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Agricultural Systems 43 (1993) 145-163

D e v e l o p m e n t , C a l i b r a t i o n a n d V a l i d a t i o n o f a G r e e n h o u s eT o m a t o G r o w t h M o d e l : I . D e s c r i p t i o n o f t h e M o d e l *

E . D ayan, :~ H. van K eu len , b J . W . Jon e s , ~ I . Z ip or i , aD . S h m u e l & H . C h a l l a dB eso r E x p er im en ta l S t a t io n , A g r i cu l tu ra l R esea rch Organizat ion, Israelb D L O - C e n t r e o f A g r o b i ol o g ic a l R e s e a r c h ( C A B O - D L O ) , W ageningen, Th e Netherlands' A g r i cu ltu ra l E n g in ee rin g D ep ar tm e n t , U n iv e r s i ty o f F lo r id a , G a in esv i ll e , F lo r id a , U S Ad D e p ar tm en t o f H o r t i cu l tu re , W ag en in g en A g r i cu l tu ra l U n iv e r si ty , W ag en in g en, T h e

Netherlands(Received 29 January 1992 ; accep ted 6 November 1992)

A B S T R A C TA dynam ic crop grow th model , TO M G R O , fo r an inde termina te tomatovariety is pre sen ted The mo del describes the phenolog ical developm entand increase in dry weight of various organs (roots, stem nodes, leavesand fru i ts ) fro m plant ing t i ll m aturi ty under variable e nvironme ntal condi-t ions . Phenological development is governed by genet ic p lant propert iesand environme ntal condit ions (e .g . a ir temperature and C 02 level) and ex-pres sed in a p lastochron index, i .e . the current s tem node number. Tota ldry m atter accum ulat ion is based on a quant i ta t ive description o f the car-bon balance, including g ross C O 2 assimilation, m ainten anc e respirationand grow th respiration. Part i t ioning o f dry matte r increase over the vari-ous organ s is gov ern ed by their relative sin k strengh, defined on the basiso f a gene tically de term ine d "potential ' gro w th rate, ac hieved under non-l imiting carbohy drate supply. The m odel is both schem atic and modular inset-up. This means i t can be adap ted easily and mo st o f its subrout ines canbe replaced easily by oth ers i f bette r descriptions becom e available. It canalso be com bined with a more comprehensive m ode l describing greenhousec l imate and appears robus t fo r use in procedures o f economic op t imiza t iono f cl imate condi t ions in greenhouses o r fo r ma nage me nt purposes.

* C o n t r ib u t io n f ro m th e A g r i cu l tu ra l R esea rch O rg an iza t io n , the Volcani Center , BetDagan , Is rael . No . 3422-E , 1991 series.:~ Presen t address : H ab so r Ex per im ental S ta t ion , M obi le Po st H aneg ev 4 , Is rael 85400.

145Agricultural System s 0308-521X/93/ 06.00 1993 Elsevier Science Publishers Ltd, England.Printed in Great Britain


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146 E. Dayan et a l .

I N T R O D U C T I O NI n c r e a s i n g i n t e r n a t i o n a l c o m p e t i t i o n p u t s i n c r e a s i n g p r e s s u r e o n t o m a t og r o w e r s t o r e d u c e th e c os t s o f p r o d u c t i o n b y , a m o n g o t h e r m o v e s ,e c o n o m i z i n g o n r e s o u r c e u s e . T o t h i s e n d , n e w g r o w i n g t e c h n i q u e sa r e r e q u i r e d , i n c l u d i n g u s e o f n e w v a r i e t i e s , c l i m a t e c o n t r o l , a n d e x -t e n s i o n o f t h e g r o w i n g p e r i o d . G r o w t h o f t o m a t o p l a n t s i n a g re e n -h o u s e i s a c o m p l e x p r o c e s s , g o v e r n e d b y t h e i n t e r a c t i o n s b e t w e e np l a n t g e n e t i c p r o p e r t i e s a n d e n v i r o n m e n t a l c o n d i t i o n s , a s m o d i f i e d b yc l i m a t e c o n t r o l i n s i d e t h e g r e e n h o u s e . I t i s t h e r e f o r e d i f f i c u l t t o p r e d i c ti n t u i t i v e l y , t h e m a n a g e m e n t m e a s u r e s n e c e s s a r y t o c r e a t e c r o p g r o w i n gc o n d i t i o n s t h a t w i l l l e a d t o o p t i m a l r e s o u r c e u s e ( C h a l l a & V o o r e n ,1980).D y n a m i c c r o p g r o w t h m o d e l s i n w h i c h i n s i g h t s i n p l a n t p h y s i o l o g i c a lp r o c e s s e s a n d t h e i r d e p e n d e n c e o n e n v i r o n m e n t a l c o n d i t i o n s a r e c o m -b i n e d ( W h i s l e r e t a l . , 1 9 8 6 ; S e l i g m a n , 1 99 0), m a y p r o v i d e a p r a c t i c a l a i di n m a n a g e m e n t d e c i s i o n - m a k i n g , s o t h a t t h e e f f e c t s o f a l t e r n a t i v e m a n -a g e m e n t s t r a t e g i e s c a n b e e x a m i n e d . I n t h i s p a p e r s u c h a m o d e l f o r at o m a t o c r o p , T O M G R O , is p r e s e n te d . I n th e fi rs t p a r t a d e s c ri p t i o n o ft h e m o d e l i s g i v e n , w h i l e i n p a r t I I ( D a y a n e t a l . , 1 9 9 3 fi el d c a l i b r a t i o na n d v a l i d a t io n a r e d es c r ib e d . C a l i b r a t i o n o f th e m o d e l u n d e r c o n t r o l l e dc o n d i t i o n s h a s b e e n t h e s u b j e c t o f a s e p a r a t e s t u d y ( J o n e s e t a l . ,1 98 9a , b ), w h i l e i ts a p p l i c a t i o n f o r e c o n o m i c o p t i m i z a t i o n o f g r e e n h o u s econ t ro l i s de sc r ibed e l sewhe re (Seg ine r & Sh ina , 1989) .T h e m o d e l w a s d e s ig n e d t o d e sc r ib e g r o w t h o f a n i n d e t e r m i n a t et o m a t o v a r i e t y u n d e r t h e s p e c i f i c c o n d i t i o n s o f g r e e n h o u s e c u l t i v a t i o n i nI s ra e l. T i m i n g , q u a n t i t y a n d q u a l i t y o f t o m a t o f r u i t y i e l d a r e a f fe c t e d b yc l i m a t e c o n d i t i o n s i n t h e g r e e n h o u s e , c o n t r o l l e d b y c o o l i n g , h e a t i n g a n dC O 2 e n r i c h m e n t . T h e m o d e l d e s c r i b e s t h e e f f e c t s o f t h e s e m a n a g e m e n tm e a s u r e s t h r o u g h t h e i r in f lu e n c e o n t o t a l d r y m a t t e r a c c u m u l a t i o n a n dd i s t r i b u t i o n .T h e e f fe c ts o f w a t e r o r n u t r i e n t d e f i c i e n c y a r e n o t t r e a t e d i n th e m o d e l ,a s n e a r - o p t i m u m l ev e ls o f n u t r i e n t a n d w a t e r s u p p ly a r e m a i n t a i n e du n d e r g r e e n h o u s e c o n d i t io n s . W e e d s a re s u p p o s e d n o t t o i n f lu e n c e c r o pp e r f o r m a n c e , a n d e ff ec ts o f p e s t s a n d d i s e as e s a r e t r e a t e d i n a r u d i m e n -t a r y w a y . U n d e r t h e i n t e n s i v e m a n a g e m e n t p r a c t i c e s c o m m o n i n g r e e n -h o u s e s , w e e d s , p e s t s a n d d i s e a s e s h a r d l y i n t e r f e r e w i t h t h e g r o w t h o fc o m m e r c i a l c r o p s .A n i m p o r t a n t c r i t e r i o n i n m o d e l d e v e l o p m e n t w a s r o b u s t n e s s i n v i e wo f its a p p l ic a ti o n f o r e c o n o m i c o p t i m i z a ti o n o f g r e e n h o u s e m a n a g e m e n ta s p a r t o f a n o v e r a l l d e c i s i o n s u p p o r t s y s t em .


