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The effect of water restrictions on apple orchard productivity in British Columbia's Okanagan Valley Wigington, Ian 1987

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THE E F F E C T OF WATER RESTRICTIONS PRODUCTIVITY  IN BRITISH  ON APPLE ORCHARD  COLUMBIA'S OKANAGAN VALLEY  by IAN  A  THESIS SUBMITTED  WIGINGTON  IN PARTIAL FULFILMENT OF  THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  in THE FACULTY OF GRADUATE STUDIES Agricultural  We a c c e p t to  this the  thesis  required  THE UNIVERSITY  as  conforming  standard  OF BRITISH  April  ©  Economics  COLUMBIA  1987  Ian W i g i n g t o n ,  1987  In  presenting  this  requirements  f o r an  British freely that  Columbia, available  or  understood  that  financial  I  agree  gain  degree at  that  for extensive  by  partial  reference  purposes  Department  in  advanced  for  permission  scholarly  thesis  may  be  his  or  copying  or  shall  not  the and  allowed  Economics  The U n i v e r s i t y of B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date: A p r i l  1987  Columbia  The  of by  of  of  the  University shall  make  I further  the  Head  of it  agree  this thesis  representatives.  publication  permission.  Agricultural  study.  granted  be  the  Library  copying  her  fulfilment  of  for my  It  is  this thesis  for  without  my  1  written  Abstract  This  thesis  yield  for  examines  apples  C o l u m b i a . T.h'ifS i s simulates Two  soil  were  The  the  results  orchard lower  th'an  while  soils for  two  in  the  and  of  two  and  British  model in  water  which  tree  f r u i t s .  irrigation  systems  simulation.  water  were r e q u i r e d .  Trickle  determined  be  30%  42%  of  of  present  sprinkler  yields .  ii  are  Okanagan  substantially rates.  requirements  present  irrigation  71% o f  that  application  irrigation  to  soils  indicate  requirements  irrigation  i r r i g a t i o n ,  to  a  relationship  simulation  amounted  between  region  through  rootstocks,  the  present  sand  Okanagan  accomplished  irrigation  sprinkler loam  of  the  relationship  water/yield  types,  included  in  the  Using  for  s i l t -  application  application  requirements requirements  rates,  rates  were for  similar  Table of Contents 1.  INTRODUCTION  ,  2.  1  1.1 The Problem  ....4  1.2 Objectives  4  1.3 Research Method  5  1 .4 Thesis Guide  8  THEORETICAL CONSIDERATIONS AND THE CONCEPTUAL MODEL .10 2.1 Factor Demand Theory and Input Restriction 2.1.1  Factor Demand Theory  10  2.1.2  Quantitative Input Restriction  12  2.2 B i o l o g i c a l Considerations  3.  10  18  2.2.1  The Plant-Water Relationship  18  2.2.2  Determining Water Stress  20  2.2.3  Calculating the S o i l Moisture Level  22  2.3 T r i c k l e versus Sprinkler I r r i g a t i o n  26  2.4 Hypothesized Water/Yield Relationship  28  2.5 Generalized Model  33  ANALYTICAL MODEL  37  3.1 The Orchard Components Comprising the Model  37  3.1.1  Tree Rootstocks  38  3.1.2  S o i l Type  41  3.1.3  I r r i g a t i o n Method  43  3.1.4  Orchard System Summary  46  3.2 Calculation of Water Application Rates For Eight Base Cases  48  3.2.1  Sprinkler Systems  48  3.2.2  T r i c k l e Systems  51  3.3 Calculation of S o i l Moisture Level iii  54  3.4 C a l c u l a t i o n o f Y i e l d s 3.4.1  D e t e r m i n i n g Growth R e d u c t i o n F a c t o r  3.4.2 D e t e r m i n i n g 3.4.3  56  the Y i e l d  Reduction Factor  58 ....59  T o t a l Growth and T o t a l Y i e l d  63  3.5 Weather G e n e r a t o r  64  3.6 D e r i v i n g P o t e n t i a l E v a p o t r a n s p i r a t i o n Evaporation  4.  from Pan 68  3.7 Summary o f P a r a m e t e r R e l a t i o n s h i p s  71  RESULTS  76  4.1 The Base Case  77  4.2 R e s u l t s  80  o f t h e Water R e s t r i c t e d C a s e s  4.3 V a l i d a t i o n o f t h e Water R e s t r i c t e d C a s e s  88  4.4 S e n s i t i v i t y  90  4.4.1  Analysis  The E v a p o t r a n s p i r a t i o n  Factor  K  91  4.4.2 A c t u a l v e r s u s P o t e n t i a l E v a p o t r a n s p i r a t i o n S l o p e C o e f f i c i e n t f ....94 4.4.3 The T i m i n g  of S t r e s s  Factor  T  96  4.4.4 The D e g r e e o f S t r e s s  Factor  d  98  4.5 P o l i c y I m p l i c a t i o n s 5.  100  -SUMMARY, CONCLUSIONS, AND  SUGGESTIONS FOR FUTURE  RESEARCH  101  5 .1  Summary  101  5.2 C o n c l u s i o n s  105  5.3 Recommendations  f o r Future  REFERENCES  Research  108 112  i v  LIST OF TABLES 3.1 Average Y i e l d s per Acre Over 20 Years For Different Rootstocks  Two  40  3.2 A v a i l a b l e Water Storage C a p a c i t y and Maximum S o i l Water D e f i c i t by S o i l Type  42  3.3 D e f i n i t i o n of E i g h t Orchard Systems and T h e i r Components  47  3.4 D e r i v a t i o n of E v a p o t r a n s p i r a t i o n C o e f f i c i e n t K Which V a r i e s W i t h P e r i o d Of Growing Season  69  3.5 Model P a r a m e t e r s , A b r e v i a t i o n s , and U n i t s of Measurement  72  4.1 R e s u l t s of Water R e d u c t i o n s on M2 Orchard Y i e l d s Showing Base Case and Water R e s t r i c t e d Case Annual I r r i g a t i o n L e v e l s and Y i e l d s  78  4.2 C r i t i c a l P o i n t s For Orchard Systems With M2 Rootstocks  87  4.3 R e s u l t s of Parameter S e n s i t i v i t y A n a l y s i s on Orchards Systems i n Year 4 of Tree L i f e  v  M2  92  LIST OF FIGURES 2.1  Hypothesized Orchard Production F u n c t i o n  17  2.2 Hypothesized R e s t r i c t e d Orchard Production Function 2.3 Hypothesized T r i c k l e and S p r i n k l e r Functions  Production  31  2.4 Hypothesized R e s t r i c t e d v s . U n r e s t r i c t e d Orchard Production F u n c t i o n s 2.5 General Flowchart 3.1  Derivation  of the Orchard Production Model  ..29  31 ....34  of S o i l Moisture F a c t o r p  57  3.2 R e l a t i o n s h i p Between Growth Reduction Factor g and S o i l Moisture L e v e l  60  3.3 D e r i v a t i o n  62  of Timing of S t r e s s F a c t o r T  3.4 R e l a t i o n s h i p Between E v a p o t r a n s p i r a t i o n C o e f f i c i e n t K and Percent of Growing Season 70 3.5  I n t e r a c t i o n of F a c t o r s Comprising the Model  73  4.1  Production F u n c t i o n s For M2 Orchard Systems Showing E f f e c t of Reducing Water A p p l i c a t i o n L e v e l s on Yields  83  4.2 E v a p o t r a n s p i r a t i o n C o e f f i c i e n t Systems  K f o r M2 Orchard  4.3 E v a p o t r a n s p i r a t i o n C o e f f i c i e n t S e n s i t i v i t y A n a l y s i s Cases  K f o r the Control and  85 93  4.4 A c t u a l v s . P o t e n t i a l E v a p o t r a n s p i r a t i o n C o e f f i c i e n t f and I t s R e l a t i o n s h i p to the E v a p o t r a n s p i r a t i o n Factor p for the C o n t r o l and S e n s i t i v i t y A n a l y s i s Cases 95 4.5 L e v e l of S t r e s s F a c t o r T Over the Growing Season: C o n t r o l Case and Value Assumed for S e n s i t i v i t y Case 4.6 Degree of S t r e s s F a c t o r d for the C o n t r o l Case and the S e n s i t i v i t y A n a l y s i s Case  vi  ..97 99  I  dedicate  this  Wigington, Eija,  I  for their  f o r never  would  John  work  like  doubting  Tim  expertise  and  the  thing.  I  also  much  wish  my  gratitude claims  researching  this  to Rick  made  to  on  Roger  for funding  for  and  and  time  to  initiating  Pipe  I would  Gwen and  thier  for  like  to  Sykes f o r  patience  in  Shynkaryk f o r  McNeill  provided.  for  Roger  Finally,  Kathy  and  commitee,  Novak,  Short,  Lymer  vii  my  Mike  their  to  Dorothy  understanding.  of  Riemann  support.  thesis,  and  Cam  and  encouragement,  members  Walter  moral  innumerable  Directorate  the  James  always  H a z l e d i n e , and  to thank  encouragement,  and  and  g u i d a n c e , and  appreciated  express  parents,  support  to thank  Graham,  whole  t o my  and  the  Inland  Waters  Chapter  1  INTRODUCTION The 8.2%  of  tree  fruit  total  farm c a s h  Canada,  1985).  growing  area  climate,  The  Apples  Columbia  in  fruits  for of  99.3%  receipts  i n B r i t i s h Columbia  i n the  because  (1981  c e n s u s ) . The  and  i s i n demand  recreational  future,  part  demands.  of a l a r g e r  production  water  use  2  particularly T h i s study  planted  accounts  (B.C.  Ministry  industrial, as  sectors  with  f o c u s e s on  o f w a t e r use  this  study  by  a  to other  The  for  study i s  a l l sectors in apple  forms o f  s p e c i f i c a l l y concerns  for apple orchards  c o u l d be  water u s e d  Because of the predominance of region r e l a t i v e  agricultural  expanding  i n t h e Okanagan V a l l e y .  assessment  in this  agriculture,  1  purposes  the Okanagan.  on  region  from  u s e r s as w e l l  problem  agricultural  rely  apple crop  t h e needs of a l l t h e s e  residential  i t s dry  of the a c r e a g e  Okanagan  users. Meeting i n the  fruit  1985).  i n t h e Okanagan  residential,  (Stats  a r e t h e major o r c h a r d c r o p grown i n  of the B r i t i s h Columbia  Water  of  r e g i o n must  a c c o u n t i n g f o r 68.7%  Agriculture,  for approximately  Okanagan r e g i o n i s t h e p r i m a r y  producers  British tree  accounted  i n t h e P r o v i n c e and,  fruit  irrigation.  industry  itself  with  i n t h e Okanagan r e g i o n .  R. M c N e i l l , Water Use Optimization Model, Working Paper, E n v i r o n m e n t Canada, 1983. T h i s s t u d y i s t h e a g r i c u l t u r a l component o f a m u l t i s e c t o r w a t e r use model b e i n g d e v e l o p e d by t h e I n l a n d W a t e r s D i r e c t o r a t e , P a c i f i c & Yukon R e g i o n . 1  2  1  2  Tree  fruit  irrigation of  the  producers  systems  the  Okanagan V a l l e y r e l y  to p r o v i d e t h e i r  orchardists  irrigation  in  i n the  valley  systems c o n s i s t i n g  of  water  still  requirements.  use  older  w h i c h c a n be u n c o u p l e d and moved a b o u t  Most  new  posts  i r r i g a t i o n systems c o n s i s t (solid  over  generally time.  are  trees. not  This  mainline  set  is  systems)  S o l i d set  able  irrigate  to  to  those with  allocate  water  a lack  of  water  their  watering  orchards plays  in  the  water  factor  that  needs  under t r e e s  available  systems  are one  capacity  Hence,  basis,  and  valves  rotation  in  irrigation  in  producers  moving p i p e  This  role  o r on  orchards at  systems u s i n g  1980).  stress.  The h o t t e r  water  a plant  requires.  and t h i s  results  (Carruthers  and C l a r k ,  possibility  of  water  allowable  maximum l i m i t  is  must  be c o n s i d e r e d  When a p l a n t  from t h e  water  water  set  a key  requirements.  r e q u i r e d water  yields  sprinklers  to  method  of  practices  area.  A second fruit  permanent  systems.  of  orchard.  o r c h a r d s on a r o t a t i o n a l  solid  (Stevenson,  the  entire  t h o s e w i t h handmove s y s t e m s p h y s i c a l l y sprinklers,  'handmove'  s y s t e m s and handmove  irrigation district  f o r c e d to  of  placed either  to a p p l y water  m a i n l y due  Many  s p r i n k l e r s and s e c t i o n s  pipe  and p i p e  on  soil,  and d r i e r  it the  Water s t r e s s i n revenue 1981).  stress  d u r i n g each determined  relates  fails is  to  said  losses  to  reduce to  the  its  undergo  the  more  tree  fruit  minimizes  maximum amount  irrigation rotation. by a w o r s t  tree  producers  A producer thus  by u s i n g  obtain  weather,  can  to  case  This  scenario  for  the of  3  water  required  words,  i f a t any  equivalent the  during  to  given  the  irrigation  an  t i m e an  hottest,  during  and  can  period.  recorded  other  period to  date,  each r o t a t i o n should  method of  be  In  undergoes a  period  needs. T h i s  i s wasteful  dry  orchard  driest  water a p p l i e d  a d e q u a t e t o meet t r e e irrigation  extended hot,  tree  e n c o u r a g e d by  be  fruit the p r i c i n g  scheme f o r a g r i c u l t u r a l w a t e r . Water annual  i n the  Okanagan  f i x e d fee,  o r c h a r d i s t s may  amounts as  d e t e r m i n e d by  particular  area  the  in question.  mechanism and  because the  characterized  by  traditionally  irrigated  norm r a t h e r minimizing  than the  agricultural  i s p r i c e d by  good  the  allowable  exception  methods c o u l d  upon o v e r a l l water  demands.  Pricing incentive whether  by  the  acre  potential  generally  conditions  were  1980),  stress. t o be  thus  The  one  area  have a c o n s i d e r a b l e  to provide  any  the  where impact  economic  t o c o n s e r v e w a t e r . A volume p r i c i n g scheme,  incorporated  expense or  fails  in  the  have  i s thus c o n s i d e r e d  water c o n s e r v a t i o n  for  orchardists  water  an  water  rate  is  (Stevenson, of  For  this pricing  region  i f drought  potential risk  sector  flow  Because of  drainage,  as  acre.  l a w f u l l y apply  Okanagan  soil  the  totally  i n t o the  replacing  for s u b s t a n t i a l  e x i s t i n g set the  per  irrigation  amounts o r c h a r d i s t s p r e s e n t l y  use  acre  as  an  added  p r i c e method,  water  i n the  up  savings  Okanagan.  over  has the  4  1.1  THE PROBLEM  Water  supplies  several short  groups.  s u p p l y of  result this  user  in the  district valley  While the  water,  in l o c a l  occurs  Okanagan must meet t h e  demands  shortages  as  a whole  from c o m p e t i n g  (McNeill,  1983).  streams.  These water  by the  district  courses  systems  are  Conflicts as  any down s t r e a m s u c h as  residential  this  areas  Agricultural consideration irrigation work as  Okanagan. F l a t  The  main o b j e c t i v e  of  o r c h a r d and t h e  water  used  Arising  tree  chosen  this  thesis  fruits. the  from t h i s  from u p p e r  summer  are  demands is  highest.  during this  become  not  risk  of  tapped  months  more  This  period. frequent  increase.  a major for  water  stress  to  determine  the  requirements  and y i e l d  for  implications  as  Some  conservation.  between water  apple  is  to  interests.  rate p r i c i n g  and m i n i m i z i n g t h e  OBJECTIVES  for  to  conservation  anti-incentives  relationship  expected  expand and water  i n the  water  are  water  1.2  Columbia  of  late  fishing  is  thereof  i n terms  The Okanagan r e g i o n  study  of  an  of  area.  main o b j e c t i v e  are  the  To d e t e r m i n e  the  reduction  in y i e l d  following  that  total  British  sub-objectives: 1.  in  An example  i n some c a s e s  i n the  sport  not do  systems a c c e s s water  when a g r i c u l t u r a l i r r i g a t i o n r e q u i r e m e n t s eliminates  is  of  sectors  between a g r i c u l t u r e a n d f i s h i n g  a g r i c u l t u r a l water  entirely  valley  demands  may be  5 anticipated  if  application  regimes  and t o  level  present  application  to  below  be  trees  are  To d e t e r m i n e  sprinkler settings 3.  the  and t r i c k l e i n terms  To t e s t  key p a r a m e t e r s  of  the of  agriculture  water  and t h e  pricing  In  determine  varying that  levels  water  water  at  relative  water/yield sensitivity  the  application  which y i e l d s  begin  use  efficiencies  in apple  input/output of  the  of  orchard  relationships.  results  to changes  in  model. alternative  i n terms  policy  water  i r r i g a t i o n systems  4. To i n v e s t i g a t e  1.3  to  affected. 2.  for  subjected  of  user  water  pricing  incentives  implications  of  these  to  strategies  conserve  alternative  formulae.  RESEARCH METHOD order to  constructed cycle  to  affect  attempting trade-off  the  simulate  and d e t e r m i n e  levels  the  accomplish  yields  t o model o r between t h e of  space,  allows.  simplification  reality.  this  thesis  attempts  physiological process,  plant  water,  is  to  orchard  cycle.  application  The p r o b l e m o f  which r e a l i t y  to  The s i m u l a t i o n  represent  the  systematically  a and  computer  some d e g r e e a undertaken  reaction  when one o f  is  requires  and d a t a w h i c h the is  be  growing  any s y s t e m o r p r o c e s s  Any model  process  a model w i l l  i r r i g a t i o n water  complexity  time,  apple  in that  simulate  modelling process of  objective  an a c t u a l  how v a r i o u s  yearly  limitations  first  the  of  inputs  restricted.  a  for complex  to  that  The m o d e l l i n g  6  procedure attempts water of  level  incorporated  growing  into  from a h i s t o r i c a l  amount  day,  the  season.  model  of  water  evapotranspiration  a daily  stress  age  factor  is  and y i e l d ,  or y i e l d .  marketable  yields,  partial  and l a t e r  cropping, factor  while full  when water  and a y i e l d  combination The g r o w t h  of  the  based  crops.  factor  has  years,  proper tree  growth  is  proper  tree  branch s t r u c t u r e  year-end y i e l d  r e a c h e d mature to  fruit  the  yield.  size,  to  o r c h a r d , the  the  a weather  to  calculate on  that  the tree  calculation plant  produce  years  to  year-end  important and s i z e  growth.  yield.  determine In t h e  factor  Once a f r u i t is  not  tree a  the  early the  accommodate  reduction  new b r a n c h g r o w t h  the  in p r o v i d i n g to  full  reduction  are c a l c u l a t e d ,  to  growth  first  period prior  final  of  no  produce  a growth  on t r e e  totals.  year  daily  relate  growth,  calculated  yield  day  availability.  F o r the  is  stress  only  possible  factor  which water  F o r mature y e a r s ,  used  on p l a n t  which determines  each  generator  C a l c u l a t i o n of  occurs,  reduction  reduction  being  subsequent  stress  for  soil  f o r m e r p r o v i d i n g an  orchard years  effect  determine  it  water  of  Early  yield  a given  orchard transpires  makes  on t h e  of  and p r o v i d e s  the  rate.  p r o d u c t i o n needs w i t h Depending  set  latter  which the  rate  fruit  A weather  values,  the  effect  randomly s e l e c t s  weather d a t a  input,  evapotranspiration fruit  the  the  year-end  and t e m p e r a t u r e  exogenous water the  ascertain  on p o t e n t i a l  a predefined  rainfall  to  is  fruit. used  to  has  contributor  7  Stress carried  effects  over  considered  in  terms  from y e a r  to  year,  independent  of  past  growth r e d u c i n g s t r e s s to  subsequent  assumption  yearly  of  information affects  of  the  to  or  each growing subsequent  degree  to  determine  due t o  relative  efficiencies  of  s p r i n k l e r and t r i c k l e  is  to  hypothesize  necessary  stress  and t r e e  relationship two  i n terms  of  growing  which a f u r t h e r critical  point  at  and t r i c k l e w h i c h water  compared f o r relative  systems. provide  reduction  each water  implications mechanisms.  between  examine  rates  reductions.  become  By  the  in the  altering  results determine  of  c r i t i c a l can providing a  the  the  i r r i g a t i o n water  point  model,  s p r i n k l e r and  the  the  simulating  use  of  the  becomes  thus  for  the  orchard during  application  i r r i g a t i o n systems  water  using  reducing  determine  made t o  it  this  is  efficiency  year  i r r i g a t i o n systems,  the  restrictions  quantifiable  use  a p p l i e d to  in y i e l d  information to of  of  i r r i g a t i o n method,  An a n a l y s i s the  simplifying  water  application  i n water  Thus a  years.  In s y s t e m a t i c a l l y  an a t t e m p t  and r e s u l t s  sprinkler  water  i r r i g a t i o n water  season,  and t o  is  c a r r i e d on  i n any one  a relationship  yields,  i r r i g a t i o n systems.  amount of  of  fruit  a lack  i n subsequent the  season  not  This  which s t r e s s  not  seasons.  is  yield calculations.  growth a n d / o r y i e l d  In o r d e r  as  in maturing years  model a r i s e s  on t h e  y i e l d or growth are  pricing  be test  trickle  simulation  potential  the  will  at  8 Key than  parameters  i n the  those designated  sensitivity  of  the  strategies  are  1 .4  THESIS  GUIDE  The  next  the  model,  for  chapter  the  model.  evaluated  model a r e  at  values  simulation  to  test  Finally,  alternative  using maginal  discusses  and p r e s e n t s  set  some of  results  water  literature  on i r r i g a t i o n s y s t e m s and r e l e v a n t  findings,  determined, provides is  is  reviewed.  be  The f i n a l  pricing  appropriate of  on p r e v i o u s  section how t h e  of  to  reducing studies.  The  water-apple  model p a r a m e t e r s  d e s c r i p t i o n of  three  cycle  the  presents choice  incorporated into  determining is  discussed,  as  assumed p r e s e n t  three,  the  of the  orchard yields  Okanagan o r c h a r d s .  is  the  are  chapter  orchard  two  simulation  discussed.  role  for each  description  interact  i n the  of  Next,  stage  a detailed  of  account  following  sections  i n the  characteristics the the of  method of growing  calculating  of  in  chapter  simulation  the  chapter  weather  section  of  how t h e  v a r i o u s model  simulation.  Section  a p p l i c a t i o n amounts  and s t r u c t u r e of  The f i n a l  detailed  orchard  simulation.  day w a t e r In t h e  a n a l y t i c a l model.  specific  model p a r a m e t e r s u s e d  d e r i v e d and t h e is  water  conceptualized.  one d i s c u s s e s  the  from w h i c h t h e  a general  Chapter  to  based  theory  irrigation  yield  applications  the  analysis.  the  hypothesized  other  three  are generator  provides a  components  9  Chapter  four presents  starting  with  followed  by t h e  chapter give  the  four  discuss of  five  of  w h i c h must  cost  water  two with  further  results.  the  orchardist the  simulation,  situation,  The f i n a l  applied  to  this  and  parts  of  study  and  analysis.  of  the  possible  A discussion  be c o n s i d e r e d  other  research.  as  the  day  cases.  sensitivity  sections discuss regard to  validation  those  to  restricted  by a d i s c u s s i o n  factors of  of  b e g i n s w i t h a summary of  followed  implications  results  base case or p r e s e n t  water  results  Chapter results,  the  the  of  in measuring is  b r e a d t h of  model policy  some of the  also  presented.  the  simulation  a r e a s and c r o p s ,  and  the  overall The  final  results  and s u g g e s t i o n s  for  Chapter  2  THEORETICAL CONSIDERATIONS AND THE CONCEPTUAL MODEL This and  chapter  biological  formulation relevant  provides  theory  of  the  formulation  of  relevant  model.  literature  a discussion to  These,  of  provide hypotheses  that  in chapter  of  relationship  this  between water  and y i e l d  production.  The method used  to  the  simulate  water  yield  application  rates.  input  theory  and the  factor  p r i c e mechanisms  levels  will  the  determined the  3  resource  pp.  The  in tree  fruit  water  investigate  of  the  this  objective  trees  to  and t o  to  is  various  c a n be v i e w e d  orchardist  the  fruit  production process,  as  factor  a demand  alternative  r e s t r i c t i n g water  input  is  THEORY  of  use  point equal  of  at  Price  in this System  the  with only variable  which the  to  the  in production.  The d i s c u s s i o n  Eckert's  of  maximizing firm  level  by t h e  resource  to  the  detailed.  a profit  resource,  that  be  is  accomplish  Since  fruit  response  FACTOR DEMAND For  of  the  to  response  factor  2.1.1  to  thesis  in  of  3.  