidance from the members of my  graduate committee, Dr. F.L. B u n n e l l , Dr. P.A. J o l l i f f e , and Dr.  V.C.  Runeckles, a r e deeply a p p r e c i a t e d . S p e c i a l thanks  i s extended to Barry Wong f o r h e l p f u l suggestions fitting  and v a l u a b l e a s s i s t a n c e with computing  B r i a n Wikeem, Don Eastman, and Rick E l l i s  on  curve  difficulties.  reviewed the  word  model f o r the computer s i m u l a t i o n . F i n a n c i a l support  f o r t h i s research was p r o v i d e d by the  Research Branch of the B.C. M i n i s t r y of F o r e s t s , the N a t u r a l Sciences and E n g i n e e r i n g the  B.C.  Cattlemen's  Research C o u n c i l of Canada Association,  and  A g r i c u l t u r e at the U n i v e r s i t y of B r i t i s h  xii  (#0227),  the 1921 C l a s s of Columbia.  1. Bluebunch Scribn.  and  wheatgrass  Smith) i s a  western North America is  palatable  to  (Singleton,  Agropyron  (  key  forage  (Dayton,  both  Wilson  and  et  a l . , 1975;  e t a l . , 1966;  and  Pechanec  ,1949) a s  i t has  of  grazing  pressure  (Daubenmire,  management  i s therefore  health  p r o d u c t i v i t y of  and  The  response  defoliating  i s t o be  optimizing  plant  behaviour  quantity  of  r e g i m e , as plant  vigor  and  systems  where  wildlife  is  the  effective  the  bluebunch  Sauer,  1978;  research  1949;  Wilson  Daubenmire,  to  A  that  (Mcllvanie, a l . , 1966;  1978;  the  quality given  of  grazing  In  following has 1942;  on  grazing  livestock  must a l s o be  of and  p a r t i c u l a r regime  and  given  to  defoliation.  been t h e  focus  Blaisdell  Mueggler,  1972,  W i l l m s e t a l . , 1980a,  1  health  knowledge  herbage p r o d u c t i o n .  regrowth  and  i f grazing  plant  secure  determine  wheatgrass  et  the  climatic  maintaining  management  of  absence  in assuring  understood  practiced, consideration  Although  Pechanec,  crucial  i s a v a i l a b l e f o r any  integrated  quantity  considerable  in  to  subsequent  Blaisdell  1978). E f f e c t i v e g r a z i n g  well  e f f e c t s of  q u a l i t y and  1956;  to  Rickard  l a r g e l y i n the  production.  which  ungulates  resource.  be  needed  forage as  must  animal  is  well  this  which  e t a l . , 1981;  bluebunch wheatgrass  factors  management while  of  particularly  to  i s susceptible  Branson,  evolved  1978)  native  grass  (Caldwell  (Pursh)  indigenous  Daubenmire,  cool-season  i n j u r y , however,  spicatum  species  1937;  domestic  1976). T h i s  defoliation  INTRODUCTION  of and  1975; 1980b;  2 Caldwell 1982),  et a l . ,  existing  limited  data, i n t h e i r  guidance  identified of  1981; W i l l m s e t a l . ,  patterns  not  or  managers  strategies,  t o range  allow  animal  have  current  yearly  production  no  the  for  means  objectives.  grazing  can  only  qualitative  p e r s p e c t i v e . The e m p i r i c a l a general f a i l u r e  o f thumb  plant  transferrability  information  degrees  Because  appropriate  nature  responses, to  range  management  approximated  to consider  mechanisms u n d e r l y i n g of  be  only  in climatic  alternate  regime  objectives  plus  provide  variations  of e x p l o r i n g  optimum  et a l . ,  r e a d i n e s s and s a f e  management  data,  form,  t o range managers. G e n e r a l r u l e s  with respect  u s e . do  1981; Q u i n t o n  to  from  of  a  existing  the p h y s i o l o g i c a l  further  limit  the  o t h e r y e a r s and o t h e r  situations. This simulation  dissertation model w h i c h  wheatgrass  growth  of  Specific  1.  grazing.  properly  British 2.  dynamics  to  project  of  to  used  develop  to  a  computer  evaluate  bluebunch  i n b o t h t h e p r e s e n c e and  objectives model  of t h i s  absence  thesis are:  f o r bluebunch  responsive to climatic  Columbian  bluebunch  3.  c a n be  t o d e v e l o p a growth is  seeks  wheatgrass  conditions  which  t y p i c a l of  rangelands,  realistically wheatgrass,  both  biomass  accumulation  i n t h e p r e s e n c e and  in  absence  grazing,  t o i n v e s t i g a t e a number o f wheatgrass incomplete,  dynamics  relationships  f o r which  in  bluebunch  u n d e r s t a n d i n g i s poor o r  3 4.  to  explore  r e g i m e s on yields  implications the  availability  to w i n t e r i n g  of of  wildlife.  various  livestock grazing  c r u d e p r o t e i n and  forage  2.  2.1  GENERATION OF The  of  information Caldwell in  ASSIMILATES  e f f e c t s of  bluebunch  LITERATURE REVIEW  a b i o t i c f a c t o r s on  wheatgrass  are  net  assimilation  temperature  for photosynthesis  irradiation  was  var.  rate  spicatum  increasing  temperature  defoliation  year  of  at  20  decrease  wheatgrass  i n the  than  spring  foliage  (Caldwell  -31  leaves  on  regrowth  could  be  photosynthetic  capacity  associated 1980). only  high  of  nitrogen  with high  younger  and  or  due  rates  4  under  after  a  zero  at  the  same t i m e  plants.  of  photosynthetic  partly  of  severe  photosynthetic  to  greater et a l . ,  which are  (Bolton  and  d i f f e r e n c e s are  for d i f f e r e n t i a l  undipped  rate  wheatgrass  f o l i a g e (Caldwell  age  Trlica  approached  higher  concentrations  However, p h e n o l o g i c a l  clipped  western  greater  photosynthetic  factors responsible  between  constant  bars.  control plants  of  optimum  of  regrowing  exhibited  The  the  The  photosynthetic  photosynthesis  1981).  1981),  leaves.  for  et a l . ,  capacity  wheatgrass  smi t hi i Rydb.) p h o t o s y n t h e s i z i n g r e g i m e . Net  and  response  2 5 ° C . Brown and  in  stress  Depuit  beardless  to  rate  relevant  temperature  under c o n d i t i o n s  water p o t e n t i a l e q u a l e d  Bluebunch  rates  linear  moisture  (Agr opyr on  when s o i l  exchange  however,  inerme H e l l e r )  established  (1977) documented a  20°C  unknown;  C02  exists for a c l o s e l y related species.  (Agr opyr on  plants  the  (1975) f o u n d a n e a r p a r a b o l i c  the  with  (PHOTOSYNTHESIS)  Brown, not  assimilation Painter  and  often  the  rates  Detling  5 (1981) f o u n d undamaged  that  within  tillers  one  of  day  partially  exhibited  higher photosynthetic  leaves  control  2.2  of  of  defoliated  rates  TRANSLOCATION OF  2.2.1  ABIOTIC FACTORS  EFFECTS OF  Environmental photosynthates  stress  which are  not  the  aged  movement  of  (Moser,  environmental  indirect effects,  changes  in  of  of  the  rate  carbohydrate  of  sinks  1977). stress  appears to process  numerous  studies  assimilate  movement  following  (Weatherly  et  1971),  changes  1968). observed  al.,  1959;  have v e r y per  in  the  with  temperature  movement  water  stress  are  a  of  on  1968).  reduction i n the  1968;  generally  in plant  Sosebee  and  attributable  relationship  (Wardlaw,  the  has  phloem  severe moisture  McWilliam, stress,  on  in  effect  (Wardlaw,  Wardlaw,  source-sink  1971;  little  water d e f i c i t  even under c o n d i t i o n s Crisp,  se  indicate  such r e d u c t i o n s  Assimilate  ( C r a f t s and As  comparably  indirectly  the  development  Although  to  also  the  direct effects  through  translocation  Wiebe,  and  s i g n i f i c a n t as  mediated  Water the  plants  ASSIMILATES  control  directly  the  as  p h o t o s y n t h e s i s and (Moser,  f a c t o r s can  both  general,  are  than  treatment,  plants.  PARTITIONING AND  1977). In  clipping  the  assimilate  been stress  1968). direct  effects  translocation  of are  6 relatively  minor  partially  metabolic,  (Wardlaw,  relative  the  roots  under  27/21°C,  factor  Translocation  and  McNairn,  t o growth  in  at  1968;  Ontogenetic been  carbohydrate  no as  temperatures. formation  hirsutum  L.)  and C u r r i e r ,  obstruction  40°C and was (1972)  1968;  was  not  transitory  reported  and a p p r o a c h e d n o r m a l  BIOTIC  that  levels  within  FACTORS  changes  conflicting  i n photosynthate p a r t i t i o n i n g documented  from for  for  grasses,  on t h e p h e n o l o g i c a l  storage normally  radioactive  allocated  found  sieve plates decreased within s i x  extensively is  exported  regimes of  translocation  low  Webster  among  heating.  EFFECTS OF  using  differ  (1968)  phloem  40°C. McNairn  d e p o s i t i o n s on  evidence  not  {Gossypium  t e m p e r a t u r e s below  days of  have  from  under  cotton  Currier,  hours of heat s t r e s s  2.2.2  carbon recovered  3 2 / 2 7 ° C . Wardlaw  t e m p e r a t u r e s above  two  that  temperature  to support  be  reported  1972). However, a s s i m i l a t e  apparent  callose  (1974)  may  dependent  b l o c k a g e by h e a t - i n d u c e d c a l l o s e  reported  (McNairn  at  and  loading  temperature  did  day/night  evidence  limiting  has been  hence,  of western wheatgrass  conclusive the  and  phloem  amount o f r a d i o a c t i v e  grown  21/16°C,  though  1968). Schmer and K n i e v e l  the  plants  even  s t a g e when  takes  place.  As  have  shown,  assimilates  tracers  photosynthetic development  but  of  foliage the  are  studies  initially  s h e a t h and  further  7 expansion  of  Subsequently,  the  to  the  (Sosebee  and  Wiebe,  prior  t o culm  1973;  to  crested  minor  during  wheatgrass,  inflorescence  root  (Sosebee  ratio  of p h o t o s y n t h a t e  unity  until  and  major  and  to  The  translocation  and  translocation biomass  is  rapid vegetative 1973).  the  In  developing  and  movement  crowns becomes n e g l i g i b l e 1973).  roots  Smith  Wiebe,  at  that  upward:downward  d o e s not d r o p  using radioactive  carbohydrate Seasonal  storage,  (TNC)  of  below  of halfway  Following  early  an  Willard  carbohydrate  an  total  wheatgrass  carbohydrate through season  (1981) n o t e d  concentration  indicate  studies  i n the r o o t s  reveal  that  vegetative  depletion a sharp  storage  nonstructural  accumulation  the  a  monitoring  early  c o n c e n t r a t i o n observed  crowns o f b l u e b u n c h period  labels  trends indicate  trends  approximately  Daer and  s t a g e of  Sosebee  s t a g e of c a r b o h y d r a t e  root  1964;  1973),  1973).  to the  underground  Wiebe,  studies  carbohydrate and  Leinweber,  (Williams,  the  internodes  post-pollination.  While  date.  upper  translocated  Wiebe,  1973).  predominantly  r e a c h e s a peak a t a n t h e s i s ,  r o o t s and  seasonal  Wiebe,  is  and  translocation  time.  late  be  the  ( W i l l i a m s , 1964;  the  Smith  S o s e b e e and  carbohydrates  growth  and  elongating  elongation  1973;  relatively  to  actively  c a r b o h y d r a t e s may  Leinweber, of  (Sosebee  t h e p a t t e r n of movement  upwards  Although  leaf  of TNC  occurs stage.  reserves,  increase  once t h e p l a n t s  a  in  reached  the the  8 middle  of  the  continued  to  boot  increase  reproductive  period,  cm a n d  of  67%  completed.  until  study  current  concentration  trend.  but  that  more g r a d u a l (1981).  than  Apparently,  that  indicated the  the r e p r o d u c t i v e Willard  (1981)  carbohydrate by M c l l v a n i e  Herbage  were  stores  removal  may  Photosynthate  partitioning  different  to  of  a  phosphorus-32.  15  shifted  the  younger  leaves  cm  single It  was f a r  and  Willard  carbohydrate maturation.  in plants  observed  effective  those  was  in  in  plants  of  to that  distribution of  in  crested  heights, they  entire  with  the  applied  clipping consistently  translocates  the  plant.  (1971) c l i p p e d  which  of  the  modified  stubble  found  that  the  was  leaf  proportion so  reserves  more  parts  w h e a t g r a s s when S o s e b e e and Wiebe 10  species,  i n h i s study  seed  than  alter  to  to  increases  (1942).  photosynthates  exception  t h e end o f  same  maximum  demands  in  interrupted  Daer  until  20  been  decline  pattern  by  the  had  until  the  of root  was n o t o b s e r v e d  and  reducing  with  a similar  addition,  concentration  plants  growth  occasionally  the accumulation  In  observed  of  l e n g t h was  general  Working  (1942) r e p o r t e d  Daer  leaf  was o b s e r v e d  concentrations  Mcllvanie  by  beginning  annual a  concentrations  i n November, even t h o u g h a p p r e c i a b l e  downward  found  the  when t h e a v e r a g e  the  in carbohydrate the  Carbohydrate  Subsequently,  carbohydrate the  stage.  towards  the  upwardrdownward r a t i o o f  9 translocation  was  increased  W o r k i n g w i t h the  same s p e c i e s ,  concurred  a higher  shoot  that  system  rapid  following  approach  root  and  shoot  was  not  the  growth of  to  that  unabated  Caldwell  e t a l . (1981) and  must be  the  authors in  wheatgrass  plants  defoliation,  they  the  Painter  have  remain have  not  altered  the  Wiebe  (1971) f o r c r e s t e d  manner  the this  the  root  of did  that  that  the  Detling  new  growth  not  the  precluded  studies  the  even  structural western following possibility  compounds may  i n d i c a t e d by  of  (1981)  Thus,  and  unchanged  differ  wheagrass  Detling  wheatgrass  wheatgrass.  and  western  and  nonstructural  been  more  that  biomass y i e l d .  shown  bluebunch  a l l o c a t i o n of in  roots  n o t e d , however,  measurements of  development  that  found  proportion  undefoliated  It  b a s e d on  a  the  following defoliation  c r o w n s , and  plants.  though  in  to  p r e c l i p p i n g b a l a n c e between  the  and  (1981)  resources  with bluebunch wheatgrass,  shoots,  defoliated  plants.  al.  defoliation resulted  the  case  et  e t a l . , 1981). S i m i l a r l y , P a i n t e r  allocated  were  Caldwell  s y s t e m s . However, t h e y  reported  among  defoliated  a l l o c a t i o n of  which c o n t i n u e d  (Caldwell (1981)  to  in  Sosebee  have and  10 2.3 DRY MATTER  2.3.1  PRODUCTION  ABIOTIC CONTROLS OF DRY MATTER The  effects  accumulation established,  of  in  from  generated  numerous  field  interdependent  adverse found  that  Instead,  growth  rainy  when  that  a delayed  correlation effects  elongation Soil  analysis  than  between of s o i l  water  t o be  correlation  low  account  temperature or  was  temperatures  related  temperature,  might  soil  (1958)  e t a l . (1980a) r e p o r t e d  to soil  response  Blaisdell  between  on  variables are  and p r e c i p i t a t i o n  e l o n g a t i o n was more c l o s e l y  temperature  low  and low w i n d s .  negative  increment  weather. Willms  growth  was n o t b e l i e v e d  the  by t h e a s s o c i a t i o n  high  temperatures,  correlation  however,  (1958)  vegetative  that  skies,  high p r e c i p i t a t i o n  air  The  and f o u n d  simple  been d e r i v e d  between  clear  poorly  Blaisdell  and s i m u l t a n e o u s l y c h a n g i n g  between  tiller  of  t o growth.  explained and  factors,  manifested,  concluded  observations.  biomass  are  knowledge h a v i n g  relatively  difficulties  on  wheatgrass  were a s s o c i a t e d w i t h h i g h  precipitation,  quickly  factors  correlations  and c l i m a t i c  increments  The  bluebunch  with e x i s t i n g  primarily  growth  climatic  PRODUCTION  to  that  maximum  and suggested for  the  and t i l l e r  precipitation  poor  growth.  on  tiller  were n o t c o n s i d e r e d . temperature  determinant  in  appears  initiating  to  be  growth  a than  more soil  important moisture,  11 which al.,  i s normally recharged 1981; Q u i n t o n  bluebunch  Growth  has  been  thaws  (Stout et  initiation  reported  when  in soil  were 6°C ( Q u i n t o n e t a l . ,  and 4°C ( W i l l m s e t a l . , 1980a).  occurred  al.,  cessation  at  comparable  a  to that  to  conclude  species. provided  roots  coefficient  if  temperature  was  is  no water  is  further bluebunch  and  flexible  i n excess  reach of  of t h e  the  grass  (1972) s u g g e s t e d was due t o  a  of t h i s  that  green  et  et a l . not  cessation  found  partially  levels  Quinton  conclusion  ( 1 9 7 2 ) , who  though  (Quinton  moisture  had been w i t h i n  a  r a t e and a r e d i s t r i b u t i o n  stress  significance In f a c t ,  importance  availability spring  growth  the high s e n s i t i v i t y  questionable.  has  that  greatly o f water  the plant.  to mild moisture low  the  t o low water  reserves within  Firstly,  even  transpiration  Given  soil  mid-June. Daubenmire  the t o l e r a n c e reduced  in  l e a v e s remained  after  in early  supporting this  mid-August,  wilting  moisture  that  by D a u b e n m i r e  wheatgrass until  when  wheatgrass  observation compelled  factor  Evidence  bluebunch  observed  This  controlling  in  time  1982).  (1982)  the  e t a l . , 1982).  a t a 10 cm d e p t h  Growth  the  spring  wheatgrass  temperatures 1982)  from  o f water moisture  might  be  (Anderson of  of bluebunch  wheatgrass  and McNaughton,  moisture  l e v e l s might  t h r e e p i e c e s of evidence availability had  not  expected  in limiting  been to play  limiting, a major  1973), appear support growth. then role in  12 governing  growth  cessation,  soil  cessation.  However,  temperatures  at  12-15°C and 11-15°C a t a l o w e r air  temperatures  respective  sites  temperatures, 25°C,  were  (Quinton  a l t h o u g h lower still  photosynthetic  activity  was  they  Finally,  the c h i e f  conducted  a comparison  a wet a n d a occurred  dry at  a  factor  a  revealed  much  later  that  the  consistently bluebunch  date  in  dictated the on  The wheatgrass  been  year  when  was  2.8  times  was  abnormally  no  above  single  focus  factor  growth  cessation  of environmental factor  of the a l t e r n a t e  has  dormancy  the  discussed  for  o f any s i n g l e  conclusion  in  is in  More p r o b a b l y , g r o w t h c e s s a t i o n i s  by an i n t e r a c t i o n  the state  that  responsible  importance  season  reports  fact  wheatgrass.  regrowth  1976).  discordant on  soil  experiment.  summer  t h e y e a r when p r e c i p i t a t i o n  attention  that  of t h e p h e n o l o g i c a l development  higher  The  and  B l a i s d e l l and  watering  year  (Sauer and Uresk,  to  1975)  prevented  d u r i n g the growing  low  20  considerable  demonstrated which  two These  the o p t i m a l of  Secondly,  small  the  a l . , 1982).  precipitation than  at  ( D e p u i t and C a l d w e l l , growth.  were  grassland site;  allowed  (1949) had c o n c l u s i v e l y  moisture when  than  growth  depths  13-15°C  et  have  n o t have a r r e s t e d  Pechanec  cm  and upper  12-16°C and  would  should  10  at  of  will  depend  in  part  factors.  aestivation  related  f a c t o r s , and  to  a  in lowering  bluebunch in soil  13 temperature  (Daer and W i l l a r d ,  added  fall  that  precipitation Foliar  regrowth  which  1972),  forage a v a i l a b i l i t y  i n both  et  regrowth  a l . (1980a)  was  difference  in  initiated newly  formed  length  winter  and  removal  were  concluded in  of  the  vegetative  that fall  plants  had  effect  no  elongation  the  following  elongation  was  significantly  plants  in control  mid  than  at  April  (Willms e t a l . ,  characterized et  defoliated  the  the  and  fall  PRODUCTION  following  herbage  e t a l . (1980a),  on  stubble  the  rate  on one  in  of  fall  sampling  Since this  in  tiller tiller clipped  date  in  period  was  temperatures  growth  (Willms  previously  the higher temperature  b u n c h e s where s h a d i n g from o l d f o l i a g e  who  heights  However,  higher  1980a).  p l a n t s may r e f l e c t  c r o w n . The  soil.  t o 5 cm  superior  the  t o 7.5 cm b e f o r e t h e  by u n u s u a l l y low s o i l  a l . , 1980a),  time  spring  spring.  plants  spring.  the  Willms  clipping  early  the  growth  by  in determining  by  the  from  cm  fall  increased  emerged  examined  depth.  t h e 5 cm o f  2.3.2 DEFOLIATION EFFECTS ON DRY MATTER Rates  autumn  that  appeared  between  had  tillers  i s significant  growing  tillers  tillers  before  at the r o o t i n g  reported  already  spring-initiated  soils  (1972)  may r e a c h h e i g h t s o f up t o 25  (Evans and T i s d a l e ,  Willms  occurred  had m o i s t e n e d  regrowth,  1981). D a u b e n m i r e  was removed.  of  14 Contrary  to  and S t o d d a r t ,  reports  1953),  studies  revealed  no  stimulated  by h e r b a g e  indication  1980b; C a l d w e l l  that  t h e number o f l i v e  (2.54  which cm)  observed  had  stubble no  on  that  removal  al.,  plants  for crested  wheatgrass  bluebunch tiller  development  e t a l . , 1981). B r a n s o n slightly  repeatedly  been  heights.  Willms  significant  wheatgrass  ( B r a n s o n , 1956;  c u l m s was  Willms  depressed  c l i p p e d t o one  difference  al.  in t i l l e r  clipped  M o r t a l i t y of s p r i n g - c l i p p e d  observed e i t h e r  after  the  development  of  e t a l . , 1981). T i l l e r s  did  produce  tillers  new  w h i c h had d i e d  (Caldwell  tillers. also  e t a l . , 1981).  which  inch  density  had  water  been  tillers  stress  survived c l i p p i n g  With a s i n g l e  failed  in  d e f o l i a t i o n or  substantial  (Caldwell not  which  immediately f o l l o w i n g  et  (1980b)  plants  was  and p l a n t s  et  is  (1956) f o u n d  between u n d e f o l i a t e d i n the f a l l .  (Cook  to y i e l d  new  exception, tillers  3. Bluebunch with at  plant the  response  was n e e d e d  parameters  relationships. structured modeling also  such  grazing  has  general  factors  as  geographic Such  precision  Thornley,  were  goodness  of  interpret  processes  functions  Published physiological  by t h e  approach  the model,  climatic  does,  a  introduced pattern,  however,  tend  and g e n e r a l i t y  In  cubic  biomass  or to  (Walters,  cases,  on no  instances,  splines  were  fitting  information was  on used  15  with  curve of  was  were  their  made  to  coefficient  values  piecewise  linear  used  to  describe  conventional  bluebunch for  for  basis  attempt of  modeled  accumulation  the  significance some  was  describing  equations  primarily  which d e f i e d  processes  growth  equations  governing  In most  type.  relationships  location,  of  changes  wheatgrass  the b i o l o g i c a l  or  hierarchically I.  acknowledged  situation  of  biological  A mechanistic  Mathematical  selected  f i t .  function  of  been  mathematical  derived.  fitting  of  realism  bluebunch  physiological  mechanistic  1976).  mechanistically,  empirically  for  A  postulation  power  an a p p r o a c h  simulated  relevance  applicability  accommodate  schedule.  factors  possible.  1976).  to  mechanistically  biological  previously  (Thornley,  for  Although  or  permit  needed  sacrifice 1971;  the  heuristic  models  allowed  where  assure to  was m o d e l e d  and b i o t i c  level  to  The  growth  abiotic  and  community  property by  to  physiological  approach model  wheatgrass  METHODS  model  curves.  wheatgrass construction  16 whenever p o s s i b l e . Where  information  d a t a c o l l e c t e d f o r o t h e r members exploited. lacking  In  for  obtained  the  Agropyron  from  of  given  Subsequently,  for  During made t o  in  order  variables.  species  similarity  to  allometric against  and  biological  processes  complexity  was  information  gaps  development  increase and  decline  beyond  a  detail  by  in  in  and  of  the  reported threshold  must to  resolution  constraints,  kept  reduce both computing c o s t s  detail,  for  were  data c o l l e c t e d  components  increased  need  highest  wheatgrass.  indices  r e a s o n a b l e , model. B u n n e l l  modeling  species.  the  bluebunch  empirical  biologicaly  simulation  having  were  relationships  the  sufficient  were  entirely  plant  a conscientious  d e g r e e of  Large  geometric  g u i d a n c e was  other  precluded  a  genus  development,  simple  The  to  same  wheatgrass.  essential  complexity.  of  those  fine-tuned  model  use  capture  to  simple  and  bluebunch  the  empirical  genus, b i o l o g i c a l p r i n c i p l e s  observations  biological  postulated  of  c a s e s where q u a n t i t a t i v e  P r e c e d e n c e was degree  gaps e x i s t e d ,  be  a  to  which  and  for complexity,  need  biological constraints.  to  a  minimum  number of base  complex,  assumptions may  also yet  with well  Alternatively,  permit  realistic  objectives.  imposed  input  documented  Thus,  a compromise between  simplicity, the  undue  (1973) has  modeling  is  without  highly  resolution.  is necessarily  would  data  of  was  which  model u t i l i t y  retained  satisfy  the  number that  and  effort  by  which  the  logistical is  imposed  1 7  Process a maximum  rates  rate  representing process. the  optimality  approach 1975; et  by  the  Scalars  were d e t e r m i n e d a  series  effects  ranged  i s commonly  of  of  an  several  over  relatively  reduction  effects serious  difficulty  available The  in  (Holt  on This  eta l . ,  e t a l . , 1979; M c G i l l  et al.