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Development of a greenhouse tomato growth model: I 147

M O D E L D E S C R I P T I O NT h e m o d e l d e sc ri b es g r o w t h o f th e t o m a t o c r o p q u a n t i ta t iv e l y , b o t h b yn u m b e r o f a n d d r y m a t t e r a c c u m u l a t i o n in th e v ar i o u s p la n t c o m p o n e n t s( r o o t s , s t e m n o d e s , l e a v e s a n d f r u i t s ) . O r g a n n u m b e r s a r e d e r i v e d f r o mt h e o r d e r a n d r a t e o f a p p e a r a n c e a g ei n g, d e a th a n d d i s a p p e a ra n c e . D r ym a t t e r a c c u m u l a t i o n i s d e r i v e d f r o m t h e c a n o p y c a r b o n b a l a n c e a n d t h ep a r t it i o n i n g o f d r y m a t t e r a m o n g p l a n t o r g a n s .

T h e p l a n t d e s c r i b e d i n t h e m o d e l i s c o m p o s e d o f a s e r i e s o f s u c c e s s i v es y m p o d i a , t h e f i r s t s y m p o d i u m h a v i n g 7 - 1 5 n o d e s w i t h l e a v e s , f o l l o w e db y a t r u s s , t h e f o l l o w i n g s y m p o d i a 3 n o d e s w i t h l e a v e s p r e c e d i n g t h et r u s s . E a c h t r u s s c a r r i e s 5 - 1 2 f l o w e r s , r e s u l t i n g i n 3 - 1 2 f r u i t s ( P i c k e ne t a l . , 1 9 8 6 ; A t h e r t o n & H a r r i s , 1 98 6).T i m e s t e p o f t h e m o d e lT h e t i m e i n t e rv a l o f i n t e g r a t i o n o f th e m o d e l i s o n e d a y , i n a c c o r d a n c ew i t h t h e t i m e c o n s t a n t o f th e s y s t e m .H o w e v e r , s o m e o f t h e p r o c es s e s, l ik e a s s im i l a t io n a n d r e s p i r a ti o n r e a c tr a p i d l y t o v a r y i n g e n v i r o n m e n t a l c o n d i t i o n s s u c h a s l i g h t i n t e n s i t y a n dC O 2 c o n c e n t r a t i o n . H e n c e , t h e s e r a t e s a r e c a l c u l a t e d i n a s o - c a l l e d ' f a s tl o o p ' , t h a t i s e x e c u t e d a t h o u r l y t i m e i n t e r v a l s d u r i n g d a y t i m e i n t e g r a t e dv a l u e s a r e t h e n u s e d t o u p d a t e t h e s t a t e v a r i a b l e s o n c e a d a yS t a t e v a r i a b l e s a n d a g e c l a s s e sT h e m o d e l c a l c u l a t e s t h e t i m e c o u r s e o f b o t h w e i g h t a n d n u m b e r o fa e r i a l p l a n t c o m p o n e n t s ( s t e m n o d e s , l e a v e s a n d f r u i t s ) , w h i l e r o o tg r o w t h i s o n l y t r e a t e d s u p e r f i c i a l l y . O n l y t h e m a i n s t e m i s c o n s i d e r e d , a ss i d e s h o o t s a r e s u p p o s e d t o b e r e m o v e d ( V o o r e n e t a l . , 1986) . Each o ft h e a e r i a l p l a n t c o m p o n e n t s i s s u b d i v i d e d t o ' u n i f o r m ' c l a s s e s ( c o h o r t s ) ,c o n s i s t i n g o f i n d i v i d u a l s o f , o n a v e r a g e , t h e s a m e p h y s i o l o g i c a l a g e .S o m e o f t h e c o h o r t s c a n b e i d e n t i f i e d w i t h s p e c i f i c m o r p h o l o g i c a l s t a g e si n t h e p l a n t ' s l if e c y cl e , l i k e fl o w e r b u d s , f l o w e r s a n d r i p e n e d f r u it s .E a c h c o h o r t o f e a c h c o m p o n e n t i s c h a r a c t e r i z e d b y t w o s t a te v a r i a b le s ,r e p r e s e n t i n g it s n u m b e r a n d i ts w e i g h t. L e a f c o h o r t s a r e f u r t h e r c h a r a c -t e r i z e d b y t h e i r g r e e n a r e a . T h e t o t a l c r o p i s t h u s r e p r e s e n t e d b y s e v e nc o h o r t s o f s t a t e v a r i a b l e s : n u m b e r o f l e a v e s , n u m b e r o f s t e m n o d e s ,n u m b e r o f f r u i t s , d r y w e i g h t o f l e a v e s , d r y w e i g h t o f s t e m n o d e s , d r yw e i g h t o f fr u it s a n d a r e a o f l ea v e s ( F ig . 1). T h e g r o w t h a n d d e v e l o p m e n to f e a c h o f th e s e p l a n t c o m p o n e n t s a r e d e s c r i b e d a s c o h o r t c h a n g e s , i .e .


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F o r m a t u r e l e a v es , su s c e p ti b le t o l e a f s h e d d i n g d u e t o s h a d i n g :r d l( N ) = r d r ( N ) . Q ( N ) + r d r s . ( L a - L a x ) L a > L a x

w h e r erdr ( i )

r d r sL a

L a x

E a c h

(6)= re la t ive d ea th ra te o f l e aves in age c la s s / (day ~), fo rc in g

f u n c t i o n ;= m a x i m u m r e l a t i v e d e a t h r a t e d u e t o s h a d i n g ( d a y 1 ) ;= l e a f a r e i n d e x o f t h e c a n o p y ; a n d= c r i t ic a l l e a f a r e a i n d e x , a b o v e w h i c h l e a v e s d ie b e c a u s e o fs h a d i n g .t r u s s c o n s i s t s o f s e v e r a l f l o w e r s , i n w h i c h s e v e r a l f r u i t s a r es e t a n d d e v e l o p . T h e n u m b e r o f fl o w e r s i n i t i a te d p e r n o d e is a v a r ie t a l

