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Aquacultural Engineering 1 (1982) 245-261

COMPUTER MODELING OF THE DIURNAL OXYGEN LEVELSIN A STILLWATER AQUACULTURE POND

D. I. MEYERDepartment of Electrical Engineering, University of Calijbrnia, Davis, CA 95616, USA

andD. E. BRUN E

Department of Agricultural Engineering, The Pennsylvania State University, University Park,PA 16802, USA

ABSTRACTA dynamic model o f dissolved oxygen behavior in a stillwater aquaculture pond ispresented. Using theories and principles that have been established for aerobic waste-water treatment ponds and shallow lakes and reservoirs, equations were developed todescribe the short-term dissolved oxygen fluctuations o f an aquaculture pond. Com-ponents considered in this model include the consumption and production of oxygenby phytoplankton, fish, detritus, and the process of reaeration. Factors affecting thesecomponents can be specified by the user; these blclude meteorologic and geographicdata, and phytoplankton, .fish, and detrital characteristics. After comparing the modelto field data and analyzing the sensitivity of its components, areas of research whichmay have an impact on pond management are identified.

NOMENCLATUREAPARA TMBODTBODLCLD

a v e r a g e p h o t o s y n t h e s i s r a t es u r fa c e a r e a o f p o n d ( m 2 )a t m o s p h e r i c a t t e n u a t i o n f a c t o r ( d im e n s i o nl e ss )B O D r e m a i n i n g a f t e r o n e d a y p e r i o dt o t a l B O D a t b e g i n ni n g o f d e c a y p e r i o dc l o u d i n e s s f a c t o r ( d i m e n s i o n l e s s )w a t e r d e p t h ( m )

2 4 5Aquaeultural Engineering 0144-8609/82/0001-0245]$02.75 Applied Scie nce Publishers Ltd,England, 1982Printed in Great Britain

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2 4 6 D. I. MEYER, D. E. BRUNED1, DeDECDTECELITEREXTFRFROFW1SLJDKLK1K2LLITLITDTOPHOSOPPPHYPMA XRREREFSCSRTMPWWTMP

b o u n d a r i e s o f w a t e r c o l u m n ( m )d e c l in a t io n o f th e s u n ( r a d ia n s )t i m e o f d a y ( h )l ig h t e x t in c t io n c o e f f i c i e n t ( ly / m)e f fe c t iv e l ig h t in t e n s i ty ( ly )e n d o g e n e o u s r e s p i ra t io n r a t el ig h t e x t in c t io n c o e f f i c i e n t (m -1)f is h o x y g e n d e m a n d a s f u n c t i o n o f OPf is h o x y g e n d e m a n d a s f u n c t i o n o f FW an d WTMPf i sh we igh tin i ti a l s lo p e o f p h o to s y n th e s i s v e r s us l ig h t in t e n s i tyJ u l i a n d a te (d a y s )o x y g e n t r a n s fe r c o e f f i c i e n t ( m / h )genera l b io log ica l decay ra tet e m p e ra tu re s p e c i f i c d e c a y ra t el a t i tu d e o f p o n d lo c a t io n ( r a d ia n s )n e t s o la r r a d ia t io n p e n e t ra t in g w a te r ( ly / m)e x t ra - t e r re s t ri a l s o la r r a d ia t io n f lu x ( ly / h )l ig h t in t e n s i ty l ev e l p ro d u c in g p h o to in h ib i t io no xy g e n s o lu b i l i ty a t g ive n t e m p e ra tu re (m g / l i t e r )p o n d o xy g e n l ev el (mg / l i t e r )i n s t a n ta n e o u s p h o t o s y n t h e t i c r a tep h y t o p l a n k t o n b i om a s s ( r a g /l i te r a s c a r b o n )m a x i m u m p h o t o s y n th e s i s ra t era d iu s v e c to r (d ime n s io n le s s)r e a e r a ti o n r a t e (m g o x y g e n / h )re f l e c t iv i ty o f w a te r s u r fac e (d im e n s io n le ss )s o la r c o n s ta n t (1 .9 4 ly / min )hour ang le o f sunr ise (h )t e m p e r a t u r e m o d i f i e r f a c to rw in d s p e e d (m/ s )w a t e r t e m p e r a t u r e ( C )

INTRODUCTIONA b a s ic t a s k o f p o n d ma n a g e me n t fo r f i s h c u l tu re i s t h e ma in te n a n c e o f d i s s o lv e do xy g e n a t a l e v el s u i ta b le fo r f i sh s u rv iv al a n d g ro w th . P o n d ma n a g e rs c a n mo n i to rthe d is so lved ox yg en leve l a t a g iven po in t in t ime , bu t p red ic t ing po ten t ia l c r i tica lp e r io d s o f lo w c o n c e n t ra t io n i s d i f f ic u l t . A fe w re s e a rc h e rs h a v e d e v e lo p e d e mp i r i c alm o d e l s to p re d ic t e a r ly mo rn in g p o n d d is so lv ed o xy g e n c o n c e n t ra t io n , g iv en a n in i t ia l

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COMPUTER MODEL OF OXYGEN BEHAVIOR IN AQUACULTURE POND 2 4 7s e t o f c o n d i t i o n s ( B u s c h e t a l . , 1 9 7 7 ; B o y d e t a l . , 1 9 7 8 ; B o y d , 1 9 7 9 ) . T h e s e m o d e l sh a v e l u m p e d m a n y c h a n g e s o c c u r r i n g i n p h y s i c a l a n d b i o l o g i c a l p r o c e s s e s b y u s i n gs t a t is t i c a l te c h n i q u e s s u c h a s m u l t i p l e r e g r e s s i o n , o r b y m a k i n g s i m p l i f y i n g a s s u m p -t i o n s . T h e m o d e l s h a v e b e e n t e s t e d a n d u s e d s p e c i f ic a l l y f o r c a t fi s h p o n d s i n A u b u r n ,A l a b a m a . I n o r d e r t o g a in a b e t t e r u n d e r s t a n d i n g o f e v e n ts w h i c h c a n c o n t r i b u t et o l o w d i ss o lv e d o x y g e n c o n c e n t r a t i o n , s u c h a s p o n d d e s t r a t i fi c a t io n a n d h e a v yp h y t o p l a n k t o n b l o o m s , a m o d e l b a s e d u p o n k n o w n p h y s i c a l , c h e m i c a l , a n d b i o l o g i c a lm e c h a n i s m s h a s b e e n c r e a t e d a n d i s p r e s e n t e d h e r e . T h i s m o d e l s i m u l a t e s t h e h o u r l yf l u c t u a t i o n o f d i s s o lv e d o x y g e n i n a n a qu a c u l t u r e p o n d o v e r a 2 4 h p e r i o d , a si n f l u e n c e d b y t h e c o n s u m p t i o n a n d p r o d u c t i o n o f o x y g e n b y p h y t o p l a n k t o n , f i s h ,d e t r i t u s a n d r e a e r a t i o n . T h e m o d e l i s n e i t h e r s i t e n o r s p e c i e s s p e c i f i c a n d i n p u t p a r a -m e t e r s c a n b e a d j u s te d t o a c c o m m o d a t e m o s t p o n d c o n d i t io n s . T h e m o d e l w a sd e v e l o p e d w i t h t h r e e p r i m a r y o b j e c t iv e s i n m i n d :

1 . T h e e s t a b li s h m e n t o f a c o n c e p t u a l f r a m e w o r k w h i c h u n i f ie s th e o r i e s f r o mseveral d iscipl ines .

