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

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A COMPUTER SIMULATION OF BLUEBUNCH WHEATGRASS (AGROPYRON SP1CATUM) GROWTH DYNAMICS AND IMPLICATIONS TO INTEGRATED MANAGEMENT OF LIVESTOCK AND WILDLIFE by ANN C.(ALLAYE-CHAN A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Plant Science We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1984 © Ann C. Allaye-Chan, 1984 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 UNIVERSITY OF BRITISH 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 ex 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 gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of P l a n t Science THE UNIVERSITY OF BRITISH COLUMBIA 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: October 1984 A b s t r a c t A computer model was developed f o r bluebunch wheatgrass {Agropyron spicatum (Pursh) S c r i b n . and Smith) which simulated the growth dynamics of t h i s s p e c i e s i n both the presence and absence of g r a z i n g . Growth dynamics were m e c h a n i s t i c a l l y modeled as f u n c t i o n s of s o i l water p o t e n t i a l , s o i l and a i r temperatures, r a i n f a l l i n t e n s i t y , p hotoperiod, f o l i a r n i t r o g e n content, and p l a n t m a t u r i t y . Simulated processes i n c l u d e d growth p o t e n t i a l , p h o t o s y n t h e s i s , dark r e s p i r a t i o n , carbohydrate t r a n s l o c a t i o n between aboveground and belowground biomass, dry matter p r o d u c t i o n , shoot and root m o r t a l i t y , and l i t t e r f a l l . Model p r e d i c t i o n s of herbage p r o d u c t i o n i n the absence of g r a z i n g agreed c l o s e l y with measurements obtained from f i e l d sampling. However, erroneous s i m u l a t i o n of l i t t e r f a l l and i n a c c u r a t e p o r t r a y a l of the r e l a t i o n s h i p between s o i l water p o t e n t i a l and growth r a t e r e s u l t e d i n some d i s c r e p a n c i e s between p r e d i c t e d and observed v a l u e s . S e n s i t i v i t y a n a l y s i s of c l i m a t i c d r i v i n g v a r i a b l e s r e v e a l e d that dry matter p r o d u c t i o n i s h i g h l y s e n s i t i v e t o s o i l moisture regimes; consequently, the e f f e c t of s o i l water p o t e n t i a l on growth r a t e p a r t i c u l a r l y warrants f u r t h e r r e s e a r c h . S i m u l a t i o n r e s u l t s i n d i c a t e t hat dry matter accumulation i s p r i m a r i l y l i m i t e d by low temperatures i n e a r l y s p r i n g , low moisture a v a i l a b i l i t y i n mid-summer, and a combination of low temperatures, low f o l i a r n i t r o g e n , and short photoperiods i n l a t e f a l l . Simulated carbohydrate i i movement from the r o o t s to the shoots o c c u r r e d d u r i n g both i n i t i a t i o n of s p r i n g growth and commencement of f a l l regrowth i n one year of s i m u l a t i o n , but o c c u r r e d only d u r i n g s p r i n g i n i t i t a t i o n i n a second year of s i m u l a t i o n . Carbohydrates t r a n s l o c a t e d from the root system accounted fo r approximately 6 to 7 percent of t o t a l annual aboveground dry matter p r o d u c t i o n . Photosynthate t r a n s l o c a t i o n to the root system o c c u r r e d p r i m a r i l y before the onset of a e s t i v a t i o n , with peak carbohydrate storage c o i n c i d i n g with the stage when approximately two t h i r d s of c u r r e n t annual growth had been completed. Simulated v a l u e s of regrowth f o l l o w i n g g r o u n d - l e v e l d e f o l i a t i o n compared f a v o r a b l y with v a l u e s obtained from f i e l d sampling. Q u a n t i t a t i v e v a l i d a t i o n of dry matter accumulation f o l l o w i n g l i g h t e r d e f o l i a t i o n i n t e n s i t i e s i s p r e c l u d e d by want of s u i t a b l e d a t a . However, q u a l i t a t i v e v a l i d a t i o n of s i m u l a t i o n r e s u l t s support the b i o l o g i c a l soundness of p r o j e c t e d y i e l d s . S i m u l a t i o n r e s u l t s i n d i c a t e that s t a n d i n g crop i n the f a l l i s c o n s i d e r a b l y depressed by most g r a z i n g regimes; however, they a l s o i n d i c a t e that s p r i n g d e f o l i a t i o n s at 25% i n t e n s i t y may i n c r e a s e s t a n d i n g c r o p i n the f a l l by as much as 61%. T o t a l annual dry matter p r o d u c t i o n was s t r o n g l y a f f e c t e d by d e f o l i a t i o n date and d e f o l i a t i o n i n t e n s i t y when herbage removal o c c u r r e d before J u l y . However, the e f f e c t s of d e f o l i a t i o n date and d e f o l i a t i o n i n t e n s i t y became minor when herbage removal occurred a f t e r mid-July. S i m u l a t i o n r e s u l t s suggest that improvements in crude p r o t e i n y i e l d f o l l o w i n g s e l e c t g r a z i n g regimes surpass improvements i n forage y i e l d f o r comparable g r a z i n g treatments, s i n c e improvements i n crude p r o t e i n y i e l d are promoted by enhanced n i t r o g e n c o n c e n t r a t i o n s as w e l l as s t i m u l a t e d f o l i a r p r o d u c t i o n . Thus, d e f o l i a t i o n may occur at a higher i n t e n s i t y or at a l a t e r date f o r an improvement in crude p r o t e i n y i e l d than f o r an improvement in biomass y i e l d . S i m u l a t i o n r e s u l t s i n d i c a t e that the e f f e c t of herbage removal on dry matter p r o d u c t i o n the year f o l l o w i n g d e f o l i a t i o n c l o s e l y p a r a l l e l s the e f f e c t of herbage removal on root accumulation d u r i n g the year of treatment. In g e n e r a l , e a r l y s p r i n g or f a l l g r a z i n g are l e s s damaging than mid-season g r a z i n g at comparable d e f o l i a t i o n i n t e n s i t i e s . S i m u l a t i o n r e s u l t s support the c o n t e n t i o n that j u d i c i o u s g r a z i n g management may be used to improve bluebunch wheatgrass forage and crude p r o t e i n a v a i l a b i l i t y to w i n t e r i n g w i l d l i f e . However, improved forage q u a l i t y i s p r e d i c a t e d on the assumption that the r a t e of n i t r o g e n l o s s in regrowth w i l l not exceed the r a t e of n i t r o g e n l o s s i n s p r i n g growth. A d d i t i o n a l l y , the simulated e f f e c t of d e f o l i a t i o n on t i l l e r i n g behavior i s c r i t i c a l i n determining regrowth y i e l d . C u r r e n t l y , s i m u l a t e d t i l l e r i n g behavior i s tenuously modeled because of l a c k of data. i v Table of Contents A b s t r a c t i i L i s t of Tables v i i L i s t of F i g u r e s v i i i Acknowledgements x i i 1. INTRODUCTION 1 2. LITERATURE REVIEW 4 2.1 GENERATION OF ASSIMILATES (PHOTOSYNTHESIS) 4 2.2 PARTITIONING AND TRANSLOCATION OF ASSIMILATES ...5 2.2.1 E f f e c t s of A b i o t i c F a c t o r s 5 2.2.2 E f f e c t s of B i o t i c F a c t o r s 6 2.3 DRY MATTER PRODUCTION 10 2.3.1 A b i o t i c C o n t r o l s of Dry Matter P r o d u c t i o n ...10 2.3.2 D e f o l i a t i o n E f f e c t s on Dry Matter Product ion 13 3 . METHODS 15 4. AGGRO: SIMULATION MODEL OF BLUEBUNCH WHEATGRASS GROWTH 18 4.1 GENERAL MODEL STRUCTURE 18 4.2 ABIOTIC DRIVING VARIABLES 18 4.2.1 S o i l Water P o t e n t i a l 22 4.2.2 A i r and S o i l Temperatures 25 4.2.3 P r e c i p i t a t i o n 29 4.2.4 Daylength 29 4.3 GROWTH POTENTIAL AND DRY MATTER PRODUCTION 30 4.4 GENERATION OF ASSIMILATES 40 4.5 RESPIRATION 42 4.6 CARBOHYDRATE PARTITIONING 44 v 4.7 SHOOT AND ROOT MORTALITY 47 4.8 LITTERFALL 48 4.9 FOLIAR NITROGEN 48 4.10 EFFECTS OF DEFOLIATION 49 5. SIMULATION RESULTS, MODEL VALIDATION, SENSITIVITY ANALYSIS, AND DISCUSSION 53 5.1 BLUEBUNCH WHEATGRASS DYNAMICS IN THE ABSENCE OF GRAZING 53 5.1.1 Dry Matter Production of Aboveground Biomass 53 5.1.2 Crude P r o t e i n Y i e l d 60 5.1.3 Carbohydrate P a r t i t i o n i n g Between Above and Belowground Biomass 63 5.2 BLUEBUNCH WHEATGRASS DYNAMICS IN THE PRESENCE OF GRAZING 70 5.2.1 Regrowth F o l l o w i n g D e f o l i a t i o n 70 5.2.2 T o t a l Annual Dry Matter Pr o d u c t i o n 74 5.2.3 Crude P r o t e i n Y i e l d 74 5.2.4 Belowground Dynamics 80 5.2.5 Dry Matter Pr o d u c t i o n the Year F o l l o w i n g Herbage Removal 83 5.2.6 I m p l i c a t i o n s to I n t e g r a t e d Management of C a t t l e and W i l d l i f e 86 6. GENERAL DISCUSSION 94 LITERATURE CITED 99 APPENDICES 108 v i L i s t of Tables Table Page I. Summary of v a r i a b l e names and l i t e r a t u r e sources. ...20 I I . 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 f o r the 1968 c o n t r o l s i m u l a t ion 59 I I I . The e f f e c t of g r a z i n g regime on the November 1st a v a i l a b i l i t y of crude p r o t e i n which occurs at a minimum c o n c e n t r a t i o n of 5% f o l i a r content by weight 89 IV. The e f f e c t of g r a z i n g regime on the December 1st a v a i l a b i l i t y of crude p r o t e i n which occurs at a minimum c o n c e n t r a t i o n of 5% f o l i a r content by weight 89 v i i L i s t of F i g u r e s F i g u r e Page 1. General model s t r u c t u r e of AGGRO 19 2. S o i l water regimes used to e v a l u a t e the e f f e c t s of high, medium, and low moisture a v a i l a b i l i t y on bluebunch wheatgrass growth dynamics (From van Ryswyk and Broersma, unpublished data) 23 3. Moisture c h a r a c t e r i s t i c curve developed f o r Harper's ( 1969) bluebunch wheatgrass mesic s i t e . 24 4. Seasonal s o i l water p o t e n t i a l s generated f o r Harper's (1969) bluebunch wheatgrass mesic s i t e i n 1967 and 1968. 26 5. Simulated a i r temperatures f o r Harper's (1969) bluebunch wheatgrass mesic s i t e i n 1967 and 1968 28 6. Simulated e f f e c t of a i r temperature on growth p o t e n t i a l (Adapted from data by d e V r i e s et a l . ( 1979) ) 33 7. Simulated e f f e c t of s o i l water on growth p o t e n t i a l (Adapted from data by Majerus (1975) ) 35 8. Simulated e f f e c t of f o l i a r n i t r o g e n on growth p o t e n t i a l (Adapted from data by Wilson (1975) ) 37 v i i i 9. Simulated e f f e c t of p l a n t m a t u r i t y on belowground hormonal a c t i v i t y and i n c i d e n c e of t i l l e r i n g 39 10. Simulated e f f e c t of a i r temperature on phot o s y n t h e s i s (Adapted from data by Depuit and C a l d w e l l (1975) ). ..41 11. Simulated e f f e c t of water p o t e n t i a l on ph o t o s y n t h e s i s (Adapted from data by Brown and T r l i c a (1977) ) 43 12. Simulated e f f e c t of temperature on r e s p i r a t i o n (Adapted from data by Depuit and C a l d w e l l ( 1975) ) 45 13. Simulated f o l i a r n i t r o g e n over time 50 14. Simulated e f f e c t of d e f o l i a t i o n on p h o t o s y n t h e s i s . ...51 15. Comparison of simulated and measured shoot biomass of bluebunch wheatgrass f o r 1967 and 1968 .....54 16. Simulated growth p o t e n t i a l and simulated e f f e c t s of temperature, s o i l water p o t e n t i a l , daylength, and f o l i a r n i t r o g e n on maximum growth r a t e f o r Harper's bluebunch wheatgrass mesic s i t e i n 1967 56 17. Simulated growth p o t e n t i a l and simulated e f f e c t s of temperature, s o i l water p o t e n t i a l , daylength, and f o l i a r n i t r o g e n on maximum growth r a t e f o r Harper's bluebunch wheatgrass mesic s i t e i n 1968 57 18. Simulated crude p r o t e i n y i e l d f o r 1 967 61 19. Simulated crude p r o t e i n y i e l d f o r 1968 62 ix 20. Simulated crude p r o t e i n percentages i n f o l i a r biomass and f a l l regrowth i n 1967 and 1968 64 21. Simulated movement of carbohydrates between aboveground and belowground biomass, and cumulative movement of carbohydrates i n t o belowground biomass f o r Harper's bluebunch wheatgrass mesic s i t e i n 1967 65 22. Simulated movement of carbohydrates between aboveground and belowground biomass, and cumulative movement of carbohydrates i n t o belowground biomass f o r Harper's bluebunch wheatgrass mesic s i t e i n 1968 67 23. Comparison of simulated and measured val u e s of regrowth f o l l o w i n g g r o u n d - l e v e l d e f o l i a t i o n on May 31, June 14, and June 28, 1967 71 24. Simulated e f f e c t of d e f o l i a t i o n date and d e f o l i a t i o n i n t e n s i t y on November 1st forage a v a i l a b i l i t y 73 25. Simulated e f f e c t of d e f o l i a t i o n date and d e f o l i a t i o n i n t e n s i t y on t o t a l annual dry matter p r o d u c t i o n 75 26. Simulated crude p r o t e i n y i e l d s f o l l o w i n g d e f o l i a t i o n at four i n t e n s i t i e s on May 1 and May 30 76 27. Simulated crude p r o t e i n y i e l d s f o l l o w i n g d e f o l i a t i o n at four i n t e n s i t i e s on June 14 and June 28 77 28. Simulated crude p r o t e i n y i e l d s f o l l o w i n g d e f o l i a t i o n at four i n t e n s i t i e s on J u l y 15 and September 15 78 x 29. Simulated e f f e c t of d e f o l i a t i o n date and d e f o l i a t i o n i n t e n s i t y on November 1st root biomass 81 30. Simulated root accumulation f o l l o w i n g g r o u n d - l e v e l d e f o l i a t i o n at v a r i o u s dates 82 31. Simulated e f f e c t of d e f o l i a t i o n date and d e f o l i a t i o n i n t e n s i t y on dry matter p r o d u c t i o n the year f o l l o w i n g herbage removal 84 32. Forage a v a i l a b i l i t y f o r c a t t l e versus forage a v a i l a b i l i t y f o r w i l d l i f e on November 1st f o l l o w i n g l i v e s t o c k g r a z i n g on s i x d i f f e r e n t dates at four d i f f e r e n t i n t e n s i t i e s 91 33. Crude p r o t e i n a v a i l a b i l i t y (minimum c o n c e n t r a t i o n of 5% f o l i a r content by weight) f o r c a t t l e versus w i l d l i f e f o l l o w i n g l i v e s t o c k g r a z i n g on s i x d i f f e r e n t dates and four d i f f e r e n t i n t e n s i t i e s 92 x i Acknowledgements I wish to thank my supervisor, Dr. M.D. P i t t , for his assistance, counsel, and support throughout t h i s study. Constructive c r i t i c i s m s and guidance from the members of my graduate committee, Dr. F.L. Bunnell, Dr. P.A. J o l l i f f e , and Dr. V.C. Runeckles, are deeply appreciated. Special thanks is extended to Barry Wong for helpful suggestions on curve f i t t i n g and valuable assistance with computing d i f f i c u l t i e s . Brian Wikeem, Don Eastman, and Rick E l l i s reviewed the word model for the computer simulation. Financial support for t h i s research was provided by the Research Branch of the B.C. Ministry of Forests, the Natural Sciences and Engineering Research Council of Canada (#0227), the B.C. Cattlemen's Association, and the 1921 Class of Agriculture at the University of B r i t i s h Columbia. x i i 1. INTRODUCTION Bluebunch wheatgrass ( Agropyron spicatum (Pursh) S c r i b n . and Smith) i s a key forage s p e c i e s indigenous to western North America (Dayton, 1937; Daubenmire, 1978) which i s p a l a t a b l e to both domestic and n a t i v e ungulates ( S i n g l e t o n , 1976). T h i s cool-season grass i s s u s c e p t i b l e to d e f o l i a t i o n i n j u r y , however, ( C a l d w e l l et a l . , 1981; R i c k a r d et a l . , 1975; Wilson et a l . , 1966; Branson, 1956; B l a i s d e l l and Pechanec ,1949) as i t has e v o l v e d l a r g e l y i n the absence of g r a z i n g p r e s s u r e (Daubenmire, 1978). E f f e c t i v e g r a z i n g management i s t h e r e f o r e p a r t i c u l a r l y c r u c i a l i n a s s u r i n g the h e a l t h and p r o d u c t i v i t y of t h i s r e s o u r c e . The response of bluebunch wheatgrass to c l i m a t i c and d e f o l i a t i n g f a c t o r s must be w e l l understood i f g r a z i n g management i s to be e f f e c t i v e i n m a i n t a i n i n g p l a n t h e a l t h while o p t i m i z i n g animal p r o d u c t i o n . A secure knowledge of p l a n t behaviour i s needed to determine the q u a l i t y and q u a n t i t y of forage which i s a v a i l a b l e f o r any given g r a z i n g regime, as w e l l as the e f f e c t s of t h a t p a r t i c u l a r regime on p l a n t v i g o r and subsequent herbage p r o d u c t i o n . In g r a z i n g systems where i n t e g r a t e d management of l i v e s t o c k and w i l d l i f e i s p r a c t i c e d , c o n s i d e r a t i o n must a l s o be given to the q u a l i t y and q u a n t i t y of regrowth f o l l o w i n g d e f o l i a t i o n . Although bluebunch wheatgrass has been the focus of c o n s i d e r a b l e r e s e a r c h ( M c l l v a n i e , 1942; B l a i s d e l l and Pechanec, 1949; Wilson et a l . , 1966; Mueggler, 1972, 1975; Sauer, 1978; Daubenmire, 1978; Willms et a l . , 1980a, 1980b; 1 2 C a l d w e l l et a l . , 1981; Willms et a l . , 1981; Quinton et a l . , 1982), e x i s t i n g data, i n t h e i r c u r r e n t form, p r o v i d e only l i m i t e d guidance to range managers. General r u l e s of thumb i d e n t i f i e d with respect to range r e a d i n e s s and sa f e degrees of use. do not allow f o r y e a r l y v a r i a t i o n s i n c l i m a t i c p a t t e r n s or animal p r o d u c t i o n o b j e c t i v e s . Because range managers have no means of e x p l o r i n g a l t e r n a t e management s t r a t e g i e s , the optimum g r a z i n g regime a p p r o p r i a t e to management o b j e c t i v e s can only be approximated from a q u a l i t a t i v e p e r s p e c t i v e . The e m p i r i c a l nature of e x i s t i n g data, p l u s a general f a i l u r e t o c o n s i d e r the p h y s i o l o g i c a l mechanisms u n d e r l y i n g p l a n t responses, f u r t h e r l i m i t the t r a n s f e r r a b i l i t y of i n f o r m a t i o n to other years and other s i t u a t i o n s . T h i s d i s s e r t a t i o n seeks to develop a computer s i m u l a t i o n model which can be used to e v a l u a t e bluebunch wheatgrass growth dynamics i n both the presence and absence of g r a z i n g . S p e c i f i c o b j e c t i v e s of t h i s t h e s i s a r e : 1. to develop a growth model f o r bluebunch wheatgrass which i s p r o p e r l y responsive to c l i m a t i c c o n d i t i o n s t y p i c a l of B r i t i s h Columbian rangelands, 2. to p r o j e c t r e a l i s t i c a l l y biomass accumulation i n bluebunch wheatgrass, both i n the presence and absence of g r a z i n g , 3. to i n v e s t i g a t e a number of r e l a t i o n s h i p s i n bluebunch wheatgrass dynamics f o r which understanding i s poor or incomplete, 3 4. to explore i m p l i c a t i o n s of v a r i o u s l i v e s t o c k g r a z i n g regimes on the a v a i l a b i l i t y of crude p r o t e i n and forage y i e l d s to w i n t e r i n g w i l d l i f e . 2. LITERATURE REVIEW 2.1 GENERATION OF ASSIMILATES (PHOTOSYNTHESIS) The e f f e c t s of a b i o t i c f a c t o r s on the C02 exchange rate of bluebunch wheatgrass are unknown; however, r e l e v a n t i n f o r m a t i o n e x i s t s f o r a c l o s e l y r e l a t e d s p e c i e s . Depuit and C a l d w e l l (1975) found a near p a r a b o l i c temperature response in the net a s s i m i l a t i o n r a t e of b e a r d l e s s wheatgrass (Agr opyr on spicatum var. inerme H e l l e r ) l e a v e s . The optimum temperature f o r p h o t o s y n t h e s i s under c o n d i t i o n s of constant i r r a d i a t i o n was e s t a b l i s h e d at 20 to 25°C. Brown and T r l i c a (1977) documented a l i n e a r decrease in p h o t o s y n t h e t i c r a t e with i n c r e a s i n g moisture s t r e s s f o r western wheatgrass p l a n t s (Agr opyr on smi t hi i Rydb.) p h o t o s y n t h e s i z i n g under a 20°C temperature regime. Net p h o t o s y n t h e s i s approached zero when s o i l water p o t e n t i a l equaled -31 bars. Bluebunch wheatgrass leaves regrowing a f t e r severe d e f o l i a t i o n i n the s p r i n g e x h i b i t e d higher p h o t o s y n t h e t i c r a t e s than f o l i a g e on c o n t r o l p l a n t s at the same time of year ( C a l d w e l l et a l . , 1981). The g r e a t e r p h o t o s y n t h e t i c c a p a c i t y of regrowth c o u l d be due p a r t l y to g r e a t e r p h o t o s y n t h e t i c c a p a c i t y of younger f o l i a g e ( C a l d w e l l et a l . , 1981), the h i g h n i t r o g e n c o n c e n t r a t i o n s of which are o f t e n a s s o c i a t e d with h i g h p h o t o s y n t h e t i c r a t e s ( B o l t o n and Brown, 1980). However, p h e n o l o g i c a l or age d i f f e r e n c e s are not the only f a c t o r s r e s p o n s i b l e f o r d i f f e r e n t i a l a s s i m i l a t i o n r a t e s between c l i p p e d and u n d i p p e d p l a n t s . P a i n t e r and D e t l i n g 4 5 (1981) found that w i t h i n one day of c l i p p i n g treatment, undamaged t i l l e r s of p a r t i a l l y d e f o l i a t e d p l a n t s a l s o e x h i b i t e d higher p h o t o s y n t h e t i c r a t e s than comparably aged leaves of c o n t r o l p l a n t s . 2.2 PARTITIONING AND TRANSLOCATION OF ASSIMILATES 2.2.1 EFFECTS OF ABIOTIC FACTORS Environmental f a c t o r s can c o n t r o l the movement of photosynthates both d i r e c t l y and i n d i r e c t l y (Moser, 1977). In g e n e r a l , the d i r e c t e f f e c t s of environmental s t r e s s are not as s i g n i f i c a n t as the i n d i r e c t e f f e c t s , which are mediated through changes i n the r a t e of p h o t o s y n t h e s i s and the development of carbohydrate s i n k s (Moser, 1977). Water s t r e s s appears to have very l i t t l e e f f e c t on the t r a n s l o c a t i o n process per se (Wardlaw, 1968). Although numerous s t u d i e s i n d i c a t e a r e d u c t i o n i n a s s i m i l a t e movement f o l l o w i n g water d e f i c i t i n the p l a n t (Weatherly et a l . , 1959; Wardlaw, 1968; Sosebee and Wiebe, 1971), such r e d u c t i o n s are g e n e r a l l y a t t r i b u t a b l e to changes i n the s o u r c e - s i n k r e l a t i o n s h i p (Wardlaw, 1968). A s s i m i l a t e movement i n the phloem has been observed even under c o n d i t i o n s of severe moisture s t r e s s ( C r a f t s and C r i s p , 1971; McWilliam, 1968). As with water s t r e s s , the d i r e c t e f f e c t s of temperature s t r e s s on a s s i m i l a t e t r a n s l o c a t i o n are 6 r e l a t i v e l y minor even though phloem l o a d i n g may be p a r t i a l l y m e tabolic, and hence, temperature dependent (Wardlaw, 1968). Schmer and K n i e v e l (1974) r e p o r t e d that the r e l a t i v e amount of r a d i o a c t i v e carbon recovered from the r o o t s of western wheatgrass d i d not d i f f e r among p l a n t s grown under day/night temperature regimes of 21/16°C, 27/21°C, and 32/27°C. Wardlaw (1968) found no c o n c l u s i v e evidence to support phloem t r a n s l o c a t i o n as the l i m i t i n g f a c t o r to growth under low temperatures. T r a n s l o c a t i o n blockage by heat-induced c a l l o s e formation has been r e p o r t e d i n c o t t o n {Gossypium hirsutum L.) (McNairn and C u r r i e r , 1968; Webster and C u r r i e r , 1968; McNairn, 1972). However, a s s i m i l a t e o b s t r u c t i o n was not apparent at temperatures below 40°C and was t r a n s i t o r y at temperatures above 40°C. McNairn (1972) r e p o r t e d that c a l l o s e d e p o s i t i o n s on s i e v e p l a t e s decreased w i t h i n s i x hours of heat s t r e s s and approached normal l e v e l s w i t h i n two days of h e a t i n g . 