(l979) process  rate.  rate  has might  cautioned ensue when  among  controlling  omission cannot  in  be  this  factors  model.  obviated  given  may  be a  Unfortunately, the paucity  model o p e r a t e s on a d a i l y t i m e - s t e p . V a l i d a t i o n by c o m p a r i n g  collected  by H a r p e r  wheatgrass mesic  validation  simulation  of  results  i n the Ashnola  Sensitivity rates  analysis as w e l l  field  Region  of s u i t a b l e data p r e c l u d e d  o f model, q u a l i t a t i v e v a l i d a t o n simulation  with  was data  (1969) i n 1967 and 1968 f o r a b l u e b u n c h  community  C o l u m b i a . Where l a c k  process  depending  data.  conducted  between  i n modeling  on t h e  c o n t r o l l i n g f a c t o r s a r e s u b o p t i m a l . The e x c l u s i o n o f  interactive  this  0 t o 1,  1977; D e t l i n g  scalars  factors  towards the p r o c e s s  a l . , 1981); however, D e t l i n g  that  from  implemented  Jameson and G r o s s ,  non-dimensional  controlling  i n value  of the f a c t o r  through m u l t i p l i c a t i o n of  results was  and  was  empirical  performed  by  of  British  quantitative carried  out  observations.  altering  a s t e m p e r a t u r e and m o i s t u r e  maximum  regimes.  4.  4.1  AGGRO:  SIMULATION MODEL OF BLUEBUNCH WHEATGRASS GROWTH  GENERAL MODEL STRUCTURE  Bluebunch  wheatgrass  functions  of  temperatures, nitrogen model  soil  content,  intensity,  carbohydrate  and  root  regrowth  between  resulting  determined  and  photosynthetic variable  Table  photoperiod,  spring  from  photosynthesis,  and  litterfall.  growth,  alters  fall  and  literature  between  production, The  model  l e v e l , but  regrowth, and  Herbivory  is  standing  biomass,  r a t e , and i n c i d e n c e o f t i l l e r i n g . names  step, the  translocation  defoliation.  explicitly  foliar  At each time  biomass, d r y matter  mortality,  as  and a i r  bluebunch wheatgrass a t the whole-plant  distinguishes  of  modeled soil  1) computes g r o w t h p o t e n t i a l ,  a b o v e g r o u n d and b e l o w g r o u n d  considers  were  potential,  and p l a n t m a t u r i t y .  respiration,  shoot  dynamics  water  rainfall  (Figure  dark  growth  sources  A  user  summary  i s provided i n  1.  4.2 ABIOTIC DRIVING VARIABLES With  the exception  climatic  conditions  AGGRO. A b i o t i c weather The  first  precise  of a s t o c h a s t i c p r e c i p i t a t i o n  driving  records method input  modification  are  not  modeled  variables are  generator,  mechanistically  either  read  or approximated w i t h . g e n e r a l i z e d i s employed when model v a l u e s . The s e c o n d method  of c l i m a t i c  patterns  18  validation  in  from  equations. demands  i s u s e d when  i s desired.  in  quick  19  Growth potential of aboveground biomass  <G  > G  DMP=G - CHO deficit  DMP =  Belowground carbohydrate storage  Foliar carbohydrate  Dry matter production (DMP)  > 0  yes  no  Respiration Spring growth  Fall regrowth  yes  Standing dead  FIGURE 1 .  Regrowth after defoliation Photosynthesi;  no  Mortality Fallen litter  General model s t r u c t u r e  of AGGRO.  TABLE I. Summary of variable names and literature sources. VARIABLE  BRIEF DESCRIPTION  DEFINITION  WPOT TEMP  soil water potential air temperature soil temperature  EQ. (1), EQ. (3) EQ. (4) EQ. (5) EQ. (7) EQ. (8)  STEMP RP DL G GA GB GMAX TG WG  rainfall duration daylength aboveground biomass growth potential contribution of aboveground biomass to growth potential contribution of belowground biomass to growth potential maximum growth rate  SOURCE  EQ. (9) EQ. (TO) EQ. (14) 0.086 g g d  Quinton et al. (1982) deVries et al. (1979)  EQ. (11) EQ. (12)  Majerus (1975)  NG  effect of temperature on growth effect of soil water potential on growth effect of foliar nitrogen on growth  EQ. (13)  Wilson (1975)  DLG  effect of photoperiod on growth  BGMAX  maximum GB  Walton (1983) 0.0054 - 0.08 gg"'d"' Fine-tuned EQ. (24) ... continued o  TABLE I. conti nued ...  VARIABLE  BRIEF DESCRIPTION  DEFINITION  SOURCE  MB PSYN  effect of maturity on GB photosynthesis  EQ. (15)  Hypothesized  PMAX  maximum photosynthetic rate  TPSYN WPSYN  effect of temperature on PSYN effect of soil water potential photosynthesis respiration  RESP  EQ. (16) 0.016 g C0 g" hr"  Depuit and Caldwell (1975)  EQ. (17) EQ. (18)  Depuit and Caldwell (1975) Brown and Trlica (1977)  EQ. (19) EQ. (20)  Depuit and Caldwell (1975) Parton et al. (1978) Saugier et al. (1974) Fitted to data from ten studies Painter and Detling (1981)  1  2  WBM  effect of soil water potential on root mortality  LF N  litterfall seasonal foliar nitrogen  EQ. (21) EQ. (22)  GRPSYN  effect of defoliation on photosynthesis  EQ. (23)  1  22 4.2.1  SOIL WATER  POTENTIAL  Considerable  difficulty  realistic  data  studies  generally  precipitation Harper, 1981; of  on s o i l  1969; Daer  radiation  by  unknown  Ryswyck a n d  water  ( S k o v l i n , 1967; 1981; S t o u t cases,  soil  of  water  six  suction i s  for critical  soil  and  s t a t u s i s a p p r o x i m a t e d w i t h an values  measured  (1977,  unpub.  data)  in interior  British  ( F i g u r e 2) may be high,  used  intermediate,  moisture  availability  by v a n  f o r three  C o l u m b i a . The t h r e e to  evaluate  arid low s o i l  bluebunch wheatgrass growth dynamics. Curve seasonal  et a l . ,  conversion  suction  Broersma  sites  regimes  effects  values  water  describing  grassland  into  of  variables.  In AGGRO, s o i l equation  Willard,  two p a r a m e t e r s  rangeland  measurements  water p e r c e n t a g e and  i n securing  since  only  e t a l . , 1982). I n most  the l a t t e r  precluded  water p o t e n t i a l present  or s o i l  Quinton  was e n c o u n t e r e d  the  w a t e r on  fitting  was a c c o m p l i s h e d  for  with a  coefficient  WPOT  F o u r i e r s e r i e s o f t h e form: 6 = WPAO/2 + Z WPCI c o s ( i 7 r t / p ) + WPSI i =1  (1)  sin(i7rt/p) where WPOT  and  = water p o t e n t i a l  t  = time  of year  p  = one h a l f  (bars)  (Julian  date)  t h e p e r i o d f u n c t i o n o f WPOT  WPAO, WPCI, a n d WPSI a r e c o e f f i c i e n t s A moisture  developed  characteristic  f o r Harper's  curve  (Appendix 1 ) .  (Figure  3)  (1969) b l u e b u n c h w h e a t g r a s s  was study  23  i — — i —  J  i  F  •  M  •  A  .  M  J J MONTH  A  S  O  N  D  FIGURE 2. Soil water regimes used to evaluate the effects of high, medium, and low moisture availability on bluebunch wheatgrass growth dynamics (From van Ryswyk and Broersma, unpub. data).  24  FIGURE 3. Moisture characteristic curve developed for Harper's (1969) bluebunch wheatgrass mesic site.  25 site  f o r u s e i n model v a l i d a t i o n .  related  to  capacity,  soil  water  potential  a n d permanent w i l t i n g  r e l a t i o n s h i p was f i t t e d the cm"  3  soil  points.  (Israelsen  and Hansen, which  w a t e r c o n t e n t was  at  point,  t o permit  reference  porosity,  Soil  porosity,  field  and a c u r v i l i n e a r  interpolation  between  A bulk d e n s i t y  (p ) o f 1.55 cm b 1962) was u s e d t o c a l c u l a t e 3  i s d e f i n e d a s (Novak, p e r s . com.):  1 - p /2.650 b Field  capacity  (-15  bars)  content  (2)  (-0.33 b a r s ) a n d permanent w i l t i n g  point  were e s t i m a t e d a t 20 a n d 11.3 p e r c e n t  respectively  characteristic  (Harper,  curve  thus  1969).  The  derived  water  moisture  assumed  the  relationship: (0.28623 - WCON)/0.040924 WPOT  (3)  where WPOT  = soil  water p o t e n t i a l  WCON  = soil  water p e r c e n t a g e  Water 1967  = e  potential  values  a n d 1968 f i e l d  4.2.2 AIR AND SOIL Air  by B u n n e l l  f o r Harper's  TO  (1969)  a r e d e p i c t e d i n F i g u r e 4.  i s modeled w i t h t h e s i n e (1970),  function  i n which:  = TO + (TM - TO) [(1 + s i n ( a t  where TEMP  (by v o l u m e )  TEMPERATURES  temperature  described TEMP  season  generated  (bars)  = a i r temperature  + b))/2]  ( °C )  = minimum a i r t e m p e r a t u r e  ( °C )  (4)  26  FIGURE 4. Seasonal soil water potentials generated for Harper's (1969) bluebunch wheatgrass mesic site in 1967 and 1968.  27  TM  = maximum a i r t e m p e r a t u r e  a  = 2TT/365.25  t  = time  b  = -a(julian  (Julian  ( °C )  date)  d a t e o f TO + J u l i a n  date of  TM)/2 Maximum  and  minimum  -9.4°C  respectively  mesic  site  the  in  same s i t e Soil  temperatures  for  Harper's  bluebunch  1967, and e q u a l l e d  28.2  and  wheatgrass  28.2 a n d - 1 2 . 8 ° C f o r  i n 1968 ( F i g u r e 5 ) .  temperatures  temperatures  equalled  (STEMP)  with the formula  were  derived  (Novak, p e r s .  from a i r  com.):  -Z/Dd 5Tz  = 8To e where  (5)  8Tz  = amplitude  of temperature  wave a t  soil  of temperature  wave a t  soil  depth Z 6To  = amplitude surface  Z  = soil  Dd The  amplitude  depth  = damping d e p t h of the s o i l  assumed t o e q u a l t h a t  of  wave.  was  Damping  (Novak, p e r s . Dd  =  (m)  depth  (m)  surface the  temperature  atmospheric  calculated  wave was  temperature  with the formula  com.):  /pT7 7TC  where p k/c  (6 ) = period  of f u n c t i o n (s)  = diffusivity  constant [0.5X10~  d e V r i e s and A f g a n  (1975)]  7  m  2  s" , 1  28  •  J F  •  M  •  A  M  *  J J MONTH  *  A  •  S  1  O  1  N  FIGURE 5. Simulated air temperatures for Harper's (1969) bluebunch wheatgrass mesic site in 1967 and 1968.  D  29 Soil  temperature  temperature  by  was a  assumed  to  phase-shift  of  lag Z/Dd  behind  air  (Novak,  pers.  AGGRO  is  com.).  4.2.3  PRECIPITATION The  precipitation  stochastically  generator  driven  but  constraints:  (1) r a i n f a l l  exceed  maximum  the  within allowed  to  exceed  expected within intensity, allowed  intensity  (2)  the  (3)  total  for  rainfall  maximum  from  duration  the  Canada's RP  can  be e x p e c t e d  duration  to  i s not  w h i c h c a n be  i s not  monthly by  more  precipitation than  community,  intensity based  10%.  For  maximum  i s determined  on  Environment  (1969-1981) i n t e n s i t y - d u r a t i o n c h a r t : 6.6571 -1.1672 -0.031468-RN = (e )(RN ) (e )/60  where RP RN  4.2.4  equation  allowed  precipitation  fora specific  following  not  duration  Harper's bluebunch wheatgrass mesic rainfall  following  rainfall  monthly  region  the  fora specified  from t h e mean that  is  which  a 2 year p e r i o d  to deviate  established  includes  intensity  a 2 year p e r i o d ,  in  = duration = rain  of r a i n f a l l (hr)  intensity  (mm h r  - 1  )  DAYLENGTH Daylength  i s modeled w i t h  the equation:  (7)  30  DL  = DLAO/2 + DLC1 COS ( i r t / p ) +' DLS1 s i n  (8)  Ut/p) where DL  and  = daylength (hrs)  t  = time of year  p  = one h a l f  (Julian  the period  date) function  DLAO, DLC1, and DLS1 a r e c o e f f i c i e n t s .  bluebunch  wheatgrass  24.11081648,  DLC1  mesic  equals  community,  o f DL  For Harper's DLAO  equals  -3.83307714, a n d D L S I  equals  0.58219562.  4.3 GROWTH POTENTIAL AND DRY MATTER  PRODUCTION  In AGGRO, b l u e b u n c h w h e a t g r a s s g r o w t h on  the f a v o u r a b i l i t y  not a f f e c t e d therefore  both  one,  adverse.  i s reasonable  Phillips,  winter, The  as  that  i s possible  components:  GA,  aboveground  biomass  represents potent i a l :  plant.  threshold  Growth  temperature  of  an  t o an i n n a t e  pasture  for  cessation,  o c c u r s when c o n d i t i o n s  assumption  is  become  imposed  or  or spontaneous  grasses  (Wareing  and  reflect  the  1970).  A growth p o t e n t i a l , growth  the  g a i n e d , and g r o w t h  opposed  f o r many  dependent  g r o w i n g c o n d i t i o n s and i s  in  the  h a s been  and  dormancy,  traits  when  activity  summer  sufficiently enforced  by i n h e r e n t  initiated  meristematic in  of p r e v a i l i n g  i s entirely  G, was  developed  under e x i s t i n g  which to  represents growth  the c o n t r i b u t i o n  to  c o n d i t i o n s . G h a s two  the  contribution  potential,  of belowground  and  biomass  of  GB, w h i c h t o growth  31  G Although  foliar  function and  growth  i s generally biomass  1977; Wann  back  GB i n c r e a s e s vigor  reflect growth  (Holt  as a d i r e c t  e t a l . , 1975;  e t a l . , 1978; Sheehy  e s p e c i a l l y important  plant  n o t modeled  Jameson  e t a l . , 1979;  e t a l . , 1979; Sweeney e t a l . , 1981), s u c h a maneuver  which d i e s of  (9)  of belowground  Gross,  Detling is  = GA+GB  i n the case of bluebunch wheatgrass  t o t h e ground each w i n t e r . the s e n s i t i v i t y  i n the spring.  the  incidence  hormones  from  Thus,  of d r y matter production  In t h e model,  GB i s  the  root  system.  Of  are the c y t o k i n i n s ,  the  roots,  and t h e g i b b e r e l l i n s , w h i c h have  in  growth  dominant  component  biomass  is  intended  to to  o f t i l l e r i n g and t h e c o n t r i b u t i o n of  importance  initiation  inclusion  which a r e s y n t h e s i z e d  (Salisbury  inG in  early  low. GB d e c l i n e s  . particular  been  and R o s s , spring  only i n  implicated  1969). GB i s t h e when  aboveground  i n importance as f o l i a r  growth  accelerates. The  contribution  of  aboveground  potential  i s calculated  potential,  a i r temperature, f o l i a r  GA  = GMAX  where GMAX TG  as  • TG • WG  a  rate  = scalar  (g g "  soil  1  growth water  and d a y l e n g t h : (10)  day" ) 1  e f f e c t s of  on g r o w t h  representing  potential  of  nitrogen,  representing  temperature WG  function  to  • NG • DLG • LAB  = max g r o w t h = scalar  biomass  on g r o w t h  e f f e c t s of s o i l  water  32  NG  = scalar representing nitrogen  DLG  LAB  e f f e c t s of  = live  aboveground biomass  b a s e d on work by d e V r i e s perenne TG  =  (g n r ) 2  (0.31298 2  (Figure  e t a l . (1979) on p e r e n n i a l  L . ) , and d e s c r i b e d  TEMP  daylength  growth  e f f e c t s o f a i r t e m p e r a t u r e on g r o w t h r a t e  (Lolium  foliar  growth  = scalar representing on  The  on  e f f e c t s of  + 0.046723  + 0.0010382  6) a r e  ryegrass  by t h e r e l a t i o n s h i p : • TEMP - 0.0096323  • TEMP  3  •  (11)  - 0.20755E-4 •  TEMPM/4.27 In  the model,  growth c e s s a t i o n  e x c e e d s 40°C o r d r o p s below The e f f e c t s o f s o i l initially Nimlos The  modeled  (1972)  o c c u r s when  temperature  -0.5°C.  w a t e r p o t e n t i a l on g r o w t h  w i t h an e q u a t i o n  in a laboratory  relationship  air  thus  study  modeled  derived  rate  was  by Eddleman  and  on b l u e b u n c h w h e a t g r a s s . involved  an  exponential  decline  i n growth  rate with  increasing moisture s t r e s s , with  growth  stoppage  occurring  at a s o i l  bars.  However,  regimes  in simulation  typical  o f B.C.  water p o t e n t i a l of  trials  involving  grasslands,  i t was  accumulation  became  s u b s e q u e n t l y made t o r e d u c e which were  growth highly  Eddleman  negligible. the  stoppage o c c u r s , implausible,  and N i m l o s  (2)  soil since the  (1972) r e t a i n e d  A  water  point  equation 2  this where  decision potential  (1) s i m u l a t i o n  an R  water  found that  r e l a t i o n s h i p d e c i m a t e d growth p o t e n t i a l t o t h e biomass  soil  was at  results  derived  of o n l y  -12  0.40,  by (3)  33  FIGURE 6. "Simulated effect of air temperature on growth potential (Adapted from data by de Vries et al. (1979)).  34 Daubenmire  (1972) had  wheatgrass -15  plants  b a r s , and  until  approaches  -25  bluebunch from  long  (4)  continues  WG  =  water in  (Majerus,  1975). The  to moisture stress data  for  relationship  on  bluebunch  potential  crested  potential  1 - [0.8  where WG  soil  water  (1975)  linear  foliage  elongation  soil  wheatgrass  assumes t h e  after  cell  bars  Majerus'  observed green  at  wheatgrass  a  20 cm  modeled  depicted  depth  response  i s therefore  crested  reached  adapted  wheatgrass,  in Figure  and  7:  • (ABS(WPOT))]/20.0  = nondimensional effects  scalar  of s o i l  water  of  (12)  representing  the  potential  growth  on  rate WPOT A the  = soil  functional  aboveground  growth  shoot  root  (Loomis,  potential  (bars)  equilibrium  (Brouwer,  1963)  and  i s limited  while  water  by  growth  accommodated  up by dry  1953).  1961; 1979).  of  functional  foliar  The  1973;  t h e most  1968)  , and  as  of  Smith,  foliar  root  shoot,  on  rate.  nitrogen  taken  increases  in  fertilization  has  genus 1976;  which  growth  dramatic  the is  o f NG,  important element  nitrogen  f o r t h e Agropyron  Bayoumi and  effects  that  equilibrium  inclusion  nitrogen  production following  Sneva,  calculated  (Alberda,  documented  such  t h e m i n e r a l s u p p l y from  i n t h e model t h r o u g h t h e  the p l a n t  been w e l l  by  This  i s quantitatively  matter  biomass  between  the c a r b o h y d r a t e s u p p l y from the  is limited  computes t h e e f f e c t Nitrogen  belowground  exists  (Eckert  et a l . ,  W i l l i a m s et a l . , on  growth  is  35  FIGURE 7. Simulated effect of soil water on growth potential (Adapted from data by Majerus (1975)).  36 -1.0383(N-1) NG  = (100.0 - 90.Oe  where NG  = nondimensional effects  N and  = foliar  i s based  perennial  on  ryegrass  Although generally  )/l00.0  data  scalar representing  of f o l i a r  collected  acknowledged  and  of p h e n o l o g i c a l development  modeled growth by  hours  the  i s equal  at  0.086  g  the  first  by  Quinton  in  are  growth  a l . , 1979), t h e potential  rate  is  i s believed  is  implicitly  f o r decreased  p h o t o p e r i o d s , GMAX  is  reduced  r e d u c t i o n i n p h o t o p e r i o d beyond 13  from is  1  deficit  photosynthesis to  f o r bluebunch  support  exists, less  dry  of the seasonal y i e l d and  biomass t o o b t a i n r e l a t i v e  or  growth matter  w h e a t g r a s s was e s t i m a t e d  1  a l . (1982)  when  the d e f i c i t .  d a y " . T h i s v a l u e was d e t e r m i n e d  derivative et  current  t o growth p o t e n t i a l  growth g"  t o growth p o t e n t i a l  adequate  Where a c a r b o h y d r a t e  Maximum f o l i a r  standing  supply  reserves  production  et  on g r o w t h  growth  production i s equal  carbohydrate  potential.  included  rate  1983).  matter  underground  growth  o f NG. To a c c o u n t  shortened  60 m i n u t e  (Walton,  (1975) f o r  i n AGGRO. T h i s o m i s s i o n  inclusion  r a t e s under  Dry the  modeled  30% f o r e a c h  in  a l . , 1975; D e t l i n g  since a decelerating by  Wilson  commonly  effects  justified  by  changes  (Holt  explicitly  rate  (Figure8 ) .  models  not  n i t r o g e n on g r o w t h  n i t r o g e n (%)  ontogenetic  et  (13)  curve  subsequently growth  rate.  by t a k i n g presented d i v i d i n g by  37  FIGURE 8. Simulated effect of foliar nitrogen on growth potential (Adapted from data by Wilson (1975) ).  38 The  contribution  of  potential  i s calculated  potential,  soil  GB  belowground as  a  biomass  function  to  of  growth  soil  water  t e m p e r a t u r e , and m a t u r i t y :  = BGMAX  where BGMAX  • TG • WG  • MB  • LBG  (14)  = maximum c o n t r i b u t i o n o f b e l o w g r o u n d biomass (g  TG  g"  t o aboveground growth p o t e n t i a l day" )  1  1  = scalar representing  the e f f e c t of  temperature WG  = scalar representing  the e f f e c t  of s o i l  water p o t e n t i a l MB  = scalar representing  the e f f e c t of  maturity LBG In  = live  belowground biomass  the absence of r e l e v a n t  effects  of  data,  temperature  i t was  and  soil  (g m" ) 2  assumed  water  that  the  potential  underground a c t i v i t y  are  equal  to  those  on  activity.  fine-tuned  at  0.054  g g"  day"  g"  day"  growth  BGMAX  is  initiation  i n s p r i n g , a n d a t 0.08  growth  initiation  (Figure  9) i s p o s t u l a t e d MB  i n the f a l l ,  where MB  the e f f e c t  to follow  = 0.9930 - 0.14683  g  on  aboveground 1  1  of maturity  1  1  for for  on GB  ther e l a t i o n s h i p :  • KB + 0.56462E-2  = scalar representing  • KB  2  (15)  the e f f e c t of  maturity KB  = number  o f days s i n c e  activity.  initiation  of root  FIGURE 9. Simulated effect of plant maturity on belowground hormonal activity and incidence of t i l l e r i n g .  40  4.4 GENERATION Apparent air  OF ASSIMILATES  photosynthesis  temperature  i s assumed t o  and s o i l  water  depend  potential,  primarily  on  and i s c a l c u l a t e d  as: PSYN  = PMAX  where PSYN  • TPSYN  • WPSYN • DL  = generated day  PMAX  1  • 0.675  (16)  a s s i m i l a t e s (g CHO  g"  biomass  1  )  = maximum p h o t o s y n t h e t i c  rate  (g C 0  g"  1  2  biomass h r ~ ) 1  TPSYN  = scalar  r e p r e s e n t i n g e f f e c t s of  temperature  on p h o t o s y n t h e t i c  rate  (undimensioned) WPSYN  = scalar  representing effects  potential DL  biomass  hr' ) 1  (hours  = multiplier  Maximum p h o t o s y n t h e t i c  day ) 1  to convert  rate i s estimated  (Depuit  and  Caldwell,  temperature  on p h o t o s y n t h e t i c  rate i s  piecewise  linear  depicted  function  was a d a p t e d  Caldwell  (1975)  spicatum  var inerme  (if  for  data  and  t o gCHO  2  a t (0.016 g C 0 1975).  in  Figure by  wheatgrass  2  g"  1  The e f f e c t o f  calculated  collected  beardless  Heller),  gC0  from  the  10.  The  Depuit (  and  Agropyron  equals:  TEMP<0 o r TEMP>40)  TPSYN (if  function from  water  (undimensioned)  = daylength  0.675  of s o i l  =0  (17a)  0<TEMP<5)  TPSYN  = 0.1052632  • TEMP  (17b)  41  1 .0 r  TEMPERATURE ( °C ) FIGURE 10. Simulated effect of air temperature on photosynthesis (Adapted from data by Depuit and Caldwell (1975) ).  42 (if  5< TEMP<20)  TPSYN (if  = 1 - 0.03158  = 1  (I7d)  25<TEMP<35)  TPSYN (if  (17c)  20< TEMP <25)  TPSYN (if  (20-TEMP)  = 1 - 0.03421  (TEMP-25)  (I7e)  35<TEMP<40)  TPSYN  = 0.1315789  where TPSYN  (40-TEMP)  = scalar representing temperature  TEMP The (Figure western  of s o i l  i s based  wheatgrass  WPSYN  on  water  ( °C )  potential  on  on Brown a n d T r l i c a ' s  photosynthesis (1977) s t u d y on  a n d assumes t h e l i n e a r r e l a t i o n s h i p :  = 1+ 0.03226  where WPSYN  the e f f e c t of  photosynthesis  = a i r temperature  effect 11)  (I7f )  • WPOT  = effect  of s o i l  (18) water  p o t e n t i a l on  photosynthesis WPOT Despite  = soil  the obvious  photosynthesis, in  AGGRO s i n c e  on  grassland  water p o t e n t i a l importance  irradiation light  energy  ranges d u r i n g  of  effects  solar  radiation  have n o t been  i snot b e l i e v e d t o t h e growing  be  on  included limiting  season.  4.5 RESPIRATION Photorespiratory modeling  l o s s e s have been a c c o u n t e d  apparent  photosynthesis.  photosynthesis  However,  dark  rather  respiration  f o r i n AGGRO by than at  night  true and  43  -  s-  ra  1—  _J  <c  (O  t—1  1—  •z. LU 1—  (J  to T3  CL)  1 .0  o e o CC f '— </) c Bu <c < Q-  LU 1—  •1—  " 0  u_ c o  0.5  1—  o  LU  >-  U— 1/1  a.  UL. LU 3 >—•  0.0 10 20 SOIL WATER POTENTIAL  30 bars)  40  FIGURE 11. Simulated effect of water potential on photosynthesis (Adapted from data by Brown and Trlica (1977) ).  44 respiration  of belowground  independent calculated  function.  Dark  as a f u n c t i o n  carbohydrate temperature  o r g a n s must be computed respiration  of temperature  degradation  in  with  an  t h i s model  (Figure  is  12)  since  p r o c e s s and  hence,  • TEMP + 0.0013714  (19)  i s a metabolic  sensitive:  RESP  =  (-0.46107 + 0.069524 • TEMP )/10  • 0.0675  2  where RESP  = Respiratory  losses  (g CHO  g"  1  biomass  hr- ) 1  TEMP The  relationship  based  on d a t a  beardless  be  4.6  biomass,  )  temperature  In  respiration  Caldwell  (1975)  the absence of r e l e v a n t  respiratory  that  and  of  rate  of r o o t s  s h o o t s . However,  organs, r e s p i r a t i o n  was  modeled  is for  data f o r  was  assumed  i n t h e c a s e of  as a f u n c t i o n  of  of a i r t e m p e r a t u r e .  CARBOHYDRATE PARTITIONING  plant  documentation i n d i c a t e s  i s altered  Sosebee  and  favourability 1978;  Krueger,  that  1973;  Daer  (Mcllvanie,  1942;  Willard,  1981)  and  (Trlica,  1977;  and K r u e g e r ,  1980;  Singh et a l . ,  (Auda e t a l . ,  1966;  Garrison,  1974;  1980;  the carbon b a l a n c e of  i n phenology  of growing c o n d i t i o n s  removal  Singh,  by c h a n g e s  Wiebe,  E l Hassan  herbage and  to  ( °C  by D e p u i t and  temperature instead  Extensive a  presented  equal  belowground soil  between  wheatgrass.  belowground to  = Temperature  Buwai  Singh  et  and  Trlica,  al.,  1980).  1977;  Bokhari, 1980),  1966;  Bokhari  E l Hassan  Knowledge  and  of  and the  FIGURE 12. Simulated effect of temperature on respiration (Adapted from data by Depuit and Caldwell (1975) ).  