Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1987_A6_7 W53.pdf [ 5.87MB ]
Metadata
JSON: 831-1.0097228.json
JSON-LD: 831-1.0097228-ld.json
RDF/XML (Pretty): 831-1.0097228-rdf.xml
RDF/JSON: 831-1.0097228-rdf.json
Turtle: 831-1.0097228-turtle.txt
N-Triples: 831-1.0097228-rdf-ntriples.txt
Original Record: 831-1.0097228-source.json
Full Text
831-1.0097228-fulltext.txt
Citation
831-1.0097228.ris

Full Text

THE EFFECT OF WATER RESTRICTIONS ON APPLE ORCHARD PRODUCTIVITY IN BRITISH COLUMBIA'S OKANAGAN VALLEY by IAN WIGINGTON SUBMITTED IN PARTIAL FULFILMENT OF REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES A g r i c u l t u r a l Economics We accept t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d A THESIS THE THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1987 © Ian W i g i n g t o n , 1987 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the The U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree that p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my 1 w r i t t e n p e r m i s s i o n . A g r i c u l t u r a l Economics The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: A p r i l 1987 A b s t r a c t T h i s t h e s i s e x a m i n e s t h e r e l a t i o n s h i p b e t w e e n w a t e r a n d y i e l d f o r a p p l e s i n t h e O k a n a g a n r e g i o n o f B r i t i s h C o l u m b i a . T.h'ifS i s a c c o m p l i s h e d t h r o u g h a m o d e l w h i c h s i m u l a t e s t h e w a t e r / y i e l d r e l a t i o n s h i p i n t r e e f r u i t s . Two s o i l t y p e s , t w o r o o t s t o c k s , a n d t w o i r r i g a t i o n s y s t e m s w e r e i n c l u d e d i n t h e s i m u l a t i o n . T h e r e s u l t s o f t h e s i m u l a t i o n i n d i c a t e t h a t O k a n a g a n o r c h a r d i r r i g a t i o n w a t e r r e q u i r e m e n t s a r e s u b s t a n t i a l l y l o w e r t h ' a n p r e s e n t 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 . U s i n g s p r i n k l e r i r r i g a t i o n , i r r i g a t i o n r e q u i r e m e n t s f o r s i l t -l o a m s o i l s a m o u n t e d t o 30% o f p r e s e n t a p p l i c a t i o n r a t e s , w h i l e f o r s a n d s o i l s 42% o f p r e s e n t a p p l i c a t i o n r a t e s were r e q u i r e d . T r i c k l e i r r i g a t i o n r e q u i r e m e n t s w e r e d e t e r m i n e d t o be 71% o f s p r i n k l e r r e q u i r e m e n t s f o r s i m i l a r y i e l d s . i i Table of Contents 1. INTRODUCTION 1 1.1 The Problem ....4 , 1.2 Objectives 4 1.3 Research Method 5 1 .4 Thesis Guide 8 2. THEORETICAL CONSIDERATIONS AND THE CONCEPTUAL MODEL .10 2.1 Factor Demand Theory and Input Restriction 10 2.1.1 Factor Demand Theory 10 2.1.2 Quantitative Input Restriction 12 2.2 Biological Considerations 18 2.2.1 The Plant-Water Relationship 18 2.2.2 Determining Water Stress 20 2.2.3 Calculating the Soil Moisture Level 22 2.3 Trickle versus Sprinkler Irrigation 26 2.4 Hypothesized Water/Yield Relationship 28 2.5 Generalized Model 33 3. ANALYTICAL MODEL 37 3.1 The Orchard Components Comprising the Model 37 3.1.1 Tree Rootstocks 38 3.1.2 Soil Type 41 3.1.3 Irrigation 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 Trickle Systems 51 3.3 Calculation of Soil Moisture Level 54 i i i 3.4 C a l c u l a t i o n of Y i e l d s 56 3.4.1 Determining Growth Reduction F a c t o r 58 3.4.2 Determining the Y i e l d Reduction F a c t o r ....59 3.4.3 T o t a l Growth and T o t a l Y i e l d 63 3.5 Weather Generator 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 from Pan Evaporation 68 3.7 Summary of Parameter R e l a t i o n s h i p s 71 4. RESULTS 7 6 4.1 The Base Case 77 4.2 R e s u l t s of the Water R e s t r i c t e d Cases 80 4.3 V a l i d a t i o n of the Water R e s t r i c t e d Cases 88 4.4 S e n s i t i v i t y A n a l y s i s 90 4.4.1 The E v a p o t r a n s p i r a t i o n F a c t o r K 91 4.4.2 A c t u a l versus 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 Slope C o e f f i c i e n t f ....94 4.4.3 The Timing of S t r e s s F a c t o r T 96 4.4.4 The Degree of S t r e s s F a c t o r d 98 4.5 P o l i c y I m p l i c a t i o n s 100 5. -SUMMARY, CONCLUSIONS, AND SUGGESTIONS FOR FUTURE RESEARCH 101 5 .1 Summary 101 5.2 Con c l u s i o n s 105 5.3 Recommendations f o r Future Research 108 REFERENCES 112 i v LIST OF TABLES 3.1 Average Y i e l d s per Acre Over 20 Years For Two D i f f e r e n t Rootstocks 40 3.2 A v a i l a b l e Water Storage Capacity 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 Eight Orchard Systems and Their 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 Va r i e s With P e r i o d Of Growing Season 69 3.5 Model Parameters, A b r e v i a t i o n s , and Units of Measurement 72 4.1 Results of Water Reductions 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 Levels 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 Results of Parameter S e n s i t i v i t y A n a l y s i s on M2 Orchards Systems i n Year 4 of Tree L i f e 92 v LIST OF FIGURES 2.1 Hypothesized Orchard Production Function 17 2.2 Hypothesized Rest r ic ted Orchard Production Function ..29 2.3 Hypothesized T r i c k l e and Spr inkler Production Functions 31 2.4 Hypothesized Rest r ic ted vs . Unrest r ic ted Orchard Production Functions 31 2.5 General Flowchart of the Orchard Production Model . . . . 3 4 3.1 Derivat ion of S o i l Moisture Factor p 57 3.2 Relat ionship Between Growth Reduction Factor g and S o i l Moisture Level 60 3.3 Der ivat ion of Timing of Stress Factor T 62 3.4 Relat ionship Between Evapotranspirat ion Coef f ic ient K and Percent of Growing Season 70 3.5 Interact ion of Factors Comprising the Model 73 4.1 Production Functions For M2 Orchard Systems Showing E f fec t of Reducing Water Appl ica t ion Levels on Y ie lds 83 4.2 Evapotranspirat ion Coef f ic ient K for M2 Orchard Systems 85 4.3 Evapotranspirat ion Coef f ic ient K for the Control and S e n s i t i v i t y Ana lys is Cases 93 4.4 Actual vs . Po ten t ia l Evapotranspirat ion Coef f ic ient f and Its Rela t ionship to the Evapotranspirat ion Factor p for the Control and S e n s i t i v i t y Ana lys is Cases 95 4.5 Level of Stress Factor T Over the Growing Season: Control Case and Value Assumed for S e n s i t i v i t y Case ..97 4.6 Degree of Stress Factor d for the Control Case and the S e n s i t i v i t y Analys is Case 99 v i I d e d i c a t e t h i s work to my p a r e n t s , James and D o r o t h y W i g i n g t o n , f o r t h e i r s u p p o r t and encouragement, and to E i j a , f o r n e v e r d o u b t i n g and a l w a y s u n d e r s t a n d i n g . I would l i k e t o thank the members of my commitee, John Graham, Tim H a z l e d i n e , and Mike Novak, f o r t h i e r e x p e r t i s e and g u i d a n c e , and Cam S h o r t , f o r i n i t i a t i n g t h e whole t h i n g . I a l s o w i s h to thank W a l t e r Riemann and Roger P i p e f o r much a p p r e c i a t e d m o r a l s u p p o r t . F i n a l l y , I would l i k e t o e x p r e s s my g r a t i t u d e to R i c k Lymer and Gwen Sykes f o r i n n u m e r a b l e c l a i m s made on t h e i r t i m e and p a t i e n c e i n r e s e a r c h i n g t h i s t h e s i s , t o Kathy S h y n k a r y k f o r e n c o u r a g e m e n t , and to Roger M c N e i l l and t h e I n l a n d Waters D i r e c t o r a t e f o r f u n d i n g p r o v i d e d . v i i Chapter 1 INTRODUCTION The t r e e f r u i t i n d u s t r y accounted f o r approximately 8.2% of t o t a l farm cash r e c e i p t s i n B r i t i s h Columbia ( S t a t s Canada, 1985). The Okanagan r e g i o n i s the primary f r u i t growing area i n the Province and, because of i t s dry c l i m a t e , f r u i t producers i n the r e g i o n must r e l y on i r r i g a t i o n . Apples are the major o r c h a r d crop grown i n B r i t i s h Columbia accounting f o r 68.7% of the acreage p l a n t e d in t r e e f r u i t s (1981 c e n s u s ) . The Okanagan region accounts f o r 99.3% of the B r i t i s h Columbia apple crop (B.C. M i n i s t r y of A g r i c u l t u r e , 1985). Water i n the Okanagan i s i n demand from i n d u s t r i a l , r e s i d e n t i a l , and r e c r e a t i o n a l users as w e l l as a g r i c u l t u r a l u s e r s . Meeting the needs of a l l these s e c t o r s c o u l d be a problem i n the f u t u r e , p a r t i c u l a r l y with expanding r e s i d e n t i a l demands. 1 T h i s study focuses on water used f o r a g r i c u l t u r a l purposes i n the Okanagan V a l l e y . The study i s p a r t of a l a r g e r assessment of water use by a l l s e c t o r s i n the Okanagan. 2 Because of the predominance of apple p r o d u c t i o n i n t h i s r e g ion r e l a t i v e to other forms of a g r i c u l t u r e , t h i s study s p e c i f i c a l l y concerns i t s e l f with water use f o r apple orchards i n the Okanagan r e g i o n . 1R. M c N e i l l , Water Use Optimization Model, Working Paper, Environment Canada, 1983. 2 T h i s study i s the a g r i c u l t u r a l component of a m u l t i s e c t o r water use model being developed by the Inland Waters D i r e c t o r a t e , P a c i f i c & Yukon Region. 1 2 Tree f r u i t p r o d u c e r s i n the Okanagan V a l l e y r e l y on i r r i g a t i o n systems to p r o v i d e t h e i r water r e q u i r e m e n t s . Many of the o r c h a r d i s t s in the v a l l e y s t i l l use o l d e r 'handmove' i r r i g a t i o n systems c o n s i s t i n g of s p r i n k l e r s and s e c t i o n s of p i p e which can be uncoupled and moved about the o r c h a r d . Most new i r r i g a t i o n systems c o n s i s t of permanent s p r i n k l e r s and p i p e ( s o l i d set systems) p l a c e d e i t h e r under t r e e s or on p o s t s over t r e e s . S o l i d set systems and handmove systems are g e n e r a l l y not a b l e to a p p l y water to e n t i r e o r c h a r d s at one t i m e . T h i s i s main ly due to a l a c k of a v a i l a b l e c a p a c i t y i n m a i n l i n e i r r i g a t i o n d i s t r i c t water sys tems . Hence, producers are f o r c e d to i r r i g a t e t h e i r o r c h a r d s on a r o t a t i o n a l b a s i s , those w i t h handmove systems p h y s i c a l l y moving p ipe and s p r i n k l e r s , those w i t h s o l i d set systems u s i n g v a l v e s to a l l o c a t e water (Stevenson , 1980). T h i s r o t a t i o n method of w a t e r i n g o r c h a r d s p l a y s a key r o l e i n i r r i g a t i o n p r a c t i c e s i n the a r e a . A second f a c t o r that must be c o n s i d e r e d r e l a t e s to t r e e f r u i t water r e q u i r e m e n t s . When a p l a n t f a i l s to o b t a i n i t s r e q u i r e d water needs from the s o i l , i t i s s a i d to undergo water s t r e s s . The h o t t e r and d r i e r the weather , the more water a p l a n t r e q u i r e s . Water s t r e s s can reduce t r e e f r u i t y i e l d s and t h i s r e s u l t s i n revenue l o s s e s to producers ( C a r r u t h e r s and C l a r k , 1981). A p r o d u c e r thus min imizes the p o s s i b i l i t y of water s t r e s s by u s i n g the maximum amount of water a l l o w a b l e d u r i n g each i r r i g a t i o n r o t a t i o n . T h i s maximum l i m i t i s de termined by a worst case s c e n a r i o f o r 3 water r e q u i r e d d u r i n g an extended hot, dry p e r i o d . In other words, i f at any given time an o r c h a r d undergoes a p e r i o d e q u i v a l e n t to the h o t t e s t , d r i e s t p e r i o d recorded to date, the i r r i g a t i o n water a p p l i e d d u r i n g each r o t a t i o n should be adequate to meet t r e e needs. T h i s method of t r e e f r u i t i r r i g a t i o n i s w a s t e f u l and can be encouraged by the p r i c i n g scheme f o r a g r i c u l t u r a l water. Water in the Okanagan i s p r i c e d by the acre. For an annual f i x e d fee, o r c h a r d i s t s may l a w f u l l y apply water i n amounts as determined by the a l l o w a b l e flow r a t e f o r the p a r t i c u l a r area i n q u e s t i o n . Because of t h i s p r i c i n g mechanism and because the Okanagan re g i o n i s g e n e r a l l y c h a r a c t e r i z e d by good s o i l d r a i nage, o r c h a r d i s t s have t r a d i t i o n a l l y i r r i g a t e d as i f drought c o n d i t i o n s were the norm r a t h e r than the e x c e p t i o n (Stevenson, 1980), thus m i n i m i z i n g the p o t e n t i a l r i s k of water s t r e s s . The a g r i c u l t u r a l s e c t o r i s thus c o n s i d e r e d to be one area where water c o n s e r v a t i o n methods c o u l d have a c o n s i d e r a b l e impact upon o v e r a l l water demands. P r i c i n g by the acre f a i l s to p r o v i d e any economic i n c e n t i v e to conserve water. A volume p r i c i n g scheme, whether i n c o r p o r a t e d i n t o the e x i s t i n g set up as an added expense or t o t a l l y r e p l a c i n g the per acre p r i c e method, has p o t e n t i a l f o r s u b s t a n t i a l i r r i g a t i o n water savings over the amounts o r c h a r d i s t s p r e s e n t l y use i n the Okanagan. 4 1.1 THE PROBLEM Water s u p p l i e s i n the Okanagan must meet the demands of s e v e r a l user g r o u p s . Whi l e the v a l l e y as a whole i s not i n s h o r t supply of water , demands from competing s e c t o r s do r e s u l t in l o c a l s h o r t a g e s ( M c N e i l l , 1983). An example of t h i s occurs between a g r i c u l t u r e and f i s h i n g i n t e r e s t s . Some d i s t r i c t a g r i c u l t u r a l water systems acces s water from upper v a l l e y s treams . These water c o u r s e s are in some cases tapped e n t i r e l y by the d i s t r i c t systems i n the l a t e summer months when a g r i c u l t u r a l i r r i g a t i o n requ irements are h i g h e s t . T h i s e l i m i n a t e s any down stream s p o r t f i s h i n g d u r i n g t h i s p e r i o d . C o n f l i c t s such as t h i s are expec ted to become more f requent as r e s i d e n t i a l areas expand and water demands i n c r e a s e . A g r i c u l t u r a l water c o n s e r v a t i o n i s not a major c o n s i d e r a t i o n i n the Okanagan. F l a t r a t e p r i c i n g f o r i r r i g a t i o n water and m i n i m i z i n g the r i s k of water s t r e s s work as a n t i - i n c e n t i v e s to c o n s e r v a t i o n . 1.2 OBJECTIVES The main o b j e c t i v e of t h i s t h e s i s i s to determine the r e l a t i o n s h i p between water r e q u i r e m e n t s and y i e l d f o r an a p p l e o r c h a r d and the i m p l i c a t i o n s t h e r e o f i n terms of t o t a l water used f o r t r e e f r u i t s . The Okanagan r e g i o n of B r i t i s h Columbia i s chosen as the s tudy a r e a . A r i s i n g from t h i s main o b j e c t i v e are the f o l l o w i n g s u b - o b j e c t i v e s : 1. To determine the r e d u c t i o n i n y i e l d that may be 5 a n t i c i p a t e d i f t r e e s are s u b j e c t e d to v a r y i n g water a p p l i c a t i o n regimes and to de termine tha t water a p p l i c a t i o n l e v e l below p r e s e n t a p p l i c a t i o n l e v e l s at which y i e l d s b e g i n to be a f f e c t e d . 2. To determine the r e l a t i v e water use e f f i c i e n c i e s of s p r i n k l e r and t r i c k l e i r r i g a t i o n systems i n a p p l e o r c h a r d s e t t i n g s in terms of w a t e r / y i e l d i n p u t / o u t p u t r e l a t i o n s h i p s . 3. To t e s t the s e n s i t i v i t y of the r e s u l t s to changes i n key parameters of the mode l . 4. To i n v e s t i g a t e a l t e r n a t i v e water p r i c i n g s t r a t e g i e s for a g r i c u l t u r e i n terms of user i n c e n t i v e s to conserve water and the p o l i c y i m p l i c a t i o n s of these a l t e r n a t i v e p r i c i n g f o r m u l a e . 1.3 RESEARCH METHOD In o r d e r to a c c o m p l i s h the f i r s t o b j e c t i v e a model w i l l be c o n s t r u c t e d to s i m u l a t e an a c t u a l app le o r c h a r d growing c y c l e and determine how v a r i o u s i r r i g a t i o n water a p p l i c a t i o n l e v e l s a f f e c t y e a r l y y i e l d s i n that c y c l e . The problem of a t t e m p t i n g to model or s i m u l a t e any system or p r o c e s s i s a t r a d e - o f f between the c o m p l e x i t y which r e a l i t y r e q u i r e s and the l i m i t a t i o n s of t ime , space , and data which the computer m o d e l l i n g p r o c e s s a l l o w s . Any model i s to some degree a s i m p l i f i c a t i o n of r e a l i t y . The s i m u l a t i o n undertaken f o r t h i s t h e s i s a t tempts to r e p r e s e n t the r e a c t i o n of a complex p h y s i o l o g i c a l p l a n t p r o c e s s when one of the i n p u t s to t h a t p r o c e s s , water , i s s y s t e m a t i c a l l y r e s t r i c t e d . The m o d e l l i n g 6 procedure a t tempts to a s c e r t a i n the e f f e c t of a g i v e n s o i l water l e v e l on p o t e n t i a l y e a r - e n d f r u i t y i e l d for each day of a p r e d e f i n e d growing s e a s o n . A weather g e n e r a t o r i n c o r p o r a t e d i n t o the model randomly s e l e c t s a weather year from a h i s t o r i c a l weather d a t a set and p r o v i d e s d a i l y r a i n f a l l and temperature v a l u e s , the former p r o v i d i n g an exogenous water i n p u t , the l a t t e r be ing used to c a l c u l a t e the amount of water which the o r c h a r d t r a n s p i r e s on t h a t day, the e v a p o t r a n s p i r a t i o n r a t e . C a l c u l a t i o n of the e v a p o t r a n s p i r a t i o n r a t e makes i t p o s s i b l e to r e l a t e t r e e f r u i t p r o d u c t i o n needs w i t h water a v a i l a b i l i t y . Depending on the age of the o r c h a r d , the c a l c u l a t i o n of a d a i l y s t r e s s f a c t o r i s based on p l a n t growth, p l a n t growth and y i e l d , or y i e l d . E a r l y o r c h a r d y e a r s produce no marketable y i e l d s , w h i l e subsequent years produce f i r s t p a r t i a l and l a t e r f u l l c r o p s . For the p e r i o d p r i o r to f u l l c r o p p i n g , when water s t r e s s o c c u r s , a growth r e d u c t i o n f a c t o r and a y i e l d r e d u c t i o n f a c t o r are c a l c u l a t e d , the combinat ion of which d e t e r m i n e s the f i n a l y e a r - e n d y i e l d . The growth r e d u c t i o n f a c t o r i s c a l c u l a t e d to determine the e f f e c t which water s t r e s s has on t r e e growth. In the e a r l y y e a r s , proper t r e e growth i s important in p r o v i d i n g the proper t r e e branch s t r u c t u r e and s i z e to accommodate f r u i t . For mature y e a r s , o n l y the y i e l d r e d u c t i o n f a c t o r i s used to determine y e a r - e n d y i e l d t o t a l s . Once a f r u i t t r e e has reached mature s i z e , new branch growth i s not a c o n t r i b u t o r to f r u i t y i e l d . 7 S t r e s s e f f e c t s i n terms of y i e l d or growth are not c a r r i e d over from year to y e a r , as each growing season i s c o n s i d e r e d independent of pas t or subsequent s easons . Thus a growth r e d u c i n g s t r e s s in matur ing y e a r s i s not c a r r i e d on to subsequent y e a r l y y i e l d c a l c u l a t i o n s . T h i s s i m p l i f y i n g assumption of the model a r i s e s due to a l a c k of q u a n t i f i a b l e i n f o r m a t i o n on the degree to which s t r e s s i n any one year a f f e c t s growth a n d / o r y i e l d i n subsequent y e a r s . In order to de termine the r e l a t i v e water use e f f i c i e n c i e s of s p r i n k l e r and t r i c k l e i r r i g a t i o n sys tems , i t i s n e c e s s a r y to h y p o t h e s i z e a r e l a t i o n s h i p between water s t r e s s and t r e e f r u i t y i e l d s , and to examine t h i s r e l a t i o n s h i p i n terms of water a p p l i c a t i o n r a t e s u s i n g the two i r r i g a t i o n sys tems . In s y s t e m a t i c a l l y r e d u c i n g the amount of i r r i g a t i o n water a p p l i e d to the o r c h a r d d u r i n g the growing season , an attempt i s made to determine the p o i n t at which a f u r t h e r r e d u c t i o n in water a p p l i c a t i o n becomes c r i t i c a l and r e s u l t s i n y i e l d r e d u c t i o n s . By s i m u l a t i n g s p r i n k l e r and t r i c k l e i r r i g a t i o n systems in the mode l , the p o i n t at which water r e s t r i c t i o n s become c r i t i c a l can be compared f o r each i r r i g a t i o n method, thus p r o v i d i n g a t e s t of r e l a t i v e water use e f f i c i e n c y for s p r i n k l e r and t r i c k l e systems. An a n a l y s i s of the r e s u l t s of the s i m u l a t i o n w i l l p r o v i d e the i n f o r m a t i o n to determine the p o t e n t i a l i m p l i c a t i o n s of a l t e r i n g i r r i g a t i o n water p r i c i n g mechanisms. 8 Key parameters i n the model are set a t v a l u e s o ther than those d e s i g n a t e d f o r the s i m u l a t i o n to t e s t the s e n s i t i v i t y of the mode l . F i n a l l y , a l t e r n a t i v e water p r i c i n g s t r a t e g i e s are e v a l u a t e d u s i n g m a g i n a l a n a l y s i s . 1 .4 THESIS GUIDE The next c h a p t e r d i s c u s s e s some of the t h e o r y a p p r o p r i a t e to the model , and p r e s e n t s h y p o t h e s i z e d r e s u l t s of r e d u c i n g i r r i g a t i o n water a p p l i c a t i o n s based on p r e v i o u s s t u d i e s . The l i t e r a t u r e on i r r i g a t i o n systems and r e l e v a n t w a t e r - a p p l e y i e l d f i n d i n g s , from which the model parameters a r e d e t e r m i n e d , i s r e v i e w e d . The f i n a l s e c t i o n of c h a p t e r two p r o v i d e s a g e n e r a l d e s c r i p t i o n of how the o r c h a r d s i m u l a t i o n i s c o n c e p t u a l i z e d . Chapter t h r e e p r e s e n t s the a n a l y t i c a l mode l . S e c t i o n one d i s c u s s e s the c h o i c e of s p e c i f i c o r c h a r d c h a r a c t e r i s t i c s to be i n c o r p o r a t e d i n t o the s i m u l a t i o n . Next , the method of d e t e r m i n i n g o r c h a r d y i e l d s for each stage of the growing c y c l e i s d i s c u s s e d , as i s a d e t a i l e d account of c a l c u l a t i n g the assumed p r e s e n t day water a p p l i c a t i o n amounts i n Okanagan o r c h a r d s . In the f o l l o w i n g s e c t i o n s of c h a p t e r t h r e e , the model parameters used i n the s i m u l a t i o n are d e r i v e d and the r o l e and s t r u c t u r e of the weather g e n e r a t o r i s d i s c u s s e d . The f i n a l s e c t i o n of c h a p t e r t h r e e p r o v i d e s a d e t a i l e d d e s c r i p t i o n of how the v a r i o u s model components i n t e r a c t i n the s i m u l a t i o n . 9 Chapter four p r e s e n t s the r e s u l t s of the s i m u l a t i o n , s t a r t i n g w i t h the base case or presen t day s i t u a t i o n , and f o l l o w e d by the water r e s t r i c t e d c a s e s . The f i n a l p a r t s of c h a p t e r four d i s c u s s v a l i d a t i o n as a p p l i e d to t h i s s tudy and g i v e the r e s u l t s of s e n s i t i v i t y a n a l y s i s . Chapter f i v e beg ins wi th a summary of the model and r e s u l t s , f o l l o w e d by a d i s c u s s i o n of p o s s i b l e p o l i c y i m p l i c a t i o n s of those r e s u l t s . A d i s c u s s i o n of some of the f a c t o r s which must be c o n s i d e r e d i n measur ing the o v e r a l l c o s t of water to the o r c h a r d i s t i s a l s o p r e s e n t e d . The f i n a l two s e c t i o n s d i s c u s s the b r e a d t h of the s i m u l a t i o n r e s u l t s w i t h r e g a r d to o t h e r areas and c r o p s , and s u g g e s t i o n s f o r f u r t h e r r e s e a r c h . Chapter 2 THEORETICAL CONSIDERATIONS AND THE CONCEPTUAL MODEL T h i s c h a p t e r p r o v i d e s a d i s c u s s i o n of bo th the economic and b i o l o g i c a l t h e o r y r e l e v a n t to and u n d e r l y i n g the f o r m u l a t i o n of the model . These , t o g e t h e r w i t h a review of r e l e v a n t l i t e r a t u r e p r o v i d e hypotheses t h a t r e s u l t i n the f o r m u l a t i o n of a model p r e s e n t e d i n c h a p t e r 3. 2.1 FACTOR DEMAND THEORY AND INPUT RESTRICTION One of the o b j e c t i v e s of t h i s t h e s i s i s to i n v e s t i g a t e the r e l a t i o n s h i p between water and y i e l d in t r e e f r u i t p r o d u c t i o n . The method used to a c c o m p l i s h t h i s o b j e c t i v e i s to s i m u l a t e the y i e l d response of f r u i t t r e e s to v a r i o u s water a p p l i c a t i o n r a t e s . S ince water can be viewed as a f a c t o r input to the f r u i t p r o d u c t i o n p r o c e s s , f a c t o r demand theory and the response of the o r c h a r d i s t to a l t e r n a t i v e f a c t o r p r i c e mechanisms and to r e s t r i c t i n g water input l e v e l s w i l l be d e t a i l e d . 2 .1.1 FACTOR DEMAND THEORY For a p r o f i t maximiz ing f i r m w i t h o n l y one v a r i a b l e r e s o u r c e , the l e v e l of use of the v a r i a b l e r e s o u r c e w i l l be de termined by the p o i n t at which the c o s t of one more u n i t of the r e s o u r c e i s equa l to the r e t u r n o b t a i n e d from use of tha t r e s o u r c e i n p r o d u c t i o n . 3 The amount by which t o t a l 3 T h e d i s c u s s i o n i n t h i s s e c t i o n i s taken from L e f t w i c h and E c k e r t ' s The Price System and Resource Allocation, 8th e d . pp . 424-429. 