2.2.2 EFFECTS OF BIOTIC FACTORS Ontogenetic changes i n photosynthate p a r t i t i o n i n g have been e x t e n s i v e l y documented f o r g r a s s e s , but evidence i s c o n f l i c t i n g on the p h e n o l o g i c a l stage when carbohydrate storage normally takes p l a c e . As s t u d i e s using r a d i o a c t i v e t r a c e r s have shown, a s s i m i l a t e s exported from p h o t o s y n t h e t i c f o l i a g e are i n i t i a l l y a l l o c a t e d f o r development of the sheath and f u r t h e r 7 expansion of the l e a f (Sosebee and Wiebe, 1973). Subsequently, the p a t t e r n of movement i s predominantly upwards to the a c t i v e l y e l o n g a t i n g upper internodes (Sosebee and Wiebe, 1973; Smith and Leinweber, 1973). Although carbohydrates may be t r a n s l o c a t e d to the r o o t s p r i o r to culm e l o n g a t i o n ( W i l l i a m s , 1964; Smith and Leinweber, 1973; Sosebee and Wiebe, 1973), t r a n s l o c a t i o n of carbohydrates to the underground biomass i s r e l a t i v e l y minor d u r i n g the stage of r a p i d v e g e t a t i v e growth ( W i l l i a m s , 1964; Sosebee and Wiebe, 1973). In c r e s t e d wheatgrass, t r a n s l o c a t i o n to the d e v e l o p i n g i n f l o r e s c e n c e reaches a peak at a n t h e s i s , and movement to the r o o t s and root crowns becomes n e g l i g i b l e at that time. (Sosebee and Wiebe, 1973). The upward:downward r a t i o of photosynthate t r a n s l o c a t i o n does not drop below u n i t y u n t i l p o s t - p o l l i n a t i o n . While s t u d i e s u sing r a d i o a c t i v e l a b e l s i n d i c a t e a l a t e stage of carbohydrate storage, s t u d i e s m o n i t o r i n g seasonal carbohydrate trends i n d i c a t e an e a r l y storage date. Seasonal trends of t o t a l n o n s t r u c t u r a l carbohydrate (TNC) c o n c e n t r a t i o n observed i n the r o o t s and root crowns of bluebunch wheatgrass r e v e a l t h a t a major p e r i o d of carbohydrate accumulation occurs approximately halfway through the v e g e t a t i v e stage. F o l l o w i n g an e a r l y season d e p l e t i o n of TNC r e s e r v e s , Daer and W i l l a r d (1981) noted a sharp i n c r e a s e i n the carbohydrate c o n c e n t r a t i o n once the p l a n t s reached the 8 middle of the boot stage. Carbohydrate c o n c e n t r a t i o n s c o n t i n u e d t o i n c r e a s e u n t i l the beginning of the r e p r o d u c t i v e p e r i o d , when the average l e a f l e n g t h was 20 cm and 67% of the c u r r e n t annual growth had been completed. Subsequently, a g e n e r a l d e c l i n e i n carbohydrate c o n c e n t r a t i o n was observed u n t i l the end of the study i n November, even though a p p r e c i a b l e i n c r e a s e s i n carbohydrate c o n c e n t r a t i o n s o c c a s i o n a l l y i n t e r r u p t e d the downward t r e n d . Working with the same s p e c i e s , M c l l v a n i e (1942) r e p o r t e d a s i m i l a r p a t t e r n i n h i s study but found that the accumulation of root r e s e r v e s was f a r more grad u a l than that i n d i c a t e d by Daer and W i l l a r d (1981). In a d d i t i o n , the maximum carbohydrate c o n c e n t r a t i o n was not observed u n t i l seed maturation. A p p a r e n t l y , the r e p r o d u c t i v e demands i n p l a n t s observed by Daer and W i l l a r d (1981) were more e f f e c t i v e i n reducing carbohydrate s t o r e s than those i n p l a n t s observed by M c l l v a n i e (1942). Herbage removal may a l t e r the d i s t r i b u t i o n of photosynthates t o d i f f e r e n t p a r t s of the p l a n t . Photosynthate p a r t i t i o n i n g was m o d i f i e d i n c r e s t e d wheatgrass when Sosebee and Wiebe (1971) c l i p p e d e n t i r e p l a n t s t o 10 to 15 cm s t u b b l e h e i g h t s , with the ex c e p t i o n of a s i n g l e l e a f to which they a p p l i e d phosphorus-32. I t was found that c l i p p i n g c o n s i s t e n t l y s h i f t e d the p r o p o r t i o n of t r a n s l o c a t e s towards the younger l e a v e s so that the upwardrdownward r a t i o of 9 t r a n s l o c a t i o n was i n c r e a s e d i n d e f o l i a t e d p l a n t s . Working with the same s p e c i e s , C a l d w e l l et a l . (1981) concurred that a higher a l l o c a t i o n of resources to the shoot system f o l l o w i n g d e f o l i a t i o n r e s u l t e d i n a more r a p i d approach to the p r e c l i p p i n g balance between the root and shoot systems. However, they found that t h i s was not the case with bluebunch wheatgrass, the root growth of which co n t i n u e d unabated f o l l o w i n g d e f o l i a t i o n ( C a l d w e l l et a l . , 1981). S i m i l a r l y , P a i n t e r and D e t l i n g (1981) repo r t e d that the p r o p o r t i o n of new growth a l l o c a t e d to shoots, crowns, and r o o t s d i d not d i f f e r among d e f o l i a t e d and u n d e f o l i a t e d western wheagrass p l a n t s . I t must be noted, however, that the s t u d i e s of C a l d w e l l et a l . (1981) and P a i n t e r and D e t l i n g (1981) were based on measurements of biomass y i e l d . Thus, even though the authors have shown t h a t the s t r u c t u r a l development in bluebunch wheatgrass and western wheatgrass p l a n t s remain unchanged f o l l o w i n g d e f o l i a t i o n , they have not p r e c l u d e d the p o s s i b i l i t y t h a t the a l l o c a t i o n of n o n s t r u c t u r a l compounds may have been a l t e r e d i n the manner i n d i c a t e d by Sosebee and Wiebe (1971) f o r c r e s t e d wheatgrass. 10 2.3 DRY MATTER PRODUCTION 2.3.1 ABIOTIC CONTROLS OF DRY MATTER PRODUCTION The e f f e c t s of c l i m a t i c f a c t o r s on biomass accumulation i n bluebunch wheatgrass are po o r l y e s t a b l i s h e d , with e x i s t i n g knowledge having been d e r i v e d p r i m a r i l y from f i e l d o b s e r v a t i o n s . B l a i s d e l l (1958) generated numerous c o r r e l a t i o n s between v e g e t a t i v e growth and c l i m a t i c f a c t o r s , and found that high growth increments were a s s o c i a t e d with high temperatures, low p r e c i p i t a t i o n , r e l a t i v e l y c l e a r s k i e s , and low winds. The d i f f i c u l t i e s of simple c o r r e l a t i o n a n a l y s i s on interdependent and sim u l t a n e o u s l y changing v a r i a b l e s are q u i c k l y manifested, however, when B l a i s d e l l (1958) concluded that high p r e c i p i t a t i o n was not b e l i e v e d to be adverse t o growth. Instead, the negative c o r r e l a t i o n found between growth increment and p r e c i p i t a t i o n was e x p l a i n e d by the a s s o c i a t i o n between low temperatures and r a i n y weather. Willms et a l . (1980a) r e p o r t e d that t i l l e r e l o n g a t i o n was more c l o s e l y r e l a t e d to maximum a i r temperature than t o s o i l temperature, and suggested that a delayed response might account f o r the poor c o r r e l a t i o n between s o i l temperature and t i l l e r growth. The e f f e c t s of s o i l water or p r e c i p i t a t i o n on t i l l e r e l o n g a t i o n were not c o n s i d e r e d . S o i l temperature appears to be a more important determinant i n i n i t i a t i n g growth than s o i l moisture, 11 which i s normally recharged from s p r i n g thaws (Stout et a l . , 1981; Quinton et a l . , 1982). Growth i n i t i a t i o n i n bluebunch wheatgrass has been r e p o r t e d when s o i l temperatures at a 10 cm depth were 6°C (Quinton et a l . , 1982) and 4°C (Willms et a l . , 1980a). Growth c e s s a t i o n i n bluebunch wheatgrass has oc c u r r e d at a time when moisture a v a i l a b i l i t y was comparable to that observed i n e a r l y s p r i n g (Quinton et a l . , 1982). T h i s o b s e r v a t i o n compelled Quinton et a l . (1982) to conclude that s o i l moisture i s not a c o n t r o l l i n g f a c t o r i n the growth c e s s a t i o n of t h i s s p e c i e s . Evidence s u p p o r t i n g t h i s c o n c l u s i o n i s f u r t h e r p r o v i d e d by Daubenmire (1972), who found that bluebunch wheatgrass leaves remained p a r t i a l l y green and f l e x i b l e u n t i l mid-August, even though no water i n excess of the w i l t i n g c o e f f i c i e n t had been w i t h i n reach of the grass r o o t s a f t e r mid-June. Daubenmire (1972) suggested that the t o l e r a n c e to low water l e v e l s was due to a g r e a t l y reduced t r a n s p i r a t i o n r a t e and a r e d i s t r i b u t i o n of water r e s e r v e s w i t h i n the p l a n t . Given the hig h s e n s i t i v i t y of bluebunch wheatgrass to m i l d moisture s t r e s s (Anderson and McNaughton, 1973), the low s i g n i f i c a n c e of moisture l e v e l s might appear q u e s t i o n a b l e . In f a c t , three p i e c e s of evidence support the importance of water a v a i l a b i l i t y i n l i m i t i n g growth. F i r s t l y , i f moisture had not been l i m i t i n g , then temperature might be expected to p l a y a major r o l e i n 12 governing growth c e s s a t i o n . However, at growth c e s s a t i o n , s o i l temperatures at 10 cm depths were 12-15°C and 11-15°C at a lower and upper g r a s s l a n d s i t e ; a i r temperatures were 12-16°C and 13-15°C a t the two r e s p e c t i v e s i t e s (Quinton et a l . , 1982). These temperatures, although lower than the optimal of 20 to 25°C, would s t i l l have allowed c o n s i d e r a b l e p h o t o s y n t h e t i c a c t i v i t y (Depuit and C a l d w e l l , 1975) and should not have a r r e s t e d growth. Secondly, B l a i s d e l l and Pechanec (1949) had c o n c l u s i v e l y demonstrated that s o i l moisture was the c h i e f f a c t o r which prevented regrowth when they conducted a smal l watering experiment. F i n a l l y , a comparison of the p h e n o l o g i c a l development i n a wet and a dry year r e v e a l e d that summer dormancy o c c u r r e d at a much l a t e r date i n the year when p r e c i p i t a t i o n d u r i n g the growing season was 2.8 times higher than the year when p r e c i p i t a t i o n was abnormally low (Sauer and Uresk, 1976). The d i s c o r d a n t r e p o r t s d i s c u s s e d above focus a t t e n t i o n on the f a c t t h a t no s i n g l e f a c t o r i s c o n s i s t e n t l y r e s p o n s i b l e f o r growth c e s s a t i o n i n bluebunch wheatgrass. More probably, growth c e s s a t i o n i s d i c t a t e d by an i n t e r a c t i o n of environmental f a c t o r s , and the importance of any s i n g l e f a c t o r w i l l depend i n part on the s t a t e of the a l t e r n a t e f a c t o r s . The c o n c l u s i o n of a e s t i v a t i o n i n bluebunch wheatgrass has been r e l a t e d to a lowering i n s o i l 13 temperature (Daer and W i l l a r d , 1981). Daubenmire (1972) added that f a l l regrowth o c c u r r e d before autumn p r e c i p i t a t i o n had moistened s o i l s at the r o o t i n g depth. F o l i a r regrowth, which may reach h e i g h t s of up to 25 cm (Evans and T i s d a l e , 1972), i s s i g n i f i c a n t i n determining forage a v a i l a b i l i t y i n both winter and e a r l y s p r i n g . Willms et a l . (1980a) r e p o r t e d that the 5 cm of f a l l regrowth was a l r e a d y growing by the time the s p r i n g - i n i t i a t e d t i l l e r s appeared at the crown. The d i f f e r e n c e i n l e n g t h between the s p r i n g and f a l l i n i t i a t e d t i l l e r s had i n c r e a s e d to 7.5 cm before the newly formed t i l l e r s emerged from the s o i l . 2.3.2 DEFOLIATION EFFECTS ON DRY MATTER PRODUCTION Rates of v e g e t a t i v e growth f o l l o w i n g herbage removal were examined by Willms et a l . (1980a), who concluded that c l i p p i n g p l a n t s to 5 cm stu b b l e h e i g h t s in the f a l l had no e f f e c t on the r a t e of t i l l e r e l o n g a t i o n the f o l l o w i n g s p r i n g . However, t i l l e r e l o n g a t i o n was s i g n i f i c a n t l y higher i n f a l l c l i p p e d p l a n t s than i n c o n t r o l p l a n t s on one sampling date i n mid A p r i l (Willms et a l . , 1980a). Since t h i s p e r i o d was c h a r a c t e r i z e d by u n u s u a l l y low s o i l temperatures (Willms et a l . , 1980a), the s u p e r i o r growth i n p r e v i o u s l y d e f o l i a t e d p l a n t s may r e f l e c t the higher temperature of bunches where shading from o l d f o l i a g e was removed. 14 Con t r a r y to r e p o r t s f o r c r e s t e d wheatgrass (Cook and St o d d a r t , 1953), s t u d i e s on bluebunch wheatgrass r e v e a l e d no i n d i c a t i o n that t i l l e r development i s s t i m u l a t e d by herbage removal (Branson, 1956; Willms et a l . , 1980b; C a l d w e l l et a l . , 1981). Branson (1956) found t h a t the number of l i v e culms was s l i g h t l y depressed i n p l a n t s which had r e p e a t e d l y been c l i p p e d to one inch (2.54 cm) st u b b l e h e i g h t s . Willms et a l . (1980b) observed no s i g n i f i c a n t d i f f e r e n c e i n t i l l e r d e n s i t y between u n d e f o l i a t e d p l a n t s and p l a n t s which had been c l i p p e d i n the f a l l . M o r t a l i t y of s p r i n g - c l i p p e d t i l l e r s was observed e i t h e r immediately f o l l o w i n g d e f o l i a t i o n or a f t e r the development of s u b s t a n t i a l water s t r e s s ( C a l d w e l l et a l . , 1981). T i l l e r s which s u r v i v e d c l i p p i n g d i d not produce new t i l l e r s . With a s i n g l e e x c e p t i o n , t i l l e r s which had d i e d a l s o f a i l e d to y i e l d new t i l l e r s ( C a l d w e l l et a l . , 1981). 3 . METHODS B l u e b u n c h w h e a t g r a s s g r o w t h was m o d e l e d m e c h a n i s t i c a l l y w i t h p l a n t r e s p o n s e t o a b i o t i c a n d b i o t i c f a c t o r s s i m u l a t e d a t t h e p h y s i o l o g i c a l l e v e l w h e r e p o s s i b l e . A m e c h a n i s t i c a p p r o a c h was n e e d e d t o a s s u r e t h e b i o l o g i c a l r e l e v a n c e o f m o d e l p a r a m e t e r s a n d t o p e r m i t p o s t u l a t i o n o f b i o l o g i c a l r e l a t i o n s h i p s . T h e h e u r i s t i c power o f h i e r a r c h i c a l l y I. s t r u c t u r e d m o d e l s h a s p r e v i o u s l y b e e n a c k n o w l e d g e d by t h e m o d e l i n g c o m m u n i t y ( T h o r n l e y , 1 9 7 6 ) . A m e c h a n i s t i c a p p r o a c h a l s o a l l o w e d f o r g e n e r a l a p p l i c a b i l i t y o f t h e m o d e l , a p r o p e r t y n e e d e d t o a c c o m m o d a t e s i t u a t i o n c h a n g e s i n t r o d u c e d by s u c h f a c t o r s a s g e o g r a p h i c l o c a t i o n , c l i m a t i c p a t t e r n , o r g r a z i n g s c h e d u l e . S u c h an a p p r o a c h d o e s , h o w e v e r , t e n d t o s a c r i f i c e p r e c i s i o n f o r r e a l i s m a n d g e n e r a l i t y ( W a l t e r s , 1 9 7 1 ; T h o r n l e y , 1 9 7 6 ) . A l t h o u g h b l u e b u n c h w h e a t g r a s s g r o w t h was m o d e l e d m e c h a n i s t i c a l l y , m a t h e m a t i c a l e q u a t i o n s d e s c r i b i n g p h y s i o l o g i c a l p r o c e s s e s g o v e r n i n g b i o m a s s a c c u m u l a t i o n w e r e e m p i r i c a l l y d e r i v e d . M a t h e m a t i c a l e q u a t i o n s f o r c u r v e f i t t i n g w e r e s e l e c t e d p r i m a r i l y on t h e b a s i s o f t h e i r g o o d n e s s o f f i t . I n m o s t c a s e s , no a t t e m p t was made t o i n t e r p r e t t h e b i o l o g i c a l s i g n i f i c a n c e o f c o e f f i c i e n t v a l u e s o r f u n c t i o n t y p e . I n some i n s t a n c e s , p i e c e w i s e l i n e a r f u n c t i o n s o r c u b i c s p l i n e s w e r e u s e d t o d e s c r i b e r e l a t i o n s h i p s w h i c h d e f i e d f i t t i n g w i t h c o n v e n t i o n a l c u r v e s . P u b l i s h e d i n f o r m a t i o n on b l u e b u n c h w h e a t g r a s s p h y s i o l o g i c a l p r o c e s s e s was u s e d f o r m o d e l c o n s t r u c t i o n 15 16 whenever p o s s i b l e . Where i n f o r m a t i o n gaps e x i s t e d , e m p i r i c a l data c o l l e c t e d f o r other members of the same genus were e x p l o i t e d . In cases where q u a n t i t a t i v e guidance was e n t i r e l y l a c k i n g f o r the Agropyron genus, b i o l o g i c a l p r i n c i p l e s were obtained from o b s e r v a t i o n s of other p l a n t s p e c i e s . Precedence was given to those s p e c i e s having the highest degree of b i o l o g i c a l s i m i l a r i t y to bluebunch wheatgrass. Subsequently, simple a l l o m e t r i c r e l a t i o n s h i p s were p o s t u l a t e d and f i n e - t u n e d a g a i n s t e m p i r i c a l data c o l l e c t e d f o r bluebunch wheatgrass. During model development, a c o n s c i e n t i o u s e f f o r t was made to use simple i n d i c e s and components which would capture e s s e n t i a l b i o l o g i c a l p rocesses without undue complexity. The degree of complexity was kept to a minimum in order to reduce both computing c o s t s and number of input v a r i a b l e s . Large i n f o r m a t i o n gaps i n the data base a l s o precluded the development of a h i g h l y complex, yet b i o l o g i c a l y reasonable, model. Bu n n e l l (1973) has documented a geometric i n c r e a s e i n the number of assumptions with i n c r e a s e d d e t a i l , and r e p o r t e d that model u t i l i t y may w e l l d e c l i n e beyond a t h r e s h o l d r e s o l u t i o n . A l t e r n a t i v e l y , s u f f i c i e n t d e t a i l must be r e t a i n e d to permit r e a l i s t i c s i m u l a t i o n and to s a t i s f y modeling o b j e c t i v e s . Thus, modeling r e s o l u t i o n i s n e c e s s a r i l y a compromise between the need f o r s i m p l i c i t y , which i s imposed by l o g i s t i c a l c o n s t r a i n t s , and the need for complexity, which i s imposed by b i o l o g i c a l c o n s t r a i n t s . 1 7 Process r a t e s were determined through m u l t i p l i c a t i o n of a maximum ra t e by a s e r i e s of non-dimensional s c a l a r s r e p r e s e n t i n g the e f f e c t s of c o n t r o l l i n g f a c t o r s on the pro c e s s . S c a l a r s ranged i n value from 0 to 1, depending on the o p t i m a l i t y of the f a c t o r towards the process r a t e . T h i s approach i s commonly implemented i n modeling (Holt et a l . , 1975; Jameson and Gross, 1977; D e t l i n g et a l . , 1979; M c G i l l et a l . , 1981); however, D e t l i n g et a l . ( l 9 7 9 ) has ca u t i o n e d that an over r e d u c t i o n i n process r a t e might ensue when s e v e r a l c o n t r o l l i n g f a c t o r s are suboptimal. The e x c l u s i o n of i n t e r a c t i v e e f f e c t s among c o n t r o l l i n g f a c t o r s may be a r e l a t i v e l y s e r i o u s omission i n t h i s model. U n f o r t u n a t e l y , t h i s d i f f i c u l t y cannot be o b v i a t e d given the p a u c i t y of a v a i l a b l e d ata. The model operates on a d a i l y time-step. V a l i d a t i o n was conducted by comparing s i m u l a t i o n r e s u l t s with f i e l d data c o l l e c t e d by Harper (1969) i n 1967 and 1968 f o r a bluebunch wheatgrass mesic community i n the Ashnola Region of B r i t i s h Columbia. Where lack of s u i t a b l e data p r e c l u d e d q u a n t i t a t i v e v a l i d a t i o n of model, q u a l i t a t i v e v a l i d a t o n was c a r r i e d out between s i m u l a t i o n r e s u l t s and e m p i r i c a l o b s e r v a t i o n s . S e n s i t i v i t y a n a l y s i s was performed by a l t e r i n g maximum process r a t e s as w e l l as temperature and moisture regimes. 4. AGGRO: SIMULATION MODEL OF BLUEBUNCH WHEATGRASS GROWTH 4.1 GENERAL MODEL STRUCTURE Bluebunch wheatgrass growth dynamics were modeled as f u n c t i o n s of s o i l water p o t e n t i a l , s o i l and a i r temperatures, r a i n f a l l i n t e n s i t y , photoperiod, f o l i a r n i t r o g e n content, and p l a n t m a t u r i t y . At each time step, the model ( F i g u r e 1) computes growth p o t e n t i a l , p h o t o s y n t h e s i s , dark r e s p i r a t i o n , carbohydrate t r a n s l o c a t i o n between aboveground and belowground biomass, dry matter p r o d u c t i o n , shoot and root m o r t a l i t y , and l i t t e r f a l l . The model c o n s i d e r s bluebunch wheatgrass at the whole-plant l e v e l , but d i s t i n g u i s h e s between s p r i n g growth, f a l l regrowth, and regrowth r e s u l t i n g from d e f o l i a t i o n . H e rbivory i s user determined and e x p l i c i t l y a l t e r s s t a n d i n g biomass, p h o t o s y n t h e t i c r a t e , and i n c i d e n c e of t i l l e r i n g . A summary of v a r i a b l e names and l i t e r a t u r e sources i s pr o v i d e d i n Table 1. 4.2 ABIOTIC DRIVING VARIABLES With the ex c e p t i o n of a s t o c h a s t i c p r e c i p i t a t i o n generator, c l i m a t i c c o n d i t i o n s are not modeled m e c h a n i s t i c a l l y i n AGGRO. A b i o t i c d r i v i n g v a r i a b l e s are e i t h e r read i n from weather records or approximated w i t h . g e n e r a l i z e d e q u a t i o n s . The f i r s t method i s employed when model v a l i d a t i o n demands p r e c i s e input v a l u e s . The second method i s used when quick m o d i f i c a t i o n of c l i m a t i c p a t t e r n s i s d e s i r e d . 18 19 Growth potential of aboveground biomass <G > G DMP=G - CHO deficit DMP = Spring growth Dry matter production (DMP) Foliar carbohydrate Belowground carbohydrate storage > 0 no yes Fall regrowth Regrowth after defoliation Respiration Photosynthesi; yes Mortality no Standing dead Fallen litter FIGURE 1 . General model s t r u c t u r e of AGGRO. TABLE I. Summary of variable names and literature sources. VARIABLE BRIEF DESCRIPTION DEFINITION SOURCE WPOT soil water potential EQ. (1), EQ. (3) TEMP air temperature EQ. (4) STEMP soil temperature EQ. (5) RP rainfall duration EQ. (7) DL daylength EQ. (8) G aboveground biomass growth potential EQ. (9) GA contribution of aboveground biomass EQ. (TO) to growth potential GB contribution of belowground biomass EQ. (14) to growth potential GMAX maximum growth rate 0.086 g g d Quinton et al. (1982) TG effect of temperature on growth EQ. (11) deVries et al. (1979) WG effect of soil water potential EQ. (12) Majerus (1975) on growth NG effect of foliar nitrogen on growth EQ. (13) Wilson (1975) DLG effect of photoperiod on growth Walton (1983) BGMAX maximum GB 0.0054 - 0.08 gg"'d"' Fine-tuned EQ. (24) ... continued o TABLE I. conti nued ... VARIABLE BRIEF DESCRIPTION MB effect of maturity on GB PSYN photosynthesis PMAX maximum photosynthetic rate TPSYN effect of temperature on PSYN WPSYN effect of soil water potential photosynthesis RESP respiration WBM effect of soil water potential on root mortality LF litterfall N seasonal foliar nitrogen GRPSYN effect of defoliation on photosynthesis DEFINITION SOURCE EQ. (15) Hypothesized EQ. (16) 0.016 g C02 g"1 hr"1 Depuit and Caldwell (1975) EQ. (17) Depuit and Caldwell (1975) EQ. (18) Brown and Trlica (1977) EQ. (19) Depuit and Caldwell (1975) EQ. (20) Parton et al. (1978) EQ. (21) Saugier et al. (1974) EQ. (22) Fitted to data from ten studies EQ. (23) Painter and Detling (1981) 22 4.2.1 SOIL WATER POTENTIAL C o n s i d e r a b l e d i f f i c u l t y was encountered i n s e c u r i n g r e a l i s t i c data on s o i l water p o t e n t i a l s i n c e rangeland s t u d i e s g e n e r a l l y present only measurements of p r e c i p i t a t i o n or s o i l water percentage ( S k o v l i n , 1967; Harper, 1969; Daer and W i l l a r d , 1981; Stout et a l . , 1981; Quinton et a l . , 1982). In most cases, c o n v e r s i o n of the l a t t e r two parameters i n t o s o i l water s u c t i o n i s pre c l u d e d by unknown v a l u e s f o r c r i t i c a l s o i l and r a d i a t i o n v a r i a b l e s . In AGGRO, s o i l water s t a t u s i s approximated with an equation d e s c r i b i n g s u c t i o n v a l u e s measured by van Ryswyck and Broersma (1977, unpub. data) f o r three g r a s s l a n d s i t e s i n i n t e r i o r B r i t i s h Columbia. The thr e e water regimes ( F i g u r e 2) may be used to eval u a t e the e f f e c t s of hi g h , i n t e r m e d i a t e , arid low s o i l water on bluebunch wheatgrass growth dynamics. Curve f i t t i n g f o r seasonal moisture a v a i l a b i l i t y was accomplished with a s i x c o e f f i c i e n t F o u r i e r s e r i e s of the form: 6 WPOT = WPAO/2 + Z WPCI c o s ( i 7 r t / p ) + WPSI (1) i = 1 sin(i7rt/p) where WPOT = water p o t e n t i a l (bars) t = time of year ( J u l i a n date) p = one h a l f the p e r i o d f u n c t i o n of WPOT and WPAO, WPCI, and WPSI are c o e f f i c i e n t s (Appendix 1). A moisture c h a r a c t e r i s t i c curve ( F i g u r e 3) was developed f o r Harper's (1969) bluebunch wheatgrass study 23 i — — i — i • • . J F M A M J J A S O N D MONTH FIGURE 2. Soil water regimes used to evaluate the effects of high, medium, and low moisture availability on bluebunch wheatgrass growth dynamics (From van Ryswyk and Broersma, unpub. data). 24 FIGURE 3. Moisture characteristic curve developed for Harper's (1969) bluebunch wheatgrass mesic site. 25 s i t e f o r use i n model v a l i d a t i o n . S o i l water content was r e l a t e d to s o i l water p o t e n t i a l at p o r o s i t y , 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 , and a c u r v i l i n e a r r e l a t i o n s h i p was f i t t e d to permit i n t e r p o l a t i o n between the r e f e r e n c e p o i n t s . A bulk d e n s i t y (p ) of 1.55 cm 3 b cm" 3 ( I s r a e l s e n and Hansen, 1962) was used to c a l c u l a t e s o i l p o r o s i t y , which i s d e f i n e d as (Novak, p e r s . com.): 1 - p /2.650 (2) b F i e l d c a p a c i t y (-0.33 bars) and permanent w i l t i n g p o i n t (-15 bars) were estimated at 20 and 11.3 percent water content r e s p e c t i v e l y (Harper, 1969). The moisture c h a r a c t e r i s t i c curve thus d e r i v e d assumed the r e l a t i o n s h i p : (0.28623 - WCON)/0.040924 WPOT = e (3) where WPOT = s o i l water p o t e n t i a l (bars) WCON = s o i l water percentage (by volume) Water p o t e n t i a l v a l u e s generated f o r Harper's (1969) 1967 and 1968 f i e l d season are d e p i c t e d i n F i g u r e 4. 