One  of  the  result  FACTOR DEMAND THEORY AND INPUT RESTRICTION objectives  economic  with a review  2.1  the  the  and u n d e r l y i n g together  a model p r e s e n t e d  both  3  variable  resource of  return obtained  is  taken  Resource  424-429. 10  will  one more  be  unit  from use  The amount by w h i c h  section and  cost  one  of  total  from L e f t w i c h and  Allocation,  8th  ed.  11 revenue in  the  c h a n g e s when one more u n i t production process  product only  (MRP) o f  one  traces  is  variable  out  If  the  may r e s u l t  and t h u s  The above  factor where  the  factor the  up t o  different of  flat  must  be  entirely  out  rate  essential  the  to  the  to  price  production  use  resource.  factor  of  other  flat  is  rate  if  unit  rate  variable  of  pricing if  one  pricing  any amount  for  a fixed that  faced  of  system of  flat  the  price,  factor  is  then quite  In t h e  case  approach  the  following  and r e c e i v e  the  designated  substitute  production process  pay the  the  with  possible,  the  process input  t y p i c a l marginal analysis  The f i r m  of  resource  the  pricing situation.  thereby  input  production process, to  that  that  use  amount  In c a s e s where  the but  the  case  for  However,  a flat  i n the  for  revenue  mix.  input(s).  input o r ,  of  restricted  assumes a p e r  entitled  employed  marginal  variable of  is  rate  the  saving  in question  the  firm  fee  if  it  input  has  the  is  no  chooses  to  in production.  Apart the  pay the  one  product  per u n i t  pricing,  fee.  alternative  of  a change  either of  remain  is  to  level  some d e s i g n a t e d  from the  quantity  to  priced using  reconsidered.  choice:  flat  is  of  rate  the  the  MRP c u r v e  input  i n the  factor  purchaser  result  factor  discussion the  inputs  as  f i r m ' s demand s c h e d u l e  in changes  for  a resource  For the  the  t h e n any change  inputs  mechanism  defined  resource.  resource,  more t h a n one  variable,  factor  that  is  of  from c a s e s where  production process,  a factor with  flat  c a n be rate  substituted  out  p r i c i n g firms  are  12 unresponsive  to input  p r i c e changes  i n terms of p r o d u c t  mix  adjustments. An o b j e c t i v e Okanagan o r c h a r d the  of t h i s t h e s i s water  requirements  growing season i n order  actual flat  water  rate  results  application  that  being  as  t h e minimum amount o f water  irrigation pricing level  structure  application. an o r c h a r d water  fruit  will  production  irrigation  water  changes.  i s defined given  orchard rate  w a t e r . To d e t e r m i n e t h e  water a p p l i e d  restrictions will  t o an o r c h a r d model o f water  t h e amount o f w a t e r  and c o m p a r i n g  t h i s with  the p o t e n t i a l  required  by  t h e amount o f  f o r water  savings i n  be shown.  QUANTITATIVE section  process  due t o t h e f l a t  use, q u a n t i t a t i v e  By e s t i m a t i n g  actually applied,  This  Okanagan  orchard y i e l d s as a f u n c t i o n  operation  agriculture  2.1.2  water  price  to produce a  a r e not e f f i c i e n t  on i r r i g a t i o n  simulates  that  over  pointed out,  operation  needed  for irrigation  of e f f i c i e n t  be p l a c e d which  practices  tree  be compared t o  to input  use f o r an o r c h a r d  i t i s hypothesized  actual  to a production  unresponsive  efficient  then  t h e s e may  inputs  If  yield",  water  for a fruit  r a t e s . As h a s been  p r i c i n g of f a c t o r  i n firms  i s to determine  INPUT RESTRICTION deals  with  the hypothesized  of q u a n t i t a t i v e l y r e s t r i c t i n g  e f f e c t on  tree  t h e amount o f  available to orchardists.  "using a predefined density.  irrigation  system,  soil  t y p e and  tree  13 When t h e  s u p p l y of  becomes more l i m i t e d , or q u a n t i t y that  factors  in a production  assuming  i n the  b i d up t h e  demand may s h i f t  production  input  then,  regulations,  input w i l l  input  an  no  short  price.  intervening  run f i r m s  In t h e  long  and p r i c e may f a l l  are  substituted  process  as  pricing  demanding  run the  factor  other  (Hirshleifer,  1984,  pp.  228). In  the  need n o t  c a s e of  apply.  amount  a regulated  In the  in  the  of  l a n d i n any g i v e n  amount of orchard  of  i r r i g a t i o n water  actually compare  of  this  this  to  is  to  they  At p r e s e n t  are  1980).  determine  scenario regulated  can a p p l y to this  It the  it  per a c r e  and t h e  resulting  Water process.  is  allowed is  is  to  one  impact  To measure  amount o f  water  the  of  a p p l i e d to  inputs  documented  as  A set  by M c N e i l l  of  of all  To  water  i n each  other  possible  stages case.  production  altering  from an e c o n o m i c (1977).  water  successive  in a m u l t i - i n p u t  an o r c h a r d ,  viewed  amount of of  the  and  rate.  be m e a s u r e d  i m p a c t on y i e l d  are held constant.  production  in a series  on y i e l d  input  the  acre  meet  amount of  application  proposed that  be r e d u c e d  but one  water  any  regulated  more t h a n a d e q u a t e  (Stevenson,  thesis  the  applied  been  above  r e q u i r e d by an Okanagan o r c h a r d o p e r a t i o n  accomplish this  inputs  region.  requirements  the  Okanagan, o r c h a r d i s t s  i r r i g a t i o n water  objectives  market,  the  production  orchard perspective  These might  include  has the  14 following:  Q =  where  f(I,N,W,L,M)  Q = fruit  yield  I = i r r i g a t i o n water N = fertilizer W = weather  application  application  factors  L = labour M = management  Since the  the  o r c h a r d model u s e d  water-yield  allowing  water  relationship, to  vary while  conceptualized  above)  function  is  interest.  possible  reactions  of  of  available  reduce  of  irrigation  the  constant  on a p e r a c r e  faced  a degree  are considered. sale  It  i n the  only  of  inputs  (as  production  effect, with a  some curtailment  which t h r e a t e n s is  assumed  and d i s t r i b u t i o n  same and t h u s  outlined  other  resulting  this  an o r c h a r d i s t  remain the  b a s i s as  on t h e  to  considers  predicted effect  To p r e d i c t  r e g a r d i n g the water  study  holding a l l  i r r i g a t i o n water  orchard yields  regulations  in t h i s  flat  that  to the  of rate  previous  pricing  section  holds. The a d j u s t m e n t run and s h o r t to  variable  factors  run time  inputs  cannot  process  c a n be v i e w e d  frames.  are p o s s i b l e  be made  (Varian,  In t h e  i n terms  short  run,  but a d j u s t m e n t s p.8).  Short  run  of  long  adjustments to  fixed  adjustments  1 5  might  include a heightened  orchardist  of  facilitate  more f l e x i b l e  compensate  for hot,  supplies.  conditions  during  the  third  of  the  p a r t of  moisture  the levels  with  restricted  heat  of  the  times  to  water  and a v o i d i n g  day c o u l d r e d u c e  method f o r  to  s a v i n g water  water  is  worn o r m a l f u n c t i o n i n g s p r i n k l e r h e a d s . A  method t h e  reduce  and s o i l  quicker rotation  A second p o s s i b l e  replacement  on t h e  i r r i g a t i o n rotation patterns  dry periods  For example,  irrigating use.  weather  awareness  loss  a p p l i c a t i o n of of  soil  water  a mulch g r o u n d - c o v e r  to  the  atmosphere  to  (Kennedy,  1985). In t h e For is  l o n g - r u n time  example, altering  capacity  one the  allotment adverse  of  different  These adjustments  irrigation resitant  to  system  provides  are  variable.  t o an o r c h a r d i s t water  holding  matter.  examples faced  of  some of  with a  reduced  m i g h t make t o m i n i m i z e  using a given  technology  technologies,  and  production functions, include  switching  r e p l a c i n g the  to  the  set.  the Other  thus can a l s o a  be  different  orchard with trees  more  drought.  When water assumption  or  the  organic  w h i c h an o r c h a r d i s t ,  on y i e l d s  open  and t h u s  of  using d i f f e r e n t  constituting  water  texture  i r r i g a t i o n water,  effect  adjustments  made.  soil  discussion  adjustments  factors  long-run adjustment  through a d d i t i o n s  The above the  frame a l l  of  constant  is  restricted  holding a l l does not  to  orchard  such a degree  the  production inputs  provide a r e a l i s t i c  except  p r e d i c t i o n of  1 6 the  outcome of  objective  of  water-yield a  the  application  levels.  Limiting  represents begin  to  Assume lies  to  the  the  on y i e l d . be a t  within occur  all  optimal  holding  all the  of  levels  If  for  that  Qc,  the  of  for 2.1  levels  inputs region  restriction  of  of  Q * , then  purposes  No i n p u t  to  all  below w h i c h the  yields  critical  reducing Qc has  the  point.  constant  function  little  effect  condition is  of  need  the  except  to  non-binding  levels  to  rate  water  adjustments  inputs  a  P o i n t Qc  7  meet o r c h a r d n e e d s .  production holding  to  water c a n be assumed  5  at  the  one  i r r i g a t i o n constant 6  levels  irrigation application  point  sufficient the  as  level  orchard yields  of  level  than  Qc - Q * .  such  irrigation  irrigation  function.  other  except  remains  portion  at  these  represents  Q*. Clearly the  at  illustrative  allowable  down t o  orchard  reality.  defined  Qc a t  inputs  to m a i n t a i n  irrigation  and i s  goal  higher  depiction  Figure  actual  right  application  this  at  the  orchard environment,  water a p p l i c a t i o n  reduced,  that  achieve  orchard production  the  be  set,  If  mimic an a c t u a l  discussion  technology  hypothetical  to  However,  a truer the  is  i r r i g a t i o n water.  i n an a c t u a l  does not  provides  single  model  response  restriction  model  restricting  to since Thus  right  of  water  T h i s i s a v a l i d assumption i f o r c h a r d i s t s are c o n s i d e r e d to be e f f i c i e n t f a r m e r s s i n c e i n p u t s o t h e r t h a n water c a n be a n a l y s e d on a m a r g i n a l c o s t b a s i s . T h i s c o n c l u s i o n i s v a l i d i f i t i s assumed t h a t e x c e s s water a p p l i c a t i o n has no e f f e c t on y i e l d . S i n c e t h e Okanagan r e g i o n has good d r a i n a g e t h i s a s s u m p t i o n i s acceptable. S t r i c t l y s p e a k i n g t h i s i s not t r u e s i n c e f e r t i l i z e r a p p l i c a t i o n would l i k e l y d e c r e a s e as i r r i g a t i o n l e v e l s d r o p p e d and l e s s l e a c h i n g o c c u r e d . 5  6  7  yield  of  apples  F i g u r e 2.1  Hypothesized  Orchard P r o d u c t i o n  Function  18 constant  does not  compromise  the  predictive  power  of  the  model. From t h e the  degree  to  water-yield amount of of  the  that  which the  relationship  in tree  production function  Thus  will far  relevant  biological  chapter  to  the  aspects  of  c a n be c o n c l u d e d  fruits  applied. and t h e  be d i s c u s s e d  this  it  model a c c u r a t e l y  i r r i g a t i o n water  shape  theory  preceding discussion  varies  assumptions  has d e a l t  with  the shape  underlying  2.3.  w i t h the  In t h e  importance  the  The h y p o t h e s i z e d  in section  model.  represents  that  next  economic  section  in developing  the  the  model  are  discussed.  2.2 In  BIOLOGICAL  CONSIDERATIONS  order  to  conceptualize  quantity  of  i r r i g a t i o n water  yield, and  theoretical  the  in this  between w a t e r followed  and p l a n t  by t h e  m e a s u r i n g when  section.  this  yields.  2.2.1  THE PLANT-WATER  nearby  amount of  soil  is  the  the  expected  studies  Initially  relationship  of  the  be d i s c u s s e d .  a method  for  fruit  relationships  from p r e v i o u s  relationship  fruit  The  physiological  growth w i l l  derivation  between  a p p l i e d and t h e  plant-water  empirical observations  discussed  relationship  will  This  determining  becomes c r i t i c a l  for  be  is and tree  RELATIONSHIP  water  a plant  uses p l u s  evapotranspiration  evaporation  (ET) r a t e .  Less  from than  19 one p e r c e n t purposes  of  water  r e q u i r e d by p l a n t s  ( C a r r u t h e r s and C l a r k ,  transpiration plant  the  during  requires  conditions  as  is  photosynthesis.  a function  well  1981).  as  the  of  type  plant  plant  from t h e  roots  water  is  greater  the  demands  draws  water  source  limit  to  from t h e  upward f l o w .  openings  no l o n g e r  flows pore  size  capacity  and t h u s  The amount o f field  soil where  as  has  the  been  the  (generally  growth water  point  amount o f  is  water  water  into  a plant  soil  the  its  of  r e m a i n i n g water  is  or  soil  the  roots.  more water  reduce  8  is  the  The the  a  finite  there size  such that  is  a  of water  By r e d u c i n g  photosynthetic  reduced.  available  to  a plant  is  bounded by  on t h e  upper end,  and by t h e  on t h e  lower  Field  water  d r a i n a g e has  w i t h i n one  any  potential  replacement)  roots.  left  s a t u r a t e d and a l l o w e d  rate  a  constitutes  tension  reduces  and  within  through the  Most p l a n t s  soil  capacity  permanent w i l t i n g defined  when  readily  stomatal  soil  As the  water  t r a n s p i r a t i o n . As  t r a n s p i r a t i o n , the  soil.  in  cultural  system  stomata,  plant  (barring constant  this  stomatal  of  the  and  stomatal  t r a n s p i r e d through leaf  plant  the  through to  into  used  both atmospheric of  growth  The amount o f  Water forms a c o n t i n u o u s  draws w a t e r  for  Most i s  approach used.  gradient  is  in a s o i l to d r a i n  substantially  two d a y s  considered  end.  of  water  capacity  after to  soil  a  that  point  subsided  application).  t o be a v a i l a b l e  is  to  The  plants  W i n t e r g i v e s an example of a p l a n t , t h e D r o o p s y p o t a t o e , w h i c h , b e i n g u n a b l e t o c l o s e i t s s t o m a t a , i s an e x c e p t i o n the g e n e r a l c a s e . 8  to  20 provided  the  soil  water  content  permanent w i l t i n g p o i n t . defined  as  soil  irreversibly passes  water  soil  content  to  at  the  plant  capacity  water  storage  2.2.2  DETERMINING WATER STRESS  moisture water  capacity  stress falls  the  level  is  the  under g i v e n as  a level  that  1974).  soil the  occur  moisture  is  level  stress  the  drops  below  Assaf  (1975).  between water  soil  level  this  for  i n the  no  the  to  measure  soil  requires  below this  to  growth,  of  or  soil potential  where  water  content  maintain at  which water thesis  fruit  tree  water  a maximum stress  is  recommended by  feet  of  of  the  moisture  b a s e d on t h e  a linear  and f r u i t  soil  of  degree level  results  relationship  of existed  volume when t h e  soil  soil  range  was  is  by t h e minimum  The d e t e r m i n a t i o n  level  two  between  ( B r i t i s h Columbia M i n i s t r y  found that  top  longer  available  This  conditions,  u n d e r g o when t h e  level  is  in tree  the  which i r r i g a t i o n i s  1983).  defined  water  plant  The l i m i t  below  trees  Assaf  water  The r a n g e  available  and t h e r e f o r e  defined  and F o o d ,  apple  is  relationship  atmospheric  I r r i g a t i o n D e s i g n Manual  Agriculture of  water  point  plant  is  the  soil.  o c c u r i n g when t h e  level  (Winter,  below  t i m e must be d e t e r m i n e d .  activity,  to  a  water-yield  photosynthetic  assumed  roots.  provides a quantifiable  defined  below  (AWSC) of  amount of  any g i v e n  stress  since  and permanent w i l t i n g p o i n t  To d e t e r m i n e  orchard at  which the  stress  field  production,  fall  The permanent w i l t i n g  damaged by water  from t h e  does not  i n the  21  between and  permanent  AWSC). water the  30% o f  the  available  wilting  level  root  is  zone  is  4 feet.  the  10% o f  range  of  assumed  to  o r above  stress,  level,  p a r i b u s then  divided  by t h e  a means  for  moisture  the  stress  fruit growing  this  days  is  trees a  linear  Fruit is  in  yield at  moisture  in the fruit  of  when  or  level  water  i n f o r m a t i o n on  from r a i n  a function  daily  water  yield  and of  stress  growing  season  effects  that  not  on a p a r t i c u l a r day  hypothesis. of  stress levels  season  provides  from an o r c h a r d  only  that  the  is  also  important.  t i m i n g of  examining  water  on a p p l e  June d r o p ) ,  (before  and a l l  in  water  stress studies  the trees,  I r r i g a t i o n regimes  irrigation  the  Several  Goode(l975), stress  is  important  but  results.  i r r i g a t i o n , early (after  however,  yield,  interesting  irrigation  soil  soil  level  level  degree  inputs  yield  sum o f  hypothesized,  physiological provides  the  If  determining annual  determining  support  and water  number of  water  the  10%  age.  is  degree of  no  and t h u s  available.  ceteris  It  moisture  assumed.  a maximum when t h e  conditions are  a given  For apple  information,  c a n be m e a s u r e d on a d a i l y b a s i s  irrigation  at  60% AWSC.  moisture  atmospheric  during  soil  (AWSC)  recommended  zone.  60% AWSC i s  be z e r o when t h e  is  of  in Assaf  y i e l d and s o i l  AWSC t o  10% AWSC and a t  Soil  root  Based on t h i s  fruit  below  of  (PWP, d e f i n e d  60% AWSC i n t h e  between  at  storage capacity  The BCMAF I r r i g a t i o n D e s i g n M a n u a l  relationship  is  point  water  consisting  June d r o p ) ,  season  irrigation  late  22  applied that  to  C o x ' s Orange P i p p i n a p p l e  p o s t June d r o p i r r i g a t i o n r e s u l t s  yields  of  (1984)  in a study  the  concluded  regimes  that  g r o w t h was the  trees  s e a s o n was  late  on f i v e  the  late  tested.  spring.  fruit  various  i r r i g a t i o n time  encourage  vegetative  i r r i g a t i o n was  periods  studies,  d u r i n g the  occuring  during f r u i t  occuring  at  for  early  fruit part  growth  necessary  the  very  set  weights are  of  while  f o r maximum  growing is  apportioned  stress  most c r i t i c a l w h i l e  stress  or very  end of  critical.  2.2.3  CALCULATING THE SOIL MOISTURE LEVEL Attempts  various  to  crops  proposed  have  approach using  (1965) terms stress  discuss of  provides  release  relative the  p o r t i o n of  season  relationships review  curve"  of  of  rate water  depending  of  a  is  for  some of  simulation  relationship  together  y i e l d and t h e  plant  example  moisture  growth  yields the  A brief  an e a r l y  effects  harvestable  may a f f e c t  water-yield  the  the  presented.  a plant-soil  "moisture  corresponding  the  been numerous.  methods i s  Moore(l96l)  from a  determine  to  Water  beginning  season.  least  yield  trees  growth. B a s e d on t h e s e  the  and C h a l m e r s  pear  I r r i g a t i o n d u r i n g the  found to  s p r i n g a n d summer  Jerie,  old Bartlett  most c r i t i c a l  evidence  i n maximum m a r k e t a b l e  Mitchell,  year  provide  with  index. stress  in question.  a  F i s c h e r and Hagan on c r o p g r o w t h  different on what  derived  ways  that  constitutes  In p a r t i c u l a r ,  the  in  23  Fischer fresh  a n d Hagan p o i n t  fruit  weight  in turgor  of  i n the the  at  level,  which  and 2) pan  a given  (1967)  time,  in turn  they  water  c a s e of  as  stress  is is  dry weight  is  model y i e l d a function  a function  i r r i g a t i o n and o u t p u t s what  when y i e l d  measured  in  potentially fruit  due t o  a  fruit.  Mapp and Eidman plant,  that  or volume,  more d a m a g i n g t h a n loss  out  of  r e d u c t i o n on a  of:  1)  inputs  given  soil  water  from  rainfall  through e v a p o t r a n s p i r a t i o n ;  term atmospheric  stress,  which i s  and  a function  of  evaporation. Flinn(l971)  p r o v i d e d a good summary of  model w a t e r - y i e l d some of  the  experiments failed  to  problems to  production  for  total  seasonal  Response  seasonal  and t h u s  a possible  this  solution  suggested using Flinn degree of  to  a moisture  moisture  p r o p o s e d by F l i n n  ET = f  stress to  * Eo  are of  while  relationships plant  water  providing a  necessarily  Beringer(1961)  tension-crop  yield  relationship.  s i m u l a t i o n model  predict  determine  Early  l i m i t e d a p p l i c a b i l i t y . As  problem,  to  and  incorporating crop  time,  proposed a crop-water  to  in general  i n these methods.  v a r i a t i o n of  variations,  site-and-crop-specific  plants  water-yield  functions  and i r r i g a t i o n o v e r  to  for  encountered  correlate  account  requirements.  solution  relationships  attempts  the  yield.  soil  using  The model  moisture  level  is:  24 Ea = p * ET  where  ET = a t m o s p h e r i c Eo = pan  evaporation  Ea = a c t u a l f  transpiration  = crop  coefficient  p = a soil  moisture  The c r o p c o e f f i c i e n t d e p e n d s on the atmospheric a variety of  f  Atmospheric soil  crops.  demand i s  soil  is  the  soil  moisture  is  the  at  the  field  to  water  the  equal  to  atmospheric  case  of  at  soil's  crop-specific  amount  field  after  lost  provides orchard  of  water  capacity.  is  the  atmosphere. actual  the  amount  At s o i l  soil  which a c t u a l  moisture  f  fruits,  the  value  of  water  soil.  moisture  soil level  from  level  the of  capacity  Pan  and  from an  open  Actual  which a c t u a l l y levels is  drops,  evapotranspiration  demand, and t h u s p becomes l e s s  at  or  is  factor a point less  than  1.  is  near  equivalent  moisture  is  evaporation  conditions.  water  on  season.  drainage  evapotranspiration  demand, and t h u s t h e  for  atmosphere  atmospheric  and  data  Field  initial  and loss  released  when t h e  the  to  moisture  mid growing  atmosphere  water  1 . As the  reached at  the  under g i v e n  capacity,  atmospheric  is  between p l a n t  0.75  the  level  evapotranspiration lost  f  o c c u r r e d from a s a t u r a t e d  amount of  body o f  In t h e  from 0 up t o  the  has  factor  relationship  and c r o p i n t o  run-off  factor  demand. H a r g r e a v e s ( 1 9 6 6 )  of  ranges  demand  to  p is  than  is  25 The  soil  moisture  level  (SM) a t  time  t  is  calculated  as  follows:  SM  = SM t  + P  where  + C t  +1  t  t-1  t  P = effective I  -  Ea  - DR t  t  precipitation  = i r r i g a t i o n water  applied  C = upward c a p i l l a r y w a t e r DR = deep  Effective soil  (ie  moisture  is  Irrigation water  input,  a p p l i e d to of  layers  up t o  water  amount  in  an amount for  which  is  water  lost  to  wet  losses).  per  inches,  foot is  of  the  of to  the  the  Soil soil.  amount  Upward c a p i l l a r y movement  drawn from s u b - r o o t  rootzone  water  of  in acre  crop.  sufficient  interception  inches  measured the  the  of  is  accounting  measured  amount  the  percolation  precipitation after  movement  zone  is  the  soil  c r o p . Deep p e r c o l a t i o n  sub-root  of  zone s o i l  layers  the  for  is  due  to  drainage.  The F l i n n the  daily  water  soil  stress  model w i l l moisture  and t h e  calculated.  Details  measurement  used  This observed  section  be u s e d  levels  resulting of  as  basis  from w h i c h t h e effect  be g i v e n  in chapter 3.  has  reviewed  the  literature moisture  on  of be  and u n i t s  will  soil  degree  on y i e l d w i l l  these c a l c u l a t i o n s  impact which v a r i o u s  deriving  of  the  levels  have  had  26 on t r e e for  fruit  yields.  