46 mechanisms u n d e r l y i n g t h e s e c h a n g e s especially  lacking  carbohydrate  for  rangeland  partitioning  in  strategy  are  AGGRO,  implicitly without  an  of  establishing  was  by  strength  which  movement c o u l d be d e t e r m i n e d  Thus,  are translocated  therefore  been  dictated i t  properly  is  determined  responsive  conditions,  of f o l i a r  immediately  from  following  phases  growth  Carbohydrate  in  either  such  defoliation.  as  during growth  which,  s h o u l d be  phenology,  Carbohydrate  and  movement i s  growth p o t e n t i a l ,  effects.  arbitrarily,  special  biomass  Alternatively,  by t h e s i n k - s o u r c e i n d e x ,  changes  or d e f o l i a t i o n  manipulated  during  to  from  downwards when t h e s i n k - s o u r c e  satisfied.  entirely  by  upwards when t h e s i n k - s o u r c e  and g r o w t h p o t e n t i a l  are translocated  and  sources  reserve carbohydrates  of c u r r e n t p h o t o s y n t h e s i s .  have  underlying  magnitude  i s n e g a t i v e , a n d t h e demands o f f o l i a r  respiration  would  partitioning  the  the  1977)  s t r e n g t h s of c a r b o h y d r a t e  sinks.  i s positive,  that  of  biomass  allocation  carbohydrate  hypothesized  the r e l a t i v e  organs  assimilates  or  and  adopted  knowledge  carbohydrate  exceeds the supply  never  affected  was  in  detailed  carbohydrate  strength  approach changes  demanding  direction  because  w h e a t g r a s s must be  productivity  significantly  reflect  mechanisms. I t  storage  Nevertheless,  ( C a l d w e l l e t a l . , 1981; P o t t e r and J o n e s ,  In  and  however, and i s  grasses.  bluebunch  modeled a p p r o p r i a t e l y s i n c e p l a n t accumulation  i s poor,  growing  movement i s  normal  growth  i n i t i a t i o n or  47  Provisions translocation unlikely McNairn,  to 1972;  SHOOT AND  In  AGGRO,  with  daily  with  se  1977;  shoot  stress,  since  and  temperature  is  method,  effect  in  to standing below  25% o f l i v e  a critical on  water p o t e n t i a l the f r a c t i o n each u n i t  -30  in soil  growth  of -2°C.  shoot  mortality  fraction  p e r day  below  of  biomass  reduction in below  beyond  mortality 5%  -30  i n c r e a s e s by  water p o t e n t i a l  equal  and  induced  b a r s . At t e m p e r a t u r e s  cessation,  (PHENM) i s assumed t o  is  falls  with each u n i t  of biomass d y i n g  reduction  Following  biomass per  beyond  shoot  minimum  threshold  water p o t e n t i a l  2.5%  i n c r e a s e s by  calculated  and b a s e d on work by Eddleman  b i o m a s s when s o i l  p e r day  damage,  dead m a t t e r when  dying  senescence  1968;  frost  damage i s  of m o i s t u r e s t r e s s  dependent  by  which  30°C, t h e  bars.  (Wardlaw,  caused  b a r s . At t e m p e r a t u r e s above  with  the  transport i s  (1972) on b l u e b u n c h w h e a t g r a s s . M o r t a l i t y  foliar  to  1979).  senescence. Frost  i s transferred  is  30°C,  phloem  movement  Zeevaart,  mortality  (1978)  simulated  soil  respect  ROOT MORTALITY  The  in  per  temperature f a l l s  Nimlos  made  assimilate  Moser,  Sauer's  biomass  not  process limit  4.7  moisture  were  of  2% -30  due  live  to  shoot  day.  Belowground  mortality  i s modeled  as a f u n c t i o n  water p o t e n t i a l  and b a s e d on d a t a p r e s e n t e d  (1978)  grama  f o r blue  ( Bouteloua  gracilis  of  by P a r t o n  soil et a l .  (H.B.K.) L a g . ) :  48 SB WBM  = -[SY1  SB +  SB  (SY2  - SY1  ) • (1.0  -  (20)  V  (-SA(WPOT))  (-SA  e  •  75)  )/(1.0 - e  )]  **  (l/(1-SB)) where WBM  = scalar representing w a t e r p o t e n t i a l on  SY1  =  SY2  =0.98  Maximum r a t e nr  2  4.8  day  "  1  =  SB  = -9.85553  soil  mortality  assumed t o e q u a l  0.0026 g  e t a l . , 1978).  LITTERFALL  The  fall  following LF  of  standing  equation =  dead  derived  by  matter  = Transfer litter  RAIN SD  of  (g nr  • RAIN) standing  2  computed w i t h  the  et a l . (1974): • SD  (21)  dead m a t t e r  to  ha" ) 1  = P r e c i p i t a t i o n rate = Standing  is  Saugier  (0.00083 + 0.0013  where LF  4.9  of  0.70  r o o t m o r t a l i t y was  (Parton  root  effect  0.04  SA  of  the  (cm  hr  dead biomass  (g  empirically  with  _ 1  )  nr ) 2  FOLIAR NITROGEN  Foliar  nitrogen  i s modeled  regression  fitted  to the  wheatgrass  (McCall,  1932;  Beath  and  Hamilton,  data  from ten  Mcllvanie,  1952;  Blaisdell  studies  1942;  a  polynomial on  bluebunch  Stoddart,  e t a l . , 1952;  1946; Skovlin,  49 1967; and  Demarchi,  Cline,  1968;  Raleigh,  1976). The  equation  1970;  Demarchi,  thus  derived  1973;  Uresk  assumed  the  form: N  =  (105.86-1.1355 0.55393E-5  where N  Foliar 1 at  40  nitrogen  the  foliar  =  nitrogen  days  nitrogen  0.026% p e r  13)  seasonal  r e g r o w t h and  in  regrowth  start  computed was  of  day.  to achieve  The  shifting  of  this  shifted  foliar  by  decline  of  a maximum  of  d a t e of  the  date  in  removal However,  synchronization  and  growth  nitrogen  herbage  equation.  to obtain  a f t e r August  seasonal  synchrony with  following  regrowth  linearly  The  decline  with  performed fall  (22)  (%)  assumed t o d e c l i n e  initiation.  similarly  -  2  3  i n s p r i n g g r o w t h was  (Figure  • JD  J u l i a n date  was  r a t e of  + 0.0043233  • JD )/6.25  = foliar  JD  • JD  of  fall were curve  with  the  defoliation,  respect i v e l y .  4.10  EFFECTS OF  Herbage the  DEFOLIATION  removal a f f e c t s dry  photosynthetic  photosynthetic Detling, defoliation derived  is  as  production  w e l l as  (Caldwell  modeled  (Figure  by  with  Painter  14):  immediately  the and  altering  e t a l . , 1981;  Photosynthesis  from d a t a  wheatgrass  surface  activity  1981).  matter  following  Detling  by  reducing  the  rate  Painter  of and  following relationship  (1981) f o r  western  51  FIGURE 14.  Simulated effect of defoliation on photosynthesis.  52  GRPSYN  = -5.1458 + 10.780 KGR - 1.3308 KGR 0.042364 KGR  where GRPSYN  KGR  75% of  3  (% o f c o n t r o l )  = days s i n c e d e f o l i a t i o n  i s also altered  following  herbage  removal a t over  i n t e n s i t y . When h e r b a g e r e m o v a l o c c u r s w i t h i n growth  initiation,  BGMAX  = -0.0017  where BGMAX  BGMAX  D  initiation,  with  1  = number removal  BGMAX  weeks  the equation: (24)  = t h e maximimum c o n t r i b u t i o n  (g g -  herbage  i s determined  four  • D + 0.054  biomass  When  (23)  = e f f e c t o f d e f o l i a t i o n on p h o t o s y n t h e t i c rate  BGMAX  +  2  o f belowground  t o aboveground growth  potential  day" ) 1  of days s i n c e  occurs  after  i s assumed t o e q u a l  growth four  initiation  weeks o f g r o w t h  0.0054 g g " d a y " 1  1  5.  SIMULATION RESULTS, MODEL VALIDATION,  SENSITIVITY  ANALYSIS, AND DISCUSSION  5.1 BLUEBUNCH WHEATGRASS DYNAMICS  5.1.1  IN THE ABSENCE OF GRAZING  DRY MATTER PRODUCTION OF ABOVEGROUND BIOMASS Model  predictions  aboveground biomass obtained  from  good  prior  values  agreed  field  between p r e d i c t e d  of d r y matter p r o d u c t i o n  sampling  and observed  t o the onset  generally  measured v a l u e s  closely  fell  (Figure values  summer  with  within  f o r both  In  one  values  1967,  and o b s e r v e d v a l u e s  inaccurate  simulation  indicated  that  - 2  between J u l y  1969).  period.  was  not  the  26 and A u g u s t  Erroneous contributed observed  dry  error  of  Field  material  less  the onset of  discrepancy  litterfall  following  between from  measurements equalled year  43 g  (Harper  was n e g l i g i b l e f o r  l o s s of p l a n t  growth c e s s a t i o n  material in either  o f 1968.  simulation  to the  following  29 o f t h a t  Similarly, predicted  summer o r f a l l  simulated  originated primarily  the l o s s of p l a n t  apparent  especially  standard  of l i t t e r f a l l .  However, s i m u l a t e d  this  were  b i o m a s s compared  the  predicted  m  1 5 ) . Agreement  1967 a n d 1968.  measured  drought.  measurements  o f a e s t i v a t i o n , when  Model p r e d i c t i o n s of s t a n d i n g favorably  with  i n the  of  discrepancy  matter  foliar between  production.  53  Field  growth predicted  also and  observations  54  FIGURE 15. Comparison of simulated (continuous line) and measured (standard error intervals) shoot biomass of bluebunch wheatgrass for 1967 and 1968.  5 5  indicated  a  September  20  minimum of  of  24  gm"  of f a l l  2  1967;  in  contrast,  only  10  g m"  predicted  regrowth  equalled  Predicted  fall  regrowth  i n 1968. However, g r o w t h c e s s a t i o n  simulation  r e g r o w t h by  f o r t h e same  2  fall  period.  r e g r o w t h was c o m p a r a b l e t o o b s e r v e d  occurred  i n advance  of that  fall  i n t h e 1968  observed  i n the  field. Consideration stages  when  faulty the  of  model  limiting  prediction  rate.  In  the  regrowth  was  1967  excessively  September  (Figure  too  biomass  accumulation  representing growth  early  the  (Figure  relationship  The  the was  effect  of Thus,  predicted  1968  late  August  by  water  future  because  the  scalar  potential  research  availability  on  on the  and  growth  potential  on  dry  matter  i s f u r t h e r e m p h a s i z e d by s e n s i t i v i t y  simulation  was  substituted  f o r t h e 1967 s e a s o n , with  and  cessation  simulation  arrested soil  fall  w a t e r p o t e n t i a l was  between  climatic driving variables. Soil  compared  p o r t r a y a l of  be p r o f i t a b l e .  importance of water  production  regime  suggests that  16). S i m i l a r l y , growth  in  17).  when  low, s o i l  between m o i s t u r e  r a t e may w e l l  1968  poor  growth  w a t e r p o t e n t i a l and g r o w t h  simulation  occurred  of  soil  p r i n c i p a l growth d e p r e s s a n t  mid  is  during  p r e d i c t i o n s may be due t o i n a c c u r a t e  r e l a t i o n s h i p between  the  factors  the  1968  and control  analysis  water  regime f o r the  with  the s o i l  the  resulting  water output  r e s u l t s . I t was f o u n d  56 2.5 FIGURE 16a XJ  2.0 1 .5  1 .0 o  Q.  0.5 o  0.0 LEGEND  1 .0 0.8  CO  I  o  °  OO  0.6  Q  O !£  0.4 0.2 0.0  J A MONTH  FIGURE 16. Simulated growth potential (g m" ) (Figure 16a) and simulated effects of temperature (TG), soil water potential (WG), daylength (DLG), and foliar nitrogen (NG) on maximum growth rate (Figure 16b) for Harper's (1969) bluebunch wheatgrass mesic site in 1967.  57  FIGURE 17. Simulated growth potential (g m" ) (Figure 17a) simulated effects of temperature (TG), soil water potential daylength (DLG), and foliar nitrogen (NG) on maximum growth (Figure 17b) for Harper's (1969) bluebunch wheatgrass mesic in 1968.  and (WG), rate site  58 that  foliar  following (Table the  production  this  alteration  2).In contrast,  1968 s i m u l a t i o n  regime  for  biomass y i e l d herbage  the  season,  as modeled in  and  resulted  in yield  is  analysis  i n d i c a t e that sensitive  2).  increases 3%  changes  that  than  water  to to  regime.  regime with  the dry,  r e g i m e s measured by v a n data)  (Figure  d i f f e r e n c e s o f 65, 50, a n d 259  hormonal p r o d u c t i o n , (Table  appear  temperature  (unpublished  t o 120% o f t h e i r  most  the temperature  regime  was  1)  percent  a l s o p e r f o r m e d on model  p a r a m e t e r s by s y s t e m a t i c a l l y a d j u s t i n g  analysis  regime f o r  (Table 2 ) .  Sensitivity  rates  moisture  i s f a r more r e s p o n s i v e  wet m o i s t u r e  Broersma  soil  therefore  in  o f t h e 1968 s o i l  Ryswyck  increase  a 34% d i f f e r e n c e i n  moisture  differences  and  only  would  differences  intermediate,  respectively  available  216%  when t h e t e m p e r a t u r e  ensued. I t  inter-yearly Substitution  in  a  was s u b s t i t u t e d w i t h  1967  production  inter-yearly  sustained  Of  original  growth  and b i o m a s s o f other  i n maximum p r o c e s s i n biomass y i e l d s  Simulation  rates  observations  growth  initiation  rate of root  belowground  organs  examined,  20%  resulted in less  than  (Table 2 ) . 16 a n d 17)  corroborate  e t a l . , 1981; Q u i n t o n  1982). However, s i m u l a t i o n  of t h i s  accumulation  of temperature dependence (Stout  process  Results  rate,  parameters  results (Figures  field  values.  aboveground biomass  to f o l i a r  the  maximum  in spring et  r e s u l t s are inconsistent  a l . , with  59  TABLE II. Results of sensitivity analysis for the 1968 control.  CHANGE  TOTAL ANNUAL DRY MATTER PROD'N -2x % change (g nf*) (from control)  PARAMETERS: DMAX  +20%  113  0  LBG  +20%  135  +20  GMAX  +20%  172  +52  GBMAX  +20%  133  +18  PMAX  +20%  116  +3  RESP  +20%  113  -0.1  ROOT RESP  +20%  111  -1  PHENM  +20%  113  0  357  +216  DRIVING VARIABLES: Water potential  1967 regime  Water potential  Dry interior  37  -67  Water potential  Medium interior  57  -50  Water potential  Wet interior  405  +259  Air temperature  1967 regime  74  -34  60 field  observations  conclusion  of  simulations, from fall  aestivation.  in  availability in  occurred  when  both  during  bluebunch  fall  in soil  variance that  the  regrowth d u r i n g the  increases  in  has  availability  temperature  has  temperature even  though  limiting the  is  t o model  water  growth  fallacy  fall  also  growth  reportedly  i s high  been  (Daer and  simulated  the f a i l u r e  between  moisture  (Daer and  e t a l . , 1982). A d d i t i o n a l l y ,  between  correlation  resulted  and 1 7 ) . I n c o n t r a s t ,  regrowth  related  Willard,  and f i e l d  factor.  1981).  observations  i n t e r a c t i v e e f f e c t s of Alternately,  i n the simulation  potential  was  identified  Thus, s i m u l a t i o n  soil  results, as  results  the  expose  o f a s s u m i n g c a u s e and e f f e c t between  w h i c h may be  the to a  regrowth and d e c r e a s i n g  evident  and  t h e 1967 a n d 1968  t e m p e r a t u r e a n d m o i s t u r e may be m i s l e a d i n g . a  onset  t h e summer  wheatgrass  moisture  of  to  16  1981; Q u i n t o n  initiation  suggest  response  (Figures  cessation  The  In  water d e f i c i e n c i e s w h i l e  occurred  lowering  governing  growth c e s s a t i o n  soil  Willard,  on f a c t o r s  factors  correlated.  5.1.2 CRUDE PROTEIN YIELD  1967  Simulated crude p r o t e i n  y i e l d s peaked  and 1968  and  occurred late  in  (Figures early  June - e a r l y  infusion  of  fall  18  July  July  19).  twice  The  first  f o r t h e 1967 s i m u l a t i o n  for  regrowth  the  1968  resulted  i n both peak and i n  simulation.  The  i n a second  peak  61  I  1 S p r i n g growth  MONTH FIGURE 1 8 .  S i m u l a t e d crude p r o t e i n y i e l d f o r 1967.  MONTH FIGURE 19.  S i m u l a t e d crude p r o t e i n y i e l d f o r  1968.  63 between  late  August  Because  fall  regrowth  protein  yield  protein fall  yield  regrowth  regrowth crude  in  1968  in late  protein  in  1967,  and  Conversely,  crude p r o t e i n  in  much  late  as  i n 1968. F a l l yield  crude  extensive  i n a h i g h e r y i e l d of  than  as  crude  than  June.  a s much a s 20.5% o f t o t a l  i n 1967  accounted  peak.  August  of both y e a r s .  peak was l o w e r  resulted  15.7% o f c r u d e p r o t e i n  and  September  marginal  t h e second  constituted  available  was  i n the f i r s t  crude p r o t e i n  for  in  and e a r l y  available  45%  of  regrowth  by December  f o r 38% o f c r u d e p r o t e i n  Fall  total  accounted  31 o f 1967,  yield  by t h e end  of 1968. Crude comparable  protein between  percentages  respective  1968  o c c u r r e d 10 d a y s (Figure  y e a r s , even  31  were  of the  initiation in  i n advance of growth  initiation in  2 0 ) . Percent crude p r o t e i n  was, however,  h i g h e r i n t h e 1967 f a l l  fall  regrowth  though  growth  growth  0.5%  5.1.3  spring  1967 a n d 1968 by December  two  1967  of  regrowth  by t h e c o n c l u s i o n  CARBOHYDRATE  than  in  t h e 1968  of the r e s p e c t i v e  PARTITIONING  BETWEEN  years.  ABOVE  AND  BELOWGROUND BIOMASS S i m u l a t e d c a r b o h y d r a t e movement the  shoots  occurred  during  g r o w t h a n d commencement 22a).  Upward  movement  during  spring  initiation  both  of f a l l of  from  the  initiation  regrowth  roots  to  of spring  i n 1968 ( F i g u r e  carbohydrates occurred only  i n t h e 1967 s i m u l a t i o n  (Figure  FIGURE 20. Simulated crude protein percentages in foliar biomass and fall regrowth in 1967 and 1968.  65 2 r  T3 CVJ I  -4 •6 . «=c ct: Q >~  in o  -8 •  CQ CC  <c  C_3  M A  M J  J  A  S  O  N  D  800 FIGURE 21b 600 QL  Q  >- — -TIM O I  co E  Fall regrowth 400 Growth cessation  D£ O -—-  200  <_>  M  J A MONTH  FIGURE 21. Simulated movement of carbohydrates between aboveground and belowground biomass (Figure 21a) and cumulative movement of carbohydrates into belowground biomass (Figure 21b) for Harper's bluebunch wheatgrass mesic site in 1967.  66 21a).  Unfavorable  1967,  coupled  from r e s i d u a l on  root  with  either  (Daer and  for  results be  depleted  relationship  that  Jameson  by  fall  stored  tissue  have been s a t i s f i e d .  and  Sharp  translocated 6.6%  of  total  respectively. reserves  on  however,  In  from t h e annual The  root  of  tillering.  Additionally,  photosynthetic crucial  the  to  growth  biomass  herbage  season. S e n s i t i v i t y  in  in  the  of by  early  production a n a l y s i s on  of  the  yield  f o r 6.2 and  and 1968,  carbohydrate higher,  d i c t a t e s the incidence  establishment  spring  the  organic  carbohydrates  and  later  for  c o r r e l a t e d with  also  rapid  in  McKendrick  considerably  hormones  his  result  1967  effects  system  In  to i n d i c a t e  level  - model,  are  and  requirements  indexed  production  production  augmented  reserves  system accounted  root  reserves  or  In c o n t r a s t ,  this  indirect  the  Thus,  will  significantly  herbage p r o d u c t i o n  because  regrowth.  evidence  carbohydrate  that  g r o w t h , was  production.  draw  well defined.  no  i n c r e s t e d wheatgrass, as  etiolated  herbage  found  activity  carbohydrate  carbohydrates  new  of  regrowth.  found  g r o w t h once t h e  of  fall  need t o  between c a r b o h y d r a t e  additional  reserves  fall  i s c u r r e n t l y not  (1970)  the  ( M c l l v a n i e , 1942)  (1963)  additional  of  d e m o n s t r a t e why  herbage p r o d u c t i o n review,  support  W i l l a r d , 1981)  The  the  appreciable photosynthetic  s p r i n g growth, p r e c l u d e d  reserves  simulation may  growing c o n d i t i o n s d u r i n g  on  may  well  i n the  model  of of be  growing  revealed  a  67  FIGURE 22. Simulated movement of carbohydrates between above and belowground biomass (Figure 22a) and cumulative movement of carbohydrates into belowground biomass (Figure 22b) for Harper's bluebunch wheatgrass mesic site in 1968.  68 direct  relationship  carbohydrate with each  reserves: f o l i a r  percent  primarily  Although  downward  storage  (Figures  1968 in  fall,  67  carbohydrate  o c c u r r e d on J u l y  o f summer  a n d 81% o f  system  dormancy.  g r o w t h c e s s a t i o n was  to  1 and J u n e 20 i n  the  field  the  reserves c o i n c i d e d with the  observations,  stage  g r o w t h had been  f a v o u r a b l y w i t h Daer which  and  a  c o n c e n t r a t i o n i n the roots f o l l o w i n g  total  production.  translocation  major c a r b o h y d r a t e downward  pre-aestivation examination of  June  1  By  was o b s e r v e d ,  the  time  and J u l y  67% o f  is relatively  maximal  68.5 a n d 78.6% o f  s t o r a g e had a l r e a d y o c c u r r e d .  storage  peak  o f maximal  In  o f F i g u r e s 21b a n d 22b r e v e a l s t h a t  carbohydrate  when  does not r e p r e s e n t t h e s t a g e of  accumulation.  translocation  input  Willard's  indicated  Because of i t s s h o r t d u r a t i o n , the s t a g e  and  completed.  carbohydrate annual  root  1967  ( F i g u r e s 21a a n d 2 2 a ) . The peak  f i g u r e s agree  downward  was  carbohydrate  translocation  a n d 67% o f c u r r e n t a n n u a l  (1981)  root  carbohydrates  p l a c e by t h e t i m e  simulations  These  biomass.  to the  of  1%  21b and 2 2 b ) .  carbohydrate  73  movement  and  i n t h e 1967 a n d 1968 s i m u l a t i o n s , r e s p e c t i v e l y  Maximal system  producton  i s i n c r e a s e d by  b e f o r e the onset  the  had t a k e n  observed  growth  of carbohydrates  occurred  in  herbage  i n c r e a s e i n belowground  Translocation  significant  between  constant  30 i n 1967, and between May  fact,  the rate between  1 and June  69  30 i n 1968. Carbohydrate  translocation  to  root  system  remained  high  cessation  ( F i g u r e s 21b and 22b). During t h i s p e r i o d ,  additional was  f o r approximately  the  12.9 and 11.2% of annual carbohydrate  recorded  for  observations  are  which i n d i c a t e s restrictive activity  the  that  towards  Root:shoot  two  respective  consistent  (Trlica,  equalled  20 days a f t e r  with  suboptimum  conditions  ratios  f o r the Agropyron  genus al.,  (Warembourg and Paul, (1966)  by  appropriately  are  more  photosynthetic  and 3.9 i n the  water  range 1981;  from  Holechek,  1982)  reproduced  This in  to  2:1 8:1  (1969) and Brouwer  shown that root:shoot deficit.  1968  i n the l i t e r a t u r e approximately  1973). Davidson  have p r e v i o u s l y  increased  evidence  immediately p r i o r to a e s t i v a t i o n  s i m u l a t i o n . Rootrshoot r a t i o s reported  et  These  1977).  4.4 i n the 1967 s i m u l a t i o n  (Caldwell  an  storage  years.  empirical  growth than towards  growth  r a t i o s are  phenomenon  model  is  simulations:  s u b s t i t u t i o n of the 1968 s o i l water regime with the d r y , intermediate, Ryswyck and ratios regimes.  of  and  wet moisture regimes measured by van  Broersma 10.5,  (Figure  10)  yielded  8.5, and 3.5 f o r the three  root:shoot respective  70 5.2  BLUEBUNCH WHEATGRASS DYNAMICS IN THE  Defoliation  e f f e c t s are only d i s c u s s e d r e l a t i v e to the  s i m u l a t i o n of Harper's site  since  data  (1969)  for  bluebunch  quantitative  parameters i s a v a i l a b l e f o r t h i s year  5.2.1  defoliations  validation  mesic  of  model  only.  values of regrowth f o l l o w i n g g r o u n d - l e v e l on May  31  ( F i g u r e 23a)  compared extremely  field of  wheatgrass  1967  REGROWTH FOLLOWING DEFOLIATION Simulated  23b)  PRESENCE OF GRAZING  sampling.  on  w e l l with values  less  June  28  favorably  18.9  regrowth  observed  (Harper  not  g m~  growth  coincided  cessation,  observed  values  in  ground-level  with  be  due  measurable  the f i e l d at t h i s  discrepancy  divergence  may  for  by August 30,  2  1969). Because t h i s  defoliation  from  ( F i g u r e 23c). While p r e d i c t e d  regrowth approached was  obtained  However, p r e d i c t e d and measured values  regrowth compared  defoliation  and June 14 ( F i g u r e  the  occurred  approximate  between to  when  date  predicted  previously discussed  that  magnitude  also  The  regrowth  due  or the  to  an  possibility  not  readily  e f f e c t of g r a z i n g regime on the  fall  standing  is  of  be  is  measurable i n the  crop  v a l u e s may  low p r o j e c t i o n of l i t t e r f a l l , this  soil  growth r a t e . The d i s c r e p a n c y between  p r e d i c t e d and observed overly  of and  i n a c c u r a c i e s i n the simulated r e l a t i o n s h i p between water p o t e n t i a l and  time  field.  depicted  in  Figure  24.  Heavier  grazing  CM I  E CT)  CO CO  •a: s:  o  »—< CD CD t—t Q  <C  t—  co  FIGURE 23. Comparison of simulated (continuous line) and measured (standard error intervals) values of regrowth following ground-level defoliation on May 31 (Figure 23a), June 14 (Figure 23b), and June 28, 1967 (Figure 23c).  72 intensities while  resulted  progressive  resulted  in reduced  involved  generally  forage  availability.  An  exception  on  Consequently, crop even  of  early  period  spring  very  tillers  Forage depressed  by  defoliation forage  than  grazing  thereby  accumulation  Defoliation increased however, Regardless  forage increases  100%  availability  yield  period  fall  availability were  intensities fall.  of  is  stages. a  larger grazing,  lengthier  low  period  November  1 was  (Figure  by  intensity  defoliation  i n the  growth  i n t e n s i t y before  50%  removal  foliar  when  rapid  is possible.  