4.2.2 AIR AND SOIL TEMPERATURES A i r temperature i s modeled with the s i n e f u n c t i o n d e s c r i b e d by Bunnell (1970), i n which: TEMP = TO + (TM - TO) [(1 + s i n ( a t + b))/2] (4) where TEMP = a i r temperature ( °C ) TO = minimum a i r temperature ( °C ) 26 FIGURE 4. Seasonal soil water potentials generated for Harper's (1969) bluebunch wheatgrass mesic site in 1967 and 1968. 27 TM = maximum a i r temperature ( °C ) a = 2TT/365.25 t = time ( J u l i a n date) b = - a ( j u l i a n date of TO + J u l i a n date of TM)/2 Maximum and minimum temperatures e q u a l l e d 28.2 and -9.4°C r e s p e c t i v e l y f o r Harper's bluebunch wheatgrass mesic s i t e i n 1967, and e q u a l l e d 28.2 and -12.8°C f o r the same s i t e i n 1968 (F i g u r e 5 ) . S o i l temperatures (STEMP) were d e r i v e d from a i r temperatures with the formula (Novak, p e r s . com.): -Z/Dd 5Tz = 8To e (5) where 8Tz = amplitude of temperature wave at s o i l depth Z 6To = amplitude of temperature wave at s o i l s u r f a c e Z = s o i l depth (m) Dd = damping depth (m) The amplitude of the s o i l s u r f a c e temperature wave was assumed to equal that of the atmospheric temperature wave. Damping depth was c a l c u l a t e d with the formula (Novak, p e r s . com.): Dd = /pT7 7TC ( 6 ) where p = p e r i o d of f u n c t i o n (s) k/c = d i f f u s i v i t y constant [0.5X10~ 7 m2 s " 1 , d e V r i e s and Afgan (1975)] 28 • • • * * • 1 1 J F M A M J J A S O N D MONTH FIGURE 5. Simulated air temperatures for Harper's (1969) bluebunch wheatgrass mesic site in 1967 and 1968. 29 S o i l temperature was assumed to l a g behind a i r temperature by a p h a s e - s h i f t of Z/Dd (Novak, p e r s . com.). 4.2.3 PRECIPITATION The p r e c i p i t a t i o n generator i n AGGRO i s s t o c h a s t i c a l l y d r i v e n but i n c l u d e s the f o l l o w i n g c o n s t r a i n t s : (1) r a i n f a l l i n t e n s i t y i s not allowed to exceed the maximum i n t e n s i t y which can be expected w i t h i n a 2 year p e r i o d , (2) r a i n f a l l d u r a t i o n i s not allowed to exceed the maximum d u r a t i o n which can be expected w i t h i n a 2 year p e r i o d f o r a s p e c i f i e d r a i n f a l l i n t e n s i t y , (3) t o t a l monthly p r e c i p i t a t i o n i s not allowed to d e v i a t e from the mean monthly p r e c i p i t a t i o n e s t a b l i s h e d f o r that r e g i o n by more than 10%. For Harper's bluebunch wheatgrass mesic community, maximum r a i n f a l l d u r a t i o n f o r a s p e c i f i c i n t e n s i t y i s determined from the f o l l o w i n g equation based on Environment Canada's (1969-1981) i n t e n s i t y - d u r a t i o n c h a r t : 6.6571 -1.1672 -0.031468-RN RP = (e )(RN ) (e )/60 (7) where RP = d u r a t i o n of r a i n f a l l (hr) RN = r a i n i n t e n s i t y (mm h r - 1 ) 4.2.4 DAYLENGTH Daylength i s modeled with the equ a t i o n : 30 DL = DLAO/2 + DLC1 COS (irt/p) +' DLS1 s i n (8) U t/p) where DL = daylength (hrs) t = time of year ( J u l i a n date) p = one h a l f the p e r i o d f u n c t i o n of DL and DLAO, DLC1, and DLS1 are c o e f f i c i e n t s . For Harper's bluebunch wheatgrass mesic community, DLAO equals 24.11081648, DLC1 equals -3.83307714, andDLSI equals 0.58219562. 4.3 GROWTH POTENTIAL AND DRY MATTER PRODUCTION In AGGRO, bluebunch wheatgrass growth i s e n t i r e l y dependent on the f a v o u r a b i l i t y of p r e v a i l i n g growing c o n d i t i o n s and i s not a f f e c t e d by inherent t r a i t s i n the p l a n t . Growth i s t h e r e f o r e i n i t i a t e d when the t h r e s h o l d temperature f o r meristematic a c t i v i t y has been gained, and growth c e s s a t i o n , in both summer and winter, occurs when c o n d i t i o n s become s u f f i c i e n t l y adverse. The assumption of an imposed or enf o r c e d dormancy, as opposed to an innate or spontaneous one, i s reasonable f o r many past u r e grasses (Wareing and P h i l l i p s , 1970). A growth p o t e n t i a l , G, was developed to r e f l e c t the growth that i s p o s s i b l e under e x i s t i n g c o n d i t i o n s . G has two components: GA, which r e p r e s e n t s the c o n t r i b u t i o n of aboveground biomass to growth p o t e n t i a l , and GB, which r e p r e s e n t s the c o n t r i b u t i o n of belowground biomass to growth potent i a l : 31 G = GA+GB (9) Although f o l i a r growth i s g e n e r a l l y not modeled as a d i r e c t f u n c t i o n of belowground biomass (Holt et a l . , 1975; Jameson and Gross, 1977; Wann et a l . , 1978; Sheehy et a l . , 1979; D e t l i n g et a l . , 1979; Sweeney et a l . , 1981), such a maneuver i s e s p e c i a l l y important i n the case of bluebunch wheatgrass which d i e s back to the ground each wi n t e r . Thus, i n c l u s i o n of GB i n c r e a s e s the s e n s i t i v i t y of dry matter p r o d u c t i o n to p l a n t v i g o r i n the s p r i n g . In the model, GB i s intended to r e f l e c t the i n c i d e n c e of t i l l e r i n g and the c o n t r i b u t i o n of growth hormones from the root system. Of . p a r t i c u l a r importance are the c y t o k i n i n s , which are s y n t h e s i z e d only i n the r o o t s , and the g i b b e r e l l i n s , which have been i m p l i c a t e d i n growth i n i t i a t i o n ( S a l i s b u r y and Ross, 1969). GB i s the dominant component i n G i n e a r l y s p r i n g when aboveground biomass i s low. GB d e c l i n e s i n importance as f o l i a r growth a c c e l e r a t e s . The c o n t r i b u t i o n of aboveground biomass to growth p o t e n t i a l i s c a l c u l a t e d as a f u n c t i o n of s o i l water p o t e n t i a l , a i r temperature, f o l i a r n i t r o g e n , and daylength: GA = GMAX • TG • WG • NG • DLG • LAB (10) where GMAX = max growth r a t e (g g" 1 day" 1 ) TG = s c a l a r r e p r e s e n t i n g e f f e c t s of temperature on growth WG = s c a l a r r e p r e s e n t i n g e f f e c t s of s o i l water p o t e n t i a l on growth 32 NG = s c a l a r r e p r e s e n t i n g e f f e c t s of f o l i a r n i t r o g e n on growth DLG = s c a l a r r e p r e s e n t i n g e f f e c t s of daylength on growth LAB = l i v e aboveground biomass (g n r 2 ) The e f f e c t s of a i r temperature on growth r a t e (Figure 6) are based on work by d e V r i e s et a l . (1979) on p e r e n n i a l ryegrass (Lolium perenne L . ) , and d e s c r i b e d by the r e l a t i o n s h i p : TG = (0.31298 + 0.046723 • TEMP - 0.0096323 • (11) TEMP 2 + 0.0010382 • TEMP 3 - 0.20755E-4 • TEMPM/4.27 In the model, growth c e s s a t i o n occurs when a i r temperature exceeds 40°C or drops below -0.5°C. The e f f e c t s of s o i l water p o t e n t i a l on growth r a t e was i n i t i a l l y modeled with an equation d e r i v e d by Eddleman and Nimlos (1972) i n a l a b o r a t o r y study on bluebunch wheatgrass. The r e l a t i o n s h i p thus modeled i n v o l v e d an e x p o n e n t i a l d e c l i n e i n growth r a t e with i n c r e a s i n g moisture s t r e s s , with growth stoppage o c c u r r i n g at a s o i l water p o t e n t i a l of -12 ba r s . However, i n s i m u l a t i o n t r i a l s i n v o l v i n g s o i l water regimes t y p i c a l of B.C. g r a s s l a n d s , i t was found that t h i s r e l a t i o n s h i p decimated growth p o t e n t i a l to the p o i n t where biomass accumulation became n e g l i g i b l e . A d e c i s i o n was subsequently made to reduce the s o i l water p o t e n t i a l at which growth stoppage o c c u r s , s i n c e (1) s i m u l a t i o n r e s u l t s were h i g h l y i m p l a u s i b l e , (2) the equation d e r i v e d by Eddleman and Nimlos (1972) r e t a i n e d an R 2 of only 0.40, (3) 33 FIGURE 6. potential "Simulated effect of air temperature on growth (Adapted from data by de Vries et al. (1979)). 34 Daubenmire (1972) had observed green f o l i a g e on bluebunch wheatgrass p l a n t s long a f t e r s o i l water p o t e n t i a l reached -15 bars, and (4) c e l l e l o n g a t i o n i n c r e s t e d wheatgrass cont i n u e s u n t i l s o i l water p o t e n t i a l at a 20 cm depth approaches -25 bars (Majerus, 1975). The modeled response of bluebunch wheatgrass to moisture s t r e s s i s t h e r e f o r e adapted from Majerus' (1975) data f o r c r e s t e d wheatgrass, and assumes the l i n e a r r e l a t i o n s h i p d e p i c t e d i n F i g u r e 7: WG = 1 - [0.8 • (ABS(WPOT))]/20.0 (12) where WG = nondimensional s c a l a r r e p r e s e n t i n g the e f f e c t s of s o i l water p o t e n t i a l on growth r a t e WPOT = s o i l water p o t e n t i a l (bars) A f u n c t i o n a l e q u i l i b r i u m (Brouwer, 1963) e x i s t s between the aboveground and belowground biomass such that root growth i s l i m i t e d by the carbohydrate supply from the shoot, while shoot growth i s l i m i t e d by the m i n e r a l supply from the root (Loomis, 1953). T h i s f u n c t i o n a l e q u i l i b r i u m i s accommodated i n the model through the i n c l u s i o n of NG, which computes the e f f e c t of f o l i a r n i t r o g e n on growth r a t e . N i t r o g e n i s q u a n t i t a t i v e l y the most important element taken up by the p l a n t (Alberda, 1968) , and dramatic i n c r e a s e s i n dry matter p r o d u c t i o n f o l l o w i n g n i t r o g e n f e r t i l i z a t i o n has been w e l l documented f o r the Agropyron genus (E c k e r t et a l . , 1961; Sneva, 1973; Bayoumi and Smith, 1976; W i l l i a m s et a l . , 1979). The e f f e c t s of f o l i a r n i t r o g e n on growth i s c a l c u l a t e d as 35 FIGURE 7. Simulated effect of soil water on growth potential (Adapted from data by Majerus (1975)). 36 -1.0383(N-1) NG = (100.0 - 90.Oe )/l00.0 (13) where NG = nondimensional s c a l a r r e p r e s e n t i n g e f f e c t s of f o l i a r n i t r o g e n on growth r a t e N = f o l i a r n i t r o g e n (%) and i s based on data c o l l e c t e d by Wilson (1975) f o r p e r e n n i a l ryegrass ( F i g u r e 8 ) . Although ontogenetic changes i n growth rate are g e n e r a l l y acknowledged and commonly i n c l u d e d i n growth models (Holt et a l . , 1975; D e t l i n g et a l . , 1979), the e f f e c t s of p h e n o l o g i c a l development on growth p o t e n t i a l i s not e x p l i c i t l y modeled i n AGGRO. T h i s omission i s b e l i e v e d j u s t i f i e d s i n c e a d e c e l e r a t i n g growth r a t e i s i m p l i c i t l y modeled by the i n c l u s i o n of NG. To account f o r decreased growth r a t e s under shortened p h o t o p e r i o d s , GMAX i s reduced by 30% f o r each 60 minute r e d u c t i o n i n photoperiod beyond 13 hours (Walton, 1983). Dry matter p r o d u c t i o n i s equal to growth p o t e n t i a l when the carbohydrate supply from c u r r e n t p h o t o s y n t h e s i s or underground r e s e r v e s i s adequate to support growth p o t e n t i a l . Where a carbohydrate d e f i c i t e x i s t s , dry matter p r o d u c t i o n i s equal to growth p o t e n t i a l l e s s the d e f i c i t . Maximum f o l i a r growth f o r bluebunch wheatgrass was estimated at 0.086 g g" 1 day" 1. T h i s v a l u e was determined by t a k i n g the f i r s t d e r i v a t i v e of the seasonal y i e l d curve presented by Quinton et a l . (1982) and subsequently d i v i d i n g by stan d i n g biomass to o b t a i n r e l a t i v e growth r a t e . 37 FIGURE 8. Simulated effect of foliar nitrogen on growth potential (Adapted from data by Wilson (1975) ). 38 The c o n t r i b u t i o n of belowground biomass t o growth p o t e n t i a l i s c a l c u l a t e d as a f u n c t i o n of s o i l water p o t e n t i a l , s o i l temperature, and m a t u r i t y : GB = BGMAX • TG • WG • MB • LBG (14) where BGMAX = maximum c o n t r i b u t i o n of belowground biomass to aboveground growth p o t e n t i a l (g g" 1 day" 1) TG = s c a l a r r e p r e s e n t i n g the e f f e c t of temperature WG = s c a l a r r e p r e s e n t i n g the e f f e c t of s o i l water p o t e n t i a l MB = s c a l a r r e p r e s e n t i n g the e f f e c t of mat u r i t y LBG = l i v e belowground biomass (g m"2) In the absence of r e l e v a n t data, i t was assumed t h a t the e f f e c t s of temperature and s o i l water p o t e n t i a l on underground a c t i v i t y are equal to those on aboveground a c t i v i t y . BGMAX i s f i n e - t u n e d at 0.054 g g" 1 day" 1 f o r growth i n i t i a t i o n i n s p r i n g , and at 0.08 g g" 1 day" 1 f o r growth i n i t i a t i o n i n the f a l l , the e f f e c t of m a t u r i t y on GB (Fi g u r e 9) i s p o s t u l a t e d to f o l l o w the r e l a t i o n s h i p : MB = 0.9930 - 0.14683 • KB + 0.56462E-2 • KB 2 (15) where MB = s c a l a r r e p r e s e n t i n g the e f f e c t of ma t u r i t y KB = number of days s i n c e i n i t i a t i o n of root a c t i v i t y . FIGURE 9. Simulated effect of plant maturity on below-ground hormonal activity and incidence of tillering. 4 0 4.4 GENERATION OF ASSIMILATES Apparent p h o t o s y n t h e s i s i s assumed to depend p r i m a r i l y on a i r temperature and s o i l water p o t e n t i a l , and i s c a l c u l a t e d as: PSYN = PMAX • TPSYN • WPSYN • DL • 0.675 (16) where PSYN = generated a s s i m i l a t e s (g CHO g" 1 biomass d a y 1) PMAX = maximum p h o t o s y n t h e t i c r a t e (g C0 2 g" 1 biomass h r ~ 1 ) TPSYN = s c a l a r r e p r e s e n t i n g e f f e c t s of temperature on p h o t o s y n t h e t i c r a t e (undimensioned) WPSYN = s c a l a r r e p r e s e n t i n g e f f e c t s of s o i l water p o t e n t i a l (undimensioned) DL = daylength (hours d a y 1 ) 0.675 = m u l t i p l i e r t o convert gC0 2 to gCHO Maximum p h o t o s y n t h e t i c r a t e i s estimated at (0.016 g C0 2 g" 1 biomass h r ' 1 ) (Depuit and C a l d w e l l , 1975). The e f f e c t of temperature on p h o t o s y n t h e t i c r a t e i s c a l c u l a t e d from the piecewise l i n e a r f u n c t i o n d e p i c t e d i n F i g u r e 10. The f u n c t i o n was adapted from data c o l l e c t e d by Depuit and C a l d w e l l (1975) f o r b e a r d l e s s wheatgrass ( Agropyron spicatum var inerme H e l l e r ) , and e q u a l s : ( i f TEMP<0 or TEMP>40) TPSYN = 0 (17a) ( i f 0<TEMP<5) TPSYN = 0.1052632 • TEMP (17b) 41 1 .0 r TEMPERATURE ( °C ) FIGURE 10. Simulated effect of air temperature on photo-synthesis (Adapted from data by Depuit and Caldwell (1975) ). 42 ( i f 5< TEMP<20) TPSYN = 1 - 0.03158 (20-TEMP) (17c) ( i f 20< TEMP <25) TPSYN = 1 (I7d) ( i f 25<TEMP<35) TPSYN = 1 - 0.03421 (TEMP-25) (I7e) ( i f 35<TEMP<40) TPSYN = 0.1315789 (40-TEMP) (I7f ) where TPSYN = s c a l a r r e p r e s e n t i n g the e f f e c t of temperature on p h o t o s y n t h e s i s TEMP = a i r temperature ( °C ) The e f f e c t of s o i l water p o t e n t i a l on ph o t o s y n t h e s i s ( F i g u r e 11) i s based on Brown and T r l i c a ' s (1977) study on western wheatgrass and assumes the l i n e a r r e l a t i o n s h i p : WPSYN = 1+ 0.03226 • WPOT (18) where WPSYN = e f f e c t of s o i l water p o t e n t i a l on Despi t e the obvious importance of s o l a r r a d i a t i o n on ph o t o s y n t h e s i s , i r r a d i a t i o n e f f e c t s have not been i n c l u d e d i n AGGRO s i n c e l i g h t energy i s not b e l i e v e d to be l i m i t i n g on g r a s s l a n d ranges d u r i n g the growing season. 4.5 RESPIRATION P h o t o r e s p i r a t o r y l o s s e s have been accounted f o r i n AGGRO by modeling apparent p h o t o s y n t h e s i s r a t h e r than true p h o t o s y n t h e s i s . However, dark r e s p i r a t i o n at night and ph o t o s y n t h e s i s WPOT = s o i l water p o t e n t i a l 43 -s-ra _ J 1— <c (O t—1 ( J 1 — to •z. L U T 3 1 — CL) o e Q - o 'f— CC </) L U c 1 — <u <c B •1— " 0 u_ c o 1 — o L U >-U— 1/1 UL . a. L U 3 >—• 1 .0 0.5 0.0 10 SOIL WATER 20 POTENTIAL 30 bars) 40 FIGURE 11. Simulated effect of water potential on photosynthesis (Adapted from data by Brown and Trlica (1977) ). 44 r e s p i r a t i o n of belowground organs must be computed with an independent f u n c t i o n . Dark r e s p i r a t i o n i n t h i s model i s c a l c u l a t e d as a f u n c t i o n of temperature ( F i g u r e 12) s i n c e carbohydrate degradation i s a metabolic process and hence, temperature s e n s i t i v e : RESP = (-0.46107 + 0.069524 • TEMP + 0.0013714 (19) • TEMP 2)/10 • 0.0675 where RESP = R e s p i r a t o r y l o s s e s (g CHO g" 1 biomass h r - 1 ) TEMP = Temperature ( °C ) The r e l a t i o n s h i p between temperature and r e s p i r a t i o n i s based on data presented by Depuit and C a l d w e l l (1975) f o r b e a r d l e s s wheatgrass. In the absence of r e l e v a n t data f o r belowground biomass, r e s p i r a t o r y r a t e of r o o t s was assumed to be equal to that of shoots. However, in the case of belowground organs, r e s p i r a t i o n was modeled as a f u n c t i o n of s o i l temperature i n s t e a d of a i r temperature. 4.6 CARBOHYDRATE PARTITIONING E x t e n s i v e documentation i n d i c a t e s t hat the carbon balance of a p l a n t i s a l t e r e d by changes i n phenology ( M c l l v a n i e , 1942; Sosebee and Wiebe, 1973; Daer and W i l l a r d , 1981) f a v o u r a b i l i t y of growing c o n d i t i o n s ( T r l i c a , 1977; Bokhari, 1978; E l Hassan and Krueger, 1980; Singh et a l . , 1980), and herbage removal (Auda et a l . , 1966; G a r r i s o n , 1966; Bokhari and Singh, 1974; Buwai and T r l i c a , 1977; E l Hassan and Krueger, 1980; Singh et a l . , 1980). Knowledge of the FIGURE 12. Simulated effect of temperature on respiration (Adapted from data by Depuit and Caldwell (1975) ). 46 mechanisms u n d e r l y i n g these changes i s poor, however, and i s e s p e c i a l l y l a c k i n g f o r rangeland g r a s s e s . N e v e r t h e l e s s , carbohydrate p a r t i t i o n i n g i n bluebunch wheatgrass must be modeled a p p r o p r i a t e l y s i n c e p l a n t p r o d u c t i v i t y and biomass accumulation are s i g n i f i c a n t l y a f f e c t e d by a l l o c a t i o n s t r a t e g y ( C a l d w e l l et a l . , 1981; P o t t e r and Jones, 1977) In AGGRO, an approach was adopted which would i m p l i c i t l y r e f l e c t changes i n carbohydrate p a r t i t i o n i n g without demanding d e t a i l e d knowledge of the u n d e r l y i n g mechanisms. I t was hyp o t h e s i z e d that the magnitude and d i r e c t i o n of carbohydrate movement c o u l d be determined by e s t a b l i s h i n g the r e l a t i v e s t r e n g t h s of carbohydrate sources and carbohydrate s i n k s . Thus, reserve carbohydrates from storage organs are t r a n s l o c a t e d upwards when the si n k - s o u r c e s t r e n g t h i s p o s i t i v e , and growth p o t e n t i a l of f o l i a r biomass exceeds the supply of c u r r e n t p h o t o s y n t h e s i s . A l t e r n a t i v e l y , a s s i m i l a t e s are t r a n s l o c a t e d downwards when the s i n k - s o u r c e s t r e n g t h i s n e g a t i v e , and the demands of f o l i a r growth and r e s p i r a t i o n have been s a t i s f i e d . Carbohydrate movement i s t h e r e f o r e d i c t a t e d e n t i r e l y by the s i n k - s o u r c e index, which, because i t i s determined from growth p o t e n t i a l , should be p r o p e r l y r e s p o n s i v e to changes i n phenology, growing c o n d i t i o n s , or d e f o l i a t i o n e f f e c t s . Carbohydrate movement i s never manipulated a r b i t r a r i l y , e i t h e r d u r i n g normal growth or d u r i n g s p e c i a l phases such as growth i n i t i a t i o n or immediately f o l l o w i n g d e f o l i a t i o n . 47 P r o v i s i o n s were not made with re s p e c t to the t r a n s l o c a t i o n process per se s i n c e phloem t r a n s p o r t i s u n l i k e l y to l i m i t a s s i m i l a t e movement (Wardlaw, 1968; McNairn, 1972; Moser, 1977; Zeevaart, 1979). 4.7 SHOOT AND ROOT MORTALITY In AGGRO, shoot m o r t a l i t y i s caused by f r o s t damage, moisture s t r e s s , and senescence. F r o s t damage i s c a l c u l a t e d with Sauer's (1978) method, i n which 25% of l i v e shoot biomass i s t r a n s f e r r e d to s t a n d i n g dead matter when minimum d a i l y temperature f a l l s below a c r i t i c a l t h r e s h o l d of -2°C. The simulated e f f e c t of moisture s t r e s s on shoot m o r t a l i t y i s temperature dependent and based on work by Eddleman and Nimlos (1972) on bluebunch wheatgrass. M o r t a l i t y i s induced i n f o l i a r biomass when s o i l water p o t e n t i a l f a l l s below -30 b a r s . At temperatures above 30°C, the f r a c t i o n of biomass dying per day i n c r e a s e s by 2.5% with each u n i t r e d u c t i o n i n s o i l water p o t e n t i a l beyond -30 bars. At temperatures below 30°C, the f r a c t i o n of biomass dying per day i n c r e a s e s by 2% with each u n i t r e d u c t i o n i n s o i l water p o t e n t i a l beyond -30 b a r s . F o l l o w i n g growth c e s s a t i o n , m o r t a l i t y due to senescence (PHENM) i s assumed to equal 5% of l i v e shoot biomass per day. Belowground m o r t a l i t y i s modeled as a f u n c t i o n of s o i l water p o t e n t i a l and based on data presented by Parton et a l . (1978) f o r blue grama ( Bouteloua gracilis (H.B.K.) Lag.): 48 SB SB SB WBM = -[SY1 + (SY2 - SY1 ) • (1.0 - (20) V (-SA(WPOT)) (-SA • 75) e )/(1.0 - e )] ** ( l / ( 1 - S B ) ) where WBM = s c a l a r r e p r e s e n t i n g the e f f e c t of s o i l water p o t e n t i a l on root m o r t a l i t y SY1 = 0.04 SY2 =0.98 SA = 0.70 SB = -9.85553 Maximum r a t e of root m o r t a l i t y was assumed to equal 0.0026 g n r 2 day " 1 (Parton et a l . , 1978). 4.8 LITTERFALL The f a l l of standing dead matter i s computed with the f o l l o w i n g equation d e r i v e d by Saugier et a l . (1974): LF = (0.00083 + 0.0013 • RAIN) • SD (21) where LF = T r a n s f e r of standing dead matter to l i t t e r (g nr 2 ha" 1) RAIN = P r e c i p i t a t i o n r a t e (cm h r _ 1 ) SD = Standing dead biomass (g n r 2 ) 4.9 FOLIAR NITROGEN F o l i a r n i t r o g e n i s modeled e m p i r i c a l l y with a polynomial r e g r e s s i o n f i t t e d to the data from ten s t u d i e s on bluebunch wheatgrass (McC a l l , 1932; M c l l v a n i e , 1942; Stoddart, 1946; Beath and Hamilton, 1952; B l a i s d e l l et a l . , 1952; S k o v l i n , 49 1967; Demarchi, 1968; R a l e i g h , 1970; Demarchi, 1973; Uresk and C l i n e , 1976). The equation thus d e r i v e d assumed the form: N = (105.86-1.1355 • JD + 0.0043233 • JD 2 - (22) 0.55393E-5 • JD 3)/6.25 where N = f o l i a r n i t r o g e n (%) JD = J u l i a n date F o l i a r n i t r o g e n was assumed to d e c l i n e l i n e a r l y a f t e r August 1 at the r a t e of 0.026% per day. The seasonal d e c l i n e of f o l i a r n i t r o g e n i n s p r i n g growth was s h i f t e d by a maximum of 40 days ( F i g u r e 13) to achieve synchrony with date of growth i n i t i a t i o n . The seasonal d e c l i n e of f o l i a r n i t r o g e n i n f a l l regrowth and i n regrowth f o l l o w i n g herbage removal were s i m i l a r l y computed with t h i s e q uation. However, curve s h i f t i n g was performed to o b t a i n s y n c h r o n i z a t i o n with the s t a r t of f a l l regrowth and the date of d e f o l i a t i o n , r e s p e c t i v e l y . 4.10 EFFECTS OF DEFOLIATION Herbage removal a f f e c t s dry matter p r o d u c t i o n by reducing the p h o t o s y n t h e t i c s u r f a c e as w e l l as a l t e r i n g the r a t e of p h o t o s y n t h e t i c a c t i v i t y ( C a l d w e l l et a l . , 1981; P a i n t e r and D e t l i n g , 1981). Ph o t o s y n t h e s i s immediately f o l l o w i n g d e f o l i a t i o n i s modeled with the f o l l o w i n g r e l a t i o n s h i p d e r i v e d from data by P a i n t e r and D e t l i n g (1981) f o r western wheatgrass ( F i g u r e 14): 51 FIGURE 14. Simulated effect of defoliation on photosynthesis. 