2 . T h e d e t e r m i n a t i o n o f c o m p o n e n t s w h i c h h a v e t h e g r e at e s t e f f e c t o n d i ss o lv e do x y g e n .

3 . T h e i d e n t i f ic a t i o n o f a re a s o f r e s ea r c h w h i c h c o u l d i m p r o v e p o n d m a n a g e m e n t .

THE MODEL

T h e r e l a t i o n s h i p s b e t w e e n t h e c o m p o n e n t s , d e s c r i b e d q u a n t i t a t i v e l y b y t h e d i s s o l v e do xy g e n f l u x m o d e l , a r e r e p r e s e n t e d i n F i g . 1 . Wi n d , s o l a r r a d i a t i o n a n d f i s h f e e d a r et h e m a j o r c o m p o n e n t s w h i c h d i r e c tl y a f f e c t t h e r a t e s o f b i o lo g i ca l a n d p h y s i c a lp r o c e s s e s i n f l u e n c i n g p o n d w a t e r d i s s o l v e d o xy g e n ( D O ) c o n c e n t r a t i o n . T h e s o l a rr a d i a ti o n a t t h e s u r fa c e o f t h e w a t e r a t t e n u a t e s t h r o u g h t h e w a t e r c o l u m n . T h e e ff e c -t iv e l ig h t i n t e n s i ty i n t h e w a t e r c o l u m n d i r e c t ly a ff e c t s t h e p h y t o p l a n k t o n p o p u l a t i o nw h i c h i n t u r n , i n c r e a s e s D O d u r i n g t h e d a y v i a p h o t o s y n t h e s i s , a n d u t i l i z e s o xy g e n a tn i g h t t h r o u g h r e s p ir a t io n . D e c a y in g p h y t o p l a n k t o n , u n c o n s u m e d f is h f ee d , a n d fi shw a s t e p r o d u c t s a l s o d e c r e a s e D O a s r e p r e s e n t e d b y t h e s e d i m e n t o x y g e n d e m a n d . A st h e w i n d a g i t a t e s t h e w a t e r s u r f a c e , i t i n f l u e n c e s t h e o xy g e n t h r o u g h r e a e r a t i o n . T h ef i sh wi l l a l so requ i re oxygen fo r r esp i ra t ion , and wi l l inc rease the D O d e m a n d . E q u a -t i o n s d e s c r ib i n g e a c h o f t h e s e p r o c e s s e s w ill b e p r e s e n t e d i n t h e f o l l o w i n g s e c t io n s .

P o n d m o d e l e q u a t i o n s a r e t ie d t o g e t h e r b y a m a s s b a l a n c e , w h e r e t h e s u m o f t h er e a c t a n t s a n d i n f lo w c o n c e n t r a t i o n s e q u a ls th e s u m o f t h e o u t f l o w a n d a c c u m u l a t e dc o n c e n t r a t i o n s . A n o n - s t e a d y s t a t e a p p r o a c h i s u t i l i z e d t o a c c o u n t f o r c h a n g i n ge n v i r o n m e n t a l i n p u t s . Va l u e s o f r a t e c o e f f i c ie n t s u s e d i n t h e m a s s b a l a n c e e qu a t i o n sa r e s p e c i f i e d b y t h e p r o g r a m o r c a l c u l a t e d h o u r l y o v e r a 24 h p e r i o d . E a c h m a j o rc o m p o n e n t i n f l u e n c i n g d i s s o l v e d o xy g e n i s p r e s e n t e d i n a m o d u l a r s t r u c t u r e a n de v a l u a te d i n d e p e n d e n t l y o f , o r in r e la t i o n to , o t h e r c o m p o n e n t s .

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248 D.I. MEYER,D. E. BRUNE

R e o e r o t i o nF I S H ~ S O L A RR A D I A T I O N

Pho losyn fhes is ~ / ? /( ~ . f ,. ~ ! ,/ ~ , ,' ~ - M s P r o n n \ R e s p i r a t i o n /

~ W a s t e \ S e d lm e n f a x y g e n / , A l g a e .F e e , o . . e . \ p r o , o c , i o n \ e m a / / /~ / / /~ / / /~ / / /~ / / / - -~ / / /~ / / /~ / /~ , / / /~ / / /~-- / / /~ / / /~ / / /

SEDIMENTFig. 1. Pictorial representation of pond oxygen flux model.

Solar radiationThe total solar energy reaching the earth's surface is the sum of direct solar radia-tion and scattered or diffuse radiation. The amount of radiation per unit time depends

on the solar constant (1.94 ly/min), the latitude of the location (L, degrees), the timeof the year (JD, Julian date), the influence of the atmosphere (ATM), the albedo ofthe earth's surface (REF) and the elevation of the location. A Tennessee ValleyAuthority simulation study on solar radiation (1972), adapted by Orlob (1979), hasbeen implemented in the model.

The elevation of the location is assumed to be at sea level and the degree of obstruc-tion between the location and the horizon are assumed to be negligible. The declina-tion o f the sun is given as if the observation was made at the center of the earth.Atmospheric effects; reflectivity of the pond, latitude of the pond site and degree ofcloudiness (CL, 0 < CL < 1) affect the incident radiation, and can be indicated by theuser.