10 11 revenue changes when one more u n i t of a r e s o u r c e i s employed i n the p r o d u c t i o n proces s i s d e f i n e d as the m a r g i n a l revenue p r o d u c t (MRP) of tha t r e s o u r c e . For the r e s t r i c t e d case of o n l y one v a r i a b l e r e s o u r c e , the MRP c u r v e f o r t h a t r e source t r a c e s out the f i r m ' s demand schedule for t h a t r e s o u r c e . I f more than one f a c t o r input to the p r o d u c t i o n proces s i s v a r i a b l e , then any change to one v a r i a b l e f a c t o r input may r e s u l t in changes in the l e v e l of use of o t h e r v a r i a b l e f a c t o r i n p u t s and thus the p r o d u c t mix . The above d i s c u s s i o n assumes a per u n i t p r i c i n g mechanism for the f a c t o r i n p u t ( s ) . However, i f one of the f a c t o r i n p u t s i s p r i c e d u s i n g a f l a t r a t e p r i c i n g system where the p u r c h a s e r i s e n t i t l e d to use any amount of the f a c t o r up to some d e s i g n a t e d amount for a f i x e d p r i c e , then the r e s u l t of a change i n the p r i c e of t h a t f a c t o r i s q u i t e d i f f e r e n t from the per u n i t p r i c i n g s i t u a t i o n . In the case of f l a t r a t e p r i c i n g , the t y p i c a l m a r g i n a l a n a l y s i s approach must be r e c o n s i d e r e d . The f i r m i s f aced w i t h the f o l l o w i n g c h o i c e : e i t h e r pay the f l a t r a t e and r e c e i v e the d e s i g n a t e d q u a n t i t y of the input o r , i f p o s s i b l e , s u b s t i t u t e the input e n t i r e l y out of the p r o d u c t i o n p r o c e s s t h e r e b y s a v i n g the f l a t r a t e f e e . In cases where the input i n q u e s t i o n i s e s s e n t i a l to the p r o d u c t i o n p r o c e s s , the f i r m has no a l t e r n a t i v e but to pay the f l a t r a t e fee i f i t chooses to remain i n p r o d u c t i o n . A p a r t from cases where a f a c t o r can be s u b s t i t u t e d out of the p r o d u c t i o n p r o c e s s , w i t h f l a t r a t e p r i c i n g f i r m s are 1 2 unresponsive to input p r i c e changes i n terms of product mix adjustments. An o b j e c t i v e of t h i s t h e s i s i s to determine a c t u a l Okanagan orchard water requirements f o r a f r u i t t r e e over the growing season i n order that these may be compared to a c t u a l water a p p l i c a t i o n r a t e s . As has been p o i n t e d out, f l a t r a t e p r i c i n g of f a c t o r i n p u t s to a p r o d u c t i o n process r e s u l t s i n f i r m s being unresponsive to input p r i c e changes. If e f f i c i e n t water use f o r an orchard o p e r a t i o n i s d e f i n e d as the minimum amount of water needed to produce a given y i e l d " , then i t i s hypothesized that Okanagan orchard i r r i g a t i o n p r a c t i c e s are not e f f i c i e n t due to the f l a t r a t e p r i c i n g s t r u c t u r e f o r i r r i g a t i o n water. To determine the l e v e l of e f f i c i e n t water use, q u a n t i t a t i v e r e s t r i c t i o n s w i l l be p l a c e d on i r r i g a t i o n water a p p l i e d to an orchard model which s i m u l a t e s orchard y i e l d s as a f u n c t i o n of water a p p l i c a t i o n . By e s t i m a t i n g the amount of water r e q u i r e d by an o r c h a r d o p e r a t i o n and comparing t h i s with the amount of water a c t u a l l y a p p l i e d , the p o t e n t i a l f o r water savings i n a g r i c u l t u r e w i l l be shown. 2 . 1 . 2 QUANTITATIVE INPUT RESTRICTION T h i s s e c t i o n d e a l s with the hyp o t h e s i z e d e f f e c t on t r e e f r u i t p r o d u c t i o n 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 the amount of i r r i g a t i o n water a v a i l a b l e to o r c h a r d i s t s . "using a p r e d e f i n e d i r r i g a t i o n system, s o i l type and t r e e d e n s i t y . 13 When the supply of an input i n a p r o d u c t i o n p r o c e s s becomes more l i m i t e d , t h e n , assuming no i n t e r v e n i n g p r i c i n g or q u a n t i t y r e g u l a t i o n s , i n the s h o r t run f i r m s demanding tha t input w i l l b i d up the p r i c e . In the l o n g run the f a c t o r input demand may s h i f t and p r i c e may f a l l as o ther p r o d u c t i o n f a c t o r s are s u b s t i t u t e d ( H i r s h l e i f e r , 1984, pp . 228) . In the case of a r e g u l a t e d market , the above s c e n a r i o need not a p p l y . In the Okanagan, o r c h a r d i s t s are r e g u l a t e d i n the amount of i r r i g a t i o n water they can a p p l y to any a c r e of l a n d i n any g iven r e g i o n . At p r e s e n t t h i s r e g u l a t e d amount of i r r i g a t i o n water i s more than adequate to meet o r c h a r d requirements (S tevenson , 1980). I t i s one of the o b j e c t i v e s of t h i s t h e s i s to de termine the amount of water a c t u a l l y 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 and compare t h i s to the a l l o w e d water a p p l i c a t i o n r a t e . To a c c o m p l i s h t h i s i t i s proposed t h a t the amount of water a p p l i e d per a c r e be reduced i n a s e r i e s of s u c c e s s i v e s tages and the r e s u l t i n g impact on y i e l d be measured i n each c a s e . Water i s but one input i n a m u l t i - i n p u t p r o d u c t i o n p r o c e s s . To measure the impact on y i e l d of a l t e r i n g the amount of water a p p l i e d to an o r c h a r d , a l l o ther p r o d u c t i o n i n p u t s a r e h e l d c o n s t a n t . A set of p o s s i b l e o r c h a r d p r o d u c t i o n i n p u t s as viewed from an economic p e r s p e c t i v e has been documented by M c N e i l l (1977) . These might i n c l u d e the 1 4 f o l l o w i n g : Q = f ( I , N , W , L , M ) where Q = f r u i t y i e l d I = i r r i g a t i o n water a p p l i c a t i o n N = f e r t i l i z e r a p p l i c a t i o n W = weather f a c t o r s L = labour M = management S i n c e the o r c h a r d model used in t h i s s tudy c o n s i d e r s o n l y the w a t e r - y i e l d r e l a t i o n s h i p , the p r e d i c t e d e f f e c t of a l l o w i n g water to v a r y wh i l e h o l d i n g a l l o t h e r i n p u t s (as c o n c e p t u a l i z e d above) c o n s t a n t on the r e s u l t i n g p r o d u c t i o n f u n c t i o n i s of i n t e r e s t . To p r e d i c t t h i s e f f e c t , some p o s s i b l e r e a c t i o n s of an o r c h a r d i s t faced w i t h a c u r t a i l m e n t of a v a i l a b l e i r r i g a t i o n water to a degree which t h r e a t e n s to reduce o r c h a r d y i e l d s are c o n s i d e r e d . I t i s assumed tha t the r e g u l a t i o n s r e g a r d i n g the s a l e and d i s t r i b u t i o n of i r r i g a t i o n water remain the same and thus f l a t r a t e p r i c i n g on a per a c r e b a s i s as o u t l i n e d i n the p r e v i o u s s e c t i o n h o l d s . The adjustment p r o c e s s can be viewed i n terms of l o n g run and s h o r t run t ime frames. In the s h o r t r u n , adjustments to v a r i a b l e i n p u t s are p o s s i b l e but adjustments to f i x e d f a c t o r s cannot be made ( V a r i a n , p . 8 ) . Short run adjus tments 1 5 might i n c l u d e a he ightened awareness on the p a r t of the o r c h a r d i s t of weather c o n d i t i o n s and s o i l m o i s t u r e l e v e l s to f a c i l i t a t e more f l e x i b l e i r r i g a t i o n r o t a t i o n p a t t e r n s to compensate for h o t , dry p e r i o d s w i t h r e s t r i c t e d water s u p p l i e s . For example, q u i c k e r r o t a t i o n t imes and a v o i d i n g i r r i g a t i n g d u r i n g the heat of the day c o u l d reduce water use . A second p o s s i b l e method f o r s a v i n g water i s replacement of worn or m a l f u n c t i o n i n g s p r i n k l e r heads . A t h i r d method the a p p l i c a t i o n of a mulch ground-cover to reduce the l o s s of s o i l water to the atmosphere (Kennedy, 1985). In the l o n g - r u n t ime frame a l l f a c t o r s are v a r i a b l e . For example, one l o n g - r u n adjus tment open to an o r c h a r d i s t i s a l t e r i n g the s o i l t e x t u r e and thus the water h o l d i n g c a p a c i t y through a d d i t i o n s of o r g a n i c m a t t e r . The above d i s c u s s i o n p r o v i d e s examples of some of the the adjustments which an o r c h a r d i s t , f aced wi th a reduced a l l o t m e n t of i r r i g a t i o n water , might make to min imize the adverse e f f e c t on y i e l d s u s i n g a g i v e n t echno logy s e t . Other adjus tments u s i n g d i f f e r e n t t e c h n o l o g i e s , and thus c o n s t i t u t i n g d i f f e r e n t p r o d u c t i o n f u n c t i o n s , can a l s o be made. These adjustments i n c l u d e s w i t c h i n g to a d i f f e r e n t i r r i g a t i o n system or r e p l a c i n g the o r c h a r d wi th t r e e s more r e s i t a n t to d r o u g h t . When water i s r e s t r i c t e d to such a degree the assumpt ion of h o l d i n g a l l o r c h a r d p r o d u c t i o n i n p u t s except water c o n s t a n t does not p r o v i d e a r e a l i s t i c p r e d i c t i o n of 1 6 the outcome of r e s t r i c t i n g i r r i g a t i o n water . I f the o b j e c t i v e of the model i s to mimic an a c t u a l o r c h a r d w a t e r - y i e l d response i n an a c t u a l o r c h a r d env ironment , such a r e s t r i c t i o n does not a c h i e v e t h i s goa l at these 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 s . However, a t h i g h e r i r r i g a t i o n l e v e l s the model p r o v i d e s a t r u e r d e p i c t i o n of r e a l i t y . L i m i t i n g the d i s c u s s i o n f o r i l l u s t r a t i v e purposes to a s i n g l e t echno logy s e t , F i g u r e 2.1 r e p r e s e n t s one h y p o t h e t i c a l o r c h a r d p r o d u c t i o n f u n c t i o n . P o i n t Qc r e p r e s e n t s the water a p p l i c a t i o n l e v e l below which y i e l d s beg in to be r e d u c e d , and i s d e f i n e d as the critical point. Assume that the a c t u a l a l l o w a b l e 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 l i e s to the r i g h t of Qc a t Q * . C l e a r l y r e d u c i n g water a p p l i c a t i o n l e v e l s down to the l e v e l of Qc has l i t t l e e f f e c t on y i e l d . I f a l l i n p u t s o t h e r than water can be assumed to be at o p t i m a l l e v e l s at p o i n t Q * 5 , then the c o n d i t i o n of h o l d i n g a l l i n p u t s except i r r i g a t i o n c o n s t a n t i s n o n - b i n d i n g w i t h i n the r e g i o n Qc - Q * . 6 No input adjustments need to occur to m a i n t a i n o r c h a r d y i e l d s at cons tant l e v e l s 7 s i n c e i r r i g a t i o n remains s u f f i c i e n t to meet o r c h a r d needs . Thus for t h a t p o r t i o n of the p r o d u c t i o n f u n c t i o n to the r i g h t of Q c , the r e s t r i c t i o n of h o l d i n g a l l i n p u t s except water 5 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 farmers s i n c e i n p u t s o ther than water can 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 . 6 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 tha t excess 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 ince the Okanagan r e g i o n has good d r a i n a g e t h i s assumption i s a c c e p t a b l e . 7 S t r i c t l y speak ing 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 decrease as i r r i g a t i o n l e v e l s dropped and l e s s l e a c h i n g o c c u r e d . y i e l d of apples Figure 2.1 Hypothesized Orchard Production Function 18 c o n s t a n t does not compromise the p r e d i c t i v e power of the model . From the p r e c e d i n g d i s c u s s i o n i t can be c o n c l u d e d t h a t the degree to which the model a c c u r a t e l y r e p r e s e n t s the w a t e r - y i e l d r e l a t i o n s h i p i n t r e e f r u i t s v a r i e s w i t h the amount of i r r i g a t i o n water a p p l i e d . The h y p o t h e s i z e d shape of the p r o d u c t i o n f u n c t i o n and the assumptions u n d e r l y i n g t h a t shape w i l l be d i s c u s s e d in s e c t i o n 2 . 3 . Thus f a r t h i s c h a p t e r has d e a l t w i t h the economic theory r e l e v a n t to the mode l . In the next s e c t i o n the b i o l o g i c a l a s p e c t s of importance in d e v e l o p i n g the model are d i s c u s s e d . 2.2 BIOLOGICAL CONSIDERATIONS In order to c o n c e p t u a l i z e the r e l a t i o n s h i p between the q u a n t i t y of i r r i g a t i o n water a p p l i e d and the expec ted f r u i t y i e l d , t h e o r e t i c a l p l a n t - w a t e r p h y s i o l o g i c a l r e l a t i o n s h i p s and e m p i r i c a l o b s e r v a t i o n s from p r e v i o u s s t u d i e s w i l l be d i s c u s s e d i n t h i s s e c t i o n . I n i t i a l l y the r e l a t i o n s h i p between water and p l a n t growth w i l l be d i s c u s s e d . T h i s i s f o l l o w e d by the d e r i v a t i o n of a method for d e t e r m i n i n g and measuring when t h i s r e l a t i o n s h i p becomes c r i t i c a l f o r t r e e f r u i t y i e l d s . 2 .2.1 THE PLANT-WATER RELATIONSHIP The amount of water a p l a n t uses p l u s e v a p o r a t i o n from nearby s o i l i s the e v a p o t r a n s p i r a t i o n (ET) r a t e . Les s than 19 one p e r c e n t of the water r e q u i r e d by p l a n t s i s f or growth purposes ( C a r r u t h e r s and C l a r k , 1981). Most i s used i n t r a n s p i r a t i o n d u r i n g p h o t o s y n t h e s i s . The amount of water any p l a n t r e q u i r e s i s a f u n c t i o n of both a tmospher ic and s o i l c o n d i t i o n s as w e l l as the type of p l a n t and c u l t u r a l approach u s e d . Water forms a c o n t i n u o u s system w i t h i n the p l a n t from the r o o t s through to s tomata l t r a n s p i r a t i o n . As water i s t r a n s p i r e d through l e a f s tomata , a p o t e n t i a l g r a d i e n t draws water i n t o the p l a n t through the r o o t s . The g r e a t e r the demands of t r a n s p i r a t i o n , the more water the p l a n t draws from the s o i l . As the s o i l c o n s t i t u t e s a f i n i t e water source ( b a r r i n g c o n s t a n t water replacement) t h e r e i s a l i m i t to t h i s upward f l o w . Most p l a n t s reduce the s i z e of s tomata l openings when s o i l water t e n s i o n i s such t h a t water no longer f lows r e a d i l y i n t o the r o o t s . 8 By r e d u c i n g s tomata l pore s i z e a p l a n t reduces i t s p h o t o s y n t h e t i c c a p a c i t y and thus growth i s r e d u c e d . The amount of water a v a i l a b l e to a p l a n t i s bounded by the s o i l f i e l d c a p a c i t y on the upper end, and by the s o i l permanent w i l t i n g p o i n t on the lower end. F i e l d c a p a c i t y i s d e f i n e d as the amount of water l e f t in a s o i l a f t e r t h a t s o i l has been s a t u r a t e d and a l l o w e d to d r a i n to a p o i n t where the r a t e of d r a i n a g e has s u b s t a n t i a l l y s u b s i d e d ( g e n e r a l l y w i t h i n one or two days of water a p p l i c a t i o n ) . The remain ing water i s c o n s i d e r e d to be a v a i l a b l e to p l a n t s 8 W i n t e r g i v e s an example of a p l a n t , the Droopsy p o t a t o e , which , be ing unable to c l o s e i t s s tomata , i s an e x c e p t i o n to the g e n e r a l c a s e . 20 p r o v i d e d the s o i l water content does not f a l l below the permanent w i l t i n g p o i n t . The permanent w i l t i n g p o i n t i s d e f i n e d as s o i l water content at which the p l a n t i s i r r e v e r s i b l y damaged by water s t r e s s s i n c e water no l o n g e r passes from the s o i l to the p l a n t r o o t s . The range between f i e l d c a p a c i t y and permanent w i l t i n g p o i n t i s the 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 (AWSC) of a s o i l . 2 .2 .2 DETERMINING WATER STRESS To de termine the w a t e r - y i e l d r e l a t i o n s h i p i n t r e e f r u i t p r o d u c t i o n , the amount of water a v a i l a b l e to the t r e e or o r c h a r d a t any g i v e n time must be d e t e r m i n e d . T h i s s o i l m o i s t u r e l e v e l p r o v i d e s a q u a n t i f i a b l e measure of p o t e n t i a l water s t r e s s under g i v e n a tmospher ic c o n d i t i o n s , where water s t r e s s i s d e f i n e d as o c c u r i n g when the s o i l water c o n t e n t f a l l s below a l e v e l tha t the p l a n t r e q u i r e s to m a i n t a i n p h o t o s y n t h e t i c a c t i v i t y , and t h e r e f o r e growth , at a maximum l e v e l ( W i n t e r , 1974). The l i m i t below which water s t r e s s i s assumed to occur i s d e f i n e d for t h i s t h e s i s by the minimum s o i l m o i s t u r e l e v e l below which i r r i g a t i o n i s recommended by the I r r i g a t i o n Des ign Manual ( B r i t i s h Columbia M i n i s t r y of A g r i c u l t u r e and F o o d , 1983). The d e t e r m i n a t i o n of the degree of s t r e s s a p p l e t r e e s undergo when the s o i l m o i s t u r e l e v e l drops below t h i s d e f i n e d l e v e l i s based on the r e s u l t s of Assaf (1975) . A s s a f found that a l i n e a r r e l a t i o n s h i p e x i s t e d between s o i l water l e v e l and f r u i t volume when the s o i l water l e v e l i n the top two feet of s o i l was i n the range 21 between 30% of the 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 (AWSC) and permanent w i l t i n g p o i n t (PWP, d e f i n e d i n A s s a f at 10% AWSC). The BCMAF I r r i g a t i o n Des ign Manual recommended s o i l water l e v e l i s 60% AWSC in the root zone . For a p p l e t r e e s the roo t zone i s 4 f e e t . Based on t h i s i n f o r m a t i o n , a l i n e a r r e l a t i o n s h i p between f r u i t y i e l d and s o i l m o i s t u r e l e v e l i n the range of 10% of AWSC to 60% AWSC i s assumed. F r u i t y i e l d i s assumed to be zero when the s o i l m o i s t u r e l e v e l i s at or below 10% AWSC and at a maximum when the s o i l m o i s t u r e l e v e l i s at or above 60% AWSC. S o i l m o i s t u r e l e v e l , and thus the degree of water s t r e s s , can be measured on a d a i l y b a s i s when i n f o r m a t i o n on a tmospher i c c o n d i t i o n s and water i n p u t s from r a i n and i r r i g a t i o n are a v a i l a b l e . I f y i e l d i s a f u n c t i o n of s t r e s s c e t e r i s p a r i b u s then the sum of d a i l y water s t r e s s l e v e l s d i v i d e d by the number of days in the growing season p r o v i d e s a means f o r d e t e r m i n i n g annual f r u i t y i e l d from an o r c h a r d of a g i v e n age . I t i s h y p o t h e s i z e d , however, t h a t not o n l y i s the degree of water s t r e s s on a p a r t i c u l a r day important i n d e t e r m i n i n g f r u i t y i e l d , but that the t i m i n g of water s t r e s s d u r i n g the growing season i s a l s o i m p o r t a n t . S e v e r a l s t u d i e s support t h i s h y p o t h e s i s . G o o d e ( l 9 7 5 ) , examining the p h y s i o l o g i c a l e f f e c t s of water s t r e s s on a p p l e t r e e s , p r o v i d e s i n t e r e s t i n g r e s u l t s . I r r i g a t i o n regimes c o n s i s t i n g of no i r r i g a t i o n , e a r l y i r r i g a t i o n (be fore June d r o p ) , l a t e i r r i g a t i o n ( a f t e r June d r o p ) , and a l l season i r r i g a t i o n 22 a p p l i e d to C o x ' s Orange P i p p i n a p p l e t r e e s p r o v i d e ev idence that pos t June drop i r r i g a t i o n r e s u l t s i n maximum marketab le y i e l d s of the regimes t e s t e d . M i t c h e l l , J e r i e , and Chalmers (1984) i n a s tudy on f i v e year o l d B a r t l e t t pear t r e e s c o n c l u d e d t h a t the most c r i t i c a l i r r i g a t i o n t ime for f r u i t growth was l a t e s p r i n g . I r r i g a t i o n d u r i n g the e a r l y p a r t of the season was found to encourage v e g e t a t i v e growth wh i l e l a t e s p r i n g and summer i r r i g a t i o n was n e c e s s a r y f o r maximum f r u i t growth . Based on these s t u d i e s , weights are a p p o r t i o n e d to the v a r i o u s p e r i o d s d u r i n g the growing season . Water s t r e s s o c c u r i n g d u r i n g f r u i t set i s most c r i t i c a l wh i l e s t r e s s o c c u r i n g at the v e r y b e g i n n i n g or very end of the season i s l e a s t c r i t i c a l . 2 .2 .3 CALCULATING THE SOIL MOISTURE LEVEL At tempts to determine the w a t e r - y i e l d r e l a t i o n s h i p s for v a r i o u s c r o p s have been numerous. A b r i e f review of some of the proposed methods i s p r e s e n t e d . M o o r e ( l 9 6 l ) p r o v i d e s an e a r l y example of a s i m u l a t i o n approach u s i n g a p l a n t - s o i l m o i s t u r e r e l a t i o n s h i p d e r i v e d from a "moisture r e l e a s e curve" t o g e t h e r w i t h a c o r r e s p o n d i n g r e l a t i v e growth r a t e i n d e x . F i s c h e r and Hagan (1965) d i s c u s s the e f f e c t s of water s t r e s s on c r o p growth i n terms of h a r v e s t a b l e y i e l d and the d i f f e r e n t ways that s t r e s s may a f f e c t y i e l d s depending on what c o n s t i t u t e s the y i e l d p o r t i o n of the p l a n t in q u e s t i o n . In p a r t i c u l a r , 23 F i s c h e r and Hagan p o i n t out tha t when y i e l d i s measured i n f r e s h f r u i t weight or volume, water s t r e s s i s p o t e n t i a l l y more damaging than i n the case of dry weight f r u i t due to a l o s s i n t u r g o r of the f r u i t . Mapp and Eidman (1967) model y i e l d r e d u c t i o n on a g i v e n p l a n t , at a g i v e n t i m e , as a f u n c t i o n o f : 1) s o i l water l e v e l , which i n t u r n i s a f u n c t i o n of i n p u t s from r a i n f a l l and i r r i g a t i o n and outputs through e v a p o t r a n s p i r a t i o n ; and 2) what they term atmospher ic s t r e s s , which i s a f u n c t i o n of pan e v a p o r a t i o n . F l i n n ( l 9 7 1 ) p r o v i d e d a good summary of a t tempts to model w a t e r - y i e l d r e l a t i o n s h i p s for p l a n t s i n g e n e r a l and some of the problems encountered i n these methods. E a r l y exper iments to c o r r e l a t e t o t a l w a t e r - y i e l d r e l a t i o n s h i p s f a i l e d to account for s e a s o n a l v a r i a t i o n of p l a n t water r e q u i r e m e n t s . Response f u n c t i o n s i n c o r p o r a t i n g c r o p p r o d u c t i o n and i r r i g a t i o n over t i m e , w h i l e p r o v i d i n g a s o l u t i o n to s e a s o n a l v a r i a t i o n s , are n e c e s s a r i l y s i t e - a n d - c r o p - s p e c i f i c and thus of l i m i t e d a p p l i c a b i l i t y . As a p o s s i b l e s o l u t i o n to t h i s prob lem, B e r i n g e r ( 1 9 6 1 ) sugges ted u s i n g a m o i s t u r e t e n s i o n - c r o p y i e l d r e l a t i o n s h i p . F l i n n proposed a c r o p - w a t e r s i m u l a t i o n model u s i n g degree of m o i s t u r e s t r e s s to p r e d i c t y i e l d . The model proposed by F l i n n to determine the s o i l m o i s t u r e l e v e l i s : ET = f * Eo 24 Ea = p * ET where ET = a tmospher ic demand Eo = pan e v a p o r a t i o n Ea = a c t u a l t r a n s p i r a t i o n f = c r o p c o e f f i c i e n t p = a s o i l m o i s t u r e f a c t o r The c r o p c o e f f i c i e n t f a c t o r f i s c r o p - s p e c i f i c and depends on the r e l a t i o n s h i p between p l a n t m o i s t u r e l o s s and a tmospher i c demand. Hargreaves (1966) p r o v i d e s da ta for f on a v a r i e t y of c r o p s . In the case of o r c h a r d f r u i t s , the v a l u e of f ranges from 0 up to 0.75 at mid growing season . Atmospher ic demand i s the amount of water r e l e a s e d from the s o i l and c r o p i n t o the atmosphere when the water l e v e l of the s o i l i s a t the s o i l ' s f i e l d c a p a c i t y . F i e l d c a p a c i t y i s the s o i l m o i s t u r e l e v e l a f t e r the i n i t i a l d r a i n a g e and r u n - o f f has o c c u r r e d from a s a t u r a t e d s o i l . Pan e v a p o r a t i o n i s the amount of water l o s t to the atmosphere from an open body of water under g i v e n a tmospher ic c o n d i t i o n s . A c t u a l e v a p o t r a n s p i r a t i o n i s the amount of water which a c t u a l l y i s l o s t to the atmosphere . At s o i l m o i s t u r e l e v e l s at or near f i e l d c a p a c i t y , a c t u a l e v a p o t r a n s p i r a t i o n i s e q u i v a l e n t to a t m o s p h e r i c demand, and thus the s o i l m o i s t u r e f a c t o r p i s e q u a l to 1. As the s o i l m o i s t u r e l e v e l d r o p s , a p o i n t i s reached at which a c t u a l e v a p o t r a n s p i r a t i o n i s l e s s than a t m o s p h e r i c demand, and thus p becomes l e s s than 1. 25 The s o i l m o i s t u r e l e v e l (SM) at t ime t i s c a l c u l a t e d as f o l l o w s : SM = SM + P + 1 + C - Ea - DR t t -1 t t t t t where P = e f f e c t i v e p r e c i p i t a t i o n I = i r r i g a t i o n water a p p l i e d C = upward c a p i l l a r y water movement DR = deep p e r c o l a t i o n E f f e c t i v e p r e c i p i t a t i o n i s an amount s u f f i c i e n t to wet the s o i l ( i e a f t e r a c c o u n t i n g for i n t e r c e p t i o n l o s s e s ) . S o i l m o i s t u r e i s measured i n inches of water per foot of s o i l . I r r i g a t i o n i n p u t , measured in a c r e i n c h e s , i s the amount of water a p p l i e d to the c r o p . Upward c a p i l l a r y movement i s the amount of water which i s drawn from s u b - r o o t zone s o i l l a y e r s up to the rootzone of the c r o p . Deep p e r c o l a t i o n i s the amount of water l o s t to s u b - r o o t zone s o i l l a y e r s due to d r a i n a g e . The F l i n n model w i l l be used as the b a s i s for d e r i v i n g the d a i l y s o i l m o i s t u r e l e v e l s from which the degree of water s t r e s s and the r e s u l t i n g e f f e c t on y i e l d w i l l be c a l c u l a t e d . D e t a i l s of these c a l c u l a t i o n s and u n i t s of measurement used w i l l be g i v e n i n c h a p t e r 3. T h i s s e c t i o n has rev iewed the l i t e r a t u r e on the observed impact which v a r i o u s s o i l m o i s t u r e l e v e l s have had 26 on t r e e f r u i t y i e l d s . As w e l l , the g e n e r a l form of a method for c a l c u l a t i n g s o i l m o i s t u r e l e v e l s has been o u t l i n e d . The c o m b i n a t i o n of these two p r o c e d u r e s forms the b a s i s for the o r c h a r d model to be f u l l y d e v e l o p e d i n the next c h a p t e r . The f o l l o w i n g s e c t i o n examines the r e l a t i v e m e r i t s 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 . 