52 GRPSYN = -5.1458 + 10.780 KGR - 1.3308 KGR2 + (23) 0.042364 KGR3 where GRPSYN = e f f e c t of d e f o l i a t i o n on p h o t o s y n t h e t i c rate (% of c o n t r o l ) KGR = days s i n c e d e f o l i a t i o n BGMAX i s a l s o a l t e r e d f o l l o w i n g herbage removal at over 75% i n t e n s i t y . When herbage removal occurs w i t h i n four weeks of growth i n i t i a t i o n , BGMAX i s determined with the equ a t i o n : BGMAX = -0.0017 • D + 0.054 (24) where BGMAX = the maximimum c o n t r i b u t i o n of belowground biomass to aboveground growth p o t e n t i a l (g g- 1 day" 1) D = number of days s i n c e growth i n i t i a t i o n When herbage removal occurs a f t e r four weeks of growth i n i t i a t i o n , BGMAX i s assumed to equal 0.0054 g g" 1 day" 1 5. SIMULATION RESULTS, MODEL VALIDATION, SENSITIVITY  ANALYSIS, AND DISCUSSION 5.1 BLUEBUNCH WHEATGRASS DYNAMICS IN THE ABSENCE OF GRAZING 5.1.1 DRY MATTER PRODUCTION OF ABOVEGROUND BIOMASS Model p r e d i c t i o n s of dry matter p r o d u c t i o n i n the aboveground biomass agreed c l o s e l y with measurements o b t a i n e d from f i e l d sampling (Figure 15). Agreement between p r e d i c t e d and observed values were e s p e c i a l l y good p r i o r to the onset of a e s t i v a t i o n , when simulated v a l u e s g e n e r a l l y f e l l w i t h i n one standard e r r o r of measured values f o r both 1967 and 1968. Model p r e d i c t i o n s of standing biomass compared l e s s f a v o r a b l y with measured valu e s f o l l o w i n g the onset of summer drought. In 1967, the di s c r e p a n c y between p r e d i c t e d and observed values o r i g i n a t e d p r i m a r i l y from i n a c c u r a t e s i m u l a t i o n of l i t t e r f a l l . F i e l d measurements i n d i c a t e d that the l o s s of p l a n t m a t e r i a l e q u a l l e d 43 g m - 2 between J u l y 26 and August 29 of that year (Harper 1969). However, simulated l i t t e r f a l l was n e g l i g i b l e f o r t h i s p e r i o d . S i m i l a r l y , p r e d i c t e d l o s s of p l a n t m a t e r i a l was not apparent f o l l o w i n g growth c e s s a t i o n i n e i t h e r the summer or f a l l of 1968. Erroneous s i m u l a t i o n of f o l i a r growth a l s o c o n t r i b u t e d to the disc r e p a n c y between p r e d i c t e d and observed dry matter p r o d u c t i o n . F i e l d o b s e r v a t i o n s 53 54 FIGURE 15. Comparison of simulated (continuous line) and measured (standard error intervals) shoot biomass of bluebunch wheatgrass for 1967 and 1968. 5 5 i n d i c a t e d a minimum of 24 gm"2 of f a l l regrowth by September 20 of 1967; i n c o n t r a s t , p r e d i c t e d f a l l regrowth e q u a l l e d only 10 g m"2 f o r the same p e r i o d . P r e d i c t e d f a l l regrowth was comparable to observed f a l l regrowth i n 1968. However, growth c e s s a t i o n i n the 1968 s i m u l a t i o n o c c u r r e d i n advance of that observed i n the f i e l d . C o n s i d e r a t i o n of l i m i t i n g f a c t o r s d u r i n g growth stages when model p r e d i c t i o n i s poor suggests that f a u l t y p r e d i c t i o n s may be due to i n a c c u r a t e p o r t r a y a l of the r e l a t i o n s h i p between s o i l water p o t e n t i a l and growth r a t e . In the 1967 s i m u l a t i o n when p r e d i c t e d f a l l regrowth was e x c e s s i v e l y low, s o i l water p o t e n t i a l was the p r i n c i p a l growth depressant between l a t e August and mid September (F i g u r e 16). S i m i l a r l y , growth c e s s a t i o n o c c u r r e d too e a r l y i n the 1968 s i m u l a t i o n because biomass accumulation was a r r e s t e d by the s c a l a r r e p r e s e n t i n g the e f f e c t of s o i l water p o t e n t i a l on growth (F i g u r e 17). Thus, f u t u r e r e s e a r c h on the r e l a t i o n s h i p between moisture a v a i l a b i l i t y and growth r a t e may w e l l be p r o f i t a b l e . The importance of water p o t e n t i a l on dry matter p r o d u c t i o n i s f u r t h e r emphasized by s e n s i t i v i t y a n a l y s i s of c l i m a t i c d r i v i n g v a r i a b l e s . S o i l water regime f o r the 1968 s i m u l a t i o n was s u b s t i t u t e d with the s o i l water regime f o r the 1967 season, and the r e s u l t i n g output compared with the 1968 c o n t r o l r e s u l t s . I t was found 56 2.5 2.0 X J o Q . o 1 .5 1 .0 0.5 0.0 FIGURE 16a LEGEND 1 .0 0.8 ° 0.6 C O I o OO Q O !£ 0.4 0.2 0.0 J A MONTH FIGURE 16. Simulated growth potential (g m" ) (Figure 16a) and simulated effects of temperature (TG), soil water potential (WG), daylength (DLG), and foliar nitrogen (NG) on maximum growth rate (Figure 16b) for Harper's (1969) bluebunch wheatgrass mesic site in 1967. 57 FIGURE 17. Simulated growth potential (g m" ) (Figure 17a) and simulated effects of temperature (TG), soil water potential (WG), daylength (DLG), and foliar nitrogen (NG) on maximum growth rate (Figure 17b) for Harper's (1969) bluebunch wheatgrass mesic site in 1968. 58 that f o l i a r p r o d u c t i o n s u s t a i n e d a 216% in c r e a s e f o l l o w i n g t h i s a l t e r a t i o n i n a v a i l a b l e s o i l moisture (Table 2).In c o n t r a s t , when the temperature regime f o r the 1968 s i m u l a t i o n was s u b s t i t u t e d with the temperature regime f o r the 1967 season, only a 34% d i f f e r e n c e i n biomass y i e l d ensued. I t would t h e r e f o r e appear that herbage p r o d u c t i o n as modeled i s f a r more responsive to i n t e r - y e a r l y d i f f e r e n c e s i n moisture regime than to i n t e r - y e a r l y d i f f e r e n c e s i n temperature regime. S u b s t i t u t i o n of the 1968 s o i l water regime with the dry, int e r m e d i a t e , and wet moisture regimes measured by van Ryswyck and Broersma (unpublished data) ( F i g u r e 1) r e s u l t e d i n y i e l d d i f f e r e n c e s of 65, 50, and 259 percent r e s p e c t i v e l y (Table 2). S e n s i t i v i t y a n a l y s i s was a l s o performed on model parameters by s y s t e m a t i c a l l y a d j u s t i n g maximum process r a t e s to 120% of t h e i r o r i g i n a l v a l u e s . R e s u l t s of t h i s a n a l y s i s i n d i c a t e that aboveground biomass accumulation i s most s e n s i t i v e to f o l i a r growth r a t e , r a t e of root hormonal p r o d u c t i o n , and biomass of belowground organs (Table 2 ) . Of the other parameters examined, 20% i n c r e a s e s i n maximum process r a t e s r e s u l t e d i n l e s s than 3% changes i n biomass y i e l d s (Table 2 ) . Si m u l a t i o n r e s u l t s ( F i g u r e s 16 and 17) c o r r o b o r a t e f i e l d o b s e r v a t i o n s of temperature dependence i n s p r i n g growth i n i t i a t i o n (Stout et a l . , 1981; Quinton et a l . , 1982). However, s i m u l a t i o n r e s u l t s are i n c o n s i s t e n t with 59 TABLE II. Results of sensitivity analysis for the 1968 control. CHANGE TOTAL ANNUAL DRY MATTER PROD'N -2x % change (from control) (g nf*) PARAMETERS: DMAX LBG GMAX GBMAX PMAX RESP ROOT RESP PHENM DRIVING VARIABLES: Water potential Water potential Water potential Water potential Air temperature +20% 113 +20% 135 +20% 172 +20% 133 +20% 116 +20% 113 +20% 111 +20% 113 1967 regime 357 Dry interior 37 Medium interior 57 Wet interior 405 1967 regime 74 0 +20 +52 +18 +3 - 0 . 1 -1 0 +216 -67 - 5 0 +259 - 3 4 60 f i e l d o b s e r v a t i o n s on f a c t o r s governing the onset and c o n c l u s i o n of a e s t i v a t i o n . In both the 1967 and 1968 s i m u l a t i o n s , growth c e s s a t i o n d u r i n g the summer r e s u l t e d from s o i l water d e f i c i e n c i e s while regrowth d u r i n g the f a l l o c c u r r e d i n response to i n c r e a s e s i n moisture a v a i l a b i l i t y ( F i g u r e s 16 and 17). In c o n t r a s t , growth c e s s a t i o n i n bluebunch wheatgrass has r e p o r t e d l y o c c u r r e d when moisture a v a i l a b i l i t y i s high (Daer and W i l l a r d , 1981; Quinton et a l . , 1982). A d d i t i o n a l l y , the i n i t i a t i o n of f a l l regrowth has been r e l a t e d to a lowering i n s o i l temperature (Daer and W i l l a r d , 1981). The v a r i a n c e between simulated and f i e l d o b s e r v a t i o n s suggest that the f a i l u r e to model i n t e r a c t i v e e f f e c t s of temperature and moisture may be m i s l e a d i n g . A l t e r n a t e l y , a c o r r e l a t i o n between f a l l regrowth and d e c r e a s i n g s o i l temperature i s a l s o e vident i n the s i m u l a t i o n r e s u l t s , even though water p o t e n t i a l was i d e n t i f i e d as the l i m i t i n g growth f a c t o r . Thus, s i m u l a t i o n r e s u l t s expose the f a l l a c y of assuming cause and e f f e c t between f a c t o r s which may be c o r r e l a t e d . 5.1.2 CRUDE PROTEIN YIELD Simulated crude p r o t e i n y i e l d s peaked twice i n both 1967 and 1968 ( F i g u r e s 18 and 19). The f i r s t peak o c c u r r e d i n e a r l y J u l y f o r the 1967 s i m u l a t i o n and in l a t e June - e a r l y J u l y f o r the 1968 s i m u l a t i o n . The i n f u s i o n of f a l l regrowth r e s u l t e d i n a second peak 61 I 1 S p r i n g growth MONTH FIGURE 18. S imulated crude p r o t e i n y i e l d f o r 1967. MONTH FIGURE 19. S i m u l a t e d c r u d e p r o t e i n y i e l d f o r 1968. 63 between l a t e August and e a r l y September of both y e a r s . Because f a l l regrowth was marginal i n 1967, crude p r o t e i n y i e l d i n the second peak was lower than crude p r o t e i n y i e l d i n the f i r s t peak. Conversely, e x t e n s i v e f a l l regrowth i n 1968 r e s u l t e d i n a high e r y i e l d of crude p r o t e i n i n l a t e August than i n l a t e June. F a l l regrowth c o n s t i t u t e d as much as 20.5% of t o t a l a v a i l a b l e crude p r o t e i n i n 1967 and as much as 45% of t o t a l a v a i l a b l e crude p r o t e i n i n 1968. F a l l regrowth accounted f o r 15.7% of crude p r o t e i n y i e l d by December 31 of 1967, and accounted f o r 38% of crude p r o t e i n y i e l d by the end of 1968. Crude p r o t e i n percentages of s p r i n g growth were comparable between 1967 and 1968 by December 31 of the two r e s p e c t i v e y e a r s , even though growth i n i t i a t i o n i n 1968 o c c u r r e d 10 days i n advance of growth i n i t i a t i o n i n 1967 ( F i g u r e 20). Percent crude p r o t e i n was, however, 0.5% higher i n the 1967 f a l l regrowth than i n the 1968 f a l l regrowth by the c o n c l u s i o n of the r e s p e c t i v e y e a r s . 5.1.3 CARBOHYDRATE PARTITIONING BETWEEN ABOVE AND  BELOWGROUND BIOMASS Simulated carbohydrate movement from the ro o t s to the shoots o c c u r r e d d u r i n g both i n i t i a t i o n of s p r i n g growth and commencement of f a l l regrowth i n 1968 (Figure 22a). Upward movement of carbohydrates o c c u r r e d only d u r i n g s p r i n g i n i t i a t i o n i n the 1967 s i m u l a t i o n (Figure FIGURE 20. Simulated crude protein percentages in foliar biomass and fall regrowth in 1967 and 1968. 65 2 r T3 CVJ I «=c ct: Q >~ in o CQ CC <c C_3 -4 •6 . -8 • M A M J J A S O N D QL Q > - — -- T IM O I co E D£ O - — -<_> 800 600 400 200 FIGURE 21b Fall regrowth Growth cessation M J A MONTH FIGURE 21. Simulated movement of carbohydrates between aboveground and belowground biomass (Figure 21a) and cumulative movement of carbohydrates into belowground biomass (Figure 21b) for Harper's bluebunch wheatgrass mesic site in 1967. 66 21a). Unfavorable growing c o n d i t i o n s d u r i n g the f a l l of 1967, coupled with a p p r e c i a b l e p h o t o s y n t h e t i c a c t i v i t y from r e s i d u a l s p r i n g growth, p r e c l u d e d the need to draw on root r e s e r v e s f o r support of f a l l regrowth. Thus, s i m u l a t i o n r e s u l t s demonstrate why carbohydrate r e s e r v e s may e i t h e r be d e p l e t e d ( M c l l v a n i e , 1942) or augmented (Daer and W i l l a r d , 1981) by f a l l regrowth. The r e l a t i o n s h i p between carbohydrate r e s e r v e s and herbage p r o d u c t i o n i s c u r r e n t l y not w e l l d e f i n e d . In h i s review, Jameson (1963) found no evidence to i n d i c a t e that a d d i t i o n a l s t o r e d carbohydrates w i l l r e s u l t i n a d d i t i o n a l growth once the carbohydrate requirements f o r new t i s s u e have been s a t i s f i e d . In c o n t r a s t , McKendrick and Sharp (1970) found that the l e v e l of organic r e s e r v e s i n c r e s t e d wheatgrass, as indexed by the y i e l d of e t i o l a t e d growth, was s i g n i f i c a n t l y c o r r e l a t e d with herbage p r o d u c t i o n . In t h i s - model, carbohydrates t r a n s l o c a t e d from the root system accounted f o r 6.2 and 6.6% of t o t a l annual p r o d u c t i o n i n 1967 and 1968, r e s p e c t i v e l y . The i n d i r e c t e f f e c t s of carbohydrate r e s e r v e s on herbage p r o d u c t i o n are c o n s i d e r a b l y h i g h e r , however, because the root system a l s o d i c t a t e s the p r o d u c t i o n of growth hormones and i n c i d e n c e of t i l l e r i n g . A d d i t i o n a l l y , the r a p i d establishment of p h o t o s y n t h e t i c biomass i n e a r l y s p r i n g may w e l l be c r u c i a l to herbage p r o d u c t i o n l a t e r on i n the growing season. S e n s i t i v i t y a n a l y s i s on the model r e v e a l e d a 67 FIGURE 22. Simulated movement of carbohydrates between above and belowground biomass (Figure 22a) and cumulative movement of carbohydrates into belowground biomass (Figure 22b) for Harper's bluebunch wheatgrass mesic site in 1968. 68 d i r e c t r e l a t i o n s h i p between herbage producton and carbohydrate r e s e r v e s : f o l i a r growth i s i n c r e a s e d by 1% with each percent i n c r e a s e i n belowground biomass. T r a n s l o c a t i o n of carbohydrates to the root system o c c u r r e d p r i m a r i l y b e f o r e the onset of summer dormancy. Although downward movement of carbohydrates was s i g n i f i c a n t i n the f a l l , 67 and 81% of carbohydrate storage had taken p l a c e by the time growth c e s s a t i o n was observed i n the 1967 and 1968 s i m u l a t i o n s , r e s p e c t i v e l y ( F i g u r e s 21b and 22b). Maximal carbohydrate t r a n s l o c a t i o n to the root system occurred on J u l y 1 and June 20 i n the 1967 and 1968 s i m u l a t i o n s ( F i g u r e s 21a and 22a). The peak input i n carbohydrate r e s e r v e s c o i n c i d e d with the stage when 73 and 67% of c u r r e n t annual growth had been completed. These f i g u r e s agree f a v o u r a b l y with Daer and W i l l a r d ' s (1981) f i e l d o b s e r v a t i o n s , which i n d i c a t e d a peak carbohydrate c o n c e n t r a t i o n i n the r o o t s f o l l o w i n g 67% of t o t a l annual p r o d u c t i o n . Because of i t s shor t d u r a t i o n , the stage of maximal downward t r a n s l o c a t i o n does not represent the stage of major carbohydrate accumulation. By the time maximal downward t r a n s l o c a t i o n was observed, 68.5 and 78.6% of p r e - a e s t i v a t i o n s torage had a l r e a d y o c c u r r e d . In f a c t , examination of F i g u r e s 21b and 22b r e v e a l s t h a t the rate of carbohydrate storage i s r e l a t i v e l y constant between June 1 and J u l y 30 i n 1967, and between May 1 and June 69 30 in 1968. Carbohydrate translocation to the root system remained high for approximately 20 days after growth cessation (Figures 21b and 22b). During t h i s period, an additional 12.9 and 11.2% of annual carbohydrate storage was recorded for the two respective years. These observations are consistent with empirical evidence which indicates that suboptimum conditions are more r e s t r i c t i v e towards growth than towards photosynthetic a c t i v i t y ( T r l i c a , 1977). Root:shoot rat i o s immediately prior to aestivation equalled 4.4 in the 1967 simulation and 3.9 in the 1968 simulation. Rootrshoot rat i o s reported in the l i t e r a t u r e for the Agropyron genus range from approximately 2:1 (Caldwell et a l . , 1981; Holechek, 1982) to 8:1 (Warembourg and Paul, 1973). Davidson (1969) and Brouwer (1966) have previously shown that root:shoot r a t i o s are increased by water d e f i c i t . This phenomenon i s appropriately reproduced in model simulations: substitution of the 1968 s o i l water regime with the dry, intermediate, and wet moisture regimes measured by van Ryswyck and Broersma (Figure 10) yielded root:shoot r a t i o s of 10.5, 8.5, and 3.5 for the three respective regimes. 70 5.2 BLUEBUNCH WHEATGRASS DYNAMICS IN THE PRESENCE OF GRAZING Def o l i a t i o n e f f e c t s are only discussed r e l a t i v e to the 1967 simulation of Harper's (1969) bluebunch wheatgrass mesic s i t e since data for quantitative v a l i d a t i o n of model parameters i s available for t h i s year only. 5.2.1 REGROWTH FOLLOWING DEFOLIATION Simulated values of regrowth following ground-level d e f o l i a t i o n s on May 31 (Figure 23a) and June 14 (Figure 23b) compared extremely well with values obtained from f i e l d sampling. However, predicted and measured values of regrowth compared less favorably for ground-level d e f o l i a t i o n on June 28 (Figure 23c). While predicted regrowth approached 18.9 g m~2 by August 30, measurable regrowth was not observed in the f i e l d at t h i s time (Harper 1969). Because t h i s discrepancy occurred when d e f o l i a t i o n coincided with the approximate date of growth cessation, divergence between predicted and observed values may be due to previously discussed inaccuracies in the simulated r e l a t i o n s h i p between s o i l water pote n t i a l and growth rate. The discrepancy between predicted and observed values may also be due to an overly low projection of l i t t e r f a l l , or the p o s s i b i l i t y that t h i s magnitude of regrowth i s not readily measurable in the f i e l d . The effect of grazing regime on the f a l l standing crop i s depicted in Figure 24. Heavier grazing C M I E CT) CO CO •a: s: o »—< CD CD t—t Q <C t— co FIGURE 23. Comparison of simulated (continuous line) and measured (standard error intervals) values of regrowth following ground-level defoliation on May 31 (Figure 23a), June 14 (Figure 23b), and June 28, 1967 (Figure 23c). 72 i n t e n s i t i e s r e s u l t e d i n reduced forage a v a i l a b i l i t y , while p r o g r e s s i v e d e l a y s i n d e f o l i a t i o n date g e n e r a l l y r e s u l t e d i n reduced forage a v a i l a b i l i t y . An e x c e p t i o n i n v o l v e d d e f o l i a t i o n on May 31, which y i e l d e d more regrowth by November 1 than d e f o l i a t i o n on May 1 f o r a l l g r a z i n g i n t e n s i t i e s examined. These r e s u l t s suggest that bluebunch wheatgrass response to herbage removal i s r e l a t i v e l y weak at very e a r l y growth stages. Consequently, l a t e s p r i n g g r a z i n g w i l l y i e l d a l a r g e r crop of secondary t i l l e r s than e a r l y s p r i n g g r a z i n g , even though e a r l y s p r i n g g r a z i n g r e s u l t s i n a l e n g t h i e r regrowth p e r i o d than l a t e s p r i n g g r a z i n g . A d d i t i o n a l l y , e a r l y s p r i n g g r a z i n g prolongs the p e r i o d of low f o l i a r biomass, thereby d e l a y i n g the p e r i o d when r a p i d accumulation of dry matter i s p o s s i b l e . Forage a v a i l a b i l i t y on November 1 was c o n s i d e r a b l y depressed by most g r a z i n g regimes ( F i g u r e 24). However, d e f o l i a t i o n at 25% i n t e n s i t y before June 25 i n c r e a s e d forage a v a i l a b i l i t y i n the f a l l by as much as 61%. D e f o l i a t i o n at 50% i n t e n s i t y before June 5 a l s o i n c r e a s e d forage a v a i l a b i l i t y r e l a t i v e to c o n t r o l : however, i n c r e a s e s were marginal at l e s s than 10%. Regardless of d e f o l i a t i o n date, herbage removal at 75 and 100% i n t e n s i t i e s s e v e r e l y depressed forage a v a i l a b i l i t y i n the f a l l . 73 FIGURE 24. Simulated effect of defoliation date and defoliation intensity on November 1st forage availability. 74 5.2.2 TOTAL ANNUAL DRY MATTER PRODUCTION Si m u l a t i o n r e s u l t s i n d i c a t e that annual dry matter p r o d u c t i o n i s s t r o n g l y a f f e c t e d by d e f o l i a t i o n date and d e f o l i a t i o n i n t e n s i t y when herbage removal occurs between A p r i l and J u l y ( F i g u r e 25). However, the e f f e c t s of d e f o l i a t i o n date and d e f o l i a t i o n i n t e n s i t y become minor when herbage removal occurs a f t e r mid-July. Spring d e f o l i a t i o n at 25 and 50% i n t e n s i t i e s improved annual dry matter p r o d u c t i o n by as much as 65 and 21 percent, r e s p e c t i v e l y . In c o n t r a s t , s p r i n g d e f o l i a t i o n at 75 and 100% i n t e n s i t i e s c o n s i s t e n t l y depressed annual dry matter p r o d u c t i o n . In agreement with M c l l v a n i e ' s (1944) o b s e r v a t i o n s , annual dry matter p r o d u c t i o n was most s e r i o u s l y c u r t a i l e d by heavy d e f o l i a t i o n i n t e n s i t i e s at e a r l y d ates. Regardless of d e f o l i a t i o n date and d e f o l i a t i o n i n t e n s i t y , herbage removal a f t e r mid J u l y had l i t t l e e f f e c t on t o t a l annual dry matter p r o d u c t i o n . 5.2.3 CRUDE PROTEIN YIELD Because crude p r o t e i n y i e l d s are p a r t i a l l y determined by the a v a i l a b i l i t y of s t anding biomass, the e f f e c t of herbage removal on crude p r o t e i n a v a i l a b i l i t y ( F i g u r e s 26, 27, and 28) c l o s e l y resembles the e f f e c t of herbage removal on forage a v a i l a b i l i t y . However, improvements i n crude p r o t e i n y i e l d f o l l o w i n g s e l e c t g r a z i n g regimes surpass improvements in forage y i e l d f o r comparable g r a z i n g treatments, s i n c e crude p r o t e i n 75 FIGURE 25. Simulated effect of defoliation date and defoliation intensity on total dry matter production. 76 M A M J J A S O N D MONTH FIGURE 26. Simulated crude protein yields following defoliation at 4 intensities on May 1 (Figure 26a) and May 30 (Figure 26b). 77 MONTH FIGURE 27. Simulated crude protein yields following defoliation at 4 intensities on June 14 (Figure 27a) and June 28 (Figure 27b). FIGURE 28. Simulated crude protein yields following defoliation at 4 intensities on July 15 (Figure 28a) and Sept 15 (Figure 28b). 79 a v a i l a b i l i t y i s promoted by enhanced n i t r o g e n c o n c e n t r a t i o n s as w e l l as s t i m u l a t e d f o l i a r p r o d u c t i o n . S i m i l a r l y , d e f o l i a t i o n regimes which depress forage a v a i l a b i l i t y i n the f a l l are l e s s r e s t r i c t i v e towards crude p r o t e i n a v a i l a b i l i t y a t t h i s time. The d i v i s i o n between g r a z i n g regimes which suppress y i e l d and those which enhance y i e l d a l s o d i f f e r s f o r the two parameters. For example, d e f o l i a t i o n at 25% i n t e n s i t y must occur b e f o r e June 25 i f an improvement i n forage a v a i l a b i l i t y i s d e s i r e d . In c o n t r a s t , d e f o l i a t i o n at 25% i n t e n s i t y may occur as l a t e as J u l y 5 f o r an improvement i n crude p r o t e i n a v a i l a b i l i t y to develop. Thus, d e f o l i a t i o n may occur at a higher i n t e n s i t y or at a l a t e r date f o r an improvement i n crude p r o t e i n y i e l d than f o r an improvement i n biomass y i e l d . Enhancements i n crude p r o t e i n y i e l d , when they occur, g e n e r a l l y do so w i t h i n three weeks of herbage removal ( F i g u r e s 26, 27, and 28). An e x c e p t i o n i n v o l v e s d e f o l i a t i o n i n e a r l y s p r i n g when crude p r o t e i n y i e l d i s l i m i t e d by the slow accumulation i n biomass. In c o n t r a s t , high d e f o l i a t i o n s d u r i n g r a p i d v e g e t a t i v e growth r e s u l t e d i n almost immediate i n c r e a s e s i n crude p r o t e i n y i e l d . R e l a t i v e i n c r e a s e s i n p r o t e i n a v a i l a b i l i t y p e r s i s t e d u n t i l the end of the year. 80 5.2.4 BELOWGROUND DYNAMICS Spr i n g g r a z i n g at 25 and 50% i n t e n s i t i e s i n c r e a s e d root accumulation by as much as 226 and 162% r e s p e c t i v e l y ( Figure 29). In c o n t r a s t , root accumulation was s l i g h t l y a r r e s t e d by summer g r a z i n g at these i n t e n s i t i e s . D e f o l i a t i o n at 75 and 100% i n t e n s i t i e s g e n e r a l l y depressed belowground biomass r e l a t i v e to c o n t r o l ; however, d e t r i m e n t a l e f f e c t s were l e s s trenchant on root accumulation than on t o t a l annual p r o d u c t i o n in the aboveground biomass ( F i g u r e 29). Whereas annual herbage p r o d u c t i o n was reduced by up to 50%, maximum c u r t a i l m e n t of root accumulation e q u a l l e d 34% f o r the g r a z i n g regimes examined. Heavy d e f o l i a t i o n i n s p r i n g or f a l l c u r t a i l e d root accumulation l e s s s e v e r e l y than heavy d e f o l i a t i o n d u r i n g mid-season. Regardless of d e f o l i a t i o n date, recovery i n root biomass was not apparent u n t i l l a t e August or e a r l y September f o l l o w i n g g r o u n d - l e v e l d e f o l i a t i o n ( F i g u r e 30). O s t e n s i b l y , low f o l i a r growth, together with e x t e n s i v e root m o r t a l i t y and high r e s p i r a t o r y l o s s e s , prevented b u i l d - u p of root biomass i n summer. These o b s e r v a t i o n s emphasize the importance of carbohydrate stoarage i n the f a l l f o r p l a n t s which had r e c e i v e d g r o u n d - l e v e l d e f o l i a t i o n s . Root:shoot r a t i o s are r e p o r t e d l y lower on grazed than ungrazed s i t e s (Sims et a l . , 1978). The s e n s i t i v i t y of root p r o d u c t i o n to herbage removal i s apparent i n 81 FIGURE 29. Simulated effect of defoliation date and defoliation intensity on November 1st root biomass. 