regimes  i n the  that  grazing. Additionally,  the  most g r a z i n g  at  of  the  on  availability  herbage  results in a  availability  25%  1 for a l l  r e s u l t s suggest  will  spring  prolongs  matter  May  than e a r l y s p r i n g  grazing  late  y i e l d e d more  on  early  delaying  of d r y  at  which  to  spring grazing  secondary  biomass,  and  response  though e a r l y s p r i n g  regrowth  31,  1 than d e f o l i a t i o n  at  late  May  examined. These  weak  availability, date  bluebunch wheatgrass relatively  forage  in d e f o l i a t i o n  November  intensities  reduced  delays  defoliation  r e g r o w t h by grazing  in  date,  24).  However,  June 25  increased  as  before relative  marginal  at  herbage  severely  considerably  much June to less  61%.  5  also  control: than  removal  depressed  as  at  10%. 75  forage  73  FIGURE 24. Simulated effect of defoliation date and defoliation intensity on November 1st forage availability.  74 5.2.2  TOTAL ANNUAL DRY Simulation  MATTER PRODUCTION  results  indicate  that  production  is strongly  affected  by  defoliation  intensity  between A p r i l of  and  defoliation  July  date  m i n o r when h e r b a g e defoliation dry  at  matter  25  In  contrast,  intensities  matter  production.  observations,  had  little  5.2.3  In  curtailed  defoliation  on  by  effect  herbage  26,  herbage  27,  annual  and  21  percent,  at  75  and  annual  dry  with M c l l v a n i e ' s production  removal  annual dry  (1944) was  most  intensities  defoliation  protein  r e m o v a l on  and  28) on  in crude  grazing  improved  date  after matter  at  mid  and July  production.  YIELD yields of  are  standing  crude p r o t e i n  partially  biomass,  resembles  forage  availability. yield  improvements  treatments,  the  effect  following in  since  the  availability  closely  protein  regimes surpass  comparable  Spring  depressed  of  herbage  become  mid-July.  defoliation  matter  availability  removal  improvements grazing  the  65  heavy d e f o l i a t i o n  total  crude  determined  (Figures  dry  by  CRUDE PROTEIN  of  spring  Regardless  effect  much as  agreement  intensity,  Because  as  consistently  annual  dates.  by  effects  intensity  intensities  and  occurs  However, t h e  defoliation  50%  date  removal  removal o c c u r s a f t e r and  100%  early  and  25).  matter  defoliation  herbage  (Figure  production  respectively.  seriously  when  annual dry  However, select  forage y i e l d crude  of  for  protein  75  FIGURE 25. Simulated effect of defoliation date and defoliation intensity on total dry matter production.  76  M A  M J  J  A  S  O N D  MONTH FIGURE 26. Simulated crude protein yields following defoliation at 4 intensities on May 1 (Figure 26a) and May 30 (Figure 26b).  77  MONTH FIGURE 27. Simulated crude protein yields following defoliation at 4 intensities on June 14 (Figure 27a) and June 28 (Figure 27b).  FIGURE 28. Simulated crude protein yields following defoliation at 4 intensities on July 15 (Figure 28a) and Sept 15 (Figure 28b).  79 availability  is  concentrations Similarly,  promoted  as w e l l  regimes  availability  in  crude p r o t e i n  availability  between which For  grazing  example,  fall  regimes  enhance y i e l d  at this which  desired.  In  at  may o c c u r a s l a t e protein occur  contrast, as J u l y  availability  in  improvement  occur, removal  (Figures  defoliation limited contrast, growth protein  in  f o r t h e two  division  i n forage  and t h o s e  parameters.  25% i n t e n s i t y  protein  must  occur  availability  a t 25% i n t e n s i t y in  crude  yield  may  date  f o r an  than  for  an  yield. crude  protein  they  involves  slow  when c r u d e  protein  accumulation  defoliations i n almost  yield.  Relative  persisted  weeks  when  26, 27, a n d 2 8 ) . An e x c e p t i o n spring  three  yield,  herbage  resulted  availability  The  of  the  high  time.  or at a l a t e r  do so w i t h i n  in early  by  towards  t o d e v e l o p . Thus, d e f o l i a t i o n  i n biomass  generally  restrictive  5 f o r an improvement  crude  Enhancements  forage  defoliation  at a higher intensity  improvement  depress  suppress y i e l d  also differs  defoliation  nitrogen  f o l i a r production.  which  are less  b e f o r e J u n e 25 i f an improvement is  enhanced  as s t i m u l a t e d  defoliation the  by  until  in  during  immediate  yield  is  biomass.  In  rapid  vegetative  increases  increases  i n crude  in  t h e end o f t h e y e a r .  protein  80 5.2.4 BELOWGROUND Spring root  grazing  a t 25 a n d 50% i n t e n s i t i e s  accumulation  respectively was  DYNAMICS  (Figure  slightly  intensities. generally  by  summer  Defoliation  at  75  on  production  root  in  annual  the  maximum  34%  f o r the grazing spring  severely  belowground  fall  September 30).  not  extensive prevented  apparent  observations stoarage  in  until  foliar  m o r t a l i t y and of  emphasize the  on t o t a l  annual  (Figure  root  the  fall  equalled  defoliation  recovery  in  growth,  (Figure  together  respiratory  biomass  root  August o r e a r l y  defoliation  with  losses,  i n summer. T h e s e  importance  f o r plants  less  mid-season.  late  high  29).  by up t o  accumulation  date,  ground-level low  build-up  less  accumulation  during  to  were  r e g i m e s e x a m i n e d . Heavy  following  root  intensities  was r e d u c e d  root  these  relative  biomass  of root  at  100%  than  curtailed  Ostensibly,  accumulation  biomass  aboveground  a n d 162%  grazing  accumulation  t h a n heavy d e f o l i a t i o n  was  root  effects  Regardless of d e f o l i a t i o n biomass  226  detrimental  curtailment  or  as  and  herbage p r o d u c t i o n  50%,  in  much  arrested  however,  trenchant  as  2 9 ) . In c o n t r a s t ,  depressed  control;  Whereas  by  increased  of  carbohydrate  which had r e c e i v e d  ground-level d e f o l i a t i o n s . Root:shoot than of  ungrazed root  ratios  sites  production  are  reportedly  l o w e r on g r a z e d  (Sims e t a l . , 1978). The s e n s i t i v i t y to  herbage  removal  i s apparent i n  81  FIGURE 29. Simulated effect of defoliation date and defoliation intensity on November 1st root biomass.  82'  700  600 "  Control April 1 defoliation May 1 defoliation May 31 defoliation June 14 defoliation June 28 defoliation July 15 defoliation Sept. 15 defoliation  CVJ  i  CD CO  s: o  500  — II CO  o o  on  400  300 •  M  J  MONTH FIGURE 30. Simulated root accumulation following ground-level defoliation at various dates.  83 both  simulated  (1956) f o u n d t h a t when inch a  bluebunch  and  empirical  observations.  root  production  was s e v e r e l y  wheatgrass  ( 2 . 5 cm) h e i g h t s fourteen  production foliar  week  two-fold  whereas  period.  The  aestivation  between May  than  the  biomass  foliar  biomass  Similarly,  root:shoot  ratios  were r e d u c e d  approximately  impairment  root  decrease. that  were c l i p p e d t o one  s e c o n d o r f o u r t h week f o r  was much more s e v e r e  hundred-fold  curtailed  at every  production:  indicate  plants  Branson  from  3.6 i n p l a n t s  to  impairment  was  to  reduced  suffered  simulation  only  a a  results  immediately  4.4  root  prior  to  i n ungrazed p l a n t s t o  d e f o l i a t e d a t 100% i n t e n s i t y  1 and t h e end o f J u l y .  5.2.5 DRY MATTER  PRODUCTION  THE YEAR  FOLLOWING  HERBAGE  REMOVAL Simulation herbage  removal  following herbage  results on  dry  defoliation  surprising  (Figures since  inter-yearly  31 and 2 9 ) . T h i s  dynamics.  Lack  validation  of s i m u l a t i o n  validation  discloses  projected  yields.  of  to  s u i t a b l e data results; the  the  during  effect the  of year  effect  of  the year of  r e l a t i o n s h i p i s not  are perennial  bluebunch  the  production  accumulation  the roots  link  matter  that  closely parallels  r e m o v a l on r o o t  treatment  indicate  and p r o v i d e t h e  wheatgrass  growth  preclude  quantitative  however,  qualitative  biological  soundness  of  FIGURE 31. Simulated effect of defoliation date and defoliation intensity on dry matter production the year following herbage removal.  85 Simulation is  less  31).  results  damaging  This  than  herbage  spring  accumulation  less which  but  than  the year  that  late  before  spring  t h e end  wheatgrass  boot  (Blaisdell  simulated period booting  which  results  (Stoddart,  1946;  al.,  to  the flower  Pechanec,  1979)  defoliation  also  highest  on  concur  with  herbage  on  less  that  head  1949;  development  (1946) harmful  the  and the  bluebunch injury  emerges from Wilson  was  not  t h e end  explicitly in  date  (Quinton et a l . , field  Pechanec, minor  production  the  of J u n e ,  approximate  and  the  et a l . ,  disturbance  toward  31)  Blaisdell  plants  defoliation  physiological  (Figure  than  i t allowed regrowth  suggests  i n bluebunch wheatgrass  Simulation  that  produced  Stoddart  was  was  season.  susceptible  coincides  date  found  treatment  because  was  (1966)  first matter  inches high  grazing  AGGRO,  plant  al.  grazing  1966). W h i l e p h e n o l o g i c a l  dry  as c l i p p i n g  spring  and  by t h e  in  inches high.  evidence  empirical  demonstrated  affected  when 5-7  of the growing  i s most  in  et  1-2  b e f o r e or a f t e r  modeled  (1949)  least  following  when  early  Empirical  shortly  Wilson  grazing (Figure  s u p p o r t e d by  reductions  were c l i p p e d  were c l i p p e d  concluded  well  was  spring  defoliation  became more p r o n o u n c e d  which  herbage  early  Pechanec  production  delayed. Similarly, plants  is  and  clipping  that  mid-season  observation  evidence: B l a i s d e l l that  reveal  a of  1982).  observations 1949;  impact the year  West e t of  fall  following  86 defoliation. There  i s no  stimulations the  year  documentation  following  light  studies  generally  concerned with  spring  ground-level  defoliations in a  of  Rickard  are  vulnerable  al.,  1975),  phenological  31).  (1981) have p r e v i o u s l y  defoliation to  et  single  stage  are  multiple, (Stoddart,  d e f o l i a t i o n s through  (Wilson  or  Bedell  160%  1972;  severe  s i n g l e season  years  Mueggler,  to  predicted  subjected  1956), s u c c e s s i v e  1949;  up  w h i c h were  d e f o l i a t i o n (Figure  often  consecutive  et  dramatic  relatively  Plants  Branson  the  investigating defoliation effects  treatments.  number  support  i n herbage p r o d u c t i o n  However,  1946;  to  al.,  1966;  d e f o l i a t i o n s at  (Blaisdell  and  following  summer  and  and  stimulations  fall  a  Pechanec,  1975). A d d i t i o n a l l y , Ganskopp reported  a  grazing  of  at  25%  intensity.  5.2.6  IMPLICATIONS AND  INTEGRATED MANAGEMENT OF  from  consideration concomittant Under  of  optimum  desired of  matter  removal at  grazing  regime  management  management  of management  climatic  conditions  production 25%  site  was  i n t e n s i t y on  in  May  31  must  be  Thus,  entail  a  objectives.  of  Harper's  1967,  highest  cannot  outcome.  policy  discussion  bluebunch wheatgrass mesic dry  CATTLE  WILDLIFE  Selection divorced  TO  (1969)  total  annual  following  herbage  (Figure  25).  This  87  grazing  r e g i m e would t h e r e f o r e be o p t i m a l  objective  was  to  maximize  regard  t o the timing  root  production  removal  at  be  to  of concern.  stimulated Thus,  subsequent Of  to  East  grazing  Given  of forage  winter  grazing  forage  grazing  in Figures  by  protein yield  to  10%.  accommodate simultaneous  policy  availability  is a  livestock  and  has  Scherzinger,  i n such  areas  r e g i o n of the  British  effects  and crude  as  of  protein  become p a r a m o u n t .  24, 26, 27, a n d 28, j u d i c i o u s t o improve crude  i n the f a l l  minimum by a t  availability  unpub. d a t a ) and i s ,  objective,  examined, a  five  habitat for wildlife  Ashnola  be u s e d  availability  regimes  availability  the  and w i n t e r  management may  should not  The u s e o f  (Anderson  an  r e g i m e on f o r a g e  shown  30),  by more t h a n  require  importance.  or  such  herbage  variables.  t o management  Kootenays  by  examined,  available  which  Because  (Figure  regimes  production  addressed  i n the f a l l As  crude  intensity  is  improve  central  Columbia.  and  annual  without  availability.  M a l e c h e k e t a l . , 1978; P i t t ,  fact,  production  herbage p r o d u c t i o n  the season  been p r e v i o u s l y  management  stimulated  grazing  of c o n s i d e r a b l e  management  yield  24  of s e v e r a l  Frequently,  the  and  policies  maximization  in  likewise  flexibility  management  1976;  forage  date  total  some  matter  is  this  impairment  of  forage  if  three  and w i n t e r . enhanced  o f 10% w h i l e  least  the  protein  seven  same  Of 24 forage  enhanced  amount.  In  88 accordance crude  with  protein  herbage  forage  were  in early  protein  were m a x i m i z e d by  on May  less  spring  by  is  quantity,  a  abundant more  31. In  with  curtailed  y i e l d and by  deficiencies  Leege,  1982),  weight  heavy  As effects  necessarily  low p r o t e i n  protein  5%  may  forage  than  yield.  foliar in  levels  forage  must be c o n s i d e r e d i n  develop  loss  a good  Where  limitation  protein  on t h e a v a i l a b i l i t y  this  since  will  below  not  s t a n d i n g biomass.  crude  dropped  depend  is  crude  protein  Assuming  that  i f percentage  crude  content  (Nelson  animals w i l l  of crude  protein  and  therefore  which  occurs  minimum c o n c e n t r a t i o n . revealed  i n T a b l e 3,  of j u d i c i o u s  remarkable November  when  the  potential  this  parameter  1st a v a i l a b i l i t y  ungrazed  following  plants,  livestock  31.  Of  24  grazing  fall  availability  beneficial  g r a z i n g management become even is  considered.  of crude p r o t e i n  a minimum c o n c e n t r a t i o n o f 5% e q u a l l e d  in  contrast  t h a n heavy d e f o l i a t i o n s i n  serious  percentage  conjunction protein  yield  of f o r a g e q u a l i t y  masked  quality  at  production,  spring.  indicator  at  matter  p r o d u c t i o n , crude p r o t e i n  availability  Crude  be  dry  a t 25% i n t e n s i t y  dry matter  defoliations  annual  and f o r a g e a v a i l a b i l i t y  removal  to annual  late  total  but e q u a l l e d defoliation regimes  of t h i s  which  12.1  more The  occurs ha"  1  a s much a s 144 kg h a "  1  a t 25% i n t e n s i t y  examined,  parameter  by  kg  on  May  18 i n c r e a s e d t h e at  least  10%.  TABLE III. The effect of grazing regime on the November 1st availability of crude protein (Kg/ha) which occurs at a minimum concentration of 5% foliar content by weight. GRAZING INTENSITY (%) Clipping Date  25  50  70  99  May 1  34.5  24.5  14.4  12.5  May 31  144.0  97.6  51.7  51.5  June 14  98.0  67.2  36.7  35.7  June 28  48.6  35.0  14.1  22.0  July 15  18.1  15.3  12.4  14.0  Sept. 15  1.4  1.4  1.4  6.0  Control: 12.1 Kg/ha  TABLE IV. The effect of grazing regime on the December 30th availability of crude protein (Kg/ha) which occurs at a minimum concentration of 5% foliar content by weight. Clipping Date  GRAZING INTENSITY [%) 25 50 70  99  May 1  21.3  15.1  8.9  7.8  May 31  31.6  22.2  12.7  12.5  June 14  25.8  18.1  11 .0  10.5  June 28  33.0  23.6  21.3  15.0  July 15  11.4  9.5  7.6  8.9  Sept. 15  1.0  1.0  1.0  3.0  Control:  7.5 Kg/ha  90 This  relationship  (Table and  4) even  until  though d i f f e r e n t i a l  ungrazed p l a n t s diminished The  effect  partitioning in  persisted  Figures  livestock higher  values  with  of  grazing  between  livestock  forage  Similarly,  wildlife  following spring grazing  100%  intensities.  grazing  occurred  of  access  cattle  forage  on  and w i l d l i f e  Forage  i s depicted  in  livestock.  t o more f o r a g e  by l i v e s t o c k  to wildlife  summer  or  date,  resulted in  than  availability  availability  resource  defoliation  to wildlife  gained  grazed  time.  a t 25 a n d 50% i n t e n s i t i e s  availability  exceeded  between  regime  23 and 24. R e g a r d l e s s grazing  t h e end o f t h e y e a r  at  to  at  75  and  livestock  when  fall  than  livestock 75 and 100%  intensities. While forage  forage  availability  availability  to  to livestock  wildlife  f o r 17  of  24  regimes examined, crude p r o t e i n a v a i l a b i l i t y exceeded crude p r o t e i n only  8 o f 24 g r a z i n g Grazing  management Figures  livestock early  regimes which a r e u n s u i t a b l e of  two  species  i s inappropriate  i t seriously  wildlife.  to  are  to w i l d l i f e  livestock  for  i s extremely  low  Regardless  for integrated  readily  identified  fall  grazing  in by  f o r m u l t i - s p e c i e s management  depletes  Alternatively,  spring.  grazing  regimes.  32 a n d 33. F o r e x a m p l e , h e a v y  livestock because  availability  exceeded  forage forage  when of  availability availability  grazing defoliation  occurred  to to in  intensity,  91 2500  r  0  500 FORAGE AVAILABILITY  1000 1500 TO LIVESTOCK (Kg ha' ) 1  FIGURE 32. Forage availability for cattle versus forage availability for wildlife on November 1st following livestock grazing on six different dates (May 1 - 1, May 31 - 2, June 14-3, June 28-4, July 15 - 5, Sept. 15 - 6) at four different intensities.  92  FIGURE 33. Crude protein availability (minimum concentration of 5% foliar content by weight) for livestock versus wildlife following livestock grazing on six different dates (May 1-1, May 31 - 2, June 14 - 3, June 28 - 4, July 15 - 5, Sept. 15 - 6) and four different intensities.  93 livestock  g r a z i n g on May  availability  1st y i e l d e d  to both w i l d l i f e  and  low  crude  livestock.  protein  6. The matter  seemingly  accumulation  matter late  model  p r o v i d e s good p r e d i c t i o n s  of  dry  i n t h e a b s e n c e of g r a z i n g a s w e l l  as  dry  accumulation  spring  matter  or e a r l y  following  validation  biological  model validation  root:shoot  ratios  varied  of  fell  simulation  dry  defoliation  data.  results  removal.  However,  support  the  following following  all  bluebunch  wheatgrass.  supported  by  physiological simplifying  and  organismal  indices A  biomass.  carbohydrate  movement  dry matter  showed  good  empirical  undue  be  The  feature  between  94  these  production  due  both  may this  of  to the  as a d o p t i o n  of  and  production,  partly  complexity  magnitude  date  qualitative  at  as w e l l  relationship  and  observations  may  levels,  distinctive  simulated  belowground  and  dry matter  principles  where  stress  of d e f o l i a t i o n  results  biological  disadvantageous. the  available  Predicted  of p u b l i s h e d v a l u e s  to moisture  annual  removal  simulation  of  range  effects  total  herbage  with  Favourable  the  defoliation,  agreement  observance  on  also  parameters.  i n response  Simulated  intensity  is  alternate  within  appropriately  defoliation  involves  of  suitable  integrity  qualitative  the year  lighter  of  in  s o u n d n e s s of p r o j e c t e d y i e l d s .  Overall  regrowth  following  i s p r e c l u d e d by want of  qualitative  herbage  ground-level d e f o l i a t i o n  summer. Q u a n t i t a t i v e v a l i d a t i o n  accumulation  intensities  and  GENERAL DISCUSSION  of be  model  between  above  and  and  direction  of  two  components  is  95 entirely turn  dependent  the  sink-source  d e t e r m i n e d by t h e g r o w t h p o t e n t i a l .  movement in  on  is  indirectly  related,  distinctive  growth as a d i r e c t  feature  the  belowground  v i g o r , and  winter  sensitivity  dormancy,  summer  when t h e volume o f l i v e Simulation insights  into,  of  is  of  are  shoot  biomass  development, suggested  identified  judicious  periods  Simulation  revealed  different  of carbohydrate  root  results  reserves support  crude  protein  availability  wildlife  effectiveness  habitat. of  will  depend  modulate  substantially of  It  grazing  habitat  stimulation  effects  on  which factors  stages  of  s t o r a g e , and  toward  herbage  the contention improve  of i n c o r r e c t also  that  forage  year  to  to  production over  grazing  emphasized  the p r e v a i l i n g  following multiple defoliations  or  t o w i n t e r i n g w i l d l i f e , but  management  from  forage  is  of,  wheatgrass  results  at  to  removal,  confirmation  g r a z i n g management may be u s e d t o  exposes the d e v a s t a t i n g on  growth  This  i s low.  provided  the importance of  production.  and  to  foliar  following  or herbage  r e l a t i o n s h i p s i n bluebunch  limiting  effects.  production  important  aestivation,  results  t o , changes  biomass.  herbage  especially  i sin  carbohydrate  defoliation  belowground  were p r e v i o u s l y u n c l e a r . S i m u l a t i o n which  Thus,  i n v o l v e s t h e m o d e l i n g of  function  heightens  which  and r e s p o n s i v e  p h e n o l o g y , g r o w i n g c o n d i t i o n s , and  Another  index,  that  improve  not  successive  the  wildlife  c l i m a t e , which  year. may  regime  may  Additionally, materialize years.  96 Although s i m u l a t i o n of  inspection,  As  discussed e a r l i e r ,  r e s u l t s appear v a l i d at a l l  AGGRO cannot be the  s o i l water p o t e n t i a l and  regarded as  simulated  growth r a t e  fully  levels  predictive.  relationship  between  is neccessarily  a  first  approximation. Refinement of t h i s r e l a t i o n s h i p i s e s p e c i a l l y important  because  importance  of  moisture  dependability jeopardized were  sensitivity  of by  generated  on  validation  values of s o i l  from  has  availability  model  input  analysis  an  untested  (1969)  i n t r o d u c e d by apparent.  the  growth.  The  results  water  is  potential  from  bluebunch wheatgrass mesic s i t e , any  error  input  Similarly,  values  the  would  fine-textured  not  be  soil  readily  at Harper's  (1969) study s i t e may  have obscured another p o t e n t i a l  Because  potential  water  throughout such a h o r i z o n , depth  may  unlikely  be hold  for  weakness  relationships  for  is which  sensitivity analysis,  relatively  consideration  sufficient. true  is  of  error.  homogeneous  only  one  However, t h i s r e l a t i o n s h i p  a  sandy  a v a i l a b i l i t y varies dramatically Model  which  originated  faulty  soil  also  moisture c h a r a c t e r i s t i c  curve. Since both years of v a l i d a t i o n data Harper's  disclosed  also data  soil  where  with s o i l  depth.  engendered  by  are  soil will  moisture  postulated  l a c k i n g . As  revealed  root hormonal p r o d u c t i o n and  in  incidence  of t i l l e r i n g have c o n s i d e r a b l e impact on herbage p r o d u c t i o n . However, Similarly,  process  rates  shoot  erroneous s i m u l a t i o n  for  mortality  these is  factors tenuously  of t h i s p r o c e s s w i l l not  are  unknown.  modeled,  but  be apparent in  97 predicted in  y i e l d s because  the growing  mortality  s e a s o n when b i o m a s s  complete.  Alternatively,  mortality  will  storage  in  incurred biased  have  the  and  Errors  subsequent  Simulation  qualitatively  term  bluebunch wheatgrass.  by  not  been  modeled  loss  nitrogen effect  loss of  indicates  regrowth  that  close  (Cook  and  continued  The  stimulation species.  of  of  unpub.  Stoddar, does  data).  improvements  crude  that  protein  the  exceed  Although  not  exist  partially  axillary  buds must  rate  wil  and  Sneva,  result  defoliated still  of  in  tillering which  axillary  for  of  simulated  wheagrass  stimulate Hyder  of  forage  the r a t e  simulated  1953;  which  has  behavior i s c r i t i c a l  by work on c r e s t e d  conditions  elongation  observations  A d d i t i o n a l l y , the  defoliation will  documentation  wheatgrass.  this  yield.  i s substantiated  development similar  growth.  not  d e f o l i a t i o n on t i l l e r i n g  determining behavior  in spring  will  and are  i n AGGRO, i m p r o v e d  the assumption  regrowth  seriously  regimes  Pitt,  foliar  mechanistically  in  thus  crude p r o t e i n  v a l i d a t i o n of p r e d i c t e d  on  shoot  are  be  grazing  1946;  be p e r f o r m e d . B e c a u s e  nitrogen  may  empirical  still  i s predicated  biomass  improved  select  must  quality  root  of  simulations.  (Stoddart,  quantitative  late  on c a r b o h y d r a t e  production  of  following  supported  impact  in  herbage  predictions  forage a v a i l a b i l i t y  simulation  considerable  fall.  induced u n t i l  accumulation i s v i r t u a l l y  faulty  i n the case of long  However,  i s not  bud  1963),  bluebunch in  either  culms  or  be documented f o r  98 Model the  imperfections  utility  areas  above do n o t d e t r a c t  t h i s m o d e l . They m e r e l y f o c u s  which warrant f u r t h e r r e s e a r c h .  additional and  of  discussed  updated.  