c h a r a c t e r i s t i c , m o d i f i e d b y p h y s i o l o g i c a l a g e o f t h e p l a n t ( V r i e s e n g a &H o n m a , 1 97 4) a n d e n v i r o n m e n t a l c o n d i t i o n s ; fo r e x a m p l e , l o w t e m p e r -a t u r e s r e s u l t i n s p l it t i n g o f th e t r u s s a n d i n i t i a t i o n o f m o r e f r u i t s p e rt r u s s ( C a l v e r t , 1 9 5 9 ; H u r d & C o o p e r , 1 9 6 7 ) .T h e d e g r e e o f sp l i tt in g a n d h e n c e t h e n u m b e r o f f ru i ts p e r t r u s s i sa s s u m e d t o b e p o s i t iv e l y c o r r e l a t e d w i t h t im e o f e x p o s u r e t o l o w e r t h a nc r it ic a l t e m p e r a t u r e s . H e n c e , t h e r a t e o f f r u it f o r m a t i o n , r F , i s g iven by:

r F = r M . F t . c s . f t l (7)f a c t o r a c c o u n t i n g f o r t h e e f f e c t o f p l a s t o c h r o n i n d e x o n t h en u m b e r o f fr u it s p e r t r u ss ;

c s = f a c t o r a c c o u n t i n g f o r t h e e f fe ct o f lo w t e m p e r a t u r e s o n t r u ssspl i t t ing; andf t l = f a c t o r a c c o u n t i n g f o r t h e e f f e c t o f s u b - o p t i m u m t e m p e r a t u r e s o n

frui t se t .B o t h h i g h a n d l o w t e m p e r a t u r e s r e d u c e f r u i t s e t ( L e v y et al . , 1978;

R y l s k i , 1 9 7 9 ; S a w h n e y , 1 9 8 3 ; P i c k e n , 1 98 4). H e n c e , i n t h e m o d e l , t h e r a t eo f f r u i t i n i t i a t i o n i s n e g a t i v e l y c o r r e l a t e d w i t h t h e d u r a t i o n o f t h e p e r i o do f e x p o s u r e t o a b o v e - o r b e l o w - c r i t ic a l t e m p e r a t u r e s .A f t e r s e t t i n g , t h e y o u n g f r u i t s a r e s t i l l s e n s i t i v e t o s u b - o p t i m a l c o n d i -t i o n s a n d s o m e m a y b e a b o r t e d ( R u s s e ll & M o r r i s , 1 9 8 2 ; A t h e r t o n &O t h m a n , 1 98 3). T h e n u m b e r o f a b o r t e d y o u n g f ru i ts is c a l c u l a t e d as af u n c t i o n o f s i n k / s o u r c e r a t i o ( C a l v e r t & S l a c k , 1 9 7 5 ) , w h i c h w i l l b e d i s -c u s s e d l at e r. H e n c e , t h e r a t e o f f r u it a b o r t i o n , R a , is given as:

R a = r r a . F ( l ) (8)w h e r e r r a = r e l a t i v e r a t e o f f r u i t a b o r t i o n ( d a y ~ ) , a n d F ( / ) = y o u n g f r u i t sn u m b e r .A l l m a t u r e f r u i t s a r e p i c k e d a n d r e m o v e d f r o m t h e s y s t e m .

w h e r eF t =


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152 E. Dayan et al.

Dry matter productionC a l c u l a t i o n o f b i o m a s s a c c u m u l a t i o n o f th e c r o p i s b a s e d o n a q u a n -t it a ti v e d e s c r ip t i o n o f th e c a r b o n b a l a n ce , c o m p r i s i n g g r o ss c a r b o n a s-s i m i l a t i o n , m a i n t e n a n c e r e s p i r a t i o n a n d g r o w t h r e s p i r a t i o n . G r o s s a s s i m i -l a t i o n , a s w e l l a s m a i n t e n a n c e a n d g r o w t h r e s p i r a t i o n a r e d e t e r m i n e d b yt h e i n s t a n t a n e o u s ly v a r ia b le c o m b i n a t i o n o f t h e e n v i r o n m e n t a l c o n d i-t io n s t e m p e r a t u r e , r a d i a t i o n a n d C O 2 le ve l a n d t h e m o r p h o l o g y , siz e a n dp h y s i o l o g ic a l a g e o f e a c h p l a n t c o m p o n e n t ( H u r d & T h o r n l e y , 1 97 4). A se n v i r o n m e n t a l c o n d i t i o n s i n s i d e t h e g r e e n h o u s e v a r y o v e r s h o r t p e r i o d so f ti m e , a s s i m i l a t io n a n d r e s p i r a t i o n a r e c a l c u l a t e d w i t h h o u r l y t i m es t e p s , i n t h e ' f a s t l o o p ' .

D a i ly g r o s s as s i m i l at i o n is o b t a i n e d b y i n t e g r a t i o n o f in s t a n t a n e o u sa s s i m i l a t i o n r a t e s , c a l c u l a t e d a s a f u n c t i o n o f t h e p r e v a i l i n g l e v e l s o fP A R ( p h o t o s y n t h e t i c a ll y a c ti v e r a d i a t io n ) a n d C O 2 , a m b i e n t t e m p e r a t u r ea n d c r o p c h a r a c t e ri s t ic s s u c h a s l e a f a re a i n d e x , l e a f a n g l e d i s t r i b u t i o n ,l ig h t e x t i n c t i o n c o e f fi ci en t , e tc . C a l c u l a t i o n o f i n s t a n t a n e o u s g r o s s a s s im i -l a t i on r a t e , P g , i s b a s e d o n A c o c k ' s e q u a t i o n ( A c o c k et a l . , 1978).

P g = ( D . P m /K ) . ln [ (1 - m ) . P m + Q e . K . R m ] /[(1 - m ) . P m + Q e . K . R m . e x p ( - K . L a ) ] . T a (9)D -- c o n v e r s i o n f a c t o r f r o m / z m o l C O 2 m 2 s J t o g C O 2 m 2 d a y ~;K -- c a n o p y l ig h t e x t i n c t i o n c o e f fi c ie n t f o r P A R ;m = l e a f l i g h t t r a n s m i s s i o n c o e f f i c i e n t ;

P m = l i g h t s a t u r a t e d l e a f C O 2 a s s i m i l a t i o n r a t e 0 z m o l C O 2 m 2 s ~);Q e = l e a f q u a n t u m e ff ic ie n cy (/ zm o l C O 2 / ~ m o l -l p h o t o n s ) ;

R m = p h o t o s y n t h e t i c p h o t o n f lu x d e n s i t y 0 z m o l p h o t o n s m -2 s -l);L a = a c t iv e c a n o p y l e a f a r e a i n d e x ( m 2 l e a f m 2 s u r fa c e ); a n dT a = f a c t o r a c c o u n t i n g f o r t h e e ff ec t o f a m b i e n t t e m p e r a t u r e o n g r o ss

a s s i m i l a t i o n .T h e v a l u e o f P m i s d e t e r m i n e d b y p h y s i o l o g i c a l c r o p a g e , a m b i e n t t e m -p e r a tu r e a n d a m b i e n t C O2 c o n c e n t r a t i o n ( T h o r n l e y et a l . , 1981):

P m = P m c . f t p . f p i (10)w h e r e

P m c = l ig h t s a t u r a t e d l e a f C O 2 a s s i m i l a t i o n r a t e , a s a f u n c t i o n o fa m b i e n t C O 2 c o n c e n t r a t i o n (p , m o l C O 2 m 2 S 1 ;f t p -- f a c t o r a c c o u n t i n g f o r th e e ff ec t o f a m b i e n t t e m p e r a t u r e o n l ig h t -s a t u r a t e d l e a f C O 2 a s s im i l a t io n r a t e; a n df p i = f a c t o r a c c o u n t i n g f o r t h e e ff ec t o f l e a f a g e o n l i g h t - s a t u r a t e dl e a f C O ~ a s s i m u l a t i o n r a t e .