calculating  combination  of  o r c h a r d model following  As w e l l ,  soil  moisture  these to  be  section  fully  examines the  2.3  TRICKLE VERSUS SPRINKLER  One  of  and  sprinkler  objectives  of  irrigation  reviewed  are  Proebsting, physiological  sprinkler  with  effects  through  trickle terms  (in  to  irrigation  this  to this  apples  the  basis  The  for  the  next c h a p t e r .  merits  is  of  of  The  trickle  versus  thesis  are  needed  for  of  the  rootstock  growth at  irrigation, periodic  sprinkler  In  not  this  and y i e l d thesis,  from  time  Prosser  sprinkler were  results  irrigated  compared  of trees  in  Trickle  requiring  irrigated  size  methods  Of p a r t i c u l a r  favourable  trees  the  daily  two weeks)  characteristics.  and f r u i t  irrigated trees.  irrigation  measures.  sprinkler  water-yield  sprinkler  seedling  every  versus  of  trickle  (1977) measured  distinct  trickle  physiological  compare  section.  on  c a s e once  to  terms  f o u r t h year  produced bushier  occurred earlier trickle  three  g r o w t h and y i e l d  spreading  in  trickle  in t h i s  of  irrigated trees  of  systems  of  The e f f e c t s  respect  interest  thesis  i r r i g a t i o n and t r a d i t i o n a l  irrigation  the  i n the  M i d d l e t o n and R o b e r t s  Redspur D e l i c i o u s  Washington.  method  been o u t l i n e d .  forms  relative  a  IRRIGATION  this  irrigation Studies  planting  has  form of  irrigation.  relationships.  of  levels  developed  sprinkler  for  general  two p r o c e d u r e s  and  the  the  trees.  the Blossoming  were g r e a t e s t yield  on  relationships  27  for  b o t h s p r i n k l e r and t r i c k l e  compared on an e f f i c i e n c y In what  appears  to  of  and R o b e r t s  advantages  and d i s a d v a n t a g e s  irrigation  for  (1981)  i r r i g a t i o n had t h e  energy,  reduce  leeching, the  disadvantages  in  keeping  filtration and as  trickle  increased less  water  irrigation  clear  of  that  trickle 1981). this  of  nutrients  trees  i n the  i n the  into  the  effects  adequate  substantial  terms  to  water  of  the  of  be  water  event  of  of  Some  used,  a water  t r i c k l e versus  savings  identical  the  is  are  conditions effects,  in  applications.  water  l a c k of  taken.  to  costs  was  g r o u n d compared t o  t r i c k l e and s p r i n k l e r  underestimates in  due  extensive  d i r t y water  i r r i g a t i o n on o r c h a r d f r u i t s  As f o r p h y s i o l o g i c a l  study  and  maintainance  clear,  if  that  and f r u i t i n g .  increased  controls  stored  concluded  and l o s s  s y s t e m under c e r t a i n  considered  was  to  sprinkler  save water  blossoming  the  cut-off sprinkler  systems.  Research methods  risk was  t r i c k l e versus  irrigation lines  basis.  summary of  to  included  be  yield  potential  earlier  and c h e m i c a l  will  study, Middleton,  p r o v i d e a good of  erosion  and i n d u c e  of  a p p l i e d to  o r c h a r d s . The s t u d y  trickle  soil  water  be a f o l l o w - u p  Proebsting  fruit  i r r i g a t e d trees  ongoing.  possible  for  the  This  of  fruit  assumption  It  et.al.  purposes  suitable  yield  ratios.  quantifiable  of  be  yield  given  probably  gap between t r i c k l e and s p r i n k l e r a p p l i e d to  is  with a  (Middleton  irrigation will  terms  sprinkler  However,  data a n e u t r a l  systems because position  28 2.4 In  HYPOTHESIZED WATER/YIELD RELATIONSHIP this  section  the  characteristics  water/yield production function relationships  a r e b a s e d on t h e  Throughout unrestricted  will  function. as  that  the  this  section  be u s e d  A restricted  production process  inputs  With the  are  The  study  detriment  above.  restricted the  which r e s u l t s  in the  and  orchard production is  here  defined  when a l l  i r r i g a t i o n water  to  found t h a t  during  inputs  are  in  held all  been c o n s i d e r e d an a r e a  c o u l d be r e d u c e d  orchard y i e l d s .  rates  water  and a c t u a l  one  week  requirements  (1980),  in a  needs b a s e d on  was a p p l i e d as  Only d u r i n g  substantially  Stevenson  irrigation applications,  a 9 year p e r i o d i n the  as much w a t e r  o r c h a r d water  past  use  Okanagan o r c h a r d  orchards.  to  detailed  These  variable.  evapotranspiration  twice  orchard  unrestricted production function,  Okanagan has  of  terms  refer  except  where a g r i c u l t u r a l w a t e r without  findings  production function  production function  constant.  the  are hypothesized.  the  to  of  Summerland d i s t r i c t  was needed  i n the  9 year  by  the  period did  a p p r o a c h the  rate  of  irrigation  of  and t h o s e  application. Based on t h e earlier,  it  function  for  a  is  findings  hypothesized  o r c h a r d s , as  Stevenson  that  the  depicted  horizontal portion representing  from water needs.  applications  Q* i n F i g u r e  2.2  represents  restricted production  in Figure a near  beyond that  noted  2.2,  will  zero y i e l d  necessary  have  increase  for apple  tree  c u r r e n t Okanagan w a t e r  y i e l d of apples  l-'igure 2.2  H y p o t h e s i z e d R e s t r i c t e d Orchard P r o d u c t i o n F u n c t i o n  30 application  levels.  Figure  2.2  point,  Q c , below  moisture at  is  hypothesized  levels.  a point  The l e f t  equal  This to  between  research  station  at  relative  fertilizer  are a f f e c t e d  The b a s i s at  hypothesized  the  this  different  determine  levels.  Water a p p l i c a t i o n r a t e s  100% of  present  orchard watering  trees  The d e g r e e stress  that  water  will  result  this  decline  this  study.  is  of  are  2.3  not  11 y e a r  on t r e e  apple  tree it  is  the  shape  to  point,  Qc,  and s l o p e  of  be d e t e r m i n e d  in  relationship  i r r i g a t i o n and s p r i n k l e r i r r i g a t i o n .  irrigation  is  p r e d i c t e d to  water  used  to  yield  conjecture  is  b a s e d on v a r i o u s c o m p a r i s o n s  than  were  hypothesized  in y i e l d ,  hypothesized  the  p e r i o d of  response  critical  the  be more e f f i c i e n t  between  Trickle i n terms  sprinkler irrigation. of  a  growth.  the  These w i l l  is  ranging  practices  below  certain.  gives  of  Thus w h i l e  9  a p p l i c a t i o n rates in a decline  the  effects  sensitivity  uncertain.  over  lie  Canada  loss  to  to  prediction  Agricultural  attributable  soil  c u r r e n t Okanagan  to  s t u d y w i t h no d i s c e r n i b l e  trickle  for  in  critical  Summerland ( 1 9 7 4 - 8 4 )  to M c i n t o s h apple  Figure  is  some  watering  37% t o  water  point  y i e l d curve  by r e d u c e d  30% and 40% of  u n d e r t a k e n by S t e v e n s o n  the  after  critical  study  applied  drop o f f  which y i e l d s  application rates.  from  the  to  water  irrigation  p o r t i o n of  of  This t r i c k l e and  R e s u l t s o b t a i n e d by A s s a f e t . a l . ( 1 9 7 5 ) s u p p o r t a 59% d r o p i n what t h e y t e r m " c o m m e r c i a l f r u i t y i e l d " when t o t a l s e a s o n a l i r r i g a t i o n was r e d u c e d by 20%. H o w e v e r , i r r i g a t i o n a p p l i c a t i o n r a t e s were n o t c o n s t a n t d u r i n g t h e c o u r s e of t h e growing season as i s the c a s e w i t h the s i m u l a t i o n i n t h i s thesis. 9  31  yeild of appies  quantity of water Figure 2.3  Hypothesized T r i c k l e and Sprinkler Production Functions  yield of apples  quantity of water Figure 2.4  Hypothesized Restricted vs. Unrestricted Orchard Production Functions  32 sprinkler  i r r i g a t i o n methods  conversations  with Stevenson  The t r e e confined  to  this  other  condition,  restricted  process  to  allowing left-most  variable  Figure of  levels  the  given  water  left  2.4  the  form,  level the  orchard production process control  at the  levels  further is  the  other  variable  management  i n the  restricted case.  to  2.4.  inputs  conjecture non-binding  of  At t h i s  other  the  i n the  point  t h a n water  restriction  is  i n no y i e l d  By  is  r e a c h e d and increase.  This in  r e s t r i c t i o n p l a c e d on  no l o n g e r  on o t h e r  yields  increasing  production functions the  to  are  maintaining orchard  a p p l i e d , maximum y i e l d  the  In  the  practices)  those  result  form. in  to  a  chemical a p p l i c a t i o n s  above  applications  hypothesized  factors  thus  water  and  the  restricted  input,  2.1  restricted  the  (such as  h o r i z o n t a l p o r t i o n of  variable  is  water  water  figures  to change,  for  amount of  the  orchard production  i n c r e a s e d p r o d u c t i o n at  t r a n s p i r a t i o n and o t h e r  substituted  form  By r e m o v i n g r e s t r i c t i o n s  over  is  By i m p o s i n g  in diagramatic  factors  in  simulation  t a k e s on a  production curve  resulting  and  relationship  constant.  provides  other  application  unrestricted  factors  factors.  of  p o r t i o n of  to  water-yield  r e s t r i c t i n g the  water-yield  shift  the  in this  production function  result  the  of  1981)  (1984).  production process  the  form.  hypothesized  the  fruit  an a n a l y s i s  holding a l l  (Middleton e t . a l . ,  binding.  variable  inputs  This being  h o r i z o n t a l p o r t i o n of  the  hypothesized  p r o d u c t i o n c u r v e assumes t h a t  the  restriction,  33  within  this  defined  yields.  Strictly  obvious  example  must  increase  leeching in  if  Since  yields  portion  2.5 This  to  of  hindered  are  the  to  result  assumption  fertilizer  applications  remain at  the  i n increased  in t h i s  range,  imposition  of  is  false.  An which  cause  soil  same l e v e l .  c a n a change  production surface  by t h e  is  in orchard  application,  the  However,  production  i n any of  the  orchard production.  and u n r e s t r i c t e d  coincide  the  i n no c h a n g e  h o r i z o n t a l p o r t i o n of  restricted  predicted  is  i n F i g u r e 2.4  factors  the  this  this  when e x c e s s water  given  variable  results  speaking, of  no c a s e a l o n g  surface  range,  production curves analysis not  variable  of  this  deemed  input  are  to  be  restrictions.  GENERALIZED MODEL chapter  has  discussed,  among o t h e r  theoretical  relationship  between w a t e r  studies  tree  In the  for  theoretical parameters  fruits.  and e m p i r i c a l r e s u l t s of  the  orchard.  F i g u r e 2.5  water-yield  overall  picture  chapter  3. model  objective o r c h a r d to  of  the  and p l a n t  chapter,  will  yield  these  be u s e d  to  define  a c o m p u t e r - b a s e d model w h i c h a t t e m p t s  simulate  The  next  things,  of  provides what  in this  simulating  various  provide a l e v e l  of  relationship the  will  levels  reader  with a  of  generality  response  for of  i r r i g a t i o n water to  the  generalized  in d e t a i l  was d e v e l o p e d  yield  to  an Okanagan f r u i t  be d e v e l o p e d  thesis the  of  the  results,  an  in  the apple  input. several  To  34  orchard  rootstock  weather  system  irrigation type  soil  type  generator  pan  evaporation  (PAN)  \ 7  p o t e n t i a l evapotranspiration (PET) - PAN a c t u a l evapotranspiration  soil  moisture  v actual YR  « '- ^-5 U1  yield  (SM) = SM  * K  (AET) « rho * PET  + R + I - AET  0  i r r i g a t i o n input (I) e i t h e r by s o l i d s e t o r t r i c k l e systems  (AY) - f t p o t e n t i a l  : l . degree of s t r e s s 2. t i m i n g o f s t r e s s  y i e l d (PY), y i e l d reduction  (g) (T)  General Flowchart of the Orchard Production Model  (YR))  35 combinations by t h e  of  model.  components  orchard c h a r a c t e r i s t i c s  These c h a r a c t e r i s t i c s  and c o n s i s t  systems and 2 s o i l form 8 u n i q u e and the of  systems.  systems  r e s u l t i n g y i e l d as Figure  model a t choice  the  is  A list given  3.1.1).  Soil  system  irrigation  water  section  system  works is  component then  affects type  in Table  allowable 50% o r  (245  As  3.1.2).  is  impact  (see  soil  on t h e to  the  The  moisture  The c h o i c e  able  choice  indicated  yields  i m p a c t on t h e  orchard  this  of  the  amount  make use  of of  being  system  is  fashion. one  (see  level.  yield  used.  orchard  of  some p e r c e n t  some o t h e r use  the  simulation  I n i t i a l l y an  the  8 possible  orchard orchard  An i r r i g a t i o n a p p l i c a t i o n l e v e l  irrigation level  water  2.5,  c o m p r i s e d of  A s i m u l a t i o n over orchard  The  an impact on  model.  has an e f f e c t  following  combinations.  75% o r  an o r c h a r d  in Figure  i n the  chosen  chosen,  c a n have  to  components  3.2.  yearly potential  section  which the  orchard  simulation process.  has an  component  combine  3.1.3).  As d e p i c t e d process  of  orchard  2 irrigation  o r c h a r d components  i n the  and i r r i g a t i o n (see  irrigation  (see  points  rootstock  types,  s i m u l a t e d by t h e  different  different  of  section level  2.5,  termed  The o r c h a r d components  e a c h p a r t i c u l a r o r c h a r d component  the in  are here  2 rootstock  types.  orchard  8 orchard  of  c a n be a c c o m m i d a t e d  of  section These  simulation  the  3.2),  factors is  F o r e a c h day o f a weather  for  day  example  being  chosen,  derived.  20 g r o w i n g s e a s o n s  days per growing s e a s o n ) ,  present  is  for  the  chosen  each growing generator  season  provides  36  temperature historical the  and r a i n f a l l weather  data  d a i l y a d d i t i o n of  evapotranspiration calculation daily used  soil  irrigation  daily  level  yields. the  of  growing  as  soil  soil  daily  stress.  growing  (see  used  to  section  season and,  the  of  growing  season  next chapter  these  biological  day and  simulation  (see  is  the  the  affects  These are with  the  orchard  stress during  daily  table  factors  to c a l c u l a t e  water  together  are  the  user.  used  calculate 3.4).  of  for  Other  level  Water s t r e s s  yield  each  level.  is  data  incorporated into  moisture  level  o r c h a r d system y i e l d  In t h e  are  d e g r e e and t i m i n g of  season are  From t h i s  t h r o u g h 3.7  previous  by the  moisture  water  soil  potential for  3.5  moisture  on t h e  set  3.5).  from  and s u b t r a c t i o n  sections  the  the  factors  entire  section  precipitation  moisture  Both the  reduction the  of  input,  The d a i l y  randomly chosen  evapotranspiration)  calculate  of  (see  (see  calculation to  level  of  data  yield summed  the  3.1),  over  estimated the  actual  determined.  further  detail  systems  is  on the  given.  components  of  Chapter 3 ANALYTICAL MODEL This chapter orchard the  s i m u l a t i o n model.  v a r i o u s components  method of  calculating  calculation outflows,  of  methods  of  at  parameters  abreviations  3.1  o r c h a r d water based  calculation water.  end of  used  section  components the  provides  of  The f i n a l  of  the  describe  inputs yields  section  and based  on  the  discusses  the  provides model  the  the  r e q u i r e d weather  chapter,  data.  a list  together  of with  measurement.  COMPRISING THE MODEL  a detailed  model.  the  orchard systems,  actual  the  of  requirements,  in f o r m u l a t i n g the  and u n i t s  sections  on w a t e r  of  this  THE ORCHARD COMPONENTS  This  These  description  of  the  o r c h a r d components  orchard  consist  of  following:  1.  The  c o m p r i s i n g the  in generating  the  description  The f o l l o w i n g  water  soil  employed  3.5,  Table  soil  and t h e  availability  the  presents a d e t a i l e d  two  rootstocks  2. two  soil  3.  i r r i g a t i o n systems  two  choice  type, orchard  of  types  a particular rootstock,  a particular  and a p a r t i c u l a r i r r i g a t i o n s y s t e m c o m p r i s e s system.  There are  Each o r c h a r d system  is  thus  8 possible  simulated  37  in  turn.  soil a  single  orchard systems. Because  the  choice  38 of  o r c h a r d components  simulation,  providing  can a f f e c t  the  a r a n g e of  possible  achieves  some g e n e r a l i t y  note  d i s t i n c t i o n between  the  encompasses systems, set  of  3.1.1  all  the  results.  the  component  and an o r c h a r d  component  i n the  outcome  which r e f e r s  important  to  which  the  orchard  t o one  unique  choices.  of  tree  rootstock  reach m a t u r i t y , and expected  certain  tree  thesis  fruit  diseases.  are M a i l i n g  a dwarfing rootstock  schemes  if  suitable  tree  management is  26  the  view  and managed, allotted  suitable  expert  2 (M2).  for 1  0  M26  planting  M2 p r o d u c e s a s e m i - s t a n d a r d plantings  requiring  rootstock  less  schemes.  h o r t i c u l t u r a l i s t s that  of  time  of  selected  for high density  in  will,  if  any  properly  p r o d u c e a g r e e n canopy a r e a w h i c h  fills  the  orchard  areas  c a n be assumed t o  M2 and M26 p l a n t i n g s  incidence  than h i g h e r d e n s i t y  of  l e n g t h of  The r o o t s t o c k s  f o r medium d e n s i t y skill  maturity,  (M26) and M a i l i n g  orchard planting regardless out  at  cultivated properly.  tree  It  size  an i m p o r t a n t f a c t o r  required  to  tree  is  eventual  laid  is  and a l l  determining  is  It  systems  TREE ROOTSTOCKS The c h o i c e  this  the  orchard  general model,  choices  system,  of  space.  Since  produce the  in this  study  identical  canopy  same a p p l e y i e l d s , a r e assumed t o  the  produce  T h i s s e l e c t i o n was b a s e d on h i s t o r i c a l r o o t s t o c k p r o d u c t i o n from Okanagan N u r s e r i e s 1977-1983 ( S a n d e r s , 1983) and c o n v e r s a t i o n s w i t h M i k e S a n d e r s and Helmut A r n d t , d i s t r i c t h o r t i c u l t u r a l i s t s , B r i t i s h C o l u m b i a M i n i s t r y of A g r i c u l t u r e , Kelowna. 1 0  39 identical in  terms  density  per a c r e of  potential  than  tend  to  M26 r o o t s t o c k s --  the  open  Cost of  to  full  --  annual  after total  year  may be  would l i k e l y  1  4  the  decline  and  and t h u s feasible rate  percentage  after  an  earlier  used  some  M2 o r in  this  conversations for  the  in Table 3.1.  a f a i r l y constant  rootstock,  such  on e i t h e r  basis  given  returns  While i t  y i e l d at  semi-dwarfing  obtainable  8.  total  as  higher  1 2  The s o u r c e s  p r o v i d e d the  a  grown on  trees.  1 3  advantage,  of  production at  question.  f o r M2 and M26 p l a n t i n g s  yield  trees  Production Study  S t u d y assumes c o n s t a n t  or  into  that  semi-standard  with h o r t i c u l t u r a l i s t s data  is  y i e l d w h i c h c a n be e x p e c t e d is  The  1 1  p r o d u c t i o n and p r o f i t s ,  come  s t a n d a r d or  The e x a c t  thesis  on m a t u r e t r e e s .  dwarfing rootstock  rootstocks age  yields  yield The  a  constant  to  maintain  on a d w a r f i n g of  top  grades  point.  T h i s a s s u m p t i o n i s a r e s u l t of c o n v e r s a t i o n s w i t h M . S a n d e r s , h o r t i c u l t u r a l i s t , B r i t i s h C o l u m b i a M i n i s t r y of A g r i c u l t u r e , K e l o w n a . However i n p r a c t i c e c a n o p y a r e a s a r e s e l d o m i d e n t i c a l and t h e r e f o r e y i e l d s d i f f e r . M 2 6 o r c h a r d s were assumed t o come i n t o f u l l p r o d u c t i o n by y e a r 7 w h i l e M2 o r c h a r d s r e a c h f u l l p r o d u c t i o n i n y e a r 9 . The p e r a c r e y i e l d o b t a i n e d a t f u l l p r o d u c t i o n i s h i g h e r t h a n t h a t g i v e n i n t h e C o s t o f P r o d u c t i o n S t u d y (and o c c u r s a y e a r l a t e r ) and r e p r e s e n t s a compromise between t h e S t u d y f i g u r e s and i n f o r m a t i o n o b t a i n e d t h r o u g h p e r s o n a l c o m m u n i c a t i o n w i t h M . S a n d e r s . As w e l l as r e a c h i n g f u l l p r o d u c t i o n e a r l i e r , o r c h a r d s on M26 r o o t s t o c k s b e g i n m a r k e t a b l e b e a r i n g i n y e a r 3 w h i l e M2 o r c h a r d s b e g i n b e a r i n g i n y e a r 4. T h e b a s i s for d e t e r m i n i n g y i e l d s for a l l o r c h a r d systems i s t h e E s t i m a t e d C o s t s a n d R e t u r n s of A p p l e O r c h a r d E s t a b l i s h m e n t and P r o d u c t i o n , Okanagan V a l l e y , 1984. The BCMAF P r o d u c t i o n S t u d y was done u s i n g a 20 a c r e o r c h a r d w i t h 202 t r e e s p e r a c r e a n d a s p r i n k l e r i r r i g a t i o n s y s t e m . " D i s c u s s i o n s w i t h M . S a n d e r s and D . S t e v e n s o n s u p p o r t t h i s view. 1 1  1 2  1 3  1  40  TABLE  3.1:  AVERAGE Y I E L D S PER A C R E OVER 20 YEARS FOR 2 D I F F E R E N T ROOTSTOCKS (LBS./ACRE)  YEAR  ROOTSTOCK M2  M26  1 2 3 4 5 6 7 8 9 10 1 1 1 2 1 3 14 1 5 1 6 1 7 18 19 20  00000 0 0 1 600 8000 1 6000 24000 32000 35000 35000 35000 35000 35000 34300 33614 32942 32283 3 1 637 31 004 30384  00000 0 3000 6000 1 5500 32000 35000 35000 35000 35000 35000 35000 35000 34300 33614 32942 32283 31 637 3 1 004 30384  AVERAGE  24 1 34  26383  SOURCE:  A d a p t e d f r o m BCMAF " E s t i m a t e d C o s t s a n d R e t u r n s Apple Orchard Establishment and Production, O k a n a g a n V a l l e y , " May 1 9 8 3 .  Unfortunately exactly peak a  an o r c h a r d ,  production,  point.  year  when  there  However,  i s no d a t a o n M2  o r M26  or the d e c l i n e the assumption  8 and c o n t i n u i n g  over  an  available  to determine  rootstock,  in production of constant  indefinite  reaches  following yields  period is  such  after  41 unrealistic. production  On t h i s  is  assumed  Rootstock, determines soil  type  basis  i n so  a 2% p e r y e a r  from y e a r  14  far  determines  as  it  planting density. are  other  decline  onwards. tree  Tree t r a i n i n g ,  factors  that  in  determine  size,  also  nutrition,  and  eventual  tree  for  study,  size. M26 and M2, t h e are assigned  tree  respectively. used  tree  These  will  rootstocks  densities  spacings  densities  two  of  densities found i n  388  chosen and 202  this  trees  are d e r i v e d using  the  be  r e f e r r e d to  is  an i m p o r t a n t  per  commonly  Okanagan r e g i o n .  as  acre  The  h i g h and medium  two  density  plantings.  3.1.2  SOIL TYPE Soil  type  holding capacity h o l d water capacity that  m e a s u r e d by 1  water  deficit  span t h e  necessary  c r i t i c a l point (MSWD).  range  of  water  for  the  two  ability  water  thumb f o r  orchard crops  is  40% of  soils  T a b l e 3.2 Soil  maximum  considered  respect  to  to  storage  AWSC has  termed t h e  types with  soils.  A soil's  water  available  when  The two  soil  Okanagan r e g i o n .  figures  its  A r u l e of  5  i r r i g a t i o n is This  in determining  and p l a n t i n g d e n s i t y .  (AWSC).  removed.  the  is  factor  is  been soil  in this  study  AWSC f o u n d  in  p r o v i d e s AWSC and MSWD texture  absorption c h a r a c t e r i s t i c s .  affects  a  The more c o a r s e  soil's the  soil,  A more d e t a i l e d a c c o u n t of i n f o r m a t i o n c o n t a i n e d i n t h i s s e c t i o n c a n be f o u n d i n t h e B . C . M i n i s t r y of A g r i c u l t u r e ' s Irrigation Design Manual , 1983 r e v i s e d e d i t i o n . 