2.3 TRICKLE VERSUS SPRINKLER IRRIGATION One of the o b j e c t i v e s of t h i s t h e s i s i s to compare 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 systems i n terms of w a t e r - y i e l d r e l a t i o n s h i p s . S t u d i e s of t r i c k l e v e r s u s s p r i n k l e r i r r i g a t i o n are reviewed in t h i s s e c t i o n . P r o e b s t i n g , M i d d l e t o n and R o b e r t s (1977) measured the p h y s i o l o g i c a l e f f e c t s of t h r e e d i s t i n c t i r r i g a t i o n methods f o r Redspur D e l i c i o u s a p p l e s on s e e d l i n g r o o t s t o c k from time of p l a n t i n g through the f o u r t h year of growth at P r o s s e r Wash ington . The e f f e c t s of t r i c k l e i r r i g a t i o n , d a i l y s p r i n k l e r i r r i g a t i o n and t r a d i t i o n a l p e r i o d i c s p r i n k l e r i r r i g a t i o n ( i n t h i s case once every two weeks) were compared w i t h r e s p e c t to p h y s i o l o g i c a l measures . Of p a r t i c u l a r i n t e r e s t to t h i s t h e s i s are the f a v o u r a b l e r e s u l t s of t r i c k l e i r r i g a t e d t r e e s v e r s u s s p r i n k l e r i r r i g a t e d t r e e s i n terms of growth and y i e l d c h a r a c t e r i s t i c s . T r i c k l e i r r i g a t i o n produced b u s h i e r t r e e s not r e q u i r i n g the s p r e a d i n g needed for s p r i n k l e r i r r i g a t e d t r e e s . B lossoming o c c u r r e d e a r l i e r and f r u i t s i z e and y i e l d were g r e a t e s t on t r i c k l e i r r i g a t e d t r e e s . In t h i s t h e s i s , y i e l d r e l a t i o n s h i p s 27 for both s p r i n k l e r and t r i c k l e i r r i g a t e d t r e e s w i l l be compared on an e f f i c i e n c y of water a p p l i e d to y i e l d b a s i s . In what appears to be a f o l l o w - u p s t u d y , M i d d l e t o n , P r o e b s t i n g and Rober t s (1981) p r o v i d e a good summary of the advantages and d i s a d v a n t a g e s of t r i c k l e versus s p r i n k l e r i r r i g a t i o n for f r u i t o r c h a r d s . The study c o n c l u d e d tha t t r i c k l e i r r i g a t i o n had the p o t e n t i a l to save water and energy , reduce s o i l e r o s i o n and l o s s of n u t r i e n t s due to l e e c h i n g , and induce e a r l i e r b los soming and f r u i t i n g . Some of the d i s a d v a n t a g e s i n c l u d e d i n c r e a s e d mainta inance c o s t s i n keeping t r i c k l e i r r i g a t i o n l i n e s c l e a r , e x t e n s i v e f i l t r a t i o n and c h e m i c a l c o n t r o l s i f d i r t y water was used , and i n c r e a s e d r i s k to t r e e s i n the event of a water c u t - o f f as l e s s water was s t o r e d i n the ground compared to s p r i n k l e r i r r i g a t i o n systems. Research i n t o the e f f e c t s of t r i c k l e v e r s u s s p r i n k l e r methods of i r r i g a t i o n on o r c h a r d f r u i t s i s o n g o i n g . I t i s c l e a r tha t s u b s t a n t i a l water s a v i n g s are p o s s i b l e w i t h a t r i c k l e system under c e r t a i n c o n d i t i o n s ( M i d d l e t o n e t . a l . 1981). As for p h y s i o l o g i c a l e f f e c t s , for the purposes of t h i s s tudy 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 w i l l be c o n s i d e r e d to be i d e n t i c a l i n terms of f r u i t y i e l d g i v e n adequate water a p p l i c a t i o n s . T h i s assumption p r o b a b l y underes t imate s the gap between t r i c k l e and s p r i n k l e r systems i n terms of water a p p l i e d to y i e l d r a t i o s . However, because of the l a c k of s u i t a b l e q u a n t i f i a b l e da ta a n e u t r a l p o s i t i o n was t a k e n . 28 2.4 HYPOTHESIZED WATER/YIELD RELATIONSHIP In t h i s s e c t i o n the c h a r a c t e r i s t i c s of the o r c h a r d w a t e r / y i e l d p r o d u c t i o n f u n c t i o n are h y p o t h e s i z e d . These r e l a t i o n s h i p s are based on the f i n d i n g s d e t a i l e d above . Throughout t h i s s e c t i o n the terms restricted and unrestricted w i l l be used to r e f e r to the o r c h a r d p r o d u c t i o n f u n c t i o n . A r e s t r i c t e d p r o d u c t i o n f u n c t i o n i s here d e f i n e d as that p r o d u c t i o n f u n c t i o n which r e s u l t s when a l l i n p u t s in the p r o d u c t i o n p r o c e s s except i r r i g a t i o n water are h e l d c o n s t a n t . With the u n r e s t r i c t e d p r o d u c t i o n f u n c t i o n , a l l i n p u t s are v a r i a b l e . The Okanagan has i n the pas t been c o n s i d e r e d an a r e a where a g r i c u l t u r a l water use c o u l d be reduced s u b s t a n t i a l l y wi thout d e t r i m e n t to o r c h a r d y i e l d s . Stevenson (1980), i n a s tudy of Okanagan o r c h a r d water needs based on e v a p o t r a n s p i r a t i o n r a t e s and a c t u a l i r r i g a t i o n a p p l i c a t i o n s , found tha t d u r i n g a 9 year p e r i o d i n the Summerland d i s t r i c t twice as much water was a p p l i e d as was needed by the o r c h a r d s . Only d u r i n g one week i n the 9 year p e r i o d d i d o r c h a r d water r e q u i r e m e n t s approach the r a t e of i r r i g a t i o n a p p l i c a t i o n . Based on the f i n d i n g s of Stevenson and those noted e a r l i e r , i t i s h y p o t h e s i z e d t h a t the r e s t r i c t e d p r o d u c t i o n f u n c t i o n for o r c h a r d s , as d e p i c t e d i n F i g u r e 2 .2 , w i l l have a h o r i z o n t a l p o r t i o n r e p r e s e n t i n g a near zero y i e l d i n c r e a s e from water a p p l i c a t i o n s beyond tha t necessary f o r app le t r e e needs . Q* i n F i g u r e 2.2 r e p r e s e n t s c u r r e n t Okanagan water y i e l d of apples l-'igure 2 .2 Hypothesized R e s t r i c t e d Orchard Production Function 30 a p p l i c a t i o n l e v e l s . The l e f t p o r t i o n of the y i e l d c u r v e i n F i g u r e 2.2 i s h y p o t h e s i z e d to drop o f f a f t e r some c r i t i c a l p o i n t , Qc , below which y i e l d s are a f f e c t e d by reduced s o i l mo i s ture l e v e l s . T h i s c r i t i c a l p o i n t i s h y p o t h e s i z e d to l i e at a p o i n t equa l to between 30% and 40% of c u r r e n t Okanagan water a p p l i c a t i o n r a t e s . The b a s i s f o r t h i s p r e d i c t i o n i s a s tudy undertaken by Stevenson at the A g r i c u l t u r a l Canada r e s e a r c h s t a t i o n a t Summerland (1974-84) to determine the r e l a t i v e f e r t i l i z e r l o s s a t t r i b u t a b l e to d i f f e r e n t i r r i g a t i o n w a t e r i n g l e v e l s . Water a p p l i c a t i o n r a t e s r a n g i n g from 37% to 100% of p r e s e n t o r c h a r d w a t e r i n g p r a c t i c e s were a p p l i e d to M c i n t o s h a p p l e t r e e s over the 11 year p e r i o d of the s tudy w i t h no d i s c e r n i b l e e f f e c t s on t r e e growth . The degree of s e n s i t i v i t y of app le t r e e response to water s t r e s s i s u n c e r t a i n . 9 Thus w h i l e i t i s h y p o t h e s i z e d that water a p p l i c a t i o n r a t e s below the c r i t i c a l p o i n t , Qc , w i l l r e s u l t i n a d e c l i n e i n y i e l d , the shape and s l o p e of t h i s d e c l i n e are not c e r t a i n . These w i l l be de termined i n t h i s s t u d y . F i g u r e 2.3 g i v e s the h y p o t h e s i z e d r e l a t i o n s h i p between t r i c k l e 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 . T r i c k l e i r r i g a t i o n i s p r e d i c t e d to be more e f f i c i e n t i n terms of water used to y i e l d than s p r i n k l e r i r r i g a t i o n . T h i s c o n j e c t u r e i s based on v a r i o u s comparisons of t r i c k l e and 9 R e s u l t s o b t a i n e d by Assa f e t . a l . ( 1 9 7 5 ) support a 59% d r o p i n what they term "commercia l f r u i t y i e l d " when t o t a l s easona l i r r i g a t i o n was reduced by 20%. However, 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 not cons tant d u r i n g the course of the growing season as i s the case wi th the s i m u l a t i o n i n t h i s t h e s i s . 31 yeild of appies quantity of water Figure 2.3 Hypothesized Trickle and Sprinkler Production Functions yield of apples q u a n t i t y of water Figure 2.4 Hypothesized Restricted vs. Unrestricted Orchard Production Functions 32 s p r i n k l e r i r r i g a t i o n methods ( M i d d l e t o n e t . a l . , 1981) and c o n v e r s a t i o n s w i t h Stevenson (1984) . The t r e e f r u i t p r o d u c t i o n p r o c e s s i n t h i s s i m u l a t i o n i s c o n f i n e d to an a n a l y s i s of the w a t e r - y i e l d r e l a t i o n s h i p h o l d i n g a l l o t h e r v a r i a b l e f a c t o r s c o n s t a n t . By imposing t h i s c o n d i t i o n , the p r o d u c t i o n f u n c t i o n takes on a r e s t r i c t e d form. F i g u r e 2.4 p r o v i d e s in d i a g r a m a t i c form the h y p o t h e s i z e d r e s u l t of r e s t r i c t i n g the o r c h a r d p r o d u c t i o n p r o c e s s to w a t e r - y i e l d f a c t o r s . By removing r e s t r i c t i o n s and a l l o w i n g the l e v e l s of o ther f a c t o r s to change , the l e f t - m o s t p o r t i o n of the p r o d u c t i o n c u r v e i s h y p o t h e s i z e d to s h i f t to the l e f t r e s u l t i n g in i n c r e a s e d p r o d u c t i o n at a g i v e n water a p p l i c a t i o n l e v e l over the r e s t r i c t e d form. In the u n r e s t r i c t e d form, the o ther v a r i a b l e f a c t o r s in the o r c h a r d p r o d u c t i o n p r o c e s s (such as c h e m i c a l a p p l i c a t i o n s to c o n t r o l t r a n s p i r a t i o n and o ther management p r a c t i c e s ) are s u b s t i t u t e d f o r water i n p u t , thus m a i n t a i n i n g o r c h a r d y i e l d s at l e v e l s above those i n the r e s t r i c t e d c a s e . By i n c r e a s i n g the amount of water a p p l i e d , maximum y i e l d i s reached and f u r t h e r water a p p l i c a t i o n s r e s u l t i n no y i e l d i n c r e a s e . T h i s i s the h o r i z o n t a l p o r t i o n of the p r o d u c t i o n f u n c t i o n s in f i g u r e s 2.1 to 2 . 4 . At t h i s p o i n t the r e s t r i c t i o n p l a c e d on v a r i a b l e i n p u t s o t h e r than water i s no longer b i n d i n g . T h i s c o n j e c t u r e of the r e s t r i c t i o n on o ther v a r i a b l e i n p u t s be ing n o n - b i n d i n g i n the h o r i z o n t a l p o r t i o n of the h y p o t h e s i z e d r e s t r i c t e d p r o d u c t i o n c u r v e assumes tha t the r e s t r i c t i o n , 33 w i t h i n t h i s d e f i n e d range , r e s u l t s i n no change i n o r c h a r d y i e l d s . S t r i c t l y s p e a k i n g , t h i s assumpt ion i s f a l s e . An obv ious example of t h i s i s f e r t i l i z e r a p p l i c a t i o n , which must i n c r e a s e when excess water a p p l i c a t i o n s cause s o i l l e e c h i n g i f y i e l d s are to remain at the same l e v e l . However, i n no case a l o n g the h o r i z o n t a l p o r t i o n of the p r o d u c t i o n s u r f a c e g i v e n in F i g u r e 2.4 can a change i n any of the v a r i a b l e f a c t o r s r e s u l t in increased o r c h a r d p r o d u c t i o n . S i n c e the r e s t r i c t e d and u n r e s t r i c t e d p r o d u c t i o n c u r v e s are p r e d i c t e d to c o i n c i d e in t h i s range , a n a l y s i s of t h i s p o r t i o n of the p r o d u c t i o n s u r f a c e i s not deemed to be h i n d e r e d by the i m p o s i t i o n of v a r i a b l e input r e s t r i c t i o n s . 2.5 GENERALIZED MODEL T h i s c h a p t e r has d i s c u s s e d , among o t h e r t h i n g s , the t h e o r e t i c a l r e l a t i o n s h i p between water and p l a n t y i e l d s t u d i e s f o r t r e e f r u i t s . In the next c h a p t e r , these t h e o r e t i c a l and e m p i r i c a l r e s u l t s w i l l be used to d e f i n e the parameters of a computer-based model which a t tempts to s i m u l a t e the w a t e r - y i e l d r e l a t i o n s h i p of an Okanagan f r u i t o r c h a r d . F i g u r e 2.5 p r o v i d e s the reader w i t h a g e n e r a l i z e d o v e r a l l p i c t u r e of what w i l l be deve loped i n d e t a i l i n c h a p t e r 3. The model i n t h i s t h e s i s was d e v e l o p e d f o r the o b j e c t i v e of s i m u l a t i n g the y i e l d response of an a p p l e o r c h a r d to v a r i o u s l e v e l s of i r r i g a t i o n water i n p u t . To p r o v i d e a l e v e l of g e n e r a l i t y to the r e s u l t s , s e v e r a l 3 4 orchard system i r r i g a t i o n rootstock type s o i l type weather generator pan evaporation (PAN) \ 7 p o t e n t i a l evapo-t r a n s p i r a t i o n (PET) - PAN * K a c t u a l evapo-t r a n s p i r a t i o n (AET) « rho * PET s o i l moisture (SM) = SM + R + I - AET 0 v i r r i g a t i o n input (I) e i t h e r by s o l i d set or t r i c k l e systems a c t u a l y i e l d (AY) - f t p o t e n t i a l y i e l d (PY), y i e l d r e d u c t i o n (YR)) YR : l . degree of s t r e s s (g) 2. t i m i n g of s t r e s s (T) «U1'- ^-5 General Flowchart of the Orchard Production Model 35 c o m b i n a t i o n s of o r c h a r d c h a r a c t e r i s t i c s can be accommidated by the model . These c h a r a c t e r i s t i c s a r e here termed orchard components and c o n s i s t of 2 r o o t s t o c k t y p e s , 2 i r r i g a t i o n systems and 2 s o i l t y p e s . The o r c h a r d components combine to form 8 unique orchard systems. A l i s t of o r c h a r d components and the 8 o r c h a r d systems i s g i v e n i n T a b l e 3 . 2 . The c h o i c e of each p a r t i c u l a r o r c h a r d component can have an impact on the r e s u l t i n g y i e l d as s i m u l a t e d by the mode l . As i n d i c a t e d in F i g u r e 2 . 5 , the d i f f e r e n t o r c h a r d components impact the model at d i f f e r e n t p o i n t s in the s i m u l a t i o n p r o c e s s . The c h o i c e of r o o t s t o c k a f f e c t s y e a r l y p o t e n t i a l y i e l d s (see s e c t i o n 3 . 1 . 1 ) . S o i l type has an impact on the s o i l m o i s t u r e l e v e l and i r r i g a t i o n (see s e c t i o n 3 . 1 . 2 ) . The c h o i c e of the i r r i g a t i o n system component has an e f f e c t on the amount of i r r i g a t i o n water which the o r c h a r d i s a b l e to make use of (see s e c t i o n 3 . 1 . 3 ) . As d e p i c t e d in F i g u r e 2 . 5 , the o r c h a r d s i m u l a t i o n p r o c e s s works in the f o l l o w i n g f a s h i o n . I n i t i a l l y an o r c h a r d system i s chosen compr i sed of one of the 8 p o s s i b l e o r c h a r d component c o m b i n a t i o n s . 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 i s then chosen , t h i s be ing some p e r c e n t of the presen t day a l l o w a b l e i r r i g a t i o n l e v e l (see s e c t i o n 3 . 2 ) , f o r example 50% or 75% or some o ther l e v e l . These f a c t o r s be ing chosen , an o r c h a r d water use y i e l d s i m u l a t i o n i s d e r i v e d . A s i m u l a t i o n over 20 growing seasons f o r the chosen o r c h a r d system i s used . For each day of each growing season (245 days per growing s e a s o n ) , a weather generator p r o v i d e s 36 t emperature and r a i n f a l l da ta randomly chosen from h i s t o r i c a l weather data (see s e c t i o n 3 . 5 ) . From t h i s data the d a i l y a d d i t i o n of precipitation and s u b t r a c t i o n of evapotranspiration (see s e c t i o n s 3.5 through 3.7 for c a l c u l a t i o n of e v a p o t r a n s p i r a t i o n ) are i n c o r p o r a t e d i n t o the d a i l y c a l c u l a t i o n of the soil moisture l e v e l . Other f a c t o r s used to c a l c u l a t e the d a i l y s o i l m o i s t u r e l e v e l are the l e v e l of s o i l m o i s t u r e on the p r e v i o u s day and the i r r i g a t i o n i n p u t , as set by the s i m u l a t i o n u s e r . The d a i l y s o i l m o i s t u r e l e v e l i s used to c a l c u l a t e the d a i l y l e v e l of water s t r e s s . Water s t r e s s a f f e c t s o r c h a r d y i e l d s . Both the degree and t i m i n g of water s t r e s s d u r i n g the growing season are used to c a l c u l a t e d a i l y y i e l d r e d u c t i o n f a c t o r s (see s e c t i o n 3 . 4 ) . These are summed over the e n t i r e growing season and, t o g e t h e r wi th the e s t i m a t e d p o t e n t i a l o r c h a r d system y i e l d (see t a b l e 3 . 1 ) , the a c t u a l y i e l d f o r the growing season i s d e t e r m i n e d . In the next c h a p t e r f u r t h e r d e t a i l on the components of each of these b i o l o g i c a l systems i s g i v e n . C h a p t e r 3 ANALYTICAL MODEL T h i s chapter p r e s e n t s a d e t a i l e d d e s c r i p t i o n of the o r c h a r d s i m u l a t i o n model . The f o l l o w i n g s e c t i o n s d e s c r i b e the v a r i o u s components c o m p r i s i n g the o r c h a r d systems, the method of c a l c u l a t i n g o r c h a r d water r e q u i r e m e n t s , the c a l c u l a t i o n of s o i l water based on water i n p u t s and o u t f l o w s , and the c a l c u l a t i o n of a c t u a l y i e l d s based on the a v a i l a b i l i t y of s o i l water . The f i n a l s e c t i o n d i s c u s s e s the methods employed i n g e n e r a t i n g the r e q u i r e d weather d a t a . T a b l e 3 . 5 , at the end of t h i s c h a p t e r , p r o v i d e s a l i s t of the parameters used i n f o r m u l a t i n g the model toge ther w i t h a b r e v i a t i o n s and u n i t s of measurement. 3.1 THE ORCHARD COMPONENTS COMPRISING THE MODEL T h i s s e c t i o n p r o v i d e s a d e t a i l e d d e s c r i p t i o n of the orchard components of the model . These o r c h a r d components c o n s i s t of the f o l l o w i n g : 1. two r o o t s t o c k s 2. two s o i l types 3. two i r r i g a t i o n systems The c h o i c e of a p a r t i c u l a r r o o t s t o c k , a p a r t i c u l a r s o i l t y p e , and a p a r t i c u l a r i r r i g a t i o n system comprises a s i n g l e orchard system. There are thus 8 p o s s i b l e o r c h a r d systems. Each o r c h a r d system i s s i m u l a t e d i n t u r n . Because the c h o i c e 37 38 of o r c h a r d components can a f f e c t the outcome of the s i m u l a t i o n , p r o v i d i n g a range of p o s s i b l e o r c h a r d systems a c h i e v e s some g e n e r a l i t y i n the r e s u l t s . I t i s important to note the d i s t i n c t i o n between the g e n e r a l model , which encompasses a l l the component c h o i c e s and a l l the o r c h a r d systems, and an o r c h a r d sys tem, which r e f e r s to one unique set of component c h o i c e s . 3 .1 .1 TREE ROOTSTOCKS The c h o i c e of t r e e r o o t s t o c k i s an important f a c t o r i n d e t e r m i n i n g e v e n t u a l t r e e s i z e at m a t u r i t y , l e n g t h of t ime r e q u i r e d to reach m a t u r i t y , and expected i n c i d e n c e of c e r t a i n t r e e f r u i t d i s e a s e s . The r o o t s t o c k s s e l e c t e d f o r t h i s t h e s i s are M a i l i n g 26 (M26) and M a i l i n g 2 (M2). 1 0 M26 i s a dwar f ing r o o t s t o c k s u i t a b l e for h i g h d e n s i t y p l a n t i n g schemes i f c u l t i v a t e d p r o p e r l y . M2 produces a s e m i - s t a n d a r d t r e e s u i t a b l e for medium d e n s i t y p l a n t i n g s r e q u i r i n g l e s s t r e e management s k i l l than h i g h e r d e n s i t y schemes. I t i s the view of exper t h o r t i c u l t u r a l i s t s that any o r c h a r d p l a n t i n g r e g a r d l e s s of r o o t s t o c k w i l l , i f p r o p e r l y l a i d out and managed, produce a green canopy area which f i l l s the a l l o t t e d o r c h a r d s p ace . S i n c e i d e n t i c a l canopy a r e a s can be assumed to produce the same apple y i e l d s , the M2 and M26 p l a n t i n g s i n t h i s s tudy are assumed to produce 1 0 T h i s s e l e c t i o n was based 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 (Sanders , 1983) and c o n v e r s a t i o n s w i t h Mike Sanders 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 Columbia M i n i s t r y of A g r i c u l t u r e , Kelowna. 39 i d e n t i c a l per a c r e y i e l d s on mature t r e e s . 1 1 The advantage , i n terms of p o t e n t i a l p r o d u c t i o n and p r o f i t s , of a h i g h e r d e n s i t y dwar f ing r o o t s t o c k i s t h a t t r e e s grown on such r o o t s t o c k s tend to come i n t o f u l l p r o d u c t i o n a t an e a r l i e r age than s t a n d a r d or s e m i - s t a n d a r d t r e e s . 1 2 The exact y i e l d which can be expected on e i t h e r M2 or M26 r o o t s t o c k s i s open to q u e s t i o n . The sources used in t h i s t h e s i s - - the Cos t of P r o d u c t i o n S t u d y 1 3 and c o n v e r s a t i o n s w i t h h o r t i c u l t u r a l i s t s - - p r o v i d e d the b a s i s for the y i e l d data for M2 and M26 p l a n t i n g s as g i v e n i n T a b l e 3 . 1 . The Study assumes c o n s t a n t t o t a l r e t u r n s and thus a c o n s t a n t y i e l d a f t e r year 8. Whi l e i t may be f e a s i b l e to m a i n t a i n annua l total y i e l d a t a f a i r l y c o n s t a n t r a t e on a d w a r f i n g or s e m i - d w a r f i n g r o o t s t o c k , 1 4 the percentage of top grades o b t a i n a b l e would l i k e l y d e c l i n e a f t e r some p o i n t . 1 1 T h i s assumption 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. Sanders , h o r t i c u l t u r a l i s t , B r i t i s h Columbia M i n i s t r y of A g r i c u l t u r e , Kelowna. However i n p r a c t i c e canopy areas a r e seldom 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 . 1 2 M 2 6 o r c h a r d s were assumed to come i n t o f u l l p r o d u c t i o n by year 7 whi 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 year 9. The per 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 than tha t g i v e n i n the Cos t of P r o d u c t i o n Study (and o c c u r s a year l a t e r ) and r e p r e s e n t s a compromise between the Study 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 through p e r s o n a l communicat ion 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 beg in marketab le b e a r i n g i n year 3 w h i l e M2 o r c h a r d s beg in b e a r i n g i n year 4. 1 3 T h e b a s i s f o r 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 the E s t i m a t e d C o s t s and R e t u r n s of Apple 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 Study 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 per a c r e and a s p r i n k l e r i r r i g a t i o n sys tem. 1 " D i s c u s s i o n s w i t h M. Sanders and D. Stevenson support t h i s v i ew. 40 TABLE 3.1: AVERAGE YIELDS PER ACRE OVER 20 YEARS FOR 2 DIFFERENT ROOTSTOCKS (LBS./ACRE) YEAR ROOTSTOCK M2 M26 1 00000 00000 2 0 0 3 0 3000 4 1 600 6000 5 8000 1 5500 6 1 6000 32000 7 24000 35000 8 32000 35000 9 35000 35000 10 35000 35000 1 1 35000 35000 1 2 35000 35000 1 3 35000 35000 14 34300 34300 1 5 33614 33614 1 6 32942 32942 1 7 32283 32283 18 3 1 637 31 637 19 31 004 3 1 004 20 30384 30384 AVERAGE 24 1 34 26383 SOURCE: A d a p t e d from BCMAF " E s t i m a t e d C o s t s and R e t u r n s 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 , " May 1983. U n f o r t u n a t e l y t h e r e i s no d a t a a v a i l a b l e t o d e t e r m i n e e x a c t l y when an o r c h a r d , on M2 or M26 r o o t s t o c k , r e a c h e s peak p r o d u c t i o n , o r t h e d e c l i n e i n p r o d u c t i o n f o l l o w i n g such a p o i n t . However, t h e a s s u m p t i o n of c o n s t a n t y i e l d s a f t e r y e a r 8 and c o n t i n u i n g o v e r an i n d e f i n i t e p e r i o d i s 41 u n r e a l i s t i c . On t h i s b a s i s a 2% per year d e c l i n e i n p r o d u c t i o n i s assumed from year 14 onwards. R o o t s t o c k , i n so f a r as i t de termines t r e e s i z e , a l s o determines p l a n t i n g d e n s i t y . Tree t r a i n i n g , n u t r i t i o n , and s o i l type are o ther f a c t o r s tha t determine e v e n t u a l t r e e s i z e . M26 and M2, the two r o o t s t o c k s chosen for t h i s s t u d y , are a s s i g n e d t r e e d e n s i t i e s of 388 and 202 t r e e s per a c r e r e s p e c t i v e l y . These d e n s i t i e s are d e r i v e d u s i n g commonly used t r e e s p a c i n g s found i n the Okanagan r e g i o n . The two d e n s i t i e s w i l l be r e f e r r e d to as h i g h and medium d e n s i t y p l a n t i n g s . 3 .1 .2 SOIL TYPE S o i l type i s an impor tant f a c t o r in d e t e r m i n i n g water h o l d i n g c a p a c i t y and p l a n t i n g d e n s i t y . A s o i l ' s a b i l i t y to h o l d water i s measured by i t s available water storage capacity (AWSC). 1 5 A r u l e of thumb f o r o r c h a r d c r o p s i s that i r r i g a t i o n i s n e c e s s a r y when 40% of AWSC has been removed. T h i s c r i t i c a l p o i n t i s termed the maximum soil water deficit (MSWD). The two s o i l s c o n s i d e r e d i n t h i s s tudy span the range of s o i l types w i t h r e s p e c t to AWSC found i n the Okanagan r e g i o n . T a b l e 3.2 p r o v i d e s AWSC and MSWD f i g u r e s for the two s o i l s . S o i l t e x t u r e a f f e c t s a s o i l ' s water a b s o r p t i o n c h a r a c t e r i s t i c s . The more c o a r s e the s o i l , 1 5 A more d e t a i l e d account 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 can be found i n the 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 . 42 TABLE 3.2: AVAILABLE WATER STORAGE CAPACITY AND MAXIMUM SOIL WATER DEFICIT BY SOIL TYPE (IN./SOIL FT.) SOIL TYPE AVAILABLE WATER MAXIMUM SOIL STORAGE CAPACITY WATER D E F I C I T SAND 1.0 0.4 ("1.6) SILT-LOAM 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 water d e f i c i t f o r 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 , 1983. the f a s t e r t h e a b s o r p t i o n r a t e of water a p p l i e d t o the s u r f a c e . A s o i l ' s a b s o r p t i o n r a t e must be c o n s i d e r e d when d e t e r m i n i n g an i r r i g a t i o n s y s t e m f l o w r a t e ( c a l c u l a t e d i n s e c t i o n 3.2). A s e c o n d f a c t o r w h i c h i n c r e a s e s a b s o r p t i o n r a t e s i s t h e p r e s e n c e or a b s e n c e o f s u r f a c e t u r f or sod. A l l o r c h a r d s y s t e m s w i l l be assumed t o have sod c o v e r . T r e e s p l a n t e d on s i l t - l o a m s o i l s t e n d t o have more e x p a n s i v e r o o t s y s t e m s and t h u s a r e not as d e n s e l y p l a n t e d as t r e e s on sandy s o i l s . F o r t h e p u r p o s e s of t h i s s t u d y , the r e l a t i o n s h i p between s o i l t y p e and d e n s i t y w i l l not be c o n s i d e r e d . 