data  It is  become a v a i l a b l e , t h i s model  from  a t t e n t i o n on  hoped  that  as  c a n be r e f i n e d  LITERATURE  CITED  A l b e r d a , T h . 1968. Some a s p e c t s o f n i t r o g e n i n p l a n t s , s p e c i a l l y i n g r a s s . S t i k s t o f 12:97-103.  more  A n d e r s o n , E.W. and R . J . S c h e r z i n g e r . 1975. I m p r o v i n g quality of winter forage f o r e l k by c a t t l e g r a z i n g . J . Range. Manage. 28:120-125. Anderson, J . E . and S . J . McNaughton. 1973. E f f e c t s o f low s o i l t e m p e r a t u r e on t r a n s p i r a t i o n , p h o t o s y n t h e s i s , leaf relative water c o n t e n t , a n d g r o w t h among e l e v a t i o n a l l y d i v e r s e p l a n t p o p u l a t i o n s . E c o l o g y 54:1220-1233. Auda, H., R.E. B l a s e r , and R.H. Brown. 1966. T i l l e r i n g and c a r b o h y d r a t e c o n t e n t s of o r c h a r d g r a s s as i n f l u e n c e d by e n v i r o n m e n t a l f a c t o r s . C r o p S c i . 6:139-143. Bayoumi, M.A. and A.D. S m i t h . winter range vegetation Manage. 29:44-48.  1976. Response of to fertilization.  b i g game J. Range  B e a t h , O.A. and J.W. H a m i l t o n . 1952. C h e m i c a l c o m p o s i t i o n o f Wyoming f o r a g e p l a n t s . Wyoming A g r i c . Exp. Stn. Bull. 311, 40 pp. B l a i s d e l l , J . P . 1958. Seasonal development and yield of native p l a n t s on t h e upper Snake R i v e r p l a i n s and t h e i r r e l a t i o n to certain climatic factors. U.S.D.A. Tech. B u l l . 1190. B l a i s d e l l , J . P . and J . F . P e c h a n e c . 1949. E f f e c t s o f herbage removal at various dates on vigor of bluebunch w h e a t g r a s s and a r r o w l e a f b a l s a m r o o t . E c o l o g y 30:298-305. Blaisdell, J . P . , A.C. Wiese, and CW. Hodgson. 1952. Variations in chemical composition of bluebunch wheatgrass, arrowleaf b a l s a m r o o t , and a s s o c i a t e d r a n g e p l a n t s . J . Range Manage. 5:346-353. B o k h a r i , U.G. 1978. T o t a l n o n s t r u c t u r a l c a r b o h y d r a t e s i n t h e v e g e t a t i o n components o f a s h o r t g r a s s p r a i r i e ecosystem u n d e r s t r e s s . J . Range Manage. 31:224-229. B o k h a r i , U.G. and J . S . S i n g h . 1974. E f f e c t s of temperature and c l i p p i n g on g r o w t h , c a r b o h y d r a t e r e s e r v e s , and r o o t e x u d a t i o n of western wheatgrass i n hydroponic culture. C r o p S c i . 14:790-794. B o l t o n , J.K. and R.H. Brown. 1980. P h o t o s y n t h e s i s of grass species differing i n carbon d i o x i d e f i x a t i o n pathways. V.  and  Response  tall  of Pani cum  fescue  (Festuca  maximum  arundi 99  J a c q . , Pani cum  nacea)  mi I i oi des  ,  to nitrogen. Plant  100 Physiol.  66:97:100.  Branson, F.A. 1956. t r e a t m e n t s on five 9:86-88.  Quantitative effects of c l i p p i n g range grasses. J . Range Manage.  Brouwer, R. 1963. Some a s p e c t s o f t h e e q u i l i b r i u m between overground and underground plant parts. Inst. Biol. Scheikd. Onderz. Landbouwgewassen Wageningen Jaarb. 1963:31-39. Brouwer, R. 1966. Root g r o w t h o f g r a s s e s and c e r e a l s . I n : Milthorpe, F . L . a n d J.D. I v i n s ( e d s . ) The g r o w t h o f c e r e a l s and g r a s s e s . P r o c e e d i n g s o f t h e T w e l f t h Easter School in Agricultural Science, University of N o t t i n g h a m , 1965. Brown,L.F. a n d M.J. T r l i c a . 1977. I n t e r a c t i n g e f f e c t s o f s o i l w a t e r , t e m p e r a t u r e a n d i r r a d i a n c e on C02 exchange r a t e s o f two d o m i n a n t g r a s s e s o f t h e s h o r t g r a s s prairie. J . A p p l . E c o l . 14:197-204. Bunnell, F. 1970. TC0MP - An i n t e r a c t i v e model o f n u t r i e n t c y c l i n g and d e c o m p o s i t i o n i n t h e A r c t i c t u n d r a . Faculty of Forestry and I n s t i t u t e of Animal Resoure E c o l o g y , U n i v e r s i t y of B r i t i s h Columbia. B u n n e l l , F. 1973. T h e o l o g i c a l e c o l o g y w o r l d . F o r . C h r o n . 49:167-171.  or models and t h e r e a l  Buwai, M. a n d M.J. T r l i c a . 1977. M u l t i p l e defoliation e f f e c t s on h e r b a g e y i e l d , v i g o r , a n d t o t a l n o n s t r u c t u r a l carbohydrate of f i v e range s p e c i e s . J . Range Manage. 30:164-171. C a l d w e l l , M.M., J . H . R i c h a r d s , D.A. J o h n s o n , R.S. Nowak, a n d R.S. D z u r e c . 1981. C o p i n g w i t h h e r b i v o r y : photosynthetic capacity and resource allocation i n two semiarid Agropyron b u n c h g r a s s e s . O e c o l o g i a 50:14-24. Cook, C W . a n d L.A. S t o d d a r t . 1953. Some g r o w t h r e s p o n s e s o f c r e s t e d w h e a t g r a s s f o l l o w i n g h e r b a g e r e m o v a l . J . Range. Manage. 6:267-270. C r a f t s , A.S. a n d C.E. C r i s p . 1971. Phloem transport p l a n t s . W.H. Freeman and Co., San F r a n c i s c o . 481 p p .  in  Daer, T. a n d E . E . W i l l a r d . 1981. T o t a l nonstructural carbohydrate trends i n bluebunch wheatgrass r e l a t e d t o g r o w t h a n d p h e n o l o g y . J . Range Manage. 34:377-379. Daubenmire, R. 1972. A n n u a l cycles o f s o i l m o i s t u r e and temperature as r e l a t e d to grass development i n the s t e p p e o f e a s t e r n W a s h i n g t o n . E c o l o g y 53:419-424.  101 Daubenmire, R. 1978. A n n u a l v a r i a t i o n i n t h e f l o w e r i n g of Agropyron spicatum near C l a r k s t o n , W a s h i n g t o n . Northw. Sci. 52:153-155. D a v i d s o n , R.L. on  1969. E f f e c t s  root:shoot r a t i o s  repens  L.  of s o i l  i n Lolium  n u t r i e n t s and  perenne  L.  moisture  Trifolium  and  . Ann. B o t . 33:571-577.  Dayton, W.A. 1937. Range p l a n t v a r i o u s l y paged.  handbook. USDA, F o r . S e r v . ,  Demarchi, D. 1973. R e l a t i o n s h i p o f range q u a l i t y t o range c o n d i t i o n i n the C h i l c o t i n r e g i o n , B r i t i s h Columbia. J. Range Manage. 26:345-348. D e m a r c h i , R.A. 1968. C h e m i c a l c o m p o s i t i o n of b i g h o r n f o r a g e s . J . Range Manage. 21:385-388.  winter  D e p u i t , E . J . and M.M. C a l d w e l l . 1975. Gas e x c h a n g e o f three cool s e m i - d e s e r t s p e c i e s i n r e l a t i o n t o t e m p e r a t u r e and w a t e r s t r e s s . J . E c o l . 63:835-858. Detling, J.K., W.J. Parton, and H.W. Hunt. 1979. A s i m u l a t i o n model o f Bout el oua gracilis biomass dynamics on the North American Shortgrass P r a i r i e . Oecologia ( B e r l . ) 38:167-191. E d d l e m a n , L . E . and T . J . N i m l o s . 1972. Growth r a t e s o f ' n a t i v e grasses and soil water p o t e n t i a l as measured with t h e r m o c o u p l e p s y c h r o m e t e r s . In: Brown, R.W. and B.P. van Haveren (eds.) Psychrometry i n water r e l a t i o n s research Proceedings of the Symposium on T h e r m o c o u p l e P s y c h r o m e t e r s . Utah A g r i c . Exp. S t n . Eckert, R.E. J r . , A.T. Black, and J.H. R o b e r t s o n . 1961. E f f e c t s of macro- and m i c r o n u t r i e n t s on the y i e l d of c r e s t e d w h e a t g r a s s . J . Range Manage. 14:149-155. El  H a s s a n , B. and W.C. K r u e g e r . 1980. Impact of intensity and season of grazing on carbohydrate reserves of p e r e n n i a l r y e g r a s s . J . Range. Manage. 33:200-203.  Evans,  G.R.  and  characteristics  spicatum  E.W. of  Aristida  in west-central  Tisdale.  longiseta  1972.  Idaho. E c o l o g y  and  Ecological  Agropyron  53:137-142.  G a n s k o p p , D.C. and T . E . B e d e l l . 1981. An a s s e s s m e n t o f v i g o r and production of range g r a s s e s f o l l o w i n g d r o u g h t . J . Range Manage. 34:137-141. Garrison, G.A. 1966. A preliminary study of response of p l a n t r e s e r v e s t o s y s t e m s and i n t e n s i t i e s o f g r a z i n g on mountain rangeland i n n o r t h w e s t U.S.A. p.- 937-940 In: Tenth I n t . G r a s s l . Congr., P r o c .  102 H a r p e r , F . E . 1969. E f f e c t s of c e r t a i n c l i m a t i c factors on the p r o d u c t i v i t y and availability of f o r a g e s on the A s h n o l a b i g h o r n w i n t e r r a n g e s . M.Sc. Thesis. Univ. B r i t . C o l . V a n c o u v e r , B.C. 103 pp. Holechek, J.L. below-ground 35:39-42.  1982. Fertilizer biomass of f o u r  effects on aboveand s p e c i e s . J . Range Manage.  Holt, D.A., R . J . B u l a , G.E. M i l e s , M.M. S c h r e i b e r , and R.M. P e a r t . 1975. Environmental physiology, modelling and simulation of a l f a l f a growth I . C o n c e p t u a l development o f SIMED. I n d i a n a A g r i c . Exp. S t n . Res. B u l l . 907. Hyder, D.N. and F.A. Sneva. 1963. Morphological and p h y s i o l o g i c a l f a c t o r s a f f e c t i n g the grazing management of c r e s t e d w h e a t g r a s s . C r o p S c i . 3:267-271. I s r a e l s e n , O.W. and V.E. H a n s e n . 1962. I r r i g a t i o n p r i n c i p l e s and p r a c t i c e s . 3rd edition. New Y o r k , J o h n W i l e y and Sons I n c . Jameson, D.A. harvesting.  1963. Responses of individual B o t . Rev. 29:532-594.  plants  to  Jameson, D.A. and B.L. Gross. (eds). 1977. Ranges G r a s s l a n d S i m u l a t i o n Model. I n : Feedback An approach t o n a t u r a l r e s o u r c e management. Range S c i e n c e S e r i e s No. 27. C o l l e g e of F o r e s t r y and N a t u r a l R e s o u r c e s , Colorado State U n i v e r s i t y . L o o m i s , W.E. 1953. Growth c o r r e l a t i o n , p. 197-217 In: Loomis (ed.) Growth and d i f f e r e n t i a t i o n of p l a n t s . S t a t e C o l l e g e P r e s s , Ames.  W.E. Iowa  Majerus, M.E. 1975. Response of r o o t and s h o o t g r o w t h of three grass species to decreases in soil water p o t e n t i a l . J . Range Manage. 28:473-476. Malechek, J.C., K.J. Kotter, Nutrition and production m a n i p u l a t o r s of big game 31:92-96.  and CH. Jensen. 1978. of d o m e s t i c s h e e p managed as habitat. J. Range Manage.  M c C a l l , R. 1932. Seasonal variation in composition and d i g e s t i b i l i t y of c e r t a i n s p e c i e s of r a n g e bunch g r a s s e s . The A m e r i c a n S o c i e t y of Animal Production Proceedings 25:95-100. M c G i l l , W.B., H.W. Hunt, R.G. Woodmansee, and J.O. Reuss. 1981. Phoenix, A model of carbon and nitrogen in g r a s s l a n d s o i l s . In: C l a r k , F.E. and R o s s w a l l , T. ( e d s . ) Terrestrial Nitrogen Cycles. Ecol. B u l l . (Stockholm) 33:49-115.  103 M c l l v a n i e , S.K. 1942. C a r b o h y d r a t e and nitrogen trends in bluebunch w h e a t g r a s s , Agropyron spicatum , with special reference to grazing influences. Plant Physiol. 17:540-557. M c K e n d r i c k , J.D. and L.A. Sharp. 1970. Relationship of organic reserves to herbage production in crested w h e a t g r a s s . J . Range Manage. 23:434-438. McNairn, R.B. 1972. Phloem t r a n s l o c a t i o n and h e a t - i n d u c e d c a l l o s e f o r m a t i o n i n f i e l d - g r o w n Gossypium hirsutum L. . P l a n t P h y s i o l . 50:366-370. M c N a i r n , R.B. and H.B. C u r r i e r . 1968. T r a n s l o c a t i o n b l o c k a g e by s i e v e p l a t e c a l l o s e . P l a n t a ( B e r l . ) 82:369-380. M c W i l l i a m , J.R. 1968. The n a t u r e o f t h e perennial response in Mediterranean grasses. I I . Senescence, summer dormancy, and s u r v i v a l i n Phalaris. Australian Journal o f A g r i c u l t u r a l R e s e a r c h 19:397-409. Moser, L.E. 1977. Carbohydrate translocation in range plants, p. 47-71 In: R o n a l d E . Sosebee (ed.) R a n g e l a n d P l a n t P h y s i o l o g y . S o c . Range Manage. Range S c i . Series No. 4. Mueggler, W.F. 1972. Influence of response of bluebunch wheatgrass Manage. 25:88-92.  competition to c l i p p i n g .  on the J . Range  Mueggler, W.F. 1975. R a t e and p a t t e r n of v i g o r r e c o v e r y i n Idaho f e s c u e and b l u e b u n c h w h e a t g r a s s . J . Range Manage. 28:198-204. N e l s o n , J.R. and T.A. L e e g e . 1982. N u t r i t i o n a l requirements and f o o d h a b i t s . Ch. 8 In: Thomas, J a c k Ward and D a l e E . T o w e i l l (eds.) Elk of North America Ecology and Management. S t a c k p o l e B o o k s . 698 pp. Novak, M.D. A s s i s t a n t professor. Dept. of Soil Faculty o f A g r i c u l t u r e , U n i v e r s t i y of B r i t i s h Vancouver, B.C.  Science, Columbia,  P a i n t e r , E . L . and J.K. D e t l i n g . 1981. E f f e c t s of d e f o l i a t i o n on net photosynthesis and regrowth of western w h e a t g r a s s . J . Range Manage. 34:68-71. P a r t o n , W.J., J . S . S i n g h , and D.C. Coleman. 1978. A model o f production and t u r n o v e r o f r o o t s i n s h o r t g r a s s p r a i r i e . J . A p p l . E c o l . 47:515-542. Pitt, M.D. Grazing  Unpublished d a t a . Assessment of S p r i n g C a t t l e t o Improve Autumn F o r a g e Quality of Bluebunch  Wheatgrass  ( Agropyron  spicatum  ).  104 P o t t e r , J.R. and an i m p o r t a n t  J.W. J o n e s . .1977. L e a f a r e a p a r t i t i o n i n g as f a c t o r i n g r o w t h . P l a n t P h y s i o l . 59:10-14.  Quinton, D.A, A. McLean, and D.G. S t o u t . 1982. Vegetative and reproductive growth of- b l u e b u n c h wheatgrass in i n t e r i o r B r i t i s h C o l u m b i a . J . Range Manage. 35:46-51. R a l e i g h , R . J . 1970. Symposium on p a s t u r e methods f o r maximum production in beef cattle: manipulation of both livestock and forage management to give optimum p r o d u c t i o n . J . Anim. S c i . 30:108-114. R i c k a r d , W.H., D.W. U r e s k , and J . F . C l i n e . 1975. Impact of cattle grazing on three perennial grasses in s o u t h - c e n t r a l W a s h i n g t o n . J . Range Manage. 28:108-112. Salisbury, F.B. Wadsworth Pub.  and Co.,  C. Ross. 1969. Plant Physiology. I n c . , B e l m o n t , C a l i f . 747 pp.  Sauer, R.H. 1978. A s i m u l a t i o n model f o r g r a s s l a n d p r i m a r y p r o d u c e r p h e n o l o g y and b i o m a s s d y n a m i c s . In: George S. Innis (ed.) Grassland Simulation Model. Ecological S t u d i e s 26. S p r i n g e r - V e r l a g New Y o r k I n c . 298 pp. S a u e r , R.H. and D.W. U r e s k . 1976. P h e n o l o g y of s t e p p e i n wet and d r y y e a r s . Northw. S c i . 50:133-139.  plants  Saugier, B., E.A. R i p l e y , and P. L u e k e . 1974. A m e c h a n i s t i c model o f p l a n t g r o w t h and water use for the Matador grassland. Matador Project Technical Report 65. U n i v e r s i t y of Saskatchewan, Saskatoon, Saskatchewan. Schmer, D.A. and D.P. K n i e v e l . 1974. C a r b o n t r a n s l o c a t i o n i n b l u e grama, b u f f a l o g r a s s and w e s t e r n w h e a t g r a s s , p. 85 In: Agron. A b s t r . Sheehy, J . E . , J.M. Cobby, and G.J.A. R y l e . 1979. The growth of p e r e n n i a l r y e g r a s s : a m o d e l . Ann. B o t . 43:335-354. S i m s , P.L., J.S. Singh, and W.K. Lauenroth. 1978. The structure and function of ten western North American g r a s s l a n d s . I . A b i o t i c and v e g e t a t i o n a l c h a r a c t e r i s t i c s . J . E c o l . 66:251-285. S i n g h , J . S . , M.J. T r l i c a , P.G. Risser, R.E. Redmann, and J.K. M a r s h a l l . 1980. A u t o t r o p h i c s u b s y s t e m . p59-200 In: A . I . Breymeyer and G.M. van Dyne (eds.) Grasslands, systems analysis and man. International Biological Programme 19. C a m b r i d g e U n i v e r s i t y P r e s s . 950 pp. S i n g l e t o n , J . 1976. F o o d h a b i t s of w i l d u n g u l a t e s i n B r i t i s h Columbia. Environment and Land Use Committee Secretariat, Dept. of E n v i r o n , and D e p t . o f Rec. T r a v . I n d . , B r i t i s h C o l u m b i a . 51 pp..  105 S k o v l i n , J.M. 1967. F l u c t u a t i o n s i n f o r a g e q u a l i t y on summer range i n t h e B l u e M o u n t a i n s . U.S.D.A. F o r . S e r v . R e s . Pap. PNW-44 20 pp. P a c i f i c N o r t h w e s t Forest a n d Range Exp. S t n . S m i t h , A . E . and C L . L e i n w e b e r . 1973. I n c o r p o r a t i o n of "C by l i t t l e b l u e s t e m t i l l e r s a t two s t a g e s o f p h e n o l o g i c a l d e v e l o p m e n t . A g r o n . J . 65:908-910. 1  Sneva, F.A. 1973. Wheatgrass response to seasonal a p p l i c a t i o n s o f two n i t r o g e n s o u r c e s . J . Range Manage. 26:137-139. S o s e b e e , R.E. and H.H. Wiebe. 1971. E f f e c t o f w a t e r and clipping on p h o t o y s n t h a t e translocation g r a s s e s . A g r o n . J . 63:14-17.  stress i n two  Sosebee, R.E. a n d H.H. Wiebe. 1973. E f f e c t o f p h e n o l o g i c a l d e v e l o p m e n t on r a d i o p h o s p h o r u s t r a n s l o c a t i o n f r o m l e a v e s i n c r e s t e d w h e a t g r a s s . O e c o l o g i a 13:103-112. S t o d d a r t , L.A. 1946. Some p h y s i c a l a n d c h e m i c a l r e s p o n s e s o f Agropyron spicatum t o herbage removal at various s e a s o n s . U t a h S t a t e A g r i c . E x p . S t n . B u l l . 324. 24 p p . Stout, D.G., A. McLean, a n d D.A. Q u i n t o n . 1981. G r o w t h a n d p h e n o l o g i c a l development of rough fescue in interior B r i t i s h C o l u m b i a . J . Range Manage. 34:455-459. Sweeney, D.G., D.W. Hand, G. Slack, and J.H.M. T h o r n l e y . 1981. M o d e l l i n g t h e g r o w t h o f w i n t e r l e t t u c e , p . 217-229 In: Rose, D.A. and D.A. Charles-Edwards (eds.) M a t h e m a t i c s a n d P l a n t P h y s i o l o g y . Academic P r e s s . Thornley, J.H.M. 1976. M a t h e m a t i c a l models in p h y s i o l o g y . New Y o r k : Academic P r e s s . 318 p p .  plant  T r l i c a , M.J. 1977. I I I . D i s t r i b u t i o n and u t i l i z a t i o n of carbohydrate r e s e r v e i n r a n g e p l a n t s . p73-96 In: Ronald E. Sosebee (ed.) Rangeland Plant Physiology Soc. f o r Range S c i . S e r i e s No. 4. U r e s k , D.W. a n d J . F . C l i n e . 1976. M i n e r a l composition of three perennial g r a s s e s i n a s h r u b - s t e p p e community i n s o u t h - c e n t r a l W a s h i n g t o n . J . Range Manage. 29:255-256. de  Vries, D.A. a n d N.H. A f g a n . ( e d s . ) . 1975. Heat a n d mass t r a n s f e r i n t h e b i o s p h e r e . P a r t I . John W i l e y and Sons, New Y o r k , N.Y. 594 p p .  de V r i e s , F . , W.T. P e n n i n g , J.M. W i t l a g e , a n d D. Kremer. 1979. R a t e s o f r e s p i r a t i o n a n d o f i n c r e a s e i n s t r u c t u r a l d r y m a t t e r i n young wheat, r y e g r a s s a n d m a i z e p l a n t s i n relation t o temperature, t o water s t r e s s and t o t h e i r  106 s u g a r c o n t e n t . Ann. B o t . 44:595-609. W a l t e r s , C . J . 1971. S y s t e m s e c o l o g y : the systems approach and mathematical m o d e l s i n e c o l o g y . Chap. 10 In: Odum, E.P. (ed.) F u n d a m e n t a l s o f E c o l o g y . W.B. S a u n d e r s Co. 3rd e d . W a l t o n , P.D. 1983. P r o d u c t i o n a n d management f o r a g e s . R e s t o n Pub. Co. I n c . 336 pp.  of  cultivated  Wann, M., C D . Raper J r . , and H.L. L u c a l J r . 1978. A dynamic model f o r plant growth: a simulation of d r y matter accumulation f o r tobacco. Photosynthetica 12:121-136. Wardlaw, I . F . 1968. The c o n t r o l a n d p a t t e r n o f movement o f c a r b o h y d r a t e s i n p l a n t s . B o t . Rev. 34:79-105. Wareing, P.F. and I . D . J . Phillips. 1970. The c o n t r o l o f g r o w t h and d i f f e r e n t i a t i o n in plants. Pergamon Press L t d . 303 pp. Warembourg, F.R. a n d E.A. P a u l . 1977. S e a s o n a l t r a n s f e r s o f assimilated C i n grassland: plant production and turnover, translocation and r e s p i r a t i o n . In: J.K. M a r s h a l l (ed.) The b e l o w g r o u n d e c o s y s t e m : a s y n t h e s i s o f plant-associated processes. Range Science Department Science Series No. 26. C o l o r a d o S t a t e U n i v e r s i t y , F o r t C o l l i n s , Colorado. 1fl  Weatherley, P.E., A . J . P e e l , a n d G.P. H i l l . 1959. The physiology of the sieve tube: preliminary experiments u s i n g a p h i d mouth p a r t s . J . E x p . B o t . 10:1-16. W e b s t e r , D.H. a n d H.B. C u r r i e r . 1968. H e a t - i n d u c e d callose and l a t e r a l movement o f a s s i m i l a t e s from phloem. C a n . J . Bot 46:1215-1220. West, N.E., K.H. R e a , and R.O. Harniss. 1979. P l a n t demographic s t u d i e s i n sagebrush-grass communities of s o u t h e a s t e r n I d a h o . E c o l o g y 60:376-388. Williams, R.D. 1964. T r a n s l o c a t i o n O u t l o o k A g r i c . 4:136-142.  in  perennial  grass.  W i l l i a m s , R . J . , K. B r o e r s m a , and A . L . v a n Ryswyk. 1979. The effects of n i t r o g e n fertilization on w a t e r use by c r e s t e d w h e a t g r a s s . J . Range Manage. 32:98-100. Willms, W., A.W. B a i l e y , and A. McLean. 1980a. Some e f f e c t s of s o i l and a i r temperature on g r o w t h o f Agr opyr on spicatum following clipping or b u r n i n g . Can. J . Bot. 58:568-573. Willms,  W.,  A.W.  Bailey,  a n d A. M c L e a n .  1980b. E f f e c t s o f  107  clipping or characteristics 58:2309-2312.  of  burning Agropyron  on  some spicatum.  morphological Can. J . Bot.  W i l l m s , W., A.W. B a i l e y , A. McLean, and C. Kalnin. 1981. Effects o f f a l l c l i p p i n g o r b u r n i n g on t h e d i s t r i b u t i o n of c h e m i c a l c o n s t i t u e n t s i n bluebunch wheatgrass i n s p r i n g . J . Range Manage. 34:267-269. W i l s o n , A.M., G.A. H a r r i s , and D.H. G a t e s . 1966. Cumulative e f f e c t s o f c l i p p i n g on y i e l d o f b l u e b u n c h w h e a t g r a s s . J . Range Manage. 19:90-91. Wilson, J.R. 1975. Comparative response to nitrogen d e f i c i e n c y of a t r o p i c a l and temperature grass i n the interrelation between photosynthesis, g r o w t h , and t h e a c c u m u l a t i o n of n o n - s t r u c t u r a l c a r b o h y d r a t e . Neth. J . A g r i c . S c i . 23:104-112. Zeevaart, J.A.D. 1979. Regulation of assimilate partitioning. p14-17 In:Partitioning of a s s i m i l a t e s Summary r e p o r t s o f a w o r k s h o p h e l d at Michigan State U n i v e r s i t y , E a s t L a n s i n g , M i c h i g a n May 7 t o 9 ,1979.  APPENDIX I. COEFFICIENT VALUES FOR GENERATED SOIL WATER REGIMES  SOIL  WATER  REGIME  COEFFICIENT  Dry Interior  Medium Interior  Wet Interior  Harper 1967  Harper 1968  WPAO  -40.1456  -20.3599  -5.0720  0.2044  0.2561  WPCI  16.7146  13.4655  3.8462  0.0246  0.1326  WPC2  5.5584  -4.3823  -2.3227  0.0191  0.5415  WPC3  -0.2600  1.8011  0.6965  -0.6508  -0.1306  WPC4  0  0  0.3628  0.6305  0.2288  WPC5  0  0  -0.7000  -0.5588  0  WPC6  0  0  0.6108  0.2760  0  WPSI  23.2981  6.6959  1.6328  0.0205  0.7386  WPS2  -7.2709  -4.9627  -2.4904  -0.1173  -0.2572  WPS3  -3.4033  3.4738  2.3225  0.1125  0.9152  WPS4  0  0  -1.4996  -0.1110  -0.2790  WPS5  0  0  0.6428  0.1011  0  WPS6  0  0  -0.1499  -0.7291  0  109  APPENDIX II. FORTRAN COMPUTER LISTING OF MODEL AGGRO. (Documentation for this l i s t i n g i s available from the Research Branch, B.C. Ministry of Forests, 3015 Ord Road, Kamloops, B.C. V2B 8A9)  MICHIGAN 0001 0002 0OO3 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 0020 0021 0022 0023 0024 0O25 0O26 0027 0028 0029 0030 O031 0032 0033 0O34 0035 0036 0037 0038 0039 0040 0041 0042 0043 0044 0045 0046 0047 0048 0O49 0O5O 0051 0052 0053  TERMINAL  SYSTEM FORTRAN G(21.8)  MAIN  10-11-84  C GROWTH MODEL FOR BLUEBUNCH WHEATGRASS SUBROUTINE UMOOEL(JTIME > REAL N.NG.N2 REAL N03 , NH4 . LBG, NP , NAB, NLP. NL . NML , NLT , NVG REAL TNLOSS.NLO.NCYCLE.NTO REAL NAVAIL,NLOSS,LAB.NFREE,NMIN,NN,MB.NPSYN,KILL,LF REAL J,NVO,NV,N0EM,NVOLT REAL DMAX . NRECYC , NCYC . N03, NG 1 . NG2 , NG3 REAL NRGG.NRGAES.NMINY INTEGER INCR.NK.KA,KB,RK.OR.DP,WPCH INTEGER GRJD,FUN COMMON P,A1.B(10).GMAX.ITIME COMMON AB,RS,CC.SO,SS.TS.D,RSP COMMON TEMP,TO(10).TM1(10).DD(12).DL.STEMP COMMON WP0T.W1,N COMMON PSYN.TPSYN,WSYN,NPSYN,T,TNPSYN COMMON G.WG.NG.TG.T1.N2 COMMON RESP.RR COMMON OMAX.LAB COMMON TA,TB,SG,TM,NRECYC COMMON C4.C5.S4.S5.ISINK COMMON 0R(12),RM(12),RD(12) COMMON d(12).A(12),NVO(12) COMMON WPA0(6),WPC1(6),WPC2(6),WPC3(6).WPC4(6).WPC5(6),WPC6(6) COMMON WPS1(6),WPS2(6).WPS3(6),WPS4(6),WPS5(6),WPS6(6) COMMON U3.U4.N03.NH4 COMMON INCR.NK.KA.KB.RK,JR.RJ COMMON GA.GB.MB.LBG.JD COMMON NP (12).NAB<12).NOEM,NLP(12).NL*12),NML(12).NLT COMMON NVG(12),NV<12),NV0LT COMMON Z1,R3(365).R4(36S) COMMON TNLOSS.NLO(12).NCYCLE,NTO<12).TLOSSO.NAVAIL,NFREE.NMIN.NN COMMON NMV(12).FM.AM.CM,KILL.BM,LF.PHENM COMMON RN(20),RP(20),PREC,R1(20).R2(20),DP(20),PM(20) COMMON SY 1 , SY2 , SA . SB. WBM, RNDMI COMMON ISOURC.IPASS.LOCN.WPCH.RNOMI COMMON DLA0(10),DLC1(10).DLS1(10).PI.WAM.NCYC COMMON NYC.CP.UDR.CPY.GRAZINC365).KGR.GR.GRPSYN COMMON ISTT.ISTST.ISTW.GRA.KNEMP.KNEMPI.KNI COMMON GRJD,FUN,GBMAX,GGBMAX.DLG.ISHIF,NCH COMMON IAEST,AGBMAX,FUN2.RGAES.FUNS COMMON MORTJD.MORTWP,CUMAB,RGG.AMRGG.AMRG.TLAB COMMON RTSHT.PMAX.FRMAX,FRRMAX.TSSNEG COMMON KNEMP2 .KNEMP3.NRGG.NRGAES.GRAZ. AMG. AMRGA COMMON GLAB.GLABAB.RGGAB.RGAB.CPG,CPRGA.CPRGG,LF2 COMMON NMG,NMRGA.NMRGG.CPYMIN.NMINY COMMON CPYG,CPYRGA,CPYRGG,PHENM2 COMMON NG1.NG2.NG3.GA1,GA2.IAESTO,RGJD.JDAEST COMMON Z.DAMPD.GRKNI A207.DO.220.DO.241.DO.262.DO.365.00/ REAL'S WtiMEBt i1 ) / l DO.135 DO.150.00,165.00.179.06,193.DO. REAL'S WPB(11)/0.15D0.0.2O8333D0.0.173333DO.O.17166700,0.163333D0. AO. 05833306.0.6633300.6.04D0.6.62833306,6.048333DO.0. 