1 5  42  TABLE  3.2:  SOIL  A V A I L A B L E WATER STORAGE C A P A C I T Y AND MAXIMUM S O I L WATER D E F I C I T BY S O I L T Y P E ( I N . / S O I L F T . )  TYPE  A V A I L A B L E WATER STORAGE C A P A C I T Y  SAND SILT-LOAM  MAXIMUM S O I L WATER D E F I C I T  1.0  0.4  ("1.6)  2.5  1.0 ( 4 . 0 )  F i g u r e s i n b r a c k e t s d e n o t e maximum s o i l w a t e r for 4 f o o t r o o t zone. S o u r c e : BCMAF I r r i g a t i o n D e s i g n M a n u a l , 1 9 8 3 .  the  faster  surface.  the absorption  A soil's  determining section rates  an i r r i g a t i o n  3.2). A second  systems  Trees expansive as  trees  root  1  6  To c o n s i d e r complexity  rate  system  must flow  f a c t o r which  be a s s u m e d  on s i l t - l o a m and thus  soils.  between  of water  or absence  systems  on s a n d y  considered.  the  will  planted  relationship  1 6  absorption  i s the presence  orchard  rate  soil  The o r c h a r d  applied  rate  t o have  absorption  turf  or sod.  tend  and d e n s i t y soil  A l l  sod cover. t o have  a r e not as densely  system's  when  (calculated in  of surface  For the purposes type  t othe  be c o n s i d e r e d  increases  soils  deficit  of t h i s will  type  more planted study, the  n o t be  i s expected to  the s o i l type/density f a c t o r would i n c r e a s e of t h e model w h i l e c o n t r i b u t i n g l i t t l e i n the  43 have the  an e f f e c t fruit  3.1.3  on t h e  function section  available  for  use  by  trees.  was  noted  is  irrigation  to  two  they  Irrigation Okanagan v a r y  affect  implying  that  paribus.  However, due  solid  set  of  district  to  set  in  many handmove  systems are  large  the  characteristic  of  part the  to  in  1 7  the the  irrigation way  years is  1  8  used,  still  generally  Okanagan a r e a ,  systems.  generally  given  labour  practices.  producers  but  recent  of  obtain  water  sprinkler  systems  from a  implications  fruit  district,  This  interest  o r c h a r d systems  more c a p i t a l and l e s s  in  the  Handmove s y s t e m s have  solid  production  by i r r i g a t i o n m e t h o d .  s y s t e m s u s e d by t r e e  systems dominate.  operation,  all  from d i s t r i c t  to  restricted  Okanagan i r r i g a t i o n  through l o c a l  handmove a n d p e r m a n e n t  increasingly  differ  the  and d i s c u s s e s  assumes t h a t water  that  i r r i g a t i o n methods  perspective  e a c h method a s study  earlier  expected  describes  historical  sizes  water  IRRIGATION METHOD It  This  amount of  ceteris  in  small orchard  and to  the  many  ( c o n t ' d ) way of o v e r a l l r e s u l t s , as d e n s i t y i s a l r e a d y a factor that is v a r i e d . I t s h o u l d be n o t e d t h a t some o r c h a r d i s t s i n t h e Okanagan a c c e s s t h e i r own w a t e r t h r o u g h pumping o r g r a v i t y f e e d s y s t e m s . S u c h s y s t e m s would a p p e a r t o c o m p r i s e a v e r y s m a l l p e r c e n t a g e of t h e t o t a l t r e e f r u i t a c r e a g e i n t h e Okanagan ( c o n v e r s a t i o n s w i t h B i l l Ross of the S o u t h e r n Okanagan L a n d s I r r i g a t i o n D i s t r i c t p u t the e s t i m a t e a t 2% f o r t h a t d i s t r i c t ) t h o u g h l a r g e r o p e r a t i o n s s u c h as v i n e y a r d s a r e more l i k e l y t o a c c e s s t h e i r own i r r i g a t i o n n e e d s . P e r s o n a l c o m m u n i c a t i o n : D r . D . S . S t e v e n s o n , Summerland R e s e a r c h S t a t i o n a n d M r . B i l l R o s s , S o u t h Okanagan L a n d s I r r i g a t i o n D i s t r i c t , M a y , 1984. 1 6  1 7  1 8  44 family-run but,  as  operations.  yet,  their  With the postwar  the  amount of  was  kept  to  for  i r r i g a t i o n of  time  to  requirement(see peak  interval,  a minimum. T h i s  the  entire  orchard using  varies  depending  on a t m o s p h e r i c  to  a b s o r b and s t o r e  conditions  r e q u i r e more  conditions,  all  else  As c a p a c i t i e s sufficient  to  based  on t h e  followed. pipe  in the  valves  The w a t e r  to  operating  producers  to  their  water known as  irrigate  an  interval  and/or  soil  types  capacities  than c o o l e r ,  wetter  systems are  an e n t i r e  o r c h a r d at  a rotation is  not  method  generally  systems p h y s i c a l l y  water  fixed to  various  move  sprinkler  orchard sections irrigation  Okanagan a r e d e s i g n e d entire  the  atmospheric  water  those with  the  enough  9  system),  handmove  in the  irrigate  1  was  in t h e i r  requirement  allocate  sprinklers)  The peak  drier  i r r i g a t i o n of  systems of  presently  differ  district  while  to  conditions  the  interval  rotation  method.  equal.  with a t r i c k l e  peak  period,  needed  Hotter,  in  o r c h a r d once d u r i n g a  This  being  for  and  investment  i r r i g a t i o n water  Producers using  s y s t e m s use turn.  of  allow  time(except  Soils  water.  irrigation  maximum e x p e c t e d  a rotation  a particular location.  (pipe  entire  minimum t i m e  in  one  the  Stevenson,1980). is  handmove  capital  p e r i o d d e t e r m i n e d by the  found  small.  from f u r r o w t o  invested allow  i r r i g a t i o n systems are  numbers a r e  change  years,  Trickle  orchard using  in  districts to  allow  sprinklers  O t h e r f a c t o r s a f f e c t i n g the water r e q u i r e m e n t s of o r c h a r d s i n c l u d e t h e s l o p e of l a n d and d i r e c t i o n t h e s l o p e f a c e s , p r e s e n c e o r a b s e n c e of s o d c o v e r , p r o x i m i t y t o l a r g e b o d i e s o f w a t e r , and e x p o s u r e t o w i n d . 1 9  45 during year  the  peak  (1967  for  The two this  study  Sprinkler  water  is  sprinkler  considered  (solid the  set  driest  type)  recorded  i n the  be e x a m i n e d  in  and t r i c k l e .  m a j o r i t y of  orchard  O k a n a g a n . The t r i c k l e  primarily  for  its  potential  The s p r i n k l e r s y s t e m u s e d  for  this  i n terms  of  savings.  type.  advantage provides  of  an o v e r - t r e e  layer  fusion.  over-tree  crown r o t .  Okanagan  than  s h o u l d the  a c t s as  P e r h a p s the  of  fruit  of  over-tree  set  transpiration,  turgor,  ability  environmental  to  is  that to  it  due  to  this  of  below  the  latent  an the  diseases author  in recent  fruit  fall  such  as  indicates  s p r i n k l e r sytems have  systems  it  the  to  increases  certain  The  that  main d i s a d v a n t a g e  been  years  in  the  soil  as  a  more  1984).  obtain  access  and n u t r i e n t  determines  the to  water  transport  a b s o r b and r e t a i n  factors,  an  temperature  i r r i g a t i o n s y s t e m s use  from which p l a n t s  the  by c o a t i n g  a warming a g e n t  trees  under-tree  (Vander G u l i k ,  Solid  A soil's  protection  I n f o r m a t i o n conveyed  installations popular  frost  s p r i n k l e r system i s  susceptibility  is  and d i s a d v a n t a g e s .  s p r i n k l e r system  which,  level,  model  s p r i n k l e r systems are  some a d v a n t a g e s  a method of  frezing of  Over-tree  with  w i t h a water  area  hottest,  i r r i g a t i o n systems which w i l l  s y s t e m s now i n use  alternative  heat  the  Okanagan).  systems comprise  under-tree  the  the  are  irrigation system  i n t e r v a l of  the  water,  storage  necessary  for  requirements. together  frequency  and  with  46 intensity  of i r r i g a t i o n s .  Producers with  t h e aim of minimizing  accomplished can  allow  60%  during  determined  irrigations  water  called  t h e safe  f o r any o r c h a r d  and t h e s o i l  required  during  method t y p i c a l l y A trickle  water  storage.  type,  transport  i n that  f o r water  zone. Water used per  plant  orchards  on s o i l  reaches  This  interval,  together  2  c a n be  type,  climate,  with  t h e amount o f  using  a rotational  system  radically  i t does n o t r e l y the s o i l  in trickle  differs  systems unlike  from  that  on t h e s o i l f o r  i s used o n l y  from t h e p o i n t  different  irrigation  0  p e r day and t h u s , having  AWSC  peak ET, d e t e r m i n e s t h e amount o f  applies.  Rather,  a producer  (ET) r a t e s a r e a v a i l a b l e . The s a f e  irrigation  above  interval  weather p e r i o d .  i f data  irrigated  stress. This i s  the s o i l ' s  irrigation  water p e r day which a p r o d u c e r  described  of water  before  a "hottest, driest"  evapotranspiration  interval  the r i s k  by c a l c u l a t i n g t h e maximum  between  calculation,  and  i n t h e Okanagan have t r a d i t i o n a l l y  a s a medium o f  of emission  t o the root  i s measured  i n volume  s p r i n k l e r systems,  densities require  different  volumes of water.  3.1.4  ORCHARD SYSTEM SUMMARY Table  the  3.3 summarises t h e o r c h a r d  s t u d y . As i n d i c a t e d , 8 o r c h a r d  unique combinations  systems analysed i n  systems comprised of  o f one o f two r o o t s t o c k s ,  two s o i l  types  See t h e f o l l o w i n g s e c t i o n s f o r c a l c u l a t i o n s o f r o t a t i o n a l method w a t e r u s e a n d t r i c k l e water u s e . 2 0  47  TABLE  3.3:  ORCHARD SYSTEM  ROOTSTOCK  1  two i r r i g a t i o n  rootstock yearly  affects  fruit  maturity,  absorption thus  of  will  the density,  yields,  rate  typically  application.  be s i m u l a t e d . As  Soil  applied  needed  to reach  irrigation,  type  affects  holding capacity  requirements i s important  noted,  t h e volume of pre-mature  of t r i c k l e  and t h e water  system  SPRINKLER SPRINKLER SPRINKLER SPRINKLER TRICKLE TRICKLE TRICKLE TRICKLE  the l e n g t h of time  for the orchard.  the water  irrigation water  systems  SYSTEMS  IRRIGATION SYSTEM  SAND SILT-LOAM SAND SILT-LOAM SAND SILTLOAM SAND SILTLOAM  and, i n the case  requirements  and  SOIL TYPE  M2 M2 M26 M26 M2 M2 M26 M26  2 3 4 5 6 7 8  and  D E F I N I T I O N OF E I G H T ORCHARD AND T H E I R COMPONENTS  water  t h e water of the s o i l ,  f o r t h e o r c h a r d . The t y p e o f in determining  to the orchard  as well  t h e amount o f as t h e method  48 3.2  CALCULATION OF WATER APPLICATION RATES FOR EIGHT BASE CASES  This  section provides  detailed  rates  simulation.  The base c a s e s a r e  water  application  orchard  systems  irrigation British  (as  the  orchard  Manual,  systems w i t h  pertaining  sprinkler  rate  rate  water of  the  are  to the  the present  Okanagan V a l l e y of  based  on methods  of  A g r i c u l t u r e and  revision.  application  Consistent  rates  for  those  i r r i g a t i o n are a function  and s o i l  and  orchard  irrigation  under  the  the  type.  of  For o r c h a r d systems  calculation  is  a function  of  density.  SYSTEMS the  irrigation  systems,  apple  can a c c e s s  tree  to  1983  water  i r r i g a t i o n the  To c a l c u l a t e  defined.  i n T a b l e 3.3)  base c a s e  SPRINKLER  as  B r i t i s h Columbia M i n i s t r y  evapotranspiration  3.2.1  defined  gat i on Desi gn Manual,  trickle  scenarios  The c a l c u l a t i o n s  evapotranspiration using  case  of  w h i c h w o u l d be a p p l i e d  given  regulations  i n the  Irri  Food's  the  rates  Columbia.  outlined  with  for  base  application  calculations  Using the  water  application  an e f f e c t i v e water  (a  rates  storage  rooting  Manual a r o o t i n g  for  range  depth)  depth  of  sprinkler  from w h i c h an must  4 feet  be is  assumed.  For  tree  40% of section  fruits,  the  the  available  3.1.2).  maximum s o i l water  storage  The AWSC v a r i e s  water  deficit  capacity  with  soil  (MSWD)  (AWSC)  texture.  is  (see Since  the  49  model d e v e l o p e d MSWD must AWSC i s  in this  be c a l c u l a t e d  1 inch per  foot  zone.  The MSWD i s  zone.  For s i l t - l o a m ,  MSWD of  4  The (like  spacings water  Okanagan)  of  4 inches  the  moisture allowable  or  AWSC o r  a 2.5  is  rotation  1.6  inch per  each.  inches foot  types,  the  For sand,  the  over  the  root  over  the  root  AWSC r e s u l t s  soil  in a  reaches  the  and i s  as  the  basis  GA ( s a n d )  (GA) of  =  is  of  uses the as  75% of  i n the  set  set  sprinkler  the  soil.  up t o  apply a  the  rotation  MSWD ( t h e  soil  driest  for  each  rotation  thus  soil  dependent.  required is  the  equal  set  to  The the  efficiency.  1.6/.75 inches  = 4.0/.75 = 5.3  the  water  application  = 2.13  GA ( s i l t - l o a m )  is  Thus  stored  each  calculation  Water a p p l i c a t i o n  MSWD d i v i d e d by t h e  orchard  1983).  which the Manual d e f i n e s state)  climate  a p p r o x i m a t e l y 75% f o r most  requirement during  application'  To d e t e r m i n e  f o r a hot  i r r i g a t i o n method  3.1.3),  level  application.  given  soil  ( I r r i g a t i o n Design Manual,  section  'Gross  for  application efficiency  maximum o r c h a r d (see  2 soil  separately  40% of  applied actually  Because  considers  inches. water  the  thesis  expected  system,  the  inches  maximum w a t e r  requirements  maximum e x p e c t e d  for a  atmospheric  50 demand o r Peak E v a p o t r a n s p o r a t i o n determined rate The 0.23  (see  section  f o r Kelowna was PKET f o r  sand  i n c h e s per  is  of  be d e t e r m i n e d . allowable the  0.25  i n c h e s p e r day and f o r  peak  water  The peak  driest  between  the  (PI)  is  weather  conditions  PI  (sand)  =  the  /  PKET  and  thus  interval  can  maximum sets  under  on r e c o r d .  ( i n c h e s per  day)  1.6/.25 days  = 4.0/.23 =  17  days  do not  a b s o r b water  the  same r a t e .  the  soil's  the  maximum a p p l i c a t i o n  The w a t e r  absorption  a p p l i e d at  application  capacity. rates  rate  the  must  A s s u m i n g a sod  as  limited  characteristics  are  0.75  i n c h e s p e r hour  i n c h e s p e r hour  for  silt  loam  1983).  peak  irrigation rotation  = MSWD ( i n c h e s )  soils  1983).  silt-loam  evapotranspiration  interval  (days)  All  Design Manual,  depletion,  PI  (silt-loam)  be  The Peak E v a p o t r a n s p i r a t i o n  (Irrigation  = 6  PI  must  used  of  soil  interval  hottest,  rate  day.  Under c o n d i t i o n s maximum r a t e s  3.1.3).  (PKET)  (Irrigation  not turf  by s o i l for  surface exceed cover,  absorption  s a n d and  Design  at  0.35  Manual,  51 The  amount  irrigation chosen  i s the s e t time  sand  t o meet  and s i l t - l o a m  the i r r i g a t i o n  o f 12 h o u r s soils  irrigation  requirements For  efficiency  silt-loam  17 day r o t a t i o n  the  were c h o s e n f o r  soils  1.6 i n c h e s o f w a t e r a r e rooting  depth. At  is sufficient  t o meet  plant  conditions.  T h i s amount  is sufficient  d u r i n g PKET. T h e s e a p p l i c a t i o n irrigation  rates  equals for a  r a t e s w i l l be  f o r those  orchard  irrigation.  TRICKLE SYSTEMS As  was t h e c a s e  w i t h d e t e r m i n i n g t h e base c a s e  application  rates  for sprinkler  application  rates  for trickle  Irrigation  the d e r i v a t i o n  Design  comparing  sprinkler  base c a s e s  systems,  base c a s e  requirements  irrigation  versus  f o r those  i s f o r the  trickle  for sprinkler  water water  systems a r e c a l c u l a t e d  M a n u a l methods. As i n d i c a t e d  o f water  systems u s i n g t r i c k l e  The  of  2.13 i n c h e s o f water must be  required.  systems u s i n g s p r i n k l e r  the  rate  allow  while  4.0 i n c h e s MSWD a t 75% e f f i c i e n c y  a s the base case  3.2.2  a n d 24 h o u r s  f o r 6 d a y s g i v e n PKET  i n c h e s water  used  requirements  t o meet MSWD a s s u m i n g a 4 f o o t  applied. This application  5.3  t h e y must a l s o  respectively.  summarise, f o r s a n d  required  though  receives  Set times a r e  t h e maximum water a p p l i c a t i o n  The s e t t i m e s  To  75%  time  exceeding  soil.  of the r o t a t i o n .  f o r operator convenience,  sufficient not  o f t i m e a n y one o r c h a r d s e c t i o n  water use  and t r i c k l e  using  earlier,  orchard  purpose efficiencies.  systems d i f f e r i n  52 one  important  represent  respect.  present  Kelowna a r e a , differences  the  entire  uses a  rotation  trickle  sprinkler  at  one  method  a  system u s e r s without The  trickle  irrigation  the  which  of  trickle  irrigated  The  base c a s e  area  for  Therefore  used  density  requirements  first  at  a gallons  this  by  day.  Ten  prevent  of  per M2  to  sprinkler  of  water  from  which  be  critical  stress.  carried points  irrigation  tree  factor  basis  water  as  irrigation  in determining  irrigated  to  an  per  day  orchard  the  water  systems.  (g/p/d) f i g u r e  the  density  (trees  in a gallons  per  a c r e per  inch  more w a t e r  salinity  buildup.  day  results  orchard  calculations.  by  acre  for  requirements  opposed  systems,  per  out,  systems.  plant and  a  available  risk  the  use  daily  orchard  percent  irrigation  to  M26  gallons  irrigating  To  s y s t e m b a s e c a s e water a p p l i c a t i o n  then m u l t i p l i e d  resulting  to  For  not  the  respond  reductions w i l l  sprinkler  trickle  to  the  because of  3 . 1 . 3 ) . The  the  determine  a per  is a  trickle  calculated. was  for  section  results  irrigation  s t a r t i n g point  trickle  on  basis  is a  for  sprinkler  orchardist  orchard  were c a l c u l a t e d  arrive  (see  water  i s to  levels  trickle  flexibility  base c a s e  sprinkler  p r o v i d e s a means of  increasing  successive aim  and  time w h i l e  s y s t e m e n a b l e s an  weather c o n d i t i o n s ,  base c a s e  b a s e c a s e d o e s not  irrigation  orchard  the  water a p p l i c a t i o n  trickle  between  methods. T r i c k l e an  day  While  the  per  was g/p/d  figure  acre)  estimate.  i n i n c h e s of  i s added t o a l l o w  rates,  for  Dividing water  per  drainage  53 g/p/d  =  (.623  * PKET *  .75  * A *  .9)  +  where PKET = peak e v a p o t r a n s p i r a t i o n A = area .623  per  = 27152 g / a c r e  .75  = a trickle  .9  = crop  10%  = allows  M2  rootstocks  (202  gallons/plant/day gallons/acre/day  i n c h / 43560  irrigation  in.)  by  density)  feet /acre 2  correction factor  for  apples  f o r water p e r c o l a t i o n t o buildup  t r e e s per  =  (.24  (determined  coefficient  salinity  For  tree  10%  (10%  of  prevent  g/p/d).  acre):  24.0  = 24.0  g/p/d  * 202  trees/acre  = 4848 inches  For  M26  in a  will  relative  orchard  discussed  =  . 1786  =  .196  +  .195  requirements  not  be  a  acre)  inches  f r o m the  (27152 g a l s / a c r e  in.)  10%  t r e e s per  I t would appear  density,  be  (4848 g/a/d) /  f i g u r e of  water  similar.  =  (388  i s apparent  base c a s e very  day  rootstocks  resulted As  per  per  similar calculations day.  above c a l c u l a t i o n s , t h e f o r M2 that  significant  and  M26  daily  rootstocks  rootstock, determinant  and in  thus the  system w a t e r - y i e l d comparisons. T h i s  f u r t h e r i n chapter  are  will  4.  These water a p p l i c a t i o n c a l c u l a t i o n s f o r s p r i n k l e r trickle  irrigation  systems  form t h e  base c a s e s  for  the  and  54 simulation model. Successive reductions of water application levels as a percent of the base case levels are carried out for a l l orchard systems to determine the c r i t i c a l  irrigation  levels below which y i e l d s begin to be reduced. I r r i g a t i o n l e v e l i s one input into the c a l c u l a t i o n used to determine the s o i l moisture l e v e l , as outlined in the following section.  3.3 CALCULATION OF SOIL MOISTURE LEVEL In order to determine whether or not water stress i s present and, i f present, i t s effect on y i e l d , the s o i l moisture level must be determined. This section provides a detailed discussion of a l l the parameters used in the model to determine the s o i l moisture l e v e l . The function used in c a l c u l a t i n g the moisture l e v e l of the  s o i l for each period t i s adapted from Flinn(1971) and  is of the following form:  SM  t  = SM  t-1  + R  t  + I  t  - AET  t  where SM = s o i l moisture l e v e K i n . ) R = rainfall(in.) I = irrigation(in.) AET = actual evapotranspirat ion(in.) t = day of the growing season (t=1...245) and 0 < SM < FC.  55  Rainfall  each  generator  2 1  simulation  .  day  runs.  15.  were d e t e r m i n e d is  (PET)  and t h e  e x o g e n o u s l y by the is  a factor  to  The v a l u e s for  in  of  I,  initial  section  a function soil  the  of  3.2.  moisture  amount  orchard  Actual  level.  the  s e a s o n on May 1,  the  both p o t e n t i a l  weather  be v a r i e d d u r i n g  I r r i g a t i o n begins each  each day,  (AET)  set  Irrigation  ends September applied  is  of  system  and  water simulation  evapotranspiration evapotranspiration  AET i s  derived  as  follows:  AET = p * PET  p(sand)  = 3 *  (SM/FC)  p(silt-loam)  = 5 *  (SM/FC)  where  p = a soil  SM = s o i l  moisture  FC = f i e l d lOin. and  The potential  2 1  see  value  0 < p <  of  moisture  capacity for  3.5.  level  (4in.  for  sand,  silt-loam)  1.  p depends  evapotranspiration  section  factor  on the (PET),  soil  moisture  and t h e  soil  level  (SM),  type.  This  56 relationship  is  apparent  that  ratio  actual  of  given  as  the to  The p o i n t  soil  since  different field  soil  moisture  level  the  31. is  3.4  CALCULATION OF YIELDS previous  moisture  level  detailed.  the  to  beginning  the  This  to  calculate  yield  is  done  of  the  calculated.  a growth  The g r o w t h The g r o w t h  growth d u r i n g t h i s  later  years.  (depending  factor  The y i e l d  for  the  period.  from March 1  the of  soil  the  soil  use  of  the  yields.  is  the  season  at  daily  soil  moisture  The c a l c u l a t i o n depending  on the  factor  calculated  assumes w a t e r  for  is  establishing  accommodate  calculated  t h r o u g h 20.  This  age  years 1  Tree  for  of  are  pre-maturation period. important  soil  was  will  factor  to  is  stress  is  with  by  determining  growing  and number t o  on r o o t s t o c k )  also  season.  and a yield  inhibit  branch s i z e  capacity  factor  7.  sufficient  function  First,  factor  years  previous  steps.  through  growth d u r i n g e a r l y  field  yearly apple  in several  orchard,  the  the  moisture  are c a l c u l a t e d  a method  makes  soil  is  varies  p i n any p e r i o d  SM i n t h e  e a c h day of  section  level  the  (p)  decline  a given  of  levels  growing  section, for  at  of  to  it  declines,  are c h a r a c t e r i z e d  To i n i t i a t e  the  In  of  soils  value  set  moisture  evapotranspiration  The v a l u e  moisture  through October  soil  pressures  ratio.  soil  of  From F i g u r e 3 . 1 ,  which p b e g i n s  different  using  Daily  at  water  capacity  calculated  level  potential  declines. type  in Figure 3.1.  is  for the  fruit years  in 3 or 4  period  57  Figure  3- '  n«.riv.it ion of  Soil  Moisture  Factor p  58 during  which marketable  during  this  period  Once t h e reduction yield  of  factors  yearly  days  and t h u s  the  determined,  factors  to  yield.  relevant  the  calculating  reduction  absence  water  reduction  growing  factor.  from t h e  second  step  daily  growth  using  the  in  daily  season g i v e s  The y e a r l y  potential  stress)  factors  the  the  reduction  yearly  equals  d i v i d e d by  the  average factor  when  yield  (yield  in  the  actual  yearly  yield.  