82' 700 Control 600 April 1 defoliation May 1 defoliation May 31 defoliation June 14 defoliation June 28 defoliation July 15 defoliation " Sept. 15 defoliation CVJ i CD CO s: o I—I CO o o on 500 400 300 • M J MONTH FIGURE 30. Simulated root accumulation following ground-level defolia-tion at various dates. 83 both simulated and e m p i r i c a l o b s e r v a t i o n s . Branson (1956) found that root p r o d u c t i o n was s e v e r e l y c u r t a i l e d when bluebunch wheatgrass p l a n t s were c l i p p e d to one inc h (2.5 cm) h e i g h t s at every second or f o u r t h week f o r a f o u r t e e n week p e r i o d . The impairment to root p r o d u c t i o n was much more severe than the impairment to f o l i a r p r o d u c t i o n : root biomass was reduced a hundr e d - f o l d whereas f o l i a r biomass s u f f e r e d only a tw o - f o l d decrease. S i m i l a r l y , s i m u l a t i o n r e s u l t s i n d i c a t e that root:shoot r a t i o s immediately p r i o r to a e s t i v a t i o n were reduced from 4.4 i n ungrazed p l a n t s to approximately 3.6 i n p l a n t s d e f o l i a t e d at 100% i n t e n s i t y between May 1 and the end of J u l y . 5.2.5 DRY MATTER PRODUCTION THE YEAR FOLLOWING HERBAGE  REMOVAL Sim u l a t i o n r e s u l t s i n d i c a t e that the e f f e c t of herbage removal on dry matter p r o d u c t i o n the year f o l l o w i n g d e f o l i a t i o n c l o s e l y p a r a l l e l s the e f f e c t of herbage removal on root accumulation d u r i n g the year of treatment ( F i g u r e s 31 and 29). T h i s r e l a t i o n s h i p i s not s u r p r i s i n g s i n c e the r o o t s are p e r e n n i a l and p r o v i d e the i n t e r - y e a r l y l i n k t o bluebunch wheatgrass growth dynamics. Lack of s u i t a b l e data p r e c l u d e q u a n t i t a t i v e v a l i d a t i o n of s i m u l a t i o n r e s u l t s ; however, q u a l i t a t i v e v a l i d a t i o n d i s c l o s e s the b i o l o g i c a l soundness of p r o j e c t e d y i e l d s . FIGURE 31. Simulated effect of defoliation date and defoliation intensity on dry matter production the year following herbage removal. 85 S i m u l a t i o n r e s u l t s r e v e a l that e a r l y s p r i n g g r a z i n g i s l e s s damaging than mid-season d e f o l i a t i o n (Figure 31). T h i s o b s e r v a t i o n i s w e l l supported by e m p i r i c a l e v i d e n c e : B l a i s d e l l and Pechanec (1949) demonstrated t h a t herbage p r o d u c t i o n was l e a s t a f f e c t e d by the f i r s t s p r i n g c l i p p i n g but r e d u c t i o n s i n dry matter accumulation became more pronounced as c l i p p i n g date was d e l a y e d . S i m i l a r l y , Wilson et a l . (1966) found that p l a n t s which were c l i p p e d when 5-7 inches high produced l e s s herbage the year f o l l o w i n g treatment than p l a n t s which were c l i p p e d when 1-2 inches h i g h . Stoddart (1946) concluded that e a r l y s p r i n g g r a z i n g was l e s s harmful than l a t e s p r i n g g r a z i n g because i t allowed regrowth be f o r e the end of the growing season. E m p i r i c a l evidence suggests that bluebunch wheatgrass i s most s u s c e p t i b l e to d e f o l i a t i o n i n j u r y s h o r t l y before or a f t e r the flower head emerges from the boot ( B l a i s d e l l and Pechanec, 1949; Wilson et a l . , 1966). While p h e n o l o g i c a l development was not e x p l i c i t l y modeled i n AGGRO, p h y s i o l o g i c a l d i s t u r b a n c e i n the s i m u l a t e d p l a n t was h i g h e s t toward the end of June, a p e r i o d which c o i n c i d e s with the approximate date of b o o t i n g i n bluebunch wheatgrass (Quinton et a l . , 1982). S i m u l a t i o n r e s u l t s ( F i g u r e 31) and f i e l d o b s e r v a t i o n s ( S t o d d a r t , 1946; B l a i s d e l l and Pechanec, 1949; West et a l . , 1979) a l s o concur on the minor impact of f a l l d e f o l i a t i o n on herbage p r o d u c t i o n the year f o l l o w i n g 86 d e f o l i a t i o n . There i s no documentation to support the dramatic s t i m u l a t i o n s i n herbage p r o d u c t i o n which were p r e d i c t e d the year f o l l o w i n g l i g h t s p r i n g d e f o l i a t i o n (Figure 31). However, s t u d i e s i n v e s t i g a t i n g d e f o l i a t i o n e f f e c t s are g e n e r a l l y concerned with r e l a t i v e l y severe d e f o l i a t i o n treatments. P l a n t s are o f t e n s u b j e c t e d to m u l t i p l e , g r o u n d - l e v e l d e f o l i a t i o n s i n a s i n g l e season (Stoddart, 1946; Branson 1956), s u c c e s s i v e d e f o l i a t i o n s through a number of c o n s e c u t i v e years (Wilson et a l . , 1966; R i c k a r d et a l . , 1975), or s i n g l e d e f o l i a t i o n s at a v u l n e r a b l e p h e n o l o g i c a l stage ( B l a i s d e l l and Pechanec, 1949; Mueggler, 1972; 1975). A d d i t i o n a l l y , Ganskopp and B e d e l l (1981) have p r e v i o u s l y r e p o r t e d s t i m u l a t i o n s of up to 160% f o l l o w i n g summer and f a l l g r a z i n g at 25% i n t e n s i t y . 5.2.6 IMPLICATIONS TO INTEGRATED MANAGEMENT OF CATTLE  AND WILDLIFE S e l e c t i o n of optimum g r a z i n g regime cannot be d i v o r c e d from d e s i r e d management outcome. Thus, c o n s i d e r a t i o n of management p o l i c y must e n t a i l a concomittant d i s c u s s i o n of management o b j e c t i v e s . Under c l i m a t i c c o n d i t i o n s of Harper's (1969) bluebunch wheatgrass mesic s i t e i n 1967, t o t a l annual dry matter p r o d u c t i o n was h i g h e s t f o l l o w i n g herbage removal at 25% i n t e n s i t y on May 31 ( F i g u r e 25). T h i s 87 g r a z i n g regime would t h e r e f o r e be optimal i f management o b j e c t i v e was to maximize forage p r o d u c t i o n without regard to the t i m i n g of forage a v a i l a b i l i t y . Because root p r o d u c t i o n i s l i k e w i s e s t i m u l a t e d by herbage removal at t h i s date and i n t e n s i t y ( F i g u r e 30), impairment to subsequent herbage p r o d u c t i o n should not be of concern. Of 24 g r a z i n g regimes examined, f i v e s t i m u l a t e d t o t a l annual p r o d u c t i o n by more than 10%. Thus, some f l e x i b i l i t y i s a v a i l a b l e to accommodate management p o l i c i e s which r e q u i r e simultaneous maximization of s e v e r a l v a r i a b l e s . F r e q u e n t l y , the season of forage a v a i l a b i l i t y i s a matter of c o n s i d e r a b l e importance. The use of l i v e s t o c k management to improve winter h a b i t a t f o r w i l d l i f e has been p r e v i o u s l y addressed (Anderson and S c h e r z i n g e r , 1976; Malechek et a l . , 1978; P i t t , unpub. data) and i s , in f a c t , c e n t r a l to management p o l i c y i n such areas as the East Kootenays or the Ashnola region of B r i t i s h Columbia. Given such an o b j e c t i v e , the e f f e c t s of g r a z i n g regime on forage a v a i l a b i l i t y and crude p r o t e i n y i e l d i n the f a l l and winter become paramount. As shown i n F i g u r e s 24, 26, 27, and 28, j u d i c i o u s g r a z i n g management may be used to improve crude p r o t e i n and forage a v a i l a b i l i t y i n the f a l l and w i n t e r . Of 24 g r a z i n g regimes examined, three enhanced forage a v a i l a b i l i t y by a minimum of 10% while seven enhanced crude p r o t e i n y i e l d by at l e a s t the same amount. In 88 accordance with t o t a l annual dry matter p r o d u c t i o n , crude p r o t e i n and forage a v a i l a b i l i t y were maximized by herbage removal at 25% i n t e n s i t y on May 31. In c o n t r a s t to annual dry matter p r o d u c t i o n , crude p r o t e i n y i e l d and forage a v a i l a b i l i t y were l e s s c u r t a i l e d by heavy d e f o l i a t i o n s i n e a r l y s p r i n g than heavy d e f o l i a t i o n s i n l a t e s p r i n g . Crude p r o t e i n y i e l d i s not n e c e s s a r i l y a good i n d i c a t o r of forage q u a l i t y s i n c e low p r o t e i n l e v e l s may be masked by abundant s t a n d i n g biomass. Where forage q u a l i t y i s a more s e r i o u s l i m i t a t i o n than forage q u a n t i t y , percentage crude p r o t e i n must be c o n s i d e r e d i n c o n j u n c t i o n with crude p r o t e i n y i e l d . Assuming that p r o t e i n d e f i c i e n c i e s w i l l develop i f percentage crude p r o t e i n dropped below 5% f o l i a r content (Nelson and Leege, 1982), weight l o s s i n animals w i l l t h e r e f o r e depend on the a v a i l a b i l i t y of crude p r o t e i n which occurs at t h i s minimum c o n c e n t r a t i o n . As r e v e a l e d i n Table 3, the p o t e n t i a l b e n e f i c i a l e f f e c t s of j u d i c i o u s g r a z i n g management become even more remarkable when t h i s parameter i s c o n s i d e r e d . The November 1st a v a i l a b i l i t y of crude p r o t e i n which occurs at a minimum c o n c e n t r a t i o n of 5% e q u a l l e d 12.1 kg ha" 1 i n ungrazed p l a n t s , but e q u a l l e d as much as 144 kg ha" 1 f o l l o w i n g l i v e s t o c k d e f o l i a t i o n at 25% i n t e n s i t y on May 31. Of 24 g r a z i n g regimes examined, 18 i n c r e a s e d the f a l l a v a i l a b i l i t y of t h i s parameter by at l e a s t 10%. TABLE III. The effect of grazing regime on the November 1st availa-bility of crude protein (Kg/ha) which occurs at a minimum concentra-tion of 5% foliar content by weight. GRAZING INTENSITY (%) Clipping Date 25 50 70 99 May 1 34.5 24.5 14.4 12.5 May 31 144.0 97.6 51.7 51.5 June 14 98.0 67.2 36.7 35.7 June 28 48.6 35.0 14.1 22.0 July 15 18.1 15.3 12.4 14.0 Sept. 15 1.4 1.4 1.4 6.0 Control: 12.1 Kg/ha TABLE IV. The effect of grazing regime on the December 30th availability of crude protein (Kg/ha) which occurs at a minimum concentration of 5% foliar content by weight. GRAZING INTENSITY [%) Clipping Date 25 50 70 99 May 1 21.3 15.1 8.9 7.8 May 31 31.6 22.2 12.7 12.5 June 14 25.8 18.1 11 .0 10.5 June 28 33.0 23.6 21.3 15.0 July 15 11.4 9.5 7.6 8.9 Sept. 15 1.0 1.0 1.0 3.0 Control: 7.5 Kg/ha 90 T h i s r e l a t i o n s h i p p e r s i s t e d u n t i l the end of the year (Table 4) even though d i f f e r e n t i a l v a l u e s between grazed and ungrazed p l a n t s d i m i n i s h e d with time. The e f f e c t of g r a z i n g regime on resource p a r t i t i o n i n g between l i v e s t o c k and w i l d l i f e i s d e p i c t e d i n F i g u r e s 23 and 24. Regardless of d e f o l i a t i o n date, l i v e s t o c k g r a z i n g at 25 and 50% i n t e n s i t i e s r e s u l t e d i n higher forage a v a i l a b i l i t y to w i l d l i f e than l i v e s t o c k . S i m i l a r l y , w i l d l i f e gained access to more forage than c a t t l e f o l l o w i n g s p r i n g g r a z i n g by l i v e s t o c k at 75 and 100% i n t e n s i t i e s . Forage a v a i l a b i l i t y to l i v e s t o c k exceeded forage a v a i l a b i l i t y to w i l d l i f e when l i v e s t o c k g r a z i n g o c c u r r e d i n summer or f a l l at 75 and 100% i n t e n s i t i e s . While forage a v a i l a b i l i t y to w i l d l i f e exceeded forage a v a i l a b i l i t y t o l i v e s t o c k f o r 17 of 24 g r a z i n g regimes examined, crude p r o t e i n a v a i l a b i l i t y to w i l d l i f e exceeded crude p r o t e i n a v a i l a b i l i t y to l i v e s t o c k f o r only 8 of 24 g r a z i n g regimes. G r a z i n g regimes which are u n s u i t a b l e f o r i n t e g r a t e d management of two s p e c i e s are r e a d i l y i d e n t i f i e d i n F i g u r e s 32 and 33. For example, heavy f a l l g r a z i n g by l i v e s t o c k i s i n a p p r o p r i a t e f o r m u l t i - s p e c i e s management because i t s e r i o u s l y d e p l e t e s forage a v a i l a b i l i t y to w i l d l i f e . A l t e r n a t i v e l y , forage a v a i l a b i l i t y to l i v e s t o c k i s extremely low when g r a z i n g o c c u r r e d in e a r l y s p r i n g . Regardless of d e f o l i a t i o n i n t e n s i t y , 91 2500r 0 500 1000 1500 FORAGE AVAILABILITY TO LIVESTOCK (Kg ha'1) FIGURE 32. Forage availability for cattle versus forage availability for wildlife on November 1st following livestock grazing on six different dates (May 1 - 1, May 31 - 2, June 14-3, June 28-4, July 15 - 5, Sept. 15 - 6) at four different intensities. 92 FIGURE 33. Crude protein availability (minimum concentration of 5% foliar content by weight) for livestock versus wildlife following livestock grazing on six different dates (May 1-1, May 31 - 2, June 14 - 3, June 28 - 4, July 15 - 5, Sept. 15 - 6) and four different intensities. 93 livestock grazing on May 1st yielded low crude protein a v a i l a b i l i t y to both w i l d l i f e and livestock. 6. GENERAL DISCUSSION The model seemingly p r o v i d e s good p r e d i c t i o n s of dry matter accumulation i n the absence of g r a z i n g as w e l l as dry matter accumulation f o l l o w i n g g r o u n d - l e v e l d e f o l i a t i o n i n l a t e s p r i n g or e a r l y summer. Q u a n t i t a t i v e v a l i d a t i o n of dry matter accumulation f o l l o w i n g l i g h t e r d e f o l i a t i o n i n t e n s i t i e s i s p r e c l u d e d by want of s u i t a b l e d a t a . However, q u a l i t a t i v e v a l i d a t i o n of s i m u l a t i o n r e s u l t s support the b i o l o g i c a l soundness of p r o j e c t e d y i e l d s . O v e r a l l model i n t e g r i t y i s a l s o supported by q u a l i t a t i v e v a l i d a t i o n of a l t e r n a t e parameters. P r e d i c t e d root:shoot r a t i o s f e l l w i t h i n the range of p u b l i s h e d values and v a r i e d a p p r o p r i a t e l y i n response to moisture s t r e s s and herbage removal. Simulated e f f e c t s of d e f o l i a t i o n date and d e f o l i a t i o n i n t e n s i t y on t o t a l annual dry matter p r o d u c t i o n , regrowth f o l l o w i n g d e f o l i a t i o n , and dry matter p r o d u c t i o n the year f o l l o w i n g herbage removal showed good q u a l i t a t i v e agreement with a l l a v a i l a b l e e m p i r i c a l o b s e r v a t i o n s of bluebunch wheatgrass. Favourable s i m u l a t i o n r e s u l t s may be p a r t l y due to observance of b i o l o g i c a l p r i n c i p l e s at both the p h y s i o l o g i c a l and organismal l e v e l s , as w e l l as adoption of s i m p l i f y i n g i n d i c e s where undue complexity may be disadvantageous. A d i s t i n c t i v e f e a t u r e of t h i s model i n v o l v e s the simulated r e l a t i o n s h i p between above and belowground biomass. The magnitude and d i r e c t i o n of carbohydrate movement between these two components i s 94 95 e n t i r e l y dependent on the si n k - s o u r c e index, which i s i n turn determined by the growth p o t e n t i a l . Thus, carbohydrate movement i s i n d i r e c t l y r e l a t e d , and responsive t o, changes i n phenology, growing c o n d i t i o n s , and d e f o l i a t i o n e f f e c t s . Another d i s t i n c t i v e f e a t u r e i n v o l v e s the modeling of f o l i a r growth as a d i r e c t f u n c t i o n of belowground biomass. T h i s heightens the s e n s i t i v i t y of herbage pr o d u c t i o n to belowground v i g o r , and i s e s p e c i a l l y important f o l l o w i n g winter dormancy, summer a e s t i v a t i o n , or herbage removal, when the volume of l i v e shoot biomass i s low. Si m u l a t i o n r e s u l t s p r o v i d e d c o n f i r m a t i o n o f , or i n s i g h t s i n t o , r e l a t i o n s h i p s i n bluebunch wheatgrass which were p r e v i o u s l y u n c l e a r . S i m u l a t i o n r e s u l t s r e v e a l e d f a c t o r s which are l i m i t i n g to growth at d i f f e r e n t stages of development, i d e n t i f i e d p e r i o d s of carbohydrate storage, and suggested the importance of root r e s e r v e s toward herbage p r o d u c t i o n . S i m u l a t i o n r e s u l t s support the c o n t e n t i o n that j u d i c i o u s g r a z i n g management may be used to improve forage and crude p r o t e i n a v a i l a b i l i t y to w i n t e r i n g w i l d l i f e , but exposes the d e v a s t a t i n g e f f e c t s of i n c o r r e c t g r a z i n g regime on w i l d l i f e h a b i t a t . I t i s a l s o emphasized that the e f f e c t i v e n e s s of g r a z i n g management to improve w i l d l i f e h a b i t a t w i l l depend on the p r e v a i l i n g c l i m a t e , which may modulate s u b s t a n t i a l l y from year to year. A d d i t i o n a l l y , s t i m u l a t i o n of forage p r o d u c t i o n may not m a t e r i a l i z e f o l l o w i n g m u l t i p l e d e f o l i a t i o n s over s u c c e s s i v e y e a r s . 96 Although simulation results appear v a l i d at a l l levels of inspection, AGGRO cannot be regarded as f u l l y p r e d ictive. As discussed e a r l i e r , the simulated r e l a t i o n s h i p between s o i l water potential and growth rate is neccessarily a f i r s t approximation. Refinement of t h i s r e l a t i o n s h i p i s especially important because s e n s i t i v i t y analysis has disclosed the importance of moisture a v a i l a b i l i t y on growth. The dependability of model v a l i d a t i o n results i s also jeopardized by input values of s o i l water potential which were generated from an untested moisture c h a r a c t e r i s t i c curve. Since both years of v a l i d a t i o n data originated from Harper's (1969) bluebunch wheatgrass mesic s i t e , any error introduced by faulty input values would not be readily apparent. S i m i l a r l y , the fine-textured s o i l at Harper's (1969) study s i t e may have obscured another potential error. Because s o i l water potential i s r e l a t i v e l y homogeneous throughout such a horizon, consideration of only one s o i l depth may be s u f f i c i e n t . However, this r e l a t i o n s h i p w i l l u nlikely hold true for a sandy s o i l where moisture a v a i l a b i l i t y varies dramatically with s o i l depth. Model weakness is also engendered by postulated relationships for which data are lacking. As revealed in s e n s i t i v i t y analysis, root hormonal production and incidence of t i l l e r i n g have considerable impact on herbage production. However, process rates for these factors are unknown. Si m i l a r l y , shoot mortality i s tenuously modeled, but erroneous simulation of t h i s process w i l l not be apparent in 97 p r e d i c t e d y i e l d s because m o r t a l i t y i s not induced u n t i l l a t e in the growing season when biomass accumulation i s v i r t u a l l y complete. A l t e r n a t i v e l y , f a u l t y s i m u l a t i o n of shoot m o r t a l i t y w i l l have c o n s i d e r a b l e impact on carbohydrate storage i n the f a l l . E r r o r s i n root biomass are thus i n c u r r e d and subsequent herbage p r o d u c t i o n may be s e r i o u s l y b i a s e d i n the case of long term s i m u l a t i o n s . S i m u l a t i o n p r e d i c t i o n s of improved crude p r o t e i n and forage a v a i l a b i l i t y f o l l o w i n g s e l e c t g r a z i n g regimes are q u a l i t a t i v e l y supported by e m p i r i c a l o b s e r v a t i o n s of bluebunch wheatgrass. (Stoddart, 1946; P i t t , unpub. d a t a ) . However, q u a n t i t a t i v e v a l i d a t i o n of p r e d i c t e d improvements must s t i l l be performed. Because f o l i a r crude p r o t e i n has not been modeled m e c h a n i s t i c a l l y i n AGGRO, improved forage q u a l i t y i s p r e d i c a t e d on the assumption that the r a t e of n i t r o g e n l o s s i n regrowth w i l l not exceed the r a t e of n i t r o g e n l o s s i n s p r i n g growth. A d d i t i o n a l l y , the simulated e f f e c t of d e f o l i a t i o n on t i l l e r i n g behavior i s c r i t i c a l i n determining regrowth y i e l d . Although simulated t i l l e r i n g behavior i s s u b s t a n t i a t e d by work on c r e s t e d wheagrass which i n d i c a t e s that c l o s e d e f o l i a t i o n w i l l s t i m u l a t e a x i l l a r y bud development (Cook and Stoddar, 1953; Hyder and Sneva, 1963), s i m i l a r documentation does not e x i s t f o r bluebunch wheatgrass. 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COEFFICIENT VALUES FOR GENERATED SOIL WATER REGIMES SOIL WATER REGIME COEFFICIENT Dry Interior Medium Interior Wet Interior Harper 1967 Harper 1968 WPAO -40.1456 -20.3599 -5.0720 0.2044 0.2561 WPCI 16.7146 13.4655 3.8462 0.0246 0.1326 WPC2 5.5584 -4.3823 -2.3227 0.0191 0.5415 WPC3 -0.2600 1.8011 0.6965 -0.6508 -0.1306 WPC4 0 0 0.3628 0.6305 0.2288 WPC5 0 0 -0.7000 -0.5588 0 WPC6 0 0 0.6108 0.2760 0 WPSI 23.2981 6.6959 1.6328 0.0205 0.7386 WPS2 -7.2709 -4.9627 -2.4904 -0.1173 -0.2572 WPS3 -3.4033 3.4738 2.3225 0.1125 0.9152 WPS4 0 0 -1.4996 -0.1110 -0.2790 WPS5 0 0 0.6428 0.1011 0 WPS6 0 0 -0.1499 -0.7291 0 109 APPENDIX II. FORTRAN COMPUTER LISTING OF MODEL AGGRO. (Documentation for this l i s t i n g is available from the Research Branch, B.C. Ministry of Forests, 3015 Ord Road, Kamloops, B.C. V2B 8A9) MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) MAIN 10-11-84 13:27:50 PAGE P0O1 C GROWTH MODEL FOR BLUEBUNCH WHEATGRASS 1 000 0001 SUBROUTINE UMOOEL(JTIME > 2 000 0002 REAL N.NG.N2 1 000 0OO3 REAL N03 , NH4 . LBG, NP , NAB, NLP. NL . NML , NLT , NVG 2 000 0004 REAL TNLOSS.NLO.NCYCLE.NTO 3 000 0005 REAL NAVAIL,NLOSS,LAB.NFREE,NMIN,NN,MB.NPSYN,KILL,LF 4 OOO 0006 REAL J,NVO,NV,N0EM,NVOLT 5 OOO 0007 REAL DMAX . NRECYC , NCYC . N03, NG 1 . NG2 , NG3 6 000 0008 REAL NRGG.NRGAES.NMINY 6 200 0009 INTEGER INCR.NK.KA,KB,RK.OR.DP,WPCH 7 000 0010 INTEGER GRJD,FUN 8 000 0011 COMMON P,A1.B(10).GMAX.ITIME 9 000 0012 COMMON AB,RS,CC.SO,SS.TS.D,RSP 1 1 000 0013 COMMON TEMP,TO(10).TM1(10).DD(12).DL.STEMP 12 000 0014 COMMON WP0T.W1,N 13 000 0015 COMMON PSYN.TPSYN,WSYN,NPSYN,T,TNPSYN 14 000 0016 COMMON G.WG.NG.TG.T1.N2 15 000 0017 COMMON RESP.RR 16 000 0018 COMMON OMAX.LAB 17 000 0019 COMMON TA,TB,SG,TM,NRECYC 18 000 0020 COMMON C4.C5.S4.S5.ISINK 19 000 0021 COMMON 0R(12),RM(12),RD(12) 20 000 0022 COMMON d(12).A(12),NVO(12) 21 000 0023 COMMON WPA0(6),WPC1(6),WPC2(6),WPC3(6).WPC4(6).WPC5(6),WPC6(6) 22 OOO 0024 COMMON WPS1(6),WPS2(6).WPS3(6),WPS4(6),WPS5(6),WPS6(6) 23 000 0O25 COMMON U3.U4.N03.NH4 24 OOO 0O26 COMMON INCR.NK.KA.KB.RK,JR.RJ 25 000 0027 COMMON GA.GB.MB.LBG.JD 26 000 0028 COMMON NP (12).NAB<12).NOEM,NLP(12).NL*12),NML(12).NLT 27 000 0029 COMMON NVG(12),NV<12),NV0LT 28 000 0030 COMMON Z1,R3(365).R4(36S) 29 000 O031 COMMON TNLOSS.NLO(12).NCYCLE,NTO<12).TLOSSO.NAVAIL,NFREE.NMIN.NN 30 000 0032 COMMON NMV(12).FM.AM.CM,KILL.BM,LF.PHENM 32 OOO 0033 COMMON RN(20),RP(20),PREC,R1(20).R2(20),DP(20),PM(20) 33 000 0O34 COMMON SY 1 , SY2 , SA . SB. WBM, RNDMI 34 000 0035 COMMON ISOURC.IPASS.LOCN.WPCH.RNOMI 36 000 0036 COMMON DLA0(10),DLC1(10).DLS1(10).PI.WAM.NCYC 37 000 0037 COMMON NYC.CP.UDR.CPY.GRAZINC365).KGR.GR.GRPSYN 38 OOO 0038 COMMON ISTT.ISTST.ISTW.GRA.KNEMP.KNEMPI.KNI 39 000 0039 COMMON GRJD,FUN,GBMAX,GGBMAX.DLG.ISHIF,NCH 40 000 0040 COMMON IAEST,AGBMAX,FUN2.RGAES.FUNS 41 000 0041 COMMON MORTJD.MORTWP,CUMAB,RGG.AMRGG.AMRG.TLAB 42 000 0042 COMMON RTSHT.PMAX.FRMAX,FRRMAX.TSSNEG 43 OOO 0043 COMMON KNEMP2 .KNEMP3.NRGG.NRGAES.GRAZ. AMG. AMRGA 44 000 0044 COMMON GLAB.GLABAB.RGGAB.RGAB.CPG,CPRGA.CPRGG,LF2 45 000 0045 COMMON NMG,NMRGA.NMRGG.CPYMIN.NMINY 46 000 0046 COMMON CPYG,CPYRGA,CPYRGG,PHENM2 47 000 0047 COMMON NG1.NG2.NG3.GA1,GA2.IAESTO,RGJD.JDAEST 48 OOO 0048 COMMON Z.DAMPD.GRKNI 49 000 0O49 REAL'S WtiMEBt i1 ) / l DO.135 DO.150.00,165.00.179.06,193.DO. 4 000 A207.DO.220.DO.24 .DO.262.DO.365.00/ 5 OOO 0O5O REAL'S WPB(11)/0.15D0.0.2O8333D0.0.173333DO.O.17166700,0.163333D0. 6 000 AO. 05833306.0.6633300.6.04D0.6.62833306,6.048333DO.0. 1500/ 7 000 0051 REAL'S TIMEN, YZLIN.TIMEWP 8 000 0052 REAL*8 STIMEB(13)/1.DO,151.DO.154.DO,161.DO.172.DO,177.DO. 9 OOO A191 DO.203 00.22 1.00.238.DO.247.DO.262.DO.365.667 10 000 0053 REAL'S STEMPB(13)/-4.000.9.ODO.10.300.10.3D0,13.000. 1 1 OOO A 14.800.17.500.13. 100.17.000.11.400. 14.700,11 3D0,-4.000/ 12 000 MICHIGAN TERMINAL SYSTEM FORTRAN GI21.8) UMODEL 10-11-84 13:27:50 PAGE P002 0O54 REAL'S TIMEB(10)/1.DO.140.DO.189.DO.195.DO,230.DO,258.DO.278 DO. 13.000 0055 A 306.66.315.DO.365.667 REAL'8 TEMPB(10)/-2.78DO.8.3D0.14.4D0,8.3D0.21.1D0,12.2D0,15 A,-2.8D0,0.000.-2.7800/ 6D0 14.000 15.000 16.000 O056 0057 0058 EXTERNAL VZLIN ISOURC-11 CALL FTNCMD('DEFAULT 11«*S0URCE*:') 16.200 17.000 18.000 0059 OOSO REAL'S DWBM,DWPOT.DPAR15(4 I/O.7D0.