1500/ REAL'S TIMEN, YZLIN.TIMEWP REAL*8 STIMEB(13)/1.DO,151.DO.154.DO,161.DO.172.DO,177.DO. A191 DO.203 00.22 1.00.238.DO.247.DO.262.DO.365.667 REAL'S STEMPB(13)/-4.000.9.ODO.10.300.10.3D0,13.000. A 14.800.17.500.13. 100.17.000.11.400. 14.700,11 3D0,-4.000/  13:27:50 1 000 2 000 1 000 2 000 3 000 4 OOO 5 OOO 6 000 6 200 7 000 8 000 9 000 1 1 000 12 000 13 000 14 000 15 000 16 000 17 000 18 000 19 000 20 000 21 000 22 OOO 23 000 24 OOO 25 000 26 000 27 000 28 000 29 000 30 000 32 OOO 33 000 34 000 36 000 37 000 38 OOO 39 000 40 000 41 000 42 000 43 OOO 44 000 45 000 46 000 47 000 48 OOO 49 000 4 000 5 OOO 6 000 7 000 8 000 9 OOO 10 000 1 1OOO 12 000  PAGE P0O1  MICHIGAN TERMINAL 0O54 0055 O056 0057 0058 0059 OOSO 0061 O062 0063 0064 O065 0066  0067  0068 0069 6670 0071 0072 0073 0074 0075 O076 0077 O078 O079 0080 0081 0082 O083 0084 0085 0086 0087 0088 0089 0090 0091 O092 0093 0094 O095 0096  SYSTEM FORTRAN GI21.8) REAL'S  UMODEL  10-11-84  TIMEB(10)/1.DO.140.DO.189.DO.195.DO,230.DO,258.DO.278 DO.  A 306.66.315.DO.365.667  REAL'8 TEMPB(10)/-2.78DO.8.3D0.14.4D0,8.3D0.21.1D0,12.2D0,15 6D0 A,-2.8D0,0.000.-2.7800/ EXTERNAL VZLIN ISOURC-11 CALL FTNCMD('DEFAULT 11«*S0URCE*:') REAL'S DWBM,DWPOT.DPAR15(4 I/O.7D0.-9.85S53D0..0400, .9866/. ADTAU1/O.DO/,DTAU2/75.DO/ CALL FTNCMD('DEFAULT 10='SINK*;') ISINK-10 IF(IPASS.EO.O)CALL CHOICE IF(IPASS.EQ.O)NAVAIL=0.15*LBG IPASS'IPASS+1 ITIME-JTIME C'INK CALL FWRITE(ISINK,'STATEMENT #1 ITIME IS <I«4>.:'.ITIME) C'INK CALL FWRlfElISINK.'STATEMENT *1 JTIME IS <I*4>.:'.jfIME) IF(M0D(ITIME,365).E0.1)CALL REINIT C'INK CALL FWRITE(ISINK,'STATEMENT *2 ITIME IS <I*4>.:',ITIME) C'INK CALL FWRITEt ISINK, ' STATEMENT #2 JT IME IS <I'4>. : ' .JTIME) C'INK CALL FWRITEfISINK.'STATEMENT #2 JO IS <I'4>.:',JD) JD'JD+INCR C'INK CALL FWRITEfiSINK.'STATEMENT #3 ITIME IS <I'4> : ' . i t l M E ) C'INK CALL FWRITEfISINK,'STATEMENT *3 JTIME IS <I*4>.:',JTIME) C'INK CALL FWRITE(ISINK,'STATEMENT #3 JD IS <I'4>.:',JD) C COMPUTE WEATHER PARAMETERS IF((LOCN.EO.4).OR.(LOCN.EO.5))G0T0 1333 IF(M0D(ITIME,365).EO.1)CALL RAIN GOTO 1340 1333 IF(M0D(ITIME,365).E0.1)CALL ASHRN 1340 CONTINUE 4090 f EMP=f 6( LOCN j + ( TM1 ( LOCN ) -f6( LOCN j )' * ( 1 + SI N( A i * JD+B( LOCN ) ) ) / 2 4091 CONTINUE C'INK CALL FWRITE(ISINK,'THE VALUE OF TEMP IS <R*4>.:',TEMP) IF((LOCN £0.4).OR.(LOCN.EO.5)(GOTO 6005 STEMP*( TM1(LOCN)-T0(LOCN))•EXP(-Z/DAMPD)• ASIN(A1«JD+B(L0CN)-(Z/DAMPD)) GOTO 6006 6005 CONTINUE NBPS»13 IF(JD.GT.6)G6fb 4095 STEMP»-0. 4095 CONTINUE TIMEN-DFLOAf(JD) STEMP*SNGL(YZLIN(STIMEB,STEMPB.NBPS,TIMEN,ISTST.ISINK,JD,2)) 6006 CONTINUE DL'DLFNCf1) IF(LOCN.NE.10)GOTO 5001 NBPW67»11 IF ( JD . GT . 6 ) GOf6 5666 WPOT«-0.0 5000 CONTINUE fIMEWP^DFLOATfJD) WPOT = SNGL(YZLIN(WTIMEB,WPB.NBPW67,TIMEWP,ISTW,I SINK,JD,3)) GOTO 5004 5001 CONTINUE WP0T=WPA0(WPCH)/2+WPC1(WPCH)'C0S(PI'JD/P) A+WPC2(WPCH)'C0S(2»PI'JD/P)+WPC3(WPCH)*C0S(2*PI'JD/P)  13:27:50 13.000 14.000 15.000 16.000 16.200 17.000 18.000 19.000 20.000 21 .000 22.000 23.000 24 .000 25.000 26.000 27.000 28.000 29.000 30.000 31 .000 32.000 34.000 35.000 36 .000 37.000 38.000 38. 100 38.150 38.200 38.300 39.000 50.000 51 .000 52.000 52 . 100 52.20O 52.300 52 .400 52.500 53.000 54.000 55.000 56 .000 57 .000 58 .000 58.200 59.000 60.000 61 .000 62.000 63.000 64.000 65.000 66.000 67 .000 68.0O0 69 OOO 70.000  PAGE P002  MICHIGAN TERMINAL-SYSTEM FORTRAN G ( 2 1 . 8 )  0O97 0098 0O99 010O 0101 0102 0103 0104 0105 0106 0107 0108 0109 01 10 01 11 0112 01 13 01 14 01 15 01 16 0117 0118 0119 0120 0121 0122 0123 0124 0125 0126 0127 0128 0129 0130 0131  1060  IF(KNEMP.GT.213)N (6.6-6.0269737*(KNEMP-213))/6.25 IF(GLABAB.LE.O)N°0.0 IF(KNEMP2.GT.213)G0T0 1070 B  NRGG (105.86-1.i355»kNEMP2+6.6643233«kN A*KNEMP2*»3)/6.25 IF(NRGG.GT.4.16)NRGG-4.16 3  1070 iF(kNEMP2.GT.213JNRGG-<6.6-6.6266737»(KNEMP2-213))/6 25 IF(RGGAB.LE.0)NRGG=0 IF(KNEMP3.GT.213)GOTO 1080 NRGAES>(105.86-1.1355*kNEMP3+6.6643233»kNEMP A»KNEMP3«*3)/6.25 IF(NRGAE S.GT.4.16)NRGAES*4.16  0137 0138 0139 0140  10-11-84  N«(-8 5i86+3490.2/KNEMP)/6.25 IF(N.GT.4.16)N=4.16 IF(LAB.LE.O)N=0.0 GOTO 4100 224 CONTINUE 223 CONTINUE IF(KNEMP.GT.2i3)Gbtb 1060 N'i105.86-1.1355«KNEMP+0.O043233«KNEMP*»2-0.55393E-5«KNEMP**3)/6.2 IF(N.GT.4.16)N'4.16  0132 0133 0134 0135 0136  UMODEL  B+WPC4(WPCH)*C0S(4*PI*dD/P)+WPC5(WPCH)*COS(5*PI*dO/P) c»wPC6(wpcH)«cbs<G»Pi•Jb/Pi+wps i(WPCH)*SIN(PI« JO/P) D+WPS2(WPCH)*C05(2*PI*JD/P)+WPSS(WPCH)*SIN(3*PI*dD/P) E+WPS4(WPCH)*C0S(4*PI*dD/P)+WPS5(WPCH)»SIN(5*PI*dD/P) F•WPS6 rwpCH)*COS(6 * P i * J b / P ) 5004 CONTINUE IF((WPCH.NE.4).AND.(WPCH.NE.5))G0T0 4099 WPOT--EXP((.28623-WPOT)/.040924)*9782.36/100000 4099 IF(WPOT.GT.-O.4)WP0T=-O.4 C EMPIRICAL N CONC. OVER TIME IF(KA.NE.iiGOTO 222 IF(dD.LT.74)KNEMPI-=1 IF(dD.LT.74)KNI"dD iFfdD.GT.105)KNEMPi-2 IF(dO.GT.105>KNI=dD IF((dD.GE.74).AND.(dD.LE.105))KNEMPI-3 IF((db.GE.74j.AND.(db.IE.105))KN1'dD 222 CONTINUE IF(KNEMPI.LT.1)G0T0 4100 IF(KNEMPI.EQ.l)iSHiF»74-KNi IF(KNEMPI.EO-1)KNEMP-dD+ISHIF IF(KNEMPI.EO.2)KNEMP=JD-30 IF(KNEMPI.EO.3)kNEMP=db-(KNI-FUN3) KNEMP2=dD-GRdD+FUN KNEMPS=dD-RGdD+FUN2 IF(NCH.NE.1)GOtb 224 IF(KNEMP.LT.1)N=4.16 IF(KNEMP,LT.1)GOTO 224  1080  IF(KNEMP3. GT . 2 13)NRGAES«if6 .6-6.6266737*(KNEMP3-2 13) )/6 . 25 IF(RGAB.LE.0)NRGAES=0  4100 CONTINUE  CN - STAtEMENTS MARKED WITH CN OESCRIBE CN A MECHANISTIC MODEL OF FOLIAR NITROGEN CN WHICH WAS NOT INCLUDED IN THE FINAL VERSION OF AGGRO. CNNIfROGEN UPTAKE CN U3=(O.OO2OO*N03/(84+N03)+O.OOO4O*N03/(4.8tN03))*LBG*INCR CN U4=(0.OO2O0*NH4/(84+NH4)+0.OOO4O*NH4/(4.8+NH4))*LBG«INCR  13:27:50 71 72 73 74  000 000 OOO 000 75 000 76 000 77 OOO 78 o o o 79 0 0 0 80 0 0 0 81 o o o 82 0 0 0 83 o o o 84 000 85 000 86 o o o 87 000 88 0 0 0 89 o o o 89 200 9 0 000 91 o o o 92 000 93 000 94 o o o 95 0 0 0 96 000 97 000 98 o o o 99 0 0 0 100 0 0 0 101 0 0 0 102 0 0 0 103 o o o 104 000 105 000 106 o o o 107 000 108 000 109 o o o 110 000 111 0 0 0 112.000 113 0 0 0 114 000 115 000 1 16 000 117 000 1 18 000 1 19 000 120 000 121 000 121 200 121 400 121 600 122 o o o 123 000 124 000  PAGE POOS  MICHIGAN  TERMINAL  SYSTEM  FORTRAN  G(21.8)  UMODEL  10-11-84  CN IF(KA.LE. 1)N=(29.0/6.25) CN IF(KA LE.1(GOTO 4760 C N N I T R O G E N OEMAND CN NK-NK+1 CN DO 4 1 9 4 1-1,12 CN NP(I)=(105.86-1.1355*(J(I)+104)*0.0043233*(J(I)*104)»»2 CN A-0.55393E-5*(d(I)+104)**3)/6.25 CN IF(NP(I).LT.0.24) NP(I)=024 CN194 CONTINUE - . CN195 CONTINUE CN DO 4 1 9 9 1 = 1 , 1 2 CN NABU)=NP(I)*A(I)/100.0 CN199 CONTINUE CN NDEM=0.0 CN 00 4 2 3 0 1-1,12 CN NDEM=NDEM+NAB(1) CNINK C A L L F W R I T E 1 I S I N K . ' S T A T E M F N T » B NDEM I S <R*4>.:'.NDEM) CN230 CONTINUE t CNNITROGEN LEACHING CN CN CN CN285 CN300 CN CN CN CN CN CN  DO 4 2 8 5 1=1,12 I F ( A ( I ) . L E . O ) G O T O 4285 DD(I)=DD(I)+TEMP CONTINUE CONTINUE DO 4 3 6 0 1 = 1 , 1 2 Z1=R3( J0)«R4i( J D ) I F ( 0 0 ( 1 ) LE.162) NLP(I)=0.875*Z1*70/61.0 I F U O D U ) G T . 1 6 2 ) .AND. ( D D U ) L E . 3 2 4 ) ) N L P ( I ) = ( 2 . 7 5 * Z 1*70/61 .0)  I F ( ( D D ( I ) . G T . 3 2 4 ) . A N D . ( D D I I j . L E . 4 8 6 ) j N I P ( I ) = (6.25*Z1*70/61.6) IF(DD(I).GT.486) NLP(I)=(0.22746*13.192*Z1-0.61749«Z1**2)*70/61.0 CN360 CONTINUE CN DO 4 4 0 0 1 = 1 . 1 2 CN NL(I)=NLP(I)*NAB(I)/100.0 CN NML(I)=NAB(I)-NL(I) CN400 CONTINUE CN NLT=0.0 CN . DO 4 4 0 8 1=1,12 CN NLT=NLT+NL(I) CN408 CONTINUE CNN V O L A T I L I Z A T I O N CN DO 4 4 3 8 1 = 1 , 1 2 CN M U L T I P L I C ' N BY 0.7 I S FOR CDNVERS'N FROM L E A F AREA TO L E A F WT CN N V G ( I ) - E X P ( - 5 . 1 5 9 2 ) * E X P ( 0 . 1 B 3 3 0 * T E M P ) * 0 . 7*DL*INCR*.000001 CN NV(I)=NVG(I)'A(I) CN438 CONTINUE CN DO 4 4 4 8 1 = 1 , 1 2 CN NMV(I)=NML(I)-NV(i) CN448 CONTINUE CN NVOLT=0.0 CN 00 4458 I•1,12 CN NVOLT=NV0LT+NV(I) CN4S8 CONTINUE CN TNLOSS"NVOLT*NLt CN DO 4 4 8 3 1=1,12 CN I F ( A U ) . L E . O ) GOTO 4 4 8 3 CN A( I )-(*"( I )-NV( I ) - N L ( I ) ) CN IF(A(I).LEO) CN ACALL F W R I T E t I S I N K , * A ( < I * 4 > ) IS NON-POSITIVE-<R*4>. : ' , I , A ( I ) )  13:27:50 125 .000 126 .000 127 .000 128 .OOO 129 .000 130 .000 131 .000 132 • OOO 133 .000 134 .000 135 .000 136 .000 137 0 0 0 138 .000 139 0 0 0 1 4 0 OOO 14 1 0 0 0 142 .000 143 0 0 0 144 0 0 0 145 0 0 0 146 0 0 0 147 0 0 0 148 0 0 0 149 0 0 0 150 0 0 0 151 0 0 0 152 0 0 0 153 0 0 0 154 0 0 0 155 0 0 0 156 0 0 0 157 0 0 0 158 0 0 0 159 0 0 0 160 0 0 0 161 0 0 0 162 0 0 0 163 0 0 0 164 0 0 0 165 0 0 0 166 0 0 0 167 0 0 0 168 0 0 0 169 0 0 0 170 0 0 0 171 0 0 0 172 0 0 0 173 0 0 0 174 0 0 0 175 0 0 0 176 0 0 0 177 0 0 0 178 OOO 179 0 0 0 180 0 0 0 181 0 0 0 182 0 0 0  PAGE  P004  MICHIGAN  TERMINAL  S Y S T E M FORTRAN  G(21.8)  UMODEL  10-11-84  CN IF(AU).LE.O) A(I)=0 CN483 CONTINUE CN LAB=LAB-TNLOSS CN I F ( N K . L T . 2 ) GOTO 4 5 0 0 CN DO 4 4 9 5 1 = 1 . 1 2 CN NCYC=NTO(I)-TL0SS0-NAB(I) CN495 CONTINUE CN500 NAVAIL=NAVAIL+U3*U4+NCYCLE CN NRECYC'NCYCLE CN NCYCLE=0 CN TLOSS0=TNL0SS CN DO 4 5 3 5 1 - 1 , 1 2 CN NTO(I)=NAB(I) CN535 CONTINUE CN DO 4 5 4 8 1 = 1 , 1 2 CN NV0(I)=NV(I) CN548 CONTINUE CN DO 4 5 5 8 1 = 1 , 1 2 CN NLO(I)=NL(I) CN558 CONTINUE CN IF(NAVAIL.GT.NDEM)GOTO 4700 C N N A V A I L I S < DEMAND C N F I G U R E OUT MIN L E V E L OF N FOR A L L A ( I ) AND R E S E R V E T H I S AMOUNT ( N M I N ) CN NMIN=0.01*LAB CN NFREE=NAVAIL-NMIN CN IF(NFREE.GE.0)G0T0 4625 CNNFREE < 0 CN 0 0 4 6 2 0 I - 1 . 12 CN NAB(I)»NAVAIL/LAB*A(I) CN620 CONTINUE CN GOTO 4 6 5 0 CNINK C A L L F W R I T E t I S I N K , ' S T A T E M E N T # 9 N F R E E IS <R'4>.: ' . N F R E E ) CNNFREE > = 0 C N 6 2 5 DO 4 6 4 0 12 CN I F ( N F R E E . G T . N A B ( 1 3 - i ) ) G 0 t 6 4630 CNNFREE < N A B ( I ) CN NAB(13-I)=0.01»A(13-I)+NFREE CNTHE FOLLOWING HAS THE E F F E C T OF A DO LOOP WITH A NEG. INCREMENT CN L1 = 13-1 - 1 CN DO 4 6 2 4 L - 1 . L 1 CN CN624 C O N T I N U E CN GOTO 4 6 5 0 CN630 CONTINUE C N N A B ( I ) REMAINS AS N A B ( I ) CN NFREE=NFREE-NAB(I) CN640 CONTINUE CN650 CONTINUE CN NAVAIL=0 CN 0 0 4 6 6 8 1=1, 12 CN I F ( A ( I ) . L E . O ) G 0 T O 4668 CN NP(I)=NAB(I)/A(I)M00.0 CN668 CONTINUE GOTO 4 6 7 0 CN CN700 CONTINUE CNNAVAIL > NDEMAND C N N A B ( l ) REMAINS AS N A B ( I ) AND N P ( I ) AS N P ( I ) CN NAVAIL=NAVAIL-NDEM  NAB(i)=6.6i*A(i)  13:27:50 183 . 0 0 0 184 .OOO 185 . 0 0 0 186 OOO 187 . 0 0 0 188 . 0 0 0 189 . 0 0 0 190 . 0 0 0 191 . OOO 192 . 0 0 0 193 OOO 194 .000 195 . 0 0 0 196 . OOO 197 . 0 0 0 198 0 0 0 199 0 0 0 2 0 0 OOO 201 0 0 0 202 0 0 0 203 0 0 0 204 0 0 0 205 0 0 0 2 0 6 OOO 207 0 0 0 208 0 0 0 2 0 9 OOO 210 0 0 0 211 OOO 212 0 0 0 213 0 0 0 214 0 0 0 215 0 0 0 216 0 0 0 2 1 7 OOO 218 0 0 0 219 0 0 0 220 0 0 0 221 0 0 0 222 0 0 0 223 0 0 0 224 0 0 0 225 0 0 0 226 0 0 0 227 0 0 0 228 0 0 0 229 0 0 0 230 0 0 0 231 0 0 0 232 0 0 0 2 3 3 OOO 234 0 0 0 235 000 236 0 0 0 237 0 0 0 238 0 0 0 2 3 9 OOO 240 0 0 0  PAGE  P005  MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8)  0141 0142 0143 0144 0145 0146 0147 0148 0149 0150 0151 0152 0153 0154 0155 0156 0157 0158 0159 0160 0161 0162 0163 0164 0165 0166 0167 0168 0169 0170 017 1 0172 0173 0174 0175 0176  UMODEL  10-11-84  13:27:50  CN670 NN-0.0 241 .000 CN DO 4675 1-1,12 242 .000 CN NN-NN+NAB(I) 243 000 CN675 CONTINUE 244 .OOO CN IF(LAB.GE..1)G0T0 4765 245 .000 CN N-0. 246 .000 CN GOTO 4766 247 .000 CN65 CONTINUE 248 000 CN N-NN/LAB*100.0 249 000 CN IF(N.GT.4.)CALL FWRITE(ISINK.'GA=<R>,GB»<R>,N-<R>,NN-<R>. 250 000 CN ALAB"<R>.TNLOSS=<R>.AB=<R>.CM =<R>.AM»<R>.:',GA,GB,N,NN,LAB,TNLOSS, 251 .OOO CN BAB.CM,AM) 252 OOO CN66 CONTINUE 253 000 CN760 CONTINUE 254 000 C COMPUTE GROWTH POTENTIAL 255 000 IF(TEMP.LT.-.5JG0T0 226 256 000 TG-(.31298+ 046723*TEMP- .0096323*TEMP**2+ 258 000 A.00103B2*TEMP**3-.20755E-4 *TEMP* *4)/4 .27 259 000 IF(TG.LT.O)TG»0 260 000 GOTO 230 262 OOO 226 TG-0 263 OOO 230 NG-( -108.56+165.52*N-48.029*N"2+4.71 19*N**3)/100 265 000 NG1 -(-55.981+79.567 «N-9.8307 »N*•2)/100 266 000 NG2-(-55.981+79.567*NRGAES-9.8307*NRGAES*»2)/100 266 200 NG3-(-55.981 + 79.567>NRGG-9.B307*NRGG* *2)/100 266 40O CMNK CALL FWRITE ( I SINK .'STATEMENT11 N IS <R«4>.: '.N) 267 000 C'INK CALL FWRITE(ISINK.'STATEMENT 11 N2 IS <R*4>. :',N2) 268 000 IF(NG.LT.O)NG-0 269 000 IF(NG1.LT.6lNG1=6 270 000 IF(NG.GT.1)NG-1 271 000 IF(NG2.LT.O)NG2-0 271 200 IF(NG3.LT.O)NG3=0 271 400 IF(N.GT.3.3)NG1-1 272 000 IF(NRGAES.GT.3.3)NG2-1 272 200 IF(NRGG.GT.3.3)NG3-1 272 40O CMNK CALL FWRITE( ISINK.'STATEMENT 12 273 000 N IS <R»4>.: ' ,N) C*INK CALL FWRITE( ISINK, 'STATEMENT 12 274 000 N2 IS <RM>. :',N2) IFIWPbt.Gf.-i)WG=1 275 000 IF(WP0T.GT.-1)G0T0 235 276 OOO 277 OOO WG-1-O.8*(ABS(WP0T))/20.0 IF(WG.GT.1)WG-1 278 OOO IF(WG.LT.O)WG-0 279 000 235 CONTINUE 280 000 IF(KB.LT.1)MB- 1 281 000 C»INK CALL FWRITE(ISINK.'STATEMENT 13 N IS <R*4>.: ' ,N) 282 000 C*INK CALL FWRlTEdSINK.'STATEMENT 13 283 000 N2 IS <RM>. :'.N2) IF((JD.GT.182).AND.(DL.LE.13))DLG-1.0-(0.3*(13-DL)) 284 000 285 OOO IF(IAEST.E0.O)GA=GMAX*TG*WG*DLG*GLAB*NG1 285 200 IF(IAEST.EO.0)GA=GA+(GMAX*TG*WG*DLG*RGG*NG3) IF ( ( 1 AEST . EO. 1 ) • AND . (GRJD . EO. 6) ) G A = GM A X • f G * WG * D L G * R G A E S 000 * NG2 286 IF((IAEST.E0.1).AND.(GRJD.NE.0))GA=GMAX*TG*WG*DLG*RGAES*NG2 287 000 287 IF((IAEST.EO.1).AND.(GRJD.NE.0))GA=GA+(GMAX*TG*WG*DLG»RGG*NG3) 500 1020 CONTINUE 289 000 GBQBMAX*TG*WG*MB*LBG 290 000 G-GA+GB 291 000 IF( IAESTO.EO.1)G0T0 1350 291 300 IF((G.E0.O).AND.(JD.GT.151))IAESTO-1 291 600 IF((G.E0.O).AND.(JD.GT.151))JDAEST=JD 291 700 a  PAGE P006  MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) 0177 0178 0179 0180 0181 0182 0183 0184 0185 0186 0187 0188 0189 0190 0191 0192 0193 0194 0195 0196 0197 0198 0199 0200 0201 0202 0203 0204 0205 0206 0207 0208 0209 0210 021 1 0212 0213 0214 0215 0216 0217 0218 0219 0220 0221 0222 0223 0224 0225 0226 0227 0228 0229 0230  UMODEL  10-11-84  1350 CONTINUE IF( IAEST . EQ . 1 JGOtd 1355 IF((IAESTO.EO.1) AND.(G.NE.0))IAEST=1 IF((IAESTO.EO.1).AND.(G.NE.0))KB=1 IF((IAESTO.EO.1j AND.(G.NE 6))RGJD=JO IF( (IAESTO.EO.1).AND.(G.NE.0))GBMAX=AGBMAX 1355 CONTINUE 10O0 CONTINUE IFfKA.GE.1)GOTO 244 IF(G.GT .0)KA=> 1 GOfb 245 244 KA=KA+INCR 245 IF(GA.GT.O)TA-TA+GA IF(GB. GT . 6)fB = TB+GB IF (KB . GE . 1 )GOTO 250 IF(GB.GT.0)KB=1 GOTO 252 250 KB=KB+INCR IF(KB.GT.21)KB-21 IF(KB.LT.1)GOTO 260 252 MB=.99930-.14683*(KB-1)+.0056462*(KB-1)*«2 IF(MB.GT.1)MB=1 IF(KB.GT.18)MB-0 C«INK CALL FWRITE(I SINK,'STATEMENT*10 MB IS <R*4>.:•,MB) C COMPUTE PHOTOSYNTHESIS 260 IF((TEMP.LE.0).OR.(TEMP.GT.40)1G0TO 270 IF((TEMP.GE.20).AND.(TEMP.LE.25))GOTO 274 IF((TEMP.GE.5).AND.(TEMP.LT.20))GOTO 278 IF((TEMP.GT.25).AND.(TEMP.LE.35 j)GOTb 282 IF( ( TEMP. GT.O) .AND. ( TEMP . LT . 5) )TPSYN=>TEMP*0. 1052632 IF((TEMP.GT.O).AND.(TEMP.LT.5)(GOTO 300 IF ( (TEMP.GT.35).AND.(TEMP.LE.40))fPSYN=(40-TEMP)*6.1315789 IF((TEMP.GT.35).AND.(TEMP.LE.40))GOTO 300 270 TPSYN=0 GOTO 300 274 TPSYNM GOTO 300 278 TPSYN*1-(6.03158)*(20-fEMP) GOTO 300 282 TPSYN»1-(0.03421)*(TEMP-25) GOfb 300 300 IF(WP0T.LE.-3O)G0T0 330 WSYN=1+(O.O278)»WP0T IFfWSYN.Gt.i)WSYN=i GOTO 400 330 WSYN'O GOTO 400 C MULTIPLICATION BY .675 IS CONVERSION FOR C02 TO CH20 400 CONTINUE IF(KGR.NE 0)KGR=KGR+1 IF(GRAZIN(JD) NE.0.0)KGR=1 IF (KGR . LT . UGOTO 410 IFJKGR.GT.16)GRPSYN*6 0 IF(KGR.GT.16IG0T0 410 GRPSYN*(-5.1458+10.780*(KGR-1)- 1.3308*(KGR-1)**2 A+.04 2364*(KGR-1) **3)/100.0 410 PSYN=PMAX«TPSYN«WSYN*LAB*DL*0.675*(1.O+GRPSYN) T=T+PSYN  13:27:50 291,90O 292.20O 292.500 292.800 293.100 293.400 294.000 297.000 298.000 299.000 300.000 301.000 302 .000 303.000 304 .000 305.000 306.000 307 .000 308.000 309.000 310.000 311.000 312.000 313.000 314.000 315.000 316.000 317.000 318.000 319.000 320.000 321.000 322.000 323.000 324.000 325.000 326.000 327.000 328. OOO 329.000 330.000 331.000 332.000 333.000 334.000 335.000 336.000 337.000 338.000 339.000 340.000 34 1.000 342.000 343.000 344.000 345.000 346.000 347.000  PAGE P0O7  MICHIGAN  0231 0232 0233 0234 0235 0236 0237 0238 0239 0240 0241 0242 0243 0244 0245 0246 0247 0248 0249 0250 0251  0252 0253 0254 0255 0256 0257 0258 0259 0260 0261 0262 0263 0264 0265 0266 0267 0268 0269 0270 0271 0272 0273 0274 0275 0276  TERMINAL  SYSTEM  FORTRAN G ( 2 1 . B )  UMODEL  10 - 11-84  C COMPUTE R E S P I R A T I O N IF(TEMP.LT.5)GOT0 430 *LAB*(24 -DD* RESP=(-0.46107+O.069524*TEMP+O.0O13714*TEMP**2)/1000 A0.675«FRMAX GOTO 4 3 2 430 RESP-0 4 3 2 CONTINUE C COMPUTE NET PSYN NPSYN=PSYN-RESP TNPSYN=TNPSYN+NPSYN C COMPUTE ROOT R E S P I R A T I O N IF(TEMP.LT.5)RR=0 IF(STEMP.LT.5)G0TO 470 .675 RR»(-0.46107+6.66^52^*STEMP+6.0dl37'l4*StEMP»*2)/1000»LB6»DL« A*FRRMAX 4 7 0 CONTINUE CRS RS=RS-RR LBG=LBG-RR C COMPUTE SOURCE S T R E N G T H SS=G-NPSYN IF((G.GT.0).AND.(NPSYN.GT.0).AND.(SS.GT.0))SG=SG+SS IF((G.GT.O).AND.(NPSYN.LT.O).AND.(SS.GT.0))SG=SG+SS- ABS(NPSYN) IF(SS.GT.O)UDR=-0.0 IF(SS.LT.O)UDR=(PSYN-ABS(SS))/ABS(SS) C I S P S Y N ENOUGH TO SUPPORT GROWTH DEMAND IF(SS.LE.6JGOT0 540 TS-TS+SS C P S Y N I S NOT ENOUGH TO SUPPORT GROWTH RS=0.30*LBG IF(RS.LT.SS)GOTO 510 C R E S E R V E I S ENOUGH TO COVER SS CRS RS"RS-SS LBG=LBG-SS IF((IAEST.EO.O) AND.(GRdD.EO.0))GLABAB«GLABAB+G IF((IAEST.EO.O).AND.(GRjb.EO.O))GLAB=GLAB+G I F ( ( I A E S T . E O . O ) AND.(GRdD.NE.0))RGGAB"RGGAB+G IF((IAEST.EO.O).AND.(GRdD.NE.0))RGG RGG+G IF((IAEST.EO.1).AND.(GRdO.LE.RGJD))RGAB=RGAB*G I F ( ( I A E S T . E O . 1 ) AND.(GRdD.LE.RGdD))RGAES=RGAES+G I F ( ( I A E S T . EO. 1 ) .AND. (GRdO . GT . RGdD) )RGGAB=RGGAB+G IF((IAEST.EQ.1).AND.(GRdD.GT.RGdD))RGG=RGG+G CUMAB'CUMAB+G AB-=AB+G GOTO 5 7 0 C R E S E R V E S NOT ENOUGH TO COVER SS 5 1 0 O-RS-SS IF<(G+Dj.Lt.6)Gbtd 520 AB-AB+G+D LBG»LBG-SS-0 IF((IAEST.EO.O).AND.(GRdD E O O ) )GLABAB«GLABAB+G+b IF((IAEST.EO.O).AND.(GRdD.EO.O))GLAB"GLAB+G+D I F ( ( I A E S T . E O . O ) AND.(GRdD.NE.0))RGGAB=RGGAB+G+D IF((IAEST.EO.6).AND.(GRdD.NE.6))RGG RGG+G+b I F ( ( I A E S T . E O . 1 ) AND.(GRdD.LE.RGdD))RGAB=RGAB+G+D I F ( ( I A E S T . E O . 1 ) AND.(GRdO.LE.RGdD))RGAES=RGAES+G+0 I F ( ( I A E S T . E O . 1 ) . A N D . ( G R d O . G T . R G d D ) ) R G G A B = RGGAB+G+b I F ( ( I A E S T . E O . 1 ) AND.(GRdD GT.RGdD))RGG=RGG+G+D CUMAB=CUMAB+G+D S  c  PAGE  13:27:50 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 394 395 396 397 39B 399 40O 401 402 403  000 000 000 000 OOO 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 ooo 000 ooo 000 000 200 000 000 000 000 ooo 000 000 000 000 000 000 000 000 000 000 000 000 000 000 200 000 000 000 000 000 000 000 000 000  POOS  MICHIGAN  TERMINAL  0277  SYSTEM  520  0278 CPS 0279  FORTRAN  UMODEL  10-11-84  13:27:50  PAGE  404 .000  IF(G.LT.O)G»0  405  000  RS-0  407  000  408  000  GOTO C  G(21.8)  G=G+D  SOURCE  570  STRENGTH  <=  0  409  000  AB=AB+G  410  000  0281  IF((1AEST.EO.0).AND.(GRJD.EO.O))GLAB"GLAB+G  411  0282  IF((IAEST.EO.O).AND.(GRJD.EO.O))GLABAB=GLABAB+G  411  200  0283  IF((IAEST.EO.O)•AND.(GRJD.NE.0)>RGGAB=RGGAB+G  412  000  0284  0280  540  000  IF((IAEST.EO.O).AND.(GRJD.NE.0))RGG=RGG+G  413  000  0285  IF((IAEST.EO.1j.AND.(GRJD.LE.RGJD)JRGAB=RGAB+G  414  000  0286  IF((IAEST.EO.1).AND.(GRJD.LE.RGJD)JRGAES-RGAES+G  415  000  0287  I F ( ( I A E S T . E O . 1 ) . AND .( G R J D . G T . R G J D ) )RGGAB-=RGGAB+G  416  ooo  0288  IF((IAEST•EO.1).AND.(GRJD.GT.RGJD)jRGG=RGG*G  417  000  0289  TSSNEG»TSSNEG+ABS(SS)  418  000  0290  CUMAB'CUMAB+G  419  000  RS=RS+0.60*ABS(SS)  420  LBG'LBG+ABS(SS)  421  000  CONTINUE  422  000  423  000  CRS 0291 0292  570  0293 0294 0295 0296  575 C  IF(LBG.Lt.i.yRSP-6.  000  IF(LBG.LT.1.)G0T0575  424  000  RSP=RS/LBG«100.0  425  000  CONTINUE  426  000  427  000  COMPUTE  ABOVEGROUND  MORTALITY  (AM)  0297  AM-0  427  700  0298  AMG O A  428  400  0299  AMRGA-0  429  100.  0300  AMRGG=0  429  800  0301  PHENM=0.22594-0.010724*KA+0.00038151*KA"2  432  000  0302  IF(PHENM.LT.0.2)  PHENM=0.2  433  000  0303  IF(PHENM.GT.1.0)  PHENM-1.0  434  000  0304  IF(TEMP.LE.-2)FM=0.25  435  000  0305  IF(TEMP.GT.-2)  FM=0.  436  000  0306  IF(TEMP.LE.SO)  WAM=(0.02'(ABS(WPOT)-30))'PHENM  437  000  0307  I F ( t EMP.GT.30)  WAM=(6.025•(ABS(WPOT )- 3 0 ) j ' P H E N M  438  000  439  000  0308  IF(WP0T.GT.-3O)WAM=O  0309  IF(IAESTO.NE.1)GOTO  439  100  0310  AMG=(WAM+FM)'GLAB+PHENM2'GLAB  439  200  GOTO  439  300  031 1  1320  1330  0312  1320  AMG=(WAM+FM)'GLAB  439  400  0313  1330  CONTINUE  439  500  0314  AMRGA=(WAM+FM)*RGAES  441  000  0315  AMRGG=(WAM+FM)*RGG  442  000  0316  AM=AMRGA+AMRGG+AMG  443  000  0317  CM=CM+AM  444  000  C 0318 0319 0320 C  459  000  RGAES=RGAES-AMRGA  460  000  GLAB"GLAB-AMG  461  000  RGG-RGG-AMRGG  462  000  477  000  ALLOCATE  COMPUTE  MORTALITY  PROTEIN  TO  BIOMASS  TYPE  YIELD  0321  NN=N/100.0'GLABAB+RGAB'NRGAES/100.O+NRGG/100.O'RGGAB  478  000  0322  CPY=NN*6.25  479  000  0323  CPG=N*6.25  480  000  0324  CPRGA=NRGAES*6.25  481  000  0325  CPRGG=NRGG'6.25  481  100  0326  CPYG=CPG*GLABAB7I6O.6  481  200  0327  CPYRGA-CPRGA'RGAB/100.0  481  300  0328  CPYRGG=CPRGG'RGGAB/100.0  481  400  '  P009  MICHIGAN 0329 0330 0331 0332 0333 0334 0335 0336 0337 0338 0339 0340 0341 0342 0343 0344 0345 0346 0347 0348 0349 0350 0351 0352 0353 0354 0355 0356 0357 0358 0359 0360 0361 0362 0363 0364 0365 0366 0367 0368 0369 0370  TERMINAL  0375 0376 0377  G(21.8)  UMODEL  IF((N.LT.NMINY).AND.(GLABAB.GT.0)JNMG-0 IF((NRGAES LT.NMINYj.AND.(RGAB.GT.0)JNMRGA=0 IF((NRGG.LT.NMINY).AND.(RGGAB.GT.0))NMRGG=0 CPYMIN=CPYG*NMG+CPYRGA*NMRGA+CPYRGG*NMRGG C COMPUTE GRAZED M O R T A L I T Y GR=GRAZIN(i)D)/100*AB I F (GR . NE . 0 ) G R J D = J D I F ( G R . N E . 0 ) K B =1 GRKNI"GRJD-KNI IF(GRKNI.GT.28)G0T0 6000 GGBMAX O.054-GRKNI*0.0017357 6 0 0 0 CONTINUE IF(GR.NE.0)GBMAX"GGBMAX AB-AB-GR C A L L O C A T E GRAZED M O R T A L I T Y TO BIOMASS T Y P E GRAZ-GR I F ( G R A Z . E O . 6 ) G b f 0 1200 I F ( I A E S T . N E . 0 ) G 0 T 0 1100 GLAB"GLAB-GRAZ GLABAB=GLABAB-GRAZ GRAZ"0 GOTO 1 2 0 0 C IAEST.NE.O 1100 I F ( R G A E S . L T . G R A Z ) G O T O 1300 RGAES=RGAES-GRAZ RGAB"RGAB-GRAZ GRAZ=0 GOTO 1200 C RGAES.LT.GRAZ 1300 CONTINUE IF((RGAES.LT.GRAZ).AND.(RGA8.GE.GRAZ))GOTO 6010 C RGAES < GRAZ AND RGAB < GRAZ GRAZ"GRAZ-RGAB RGAES-0 RGAB=0 GOTO 6 0 2 0 6 0 1 0 CONTINUE C RGAES < GRAZ AND RGAB >" GRAZ RGAES-0 RGAB"RGAB-GRAZ a  GRAZ=6 GOTO 1200 CONTINUE I F ( G L A B . L T . GRAZ )Go"f0 GLAB"GLAB-GRAZ G L A B A B "GLABAB-GRAZ GRAZ"0 GOTO 1200 G L A B < GRAZ  6020  :  C 0371 0372 0373 0374  S Y S T E M FORTRAN  1360  1360 GLAB"6 GLABAB-GLABAB-GRAZ GRAZ"0 1200 CONTINUE C COMPUTE T O T A L L I V E ABOVEGROUND BIOMASS LAB=GLAB+RGG+RGAES C COMPUTE BELOWGRbUNb M O R T A L I T Y (BM) IF(WPOT.GT.0)WBM=0.04 IF(WP0T.GT.O)G0T0 840  10-11-84  13:27:50 482.000 483.000 484.000 485.000 4 8 6 OOO 487.000 4 8 8 . OOO 490.000 490.100 490.200 490.300 490.400 491.000 492.000 506.000 507.000 508.000 509.000 510.000 511.000 512.000 513.000 514.OOO 515.000 516.000 517.OOO 518.000 519.000 520.000 520.100 520.20O 520.300 520.400 520.500 520.600 520.700 520.800 520.900 521.000 521.10O 521.200 521.300 521.400 522.100 522.150 522.200 522.250 522.30O 522.350 522.400 522.450 522.500 525.000 526.000 527.000 528.000 529.000 530.000  PAGE  P010  MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8)  UMODEL  10-11-84  13:27:50  CWBM WBM*-(SY1**SB+(SY2**SB-SY1**SB)*<1.0-EXP(-SA* (WPOT-O)))/ CWBM «(1 0-EXP(-SA*(75-O))))*•(1/( SRI) DWPOT'DBLE(WPOT) CALL SCH15(DWBM,-DWP0T,DPAR15.DTAU1,DTAU2) WBM-SNGI. (DWBM) 840 CONTINUE BM=WBM*LBG*DMAX TM=TM+BM LBG*LBG-BM CRS RS=RS-RSP/100*BM 0385 IF(AB.LE.O)G0T0 1083 0386 RTSHT=LBG/AB 0387 1083 CONTINUE C COMPUTE LITTERFALL 0388 SD-SD+AM CRAIN IF(R3(JD).NE.0.)CALL FWRITECISINK,'R3(<I>) IS <R*4>.:',JD,R3(JD)) CRAIN IF(R4(JD).NE.O.)CALL FWRITE(I SINK.'R4(<I>) IS<R*4>. :',JD,R4(JD ) ) C*INK CALL FWRITE(ISINK,'R4(JD) IS <R*4>.:',R4(JD)) C*INK CALL FWRITEdSINK, 'Z1 IS <R*4>.:',Z1) 0389 LFM8.3E-4+1 .3E-3*R3( JD)*0. 10)*SD*R4( JD) SD-SD-LF 0390 C ALLOCATE LITTERFALL TO AB TYPE 0391 AB=AB-LF 0392 IF(LF.E0.O)G0T0 1305 0393 LF2 LF 0394 IF (GLABAB . LT . LF2 )G6TO 1310 0395 GLABAB=GLABAB-LF2 0396 LF2-0 0397 GOTO 1305 0398 1310 LF2-LF2-GLABAB 0399 GLABAB°0 0400 IF(RGG.LT.LF 2)GOf0 1315 0401 RGG=RGG-LF2 0402 LF2-0 0403 GOTO 1305 0404 1315 LF2=LF2-RGG 0405 RGG=0 0406 RGAB-RGAB-LF2 0407 1305 CONTINUE 0408 RETURN C2000 CONTINUE C STOP 0409 END •OPTIONS IN EFFECT* ID,EBCDIC,SOURCE.NOLIST,NOOECK,LOAD.NOMAP •OPTIONS IN EFFECT* NAME " UMODEL , LINECNT = 60 •STATISTICS* SOURCE STATEMENTS 409,PROGRAM SIZE • 14212 •STATISTICS* NO DIAGNOSTICS GENERATED 0378 0379 0380 0381 0382 0383 0384  3  531 000 532.000 533.000 534.000 535 000 536 000 537 000 538 000 539 000 540 000 54 1.000 542.OOO 543.000 544.000 545.000 546.000 547 000 548 000 549 000 550 000 551 000 552 000 553 000 553 050 553 100 553 150 553 200 553 260 553 270 553 280 553 300 553 350 553 400 553 450 553 500 553 550 553 600 553 650 553 700 554 000 555 000 556 000 557 000  PAGE P011  MICHIGAN TERMINAL SYSTEM FORTRAN GI21.8) 0001 0002 0003 0004  YZLIN  10-11-84  13:28:08  REAL FUNCTION YZLIN*8(X,Y.N.XL IN.I START,ISINK.JD,ICALL) IMPLicif R E A L » 8 ( A - H . b - Z ) 5 5 9 . REAL*8 X(N),Y(N) IF(ISTART.LE.0)ISTART=1 CTEST WRITE! ISiNK,35)X CTEST35 FORMAT('O'.'X='.10(1X.F7.3)) CTEST WRITEtISINK,36)Y CT EST 36 FORMAT ( ' 0 ' . 'Y=' . id( IX i F7 . 3 j ) 5 6 5 0005 NM1-N-1 0006 DO 10 I=ISTART,NM1 0007 i f ( (XLIN GE X( I )) AND. (XL IN LE X( t + 1 ) ) VGOTO 2 0 5 6 0008 10 CONTINUE 0009 WRITE(ISINK,30)XLIN,ICALL 0 0 1 0 3 0 F O R M A T ( ' - ' |''•••ERROR*** fIME=' , E 2 0 . 