9/19

Development o f a greenhouse tomato growth model: I 153T h e v a lu e o f P m c is c a l c u l at e d f r o m a m b i e n t C O 2 c o n c e n t r a t io n :

P m c = t l . C a + m a x [ O . , t 2 . ( C a - 350)] (11)w h e r eC a = am b i en t C O2 co n c en t r a t i o n ( p ~m o l t o o l 1 ):t l , t 2 = em p i r i c a l co n s t an t s ; an dm a x = t a k e s t h e m a x i m u m v a l u e o f t h e a r g u m e n t s in b r a c k e ts .

D a i l y m a i n t e n a n c e r e sp i r a ti o n is a ls o o b t a i n e d b y i n t e g r a t i o n o f t h e i n-s t an t an eo u s r a t e s , c a l cu l a t ed t o ( P en n i n g d e Vr i e s, 1 97 5):r m r - - ( W t v . r r v + W t f r r f ) . T mw h e r e

rmrW t v =

(12)d a i ly t o t a l m a i n t e n a n c e r e s p i ra t i o n ( k g CH20 m 2 day-~);t o ta l d r y w e i g h t o f l iv i n g a b o v e g r o u n d v e g e t a ti v e p l a n t o r g a n s ,co m p r i s i n g l e av es, p e t io l e s an d s t em n o d es ( k g m - 2);

r r v = m a i n t en an ce r e s p i r a t i o n co e f fi c ien t o f v eg e t a t i v e p l an t m a t e r i a l(kg CH20 k g -1 (dry mat ter ) day ~) ;W t f - - to ta l d ry weigh t o f f ru i t on the c rop (kg m 2) ;

r r f = m ain ten anc e resp i r a t ion coef fi c ien t o f f ru i t m ate r i a l (kg CH 20 kg I( d r y m a t t e r ) d ay l ) ; an dT m -- f a c t o r a c c o u n t i n g f o r t h e ef fe c t o f t e m p e r a t u r e o n m a i n t e n a n c er e s p i ra t i o n ( G o s i e w s k i e t a l . , 1982).Gr o wt h r e s p i r a t i o n i s a s s o c i a t ed w i t h t h e co n v e r s i o n o f p r i m ar y p h o t o -s y n t h a t e s i n t o s t ru c t u r a l d r y m a t t e r ( P e n n i n g d e V r ie s e t a l . , 1983).

r g = c p . ( P g - r m r ) (13)w h e r er g = r a te o f g r o w t h r e s p ir a t io n ( k g CH20 m 2 da y ~); an dc p = c a r b o n p r o d u c t i o n v a l u e ( k g d r y m a t t e r k g 1 (CH20)).

T o t a l a s s i m i l a t e ( ex p r e s s ed i n t e r m s o f d r y m a t t e r ) av a i l ab l e f o rg r o wt h o f s t r u c t u r a l p l an t m a t e r i a l , P n , i s thu s g iven by :P n = P g - r m r - r g (14)

A s s i m i l a t e d i s t r i b u t i o nP a r t i t io n i n g o f d r y w e i g h t i n c re a s e a m o n g p l a n t o r g a n s c a n b e d e s c r i b e db y t h e i r r e la t iv e s in k s t r e n g t h s ( H u r d & T h o r n l e y , 1 9 7 4 ; T a n a k a e t a l . ,1 9 7 4 a , b ; H u r d e t a l . , 1 9 7 9 ; T h o r n l e y e t a l . , 198 1; S ta rck , 1983). In themodel , f i r s t a f r ac t ion , f r t , o f t h e av a i l ab l e a s s i m i l a t e s , d e f i n ed a s af u n c t i o n o f t h e p h y s i o l o g ic a l a g e o f t h e p l a n t ( p l a s to c h r o n ) , m o d i f i e d by


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154 E. Dayan et al.

t e m p e r a t u r e a n d t h e s o u r c e / s i n k r a t i o , i s p a r t i t i o n e d t o g r o w t h o f t h er o o t s y s t e m ( N o u r a i , 1 9 8 0 ; R u s s e l l & M o r r i s 1 98 3).T h e t o t a l s i n k s t r e n g t h o f le a v e s a n d f r u it s is c a l c u l a t e d b y a d d i n g t h e

s i n k s t r e n g t h s o f t h e v a r i o u s c o h o r t s , w h i c h i s a f u n c t i o n o f t h e n u m b e ro f o r g a n s i n th e c o h o r t a n d t h e g e n e t i c al l y d e t e r m i n e d ' p o t e n t i a l g r o w t hr a t e ' p e r i n d i v i d u a l, i.e. i ts g r o w t h r a t e u n d e r n o n - l i m i t i n g c a r b o h y d r a t esupp ly (Miha i lov , 1975) .T h e a c t u a l s i n k s t r e n g t h s o f t h e f r u i t s , D f , i s o b t a i n e d a s t h e s u m o ft h e s i n k s t r e n g t h s o f a l l f r u i t c o h o r t s , c a l c u l a t e d i n d e p e n d e n c e o f t h en u m b e r o f f ru i ts i n t h e c o h o r t a n d t h e p o t e n t i a l g r o w t h r a t e p e r in -

d i v i d u a l ( W a l k e r & H o , 1 9 7 7 : H o et al., 1983) , modi f ied by the e f fec t s o fa m b i e n t t e m p e r a t u r e a n d C O 2 c o n c e n t r a t i o n ( F i s h e r, 1 9 7 7 ; H o , 1 98 0):S

D f = ~ , ( N f ( i ) . P f ( i ) . T f f C ) (15)t=lw h e r e :

Nf l i ) - - number o f f ru i t s in age c la s s i ;Pfl i ) = m a x i m u m r a te o f d r y m a t t e r a c c u m u l a t i o n p e r f r u it i n a g ec lass i (g f ru i t 1 da y l );

T f = f a c t o r a c c o u n t i n g f o r t h e e f f e c t o f t e m p e r a t u r e o n p o t e n t i a lf r u i t d r y m a t t e r a c c u m u l a t i o n r a t e ; a n df C = f a c t o r a c c o u n t i n g f o r t h e e f f e c t o f a m b i e n t C O 2 c o n c e n t r a t i o no n p o t e n t i a l f r u i t d r y m a t t e r a c c u m u l a t i o n r a t e ( s e e e q n ( 1 9 ) ) .

F o r l e a f b l a d es , p o t e n t i a l d r y m a t t e r a c c u m u l a t i o n r a t e is a s s u m e d t ob e c o n t r o l l e d b y p o t e n t i a l l e a f a r e a e x p a n s i o n r a t e in e a c h c o h o r t , rLA( i )(Hu ssey , 1963a, b 1965; C oo pe r , 1966 , 1967 ; K lap w i jk , 1981), de f ined a s :w h e r e rL A( i) = N l(i) . Pl( i). Tl . fc (16)

Nl( i ) = n u m b e r o f g r o w i n g l e a v e s i n a g e c la s s i ( m 2);Pl(i) -- m a x i m u m r a t e o f l e a f a r e a e x p a n s i o n o f a n i n d i v i d u a l l e a f i n

a g e cl as s i a t o p t i m u m t e m p e r a t u r e a n d 3 5 0 / z m o l m o l ~ C O 2c o n c e n t r a t i o n ( m 2 l e a f ~ d a y J)Tl = f a c t o r a c c o u n t i n g f o r t h e ef fe ct o f a m b i e n t t e m p e r a t u r e o n l e a fa r e a e x p a n s i o n r a t e ; a n df c - - f a c t o r a c c o u n t i n g f o r t h e e f f e c t o f a m b i e n t C O 2 c o n c e n t r a t i o no n l e a f a r e a e x p a n s i o n r a te .