Daily, the radius vector (R, eqn (1)) and the declination of the sun (December,eqn (2)) are calculated, given the Julian date and the latitude of the pond site. Timesof sunrise (SR) and sunset are calculated (eqn (3)) from the declination, radius vector,and Julian date. The rate of solar radiation for each hour of daylight is calculated(LITDT, ly/h, eqn (4)) with the maximum rate occurring close to hour 12. Theincident solar radiation at the water surface (LIT) is calculated using eqn (5). Theseequations are as follows:

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C O M P U T E R M O D E L O F O X Y G E N B E H A V I O R I N A Q U A C U L T U R E P O N D 2 4 9R = 1 + 0 . 1 7 ( c o s ( 2 z r / 36 5 ) ( 1 8 6 - - J D ) ) (1 )

D E C = 2 3 . 4 5 0 r / 1 8 0 ) ( c o s ( 2 7 r/ 3 6 5 )( 1 7 2 - - J D ) ) (2 )S R = ( 1 2 / ~ ) a r c c o s ( ( t a n L ) ( ta n D E C ) ) (3 )L I T D T = 6 0 S C [ ( (D T + 1 - - S R ) ( s i u L ) ( s i n D E C )

+ ( 1 2 u / 1 2 ( c o s L ) ( c o s D E C ) ) ( ( s i n u / 1 2 ) ( D T + 1 3)x (sin 7 r / 1 2 ) ( D r + 1 2 ) ) ] / R 2 ( 4 )

L I T = L I T D T ( A T M ) ( 1 - - R E F ) ( 1 - - 0 . 6 5 C L 2 )/ 6 0 (5 )

L i g h t a t t e n u a t io nL i g h t i n t e n s i t y w i t h in t h e w a t e r c o l u m n c a n b e d e s c ri b e d b y th e B e e r - L a m b e r tL a w , w h e r e t h e l ig h t in t e n s i t y is a t t e n u a t e d e x p o n e n t i a ll y w i t h d e p t h ( D ; W a r r e n,

1 9 71 ) . T h e l i g h t e x t i n c t i o n c o e f f i c i e n t ( E C ) i s i n f l u e n c e d b y t h e a b s o r p t i o n a n ds c a t t e r i n g o f l ig h t w i t h i n t h e w a t e r c o l u m n c a u s e d b y w a t e r i t s e lf , a n d b y t h e d i s s o lv e da n d s u s p e n d e d s u b s t a n c e s o f b io l o g i c a l a n d n o n - b i o l o g i c a l o r i g in ( J e r l o v , 1 9 6 8 ) .

I n m o d e l i n g l ig h t a t t e n u a t i o n , s p e c tr a l m o d i f i c a t i o n b e l o w th e t o p m e t e r o f li g htp e n e t r a t i o n i s s u f f i c i e n t l y sm a l l f o r t h e m e a n v e r t ic a l e x t i n c t i o n c o e f f i c i e n t o f w h i t el ig h t t o b e u s e d ( H u t c h i s o n , 1 9 5 7 ) . T h e e x t i n c t i o n c o e f f i c i e n t a n d d i s t r i b u t i o n o f e a c hs u b s t a n c e i n t h e p o n d i s a s s u m e d c o m p l e t e l y m i x e d t h r o u g h o u t t h e e u p h o t i c z o n e a n dv e r t i c a l m i g r a t i o n o f a l g a e o r c o n s u m e r s w i t h i n t h e m i xe d l a y e r a r e i g n o r e d . O n l y 5 0%o f t h e t o t a l l i g h t s p e c t r u m i s a v a i l a b l e f o r p h o t o s y n t h e s i s ( S t r i c k l a n d a n d P a r s o n s ,1 9 6 5 ) . T h e e f f e c t i v e l i g h t ( E L I T ) i s c a l c u l a t e d u s i n g e qn ( 6 ) b e l o w :

E L I T = 0 . 5 0 ( L IT ) e x p [ - - ( E C ) ( D ) ] ( 6 )

R e a e r a t i o nD e p e n d i n g o n w i n d s p e e d , p o n d o x y g e n c o n c e n t r a t i o n a n d w a t e r t e m p e r a t u r e ,

o x y g e n w i ll d i f fu s e t h r o u g h t h e p o n d s u r fa c e , te n d i n g t o m o v e in th e d i r e c ti o n w h i c hw i l l m a i n t a i n t h e p o n d d i s s o lv e d o xy g e n le v e l a t s a t u r a t i o n . T h e o v e r a l l o xy g e nt r a n s f e r c o e f f i c i e n t is s t r o n g l y d e p e n d e n t o n t h e i n t e r f a c e c o n d i t i o n s . A s w i n d s p e e da n d s u r f a c e w a t e r m o v e m e n t i n c r e a s e , p o t e n t i a l c o n v e c t i v e o x y g e n t r a n s f e r i se n h a n c e d a n d t h e o x y g e n t r a n s f e r c o e f f i c i e n t i n c r e a s e s m a n y f o l d ( O d u m , 1 9 5 6 ) . A ne m p i r i c a l r e l a t i o n s h i p b e t w e e n w i n d s p e e d ( W, m / s ) a n d t h e o xy g e n t r a n s f e r c o e f fi -c i e n t ( K L , m / h ) w a s es t ab l is h e d b y B a n k s a n d H e r r e r a ( 1 9 7 7 ) ( e q n ( 7 ) ):

K L = 0 - 0 0 3 6 ( 8 4 3 W ' s - - 3 - 6 7 W + 0 . 4 3 W 2 ) ( 7 )G i v e n t h a t t h e p o r t i o n o f t h e w a t e r c o l u m n u n d e r c o n s i d e r a t io n i s w e l l m i x e d , t h e

c o n t r i b u t i o n o f re a e r a t i o n to t h e p o n d D O l e v el c a n b e d e s c r i b e d a s f o ll o w s :R E = I O 0 0( K L ) ( A R ) ( O S - - O P ) (8 )

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2 5 0 D . I . M E Y E R , D . E . B R U N E

R e a e r a t i o n (R E , m g o x y g e n / h ) is a f u n c t i o n o f t h e o x y g e n t r a n s f e r c o e ff i c ie n t , th es u r f a c e a r e a o f t h e p o n d ( A R , m 2 ) , t h e p o n d d i s s o l v e d o xy g e n l e v e l (OP, m g / l i t e r ) a n dt h e l e v e l o f d i s s ol v e d o xy g e n t h e p o n d w i ll c o n t a i n a t s a t u r a t i o n (O S , m g / l i t e r ) .