1 6 The o r c h a r d s y s t e m ' s s o i l t y p e i s e x p e c t e d t o 1 6 To c o n s i d e r t h e s o i l t y p e / d e n s i t y f a c t o r would i n c r e a s e the c o m p l e x i t y 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 an e f f e c t on the amount of water a v a i l a b l e for use by the f r u i t t r e e s . 3 . 1 . 3 IRRIGATION METHOD I t was noted e a r l i e r that the r e s t r i c t e d p r o d u c t i o n f u n c t i o n i s expec ted to d i f f e r by i r r i g a t i o n method. T h i s s e c t i o n d e s c r i b e s two i r r i g a t i o n methods of i n t e r e s t from a h i s t o r i c a l p e r s p e c t i v e and d i s c u s s e s the i m p l i c a t i o n s of each method as they a f f e c t Okanagan i r r i g a t i o n p r a c t i c e s . T h i s s tudy assumes tha t a l l o r c h a r d systems o b t a i n i r r i g a t i o n water through l o c a l d i s t r i c t water s y s t e m s . 1 7 I r r i g a t i o n systems used by t r e e f r u i t p r o d u c e r s i n the Okanagan v a r y from d i s t r i c t to d i s t r i c t , but g e n e r a l l y the handmove and permanent s o l i d set s p r i n k l e r i r r i g a t i o n systems dominate . Handmove systems have g i v e n way i n c r e a s i n g l y to s o l i d set systems i n recen t y e a r s 1 8 i m p l y i n g t h a t more c a p i t a l and l e s s l a b o u r i s u sed , c e t e r i s  p a r i b u s . However, many handmove systems are s t i l l in o p e r a t i o n , due i n l a r g e p a r t to the g e n e r a l l y s m a l l o r c h a r d s i z e s c h a r a c t e r i s t i c of the Okanagan a r e a , and to the many 1 6 ( 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 f a c t o r tha t i s v a r i e d . 1 7 I t s h o u l d be noted t h a t some o r c h a r d i s t s i n the Okanagan acces s t h e i r own water through pumping or g r a v i t y feed sys tems. Such systems would appear to compri se a very s m a l l p e r c e n t a g e of the t o t a l t r e e f r u i t acreage i n the 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 Southern Okanagan Lands I r r i g a t i o n D i s t r i c t put the e s t imate a t 2% f o r t h a t d i s t r i c t ) though l a r g e r o p e r a t i o n s such as v i n e y a r d s are more l i k e l y to acces s t h e i r own i r r i g a t i o n needs . 1 8 P e r s o n a l communicat ion: D r . D . S . S t e v e n s o n , Summerland Research S t a t i o n and M r . B i l l Ross , South Okanagan Lands I r r i g a t i o n D i s t r i c t , May, 1984. 44 f a m i l y - r u n o p e r a t i o n s . T r i c k l e i r r i g a t i o n systems are found b u t , as y e t , t h e i r numbers are s m a l l . With the change from furrow to handmove i r r i g a t i o n in postwar y e a r s , the amount of c a p i t a l (p ipe and s p r i n k l e r s ) i n v e s t e d was kept to a minimum. T h i s investment was enough to a l l o w f o r i r r i g a t i o n of the e n t i r e o r c h a r d once d u r i n g a t ime p e r i o d de termined by the maximum expec ted water r e q u i r e m e n t ( s e e S t e v e n s o n , 1 9 8 0 ) . T h i s p e r i o d , known as the peak i n t e r v a l , i s the minimum time needed to i r r i g a t e an e n t i r e o r c h a r d u s i n g a r o t a t i o n method. The peak i n t e r v a l v a r i e s depending on atmospher ic c o n d i t i o n s a n d / o r s o i l types in a p a r t i c u l a r l o c a t i o n . S o i l s d i f f e r i n t h e i r c a p a c i t i e s to absorb and s t o r e water . H o t t e r , d r i e r a t m o s p h e r i c c o n d i t i o n s r e q u i r e more i r r i g a t i o n water than c o o l e r , wet ter c o n d i t i o n s , a l l e l s e b e i n g e q u a l . 1 9 As c a p a c i t i e s of the d i s t r i c t water systems are not s u f f i c i e n t to a l l o w for i r r i g a t i o n of an e n t i r e o r c h a r d at one t i m e ( e x c e p t w i t h a t r i c k l e sy s t em) , a r o t a t i o n method based on the peak i n t e r v a l requirement i s g e n e r a l l y f o l l o w e d . P r o d u c e r s u s i n g handmove systems p h y s i c a l l y move p i p e in the r o t a t i o n wh i l e those w i t h f i x e d s p r i n k l e r systems use v a l v e s to a l l o c a t e water to o r c h a r d s e c t i o n s in t u r n . The water systems of the v a r i o u s i r r i g a t i o n d i s t r i c t s p r e s e n t l y o p e r a t i n g in the Okanagan are d e s i g n e d to a l l o w p r o d u c e r s to i r r i g a t e t h e i r e n t i r e o r c h a r d u s i n g s p r i n k l e r s 1 9 Other 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 the s l o p e of l a n d and d i r e c t i o n the s lope f a c e s , presence or absence of sod c o v e r , p r o x i m i t y to l a r g e b o d i e s of water , and exposure to w ind . 45 d u r i n g the peak i n t e r v a l of the h o t t e s t , d r i e s t r e c o r d e d year (1967 f o r the Okanagan) . The two i r r i g a t i o n systems which w i l l be examined i n t h i s s tudy a r e s p r i n k l e r ( s o l i d set type) and t r i c k l e . S p r i n k l e r systems comprise the m a j o r i t y of o r c h a r d i r r i g a t i o n systems now in use i n the Okanagan. The t r i c k l e system i s c o n s i d e r e d p r i m a r i l y for i t s p o t e n t i a l i n terms of water s a v i n g s . The s p r i n k l e r system used for t h i s model i s the under-tree t y p e . Over-tree s p r i n k l e r systems are an a l t e r n a t i v e w i t h some advantages and d i s a d v a n t a g e s . The advantage of an o v e r - t r e e s p r i n k l e r system i s tha t i t p r o v i d e s a method of f r o s t p r o t e c t i o n by c o a t i n g the f r u i t w i t h a water l a y e r which , s h o u l d the temperature f a l l below the f r e z i n g l e v e l , a c t s as a warming agent due to the l a t e n t heat of f u s i o n . Perhaps the main d i s a d v a n t a g e of an o v e r - t r e e s p r i n k l e r system i s that i t i n c r e a s e s the s u s c e p t i b i l i t y of f r u i t t r e e s to c e r t a i n d i s e a s e s such as crown r o t . I n f o r m a t i o n conveyed to t h i s au thor i n d i c a t e s i n s t a l l a t i o n s of u n d e r - t r e e s p r i n k l e r sytems have been more p o p u l a r than o v e r - t r e e systems i n recent y e a r s in the Okanagan (Vander G u l i k , 1984). S o l i d se t i r r i g a t i o n systems use the s o i l as a s torage a r e a from which p l a n t s o b t a i n access to water neces sary for t r a n s p i r a t i o n , t u r g o r , and n u t r i e n t t r a n s p o r t r e q u i r e m e n t s . A s o i l ' s a b i l i t y to absorb and r e t a i n water , t oge ther wi th e n v i r o n m e n t a l f a c t o r s , de termines the f requency and 46 i n t e n s i t y of i r r i g a t i o n s . Producers i n the Okanagan have t r a d i t i o n a l l y i r r i g a t e d with the aim of minimizing the r i s k of water s t r e s s . T h i s i s accomplished by c a l c u l a t i n g the maximum i n t e r v a l a producer can a l l o w between i r r i g a t i o n s before the s o i l ' s AWSC reaches 60% d u r i n g a " h o t t e s t , d r i e s t " weather p e r i o d . T h i s c a l c u l a t i o n , c a l l e d the safe irrigation interval, can be determined f o r any orchard i f data on s o i l type, c l i m a t e , and e v a p o t r a n s p i r a t i o n (ET) r a t e s are a v a i l a b l e . The safe i n t e r v a l and the s o i l type, together with the amount of water r e q u i r e d d u r i n g peak ET, determines the amount of water per day which a producer u s i n g a r o t a t i o n a l i r r i g a t i o n method t y p i c a l l y a p p l i e s . 2 0 A t r i c k l e i r r i g a t i o n system r a d i c a l l y d i f f e r s from that d e s c r i b e d above i n that i t does not r e l y on the s o i l f o r water s t o r a g e . Rather, the s o i l i s used on l y as a medium of t r a n s p o r t f o r water from the p o i n t of emission to the root zone. Water used i n t r i c k l e systems i s measured i n volume per p l a n t per day and thus, u n l i k e s p r i n k l e r systems, orchards having d i f f e r e n t d e n s i t i e s r e q u i r e d i f f e r e n t volumes of water. 3.1.4 ORCHARD SYSTEM SUMMARY Table 3.3 summarises the orch a r d systems analysed i n the study. As i n d i c a t e d , 8 orchard systems comprised of unique combinations of one of two r o o t s t o c k s , two s o i l types 2 0 See the 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 of r o t a t i o n a l method water use and t r i c k l e water use. 47 TABLE 3.3: DEFINITION OF EIGHT ORCHARD SYSTEMS AND THEIR COMPONENTS ORCHARD SYSTEM ROOTSTOCK SOIL TYPE IRRIGATION SYSTEM 1 2 3 4 5 6 7 8 M2 M2 M26 M26 M2 M2 M26 M26 SAND SILT-LOAM SAND SILT-LOAM SAND SILTLOAM SAND SILTLOAM SPRINKLER SPRINKLER SPRINKLER SPRINKLER TRICKLE TRICKLE TRICKLE TRICKLE and two i r r i g a t i o n s y s t e m s w i l l be s i m u l a t e d . As n o t e d , r o o t s t o c k a f f e c t s t h e d e n s i t y , t h e volume of pre-mature y e a r l y f r u i t y i e l d s , t h e l e n g t h o f t i m e needed t o r e a c h m a t u r i t y , and, i n t h e c a s e of t r i c k l e i r r i g a t i o n , water r e q u i r e m e n t s f o r t h e o r c h a r d . S o i l t y p e a f f e c t s the water a b s o r p t i o n r a t e and t h e water h o l d i n g c a p a c i t y of t h e s o i l , and t h u s the water r e q u i r e m e n t s f o r t h e o r c h a r d . The typ e of i r r i g a t i o n s y s t e m i s i m p o r t a n t i n d e t e r m i n i n g the amount of water t y p i c a l l y a p p l i e d t o t h e o r c h a r d as w e l l as the method of a p p l i c a t i o n . 48 3.2 CALCULATION OF WATER APPLICATION RATES FOR EIGHT BASE  CASES T h i s s e c t i o n p r o v i d e s d e t a i l e d c a l c u l a t i o n s of water a p p l i c a t i o n r a t e s for the base case s c e n a r i o s of the o r c h a r d s i m u l a t i o n . The base cases are d e f i n e d as the i r r i g a t i o n water a p p l i c a t i o n r a t e s which would be a p p l i e d to the o r c h a r d systems (as g i v e n i n T a b l e 3.3) under the present i r r i g a t i o n r e g u l a t i o n s p e r t a i n i n g to the Okanagan V a l l e y of B r i t i s h C o l u m b i a . The c a l c u l a t i o n s are based on methods o u t l i n e d i n the B r i t i s h Columbia M i n i s t r y of A g r i c u l t u r e and F o o d ' s Irri gat i on Desi gn Manual, 1983 r e v i s i o n . C o n s i s t e n t w i t h the Manual, base case water a p p l i c a t i o n r a t e s for those o r c h a r d systems wi th s p r i n k l e r i r r i g a t i o n are a f u n c t i o n of e v a p o t r a n s p i r a t i o n r a t e and s o i l t y p e . For o r c h a r d systems u s i n g t r i c k l e i r r i g a t i o n the c a l c u l a t i o n i s a f u n c t i o n of e v a p o t r a n s p i r a t i o n r a t e and d e n s i t y . 3 .2 .1 SPRINKLER SYSTEMS To c a l c u l a t e the water a p p l i c a t i o n r a t e s for s p r i n k l e r i r r i g a t i o n systems, an e f f e c t i v e s torage range from which an a p p l e t r e e can access water (a r o o t i n g depth) must be d e f i n e d . U s i n g the Manual a r o o t i n g depth of 4 feet i s assumed. For t r e e f r u i t s , the maximum s o i l water d e f i c i t (MSWD) i s 40% of the 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 (AWSC) (see s e c t i o n 3 . 1 . 2 ) . The AWSC v a r i e s w i t h s o i l t e x t u r e . S i n c e the 49 model deve loped i n t h i s t h e s i s c o n s i d e r s 2 s o i l t y p e s , the MSWD must be c a l c u l a t e d s e p a r a t e l y for each . For sand , the AWSC i s 1 i n c h per foot of s o i l or 4 inches over the root zone . The MSWD i s 40% of AWSC or 1.6 inches over the root zone . For s i l t - l o a m , a 2.5 i n c h per foot AWSC r e s u l t s i n a MSWD of 4 i n c h e s . The water a p p l i c a t i o n e f f i c i e n c y for a hot c l i m a t e ( l i k e the Okanagan) i s a p p r o x i m a t e l y 75% for most s p r i n k l e r s p a c i n g s ( I r r i g a t i o n Des ign M a n u a l , 1983). Thus 75% of the water a p p l i e d a c t u a l l y reaches and i s s t o r e d i n the s o i l . Because the r o t a t i o n i r r i g a t i o n method i s set up to a p p l y a maximum o r c h a r d requirement d u r i n g each set of the r o t a t i o n (see s e c t i o n 3 . 1 . 3 ) , the c a l c u l a t i o n uses the MSWD (the s o i l m o i s t u r e l e v e l which the Manual d e f i n e s as the d r i e s t a l l o w a b l e s o i l s t a t e ) as the b a s i s for each r o t a t i o n set a p p l i c a t i o n . Water a p p l i c a t i o n i s thus s o i l dependent . The ' G r o s s a p p l i c a t i o n ' (GA) of water r e q u i r e d i s equa l to the MSWD d i v i d e d by the a p p l i c a t i o n e f f i c i e n c y . GA (sand) = 1 .6 / . 75 = 2.13 inches GA ( s i l t - l o a m ) = 4 . 0 / . 7 5 = 5.3 inches To de termine the expected maximum water requ irements f o r a g i v e n o r c h a r d system, the maximum expected a tmospher ic 50 demand or Peak E v a p o t r a n s p o r a t i o n (PKET) r a t e must be de termined (see s e c t i o n 3 . 1 . 3 ) . The Peak E v a p o t r a n s p i r a t i o n r a t e for Kelowna was used ( I r r i g a t i o n Des ign M a n u a l , 1983). The PKET f o r sand i s 0.25 i n c h e s per day and f o r s i l t - l o a m 0.23 inches per day . Under c o n d i t i o n s of peak e v a p o t r a n s p i r a t i o n and thus maximum r a t e s of s o i l water d e p l e t i o n , the peak i n t e r v a l can be d e t e r m i n e d . The peak i n t e r v a l (PI) i s the maximum a l l o w a b l e i n t e r v a l between i r r i g a t i o n r o t a t i o n se t s under the h o t t e s t , d r i e s t weather c o n d i t i o n s on r e c o r d . PI (days) = MSWD ( i n c h e s ) / PKET ( inches per day) PI (sand) = 1 . 6 / . 2 5 = 6 days PI ( s i l t - l o a m ) = 4 . 0 / . 2 3 = 17 days A l l s o i l s do not a b s o r b water a p p l i e d at the s u r f a c e at the same r a t e . The water a p p l i c a t i o n r a t e must not exceed the s o i l ' s a b s o r p t i o n c a p a c i t y . Assuming a sod t u r f c o v e r , the maximum a p p l i c a t i o n r a t e s as l i m i t e d by s o i l a b s o r p t i o n c h a r a c t e r i s t i c s are 0.75 i n c h e s per hour for sand and 0.35 inches per hour for s i l t loam ( I r r i g a t i o n Des ign M a n u a l , 1983). 51 The amount of time any one orchard s e c t i o n r e c e i v e s i r r i g a t i o n i s the set time of the r o t a t i o n . Set times are chosen f o r operator convenience, though they must a l s o a l l o w s u f f i c i e n t time to meet the i r r i g a t i o n requirements while not exceeding the maximum water a p p l i c a t i o n r a t e of the s o i l . The set times of 12 hours and 24 hours were chosen f o r sand and s i l t - l o a m s o i l s r e s p e c t i v e l y . To summarise, f o r sand s o i l s 1.6 inches of water are r e q u i r e d to meet MSWD assuming a 4 foot r o o t i n g depth. At 75% i r r i g a t i o n e f f i c i e n c y 2.13 inches of water must be a p p l i e d . T h i s a p p l i c a t i o n i s s u f f i c i e n t to meet p l a n t requirements f o r 6 days given PKET c o n d i t i o n s . For s i l t - l o a m 4.0 inches MSWD at 75% e f f i c i e n c y equals 5.3 inches water r e q u i r e d . T h i s amount i s s u f f i c i e n t f o r a 17 day r o t a t i o n d u r i n g PKET. These a p p l i c a t i o n r a t e s w i l l be used as the base case i r r i g a t i o n r a t e s f o r those o r c h a r d systems using s p r i n k l e r i r r i g a t i o n . 3.2.2 TRICKLE SYSTEMS As was the case with determining the base case water a p p l i c a t i o n r a t e s f o r s p r i n k l e r systems, base case water a p p l i c a t i o n r a t e s f o r t r i c k l e systems are c a l c u l a t e d u s i n g the I r r i g a t i o n Design Manual methods. As i n d i c a t e d e a r l i e r , the d e r i v a t i o n of water requirements for those o r c h a r d systems using t r i c k l e i r r i g a t i o n i s f o r the purpose comparing s p r i n k l e r versus t r i c k l e water use e f f i c i e n c i e s . The base cases f o r s p r i n k l e r and t r i c k l e systems d i f f e r i n 52 one important r e s p e c t . While the base case s p r i n k l e r r e s u l t s represent present day water a p p l i c a t i o n l e v e l s f o r the Kelowna area, the t r i c k l e base case does not because of the d i f f e r e n c e s between s p r i n k l e r and t r i c k l e i r r i g a t i o n methods. T r i c k l e i r r i g a t i o n p r o v i d e s a means of i r r i g a t i n g an e n t i r e o rchard at one time while s p r i n k l e r i r r i g a t i o n uses a r o t a t i o n method (see s e c t i o n 3.1.3). The use of a t r i c k l e system enables an o r c h a r d i s t to respond to d a i l y weather c o n d i t i o n s , a f l e x i b i l i t y not a v a i l a b l e to s p r i n k l e r system users without i n c r e a s i n g the r i s k of water s t r e s s . The t r i c k l e base case i s a s t a r t i n g p o i n t from which s u c c e s s i v e i r r i g a t i o n water r e d u c t i o n s w i l l be c a r r i e d out, the aim of which i s to determine the c r i t i c a l p o i n t s f o r t r i c k l e i r r i g a t e d o r c h a r d systems. The base case t r i c k l e i r r i g a t i o n water requirements were c a l c u l a t e d on a per t r e e b a s i s as opposed to an o r c h a r d area b a s i s used f o r s p r i n k l e r i r r i g a t i o n c a l c u l a t i o n s . T herefore d e n s i t y i s a f a c t o r i n determining the water requirements f o r t r i c k l e i r r i g a t e d orchard systems. To a r r i v e at t r i c k l e system base case water a p p l i c a t i o n r a t e s , f i r s t a g a l l o n s per p l a n t per day (g/p/d) f i g u r e was c a l c u l a t e d . For M2 and M26 orchard systems, the g/p/d f i g u r e was then m u l t i p l i e d by the d e n s i t y ( t r e e s per acre) r e s u l t i n g i n a g a l l o n s per acre per day e s t i m a t e . D i v i d i n g t h i s by g a l l o n s per a c r e i n c h r e s u l t s i n inches of water per day. Ten percent more water i s added to allow f o r drainage to prevent s a l i n i t y b u i l d u p . 53 g/p/d = (.623 * PKET * .75 * A * .9) + 10% where PKET = peak e v a p o t r a n s p i r a t i o n (.24 i n . ) A = area per t r e e (determined by d e n s i t y ) .623 = 27152 g/acre inch / 43560 f e e t 2 / a c r e .75 = a t r i c k l e i r r i g a t i o n c o r r e c t i o n f a c t o r .9 = crop c o e f f i c i e n t f o r apples 10% = a l l o w s f o r water p e r c o l a t i o n to prevent s a l i n i t y b u i l d u p (10% of g/p/d). For M2 r o o t s t o c k s (202 t r e e s per a c r e ) : g a l l o n s / p l a n t / d a y = 24.0 g a l l o n s / a c r e / d a y = 24.0 g/p/d * 202 t r e e s / a c r e = 4 8 4 8 inches per day = (4848 g/a/d) / (27152 g a l s / a c r e i n . ) = . 1786 + 10% = .196 For M26 r o o t s t o c k s (388 t r e e s per acre) s i m i l a r c a l c u l a t i o n s r e s u l t e d i n a f i g u r e of .195 inches per day. As i s apparent from the above c a l c u l a t i o n s , the d a i l y base case water requirements f o r M2 and M26 r o o t s t o c k s are very s i m i l a r . I t would appear that r o o t s t o c k , and thus d e n s i t y , w i l l not be a s i g n i f i c a n t determinant in the r e l a t i v e o r c h a r d system w a t e r - y i e l d comparisons. T h i s w i l l be d i s c u s s e d f u r t h e r i n chapter 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 and t r i c k l e i r r i g a t i o n systems form the base cases f o r the 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 yields begin to be reduced. Irrigation level is one input into the calculation used to determine the s o i l moisture level, as outlined in the following section. 3.3 CALCULATION OF SOIL MOISTURE LEVEL In order to determine whether or not water stress is present and, i f present, i t s effect on yield, 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 level. The function used in calculating the moisture level of the s o i l for each period t is adapted from Flinn(1971) and is of the following form: SM = SM + R + I - AET t t-1 t t 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 R a i n f a l l each day i s set exogenously by the weather g e n e r a t o r 2 1 . I r r i g a t i o n i s a f a c t o r to be v a r i e d d u r i n g the s i m u l a t i o n r u n s . I r r i g a t i o n beg ins each season on May 1, and ends September 15. The v a l u e s of I , the amount of water a p p l i e d each day , for the i n i t i a l o r c h a r d system s i m u l a t i o n were de termined i n s e c t i o n 3 . 2 . A c t u a l e v a p o t r a n s p i r a t i o n (AET) i s a f u n c t i o n of both 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 (PET) and the s o i l m o i s t u r e l e v e l . AET i s d e r i v e d as f o l l o w s : AET = p * PET p(sand) = 3 * (SM/FC) p ( s i l t - l o a m ) = 5 * (SM/FC) where p = a s o i l m o i s t u r e f a c t o r SM = s o i l m o i s t u r e l e v e l FC = f i e l d c a p a c i t y ( 4 i n . f or sand , l O i n . for s i l t - l o a m ) and 0 < p < 1. The v a l u e of p depends on the s o i l m o i s t u r e l e v e l (SM), 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 ( P E T ) , and the s o i l t y p e . T h i s 2 1 see s e c t i o n 3 . 5 . 56 r e l a t i o n s h i p i s g i v e n in F i g u r e 3 . 1 . From F i g u r e 3 . 1 , i t i s apparent t h a t as the l e v e l of s o i l m o i s t u r e d e c l i n e s , the r a t i o of a c t u a l to 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 (p) a l s o d e c l i n e s . The p o i n t a t which p beg ins to d e c l i n e v a r i e s w i th s o i l type s i n c e d i f f e r e n t s o i l s are c h a r a c t e r i z e d by d i f f e r e n t s o i l water p r e s s u r e s at a g i v e n s o i l m o i s t u r e to f i e l d c a p a c i t y r a t i o . The v a l u e of p i n any p e r i o d i s c a l c u l a t e d u s i n g the va lue of SM i n the p r e v i o u s p e r i o d . D a i l y s o i l m o i s t u r e l e v e l s are c a l c u l a t e d from March 1 through October 31. To i n i t i a t e the f u n c t i o n the s o i l m o i s t u r e l e v e l i s set to the f i e l d c a p a c i t y of the s o i l at the b e g i n n i n g of the growing season . 3.4 CALCULATION OF YIELDS In the p r e v i o u s s e c t i o n , a method for d e t e r m i n i n g the s o i l m o i s t u r e l e v e l f o r each day of the growing season was d e t a i l e d . T h i s s e c t i o n makes use of the d a i l y s o i l m o i s t u r e l e v e l to c a l c u l a t e y e a r l y a p p l e y i e l d s . The c a l c u l a t i o n of y i e l d i s done i n s e v e r a l s t e p s . F i r s t , depending on the age of the o r c h a r d , a growth factor and a yield factor are c a l c u l a t e d . The growth f a c t o r i s c a l c u l a t e d for years 1 through 7. The growth f a c t o r assumes water s t r e s s w i l l i n h i b i t growth d u r i n g t h i s p r e - m a t u r a t i o n p e r i o d . Tree growth d u r i n g e a r l y y e a r s i s important f o r e s t a b l i s h i n g s u f f i c i e n t branch s i z e and number to accommodate f r u i t in l a t e r y e a r s . The y i e l d f a c t o r i s c a l c u l a t e d for y e a r s 3 or 4 (depending on r o o t s t o c k ) through 20. T h i s i s the p e r i o d 57 Figure 3- ' n«.riv.it ion of S o i l Moisture Factor p 58 d u r i n g which marketab le f r u i t y i e l d s o c c u r . T r e e growth d u r i n g t h i s p e r i o d i s not a c o n t r i b u t i n g f a c t o r to y i e l d . Once the age of the t r e e and thus the r e l e v a n t r e d u c t i o n f a c t o r s have been d e t e r m i n e d , the second s tep i n y i e l d d e t e r m i n a t i o n i n v o l v e s c a l c u l a t i n g d a i l y growth r e d u c t i o n a n d / o r y i e l d r e d u c t i o n f a c t o r s u s i n g the d a i l y s o i l m o i s t u r e l e v e l s . The sum of the d a i l y r e d u c t i o n f a c t o r s d i v i d e d by the number of days in the growing season g i v e s the average y e a r l y r e d u c t i o n f a c t o r . The y e a r l y r e d u c t i o n f a c t o r when s u b t r a c t e d from the p o t e n t i a l y e a r l y y i e l d ( y i e l d i n the absence of water s t r e s s ) e q u a l s the a c t u a l y e a r l y y i e l d . 3 .4 .1 DETERMINING GROWTH REDUCTION FACTOR The model assumes t h a t , i n the absence of water s t r e s s , t r e e growth w i l l proceed unh indered d u r i n g each growing season . However, i f water s t r e s s o c c u r s growth w i l l be a f f e c t e d to a degree de termined by the f o l l o w i n g r e l a t i o n s h i p : g = 1 .2 - (2 .0*(SM / F C ) ) t t where g = a growth r e d u c t i o n f a c t o r ( expressed as a r a t i o of p o t e n t i a l d a i l y growth) SM = s o i l m o i s t u r e l e v e l FC = f i e l d c a p a c i t y (10 i n . f or s i l t - l o a m , 4 i n . for sand s o i l s ) 59 t = day of growing season ( t = 1 . . . 2 4 5 ) and 0 < g < 1 . T h i s r e l a t i o n s h i p i s d e s c r i b e d g r a p h i c a l l y i n F i g u r e 3.2 where permanent w i l t i n g p o i n t i s assumed to be 10% of the s o i l ' s a v a i l a b l e water s torage c a p a c i t y , AWSC (see s e c t i o n 3 . 1 . 2 ) . F u l l p o t e n t i a l growth o c c u r s at or above 60% of AWSC (when the growth r e d u c t i o n , f a c t o r ' g ' i s z e r o ) . T h i s i s the recommended minimum s o i l water l e v e l 2 2 f or t r e e f r u i t s i n the Okanagan. When g i s 1.00 (at or below permanent w i l t i n g p o i n t ) no growth o c c u r s . 3 . 4 . 2 DETERMINING THE YIELD REDUCTION FACTOR As with, growth d e t e r m i n a t i o n , y i e l d s are assumed to be u n a f f e c t e d i n the absence of water s t r e s s . When water s t r e s s i s p r e s e n t two f a c t o r s are c o n s i d e r e d , the degree and the t i m i n g of s t r e s s . . 1. degree of stress T h i s f a c t o r i s i d e n t i c a l to the growth r e d u c t i o n f a c t o r . T h i s assumes tha t growth and y i e l d a r e a f f e c t e d to the same degree at a g iven s o i l water l e v e l . 