D r y m a t t e r d e m a n d o n e a c h l e a f a g e cl as s ( 's i n k s t r e n g t h ' ) i s d e r i v e df r o m i ts p o t e n t i a l e x p a n s i o n r a te , t a k i n g i n t o a c c o u n t i ts s p ec if ic l e a f a r e a :rDp(i) = rL A ( i) /Ls(i) (17)


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w h e r e rDp( i ) = po ten t ia l r a te o f inc rea se in d ry we igh t o f l eaves in age c las si (kg m 2 day- l ) ; and Ls( i ) - spec if ic lea f a rea o f leaves in age c lass i(m 2 g -l).S p e c if ic l e a f a r e a f o r e a c h l e a f c o h o r t is d e f in e d a s a f u n c t i o n o f a m b i -

e n t t e m p e r a t u r e a n d C O 2 c o n c e n t r a t i o n a n d t h e p r e v a i l i n g p h o t o n f l u xd e n s i t y ( H u r d & T h o r n l e y , 1 9 7 4 ; C h a r l e s - E d w a r d s & L u d w i g , 1 9 7 5 ) :L s ( i) = L s s . f C . T s l . f R (18)w h e r e

L s s -- ' s t a n d a r d ' s p ec if ic l e a f a r e a ( m 2 g ~ ) ;f C = f a c t o r a c c o u n t i n g f o r t h e e f f e c t o f a m b i e n t C O 2 c o n c e n t r a t i o non spec i fic l e a f a rea ;T s = f a c t o r a c c o u n t i n g f o r t h e e f f e c t o f a m b i e n t t e m p e r a t u r e o n

spec i f ic l e a f a rea ; andf R -- f a c t o r a c c o u n t i n g f o r t h e e ff ec t o f p h o t o s y n t h e t i c p h o t o n f lu xd e n s i t y o n s p ec if ic l e a f a r e a .

T h e e f f ec t o f a m b i e n t C O 2 c o n c e n t r a t i o n o n s p ec if ic l e a f a r e a is d e f i n e da s a li n e a rl y i n c r e a si n g f u n c t i o n o f CO 2 c o n c e n t r a t i o n ( G o u d r i a a n & d eRui te r , 1983) :f C = 1/(1 + B c ( C a - 350)) (19)

w h e r e B c -- c h a n g e i n s p e ci fi c l e a f a r e a p e r / z m o l m o l -~ c h a n g e i n a m b i -en t CO2.T e m p e r a t u r e h a s a d i f fe r e n ti a l e ff ec t o n l e a f a r e a e x p a n s i o n a n d d r ym a t t e r p r o d u c t i o n , i . e . l e a f t h i c k n e s s d e c r e a s e s w i t h i n c r e a s i n g t e m p e r a -t u r e s ( F r i e n d , 1 9 6 6 ; H u r d & T h o r n l e y , 1 9 7 4 ) :

f T = 1 /(1 + B T ( 2 4 - T )) (2 0)w h e r e B T = c h a n g e i n s p ec if ic l e a f a r e a p e r C c h a n g e i n t e m p e r a t u r e( H u r d & T h o r n l e y , 1 9 7 4 ) ; a n d T = a m b i e n t t e m p e r a t u r e ( C ) .

T h e r e f e r e n c e t e m p e r a t u r e o f 2 4 C w a s c h o s e n r a t h e r a r b i t ra r i l y , b a s e do n t h e r e s u lt s o f c o n t r o l l e d c o n d i t i o n e x p e r i m e n t s ( Jo n e s et a l . , 1989b).B e c a u s e o f th e r e l a ti v e i n d e p e n d e n c e o f le a f a r e a d e v e l o p m e n t a n d l e a fw e i g h t i n c r e a s e , h i g h e r a s s i m i l a t i o n r a t e s , i n d u c e d b y i n c r e a s e d p h o t o nf lu x d e n s i t y , le a d t o t h i c k e r l e a v e s ( C o o p e r , 1 96 6, 1 9 6 7 ; T h o r n l e y &H u r d , 1 97 4; K l a p w i j k , 1 98 1). I n t h e m o d e l a m o d i f i e d v e r s i o n o f a ne m p i r i c a l e q u a t i o n d e v e l o p e d b y B o o t e a n d c o - w o r k e r s ( K . J . B o o t e , J .W . J o n e s & G . H o g e n b o o m , u n p u b l i s h e d d a t a ) i s u s e d :

f R = L s m + ( L s x - L s m ) . e x p ( - 0 . 4 1 7 . R m ) (2 1)w h e r e L s m , L s x = m i n i m u m a n d m a x i m u m v a l u e s o f sp e ci fi c l e a f a r e a ,r e spec t ive ly (g m-2) ; and R m = p h o t o s y n t h e t i c p h o t o n f l u x d e n s i t y ( / x m o lp h o to n s m -2 s ~).


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156 E . D a y a n et al.

T o t a l d r y m a t t e r d e m a n d f o r le a f g r o w t h , DI, i s o b t a i n e d b y a d d i n gt h e d e m a n d s o f all a ge cl as se s, a n d t a k i n g i n to a c c o u n t t h e r e q u i r e m e n t sf o r g r o w t h o f t h e p e t io l e s , t h a t a r e a s s u m e d t o b e p a r t o f th e l e a f b l ad e s :

ND l = (1 + p f ) ~ ( r D p (i )) (22)Ix lw h e r e p f -- f r a c t i o n o f p e t i o l e i n t o t a l l e a f b l a d e w e i g h t .

T o t a l d r y m a t t e r d e m a n d o f t h e g r o w i n g s t e m n o d e s i s d e r i v e d f r o mt h e d e m a n d o f t h e l ea v es b y a s s u m i n g a f ix ed r a ti o b e t w e e n l e a f a n d s t emn o d e s i n k s t r e n g t h ( H e u v e l i n k & M a r c e l is , 1 98 9):

Ds = ~ , , ( rDs( i ) ) (23)t=I

rOs( i ) = rDp( i ) . Ns( i)/N l( i).fs" (24)w h e r e

D s = t o t a l d r y m a t t e r d e m a n d f o r st e m g r o w t h ( k g m 2 d a y i);rDs( i ) - - d r y m a t t e r d e m a n d f o r s t e m g r o w t h i n a g e c l a s s i ( k g p l a n t

day ~);N s (i ) -- n u m b e r o f g r o w i n g s t e m n o d e s i n a g e c la s s i; a n df s ~ = r a ti o o f d r y m a t t e r d e m a n d o f l e af b l a d e a n d s t em n o d e .