Phy toplanktonF a c t o r s i n f l u e n c i n g g r o s s p h y t o p l a n k t o n p r o d u c t i o n r a t e s i n c l u d e p h y t o p l a n k t o n

d e n s i t y , s p e c i e s c o m p o s i t i o n , a g e a n d p h y s i o l o g i c a l s t a g e , a s w e l l a s v a r i a t i o n s i ni n c i d e n t s o l a r ra d i a t i o n , l i g h t a t t e n u a t i o n i n t h e w a t e r c o l u m n , w a t e r t e m p e r a t u r e an dn u t r i e n t c o n d i t i o n s . I n m o d e l i n g t h e e f f e c t o f e n v i r o n m e n t a l f a c t o r s o n t h e r a t e o fp h o t o s y n t h e s i s , o n e o f tw o m a t h e m a t i c a l f u n c t i o n s m a y b e c h o s e n . F o r e x a m p l e ,d e p e n d i n g o n t h e e f f e c t i v e l i g h t i n t e n s i t y , t h e p h o t o p l a n k t o n m a y b e l ig h t l i m i t e d o rp h o t o i n h i b i t e d ; t h e p r o p e r r e s p o n se is s e le c t ed a n d t h e a v e ra g e r a t e o f p h o t o s y n t h e s i so v e r a s p e c i fi e d d e p t h r a n g e is c a l c u l a t e d . G i v e n t h e a v e r a g e r a t e o f p h o t o s y n t h e s i s , t h er a t e o f o x y g e n p r o d u c t i o n d u e t o p h o t o s y n t h e s i s a n d t h e b i o m a s s o f f ix e d p h y t o -p l a n k t o n i s c a l c u l a t e d . T h e c o n t r i b u t i o n o f p h y t o p l a n k t o n t o t h e p o n d DO level ist h e d i f f e re n c e b e t w e e n o x y g e n e v o lv e d t h r o u g h p h o t o s y n t h e s i s a n d t h a t o x y g e n u s e df o r r e s p i r a t i o n . F i r s t , t h e t w o m a j o r e qu a t i o n s m o d e l i n g p h o t o s y n t h e s i s a r e d e s c r i b e d ,i n c l u d i n g t e m p e r a t u r e a n d l i g h t e f f e c t s . P h y t o p l a n k t o n r e s p i r a t i o n f o l l o w s p h o t o -s y n t h e s i s . T h e e qu a t i o n s a r e u s e d t o s i m u l a t e t h e r a t e o f p h o t o s y n t h e s i s ( P , h - ~ ) .S m i t h ' s e qn ( 1 0 ) i s u s e d t o s i m u l a t e p r o d u c t i v i t y a t l o w l i g h t i n t e n s i t i e s w h e r e t h ep h o t o s y n t h e t i c r a t e d e p e n d s l i n e ar l y u p o n t h e l ig h t i n te n s i t y ( S m i t h , 1 9 3 6 ):

( ISL ) (ELIT )P = [ ( IS L) (E LIT) ] o .s ( 1 0 )1 + [ (PM AX)(TMP) 2J

S t e e l e ' s e qn ( 1 1 ) i s u s e d a t l i g h t i n t e n s i t i e s g r e a t e r t h a n t h e v a l u e w h e r e t h e p h o t o -s y n t h e t i c r a t e b e c o m e s l i g h t - s a t u r a t e d (S t e e l e , 1 9 6 2 ) :

(ELIT)(PMAX ) ( TMPe = ( 1 1 )e x p 1

S t e e l e ' s e qu a t i o n i n c l u d e s p h o t o i n h i b i t i o n e f f e c t s a t h i g h l i g h t i n t e n s i t i e s . N e c e s -s a r y p a r a m e t e r s f o r e qn s ( 1 0 ) a n d ( 1 1 ) i n c l u d e t h e l i g h t e x t i n c t i o n c o e f f i c i e n t (EXT,m - l ) , s o l ar r a d i a t i o n i n t e n s i t y a t a g i v e n t i m e (LIT, l y / m i n ) , a n d t h e t e m p e r a t u r em o d i f i e r ( TM P , O < T M P < 1) and use r - spec i f i ed inpu ts w hich a re sp ec ies spec i f i c( m a x i m u m p h o t o s y n t h e t i c r a t e (P M A X, h - l ) , i n i t i a l s l o p e o f t h e p h o t o s y n t h e s i s v e r s u sl i g h t i n t e n s i t y c u r v e (ISL, 1 / h / l y / m i n ) , l i g h t i n t e n s i t y o c c u r r i n g a t th e o n s e t o f p h o t o -i n h i b i t i o n (O P H, l y / m i n ) a n d b o u n d a r i e s o f t h e w a t e r c o l u m n u n d e r c o n s i d e r a ti o n(D 1, D2 , m )) .

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C O M P U T E R M O D E L O F O X Y G E N B E H A V I O R I N A Q U A C U L T U R E P O N D

T h i s a ve r ag e p h o t o s y n t h e t i c r a t e ( A P , h - 1 ) f o r a s i m u l a t e d p o n d s e c t i o n i s:

A P - ( D 2 D r ) P d D1

251

(1 : )

(a ) Tem perature e f fects . T h e r a te o f p h o t o s y n t h e s i s e x h i b i ts a n o n -l i n ea r re s p o n s et o w a t e r t e m p e r a t u r e , a n d t h e r e s p o n se c u r v e is s k e w e d t o t h e r ig h t ( T h o r n t o n a n dL e s s e m , 1 9 7 8) . T h e m a x i m u m t e m p e r a t u r e a n d o p t i m a l t e m p e r a t u r e r a n g e h a v e b e e nu s e d a s p a r a m e t e r s t o m o d i f y t h e c u r v e t o m e e t t h e t e m p e r a t u r e c r i te r ia f o r a g i ve nd o m i n a n t p h y t o p l a n k t o n s p e ci es . A t e m p e r a t u r e m u l t ip l i e r, a d i m e n s io n l e ss n u m b e rb e t w e e n 0 a n d 1 , m o d i f i e s t h e r a t e o f p h o t o s y n t h e s i s . U n d e r o p t i m a l c o n d i t i o n s ,t e m p e r a t u r e d o e s n o t i n h i b i t p h o t o s y n t h e s i s a n d t h e m u l t i p l ie r e qu a l s 1. T h e m u l t i -p l ie r d i m i n is h e s i n v al u e a s t h e w a t e r t e m p e r a t u r e m o v e s a w a y f r o m t h e o p t i m a lt e m p e r a t u r e . T h e m a x i m u m r a t e o f p h o t o s y n t h e s i s is m u l t i p l ie d b y t h e t e m p e r a t u r em u l t i p l i e r t o m o d e l t h i s m a j o r e f f e c t o f t h e a c t u a l r a t e o f p h o t o s y n t h e s i s f o r a g i v e nt i m e p e r i o d i n e qn s ( 1 0 ) a n d ( 1 1 ) .