1 0 . ' - - O U T OF fNT FRpbLAf I O N ' / 5 A' RANGE--CALL NUMBER ' , 1 1 0 . ' . ' ) 0011 WRITE(ISINK.40)JD,ISTART,I,N.NM1 0 0 1 2 4 0 F O R M A T ( ' - ' . ' JD^ ' . I 10. ' : I ST AR1 - ' , I 1 0 , ' ; 1= ' . I 10 J ' •' N= ' ,1 ioT': ' 7 A' NM1-'.I10) C STOP 0 0 1 3 2 0 C O N T I N U E 5 7 7 . 0 0014 SL0PE'(Y(I+1)-Y(I))/(X(I+1)-X(I)) 0015 YZLIN'SLOPE*XLIN+(Y(I)-SL0PE*X(I)) 0 0 1 6 1 S T ART = 1 5 8 0 . 0 0 CTEST WRITE(ISINK,40)JD.ISTART,I,N.NM1 0017 RETURN 0 0 1 8 E N D 5 8 3 •OPTIONS IN EFFECT* ID,EBCDIC,SOURCE.NOLIST,NODECK,LOAD.NOMAP •OPTIONS IN EFFECT* NAME = YZLIN , LINECNT = 60 * S T A T l s t l C S * S O U R C E ST AT EMENtS ' 1 8 .PROGRAM S I Z E ' = 9 6 2 •STATISTICS* NO DIAGNOSTICS GENERATED  558.000 O O O 560.000 561.000 562.000 563.000 564.000 000 566.000 567.000 8 OOO 569.000 570.000 7 i OOO 572.000 573.000 5 7 4 . 0 0 0 575.000 576.000 0 0 578.000 579.000 0 581.000 582.000 .666  PAGE P001  M I C H I G A N  0 0 0 1 0 0 0 2  T E R M I N A L  S Y S T E M  F O R T R A N  S U B R O U T I N E •  G ( 2 1 . 8 )  R E I N I T  1 0 - 1 1 - 8 4  1 3 : 2 8 : 0 9  5 8 4  R E I N I T  R E A L  N . N G . N 2  0 0 0 3  R E A L  N 0 3 . N H 4 . L B G . N P , N A B , N L P , N L . N M L . N L T . N V G  2  0 0 0 4  R E A L  T N L O S S . N L O . N C Y C L E , N T O  3  1  P A G E  . 0 0 0  0 0 0 0 0 0 .OOO  0 0 0 5  R E A L  0 0 0 6  R E A L  J . N V O . N V . N O E M . N V O L T  5 . 0 0 0  0 0 0 7  R E A L  D M A X , N R E C Y C . N C Y C , N 0 3 , N G 1 , N G 2 , N G 3  6  N A V A I L , N L O S S . L A B , N F R E E , N M I N . N N . M B . N P S Y N . K I L L . L F  0 0 0 8  R E A L  0 0 0 9  I N T E G E R  0 0 1 0  0 0 1  1  N R G G , N R G A E S  I N T E G E R  , N M I N Y  I N C R , N K . K A . K B . R K , J R . D P . W P C H  0 0 0  6  2 0 O  7  O O O  8  O O O  9  0 0 0  11  0 0 0  12  0 0 0  1 3  0 0 0  P S Y N . T P S Y N . W S Y N , N P S Y N , T . T N P S Y N  14  0 0 0  C O M M O N  G . W G . N G . T G . T 1 , N 2  15  0 0 0  C O M M O N  R E S P . R R  1 6  0 0 0  C O M M O N  D M A X , L A B  17  0 0 0  18  0 0 0  C O M M O N  G R J D . F U N  4 . 0 0 0  P , A 1 , B ( 1 0 ) . G M A X , I T I M E  0 0 1 2  C O M M O N  0 0 1 3  C O M M O N  0 0 1 4  C O M M O N  W P 0 T . W 1 , N  0 0 1 5  C O M M O N  0 0 1 6 0 0 1 7 0 0 1 8  A B . R S . C C . S D . S S . T S . D . R S P T E M P , T O ( 1 0 ) , T M 1 ( 1 0 ) , D D I 1 2 ) , D L , S T E M P  0 0 1 9  C O M M O N  T A , T B , S G , T M , N R E C Y C  0 0 2 0  C O M M O N  C 4 , C 5 , S 4 . S 5 , I S I N K  0 0 2 1  C O M M O N  D R ( 1 2 ) , R M ( 1 2 ) . R D ( 1 2 )  2 0  0 0 0  0 0 2 2  C O M M O N  J ( 1 2 ) . A ( 1 2 ) , N V 0 ( 1 2 )  2 1  0 0 0  0 0 2 3  C O M M O N  W P A O ( 6 ) . W P C  2 2  0 0 0  0 0 2 4  C O M M O N  W P S  2 3  0 0 0  0 0 2 5  C O M M O N  U 3 . U 4 . N 0 3 . N H 4  2 4  0 0 0  0 0 2 6  C O M M O N  I N C R , N K , K A , K B , R K , J R , R J  2 5  0 0 0  1 9  1 ( 6 ) . WPC2"(6 ) , W P C 3 ( 6 ) . WPC4'(6 ) . W P C 5 ( 6 ) . W P C 6 ( 6 )  1 ( 6 ) , W P S 2 ( 6 ) , W P S 3 ( 6 ) , W P S 4 ( 6 ) . W P S 5 ( 6 ) , W P S 6 ( 6 )  0 0 0  0 0 2 7  C O M M O N  G A , G B , M B , L B G , J D  2 6  o o o  0 0 2 8  C O M M O N  N P ( 1 2 ) , N A B ( 1 2 ) , N D E M , N L P ( 1 2 ) , N L ( 1 2 ) , N M L ( 1 2 ) , N L T  2 7  0 0 0  2 8  o o o  0 0 2 9  COMMON  0 0 3 0  C O M M O N  0 0 3 1  C O M M O N  N V G ( i 2 ) . N V ( i i j . N V O L f  2 9  Z 1 , R 3 ( 3 6 5 ) , R 4 ( 3 6 5 )  0 0 3 3  C O M M O N C O M M O N  0 0 0  3 0  0 0 0  3 2  0 0 0  R N ( 2 0 ) , R P ( 2 0 ) . P R E C , R 1 ( 2 0 ) . R 2 ( 2 0 ) , 0 P ( 2 0 ) , P M ( 2 0 )  3 3  0 0 0  T N L O S S , N L O ( 1 2 ) . N C Y C L E , N T O ( 1 2 ) , T L O S S O , N A V A I L , N F R E E . N M I N , N N  0 0 3 2  KIMv(12),FM,AM,CM,KILL,BM.LF  . P H E N M  0 0 3 4  C O M M O N  S Y 1 , S Y 2 , S A , S B , W B M . R N D M I  3 4  0 0 3 5  C O M M O N  I S O U R C . I P A S S . L O C N . W P C H , R N O M I  3 6  0 0 0  0 0 3 6  C O M M O N  3 7  0 0 0  D L A O ( 1 0 ) , D L C 1 ( 1 0 ) , D L S 1 ( 1 0 ) . P I . W A M . N C Y C  0 0 0  0 O 3 7  C O M M O N  3 8  0 0 0  0 0 3 8  C O M M O N  I S T T . I S T S T , I S T W . G R A , K N E M P , K N E M P I . K N I  3 9  0 0 0  0 0 3 9  C O M M O N  G R J D . F U N , G B M A X . G G B M A X . D L G . I S H I F . N C H  4 0  0 0 0  0 0 4 0  C O M M O N  I A E S T , A G B M A X , F U N 2 . R G A E S , F U N S  4 1  0 0 0  0 0 4 1  C O M M O N  M O R T J O , M O R T W P , C U M A B . R G G . A M R G G , A M R G , f L A B  4 2  0 0 0  0 0 4 2  C O M M O N  R T S H T . P M A X , F R M A X , F R R M A X , T S S N E G  4 3  0 0 0  0 0 4 3  C O M M O N  K N E M P 2 . K N E M P S . N R G G , N R G A E S . G R A Z . A M G , A M R G A  4 4  0 0 0  0 O 4 4  C O M M O N  G L A B . G L A B A B . R G G A B . R G A B . C P G . C P R G A , C P R G G . L F 2  4 5  0 0 4 5  C O M M O N  N M G . N M R G A . N M R G G . C P Y M I N , N M I N Y  4 6  0 0 0  0 0 4 6  C O M M O N  C P Y G , C P Y R G A , C P Y R G G , P H E N M 2  4 7  0 0 0  0 0 4 7  C O M M O N  N G 1 . N G 2 . N G 3 . G A 1 , G A 2 . I A E S T O . R G J D . J D A E S T  4 8  0 0 0  C O M M O N  Z , D A M P D . G R K N I  N Y C , C P , U O R . C P Y , G R A Z I N ( 3 6 5 ) . K G R , G R . G R P S Y N  0 0 0  4 9  0 0 0  0 0 4 9  J D * 0  5 8 6  0 0 0  0 0 5 0  K A = 0  5 8 7  0 0 0  0 0 5 1  K B = 0  5 8 8  0 0 0  0 0 5 2  N D E M = 0  5 8 9  0 0 0  0 0 5 3  N L T = 0  5 9 0  o o o  0 0 5 4  N V O L T - 0  5 9 1  0 0 0  0 0 5 5  T A = 0  5 9 2  0 0 5 6  T B ' O  5 9 3  0 0 0  0 0 5 7  S G = 0  5 9 4  0 0 0  0 0 5 8  T S ' O  5 9 5  o o o  0 0 4 8  0 0 0  P 0 0 1  MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8)  REINIT  0059 AB-0 0060 CM-0 0O61 TM=0 0062 KGR-0 0063 T=0 0064 CUMAB-0 0065 IAEST-0 0066 GRUD-0 0067 RGdD-0 0068 KNI-0 0069 KNEMPI-0 0O70 IAESTO-0 0071 JDAEST-0 0072 DLGM.O 0073 TSSNEG-0 0O74 GLAB-0 0075 RGG=0 0O76 RGAES=0 0077 GLABA8-0 0078 RGAB-0 0079 RGGAB-0 GBMAX-.054 0080 0081 TNPSYN-0 0082 DO 900 1-1.12 0083 DD(I)»0 0084 900 CONTINUE 0085 00 905 1-1,365 0086 R3(I )=0 0087 R4(I)-0 0088 905 CONTINUE 0089 DO 910 1-1.20 PM(I)=0 0090 DP(I)-0 0091 0092 910 CONTINUE 0093 GGBMAX -0.0054 0094 RETURN 0095 END •OPTIONS IN EFFECT' ID. EBCDIC, SOURCE .NOLIST ,NODECK. LOAD.NOMAP •OPTIONS IN EFFECT' NAME = REINIT . LINECNT » 60 •STATISTICS* SOURCE STATEMENTS 95.PROGRAM SIZE • S T A T I S T I C S ' N O 01 AGNOSTICS GENERATED  tO-11-84  13:28:09 596.000 597 000 598 000 599 000 600 000 600 050 600 100 600 150 600 200 600 250 600 300 600 350 600 400 600 450 600 500 600 550 600 600 600 650 600 700 600 750 600 800 600 850 601 000 602 000 603 000 604 000 605 000 606 000 607 000 608 000 609 000 610 000 611 000 612 000 612 200 613 000 614 000  730  PAGE P002  MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) 0OO1 0002 0003 00O4 0005 0006 0007 0008 0009 0010 001 1 0012 0O13 0014 0015 0016 0017 0018 0019 0020 0021 0022 0023 0024 0025 0026 0027 0028 0029 0030 0031 0032 0033 0034 0035 0036 0037 0038 0039 0040 0041 0042 0043 0044 0045 0046 0047 0048 0049 0050 0051 0052 0053 0054 0055 0056 0057 0058  ASHRN  10-11-84  SUBROUTINE ASHRN REAL N.NG.N2 REAL N03. NH4 , LBG. NP.NAB . NLP , NL .NML. NLT, NVG REAL TNL0S5.NLO.NCYCLE,NTO REAL NAVAIL.NLOSS.LAB.NFREE.NMIN.NN,MB.NPSYN,KILL,LF REAL d.NVO.NV.NDEM.NVOLT REAL DMAX,NRECYC.NCYC.N03.NG1,NG2,NG3 REAL NRGG.NRGAES.NMINY INTEGER INCR.NK.KA.KB.RK,JR,DP.WPCH INTEGER GRJD.FUN COMMON P,A1.B(10).GMAX,ITIME COMMON AB.RS.CC.SD.SS.TS.D.RSP COMMON TEMP.TO(10),TM1(10).DD(12).DL,STEMP COMMON WPOT,W1,N COMMON PSYN.TPSYN.WSYN,NPSYN,T.TNPSYN COMMON G.WG.NG.TG.T1,N2 COMMON RESP,RR COMMON DMAX.LAB COMMON TA.TB.SG.TM,NRECYC COMMON C4,C5,S4,S5,ISINK COMMON 0R(12),RM(12),R0(12) COMMON J(12),A<12).NV0(12) COMMON WPA0(6).WPCI(6).WPC2(6).WPC3I6),WPC4(6),WPC5(6),WPC6<6> COMMON WPS1(6),WPS2(6),WPS3(6).WPS4(6).WPS5(6).WPS6I6) COMMON U3,U4,N03,NH4 COMMON INCR.NK.KA.KB.RK.JR.RJ COMMON GA,GB,MB,LBG,JD COMMON NP(12),NAB(12),NDEM,NLP(12),NL(12),NML(12).NLT COMMON NVG(12),NV(12J.NV0LT COMMON Z1,R3<365),R4(365) COMMON TNLOSS,NLOC12),NCYCLE,NTO(12),TLOSSO,NAVAIL .NFREE.NMIN.NN COMMON NMV(12),FM,AM,CM,KILL,BM.LF,PHENM COMMON RN(20).RP(20).PREC.R1(20),R2(20).DP(20).PM(20) COMMON SY1,SY2,SA,SB.WBM,RNDMI COMMON ISOURC.IPASS,LOCN.WPCH.RNOMI COMMON DLAOt10).DLC1(10),DLS1(10).PI,WAM,NCYC COMMON NYC,CP,UDR,CPY.GRAZIN(365),KGR,GR,GRPSYN COMMON ISTT,ISTST,ISTW,GRA,KNEMP,KNEMPI,KNI COMMON GRJD,FUN,GBMAX,GGBMAX.DLG,ISHIF,NCH COMMON IAEST,AGBMAX.FUN2.RGAES.FUN3 COMMON MORTJD.MORTWP,CUMAB.RGG.AMRGG,AMRG.TLAB COMMON RTSHT,PMAX,FRMAX,FRRMAX.TSSNEG COMMON KNEMP2.KNEMP3.NRGG,NRGAES.GRAZ,AMG,AMRGA COMMON GLAB.GLABAB,RGGAB.RGAB.CPG.CPRGA.CPRGG.LF2 COMMON NMG,NMRGA,NMRGG,CPYMIN.NMINY COMMON CPYG,CPYRGA,CPYRGG,PHENM2 COMMON NG1,NG2.NG3.GA1.GA2.IAESTO.RGJO.JOAEST COMMON Z.DAMPD,GRKNI IF(LOCN.E0.5)G0T0 100 R3(148)=10 R4(148)>0.127 R3(154)-5. R4(154)=0.508 R3(165)=7. R4(165)=3.084 R3(177)=1S. R4( 177) = 3.556 R3(202)=2.3  13:28:15  PAGE P001  614 .007 1 000 2 000 3 .000 4 OOO 5 OOO 6 000 6 200 7 000 8 000 9 000 1 1 000 12 000 13 000 14 000 15 000 16 000 17 000 18 000 19 OOO 20 000 21 000 22 000 23 000 24 000 25 000 26 000 27 000 28 000 29 000 30 000 32 000 33 000 34 000 36 000 37 000 38 000 39 000 40 000 4 1 000 42 000 43 000 44 000 45.000 46.000 47.000 48 000 49 000 614 343 614 350 614 357 614 364 614 371 614 378 614 385 614 392 614 399 614 406  ro  MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) 0059 0060 0061 0062 0063 0064 0065 0066 0067 0068 0069 0070 0071 0072 0073 0074 0075 0O76 0077 0078 0079 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 0095 0096 0097 0098 0099 0100 0101 0102 0103 0104 0105 0106 0107 0108 0109 0110 0111 0112 01 13 0114 0115 01 16  R4(202)-4.417 R3(260)°13. R4(260)=0.6845 R3(289)=7. R4(289)=2.358 GOTO 200 100 CONTINUE R3(140)=3. R4(1401-13.54 R3(142)=8. R4(142)»7.937 R3(143)-15. R4(143)*0.169 R3(144)=25. R4(144)=0.152 R3(145)-=3. R4(145 j=6.847 R3(160)-3. R4(160)=2.12 R3(161j=2 R4(161)"3.175 R3(173)=13. R4( 173)=6 977 R3(174)=14. R4(174)=0.091 R3(177)=6. R4( 177)=0.423 R3(1B0)*29. R4(186j=0.043 R3(195)»8. R4(195)=0.635 R3(197)=4 R4(197)=0.635 R3(199)=7. R4(199)»0.725 R3(202)=8. R4(2O2)=0.159 R3(221j=3. R4(221)=2.54 R3(222)=9. R4(222)=6.564 R3(225)=7. R4(225)=0.141 R3(226)=i.1 R4(226)=1.15 R3(228)=1.9 R4(228)-13.36 R3(230)=7. R4(230)=-0.363 R3(231)"7. R4(231)=0.544 R3(236)»4. R4(236)=6.9525 R3(237)=5. R4(237)»1.016 R3(239)=5. R4<239)*1.524 R3(247)=4.  ASHRN  10-11-84  13:28: 15  PAGE P0O2  614.413 614.420 614.427 614.434 614.441 614.448 614.455 614.462 614.469 614.476 614.483 614.490 614.497 614.504 614.511 614.518 614.525 614.532 614.539 614.546 614.553 614.560 614.567 614.574 614.581 614.588 614.595 614.602 614.609 614.616 614.623 614.630 614.637 614.644 614.651 614.658 614.665 614.672 614.679 614.686 614.693 614.70O 614.707 614.714 614.721 614.728 614.735 614.742 614.749 614.756 614.763 614.770 614.777 614.784 614.791 614.798 614.805 614.812  ro  MICHIGAN TERMINAL  SYSTEM FORTRAN GI21.8)  ASHRN  10-11-84  0117 R4(247)=3.175 01 18 R3(253)=2 8 6 1 4 . 0119 R4(253)=5.89 0120 R3(256)=6. ' 0121 R 4 ( 2 S 6 ) = 0 . 4 2 0122 R3(258)»1. 0123 R4(258)°2.54 0124 200 CONTINUE 0125 RETURN 0126 END 'OPTIONS IN E F F E C T ' 1 0 .EBCDIC! SOURCE. NOL if's"f ^NObECKVLOAbTmMAp' •OPTIONS IN EFFECT* NAME - ASHRN , LINECNT * 60 •STATISTICS* SOURCE STATEMENTS • 126,PROGRAM S I Z E = 1094 • S T A T I S T I C S ' N O DIAGNOSTICS GENERATED  13:28:15 8  3  6  1  614.819 2 6 614.833 614.840 4 847 614.854 614.861 614.868 614.875 614.882  PAGE POOS  M I C H I G A N  TERMINAL  SYSTEM  FORTRAN  0 0 0 1  SUBROUTINE  0OO2  REAL  0 0 0 3  REAL  0 0 0 4  REAL  G ( 2 1 . 8 )  R A I N  1 0 - 1 1 - 8 4  R A I N  1 3 : 2 8 : 2 1  PAGE  6 1 5 . 0 0 0  N . N G . N 2  1 . 0 0 0  N 0 3 . N H 4 , L B G . N P . N A B . N L P . N L . NML, NLT,  NVG  T N L O S S , N L O . N C Y C L E , N T O  2  0 0 0  3  0 0 0  0 0 0 5  REAL  N A V A I L . N L O S S . L A B , N F R E E . N M I N . N N . M B . N P S Y N . K I L L , L F  4  0 0 0  0 0 0 6  REAL  d . N V O . N V . N O E M . N V O L T  5  0 0 0  00O7  REAL  D M A X . N R E C Y C . N C Y C . N 0 3 . N G 1 . N G 2 . N G 3  6  0 0 0  0 0 0 8  REAL  N R G G . N R G A E S . N M I N Y  6 . 2 0 0  0 0 0 9  INTEGER  I N C R . N K . K A . K B , R K . J R . D P . W P C H  0 0 1 0  INTEGER  0 0 1 1  COMMON  P , A 1 , B ( 1 0 ) . G M A X , I T I M E  G R J D , F U N  7  OOO  8  0 0 0  9  OOO  0 O 1 2  COMMON  A B . R S . C C . S D . S S . T S . D . R S P  1 1  0 0 0  0 0 1 3  COMMON  T E M P . T O I 1 0 ) , T M 1 ( 1 0 ) , 0 D ( 1 2 ) , D L , S T E M P  12  0 0 0  0 O 1 4  COMMON  W P 0 T . W 1 . N  13  0 0 0  0 0 1 3  COMMON  P S Y N . T P S Y N . W S Y N , N P S Y N . T . T N P S Y N  14  0 0 0  0 0 1 6  COMMON  G . W G . N G . T G . T 1 , N 2  15  0 0 0  0 0 1 7  COMMON  R E S P . R R  16  0 0 0  0 0 1 8  COMMON  D M A X , L A B  17  0 0 0  0 O 1 9  COMMON  T A . T B . S G . T M , N R E C Y C  18  0 0 0  0 0 2 0  COMMON  C 4 , C 5 , S 4 . S 5 . I S I N K  19  0 0 0  0 0 2 1  COMMON  D R ( 1 2 ) , R M ( 1 2 ) . R D ( 1 2 )  2 0  0 0 0  0 0 2 2  COMMON  J ( 1 2 ) , A ( 1 2 ) , N V 0 ( 1 2 )  21  0 0 2 3 0 0 2 4  COMMON COMMON  0 0 2 5  COMMON  W P A O ( 6 ) . W P C i ( 6 ) . WPC2"( 6 ) , W P C 3 ( 6') , W P C 4 ( 6 ) , W P C 5 ( 6 ) . W P C 6 < 6 ) WPS 1 ( 6 ) , W P S 2 ( 6 ) , W P S 3 ( 6 ) . W P S 4 ( 6 ) . W P S 5 ( 6 ) . W P S 6 ( 6 ) U 3 , U 4 , N 0 3 , N H 4  22 23  ooo ooo 0 0 0  24  0 0 0  25  0 0 0  26  0 0 0  27  0 0 0  0 0 2 6  COMMON  0 0 2 7  COMMON  0 0 2 8  COMMON  0 0 2 9  COMMON  N V G ( 1 2 ) , N V ( 1 2 ) , N V O L T  28  0 0 0  0 0 3 0  COMMON  Z 1 . R 3 ( 3 6 5 ) , R 4 ( 3 6 5 )  2 9  0 0 0  0 0 3 1  COMMON  30  0 0 0  0 0 3 2  COMMON  I N C R . N K . K A . K B . R K . J R . R J G A . G B . M B . L B G , J D N P ( 1 2 ) , N A B ( 1 2 ) , N D E M . N L P ( 1 2 ) , N L ( 1 2 ) , N M L (  1 2 ) . N L T  T N L O S S . N L O ( 1 2 ) . N C Y C L E , N T O ( 1 2 ) . T L O S S O . N A V A I L . N F R E E . N M I N , N N N M V ( 1 2 ) . F M . A M , C M . K I L L . B M , L F . P H E N M  32  0 0 0  0 O 3 3  COMMON  R N ( 2 0 ) . R P ( 2 0 ) . P R E C , R 1 ( 2 0 ) , R 2 ( 2 O ) , 0 P ( 2 0 ) , P M ( 2 O )  33  0 0 0  0 0 3 4  COMMON  S Y 1 , S Y 2 , S A , S B . W B M . R N O M I  34  0 0 0  0 0 3 5  COMMON  I S O U R C . I P A S S , L O C N . W P C H . R N O M I  36  0 0 0  0 0 3 6  COMMON  D L A O ( 1 0 ) , D L C 1 ( 1 0 ) , D L S 1 ( 1 0 ) , P I . W A M . N C Y C  37  0 0 3 7  COMMON  N Y C , C P , U D R , C P Y , G R A Z I N ( 3 6 5 ) , K G R , G R . G R P S Y N  38  0 0 0  0 0 3 8  COMMON  I S T T , I S T S T , I S T W , G R A , K N E M P , K N E M P I . K N I  39  0 0 0  0 0 3 9  COMMON  G R J D , F U N , G B M A X , G G B M A X . D L G . I S H I F . N C H  4 0 41  0 0 4 0  COMMON COMMON  MORTJD.MORTWP.CUMAB.RGG.AMRGG.AMRG.TLAB  42  0 0 0  0 0 4 2  COMMON  R T S H T . P M A X . F R M A X . F R R M A X . T S S N E G  4 3  0 0 0  0 0 4 3 0 0 4 4  COMMON  K N E M P 2 . K N E M P 3 . N R G G . N R G A E S . G R A Z . A M G . A M R G A  44  0 0 0  COMMON  G L A B , G L A B A B , R G G A B , R G A B , C P G . C P R G A , C P R G G , L F 2  4 5  0 0 4 5  COMMON  NMG,NMRGA,NMRGG.CPYMIN.NMINY  46  0 0 0  0 0 4 6  COMMON  C P Y G , C P Y R G A , C P Y R G G , P H E N M 2  47  0 0 0  0 0 4 7  COMMON  N G 1 , N G 2 . N G 3 . G A 1 , G A 2 , I A E S T O . R G J D . J D A E S T  48  0 0 4 8  COMMON  Z,DAMPD,GRKNI  ooo  0 0 4 9  R N O M I = R A N D ( 1 . 0 )  6 4 3  2 0 0  0 0 5 0  DO  6 4 3  8 0 0  0 0 5 2  49  1 = 1 . 1 2  R K - 1 5 0 3 5  0 0 5 3  CONTINUE R N ( R k ) = F R A N D T 6 ) * 3 . 1 • 1 0  0 0 5 4  I F ( R N ( R K ) . L T . 0 . 8 ) G 0 T 0 C M N K  0 0 5 5  5 3 5 0  S T , A G B M A X . F U N 2 , R G A E S . F U N 3  ooo  0 0 4 1  0 0 5 1  IAE  0 0 0  C*INK  C A L L  5 0 3 5  FWRITE ( I S INK , ' S T A T E M E N T S  I  IS  < I " 4 > .  : ' , I )  C A L L FWRIf E ( I S I N K , ' S T A T E M E N T S RK IS < I * 4 > . : ' ,RK) R P ( R K ) = ( ( 2 . 7 1 8 2 8 1 8 * * 6 . 6 5 7 1 ) « ( R N ( R K ) • « ( - 1 . 1 6 7 2 ) ) * A ( 2 . 7 1 B 2 8 1 8 * « ( - O . 0 3 1 4 6 8 * R N ( R K ) ) ) ) / 6 0  0 0 0  0 0 0  0 0 0  6 4 4  4 0 0  6 4 5  0 0 0  6 4 5  6 0 0  6 4 6  2 0 0  6 4 6  8 0 0  6 4 7  4 0 0  6 4 8  0 0 0  6 4 8  60O  P001  MICHIGAN TERMINAL SYSTEM FORTRAN G(21.B) 0056 0057  RAIN  10-11- 84  RP(RK)"FRAND(0)*RP(RK) PREC=RN(RK)*RP(RK) C'INK CALL FWRITE(ISINK,'RP(RK)=<R*4>, RN(RK)=<R*4>, PREC=<R*4>, RM(I)=< C ' I N K A R » 4 > . OR(I)-=<R*4>.:'.RP(RK).RN(RK),PREC,RM(I),0R(I)) C'INK I F ( P R E C . G T . ( 4 « R M ( I ) / 0 R ( I ) ) ) C A L L FWRITE(I SINK,'STATEMENT #4B PREC C'INKATOO LARGE - R E J E C T . : ' ) 0058 IF(PREC.GT.(4*RM(I)/DR(I)))G0TO 5035 0O59 PM(I)»PM(I)+PREC 0060 I F ( ( ( R M ( I ) - 0 . 1 0 ' R M d )) LT.PMd)).AND.((RM(I)+0.10*RM(I)) .GT. APM(I))) GOTO 5130 0061 5110 I F ( P M ( I ) . G T . R M ( I ) ) PM(I)=PM(I)-PREC C'INK IF(PM(I).GT.RM(I))CALL FWRITE(ISINK,'STATEMENT #4A REJECT C'INKAMONTHLY RAIN - TOO L A R G E . : ' ) 0OG2 IF(PM(I).GT.RM(I))G0TO 5035 0O63 RK=RK+1 0064 DPI I)-RK 0065 GOTO 5035 0066 5130 CONTINUE C ASSIGN DATES TO RAIN C'INK CALL FWRITE(I SINK,'STATEMENT*5 ASSIGN DATES TO RAIN. : ' C'INK CALL FWRITE( ISINK, 'STATEMENT#5 OAYSWRAIN CONST IS <R*4>. : ' , D R ( I ) ) C'INK CALL FWRITEdSINK,'STATEMENT#5 OAYSWRAIN IS < I « 4 > . : ' , D P ( D ) 0067 DO 5340 L ' l . R K 0068 IF(I.EO.I) R1(L)»FRAND(0)*31 0069 IF(I.E0.2) R1(L)»FRAND(0)*28 0070 I F < I . E 0 . 3 ) Ri(L)=FRAND(0)*31 0071 •• IF(1 E 0 . 4 ) R1(L)=FRAND(0)*30 0072 I F d . E Q . 5 ) R1(L)"FRAND(0)*31 0073 IF(I.E0.6) R1(L)»FRAND(0)'30 0074 I F d . E Q . 7 ) R1(L)"FRAND(0)*31 0075 I F d . E Q . 8 ) R1(L)=FRAND(0)'3t 0076 IF d . E O . 9 ) R1(L)•FRAND(6)*30 0077 I F ( I . E O . I O ) R1(L)=FRAND(0)'31 I F d . E 0 . 1 1 ) R1(L)"FRAND(0)'30 0078 0079 I F d . EO. 12) R1(L)"FRANb(6)'31 0080 I F ( I . E O . 1 ) R2(L)=0 IFCI.E0.2) R2(L)'31 0081 0082 IF( I . F.b. 3) R2(L)=59 0083 I F d . E 0 . 4 ) R2(L)"90 0084 I F ( I . E 0 . 5 ) R2(L)=120 0O85 IF(I E 0 . 6 ) R2(L)'151 0086 I F ( I . E 0 . 7 ) R2(L)-181 0087 I F ( I . E 0 . 8 ) R2(L)=212 0088 IF(I.E0.9) R2(Li-243 0089 IF(I EO.10) R2(L)*273 0090 • I F d . E O . 11) R 2 ( L ) » 3 0 4 0091 IF(I.EO.12) R2(C)'334 0092 RJ=R1(L)+R2(L) 0093 JR=INT(RJ+0.5) C* INK CALL F W R i f E d S i N K , ' S T A t E M E N f * 6 JR IS <I'4>. : ' . JR) C'INK CALL FWRITE(ISINK,'STATEMENT#6 L IS < I * 4 > . : ' , L ) 0094 R3(JR)'RN(L) 0O9S R4(JR)»RPJL) 0096 5340 CONTINUE 0097 5350 CONTINUE 0098 RETURN 0099 END •OPTIONS IN EFFECT' ID.EBCDIC.SOURCE.NOLIST.NODECK,LOAD.NOMAP  13 28:21 649.200 649.800 650.40O 651.000 651.600 652.200 652.800 653.400 654.000 654.600 655.200 655.800 656.400 657.000 657.600 658.200 658.800 659.400 660.000 660.600 .661.200 661.800 662.400 663.000 663.600 664.200 664.800 665.400 666.000 666.600 667.200 667.800 668.400 669.000 669.600 670.200 670.800 671.400 672.000 672.600 673.200 673.800 674.400 675 .000 675.600 676.200 676.800 677.400 678.000 678.600 679.200 679.800 680.400 681.000 681.600 682.200 682.800  PAGE P002  •  ro oo  MICHIGAN 0001 0002 0OO3 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 0016 0017 0018 0020 0021 0O22 0023 0024 0025 0O26 0027 0028 0029 0030 0031 0032 0033 0034 0035 0036 0037 0038 0039 0040 0041 0042 0043 0044 0045 0O46 0047 0048 0049 0050 0051 0052 0053 0054  TERMINAL  SYSTEM  FORTRAN  G(21.8)  CHOICE  SUBROUTINE CHOICE R E A L N.NG.N2 REAL N03.NH4.LBG.NP.NAB,NLP,NL.NML,NLT.NVG REAL TNLOSS.NLO,NCYCLE,NTO REAL N A V A I L , N L O S S . L A B . N F R E E . N M I N . N N , M B . N P S Y N . K I L L REAL J,NVO,NV.NDEM,NVOLT REAL DMAX,NRECYC.NCYC,N03,NG1,NG2.NG3 R E A L NRGG,NRGAES,NMINY I N T E G E R INCR,NK,KA,KB.RK,dR,DP.WPCH INTEGER GRJD.FUN COMMON P . A 1 . B ( 1 0 ) , G M A X , I T I M E COMMON A B . R S . C C , S D , S S . T S . D . R S P COMMON T E M P . T O C 1 0 ) , T M 1 ( 1 0 ) , D D ( 1 2 ) , 0 L . S T E M P COMMON WPOT,W1,N COMMON P S Y N , T P S Y N , W S Y N , N P S Y N , T , T N P S Y N COMMON G.WG,NG,TG,T1.N2 COMMON RESP,RR COMMON DMAX,LAB  10-11-84  LF  COMMON C 4 . C 5 . 5 4 , S 5 . I S I N K COMMON D R ( t 2 ) , R M ( 1 2 ) , R D ( 1 2 ) COMMON J ( 1 2 ) , A ( 1 2 ) , N V O ( 1 2 ) COMMON WPA016),WPC1(6),WPC2(6).WPC3(6),WPC4(6),WPC5(6),WPC6(6) COMMON WPS1(6),WPS2(6).WPS3(6),WPS4(6).WPS5I6),WPS6<6) COMMON U3,U4,N03,NH4 COMMON I N C R . N K . K A . K B . R K . d R . R d COMMON GA.GB.MB.LBG.dD COMMON N P ( 1 2 ) . N A B ( 1 2 ) , N D E M , N L P ( 1 2 ) , N L ( 1 2 ) , N M L ( 1 2 ) , N L T COMMON N V G ( 1 2 ) . N V ( 1 2 ) . N V O L T COMMON Z 1 , R 3 ( 3 6 5 ) , R 4 ( 3 6 5 ) COMMON TNLOSS,NLO(12),NCYCLE,NTO(12).TLOSSO,NAVAIL,NFREE.NMIN.NN COMMON N M V ( 1 2 ) , F M , A M . C M , K I L L , B M . L F . P H E N M COMMON R N ( 2 0 ) , R P ( 2 0 ) , P R E C . R 1 ( 2 O ) , R 2 ( 2 O ) . 0 P ( 2 0 ) . P M ( 2 0 ) COMMON SY1,SY2,SA,SB.WBM.RNDMI COMMON ISOURC, IPASS.LOCN,WPCH.RNOMI COMMON D L A O f 1 0 ) . D L C 1 ( 1 0 ) . D L S 1 ( 1 0 ) . P I . W A M . N C Y C COMMON N Y C , C P , U D R , C P Y , G R A Z I N ( 3 6 5 ) , K G R . G R . G R P S Y N COMMON I S T T , 1ST S T , ISTW, GRA ,KNEMP ,KNEMP I , KNI COMMON GRJD,FUN,GBMAX,GGBMAX,DLG,I S H I F . N C H COMMON I A E S T . A G B M A X . F U N 2 , R G A E S , F U N 3 COMMON MORTJD,MORTWP,CUMAB,RGG.AMRGG,AMRG,fLAB COMMON RTSHT.PMAX,FRMAX,FRRMAX.TSSNEG COMMON KNEMP2,KNEMP3.NRGG.NRGAES.GRAZ,AMG.AMRGA COMMON G L A B . G L A B A B , RGGAB. RGAB. CPG, CPRGA . CPRGG. L F 2 COMMON NMG,NMRGA,NMRGG,CPYMIN.NMINY COMMON CPYG.CPYRGA,CPYRGG,PHENM2 COMMON N G 1 . N G 2 . N G 3 . G A 1 , G A 2 , I A E S T O . R G J D . J D A E S T COMMON Z.DAMPD,GRKNI LOGICAL'I S T A R ( 1 ) / ' « ' / 15 C O N T I N U E WRITE!ISINK.5) 5 FORMAT('-','CHOOSE GEOGRAPHIC LOCATION') WRITEfISINK,10) 10 F O R M A T ( ' - ' . ' P L E A S E ENTER NUMBER S E L E C T I O N : ' / A' 1 - KAMLOOPS'/ B ' 2 - CRANBROOk'/ C 3 - BRANSON L A B S T U D Y ' / D' 4 - ASHNOLA 1 9 6 8 ' /  1  13:28:29 6 8 4 .000 1 000 2 .000 3 000 4 000 S 000 6 000 6 200 7 000 a 000 9 000 H 000 12 0 0 0 13 0 0 0 14 0 0 0 15 0 0 0 16 0 0 0 17 0 0 0 18 19 0 0 0 20 000 21 0 0 0 22 0 0 0 23 0 0 0 24 0 0 0 25 0 0 0 26 0 0 0 27 0 0 0 28 OOO 29 0 0 0 3 0 OOO 32 OOO 33 000 34 0 0 0 36 0 0 0 37 0 0 0 38 0 0 0 39.000 40.000 41 .000 42 OOO 43 0 0 0 44 0 0 0 45.000 46.000 47.000 48.000 49.000 686.000 687 0 0 0 688 000 689 000 690 000 691 0 0 0 692 0 0 0 693.000 6 9 4 .000 695.000  PAGE P 0 0 1  M I C H I G A N  TERMINAL  SYSTEM E'  0 0 5 5  30  -  G ( 2 1 . 8 )  ASHNOLA  PAGE  1 9 6 7 ' )  696  CONTINUE  0 0 5 6 0 0 5 7 0 0 5 8  5  FORTRAN  6 9 8 . O O O  W R I T E ( I S I N K , 2 0 )  6 9 9 . 0 0 0  FORMAT  ( ' - ' , ' C H O O S E  WATER  7 0 0 . O O O  P O T E N T I A L ' )  7 0 1 . 0 0 0  W R I T E ( I S I N K , 2 5 )  0 0 6 0  COO  6 9 7 . 0 0 0  R E A D ( I S 0 U R C . S T A R . E N D " 1 5 ) L 0 C N 2 0  0 0 5 9 25  F O R M A T ( ' - ' , ' P L E A S E  ENTER  NUMBER  7 0 2 . 0 0 0  S E L E C T I O N : ' /  A '  1  -  INTERIOR  D R Y ' /  7 0 3 . 0 0 0  B'  2  -  INTERIOR  I N T E R M E D . ' /  7 0 4 . 0 0 0  C  3  -  INTERIOR  W E T ' /  7 0 5 . 0 0 0  0 '  4  -  ASHNOLA  1 9 6 8 ' /  7 0 6 . 0 0 0  E'  5  -  ASHNOLA  1 9 6 7 ' )  7 0 7 . 0 0 0  0 0 6 1  R E A D ( I S O U R C . S T A R . E N D » 3 0 ) W P C H  7 0 8 . 0 0 0  0 0 6 2  RETURN  7 0 9 . 0 0 0  • O P T I O N S • O P T I O N S  7 1 0 . O O O  END  0 0 6 3 I N I N  E F F E C T * E F F E C T *  • S T A T I S T I C S * • S T A T I S T I C S *  1 0 . E B C D I C , S O U R C E . N O L I S T . N O D E C K , L O A D . N O M A P NAME  SOURCE NO  P 0 0 2  «  CHOICE  STATEMENTS  D I A G N O S T I C S  . •  LINECNT  *  63,PROGRAM  6 0 S I Z E  »  772  GENERATED  CO  O  M I C H I G A N  TERMINAL  SYSTEM  0 0 0 1  REAL  0 0 0 2  REAL  0 0 0 3  REAL  FORTRAN  G ( 2 1 . 