DETERMINING GROWTH REDUCTION FACTOR The  tree  been  daily  i n the  subtracted  3.4.1  tree  involves  the  reduction  of  o c c u r . T r e e growth  levels.  sum o f  number of  yields  a contributing factor  the  and/or y i e l d  moisture The  not  have  determination  reduction soil  age  is  fruit  model assumes t h a t ,  growth w i l l  season. affected  However, to  proceed if  i n the  a b s e n c e of  water  u n h i n d e r e d d u r i n g each  water  stress  occurs  a d e g r e e d e t e r m i n e d by t h e  stress,  growing  growth w i l l  be  following  relat ionship:  g  = 1 .2  -  (2.0*(SM  t where  /FC)) t  g = a growth r e d u c t i o n as  a ratio  SM = s o i l  moisture  FC = f i e l d for  of  potential  (expressed  daily  growth)  level  capacity  sand  factor  soils)  (10  in.  for  silt-loam,  4 in.  59  t and  This  = day of  permanent  soil's  (when  Full  the  is  described  wilting  point  water  storage  available  3.1.2).  potential  growth  3.4.2  no g r o w t h  graphically is  assumed  water 1.00  at  'g'  level  (at  2 2  in Figure  to  capacity,  reduction, factor  O k a n a g a n . When g i s  point)  (t=1...245)  growth o c c u r s  recommended minimum s o i l the  season  0 < g < 1.  relationship  where  growing  be  10% of  AWSC (see o r above  is  zero).  for  o r below  3.2  tree  the  section  60% of This  is  fruits  permanent  AWSC the in  wilting  occurs.  DETERMINING THE YIELD REDUCTION FACTOR As  with, growth d e t e r m i n a t i o n ,  unaffected  i n the  is  two  present  timing  of  1. degree  factors  are  water  stress.  considered,  the  a r e assumed  to  be  When water  stress  d e g r e e and  the  stress..  of  stress  This  factor  This  assumes t h a t  degree at  a b s e n c e of  yields  is  identical  a given  to  the  growth  reduction  g r o w t h and y i e l d a r e a f f e c t e d soil  water  level.  factor. to  the  same  2 3  s e e I r r i g a t i o n Design Manual, B . C . M i n i s t r y of Agriculture, 1983. T h e r e i s some e v i d e n c e t o s u g g e s t t h a t an e a r l y s e a s o n t r e e g r o w t h p e r i o d f o l l o w e d by a l a t e r f r u i t g r o w t h s t a g e m a t u r e t r e e s has i m p l i c a t i o n s f o r o r c h a r d i r r i g a t i o n p r a c t i c e s ( M i t c h e l l e t . a l . 1 9 8 4 ) . The g r o w t h r e d u c t i o n f a c t o r as c a l c u l a t e d i n t h i s t h e s i s o n l y has an e f f e c t on y i e l d i n non-mature t r e e s . 2 2  2 3  in  60  Growth Reduction Factor | ( r a t i o of potential d a i l y growth)  t.00  0.75  +  0.50 .+  0.25  +  0.10  F  U  u 8  r  e  3.2  0.25  0.50  0.60  RelolJm^LilLJ^L^" "" .n.i s » i 1 M o i s t u r e C r  t h  .00  0.75  9  o  i  l  •oisture (as f r a c t i o n of f i e l d capacity)  *°" Level.  F  a  c  t  0  r  *-  61 d e g r e e of  stress  (d  ) = 1.2  -  (2.0*(SM  t where  SM = t h e  soil  FC = f i e l d and 0 < d <  2.  timing  of  moisture  capacity  level  (inches)  (inches)  1.  stress  The d a t e d u r i n g t h e  growing  s e a s o n when  important  for  yields.  The r e l a t i o n s h i p  occurrence  of  following  fruit  and t h e  timing  of  stress  stress  is  is  between  given  w < 15 t h e n  T t  = 0.25  + 0.05  * w  if  15 < w < 27 t h e n  T t  = 1.75  -  0.05  * w  if  27 > w < 30 t h e n  T t  = 7.75  -  0.25  * w  T t  = 1.15  -  0.03  * w  if  where  occurs  by  the  equations:  if  w > 30 t h e n  T = t i m i n g of ratio will  of  stress the  impact  w = week number and 0 < T <  This  /FC)) t  relationship  factor  degree upon  to  e x p r e s s e d as w h i c h water  a  stress  yield  in growing  season  1.  is  described  graphically  in Figure  3.3.  F i (jurc  3•3  63 The  value  of  T , and t h u s  stress  factor,  second  week  period  is  ultimate  3.4.3  peaks  i n June)  assumed fruit  to  the  i n week  a daily  sum of  be t h e  most  days per  timing  growing set  critical  of  season  occurs.  i n terms  (the  This of  2  the  YIELD  growth r e d u c t i o n  factor  (g)  the  of  daily  factors  these  the  the  yield. "  basis,  reduction  15 o f  of  d u r i n g which f r u i t  TOTAL GROWTH AND TOTAL Since  strength  total g over  factors  for  effect  the  is  calculated growth  the  entire  growing  all  t  d i v i d e d by t h e  days  on  season  is  the  number of  season. n  G  =Z  i  [g  ]/n  t  t  where G = a n n u a l g r o w t h n = number o f i  = the  Each y e a r ' s previous  year  a growth  factor  determined  G i  2 < t  i =1 j  and t h u s is  days per  current  growth  reduction  is for  tree  growing  year  assumed years  applicable,  factor  be d e p e n d e n t t h r o u g h seven  s e e Goode,  ]/i  for  all  i=1...7  j  1975  and M i t c h e l l  on  et.al.,  1984.  the  for  a carrythrough effect  by:  [G  (245)  (i=1...20)  to  one  season  which is  64 Total stage  yield  i n any y e a r  of the t r e e as w e l l as the y i e l d  previously related  i  yield  d and T t o be  =E[d *T ]/n t t  total  growth  determining equations  yield  yield  reduction  reduction factor together  with  G i s also a factor in  t h e YR f a c t o r .  describe the r e l a t i o n s h i p  determining  year-end  = PY i  AY  factors  r e d u c t i o n i n t h e f o l l o w i n g manner:  where YR = a n n u a l  AY  on t h e g r o w t h  d e s c r i b e d . F a c t o r s d and T a r e c o n s i d e r e d  to total  YR  The  i s dependent  (1-G -YR i i  i  (1-YR i  where AY  o f G a n d YR i n  yield..  i = PY  i  The f o l l o w i n g  )  )  f o r a l l i=4...7  f o r a l l i=8...20  = actual yield  i n year i  i PY  = potential  yield  i n year  i ( i n the  "absence o f w a t e r  stress,  see T a b l e  i  3.5 As  3.1)  WEATHER GENERATOR inputs  into  the s o i l  moisture  and e v a p o t r a n s p i r a t i o n d a t a simulation  calculation,  data.  rainfall  a r e r e q u i r e d by t h e o r c h a r d  m o d e l . One method o f g e n e r a t i n g  use h i s t o r i c a l  daily  F o r t h e Kelowna  area,  such  data  historical  i s to  65  records  of  period  daily  1971  through  much f u r t h e r . derive  pan e v a p o r a t i o n 1983.  2  section.  In o r d e r  relationship  was  to  available  Daily r a i n f a l l  5  Pan e v a p o r a t i o n  evapotranspiration  are  as  extend  has  hypothesized  be d e s c r i b e d  exist  and r a i n f a l l and t e m p e r a t u r e .  evaporation  was  maximum t e m p e r a t u r e for  the  13 y e a r  Several forms  for  period  functional  the  sets.  Linear  first  order  p e r f o r m e d and t h e  models  later  data  set,  r a i n f a l l and  April  through  daily  September  1983.  due  zero  to  the  presence  and d e p e n d e n t  using  possess  the  were  a Maximum  Cochrane O r c u t t  iterative  procedure.  results  all  are  below,  given  data  found to  tested using  re-estimated  values  variable  e s t i m a t i o n s were when  of  Correction procedures  regressions  a  D a i l y pan  Likelihood of  to  Log-linear  correlation  statistic.  in a  total  through  explanatory  serial  back  forms were c o n s i d e r e d .  and q u a d r a t i c  Durbin-Watson  months  1971  proved u n s u i t a b l e  both w i t h i n  on d a i l y  the  go  between pan  evaporation  regressed  records  pan e v a p o r a t i o n  to  the  been and c a n be u s e d  will the  for  with  2  6  The t-ratios  in  brackets.  OLS  PAN = - 8 . 1 1 2 2  + .25129T  (-6.4998) R =.5411 2  (48.061)  -  .10544R (-9.0286)  D-W=1.3711  A 1 1 w e a t h e r d a t a was o b t a i n e d from t h e C a n a d i a n C l i m a t e C e n t r e , A t m o s p h e r i c E n v i r o n m e n t S e r v i c e , E n v i r o n m e n t Canada a t Downsview O n t a r i o . s e e C M . B e a c h and J . G . MacKinnon "A Maximum L i k e l i h o o d Procedure for Regression with A u t o c o r r e l a t e d E r r o r s , " E c o n o m e t r i c a , 46:1 ( J a n . 1 9 7 8 ) . 2 5  2 6  OLS  PAN =13.542  + .41605E-3T  . (309105)  (6.2309)  .85941E-4RT (.36862)  .30423R  (1.8516) +  .13579E-2R  (-5.6759)  R =.5581  (7.1478)  PAN = - 1 0 . 6 3 6 + .26161T (-6.6534)  2  D-W=1.3799  2  AUTO  + .57254T +  2  -  .74765E-1R  (39.134)  (-6.6987)  R =.5883 2  AUTO  PAN = 7.0700  + .32341E-3T  (1.7342) .39804E-4RT (.18071)  + .10800T +  2  (4.1087) .27828R  +  (-5.5083)  (2.9745) .14064E-2R  2  (8.0441)  R =.6021 2  where AUTO = c o r r e c t e d  for  autocorrelation  PAN = pan e v a p o r a t i o n R = daily  rainfall  (predicted) (.1 mm) o  T = d a i l y maximum t e m p e r a t u r e  (.1  C)  D-W = D u r b i n - W a t s o n s t a t i s t i c number o f  observations  = 2316  Though t h e R s o b t a i n e d 2  larger  than  quadratic range  of  those obtained  function  with  the q u a d r a t i c  the  linear  forms a r e  forms,  the  was f o u n d t o r e a c h a maximum w i t h i n  the r e l e v a n t  form c o r r e c t e d  with  data  set.  For t h i s  reason  f o r a u t o c o r r e l a t i o n was c h o s e n  the  as t h e  the  linear point  67 predictor  to  be  OLS p o i n t regression accurate  predictors,  model  predictor  generator  is  pan e v a p o r a t i o n  to  prediction,  Y f  of  is  values.  is  the of  linear  violated,  are  dependent  Since  actual  the  the  A point variable  purpose  given  of  2  1  The v a r i a t i o n  of  by  (X X)  X  1  0  0  ]  -1 where  2  matrix In o r d e r  to  'capture'  prediction, multiplied generated  the  is  a (X X) 1  of  the  some of  the  s t a n d a r d e r r o r of  is  included  coefficients.  variation the  by a n o r m a l l y d i s t r i b u t e d number  co-variance  estimated this  i n the  point [N  in  the  predictor  (0,1)] r a n d o m l y  prediction  of  pan  evaporat i o n . The  final  evaporation temperature  form of  values is:  the  predictor  from d a t a  the  predicted  -1 O [1+X  for  r a i n f a l l and  v a r i a t i o n around the  interest.  most  values  variables.  the  simulate  rates,  value  not  explanatory  variable  evapotranspiration  point  the  classical  i n d i v i d u a l dependent  an e x p e c t e d v a l u e  independent  weather  of  the are  predicting  values  is  if  assumptions  means of  from a c t u a l  given  used.  for  generating  on r a i n f a l l and maximum  pan  a  68  PAN = 0  where  + 0 , T + 0 R + SEP*Rand  O  2  PAN = pan SEP  evaporation  = standard error  of  the  Rand = a randomly g e n e r a t e d  prediction number  with normal d i s t r i b u t i o n .  3.6  DERIVING  POTENTIAL EVAPOTRANSPIRATION  FROM PAN  EVAPORATION The  method  evaporation  of  deriving evapotranspiration  values  is  of  the  following  from pan  form:  PET = K * PAN  where  PET = p o t e n t i a l PAN = pan  evaporation  K = PET  Hargreaves(1968) various  points  groupings, Since  i_  coefficient  provides  i n the  growing  a table season  i n c l u d i n g deciduous the  season,  the  of  study  this  evapotranspiration  K value  growing the  31  (245  days).  growing  season  derived  from H a r g r e a v e s  a variety  stage  be d e f i n e d .  ( e x p r e s s e d as  for of  i n the  For the  season begins March  The r e l a t i o n s h i p  is  K values  plant  fruits.  s e a s o n must  October  for  depends upon t h e  growing  of  purposes  1 and ends  between K and  a percentage  given  growing  of  the  in Table 3.4.  the  total)  The  as  69  relationship  i s shown  Predicted daily  from  randomly Kelowna  equal year  maximum  by y e a r area  Data used  values  dating  identically weather orchard  75 y e a r s  back  life.  Each  2  selected  data  for  the  7  i s stored  i n a 20 y e a r  models,  a l l models  'test  data  of h i s t o r i c a l  f o ra l l 8 orchard across  are generated  and r a i n f a l l  t o 1899.  randomly  factor  i n F i g u r e 3.4.  f o r pan e v a p o r a t i o n  temperature  from  selected  graphically  thus  during  scenario',  b l o c k and  a s s u r i n g an  a n y o n e 20  i n c o r p o r a t i n g an  T h e y e a r s c o v e r e d a r e 1899, 1900, 1903-1932, 1934-1961, 1969-1983. M i s s i n g y e a r s a r e due t o a b s e n c e o r incompleteness of data. 2 7  TABLE  3.4:  D E R I V A T I O N OF E V A P O T R A N S P I R A T I O N C O E F F I C I E N T K WHICH V A R I E S WITH P E R I O D OF GROWING SEASON  PORTION OF GROWING SEASON ( X ) 0 0, 0, 0, 0, 0, 0,  Source:  EQUATION TO D E R I V E POTENTIAL EVAPOTRANSPRATION COEFFICIENT  0 0 0, 0, 0, 0, 1,  Hargreaves,  K K K K K K K  1968.  0 0 0, 0,  1 , 1 ,  2,  0*X  o*x -  5*X 5*X 0.5*X ,0*X 0*X  70  K 1 .00  0.75  0.50  0.25  % of growing season  Figure 3.4  Relationship Between Evapotranspiration Coefficient K and % of Crowing Season  71 explicit orchard  set life  randomly should  assumptions,  times,  each  of  s e l e c t e d weather  stabilize  sound b a s i s  3.7  of  for  the  consists  10 of  these  which uses a unique  years.  This  v a r i a t i o n of  set  20  year  of  m u l t i - r u n method  results  and p r o v i d e a  o r c h a r d system performance  comparisons.  SUMMARY OF PARAMETER RELATIONSHIPS  Appendix B provides  results  growing  days)  season  (245  on a l l  for  ( s y s t e m 5)  w i t h M2 r o o t s t o c k ,  irrigation  and .sand s o i l .  parameters  used  Figure  g i v e s a flow  3.5  parameters chapter,  chart,  relate  to  a sample 202  trees/acre,  T a b l e 3.5  chart of  model,  another  see  rate  section  remain constant Since  each  years  of  3.2)  for  245  days  the  orchard l i f e .  historic  used c o u n t e r s  a "weather  weather  consists  of  data daily  derived  hand c o r n e r of  the  (see  set  to  is  (see  total  various  the  T a b l e 3.3)  flow and an  base c a s e  irrigation  Once s e t ,  these  the of  simulation  20 g r o w i n g  keep  of  s e l e c t e d at section  rainfall  by  t r a c k of  For each year  year"  measurement.  how the  YEAR and DAY ( d e n o t e d  are  simulation,  as  of  run.  d u r a t i o n of  subscripts) 20 y e a r  units  of  during a simulation  run c o n s i s t s  each,  a list  this  are chosen.  the  simulation  of  single  in  upper r i g h t  (some r a t i o  a  trickle  provides  summary of  the  for  o r c h a r d system  model and t h i e r  one  i n the  parameters  i n i t i a l l y an o r c h a r d s y s t e m  irrigation rate,  i n the  and f a c t o r s  Starting  year  of  3.5).  the  run.  seasons  or  i and t  in  the 20  factors  stage year  random from a This  and maximum  weather  in  72  T a b l e 3.5 M o d e l P a r a m e t e r s , A b r e v i a t i o n s , and U n i t s o£ M e a s u r e m e n t  Abreviation  Parameter Actual Evapotranspiration A v a i l a b l e Water S t o r a g e C a p a c i t y Degree o f S t r e s s PET S l o p e C o e f f i c i e n t Field Capacity Growth Reduction Factor Gross A p p l i c a t i o n Rate PET C o e f f i c i e n t Mailing 2 Rootstock M a i l i n g 26 R o o t s t o c k Maximum S o i l W a t e r D e f i c i t Pan Evaporation Potential Evapotranspiration Peak I n t e r v a l Peak E v a p o t r a n s p i r a t i o n Permanent W i l t i n g P o i n t Potential Yield S o i l Moisture Level Timing of S t r e s s Factor Annual Y i e l d Reduction S o i l Moisture Factor  AET AWSC d f FC g GA K  M2 M26 MSWD PAN PET PI PKET PWP PY  SM T YR  precipitation  data  season  1 through  used  (March  f o r two  simulation the  and  predictor  estimate  a  f o r the period  separate  process,  rainfall  point  U n i t s o f Measurement  pan  October  inputs  deriving  in. of water/ft of s o i l inches of water inches of water days inches of water/day i n . of w a t e r / f t of s o i l Ibs/acre/year in. of water/ft of s o i l r a t i o o f p o t e n t i a l growth r a t i o of p o t e n t i a l growth  3 1 ) . The  into  as  data,  (see sections  3.5  PAN,  stage  moisture  through and  the  weather  the next  the soil  rate,  in. of water/ft of soi 1 r a t i o o f p o t e n t i a l growth inches  defined  temperature  evaporation  inches of water i n . of water/ft of s o i l r a t i o o f p o t e n t i a l growth  3.6),  growing data  is  of the  level.  Both  the use o f a a r e used  f o r each  to  growing  irrtga-  choose orchard system  ATT,  1-1*1 year(i)-0  dey(O-0  choose Irrigation level  res  growth  factor  g -f(SM ) t  a c t u a l y i e l d (AY) p o t e n t i a l yield (PY)  I  <Jyes  a n n u a l growth factor  <]yes  AT -PY *(l-<; -rR ) i  i  1  i  F i g u r e 3.5  t  Interaction  of F a c t o r s Comprising the Hodel  annual y i e l d reduction factor  74 season day. estimate  potential  potential 3.7),  The d e r i v e d pan e v a p o r a t i o n  as  d e r i v e d by H a r g r e a v e s  ratio  of  the  the  potential  estimated near  field  (see  section  derived  capacity 3.3).  level,  moisture  on t h e  section  3.3).  The d a i l y fruit  under  8 years  level  is  and t h e  period  (T)  used  (YR). growth the  an  soil  trees  Daily  (d)  as  during to  day a r e  p e r i o d of  loss  of  the  stress.  based  day's  growing  and  inputs  an annual  soil  soil  (see  trees  moisture  the  season  both the  soil  yield soil  (G).  degree  moisture  occurs  reduction moisture  days).  factor level,  continues At the  of  level  when s t r e s s  factors  (245  daily  both growing and  on t h e  season  as  the  F o r young  and o v e r ,  or  soil  and c u m u l a t e d a n n u a l l y  age  of  at  rate,  irrigation, other  and  conditions  previous  affects  and t i m i n g and y i e l d growing  level  d e r i v a t i o n of  d e t e r m i n e d by the  calculate  the  moisture  the  level  (g)  The d a i l y c a l c u l a t i o n factor,  the  rainfall,  factor  8 years  level  the  is  moisture  moisture  and the  t h r o u g h water  daily  the  with a moisture  into  moisture  a growth  AET i s  p  AET, versus  evapotranspiration  data  input  previous  trees  stress  are  is  calculated  F o r mature water  weather  section  rate,  s i m i l a r atmospheric  The a c t u a l  level.  moisture  mature  under  a  soil  PET i s  form a s o i l  to  The c o e f f i c i e n t  rate.  a given  while  used  K (see  evapotranspiration  occur at  occur  from t h e  moisture soil  to  conditions  to  (1968).  evapotranspiration  estimated  atmospheric  actual  is  PET, using  evapotranspiration coefficient,  the  loss  evapotranspiration,  rate  for  end of  75  the  growing  yields years  (this is  growth used  given  the  the  the  stress of  s t o p s and t h e is  the  (see the  yield,  the  cumulative  factor  been  tabulated.  random and the  If  YR a r e  AY. A t h i r d PY, the  Following this have  give  though 4  s y s t e m under c o n d i t i o n s  simulation  s e l e c t e d at  yield,  to  used,  3.5),  reduction  annual  3.1).  are  being  figure  potential  orchard  results  in  yield  actual  Table  a r e m a t u r e enough  rootstock  an example  G and/or  for  trees  on t h e  d e t e r m i n i n g AY i s  "years"  year  as  to c a l c u l a t e  obtainable  20  if  depends  factor  factor  water  season,  simulation  of  no  calculation,  r u n , the not,  yield  procedure  a new  weather  continues.  if  Chapter  4  RESULTS The p u r p o s e chapter  is  different case for  to  of  water  application  agriculture  orchard  cases  is  resulting  and subsequent of  the  the  systems,  be an  water  applied within  are  of  o r c h a r d water  as  sensitivity  each  case  trials. irrigation  analysis  on  incorporated 8  2 i r r i g a t i o n system t y p e s , However,  factor  rootstock  in determining water  o r on t h e  requirements  b a s e c a s e water  for  irrigation  (see  of  i r r i g a t i o n base c a s e  section  76  it  application 3.2.2).  the rates  effect  of  orchard systems.  significant since  2  was  application  between d i f f e r e n t  a potentially  application  trickle  base  restricted  i n the  calculation  8  recorded.  the  determinant trickle  for  irrigation  o r c h a r d system,  rates  was c h o s e n  of  procedure  types.  insignificant  a single  were  all  water  reduced  yields  rates  presented.  c o m p r i s e d of  application  Rootstock  results,  results  and r e s u l t s  for  of A base  application  simulated  v a r i a t i o n between d i f f e r e n t  relative  similar  on o r c h a r d y i e l d s .  b a s e c a s e s and the  discussed  to  effects  restricted  t y p e s and 2 r o o t s t o c k  found  the  base c a s e  The o r i g i n a l s i m u l a t i o n  soil  analysing  Okanagan was  presents  s e l e c t e d parameters  orchard  previous  r a t e s were s y s t e m a t i c a l l y  This chapter  Validation  the  levels  From t h e s e  s y s t e m and t h e  scenarios  of  in  current allowable  in the  systems.  application  model d e s c r i b e d  p r o v i d e a means  representing  orchard  the  is  factor  in  a  calculation  However, water  77  requirements gave  for orchard  nearly identicalresults.  relationship zones.  tree.  between  Larger,  number,  for  have  Thus,  less  densely  l a r g e r root for a l l  average  results of  the  orchard  20 of  these  unique  set  system are  The  results  weather the  of  data.  tree  more w a t e r  root  water  in  per  requirements  i d e n t i c a l . Therefore,  only  are r e p o r t e d h e r e .  lifes,  c h a p t e r a r e b a s e d on  each  The r e s u l t s of  the  t h o u g h fewer  over  Each s i m u l a t i o n r e s u l t  average  400  the  the  20  consists  of  incorporating f o r each  a  orchard  observations.  CASE of  the  base  case  simulation for orchard  are presented  r e s t r i c t e d case,  to  in Table  be d i s c u s s e d  4.1.  systems  Results  for  in the  next  section  are  c a s e water a p p l i c a t i o n l e v e l s  were  arrived  at  presented. The  using  base  the  sprinkler region  twenty is  Irrigation  D e s i g n Manual  and t r i c k l e  (see  identical  This  requiring  in t h i s  orchard  u s i n g M2 r o o t s t o c k s  also  and s i z e  accumulated y e a r l y y i e l d t o t a l s  thus  THE BASE  a t t r i b u t a b l e to  systems the  were  presented  20 y e a r  4.1  the  zones  orchard  life-span.  of  is  spaced t r e e s ,  s y s t e m s on M2 r o o t s t o c k s  The  year  This  orchard density  M2 and M26 r o o t s t o c k s  orchard  the  s y s t e m s u s i n g M2 a n d M26 r o o t s t o c k s  section  to  the  year  expected  irrigation  3.2).  average life  of  since  recommendations  systems  The base  i n the  for  Kelowna  case y i e l d r e s u l t s  potential yields M2 o r c h a r d s ,  as  (per  given  in both cases y i e l d s  acre)  are over  in Table  are not  3.1.  subject  T A B L E 4.1  RESULTS OF WATER REDUCTIONS ON M2 ORCHARD Y I E L D S SHOWING BASE C A S E AND WATER R E S T R I C T E D C A S E ANNUAL IRRIGATION L E V E L S AND Y I E L D S  [rr igat ion type  Soil type  spr i n k i e r  sand  n  M  m  M  m  n  m  «  sprinkler  silt-loam  H  N  m  n  m  m  m  "  m  m  tr ickle »  sand N  M  *•  m  «  m  m  trickle  silt-loam  Water Applied as % of Base C a s e base  case  55% 50% 45% 40%  Annua 1 Irr igat ion (inches)  53.33 29.33 26.68 24 .00 21.33  base c a s e  48.00 21 .60  40%  19.20  30% 20%  Avg. Y i e l d p e r Acre f o r 20yrs (lbs) 24138 24 111 24061 23893 23579  (0.78)*  Critical Po i n t (inches) 22 .5  (16.28) (49.98) (104.45) (166.06) 14.5  16.80 14.40 9.60  24138 (0.01) 24 1 27 (19.57) (34.90) 24083 23969 (76.31) 23638 (157.91 ) 2251 5 ( 4 0 8 . 7 2 )  base case 65% 55% 50% 45%  29.79 19.36 16.39 1 4 .90 13.41  24138 24063 23703 23296 22924  (3.11) (40.08) (156.10) (252.46) (257.95)  16.0  base case  29.79  24138 24098 23951 23703 23267  (0.04 ) ( 4 3 . 