(b ) Light e fJbcts . L i g h t i s a n o t h e r i m p o r t a n t f a c t o r a f f e c t i n g p h o t o s y n t h e s i s . A tl o w l i g h t i n t e n s i t i e s t h e a b s o r p t i o n o f l ig h t e n e r g y l i m i t s t h e r a t e o f p h o t o s y n t h e s i s ,i n d e p e n d e n t o f t e m p e r a t u r e . T h e r a t e o f p h o t o s y n t h e s i s e x h i b i t s a l i n e a r r e s p o n s e t ol ig h t i n t e n s it y , p r o p o r t i o n a l t o t h e l ig h t a b s o r b e d b y t h e p h o t o s y n t h e t i c p i g m e n t s .A f t e r r e a c h i n g a s p e c i e s - s p e c i f i e d l i g h t l e v e l , t h e r a t e o f p h o t o c h e m i c a l p r o c e s s e se x c e e d s t h e r a te o f e n z y m a t i c r e a c ti o n s a n d t h e r a t e o f p h o t o s y n t h e s i s is n o lo n g e rl i g h t - li m i t e d . T h e m a x i m u m r a t e o f p h o t o s y n t h e s i s , g i v e n n o n - l i g h t l i m i t in g o r l i g h ti n h i b i ti n g c o n d i t i o n s , i s l i m i t e d b y t h e w a t e r t e m p e r a t u r e . I n e xc e e d i n g l y b r i g h t l i g h t,t h e r a te o f p h o t o s y n t h e s i s d e c r ea s e s a s a r es u lt o f t h e p h o t o o x i d a t i o n o f c r it ic a le n z y m e s a n d t h e i n a c t i v a t i o n o f c h l o r o p h y l l ( G r o d e n , 1 9 77 ) . G i v e n t h e i n it ia l sl o p e o ft h e l i n e ar r e s p o n s e o f t h e p h o t o s y n t h e s i s r a t e t o l i g ht i n t e n s it y , t h e m a x i m u m r a t e o fp h o t o s y n t h e s i s a n d t h e l i g h t i n t e n s i t y a t t h e o n s e t o f p h o t o i n h i b i t i o n , a c u r v e m a y b ed e s c r i b e d r e f l e c ti n g t h e r a t e o f p h o t o s y n t h e s i s a g a i n st l ig h t i n t e n s i t y . T h i s f u n c t i o n i sa s s u m e d t o b e c o n s t a n t o v e r d e p t h a n d t i m e , a n d i s i n c o r p o r a t e d i n t o e q n ( 1 0 ) .

(c ) Phytoplankton respirat ion. U s i n g l a b o r a t o r y f r e s h w a t e r c u l t u r e s y s t e m s ,r e s p i r a t i o n r a t e s h a v e b e e n r e c o r d e d i n r e s p o n s e t o p h o t o s y n t h e s i s , p h y t o p l a n k t o ns p e c i e s , w a t e r t e m p e r a t u r e a n d c e l l u l a r s t o r e s . E n d o g e n o u s r e s p i r a t i o n , t h e e n e r g yr e qu i r e d t o m a i n t a i n a c e r t a i n le v e l o f b i o m a s s , i n c r e a s es e xp o n e n t i a l l y w i t h t e m p e r a -t u r e ( W T M P , C ) ( a c c o r d i n g t o R i l e y ( 1 9 4 6 ) a n d A r u g a ( 1 9 6 5 ) ) . J e w e l l a n d M c C a r t y( 1 9 7 1 ) m e a s u r e d t h e i n i t ia l r e s p i r a t i o n r a t e i n t h e i r s t u d y d e a l in g w i t h t h e r a t e a n de x t e n t o f al ga l d e c o m p o s i t i o n . U s in g t h e e x p o n e n t i a l f u n c t i o n b y R i l e y ( 1 9 5 6 ) a n d t h e

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2 5 2 D.I. MEYER, D. E. BRUNEi n i t i a l r e s p i ra t io n b y J e w e l l a n d Mc C a r ty (1 9 71 ) , t h e e n d o g e n e o u s r e s p i ra t io n r a t e(ER) f o r t h e p h y t o p l a n k t o n b io m a ss (PHY, mg / l i t e r ) ca n b e c a lc u la t e d ( e qn (1 5 ) ) :

ER = 0.0012(PHY) e x p ( 0 -0 6 9 ) ( w r M e ) ( 1 5)P h o to re s p i ra t io n , o c c u r r in g d u r in g p h o to s y n th e s i s , i s u s e d i~o o x id iz e o rg a n ic

c o m p o n e n t s , a n d i s a s s u m e d t o b e p r o p o r t i o n a l t o g r o s s p h o t o s y n t h e s i s . E n d o g e n o u sr e s p i r a ti o n a n d p h o t o r e s p i r a t i o n a r e a d d i t iv e i n t h i s m o d e l .

In th e p re s e n t s tu d y , a d ju s t e d f i r s t -o rd e r d e c a y ra t e s w e re u s e d to r e p re s e n t o xy g e nu p t a k e b y d e t r i t a l d e c a y . T h e r a t e o f d e c a y a n d b i o l o g i c a l o x y g e n d e m a n d (BOD)r e q u i r e d f o r d e c a y is d e t e r m i n e d b y t h e t y p e o f m a t t e r d e c a y i n g , t h e m e d i u m i n w h i c hth e d e c a y t a ke s p la c e a n d th e t e m p e ra tu re o f th e m e d iu m . In a ss es sing th e b io lo g ic a lo x y g e n d e m a n d a t t i m e T (BODT) o f e a c h c o m p o n e n t f o r a n a q u a c u l t u r e s y s t e m , th efo l lo w in g fa c to r s h a v e b e e n e s t ima te d : th e qu a n t i ty o f d e c a y in g ma te r i a l p re s e n t ; it su l t i m a t e BOD (BODL, m g O 2 / m g m a t e r ia l ) a n d t h e r a t e o f d e c a y ( K , h - l ) ; an d t h ew a t e r t e m p e r a t u r e (WTMP, C) . D e t r i t a l c o m p o n e n t s i n c l ud e d e c a y i n g p h y t o p l a n k t o n ,u n c o n s u m e d f is h f e e d a n d f i sh w a s t e p r o d u c t s .