8 )  FUNCTION  1 0 - 1 1 - 8 4  DLFNC  D L F N C ( I C O D E )  71 1  0 0 0  1  0 0 0  2  0 0 0  N . N G . N 2 N03 ,NH4 , L B G . NP. NAB . N L P , NL .NML , NLT,  NVG  PAGE  1 3 : 2 8 : 3 2  0 0 0 4  REAL  T N L O S S . N L O . N C Y C L E , N T O  3  0 0 0  0 0 0 5  REAL  N A V A I L . N L O S S . L A B , N F R E E . N M I N , N N , M B , N P S Y N , K I L L .LF  4  OOO  0 0 0 6  REAL  d . N V O . N V . N D E M . N V O L T  5  0 0 0  0 0 0 7  REAL  D M A X , N R E C Y C , N C Y C . N 0 3 , N G 1 , N G 2 , N G 3  6  0 0 0  0 0 0 8  REAL  N R G G . N R G A E S , N M I N Y  6  2 0 0  0 0 0 9  INTEGER  7  0 0 0  8  0 0 0  0 0 1 0  INTEGER  0 0 1 1  COMMON  0 0 1 2  COMMON  0 0 1 3  COMMON  0 0 1 4  COMMON  I N C R . N K . K A , K B , R K , J R . D P , W P C H G R J D , F U N  9  0 0 0  A B , R S . C C . S D , S S , T S , D . R S P  1 1  ooo  T E M P , T O ( 1 0 ) , T M 1 ( 1 0 ) , D D I 1 2 ) , D L . S T E M P  12  0 0 0  W P 0 T . W 1 , N  13  0 0 0 0 0 0  P,A  1 . B ( 1 0 ) , G M A X , I T I M E  0 0 1 5  COMMON  P S Y N . T P S Y N . W S Y N . N P S Y N , T , T N P S Y N  14  0 O 1 6  COMMON  G , W G , N G , T G , T 1 . N 2  15  0 0 0  0 0 1 7  COMMON  R E S P . R R  16  0 0 0  0 O 1 8  COMMON  D M A X , L A B  17  0 0 0  0 0 1 9  COMMON  T A , T B , S G , T M , N R E C Y C  18  ooo  0 0 2 0  COMMON  C 4 . C 5 . S 4 . S S . I S I N K  19  0 0 0  0 0 2 1  COMMON  D R ( 1 2 ) . R M ( 1 2 ) . R D ( 1 2 )  20  ooo  0 0 2 2  COMMON  J ( 1 2 ) , A ( 1 2 ) , N V O ( 1 2 )  21  0 0 0  0 0 2 3  COMMON  W P A 0 I 6 ) , W P C 1 ( 6 ) . W P C 2 ( 6 ) , W P C 3 ( 6 ) , W P C 4 ( 6 ) . W P C 5 ( 6 ) . W P C 6 ( 6 )  22  0 0 0  0 0 2 4  COMMON  23  0 0 0  0 0 2 5  COMMON  24  0 0 0  0 0 2 6  COMMON  25  0 0 0  0 0 2 7  COMMON  G A . G B . M B . L B G , J D  26  0 0 0  0 0 2 8  COMMON  N P ( 1 2 ) , N A B ( 1 2 ) , N D E M , N L P ( 1 2 ) , N L ( 1 2 ) , N M L ( 1 2 ) . N L T  27  0 0 0  0 0 2 9  COMMON  N V G ( 1 2 ) . N V ( 1 2 ) , N V 0 L T  28  0 0 0  0 0 3 0  COMMON  Z 1 , R 3 ( 3 6 5 ) , R 4 ( 3 6 5 )  29  0 0 0  0 0 3 1  COMMON  T N L O S S , N L O ( 1 2 ) , N C Y C L E , N T O ( 1 2 ) , T L O S S O . N A V A I L . N F R E E . N M I N . N N  30  0 0 0  0 0 3 2  COMMON  N M V ( 1 2 ) . F M . A M . C M . K I L L , B M . L F , P H E N M  32  0 0 0  0 0 3 3  COMMON  R N ( 2 0 ) , R P ( 2 0 ) . P R E C , R 1 ( 2 0 ) , R 2 ( 2 0 ) . D P ( 2 0 ) , P M ( 2 0 )  33  0 0 0  0 0 3 4  COMMON  S Y 1 , S Y 2 , S A . S B , W B M , R N D M I  34  0 0 0  0 0 3 5  COMMON  I S O U R C , I P A S S , L O C N , W P C H , R N O M I  36  0 0 0 0 0 0 0 0 0  W P S K 6 )  , W P S 2 ( 6 ) . W P S 3 ( 6 ) . W P S 4 ( 6 ) . W P S 5 ( 6 ) , W P S 6 ( 6 )  U 3 . U 4 . N 0 3 . N H 4 INCR ,NK, KA, KB, RK, JR . R J  0 0 3 6  COMMON  D L A O ( 1 0 ) , D L C 1 ( 1 0 ) , D L S 1 ( 1 0 ) . P I . W A M . N C Y C  37  0 0 3 7  COMMON  N Y C , C P , U D R , C P Y . G R A Z I N ( 3 6 5 ) , K G R . G R . G R P S Y N  38  0 0 3 8  COMMON  I S T T . I S T S T . I S T W , G R A . K N E M P . K N E M P I . K N I  39  ooo  4 0  0 0 0  4 1  0 0 0 0 0 0  0 O 3 9  COMMON  0 0 4 0  COMMON  G R J D . F U N . G B M A X . G G B M A X , D L G . I  S H I F . N C H  0 0 4 1  COMMON  0 0 4 2  COMMON  R T S H T , P M A X , F R M A X . F R R M A X . T S S N E G  43  0 0 4 3  COMMON  K N E M P 2 , K N E M P 3 , N R G G . N R G A E S , G R A Z , A M G , A M R G A  44  ooo ooo  0 0 4 4  COMMON  G L A B . G L A B A B . R G G A B . R G A B . C P G . C P R G A , C P R G G . L F 2  45  0 0 0  0 0 4 5  COMMON  NMG.NMRGA.NMRGG.CPYMIN,NMINY  46  0 0 0 0 0 0  I A E S T . A G B M A X . F U N 2 . R G A E S , F U N 3 MORT J D , MORTWP . C U M A B . RGG, AMRGG, AMRG,  TLAB  42  0 0 4 6  COMMON  C P Y G , C P Y R G A , C P Y R G G , P H E N M 2  47  0 0 4 7  COMMON  N G 1 . N G 2 . N G 3 , G A 1 . G A 2 . I A E S T O . R G J D . J D A E S T  48  0 0 0  0 0 4 8  COMMON  Z,DAMPD,GRKNI  49  ooo  0 0 4 9  G O T O ( 1 0 , 2 0 . 3 0 . 4 0 . 5 0 ) , L O C N  713  0 0 0 0 0 0  0 0 5 0  10  CONTINUE  714  0 0 5 1  2 0  CONTINUE  715  0 0 0  0 0 5 2  4 0  CONTINUE  716  0 0 0  0 0 5 3  5 0  717  0 0 0  718  0 0 0  719 7 2 0  ooo ooo  721  0 0 0 '  722  0 0 0  0 0 5 4  CONTINUE D L F N C = D L A O ( L 0 C N ) / 2 . O + D L C 1 ( L O C N ) * C O S ( P I A - S I N ( P I ' J D / P )  0 0 5 5  RETURN  0 0 5 6  3 0 C  CONTINUE B R A N S O N ( 1 9 5 6 )  LAB  STUDY  * J D / P ) + D L S 1 ( L O C N )  P 0 0 1  M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G(21.B)  D L F N C  1 0 1 1 8 4  0057 D L F N C 1 6 . 0 0 0 5 8 R E T U R N 7 0059 E N D • O P T I O N S I N EFFECT* ID, EBCDIC, S O U R C E . N O L I S T.N O D E C K, L O A D ,N O M A P ' O P T I O N S I N EFFECT*NAME D L F N C L I N F C N T * 60 •STATISTICS* S O U R C ES T A T E M E N T S * 5 9 . P R O G R A M SIZE 620 •STATISTICS* N O D I A G N O S T I C S G E N E R A T E D 3  3  2  1 3 : 2 8 : 3 2  4  723.000 .000 725.000  P A G E P 0 0 2  M I C H I G A N  TERMINAL  SYSTEM  FORTRAN  G ( 2 1 . B )  U I N I T  1 0 - 1 1 - 8 4  0 0 0 1  SUBROUTINE  U I N I T  0 0 0 2  REAL  0 0 0 3  REAL  N 0 3 , N H 4 , L B G . N P , N A B , N L P . N L . N M L . N L T . N V G  0 0 0 4  REAL  0 0 0 5  REAL  0 0 0 6  REAL  0 0 0 7  REAL  0 0 0 8  REAL  0 0 0 9  INTEGER  PAGE  1 3 : 2 8 : 3 9 726  0 0 0  1  0 0 0  2  0 0 0  T N L O S S . N L O . N C Y C L E , N T O  3  0 0 0  N A V A I L . N L O S S . L A B . N F R E E . N M I N . N N . M B , N P S Y N . K I L L . L F  4  0 0 0  d . N V O . N V , N D E M . N V O L T  5  0 0 0  D M A X , N R E C Y C . N C Y C , N 0 3 , N G 1 , N G 2 , N G 3  6  0 0 0  N . N G . N 2  NRGG, NRGAES , NMINY INCR , NK, KA . KB , RK , JR , DP . WPCH G R J D , F U N  6  20O  7  0 0 0  8  0 0 0  9  0 0 0  11  0 0 0  0 0 1 0  INTEGER  001 1  COMMON  P . A t , 8 ( 1 0 ) , G M A X , I T I M E  0 0 1 2  COMMON  A B . R S . C C . S D . S S . T S . D . R S P  0 0 1 3  COMMON  T E M P , T O ( 1 0 ) , T M 1 ( 1 0 ) , D D ( 1 2 ) , D L , S T E M P  12  0 0 0  0 0 1 4  COMMON  13  0 0 0 0 0 0 0 0 0  W P 0 T . W 1 . N  0 0 1 5  COMMON  P S Y N , T P S Y N , W S Y N . N P S Y N . T . T N P S Y N  14  0 0 1 6  COMMON  G . W G . N G . T G . T I , N 2  15  0 0 1 7  COMMDN  R E S P , R R  16  0 0 0  0 0 1 8  COMMON  D M A X , L A B  17  0 0 0  0 0 1 9  COMMON  T A , T B , S G , T M , N R E C Y C  18  0 0 0  0 0 2 0  COMMON  C 4 , C 5 . S 4 , S 5 . I S I N K  19  0 0 0  D R ( 1 2 ) , R M ( 1 2 ) , R D ( 1 2 )  20  0 0 0  J ( 1 2 ) , A ( 1 2 ) , N V O ( 1 2 )  21  OOO  22  0 0 0  23  0 0 0  24  0 0 0  25  0 0 0  G A , G B , M B , L B G , J D  26  0 0 0  COMMON  0 0 2 1 0 0 2 2  COMMON  0 0 2 3  COMMON  0 0 2 4  COMMON  0 0 2 5  COMMON  0 0 2 6  COMMON  0 0 2 7  COMMON  0 0 2 8  COMMON  N P ( 1 2 ) , N A 8 ( 1 2 ) , N D E M , N L P ( 1 2 ) , N L ( ( 2 ) , N M L ( 1 2 ) , N L T  27  0 0 0  0 0 2 9  COMMON  N V G ( 1 2 ) , N V ( 1 2 ) . N V O L T  28  OOO  0 0 3 0  COMMON  Z 1 , R 3 ( 3 6 5 ) , R 4 ( 3 6 5 )  29  0 0 0  0 0 3 1  COMMON  T N L O S S . N L O ( 1 2 ) . N C Y C L E . N T O ( 1 2 ) , T L O S S O , N A V A I L , N F R E E , N M I N , N N  3 0  0 0 0  N M V ( 1 2 ) , F M , A M , C M , K I L L , B M , L F , P H E N M  32  0 0 0  33  0 0 0  S Y 1 , S Y 2 , S A , S B , W B M , R N D M I  34  0 0 0  W P A b i 6 ) . W P C 1 ( 6 ) , W P C 2 ' ( 6 ) . W P C 3 ( 6 )'. W P C 4 < 6 ) . W P C 5 ( 6 >. W P C 6 < 6 V W P S 1 ( 6 ) . W P S 2 ( 6 ) , W P S 3 ( 6 ) . W P S 4 ( 6 ) . W P S 5 ( 6 ) . W P S 6 ( 6 ) U 3 . U 4 . N 0 3 . N H 4 I NCR ,N K , KA , K B , RK, JR , R J  0 0 3 2  COMMON  0 0 3 3  COMMON  0 0 3 4  COMMON  0 0 3 5  COMMON  I S O U R C . I P A S S . L O C N . W P C H , R N O M I  36  0 0 0  0 0 3 6  COMMON  D L A O ( 1 0 ) , D L C 1 ( 1 0 ) , D L S 1 ( 1 0 ) . P I . W A M . N C Y C  37  0 0 0  0 0 3 7  COMMON  N Y C , C P , U D R . C P Y , G R A Z I N ( 3 6 5 ) , K G R . G R , G R P S Y N  38  OOO  0 0 3 8  COMMON  I S T T , I S T S T . I S T W . G R A , K N E M P . K N E M P I . K N I  39  0 0 0  0 0 3 9  COMMON  40  0 0 0  0 0 4 0  COMMON  41  0 0 0  0 0 4 1  COMMON  MORT J D . MORT WP, CUMAB , R G G , AMRGG, AMRG, f t  42  0 0 0  0 0 4 2  COMMON  RTSHT , PMAX , FRMAX, FRRMAX , TSSNEG  43  0 0 0  0 0 4 3  COMMON  K N E M P 2 , K N E M P 3 , N R G G , N R G A E S , G R A Z , A M G , A M R G A  44  0 0 0  0 0 4 4  COMMON  G L A B , G L A B A B , R G G A B . R G A B . C P G . C P R G A . C P R G G . L F 2  45  0 0 0  0 0 4 5  COMMON  0 0 4 6  COMMON  0 0 4 7  COMMON  0 0 4 8  COMMON  0 0 4 9  C A L L  R N ( 2 0 ) , R P ( 2 0 )  . P R E C . R K 2 0 )  , R 2 ( 2 0 )  G R J D . F U N , G B M A X , G G B M A X . D L G . I  ,DP( 2 0 ) . PM(  2 0 )  S H I F . N C H  I A E S T , A G B M A X . F U N 2 , R G A E S , F U N 3  NMG.NMRGA , NMRGG. C P Y M I N .  AB  46  NMINY  C P Y G , C P Y R G A . C P Y R G G , P H E N M 2 N G 1. N G 2 , N G 3 . G A 1. G A 2 . I A E S T O . R G J D .  JDAEST  Z . D A M P D , G R K N I  D F A U L T ( ' 1 - M O D E L . O  ' )  0 0 0  47  0 0 0  48  0 0 0  4 9  0 0 0  728  0 0 0  7 2 9  0 0 0  0 0 5 0  C A L L  0 0 5 1  RETURN  7 3 0  0 0 0  0 0 5 2  END  731  OOO  C M R E A D ( ' M O D E L . C 2  ' )  • O P t i O N S  IN  EFFECT •  I D , EBCDIC , SOURCE , NOLI ST , NODECK, LOAD . NOMAP  •OPTIONS  IN  E F F E C T  NAME  SOURCE  • S T A T I S T I C S * • S T A T I S T I C S *  4  NO  *  U I N I T  STATEMENTS  D I A G N O S T I C S  . "  GENERATED  LINECNT  *  52.PROGRAM  6 0 S I Z E  -  3 3 0  P001  MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) 0001  SCH15  10-11-84  SUBROUTINE SCH15(F,X.P,TAU1,TAU2) C SUBROUTINE SCHI5 WAS WRITTEN B. WONG, FACULTY OF FORESTRY 0002 IMPLICIT REAL*8(A-H,0-Z) DIMENSION P(4) 0OO3 0004 CALL FTNCMD!'DEFAULT ib»*SINK*:') IOUT-10 0005 Y1B=P0WER(P(3),P(2),IERR1,I0UT,1) 0006 0O07 1FUERR1 NE.0)G0T0l6 0008 . Y2B=P0WER(P(4),P(2),IERR2,10UT,2) 0009 IF(IERR2.NE.O)GOT020 0O10 ET=1 DO-DEXP(-P(1)*(X-TAU1)) 001 1 ET2-1.D0-DEXP(-P(1)*(TAU2-TAU1)) 0012 F* POWER ( (Y1B+(Y2B-Y1B)*(ET/ET2M,(1. DO/P( 2) ), IERRF , I OUT, 3 ) 0O13 IF(IERRF NE O)G0rO3O 0O14 RETURN 10 CONTINUE 0015 0016 20 CONTINUE 0017 30 CONTINUE 0018 WRITE!10.50)P 0O19 50 FORMAT!' '.'THE PARAMETERS ARE ( l THROUGH 4j:'/IX,4D20•i6) STOP 0O2O END 0021 •OPTIONS IN EFFECT* ID,EBCDIC,SOURCE.NOLI ST.NODECK.LOAD.NOMAP •OPTIONS IN EFFECT* NAME • SCH15 . LINECNT = 60 •STATISTICS* SOURCE STATEMENTS • 21,PROGRAM SIZE » 10O6 •STATISTICS* NO DIAGNOSTICS GENERATED  13:28:42 732 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752  OOO 200 000 000 000 OOO 000 000  ooo  000 000 000 000 000 000 000 000 000  ooo 000 ooo 000  PAGE P001  MICHIGAN  TERMINAL  0001 C C C C C C C C C C C C C  0002 0003 0O04 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 0O16 0017 0018 0019 0020 0021 0022 0023 0024 0025 0O26 0027 0028 0029 0030 0031  c c c c c c c c c c c c  SYSTEM  FORTRAN  G(21.8)  POWER  10-11-84  REAL FUNCTION P0WER*8(X,Y,I ERR,IOUT,ICOUNT) F U N C T I O N POWER WAS WRITTEN BY B . WONG, F A C U L T Y OF F O R E S T R Y . AND I S STORED I N THE ROKA L I B R A R Y . THE F U N C T I O N SUBPROGRAM, POWER. E V A L U A T E S THE R E A L - V A L U E O POWER. X " Y , WHERE P O S S I B L E . C U R R E N T L Y , THE F U N C T I O N I S NOT E Q U I P P E D TO HANDLE COMPLEX WITH NON-ZERO IMAGINARY COMPONENTS. I ERR  MEANING  0  -1 -2  N  -  0  E R R O R S  0."Y I S U N D E F I N E D . WHEN Y<0.. X<0. , AND Y I S NOT AN I N T E G E R , SO THE IMAGINARY COMPONENT OF THE POWER IS NON-ZERO.  I F THE I E R R - V A L U E RETURNEO I S NOT I N THE ABOVE T A B L E , T H E RETURNED I E R R - V A L U E I S THE SUM OF T A B U L A T E D I E R R - V A L U E S CORRESPONDING ERRORS ARE OCCURRING I N COMBINATION.  IMPLICIT REAL*8(A-H.0-Z) LOGICAL*1 XLTO,YLTO,ERROUT ERROUT".TRUE. IF(IOUT.LT.0)ERROUT".FALSE. IERR=0  i F (V. NE. 6. boTcsof 616  c  WHOSE  IOUT R E L A T E S TO D I A G N O S T I C OUTPUT: I F IOUT I S N E G A T I V E . T H E N THE D I A G N O S T I C OUTPUT I S D I S A B L E D . I F IOUT I S N O N N E G A T I V E , THEN IOUT I S THE NUMBER OF THE L O G I C A L I N P U T / O U T P U T U N I T ONTO WHICH D I A G N O S T I C OUTPUT I S WRITTEN.  POWER'1.DO CALL RTNCHK(X,Y,IERR,IOUT,ICOUNT,ERROUT,860,8120) CONTINUE 10 IF(X.LE.O.DO)G0T02O POWER"X"Y CALL RTNCHk(X,Y,IERR,IOUT.ICOUNT,ERROUT,870.& 130) 20 CONTINUE XLTO'(X.LT.O.OO) YLtO'(V.Lt.O.DO) IF(XLTO.AND.(.N0T.(YLTO)))GOT030 IF(XLTO.AND.YLTO)G0T04O I F ( ( .NOT . ( X L T O ) ) . AND . ( . NOT . ( Y L T O ) ) ) G O T 0 5 0 ( 0 . " Y ) I S U N D E F I N E D WHEN Y<0--ERROR RETURN - 1 . IERR-IERR-1 S E T D E F A U L T ("ERROR") V A L U E OF "POWER" TO 1. POWER"1.DO CALL RTNCHK(X,Y.I ERR,IOUT.ICOUNT.ERROUT.880,8140) CONTINUE 30 . P O W E R " ( ( D A B S ( X ) ) * * Y ) * O N E N E G ( Y , I ERR) CALL RTNCHK(X,Y,IERR,IOUT,ICOUNT,ERROUT,890,8150) CONTINUE 40 POWER" 1 . 0 0 / ( ( ( D A B S ( X ) ) " D A B S ( Y ) ) ' 0 N E N E G ( D A B S ( Y ) , I E R R ) ) CALL RTNCHK(X,Y,IERR,IOUT,ICOUNT,ERROUT.8100.8160) CONTINUE 50 POWER"0.00 CALL RTNCHK(X,Y,I ERR,IOUT,ICOUNT,ERROUT,8110,8170)  c  VALUES  13:28:43 753 753 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808  PAGE 000 20O 400 000 000 OOO 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000  P001  , '  ooo 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000  ooo 000 000 000 000 000 000 000 000  ooo CO  cn  MICHIGAN  TERMINAL  SYSTEM  FORTRAN  G<21.8)  0032 60 CONTINUE 7 0 C O N T I N U E 0033 80 CONTINUE 0034 90 CONTINUE 0035 0036 100 CONTINUE 0O37 1 10 CONTINUE 0038 RETURN 120 CONTINUE 0039 0040 130 CONTINUE 0041 140 CONTINUE 0042 150 CONTINUE 0043 160 CONTINUE 0044 170 CONTINUE 0045 RETURN 0046 END •OPTIONS I N E F F E C T * I D , E B C D I C , SOURCE .NOLIST ,NODECK , LOAD, NOMAP •OPTIONS I N E F F E C T * NAME - POWER . LINECNT « 60 •STATISTICS* SOURCE S T A T E M E N T S 46,PROGRAM S I Z E •STATISTICS* NO D I A G N O S T I C S G E N E R A T E D  PAGE  P002  809.000 810000 811.000 812.000 8 1 3 OOO 814.000 815.000  816.656  817.OOO 818.OOO 819 0 0 0 820.000 821.000  822.666 823.000  CO  cn  M I C H I G A N  TERMINAL  SYSTEM  0 0 0 1  FORTRAN  REAL C  FUNCTION  C  FORESTRY,  C  FOR  C C  AND  C  AN  AND  ONENEG  ( 2 ) IF  C  ONENEG  WAS  IS  ONENEG  Y  IS A  NOT  +  8 ( Y , I  WRITTEN  STORED  IN  1.  BY THE  IF  EQUALS  - 1 .  Y  IF  I S V  I N T E G E R - V A L U E D .  B.  WONG,  1 " / " 0 D D  Y - - >  E V E N .  IS  FACULTY  824  OF  L I B R A R Y . AND  -2  IS  ADDED  OF  Y  IS  PAGE  2 0 0  824  4 0 0  8 2 5  0 0 0  826  OOO  827  0 0 0  TO  I ERR,  828  0 0 0  FOR  8 2 9  0 0 0  8 3 0  0 0 0  E V A L U A T I O N .  0002  I M P L I C I T  831  0 0 0  0 0 0 3  T L R N C E - O . D O  8 3 2  0 0 0  0 0 0 4  Y1NEG»Y  8 3 3  0 0 0 5  I F ( D A B S ( Y - D F L I N T ( Y ) ) . L E . T L R N C E ) G 0 T O 2 O C  IF  R E A L M S ( A - H . O - Z )  X  IS  N E G A T I V E ,  C  Y  IS  NOT  C  THEN  THE  AN  POWER  C  IN  T H I S  C  TO  EVALUATE  C A S E .  C  I N S T E A D ,  Y  C  AND  IS  ANO  INTEGER, IS  IS  C O M P L E X - V A L U E D .  THESE  T H I S  ROUTINES  POWER  ROUNDED  MAKE  NO  ATTEMPT  EXACTLY; TO  THE  NEAREST  0 0 0  834  0 0 0  8 3 5  0 0 0  8 3 6  0 0 0  8 3 7  0 0 0  8 3 8  0 0 0  8 3 9  0 0 0  8 4 0  INTEGER,  0 0 0  84 1  OOO  0 0 0 6  I E R R - I E R R - 2  842  0 0 0  0 0 0 7  Y 1 N E G - R N D E 0 ( Y , 1 . D O )  8 4 3  0 0 0  844  0 0 0  0 0 0 8  20  A  - 2  ADDED  TO  THE  ERROR-TYPE  INDICATOR,  I ERR.  CONTINUE  0 0 0 9  REM*DMOD(Y1NEG,2.00)  8 4 5  0 0 0  0 0 1 0  I F ( R E M . E 0 . 0 . D 0 ) G D T 0 1 0  8 4 6  0 0 0  0 0 1 1  0 N E N E G - - 1 . 0 0  8 4 7  0 0 1 2 10  0 0 0 0 0 0  O N E N E G - 1 . 0 0  8 5 0  0 0 0  RETURN  851  0 0 0  END  852  0 0 0  CONTINUE  0 0 1 4 0 0 1 5 0 0 1 6 • O P T I O N S  I N  EFFECT^  •OPTIONS  IN  EFFECT^  • S T A T I S T I C S ^ • S T A T I S T I C S ^  I D . E B C D I C , S O U R C E , N O L I S T , N O D E C K , L O A D , N O M A P NAME  SOURCE NO  0 0 0  8 4 8 8 4 9  RETURN  0 0 1 3  P 0 0 1  0 0 0  USED  ODD. COPY  - 1 "  1 3 : 2 8 : 4 4 824  ROKA  THEN  ( I N T E G E R - V A L U E D )  Y - - >  1 0 - 1 1 - 8 4  ERR)  Y.  EQUALS  ROUNDED  " E V E N  ONENEG  0 N E N E G  I N T E G E R - V A L U E D  ( 1 )  C  G ( 2 1 . 8 )  FUNCTION  =• O N E N E G  STATEMENTS  D I A G N O S T I C S  , "  L1NECNT  -  16.PROGRAM  6 0 S I Z E  »  5 6 6  GENERATED  CO  M I C H I G A N  TERMINAL  SYSTEM  FORTRAN  REAL  0 0 0 1  G ( 2 1 . B )  FUNCTION  C  FUNCTION  C  FORESTRY,  D F L I N T AND  F U N C T I O N ,  D F L I N T * 8 ( R D P I N )  WAS  IS  C  THE  C  D O U B L E - P R E C I S I O N  C  THE  I N P U T - V A L U E  C  AND  THE  C  D O U B L E - P R E C I S I O N  WRITTEN  STORED  D F L I N T ,  IN  BY  ACCEPTS  A  TRUNCATED  INTEGER  VALUE  END I N  E F F E C T NO  IS  CONVERTED  TO  A  R E A L - V A L U E D  854  . 0 0 0  8 5 5  0 0 0  8 5 7 . 0 0 0  8 6 0 . 0 0 0 '  8 6 1 . 0 0 0 8 6 2 . 0 0 0  I D , E B C D I C . S O U R C E , N O L I S T , N O D E C K , L O A D , N O M A P NAME  SOURCE  4  R E A L - V A L U E D  8 5 9 . 0 0 0  RETURN  • S T A T I S T I C S ^  8 5 3 . 4 0 0  8 5 8 . 0 0 0  0 0 0 5  • S T A T I S T I C S  8 5 3 . 2 0 0  OUTPUT.  0 0 0 4  • O P T I O N S  OF  R E A L * 8 ( A - H , 0 - Z )  D F L I N T = D F L O A T ( I D I N T ( R D P I N ) )  1  PAGE  8 5 8 . 0 0 0  0 0 0 3  EFFECT^  FACULTY  L I B R A R Y .  TRUNCATED.  I M P L I C I T  I N  WONG,  ROKA  INPUT. IS  1 3 : 2 8 : 4 4 8 5 3 . 0 0 0  B.  THE  0 0 0 2  • O P T I O N S  1 0 - 1 1 - 8 4  D F L I N T  •  D F L I N T  STATEMENTS  D I A G N O S T I C S  , •  GENERATED  LINECNT  =  5,PROGRAM  6 0 S I Z E  »  3 5 0  P001  MICHIGAN  TERMINAL  SYSTEM  FORTRAN  0001  G(21.8)  RNDEO  10-11-84  REAL FUNCTION RNDE0 8<X.PWR10) C F U N C T I O N RNDEO WAS W R I T T E N BY B. WONG, F A C U L T Y OF C F O R E S T R Y , AND I S STORED I N THE ROKA L I B R A R Y . C THE F U N C T I O N , RNDEO. ROUNDS O F F A V A L U E , "X", TO T H E N E A R E S T C POWER OF 10, "PWR10". I T U S E S THE "EVEN-ODD" C R I T E R I O N FOR ROUNDING C A D I G I T THAT I S I M M E D I A T E L Y L E F T OF A " 5 " : C . . . { E V E N DIGIT)(5) --> ...{EVEN D I G I T ) C ...{ODD D I G I T ) ( 5 > --> ...{ODD D I G I T + 1 ) C E . G., RNDE0(2O.O5ODO.O.1D0) = 20.0, C RNDEO(20.649DO,0.1D0) • 20.6, C R N D E 0 ( 2 O . 6 5 3 D 0 . 0 . 1 D 0 ) « 20.6. C AND R N D E 0 ( 2 O . 7 5 3 D O . O . 1 D 0 ) » 20.8. WHERE THE " 0 . 1 D 0 " R E Q U E S T S ROUNDING TO T H E N E A R E S T "TENTH". C I M P L I C I T REAL^8(A-H,0-Z) 0OO2 0003 L O G I C A L 1 EVEN 0004 X10-X/PWR10 0005 xibiNf"biNfCxio) OOOS RNDDGT-DINT((X10-X10INT)M0.D0) IF (RNDDGT . NE . 5 . DO) GOT010 0 0 O 7 C "RNDDGT" 'EQUALS' 5 . 0008 E V E N - ( D A B S ( D M 0 D ( X 1 O I N T . 2 . D O ) ) EQ.O.DO) 0009 IF(EVEN)RNDE0=X1OINT^PWR1O I F ( . N O T . EVEN)RNDEO=(X10INT+1.DO I*PWR10 0010 RETURN 0011 0012 10 CONTINUE C •RNDDGT" DOES NOT 'EQUAL' 5. 0013 RNDEO-(DINT(X10+0.500)(•PWRIO 0014 RETURN 0015 END ID.EBCDIC.SOURCE.NOLIST.NODECK,LOAD.NOMAP •OPTIONS IN E F F E C T ^ NAME ' RNDEO . LINECNT < = GO •OPTIONS IN E F F E C T ^ SOURCE S T A T E M E N T S 15.PROGRAM S I Z E = 668 •STATISTICS^ •STATISTICS* NO D I A G N O S T I C S G E N E R A T E D 4  1  13:28:45 863 863 863 864 865 866 867 868 869 870 87 1 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889  000 200 400 000 OOO 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000  PAGE P 0 0 1  M I C H I G A N  TERMINAL  SYSTEM  SUBROUTINE  0001 C  SUBROUTINE  C  FORESTRY,  C  THIS  C  AFTER  TO CHECK  C  ICOUNT«AN  0  2  I  CALL  THE SOURCE  C  A  C  I F  NO ERRORS  I F  A N ERROR  L  E  I  A  6r  IERR  LOGICAL  P  I  CALL  1 3 : 2 8 . 4 5  1 0 - 1 1 - 8 4  E  CALL  UNIT  T  T  PWRERR  PWRERR L  *  890.200 890.400  P  10  W  E  R  R  '  892.000 .  P  ( E . G . . W  R  WHICH  E  R  R  .  E  N  8  9  5  .  0  .  OUT A -  CALL CALL  NUMBER  8  9  NORMAL  RETURN  H  0  .  8  .  0  0  RETURN.  1.  900.000 -  b  I N EFFECT*  •OPTIONS  I N EFFECT*  • S T A T I S T I C S * S O U R C E • S T A T I S T I C S *  0  899.000  Z  )  9  0  RETURN  FROM  E  SUBPROGRAM  R  R  )  1  POWER/ 9  0  Y » < R * S > : ' , X , Y )  .000 903.000  4  000 905.000  1  0  •OPTIONS  ERROR  1 E R R ' < l"> : i c O U N T . I  FWRITE(IOUT,'X=<R*8>,  RETURN  0006  < I > j','  0  897.000  902.000  F W R I T E ( I O U T , ' • • • E R R O R ' * *  A l C A L L 0005  0  896.000 DIAGNOSTICS  OUT A  A  000  894.000  I F ( I E R R . E 0 . O ) R E T U R N  0004  893  I N OUTPUT)  POWER.  ONTO  CARRIES (  R  891.000  IERR.  CARRIES  8  OF  OF DIAGNOSTICS.  IDENTIFY  THE FUNCTION,  I  A  A  FLAG.  TO HELP  PAGE P 0 0 1  890.000  FACULTY  LIBRARY.  TO SUBROUTINE  BY  DETECTED,  R  WONG.  ONE ISSUES  INPUT/OUTPUT R  B  THE PRODUCTION  CODE  A R E DETECTED, I S  T  B v  I N THE ROKA  T H E ERROR  RETURNED  W  C  OF  U S E R - O E F I N E O  I E R R ' T H E  0003  0  TO POWER,  T H E VALUE  IOUT=THE  M  WAS WRITTEN STORED  F A C I L I T A T E S  C  R  PWRERR  PWRERRf X ,Y , IERR. IOUT , ICOUNT ,* )  PWRERR  C  C 0  A  G ( 2 t . 8 )  AND I S  SUBROUTINE  C C  0  FORTRAN  906.000 E  7  N  D  9  0  7  .000  I D , E B C D I C , S O U R C E . N O L I S T , N O D E C K , L O A D , N O M A P NAME  -  PWRERR  STATEMENTS  NO DIAGNOSTICS  , •  LINECNT 7  =  .PROGRAM  60 S  I  Z  E  =  5  8  0  GENERATED  O  MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8)  RTNCHK  10-11-84  SUBROUTINE RTNCHK(X.Y,IERR,IOUT.ICOUNT,ERROUT,•.•) SUBROUTINE'RTNCHK WAS WRITTEN BY B. WONG. FACULTY OF FORESTRY, AND IS STORED IN THE ROKA LIBRARY. THE SUBROUTINE, RTNCHK, EVALUATES WHETHER THE DIAGNOSTIC OUTPUT SUBROUTINE, PWRERR, SHOULD BE CALLED. ONLY TWO RETURNS ARE POSSIBLE FROM THE SUBROUTINE. RTNCHK: ( 1 ) IF IERR-0 (NO ERRORS), THEN A RETURN 1 OCCURS. (2) IF IERR DOES NOT EQUAL O (COMPUTATIONAL ERRORS PRESENT). • THEN A RETURN 2 OCCURS. 0002 IMPLICIT REAL*B(A-H.O-Z) 6663 LOGICAL*1 ERROUT 0004 IF(ERROUT)CALL PWRERR(X,Y,IERR,IOUT,IC0UNT.S10) 0005 IF(IERR.NE.0)G0T020 0006 RETURN 1 0007 10 CONTINUE 0008 20 CONTINUE 0009 RETURN 2 0010 END •OPTIONS IN EFFECT* ID, EBCDIC , SOURCE . NOLIST , NODECK, LOAD .NOMAP •OPTIONS IN E F F E C T * N A M E - RTNCHK LtNECNf ' » 6 0 •STATISTICS* SOURCE STATEMENTS 10.PROGRAM SIZE " 550 •STATISTICS* NO DIAGNOSTICS GENERATED C C C C C C C C  NO STATEMENTS FLAGGED IN THE ABOVE COMPILATIONS.  $COPY «SKIPFRONT  PAGE P001 908.000 908.200 908.400 909.000 910.000 911.000 912.000 913.000 914.000 915.000 916.000 917.000 918.000 919.000 920.000 921.000 922 000 923.000  L i s t i n g Of MODEL.D at 13:28:52 on OCT 11. 1984 for CC1d=ANNA Page 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58  SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET  1  P-182.5 A1=.0172024238 Et( 1 . . .4) = - 1 .570796327 B(5)--1.88796 TOO. . 5)=-9.8 -14.4 0 0 -12.8 -9.4 TM1(1...51=28.8 26.8 0 0 28.2 28.2 TNPSYN=0 T=0 KNEMP"-0 KNEMP1=0 DMAX=0.0026 LAB=0 LBQ=426 RS=144 INCR-1 N03=1.40 NH4=0.12 NK=0 A(ALL)=0 NK=0 KA=0 KB=0 PM(ALL)=6  LF=0 R3(ALL)=0 R4(ALL)=0 NDEM=0 DD(ALL)=0 NLT=0 NVOLT'O TA=0 GMAX".085 NAVAIL'O NFREE=0 TNL0SS=O NRECYC=-0.0 TB=0 U0R=-O CP=-0.0 SG=0 TS=0 AB=0 CM=0 TM=0 SD=0 NCYCLE=0 NN=0 LAB=0 GA=0 WBM=0 SY1=0.04 SY2=0.98 SA=0.70 SB=-9.85553 DP(ALL)=0 NP(ALL)=O  NAB(ALL)=0 <J(ALL)=0  ro  Listing  of  MODEL.D a t  59  SET  61 62  SET SET  6 0 S E T  *  S  S  S  S  S  SET SET SET SET SET SET SET SET E T SET SET E T SET SET E T SET SET E T SET SET E T SET SET  8 7 S E T 88 89 9 0 91 92 9 3 94 95 9 6 97 98 9 9 100 101 1 0 2 103 104 1 0 5 106 107 1 0 8  109  on  OCT  11,  1981  for  CC1d=ANNA  Page  2  NLTALL7=6  NL(ALL)=0 NML(ALL)-0  SET N V G ( A L L ) * 6  63 64 65 66 67 68 6 9 70 71 7 2 73 74 7 5 76 77 7 8 79 80 8 1 82 83 8 4 85 86  13:28:52  NLP(ALL)=0  S  S  S  S  S  S  S  SET SET E T SET SET E T SET SET E T SET SET E T SET SET E T SET SET E T SET SET E T  WAM»0 IPASS-0 DLA6(i...5)=24.01295687 24 1 6 7 6 5 2 4 7 6 6 2 4 . 1 1 0 8 1 6 4 8 24 1 1 0 8 1 6 4 8 DLC1(1...5)»-3.94957182 - 3 . 7 0 5 1 9 6 0 4 0.0 -3.83307714-3.83307714 D L S 1 ( 1 ... 5 ) = 0 . 6 2 0 6 6 3 3 0 . 5 3 8 2 9 2 2 6 0.0 0.58219562 0.58219562 W P A O J 1 . . . 4 ) « - 4 0 1456043956 -20.35989011 -5.6719780220 .2043686247 WPC1( 1 . . , 4 ) » 1 6 . 7 1 4 6 2 4 9 8 13.46548877 3.84621018 .0245794138 WPC2(1 ... 4 ) * 5 . 5 5 8 3 7 0 8 1 -4.382303985 -2.32273982 .0191259285 W P C 3 ( 1 . .!'4)«-0. 7 5 9 9 6 1 6 1 4 1 . 8 0 1 1 0 6 8 2 6 . 6 9 6 4 8 6 6 6 4 - . 6 5 0 8 4 4 1 9 E - 2 WPC4(1...4)-0 0 .36282565 .63051099E-2 WPCS(1...4)=0 0 -.70004217 -.55880747E-3 WPC6(i 7.4)=0 6 .61684175 27603917E-3 WPSK1...4)=23.29805172 6.69591130 1.63276317 .020541403 WPS2(1. . . 4 ) » - 7 . 2 7 0 9 4 4 8 6 -4.96270366 -2.4903767 -. 1 1 7 2 8 6 3 8 E - 1 WPS3(1. . ! 4 ) » - 3 . 4 0 3 2 6 i 5 2 3 47377280 2 32251251 11250596E- 1 W P S 4 ( 1 . . . 4 ) » 0 0 -1.49957215 -.11102197E-1 W P S 5 I 1 . . . 4 ) « 0 O .64275640 .10105648E-1 WPS6( ' • • )"»b""6 1 4 9 9 4 2 4 4 - . 77907707f-2 WPAO(S)«.25612601 WPC1(5)».13261694E-1 WPC215) • ! 54 148853E-.2 WPC3(5)°-0.13058056E-2 WPC4(5)-.22883572E-2 4  WPC5(5)»6!6 WPC6(5)"0.0 WPS1(5)-.73856391E-1 W P S 2 ( 5 ) » - . 257 1 5 0 6 8 E - 1 WPS3(5)».91524001E-2 WPS4(5)--.27902489E-2 WPS5(5j=6.6 WPS6(5)»0.0 PI*3.1415926536 iSTT-6 ISTST-0 ISTW«0 bR(l .12 5-12 7 6 5 8 9 7 8 7 7 9 11 RM(1 ... 1 1 ) » 3 1 . 6 16.0 9.7 10.4 18.0 2 9 . 9 2 2 . 5 2 7 . 5 21.4 15.2 2 2 . 0 RM(12)»32.3 R D ( 1 . . . 1 1 ) - 3 3 : 8 2 0 . 6 13.5 19.3 12.4 2 i . 1 4 2 . 2 48.6 18.6 14.5 2 6 . 5 RD(12)-23.4 GRAZIN(ALL)-0.0 KGR*0 GR=-0.0 GRPSYN--0.0 *lbUMP=bN  S E T GRAx-0.0  110 S E T KNI'O 11 1 S E T GRJD-0 112 SET F U N » 9 0 113 SET #NLINE=126 1 1 4 S E T GBMAX =6.054 115 S E T GGBMAX-0.0054 1 16 S E T DLG= 1 .0  L i s t i n g  Of  M O D E L . 0  a t  1 3 : 2 8 : 5 2  117  SET  ISHIF=-0  118  SET  N C H - 0  119  SET  I A E S T = 0  120  SET  A G B M A X - 0 . 0 8  121  SET  FUN2=90  122  SET  R G A E S ' O  123  SET  FUN3=76  124  SET  M0RTvJD=12O  125  SET  M0RTWP-=-30  126  SET  C U M A B - 0  127  SET  RGG=0  128  SET  T L A B  129  SET  RTSHT=0  130  SET  P M A X = 0 . 0 1 6  131  SET  FRMAX-1  132  SET  F R R M A X = 1 . 0  133  SET  T S S N E G - 0  s  134  SET SET  K N E M P 3 - 0  SET  NRGG=0  137  SET  N R G A E S - 0  138  SET  GRAZ=0  139  SET  AMG'O  140  SET  141  SET  AMRGG-0  142  SET  GLAB=0  143  SET  G L A B A B  144  SET  R G G A B  145  SET  R G A B ° 0  146  SET  C P G - - 0  147  SET  C P R G A » - 0  148  SET  C P R G G « - 0  B  e  L F 2 = 0 N M I N Y = 0 . 8  151  SET  NMG»1  152  SET  NMRGA»1  153  SET  NMRGG=1  154  SET  C P Y M I N ' O  SET  C P Y R G A - 0 C P Y R G G - 0  158  SET  P H E N M 2 » 0 . 0 5  SET  N - 0  160  SET  G A 1 - 0  161  SET  G A 2 - 0  162  SET  163  SET  R G J D - 0  164  SET  C P Y - 0  165  SET  166  SET  Z - . 6  167  SET  D A M P D - 0 . O 7 0 8 4 5 6 7 9  168  SET  G R K N I ' 1 0 0 0  - A  A l l o t t e d  3  CPYG=0  159  $ R E N  P a g e  O  SET  SET  CCfd=ANNA  0  SET  157  f o r  AMRGA*0  150  SET  1984  KNEMP2=0  149  .  11,  . 0  136  156  OCT  O  135  155  o n  I A E S T 0 = 0  J D A E S T - 0  S P R I N T 9 f i l e  s p a c e  e x c e e d e d  f o r  Id  ANNA.  -pi  

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