-9.85S53D0..0400, .9866/. ADTAU1/O.DO/,DTAU2/75.DO/ CALL FTNCMD('DEFAULT 10='SINK*;') 19.000 20.000 21 .000 0061 O062 0063 ISINK-10 IF(IPASS.EO.O)CALL CHOICE IF(IPASS.EQ.O)NAVAIL=0.15*LBG 22.000 23.000 24 .000 0064 O065 IPASS'IPASS+1 ITIME-JTIME C'INK CALL FWRITE(ISINK,'STATEMENT #1 ITIME IS <I«4>.:'.ITIME) 25.000 26.000 27.000 0066 C'INK CALL FWRlfElISINK.'STATEMENT *1 JTIME IS <I*4>.:'.jfIME) IF(M0D(ITIME,365).E0.1)CALL REINIT C'INK CALL FWRITE(ISINK,'STATEMENT *2 ITIME IS <I*4>.:',ITIME) 28.000 29.000 30.000 0067 C'INK CALL FWRITEt ISINK, ' STATEMENT #2 JT IME IS <I'4>. : ' .JTIME) C'INK CALL FWRITEfISINK.'STATEMENT #2 JO IS <I'4>.:',JD) JD'JD+INCR 31 .000 32.000 34.000 C'INK CALL FWRITEfiSINK.'STATEMENT #3 ITIME IS <I'4> :'.itlME) C'INK CALL FWRITEfISINK,'STATEMENT *3 JTIME IS <I*4>.:',JTIME) C'INK CALL FWRITE(ISINK,'STATEMENT #3 JD IS <I'4>.:',JD) 35.000 36 .000 37.000 0068 0069 C COMPUTE WEATHER PARAMETERS IF((LOCN.EO.4).OR.(LOCN.EO.5))G0T0 1333 IF(M0D(ITIME,365).EO.1)CALL RAIN 38.000 38. 100 38.150 6670 0071 0072 GOTO 1340 1333 IF(M0D(ITIME,365).E0.1)CALL ASHRN 1340 CONTINUE 38.200 38.300 39.000 0073 0074 4090 f EMP=f 6( LOCN j + ( TM1 ( LOCN ) -f6( LOCN j )' * ( 1 + SI N( A i * JD+B( LOCN )))/2 4091 CONTINUE C'INK CALL FWRITE(ISINK,'THE VALUE OF TEMP IS <R*4>.:',TEMP) 50.000 51 .000 52.000 0075 O076 IF((LOCN £0.4).OR.(LOCN.EO.5)(GOTO 6005 STEMP*( TM1(LOCN)-T0(LOCN))•EXP(-Z/DAMPD)• ASIN(A1«JD+B(L0CN)-(Z/DAMPD)) 52 . 100 52.20O 52.300 0077 O078 O079 GOTO 6006 6005 CONTINUE NBPS»13 52 .400 52.500 53.000 0080 0081 0082 IF(JD.GT.6)G6fb 4095 STEMP»-0. 4095 CONTINUE 54.000 55.000 56 .000 O083 0084 0085 TIMEN-DFLOAf(JD) STEMP*SNGL(YZLIN(STIMEB,STEMPB.NBPS,TIMEN,ISTST.ISINK,JD,2)) 6006 CONTINUE 57 .000 58 .000 58.200 0086 0087 0088 DL'DLFNCf1) IF(LOCN.NE.10)GOTO 5001 NBPW67»11 59.000 60.000 61 .000 0089 0090 0091 IF ( JD . GT . 6 ) GOf6 5666 WPOT«-0.0 5000 CONTINUE 62.000 63.000 64.000 O092 0093 0094 fIMEWP^DFLOATfJD) WPOT = SNGL(YZLIN(WTIMEB,WPB.NBPW67,TIMEWP,ISTW,I SINK,JD,3)) GOTO 5004 65.000 66.000 67 .000 O095 0096 5001 CONTINUE WP0T=WPA0(WPCH)/2+WPC1(WPCH)'C0S(PI'JD/P) A+WPC2(WPCH)'C0S(2»PI'JD/P)+WPC3(WPCH)*C0S(2*PI'JD/P) 68.0O0 69 OOO 70.000 MICHIGAN TERMINAL-SYSTEM FORTRAN G(21.8) UMODEL 10-11-84 13:27:50 PAGE POOS B+WPC4(WPCH)*C0S(4*PI*dD/P)+WPC5(WPCH)*COS(5*PI*dO/P) 71 000 c»wPC6(wpcH)«cbs<G»Pi•Jb/Pi+wps i(WPCH)*SIN(PI« JO/P) 72 000 D+WPS2(WPCH)*C05(2*PI*JD/P)+WPSS(WPCH)*SIN(3*PI*dD/P) 73 OOO E+WPS4(WPCH)*C0S(4*PI*dD/P)+WPS5(WPCH)»SIN(5*PI*dD/P) 74 000 F•WPS6 rwpCH)*COS(6 * P i * Jb/P) 75 000 0O97 5004 CONTINUE 76 000 0098 IF((WPCH.NE.4).AND.(WPCH.NE.5))G0T0 4099 77 OOO 0O99 WPOT--EXP((.28623-WPOT)/.040924)*9782.36/100000 78 ooo 010O 4099 IF(WPOT.GT.-O.4)WP0T=-O.4 79 000 C EMPIRICAL N CONC. OVER TIME 80 000 0101 IF(KA.NE.iiGOTO 222 81 ooo 0102 IF(dD.LT.74)KNEMPI-=1 82 000 0103 IF(dD.LT.74)KNI"dD 83 ooo 0104 iFfdD.GT.105)KNEMPi-2 84 000 0105 IF(dO.GT.105>KNI=dD 85 000 0106 IF((dD.GE.74).AND.(dD.LE.105))KNEMPI-3 86 ooo 0107 IF((db.GE.74j.AND.(db.IE.105))KN1'dD 87 000 0108 222 CONTINUE 88 000 0109 IF(KNEMPI.LT.1)G0T0 4100 89 ooo 01 10 IF(KNEMPI.EQ.l)iSHiF»74-KNi 89 200 01 11 IF(KNEMPI.EO-1)KNEMP-dD+ISHIF 90 000 0112 IF(KNEMPI.EO.2)KNEMP=JD-30 91 ooo 01 13 IF(KNEMPI.EO.3)kNEMP=db-(KNI-FUN3) 92 000 01 14 KNEMP2=dD-GRdD+FUN 93 000 01 15 KNEMPS=dD-RGdD+FUN2 94 ooo 01 16 IF(NCH.NE.1)GOtb 224 95 000 0117 IF(KNEMP.LT.1)N=4.16 96 000 0118 IF(KNEMP,LT.1)GOTO 224 97 000 0119 N«(-8 5i86+3490.2/KNEMP)/6.25 98 ooo 0120 IF(N.GT.4.16)N=4.16 99 000 0121 IF(LAB.LE.O)N=0.0 100 000 0122 GOTO 4100 101 000 0123 224 CONTINUE 102 000 0124 223 CONTINUE 103 ooo 0125 IF(KNEMP.GT.2i3)Gbtb 1060 104 000 0126 N'i105.86-1.1355«KNEMP+0.O043233«KNEMP*»2-0.55393E-5«KNEMP**3)/6.2 105 000 0127 IF(N.GT.4.16)N'4.16 106 ooo 0128 1060 IF(KNEMP.GT.213)N B(6.6-6.0269737*(KNEMP-213))/6.25 107 000 0129 IF(GLABAB.LE.O)N°0.0 108 000 0130 IF(KNEMP2.GT.213)G0T0 1070 109 ooo 0131 NRGG3(105.86-1.i355»kNEMP2+6.6643233«kN 110 000 A*KNEMP2*»3)/6.25 111 000 0132 IF(NRGG.GT.4.16)NRGG-4.16 112.000 0133 1070 iF(kNEMP2.GT.213JNRGG-<6.6-6.6266737»(KNEMP2-213))/6 25 113 000 0134 IF(RGGAB.LE.0)NRGG=0 114 000 0135 IF(KNEMP3.GT.213)GOTO 1080 115 000 0136 NRGAES>(105.86-1.1355*kNEMP3+6.6643233»kNEMP 1 16 000 A»KNEMP3«*3)/6.25 117 000 0137 IF(NRGAE S.GT.4.16)NRGAES*4.16 1 18 000 0138 1080 IF(KNEMP3. GT . 2 13)NRGAES«if6 .6-6.6266737*(KNEMP3-2 13) )/6 . 25 1 19 000 0139 IF(RGAB.LE.0)NRGAES=0 120 000 0140 4100 CONTINUE 121 000 CN - STAtEMENTS MARKED WITH CN OESCRIBE 121 200 CN A MECHANISTIC MODEL OF FOLIAR NITROGEN 121 400 CN WHICH WAS NOT INCLUDED IN THE FINAL VERSION OF AGGRO. 121 600 CNNIfROGEN UPTAKE 122 ooo CN U3=(O.OO2OO*N03/(84+N03)+O.OOO4O*N03/(4.8tN03))*LBG*INCR 123 000 CN U4=(0.OO2O0*NH4/(84+NH4)+0.OOO4O*NH4/(4.8+NH4))*LBG«INCR 124 000 MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) UMODEL 10-11-84 13:27:50 PAGE P004 CN I F ( K A . L E . 1)N=(29.0/6.25) 125 .000 CN IF(KA LE.1(GOTO 4760 126 .000 CNNITROGEN OEMAND 127 .000 CN NK-NK+1 128 .OOO CN DO 4194 1-1,12 129 .000 CN N P ( I ) = ( 1 0 5 . 8 6 - 1 . 1 3 5 5 * ( J ( I ) + 1 0 4 ) * 0 . 0 0 4 3 2 3 3 * ( J ( I ) * 1 0 4 ) » » 2 130 .000 CN A - 0 . 5 5 3 9 3 E - 5 * ( d ( I ) + 1 0 4 ) * * 3 ) / 6 . 2 5 131 .000 CN I F ( N P ( I ) . L T . 0 . 2 4 ) N P ( I ) = 0 2 4 132 • OOO CN194 CONTINUE - . 133 .000 CN195 CONTINUE 134 .000 CN DO 4199 1=1,12 135 .000 CN N A B U ) = N P ( I ) * A ( I ) / 1 0 0 . 0 136 .000 CN199 CONTINUE 137 000 CN NDEM=0.0 138 .000 CN 00 4230 1-1,12 139 000 CN NDEM=NDEM+NAB(1) 140 OOO CNINK CALL F W R I T E 1 I S I N K . ' S T A T E M F N T » B NDEM IS <R*4>.:'.NDEM) 14 1 000 CN230 CONTINUE t 142 .000 CNNITROGEN LEACHING 143 000 CN DO 4285 1=1,12 144 000 CN I F ( A ( I ) . L E . O ) G O T O 4285 145 000 CN DD(I)=DD(I)+TEMP 146 000 CN285 CONTINUE 147 000 CN300 CONTINUE 148 000 CN DO 4360 1=1,12 149 000 CN Z1=R3( J0)«R4i( JD) 150 000 CN I F ( 0 0 ( 1 ) LE.162) NLP(I)=0.875*Z1*70/61.0 151 000 CN I F U O D U ) GT. 162) .AND. ( D D U ) LE .324)) NLP( I ) = (2 . 75* Z 1*70/61 .0) 152 000 CN IF((D D ( I ) . G T . 3 2 4 ) . A N D . ( D D I I j . L E . 4 8 6 ) j N I P ( I ) = (6.25*Z1*70/61.6) 153 000 CN I F ( D D ( I ) . G T . 4 8 6 ) N L P ( I ) = ( 0 . 2 2 7 4 6 * 1 3 . 1 9 2 * Z 1 - 0 . 6 1 7 4 9 « Z 1 * * 2 ) * 7 0 / 6 1 . 0 154 000 CN360 CONTINUE 155 000 CN DO 4400 1=1.12 156 000 CN N L ( I ) = N L P ( I ) * N A B ( I ) / 1 0 0 . 0 157 000 CN N M L ( I ) = N A B ( I ) - N L ( I ) 158 000 CN400 CONTINUE 159 000 CN NLT=0.0 160 000 CN . DO 4408 1=1,12 161 000 CN NLT=NLT+NL(I) 162 000 CN408 CONTINUE 163 000 CNN VOLATILIZATION 164 000 CN DO 4438 1=1,12 165 000 CN MULTIPLIC'N BY 0.7 IS FOR CDNVERS'N FROM LEAF AREA TO LEAF WT 166 000 CN NVG(I)-EXP(-5.1592)*EXP(0.1B330*TEMP)*0. 7*DL*INCR*.000001 167 000 CN N V ( I ) = N V G ( I ) ' A ( I ) 168 000 CN438 CONTINUE 169 000 CN DO 4448 1=1,12 170 000 CN NMV(I)=NML(I)-NV ( i ) 171 000 CN448 CONTINUE 172 000 CN NVOLT=0.0 173 000 CN 00 4458 I•1,12 174 000 CN NVOLT=NV0LT+NV(I) 175 000 CN4S8 CONTINUE 176 000 CN TNLOSS"NVOLT*NLt 177 000 CN DO 4483 1=1,12 178 OOO CN I F ( A U ) . L E . O ) GOTO 4483 179 000 CN A( I )-(*"( I )-NV( I )-NL( I )) 180 000 CN I F ( A ( I ) . L E O ) 181 000 CN ACALL FWRITEtISINK,*A(<I*4>) IS NON-POSITIVE-<R*4>. : ' , I , A ( I ) ) 182 000 MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) UMODEL 10-11-84 13:27:50 PAGE P005 CN I F ( A U ) . L E . O ) A ( I ) = 0 183 .000 CN483 CN CN CONTINUE LAB=LAB-TNLOSS IF( N K . L T . 2 ) GOTO 4500 184 185 186 .OOO .000 OOO CN CN CN495 DO 4495 1=1.12 NCYC=NTO(I)-TL0SS0-NAB(I) CONTINUE 187 188 189 .000 .000 .000 CN500 CN CN NAVAIL=NAVAIL+U3*U4+NCYCLE NRECYC'NCYCLE NCYCLE=0 190 191 192 .000 . OOO .000 CN CN CN TLOSS0=TNL0SS DO 4535 1-1,12 NTO(I)=NAB(I) 193 194 195 OOO .000 .000 CN535 CN CN CONTINUE DO 4548 1=1,12 N V 0 ( I ) = N V ( I ) 196 197 198 . OOO .000 000 CN548 CN CN CONTINUE DO 4558 1=1,12 N L O ( I ) = N L ( I ) 199 200 201 000 OOO 000 CN558 CONTINUE CN IF(NAVAIL.GT.NDEM)GOTO 4700 CNNAVAIL IS < DEMAND 202 203 204 000 000 000 CNFIGURE OUT MIN LEVEL OF N FOR ALL A ( I ) AND CN NMIN=0.01*LAB CN NFREE=NAVAIL-NMIN RESERVE THIS AMOUNT (NMIN) 205 206 207 000 OOO 000 CN IF(NFREE.GE.0)G0T0 4625 CNNFREE < 0 CN 0 0 4620 I - 1 . 12 208 209 210 000 OOO 000 CN CN620 CN N A B ( I ) » N A V A I L / L A B * A ( I ) CONTINUE GOTO 4650 211 212 213 OOO 000 000 CNINK CALL FWRITEtISINK,'STATEMENT#9 CNNFREE > = 0 CN625 DO 4640 12 NFREE IS <R'4>.: '.NFREE) 214 215 216 000 000 000 CN I F ( N F R E E . G T . N A B ( 1 3 - i ) ) G 0 t 6 4630 CNNFREE < NAB(I) CN N A B ( 1 3 - I ) = 0 . 0 1 » A ( 1 3 - I ) + N F R E E 217 218 219 OOO 000 000 CNTHE CN CN FOLLOWING HAS THE EFFECT OF A DO L1 = 13-1 - 1 DO 4624 L-1.L1 LOOP WITH A NEG. INCREMENT 220 221 222 000 000 000 CN CN624 CN NAB(i)=6.6i*A(i) CONTINUE GOTO 4650 223 224 225 000 000 000 CN630 CONTINUE CNNAB(I) REMAINS AS NAB(I) CN NFREE=NFREE-NAB(I) 226 227 228 000 000 000 CN640 CN650 CN CONTINUE CONTINUE NAVAIL=0 229 230 231 000 000 000 CN CN CN 00 4668 1=1, 12 I F ( A ( I ) . L E . O ) G 0 T O 4668 N P ( I ) = N A B ( I ) / A ( I ) M 0 0 . 0 232 233 234 000 OOO 000 CN668 CN CN700 CONTINUE GOTO 4670 CONTINUE 235 236 237 000 000 000 CNNAVAIL > NDEMAND CNNAB(l) REMAINS AS NAB(I) AND N P ( I ) AS CN NAVAIL=NAVAIL-NDEM N P ( I ) 238 239 240 000 OOO 000 MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) UMODEL 10-11-84 13:27:50 PAGE P006 CN670 NN-0.0 241 .000 CN DO 4675 1-1,12 CN NN-NN+NAB(I) CN675 CONTINUE 242 243 244 .000 000 .OOO CN IF(LAB.GE..1)G0T0 4765 CN N-0. CN GOTO 4766 245 246 247 .000 .000 .000 CN65 CONTINUE CN N-NN/LAB*100.0 CN IF(N.GT.4.)CALL FWRITE(ISINK.'GA=<R>,GB»<R>,N-<R>,NN-<R>. 248 249 250 000 000 000 CN ALAB"<R>.TNLOSS=<R>.AB=<R>.CM CN BAB.CM,AM) CN66 CONTINUE =<R>.AM»<R>.:',GA,GB,N,NN,LAB,TNLOSS, 251 252 253 .OOO OOO 000 0141 CN760 CONTINUE C COMPUTE GROWTH POTENTIAL IF(TEMP.LT.-.5JG0T0 226 254 255 256 000 000 000 0142 0143 TG-(.31298+ 046723*TEMP- .0096323*TEMP**2+ A.00103B2*TEMP**3-.20755E-4 *TEMP* *4)/4 .27 IF(TG.LT.O)TG»0 258 259 260 000 000 000 0144 0145 0146 GOTO 230 226 TG-0 230 NG-( -108.56+165.52*N-48.029*N"2+4.71 19*N**3)/100 262 263 265 OOO OOO 000 0147 0148 0149 NG1 -(-55.981+79.567 «N-9.8307 »N*•2)/100 NG2-(-55.981+79.567*NRGAES-9.8307*NRGAES*»2)/100 NG3-(-55.981 + 79.567>NRGG-9.B307*NRGG* *2)/100 266 266 266 000 200 40O 0150 CMNK CALL FWRITE ( I SINK .'STATEMENT C'INK CALL FWRITE(ISINK.'STATEMENT IF(NG.LT.O)NG-0 11 N IS <R«4>.: 11 N2 IS <R*4>. '.N) :',N2) 267 268 269 000 000 000 0151 0152 0153 IF(NG1.LT.6lNG1=6 IF(NG.GT.1)NG-1 IF(NG2.LT.O)NG2-0 270 271 271 000 000 200 0154 0155 0156 IF(NG3.LT.O)NG3=0 IF(N.GT.3.3)NG1-1 IF(NRGAES.GT.3.3)NG2-1 271 272 272 400 000 200 0157 IF(NRGG.GT.3.3)NG3-1 CMNK CALL FWRITE( ISINK.'STATEMENT C*INK CALL FWRITE( ISINK, 'STATEMENT 12 N IS <R»4>.: 12 N2 IS <RM>. ' ,N) :',N2) 272 273 274 40O 000 000 0158 0159 0160 IFIWPbt.Gf.-i)WG=1 IF(WP0T.GT.-1)G0T0 235 WG-1-O.8*(ABS(WP0T))/20.0 275 276 277 000 OOO OOO 0161 0162 0163 IF(WG.GT.1)WG-1 IF(WG.LT.O)WG-0 235 CONTINUE 278 279 280 OOO 000 000 0164 IF(KB.LT.1)MB- 1 C»INK CALL FWRITE(ISINK.'STATEMENT C*INK CALL FWRlTEdSINK.'STATEMENT 13 N IS <R*4>.: 13 N2 IS <RM>. ' ,N) :'.N2) 281 282 283 000 000 000 0165 0166 0167 IF((JD.GT.182).AND.(DL.LE.13))DLG-1.0-(0.3*(13-DL)) IF(IAEST.E0.O)GA=GMAX*TG*WG*DLG*GLAB*NG1 IF(IAEST.EO.0)GA=GA+(GMAX*TG*WG*DLG*RGG*NG3) 284 285 285 000 OOO 200 0168 0169 0170 IF ( ( 1 AEST . EO. 1 ) • AND . (GRJD . EO. 6) ) G A = GM A X • f G * WG * D L G * R G A E S * N G 2 IF((IAEST.E0.1).AND.(GRJD.NE.0))GA=GMAX*TG*WG*DLG*RGAES*NG2 IF((IAEST.EO.1).AND.(GRJD.NE.0))GA=GA+(GMAX*TG*WG*DLG»RGG*NG3) 286 287 287 000 000 500 017 1 0172 0173 1020 CONTINUE GBaQBMAX*TG*WG*MB*LBG G-GA+GB 289 290 291 000 000 000 0174 0175 0176 IF( IAESTO.EO.1)G0T0 1350 IF((G.E0.O).AND.(JD.GT.151))IAESTO-1 IF((G.E0.O).AND.(JD.GT.151))JDAEST=JD 291 291 291 300 600 700 MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) UMODEL 10-11-84 13:27:50 PAGE P0O7 0177 1350 CONTINUE 291,90O 0178 0179 0180 IF( IAEST . EQ . 1 JGOtd 1355 IF((IAESTO.EO.1) AND.(G.NE.0))IAEST=1 IF((IAESTO.EO.1).AND.(G.NE.0))KB=1 292.20O 292.500 292.800 0181 0182 0183 1355 IF((IAESTO.EO.1j AND.(G.NE 6))RGJD=JO IF( (IAESTO.EO.1).AND.(G.NE.0))GBMAX=AGBMAX CONTINUE 293.100 293.400 294.000 0184 0185 0186 10O0 CONTINUE IFfKA.GE.1)GOTO 244 IF(G.GT .0)KA=> 1 297.000 298.000 299.000 0187 0188 0189 244 245 GOfb 245 KA=KA+INCR IF(GA.GT.O)TA-TA+GA 300.000 301.000 302 .000 0190 0191 0192 IF(GB. GT . 6)fB = TB+GB IF (KB . GE . 1 )GOTO 250 IF(GB.GT.0)KB=1 303.000 304 .000 305.000 0193 0194 0195 250 GOTO 252 KB=KB+INCR IF(KB.GT.21)KB-21 306.000 307 .000 308.000 0196 0197 0198 252 IF(KB.LT.1)GOTO 260 MB=.99930-.14683*(KB-1)+.0056462*(KB-1)*«2 IF(MB.GT.1)MB=1 309.000 310.000 311.000 0199 IF(KB.GT.18)MB-0 C«INK CALL FWRITE(I SINK,'STATEMENT*10 MB IS <R*4>.:•,MB) C COMPUTE PHOTOSYNTHESIS 312.000 313.000 314.000 0200 0201 0202 260 IF((TEMP.LE.0).OR.(TEMP.GT.40)1G0TO 270 IF((TEMP.GE.20).AND.(TEMP.LE.25))GOTO 274 IF((TEMP.GE.5).AND.(TEMP.LT.20))GOTO 278 315.000 316.000 317.000 0203 0204 0205 IF((TEMP.GT.25).AND.(TEMP.LE.35 j)GOTb 282 IF( ( TEMP. GT.O) .AND. ( TEMP . LT . 5) )TPSYN=>TEMP*0. 1052632 IF((TEMP.GT.O).AND.(TEMP.LT.5)(GOTO 300 318.000 319.000 320.000 0206 0207 0208 270 IF ( (TEMP.GT.35).AND.(TEMP.LE.40))fPSYN=(40-TEMP)*6.1315789 IF((TEMP.GT.35).AND.(TEMP.LE.40))GOTO 300 TPSYN=0 321.000 322.000 323.000 0209 0210 021 1 274 GOTO 300 TPSYNM GOTO 300 324.000 325.000 326.000 0212 0213 0214 278 282 TPSYN*1-(6.03158)*(20-fEMP) GOTO 300 TPSYN»1-(0.03421)*(TEMP-25) 327.000 328. OOO 329.000 0215 0216 0217 300 GOfb 300 IF(WP0T.LE.-3O)G0T0 330 WSYN=1+(O.O278)»WP0T 330.000 331.000 332.000 0218 0219 0220 330 IFfWSYN.Gt.i)WSYN=i GOTO 400 WSYN'O 333.000 334.000 335.000 0221 0222 GOTO 400 C MULTIPLICATION BY .675 IS CONVERSION FOR C02 TO CH20 400 CONTINUE 336.000 337.000 338.000 0223 0224 0225 IF(KGR.NE 0)KGR=KGR+1 IF(GRAZIN(JD) NE.0.0)KGR=1 IF (KGR . LT . UGOTO 410 339.000 340.000 34 1.000 0226 0227 0228 IFJKGR.GT.16)GRPSYN*6 0 IF(KGR.GT.16IG0T0 410 GRPSYN*(-5.1458+10.780*(KGR-1)- 1.3308*(KGR-1)**2 342.000 343.000 344.000 0229 0230 A+.04 2364*(KGR-1) **3)/100.0 410 PSYN=PMAX«TPSYN«WSYN*LAB*DL*0.675*(1.O+GRPSYN) T=T+PSYN 345.000 346.000 347.000 MICHIGAN TERMINAL SYSTEM FORTRAN G(21.B) UMODEL 10 - 11-84 13:27:50 PAGE POOS C COMPUTE RESPIRATION 348 000 0231 0232 IF(TEMP.LT.5)GOT0 430 RESP=(-0.46107+O.069524*TEMP+O.0O13714*TEMP**2)/1000 A0.675«FRMAX *LAB*(24 -DD* 349 350 351 000 000 000 0233 0234 0235 GOTO 432 430 RESP-0 432 CONTINUE 352 353 354 OOO 000 000 0236 0237 C COMPUTE NET PSYN NPSYN=PSYN-RESP TNPSYN=TNPSYN+NPSYN 355 356 357 000 000 000 0238 0239 C COMPUTE ROOT RESPIRATION IF(TEMP.LT.5)RR=0 IF(STEMP.LT.5)G0TO 470 358 359 360 000 000 000 0240 0241 RR»(-0.46107+6 .66^52^*STEMP+6.0dl37'l4*StEMP»*2)/1000»LB6»DL« A*FRRMAX 470 CONTINUE .675 361 362 363 000 000 000 0242 CRS RS=RS-RR LBG=LBG-RR C COMPUTE SOURCE STRENGTH 364 365 366 000 000 000 0243 0244 0245 SS=G-NPSYN IF((G.GT.0).AND.(NPSYN.GT.0).AND.(SS.GT.0))SG=SG+SS IF((G.GT.O).AND.(NPSYN.LT.O).AND.(SS.GT.0))SG=SG+SS- ABS(NPSYN) 367 368 369 000 000 000 0246 0247 IF(SS.GT.O)UDR=-0.0 IF(SS.LT.O)UDR=(PSYN-ABS(SS))/ABS(SS) C IS PSYN ENOUGH TO SUPPORT GROWTH DEMAND 370 371 372 000 o o o 000 0248 0249 IF(SS.LE.6JGOT0 540 TS-TS+SS C PSYN IS NOT ENOUGH TO SUPPORT GROWTH 373 374 375 o o o 000 000 0250 0251 RS=0.30*LBG IF(RS.LT.SS)GOTO 510 C RESERVE IS ENOUGH TO COVER SS 375 376 377 200 000 000 0252 0253 CRS RS"RS-SS LBG=LBG-SS I F ( ( I A E S T . E O . O ) A N D . ( G R d D . E O . 0 ) ) G L A B A B « G L A B A B + G 378 379 380 000 000 o o o 0254 0255 0256 IF((IAEST.EO.O).AND.(GRjb.EO.O))GLAB=GLAB+G I F ( ( I A E S T . E O . O ) AND.(GRdD.NE.0))RGGAB"RGGAB+G IF((IAEST.EO.O).AND.(GRdD.NE.0))RGG SRGG+G 381 382 383 000 000 000 0257 0258 0259 IF((IAEST.EO.1).AND.(GRdO.LE.RGJD))RGAB=RGAB*G I F ( ( I A E S T . E O . 1 ) AND.(GRdD.LE.RGdD))RGAES=RGAES+G I F ( ( IAEST. EO. 1 ) .AND. (GRdO . GT . RGdD) )RGGAB=RGGAB+G 384 385 386 000 000 000 0260 0261 0262 IF((IAEST.EQ.1).AND.(GRdD.GT.RGdD))RGG=RGG+G CUMAB'CUMAB+G AB-=AB+G 387 388 389 000 000 000 0263 0264 GOTO 570 C RESERVES NOT ENOUGH TO COVER SS 510 O-RS-SS 390 391 392 000 000 000 0265 0266 0267 IF<(G+Dj.Lt.6)Gbtd 520 AB-AB+G+D L B G » L B G - S S - 0 393 394 394 000 000 200 0268 0269 0270 IF((IAEST.EO.O).AND.(GRdD E O O ) )GLABAB«GLABAB+G+b IF((IAEST.EO.O).AND.(GRdD.EO.O))GLAB"GLAB+G+D I F ( ( I A E S T . E O . O ) AND.(GRdD.NE.0))RGGAB=RGGAB+G+D 395 396 397 000 000 000 0271 0272 0273 IF((IAEST.EO.6).AND.(GRdD.NE.6))RGG cRGG+G+b I F ( ( I A E S T . E O . 1 ) AND.(GRdD.LE.RGdD))RGAB=RGAB+G+D I F ( ( I A E S T . E O . 1 ) AND.(GRdO.LE.RGdD))RGAES=RGAES+G+0 39B 399 40O 000 000 000 0274 0275 0276 IF((IAEST.EO.1).AND.(GRdO.GT.RGdD))RGGAB = RGGAB+G+b I F ( ( I A E S T . E O . 1 ) AND.(GRdD GT.RGdD))RGG=RGG+G+D CUMAB=CUMAB+G+D 401 402 403 000 000 000 M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 2 1 . 8 ) U M O D E L 1 0 - 1 1 - 8 4 1 3 : 2 7 : 5 0 P A G E P 0 0 9 0 2 7 7 5 2 0 G = G + D 4 0 4 . 0 0 0 0 2 7 8 0 2 7 9 C P S I F ( G . L T . O ) G » 0 R S - 0 G O T O 5 7 0 4 0 5 4 0 7 4 0 8 0 0 0 ' 0 0 0 0 0 0 0 2 8 0 0 2 8 1 C S O U R C E S T R E N G T H <= 0 5 4 0 A B = A B + G I F ( ( 1 A E S T . E O . 0 ) . A N D . ( G R J D . E O . O ) ) G L A B " G L A B + G 4 0 9 4 1 0 4 1 1 0 0 0 0 0 0 0 0 0 0 2 8 2 0 2 8 3 0 2 8 4 I F ( ( I A E S T . E O . O ) . A N D . ( G R J D . E O . O ) ) G L A B A B = G L A B A B + G I F ( ( I A E S T . E O . O ) • A N D . ( G R J D . N E . 0 ) > R G G A B = R G G A B + G I F ( ( I A E S T . E O . O ) . A N D . ( G R J D . N E . 0 ) ) R G G = R G G + G 4 1 1 4 1 2 4 1 3 2 0 0 0 0 0 0 0 0 0 2 8 5 0 2 8 6 0 2 8 7 I F ( ( I A E S T . E O . 1 j . A N D . ( G R J D . L E . R G J D ) J R G A B = R G A B + G I F ( ( I A E S T . E O . 1 ) . A N D . ( G R J D . L E . R G J D ) J R G A E S - R G A E S + G I F ( ( I A E S T . E O . 1 ) . AND . ( G R J D . G T . R G J D ) )RGGAB-=RGGAB+G 4 1 4 4 1 5 4 1 6 0 0 0 0 0 0 o o o 0 2 8 8 0 2 8 9 0 2 9 0 I F ( ( I A E S T • E O . 1 ) . A N D . ( G R J D . G T . R G J D ) j R G G = R G G * G T S S N E G » T S S N E G + A B S ( S S ) C U M A B ' C U M A B + G 4 1 7 4 1 8 4 1 9 0 0 0 0 0 0 0 0 0 0 2 9 1 0 2 9 2 C R S 5 7 0 R S = R S + 0 . 6 0 * A B S ( S S ) L B G ' L B G + A B S ( S S ) C O N T I N U E 4 2 0 4 2 1 4 2 2 0 0 0 0 0 0 0 0 0 0 2 9 3 0 2 9 4 0 2 9 5 I F ( L B G . L t . i . y R S P - 6 . I F ( L B G . L T . 1 . ) G 0 T 0 5 7 5 R S P = R S / L B G « 1 0 0 . 0 4 2 3 4 2 4 4 2 5 0 0 0 0 0 0 0 0 0 0 2 9 6 0 2 9 7 5 7 5 C O N T I N U E C C O M P U T E A B O V E G R O U N D M O R T A L I T Y ( A M ) AM-0 4 2 6 4 2 7 4 2 7 0 0 0 0 0 0 7 0 0 0 2 9 8 0 2 9 9 0 3 0 0 A M G A O A M R G A - 0 A M R G G = 0 4 2 8 4 2 9 4 2 9 4 0 0 1 0 0 . 8 0 0 0 3 0 1 0 3 0 2 0 3 0 3 P H E N M = 0 . 2 2 5 9 4 - 0 . 0 1 0 7 2 4 * K A + 0 . 0 0 0 3 8 1 5 1 * K A " 2 I F ( P H E N M . L T . 0 . 2 ) P H E N M = 0 . 2 I F ( P H E N M . G T . 1 . 0 ) P H E N M - 1 . 0 4 3 2 4 3 3 4 3 4 0 0 0 0 0 0 0 0 0 0 3 0 4 0 3 0 5 0 3 0 6 I F ( T E M P . L E . - 2 ) F M = 0 . 2 5 I F ( T E M P . G T . - 2 ) F M=0. I F ( T E M P . L E . S O ) W A M = ( 0 . 0 2 ' ( A B S ( W P O T ) - 3 0 ) ) ' P H E N M 4 3 5 4 3 6 4 3 7 0 0 0 0 0 0 0 0 0 0 3 0 7 0 3 0 8 0 3 0 9 I F ( t E M P . G T . 3 0 ) W A M = ( 6 . 0 2 5 • ( A B S ( W P O T ) - 3 0 ) j ' P H E N M I F ( W P 0 T . G T . - 3 O ) W A M = O I F ( I A E S T O . N E . 1 ) G O T O 1 3 2 0 4 3 8 4 3 9 4 3 9 0 0 0 0 0 0 1 0 0 0 3 1 0 0 3 1 1 0 3 1 2 1 3 2 0 A M G = ( W A M + F M ) ' G L A B + P H E N M 2 ' G L A B G O T O 1 3 3 0 A M G = ( W A M + F M ) ' G L A B 4 3 9 4 3 9 4 3 9 2 0 0 3 0 0 4 0 0 0 3 1 3 0 3 1 4 0 3 1 5 1 3 3 0 C O N T I N U E A M R G A = ( W A M + F M ) * R G A E S A M R G G = ( W A M + F M ) * R G G 4 3 9 4 4 1 4 4 2 5 0 0 0 0 0 0 0 0 0 3 1 6 0 3 1 7 AM=AMRGA+AMRGG+AMG CM=CM+AM C A L L O C A T E M O R T A L I T Y T O B I O M A S S T Y P E 4 4 3 4 4 4 4 5 9 0 0 0 0 0 0 0 0 0 0 3 1 8 0 3 1 9 0 3 2 0 R G A E S = R G A E S - A M R G A G L A B " G L A B - A M G R G G - R G G - A M R G G 4 6 0 4 6 1 4 6 2 0 0 0 0 0 0 0 0 0 0 3 2 1 0 3 2 2 C C O M P U T E P R O T E I N Y I E L D N N = N / 1 0 0 . 0 ' G L A B A B + R G A B ' N R G A E S / 1 0 0 . O + N R G G / 1 0 0 . O ' R G G A B C P Y = N N * 6 . 2 5 4 7 7 4 7 8 4 7 9 0 0 0 0 0 0 0 0 0 0 3 2 3 0 3 2 4 0 3 2 5 C P G = N * 6 . 2 5 C P R G A = N R G A E S * 6 . 2 5 C P R G G = N R G G ' 6 . 2 5 4 8 0 4 8 1 4 8 1 0 0 0 0 0 0 1 0 0 0 3 2 6 0 3 2 7 0 3 2 8 CPYG=CPG*GLABAB7I6O.6 C P Y R G A - C P R G A ' R G A B / 1 0 0 . 0 C P Y R G G = C P R G G ' R G G A B / 1 0 0 . 0 4 8 1 4 8 1 4 8 1 2 0 0 3 0 0 4 0 0 MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) UMODEL 10-11-84 13:27:50 PAGE P010 0329 IF((N.LT.NMINY).AND.(GLABAB.GT.0)JNMG-0 482.000 0330 0331 0332 IF((NRGAES LT.NMINYj.AND.(RGAB.GT.0)JNMRGA=0 IF((NRGG.LT.NMINY).AND.(RGGAB.GT.0))NMRGG=0 CPYMIN=CPYG*NMG+CPYRGA*NMRGA+CPYRGG*NMRGG 483.000 484.000 485.000 0333 0334 C COMPUTE GRAZED MORTALITY GR=GRAZIN( i)D)/100*AB IF (GR . NE . 0)GRJD=JD 486 OOO 487.000 488. OOO 0335 0336 0337 IF(GR.NE.0)KB =1 GRKNI"GRJD-KNI IF(GRKNI.GT.28)G0T0 6000 490.000 490.100 490.200 0338 0339 0340 GGBMAX aO.054-GRKNI*0.0017357 6000 CONTINUE IF(GR.NE.0)GBMAX"GGBMAX 490.300 490.400 491.000 0341 0342 AB-AB-GR C ALLOCATE GRAZED MORTALITY TO BIOMASS TYPE GRAZ-GR 492.000 506.000 507.000 0343 0344 0345 IF(GRAZ.EO.6)Gbf0 1200 I F ( I A E S T . N E . 0 ) G 0 T 0 1100 GLAB"GLAB-GRAZ 508.000 509.000 510.000 0346 0347 0348 GLABAB=GLABAB-GRAZ GRAZ"0 GOTO 1200 511.000 512.000 513.000 0349 0350 C IAEST.NE.O 1100 IF(RGAES.LT.GRAZ)GOTO 1300 RGAES=RGAES-GRAZ 514.OOO 515.000 516.000 0351 0352 0353 RGAB"RGAB-GRAZ GRAZ=0 GOTO 1200 517.OOO 518.000 519.000 0354 0355 C RGAES.LT.GRAZ 1300 CONTINUE IF((RGAES.LT.GRAZ).AND.(RGA8.GE.GRAZ))GOTO 6010 520.000 520.100 520.20O 0356 0357 C RGAES < GRAZ AND RGAB < GRAZ GRAZ"GRAZ-RGAB RGAES-0 520.300 520.400 520.500 0358 0359 0360 RGAB=0 GOTO 6020 6010 CONTINUE 520.600 520.700 520.800 0361 0362 C RGAES < GRAZ AND RGAB >" GRAZ RGAES-0 RGAB"RGAB-GRAZ 520.900 521.000 521.10O 0363 0364 0365 GRAZ=6 GOTO 1200 6020 CONTINUE 521.200 521.300 521.400 0366 0367 0368 IF (GLAB . LT . GRAZ: )Go"f0 1360 GLAB"GLAB-GRAZ GLABAB "GLABAB-GRAZ 522.100 522.150 522.200 0369 0370 GRAZ"0 GOTO 1200 C GLAB < GRAZ 522.250 522.30O 522.350 0371 0372 0373 1360 GLAB"6 GLABAB-GLABAB-GRAZ GRAZ"0 522.400 522.450 522.500 0374 0375 1200 CONTINUE C COMPUTE TOTAL L I V E ABOVEGROUND BIOMASS LAB=GLAB+RGG+RGAES 525.000 526.000 527.000 0376 0377 C COMPUTE BELOWGRbUNb MORTALITY (BM) IF(WPOT.GT.0)WBM=0.04 IF(WP0T.GT.O)G0T0 840 528.000 529.000 530.000 MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) UMODEL 10-11-84 13:27:50 PAGE P011 CWBM WBM*-(SY1**SB+(SY2**SB-SY1**SB)*<1.0-EXP(-SA* (WPOT-O)))/ 531 000 0378 0379 CWBM «(1 0-EXP(-SA*(75-O))))*•(1/( SRI) DWPOT'DBLE(WPOT) CALL SCH15(DWBM,-DWP0T,DPAR15.DTAU1,DTAU2) 532.000 533.000 534.000 0380 0381 0382 840 WBM-SNGI. (DWBM) CONTINUE BM=WBM*LBG*DMAX 535 536 537 000 000 000 0383 0384 CRS TM=TM+BM LBG*LBG-BM RS=RS-RSP/100*BM 538 539 540 000 000 000 0385 0386 0387 1083 IF(AB.LE.O)G0T0 1083 RTSHT=LBG/AB CONTINUE 54 1.000 542.OOO 543.000 0388 C COMPUTE LITTERFALL SD-SD+AM CRAIN IF(R3(JD).NE.0.)CALL FWRITECISINK,'R3(<I>) IS <R*4>.:',JD,R3(JD)) 544.000 545.000 546.000 CRAIN C*INK C*INK IF(R4(JD).NE.O.)CALL FWRITE(I SINK.'R4(<I>) IS CALL FWRITE(ISINK,'R4(JD) IS <R*4>.:',R4(JD)) CALL FWRITEdSINK, 'Z1 IS <R*4>.:',Z1) <R*4>. :',JD,R4(JD ) ) 547 548 549 000 000 000 0389 0390 LFM8.3E-4+1 .3E-3*R3( JD)*0. 10)*SD*R4( JD) SD-SD-LF C ALLOCATE LITTERFALL TO AB TYPE 550 551 552 000 000 000 0391 0392 0393 AB=AB-LF IF(LF.E0.O)G0T0 1305 LF23LF 553 553 553 000 050 100 0394 0395 0396 IF (GLABAB . LT . LF2 )G6TO 1310 GLABAB=GLABAB-LF2 LF2-0 553 553 553 150 200 260 0397 0398 0399 1310 GOTO 1305 LF2-LF2-GLABAB GLABAB°0 553 553 553 270 280 300 0400 0401 0402 IF(RGG.LT.LF 2)GOf0 1315 RGG=RGG-LF2 LF2-0 553 553 553 350 400 450 0403 0404 0405 1315 GOTO 1305 LF2=LF2-RGG RGG=0 553 553 553 500 550 600 0406 0407 0408 1305 RGAB-RGAB-LF2 CONTINUE RETURN 553 553 554 650 700 000 0409 C2000 C CONTINUE STOP END 555 556 557 000 000 000 •OPTIONS IN EFFECT* ID,EBCDIC,SOURCE.NOLIST,NOOECK,LOAD.NOMAP •OPTIONS IN EFFECT* NAME " UMODEL , LINECNT = 60 •STATISTICS* SOURCE STATEMENTS - 409,PROGRAM SIZE • 14212 •STATISTICS* NO DIAGNOSTICS GENERATED MICHIGAN TERMINAL SYSTEM FORTRAN GI21.8) YZLIN 10-11-84 13:28:08 PAGE P001 0001 REAL FUNCTION YZLIN*8(X,Y.N.XL IN.I START,ISINK.JD,ICALL) 558.000 0002 IMPLic i f R E A L » 8 ( A - H . b - Z ) 5 5 9 . O O O 0003 REAL*8 X(N),Y(N) 560.000 0004 IF(ISTART.LE.0)ISTART=1 561.000 CTEST WRITE! ISiNK,35)X 562.000 CTEST35 FORMAT('O'.'X='.10(1X.F7.3)) 563.000 CTEST WRITEtISINK,36)Y 564.000 CT EST 36 FORMAT ( ' 0 ' . 'Y=' . id( IX i F7 . 3 j ) 5 6 5 000 0005 NM1-N-1 566.000 0006 DO 10 I=ISTART,NM1 567.000 0007 i f ( (XLIN GE X( I )) AND. (XL IN LE X( t + 1 ) ) VGOTO 2 0 5 6 8 OOO 0008 10 CONTINUE 569.000 0009 WRITE(ISINK,30)XLIN,ICALL 570.000 0 0 1 0 3 0 F O R M A T ( ' - ' |''•••ERROR*** fIME=' ,E20. 10 . ' - -OUT OF fNT FRpbLAf I O N ' / 5 7 i OOO A' RANGE--CALL NUMBER ' , 1 1 0 . ' . ' ) 572.000 0011 WRITE(ISINK.40)JD,ISTART,I,N.NM1 573.000 0 0 1 2 4 0 F O R M A T ( ' - ' . ' JD^ ' . I 10. ' : I ST AR1 - ' , I 1 0 , ' ; 1= ' . I 10 J ' •' N= ' ,1 ioT': ' 7 5 7 4 . 0 0 0 A' NM1-'.I10) 575.000 C STOP 576.000 0 0 1 3 2 0 C O N T I N U E 5 7 7 . 