T h e d e c a y r a t e c o n s t a n t is a l t er e d ( K 2 , h - l ) , t o a c c o u n t f o r p o n d w a t e r te m p e r a -tu re , i n e q n (1 3 ) . T h e g e n e ral r e l a t io n s h ip d e s c r ib in g f ir s t -o rd e r d e c a y o v e r t ime (T ,d a y s ) i s giv e n in e q n (1 4 ) :

K2 = KI (1 " 0 5 6 ) W T M P - 2 0 ( 1 3 )BODT = BODL(1 -- e x p ( - - T(K))) ( 1 4 )

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

t e m p e r a tu re a n d o xy g e n c o n t e n t , c a rb o n d io x id e le v e l, s iz e o f f i sh , a c t iv i ty a n d p h o to -per iod . Us ing resp i ra t ion f la sks , re sea rchers have been ab le to es tab l ish re la t ionsh ipsa mo n g v a r io u s f a c to r s , a n d min im u m d is so lv ed o xy g e n re qu i re m e n t s a re kn o w n fo rm an y f ish spec ies (Davis, 197 5; Fr y , 1971 ) . Ca tf ish were used as a te s t spec ies fo r thep o n d m o d e l . A n d r e w s a n d M a t s u da ( 1 9 7 5 ) s t u d i ed t h e e f f e c t o f w a t e r t e m p e r a t u r e ,f i sh we igh t and d isso lved ox yg en on f ish resp i ra t io n ; the ca t f ish were s tock ed in 2 -5-md ia m e te r c u l tu re t a n ks to s imu la te p o n d c o n d i t io n s . U sing th e s e d a ta f ro m th ise x p e r i m e n t , B o y d ( 1 9 7 9 ) p e r f o r m e d a m u l t ip l e r e g r es s io n a n d d e v e lo p e d a n e q u a t i o nfo r c a t f i s h r e s p i ra t io n (FR) using fish we ight (FW, g ) , w a t e r t e m p e r a t u r e (WTMP) an dd i ss o lve d o x y g e n (OP,mg 0 2 ) a s v a r ia b les , c o mb in in g th e e f fe c t s o f f e d a n d u n fe d f is h .T h e s e e qu a t io n s a re :

FR = 10x (1 6 )w h e r e :

x = ( - - 0 - 9 9 9 ) - - ( 0 - 0 0 0 9 5 7 ) ( F W ) + ( 6 x 1 0 - 7 ) ( F W ) 2 + (O.0327)(WTMP)- - (8 .7 x I O-6)(WTMP)2 + (3 I O-v)(WTMP)(FW)

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and:C O M P U T E R M O D E L O F O X Y G E N B E H A V I O R I N A Q U A C U L T U R E P O N D 253

( F R O ) ( O P )F R - if D O < 7 .07F R = ( F R O ) i f D O > 7.0

R E S U L T S

When developing the D O flux model, both a component sensitivity analysis and a fielddata verification study were completed. Validity of assumptions and constructs used inmodel development lead to an analysis of areas of emphasis for the development ofa more comprehensive analysis of D O fluctuations, as described in the componentevaluation section.S e n s i t i v i ty a n a l y si s

Holding other parameters constant , the level of cloudiness was varied. As the levelof cloudiness increased, the pond D O decreased. A total cloud cover reduced the ponddissolved oxygen by as much as 2 mg Oz/liter as compared to pond D O on a clear,sunny day. The difference demonstrated the effect of solar radiation on net oxygenproduction by phytoplankton (Fig. 2). The D O trend is similar to that produced ina study on solar radiation effects (Boyd e t a l . , 1978).

A second set of simulation runs were performed to determine how much influencewind would have on the pond D O at different depths, given reaeration as the solecontributor to pond D O (Fig. 3). As the wind speed increased, the time elapsed beforereaching saturation decreased. In all cases, the rate of aeration was greatest when pondD O was furthest from saturation. The effect of the reaeration rate was found to be lesssignificant as pond depth was increased.

A third set of simulation runs looked at component sensitivity, the relative effectsof phytoplankton biomass, wind speed and B O D on pond oxygen conditions over aperiod of 24 h. These three components appeared to have the greatest effect on pondD O ; specific tests and results are described in detail by Meyer (1980).F i e l d v e r i f ic a t i o n

In his study of metabolic rates of pond ecosystems under intensive catfish cultiva-tion, Mezainis (1977) monitored the dissolved oxygen levels at 0-3 m intervals ofdepth every 3 h, for a 24 h period. Concurrent chlorophyll measurements were byAugusto (1975). The catfish pond was located at the Auburn University ExperimentalStation, Alabama, and had an average depth of 1-5 m. Using the data collected byMezainis and Augusto, dissolved oxygen levels from the months of April and Novemberwere simulated. During April, the pond was stratified, and the upper mixed layer (to0.6 m) was simulated. During November the pond was totally mixed and the entire

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2 5 4 13. I . M E Y E R , D . E . B R U N E

E,_ IwbJ. JZwox0c~w> ,0( t )

8

4

l:ig. 2.

C L = 0

C L - - 1 . 0

I I8 0 0 1 6 0 0T I M E O F D A Y ( H O U R S )

The effect of cloudiness on pond oxygen levels.

w a t e r c o l u m n w a s s i m u l a t e d ( t o 1 .5 m ) . D a t a o n s e c c h i d i s k m e a s u r e m e n t s a n d B O Dm e a s u r e m e n t s w e r e i n c o m p l e t e , a n d a fe w in p u t p a r a m e t e r s w e r e e s t i m a t e d .

F i g u r e 4 i l lu s t r a te s t h a t t h e c o m p u t e r m o d e l i s a b l e to s i m u l a t e t h e f ie l d d a t a f o rA p r i l . T h e s o li d li n e r e p r e s e n t s t h e r e s u l t s f ro m t h e c o m p u t e r s i m u l a t i o n . T h e d a s h e dl in e s b o u n d t h e r a ng e o f v a l u e s a t s a m p l i n g s t a t i o n s in th e p o n d . I n t h e m o r n i n g h o u r st h e p o n d d i s s o lv e d o x y g e n i s f a il in g d u e t o t h e p h y t o p l a n k t o n a n d f i sh r e s p i r a ti o n a n dd e t r i t a l d e c a y . F o l l o w i n g s u n r i s e , t h e p o n d DO c o n c e n t r a t i o n i n c r e a s e s a s t h e p h y t o -p l a n k t o n p r o d u c e m o r e o x y g e n t h r o u g h p h o t o s y n t h e s i s t h a n is c o n s u m e d t h r o u g hr e s p i ra t i o n a n d d e c a y . T h e p h y t o p l a n k t o n p h o t o s y n t h e s i s d e cr e a se s a s t h e i n t e n s it y o ft h e s o l a r r a d i a t i o n d e c r e a s e s i n t h e l a t e a f t e r n o o n . N o v e m b e r r e s u l t s ( F i g . 5 ) f o l l o wt h e b a s i c t re n d o f a 2 4 h o x y g e n f l u x a s r e p o r t e d b y M e z a i n is , b u t a r e n o t a s a c c u r a t e

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COMPUTER MODEL OF OXYGEN BEHAVIOR IN AQUACU LTURE POND 255

l o bE- 8-JIJ JIJ J_JZta J> -x0r,,, , , 70

1l m d e p t h

~ 2 m d e p t h

/ ///

J

/ I

/

11 rn ls

6 m / s//// j

/ j J/

1 m l s//

I I I I I10 2 0 3 0 4 0 5 0E L A P S E D T IME (H O U RS )