14) ( 1 18.86)  10.3  45%  35%  w  •t  45%  M  M  M  m  It  M  40% 35% 30%  13.41 1 1 .92 10.43 8.94  (168.62)  (284.70)  * standard deviations f o r y i e l d s a r e given i n brackets. R e s u l t s a r e a v e r a g e s o f 400 o b s e r v a t i o n s u s i n g 20 r a n d o m l y s e l e c t e d w e a t h e r d a t a s e t s e a c h c o n s i s t i n g o f 20 y e a r s o f d a i l y w e a t h e r d a t a . A l l o r c h a r d s y s t e m s were s i m u l a t e d u s i n g i d e n t i c a l w e a t h e r d a t a s e t s .  79 to  water  stress.  definition applied thus  The a v e r a g e  a stress-free  i n the  results  in chapter  application  on t h e  systematically  the  application Model  by  yield,  allotment,  stress  as  and  hypothesized  2 8  the  the  o r not  a p p l i e d to  Y i e l d s are  of  water  functions.  each o r c h a r d  a function  p r o c e d u r e by w h i c h i t  a model a d e q u a t e l y  r e a l world system  Ideally,  data  used  not  to  best" method,  data p r e v i o u s l y  water  reduced.  is  s h o u l d be u s e d  As a "next  point  of  level.  whether of  a single  orchard production  amount of  validation  determined  process  i n no water  determine  respective  system  simulate.  results  results  point  behaviour  is  The maximum w a t e r  maximum p o t e n t i a l  From t h i s  water  yield  2.  The b a s e c a s e  is  yield.  base c a s e s ,  i n the  potential  in  it  mimics  was d e s i g n e d  i n c o r p o r a t e d i n the  validate  is  the  a model m i g h t  the to  modelling  simulation  results.  be v a l i d a t e d  f o r m u l a t i n g the  model  using  (Anderson  ,1974). The b a s e c a s e  results  and i n f o r m a t i o n t a k e n Okanagan V a l l e y .  from t h e  and F o o d ' s  recommendations. year  life-spans  the  The e x p e c t e d of  of  water  British  (BCMAF)  using  orchard industry  The q u a n t i t i e s  cases are d e r i v e d using Agriculture  were a r r i v e d a t  parameters in  applied  i n the  Columbia M i n i s t r y  I r r i g a t i on'Design yields  the  in each  M2 and M26 o r c h a r d s  (as  of  Manual year  given  of  the  in Table  T h i s d i s c u s s i o n i s t a k e n i n p a r t from J . R . A n d e r s o n ' s " S i m u l a t i o n : M e t h o d o l o g y and A p p l i c a t i o n i n A g r i c u l t u r a l Economics", 1974. 2 8  base  20  80 3.1)  were  Study  determined using  for  Apples  and r e v i s e d  Okanagan V a l l e y Manual  hot,  water  to  dry  periods.  The  potential  since  it  system  is  the  using  ensure  relative  stress  yield differences  of  base c a s e  this  section  move a l o n g tracing  in  the  out  determine  the  Table  at  presents  decline  the  point o r above  Orchard irrigation, through  w i t h i n an  orchard  water  on e a c h of  water/yield  The  relationships  the results as  The p r i m e p u r p o s e in this  w h i c h f u r t h e r water  manner  they for  is  to  reductions  result  successive  water  yields.  which y i e l d s  at  importance  production functions.  the  results  on e a c h o r c h a r d s y s t e m .  critical  point  production functions  point  4.1  reductions  determine  one  production function.  the  declining  stable  determine  during  interest.  The  in  occur  systems under v a r i o u s  RESULTS OF THE WATER RESTRICTED CASES  o r c h a r d system  will  secondary  4.2  respective  from  The I r r i g a t i o n D e s i g n  no water  which are  results  Production  information acquired  y i e l d data are of  levels,  of  a r e b a s e d on p r o v i d i n g o r c h a r d s w i t h  and between o r c h a r d  application  BCMAF Cost  horticulturalists.  recommendations  sufficient  the  system  2% below  for  the  simulation  The i r r i g a t i o n l e v e l  Y i e l d s are  base c a s e  1 on s a n d s o i l  w i t h M2 r o o t s t o c k ,  the  base c a s e y i e l d s  irrigation.  98% of  of  r u n s w i t h water  defined  as  considered  level.  and u s i n g  exhibits  is  at  sprinkler  stability  reductions  of  yields  amounting  to  81 42%  of  the  base c a s e  Orchard irrigation, water  system  2,  w i t h M2  reductions  level. on  silt-loam  rootstock,  down t o 30%  In a l l c a s e s  standard  gives  of  the  the  undertakes at Results irrigation  level the  yield  the  be  two  orchard  systems. T r i c k l e  flow  f o r the  given  by  trickle  the  base c a s e a t  Irrigation  irrigation  w e a t h e r and  soil  environments,  base c a s e  worst  case  scenario  rather  rate.  This  flexibility the  approach the  the  system  Water using  98%  of  a  "no  the  critical  since  varied for orchard  systems  than a p r e s e n t  represents  a  day a p p l i c a t i o n  s y s t e m water a p p l i c a t i o n  critical  carried  irrigation  s u s t a i n the  easily  in actual  for t r i c k l e  points  were  out  yield  at a  s t r e s s " case p o i n t ) . The  (2%  on  f o r the  minimum w a t e r a p p l i c a t i o n l e v e l could  (as  as  for  trickle  determined  in  simulations.  reductions  trickle  constant  1983). However,  actual a p p l i c a t i o n rates  systems can orchard  set at a  using  requirement  rates are  in t r i c k l e  trickle  from those  was  peak  moisture c o n d i t i o n s  the  r a t e s means t h a t  flow  orchardist  systems u s i n g  the  as  level.  Design Manual,  system  increased  deviation  w h i c h an  irrigation  through  level.  yield  interpreted differently  sprinkler rate  base case  standard  risk  using s p r i n k l e r  stable returns  indicated irrigation  from  can  of  and  d e v i a t i o n of  w a t e r a p p l i c a t i o n s d e c r e a s e d . The represents  soil  orchard  the  trickle  equivalent  l o s s of  systems  p u r p o s e s of d e f i n i n g a  at which  level  trickle  those  yield  results  are  to at  being  system least  defined  termed  as  82  efficiency points (on  points  of  use  soil  type)  efficiency  approximate a constant not  t h e y c a n be  compared w i t h  those o r c h a r d systems u s i n g  identical  water  as  since daily  account  for  of  the  the  of  the two  model  rate the  for  sprinkler  purposes systems.  constrains  application.  potential the  water  periodic  adjustments  to  trickle  climatic  variations.  The e f f i c i e n t  in key  significant result  of  simulation  yield the  results  for  water a p p l i e d h o l d i n g constant.  F i g u r e 4.1  sytems p r o d u c t i o n critical  points  down-turn  of  reduced.  The f l a t  critical  points  reductions  points  for  of  any y i e l d  orchardist's  each  out  as of  input  behavioural  begins  plots  except  irrigation  the  which the  response  result is  to  of  The the  right  are of  not to  these  restriction  in adjusting  the  water  be e x p e c t e d  Thus f o r the  2.  rates  orchardist,  would not  of  orchard  with  the  result  the  water  restricted  in chapter  curves  function,  to  the  water a p p l i c a t i o n  adjustments.  production  10.25  versus quantity  defined  reduction,  seasonal  c r i t i c a l point,  a predicted  for  with  to  respectively.  apples  the  system  trickle  o r c h a r d system occur  portion  range  as  is  16 i n c h e s and  F i g u r e 4.1 of  trickle  rates  represents  function  make any p r o d u c t i o n portions  each  the  flow  the  inputs  thus  trace  i n the  experiencing  all  functions  for  each  yield  The r a t i n g  restriction  simulation.  the  with  soils  reductions,  rating  savings possible  sand and s i l t - l o a m which water  irrigation  does  inches  at  critical  model  s y s t e m s were e s t a b l i s h e d a t  The p o i n t  of  Thus the  irrigation for  the  the  on an  orchard  83 yir?ld per acre (OU's lb-j)  10  20  30  «0  50  q u a n t i ty o f water (inches)  F i g u r e 4.1  P r o d u c t i o n I-'utctioiia for M2 Orcliarc! S y s l a i u ; Showing lil'fcTt LPVPIS  nit  i>l  Y if? I (Is  l.'i.ilm. i UK W;tlri  A[)p I i c:i t i o n  84 production For left  mix  i s not  those  p o r t i o n s of  of the c r i t i c a l  r e d u c t i o n s w o u l d be practices  considered  expected  orchardist  behavioural  portion  the c u r v e .  behavioural curve the  out  production  left.  provides  curves  f o r each orchard  From T a b l e which determine factor  is soil  water, are in  the  given  be  two  the  critical  4.2  p o r t i o n of  are  being  earlier  under  orchard  the c r i t i c a l  22.5  i n c h e s as compared  (55%  higher). Trickle inches  than  point with  (MPP) derived  similar).  important  factors The  stress  i s the case  f o r sandy inches  less levels  with and  sprinkler  soils  occurred  for s i l t - l o a m  s y s t e m s showed a s i m i l a r f o r s a n d and  first  able to r e t a i n  s y s t e m s on  14.5  from  forms.  e q u i v a l e n t weather c o n d i t i o n s  systems. For  10.25  stage  silt-loam  the  the  concluded  p o i n t s are apparent.  soils,  this  removing  r o o t s t o c k s as  and  Sand  of  for  p h y s i c a l product  4.1  water  The  restricted  results  type.  soils  irrigation,  56%  of t h i s  s y s t e m on M2  Figure  the  management  binding  s u b j e c t t o d e p l e t i o n down t o water  irrigation  (16 and  i s thus  f u n c t i o n s (M26  model a t an  silt-loam  is a shift  the m a r g i n a l  production  to  restriction.  p r e d i c t e d response  functions in their  4.2  from the  water  orchard  However, much can  Figure  4.1  o r c h a r d i s t faced with  restriction The  in Figure  to modify  f o r the  restriction  to the  curves  p o i n t s , the  t o compensate  of  the  binding.  at soils  relationship  respectively,  higher). The  level  second  i s the  factor  type  of  found  to  irrigation  i n f l u e n c e the c r i t i c a l s y s t e m . Under t h e  water  assumption  Marginal Physical Product (lb/acre)  300 ••  250 -•  200 -•  D  CO  O  DO  •  ISO  ••  ••  100 •-  irrigation  soil  sustain  type  sprinkler  silt-loam  sprinkler trickle _  sand silt-loam  trickle  sard  • • • O  50 •O  10  20  30  40  50  quantity of water (inches)  Figure 4.2  Marginal Physical Product Curves for M2 Orchards  86  of  constant  b e h a v i o u r on t h e  s y s t e m s were applied  ratio  Table system  found to  than s p r i n k l e r  4.2  gives  Assuming  irrigation  critical  points, system  flow  throughout  The f l e x i b i l i t y  the  sprinkler into  the  risk  a trickle  model,  the  If  in a y i e l d to  water  of  system  each  this  orchard  simulation  about  (assuming  runs.  flow  71% o f a  allows  cases).  for a l t e r i n g  were  t r i c k l e s y s t e m water  flow  conditions  rate adjustment  flexibility  the  constant  period in a l l  d e p e n d i n g on weather for  soils.  could approach these  irrigation  inherent  methods.  trickle  d e r i v e d from t h e  requirements  the  on a d a i l y b a s i s  without  points  t r i c k l e s y s t e m s use  water  of  critical  as  orchardist,  s y s t e m s on s i m i l a r  efficiencies  sprinkler  rates  the  the  the  be more e f f i c i e n t  on M2 r o o t s t o c k  rate  p a r t of  with  incorporated  requirements  would  be r e d u c e d . The a s s u m p t i o n o f water  a p p l i c a t i o n constant  restrictions the  assumed  chapter  is  essential  sprinkler  2 could shift  reducing while  holding a l l  the  fine  for  successive  this  irrigation  result.  practices  t h e MPP c u r v e t o  t r i c k l e versus  tuning t r i c k l e  a daily basis  during  inputs except  sprinkler  system  water  the  irrigation  water  Modifications as  discussed  left  water  in  thus  efficiency  gap  application rates  would u n d o u b t e d l y i n c r e a s e  this  to  on  efficiency  difference. The r e a l potential irrigation  significance  f o r water  of  savings.  the  simulation results  The m a j o r i t y of  s y s t e m s now i n o p e r a t i o n  the  is  the  orchard  i n t h e Okanagan r e g i o n  87  TABLE  4.2:  CRITICAL  Irr igat ion System  POINTS WITH M2  Base Applicat ion Level (in.)  spr i n k i e r trickle spr i n k i e r trickle  sprinkler  systems.  the  base  levels  irrigation  far  on  day  to the  sand  right  determined  by  systems  sand  on  critical level.  For  sprinkler case water  water  of  of  of  the  water  using  systems the  indicates  t o Okanagan  4.1  i t can  water  level on  a  seen  For  level  o r c h a r d s i s not  as  the  base  case  using  i s 30%  substantial  levels  orchard  the  soils  the  region) l i e  irrigation, of  that  sprinkler  application  silt-loam  that  30%  be  i n the  i s 42%  critical  for  runs.  sprinkler  of Base Case  42%  (representing  application  simulation  %  22.50 16.00 14.50 10.25  soils  critical  application  irrigation,  applied  Critical Point (inches)  application  silt-loam  the  soils  This  Type  Figure  water  orchard  orchard  level.  From  and  levels  SYSTEMS  sand sand silt-loam s ilt-loam  are  present  Soil  53.33 48.00 29.79 29.79  case  FOR ORCHARD ROOTSTOCKS  of  the  amount  required  base  of  for  fruit  88  production. of  This  the marginal  t h e MPP water  curve  physical  product  the p r i c e  infinity.  volume c h a r g e  shown by  is horizontal,  i s z e r o and  approaches  use  is clearly  on  the h o r i z o n t a l p o r t i o n s  curves  the m a r g i n a l elasticity  T h i s means t h a t  irrigation  would t h e o r e t i c a l l y  be  i n F i g u r e 4.2.  water  value product  of  of demand f o r w a t e r  were a s m a l l  t o be  positive  implemented,  significantly  where the q u a n t i t y of w a t e r u s e d  Where  c u t back  would a p p r o a c h  water  to a point  the  critical  level. It  i s important  theoretically  occur  t o note  b e f o r e any  come i n t o p l a y were t h e y significantly 4.2  reduced  i t i s noted  increasing  as  that  account  f o r more t h a n  points.  Thus w h i l e  water a p p l i c a t i o n  this  of t h e  result  behavioural aspects  affecting  yields.  application  0.1%  risk  of  total  to producers  of y i e l d ) i s reduced,  i s reduced, yield  at the  (as m e a s u r e d  the  yield.  THE  f o r the water  accomplish  as  yields  under w a t e r  does e x i s t  few  restricted  cases  d a t a were a v a i l a b l e  input r e s t r i c t i o n s .  for apple  while  do  not  critical by  the  levels  is  WATER RESTRICTED CASES  Validation  very  Table  increased risk associated  insignificant  VALIDATION OF  be  i n c r e a s e s i n t h e model when  r a t e s at the c r i t i c a l  to t o t a l  can  From  s t a n d a r d d e v i a t i o n s of y i e l d ,  w i t h water a p p l i c a t i o n  4.3  would  not c o n s t r a i n e d . Water use  without  irrigation  standard d e v i a t i o n  that  was on  difficult apple  However, one  to  orchard data  t r e e s i n t h e Okanagan r e g i o n , and  set  this  89  data  set  is  not  incorporated into  The C a n a d i a n A g r i c u l t u r a l carried  out  lysimeters  some w a t e r to  measure  on M c i n t o s h a p p l e regimes.  The d a t a  2 9  beginning  in  experiment, 37% of  the  1974. trees  of  the  drainage  F o r the  water  were t h e n  district's  allowable  seasons  reduced u n t i l  50% of  entire  increased  experiment  the the to  date,  though  recently  resulted  While conclusion  these of  overwatering  the in  root  results  this  thesis  water  4 years  of  limit  level  was  stress  the  to  Water  was  until  was  effect has  lysimeter  100%  reached. again  reached.  no d i s c e r n i b l e  to water  years  amounting  stages  limit  leaching  the  in annual  During on  tree  been have  boundedness. tend to that  support  there  i n Okanagan o r c h a r d s ,  is  the  general  differences  procedures  this  the  to  attempt  the  substantial  restriction  limit  11  rate.  S t e v e n s o n ' s water thesis  field  allowable  of  model.  application  application  limitations  the  Summerland has  applications  allowable  growth or y i e l d a t t r i b u t a b l e observed,  using  application  water  at  d u r i n g over  initial  received  of  and f e r t i l i z e r  under v a r i o u s  was c o l l e c t e d  In s u b s e q u e n t  the  water  studies  Summerland d i s t r i c t ' s  applications  design  Research S t a t i o n  related  trees  the  validate  in  and t h o s e u s e d this  in  study..  R e s u l t s o f t h i s e x p e r i m e n t up t o 1980 c a n be f o u n d i n S t e v e n s o n ' s CWRJ a r t i c l e ( 1 9 8 0 ) . S u b s e q u e n t conversations p r o v i d e d f u r t h e r i n f o r m a t i o n and more r e c e n t results. 2 9  90  4.4  S E N S I T I V I T Y ANALYSIS  A model's varied  reaction  over  simulation  a range  for  considered  of  in t h i s  importance  the  determine timing  intercept  the  d e g r e e of  was  discussed here.  case  earlier,  Sensitivity  similar f,  the  results.  scenario  to  4)  analysis  Sensitivity  rather  than  predicted  to  water  sensitivity critical system. inches  reductions  points  as  Seasonal and  most  analyses  17  and  and  the  inches  13  inches  silt-loam  soils.  to  those  for  rates  trickle  and  d. results  considered gave  parameters K,  season run set  such a  at  affect  sprinkler soils  of  yields  determined  application  for  slope  orchard l i f e  on t h e s e p a r a m e t e r s  water  potential  large  these parameters  significantly  previously  the  a single  full  Since  crucial  s y s t e m s on s a n d and s i l t - l o a m inches  using  for  the  f a c t o r K,  simulation  problems a n a l y s i s  d a t a would e n t a i l . the  analyses  For was  f o r M26 o r c h a r d s y s t e m s  amount of  where  the  versus  factor  of  most  analysis  o n l y M2 o r c h a r d s y s t e m s a r e  a v o i d the  be  is  T , and the  stress  are  strength  uncertain.  actual  factor  in analysing  T , and d were c a r r i e d out  (orchard year  the  evapotranspiration  the  As  are  sensitivity  evapotranspiration, determing  to  testing  whose v a l u e s study,  to  outcomes when p a r a m e t e r s  sensitivity  a p p r o p r i a t e for coefficient  of  key  Model  parameters  model d e v e l o p e d  slope  is  results.  important  the  i n terms  that  were point  yields,  the  was  performed  for  each o r c h a r d  were h e l d  to  at  24  i r r i g a t e d orchard  respectively,  and t o  i r r i g a t e d o r c h a r d s on  18  sand  91 The orchard in  results  r a n g i n g of  these  parameters  s y s t e m s on y e a r - e n d a c t u a l  yield  (year  Table 4.3,  set  to  4.4.1  the  of  where  values  the  used  "control for  the  evapotranspiration  Hargreaves  (1968),  value  of  evapotranspiration  relationship varies  season.  To d e t e r m i n e  results  to  relationship,  throughout graphical  the  given  analysis in table  significant s y s t e m s as figures. rates  By s e t t i n g  control  approximately for  greater  soils.  soil  case.  of  given  runs.  case.  K was  the  K=0.75,  control of  losses  o r c h a r d s y s t e m s on s a n d retention  the  simulation at  0.75  a  c a s e and  the  this  restriction a  in a l l  orchard  control  case  evapotranspiration  occur  than o c c u r r e d  case average of  The  provides  from the  much h i g h e r  The m a g n i t u d e  the  on K has  yield  % change  moisture  of  held constant  The r e s t r i c t i o n  by t h e  by  evaporation  p e r i o d of  F i g u r e 4.3  year-end  data.  between pan  The r e s u l t s  The c o n t r o l  0.53.  water  derived  determining  sensitivity  both the  on the  indicated  within  season.  4.3.  impact  and t h u s  greatest  growing  description  sensitivity  the  all  parameters  from pan e v a p o t r a n s p i r a t i o n  K a n d t h u s the  this  K , as  a means of  growing  the  all  are  orchard simulation  coefficient  provides  evapotranspiration  are  c a s e " has  4)  for  THE EVAPOTRANSPIRATION FACTOR K The  and  the  yield soils.  characteristics  K value  was  reduction This of  is  in  is due  silt-loam  to  TABLE 4.3i  RESULTS OF PARAMETER 8EN8ITIVITY ANALYSIS ON M2 ORCHARD 8Y8TEM8 IN YEAR 4 OF TREE LIFE  CONTROL CASE  EVAP0TRAN8PIRATION FACTOR 'K' - 0.73  ACTUAL VS POTENTIAL ET SLOPE COEF. - \  . IRRIGATION SYSTEM  SOIL TYPE  YIELD <LB8/ACRE>  . SPRINKLER  8 AND  13*7.62  1129.34  -29.3X  1600.00  •0. IX  . SPRINKLER  SILT-LOAM  1388.09  1204.60  -22.7X  1396.72  •2.3X  1366.88  1086.29  -30.BX  1600.00  •2. OX  1389.21  1239.66  -22. OX  16OO.0O  •0. 7X  .  TRICKLE  .  TRICKLE  .  6 AND SILT-LOAM  .  YIELD (LBS/ACRE)  ACTUAL VS POTENTIAL ET SLOPE COEF. - 20  X CHANGE FROM CONTROL  TIMING OF 8TRE88 FACTOR 'T* - 0.73  . IRRIGATION SYSTEM  SOIL TYPE  YIELD (LBS/ACRE)  X CHANGE FROM CONTROL  . SPRINKLER  SAND  1479.79  -7.4X  \  1363.40  -2. IX  . SPRINKLER  SILT-LOAM  1462.43  -6. IX  \  1302.83  1437.10  -7. IX  1309.19  -3. OX  TRICKLE  SAND  TRICKLE  SILT-LOAM  .  .  YIELD <LBS/ACRE)  YIELD (LBS/ACRE)  X CHANGE FROM CONTROL  DEGREE OF 8TREB8 FACTOR g - 1.18 - 1.67*801L MOISTURE  X CHANGE FROM CONTROL  YIELD <LBS/ACRE) '.  X CHANGE FROM CONTROL  1407.07  -11.9X  -3.3X  1331.63  -13.2X  1340.43  -1.8X  1334.80  -13.6X  1380.92  -0.3X  1419.03  -10.7X  '.  93  K 1.00  sensitivity 0.75  H  0.50 +  0.25  T  50  25  75  100  % of growing season  F i g u r e A.3  Evapotranspiration Sensitivity  Coefficient  A n a l y s i s Cases  K f o r the C o n t r o l and  94 4.4.2  ACTUAL VERSUS  POTENTIAL EVAPOTRANSPIRATION  SLOPE  COEFFICIENT F The (PET)  relationship  and a c t u a l  following  between p o t e n t i a l  evapotranspiration  equation  (see  section  evapotranspiration  (AET) i s  given  by  the  3.3):  AET = p * PET  The  value  moisture with  of  the  and s o i l  soil  type  p = f * where  soil  type  and i s  as  moisture well  described  the  SM = s o i l  moisture  control case,  silt-loam and  soils  retension  sensitivity on  diagramatic moisture  The 4.3.  With  factor  soil  varies  below:  water  f was  set  respectively  the  types  model,  p,  soil  storage  to  to of  capacity  3 and 5 f o r  account the  for  soils.  f was a s s i g n e d  in successive  description  factor  coefficient  P E T . The f  on  level  characteristics  of  both s o i l  p depends  (SM/AWSC)  AWSC = a v a i l a b l e  For  as  factor  of  the  runs.  water  holding  To t e s t  values  Figure  relationship  moisture  s a n d and  SM and t h e  of  4.4  the 1 and  20  provides  between t h e AET-PET  a  soil  slope  f.  results f=1,  of  the  setting actual  f at  yield  1 and 20 a r e g i v e n increases  relative  in to  table the  95  0.05  0.20  0.30  0.40  0.50  1.00 soil moisture (fraction of field capacity)  Figure 4.4  Actual vs. Potential Evapotranspiration Coefficient f and its Relationship to the Evapotranspiration Factor P and Soil Moisture for the Control and Sensitivity Cases  96  control small  case  since  for a l l the  c o n t r o l case  maximum p o t e n t i a l 3.1).  below the  to  the  lower  the  results  are very c l o s e  p,  lbs  but v e r y  the  for a l l p is  the  low  value  soil  than the  c o n t r o l case  affected  ranges  appear to  of  4,  lower soil  is  see  to  the  Table  p values  moisture the  the  are  levels  ratio  level  AET/PET,  of  A E T , the  model.  p is  levels.  year  equal to  lower  moisture  between  for  due t o  d e p l e t i o n mechanism i n t h e When f=20,  not  Since  of  The i n c r e a s e s  is  c o n t r o l case  value  systems.  (1600  in y i e l d  field capacity.  water  all  yield  The i n c r e a s e  relative  orchard  equal  levels.  to  5.0% and 7.4%. to  (0<p<  Thus y i e l d s  The d e g r e e  be o v e r l y s e n s i t i v e  1.0  to  are  at lower  which y i e l d s  Thus t h e  the  1)  model  AET-PET  are  does  slope  coef f ic i e n t .  