2 3 2 2 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 A g r i c u l t u r e , 1983. 2 3 T h e r e i s some ev idence to suggest t h a t an e a r l y season t r e e growth 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 growth s tage in mature 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 . 1984). The growth 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 . 60 Growth Reduction Factor | (ratio of potential daily growth) t.00 0.75 + 0.50 .+ 0.25 + 0.10 0 .25 0.50 0.60 0.75 .00 9 o i l • o i s t u r e (as f r a c t i o n of f i e l d c a p a c i t y ) F U u r e 3.2 R e l o l J m ^ L i l L J ^ L ^ " C r " " t h *°" F a c t 0 r *-8 .n.i s » i 1 Moisture Level. 61 degree of s t r e s s (d ) = 1.2 - (2 .0*(SM / F C ) ) t t where SM = the s o i l m o i s t u r e l e v e l ( inches ) FC = f i e l d c a p a c i t y ( i n c h e s ) and 0 < d < 1. 2. timing of stress The date d u r i n g the growing season when s t r e s s o c c u r s i s important for f r u i t y i e l d s . The r e l a t i o n s h i p between o c c u r r e n c e of and the t i m i n g of s t r e s s i s g i v e n by the f o l l o w i n g e q u a t i o n s : i f w < 15 then T = 0.25 + 0.05 * w t i f 15 < w < 27 then T = 1.75 - 0.05 * w t i f 27 > w < 30 then T = 7.75 - 0.25 * w t i f w > 30 then T = 1.15 - 0.03 * w t where T = t i m i n g of s t r e s s f a c t o r expressed as a r a t i o of the degree to which water s t r e s s w i l l impact upon y i e l d w = week number i n growing season and 0 < T < 1. T h i s r e l a t i o n s h i p i s d e s c r i b e d g r a p h i c a l l y i n F i g u r e 3 . 3 . F i (jurc 3 • 3 63 The va lue of T , and thus the s t r e n g t h of the t i m i n g of s t r e s s f a c t o r , peaks i n week 15 of the growing season (the second week i n June) d u r i n g which f r u i t set o c c u r s . T h i s p e r i o d i s assumed to be the most c r i t i c a l i n terms of u l t i m a t e f r u i t y i e l d . 2 " 3 .4 .3 TOTAL GROWTH AND TOTAL YIELD S i n c e the growth r e d u c t i o n f a c t o r (g) i s c a l c u l a t e d on a d a i l y b a s i s , the t o t a l e f f e c t of the d a i l y growth r e d u c t i o n f a c t o r s g over the e n t i r e growing season i s the sum of these f a c t o r s for a l l t days d i v i d e d by the number of days per season . n G =Z [g ] /n i t t where G = annua l growth r e d u c t i o n f a c t o r n = number of days per growing season (245) i = the c u r r e n t t r e e year ( i = 1 . . . 2 0 ) Each y e a r ' s growth i s assumed to be dependent on the p r e v i o u s year and thus for y e a r s one through seven for which a growth f a c t o r i s a p p l i c a b l e , a c a r r y t h r o u g h e f f e c t i s de termined by: i G =1 [G ] / i f o r a l l i = 1 . . . 7 i j j 2 < t see Goode, 1975 and M i t c h e l l e t . a l . , 1984. 64 T o t a l y i e l d i n any year i s dependent on the growth stage of the t r e e as w e l l as the y i e l d f a c t o r s d and T p r e v i o u s l y d e s c r i b e d . F a c t o r s d and T are c o n s i d e r e d to be r e l a t e d to t o t a l y i e l d r e d u c t i o n i n the f o l l o w i n g manner: YR =E[d *T ]/n i t t where YR = annual y i e l d r e d u c t i o n The t o t a l growth r e d u c t i o n f a c t o r G i s a l s o a f a c t o r i n determining y i e l d together with the YR f a c t o r . The f o l l o w i n g equations d e s c r i b e the r e l a t i o n s h i p of G and YR i n determining year-end y i e l d . . AY = PY (1-G -YR ) f o r a l l i=4...7 i i i i AY = PY (1-YR ) f o r a l l i=8...20 i i i where AY = a c t u a l y i e l d i n year i i PY = p o t e n t i a l y i e l d in year i ( i n the i "absence of water s t r e s s , see Table 3.1) 3.5 WEATHER GENERATOR As inputs i n t o the s o i l moisture c a l c u l a t i o n , d a i l y r a i n f a l l and e v a p o t r a n s p i r a t i o n data are r e q u i r e d by the or c h a r d s i m u l a t i o n model. One method of generating such data i s to use h i s t o r i c a l d a ta. For the Kelowna area, h i s t o r i c a l 65 r e c o r d s of d a i l y pan e v a p o r a t i o n are a v a i l a b l e for the p e r i o d 1971 t hrough 1983. 2 5 D a i l y r a i n f a l l r e c o r d s go back much f u r t h e r . Pan e v a p o r a t i o n has been and can be used to d e r i v e e v a p o t r a n s p i r a t i o n as w i l l be d e s c r i b e d i n a l a t e r s e c t i o n . In o r d e r to extend the pan e v a p o r a t i o n d a t a s e t , a r e l a t i o n s h i p was h y p o t h e s i z e d to e x i s t between pan e v a p o r a t i o n and r a i n f a l l and t e m p e r a t u r e . D a i l y pan e v a p o r a t i o n was r e g r e s s e d on d a i l y t o t a l r a i n f a l l and d a i l y maximum temperature f o r the months A p r i l through September for the 13 year p e r i o d 1971 through 1983. S e v e r a l f u n c t i o n a l forms were c o n s i d e r e d . L o g - l i n e a r forms proved u n s u i t a b l e due to the presence of z e r o v a l u e s both w i t h i n the e x p l a n a t o r y and dependent v a r i a b l e da ta s e t s . L i n e a r and q u a d r a t i c e s t i m a t i o n s were found to possess f i r s t o r d e r s e r i a l c o r r e l a t i o n when t e s t e d u s i n g the Durbin-Watson s t a t i s t i c . C o r r e c t i o n p r o c e d u r e s were performed and the models r e - e s t i m a t e d u s i n g a Maximum L i k e l i h o o d Cochrane O r c u t t i t e r a t i v e p r o c e d u r e . 2 6 The r e s u l t s of a l l r e g r e s s i o n s are g i v e n below, w i t h t - r a t i o s i n b r a c k e t s . OLS PAN = -8 .1122 + .25129T - .10544R (-6 .4998) (48.061) ( -9 .0286) R 2 =.5411 D-W=1.3711 2 5 A 1 1 weather d a t a was o b t a i n e d from the Canadian C l i m a t e C e n t r e , Atmospher i c Environment S e r v i c e , Environment Canada at Downsview O n t a r i o . 2 6 s e e C M . Beach and J . G . MacKinnon "A Maximum L i k e l i h o o d Procedure f o r R e g r e s s i o n wi th 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 . 1978). OLS PAN =13.542 + . 4 1 6 0 5 E - 3 T 2 + .57254T + . (309105) (6.2309) (1.8516) .85941E-4RT - .30423R + .13579E-2R 2 (.36862) (-5.6759) (7.1478) R 2 =.5581 D-W=1.3799 AUTO PAN = -10 .636 + .26161T - .74765E-1R (-6.6534) (39.134) ( -6 .6987) R 2 =.5883 AUTO PAN = 7.0700 + . 3 2 3 4 1 E - 3 T 2 + .10800T + (1.7342) (4.1087) (2.9745) .39804E-4RT - .27828R + .14064E-2R 2 (.18071) ( -5 .5083) (8.0441) R 2 =.6021 where AUTO = c o r r e c t e d for a u t o c o r r e l a t i o n PAN = pan e v a p o r a t i o n ( p r e d i c t e d ) R = d a i l y r a i n f a l l (.1 mm) o T = d a i l y maximum temperature (.1 C) D-W = Durbin-Watson s t a t i s t i c number of o b s e r v a t i o n s = 2316 Though the R 2 s o b t a i n e d w i t h the q u a d r a t i c forms are l a r g e r than those o b t a i n e d w i t h the l i n e a r forms , the q u a d r a t i c f u n c t i o n was found to reach a maximum w i t h i n the range of the r e l e v a n t data s e t . For t h i s reason the l i n e a r form c o r r e c t e d for a u t o c o r r e l a t i o n was chosen as the p o i n t 67 p r e d i c t o r to be u s e d . OLS p o i n t p r e d i c t o r s , i f the c l a s s i c a l l i n e a r r e g r e s s i o n model assumptions are not v i o l a t e d , are the most a c c u r a t e means of p r e d i c t i n g i n d i v i d u a l dependent va lues from a c t u a l v a l u e s of the e x p l a n a t o r y v a r i a b l e s . A p o i n t p r e d i c t o r i s an expected v a l u e of the dependent v a r i a b l e for g i v e n independent v a r i a b l e v a l u e s . S i n c e the purpose of the weather g e n e r a t o r i s to s i m u l a t e a c t u a l r a i n f a l l and e v a p o t r a n s p i r a t i o n r a t e s , the v a r i a t i o n around the p r e d i c t e d pan e v a p o r a t i o n v a l u e i s of i n t e r e s t . The v a r i a t i o n of a p o i n t p r e d i c t i o n , Y i s g iven by f -1 O 2 [ 1 + X 1 0 ( X 1 X ) X 0 ] -1 where a 2 ( X 1 X ) i s the c o - v a r i a n c e m a t r i x of the e s t i m a t e d c o e f f i c i e n t s . In o r d e r to ' c a p t u r e ' some of t h i s v a r i a t i o n in the p r e d i c t i o n , the s t a n d a r d e r r o r of the p o i n t p r e d i c t o r m u l t i p l i e d by a n o r m a l l y d i s t r i b u t e d [N (0,1)] randomly genera ted number i s i n c l u d e d i n the p r e d i c t i o n of pan evaporat i o n . The f i n a l form of the p r e d i c t o r f o r g e n e r a t i n g pan e v a p o r a t i o n v a l u e s from data on r a i n f a l l and maximum temperature i s : 68 PAN = 0 O + 0 , T + 0 2 R + SEP*Rand where PAN = pan e v a p o r a t i o n SEP = s t a n d a r d e r r o r of the p r e d i c t i o n Rand = a randomly generated number wi th normal d i s t r i b u t i o n . 3.6 DERIVING POTENTIAL EVAPOTRANSPIRATION FROM PAN  EVAPORATION The method of d e r i v i n g e v a p o t r a n s p i r a t i o n from pan e v a p o r a t i o n v a l u e s i s of the f o l l o w i n g form: PET = K * PAN where PET = 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 PAN = pan e v a p o r a t i o n K = PET c o e f f i c i e n t Hargreaves (1968) p r o v i d e s a t a b l e of K v a l u e s for v a r i o u s p o i n t s i n the growing season for a v a r i e t y of p l a n t g r o u p i n g s , i n c l u d i n g dec iduous f r u i t s . S i n c e the K va lue depends upon the s tage i n the growing season , the growing season must be d e f i n e d . For the purposes of t h i s s tudy the growing season beg ins March 1 and ends October 31 (245 d a y s ) . The r e l a t i o n s h i p between K and the growing season (expressed as a percentage of the t o t a l ) as i _ d e r i v e d from Hargreaves i s g i v e n i n T a b l e 3 . 4 . The 69 r e l a t i o n s h i p i s shown g r a p h i c a l l y i n F i g u r e 3.4. P r e d i c t e d v a l u e s f o r pan e v a p o r a t i o n a r e g e n e r a t e d d a i l y from maximum t e m p e r a t u r e and r a i n f a l l d a t a s e l e c t e d randomly by y e a r from 75 y e a r s of h i s t o r i c a l d a t a f o r t h e Kelowna a r e a d a t i n g back t o 1899. 2 7 Data s e l e c t e d r andomly i s s t o r e d i n a 20 y e a r b l o c k and used i d e n t i c a l l y f o r a l l 8 o r c h a r d m o d e l s , t h u s a s s u r i n g an e q u a l weather f a c t o r a c r o s s a l l m o d e l s d u r i n g any one 20 y e a r o r c h a r d l i f e . E a c h ' t e s t s c e n a r i o ' , i n c o r p o r a t i n g an 2 7 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 or i n c o m p l e t e n e s s of d a t a . TABLE 3.4: DERIVATION OF EVAPOTRANSPIRATION COEFFICIENT K WHICH VARIES WITH PERIOD OF GROWING SEASON PORTION OF GROWING SEASON (X) EQUATION TO DERIVE POTENTIAL EVAPOTRANSPRATION COEFFICIENT 0 0, 0, 0, 0, 0, 0, 0 0 0, 0, 0, 0, 1, K K K K K K K 0 0 0, 0, 1 , 1 , 2, 0*X o * x 5*X 5*X - 0.5*X ,0*X 0*X S o u r c e : H a r g r e a v e s , 1 9 6 8 . 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 e x p l i c i t set of a s sumpt ions , c o n s i s t s of 10 of these 20 year o r c h a r d l i f e t i m e s , each of which uses a unique set of randomly s e l e c t e d weather y e a r s . T h i s m u l t i - r u n method s h o u l d s t a b i l i z e the v a r i a t i o n of r e s u l t s and p r o v i d e a sound b a s i s for o r c h a r d system performance c o m p a r i s o n s . 3.7 SUMMARY OF PARAMETER RELATIONSHIPS Appendix B p r o v i d e s r e s u l t s on a l l parameters for a s i n g l e growing season (245 days) for a sample o r c h a r d system (system 5) w i th M2 r o o t s t o c k , 202 t r e e s / a c r e , t r i c k l e i r r i g a t i o n and .sand s o i l . T a b l e 3.5 p r o v i d e s a l i s t of parameters used in the model and t h i e r u n i t s of measurement. F i g u r e 3 .5 g i v e s a f low c h a r t summary of how the v a r i o u s parameters and f a c t o r s of the model , as d e r i v e d i n t h i s c h a p t e r , r e l a t e to one another d u r i n g a s i m u l a t i o n r u n . S t a r t i n g i n the upper r i g h t hand c o r n e r of the flow c h a r t , i n i t i a l l y an o r c h a r d system (see T a b l e 3.3) and an i r r i g a t i o n r a t e (some r a t i o of the base case i r r i g a t i o n r a t e , see s e c t i o n 3.2) are c h o s e n . Once s e t , these f a c t o r s remain c o n s t a n t for the d u r a t i o n of the s i m u l a t i o n r u n . S i n c e each s i m u l a t i o n run c o n s i s t s of 20 growing seasons or y e a r s of 245 days e a c h , YEAR and DAY (denoted by i and t i n s u b s c r i p t s ) are used c o u n t e r s to keep t r a c k of the stage i n the 20 year o r c h a r d l i f e . For each year of the 20 year s i m u l a t i o n , a "weather year" i s s e l e c t e d at random from a h i s t o r i c weather da ta set (see s e c t i o n 3 . 5 ) . T h i s weather year c o n s i s t s of d a i l y t o t a l r a i n f a l l and maximum 72 T a b l e 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 o£ Measurement A b r e v i a t i o n Parameter U n i t s of Measurement AET A c t u a l E v a p o t r a n s p i r a t i o n i n c h e s of water AWSC 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 i n . of w a t e r / f t of s o i l d Degree of S t r e s s r a t i o of p o t e n t i a l growth f PET S l o p e C o e f f i c i e n t FC F i e l d C a p a c i t y i n . of w a t e r / f t of s o i 1 g Growth R e d u c t i o n F a c t o r r a t i o of p o t e n t i a l growth GA Gross A p p l i c a t i o n Rate i n c h e s K PET C o e f f i c i e n t M2 M a i l i n g 2 R o o t s t o c k M26 M a i l i n g 26 R o o t s t o c k MSWD Maximum S o i l Water D e f i c i t i n . o f w a t e r / f t of s o i l PAN Pan E v a p o r a t i o n i n c h e s of water PET 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 i n c h e s of water PI Peak I n t e r v a l days PKET Peak E v a p o t r a n s p i r a t i o n i n c h e s of water/day PWP Permanent W i l t i n g P o i n t i n . of w a t e r / f t of s o i l PY P o t e n t i a l Y i e l d I b s / a c r e / y e a r SM S o i l M o i s t u r e L e v e l i n . of w a t e r / f t of s o i l T Tim i n g of S t r e s s F a c t o r r a t i o of p o t e n t i a l growth YR Annual Y i e l d R e d u c t i o n S o i l M o i s t u r e F a c t o r r a t i o of p o t e n t i a l growth p r e c i p i t a t i o n d a t a f o r t h e p e r i o d d e f i n e d as the growing se a s o n (March 1 t h r o u g h O c t o b e r 3 1 ) . The weather d a t a i s used f o r two s e p a r a t e i n p u t s i n t o t h e n e x t s t a g e of t h e s i m u l a t i o n p r o c e s s , d e r i v i n g t h e s o i l moisture l e v e l . Both the r a i n f a l l and t e m p e r a t u r e d a t a , t h r o u g h the use of a p o i n t p r e d i c t o r ( see s e c t i o n s 3.5 and 3 . 6 ) , a r e used t o e s t i m a t e a pan evaporation r a t e , PAN, f o r e a c h growing choose orchard system choose I r r i g a t i o n l e v e l y e a r ( i ) - 0 a c t u a l y i e l d (AY) p o t e n t i a l y i e l d (PY) A T i - P Y i * ( l - < ; 1 - r R i ) <Jyes 1-1*1 dey(O-0 <]yes F i g u r e 3.5 I n t e r a c t i o n of F a c t o r s Comprising the Hodel annual y i e l d r e d u c t i o n f a c t o r res i r r t g a - ATT, growth f a c t o r g t - f ( S M t ) I annual growth f a c t o r 74 season day . The d e r i v e d pan e v a p o r a t i o n r a t e i s used to e s t imate potential evapotranspiration, PET, u s i n g a 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 , K (see s e c t i o n 3 . 7 ) , as d e r i v e d by Hargreaves (1968) . The c o e f f i c i e n t p i s the r a t i o of the actual evapotranspiration r a t e , A E T , v e r s u s the 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 r a t e . AET i s the m o i s t u r e l o s s e s t i m a t e d to o c c u r at a g i v e n s o i l m o i s t u r e l e v e l and a tmospher ic c o n d i t i o n s w h i l e PET i s the m o i s t u r e l o s s e s t i m a t e d to occur form a s o i l w i th a m o i s t u r e l e v e l a t or near f i e l d c a p a c i t y under s i m i l a r a tmospher ic c o n d i t i o n s (see s e c t i o n 3 . 3 ) . The a c t u a l e v a p o t r a n s p i r a t i o n r a t e , as d e r i v e d from the weather da ta and the p r e v i o u s d a y ' s s o i l m o i s t u r e l e v e l , i s an input i n t o the d e r i v a t i o n of the d a i l y s o i l m o i s t u r e l e v e l . D a i l y r a i n f a l l , i r r i g a t i o n , and s o i l m o i s t u r e on the p r e v i o u s day are the o ther i n p u t s (see s e c t i o n 3 . 3 ) . The d a i l y s o i l m o i s t u r e l e v e l a f f e c t s both growing and mature f r u i t t r e e s through water s t r e s s . For young t r e e s under 8 y e a r s a growth factor based on the s o i l m o i s t u r e l e v e l i s c a l c u l a t e d d a i l y (g) and cumulated a n n u a l l y ( G ) . For mature t r e e s 8 y e a r s of age and o v e r , both the degree of water stress (d) as d e t e r m i n e d by the s o i l m o i s t u r e l e v e l and the period during the growing season when s t r e s s o c c u r s (T) are used to c a l c u l a t e an annual yield reduction factor (YR) . The d a i l y c a l c u l a t i o n of the s o i l m o i s t u r e l e v e l , growth f a c t o r , and t i m i n g and y i e l d f a c t o r s c o n t i n u e s f o r the p e r i o d of the growing season (245 d a y s ) . At the end of 75 the growing season , i f the t r e e s are mature enough to g i v e y i e l d s ( t h i s depends on the r o o t s t o c k b e i n g used , though 4 y e a r s i s g i v e n as an example in f i g u r e 3 . 5 ) , the c u m u l a t i v e growth f a c t o r G a n d / o r the y i e l d r e d u c t i o n f a c t o r YR are used to c a l c u l a t e the actual annual yield, AY. A t h i r d f a c t o r d e t e r m i n i n g AY i s potential yield, PY, the y i e l d o b t a i n a b l e f o r the o r c h a r d system under c o n d i t i o n s of no water s t r e s s (see T a b l e 3 . 1 ) . F o l l o w i n g t h i s c a l c u l a t i o n , i f 20 "years" of the s i m u l a t i o n have been r u n , the p r o c e d u r e s tops and the r e s u l t s are t a b u l a t e d . I f n o t , a new weather year i s s e l e c t e d at random and the s i m u l a t i o n c o n t i n u e s . Chapter 4 RESULTS The purpose of the model d e s c r i b e d i n the p r e v i o u s c h a p t e r i s to p r o v i d e a means of a n a l y s i n g the e f f e c t s of d i f f e r e n t water a p p l i c a t i o n l e v e l s on o r c h a r d y i e l d s . A base case r e p r e s e n t i n g c u r r e n t a l l o w a b l e water a p p l i c a t i o n r a t e s for a g r i c u l t u r e i n the Okanagan was s i m u l a t e d f o r a l l 8 o r c h a r d sys tems. From these base case r e s u l t s , water a p p l i c a t i o n r a t e s were s y s t e m a t i c a l l y reduced f o r each o r c h a r d system and the r e s u l t i n g y i e l d s were r e c o r d e d . T h i s c h a p t e r p r e s e n t s the r e s u l t s of the base case s c e n a r i o s and subsequent r e s t r i c t e d i r r i g a t i o n t r i a l s . V a l i d a t i o n of the base cases and the r e s t r i c t e d i r r i g a t i o n cases i s d i s c u s s e d and r e s u l t s of s e n s i t i v i t y a n a l y s i s on s e l e c t e d parameters a r e p r e s e n t e d . The o r i g i n a l s i m u l a t i o n procedure i n c o r p o r a t e d 8 o r c h a r d sys tems , c o m p r i s e d of 2 i r r i g a t i o n system t y p e s , 2 s o i l types and 2 r o o t s t o c k t y p e s . However, r o o t s t o c k was found to be an i n s i g n i f i c a n t f a c t o r i n d e t e r m i n i n g the relative v a r i a t i o n between d i f f e r e n t water a p p l i c a t i o n r a t e s a p p l i e d w i t h i n a s i n g l e o r c h a r d system, or on the e f f e c t of s i m i l a r a p p l i c a t i o n r a t e s between d i f f e r e n t o r c h a r d sys tems. Root s tock was chosen as a p o t e n t i a l l y s i g n i f i c a n t f a c t o r in o r c h a r d water a p p l i c a t i o n requirements s i n c e i t i s a de terminant in the base case water a p p l i c a t i o n c a l c u l a t i o n for t r i c k l e i r r i g a t i o n (see s e c t i o n 3 . 2 . 2 ) . However, c a l c u l a t i o n of t r i c k l e i r r i g a t i o n base case water 76 77 requirements f o r o r c h a r d systems u s i n g M2 and M26 r o o t s t o c k s gave n e a r l y i d e n t i c a l r e s u l t s . T h i s i s a t t r i b u t a b l e to the r e l a t i o n s h i p between o r c h a r d d e n s i t y and s i z e of t r e e roo t zones . L a r g e r , l e s s d e n s e l y spaced t r e e s , though fewer i n number, have l a r g e r root zones r e q u i r i n g more water per t r e e . T h u s , f o r a l l o r c h a r d systems the water r e q u i r e m e n t s for M2 and M26 r o o t s t o c k s were i d e n t i c a l . T h e r e f o r e , o n l y o r c h a r d systems on M2 r o o t s t o c k s are r e p o r t e d h e r e . The r e s u l t s p r e s e n t e d in t h i s c h a p t e r are based on the average of the accumulated y e a r l y y i e l d t o t a l s over the 20 year o r c h a r d l i f e - s p a n . Each s i m u l a t i o n r e s u l t c o n s i s t s of 20 of these 20 year o r c h a r d l i f e s , each i n c o r p o r a t i n g a unique set of weather d a t a . The r e s u l t s f o r each o r c h a r d system are thus the average of 400 o b s e r v a t i o n s . 4.1 THE BASE CASE The r e s u l t s of the base case s i m u l a t i o n f o r o r c h a r d systems u s i n g M2 r o o t s t o c k s are p r e s e n t e d in T a b l e 4 . 1 . R e s u l t s f or the r e s t r i c t e d c a s e , to be d i s c u s s e d i n the next s e c t i o n are a l s o p r e s e n t e d . The base case water a p p l i c a t i o n l e v e l s were a r r i v e d at u s i n g the I r r i g a t i o n Des ign Manual recommendations for s p r i n k l e r and t r i c k l e i r r i g a t i o n systems i n the Kelowna r e g i o n (see s e c t i o n 3 . 2 ) . The base case y i e l d r e s u l t s are i d e n t i c a l to the average p o t e n t i a l y i e l d s (per a c r e ) over the twenty year l i f e of M2 o r c h a r d s , as g i v e n i n T a b l e 3 . 1 . T h i s i s expec ted s i n c e in both cases y i e l d s are not s u b j e c t TABLE 4.1 RESULTS OF WATER REDUCTIONS ON M2 ORCHARD YIELDS SHOWING BASE CASE AND WATER RESTRICTED CASE ANNUAL IRRIGATION LEVELS AND YIELDS [ r r i g a t i o n S o i l Water Annua 1 Avg. Y i e l d per C r i t i c a l type type A p p l i e d a s % I r r i g a t i o n A c r e f o r 20yrs Po i nt of Base Case ( i n c h e s ) ( l b s ) ( i n c h e s ) spr i n k i e r sand base c a s e 53.33 24138 (0.78)* 22 .5 n M 55% 29.33 24 111 (16.28) m M 50% 26.68 24061 (49.98) m n 45% 24 .00 23893 (104.45) m « 40% 21.33 23579 (166.06) s p r i n k l e r s i l t - l o a m base c a s e 48.00 24138 (0.01) 14.5 H N 45% 21 .60 24 1 27 (19.57) m n 40% 19.20 24083 (34.90) m m 35% 16.80 23969 (76 .31) m " 30% 14.40 23638 (157.91 ) m m 20% 9.60 2251 5 (408.72) t r i c k l e sand base c a s e 29.79 24138 (3.11) 16.0 » N 65% 19.36 24063 (40.08) M *• 55% 16.39 23703 (156.10) m « 50% 1 4 .90 23296 (252.46) m m 45% 13.41 22924 (257.95) t r i c k l e s i l t - l o a m base c a s e 29.79 24138 (0.04 ) 10.3 w •t 45% 13.41 24098 (43. 14) M M 40% 1 1 .92 23951 ( 1 18.86) M m 35% 10.43 23703 (168.62) It M 30% 8.94 23267 (284.70) * s t a n d a r d d e v i a t i o n s f o r y i e l d s a r e g i v e n i n b r a c k e t s . R e s u l t s a r e averages of 400 o b s e r v a t i o n s u s i n g 20 randomly s e l e c t e d weather da t a s e t s each c o n s i s t i n g of 20 y e a r s of d a i l y weather d a t a . A l l o r c h a r d systems were s i m u l a t e d u s i n g i d e n t i c a l weather d a t a s e t s . 79 to water s t r e s s . The average p o t e n t i a l y i e l d i s by d e f i n i t i o n a s t r e s s - f r e e y i e l d . The maximum water a l l o t m e n t , a p p l i e d i n the base c a s e s , r e s u l t s i n no water s t r e s s and thus r e s u l t s i n the maximum p o t e n t i a l y i e l d , as h y p o t h e s i z e d in c h a p t e r 2. The base case r e s u l t s de termine a s i n g l e p o i n t of water a p p l i c a t i o n on the r e s p e c t i v e o r c h a r d p r o d u c t i o n f u n c t i o n s . From t h i s p o i n t the amount of water a p p l i e d to each o r c h a r d system i s s y s t e m a t i c a l l y r e d u c e d . Y i e l d s are a f u n c t i o n of water a p p l i c a t i o n l e v e l . Model v a l i d a t i o n i s the p roced u re by which i t i s de termined whether or not a model a d e q u a t e l y mimics the behav iour of the r e a l wor ld system i t was d e s i g n e d to s i m u l a t e . 2 8 I d e a l l y , data not i n c o r p o r a t e d i n the m o d e l l i n g p r o c e s s s h o u l d be used to v a l i d a t e the s i m u l a t i o n r e s u l t s . As a "next best" method, a model might be v a l i d a t e d u s i n g data p r e v i o u s l y used i n f o r m u l a t i n g the model (Anderson , 1974) . The base case r e s u l t s were a r r i v e d a t u s i n g parameters and i n f o r m a t i o n taken from the o r c h a r d i n d u s t r y i n the Okanagan V a l l e y . The q u a n t i t i e s of water a p p l i e d i n the base cases a r e d e r i v e d u s i n g the B r i t i s h Columbia M i n i s t r y of A g r i c u l t u r e and F o o d ' s (BCMAF) I r r i g a t i on'Design Manual recommendations . The expected y i e l d s i n each year of the 20 year l i f e - s p a n s of M2 and M26 o r c h a r d s (as g i v e n i n T a b l e 2 8 T h i s d i s c u s s i o n i s taken in 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 : Methodology 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. 80 3.1) were de termined u s i n g the BCMAF Cost of Production Study for Apples and r e v i s e d u s i n g i n f o r m a t i o n a c q u i r e d from Okanagan V a l l e y h o r t i c u l t u r a l i s t s . The I r r i g a t i o n Des ign Manual recommendations are based on p r o v i d i n g o r c h a r d s w i t h s u f f i c i e n t water to ensure no water s t r e s s w i l l occur d u r i n g h o t , d r y p e r i o d s . The p o t e n t i a l y i e l d data are of secondary importance s i n c e i t i s the r e l a t i v e y i e l d d i f f e r e n c e s w i t h i n an o r c h a r d system and between o r c h a r d systems under v a r i o u s water a p p l i c a t i o n l e v e l s , which are of i n t e r e s t . 