Fig. 3. The effect of wind speed on pond oxyg en levels.

a t r e p r e s e n t in g t h e d a t a . T h i s d i s c r e p a n c y i s l i k e ly d u e t o t h e f a c t t h a t t h e p o n d m a yn o t h a v e b e e n a s w e l l m i x e d d u r i n g t h i s t im e p e r i o d a s p r e v i o u s l y s u g g e s t ed b yM e z a in i s .Component evaluation

(a ) Solar radiation. T h e s e t o f e q u a t i o n s d e s c r i b i n g s o l a r r a d i a t i o n ( e q n s ( 1 ) - ( 5 ) )a r e b a se d o n a s o u n d t h e o r e t i c a l a n d e x p e r i m e n t a l b a si s, a n d h a v e b e e n a p p l i e d t os o la r r a d i a t io n m o d e l i n g s t u d ie s . T h e s o la r r a d i a t i o n m o d e l is a d e q u a t e , e s p e c ia l l y f o ri t s i n t e n d e d u s e i n t h is m o d e l . I t s im p o r t a n c e l ie s i n t h e f a c t t h a t s o l a r r a d i a t i o n isa f o r c in g f u n c t i o n w h i c h a l lo w s f l e x i b il i t y i n a n a l y z i n g p o n d c o n d i t i o n s t h r o u g h o u tt h e w o r l d .

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256 D . I . M E Y E R , D . E . B R U N E_

Fig. 4.

A \

- - I \S

E I " ,I

- - I - - I I IL l> 6,,,. / / \Z r --/.. _ \t u , " / / - ~" . . . . \~" j l /

. . . . . , , , , , , / \aI .ul ~ "-~, ' ,1/" " - - . . X " /0 J ' f_mo 4

. . . . . 95% Confidence infervols, pond s-14- - C o m p u f e r s i m u l o f i o n

0 4 0 0 1 20 0 2 0 0 0T I M E OF D A Y ( HOU R S )

A comparison of field data collected by M ezainis (for the mo nth o f April) to com putersimulation.

( b ) A t t e n u a t i o n o f so la r r a d ia t io n . T h e m a j o r f a c t o r l i m i ti n g t h e a c c u r a c y o f t h el i gh t a t t e n u a t i o n f u n c t i o n i s t h e e x t i n c t i o n c o e f f i c i e n t . U si n g a r e l a t io n s h i p d e v e l o p e db y P o o l e a n d A t k i n s ( 1 9 2 9 ) , t h e s e c c h i d i s k r e a d i n g is u s e d t o d e t e r m i n e t h e e x t i n c t i o nc o e f f i c i e n t . T h e c o m p o n e n t s a f f e c t i n g t h e s e c c h i d i s k r e a d i n g a r e n o t c o m p a r a b l e f r o mo n e p o n d t o a n o t h e r ( S t e e m a n N i e l s e n , 1 9 7 5 ) . F o r e x a m p l e , t u r b i d i t y c a u s e d b y t h ep r e s e n c e o f c l a y p a r t ic l e s m a y a l t e r t h e l i g h t e x t i n c t i o n c o e f f i c i e n t o f o n e p o n d ;a p h y t o p l a n k t o n p o p u l a t i o n m a y a l te r th e l i gh t e x t i n c t io n c o e f f i c i e n t in a n o t h e r p o n d .S h o r t - t e r m a n s w e r s i n a n y o n e p o n d m a y b e h a n d l e d u s i n g s e c c h i r e a d in g s b e c a u s et h e se c o m p o n e n t s m a y n o t v a r y w i d e ly w i t h a si ng le l o c a t io n . F o r r e s e ar c h a n d ag e n er a l c o m p a r i s o n , f u r t h e r e x p e r i m e n t a t i o n o n f a c t o r s a f f e c ti n g th e e x t i n c t i o nc o e f f i c i e n t is n e c e s sa r y . E a r l y f i el d s tu d i e s b y R i l e y ( 1 9 5 6 ) , L o r e n z e n ( 1 9 7 2 ) a n d

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C O M P U T E R M O D E L O F O X Y G E N B E H A V I O R I N A Q U A C U L T U R E P O N D

1 0 -2 5 7

Fig. 5.

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9 5 0 C o n f i d e n c e i n t e r v o l s , p o n d s - 1 4C o m p u t e r s i m u l o t i o n

6 _ _ / 1 , I I I0 400 1 2 0 0 2 0 0 0

TIME OF DAY ( H O U R S )A comparison o f field data collected b y Mezainis (for the mo nth of November) tocomputer simulation.

S a k a m o t o ( 1 9 6 6 ) e s t a b l i s h e d e m p i r i c a l r e l a t i o n s h i p s b e t w e e n t h e e x t i n c t i o n c o e f f i -c i e n t a n d f a c t o r s s u c h a s c h l o r o p h y l l A a n d i n o r g a n i c a n d o r g a n i c m a t t e r . M a n y s t u d i e sh a v e l i m i t e d a p p l i c a t i o n b e c a u s e t h e l ig h t c o m p a r i s o n d e p t h a n d c h l o r o p h y l l A c o n -c e n t r a t i o n h a v e t o b e m e a s u r e d b e f o r e t h e i n f lu e n c e o f t h e e x t i n c t i o n f a c t o r s c a n b ec a l c u l a t e d .

( c ) Reaeration. T h e r e l a t io n s h i p u s e d t o d e s c ri b e t h e r e a e r a t i o n c o e f f i c i e n t is b a s e do n d a t a f r o m l a r ge , w e l l - m i x e d b o d i e s o f w a t e r . D i r e c t m e a s u r e m e n t s o f r e a e r a t i o n ina q u a c u l t u r e p o n d s ( s m a l le r w a t e r b o d i e s ) is n o t a v a i la b le . T h e i n f l u e n c e o f t h e w i n ds t ir r in g u p s e d i m e n t s a t t h e b o t t o m o f p o n d s a l so n e e d s f u r t h e r i n v e s t ig a t i o n .