4.4.3  THE TIMING OF STRESS One  of  be a f f e c t e d  the  by b o t h t h e  stress during varies apple  the  between  the  the  entire  and  sensitivity The  case  4.3. range  the  degree  and 1.00,  least  sensitivity  analyses,  analysis of  from 0.5%  to  is  that  t i m i n g of  For the  v u n e r a b l e to T was  set  4.5  y i e l d can water  control case,  i n d i c a t i n g the  Figure  periods water  equal to  presents  T  when  stress. 0.75  the  for  control  cases.  setting  The d e c r e a s e s  model  and t h e  a n d most  growing season.  results  of  growing season.  0.10  trees are  For  Table  assumptions  FACTOR T  T equal  to  0.75  in y i e l d r e l a t i v e 3.5%.  Thus t h e  are given to  the  t i m i n g of  in  control stress  97  1.00  -r  0.75 sensitivity case control case  0.50  --  0.25  , 10  15  20  25  30  35  week of growing season  F i g u r e U .5  L e v e l of S t r e s s F a c t o r T Over Growing Season: C o n t r o l or Base Case and Value Assumed f o r S e n s i t i v i t y Case  98 factor  does not  parameter  4.4.4  variation  water  was  i n the  range  in  the  on y i e l d  is  assumed  factor.  form of  (d=1.0),  The d e g r e e  a linear  when t h e  available  water  permanent  when SM i s  sensitive  to  tested.  soil  to  AWSC.  70% of given  analysis from  the  are to  shown  control  case  begins water stress  to  It  occur.  parameter yield  AWSC  of  was  The r e s u l t s  at  sensitive  to  this  parameter for  chosen of  The f a c t levels, ranging  the  is  level  and  take  10% o f is  termed  (d=0.0)  this  relationship,  of  the  stage the  below  determination.  of  r a n g i n g . The Design  felt  to  to  concern  at the  these  it  stress  critical  degree  since  soil  be a  which water  model,  range  The model  Irrigation  was  cases  reductions  minimum o r c h a r d it  AWSC  sensitivity  parameter  sensitive not  analysis  the  the  the  from 60% of  control case.  is  since  that is  to  o r below  (this  The y i e l d the  was  factor  assumed  increased  to  estimate  application  to a c t u a l  level  recommendation  level.  conservative  SM, i s  relative  no-stress  of  AWSC.  in Table 4.3.  13.6%  relatively  moisture  is  The c o n t r o l a n d s e n s i t i v i t y  appears  (1983)  a degree  effect  between maximum s t r e s s  sensitivity  moisture  d,  the  PWP), and n o - s t r e s s  60% of  in Figure 4.6.  10.7%  Manual  point,  section,  have  factor,  moisture,  o r above  no-stress  to  storage capacity,  wilting  at  previous  relationship  soil  To d e t e r m i n e  are  be e x t r e m e l y  indicated  stress  a timing  the  to  THE DEGREE OF STRESS FACTOR D As  the  appear  of is  a  key  99  F i g u r e 4.6  Degree of S t r e s s F a c t o r d f o r the C o n t r o l Case and the S e n s i t i v i t y A n a l y s i s Case  100 The  general  analysis  p e r f o r m e d on t h e  stability the  and r o b u s t n e s s  results  of  fluctuations  4.5  conclusion  POLICY  the  with  results  was  of  to  Risk lower  the  the  savings  levels  that,  results  use  where  of  yield  the of  on a v e r a g e ,  of  of  the  reductions  water  mechanism.  region  is  of  yield  is  of  the  given  use  that  would  profit  (2% y i e l d  than  risk by  of  the  For s p r i n k l e r  0.01%.  risk  reduction  silt-loam) This  would  result  reduction. show t h a t  adversely  method of to  significant  affect  in  i n t r o d u c e a per  half.  Okanagan  encouraging  Such a p r i c i n g scheme has t h e  a g r i c u l t u r a l water  equal,  water.  levels  little  simulations  would not  averse,  producers  A measure  less  very  the  in  being  sand and 30% f o r  y i e l d was  conservation  cut  less  in Table 4.1.  42% f o r  of  loss  c r i t i c a l points  One p o s s i b l e  to  changes.  else  the  from u s i n g  orchard y i e l d s .  pricing  all  be c o n s i d e r e d .  from t h e s e m a g n i t u d e s  water  that  interpreted.  t h r o u g h r e d u c i n g water  standard d e v i a t i o n  The  of  large  m a x i m i z e r s and r i s k  implies,  a level  also  systems at  indicates  to  value  one  indicates  was p r i c e d by v o l u m e ,  to  standard deviations  w i t h water  This  subject  model may be  use  must  yields  orchard  model.  not  profit  maximization  water  equal  the  s m a l l parameter  a g r i c u l t u r a l water  reduce  of  is  IMPLICATIONS  Profit if  sensitivity  s e l e c t e d parameters  model a r e  Assuming p r o d u c e r s are the  drawn from t h e  water  unit  water  potential  Chapter SUMMARY,  5.1  CONCLUSIONS,  AND SUGGESTIONS FOR FUTURE RESEARCH  SUMMARY  Water  i n the  Okanagan V a l l e y o f  demand from c o m m e r c i a l , agricultural water  use  fishing.  interest  conflicts, District  use  of  the  extent  having  of  groups.  streams  potential  to  (McNeill,  Current  flat water  fishing  and resulted and  in  sport  areas  has  been  water  use  the  water  flow  d u r i n g the  summer  designated below  to  as  current  1983).  This  is  commonly u s e d ,  of  allotted the  water  mechanism.  t o make use  using  have  in  is  due  to  priced,  the  irrigation  and t h e  the  do  not  method by  environmental  influences  area.  rate  during  demands  can d e p l e t e  conservation.  Agricultural  water  recreational  between a g r i c u l t u r e  reduce  w h i c h a g r i c u l t u r a l water  flat  is  Okanagan i r r i g a t i o n p r i c i n g p r a c t i c e s  water  technology  Columbia  a g r i c u l t u r a l i r r i g a t i o n s y s t e m s w h i c h make  eliminating  requirements  the  These  The a g r i c u l t u r a l s e c t o r the  promote  British  residential,  notably  upper v a l l e y  months.  in  5  per  fee,  user  is  is  determined  by t h e  water  driest  historical  period  i n the  to  this  growing  The u s e r  has,  101  regardless  of  of  required region for  maximum r e q u i r e d amount season,  a  allowed  The amount  i r r i g a t i o n method.  the  the  water.  access  throughout  volume  fee,  p r i c e d using  of  acre  hottest,  Okanagan i s  For a per a c r e  a designated  a rotational rate  i n the  the  of  weather  1 02 conditions. The most the  common i r r i g a t i o n t e c h n o l o g y  Okanagan i s  sprinkler  i r r i g a t i o n . Because  irrigation  systems are unable  flow  rates  to  time  using  sprinklers,  practiced. in  enable  This  a systematic  conditions risk  of  orchard this  the  amount  excess  rotational  forcast  d u r i n g each  of  Thus t h e agricultural  were:  use  certainty,  the  m i n i m i z e d by  Only very  to  each  rarely trees  is  from  characteristically  good  of  s p r i n k l e r i r r i g a t i o n under the p r i c i n g scheme  present  encourages  use. of  relationship  this  thesis  in tree  determine  actual water  was  fruits.  a model was c o n s t r u c t e d  these with present sprinkler  weather  region.  production process.  to  sections  Because  Damage t o  to  one  be  i r r i g a t i o n allotment  m i n i m a l due  The m a i n o b j e c t i v e  orchard  is  rotation.  i r r i g a t i o n water  maximum w a t e r  objective,  stress  i r r i g a t i o n necessary.  i n the  water-yield  with absolute  from w a t e r  water  orchard in  days.  in  district  o r c h a r d s at  i r r i g a t i o n must  a p e r i o d of  be  the  used  sufficient  entire  way o v e r  i r r i g a t i o n is  drainage  i r r i g a t i o n of  maximum a l l o w a b l e  section  provide  i r r i g a t i n g the  c r o p damage  applying  to  involves  cannot  presently  to  to  simulate  o r c h a r d water  i r r i g a t i o n and t r i c k l e  water-yield  input/output  alternative  a g r i c u l t u r a l water  of  an  this  actual  the  thesis  needs and compare  rates;  to  compare  i r r i g a t i o n i n terms  relationships;  the  To a c c o m p l i s h  Other o b j e c t i v e s  application  analyse  and t o  of  investigate  pricing strategies  with  the  1 03  aim o f  p r o m o t i n g water  The  conservation.  r e s e a r c h method c o n s i s t e d  response  of  decreasing  several  orchard  of  one  of  and two  i r r i g a t i o n types.  at  irrigation level  each  according  to  water-yield  the  production  water  growing  stress  was  the  determination  the  growing  a series  levels.  thereby  and t h e  t i m i n g of into  stress) The d a t a  determining the  of  on F l i n n  the  a yield  daily  presence  (1971). level  categories. British  3 0  Assaf  the  growing  c a n be  for  Y i e l d data  al  when  of  (1975),  and d e g r e e  This  method  soil  moisture  season,  yield  less  involved during inputs  By c a l i b r a t i n g taking  water a value  yield  of  into  stress, for  lost  and  year  due  end  to  calculated. this for  Columbia M i n i s t r y  et  of  the  i r r i g a t i o n and r a i n f a l l  reduction  no-stress  used  run  stress during  consideration  b o t h d e g r e e and t i m i n g o f  water  both  3 0  water  factor,  (potential  simulation  studies,  soil  yield  types,  orchard y i e l d .  based  summing t h e s e o v e r  soil  and g r a p h e d  outflow.  consideration  two  the  and s u b t r a c t i n g e v a p o t r a n s p i r a t i o n to  of  producing a series  from o t h e r  s e a s o n by a d d i n g  moisture  yield  Each o r c h a r d  rootstocks, of  the  functions.  stress  The method of  to  were t a b u l a t e d  results  yearly  simulating  The r e s u l t s  s e a s o n were t a k e n  calculating  water  two  orchard system,  B a s e d on t h e d e g r e e of  systems  irrigation application  system c o n s i s t e d  of  thesis apple  of  Goode  c a n be g r o u p e d i n t o  trees  was  obtained  A g r i c u l t u r e and F o o d  (1975),  Michell  (1984)  three  from  (BCMAF)  the  1 04 Estimated  Costs  and Returns  and Production, adjusted to  after  better  over  20  Okanagan  was  reflect  actual  Canada.  yields  base c a s e w a t e r  last  This  data c o n s i s t e d  British  Columbia  1934-1961,  weather  and/or  generator  evapotranspiration moisture  levels.  The  results  current reducing  for  is  BCMAF Irri  data category  unavailability  orchards  1984).  Establishment This data  was  horticulturalists  M2 and M26  the  rootstocks  technical  is  the  of  weather  i n the  (degrees the  precipitation  1899,  data.  This  for  1900,  incomplete  were due  data  was  which p r o v i d e d p r e c i p i t a t i o n  the  for  the  calculation  simulation  Okanagan r e g i o n ,  runs  of  or c h a n g i n g p r e s e n t  soil  that,  are p o s s i b l e  for in  without  irrigation  systems. For  sprinkler  applications rates in  i r r i g a t e d orchard systems,  amounting to  on s a n d s o i l s  a 2% r e d u c t i o n  42% of  present  day  and 30% on on s i l t - l o a m  i n the  average  y i e l d over  water irrigation  soils a 20  by  and  reductions  sprinkler  to  used  daily  indicated  substantial  applications  (1983).  obtained  C) r e a d i n g s  years  data  Environment  M i s s i n g years  i r r i g a t i o n water yields  total  This  data  of  needed  Manual  1969-1983.  input  of  for  daily  data  rates.  gati on Design  Atmospheric Environment S e r v i c e  1903-1932,  the  (May,  application  (mm) and maximum t e m p e r a t u r e Kelowna,  Orchard  with d i s t r i c t  data category  a c q u i r e d from t h e  from t h e  Apple  years.  determine  The  Valley  discussions  The s e c o n d to  for  resulted year  1 05 period. To a c h i e v e irrigation growing  season)  CONCLUSIONS  The  findings  reductions that  without levels fees, on  p a r t of  water  decrease  point  c a n be  on the is  large  application  water  use  unknown.  the  i n terms  of  fruit use  use  fixed  conservation  analysis  50% r e s u l t e d If  water  y i e l d per  in  show  in  of  pay  quantities approaches  reduced to  unit  no  producers  product  be  user  water  a more applied,  function derived.  that  of  demand f o r  water  day  irrigation  water  at  the the  water  However, is  this  marginal value  of  sector,  water  water  yields. of  use  accomplished  annual  for  rates.  water  fruit  the  marginal p h y s i c a l product  levels  for  use.  of  o r d e r of  for  sprinkler  Current  demand c o u l d t h e o r e t i c a l l y  level  water  result  Results  in tree  where  throughout  substantial  incentive  i n the  i r r i g a t i o n fee  water  fee  the  orchardists.  rate  Okanagan t r e e  reductions  be  trickle  r e q u i r e 71% of  indicate  little  reductions  unit  very  user  to  soils,  a constant  i n the  use  which p r o v i d e  assertion is  study  on l i k e  r e d u c i n g mean o r c h a r d y i e l d s .  efficient based  this  s u c h water  b e y o n d the zero,  of  at  found to  are p o s s i b l e  significant a per  was  would a p p e a r  the  that  same y i e l d s  ( a p p l y i n g water  5.2  and  the  price point  of  and t h u s  present  the  would r e s u l t the  uncertain  Present  elasticity  a d d i t i o n of in a large  predicted since  the  impact  a s m a l l per reduction  unit  in  upon i r r i g a t i o n  marginal value  a g r i c u l t u r a l water  The  charges  of  cover  water the  is  1 06 variable  costs  of  supply.  structure,  based  w o u l d have  on w a t e r  water  costs  costs  (generally  perceived water  on p r e s e n t use  represent  risk  costs  than  water  through  regionally  marginal water set  values,  thesis  not  conservation, the  suggest  irrigation  the  of  what  with  water  orchard's  level  Okanagan  of  water  while  the  policy  of  The  savings  in  likely  of  pricing irrigation  pricies  should  results  of  such a p o l i c y  be  this  for promoting  t r i c k l e versus  respect  (apart  to  water  depends  on  water  affect  in  water  the  the  exists  requirements.  use  adoption  efficiency of  longer  for  levels.  rate  of  trickle  one  of  is  not  by a p p l y i n g water  In t h e  short  Okanagan  term. the  producers to This  user  trickle  in decreased  p r i c i n g is  zero cost  sprinkler  from i m p l e m e n t i n g a p e r u n i t  could result  use  incentive  incurs  production  outweigh  i n the  promoting the  by r e d u c i n g a p p l i c a t i o n producer  total  Orchard  water.  results  adoption)  The method of why l i t t l e  clear.  not  volumes,  a n n u a l l y per a c r e ) .  water  effectiveness  policies  systems  agricultural  is  p r e d i c t e d outcome  w h i c h may p o s i t i v e l y  irrigation  and  price  reductions.  toward a p o s s i b l e  methods  that  of  water  prices  s t r e s s may w e l l  Therefore,  favourable  irrigation  fee  the  marginal value The  $100  unit  w i t h demand. W i t h o u t i n f o r m a t i o n on  certain.  point  rate  Valley  irrigation  by volume and a t  is  a per  a s m a l l p o r t i o n of  less  of  flat  i n the  The m a r g i n a l v a l u e varies  The e f f e c t  key  reasons  conserve to  water  imply that  beyond  the  run, f e r t i l i z e r  loss  a  1 t h r o u g h water longer  drainage  run e f f e c t  substantial  indirect  environmental  impact valley  recreational  from l a t e  lakes  a l s o an  discussion  of  the  unit,  producer pareto  region  region.  to  the  it  is  of  yields  thus  far  and,  be c o n s i d e r e d .  the  sport  fishing  w h i c h s h o u l d be  the not  and  included  in a  over-watering.  prospect  of  detrimental  and p r o f i t s ,  and  i n streams  p r o d u c e r of  The  chemicals  health  shortages  section  in p r i n c i p l e ,  to  the  water to  pricing  the  would a p p e a r  is  all  to  costs  related  often  exists  are  to  i n hot  used.  there  to  be  an  the  within  outlined  apply,  at  dry areas  is  implicit  and t h u s more e f f i c i e n t  is  least  of  the  delivered  an a b s e n c e of use. per  in  where  The u n i q u e n e s s  i r r i g a t i o n water  present,  to  toward  growing  implications  i r r i g a t i o n water  u s e r s and t h u s  pumping c o s t s a r e already  fees  fruit  generalized  agriculture  that  pressurized  been d i r e c t e d  policy  c a n be  i r r i g a t i o n user  Okanagan c a s e  have  in p a r t i c u l a r ,  However,  previous  fixed  also  be  with  and o t h e r  to  the  While t h e s e might  s y s t e m may have Losses  is  optimal.  Okanagan  the  fertilizer  included, as  orchard operation. A  application  must  summer w a t e r  costs  the  producer bears  effects  water  insofar  The r e s u l t s  that  of  are  i n terms  to  pH l e v e l s .  'externality'  When t h e s e c o s t s by t h e  soil  consequences.  industry is  of  c o s t s which the  over-watering,  the  a cost  e x c e s s water  lowering  termed d i r e c t  entering  of  is  07  Where  unit  water  use  such  user is  pumping  fee likely.  1 08 5 . 3 RECOMMENDATIONS While  simulation  yield  response  wheat, found  FOR FUTURE RESEARCH  has  been  literature  therefore  represent  of  an  system for  fruit  point  at  water  stress,  to  the  soil  of  moisture  calculated Apart process lies those are  level  being the  by t h e  for  Okanagan t r e e  water  degree  of  t h e s i s may  simulate  of  weather  data of  The use  stress is  present  the  result  of of B . C .  on t h e  probably errs the  a  model,  a "safety  actually  from  using  will  B.C. Ministry  assumption  variety  and a  the  level  an  the  results  relationships  provides  of  factor" threshold toward  case.  day o v e r w a t e r i n g  This as  model. insights  into  the  apple  model p r o v i d e s ,  the  main v a l u e  simulation  they  to  moisture  from t h e  r e q u i r e d than  from t h e  results.  that  taken  soil  The c o n s e r v a t i v e  which the  i n the  the  This  simulation  A key a s s u m p t i o n  A g r i c u l t u r e sources  would l e s s e n  at  I r r i g a t i o n Design Manual.  results.  more water  is  author.  p r o d u c t i o n uses a  physiological  process.  predict  p r o d u c t i o n were  The model makes use  which l o w e r i n g  Agriculture's Ministry  in apple  incorporating historical  random s e l e c t i o n  fruit  The model d e v e l o p e d  relationship  on t r e e  tree  i n i t i a l attempt  information sources.  studies  in  simulating  to  p a r t i c u l a r l y c o r n and  s e a r c h e s by t h i s  orchard environment. water-yield  a technique  i n many a n n u a l c r o p s ,  no a t t e m p t s a t in  u s e d as  p r o c e d u r e and the  The i m p l i c a t i o n s indicate fruit  that  of  the  of  the  implications  results  e x c e s s water  production. This  production  use  for  occurs  situation,  work  of  policy in  which  109 appears  to  together  be  the  result  with other  of  a flat  environmental  c o u l d be  remedied  p r i c i n g regime.  However,  the  water  value  depend on t h e  the  simulating  results  tree  fruit  thoroughly  available results these  validating  data  against  position  of  support  the  of  the  the  model.  studies  the  estimated  model  The "next  model  4,  means  best" the  model  by S t e v e n s o n  (1980).  results,  exact  the  in  in chapter  which c o u l d p r o v i d e a  w h i c h a c o m p a r i s o n of  c a n be made a r e  studies  validity  p r o d u c t i o n . As was n o t e d  no d a t a a r e c u r r e n t l y a v a i l a b l e of  p r i c i n g mechanism  factors,  t h r o u g h a p e r volume of  rate  production function  are  While  shape open  and  to  question. The p o i n t production model.  (the  This  studies,  at  w h i c h water  c r i t i c a l point)  result  as  has  discussed  production  function  simulation  results  more water  is  supportable.  in  t r e e development  applications  were  levels.  implies  i n the  application  the  the  F o r the  right  constant  Stevenson  key  result  of  from  p o r t i o n of the  average  reduced to that  one  the  the  other the  yearly yields  c r i t i c a l point  (1980)  of  c r i t i c a l point,  third  of  no  the  when  water  found that  o r p r o d u c t i o n o c c u r e d when  experiment  level  decline  water  normal a p p l i c a t i o n  production function  was h o r i z o n t a l w i t h i n  for  this  the  water  range.  Referring the  above.  a p p l i e d beyond t h e  also  trees  is  some s u p p o r t i n g d a t a  to of  is  This  becomes c r i t i c a l t o o r c h a r d  to  F i g u r e 2.2  production function  to  in chapter  the  left  of  2, the  the  portion  critical  of  point  1 10 falls  off  sharply with  application this  levels.  portion  constraint constant, levels.  of  the  holding  levels  to  adjusting  T h i s type of production  since  all  bias  technology  set,  From the of  is  the  "other  to as  the  right  process.  The v a l u e  likelihood  of  Okanagan t r e e regimes over  fruits  data  for set  validation  is  future  production  not  that  accounted  portion  of  point  point  Q* f o r  given  be  increased.  right  yields  a  the  the  are  unaffected  levels. is  growth to  the  that  there  purposes.  and y i e l d  a variety  Without  is  of  a  lack  The  data  for  irrigation  available  such data  in  the  thorough  possible.  work r e l a t e s function  of  critical  p e r i o d becoming  The s e c o n d m a j o r a r e a from  of  is  the  validation  seems r e m o t e .  not  on y i e l d  water  orchard production  that  model  subjected  a multi-year  future  is  the  water a p p l i c a t i o n  a detailed  forseeable  at  only  of  depicts  available  irrigation  the  accurately  readily  of  inputs  to  point  of  the  that  critical  the  to  concluded  function  The major weakness of  is  is  production  current  it  it  the  by h a l v i n g  these  for  and c a n n o t  policy  due  by a l l o w i n g  occur  above d i s c u s s i o n ,  for  at  effect  depicted  attained  which,  i n p u t " mix  does not  function  water  orchard production  since,  change,  a maximum y i e l d ,  portion  function  other  arises  the  in  been d i s c u s s e d e a r l i e r ,  production  This situation  orchardist  the  As has  decreases  under-estimates production  application  for.  of  further  to  to  the  of  the  that left  model  which c o u l d  portion of  the  of  the  critical  benefit  estimated point.  This  111 region  is  considered  inability  of  the  non-irrigation  to  model  inputs  have a downwards to  incorporate  bias  changes  d u r i n g h i g h water to  to  e x t e n s i v e model  model  benefits dynamic  of  require  incorporating  framework  required present  would  given model.  Finally,  may not  the  fruits.  irrigation question.  3 1  outweigh the  periods.  policy  aspect  reworking. aspects  the  breadth  This  of  provide a s p a t i a l  The  in a  considerable  work  implications  of  the would  of  model  to  involve  weather data breadth  the  to  for  present handle  results crops  altering the  other  the  p a r t i c u l a r crop regions  be  than  water-yield  from d i f f e r e n t the  could  and  in would  model.  A v e r s i o n o f t h e model u s e d f o r t h i s t h e s i s entitled WYSPAC (Water Y i e l d S i m u l a t i o n f o r P e r e n n i a l and A n n u a l C r o p s ) has s i n c e been d e v e l o p e d f o r t h e I n l a n d W a t e r s D i r e c t o r a t e , Vancouver. 3 1  The  '  system parameters Use  the  such a r e a c t i v e  such b e h a v i o r a l  considerable  e x t e n d e d by a d a p t i n g tree  include  to  to  stress  dynamic a p p r o a c h n e c e s s a r y the  due  REFERENCES  Agrawal,  R.C.  and  E.O.  Heady.  Operati  for Agricultural Decisions. University Press, 1972.  Ames,  ons  Research  Iowa:  Iowa  Methods  State'  A n d e r s o n , J . R . " S i m u l a t i o n : M e t h o d o l o g y and A p p l i c a t i o n A g r i c u l t u r a l E c o n o m i c s , " Review of M a r k e t i n g and A g r i c u l t u r a l E c o n o m i c s , 42:1 (March 1 9 7 4 ) : 3 ~ 3 8 .  