4.2 RESULTS OF THE WATER RESTRICTED CASES The base case r e s u l t s determine one p o i n t on each of the r e s p e c t i v e o r c h a r d system p r o d u c t i o n f u n c t i o n s . The r e s u l t s i n t h i s s e c t i o n determine w a t e r / y i e l d r e l a t i o n s h i p s as they move a l o n g the p r o d u c t i o n f u n c t i o n . The prime purpose for t r a c i n g out the p r o d u c t i o n f u n c t i o n s i n t h i s manner i s to de termine the p o i n t at which f u r t h e r water r e d u c t i o n s r e s u l t i n d e c l i n i n g y i e l d s . T a b l e 4.1 p r e s e n t s the r e s u l t s of the s u c c e s s i v e water r e d u c t i o n s on each o r c h a r d sys tem. The i r r i g a t i o n l e v e l at which y i e l d s d e c l i n e 2% below base case y i e l d s i s d e f i n e d as the critical point f or i r r i g a t i o n . Y i e l d s a r e c o n s i d e r e d s t a b l e a t or above 98% of the base case l e v e l . O r c h a r d system 1 on sand s o i l and u s i n g s p r i n k l e r i r r i g a t i o n , w i t h M2 r o o t s t o c k , e x h i b i t s s t a b i l i t y of y i e l d s t h r o u g h s i m u l a t i o n runs w i t h water r e d u c t i o n s amounting to 81 42% of the base case l e v e l . Orchard system 2, on s i l t - l o a m s o i l and using s p r i n k l e r i r r i g a t i o n , with M2 r o o t s t o c k , g i v e s s t a b l e r e t u r n s through water r e d u c t i o n s down to 30% of the base case l e v e l . In a l l cases standard d e v i a t i o n of y i e l d i n c r e a s e d as water a p p l i c a t i o n s decreased. The standard d e v i a t i o n r e p r e s e n t s the l e v e l of y i e l d r i s k which an o r c h a r d i s t undertakes at the i n d i c a t e d i r r i g a t i o n l e v e l . R e s u l t s from the two o r c h a r d systems u s i n g t r i c k l e i r r i g a t i o n can be i n t e r p r e t e d d i f f e r e n t l y from those using s p r i n k l e r systems. T r i c k l e i r r i g a t i o n was set at a constant flow r a t e f o r the base case at the peak requirement (as g i v e n by the I r r i g a t i o n Design Manual, 1983). However, s i n c e t r i c k l e i r r i g a t i o n system flow r a t e s are e a s i l y v a r i e d f o r weather and s o i l moisture c o n d i t i o n s i n a c t u a l orchard environments, the base case f o r t r i c k l e systems represents a worst case s c e n a r i o rather than a present day a p p l i c a t i o n r a t e . T h i s f l e x i b i l i t y i n t r i c k l e system water a p p l i c a t i o n r a t e s means that the a c t u a l a p p l i c a t i o n r a t e s f o r t r i c k l e systems can approach the c r i t i c a l p o i n t s as determined in the o r c h a r d system s i m u l a t i o n s . Water r e d u c t i o n s c a r r i e d out on those orchard systems u s i n g t r i c k l e i r r i g a t i o n were f o r the purposes of d e f i n i n g a minimum water a p p l i c a t i o n l e v e l at which the t r i c k l e system c o u l d s u s t a i n the y i e l d at a l e v e l e q u i v a l e n t to at l e a s t 98% of a "no s t r e s s " case (2% l o s s of y i e l d being d e f i n e d as the c r i t i c a l p o i n t ) . The t r i c k l e r e s u l t s are termed 82 efficiency points as they can be compared wi th the c r i t i c a l p o i n t s of those o r c h a r d systems u s i n g s p r i n k l e r i r r i g a t i o n (on i d e n t i c a l s o i l type) f o r the purposes of r a t i n g the water use e f f i c i e n c y of the two sys tems. The r a t i n g i s approx imate s i n c e the model c o n s t r a i n s the t r i c k l e system to a c o n s t a n t d a i l y r a t e of a p p l i c a t i o n . Thus the model does not account for the p o t e n t i a l water s a v i n g s p o s s i b l e w i t h p e r i o d i c adjustments to the t r i c k l e flow r a t e s w i th s e a s o n a l c l i m a t i c v a r i a t i o n s . The e f f i c i e n t p o i n t s for t r i c k l e i r r i g a t i o n systems were e s t a b l i s h e d at 16 inches and 10.25 inches f o r sand and s i l t - l o a m s o i l s r e s p e c t i v e l y . The p o i n t at which water r e s t r i c t i o n begins to r e s u l t i n s i g n i f i c a n t y i e l d r e d u c t i o n s , the c r i t i c a l p o i n t , i s the key r e s u l t of the s i m u l a t i o n . F i g u r e 4.1 p l o t s the s i m u l a t i o n r e s u l t s f o r y i e l d of a p p l e s versus q u a n t i t y of water a p p l i e d h o l d i n g a l l i n p u t s except i r r i g a t i o n water c o n s t a n t . F i g u r e 4.1 thus r e p r e s e n t s the restricted o r c h a r d sytems p r o d u c t i o n f u n c t i o n s as d e f i n e d in c h a p t e r 2. The c r i t i c a l p o i n t s for each o r c h a r d system occur w i t h the down-turn of each f u n c t i o n as water a p p l i c a t i o n r a t e s are r e d u c e d . The f l a t p o r t i o n of the c u r v e s to the r i g h t of the c r i t i c a l p o i n t s t r a c e out a p r e d i c t e d r e s u l t of water r e d u c t i o n s i n the range f o r which the o r c h a r d i s t , not e x p e r i e n c i n g any y i e l d r e d u c t i o n , would not be expected to make any p r o d u c t i o n input a d j u s t m e n t s . Thus for these p o r t i o n s of each p r o d u c t i o n f u n c t i o n , the r e s t r i c t i o n on an o r c h a r d i s t ' s behavioural response i n a d j u s t i n g the o r c h a r d 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- 'utct ioi ia for M2 Orcliarc! Sys la iu ; Showing lil 'fcTt i>l l.'i.ilm. i UK W;tlri A[)p I i c:i t ion L P V P I S nit Y if? I (Is 84 p r o d u c t i o n mix i s not c o n s i d e r e d b i n d i n g . For those p o r t i o n s of the curves i n F i g u r e 4.1 to the l e f t of the c r i t i c a l p o i n t s , the o r c h a r d i s t faced with water r e d u c t i o n s would be expected to modify orchard management p r a c t i c e s to compensate f o r the water r e s t r i c t i o n . The o r c h a r d i s t b e h a v i o u r a l r e s t r i c t i o n i s thus b i n d i n g f o r t h i s p o r t i o n of the curve. The p r e d i c t e d response of removing the b e h a v i o u r a l r e s t r i c t i o n i s a s h i f t of t h i s p o r t i o n of the curve out to the l e f t . However, much can be concluded from the p r o d u c t i o n f u n c t i o n s i n t h e i r given r e s t r i c t e d forms. F i g u r e 4.2 p r o v i d e s the marginal p h y s i c a l product (MPP) curves f o r each orchard system on M2 r o o t s t o c k s as d e r i v e d from the p r o d u c t i o n f u n c t i o n s (M26 r e s u l t s are s i m i l a r ) . From Table 4.1 and F i g u r e 4.2 two important f a c t o r s which determine the c r i t i c a l p o i n t s are apparent. The f i r s t f a c t o r i s s o i l type. Sand s o i l s , being able to r e t a i n l e s s water, are s u b j e c t to d e p l e t i o n down to water s t r e s s l e v e l s i n the model at an e a r l i e r stage than i s the case with s i l t - l o a m s o i l s under e q u i v a l e n t weather c o n d i t i o n s and i r r i g a t i o n systems. For o r c h a r d systems on s p r i n k l e r i r r i g a t i o n , the c r i t i c a l p o i n t f o r sandy s o i l s o c c u r r e d at 22.5 inches as compared with 14.5 inches f o r s i l t - l o a m s o i l s (55% h i g h e r ) . T r i c k l e systems showed a s i m i l a r r e l a t i o n s h i p (16 and 10.25 inches f o r sand and s i l t - l o a m r e s p e c t i v e l y , 56% h i g h e r ) . The second f a c t o r found to i n f l u e n c e the c r i t i c a l water l e v e l i s the type of i r r i g a t i o n system. Under the assumption Marginal Physical Product (lb/acre) 300 •• 250 -• D CO 200 -• D O O • • ISO • • • 100 •- i r r i g a t i o n s o i l sustain type sprinkler silt-loam • sprinkler sand • tr i c k l e silt-loam • _ t r i c k l e 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 c o n s t a n t behav iour on the p a r t of the o r c h a r d i s t , t r i c k l e systems were found to be more e f f i c i e n t i n a y i e l d to water a p p l i e d r a t i o than s p r i n k l e r systems on s i m i l a r s o i l s . T a b l e 4.2 g i v e s the c r i t i c a l p o i n t s of each o r c h a r d system on M2 r o o t s t o c k as d e r i v e d from the s i m u l a t i o n r u n s . Assuming i r r i g a t i o n e f f i c i e n c i e s c o u l d approach these c r i t i c a l p o i n t s , the t r i c k l e systems use about 71% of the s p r i n k l e r system water requirements (assuming a c o n s t a n t flow r a t e throughout the i r r i g a t i o n p e r i o d i n a l l c a s e s ) . The f l e x i b i l i t y of a t r i c k l e system a l l o w s f o r a l t e r i n g flow r a t e s on a d a i l y b a s i s depending on weather c o n d i t i o n s wi thout the r i s k i n h e r e n t for flow r a t e adjustment w i t h s p r i n k l e r methods. I f t h i s f l e x i b i l i t y were i n c o r p o r a t e d i n t o the model , the t r i c k l e system water requ irements would be reduced . The assumpt ion of h o l d i n g a l l i n p u t s except i r r i g a t i o n water a p p l i c a t i o n c o n s t a n t d u r i n g s u c c e s s i v e water r e s t r i c t i o n s i s e s s e n t i a l f o r t h i s r e s u l t . M o d i f i c a t i o n s to the assumed s p r i n k l e r i r r i g a t i o n p r a c t i c e s as d i s c u s s e d i n c h a p t e r 2 c o u l d s h i f t the MPP c u r v e to the l e f t thus r e d u c i n g the t r i c k l e v e r s u s s p r i n k l e r water e f f i c i e n c y gap wh i l e f i n e t u n i n g t r i c k l e system water a p p l i c a t i o n r a t e s on a d a i l y b a s i s would undoubted ly i n c r e a s e t h i s e f f i c i e n c y d i f f e r e n c e . The r e a l s i g n i f i c a n c e of the s i m u l a t i o n r e s u l t s i s the p o t e n t i a l f or water s a v i n g s . The m a j o r i t y of the o r c h a r d i r r i g a t i o n systems now i n o p e r a t i o n in the Okanagan r e g i o n 87 TABLE 4.2: CRITICAL POINTS FOR ORCHARD SYSTEMS WITH M2 ROOTSTOCKS I r r i g a t i o n System sp r i n k i e r t r i c k l e s pr i n k i e r t r i c k l e Base A p p l i c a t i o n L e v e l ( i n . ) 53.33 48.00 29.79 29.79 S o i l Type C r i t i c a l P o i n t ( i n c h e s ) s a n d s a n d s i l t - l o a m s i l t - l o a m 22.50 16.00 14.50 10.25 % of Base Case 42% 30% a r e s p r i n k l e r s y s t e m s . From F i g u r e 4.1 i t can be seen t h a t the base c a s e l e v e l s o f w a t e r a p p l i c a t i o n f o r s p r i n k l e r i r r i g a t i o n on sand and s i l t - l o a m s o i l s ( r e p r e s e n t i n g the p r e s e n t day l e v e l s o f w a t e r a p p l i c a t i o n i n t h e r e g i o n ) l i e f a r t o t h e r i g h t of t h e c r i t i c a l water a p p l i c a t i o n l e v e l s as d e t e r m i n e d by t h e o r c h a r d s i m u l a t i o n r u n s . F o r o r c h a r d systems on s a n d s o i l s u s i n g s p r i n k l e r i r r i g a t i o n , t h e c r i t i c a l w a t er a p p l i c a t i o n l e v e l i s 42% of the base c a s e l e v e l . F o r o r c h a r d s y s t e m s on s i l t - l o a m s o i l s u s i n g s p r i n k l e r i r r i g a t i o n , t h e c r i t i c a l l e v e l i s 30% of t h e base c a s e l e v e l . T h i s i n d i c a t e s t h a t a s u b s t a n t i a l amount of water a p p l i e d t o Okanagan o r c h a r d s i s not r e q u i r e d f o r f r u i t 88 p r o d u c t i o n . T h i s i s c l e a r l y shown by the h o r i z o n t a l p o r t i o n s of the marginal p h y s i c a l product curves i n F i g u r e 4.2. Where the MPP curve i s h o r i z o n t a l , the marginal value product of water i s zero and the p r i c e e l a s t i c i t y of demand f o r water approaches i n f i n i t y . T h i s means that were a small p o s i t i v e volume charge on i r r i g a t i o n water to be implemented, water use would t h e o r e t i c a l l y be s i g n i f i c a n t l y cut back to a p o i n t where the q u a n t i t y of water used would approach the c r i t i c a l l e v e l . I t i s important to note that t h i s r e s u l t would t h e o r e t i c a l l y occur before any of the b e h a v i o u r a l aspects come i n t o p l a y were they not c o n s t r a i n e d . Water use can be s i g n i f i c a n t l y reduced without a f f e c t i n g y i e l d s . From Table 4.2 i t i s noted that standard d e v i a t i o n s of y i e l d , while i n c r e a s i n g as i r r i g a t i o n a p p l i c a t i o n i s reduced, do not account f o r more than 0.1% of t o t a l y i e l d at the c r i t i c a l p o i n t s . Thus while r i s k to producers (as measured by the standard d e v i a t i o n of y i e l d ) i n c r e a s e s i n the model when water a p p l i c a t i o n i s reduced, the i n c r e a s e d r i s k a s s o c i a t e d with water a p p l i c a t i o n r a t e s at the c r i t i c a l l e v e l s i s i n s i g n i f i c a n t to t o t a l y i e l d . 4.3 VALIDATION OF THE WATER RESTRICTED CASES V a l i d a t i o n f o r the water r e s t r i c t e d cases was d i f f i c u l t to accomplish as very few data were a v a i l a b l e on apple orchard y i e l d s under water input r e s t r i c t i o n s . However, one data set does e x i s t f o r apple t r e e s i n the Okanagan r e g i o n , and t h i s 89 data set i s not i n c o r p o r a t e d i n t o the d e s i g n of the model . The Canadian A g r i c u l t u r a l Research S t a t i o n a t Summerland has c a r r i e d out some water r e l a t e d s t u d i e s u s i n g f i e l d l y s i m e t e r s to measure water d r a i n a g e and f e r t i l i z e r l e a c h i n g on M c i n t o s h a p p l e t r e e s under v a r i o u s water a p p l i c a t i o n r e g i m e s . 2 9 The d a t a was c o l l e c t e d d u r i n g over 11 y e a r s b e g i n n i n g i n 1974. For the i n i t i a l 4 y e a r s of the exper iment , t r e e s r e c e i v e d water a p p l i c a t i o n s amounting to 37% of the Summerland d i s t r i c t ' s a l l o w a b l e r a t e . Water a p p l i c a t i o n s were then i n c r e a s e d i n annual s tages u n t i l 100% of the d i s t r i c t ' s a l l o w a b l e a p p l i c a t i o n l i m i t was r e a c h e d . In subsequent seasons the water a p p l i c a t i o n l e v e l was a g a i n reduced u n t i l 50% of the a l l o w a b l e l i m i t was r e a c h e d . D u r i n g the e n t i r e exper iment to d a t e , no d i s c e r n i b l e e f f e c t on t r e e growth or y i e l d a t t r i b u t a b l e to water s t r e s s has been o b s e r v e d , though the l i m i t a t i o n s of the l y s i m e t e r have r e c e n t l y r e s u l t e d i n root boundedness . W h i l e these r e s u l t s t end to support the g e n e r a l c o n c l u s i o n of t h i s t h e s i s that there i s s u b s t a n t i a l o v e r w a t e r i n g i n Okanagan o r c h a r d s , the d i f f e r e n c e s in S t e v e n s o n ' s water r e s t r i c t i o n p r o c e d u r e s and those used i n t h i s t h e s i s l i m i t the attempt to v a l i d a t e t h i s s t u d y . . 2 9 R e s u l t s of t h i s experiment up to 1980 can be found in S t e v e n s o n ' s CWRJ a r t i c l e (1980) . Subsequent c o n v e r s a t i o n s 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 recen t r e s u l t s . 90 4.4 SENSITIVITY ANALYSIS A model ' s r e a c t i o n in terms of outcomes when parameters are v a r i e d over a range i s of key importance to the s t r e n g t h of s i m u l a t i o n r e s u l t s . Model s e n s i t i v i t y t e s t i n g i s most important for parameters whose v a l u e s are u n c e r t a i n . For the model deve loped in t h i s s t u d y , s e n s i t i v i t y a n a l y s i s was c o n s i d e r e d a p p r o p r i a t e for the e v a p o t r a n s p i r a t i o n f a c t o r K, the s lope c o e f f i c i e n t to determine 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 , the t i m i n g f a c t o r T , and the s l o p e and i n t e r c e p t de terming the degree of s t r e s s f a c t o r d . As was the case in a n a l y s i n g the s i m u l a t i o n r e s u l t s d i s c u s s e d e a r l i e r , o n l y M2 o r c h a r d systems a r e c o n s i d e r e d h e r e . S e n s i t i v i t y a n a l y s i s f or M26 o r c h a r d systems gave s i m i l a r r e s u l t s . S e n s i t i v i t y a n a l y s e s f o r the parameters K, f, T , and d were c a r r i e d out u s i n g a s i n g l e season run ( o r c h a r d year 4) r a t h e r than the f u l l o r c h a r d l i f e set s c e n a r i o to a v o i d the problems a n a l y s i s of such a l a r g e amount of d a t a would e n t a i l . S ince these parameters were p r e d i c t e d to be the most c r u c i a l to y i e l d s a t tha t p o i n t where water r e d u c t i o n s s i g n i f i c a n t l y a f f e c t y i e l d s , the s e n s i t i v i t y a n a l y s e s on these parameters was performed at c r i t i c a l p o i n t s as p r e v i o u s l y de termined f o r each o r c h a r d sys tem. S e a s o n a l water a p p l i c a t i o n r a t e s were h e l d to 24 inches and 17 inches for those s p r i n k l e r i r r i g a t e d o r c h a r d systems on sand and s i l t - l o a m s o i l s r e s p e c t i v e l y , and to 18 inches and 13 inches for t r i c k l e i r r i g a t e d o r c h a r d s on sand and s i l t - l o a m s o i l s . 91 The r e s u l t s of the r a n g i n g of these parameters for a l l o r c h a r d systems on y e a r - e n d a c t u a l y i e l d (year 4) are g i v e n in T a b l e 4 . 3 , where the " c o n t r o l case" has a l l parameters set to the v a l u e s used for the o r c h a r d s i m u l a t i o n r u n s . 4 .4 .1 THE EVAPOTRANSPIRATION FACTOR K The 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, as d e r i v e d by Hargreaves (1968) , p r o v i d e s a means of d e t e r m i n i n g e v a p o t r a n s p i r a t i o n from pan e v a p o t r a n s p i r a t i o n d a t a . The v a l u e of K and thus the r e l a t i o n s h i p between pan e v a p o r a t i o n and e v a p o t r a n s p i r a t i o n v a r i e s w i t h i n the p e r i o d of the growing season . To determine s e n s i t i v i t y of the s i m u l a t i o n r e s u l t s to t h i s r e l a t i o n s h i p , K was h e l d c o n s t a n t at 0.75 throughout the growing season . F i g u r e 4.3 p r o v i d e s a g r a p h i c a l d e s c r i p t i o n of both 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 c a s e . The r e s u l t s of t h i s r e s t r i c t i o n are g i v e n i n t a b l e 4 . 3 . The r e s t r i c t i o n on K has a s i g n i f i c a n t impact on the y e a r - e n d y i e l d i n a l l o r c h a r d systems as i n d i c a t e d by the % change from the c o n t r o l case f i g u r e s . By s e t t i n g K=0.75, much h i g h e r e v a p o t r a n s p i r a t i o n r a t e s and thus s o i l m o i s t u r e l o s s e s occur than o c c u r r e d i n the c o n t r o l c a s e . The c o n t r o l case average K v a l u e was a p p r o x i m a t e l y 0 .53 . The magnitude of y i e l d r e d u c t i o n i s g r e a t e s t f o r o r c h a r d systems on sand s o i l s . T h i s i s due to the g r e a t e r water r e t e n t i o n c h a r a c t e r i s t i c s of s i l t - l o a m s o i l s . TABLE 4.3i RESULTS OF PARAMETER 8EN8ITIVITY ANALYSIS ON M2 ORCHARD 8Y8TEM8 IN YEAR 4 OF TREE LIFE CONTROL CASE EVAP0TRAN8PIRATION ACTUAL VS POTENTIAL FACTOR 'K' - 0.73 ET SLOPE COEF. - \ . IRRIGATION SYSTEM SOIL TYPE YIELD <LB8/ACRE> YIELD (LBS/ACRE) X CHANGE FROM CONTROL YIELD <LBS/ACRE) X CHANGE FROM CONTROL . 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 . TRICKLE 6 AND 1366.88 1086.29 -30.BX 1600.00 •2. OX . TRICKLE SILT-LOAM . 1389.21 1239.66 -22. OX 16OO.0O •0. 7X ACTUAL VS POTENTIAL TIMING OF 8TRE88 DEGREE OF 8TREB8 FACTOR ET SLOPE COEF. - 20 FACTOR 'T* - 0.73 g - 1.18 - 1.67*801L MOISTURE . IRRIGATION SYSTEM SOIL TYPE YIELD (LBS/ACRE) X CHANGE FROM CONTROL YIELD (LBS/ACRE) X CHANGE FROM CONTROL YIELD <LBS/ACRE) X CHANGE FROM CONTROL . SPRINKLER SAND 1479.79 -7.4X \ 1363.40 -2. IX '. 1407.07 -11.9X '. . SPRINKLER SILT-LOAM . 1462.43 -6. IX \ 1302.83 -3.3X 1331.63 -13.2X TRICKLE SAND 1437.10 -7. IX 1340.43 -1.8X 1334.80 -13.6X TRICKLE SILT-LOAM . 1309.19 -3. OX 1380.92 -0.3X 1419.03 -10.7X 9 3 K 1.00 0.75 H 0.50 + 0.25 T 25 50 s e n s i t i v i t y 75 100 % of growing season Figure A.3 Evapotranspiration C o e f f i c i e n t K for the Control and S e n s i t i v i t y Analysis Cases 94 4 . 4 . 2 ACTUAL VERSUS POTENTIAL EVAPOTRANSPIRATION SLOPE  COEFFICIENT F The r e l a t i o n s h i p between 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 (PET) and a c t u a l e v a p o t r a n s p i r a t i o n (AET) i s g i v e n by the f o l l o w i n g e q u a t i o n (see s e c t i o n 3 . 3 ) : AET = p * PET The v a l u e of the s o i l m o i s t u r e f a c t o r p depends on s o i l m o i s t u r e and s o i l type as w e l l as PET. The f f a c t o r v a r i e s w i t h s o i l type and i s d e s c r i b e d below: p = f * (SM/AWSC) where SM = s o i l m o i s t u r e l e v e l AWSC = a v a i l a b l e water s torage c a p a c i t y F o r the c o n t r o l c a s e , f was se t to 3 and 5 for sand and s i l t - l o a m s o i l s r e s p e c t i v e l y to account for water h o l d i n g and r e t e n s i o n c h a r a c t e r i s t i c s of the s o i l s . To t e s t the s e n s i t i v i t y of the model , f was a s s i g n e d v a l u e s of 1 and 20 on both s o i l types in s u c c e s s i v e r u n s . F i g u r e 4.4 p r o v i d e s a d i a g r a m a t i c d e s c r i p t i o n of the r e l a t i o n s h i p between the s o i l m o i s t u r e f a c t o r p, s o i l m o i s t u r e SM and the AET-PET s lope c o e f f i c i e n t f . The r e s u l t s of s e t t i n g f at 1 and 20 are g i v e n i n t a b l e 4 . 3 . With f=1, the a c t u a l y i e l d i n c r e a s e s r e l a t i v e to 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 c o n t r o l case for a l l o r c h a r d systems. The i n c r e a s e s are s m a l l s i n c e the c o n t r o l case r e s u l t s are very c l o s e to the maximum p o t e n t i a l y i e l d (1600 l b s for year 4, see T a b l e 3 . 1 ) . The i n c r e a s e i n y i e l d i s due to lower p v a l u e s r e l a t i v e to the c o n t r o l case f o r a l l s o i l m o i s t u r e l e v e l s below f i e l d c a p a c i t y . S i n c e p i s equa l to the r a t i o A E T / P E T , the lower the v a l u e of p, the lower i s the l e v e l of A E T , the water d e p l e t i o n mechanism in the model . When f=20, the v a l u e of p i s equa l to 1.0 (0<p< 1) a t a l l but very low s o i l m o i s t u r e l e v e l s . Thus y i e l d s are lower than the c o n t r o l case l e v e l s . The degree to which y i e l d s are a f f e c t e d ranges between 5.0% and 7.4%. Thus the model does not appear to be o v e r l y s e n s i t i v e to the A E T - P E T s lope coef f i c i e n t . 4 .4 .3 THE TIMING OF STRESS FACTOR T One of the assumpt ions of the model i s t h a t y i e l d can be a f f e c t e d by both the degree and the t i m i n g of water s t r e s s d u r i n g the growing s e a s o n . For the c o n t r o l c a s e , T v a r i e s between 0.10 and 1.00, i n d i c a t i n g the p e r i o d s when apple t r e e s are l e a s t and most v u n e r a b l e to water s t r e s s . For the s e n s i t i v i t y a n a l y s e s , T was set e q u a l to 0.75 f o r the e n t i r e growing season . F i g u r e 4.5 p r e s e n t s 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 c a s e s . The r e s u l t s of s e t t i n g T e q u a l to 0.75 are g i v e n i n T a b l e 4 . 3 . The d e c r e a s e s i n y i e l d r e l a t i v e to the c o n t r o l case range from 0.5% to 3.5%. Thus the t i m i n g of s t r e s s 97 1.00 -r 0.75 c o n t r o l case 0.50 --0.25 s e n s i t i v i t y case , 10 15 20 25 30 35 week of growing season Figure U .5 Le v e l of Stress Factor T Over Growing Season: Control or Base Case and Value Assumed f o r S e n s i t i v i t y Case 98 f a c t o r does not appear to be extremely s e n s i t i v e to parameter v a r i a t i o n i n the range t e s t e d . 4 .4 .4 THE DEGREE OF STRESS FACTOR D As was i n d i c a t e d i n the p r e v i o u s s e c t i o n , the e f f e c t of water s t r e s s on y i e l d i s assumed to have a degree f a c t o r and a t i m i n g f a c t o r . The degree f a c t o r , d , i s assumed to take the form of a l i n e a r r e l a t i o n s h i p between maximum s t r e s s (d=1.0) , when the s o i l m o i s t u r e , SM, i s at or below 10% of 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 , AWSC ( t h i s l e v e l i s termed the permanent w i l t i n g p o i n t , PWP), and n o - s t r e s s (d=0.0) when SM i s at or above 60% of AWSC. To determine the s e n s i t i v i t y of t h i s r e l a t i o n s h i p , the n o - s t r e s s s o i l m o i s t u r e l e v e l was i n c r e a s e d from 60% of AWSC to 70% of AWSC. 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 are g iven i n F i g u r e 4 . 6 . The r e s u l t s of the s e n s i t i v i t y a n a l y s i s are shown i n T a b l e 4 . 3 . The y i e l d r e d u c t i o n s range from 10.7% to 13.6% r e l a t i v e to the c o n t r o l c a s e . The model appears r e l a t i v e l y s e n s i t i v e to t h i s parameter r a n g i n g . The c o n t r o l case n o - s t r e s s parameter i s the I r r i g a t i o n Des ign Manual (1983) recommendation for the minimum o r c h a r d s o i l m o i s t u r e l e v e l . I t was chosen s i n c e i t was f e l t to be a c o n s e r v a t i v e e s t i m a t e of the stage below which water s t r e s s beg ins to o c c u r . The f a c t tha t the model , at these c r i t i c a l water a p p l i c a t i o n l e v e l s , i s s e n s i t i v e to the degree of s t r e s s parameter r a n g i n g i s not of concern s i n c e i t i s a key to a c t u a l y i e l d d e t e r m i n a t i o n . 99 Figure 4.6 Degree of Stress Factor d for the Control Case and the S e n s i t i v i t y Analysis Case 100 The g e n e r a l c o n c l u s i o n drawn from the s e n s i t i v i t y a n a l y s i s per formed on the s e l e c t e d parameters i s one of s t a b i l i t y and r o b u s t n e s s of the model . T h i s i n d i c a t e s that the r e s u l t s of the model are not s u b j e c t to l a r g e f l u c t u a t i o n s w i t h s m a l l parameter v a l u e changes . 