T o t a l d r y m a t t e r d e m a n d f o r g r o w t h o f th e a e ri al p l a n t p a r t s i s t h es u m o f th e d e m a n d s o f th e c o m p o n e n t s :

T D = D l + D s + D f (25)T h e a c t u a l g r o w t h r a te s o f a ll c o h o r t s o f le a v es ( p l u s p et io l e s) , s t e m

n o d e s a n d f r u it s ar e d e r i v e d f r o m t h e p o t e n t i a l r a t e b y m u l t i p l y i n g w i t ht h e r a t i o P n / T D , i . e . t h e s u p p l y / d e m a n d r a t i o .

R ( p ) = P ( p ) . P n / T D (26)w h e r e R ( p ) = a c t u a l g r o w t h r a t e o f e a c h c o h o r t o f o r g a n s ( k g m 2 d a y 1);a n d P ( p ) -- p o t e n t i a l g r o w t h r a te o f e a c h c o h o r t o f o r g a n s ( k g m 2 d ay -~ ).

I f n e t a s s i m i l a t io n e x c e e d s t o t a l c r o p d e m a n d f o r a s s im i l a te s , a s s im i l a -t i o n i s i n s t a n t a n e o u s l y a d j u s t e d t o s a t i s f y d e m a n d e x a c t l y , i . e . s u r p l u sa s s i m i l a t e s a r e n o t s t o r e d i n a r e s e r v e p o o l f o r l a t e r u s e ( W a l k e r & H o ,1 9 7 7 ; W a l k e r et al . , 1 9 7 8 ; G o s i e w s k i et al . , 1981).

D I S C U S S I O NT h e p r e s e n t m o d e l i s b a s e d o n t h e a s s u m p t i o n t h a t a s s i m i l a t e a v a i l a b i l i t yis t h e m a j o r c o n s t r a i n t f o r g r o w t h a n d y i el d o f g r e e n h o u s e t o m a t o c r o p s .


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Developmen t o f a greenhouse tomato g row th model." I 157

F o r m a n y s i tu a t i o n s i n t h e t e m p e r a t e z o n e a l in e a r r e l a ti o n b e t w e e n l ig h ti n t e r c e p t i o n a n d d r y m a t t e r p r o d u c t i o n h a s b e e n e s t a b l i s h e d ( M o n t e i t h ,1 9 7 7 ; Wa l k e r e t a l . , 1 9 7 8 ; Go s i ews k i e t a l . , 1981; K eu len & S to l , 1991).U n d e r w i n t e r c o n d i t i o n s i n I s r a e l i g r e e n h o u s e s t h i s p h e n o m e n o n w a sa l s o o b s e r v e d ( D a y a n e t a l . , 1 9 8 6 ) . T h e r e f o r e , i n t h e p r e s en t m o d e ll i m i t ed a s s i m i l a t e av a i l ab i l i t y i s a s s u m ed , an d h en ce a s t r o n g i n t e r n a lc o m p e t i t i o n f o r a s s i m i l a t e s b e t w e e n v e g e t a t i v e a n d r e p r o d u c t i v e p l a n to r g a n s a n d n o a c c u m u l a t i o n o f r e s e r v e c a r b o h y d r a t e s .T h e m o d e l d e s c r i b e d h e r e i s v e r y s i m i l a r t o o t h e r s i n c a l c u l a t i n g d r ym a t t e r a c c u m u l a t i o n i n t h e c r o p f r o m a q u a n t i ta t i v e d e s c r i p ti o n o f t h eca r b o n b a l an ce , i .e . g r o s s p h o t o s y n t h e s i s m i n u s l o s se s t h r o u g h r e s p i r a -t i o n f o r g r o w t h a n d m a i n t e n a n c e . T h e p r i n c ip l e o f d r y m a t t e r p a r t i ti o n -i n g a m o n g t h e v a r i o u s p l a n t o r g a n s , b a s e d o n a s o u r c e / s i n k a p p r o a c h i sa l s o s i m i l a r t o s o m e o t h e r m o d e l s ( D a y a n e t a l . , 1981; Keulen & Se l ig -m an , 1 9 8 7 ; M ar ce l i s e t a l . , 1 98 9). I n m o d e l s f o r d e t e r m i n a t e c ro p s , t h ev a r i ab l e s i n k / s o u r ce r e l a t i o n s a r e o f t en d e s c r i b ed i n t e r m s o f f i x ed d ev e l -o p m e n t s t a g e s ( J o n e s e t aL ,1984; Keulen & Se l igman , 1987) and par t i -t i o n i n g i s d i r ec t ly r e l a t ed t o t h e s e d ev e l o p m en t s t ag es b y em p i r i c a lf u n c t i o n s ( M ar ce l i s e t a l . , 1989; Spi t ters e t a l . , 1 9 8 9 ) . I n i n d e t e r m i n a t ec r o p s , b e c a u s e g r o w t h o f v e g e t a t i v e a n d r e p r o d u c t i v e o r g a n s p r o c e e d ss i m u l t a n e o u s l y a n d c o n t i n u o u s l y , t h e p l a n t ' s l if e cy c le d o e s n o t h a v e af ix e d l e n g th . T h i s m e a n s t h a t d e v e l o p m e n t h a s t o b e r e l a t e d t o t h e l if ec y -c le o f t h e c o m p o n e n t o r g a n s. T h e r e f o r e , in t h e m o d e l p r e s e n t e d h e re , t h ep h y s i o l o g i ca l ag e o f t h e c r o p a s a wh o l e i s d e s c r i b ed i n t e r m s o f t h e l i f e -cy c l e o f t h e v a r i o u s o r g an s , s t em n o d es , l e av es an d f r u i t s . T h e p h y s i o -l o g i c a l a g e o f e a c h o f t h e o r g a n p o p u l a t i o n s p r e s e n t a t a n y m o m e n t , i sd e f i n ed b y i ts n u m b e r an d t h e p h y s i o l o g i ca l ag e o f i ts i n d i v i d u a l s .T h e p h y s i o l o g ic a l a g e o f e a c h i n d i v i d u a l is d e s c r ib e d b y t h e i n t e g r a t e da n d i n t er a c t iv e e ff ec ts o f t h e e n v i r o n m e n t a l c o n d i t i o n s , t e m p e r a t u r e , l ig h tan d C O2 co n cen t r a t i o n s i n ce i t s ap p ea r an ce . B as i ca l l y , t h i s d e s c r i p t i o ni s s i m i l a r t o t h e o n e u s i n g a c c u m u l a t e d h e a t s u m , a s i n o t h e r m o d e l s ,e x c e p t t h a t t h e h e a t s u m b e t w e e n i n it i a ti o n a n d p h y s i o l o g ic a l m a t u r i t y ism o d i f i e d b y r a d i a t i o n l ev e l a n d C O 2 c o n c e n t r a t i o n , c o n d i t i o n s t h a t c a ng e n e r a ll y b e c o n t r o l l e d u n d e r g r e e n h o u s e c o n d i t io n s .D e f i n i n g si n k s t re n g t h o n t h e b a s is o f n u m b e r a n d p h y s i o l o g i c a l a g e o ft h e v a r i o u s o r g an s r e s u l t s i n v a r i ab l e s i n k s t r en g t h , b o t h t o t a l an d f o r t h ed i f f e r en t o r g an s , i n t h e co u r s e o f t h e p l an t ' s g r o wt h cy c l e , wh i ch i s i na c c o r d a n c e w i t h t h e o b s e r v e d p a t t e r n o f g r o w t h o f v e g e t a ti v e a n d r e p r o -d u c t i v e p l an t o r g an s .U s e o f a d y n a m i c s u p p l y / d e m a n d r a t io t o g o v e r n d r y m a t t e r p a r ti ti o n -i n g , r a t h e r t h an p h y s i o l o g i ca l ag e o n l y , l e ad s t o v a r i ab l e p a r t i t i o n i n gp a t t e r n s i n t h e co u r s e o f t h e p l an t ' s g r o wt h cy c l e , M o r eo v e r , i t a f f ec t s


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158 E. Dayan et al.i n i t ia t i o n a n d a b o r t i o n o f o rg a n s , t h u s i n f lu e n c i n g a l so t h e g r o w t hp a t t e r n .