0 0 0 0014 SL0PE'(Y ( I+1)-Y ( I))/(X ( I+1 ) -X(I)) 578.000 0015 YZLIN'SLOPE*XLIN+(Y(I)-SL0PE*X(I)) 579.000 0 0 1 6 1 S T ART = 1 5 8 0 . 0 0 0 CTEST WRITE(ISINK,40)JD.ISTART,I,N.NM1 581.000 0017 RETURN 582.000 0 0 1 8 E N D 5 8 3 .666 •OPTIONS IN EFFECT* ID,EBCDIC,SOURCE.NOLIST,NODECK,LOAD.NOMAP •OPTIONS IN EFFECT* NAME = YZLIN , LINECNT = 60 * S T A T l s t l C S * S O U R C E ST AT EMENtS ' 1 8 .PROGRAM S I Z E ' = 9 6 2 •STATISTICS* NO DIAGNOSTICS GENERATED M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 2 1 . 8 ) R E I N I T 1 0 - 1 1 - 8 4 1 3 : 2 8 : 0 9 P A G E P 0 0 1 0 0 0 1 S U B R O U T I N E R E I N I T 5 8 4 . 0 0 0 0 0 0 2 • R E A L N . N G . N 2 1 0 0 0 0 0 0 3 R E A L N 0 3 . N H 4 . L B G . N P , N A B , N L P , N L . N M L . N L T . N V G 2 0 0 0 0 0 0 4 R E A L T N L O S S . N L O . N C Y C L E , N T O 3 . O O O 0 0 0 5 R E A L N A V A I L , N L O S S . L A B , N F R E E , N M I N . N N . M B . N P S Y N . K I L L . L F 4 . 0 0 0 0 0 0 6 R E A L J . N V O . N V . N O E M . N V O L T 5 . 0 0 0 0 0 0 7 R E A L D M A X , N R E C Y C . N C Y C , N 0 3 , N G 1 , N G 2 , N G 3 6 0 0 0 0 0 0 8 R E A L N R G G , N R G A E S , N M I N Y 6 2 0 O 0 0 0 9 I N T E G E R I N C R , N K . K A . K B . R K , J R . D P . W P C H 7 O O O 0 0 1 0 I N T E G E R G R J D . F U N 8 O O O 0 0 1 1 C O M M O N P , A 1 , B ( 1 0 ) . G M A X , I T I M E 9 0 0 0 0 0 1 2 C O M M O N A B . R S . C C . S D . S S . T S . D . R S P 1 1 0 0 0 0 0 1 3 C O M M O N T E M P , T O ( 1 0 ) , T M 1 ( 1 0 ) , D D I 1 2 ) , D L , S T E M P 1 2 0 0 0 0 0 1 4 C O M M O N W P 0 T . W 1 , N 1 3 0 0 0 0 0 1 5 C O M M O N P S Y N . T P S Y N . W S Y N , N P S Y N , T . T N P S Y N 1 4 0 0 0 0 0 1 6 C O M M O N G . W G . N G . T G . T 1 , N 2 1 5 0 0 0 0 0 1 7 C O M M O N R E S P . R R 1 6 0 0 0 0 0 1 8 C O M M O N D M A X , L A B 1 7 0 0 0 0 0 1 9 C O M M O N T A , T B , S G , T M , N R E C Y C 1 8 0 0 0 0 0 2 0 C O M M O N C 4 , C 5 , S 4 . S 5 , I S I N K 1 9 0 0 0 0 0 2 1 C O M M O N D R ( 1 2 ) , R M ( 1 2 ) . R D ( 1 2 ) 2 0 0 0 0 0 0 2 2 C O M M O N J ( 1 2 ) . A ( 1 2 ) , N V 0 ( 1 2 ) 2 1 0 0 0 0 0 2 3 C O M M O N W P A O ( 6 ) . W P C 1 ( 6 ) . W P C 2 " ( 6 ) , W P C 3 ( 6 ) . W P C 4 ' ( 6 ) . W P C 5 ( 6 ) . W P C 6 ( 6 ) 2 2 0 0 0 0 0 2 4 C O M M O N W P S 1 ( 6 ) , W P S 2 ( 6 ) , W P S 3 ( 6 ) , W P S 4 ( 6 ) . W P S 5 ( 6 ) , W P S 6 ( 6 ) 2 3 0 0 0 0 0 2 5 C O M M O N U 3 . U 4 . N 0 3 . N H 4 2 4 0 0 0 0 0 2 6 C O M M O N I N C R , N K , K A , K B , R K , J R , R J 2 5 0 0 0 0 0 2 7 C O M M O N G A , G B , M B , L B G , J D 2 6 o o o 0 0 2 8 C O M M O N N P ( 1 2 ) , N A B ( 1 2 ) , N D E M , N L P ( 1 2 ) , N L ( 1 2 ) , N M L ( 1 2 ) , N L T 2 7 0 0 0 0 0 2 9 C O M M O N N V G ( i 2 ) . N V ( i i j . N V O L f 2 8 o o o 0 0 3 0 C O M M O N Z 1 , R 3 ( 3 6 5 ) , R 4 ( 3 6 5 ) 2 9 0 0 0 0 0 3 1 C O M M O N T N L O S S , N L O ( 1 2 ) . N C Y C L E , N T O ( 1 2 ) , T L O S S O , N A V A I L , N F R E E . N M I N , N N 3 0 0 0 0 0 0 3 2 C O M M O N K I M v ( 1 2 ) , F M , A M , C M , K I L L , B M . L F . P H E N M 3 2 0 0 0 0 0 3 3 C O M M O N R N ( 2 0 ) , R P ( 2 0 ) . P R E C , R 1 ( 2 0 ) . R 2 ( 2 0 ) , 0 P ( 2 0 ) , P M ( 2 0 ) 3 3 0 0 0 0 0 3 4 C O M M O N S Y 1 , S Y 2 , S A , S B , W B M . R N D M I 3 4 0 0 0 0 0 3 5 C O M M O N I S O U R C . I P A S S . L O C N . W P C H , R N O M I 3 6 0 0 0 0 0 3 6 C O M M O N D L A O ( 1 0 ) , D L C 1 ( 1 0 ) , D L S 1 ( 1 0 ) . P I . W A M . N C Y C 3 7 0 0 0 0 O 3 7 C O M M O N N Y C , C P , U O R . C P Y , G R A Z I N ( 3 6 5 ) . K G R , G R . G R P S Y N 3 8 0 0 0 0 0 3 8 C O M M O N I S T T . I S T S T , I S T W . G R A , K N E M P , K N E M P I . K N I 3 9 0 0 0 0 0 3 9 C O M M O N G R J D . F U N , G B M A X . G G B M A X . D L G . I S H I F . N C H 4 0 0 0 0 0 0 4 0 C O M M O N I A E S T , A G B M A X , F U N 2 . R G A E S , F U N S 4 1 0 0 0 0 0 4 1 C O M M O N M O R T J O , M O R T W P , C U M A B . R G G . A M R G G , A M R G , f L A B 4 2 0 0 0 0 0 4 2 C O M M O N R T S H T . P M A X , F R M A X , F R R M A X , T S S N E G 4 3 0 0 0 0 0 4 3 C O M M O N K N E M P 2 . K N E M P S . N R G G , N R G A E S . G R A Z . A M G , A M R G A 4 4 0 0 0 0 O 4 4 C O M M O N G L A B . G L A B A B . R G G A B . R G A B . C P G . C P R G A , C P R G G . L F 2 4 5 0 0 0 0 0 4 5 C O M M O N N M G . N M R G A . N M R G G . C P Y M I N , N M I N Y 4 6 0 0 0 0 0 4 6 C O M M O N C P Y G , C P Y R G A , C P Y R G G , P H E N M 2 4 7 0 0 0 0 0 4 7 C O M M O N N G 1 . N G 2 . N G 3 . G A 1 , G A 2 . I A E S T O . R G J D . J D A E S T 4 8 0 0 0 0 0 4 8 C O M M O N Z , D A M P D . G R K N I 4 9 0 0 0 0 0 4 9 J D * 0 5 8 6 0 0 0 0 0 5 0 K A = 0 5 8 7 0 0 0 0 0 5 1 K B = 0 5 8 8 0 0 0 0 0 5 2 N D E M = 0 5 8 9 0 0 0 0 0 5 3 N L T = 0 5 9 0 o o o 0 0 5 4 N V O L T - 0 5 9 1 0 0 0 0 0 5 5 T A = 0 5 9 2 0 0 0 0 0 5 6 T B ' O 5 9 3 0 0 0 0 0 5 7 S G = 0 5 9 4 0 0 0 0 0 5 8 T S ' O 5 9 5 o o o MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) REINIT tO-11-84 13:28:09 PAGE P002 0059 AB-0 596.000 0060 CM-0 597 000 0O61 TM=0 598 000 0062 KGR-0 599 000 0063 T=0 600 000 0064 CUMAB-0 600 050 0065 IAEST-0 600 100 0066 GRUD-0 600 150 0067 RGdD-0 600 200 0068 KNI-0 600 250 0069 KNEMPI-0 600 300 0O70 IAESTO-0 600 350 0071 JDAEST-0 600 400 0072 DLGM.O 600 450 0073 TSSNEG-0 600 500 0O74 GLAB-0 600 550 0075 RGG=0 600 600 0O76 RGAES=0 600 650 0077 GLABA8-0 600 700 0078 RGAB-0 600 750 0079 RGGAB-0 600 800 0080 GBMAX-.054 600 850 0081 TNPSYN-0 601 000 0082 DO 900 1-1.12 602 000 0083 DD(I)»0 603 000 0084 900 CONTINUE 604 000 0085 00 905 1-1,365 605 000 0086 R3(I )=0 606 000 0087 R4(I)-0 607 000 0088 905 CONTINUE 608 000 0089 DO 910 1-1.20 609 000 0090 PM(I)=0 610 000 0091 DP(I)-0 611 000 0092 910 CONTINUE 612 000 0093 GGBMAX -0.0054 612 200 0094 RETURN 613 000 0095 END 614 000 •OPTIONS IN EFFECT' ID. EBCDIC, SOURCE .NOLIST ,NODECK. LOAD.NOMAP •OPTIONS IN EFFECT' NAME = REINIT . LINECNT » 60 •STATISTICS* SOURCE STATEMENTS - 95.PROGRAM SIZE - 730 •STATISTICS'NO 01 AGNOSTICS GENERATED MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) ASHRN 10-11-84 13:28:15 PAGE P001 0OO1 SUBROUTINE ASHRN 614 .007 0002 0003 00O4 REAL N.NG.N2 REAL N03. NH4 , LBG. NP.NAB . NLP , NL .NML. NLT, NVG REAL TNL0S5.NLO.NCYCLE,NTO 1 2 3 000 000 .000 0005 0006 0007 REAL NAVAIL.NLOSS.LAB.NFREE.NMIN.NN,MB.NPSYN,KILL,LF REAL d.NVO.NV.NDEM.NVOLT REAL DMAX,NRECYC.NCYC.N03.NG1,NG2,NG3 4 5 6 OOO OOO 000 0008 0009 0010 REAL NRGG.NRGAES.NMINY INTEGER INCR.NK.KA.KB.RK,JR,DP.WPCH INTEGER GRJD.FUN 6 7 8 200 000 000 001 1 0012 0O13 COMMON P,A1.B(10).GMAX,ITIME COMMON AB.RS.CC.SD.SS.TS.D.RSP COMMON TEMP.TO(10),TM1(10).DD(12).DL,STEMP 9 1 1 12 000 000 000 0014 0015 0016 COMMON WPOT,W1,N COMMON PSYN.TPSYN.WSYN,NPSYN,T.TNPSYN COMMON G.WG.NG.TG.T1,N2 13 14 15 000 000 000 0017 0018 0019 COMMON RESP,RR COMMON DMAX.LAB COMMON TA.TB.SG.TM,NRECYC 16 17 18 000 000 000 0020 0021 0022 COMMON C4,C5,S4,S5,ISINK COMMON 0R(12),RM(12),R0(12) COMMON J(12),A<12).NV0(12) 19 20 21 OOO 000 000 0023 0024 0025 COMMON WPA0(6).WPCI(6).WPC2(6).WPC3I6),WPC4(6),WPC5(6),WPC6<6> COMMON WPS1(6),WPS2(6),WPS3(6).WPS4(6).WPS5(6).WPS6I6) COMMON U3,U4,N03,NH4 22 23 24 000 000 000 0026 0027 0028 COMMON INCR.NK.KA.KB.RK.JR.RJ COMMON GA,GB,MB,LBG,JD COMMON NP(12),NAB(12),NDEM,NLP(12),NL(12),NML(12).NLT 25 26 27 000 000 000 0029 0030 0031 COMMON NVG(12),NV(12J.NV0LT COMMON Z1,R3<365),R4(365) COMMON TNLOSS,NLOC12),NCYCLE,NTO(12),TLOSSO,NAVAIL .NFREE.NMIN.NN 28 29 30 000 000 000 0032 0033 0034 COMMON NMV(12),FM,AM,CM,KILL,BM.LF,PHENM COMMON RN(20).RP(20).PREC.R1(20),R2(20).DP(20).PM(20) COMMON SY1,SY2,SA,SB.WBM,RNDMI 32 33 34 000 000 000 0035 0036 0037 COMMON ISOURC.IPASS,LOCN.WPCH.RNOMI COMMON DLAOt10).DLC1(10),DLS1(10).PI,WAM,NCYC COMMON NYC,CP,UDR,CPY.GRAZIN(365),KGR,GR,GRPSYN 36 37 38 000 000 000 0038 0039 0040 COMMON ISTT,ISTST,ISTW,GRA,KNEMP,KNEMPI,KNI COMMON GRJD,FUN,GBMAX,GGBMAX.DLG,ISHIF,NCH COMMON IAEST,AGBMAX.FUN2.RGAES.FUN3 39 40 4 1 000 000 000 0041 0042 0043 COMMON MORTJD.MORTWP,CUMAB.RGG.AMRGG,AMRG.TLAB COMMON RTSHT,PMAX,FRMAX,FRRMAX.TSSNEG COMMON KNEMP2.KNEMP3.NRGG,NRGAES.GRAZ,AMG,AMRGA 42 43 44 000 000 000 0044 0045 0046 COMMON GLAB.GLABAB,RGGAB.RGAB.CPG.CPRGA.CPRGG.LF2 COMMON NMG,NMRGA,NMRGG,CPYMIN.NMINY COMMON CPYG,CPYRGA,CPYRGG,PHENM2 45.000 46.000 47.000 0047 0048 0049 COMMON NG1,NG2.NG3.GA1.GA2.IAESTO.RGJO.JOAEST COMMON Z.DAMPD,GRKNI IF(LOCN.E0.5)G0T0 100 48 49 614 000 000 343 0050 0051 0052 R3(148)=10 R4(148)>0.127 R3(154)-5. 614 614 614 350 357 364 0053 0054 0055 R4(154)=0.508 R3(165)=7. R4(165)=3.084 614 614 614 371 378 385 0056 0057 0058 R3(177)=1S. R4( 177) = 3.556 R3(202)=2.3 614 614 614 392 399 406 ro MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) ASHRN 10-11-84 13:28: 15 PAGE P0O2 0059 R4(202)-4.417 614.413 0060 0061 0062 R3(260)°13. R4(260)=0.6845 R3(289)=7. 614.420 614.427 614.434 0063 0064 0065 R4(289)=2.358 GOTO 200 100 CONTINUE 614.441 614.448 614.455 0066 0067 0068 R3(140)=3. R4(1401-13.54 R3(142)=8. 614.462 614.469 614.476 0069 0070 0071 R4(142)»7.937 R3(143)-15. R4(143)*0.169 614.483 614.490 614.497 0072 0073 0074 R3(144)=25. R4(144)=0.152 R3(145)-=3. 614.504 614.511 614.518 0075 0O76 0077 R4(145 j=6.847 R3(160)-3. R4(160)=2.12 614.525 614.532 614.539 0078 0079 0080 R3(161j=2 R4(161)"3.175 R3(173)=13. 614.546 614.553 614.560 0081 0082 0083 R4( 173)=6 977 R3(174)=14. R4(174)=0.091 614.567 614.574 614.581 0084 0085 0086 R3(177)=6. R4( 177)=0.423 R3(1B0)*29. 614.588 614.595 614.602 0087 0088 0089 R4(1 8 6 j=0.043 R3(195)»8. R4(195)=0.635 614.609 614.616 614.623 0090 0091 0092 R3(197)=4 R4(197)=0.635 R3(199)=7. 614.630 614.637 614.644 0093 0094 0095 R4(199)»0.725 R3(202)=8. R4(2O2)=0.159 614.651 614.658 614.665 0096 0097 0098 R3(221j=3. R4(221)=2.54 R3(222)=9. 614.672 614.679 614.686 0099 0100 0101 R4(222)=6.564 R3(225)=7. R4(225)=0.141 614.693 614.70O 614.707 0102 0103 0104 R3(226)=i.1 R4(226)=1.15 R3(228)=1.9 614.714 614.721 614.728 0105 0106 0107 R4(228)-13.36 R3(230)=7. R4(230)=-0.363 614.735 614.742 614.749 0108 0109 0110 R3(231)"7. R4(231)=0.544 R3(236)»4. 614.756 614.763 614.770 0111 0112 01 13 R4(236)=6.9525 R3(237)=5. R4(237)»1.016 614.777 614.784 614.791 0114 0115 01 16 R3(239)=5. R4<239)*1.524 R3(247)=4. 614.798 614.805 614.812 ro MICHIGAN TERMINAL SYSTEM FORTRAN GI21.8) ASHRN 10-11-84 13:28:15 PAGE POOS 0117 R4(247)=3.175 614.819 01 18 R3(253)=2 8 6 1 4 . 8 2 6 0119 R4(253)=5.89 614.833 0120 R3(256)=6. ' 614.840 0121 R 4 ( 2 S 6 ) = 0 . 4 2 3 6 1 4 847 0122 R3(258)»1. 614.854 0123 R4(258)°2.54 614.861 0124 200 CONTINUE 614.868 0125 RETURN 614.875 0126 END 614.882 'OPTIONS IN EFFECT'10 .EBCDIC! SOURCE. NOL if's"f ^ NObECKVLOAbTmMAp' •OPTIONS IN EFFECT* NAME - ASHRN , LINECNT * 60 •STATISTICS* SOURCE STATEMENTS • 126,PROGRAM SIZE = 1094 •STATISTICS'NO DIAGNOSTICS GENERATED M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 2 1 . 8 ) R A I N 1 0 - 1 1 - 8 4 1 3 : 2 8 : 2 1 P A G E P 0 0 1 0 0 0 1 S U B R O U T I N E R A I N 6 1 5 . 0 0 0 0 O O 2 R E A L N . N G . N 2 1 . 0 0 0 0 0 0 3 R E A L N 0 3 . N H 4 , L B G . N P . N A B . N L P . N L . N M L , N L T , N V G 2 0 0 0 0 0 0 4 R E A L T N L O S S , N L O . N C Y C L E , N T O 3 0 0 0 0 0 0 5 R E A L N A V A I L . N L O S S . L A B , N F R E E . N M I N . N N . M B . N P S Y N . K I L L , L F 4 0 0 0 0 0 0 6 R E A L d . N V O . N V . N O E M . N V O L T 5 0 0 0 0 0 O 7 R E A L D M A X . N R E C Y C . N C Y C . N 0 3 . N G 1 . N G 2 . N G 3 6 0 0 0 0 0 0 8 R E A L N R G G . N R G A E S . N M I N Y 6 . 2 0 0 0 0 0 9 I N T E G E R I N C R . N K . K A . K B , R K . J R . D P . W P C H 7 O O O 0 0 1 0 I N T E G E R G R J D , F U N 8 0 0 0 0 0 1 1 C O M M O N P , A 1 , B ( 1 0 ) . G M A X , I T I M E 9 O O O 0 O 1 2 C O M M O N A B . R S . C C . S D . S S . T S . D . R S P 1 1 0 0 0 0 0 1 3 C O M M O N T E M P . T O I 1 0 ) , T M 1 ( 1 0 ) , 0 D ( 1 2 ) , D L , S T E M P 1 2 0 0 0 0 O 1 4 C O M M O N W P 0 T . W 1 . N 1 3 0 0 0 0 0 1 3 C O M M O N P S Y N . T P S Y N . W S Y N , N P S Y N . T . T N P S Y N 1 4 0 0 0 0 0 1 6 C O M M O N G . W G . N G . T G . T 1 , N 2 1 5 0 0 0 0 0 1 7 C O M M O N R E S P . R R 1 6 0 0 0 0 0 1 8 C O M M O N D M A X , L A B 1 7 0 0 0 0 O 1 9 C O M M O N T A . T B . S G . T M , N R E C Y C 1 8 0 0 0 0 0 2 0 C O M M O N C 4 , C 5 , S 4 . S 5 . I S I N K 1 9 0 0 0 0 0 2 1 C O M M O N D R ( 1 2 ) , R M ( 1 2 ) . R D ( 1 2 ) 2 0 0 0 0 0 0 2 2 C O M M O N J ( 1 2 ) , A ( 1 2 ) , N V 0 ( 1 2 ) 2 1 ooo 0 0 2 3 C O M M O N W P A O ( 6 ) . W P C i ( 6 ) . W P C 2 " ( 6 ) , W P C 3 ( 6 ' ) , W P C 4 ( 6 ) , W P C 5 ( 6 ) . W P C 6 < 6 ) 2 2 ooo 0 0 2 4 C O M M O N W P S 1 ( 6 ) , W P S 2 ( 6 ) , W P S 3 ( 6 ) . W P S 4 ( 6 ) . W P S 5 ( 6 ) . W P S 6 ( 6 ) 2 3 0 0 0 0 0 2 5 C O M M O N U 3 , U 4 , N 0 3 , N H 4 2 4 0 0 0 0 0 2 6 C O M M O N I N C R . N K . K A . K B . R K . J R . R J 2 5 0 0 0 0 0 2 7 C O M M O N G A . G B . M B . L B G , J D 2 6 0 0 0 0 0 2 8 C O M M O N N P ( 1 2 ) , N A B ( 1 2 ) , N D E M . N L P ( 1 2 ) , N L ( 1 2 ) , N M L ( 1 2 ) . N L T 2 7 0 0 0 0 0 2 9 C O M M O N N V G ( 1 2 ) , N V ( 1 2 ) , N V O L T 2 8 0 0 0 0 0 3 0 C O M M O N Z 1 . R 3 ( 3 6 5 ) , R 4 ( 3 6 5 ) 2 9 0 0 0 0 0 3 1 C O M M O N T N L O S S . N L O ( 1 2 ) . N C Y C L E , N T O ( 1 2 ) . T L O S S O . N A V A I L . N F R E E . N M I N , N N 3 0 0 0 0 0 0 3 2 C O M M O N N M V ( 1 2 ) . F M . A M , C M . K I L L . B M , L F . P H E N M 3 2 0 0 0 0 O 3 3 C O M M O N R N ( 2 0 ) . R P ( 2 0 ) . P R E C , R 1 ( 2 0 ) , R 2 ( 2 O ) , 0 P ( 2 0 ) , P M ( 2 O ) 3 3 0 0 0 0 0 3 4 C O M M O N S Y 1 , S Y 2 , S A , S B . W B M . R N O M I 3 4 0 0 0 0 0 3 5 C O M M O N I S O U R C . I P A S S , L O C N . W P C H . R N O M I 3 6 0 0 0 0 0 3 6 C O M M O N D L A O ( 1 0 ) , D L C 1 ( 1 0 ) , D L S 1 ( 1 0 ) , P I . W A M . N C Y C 3 7 0 0 0 0 0 3 7 C O M M O N N Y C , C P , U D R , C P Y , G R A Z I N ( 3 6 5 ) , K G R , G R . G R P S Y N 3 8 0 0 0 0 0 3 8 C O M M O N I S T T , I S T S T , I S T W , G R A , K N E M P , K N E M P I . K N I 3 9 0 0 0 0 0 3 9 C O M M O N G R J D , F U N , G B M A X , G G B M A X . D L G . I S H I F . N C H 4 0 ooo 0 0 4 0 C O M M O N I A E S T , A G B M A X . F U N 2 , R G A E S . F U N 3 4 1 0 0 0 0 0 4 1 C O M M O N M O R T J D . M O R T W P . C U M A B . R G G . A M R G G . A M R G . T L A B 4 2 0 0 0 0 0 4 2 C O M M O N R T S H T . P M A X . F R M A X . F R R M A X . T S S N E G 4 3 0 0 0 0 0 4 3 C O M M O N K N E M P 2 . K N E M P 3 . N R G G . N R G A E S . G R A Z . A M G . A M R G A 4 4 0 0 0 0 0 4 4 C O M M O N G L A B , G L A B A B , R G G A B , R G A B , C P G . C P R G A , C P R G G , L F 2 4 5 0 0 0 0 0 4 5 C O M M O N N M G , N M R G A , N M R G G . C P Y M I N . N M I N Y 4 6 0 0 0 0 0 4 6 C O M M O N C P Y G , C P Y R G A , C P Y R G G , P H E N M 2 4 7 0 0 0 0 0 4 7 C O M M O N N G 1 , N G 2 . N G 3 . G A 1 , G A 2 , I A E S T O . R G J D . J D A E S T 4 8 ooo 0 0 4 8 C O M M O N Z , D A M P D , G R K N I 4 9 0 0 0 0 0 4 9 R N O M I = R A N D ( 1 . 0 ) 6 4 3 2 0 0 0 0 5 0 D O 5 3 5 0 1 = 1 . 1 2 6 4 3 8 0 0 0 0 5 1 R K - 1 6 4 4 4 0 0 0 0 5 2 5 0 3 5 C O N T I N U E 6 4 5 0 0 0 0 0 5 3 R N ( R k ) = F R A N D T 6 ) * 3 . 1 • 1 0 6 4 5 6 0 0 0 0 5 4 I F ( R N ( R K ) . L T . 0 . 8 ) G 0 T 0 5 0 3 5 6 4 6 2 0 0 C M N K C A L L F W R I T E ( I S I N K , ' S T A T E M E N T S I I S < I " 4 > . : ' , I ) 6 4 6 8 0 0 C * I N K C A L L F W R I f E ( I S I N K , ' S T A T E M E N T S R K I S < I * 4 > . : ' , R K ) 6 4 7 4 0 0 0 0 5 5 R P ( R K ) = ( ( 2 . 7 1 8 2 8 1 8 * * 6 . 6 5 7 1 ) « ( R N ( R K ) • « ( - 1 . 1 6 7 2 ) ) * 6 4 8 0 0 0 A ( 2 . 7 1 B 2 8 1 8 * « ( - O . 0 3 1 4 6 8 * R N ( R K ) ) ) ) / 6 0 6 4 8 6 0 O MICHIGAN TERMINAL SYSTEM FORTRAN G(21.B) RAIN 10-11- 84 13 28:21 PAGE P002 0056 RP(RK)"FRAND(0)*RP(RK) 649.200 0057 PREC=RN(RK)*RP(RK) C'INK CALL FWRITE(ISINK,'RP(RK)=<R*4>, RN(RK)=<R*4>, PREC=<R*4>, RM(I)=< C ' I N K A R » 4 > . OR(I)-=<R*4>.:'.RP(RK).RN(RK),PREC,RM(I),0R(I)) 649.800 650.40O 651.000 0058 C'INK I F ( P R E C . G T . ( 4 « R M ( I ) / 0 R ( I ) ) ) C A L L FWRITE(I SINK,'STATEMENT C'INKATOO LARGE - REJECT . : ' ) IF(PREC.GT.(4*RM(I)/DR(I)))G0TO 5035 #4B PREC 651.600 652.200 652.800 0O59 0060 P M ( I ) » P M ( I ) + P R E C IF ( ( (RM( I ) -0 .10 'RMd )) LT.PMd)).AND.((RM(I)+0.10*RM(I)) APM(I))) GOTO 5130 .GT. 653.400 654.000 654.600 0061 5110 IF(PM(I).GT.RM(I)) PM(I)=PM(I)-PREC C'INK IF(PM(I).GT.RM(I))CALL FWRITE(ISINK,'STATEMENT #4A REJECT C'INKAMONTHLY RAIN - TOO LARGE. : ' ) 655.200 655.800 656.400 0OG2 0O63 0064 IF(PM(I).GT.RM(I))G0TO 5035 RK=RK+1 DPI I)-RK 657.000 657.600 658.200 0065 0066 GOTO 5035 5130 CONTINUE C ASSIGN DATES TO RAIN 658.800 659.400 660.000 C'INK CALL FWRITE(I SINK,'STATEMENT*5 ASSIGN DATES TO RAIN. : ' C'INK CALL FWRITE( ISINK, 'STATEMENT#5 OAYSWRAIN CONST IS <R*4>. C'INK CALL FWRITEdSINK,'STATEMENT#5 OAYSWRAIN IS < I « 4 > . : ' : ' ,DR( I ) ) , D P ( D ) 660.600 .661.200 661.800 • 0067 0068 0069 DO 5340 L ' l . R K IF( I .EO. I ) R 1 ( L ) » F R A N D ( 0 ) * 3 1 IF ( I .E0 .2) R 1 ( L ) » F R A N D ( 0 ) * 2 8 662.400 663.000 663.600 0070 0071 0072 IF<I.E0.3) Ri(L)=FRAND(0)*31 •• IF(1 E0.4) R1(L)=FRAND(0)*30 I F d . E Q . 5 ) R1(L)"FRAND(0)*31 664.200 664.800 665.400 0073 0074 0075 IF ( I .E0 .6) R 1 ( L ) » F R A N D ( 0 ) ' 3 0 I F d . E Q . 7 ) R1(L)"FRAND(0)*31 I F d . E Q . 8 ) R1(L)=FRAND(0)'3t 666.000 666.600 667.200 0076 0077 0078 IF d . E O . 9 ) R1(L)•FRAND(6)*30 IF(I .EO.IO) R1(L)=FRAND(0)'31 I F d . E 0 . 1 1 ) R1(L)"FRAND(0)'30 667.800 668.400 669.000 0079 0080 0081 I F d . EO. 12) R1(L)"FRANb(6)'31 IF( I .EO.1) R2(L)=0 IFCI .E0.2) R2(L)'31 669.600 670.200 670.800 0082 0083 0084 IF( I . F.b. 3) R2(L)=59 I F d . E 0 . 4 ) R2(L)"90 IF ( I .E0 .5) R2(L)=120 671.400 672.000 672.600 0O85 0086 0087 IF(I E0.6) R2(L)'151 IF ( I .E0 .7) R2(L)-181 IF ( I .E0 .8) R2(L)=212 673.200 673.800 674.400 0088 0089 0090 • IF ( I .E0 .9) R2(Li -243 IF(I EO.10) R2(L)*273 I F d . E O . 11) R 2 ( L ) » 3 0 4 675 .000 675.600 676.200 0091 0092 0093 IF( I .EO.12) R2( C ) '334 RJ=R1(L)+R2(L) JR=INT(RJ+0.5) 676.800 677.400 678.000 0094 C* INK CALL FWRifEdSiNK,'STAtEMENf*6 JR IS <I'4>. : ' . JR) C'INK CALL FWRITE(ISINK,'STATEMENT#6 L IS <I*4>.: ' ,L) R3(JR)'RN(L) 678.600 679.200 679.800 0O9S 0096 0097 R 4 ( J R ) » R P J L ) 5340 CONTINUE 5350 CONTINUE 680.400 681.000 681.600 0098 0099 •OPTIONS RETURN END IN EFFECT' ID.EBCDIC.SOURCE.NOLIST.NODECK,LOAD.NOMAP 682.200 682.800 r o oo MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) CHOICE 10-11-84 13:28:29 PAGE P001 0001 SUBROUTINE CHOICE 684 .000 0002 0OO3 0004 REAL N.NG.N2 REAL N03.NH4.LBG.NP.NAB,NLP,NL.NML,NLT.NVG REAL TNLOSS.NLO,NCYCLE,NTO 1 2 3 000 .000 000 0005 0006 0007 REAL NAVAIL,NLOSS.LAB.NFREE.NMIN.NN,MB.NPSYN.KILL REAL J,NVO,NV.NDEM,NVOLT REAL DMAX,NRECYC.NCYC,N03,NG1,NG2.NG3 LF 4 S 6 000 000 000 0008 0009 0010 REAL NRGG,NRGAES,NMINY INTEGER INCR,NK,KA,KB.RK,dR,DP.WPCH INTEGER GRJD.FUN 6 7 a 200 000 000 0011 0012 0013 COMMON COMMON COMMON P.A1.B(10),GMAX,ITIME AB.RS.CC,SD,SS.TS.D.RSP TEMP.TOC10),TM1(10),DD(12),0L.STEMP 9 H 12 000 000 000 0014 0015 0016 COMMON COMMON COMMON WPOT,W1,N PSYN,TPSYN,WSYN,NPSYN,T,TNPSYN G.WG,NG,TG,T1.N2 13 14 15 000 000 000 0017 0018 COMMON COMMON RESP,RR DMAX,LAB 16 17 18 000 000 0020 0021 0O22 COMMON C4.C5.54,S5.ISINK COMMON DR(t2),RM(12),RD(12) COMMON J ( 1 2 ) , A ( 1 2 ) , N V O ( 1 2 ) 19 20 21 000 000 000 0023 0024 0025 COMMON WPA016),WPC1(6),WPC2(6).WPC3(6),WPC4(6),WPC5(6),WPC6(6) COMMON WPS1(6),WPS2(6).WPS3(6),WPS4(6).WPS5I6),WPS6<6) COMMON U3,U4,N03,NH4 22 23 24 000 000 000 0O26 0027 0028 COMMON INCR.NK.KA.KB.RK.dR.Rd COMMON GA.GB.MB.LBG.dD COMMON NP(12).NAB(12),NDEM,NLP(12),NL(12),NML(12),NLT 25 26 27 000 000 000 0029 0030 0031 COMMON NVG(12).NV(12).NVOLT COMMON Z1, R 3 ( 3 6 5 ) , R 4 ( 3 6 5 ) COMMON TNLOSS,NLO(12),NCYCLE,NTO(12).TLOSSO,NAVAIL,NFREE.NMIN.NN 28 29 30 OOO 000 OOO 0032 0033 0034 COMMON COMMON COMMON NMV(12),FM,AM.CM,KILL,BM.LF.PHENM RN(20),RP(20),PREC.R1(2O),R2(2O).0P(20).PM(20) SY1,SY2,SA,SB.WBM.RNDMI 32 33 34 OOO 000 000 0035 0036 0037 COMMON COMMON COMMON ISOURC, IPASS.LOCN,WPCH.RNOMI DLAOf10).DLC1(10).DLS1(10).PI.WAM.NCYC NYC,CP,UDR,CPY,GRAZIN(365),KGR.GR.GRPSYN 36 37 38 000 000 000 0038 0039 0040 COMMON COMMON COMMON ISTT, 1ST ST, ISTW, GRA ,KNEMP ,KNEMP I , KNI GRJD,FUN,GBMAX,GGBMAX,DLG,I SHIF.NCH IAEST.AGBMAX.FUN2,RGAES,FUN3 39.000 40.000 41 .000 0041 0042 0043 COMMON COMMON COMMON MORTJD,MORTWP,CUMAB,RGG.AMRGG,AMRG,fLAB RTSHT.PMAX,FRMAX,FRRMAX.TSSNEG KNEMP2,KNEMP3.NRGG.NRGAES.GRAZ,AMG.AMRGA 42 43 44 OOO 000 000 0044 0045 0O46 COMMON COMMON COMMON GLAB . GLABAB , RGGAB. RGAB. CPG, CPRGA . CPRGG. LF2 NMG,NMRGA,NMRGG,CPYMIN.NMINY CPYG.CPYRGA,CPYRGG,PHENM2 45.000 46.000 47.000 0047 0048 0049 COMMON NG1.NG2.NG3.GA1,GA2,IAESTO.RGJD.JDAEST COMMON Z.DAMPD,GRKNI LOGICAL'I S T A R ( 1 ) / ' « ' / 48.000 49.000 686.000 0050 0051 0052 15 CONTINUE WRITE!ISINK.5) 5 FORMAT('-','CHOOSE GEOGRAPHIC LOCATION') 687 688 689 000 000 000 0053 0054 WRITEfISINK,10) 10 FORMAT('-'.'PLEASE ENTER NUMBER SELECTION:'/ A' 1 - KAMLOOPS'/ 690 691 692 000 000 000 B' 2 - CRANBROOk'/ C 3 - BRANSON LAB STUDY'/ D' 4 - ASHNOLA 1968'/ 693.000 694 .000 695.000 1 M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 2 1 . 8 ) P A G E P 0 0 2 E ' 5 - A S H N O L A 1 9 6 7 ' ) 3 0 C O N T I N U E R E A D ( I S 0 U R C . S T A R . E N D " 1 5 ) L 0 C N W R I T E ( I S I N K , 2 0 ) 6 9 6 C O O 6 9 7 . 0 0 0 6 9 8 . O O O 6 9 9 . 0 0 0 7 0 0 . O O O 7 0 1 . 0 0 0 7 0 2 . 0 0 0 0 0 5 5 0 0 5 6 0 0 5 7 0 0 5 8 0 0 5 9 0 0 6 0 2 0 F O R M A T ( ' - ' , ' C H O O S E W A T E R P O T E N T I A L ' ) W R I T E ( I S I N K , 2 5 ) 2 5 F O R M A T ( ' - ' , ' P L E A S E E N T E R N U M B E R S E L E C T I O N : ' / A ' 1 - I N T E R I O R D R Y ' / B ' 2 - I N T E R I O R I N T E R M E D . ' / C 3 - I N T E R I O R W E T ' / 7 0 3 . 0 0 0 7 0 4 . 0 0 0 7 0 5 . 0 0 0 0 0 6 1 0 0 6 2 0 0 6 3 • O P T I O N S I N 0 ' 4 - A S H N O L A 1 9 6 8 ' / E ' 5 - A S H N O L A 1 9 6 7 ' ) R E A D ( I S O U R C . S T A R . E N D » 3 0 ) W P C H 7 0 6 . 0 0 0 7 0 7 . 0 0 0 7 0 8 . 0 0 0 7 0 9 . 0 0 0 7 1 0 . O O O R E T U R N E N D E F F E C T * 1 0 . E B C D I C , S O U R C E . N O L I S T . N O D E C K , L O A D . N O M A P • O P T I O N S I N E F F E C T * N A M E « C H O I C E . L I N E C N T * 6 0 • S T A T I S T I C S * S O U R C E S T A T E M E N T S • 6 3 , P R O G R A M S I Z E » • S T A T I S T I C S * N O D I A G N O S T I C S G E N E R A T E D 7 7 2 CO O M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 2 1 . 8 ) D L F N C 1 0 - 1 1 - 8 4 1 3 : 2 8 : 3 2 P A G E P 0 0 1 0 0 0 1 R E A L F U N C T I O N D L F N C ( I C O D E ) 7 1 1 0 0 0 0 0 0 2 0 0 0 3 0 0 0 4 R E A L N . N G . N 2 R E A L N 0 3 , N H 4 , L B G . N P . N A B . N L P , N L . N M L , N L T , N V G R E A L T N L O S S . N L O . N C Y C L E , N T O 1 2 3 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 6 0 0 0 7 R E A L N A V A I L . N L O S S . L A B , N F R E E . N M I N , N N , M B , N P S Y N , K I L L . R E A L d . N V O . N V . N D E M . N V O L T R E A L D M A X , N R E C Y C , N C Y C . N 0 3 , N G 1 , N G 2 , N G 3 L F 4 5 6 O O O 0 0 0 0 0 0 0 0 0 8 0 0 0 9 0 0 1 0 R E A L N R G G . N R G A E S , N M I N Y I N T E G E R I N C R . N K . K A , K B , R K , J R . D P , W P C H I N T E G E R G R J D , F U N 6 7 8 2 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 2 0 0 1 3 C O M M O N P , A 1 . B ( 1 0 ) , G M A X , I T I M E C O M M O N A B , R S . C C . S D , S S , T S , D . R S P C O M M O N T E M P , T O ( 1 0 ) , T M 1 ( 1 0 ) , D D I 1 2 ) , D L . S T E M P 9 1 1 1 2 0 0 0 ooo 0 0 0 0 0 1 4 0 0 1 5 0 O 1 6 C O M M O N W P 0 T . W 1 , N C O M M O N P S Y N . T P S Y N . W S Y N . N P S Y N , T , T N P S Y N C O M M O N G , W G , N G , T G , T 1 . N 2 1 3 1 4 1 5 0 0 0 0 0 0 0 0 0 0 0 1 7 0 O 1 8 0 0 1 9 C O M M O N R E S P . R R C O M M O N D M A X , L A B C O M M O N T A , T B , S G , T M , N R E C Y C 1 6 1 7 1 8 0 0 0 0 0 0 ooo 0 0 2 0 0 0 2 1 0 0 2 2 C O M M O N C 4 . C 5 . S 4 . S S . I S I N K C O M M O N D R ( 1 2 ) . R M ( 1 2 ) . R D ( 1 2 ) C O M M O N J ( 1 2 ) , A ( 1 2 ) , N V O ( 1 2 ) 1 9 2 0 2 1 0 0 0 ooo 0 0 0 0 0 2 3 0 0 2 4 0 0 2 5 C O M M O N W P A 0 I 6 ) , W P C 1 ( 6 ) . W P C 2 ( 6 ) , W P C 3 ( 6 ) , W P C 4 ( 6 ) . W P C 5 ( 6 ) . W P C 6 ( 6 ) C O M M O N W P S K 6 ) , W P S 2 ( 6 ) . W P S 3 ( 6 ) . W P S 4 ( 6 ) . W P S 5 ( 6 ) , W P S 6 ( 6 ) C O M M O N U 3 . U 4 . N 0 3 . N H 4 2 2 2 3 2 4 0 0 0 0 0 0 0 0 0 0 0 2 6 0 0 2 7 0 0 2 8 C O M M O N I N C R , N K , K A , K B , R K , J R . R J C O M M O N G A . G B . M B . L B G , J D C O M M O N N P ( 1 2 ) , N A B ( 1 2 ) , N D E M , N L P ( 1 2 ) , N L ( 1 2 ) , N M L ( 1 2 ) . N L T 2 5 2 6 2 7 0 0 0 0 0 0 0 0 0 0 0 2 9 0 0 3 0 0 0 3 1 C O M M O N N V G ( 1 2 ) . N V ( 1 2 ) , N V 0 L T C O M M O N Z 1 , R 3 ( 3 6 5 ) , R 4 ( 3 6 5 ) C O M M O N T N L O S S , N L O ( 1 2 ) , N C Y C L E , N T O ( 1 2 ) , T L O S S O . N A V A I L . N F R E E . N M I N . N N 2 8 2 9 3 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 3 3 0 0 3 4 C O M M O N N M V ( 1 2 ) . F M . A M . C M . K I L L , B M . L F , P H E N M C O M M O N R N ( 2 0 ) , R P ( 2 0 ) . P R E C , R 1 ( 2 0 ) , R 2 ( 2 0 ) . D P ( 2 0 ) , P M ( 2 0 ) C O M M O N S Y 1 , S Y 2 , S A . S B , W B M , R N D M I 3 2 3 3 3 4 0 0 0 0 0 0 0 0 0 0 0 3 5 0 0 3 6 0 0 3 7 C O M M O N I S O U R C , I P A S S , L O C N , W P C H , R N O M I C O M M O N D L A O ( 1 0 ) , D L C 1 ( 1 0 ) , D L S 1 ( 1 0 ) . P I . W A M . N C Y C C O M M O N N Y C , C P , U D R , C P Y . G R A Z I N ( 3 6 5 ) , K G R . G R . G R P S Y N 3 6 3 7 3 8 0 0 0 0 0 0 0 0 0 0 0 3 8 0 O 3 9 0 0 4 0 C O M M O N I S T T . I S T S T . I S T W , G R A . K N E M P . K N E M P I . K N I C O M M O N G R J D . F U N . G B M A X . G G B M A X , D L G . I S H I F . N C H C O M M O N I A E S T . A G B M A X . F U N 2 . R G A E S , F U N 3 3 9 4 0 4 1 ooo 0 0 0 0 0 0 0 0 4 1 0 0 4 2 0 0 4 3 C O M M O N M O R T J D , M O R T W P . C U M A B . R G G , A M R G G , A M R G , T L A B C O M M O N R T S H T , P M A X , F R M A X . F R R M A X . T S S N E G C O M M O N K N E M P 2 , K N E M P 3 , N R G G . N R G A E S , G R A Z , A M G , A M R G A 4 2 4 3 4 4 0 0 0 ooo ooo 0 0 4 4 0 0 4 5 0 0 4 6 C O M M O N G L A B . G L A B A B . R G G A B . R G A B . C P G . C P R G A , C P R G G . L F 2 C O M M O N N M G . N M R G A . N M R G G . C P Y M I N , N M I N Y C O M M O N C P Y G , C P Y R G A , C P Y R G G , P H E N M 2 4 5 4 6 4 7 0 0 0 0 0 0 0 0 0 0 0 4 7 0 0 4 8 0 0 4 9 C O M M O N N G 1 . N G 2 . N G 3 , G A 1 . G A 2 . I A E S T O . R G J D . J D A E S T C O M M O N Z , D A M P D , G R K N I G O T O ( 1 0 , 2 0 . 