4.5 POLICY IMPLICATIONS Assuming p r o d u c e r s are p r o f i t maximizers and r i s k a v e r s e , the r e s u l t s of the model may be i n t e r p r e t e d . P r o f i t m a x i m i z a t i o n i m p l i e s , a l l e l s e b e i n g e q u a l , that i f a g r i c u l t u r a l water was p r i c e d by volume, p r o d u c e r s would reduce water use to a l e v e l where the l o s s of y i e l d p r o f i t was equa l to the s a v i n g s from u s i n g l e s s water . R i s k must a l s o be c o n s i d e r e d . A measure of the r i s k of lower y i e l d s through r e d u c i n g water l e v e l s i s g i v e n by the s t a n d a r d d e v i a t i o n s of y i e l d i n T a b l e 4 . 1 . For s p r i n k l e r o r c h a r d systems at the c r i t i c a l p o i n t s (2% y i e l d r e d u c t i o n w i t h water l e v e l s of 42% for sand and 30% f o r s i l t - l o a m ) s t a n d a r d d e v i a t i o n of y i e l d was l e s s than 0.01%. T h i s i n d i c a t e s t h a t , on a v e r a g e , very l i t t l e r i s k would r e s u l t from these magnitudes of water r e d u c t i o n . The r e s u l t s of the s i m u l a t i o n s show t h a t s i g n i f i c a n t water use r e d u c t i o n s would not a d v e r s e l y a f f e c t Okanagan o r c h a r d y i e l d s . One p o s s i b l e method of e n c o u r a g i n g water c o n s e r v a t i o n i n the r e g i o n i s to i n t r o d u c e a per u n i t water p r i c i n g mechanism. Such a p r i c i n g scheme has the p o t e n t i a l to c u t a g r i c u l t u r a l water use in h a l f . Chapter 5 SUMMARY, CONCLUSIONS, AND SUGGESTIONS FOR FUTURE RESEARCH 5.1 SUMMARY Water i n the Okanagan V a l l e y of B r i t i s h Columbia i s in demand from c o m m e r c i a l , r e s i d e n t i a l , r e c r e a t i o n a l and a g r i c u l t u r a l i n t e r e s t groups . These demands have r e s u l t e d in water use c o n f l i c t s , n o t a b l y between a g r i c u l t u r e and sport f i s h i n g . D i s t r i c t a g r i c u l t u r a l i r r i g a t i o n systems which make use of upper v a l l e y streams can d e p l e t e the water flow to the ex tent of e l i m i n a t i n g f i s h i n g areas d u r i n g the summer months. The a g r i c u l t u r a l s e c t o r has been d e s i g n a t e d as h a v i n g the p o t e n t i a l to reduce water use below c u r r e n t requ irements ( M c N e i l l , 1983). C u r r e n t 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 do not promote water c o n s e r v a t i o n . T h i s i s due to the method by which a g r i c u l t u r a l water i s p r i c e d , the i r r i g a t i o n t echno logy commonly used , and the e n v i r o n m e n t a l i n f l u e n c e s i n the a r e a . A g r i c u l t u r a l water in the Okanagan i s p r i c e d u s i n g a f l a t r a t e mechanism. For a per a c r e f ee , the user i s a l l owed to make use of a d e s i g n a t e d volume of w a t e r . The amount of water a l l o t t e d per acre i s de termined by the water r e q u i r e d d u r i n g the h o t t e s t , d r i e s t h i s t o r i c a l p e r i o d i n the r e g i o n u s i n g a r o t a t i o n a l i r r i g a t i o n method. The user has , f or the f l a t r a t e f e e , a c c e s s to t h i s maximum r e q u i r e d amount of water throughout the growing season , r e g a r d l e s s of weather 101 1 02 c o n d i t i o n s . The most common i r r i g a t i o n t e c h n o l o g y p r e s e n t l y used in the Okanagan i s s p r i n k l e r i r r i g a t i o n . Because the d i s t r i c t i r r i g a t i o n systems are unable to p r o v i d e s u f f i c i e n t water f low r a t e s to enable i r r i g a t i o n of e n t i r e o r c h a r d s at one t ime u s i n g s p r i n k l e r s , r o t a t i o n a l i r r i g a t i o n must be p r a c t i c e d . T h i s i n v o l v e s i r r i g a t i n g the o r c h a r d i n s e c t i o n s i n a s y s t e m a t i c way over a p e r i o d of d a y s . Because weather c o n d i t i o n s cannot be f o r c a s t w i t h a b s o l u t e c e r t a i n t y , the r i s k of c r o p damage from water s t r e s s i s m i n i m i z e d by a p p l y i n g the maximum a l l o w a b l e i r r i g a t i o n a l l o t m e n t to each o r c h a r d s e c t i o n d u r i n g each r o t a t i o n . Only v e r y r a r e l y i s t h i s amount of i r r i g a t i o n n e c e s s a r y . Damage to t r e e s from excess i r r i g a t i o n i s minimal due to c h a r a c t e r i s t i c a l l y good d r a i n a g e i n the r e g i o n . Thus the use of s p r i n k l e r i r r i g a t i o n under the presen t a g r i c u l t u r a l i r r i g a t i o n water p r i c i n g scheme encourages maximum water use . The main o b j e c t i v e of t h i s t h e s i s was to a n a l y s e the w a t e r - y i e l d r e l a t i o n s h i p i n t r e e f r u i t s . To a c c o m p l i s h t h i s o b j e c t i v e , a model was c o n s t r u c t e d to s i m u l a t e an a c t u a l o r c h a r d p r o d u c t i o n p r o c e s s . Other o b j e c t i v e s of the t h e s i s were: to de termine a c t u a l o r c h a r d water needs and compare these w i t h p r e s e n t water a p p l i c a t i o n r a t e s ; to compare s p r i n k l e r i r r i g a t i o n and t r i c k l e i r r i g a t i o n i n terms of w a t e r - y i e l d i n p u t / o u t p u t r e l a t i o n s h i p s ; and to i n v e s t i g a t e a l t e r n a t i v e a g r i c u l t u r a l water p r i c i n g s t r a t e g i e s w i th the 1 03 aim of promot ing water c o n s e r v a t i o n . The r e s e a r c h method c o n s i s t e d of s i m u l a t i n g the y i e l d response of s e v e r a l orchard systems to a s e r i e s of d e c r e a s i n g 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 s . Each o r c h a r d system c o n s i s t e d of one of two r o o t s t o c k s , two s o i l t y p e s , and two i r r i g a t i o n t y p e s . The r e s u l t s of the s i m u l a t i o n run at each i r r i g a t i o n l e v e l were t a b u l a t e d and graphed a c c o r d i n g to o r c h a r d system, thereby p r o d u c i n g a s e r i e s of w a t e r - y i e l d p r o d u c t i o n f u n c t i o n s . Based on the r e s u l t s from o t h e r s t u d i e s , 3 0 both the degree of water s t r e s s and the t i m i n g of water s t r e s s d u r i n g the growing season were taken i n t o c o n s i d e r a t i o n when c a l c u l a t i n g y e a r l y o r c h a r d y i e l d . The method of d e t e r m i n i n g the presence and degree of water s t r e s s was based on F l i n n (1971) . T h i s method i n v o l v e d the d e t e r m i n a t i o n of the d a i l y l e v e l of s o i l mo i s ture d u r i n g the growing season by add ing i r r i g a t i o n and r a i n f a l l i n p u t s 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 o u t f l o w . By c a l i b r a t i n g s o i l m o i s t u r e to a yield reduction factor, t a k i n g i n t o c o n s i d e r a t i o n both degree and t i m i n g of water s t r e s s , and summing these over the growing s eason , a v a l u e for year end y i e l d ( p o t e n t i a l n o - s t r e s s y i e l d l e s s y i e l d l o s t due to water s t r e s s ) can be c a l c u l a t e d . The da ta used for t h i s t h e s i s can be grouped i n t o three c a t e g o r i e s . Y i e l d data for a p p l e t r e e s was o b t a i n e d from the B r i t i s h Columbia M i n i s t r y of A g r i c u l t u r e and Food (BCMAF) 3 0 A s s a f et a l (1975) , Goode (1975) , M i c h e l l (1984) 1 04 Estimated Costs and Returns for Apple Orchard Establishment and Production, Okanagan Valley (May, 1984). T h i s data was a d j u s t e d a f t e r d i s c u s s i o n s w i t h 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 to b e t t e r r e f l e c t a c t u a l y i e l d s for M2 and M26 r o o t s t o c k s over 20 y e a r s . The second data c a t e g o r y i s the t e c h n i c a l data needed to de termine base case water a p p l i c a t i o n r a t e s . T h i s data was a c q u i r e d from the BCMAF Irri gati on Design Manual (1983) . The l a s t data c a t e g o r y i s the weather data o b t a i n e d from the Atmospher ic Environment S e r v i c e of Environment Canada . T h i s data c o n s i s t e d of d a i l y t o t a l p r e c i p i t a t i o n (mm) and maximum temperature (degrees C) r e a d i n g s for Kelowna, B r i t i s h Columbia f o r the y e a r s 1899, 1900, 1903-1932, 1934-1961, 1969-1983. M i s s i n g years were due to u n a v a i l a b i l i t y a n d / o r incomple te d a t a . T h i s data was used by the weather generator which p r o v i d e d p r e c i p i t a t i o n and e v a p o t r a n s p i r a t i o n input for the c a l c u l a t i o n of d a i l y s o i l m o i s t u r e l e v e l s . The r e s u l t s of the s i m u l a t i o n runs i n d i c a t e d t h a t , f o r o r c h a r d s i n the Okanagan r e g i o n , s u b s t a n t i a l r e d u c t i o n s in c u r r e n t i r r i g a t i o n water a p p l i c a t i o n s are p o s s i b l e wi thout r e d u c i n g y i e l d s or chang ing p r e s e n t s p r i n k l e r i r r i g a t i o n sys tems . For s p r i n k l e r i r r i g a t e d o r c h a r d systems, water a p p l i c a t i o n s amounting to 42% of p r e s e n t day i r r i g a t i o n r a t e s on sand s o i l s and 30% on on s i l t - l o a m s o i l s r e s u l t e d i n a 2% r e d u c t i o n i n the average y i e l d over a 20 year 1 05 p e r i o d . To a c h i e v e the same y i e l d s on l i k e s o i l s , t r i c k l e i r r i g a t i o n ( a p p l y i n g water a t a c o n s t a n t r a t e throughout the growing season) was found to r e q u i r e 71% of s p r i n k l e r r a t e s . 5.2 CONCLUSIONS The f i n d i n g s of t h i s s tudy i n d i c a t e s u b s t a n t i a l water use r e d u c t i o n s are p o s s i b l e i n the Okanagan t r e e f r u i t s e c t o r , and t h a t such water use r e d u c t i o n s can be a c c o m p l i s h e d wi thout r e d u c i n g mean o r c h a r d y i e l d s . C u r r e n t water use l e v e l s would appear to be the r e s u l t of annual f i x e d user f e e s , which p r o v i d e l i t t l e i n c e n t i v e for water c o n s e r v a t i o n on the p a r t of o r c h a r d i s t s . R e s u l t s of t h i s a n a l y s i s show t h a t water r e d u c t i o n s i n the o r d e r of 50% r e s u l t e d i n no s i g n i f i c a n t decrease i n t r e e f r u i t y i e l d s . I f p r o d u c e r s pay a per u n i t i r r i g a t i o n fee f o r use of water i n q u a n t i t i e s beyond the p o i n t where the m a r g i n a l v a l u e product approaches z e r o , water demand c o u l d t h e o r e t i c a l l y be reduced to a more e f f i c i e n t l e v e l in terms of y i e l d per u n i t of water a p p l i e d , based on the m a r g i n a l p h y s i c a l p r o d u c t f u n c t i o n d e r i v e d . The a s s e r t i o n i s tha t the p r i c e e l a s t i c i t y of demand for water i s very l a r g e at the p o i n t of p r e s e n t day i r r i g a t i o n water a p p l i c a t i o n l e v e l s and thus the a d d i t i o n of a s m a l l per u n i t user fee for water would r e s u l t i n a l a r g e r e d u c t i o n i n water use . However, the p r e d i c t e d impact upon i r r i g a t i o n water use i s u n c e r t a i n s i n c e the m a r g i n a l va lue of water i s unknown. Present a g r i c u l t u r a l water charges cover the 1 06 v a r i a b l e c o s t s of s u p p l y . The e f f e c t a per u n i t water p r i c e s t r u c t u r e , based on presen t f l a t r a t e p r i c e s and vo lumes , would have on water use i n the V a l l e y i s not c l e a r . O r c h a r d water c o s t s r e p r e s e n t a s m a l l p o r t i o n of t o t a l p r o d u c t i o n c o s t s ( g e n e r a l l y l e s s than $100 a n n u a l l y per a c r e ) . The p e r c e i v e d r i s k of water s t r e s s may w e l l outweigh s a v i n g s i n water c o s t s through i r r i g a t i o n r e d u c t i o n s . The m a r g i n a l v a l u e of water i n the Okanagan l i k e l y v a r i e s r e g i o n a l l y w i t h demand. Without i n f o r m a t i o n on m a r g i n a l v a l u e s , the p r e d i c t e d outcome of p r i c i n g i r r i g a t i o n water by volume and at what l e v e l water p r i c i e s s h o u l d be set i s not c e r t a i n . T h e r e f o r e , w h i l e the r e s u l t s of t h i s t h e s i s p o i n t toward a p o s s i b l e p o l i c y for promot ing water c o n s e r v a t i o n , the e f f e c t i v e n e s s of such a p o l i c y depends on the m a r g i n a l v a l u e of water . The f a v o u r a b l e r e s u l t s of t r i c k l e v e r s u s s p r i n k l e r i r r i g a t i o n methods w i t h r e s p e c t to water use e f f i c i e n c y suggest that p o l i c i e s promot ing the a d o p t i o n of t r i c k l e i r r i g a t i o n systems (apart from implement ing a per u n i t user fee which may p o s i t i v e l y a f f e c t the r a t e of t r i c k l e i r r i g a t i o n a d o p t i o n ) c o u l d r e s u l t i n decreased Okanagan a g r i c u l t u r a l water use i n the l onger t erm. The method of water p r i c i n g i s one of the key reasons why l i t t l e i n c e n t i v e e x i s t s for p r o d u c e r s to conserve water by r e d u c i n g a p p l i c a t i o n l e v e l s . T h i s i s not to imply t h a t a p r o d u c e r i n c u r s zero c o s t by a p p l y i n g water beyond the o r c h a r d ' s r e q u i r e m e n t s . In the s h o r t r u n , f e r t i l i z e r l o s s 1 07 through water d r a i n a g e i s a c o s t to the o r c h a r d o p e r a t i o n . A longer run e f f e c t of excess water a p p l i c a t i o n i s the s u b s t a n t i a l l o w e r i n g of s o i l pH l e v e l s . Whi le these might be termed d i r e c t c o s t s which the producer bears w i t h o v e r - w a t e r i n g , i n d i r e c t e f f e c t s must a l s o be c o n s i d e r e d . The e n v i r o n m e n t a l impact of f e r t i l i z e r and other c h e m i c a l s e n t e r i n g the v a l l e y water system may have h e a l t h and r e c r e a t i o n a l consequences . L o s s e s to the s p o r t f i s h i n g i n d u s t r y from l a t e summer water shor tages i n streams and l a k e s i s a l s o an ' e x t e r n a l i t y ' which shou ld be i n c l u d e d i n a d i s c u s s i o n of the c o s t s to the producer of o v e r - w a t e r i n g . When these c o s t s are i n c l u d e d , the p r o s p e c t of water p r i c i n g by the u n i t , i n s o f a r as i t i s not d e t r i m e n t a l to the producer in terms of y i e l d s and p r o f i t s , would appear to be p a r e t o o p t i m a l . The r e s u l t s thus f a r have been d i r e c t e d toward the Okanagan r e g i o n a n d , i n p a r t i c u l a r , f r u i t growing w i t h i n tha t r e g i o n . However, the p o l i c y i m p l i c a t i o n s o u t l i n e d i n the p r e v i o u s s e c t i o n can be g e n e r a l i z e d to a p p l y , at l e a s t i n p r i n c i p l e , to a l l a g r i c u l t u r e i n hot dry areas where f i x e d i r r i g a t i o n user fees a r e u s e d . The uniqueness of the Okanagan case i s tha t i r r i g a t i o n water i s d e l i v e r e d p r e s s u r i z e d to users and thus there i s an absence of pumping c o s t s o f t e n r e l a t e d to i r r i g a t i o n water use . Where such pumping c o s t s are p r e s e n t , an i m p l i c i t per u n i t user fee a l r e a d y e x i s t s and thus more e f f i c i e n t water use i s l i k e l y . 1 08 5.3 RECOMMENDATIONS FOR FUTURE RESEARCH Whi le s i m u l a t i o n has been used as a t echn ique to p r e d i c t y i e l d response i n many annua l c r o p s , p a r t i c u l a r l y c o r n and wheat, no a t tempts at s i m u l a t i n g t r e e f r u i t p r o d u c t i o n were found i n l i t e r a t u r e s earches by t h i s a u t h o r . T h i s t h e s i s may t h e r e f o r e r e p r e s e n t an i n i t i a l attempt at s i m u l a t i o n of an o r c h a r d env ironment . The model deve loped to s i m u l a t e the w a t e r - y i e l d r e l a t i o n s h i p i n apple p r o d u c t i o n uses a v a r i e t y of i n f o r m a t i o n s o u r c e s . The model makes use of r e s u l t s from s t u d i e s on t r e e f r u i t p h y s i o l o g i c a l r e l a t i o n s h i p s and a system for i n c o r p o r a t i n g h i s t o r i c a l weather da ta u s i n g a random s e l e c t i o n p r o c e s s . A key assumption of the mode l , the p o i n t at which l o w e r i n g the s o i l moi s ture l e v e l w i l l r e s u l t i n water s t r e s s , i s taken from the B . C . M i n i s t r y of A g r i c u l t u r e ' s I r r i g a t i o n Des ign Manua l . The use of B . C . M i n i s t r y of A g r i c u l t u r e sources p r o v i d e s a "safe ty f a c t o r " to the r e s u l t s . The c o n s e r v a t i v e assumption on the t h r e s h o l d s o i l m o i s t u r e l e v e l f o r water s t r e s s p r o b a b l y e r r s toward more water b e i n g r e q u i r e d than i s a c t u a l l y the c a s e . T h i s would l e s s e n the degree of presen t day o v e r w a t e r i n g as c a l c u l a t e d by the mode l . A p a r t from the i n s i g h t s i n t o the app le p r o d u c t i o n p r o c e s s which the model p r o v i d e s , the main va lue of the work l i e s i n the s i m u l a t i o n p r o c e d u r e and the i m p l i c a t i o n s of those r e s u l t s . The i m p l i c a t i o n s of the r e s u l t s for p o l i c y are that they i n d i c a t e t h a t excess water use o c c u r s i n Okanagan t r e e f r u i t p r o d u c t i o n . T h i s s i t u a t i o n , which 109 appears to be the r e s u l t of a f l a t r a t e p r i c i n g mechanism toge ther w i t h o t h e r e n v i r o n m e n t a l f a c t o r s , c o u l d be remedied through a per volume water p r i c i n g reg ime. However, the v a l u e of the r e s u l t s depend on the v a l i d i t y of the model i n s i m u l a t i n g t r e e f r u i t p r o d u c t i o n . As was noted i n c h a p t e r 4, no data are c u r r e n t l y a v a i l a b l e which c o u l d p r o v i d e a means of t h o r o u g h l y v a l i d a t i n g the model . The "next best" a v a i l a b l e da ta a g a i n s t which a comparison of the model r e s u l t s can be made are s t u d i e s by Stevenson (1980) . W h i l e these s t u d i e s suppor t the model r e s u l t s , the exact shape and p o s i t i o n of the e s t i m a t e d p r o d u c t i o n f u n c t i o n are open to q u e s t i o n . The p o i n t a t which water becomes c r i t i c a l to o r c h a r d p r o d u c t i o n (the c r i t i c a l p o i n t ) i s the key r e s u l t of the model . T h i s r e s u l t has some s u p p o r t i n g da ta from o t h e r s t u d i e s , as d i s c u s s e d above . For the p o r t i o n of the p r o d u c t i o n f u n c t i o n to the r i g h t of the c r i t i c a l p o i n t , the s i m u l a t i o n r e s u l t s of c o n s t a n t average y e a r l y y i e l d s when more water i s a p p l i e d beyond the c r i t i c a l p o i n t water l e v e l i s a l s o s u p p o r t a b l e . Stevenson (1980) found tha t no d e c l i n e i n t r e e development or p r o d u c t i o n o c c u r e d when water a p p l i c a t i o n s were reduced to one t h i r d of normal a p p l i c a t i o n l e v e l s . T h i s i m p l i e s tha t the p r o d u c t i o n f u n c t i o n f o r the t r e e s i n the exper iment was h o r i z o n t a l w i t h i n t h i s water a p p l i c a t i o n range . R e f e r r i n g to F i g u r e 2.2 i n chapter 2, the p o r t i o n of the p r o d u c t i o n f u n c t i o n to the l e f t of the c r i t i c a l p o i n t 1 10 f a l l s o f f s h a r p l y w i t h f u r t h e r decreases i n water a p p l i c a t i o n l e v e l s . As has been d i s c u s s e d e a r l i e r , i t i s t h i s p o r t i o n of the p r o d u c t i o n f u n c t i o n w h i c h , due to the c o n s t r a i n t of h o l d i n g a l l o ther o r c h a r d p r o d u c t i o n i n p u t s c o n s t a n t , u n d e r - e s t i m a t e s p r o d u c t i o n at these i r r i g a t i o n l e v e l s . T h i s s i t u a t i o n a r i s e s s i n c e , by a l l o w i n g o n l y water a p p l i c a t i o n l e v e l s to change, the e f f e c t on y i e l d of the o r c h a r d i s t a d j u s t i n g the "other input" mix i s not accounted f o r . T h i s type of b i a s does not occur f o r t h a t p o r t i o n of the p r o d u c t i o n f u n c t i o n to the r i g h t of the c r i t i c a l p o i n t s i n c e a maximum y i e l d , as d e p i c t e d at p o i n t Q* f o r a g i v e n t echno logy s e t , i s a t t a i n e d and cannot be i n c r e a s e d . From the above d i s c u s s i o n , i t i s c o n c l u d e d t h a t the p o r t i o n of the p r o d u c t i o n f u n c t i o n to the r i g h t of the c r i t i c a l p o i n t a c c u r a t e l y d e p i c t s the o r c h a r d p r o d u c t i o n p r o c e s s . The v a l u e f o r p o l i c y i s that y i e l d s are u n a f f e c t e d by h a l v i n g c u r r e n t water a p p l i c a t i o n l e v e l s . The major weakness of the model i s t h a t t h e r e i s a l a c k of r e a d i l y a v a i l a b l e da ta for v a l i d a t i o n p u r p o s e s . The l i k e l i h o o d of a d e t a i l e d set of growth and y i e l d da ta f o r Okanagan t r e e f r u i t s s u b j e c t e d to a v a r i e t y of i r r i g a t i o n regimes over a m u l t i - y e a r p e r i o d becoming a v a i l a b l e in the f o r s e e a b l e f u t u r e seems remote. Without such d a t a thorough v a l i d a t i o n i s not p o s s i b l e . The second major a r e a of the model which c o u l d b e n e f i t from f u t u r e work r e l a t e s to tha t p o r t i o n of the e s t i m a t e d p r o d u c t i o n f u n c t i o n to the l e f t of the c r i t i c a l p o i n t . T h i s 111 r e g i o n i s c o n s i d e r e d to have a downwards b i a s due to the i n a b i l i t y of the model to i n c o r p o r a t e changes to n o n - i r r i g a t i o n i n p u t s d u r i n g h i g h water s t r e s s p e r i o d s . The dynamic approach n e c e s s a r y to i n c l u d e such a r e a c t i v e aspec t to the model would r e q u i r e e x t e n s i v e model r e w o r k i n g . The b e n e f i t s of i n c o r p o r a t i n g such b e h a v i o r a l a s p e c t s in a dynamic framework may not outweigh the c o n s i d e r a b l e work r e q u i r e d g i v e n the c o n s i d e r a b l e p o l i c y i m p l i c a t i o n s of the presen t mode l . ' F i n a l l y , the b r e a d t h of the presen t r e s u l t s c o u l d be extended by a d a p t i n g the model to handle c r o p s o ther than t r e e f r u i t s . 3 1 T h i s would i n v o l v e a l t e r i n g w a t e r - y i e l d and i r r i g a t i o n system parameters for the p a r t i c u l a r c r o p in q u e s t i o n . Use of weather data from d i f f e r e n t r e g i o n s would p r o v i d e a s p a t i a l b r e a d t h to the mode l . 3 1 A v e r s i o n of the model used for t h i s t h e s i s e n t i t l e d WYSPAC (Water Y i e l d S i m u l a t i o n for P e r e n n i a l and Annual Crops) has s i n c e been deve loped for the I n l a n d Waters D i r e c t o r a t e , V a n c o u v e r . REFERENCES A g r a w a l , R . C . and E . O . Heady. Operati ons Research Methods for Agricultural Decisions. Ames, Iowa: Iowa State' U n i v e r s i t y P r e s s , 1972. A n d e r s o n , J . R . " S i m u l a t i o n : Methodology and A p p l i c a t i o n in 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 Economics , 42:1 (March 1974):3~38. A s s a f , R . , I . L e v i n and B. B r a v d o . " E f f e c t of I r r i g a t i o n Regimes on Trunk and F r u i t Growth R a t e s , Q u a l i t y and Y i e l d of Apple T r e e s , " J . of H o r t . S c . 50 (19 7 5 ) : 4 8 1 - 9 3 . B e t h e l , R . , et a l . "Water C o n s e r v a t i o n and Management for F o o t h i l l O r c h a r d s , " C a l i f o r n i a A g r i c u l t u r e 33:10 ( 1 9 7 9 ) : 7 - 9 . 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 and F o o d , A g r i c u l t u r a l E n g i n e e r i n g B r a n c h . Irrigation Design Manual, r e v i s e d 1983. 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 and F o o d , Economics B r a n c h . Est imat ed Costs and Returns Apple Orchard Establishment and Production, Okanagan Valley. May 1984. 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 and F o o d , A g r i c u l t u r a l E n g i n e e r i n g B r a n c h . Engineering Notes. V a r i o u s pamphle t s . Canada . Department of the Env ironment , Atmospher i c Environment S e r v i c e . Temperature and Precipitation Bri t i sh Col umbi a 1941-1970. C a r r u t h e r s , I . and C . C l a r k . The Economi cs of Irrigation. 2d e d . L i v e r p o o l : L i v e r p o o l U n i v e r s i t y P r e s s , 1981. C h i l d s , R . A . , et a l . "A Dynamic Programming Approach To Apple O r c h a r d Replacement ." A . E . Res . 83 -11 . I t h a c a N . Y . : Department of A g r i c u l t u r a l E c o n o m i c s , N . Y . C o l l e g e of A g r i c u l t u r e and L i f e S c i e n c e s , C o r n e l l U n i v e r s i t y , January 1983. C o p e l a n d , T . E . and J . F . Weston. Financial Theory and Corporate Policy. 2d e d . R e a d i n g , M a s s . : Add i son-Wes l ey Pub. C o . , 1983. E n g l i s h , B . C . and D. D v o s k i n . " N a t i o n a l and R e g i o n a l Water P r o d u c t i o n F u n c t i o n s R e f l e c t i n g Weather C o n d i t i o n s . . . M i s c e l l a n e o u s R e p o r t . " Ames Iowa: The C e n t r e for A g r i c u l t u r a l and R u r a l Development , Iowa S t a t e U n i v e r s i t y , 1977. 112 1 1 3 F u n t , R . C , D . S . Ross and H . L . B r o d i e . "Economic Comparison 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 of S i x F r u i t Crops i n M a r y l a n d . " MP950, C o l l e g e Park M a r y l a n d : U n i v e r s i t y of M a r y l a n d , J u l y 1980. G e r l i n g , W.D. "An A n a l y s i s of Apple O r c h a r d R e p l a n t i n g C o s t s and P o t e n t i a l P r o f i t a b i l i t y . " A . E . E x t . 81-26, r e v i s e d , I t h a c a N . Y . : Department of A g r i c u l t u r a l Economics , N . Y . S t a t e C o l l e g e of A g r i c u l t u r e and L i f e S c i e n c e s , C o r n e l l U n i v e r s i t y , 1981. Goode, J . E . "Water S t o r a g e , Water S t r e s s and Crop Responses to I r r i g a t i o n . " In Climate and the Orchard; Effects of climate on fruit tree growth and cropping in Eastern England, r e s e a r c h review n o . 