A l t h o u g h t h e p r e s e n t m o d e l p e r f o r m s s a t i s f a c t o r i l y , b o t h u n d e r I s r a e l ig r e e n h o u s e ( D a y a n e t a l . , 1 9 9 3 ) a n d c o n t r o l l e d c h a m b e r c o n d i t i o n s( J o n e s e t a l . , 1 9 8 9 a ) , s e v e r a l p h y s i o l o g i c a l a n d p h y s i c a l a s p e c t s w a r r a n tf u r t h e r a t t e n t i o n .

L e a f a p p e a r a n c e a n d l e a f d e v e l o p m e n t a r e a t r e a t e d d e s c ri p t iv e l y , b yu s i n g e m p i r i c a l f u n c t i o n s r e l a t i n g s p e ci fi c l e a f a r e a t o e n v i r o n m e n t a l c o n -d i t io n s , t h u s d i s r e g a r d i n g n u m b e r a n d r a t e o f d e v e l o p m e n t o f l ea fl et s o nt h e c o m p o s i t e l e a f . A m o r e m e c h a n i s t i c a p p r o a c h b a s e d o n c e l l n u m b e r ,c e l l e x p a n s i o n r a t e a n d c a r b o h y d r a t e a v a i l a b i l i t y a s a f f e c t e d b y e n v i r o n -m e n t a l c o n d i t i o n s a n d l e a f l e t p o s i t i o n w o u l d b e p r e f e r a b l e ( H o & S h a w ,1977).D e s c r i p t i o n o f f r u it i n i t i a ti o n a n d f r u it d e v e l o p m e n t r e q u ir e s m o r e d e t a il ,a s th e p a t t e r n o f f ru i t i n i ti a t io n w i t h i n th e t r us s , a n d e n v i r o n m e n t a le f f e c t s o n f l o w e r i n g a n d f r u i t s e t , e . g . v i a b i l i t y o f t h e p o l l e n , t r a n s f e r o fp o l l e n f r o m t h e a n t h e r t o t h e o v a r i e s , e t c . ( L e v y e t a l . , 1 9 7 8 ; R y l s k i ,1 9 7 9; S a w h n e y , 1 9 8 3 ; P i c k e n , 1 98 4), a r e n o t t a k e n i n t o a c c o u n t . T h e s ep r o c e s s e s m a y h a v e c o n s i d e r a b l e e f f e c t s o n f r u i t n u m b e r s u n d e r g r e e n -h o u s e c o n d i t io n s .

D r y m a t t e r a l l o c a t i o n t o t h e r o o t s a n d r o o t a c t i v i t y a r e t r e a t e d i n ar u d i m e n t a r y w a y , a s i n m o s t p u b l i s h e d c r o p g r o w t h m o d e l s ( c f . K e u l e n& S e l i g m a n , 1 9 8 7 ) . A m o r e e x p l a n a t o r y d e s c r i p t i o n , t a k i n g i n t o a c c o u n tt h e i n t e r a c t i o n s b e t w e e n a b o v e g r o u n d a n d b e l o w g r o u n d p l a n t o r g a n s ,a s w e l l a s t h e e f f e c t s o f e n v i r o n m e n t a l c o n d i t i o n s o n r o o t g r o w t h a n df u n c t i o n i n g , w o u l d w i d e n a p p l i c a b i l i t y o f t h e m o d e l , e s p e c i a l l y f o r s o i l -l e s s c u l t u r e s , w h e r e r o o t f u n c t i o n i n g m a y b e a c o n s t r a i n t f o r o p t i m u mc r o p p e r f o r m a n c e ( C r a p o & K e t e l l a p p e r , 1 9 8 1 ) .

P l a n t g e n e t i c c h a r a c t e r i s t i c s , e i t h e r d i r e c t l y o r t h r o u g h t h e i r r e s p o n s et o e n v i r o n m e n t a l c o n d i t io n s , g o v e r n t h e p a t t e rn o f g r o w t h a n d d e v e lo p -m e n t o f t h e c r o p . T h e s e c h a r a c t e r i s t i c s a r e m o s t l ik e l y c u l t iv a r - sp e c i fi c ,s o t h a t t h e m o d e l n e e d r e - c a l i b r a t i o n f o r u s e w i t h e a c h d i f f e r e n t v a r i e t y( A u g u s t i n e e t a l . , 1 9 7 9 ; B a n g e r t h & H o , 1 98 4).

A l s o s o m e p h y s i c a l p r o c e s s e s a r e t r e a t e d r a t h e r s u p e r f i c i a l l y . E f f e c t so f a ir h u m i d i t y a r e n o t t r e a t e d a t a l l. T h i s c o u l d b e o v e r - s im p l i f ic a t i o n ,e s p e c i a l l y u n d e r g r e e n h o u s e c o n d i t i o n s , a s h i g h h u m i d i t i e s , s u c h a s m a yo c c u r d u r i n g c l o s i n g o f t h e w i n d o w s e i t h e r t o a l l o w C O 2 e n r i c h m e n t o rt o r e d u c e h e a t d i s s i p a t i o n d u r i n g c o l d n i g h t s , m a y i n t e r f e r e w i t h v a r i o u sprocesse s , such a s ion up take , a s s imi la t ion , f e r t i l i z a t ion , f ru i t s e t , e tc .(K lapw i jk , 1975 ; P icke n , 1984).

S i n c e e x c h a n g e p r o c e s s e s o f e n e r g y , w a t e r a n d c a r b o n d i o x i d e w i t h i nt h e c a n o p y a r e n o t c o n s i d e r e d i n t h e m o d e l , t e m p e r a t u r e a n d c a r b o n


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Development o f a greenhouse tomato growth model: I 159

d i o x i d e c o n c e n t r a t i o n a r e a s s u m e d c o n s t a n t t h r o u g h o u t , a n d e x t i n c t i o no f p h o t o s y n t h e t i c a l l y a c ti v e r a d i a t io n is b a s e d o n a h o m o g e n e o u s c r o p ,w i t h o u t t a k i n g t h e r o w s t r u c t u r e i n t o a c c o u n t ( G o u d r i a a n , 1 9 7 7 ; G i j z e n& G o u d r i a a n , 1 98 9) .O r g a n f o r m a t i o n i s d e s c r i b e d e x p li c it l y i n t h e m o d e l , a n d p r o v i d e sp h y s i o l o g i c a l a g e d i s t r i b u t i o n o f t h e e x i s t in g l e a f m a s s ; h e n c e i t a l s oa l l o w s e v a l u a t i o n o f th e p o s i t i o n o f t h e l e av e s re l a t iv e t o e a c h o t h e r a n d ,i f c o m b i n e d w i t h i n f o r m a t i o n o n s t e m n o d e l e n gt h , a ls o in a b s o l u tet e rm s . T h i s c h a r a c t e r iz a t i o n o f t h e c a n o p y w i t h i n t h e m o d e l m a y p r o v i d ea g o o d s t a r t in g p o i n t f o r th e i m p r o v e m e n t o f m o d e l d e s c ri p t i o n s f o r l e a fa r e a d e v e l o p m e n t , f r u i t i n i t i a t i o n a n d d e v e l o p m e n t , e n e r g y b a l a n c e , e t c . ,e a r l i e r d e s c r i b e d a s u n s a t i s f a c t o r y i n t h e p r e s e n t m o d e l .