3 0 . 4 0 . 5 0 ) , L O C N 4 8 4 9 7 1 3 0 0 0 ooo 0 0 0 0 0 5 0 0 0 5 1 0 0 5 2 1 0 C O N T I N U E 2 0 C O N T I N U E 4 0 C O N T I N U E 7 1 4 7 1 5 7 1 6 0 0 0 0 0 0 0 0 0 0 0 5 3 0 0 5 4 5 0 C O N T I N U E D L F N C = D L A O ( L 0 C N ) / 2 . O + D L C 1 ( L O C N ) * C O S ( P I * J D / P ) + D L S 1 ( L O C N ) A - S I N ( P I ' J D / P ) 7 1 7 7 1 8 7 1 9 0 0 0 0 0 0 ooo 0 0 5 5 0 0 5 6 R E T U R N 3 0 C O N T I N U E C B R A N S O N ( 1 9 5 6 ) L A B S T U D Y 7 2 0 7 2 1 7 2 2 ooo 0 0 0 ' 0 0 0 MICHIGAN TERMINAL SYSTEM FORTRAN G(21.B) DLFNC 10-11-84 13:28:32 PAGE P002 0057 DLFNC-16.0 723.000 0 0 5 8 R E T U R N 7 2 4 .000 0059 END 725.000 •OPTIONS IN EFFECT* ID, EBCDIC, SOURCE .NOLIST . NODECK , LOAD, NOMAP 'OPTIONS IN EFFECT*NAME 3 DLFNC LINFCNT * 60 •STATISTICS* SOURCE STATEMENTS * 59.PROGRAM SIZE 3 620 •STATISTICS* NO DIAGNOSTICS GENERATED M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 2 1 . B ) U I N I T 1 0 - 1 1 - 8 4 1 3 : 2 8 : 3 9 P A G E P 0 0 1 0 0 0 1 S U B R O U T I N E U I N I T 7 2 6 0 0 0 0 0 0 2 0 0 0 3 0 0 0 4 R E A L N . N G . N 2 R E A L N 0 3 , N H 4 , L B G . N P , N A B , N L P . N L . N M L . N L T . N V G R E A L T N L O S S . N L O . N C Y C L E , N T O 1 2 3 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 6 0 0 0 7 R E A L N A V A I L . N L O S S . L A B . N F R E E . N M I N . N N . M B , N P S Y N . K I L L . L F R E A L d . N V O . N V , N D E M . N V O L T R E A L D M A X , N R E C Y C . N C Y C , N 0 3 , N G 1 , N G 2 , N G 3 4 5 6 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 9 0 0 1 0 R E A L N R G G , N R G A E S , N M I N Y I N T E G E R I N C R , N K , K A . K B , R K , J R , D P . W P C H I N T E G E R G R J D , F U N 6 7 8 2 0 O 0 0 0 0 0 0 0 0 1 1 0 0 1 2 0 0 1 3 C O M M O N P . A t , 8 ( 1 0 ) , G M A X , I T I M E C O M M O N A B . R S . C C . S D . S S . T S . D . R S P C O M M O N T E M P , T O ( 1 0 ) , T M 1 ( 1 0 ) , D D ( 1 2 ) , D L , S T E M P 9 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 1 4 0 0 1 5 0 0 1 6 C O M M O N W P 0 T . W 1 . N C O M M O N P S Y N , T P S Y N , W S Y N . N P S Y N . T . T N P S Y N C O M M O N G . W G . N G . T G . T I , N 2 1 3 1 4 1 5 0 0 0 0 0 0 0 0 0 0 0 1 7 0 0 1 8 0 0 1 9 C O M M D N R E S P , R R C O M M O N D M A X , L A B C O M M O N T A , T B , S G , T M , N R E C Y C 1 6 1 7 1 8 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 1 0 0 2 2 C O M M O N C 4 , C 5 . S 4 , S 5 . I S I N K C O M M O N D R ( 1 2 ) , R M ( 1 2 ) , R D ( 1 2 ) C O M M O N J ( 1 2 ) , A ( 1 2 ) , N V O ( 1 2 ) 1 9 2 0 2 1 0 0 0 0 0 0 O O O 0 0 2 3 0 0 2 4 0 0 2 5 C O M M O N W P A b i 6 ) . W P C 1 ( 6 ) , W P C 2 ' ( 6 ) . W P C 3 ( 6 ) ' . W P C 4 < 6 ) . W P C 5 ( 6 > . W P C 6 < 6 V C O M M O N W P S 1 ( 6 ) . W P S 2 ( 6 ) , W P S 3 ( 6 ) . W P S 4 ( 6 ) . W P S 5 ( 6 ) . W P S 6 ( 6 ) C O M M O N U 3 . U 4 . N 0 3 . N H 4 2 2 2 3 2 4 0 0 0 0 0 0 0 0 0 0 0 2 6 0 0 2 7 0 0 2 8 C O M M O N I N C R , N K , K A , K B , R K , J R , R J C O M M O N G A , G B , M B , L B G , J D C O M M O N N P ( 1 2 ) , N A 8 ( 1 2 ) , N D E M , N L P ( 1 2 ) , N L ( ( 2 ) , N M L ( 1 2 ) , N L T 2 5 2 6 2 7 0 0 0 0 0 0 0 0 0 0 0 2 9 0 0 3 0 0 0 3 1 C O M M O N N V G ( 1 2 ) , N V ( 1 2 ) . N V O L T C O M M O N Z 1 , R 3 ( 3 6 5 ) , R 4 ( 3 6 5 ) C O M M O N T N L O S S . N L O ( 1 2 ) . N C Y C L E . N T O ( 1 2 ) , T L O S S O , N A V A I L , N F R E E , N M I N , N N 2 8 2 9 3 0 O O O 0 0 0 0 0 0 0 0 3 2 0 0 3 3 0 0 3 4 C O M M O N N M V ( 1 2 ) , F M , A M , C M , K I L L , B M , L F , P H E N M C O M M O N R N ( 2 0 ) , R P ( 2 0 ) . P R E C . R K 2 0 ) , R 2 ( 2 0 ) , D P ( 2 0 ) . P M ( 2 0 ) C O M M O N S Y 1 , S Y 2 , S A , S B , W B M , R N D M I 3 2 3 3 3 4 0 0 0 0 0 0 0 0 0 0 0 3 5 0 0 3 6 0 0 3 7 C O M M O N I S O U R C . I P A S S . L O C N . W P C H , R N O M I C O M M O N D L A O ( 1 0 ) , D L C 1 ( 1 0 ) , D L S 1 ( 1 0 ) . P I . W A M . N C Y C C O M M O N N Y C , C P , U D R . C P Y , G R A Z I N ( 3 6 5 ) , K G R . G R , G R P S Y N 3 6 3 7 3 8 0 0 0 0 0 0 O O O 0 0 3 8 0 0 3 9 0 0 4 0 C O M M O N I S T T , I S T S T . I S T W . G R A , K N E M P . K N E M P I . K N I C O M M O N G R J D . F U N , G B M A X , G G B M A X . D L G . I S H I F . N C H C O M M O N I A E S T , A G B M A X . F U N 2 , R G A E S , F U N 3 3 9 4 0 4 1 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 4 2 0 0 4 3 C O M M O N M O R T J D . M O R T W P , C U M A B , R G G , A M R G G , A M R G , f t A B C O M M O N R T S H T , P M A X , F R M A X , F R R M A X , T S S N E G C O M M O N K N E M P 2 , K N E M P 3 , N R G G , N R G A E S , G R A Z , A M G , A M R G A 4 2 4 3 4 4 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 4 5 0 0 4 6 C O M M O N G L A B , G L A B A B , R G G A B . R G A B . C P G . C P R G A . C P R G G . L F 2 C O M M O N N M G . N M R G A , N M R G G . C P Y M I N . N M I N Y C O M M O N C P Y G , C P Y R G A . C P Y R G G , P H E N M 2 4 5 4 6 4 7 0 0 0 0 0 0 0 0 0 0 0 4 7 0 0 4 8 0 0 4 9 C O M M O N N G 1 . N G 2 , N G 3 . G A 1 . G A 2 . I A E S T O . R G J D . J D A E S T C O M M O N Z . D A M P D , G R K N I C A L L D F A U L T ( ' 1 - M O D E L . O ' ) 4 8 4 9 7 2 8 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 5 1 0 0 5 2 C A L L C M R E A D ( ' M O D E L . C 2 ' ) R E T U R N E N D 7 2 9 7 3 0 7 3 1 0 0 0 0 0 0 O O O • O P t i O N S I N • O P T I O N S I N • S T A T I S T I C S * E F F E C T • I D , E B C D I C , S O U R C E , N O L I S T , N O D E C K , L O A D . N O M A P E F F E C T 4 N A M E * U I N I T . L I N E C N T * 6 0 S O U R C E S T A T E M E N T S " 5 2 . P R O G R A M S I Z E - 3 3 0 • S T A T I S T I C S * N O D I A G N O S T I C S G E N E R A T E D MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) SCH15 10-11-84 13:28:42 PAGE P001 0001 SUBROUTINE SCH15(F,X.P,TAU1,TAU2) 732 OOO 0002 0OO3 C SUBROUTINE SCHI5 WAS WRITTEN B. WONG, FACULTY OF FORESTRY IMPLICIT REAL*8(A-H,0-Z) DIMENSION P(4) 732 733 734 200 000 000 0004 0005 0006 CALL FTNCMD!'DEFAULT ib»*SINK*:') IOUT-10 Y1B=P0WER(P(3),P(2),IERR1,I0UT,1) 735 736 737 000 OOO 000 0O07 0008 . 0009 1FUERR1 NE.0)G0T0l6 Y2B=P0WER(P(4),P(2),IERR2,10UT,2) IF(IERR2.NE.O)GOT020 738 739 740 000 ooo 000 0O10 001 1 0012 ET=1 DO-DEXP(-P(1)*(X-TAU1)) ET2-1.D0-DEXP(-P(1)*(TAU2-TAU1)) F* POWER ( (Y1B+(Y2B-Y1B)*(ET/ET2M,(1. DO/P( 2) ), IERRF , I OUT, 3 ) 741 742 743 000 000 000 0O13 0O14 0015 IF(IERRF NE O)G0rO3O RETURN 10 CONTINUE 744 745 746 000 000 000 0016 0017 0018 20 CONTINUE 30 CONTINUE WRITE!10.50)P 747 748 749 000 000 ooo 0O19 0O2O 0021 50 FORMAT!' '.'THE PARAMETERS ARE (l THROUGH 4j:'/IX,4D20•i6) STOP END 750 751 752 000 ooo 000 •OPTIONS IN EFFECT* ID,EBCDIC,SOURCE.NOLI ST.NODECK.LOAD.NOMAP •OPTIONS IN EFFECT* NAME • SCH15 . LINECNT = 60 •STATISTICS* SOURCE STATEMENTS • 21,PROGRAM SIZE » 10O6 •STATISTICS* NO DIAGNOSTICS GENERATED MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) POWER 10-11-84 13:28:43 PAGE P001 0001 REAL FUNCTION P0WER*8(X,Y,I ERR,IOUT,ICOUNT) 753 000 C C C FUNCTION POWER WAS WRITTEN BY B. WONG, FACULTY OF FORESTRY. AND IS STORED IN THE ROKA LIBRARY. THE FUNCTION SUBPROGRAM, POWER. EVALUATES THE REAL-VALUEO 753 753 754 20O 400 000 C C C POWER. X " Y , WHERE POSSIBLE. CURRENTLY, THE FUNCTION IS NOT EQUIPPED TO HANDLE COMPLEX VALUES WITH NON-ZERO IMAGINARY COMPONENTS. 755 756 757 000 OOO 000 , ' C C C I ERR MEANING 0 N 0 E R R O R S 758 759 760 000 000 000 C C C -1 0 . " Y IS UNDEFINED. WHEN Y<0.. -2 - X<0. , AND Y IS NOT AN INTEGER, SO THE 761 762 763 000 000 000 C c c IMAGINARY COMPONENT OF THE POWER IS NON-ZERO. 764 765 766 000 000 000 c c c IF THE IERR-VALUE RETURNEO IS NOT IN THE ABOVE TABLE, THE RETURNED IERR-VALUE IS THE SUM OF TABULATED I ERR-VALUES WHOSE CORRESPONDING ERRORS ARE OCCURRING IN COMBINATION. 767 768 769 000 000 000 c c c IOUT RELATES TO DIAGNOSTIC OUTPUT: IF IOUT IS NEGATIVE. THEN THE DIAGNOSTIC OUTPUT IS DISABLED. 770 771 772 000 000 000 c c c IF IOUT IS NONNEGATIVE, THEN IOUT IS THE NUMBER OF THE LOGICAL INPUT/OUTPUT UNIT ONTO WHICH DIAGNOSTIC OUTPUT IS WRITTEN. 773 774 775 000 000 000 0002 0003 c IMPLICIT REAL*8(A-H.0-Z) LOGICAL*1 XLTO,YLTO,ERROUT 776 777 778 000 000 000 0O04 0005 0006 ERROUT".TRUE. IF(IOUT.LT.0)ERROUT".FALSE. IERR=0 779 780 781 000 000 ooo 0007 0008 0009 i F (V. NE. 6. boTcsof 616 POWER'1.DO CALL RTNCHK(X,Y,IERR,IOUT,ICOUNT,ERROUT,860,8120) 782 783 784 000 000 000 0010 0011 0012 10 CONTINUE IF(X.LE.O.DO)G0T02O POWER"X"Y 785 786 787 000 000 000 0013 0014 0015 20 CALL RTNCHk(X,Y,IERR,IOUT.ICOUNT,ERROUT,870.& 130) CONTINUE XLTO'(X.LT.O.OO) 788 789 790 000 000 000 0O16 0017 0018 YLtO'(V.Lt.O.DO) IF(XLTO.AND.(.N0T.(YLTO)))GOT030 IF(XLTO.AND.YLTO)G0T04O 791 792 793 000 000 000 0019 0020 c I F ( ( .NOT . ( XLTO) ) . AND . ( . NOT . ( YLTO) ) )GOT050 ( 0 . " Y ) IS UNDEFINED WHEN Y<0--ERROR RETURN -1. IERR-IERR-1 794 795 796 000 000 000 0021 0022 c SET DEFAULT ("ERROR") VALUE OF "POWER" TO 1. POWER"1.DO CALL RTNCHK(X,Y.I ERR,IOUT.ICOUNT.ERROUT.880,8140) 797 798 799 000 000 ooo 0023 0024 0025 30 CONTINUE .POWER"((DABS(X))**Y)*ONENEG(Y,I ERR) CALL RTNCHK(X,Y,IERR,IOUT,ICOUNT,ERROUT,890,8150) 800 801 802 000 000 000 0O26 0027 0028 40 CONTINUE POWER" 1 . 0 0 / ( ( ( D A B S ( X ) ) " D A B S ( Y ) ) ' 0 N E N E G ( D A B S ( Y ) , IERR)) CALL RTNCHK(X,Y,IERR,IOUT,ICOUNT,ERROUT.8100.8160) 803 804 805 000 000 000 0029 0030 0031 50 CONTINUE POWER"0.00 CALL RTNCHK(X,Y,I ERR,IOUT,ICOUNT,ERROUT,8110,8170) 806 807 808 000 000 ooo CO cn MICHIGAN TERMINAL SYSTEM FORTRAN G<21.8) 0032 0033 0034 0035 0036 0O37 0038 0039 0040 0041 0042 0043 0044 60 CONTINUE 7 0 C O N T I N U E 80 CONTINUE 90 CONTINUE 100 CONTINUE 1 10 CONTINUE RETURN 120 CONTINUE 130 CONTINUE 140 CONTINUE 150 CONTINUE 160 CONTINUE 170 CONTINUE 0045 RETURN 0046 END •OPTIONS IN EFFECT* ID, EBCDIC , SOURCE .NOLIST ,NODECK , LOAD, NOMAP •OPTIONS IN EFFECT* NAME - POWER . LINECNT « 60 •S T A T I S T I C S * SOURCE STATEMENTS - 46,PROGRAM SIZE • S T A T I S T I C S * NO DIAGNOSTICS GENERATED PAGE P002 809.000 8 1 0 0 0 0 811.000 812.000 813 OOO 814.000 815.000 816.656 817.OOO 818.OOO 819 000 820.000 821.000 822.666 823.000 CO cn M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 2 1 . 8 ) O N E N E G 1 0 - 1 1 - 8 4 1 3 : 2 8 : 4 4 P A G E P 0 0 1 0 0 0 1 R E A L F U N C T I O N 0 N E N E G + 8 ( Y , I E R R ) 8 2 4 0 0 0 C F U N C T I O N O N E N E G W A S W R I T T E N B Y B . W O N G , F A C U L T Y O F C F O R E S T R Y , A N D I S S T O R E D I N T H E R O K A L I B R A R Y . C F O R I N T E G E R - V A L U E D Y . 8 2 4 8 2 4 8 2 5 2 0 0 4 0 0 0 0 0 C ( 1 ) O N E N E G E Q U A L S 1 . I F Y I S E V E N . A N D C ( 2 ) O N E N E G E Q U A L S - 1 . I F V I S O D D . C I F Y I S N O T I N T E G E R - V A L U E D . T H E N - 2 I S A D D E D T O I E R R , 8 2 6 8 2 7 8 2 8 O O O 0 0 0 0 0 0 0002 C A N D A R O U N D E D ( I N T E G E R - V A L U E D ) C O P Y O F Y I S U S E D F O R C A N " E V E N Y - - > 1 " / " 0 D D Y - - > - 1 " E V A L U A T I O N . I M P L I C I T R E A L M S ( A - H . O - Z ) 8 2 9 8 3 0 8 3 1 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 4 0 0 0 5 T L R N C E - O . D O Y 1 N E G » Y I F ( D A B S ( Y - D F L I N T ( Y ) ) . L E . T L R N C E ) G 0 T O 2 O 8 3 2 8 3 3 8 3 4 0 0 0 0 0 0 0 0 0 C I F X I S N E G A T I V E , A N O C Y I S N O T A N I N T E G E R , C T H E N T H E P O W E R I S C O M P L E X - V A L U E D . 8 3 5 8 3 6 8 3 7 0 0 0 0 0 0 0 0 0 C I N T H I S C A S E . T H E S E R O U T I N E S M A K E N O A T T E M P T C T O E V A L U A T E T H I S P O W E R E X A C T L Y ; C I N S T E A D , Y I S R O U N D E D T O T H E N E A R E S T I N T E G E R , 8 3 8 8 3 9 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 7 C A N D A - 2 I S A D D E D T O T H E E R R O R - T Y P E I N D I C A T O R , I E R R . I E R R - I E R R - 2 Y 1 N E G - R N D E 0 ( Y , 1 . D O ) 8 4 1 8 4 2 8 4 3 O O O 0 0 0 0 0 0 0 0 0 8 0 0 0 9 0 0 1 0 2 0 C O N T I N U E R E M * D M O D ( Y 1 N E G , 2 . 0 0 ) I F ( R E M . E 0 . 0 . D 0 ) G D T 0 1 0 8 4 4 8 4 5 8 4 6 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 2 0 0 1 3 0 N E N E G - - 1 . 0 0 R E T U R N 1 0 C O N T I N U E 8 4 7 8 4 8 8 4 9 0 0 0 0 0 0 0 0 0 0 0 1 4 0 0 1 5 0 0 1 6 O N E N E G - 1 . 0 0 R E T U R N E N D 8 5 0 8 5 1 8 5 2 0 0 0 0 0 0 0 0 0 • O P T I O N S I N E F F E C T ^ I D . E B C D I C , S O U R C E , N O L I S T , N O D E C K , L O A D , N O M A P • O P T I O N S I N E F F E C T ^ N A M E =• O N E N E G , L 1 N E C N T - 6 0 • S T A T I S T I C S ^ S O U R C E S T A T E M E N T S " 1 6 . P R O G R A M S I Z E » 5 6 6 • S T A T I S T I C S ^ N O D I A G N O S T I C S G E N E R A T E D CO M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 2 1 . B ) D F L I N T 1 0 - 1 1 - 8 4 1 3 : 2 8 : 4 4 P A G E P 0 0 1 0 0 0 1 R E A L F U N C T I O N D F L I N T * 8 ( R D P I N ) 8 5 3 . 0 0 0 C F U N C T I O N D F L I N T W A S W R I T T E N B Y B . W O N G , F A C U L T Y C F O R E S T R Y , A N D I S S T O R E D I N T H E R O K A L I B R A R Y . C T H E F U N C T I O N , D F L I N T , A C C E P T S A R E A L - V A L U E D O F 8 5 3 . 2 0 0 8 5 3 . 4 0 0 8 5 4 . 0 0 0 C D O U B L E - P R E C I S I O N I N P U T . C T H E I N P U T - V A L U E I S T R U N C A T E D . C A N D T H E T R U N C A T E D I N T E G E R V A L U E I S C O N V E R T E D T O A R E A L - V A L U E D 8 5 5 0 0 0 8 5 8 . 0 0 0 8 5 7 . 0 0 0 0 0 0 2 0 0 0 3 C D O U B L E - P R E C I S I O N O U T P U T . I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) D F L I N T = D F L O A T ( I D I N T ( R D P I N ) ) 8 5 8 . 0 0 0 8 5 9 . 0 0 0 8 6 0 . 0 0 0 0 0 0 4 R E T U R N ' 8 6 1 . 0 0 0 0 0 0 5 E N D 8 6 2 . 0 0 0 • O P T I O N S I N E F F E C T ^ I D , E B C D I C . S O U R C E , N O L I S T , N O D E C K , L O A D , N O M A P • O P T I O N S I N E F F E C T 1 N A M E • D F L I N T , L I N E C N T = 6 0 • S T A T I S T I C S 4 S O U R C E S T A T E M E N T S • 5 , P R O G R A M S I Z E » 3 5 0 • S T A T I S T I C S ^ N O D I A G N O S T I C S G E N E R A T E D MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) RNDEO 10-11-84 13:28:45 PAGE P001 0001 REAL FUNCTION RNDE0 48<X.PWR10) 863 000 C C C FUNCTION RNDEO WAS WRITTEN BY B. WONG, FACULTY OF FORESTRY, AND IS STORED IN THE ROKA LIBRARY. THE FUNCTION, RNDEO. ROUNDS OFF A VALUE, "X", TO THE NEAREST 863 863 864 200 400 000 C C C POWER OF 10, "PWR10". IT USES THE "EVEN-ODD" CRITERION FOR ROUNDING A DIGIT THAT IS IMMEDIATELY LEFT OF A "5": ...{EVEN DIGIT)(5) --> ...{EVEN DIGIT) 865 866 867 OOO 000 000 C C C ...{ODD D I G I T ) ( 5 > --> ...{ODD DIGIT+1) E. G., RNDE0(2O.O5ODO.O.1D0) = 20.0, RNDEO(20.649DO,0.1D0) • 20.6, 868 869 870 000 000 000 C C C RNDE0(2O.653D0.0.1D0) « 20.6. AND RNDE0(2O.753DO.O.1D0) » 20.8. WHERE THE "0.1D0" REQUESTS ROUNDING TO THE NEAREST "TENTH". 87 1 872 873 000 000 000 0OO2 0003 0004 IMPLICIT REAL^8(A-H,0-Z) LOGICAL 11 EVEN X10-X/PWR10 874 875 876 000 000 000 0005 OOOS 00O7 x i b i N f " b i N f C x i o ) RNDDGT-DINT((X10-X10INT)M0.D0) IF (RNDDGT . NE . 5 . DO) GOT010 877 878 879 000 000 000 0008 0009 C "RNDDGT" 'EQUALS' 5. EVEN-(DABS(DM0D(X1OINT.2.DO)) EQ.O.DO) IF(EVEN)RNDE0=X1OINT^PWR1O 880 881 882 000 000 000 0010 0011 0012 IF(.NOT. EVEN)RNDEO=(X10INT+1.DO I*PWR10 RETURN 10 CONTINUE 883 884 885 000 000 000 0013 0014 C •RNDDGT" DOES NOT 'EQUAL' 5. RNDEO-(DINT(X10+0.500)(•PWRIO RETURN 886 887 888 000 000 000 0015 •OPTIONS •OPTIONS END IN EFFECT^ ID.EBCDIC.SOURCE.NOLIST.NODECK,LOAD.NOMAP IN EFFECT^ NAME ' RNDEO . LINECNT <= GO 889 000 • S T A T I S T I C S ^ • S T A T I S T I C S * SOURCE STATEMENTS - 15.PROGRAM SIZE = 668 NO DIAGNOSTICS GENERATED M I C H I G A N T E R M I N A L S Y S T E M F O R T R A N G ( 2 t . 8 ) P W R E R R 1 0 - 1 1 - 8 4 1 3 : 2 8 . 4 5 P A G E P 0 0 1 0001 S U B R O U T I N E P W R E R R f X , Y , I E R R . I O U T , I C O U N T , * ) 890.000 C S U B R O U T I N E P W R E R R W A S W R I T T E N B v B W O N G . F A C U L T Y O F 890.200 C F O R E S T R Y , A N D I S S T O R E D I N T H E R O K A L I B R A R Y . 890.400 C T H I S S U B R O U T I N E F A C I L I T A T E S T H E P R O D U C T I O N O F D I A G N O S T I C S . 891.000 C A F T E R A C A L L T O P O W E R , O N E I S S U E S A C A L L 10 P W R E R R ' 892.000 C T O C H E C K T H E V A L U E O F T H E E R R O R F L A G . I E R R . . 893 000 C I C O U N T « A N U S E R - O E F I N E O C O D E T O H E L P I D E N T I F Y ( E . G . . I N O U T P U T ) 894.000 C T H E S O U R C E 6r A C A L L T O S U B R O U T I N E P W R E R R . 8 9 5 . 0 0 0 C I E R R ' T H E I E R R R E T U R N E D B Y T H E F U N C T I O N , P O W E R . 896.000 C I O U T = T H E L O G I C A L I N P U T / O U T P U T U N I T O N T O W H I C H D I A G N O S T I C S 897.000 C A R E W R I T T E N . 8 9 8 . 0 0 0 C I F N O E R R O R S A R E D E T E C T E D , P W R E R R C A R R I E S O U T A N O R M A L R E T U R N . 899.000 C I F A N E R R O R I S D E T E C T E D , P W R E R R C A R R I E S O U T A R E T U R N 1. 900.000 0 0 0 2 I M P L I C I T R E A L * 8 ( A - H . b - Z ) 9 0 1 .000 0003 I F ( I E R R . E 0 . O ) R E T U R N 902.000 0004 C A L L F W R I T E ( I O U T , ' • • • E R R O R ' * * E R R O R R E T U R N F R O M S U B P R O G R A M P O W E R / 903.000 A l C A L L N U M B E R < I > j',' 1 E R R ' < l"> : i c O U N T . I E R R ) 9 0 4 000 0005 C A L L F W R I T E ( I O U T , ' X = < R * 8 > , Y » < R * S > : ' , X , Y ) 905.000 0006 R E T U R N 1 906.000 0 0 0 7 E N D 9 0 7 .000 • O P T I O N S I N E F F E C T * I D , E B C D I C , S O U R C E . N O L I S T , N O D E C K , L O A D , N O M A P • O P T I O N S I N E F F E C T * N A M E - P W R E R R , L I N E C N T = 60 • S T A T I S T I C S * S O U R C E S T A T E M E N T S • 7 . P R O G R A M S I Z E = 5 8 0 • S T A T I S T I C S * N O D I A G N O S T I C S G E N E R A T E D O MICHIGAN TERMINAL SYSTEM FORTRAN G(21.8) RTNCHK 10-11-84 PAGE P001 SUBROUTINE RTNCHK(X.Y,IERR,IOUT.ICOUNT,ERROUT,•.•) C SUBROUTINE'RTNCHK WAS WRITTEN BY B. WONG. FACULTY OF C FORESTRY, AND IS STORED IN THE ROKA LIBRARY. C THE SUBROUTINE, RTNCHK, EVALUATES WHETHER THE DIAGNOSTIC OUTPUT 908.000 908.200 908.400 909.000 C SUBROUTINE, PWRERR, SHOULD BE CALLED. ONLY TWO RETURNS ARE POSSIBLE C FROM THE SUBROUTINE. RTNCHK: C ( 1 ) IF IERR-0 (NO ERRORS), THEN A RETURN 1 OCCURS. 910.000 911.000 912.000 913.000 914.000 915.000 916.000 917.000 918.000 919.000 920.000 921.000 922 000 923.000 0002 6663 0004 0005 C (2) IF IERR DOES NOT EQUAL O (COMPUTATIONAL ERRORS PRESENT). C • THEN A RETURN 2 OCCURS. IMPLICIT REAL*B(A-H.O-Z) LOGICAL*1 ERROUT IF(ERROUT)CALL PWRERR(X,Y,IERR,IOUT,IC0UNT.S10) IF(IERR.NE.0)G0T020 0006 0007 0008 RETURN 1 10 CONTINUE 20 CONTINUE 0009 RETURN 2 0010 END •OPTIONS IN EFFECT* ID, EBCDIC , SOURCE . NOLIST , NODECK, LOAD .NOMAP •OPTIONS IN EFFECT*NAME - RTNCHK LtNECNf ' » 6 0 •STATISTICS* SOURCE STATEMENTS - 10.PROGRAM SIZE " •STATISTICS* NO DIAGNOSTICS GENERATED 550 NO STATEMENTS FLAGGED IN THE ABOVE COMPILATIONS. $COPY «SKIPFRONT Listing Of MODEL.D at 13:28:52 on OCT 11. 1984 for CC1d=ANNA Page 1 1 SET P-182.5 2 SET A1=.0172024238 3 SET Et( 1 . . .4) = - 1 .570796327 4 SET B(5)--1.88796 5 SET TOO. . 5)=-9.8 -14.4 0 0 -12.8 -9.4 6 SET TM1(1...51=28.8 26.8 0 0 28.2 28.2 7 SET TNPSYN=0 8 SET T=0 9 SET KNEMP"-0 10 SET KNEMP1=0 11 SET DMAX=0.0026 12 SET LAB=0 13 SET LBQ=426 14 SET RS=144 15 SET INCR-1 16 SET N03=1.40 17 SET NH4=0.12 18 SET NK=0 19 SET A(ALL)=0 20 SET NK=0 21 SET KA=0 22 SET KB=0 23 SET PM(ALL)=6 24 SET LF=0 25 SET R3(ALL)=0 26 SET R4(ALL)=0 27 SET NDEM=0 28 SET DD(ALL)=0 29 SET NLT=0 30 SET NVOLT'O 31 SET TA=0 32 SET GMAX".085 33 SET NAVAIL'O 34 SET NFREE=0 35 SET TNL0SS=O 36 SET NRECYC=-0.0 37 SET TB=0 38 SET U0R=-O 39 SET CP=-0.0 40 SET SG=0 41 SET TS=0 42 SET AB=0 43 SET CM=0 44 SET TM=0 45 SET SD=0 46 SET NCYCLE=0 47 SET NN=0 48 SET LAB=0 49 SET GA=0 50 SET WBM=0 51 SET SY1=0.04 52 SET SY2=0.98 53 SET SA=0.70 54 SET SB=-9.85553 55 SET DP(ALL)=0 56 SET NP (ALL ) =O 57 SET NAB(ALL)=0 58 SET <J(ALL)=0 ro L i s t i n g of MODEL.D a t 13:28:52 on OCT 11, 1981 for CC1d=ANNA Page 2 59 SET N L P ( A L L)=0 6 0 S E T NLTALL7=6 61 SET N L ( A L L)=0 62 SET N M L ( A L L)-0 63 SET NVG(ALL)*6 64 SET W A M » 0 65 SET IPASS-0 66 SET DLA6( i...5)=24.01295687 24 16765247 6 6 24.11081648 24 11081648 67 SET D L C 1 ( 1 . . . 5 ) » - 3 . 9 4 9 5 7 1 8 2 -3.70519604 0.0 -3.83307714-3.83307714 68 SET DLS1(1 ... 5)=0.6206633 0.53829226 0.0 0.58219562 0.58219562 6 9 * SET W P A O J 1 . . . 4 ) « - 4 0 1456043956 -20.35989011 -5.6719780220 .2043686247 70 SET WPC1( 1 . . , 4 ) » 1 6 . 7 1 4 6 2 4 9 8 13.46548877 3.84621018 .0245794138 71 SET WPC2(1 ... 4)*5.55837081 -4.382303985 -2.32273982 .0191259285 7 2 S E T WPC3(1. .!'4)«-0. 7 5 9 9 6 1 6 1 4 1 . 8 0 1 1 0 6 8 2 6 . 6 9 6 4 8 6 6 6 4 - . 6 5 0 8 4 4 1 9 E - 2 73 SET WPC4(1...4)-0 0 .36282565 .63051099E-2 74 SET WPCS(1...4)=0 0 -.70004217 -.55880747E-3 7 5 S E T WPC6(i 7.4)=0 6 .61684175 27603917E-3 76 SET WPSK1...4)=23.29805172 6.69591130 1.63276317 .020541403 77 SET WPS2(1. . . 4 ) » - 7 . 2 7 0 9 4 4 8 6 -4.96270366 -2.4903767 -. 11728638E-1 7 8 S E T WPS3(1. . ! 4 ) » - 3 . 4 0 3 2 6 i 5 2 3 47377280 2 32251251 11250596E- 1 79 SET W P S 4 ( 1 . . . 4 ) » 0 0 -1.49957215 -.11102197E-1 80 SET W P S 5 I 1 . . . 4 ) « 0 O .64275640 .10105648E-1 8 1 S E T WPS6( ' • • 4)"»b""6 1 4 9 9 4 2 4 4 - . 77907707f-2 82 SET W P A O ( S ) « . 2 5 6 1 2 6 0 1 83 SET W P C 1 ( 5 ) » . 1 3 2 6 1 6 9 4 E - 1 8 4 S E T WPC215) • ! 54 148853E-.2 85 SET W P C 3 ( 5 ) ° - 0 . 1 3 0 5 8 0 5 6 E - 2 86 SET WPC4(5)-.22883572E-2 8 7 S E T WPC5(5)»6!6 88 SET WPC6(5)"0.0 89 SET WPS1(5)-.73856391E-1 9 0 S E T W P S 2 ( 5 ) » - . 257 15068E- 1 91 SET W P S 3 ( 5 ) » . 9 1 5 2 4 0 0 1 E - 2 92 SET WPS4(5)--.27902489E-2 9 3 S E T WPS5(5j=6.6 94 SET W P S 6 ( 5 ) » 0 . 0 95 SET PI*3.1415926536 9 6 S E T i S T T - 6 97 SET ISTST-0 98 SET I S T W « 0 9 9 S E T bR(l .12 5-12 7 6 5 8 9 7 8 7 7 9 11 100 SET RM(1 ... 11)»31.6 16.0 9.7 10.4 18.0 29.9 22.5 27.5 21.4 15.2 22.0 101 SET R M (12)»32.3 1 0 2 S E T RD(1. . .11)-33:8 20.6 13.5 19.3 12.4 2 i . 1 42.2 48.6 18.6 14.5 26.5 103 SET RD(12)-23.4 104 SET GRAZIN(ALL)-0.0 1 0 5 S E T KGR*0 106 SET GR=-0.0 107 SET GRPSYN--0.0 1 0 8 S E T *lbUMP=bN 109 SET GRAx-0.0 110 SET KNI'O 1 1 1 S E T GRJD-0 112 SET F U N » 9 0 113 SET #NLINE=126 1 1 4 S E T GBMAX =6.054 115 SET GGBMAX-0.0054 1 16 SET DLG= 1 .0 L i s t i n g O f M O D E L . 0 a t 1 3 : 2 8 : 5 2 o n O C T 1 1 , 1 9 8 4 f o r CCfd=ANNA P a g e 3 1 1 7 S E T I S H I F = - 0 1 1 8 S E T N C H - 0 1 1 9 S E T I A E S T = 0 1 2 0 S E T A G B M A X - 0 . 0 8 1 2 1 S E T F U N 2 = 9 0 1 2 2 S E T R G A E S ' O 1 2 3 S E T F U N 3 = 7 6 1 2 4 S E T M 0 R T v J D = 1 2 O 1 2 5 S E T M 0 R T W P - = - 3 0 1 2 6 S E T C U M A B - 0 1 2 7 S E T R G G = 0 1 2 8 S E T T L A B s O 1 2 9 S E T R T S H T = 0 1 3 0 S E T P M A X = 0 . 0 1 6 1 3 1 S E T F R M A X - 1 . 0 1 3 2 S E T F R R M A X = 1 . 0 1 3 3 S E T T S S N E G - 0 1 3 4 S E T K N E M P 2 = 0 1 3 5 S E T K N E M P 3 - 0 1 3 6 S E T N R G G = 0 1 3 7 S E T N R G A E S - 0 1 3 8 S E T G R A Z = 0 1 3 9 S E T A M G ' O 1 4 0 S E T A M R G A * 0 1 4 1 S E T A M R G G - 0 1 4 2 S E T G L A B = 0 1 4 3 S E T G L A B A B e O 1 4 4 S E T R G G A B B 0 1 4 5 S E T R G A B ° 0 1 4 6 S E T C P G - - 0 1 4 7 S E T C P R G A » - 0 1 4 8 S E T C P R G G « - 0 1 4 9 S E T L F 2 = 0 1 5 0 S E T N M I N Y = 0 . 8 1 5 1 S E T N M G » 1 1 5 2 S E T N M R G A » 1 1 5 3 S E T N M R G G = 1 1 5 4 S E T C P Y M I N ' O 1 5 5 . S E T C P Y G = 0 1 5 6 S E T C P Y R G A - 0 1 5 7 S E T C P Y R G G - 0 1 5 8 S E T P H E N M 2 » 0 . 0 5 1 5 9 S E T N - 0 1 6 0 S E T G A 1 - 0 1 6 1 S E T G A 2 - 0 1 6 2 S E T I A E S T 0 = 0 1 6 3 S E T R G J D - 0 1 6 4 S E T C P Y - 0 1 6 5 S E T J D A E S T - 0 1 6 6 S E T Z - . 6 1 6 7 S E T D A M P D - 0 . O 7 0 8 4 5 6 7 9 1 6 8 S E T G R K N I ' 1 0 0 0 $ R E N - A S P R I N T 9 A l l o t t e d f i l e s p a c e e x c e e d e d f o r I d A N N A . -pi 

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