in  A s s a f , R . , I . L e v i n and B . B r a v d o . 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E c o n . 58:1 (Feb. 1976):391-402. M i d d l e t o n , J . E . , E . L . P r o e b s t i n g and S. R o b e r t s . "A C o m p a r i s o n of T r i c k l e and S p r i n k l e r I r r i g a t i o n f o r A p p l e O r c h a r d s . " b u l . n o . 0 8 9 5 , P r o s s e r W a s h i n g t o n : C o l l e g e of A g r i c u l t u r e Research C e n t r e , Washington S t a t e University, 1981. M i t c h e l l , P . D . , P . H . J e r i e , and D . J . C h a l m e r s . "The E f f e c t s o f R e g u l a t e d Water D e f i c i t s on Pear T r e e G r o w t h , F l o w e r i n g , F r u i t G r o w t h , and Y i e l d , " J . Amer. S o c . H o r t . S c i . 109:5 (1984):604-606. M o o r e , C V . "A G e n e r a l A n a l y t i c a l Framework f o r E s t i m a t i n g the P r o d u c t i o n F u n c t i o n f o r Crops U s i n g I r r i g a t i o n W a t e r , " J . Farm E c o n . 43 ( 1 9 6 1 ) : 8 7 6 - 8 8 . P r o e s t i n g , E . L . , J . E . M i d d l e t o n and S. 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BCMAF  of A g r i c u l t u r a l  Engineering  Economics,  Branch,  U.B.C,  A b b o t s f o r d , B.C.  115 Appendijt A:  Model Ctxig  Dt M E N S I O N A C T Y L D ( t 7 ) , D M 2 ( 2 0 , 3 ) , D M 2 6 ( 2 0 , 3 ) , G T O T ( I 7 ) , Y L D R E D ( 1 7 ) , J AWSC (1 7 ) , I W E A C ( 3 5 ) , W E A G E N ( I 2 0 0 , 3 5 ) , X M 2 ( 3 ) , X M 2 6 ( 3 ) , N P V O U T ( 8 ) REAL AYTOT,HARVC,NET,F,FC,INTCPT,SLOPE,WATER,IRRG(17,17).WATSAV 11RRTOT, N P V , N P V T O T , N P V O U T , PAN(20,245),RAIN(20,245),TWATER,EXIRR 2YLDTOT, W A T T O T , O N E ( 5 0 , 9 ) , T W O ( 5 0 , 9 ) , T H R E E ( 5 0 , 9 ) , F O U R ( 5 0 , 9 ) , 3FIVE(50,9),SIX(50,9),SEVEN(50,9) ,EIGHT(50,9),OUT(9),SEED, 4 N P V Y L D , N P V W A T , O U T 2 ( 2 ) , Y W N P V ! ( 5 0 , 2) , Y W N P V 2 ( 5 0 , 2 ) , Y W N P V 3 ( 5 0 , 2 ) , 5YWNPV4(50,2),YWNPV5(50,2),YWNPV6(50,2),YWNPV7(50,2),YWNPV8(50,2 INTEGER YEAR,I,MODEL,DAY,J,COUNT,N,Y,WEAGEN,IRRDAY 91 FORMAT(2F8.2,F10.2) 92 FORMAT( ' MODEL -',12) 93 FORMAT ( ' 0 NPV ',' AVG ' , ' SD ',' YIELD ', 1 ' AVG ' , ' SD ',' WATER ',' AVG ',' SD') 94 FORMAT(I7,I3,I2,I3,I6,30I7) 95 FORMAT('O') 96 FORMAT( ' 1 ) 97 FORMAT(F16.2,F10.2,F6.2,2F10.2,F6.2,2F7.2,F6.2) 98 F0RMAT(F16.2,FI2.2) 99 FORMAT ( ' 0 NPV Y I E L D ' , ' NPV WATER") DO 10 1 - 1 , 1 2 0 0 READ(2,94)IWEAG DO 11 J = 1 , 3 5 WEAGEN(I,J) IWEAG(J) 11 CONTINUE 10 CONTINUE DO 20 1 - 1 , 2 0 READ(3,9l)XM2 READ(4,91)XM26 DO 21 '-J-1 , 3 DM2(I,J)-XM2(J) DM26(I,J)-XM26(J) 21 CONTINUE 20 CONTINUE C DM2 AND DM26 A R E 5 B Y 2 0 ( Y E A R S ) C O S T M A T I C E S F O R M2 A N D M26 O R C H A R T SEED-1.1 1  1  DO 90  Y-1,10  CALL WEATHR(PAN,RAIN,WEAGEN,SEED) DO 100 MODEL-1,8 C 8 MODELS REPRESENTING 2 S O I L T Y P E S , 2 I R R I G A T I O N C STOCKS. HARVC=0 • C I N I T I A L I Z E HARVEST COSTS NPVTOT-0 C I N I T I A L I Z E THE NET NPV T O T A L NPVYLD-0 C N P V Y L D IS T H E NPV O F YIELD NPVWAT-0 C N P V W A T IS T H E N P V O F W A T E R DO 110 1-1,17 GTOT(I)-0 C I N I T I A L I Z E GROWTH F A C T O R T O T A L 110 CONTINUE CALL MODELS(N, F , F C , W A T E R , M O D E L , T W A T E R ) CALL IRRGAT(N,WATER,TWATER,IRRG) YLDTOT-0 WATTOT-0 DO 120 YEAR-1,20  SYSTEMS  AND  2  ROO:  116  Appendix A (continued) C  20  YEARS CONSTITUTES  ONE ORCHARD  LIFE.  EXIRR=>0 C EXIRR K E E P S T R A C K O F E X C E E S S IRRIGATION DO 1 3 0 I • 1 , N C N R E P R E S E N T S T H E NUMBER O F I R R I G A T I O N R O T A T I O N S YLDRED(I)« 0 C I N I T I A L I Z E Y I E L D REDUCTION FACTOR AWSC(I)=FC C S E T I N T I A L AWSC T O F I E L D C A P A C I T Y 130 CONTINUE IRRDAY*0 C I R R D A Y C O U N T S T H E NUMBER O F I R R I G A T I O N D A Y S P E R S E A S O N . J«0 C J I S A ROW C O U N T E R F O R T H E I R R I G A T I O N MATRIX DO 1 4 0 D A Y « 1 , 2 4 5 C 2 4 5 D A Y S P E R GROWING S E A S O N ( Y E A R )  J-J+1  140  IF ( J . G T . N ) J«! CALL YIELD{N,AWSC,F,FC,J,GTOT,YLDRED,DAY,IRRG,PAN,RAIN,IRRDAY, 1 YEAR,EXIRR) CONTINUE CALL WATUSE(N,WATER,TWATER,IRRTOT,EXIRR,IRRDAY,WATSAV) CALL YRTOT(MODEL,N,YEAR,ACTYLD,GTOT,YLDRED,DM2,DM26,AYTOT,HARV 1NET) NPV*NET/((1+.06)**YEAR) NPVTOT=NPVTOT+NPV  120  C C  C  901  902  the  •NPVYLD»NPVYLD+AYTOT/((1+.06)**YEAR) NPVWAT=NPVWAT+WATSAV/((1 + . 0 6 ) * * Y E A R ) YLDTOT=YLDTOT+AYTOT WATTOT-WATTOT+WATSAV CONTINUE YLDTOT= Y L D T O T / 2 0 WATTOT=WATTOT/20 * following  f i l l s  a  50x8  matrix  IF (MODEL.NE.1) G O T O 901 ONE(Y,1)=NPVT0T-5691.97 ONE(Y,4)"YLDTOT ONE(Y,7)=WATTOT CALL MATCAL(ONE,Y) YWNPV1(Y,1)«NPVYLD YWNPVl.(Y,2)=NPVWAT GOTO 100 I F ( M O D E L . N E . 2 ) GOTO 902 TWO(Y,1)=NPVTOT-569l.97 TWO(Y,4)«YLDTOT TWO(Y,7)=WATTOT CALL MATCAL(TWO,Y) YWNPV2(Y,1)=NPVYLD YWNPV2(Y,2)-NPVWAT GOTO 100 I F (MODEL.NE.3) GOTO 903 THREE(Y,1)-NPVTOT-5736.83 THREE(Y,4)•YLDTOT THREE(Y,7)«WATTOT CALL MATCAL(THREE,Y)  of  NPVs  for a l l orchard models  117 Appendix A  903  904  905  906  907  C 100 90  (continued)  YWNPV3(Y,1)=NPVYLD YWNPV3(Y,2)»NPVWAT G O T O 100 I F ( M O D E L . N E . 4 ) GOTO 9 0 4 FOUR(Y,1)=NPVTOT-57 36.83 FOUR(Y,4)=YLDTOT FOUR(Y,7)=WATTOT CALL MATCAL(FOUR,Y) YWNPV4(Y,1)=NPVYLD YWNPV4(Y,2)=NPVWAT G O T O 100 I F ( M O D E L . N E . 5 ) GOTO 9 0 5 FIVE(Y,1)=NPVTOT-6150.53 FIVE(Y,4)-YLDTOT FIVE(Y,7)=WATTOT CALL M A T C A L ( F I V E , Y ) YWNPV5(Y,1)=NPVYLD YWNPV5(Y,2)=NPVWAT G O T O 100 I F ( M O D E L . N E . 6 ) GOTO 9 0 6 SIX(Y,1)=NPVTOT-6150.53 SI X ( Y , 4 ) = Y L D T O T SIX(Y,7)=WATTOT CALL MATCAL(SIX,Y) YWNPV6(Y,1)=NPVYLD YWNPV6(Y,2)=NPVWAT G O T O 100 I F ( M O D E L . N E . 7 ) GOTO 9 0 7 SEVEN(Y,1)=NPVTOT-6180.05 SEVEN(Y, 4 )«YLDTOT SEVEN(Y,7)-WATTOT CALL MATCAL(SEVEN,Y) YWNPV7(Y,1)=NPVYLD YWNPV7(Y,2)=NPVWAT G O T O 100 EIGHT(Y, 1 )=NPVTOT-6180.05 EIGHT(Y,4)=YLDTOT EIGHT(Y,7)=WATTOT CALL MATCAL(EIGHT,Y) YWNPV8(Y,1)=NPVYLD YWNPV8(Y,2)=NPVWAT CONTINUE CONTINUE DO 9 9 0 M O D E L = 1 , 8 WRITE(6,96) WRITE(6,95) WRITE(6,95) WRITE(6,92)MODEL WRITE(6,93) DO 991 1=1,10 DO 9 9 2 J = 1 , 9 I F ( M O D E L . E Q . 1 ) O U T ( 3 )-ONE(I", J ) IF (MODEL.EQ.2) OUT(3)*TWO(I,J ) IF (MODEL.EQ.3) O U T ( J ) - T H R E E ( I , J ) IF (MODEL.EQ.4) OUT(3)-FOUR(I,J) IF (MODEL.EQ.5) O U T ( J ) - F I V E ( I , J ) IF (MODEL.EQ.6) OUT(J)«SIX(I,J)  118 Appendix*  992 991  994 993 990  (continued)  IF (MODEL.EQ.7) OUT(J)-SEVEN(I,J) IP (MODEL.EQ.8) OUT(J)"EIGHT(I,J) CONTINUE WRITE(6,97)OUT CONTINUE WRITE(6,96) WRITE(6,95) WRITE(6,95) WRITE(6,92)MODEL WRITE(6,99) DO 993 1=1,10 DO 994 J»1,2 IF (MODEL.EQ.1) OUT2(J)-YWNPV1(I,J) IF (MODEL.EQ.2) OUT2(J)-YWNPV2(I,J) IF (MODEL.EQ.3) OUT2(J)-YWNPV3(I,J) IF (MODEL.EQ.4) OUT2(J)=YWNPV4(I,J) IF (MODEL.EQ.5) OUT2(J)-YWNPV5(I,J) IF (MODEL.EQ.6) OUT2(J)»YWNPV6(I,J) IF (MODEL.EQ.7) OUT2(J)-YWNPV7(I,J) IF (MODEL.EQ.8) OUT2 (J) «=YWNPV8 ( I , J ) CONTINUE WRITE(6,98)OUT2 CONTINUE CONTINUE STOP END  SUBROUTINE WEATHR(/PAN/,/RAIN/,/WEAGEN/,/SEED/) DIMENSION WEAGEN(1200,35) INTEGER Z, YR, D, C,WEAGEN,T,L REAL PAN(20,245),RAIN(20,245),SEED,ET(245),U,X SEED-SEED+SEED Z=IRAND(0) C i n i t i a l i z e random number g e n e r a t o r w i t h t i m e - o f - d a y c l o c k X-RANDN(SEED) C i n i t i a l i z e Pan Evap v a r i a t i o n component random number g e n e r a t o r DO 10 YR«1,20 C 20 y e a r s needed Z-IRAND(75)-1 C s e l e c t a random number from 0 t o 74 J--1 K-0 T»0 C T keeps t r a c k of t h i r t y - d a y months C J and K a r e c u r s e r s f o r t e m p e r a t u r e and r a i n f a l l r e s p e c t i v e l y DO 1 5 D-1, 218,31 C f i l l s r a i n and p e t w i t h 245 days(one season) a c c r o s s J«J + 2 K-K + 2 DO 20 I * 5,35 C 31 days per month ( s t a r t s on 5 s i n c e i n f o , i n f i r s t 4 c o l s . ) C the f o l l o w i n g l o o p c h e c k s f o r m i s s i n g data and 30 day months. £********** IF (WEAGEN(16*Z+J,I).NE.888> GOTO 11 T=T+ 1 GOTO 20 Q  11  **********  X=FRANDN(0)  •  119  Appendix A  (continued)  U - . 0 0 0 0 4 4 7 6 * ( W E A G E N ( 1 6 * 2 • J , I ) * * 2) . 0 2 0 4 8 * W E A G E N ( 1 6 * Z J , I) • . 0000364'WEAGEN(16* Z * J , I ) • WEAGEN(16*Z*K,I) .010808*WEAGEN(I 6*Z*R,I) • .000 I 2 4 7 * ( W E A G E N ( i 6 * Z + K , I ) * * 2 ) • 2 . 5 5 9 • 214.21 2 U-ABS(U) P A N ( Y R , D - T - 5 + I) = -1.0636 • . 0 2 6 1 6 1 *WEAGEN(1 6 * Z + J , I ) 1 - 007477*WEAGEN(16*Z+K,I) + (SQRT(U))*X*.I pan u s e s s e a s o n Z ' s maximum t e m p e r a t u r e a n d r a i n d a t a p l u s v a r i a n c e component (the SE of the e s t i m a t e times a random 1 2 3  C C  +  a number)  PAN(YR,D-T-5+I ) = PAN(YR, D - T - 5 + 1 ) / 2 5 . 4 IF (PAN(YR.D-T-5 +I ) . L T . 0 ) PAN(YR,D-T-5*1)-0 C P A N i s now i n inches. RAIN(YR,D-T-5 +I ) = WEAGEN((16*Z)+K,I ) RAIN(YR,D-T-5 +1 ) = RAIN(YR,D-T-5+I)/254 C R A I N i s now i n inches. 20 CONTINUE 15 CONTINUE JO CONTINUE RETURN END SUBROUTINE MODELS(N,F,FC,WATER,/MODEL/,TWATER) C D E P E N D I N G ON T H E M O D E L N U M B E R , M O D E L S S E T S T H E R O T A T I O N AMOUNT(N), C C H O O S E S P A R A M E T E R S FOR T H E AWSC R E L A T I O N ( D E P E N D I N G ON S O I L T Y P E ) , C A N D WATER I N P U T ( D E P E N D S ON S O I L T Y P E A N D I R R I G A T I O N T Y P E ) . INTEGER MODEL,N REAL F C , W A T E R , M , T W A T E R , F IF (MODEL.EQ.1.OR.MODEL.EQ.3) N=6 IF ( M O D E L . E Q . 2 . O R . M O D E L . E Q . 4) N-1 7 IF (MODEL.EQ. 5.OR.MODEL.EQ. 6.OR.MODEL.EQ.7.OR.MODEL.EQ.8) N-1 M N IF (MODEL.EQ.1.OR.MODEL.EQ.3.OR.MODEL.EQ.5.OR.MODEL.EQ.7) GOTO C I M M E D I A T L Y BELOW A R E P A R A M E T E R S FOR S I L T - L O A M SOILS F-5 FC-10 TWATER=.198 WATER=5.333 RETURN C THE P A R A M E T E R S BELOW A R E FOR S A N D S O I L S 200 FC-4 F-3 TWATER=.198 WATER=2.133 RETURN END B  SUBROUTINE IRRGAT(/N/,/WATER/,/TWATER/,IRRG) ROUTINE F I L L S T H E I R R I G A T I O N M A T R I X FOR N DAYS INTEGER N REAL WATER, I R R G ( N , N ) , W A T A P L , T W A T E R IF ( N . E Q . 6 . 0 R . N . E Q . 17) WATAPL«=WATER* . 75 SOLID SET IRRIGATION, E F F I C I E N C Y I S O N L Y 75% O F T O T A L IF (N.EQ.1) WATAPL*TWATER DO 300 J - 1 , N DO 3 1 0 I - l ,N IRRG(I,J)-0 IF (I.EQ.J) IRRG(I,J)-WATAPL CONTINUE  C  THIS  C  IF  310  WATER  USEI  120  Appendix A (con: inue-.l ) 300  CONTINUE RETURN END  SUBROUTINE V I E L D ( / N / , / A W S C / , / ? / , / F C / , / J / , / G T O T / I ,/YLDRED/,/DAY/,/IRRG/,/PAN/,/RA I N/,/1RRDAY/,/YEAR/,/EXIRR/) C DETERMINES AWSC FOR EACH ROTATION FOR EACH DAY, C A L C U L A T E S A GROWTH C FACTOR AND STORES IT IN G T O T , AND DETERMINES A Y I E L D REDUCTION C FACTOR YLDRED. INTEGER J , I , D A Y , W E E K , N , Y E A R , I R R D A Y DIMENSION AWSC(N),GTOT(N),YLDRED(N) REAL AET,RHO,G,T,FC,IRRG(N,N),EXIRR,PAN(20,245),RAIN(20,245), 1D,K,PET,F .IF (DAY.GE.62.AND.DAY.LE.214) IRRDAY=IRRDAY*1 C IRRDAY c o u n t s t h e number o f i r r i g a t i o n d a y s . DO 400 I « 1 ,N RHO=F*AWSC(I ) / F C IF ( R H O . G T . 1 ) RHO-1 C RHO IS A C O E F F I C I E N T R E L A T I N G ACTUAL EVAPOTRANSPIRATION AND C POTENTIAL E V A P O T R A N S P I R A T I O N . D=DAY K - . 7 5 - .0002962 * ( D / 2 . 4 5 - 5 0 ) * * 2 C K i s an e v a p o t r a n s p i r a t i o n coefficient r e l a t i n g pan evap t o P E T . P E T - K * P A N ( YEAR , DAY ) * 2 AET-RHO*PET AWSC(I)-AWSC(I)+RAIN(YEAR,DAY)-AET IF ( D A Y . G E . 6 2 . A N D . D A Y . L E . 2 1 4 ) AWSC(I)-AWSC(I)+1RRG(I,J) C i r r i g a t i o n s t a r t s May 1 a n d e n d s S e p t . 30 IF (I.EQ.J.AND.AWSCfI).GT.FC.AND.DAY.GE.62.AND.DAY.LE.214) '.1EXIRR=EXIRR+AWSC(I)-FC C s t o r e any e x c c e s s i r r i g a t i o n i n EXIRR IF ( A W S C ( I ) . L T . 0 ) A W S C ( I ) « 0 C AWSC CAN NEVER BE L E S S THAN 0 INCHES IF ( A W S C ( I ) . G T . F C ) AWSC(I)=FC C . . . A N D I T CAN NEVER EXCEED F I E L D C A P A C I T Y G=1 . 2 - ( ' 2 . 0 * ( A W S C ( I ) / F C ) ) IF ( G . L T . 0 ) G - 0 IF ( G . G T . 1 ) G=1 C THE DAILY GROWTH REDUCTION FACTOR G L I E S BETWEEN 0 ( L E A S T ) AND 1 . GTOT(I)-GTOT(I)+G WEEK=(DAY/7)+1 C INTEGER D I V I S I O N ON DAY TO DETERMINE WEEK IF ( W E E K . L E . 1 5 ) T = . 2 5 + ( . 0 5 » W E E K ) IF ( W E E K . G T . 1 5 . A N D . W E E K . L T . 3 0 ) T-1.75-(.05*WEEK) IF ( W E E K . G E . 30) T - 1 . 1 5 - ( . 03*WEEK) IF ( T . G T . 1 ) T=1 C T IS A SEASONAL Y I E L D REDUCTION FACTOR YLDREDd )-YLDRED(I ) + (G*T) 400 CONTINUE RETURN END SUBROUTINE W A T U S E ( / N / , / W A T E R / , / T W A T E R / , / I R R T O T / , / E X I R R / , / I R R D A J REAL W A T E R , T W A T E R , I R R T O T , E X I R R , W A T S A V , M INTEGER N,IRRDAY M=N IF ( N . E Q . 1 ) GOTO 800 I R R T O T - ( W A T E R / M ) * IRRDAY  121 Appendix *  800  (onurui'J)  EX:RS«EX:RS/M WATSAV»IRR7CT-EX I RR RETURN I RRT0T« I R3DA Y *?WATZ3 WATSAV»IRRTOT-EXI RR RETURN END  SUBROUTI NE YRTOT (/MODEL/, /N/, /YEAR/, ACTYLD, /GTOT/, I /YLDRED/, /DM2/, /DM2 6/, AY TOT, /HARVC/, NET) C CALCULATES END OF YEAR TOTALS FOR ACTUAL YIELD, HARVEST COSTS C AND NET RETURNS USING POTENTIAL YIELD AND COST FIGURES INTEGER MODEL,YEAR,I , N DIMENSION ACTYLD (N ), GTOT (N) , YLDRED(N) , DM2 ( 20 , 3 ) , DM26 (20 , 3 ) REAL AYTOT, HARVC,NET, M M-N AYTOT-0 IF (MODEL.EQ.3.OR.MODEL.EQ.4.OR.MODEL.EQ.7.OR.MODEL.EQ.8) GOTO C MODELS 3,4,7,AND 8 ARE ON M26 ROOTSTOCKS, HAVE 388 TREES/ACRE C AND DIFFER IN COSTS FROM MODELS 1,2,5 AND 6 WHICH ARE ON M2 C ROOTSTOCKS WITH 202 TREES/ACRE. DO 510 1-1 ,N IF (YEAR.LT.8) ACTYLD(I)-(DM2(YEAR, 3)/M)*(1-GTOT{I)/ 1 (YEAR*245*M)-YLDRED(I )/(24 5*M)) C IF TREES ARE STILL IN THE GROWTH STAGE, ACTUAL YIELD IS DETERMINED C BY POTENTIAL YI ELD (FROM COST MATRIX DM2) LESS THE GROWTH AND YIELD C REDUCTION FACTORS. IF (YEAR.GE.8) ACTYLD(I)-(DM2(YEAR, 3)/M)*(1-YLDRED(I)/(24 5*M)) C IF TREES ARE MATURE ONLY A YIELD REDUCTION FACTOR IS CONSIDERED. C YLDRED IS A DAILY CUMMULATIVE FACTOR AND THUS IS DIVIDED BY THE C NUMBER OF DAYS PER GROWING SEASON. GTOT, THE GROWTH FACTOR, IS C BOTH DAILY AND YEARLY CUMULATIVE AND THUS I S DIVIDED BY YEAR*245. A YTOT-ACTYLD (I ) •AYTOT C TOTAL ACTUAL YIELD I S THE SUM OF THE ACTUAL YIELDS OF EACH ROTATION IF (YEAR.GE.4) HARVC-DM2(YEAR,2)MAYTOT/DM2{YEAR,3)) C HARVESTING AND THUS HARVEST COSTS ONLY OCCUR FROM YEAR 4 ON. NET-AYTOT*.1-HARVC-DM2 (YEAR,I)-70.00 C NET RETURNS (PER ACRE) - ACTUAL YIELD * PRICE PER POUND - CASH COSTS C - water c h a r g e s . 510 CONTINUE RETURN 500 DO 520 1-1,N IF (YEAR.LT.6) ACTYLD(I)•(DM26(YEAR,3)/M)*(1-GTOT(I ) / t (YEAR*24 5*M)-YLDRED(I )/(24 5*M)) IF (YEAR .GE . 6 ) ACTYLD ( I ) - (DM26 (YEAR, 3 )/M) * ( 1 - YLDRED (I )/( 245*M)) A YTOT-ACTYLD(I )•AYTOT IF (YEAR.GE.3) HARVC-DM26(YEAR,2)*(AYTOT/DM26(YEAR, 3 ) ) NET-AYTOT*.1-HARVC-DM26(YEAR,1)-70.00 520 CONTINUE RETURN END SUBROUTINE MATCAL(MAT, Y) C T h i s r o u t i n e computes the average and s t a n d a r d s d e v i a t i o n of C NPV, y i e l d and water used over each 20 year s i m u l a t i o n . REAL MAT(50,9),NPVAVG , YLDAVG,WATAVG, X, A, B,C INTEGER Y IF (Y.NE.1) GOTO 800  122  Appendix A  800  801  802  (continued)  MAT(Y,2)=MAT(Y , 1 ) MAT(Y,3)=0 MAT(Y,5)=MAT(Y,4) MAT(Y,6)=0 MAT(Y,8)=MAT(Y,7) MAT(Y,9)=0 RETURN NPVAVG=0 YLDAVG=0 WATAVG=0 DO 801 I = 1 , Y NPVAVG=MAT(I,1)+NPVAVG YLDAVG=MAT(1,4)+YLDAVG WATAVG=MAT(1,7)+WATAVG CONTINUE X=Y NPVAVG=NPVAVG/X YLDAVG=YLDAVG/X WATAVG=WATAVG/X MAT(Y,2)=NPVAVG MAT(Y,5)=YLDAVG MAT(Y,8)=WATAVG A=0 B=0 C=0 DO 802 1=1,Y A=A+(MAT(I,1)-NPVAVG)**2 B=B+(MAT(I,4)-YLDAVG)**2 C=C+(MAT(I,7)-WATAVG)**2 CONTINUE MAT(Y,3)=SQRT(A/(X-1)) MAT(Y,6)=SQRT(B/(X-1)) MAT(Y,9)=SQRT(C/(X-1)) RETURN END  A p p e n d i x B: S A M P L E O N E S E A S O N RUN R E S U L T S F O R ORCHARD S Y S T E M 5 (M2,trickle,sand)  DAY  RHO  1  1 .000 1 .000 2 1 .000 3 4 1 .000 1 .000 5 1 .000 6 7 1 .000 1 .000 8 1 .000 9 1 .000 IC 1 1 1 .000 1 2 ' 1 .000 1 3 1 .000 1 .000 1 4 1 5 1 .000 1 6 1 .000 1 7 1 .000 1 .000 18 1 .000 1 9 1 .000 20 1 .000 21 22 1 .000 1 .000 23 1 .000 24 1 . 000 25 1 .000 26 27 1 .000 28 1 .000 1 .000 29 1 .000 30 1 .000 31 1 .000 32 1 .000 33 1 .000 34 1 .000 35 36 1 .000 37 1 .000 1 .000 38 1 .000 39 1 .000 40 1 .000 4 1 1 .000 42 1 .000 43 1 .000 44 1 .000 45 1 .000 46 47 1 .000 1 .000 48  49  1.000  AWSC (in) 3.908 3.966 4.000 4.000 4.000 3 . 986 3.986 3.976 4.000 4.000 4.000 3.985 3.950 3.944 3.944 3.952 3.959 3.983 3.957 3.957 3.939 3.918 3.896 3.878 3.877 3.948 3.956 3.956 4.000 3.975 3.948 3.927 3.900 3.884 3.825 3.888 3.879 3.840 3.784 3.882 3.814 3.769 3.681 3.567 3.693 3.701 3.629 3.519 3 . 458  RAIN (in) 0.0 0.0 0.055 0.0 0.0 0.0 0.0 0.0 0.079 0.016 0.016 0.0 0.0 0.0 0 .0 0 . 008 0.008 0 .024 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.071 0 .008 0 .0 0.047 0.0 0.0 0.0 0.0 0.0 0.0 0.063 0.0 0.0 0.0 0 . 098 0.0 0.0 0.0  0.0 0 . 126 0 . 008 0.0 0.0  0.0  PET (in)  K  G  T  0 .012 0 . 002 0 .0 0 .0 0 .0 0 .014 0 . 0 0 .009 0 .0 0 .0 0. 0 0 .015 0 .035 0 .006 0 .0 0 .0 0 .0 0 .0 0 .026 0 .0 0 .018 0 .022 0 .02 1 0 .018 0 .001 0 .0 0. 0 0 .0 0 .0 0 . 025 0 . 027 0 .02 1 0 .027 0 .016 0 .059 0 .0 0 .009 0 .039 0 .056 0 .0 0 .068 0 .045 0 .089 0 .113 0 .0 0. 0 0 .072 0 .110 0 .061  0 . 204 0. 208 0.212 0 . 2 16 0.220 0.224 0.229 0.233 0.237 0.24 1 0.245 0.249 0.253 0.257 0.26 1 0.265 0.269 0.273 0. 270 0.282 0.286 0.290 0 . 294 0.298 0.304 0.312 0.320 0.329 0.337 0.345 0.353 0.361 0.369 0.378 0. 386 0.394 0.402 0.410 0.418 0.427 0.435 0.443 0.451 0.459 0.467 0.476 0.484 0.492 0.400  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  0. 300 0.300 0.300 0.300 0.300 0.300 0.350 0.350 0.350 0.350 0.350 0.350 0.350 0.400 0.400 0.400 0.400 0.400 0.400 0.400 0 .450 0.450 0.450 0.450 0 .450 0.450 0.450 0 .500 0.500 0. 500 0.500 0.500 0.500 0.500 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0,650  0.0 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0  0.0 0.0  Appendix B: SAMPLE ONE SEASON' RUN RESULTS FOP. ORCHARC SYSTEM 5 ( M 2 , t r i c k l e , s a n e ) day  00 01 02 03 04 05 06 07 08  09 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  rain moisture moisture ( i n ) factor p Level Un) soil  1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000  1 .000  1 .000 .000 1 .000 1 .000  1  Soil  4 .000 4 .000 4 .000 4 .000 4 .000 3 .983 4 .000 4 .000 4 .000 4 .000 4 .000 3 .997 4 .000 4 .000 4 .000 4 .000 4 .000 4 .000 4 .000 4 .000 4 .000 4 .000 4 .000 3 .564 4 .000 4 .000 4 .000 4 .000 4 .000 4 .000 3 .972 4 .000 4 .000 4 .000 4 .000 4 .000 4 .000 4 .000 4 .000  1 .000 4.000 1 .000 4 . 0 0 0 1 .000 4 . 0 0 0 1 .000 3 .969 1 .000 3 .916 1 .000 1 .000 1 .000 1 .000 1 .000  4 .000 4 .000 4 .000 4 .000 3 .939  0. 03 1 0. 528 0 . 205 0. 0 0. 0 0. 0 0 . 055 0. 0 0. 087 0. 071 0. 0 0. 0 0. 0 0 . 008 0. 055 0. 0 0. 0 0 . 094 0. 0 39 0. 157 0. 0 0 . 047 0 . 016 0. 0 0 . 008 0. 567 0. 7 1 7 0 . 031 0. 0 0. 0 0. 0 0 . 055 0 . 047 0 . 591 0. 024 0 . 008 0 . 055 0. 0  0. 0 0. 0 0. 063 0. 039 0. 0 0. 0. 0. 0.  0 039 0 0  0. 0 0. 0  p o t e n t i a l evapo growth evapotrans. reduction trar.s. coet"f . factor (in) K G -  0 .0 0. 0 0. 0 0. 04 1 0. 1 94 0. 215 0. 0 0. 143 0. 0 0. 0 0. 172 0 . 201 0 . 102 0. 0 0. 0 0 . 179 0 . 1 38 0. 0 0. 0 0. 0 0. 1 1 6 0. 0 0. 0 0. 234 0. 0 0. 0 0. 0 0. 0 0 . 031 0 . 106 0 . 226 0. 0  0. 0 0. 0 0. 0 0. 0 0. 0 0. 093 0. 140 0. 167 0. 0 0. 0 0. 229 0. 251 0. 0  0 . 1 29 78 0 . 195 0. 259  0. 1  0.704 0.706 0.708 0.710 0.712 0.714 0.716 0.718 0.720 0.722 0.724 0.727 0.729 0.731 0.733 0.735 0.737 0.739 0.741 0.743 0.745 0.747 0.749 0.749 0.747 0.745 0.743 0.741 0.739 0.737 0.735 0.733 0.731 0.729 0.727 0.724 0.722 0.720 0.718 0.716 0.714 0.712 0.710 0.708 0.706 0.704 0.702 0.700 0.696  0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0.0  0.0 0.0 0. 0 0.0 0. 0 0.0 0.0 0.0 0. 0  0 .0 0.0 0. 0 0 .0 0 .0 0 .0  0.0  timing of stress factor T 1 .000 1 .000 1 .000 1 .000 1 .000 0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.850 0.850 0.850 0.850 0.850 0.850 0.850 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.750 0.750 0.750 0.750 0.750 0.750 0.750 0.700 0.700 0.700 0.700 0.700 0.700 0.700 0.650 0.650  Appemllx B: SAMPLE ONE SEASON RUN R E S U L T S FOR ORCHARD SYSTEM 5 ( M 2 , t r i c K L e , s a n d ) day  149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196  soil SC i I rain moisture moisture (in) factor p Le ve I (in) 1 .000 1 .000 1 .000 1 .000 1 1 1 1 1 1  .000 .000 .000 .000 .000 .000  1 .000 1 .000 1 .000 1 .000 1.000 1 .000 1 .000 1 .000 1 .000 1 .000 T.OOO 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1.000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1.000 1 .000 1.000 1.000  3.977 0.0 3.907 0.0 3.901 - 0.0 0.0 3.949 3.920 0.0 0.0 3.929 4.000 0.094 0.0 4.000 0.0 4.000 4.000 0.024 0.0 4.000 0.0 4.000 4.000 0.0 0.0 3.991 3.997 0.0. 0.110 4.000 0.0 4.000 0.0 4.000 0.0 4.000 0.0 4.000 0.0 4.000 4.000 4.000  0.465 0.047  4.000 4.000 4.000 4.000 4.000  0.0 0.0 0.0 0.0 0.0  4.000  0.0  4.000  0.0  4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000  0.0 0.055 0 . 122 0.0 0.0 0.008 0.421 0 . 126 0.0 0.0 0.0 0.0 0.181 0.0 0.0 0.0 0.008 0.220  poteni Lei I evap growth t£«! mg t rc\ns. reduc t ion st ress evapotrans. coef f. factor factor (in) T K G 0. 1 60 0.268 0.204 0.151 0.227 0.189  0.0 0. 1 25 0.125 0.0 0.091 0. 167 0. 1 5 5 0.207 0. 1 92 0.0 0. 1 96 0.141 0.176 0.141  0.692 0.688 0.684  0 . 680 0.676 0.671 0.667 0.663 0.659 0.655 0.651  0.647 0.643 0.639 0.635 0.631  0.627 0.622 0.618 0.614  0 . 1 30 0.0 0.0 0. 1 5 5 0.145  0.610 0.606 0.602  0.141  0.590 0.586 0.582 0.578 0.573 0.569 0.565 0.561 0.557  0 . 163 0. 1 30 0 . 109 0.114 0.098 0.0 0.0 0 . 152 0 . 125 0.0 0.0 0.0 0.134 0.092 0.111 0 . 136 0.0 0.059 0 . 128 0.090 0.0 0.0  0.598 0.594  0.553 0.549 0.545 0.54 1 0.537 0.533 0.529 0.524 0.520 0.516 0.512 0.508 0.504 0.500  0.0 0.0 0.0 0.0 0.0 0.0  0 . 650 0.650 0.650 0. 650 0.650 0.600 0.600 0.6C0 0. 600 0.600 0.600 0.600 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.500 0.500  0.0 0.0  0.0 0.0 0.0 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0. 0.0 0.0  0.500  0.500 0.500 0.500 0.500 0 . 450 0.450 0.450 0.450 0.450 0.450 0.450 0.400 0.400 0.400 0.400 0.400 0.400 0.400 0.350 0.350 0.350  .  0.350 0.350 0.350 0.350 0.300  Appendix  day  B:  SAMPLE ONE S E A S O N RUN RESULTS FOR ORCHARD S Y S T E M 5 ( M 2 , t r i c k l e , s a n d )  soil soil r a i n p o t e n t i a l , evapogrowth moisture moisture ( i n ) evapotrans, reduction factor p l e v e l trar.s. coeff. .factor £Ln) (in} £ _G .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000  000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 955 915 860 840 718 3.611 3.537 3 545 3, 465 3 425 3. 358 3 405 3. 507 3. 451 3 434 3.400 3.400 3.448 3.400 3.471 3.542 3.51 1 3.506 3.561 3.600 3.562 3.556 3.556 3.525 3.516 3.563  882 0 0 0 0 0 0.055 0.031 0, 0 0, 134 0..0 0, 0 0, 0 0,.0 0,,0 0.0 0.0  0.0 0.0 008 0 0 0 047 102 0 0 0.0 0.0 0,,047 0,,0 0,,071 0,,071 0,,0 0.0 0.055 0,.039 0..0 0..0 0..0 0,,0 0, 0 0,,047  0, 0 0, 072 0, 077 0. 105 0.072 0, 091 0,.0 0, 0 0, 083 0 ,0 0.095 0.051 0, 048 0, 063 0, 061 0, 045 0, 065 0, 061 0, 045 0, 040 0, 055 0.020 0. 122 0 ,107 0, 073 0,,0 0, 081 0,,039 0 ,068 0,,0 0 ,0 0,,056 0.017 0.034 0.0 0.0 0.047 0.0 0.0 0.031 0, 005 0,,0 0 ,0 0,,038 0.007 0.0 0.031 0.009 0.0  0 . 496 0.492 0.483 0. 484 0.430 0.476 0.471 0,,467 0, 463 0,,459 0,,455 0,,451 0 ,447 0,,443 0.,439 0.,435 0.431 0.427 0.422 0.418 0.414 0 .410 0 ,406 0.402 0.396 0 ,388 0 ,380 0 ,371 0 ,363 0.355 0.347 0.339 0.331 0.322 0.314 0.306 0.298 0.290 0.282 0.273 0.265 0.257 0.249 0.24 1 0.233 0.224 0.216 0.208 0.200  0.0 0.0 0.0 0.0 0. 0 0 .0 0, 0, 0,  o.  0, 0 0.0 0.0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  t i m i n g of stress factor J___  0 . 300 0.300 0.300 0.,300 0 , 300 0,,300 0 ,250 , 0,.250 0,,250 0,,250 0.,250 0,,250 0,,250 0,,220 0,.220 0,,220 0,,220 0,.220 0,,220 0,.220 0, I 90 0, 90 0, 90 0, 90 0, 90 0, 90 0, 90 0, 60 0, 60 0, 60 0, 60 0, 60 0, 60 0, 60 0, 30 0, 30 0, 30 0, 30 0, 30 0, 30 0, 30 0, 00 0 00 0 00 0 00 0, 00 0, 00 0, 00 0, 070  

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