T h e m o d u l a r s e t -u p o f t h e m o d e l p r o v i d e s f le xi bi li ty a s n ew m o d u l e sc a n e a si l y b e a d d e d ( e. g. t r a n s p i r a t i o n ) a n d m o d u l e s f o r s p e ci fi c p r o c e s s e s( e. g. a ss i m i l a t i o n , o r g a n f o r m a t i o n ) c a n e a si ly b e r e p l a c e d i f i m p r o v e dd e s c r i p t i o n s b e c o m e a v a i l a b l e .

T h e m o d e l p r o v i d e s a c o n s i s te n t s c h e m a t i c d e s c r i p t io n o f t h e t o m a t oc r o p , w h i c h fa c i li t a te s s im p l i f i c a t i o n , g e n e r a l i z a t i o n , a d a p t a t i o n t o o t h e rc r o p s o r a p p l i c a t i o n s a n d t r a n s f e r t o o t h e r s o f t w a r e a n d i n c o r p o r a t i o n i no t h e r s o f t w a r e s y s t e m s , e . g . f o r e c o n o m i c o p t i m i z a t i o n a n d g r e e n h o u s ec l i m a t e c o n t r o l .

R E F E R E N C E SAcock, B. , Charles Edwards , D. A. , Fit ter , D. J . , Hand, D. W., Ludwig, L. J . ,W arren-Wilson J . & W ithers , A. C . (1978). The co n tr ibu t ion o f leaves f romdif fe ren t leve ls wi th in a tomato c rop to canopy ne t pho tosyn thes is : Anex p e r imen ta l ex amin a t io n o f two can o p y m o d e l s. J . exp . Bot . , 29, 815-27.Atherton, J . G. & Harr is , G. P. (1986) . Flowering. In T h e T o ma t o C r o p , eds. J.

G . Ath e r to n & J . Ru d ich . Ch ap man an d Ha l l , New Yo rk , p p . 1 6 7 -2 0 0Ather ton , J . G. & Othman , S . (1983) . Ef fec ts o f i r rad iance and water s t res s onf lower abor t ion in the g lasshouse tomato . A c t a H o r t . , 134, 133-8.Augustine, J . J . , Stevens , M. A. & Breidenbach, R. W. (1979) . Physiological ,mo rp h o lo g ica l , an d an a to mica l , s tu d ie s o f to ma to g en o ty p es v a ry in g incarb oxy lation effic iency. J . Am. Soc . Hor t . Sc i . , 104, 338-41.Bangerth , F. & Ho, L. C. (1984) . Fruit pos it ion and fru it sequence in a truss asfac to rs de te rm in ing s ize o f tom ato f ru it s . Ann. Bot . , 53, 315-19.Calver t , A. (1959) . Ef fec t o f the ear ly env i ronm ent on deve lopm ent o f flower ingin tomato . I I . L igh t and tempera tu re in te rac t ion . J . Hor t . Sc i . , 34, 154-62.Calver t , A. (1965) . F lowe r in i t ia t ion and deve lopm ent in the toma to . Nat l .Agr ic . Adv . Serv ice Quar t . Rev . , 70, 79-80.Calver t , A. & Slack , G. (1975) . Ef fec ts o f ca rbon d iox ide en r ichm ent on g row th ,deve lopment and y ie ld o f g lasshouse tomatoes . I . Responses to con tro l ledconcen tra t ion . J . Hor t . Sc i . , 50, 61-71.


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Challa, H. Vooren, J. van de (1980). A strategy for climate control in green-houses in early winter. Acta Hort . , 106, 159-64.Charles-Edwards, D. A. Ludwig, L. J. (1975). The basis of expression of leafphotosynthetic activities. In Environmental and Biological Control o f Ph oto-synthesis, ed. R. Marcelle. Dr W. Junk, The Hague, pp. 3744.Coleman, W. K. Greyson, R. I. (1976). The growth and development of theleaf in tomato (Lycopersicon esculentum). I. The plastochron index, a suit-able basis for description. Can. J. Bot., 54, 2421-9.Cooper, A. J. (1966). Seasonal changes in net assimilation and leaf growth ofyoung tomato plants. Acta. Hort . , 4, 76-8.Cooper, A. J. (1967). Effects of shading and time of year on net assimilationrates of young glasshouse tomato plants. Ann. Appl. Biol., 59, 85-90.Crapo, N L. Ketellapper, H. J. (1981). Metabolic priorities with respect ofgrowth and mineral uptake in roots of Hordeum, Triticum and Lycopersicon.Am. J. Bot., 68, 10-16.Dayan, E., van Keulen H. Dovrat, A. (1981). Tiller dynamics and growth ofRhodes grass after defoliation: a model named TILDYN. Agro-ecosystems,7, 101-12.Dayan, E., Enoch, Z., Fuchs, M. Zipori, I. (1986). Suitability of greenhousebuilding types and roof cover materials for growth of export tomatoes inthe Besor region of Israel. 2. Effect on fresh and dry matter production.Biotronics, 15, 71-9.Dayan, E., van Keulen, H., Jones, J. W., Zipori, I., Shmueli, D. Challa, H.(1993). Development, calibration and validation of a greenhouse tomatogrowth model: II Field calibration and validation. Agric. Syst . , 43, 165-83,this issue.Fisher, K. J. (1977). Competition effect between fruit trusses o f the tomatoplant. Sci. Hort., 7, 37~,2.Friend, D. J. C. (1966). The effects of light and temperature on the growth ofcereals. In The Growth of Cereals and Grasses, eds. F. L. Milthorpe J. D.Ivins. Butterworths, London, pp. 181-99.Gijzen, H. Groudriaan, J. (1989). A flexible and explanatory model of lightdistribution and photosynthesis in row crops. Agric. F or . M eteorol., 48,1 - 2 0 .Gosiewski, W., Nilwik, H. J. M. Bierhuizen, J. F. (1981). Effects of irradianceon photosynthesis of outdoor tomato cultivars. Gartenbauwissenschaft, 46,213-17.Gosiewski, W., Nilwik, H. J. M. Bierhuizen, J. F. (1982). The influence oftemperature on photosynthesis of different tomato genotypes. ScientiaHort . , 16, 109-15.Goudriaan, J. (1977). Crop Micrometerology: A Simulation Study. SimulationMonographs, Pudoc, Wageningen, 249 pp.Goudriaan, J. de Ruiter, H.E. (1983). Plant growth in response to CO 2enrichment, at two levels of nitrogen and phosphorus supply. I. Drymatter, leaf area and development. Neth. J. Agric. Sci., 31, 157-69,

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