5 , e d . H . C P e r e i r a . Eas t M a i l i n g , Kent E n g l a n d : Commonwealth Bureau of H o r t i c u l t u r e and P l a n t a t i o n C r o p s , 1975. H a r g r e a v e s , G . H . "Consumption Use D e r i v e d From E v a p o r a t i o n Pan D a t a , " J . of the I r r i g a t i o n and D r a i n a g e D i v i s i o n , P r o c e e d i n g s of the American S o c i e t y of C i v i l E n g i n e e r s , 1 (Mar 1968): 97-105. L e f t w i c h , R . H . and R . D . E c k e r t . The Price System and Resource Allocation. New Y o r k : Dryden P r e s s , 1982. Mapp, H . P . and V . R . Eidman. "A Bioeconomic S i m u l a t i o n A n a l y s i s of R e g u l a t i n g Groundwater I r r i g a t i o n , " Amer. J . A g r . 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 Comparison 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 for Apple O r c h a r d s . " b u l . no .0895 , P r o s s e r Washington: 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 U n i v e r s i t y , 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 of R e g u l a t e d Water D e f i c i t s on Pear T r e e Growth, F l o w e r i n g , F r u i t Growth, and Y i e l d , " J . Amer. Soc . H o r t . S c i . 109:5 (1984):604-606. Moore , C V . "A G e n e r a l A n a l y t i c a l Framework for 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 for 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 (1961):876-88 . P r o e s t i n g , E . L . , J . E . M i d d l e t o n and S. R o b e r t s . " A l t e r e d F r u i t i n g C h a r a c t e r i s t i c s of D e l i c i o u s A p p l e A s s o c i a t e d w i t h I r r i g a t i o n Method ," H o r t s c i e n c e 12:4 (Aug. 1977):349-50. S t e v e n s o n , D . S . " P r i n c i p l e s of T r i c k l e I r r i g a t i o n D e s i g n . " Paper p r e s e n t e d to Canadian S o c i e t y of A g r i c u l t u r a l E n g i n e e r s , V i c t o r i a B . C . , Aug . 1973. 1 1 4 S t e v e n s o n , D.S. and D.M. Munn. Evapotranspiration and Evaporation: Weekly summaries for Southern British Columbia from 1969 to 1977. A g r i c u l t u r e Canada, S o i l S c i e n c e and A g r i c u l t u r a l E n g i n e e r i n g S e c t i o n , A g r i c u l t u r e Canada R e s e a r c h S t a t i o n , Summerland B.C., Nov. 1978. S t e v e n s o n , D.S. " I r r i g a t i o n E f f i c i e n c y i n O r c h a r d s , " C a n a d i a n Water R e s o u r c e s J . 5:3 ( 1 9 8 0 ) : 102-10. S w a l e s , J . E . Commercial Apple Growing in British Columbia. V i c t o r i a B.C.: B.C. Dep t . -of A g r i c u l t u r e , H o r t i c u l t u r a l B r a n c h , 1978. V a r i a n , H.R. Micr oeconomi c Analysis. 2d e d . New Y o r k : W.W. N o r t o n & Co. I n c . , 1984. W i n t e r , E . J . Water, Soil and the Plant. London: M a c M i l l a n P r e s s , 1974. PERSONAL COMMUNICATION Kennedy, G. P r o f e s s o r o f A g r i c u l t u r a l E c o n o m i c s , U . B . C , V a n c o u v e r , B.C. Van d e r G u l i k , T. BCMAF E n g i n e e r i n g B r a n c h , A b b o t s f o r d , B.C. 115 Appendijt A: Model Ctxig Dt MENSION 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 ) R E A L A Y T O T , H A R V C , N E T , F , F C , I N T C P T , S L O P E , W A T E R , I R R G ( 1 7 , 1 7 ) . W A T S A V 11RRTOT, N P V , N P V T O T , N P V O U T , P A N ( 2 0 , 2 4 5 ) , R A I N ( 2 0 , 2 4 5 ) , T W A T E R , E X I R R 2 Y L D T O T , 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 ) , 3 F I V E ( 5 0 , 9 ) , S I X ( 5 0 , 9 ) , S E V E N ( 5 0 , 9 ) , E I G H T ( 5 0 , 9 ) , O U T ( 9 ) , S E E D , 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 ) , 5 Y W N P V 4 ( 5 0 , 2 ) , Y W N P V 5 ( 5 0 , 2 ) , Y W N P V 6 ( 5 0 , 2 ) , Y W N P V 7 ( 5 0 , 2 ) , Y W N P V 8 ( 5 0 , 2 INTEGER Y E A R , I , M O D E L , D A Y , J , C O U N T , N , Y , W E A G E N , I R R D A Y 91 F O R M A T ( 2 F 8 . 2 , F 1 0 . 2 ) 92 FORMAT( ' MODEL - ' , 1 2 ) 93 FORMAT ( ' 0 NPV ' , ' A V G ' , ' SD ' , ' Y I E L D ' , 1 ' AVG ' , ' SD ' , ' WATER ' , ' A V G ' , ' S D ' ) 94 F O R M A T ( I 7 , I 3 , I 2 , I 3 , I 6 , 3 0 I 7 ) 95 F O R M A T ( ' O ' ) 96 FORMAT( ' 1 1 ) 97 F O R M A T ( F 1 6 . 2 , F 1 0 . 2 , F 6 . 2 , 2 F 1 0 . 2 , F 6 . 2 , 2 F 7 . 2 , F 6 . 2 ) 98 F 0 R M A T ( F 1 6 . 2 , F I 2 . 2 ) 99 FORMAT ( ' 0 N P V Y I E L D ' , ' N P V W A T E R " ) DO 10 1 - 1 , 1 2 0 0 R E A D ( 2 , 9 4 ) I W E A G DO 11 J =1 ,35 W E A G E N ( I , J ) 1 I W E A G ( J ) 11 C O N T I N U E 10 CONTINUE DO 20 1 - 1 , 2 0 R E A D ( 3 , 9 l ) X M 2 R E A D ( 4 , 9 1 ) X M 2 6 DO 21 '-J-1 , 3 D M 2 ( I , J ) - X M 2 ( J ) D M 2 6 ( I , J ) - X M 2 6 ( J ) 21 C O N T I N U E 20 C O N T I N U E C DM2 AND DM26 A R E 5 BY 2 0 ( Y E A R S ) C O S T M A T I C E S FOR M2 AND M26 ORCHART S E E D - 1 . 1 DO 90 Y - 1 , 1 0 C A L L W E A T H R ( P A N , R A I N , W E A G E N , S E E D ) DO 100 M O D E L - 1 , 8 C 8 M O D E L S R E P R E S E N T I N G 2 S O I L T Y P E S , 2 I R R I G A T I O N S Y S T E M S AND 2 ROO: C S T O C K S . HARVC=0 • C I N I T I A L I Z E H A R V E S T C O S T S N P V T O T - 0 C I N I T I A L I Z E T H E N E T N P V T O T A L N P V Y L D - 0 C N P V Y L D IS T H E NPV O F Y I E L D N P V W A T - 0 C NPVWAT IS T H E NPV O F WATER DO 110 1 - 1 , 1 7 G T O T ( 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 C O N T I N U E C A L L M O D E L S ( N , F , F C , W A T E R , M O D E L , T W A T E R ) C A L L I R R G A T ( N , W A T E R , T W A T E R , I R R G ) Y L D T O T - 0 W A T T O T - 0 DO 120 Y E A R - 1 , 2 0 116 Appendix A (continued) C 20 Y E A R S C O N S T I T U T E S O N E ORCHARD L I F E . EXIRR=>0 C EXIRR K E E P S T R A C K OF E X C E E S S I R R I G A T I O N DO 130 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 Y L D R E D ( I ) « 0 C I N I T I A L I Z E Y I E L D R E D U C T I O N F A C T O R A W S C ( I ) = F C 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 C O N T I N U E I R R D A Y * 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 FOR T H E I R R I G A T I O N M A T R I X DO 140 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 I F ( J . G T . N ) J « ! C A L L Y I E L D { N , A W S C , F , F C , J , G T O T , Y L D R E D , D A Y , I R R G , P A N , R A I N , I R R D A Y , 1 Y E A R , E X I R R ) 140 C O N T I N U E C A L L 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 Y , W A T S A V ) C A L L Y R T O T ( M O D E L , N , Y E A R , A C T Y L D , G T O T , Y L D R E D , D M 2 , D M 2 6 , A Y T O T , H A R V 1 N E T ) N P V * N E T / ( ( 1 + . 0 6 ) * * Y E A R ) N P V T O T = N P V T O T + N P V • N P V Y L D » N P V Y L D + A Y T O T / ( ( 1 + . 0 6 ) * * Y E A R ) N P V W A T = N P V W A T + W A T S A V / ( (1 + . 0 6 ) * * Y E A R ) Y L D T O T = Y L D T O T + A Y T O T W A T T O T - W A T T O T + W A T S A V 120 C O N T I N U E Y L D T O T = Y L D T O T / 2 0 W A T T O T = W A T T O T / 2 0 * C C the f o l l o w i n g f i l l s a 5 0 x 8 matrix of N P V s for a l l orchard models C I F ( M O D E L . N E . 1 ) G O T O 901 O N E ( Y , 1 ) = N P V T 0 T - 5 6 9 1 . 9 7 O N E ( Y , 4 ) " Y L D T O T O N E ( Y , 7 ) = W A T T O T C A L L M A T C A L ( O N E , Y ) Y W N P V 1 ( Y , 1 ) « N P V Y L D Y W N P V l . ( Y , 2 ) = N P V W A T G O T O 100 901 I F ( M O D E L . N E . 2 ) G O T O 9 0 2 T W O ( Y , 1 ) = N P V T O T - 5 6 9 l . 9 7 T W O ( Y , 4 ) « Y L D T O T T W O ( Y , 7 ) = W A T T O T C A L L M A T C A L ( T W O , Y ) Y W N P V 2 ( Y , 1 ) = N P V Y L D Y W N P V 2 ( Y , 2 ) - N P V W A T G O T O 100 902 I F ( M O D E L . N E . 3 ) G O T O 9 0 3 T H R E E ( Y , 1 ) - N P V T O T - 5 7 3 6 . 8 3 T H R E E ( Y , 4 ) • Y L D T O T T H R E E ( Y , 7 ) « W A T T O T C A L L M A T C A L ( T H R E E , Y ) 117 Append ix A (continued) Y W N P V 3 ( Y , 1 ) = N P V Y L D Y W N P V 3 ( Y , 2 ) » N P V W A T GOTO 100 9 0 3 I F ( M O D E L . N E . 4 ) GOTO 904 F O U R ( Y , 1 ) = N P V T O T - 5 7 3 6 . 8 3 F O U R ( Y , 4 ) = Y L D T O T F O U R ( Y , 7 ) = W A T T O T C A L L M A T C A L ( F O U R , Y ) Y W N P V 4 ( Y , 1 ) = N P V Y L D Y W N P V 4 ( Y , 2 ) = N P V W A T GOTO 100 9 0 4 I F ( M O D E L . N E . 5 ) GOTO 9 0 5 F I V E ( Y , 1 ) = N P V T O T - 6 1 5 0 . 5 3 F I V E ( Y , 4 ) - Y L D T O T F I V E ( Y , 7 ) = W A T T O T C A L L M A T C A L ( F I V E , Y ) Y W N P V 5 ( Y , 1 ) = N P V Y L D Y W N P V 5 ( Y , 2 ) = N P V W A T GOTO 100 9 0 5 I F ( M O D E L . N E . 6 ) GOTO 9 0 6 S I X ( Y , 1 ) = N P V T O T - 6 1 5 0 . 5 3 SI X ( Y , 4 ) = Y L D T O T S I X ( Y , 7 ) = W A T T O T C A L L M A T C A L ( S I X , Y ) Y W N P V 6 ( Y , 1 ) = N P V Y L D Y W N P V 6 ( Y , 2 ) = N P V W A T GOTO 100 9 0 6 I F ( M O D E L . N E . 7 ) GOTO 9 0 7 S E V E N ( Y , 1 ) = N P V T O T - 6 1 8 0 . 0 5 S E V E N ( Y , 4 ) « Y L D T O T S E V E N ( Y , 7 ) - W A T T O T C A L L M A T C A L ( S E V E N , Y ) Y W N P V 7 ( Y , 1 ) = N P V Y L D Y W N P V 7 ( Y , 2 ) = N P V W A T GOTO 100 907 E I G H T ( Y , 1 ) = N P V T O T - 6 1 8 0 . 0 5 E I G H T ( Y , 4 ) = Y L D T O T E I G H T ( Y , 7 ) = W A T T O T C A L L M A T C A L ( E I G H T , Y ) Y W N P V 8 ( Y , 1 ) = N P V Y L D Y W N P V 8 ( Y , 2 ) = N P V W A T C 100 C O N T I N U E 90 C O N T I N U E DO 9 9 0 M O D E L = 1 , 8 W R I T E ( 6 , 9 6 ) W R I T E ( 6 , 9 5 ) W R I T E ( 6 , 9 5 ) W R I T E ( 6 , 9 2 ) M O D E L W R I T E ( 6 , 9 3 ) DO 991 1 = 1 , 1 0 DO 992 J = 1 , 9 I F ( M O D E L . E Q . 1 ) OUT(3 )-ONE(I", J ) I F ( M O D E L . E Q . 2 ) O U T ( 3 ) * T W O ( I , J ) I F ( M O D E L . E Q . 3 ) O U T ( J ) - T H R E E ( I , J ) I F ( M O D E L . E Q . 4 ) O U T ( 3 ) - F O U R ( I , J ) I F ( M O D E L . E Q . 5 ) O U T ( J ) - F I V E ( I , J ) I F ( M O D E L . E Q . 6 ) O U T ( J ) « S I X ( I , J ) 118 A p p e n d i x * ( c o n t i n u e d ) IF (MODEL.EQ.7) OUT(J)-SEVEN( I ,J) IP (MODEL.EQ.8) OUT(J)"EIGHT( I,J) 992 CONTINUE WRITE(6,97)OUT 991 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) 994 CONTINUE WRITE(6,98)OUT2 993 CONTINUE 990 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 generator with time-of-day clock 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 generator DO 10 YR«1,20 C 20 years needed Z-IRAND(75)-1 C select a random number from 0 to 74 J--1 K-0 T»0 C T keeps track of t h i r t y - d a y months C J and K are cursers for temperature 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 pet with 245 days(one season) accross J«J + 2 K-K + 2 DO 20 I* 5,35 C 31 days per month ( s t a r t s on 5 since i n f o , in f i r s t 4 c o l s . ) C the following loop checks for missing 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 ( 16* 2 • J , I ) * * 2) 1 - . 0 2 0 4 8 * W E A G E N ( 1 6 * Z + J , I ) • . 0 0 0 0 3 6 4 ' W E A G E N ( 1 6 * Z * J , I ) 2 • W E A G E N ( 1 6 * Z * K , I ) - . 0 1 0 8 0 8 * W E A G E N ( I 6 * Z * R , I ) 3 • . 0 0 0 I 2 4 7 * ( W E A G E N ( i 6 * Z + K , I ) * * 2 ) • 2 . 5 5 9 • 2 1 4 . 2 1 2 U - A B S ( U ) P A N ( Y R , D - T - 5 + I ) = - 1 . 0 6 3 6 • . 0 2 6 1 6 1 * W E A G E N (1 6 * Z + J , I ) 1 - 0 0 7 4 7 7 * W E A G E N ( 1 6 * Z + K , I ) + ( S Q R T ( U ) ) * X * . I C 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 a C v a r i a n c e c o m p o n e n t ( t h e S E o f t h e e s t i m a t e t i m e s a r a n d o m n u m b e r ) P A N ( Y R , D - T - 5 + I ) = P A N ( Y R , D - T - 5 + 1 ) / 2 5 . 4 IF ( P A N ( Y R . D - T - 5 + I ) . L T . 0 ) P A N ( Y R , D - T - 5 * 1 ) - 0 C P A N i s now i n i n c h e s . R A I N ( Y R , D - T - 5 + I ) = W E A G E N ( ( 1 6 * Z ) + K , I ) R A I N ( Y R , D - T - 5 + 1 ) = R A I N ( Y R , D - T - 5 + I ) / 2 5 4 C R A I N i s now i n i n c h e s . 20 C O N T I N U E 15 C O N T I N U E JO C O N T I N U E RETURN END S U B R O U T I N E M O D E L S ( N , F , F C , W A T E R , / M O D E L / , T W A T E R ) C D E P E N D I N G ON T H E MODEL 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 A M O U N T ( 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 AND I R R I G A T I O N T Y P E ) . I N T E G E R M O D E L , N R E A L F C , W A T E R , M , T W A T E R , F I F ( M O D E L . E Q . 1 . O R . M O D E L . E Q . 3 ) N=6 I F ( M O D E L . E Q . 2 . O R . M O D E L . E Q . 4) N-1 7 I F ( M O D E L . E Q . 5 . O R . M O D E L . E Q . 6 . O R . M O D E L . E Q . 7 . O R . M O D E L . E Q . 8 ) N-1 M B N I F ( M O D E L . E Q . 1 . O R . M O D E L . E Q . 3 . O R . M O D E L . E Q . 5 . O R . M O D E L . E Q . 7 ) G O T O 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 S O I L S F - 5 F C - 1 0 TWATER=.198 W A T E R = 5 . 3 3 3 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 F C - 4 F - 3 T W A T E R = . 1 9 8 W A T E R = 2 . 1 3 3 RETURN END S U B R O U T I N E I R R G A T ( / N / , / W A T E R / , / T W A T E R / , I R R G ) C T H I S R O U T I N E 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 D A Y S I N T E G E R N R E A L W A T E R , I R R G ( N , N ) , W A T A P L , T W A T E R I F ( N . E Q . 6 . 0 R . N . E Q . 17) WATAPL«=WATER* . 75 C IF S O L I D S E T I R R I G A T I O N , E F F I C I E N C Y I S ONLY 75% O F T O T A L WATER USEI I F ( N . E Q . 1 ) W A T A P L * T W A T E R DO 300 J - 1 , N DO 310 I - l , N I R R G ( I , J ) - 0 IF ( I . E Q . J ) I R R G ( I , J ) - W A T A P L 310 C O N T I N U E 120 Appendix A (con: inue-.l ) 300 CONTINUE RETURN END SUBROUTINE VI E L D ( / N / , / A W S C / , / ? / , / F C / , / J / , / G T O T / I , / Y L D R E D / , / D A Y / , / I R R G / , / P A N / , / R A I N / , / 1 R R D A Y / , / Y E A R / , / E X I R R / ) C DETERMINES AWSC FOR EACH ROTATION FOR EACH DAY, CALCULATES A GROWTH C FACTOR AND STORES IT IN GTOT, AND DETERMINES A Y IELD 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 A E T , R H O , G , T , F C , I R R G ( N , N ) , E X I R R , P A N ( 2 0 , 2 4 5 ) , R A I N ( 2 0 , 2 4 5 ) , 1 D , K , P E T , F . I F ( D A Y . G E . 6 2 . A N D . D A Y . L E . 2 1 4 ) IRRDAY=IRRDAY*1 C IRRDAY c o u n t s the number of 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 (RHO.GT.1) RHO-1 C RHO IS A COEFFICIENT RELATING ACTUAL EVAPOTRANSPIRATION AND C POTENTIAL EVAPOTRANSPIRATION. 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 c o e f f i c i e n t r e l a t i n g pan evap t o P E T . PET-K*PAN ( 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 and ends S e p t . 30 IF ( I . E Q.J.A N D . A W S C f I ) . G T . F C . A N D . D A Y . G E . 6 2 . A N D . D A Y . L E . 2 1 4 ) ' .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 LESS THAN 0 INCHES IF ( A W S C ( I ) . G T . F C ) AWSC(I)=FC C . . . A N D IT CAN NEVER EXCEED F I E L D CAPACITY G=1 .2 - ( ' 2 .0 * (AWSC( 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 (LEAST) AND 1 . GTOT( I ) -GTOT( I )+G WEEK=(DAY/7)+1 C INTEGER DIVISION ON DAY TO DETERMINE WEEK IF (WEEK.LE .15 ) 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 . 7 5 - ( . 0 5 * W E E K ) IF (WEEK.GE. 30) T-1 . 1 5 - ( . 03*WEEK) IF ( T . G T . 1 ) T=1 C T IS A SEASONAL YIELD 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 WATER,TWATER, IRRTOT,EXIRR,WATSAV,M INTEGER N,IRRDAY M=N IF ( N . E Q . 1 ) GOTO 800 IRRTOT-(WATER/M)* IRRDAY 121 Appendix * ( o n u r u i ' J ) EX:RS«EX:RS/M WATSAV»IRR7CT-EX I RR RETURN 800 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 IS DIVIDED BY YEAR*245. A YTOT-ACTYLD (I ) •AYTOT C TOTAL ACTUAL YIELD IS 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 charges. 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 Th is routine computes the average and standards dev ia t ion of C NPV, y i e l d and water used over each 20 year s imu la t ion . REAL MAT(50,9),NPVAVG , YLDAVG,WATAVG, X, A, B,C INTEGER Y IF (Y.NE.1) GOTO 800 122 A p p e n d i x A (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 800 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 801 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)**2 802 CONTINUE MAT(Y,3)=SQRT(A/(X-1)) MAT(Y,6)=SQRT(B/(X-1)) MAT(Y,9)=SQRT(C/(X-1)) RETURN END Appendix B: S A M P L E ONE S E A S O N RUN R E S U L T S FOR ORCHARD S Y S T E M 5 ( M 2 , t r i c k l e , s a n d ) DAY RHO AWSC ( i n ) R A I N ( i n ) P E T ( i n ) K G T 1 1 . 0 0 0 3 . 9 0 8 0 . 0 0 . 0 1 2 0 . 204 0 . 0 0 . 300 2 1 . 0 0 0 3 . 9 6 6 0 . 0 0 . 002 0 . 208 0 . 0 0 . 3 0 0 3 1 . 0 0 0 4 . 0 0 0 0 . 0 5 5 0 .0 0 . 2 1 2 0 . 0 0 . 3 0 0 4 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 0 0 . 2 16 0 . 0 0 . 3 0 0 5 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 0 0 . 2 2 0 0 . 0 0 . 3 0 0 6 1 . 0 0 0 3 . 986 0 . 0 0 . 0 1 4 0 . 2 2 4 0 . 0 0 . 3 0 0 7 1 . 0 0 0 3 . 9 8 6 0 . 0 0 . 0 0 . 2 2 9 0 . 0 0 . 3 5 0 8 1 . 0 0 0 3 . 9 7 6 0 . 0 0 . 0 0 9 0 . 2 3 3 0 . 0 0 . 3 5 0 9 1 . 0 0 0 4 . 0 0 0 0 . 0 7 9 0 . 0 0 . 2 3 7 0 . 0 0 . 3 5 0 IC 1 . 0 0 0 4 . 0 0 0 0 . 0 1 6 0 . 0 0 . 2 4 1 0 . 0 0 . 3 5 0 1 1 1 . 0 0 0 4 . 0 0 0 0 . 0 1 6 0 . 0 0 . 2 4 5 0 . 0 0 . 3 5 0 1 2 ' 1 . 0 0 0 3 . 9 8 5 0 . 0 0 . 0 1 5 0 . 2 4 9 0 . 0 0 . 3 5 0 1 3 1 . 0 0 0 3 . 9 5 0 0 . 0 0 . 0 3 5 0 . 2 5 3 0 . 0 0 . 3 5 0 1 4 1 . 0 0 0 3 . 9 4 4 0 . 0 0 . 0 0 6 0 . 2 5 7 0 . 0 0 . 4 0 0 1 5 1 . 0 0 0 3 . 9 4 4 0 . 0 0 . 0 0 . 2 6 1 0 . 0 0 . 4 0 0 1 6 1 . 0 0 0 3 . 9 5 2 0 . 008 0 . 0 0 . 2 6 5 0 . 0 0 . 4 0 0 1 7 1 . 0 0 0 3 . 9 5 9 0 . 0 0 8 0 . 0 0 . 2 6 9 0 . 0 0 . 4 0 0 18 1 . 0 0 0 3 . 9 8 3 0 . 0 2 4 0 . 0 0 . 2 7 3 0 . 0 0 . 4 0 0 1 9 1 . 0 0 0 3 . 9 5 7 0 . 0 0 . 0 2 6 0 . 270 0 . 0 0 . 4 0 0 20 1 . 0 0 0 3 . 9 5 7 0 . 0 0 . 0 0 . 2 8 2 0 . 0 0 . 4 0 0 21 1 . 0 0 0 3 . 9 3 9 0 . 0 0 . 0 1 8 0 . 2 8 6 0 . 0 0 . 4 5 0 22 1 . 0 0 0 3 . 9 1 8 0 . 0 0 . 0 2 2 0 . 2 9 0 0 . 0 0 . 4 5 0 23 1 . 0 0 0 3 . 8 9 6 0 . 0 0 . 0 2 1 0 . 294 0 . 0 0 . 4 5 0 24 1 . 0 0 0 3 . 8 7 8 0 . 0 0 . 0 1 8 0 . 2 9 8 0 . 0 0 . 4 5 0 25 1 . 000 3 . 8 7 7 0 . 0 0 .001 0 . 3 0 4 0 . 0 0 . 4 5 0 26 1 . 0 0 0 3 . 9 4 8 0 . 0 7 1 0 .0 0 . 3 1 2 0 . 0 0 . 4 5 0 27 1 . 0 0 0 3 . 9 5 6 0 . 0 0 8 0 . 0 0 . 3 2 0 0 . 0 0 . 4 5 0 28 1 . 0 0 0 3 . 9 5 6 0 . 0 0 . 0 0 . 3 2 9 0 . 0 0 . 5 0 0 29 1 . 0 0 0 4 . 0 0 0 0 . 0 4 7 0 . 0 0 . 3 3 7 0 . 0 0 . 5 0 0 30 1 . 0 0 0 3 . 9 7 5 0 . 0 0 . 025 0 . 3 4 5 0 . 0 0 . 500 31 1 . 0 0 0 3 . 9 4 8 0 . 0 0 . 027 0 . 3 5 3 0 . 0 0 . 5 0 0 32 1 . 0 0 0 3 . 9 2 7 0 . 0 0 . 0 2 1 0 . 3 6 1 0 . 0 0 . 5 0 0 33 1 .000 3 . 9 0 0 0 . 0 0 . 0 2 7 0 . 3 6 9 0 . 0 0 . 5 0 0 34 1 .000 3 . 8 8 4 0 . 0 0 . 0 1 6 0 . 3 7 8 0 . 0 0 . 5 0 0 35 1 . 0 0 0 3 . 8 2 5 0 . 0 0 . 0 5 9 0 . 386 0 . 0 0 . 5 5 0 36 1 . 0 0 0 3 . 8 8 8 0 . 0 6 3 0 . 0 0 . 3 9 4 0 . 0 0 . 5 5 0 37 1 . 0 0 0 3 . 8 7 9 0 . 0 0 . 0 0 9 0 . 4 0 2 0 . 0 0 . 5 5 0 38 1 . 0 0 0 3 . 8 4 0 0 . 0 0 . 0 3 9 0 . 4 1 0 0 . 0 0 . 5 5 0 39 1 . 0 0 0 3 . 7 8 4 0 . 0 0 . 0 5 6 0 . 4 1 8 0.0 0 . 5 5 0 40 1 . 0 0 0 3 . 8 8 2 0 . 098 0 . 0 0 . 4 2 7 0 . 0 0 . 5 5 0 4 1 1 . 0 0 0 3 . 8 1 4 0 . 0 0 . 0 6 8 0 . 4 3 5 0 . 0 0 . 5 5 0 42 1 . 0 0 0 3 . 7 6 9 0 . 0 0 . 0 4 5 0 . 4 4 3 0.0 0 . 6 0 0 43 1 . 0 0 0 3 .681 0 . 0 0 . 0 8 9 0 . 451 0.0 0 . 6 0 0 44 1 . 0 0 0 3 . 5 6 7 0.0 0 . 1 1 3 0 . 4 5 9 0 . 0 0 . 6 0 0 45 1 . 0 0 0 3 . 6 9 3 0 . 126 0 . 0 0 . 4 6 7 0 . 0 0 . 6 0 0 46 1 . 0 0 0 3 . 7 0 1 0 . 008 0 . 0 0 . 4 7 6 0 . 0 0 . 6 0 0 47 1 . 0 0 0 3 . 6 2 9 0 . 0 0 . 0 7 2 0 . 4 8 4 0 . 0 0 . 6 0 0 48 1 . 0 0 0 3 . 5 1 9 0 . 0 0 . 1 1 0 0 . 4 9 2 0.0 0 . 6 0 0 49 1.000 3 . 458 0.0 0 . 0 6 1 0 . 4 0 0 0.0 0 , 6 5 0 Appendix B: SAMPLE ONE SEASON' RUN RESULTS FOP. ORCHARC SYSTEM 5 ( M 2 , t r ick l e , s a n e ) d a y s o i l S o i l moisture m o i s t u r e f a c t o r p Level U n ) r a i n p o t e n t i a l e v a p o -( i n ) evapo- t r a n s . trar.s. coet"f . (in) K growth t i m i n g of re d u c t i o n s t r e s s f a c t o r f a c t o r G T 00 1 .000 4 .000 0. 03 1 0 . 0 0 .704 0 .0 1 .000 01 1 .000 4 .000 0. 528 0. 0 0 .706 0 .0 1 .000 02 1 .000 4 .000 0. 205 0. 0 0 .708 0 .0 1 .000 03 1 .000 4 .000 0. 0 0. 04 1 0 .710 0 .0 1 .000 04 1 .000 4 .000 0. 0 0. 1 94 0 .712 0 .0 1 .000 05 1 .000 3 .983 0. 0 0. 215 0 .714 0 .0 0 .950 06 1 .000 4 .000 0. 055 0. 0 0 . 7 1 6 0 .0 0 .950 07 1 .000 4 .000 0. 0 0. 143 0 .718 0 .0 0 .950 08 1 .000 4 .000 0. 087 0. 0 0 .720 0 .0 0 .950 09 1 .000 4 .000 0. 071 0. 0 0 .722 0 .0 0 .950 10 1 .000 4 . 000 0. 0 0. 172 0 .724 0 .0 0 .950 1 1 1 .000 3 .997 0. 0 0. 201 0 .727 0 .0 0 .950 12 1 .000 4 .000 0. 0 0. 102 0 . 7 2 9 0 .0 0 .900 13 1 .000 4 .000 0. 008 0. 0 0.731 0 .0 0 .900 14 1 .000 4 .000 0. 055 0. 0 0 .733 0 .0 0 .900 15 1 .000 4 .000 0. 0 0. 179 0 . 735 0 .0 0 .900 16 1 .000 4 .000 0. 0 0. 1 38 0 .737 0 .0 0 .900 17 1 .000 4 .000 0. 094 0. 0 0 . 739 0 .0 0 .900 18 1 .000 4 .000 0. 0 39 0. 0 0.741 0 .0 0 .900 19 1 .000 4 .000 0. 157 0. 0 0 .743 0 .0 0 .850 20 1 .000 4 .000 0. 0 0. 1 1 6 0 .745 0 .0 0 .850 21 1 .000 4 .000 0. 047 0. 0 0 . 7 4 7 0 .0 0 .850 22 1 .000 4 .000 0. 016 0. 0 0 . 749 0 .0 0 .850 23 1 .000 3 .564 0. 0 0. 234 0 .749 0 .0 0.850 24 1 .000 4 .000 0. 008 0. 0 0 .747 0 .0 0 .850 25 1 .000 4 .000 0. 567 0. 0 0 .745 0 .0 0 .850 26 1 .000 4 .000 0. 7 1 7 0. 0 0 .743 0 .0 0 .800 27 1 .000 4 .000 0. 031 0. 0 0.741 0 .0 0.800 28 1 .000 4 .000 0. 0 0. 031 0 . 7 3 9 0 .0 0 .800 29 1 .000 4 .000 0. 0 0. 106 0 .737 0 .0 0.800 30 1 .000 3 .972 0. 0 0. 226 0 . 7 3 5 0 .0 0.800 31 1 .000 4 .000 0. 055 0. 0 0 .733 0 .0 0 .800 32 1 .000 4 .000 0. 047 0. 0 0.731 0 .0 0.800 33 1 .000 4 .000 0. 591 0. 0 0 .729 0 .0 0.750 34 1 .000 4 .000 0. 024 0. 0 0 .727 0 .0 0.750 35 1 .000 4 .000 0. 008 0. 0 0 .724 0 .0 0 .750 36 1 .000 4 .000 0. 055 0. 0 0 .722 0 .0 0.750 37 1 .000 4 .000 0. 0 0. 093 0 .720 0 .0 0 .750 38 1 .000 4 .000 0. 0 0. 140 0 .718 0 .0 0.750 39 1 .000 4 .000 0. 0 0. 167 0 .716 0 .0 0.750 40 1 .000 4 .000 0. 063 0. 0 0 .714 0 .0 0.700 41 1 .000 4 .000 0. 039 0. 0 0 .712 0 .0 0.700 42 1 .000 3 . 9 6 9 0. 0 0. 229 0 .710 0 .0 0.700 43 1 .000 3 . 916 0. 0 0. 251 0 .708 0 .0 0.700 44 1 .000 4 .000 0. 039 0. 0 0 .706 0 .0 0.700 45 1 .000 4 .000 0. 0 0. 1 29 0 .704 0 .0 0.700 46 1 .000 4 .000 0. 0 0. 1 78 0 .702 0 .0 0.700 47 1 .000 4 .000 0. 0 0. 195 0 .700 0 .0 0.650 48 1 .000 3 . 9 3 9 0. 0 0. 259 0 .696 0 .0 0.650 Appemllx B: SAMPLE ONE SEASON RUN RESULTS FOR ORCHARD SYSTEM 5 ( M 2 , t r i cK L e , s a n d ) day s o i l S C i I rain poteni Lei I evap - growth t£«! mg moisture moisture (in) evapo- t rc\ns. reduc t ion st ress factor p Le ve I trans. coef f. factor factor (in) (in) K G T 149 1 .000 3.977 0.0 0. 1 60 0.692 0.0 0 . 650 150 1 .000 3.907 0.0 0.268 0 . 6 8 8 0.0 0.650 151 1 .000 3.901 - 0.0 0.204 0 . 6 8 4 0.0 0.650 152 1 .000 3 . 9 4 9 0.0 0.151 0 . 680 0.0 0. 650 153 1 .000 3.920 0.0 0.227 0.676 0.0 0.650 154 1 .000 3.929 0.0 0 . 1 8 9 0.671 0.0 0.600 155 1 .000 4.000 0.094 0.0 0.667 0 . 0 0.600 156 1 .000 4.000 0.0 0. 1 25 0.663 0 . 0 0.6C0 157 1 .000 4.000 0.0 0.125 0.659 0.0 0. 600 158 1 .000 4.000 0.024 0.0 0.655 0.0 0.600 159 1 . 0 0 0 4.000 0.0 0.091 0 . 6 5 1 0 . 0 0.600 160 1 . 0 0 0 4.000 0.0 0. 167 0.647 0 . 0 0.600 161 1 . 0 0 0 4.000 0.0 0. 1 5 5 0.643 0 . 0 0.550 162 1 . 0 0 0 3 . 9 9 1 0.0 0.207 0.639 0.0 0.550 163 1 . 0 0 0 3 . 9 9 7 0.0. 0. 1 92 0.635 0.0 0.550 164 1 . 0 0 0 4.000 0 . 1 1 0 0.0 0 . 6 3 1 0 . 0 0.550 165 1 . 0 0 0 4.000 0.0 0. 1 96 0.627 0 . 0 0.550 166 1 . 0 0 0 4.000 0.0 0.141 0.622 0 . 0 0.550 167 1 . 0 0 0 4.000 0.0 0.176 0.618 0.0 0.550 168 1 . 0 0 0 4.000 0.0 0.141 0.614 0.0 0.500 169 T.OOO 4 . 0 0 0 0.0 0 . 1 30 0 . 6 1 0 0 . 0 0.500 170 1 . 0 0 0 4 . 0 0 0 0.465 0 . 0 0 . 6 0 6 0 . 0 0.500 171 1 . 0 0 0 4 . 0 0 0 0.047 0 . 0 0 . 6 0 2 0 . 0 0.500 172 1 . 0 0 0 4.000 0.0 0. 1 5 5 0.598 0 . 0 0.500 173 1 . 0 0 0 4.000 0.0 0 . 1 4 5 0.594 0 . 0 0.500 174 1 . 0 0 0 4.000 0.0 0.141 0 . 5 9 0 0 . 0 0.500 175 1 . 0 0 0 4.000 0.0 0 . 163 0 . 5 8 6 0 . 0 0 . 450 176 1 . 0 0 0 4.000 0.0 0 . 1 30 0 . 5 8 2 0 . 0 0.450 177 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 109 0 . 5 7 8 0 . 0 0.450 178 1 . 0 0 0 4.000 0.0 0 . 1 1 4 0 . 5 7 3 0 . 0 0.450 179 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 0 9 8 0 . 5 6 9 0 . 0 0.450 180 1 . 0 0 0 4 . 0 0 0 0.055 0 . 0 0 . 5 6 5 0 . 0 0.450 181 1 . 0 0 0 4 . 0 0 0 0 . 122 0 . 0 0.561 0 . 0 0.450 182 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 152 0 . 5 5 7 0 . 0 0.400 183 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 125 0 . 5 5 3 0 . 0 0.400 184 1 . 0 0 0 4 . 0 0 0 0.008 0 . 0 0 . 5 4 9 0 . 0 0.400 185 1 . 0 0 0 4 . 0 0 0 0.421 0 . 0 0 . 5 4 5 0 . 0 0.400 186 1 . 0 0 0 4 . 0 0 0 0 . 126 0 . 0 0.54 1 0 . 0 0.400 187 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 1 3 4 0 . 5 3 7 0 . 0 0.400 188 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 0 9 2 0 . 5 3 3 0 . 0 0.400 189 1 . 0 0 0 4 . 0 0 0 0 . 0 0.111 0 . 5 2 9 0 . 0 0.350 190 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 136 0 . 5 2 4 0 . 0 0.350 191 1 . 0 0 0 4 . 0 0 0 0.181 0 . 0 0 . 5 2 0 0 . 0 0.350 192 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 0 5 9 0 . 5 1 6 0 . 0 0.350 193 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 128 0 . 5 1 2 0 . 0 0.350 194 1 . 0 0 0 4 . 0 0 0 0 . 0 0 . 0 9 0 0 . 5 0 8 0 . 0 . . 0.350 195 1 . 0 0 0 4 . 0 0 0 0.008 0 . 0 0 . 5 0 4 0 . 0 0.350 196 1 . 0 0 0 4 . 0 0 0 0 . 2 2 0 0 . 0 0 . 5 0 0 0 . 0 0.300 Appendix 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 ) day s o i l s o i l rain potential, evapo- growth timing of moisture moisture (in) evapo- trans, reduction stress factor p l e v e l trar.s. coeff. . f a c t o r factor £Ln) ( in} £ _G J _ _ _ .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 3.537 545 465 425 358 405 507 451 434 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 3 3, 3 3. 3 3. 3. 3 0, 0, 0. 0, 0, 0, 0, 882 0 0 0 0 0 0.055 0.031 0 134 .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 ,047 ,0 ,071 ,071 ,0 0.0 0.055 .039 .0 .0 .0 ,0 0 ,047 0, 0, 0, 0, 0, 0, 0. 0. 0. 0, 0, 0, 0, 0, 0, 0 072 077 0. 105 0.072 091 .0 0 083 ,0 0.095 0.051 048 063 061 045 065 061 045 040 055 0.020 0. 122 ,107 073 ,0 081 ,039 ,068 ,0 ,0 ,056 0.017 0.034 0.0 0.0 0.047 0.0 0.0 0.031 005 ,0 ,0 ,038 0.007 0.0 0.031 0.009 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 . 496 0.492 0.483 0. 484 0.430 0.476 0.471 ,467 463 ,459 ,455 ,451 ,447 ,443 ,439 ,435 0.431 0.427 0.422 0.418 0.414 .410 ,406 0.402 0.396 ,388 ,380 ,371 ,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 . 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, 0 . 300 0.300 0.300 ,300 , 300 ,300 ,250 .250 ,250 ,250 ,250 ,250 ,250 ,220 .220 ,220 ,220 .220 ,220 .220 I 90 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, 90 90 90 90 90 90 60 60 60 60 60 60 60 30 30 30 30 30 30 30 00 00 00 00 00 00 00 070 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0097228/manifest

Comment

Related Items