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2 5 8 D . I . M E Y E R , D . E . B R U N E(d ) P h y t o p l a n k t o n . T h e e q u a t i o n s d e s c r i b i n g p h y t o p l a n k t o n p h o t o s y n t h e s i s a n d

g r o w t h r e s p o n se s t o t e m p e r a t u r e a n d l ig h t u se th e c u r r e n t s t a t e o f th e a r t a p p r o a c h .U n f o r t u n a t e l y s t u d i e s a d d r e s s i n g s p e c i f i c o c c u r r e n c e s o n a n h o u r l y b a s i s o v e r a 2 4 hp e r i o d a r e s c a r c e a n d e x p e r i m e n t a l d a t a i s d i f f i c u l t t o c o l l e c t a n d i n t e r p r e t . Fa c t o r s inn e e d o f f u r th e r d e v e l o p m e n t i nc l u de p h y t o p l a n k t o n p r o d u c t i o n a n d s in k r a te s . F o re x a m p l e , p h y t o p l a n k t o n r e s p i r a t i o n r a t e s m a y i n c r e a s e e x p o n e n t i a l l y a t h i g h e rt e m p e r a t u r e s . I n t h e l o w e r r a n g e o f t e m p e r a t u r e s a l in e a r a p p r o x i m a t i o n m a y b e m o r erea l i s t i c (Cana le e t a l . , 1 9 76 ) . P r e s e n t l y , a n e xp o n e n t i a l r e s p o n s e c u r v e h a s b e e ni n c o r p o r a t e d i n t o t h e D O f l u x m o d e l .

I n a s i m u l a t io n s t u d y b y G r o d e n ( 1 9 7 7 ) b o t h t h e m a x i m u m t e m p e r a t u r e , i n it ia ls l o p e a n d o n s e t o f i n h i b i t i o n o f t h e p h y t o p l a n k t o n - l i g h t c u r v e a r e c a l c u l a t e d , g i v e n t h ew a t e r t e m p e r a t u r e , o p t i m u m t e m p e r a t u r e a n d m a x i m u m r a t e o f p h o t o s y n t h es i s .A p p l i c a b i l it y o f t h e r e l a t i o n sh i p i s u n k n o w n a n d a c ce s s t o d a t a t h a t m u s t b e s u p p li e db y t h e u s e r is l i m i t e d . H o w e v e r , c o m p o s i t e v a lu e s a v a il ab l e f o r v a r io u s p h y t o p l a n k t o ns p e c i e s t h r o u g h o u t t h e w o r l d a n d i n l a b o r a t o r y s t u d i e s a r e s u m m a r i z e d b y P a r s o n se t a l . ( 1 9 7 7 ) .

A l g a e r e s p o n d t o t h e d a i ly c y c l e o f li g h t i n t e n s i t y a n d w i ll r e a c h t h e i r m a x i m u mr a t e o f p h o t o s y n t h e s i s a t a l ig h t i n t e n s i t y w h i c h is a f u n c t i o n o f t h e d a i l y s o l a r r a d ia -t i o n ( I c h i m u r a , 1 9 6 0 ) . S e a s o n a l s o la r r a d i a ti o n a l so a f f e c t s p h y t o p l a n k t o n p o p u l a t i o n s .A s s e as o n al s o la r r a d i a t io n b e c o m e s p r o n o u n c e d , c e ll u la r c o n c e n t r a t i o n o f c h l o r o p h y l lw i l l v a r y a f f e c t i n g t h e c h l o r o p h y l l t o c a r b o n r a t i o ; a r a t i o w h i c h m u s t b e u s e d t oc o n v e r t f i e ld d a t a t o a m o d e l i n p u t p a r a m e t e r . T h i s r a t io c a n b e s e t b y t h e u s e r t o b es e a s o n - s p e c if i c r e p r e s e n t i n g t h e t i m e o f y e a r u n d e r s t u d y .

T h e p h y t o p l a n k t o n p r o d u c t i o n r a t e i s b a s e d s o le l y o n t h e ra t e o f p h o t o s y n t h e s i sa n d i n c o r p o r a t e s t w o u s e r- s p ec i fi e d r a t i o s : c h l o r o p h y l l A - t o -a l ga e a n d o x y g e n - t o -a l g a e . Va r y i n g e i t h e r w i l l e f f e c t t h e D O f l u x . T h e f i r s t o n e i s u s e d w h e n i n t e r p r e t i n gf ie l d d a t a o n p h y t o p l a n k t o n b i o m a s s , g e n e r al ly r e p o r t e d a s m g c h l o r o p h y l l A / r a g C h .C h l o r o p h y l l A c o n t e n t v a ri e s w i t h t h e l ig h t i n t e n s it y t o w h i c h t h e p h y t o p l a n k t o n a r ea d a p t e d ; i t a l so v a r i es a m o n g s p e c i e s . T h e o xy g e n - t o - a l g a e r a t i o i s b a s e d o n a t h e r m o -d y n a m i c a n a l y si s o f p h o t o s y n t h e s i s a s p r e s e n t e d b y H e n d r i c k s a n d P o t e ( 1 9 7 4 ) .

The a lga l s ink ra te i s a l so a use r - spec i f i ed coef f ic ien t . A lga l decay i s in f luenced byc e ll s i z e , 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 t h e p h y s i o l o g i c a l c o n d i t i o n o f t h e a l ga e . A f e wo f t h e s e f a c t o r s h a v e b e e n d e s c ri b e d q u a n t i ta t i v e l y i n m o d e l s b y D e P i n t o e t a l . ( 1 9 7 6 )a n d C a n a l e e t a l . ( 1 9 7 6 ) . T h e i m p o r t a n c e a n d a c c u r a c y o f t h e m a t h e m a t i c a l r e p r e-s e n t a t i o n h a s n o t b e e n e v a l u a te d i n p o n d s y s t e m s .

( e ) S e d i m e n t o x y g e n d e m a n d . T h e p r o d u c t i o n o f d e c a y i n g m a t e r i a l , t h e u l t i m a t eB O D o f t h a t m a t e r ia l a n d i ts ra t e o f d e c a y d e t e r m i n e t h e B O D o f t h e d e t r i t u s . A c c o r d -i n g t o S c a v i a ( 1 9 79 ) , f i r s t - o r d e r r a t e s r e p r e s e n t a c t u a l d a t a b e t t e r t h a n c o n s t a n t c o e f f i -c i e n ts a l t h o u g h t h e d e c a y r a t e f u n c t i o n h a s n o t b e e n q u a n t i ta t i v e l y v a l i d a te d th r o u g hf i e l d a n d l a b o r a t o r y s t u d i e s . S o u r c e s o f B O D i n c l u d e d i n t h e D O f l u x m o d e l i n c l u d ef is h m a n u r e , u n c o n s u m e d f is h f e e d a n d p h y t o p l a n k t o n d e c a y . T h e u l t i m a t e B O D a n d

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C O M P U T E R M O D E L O F O X Y G E N B E H A V I O R I N A Q U A C U L T U R E P O N D 2 5 9d e c a y r a t e o f e a c h o f t h e s e s o u r c e s a r e n o t w e l l - d e f i n e d a n d n e e d t o b e c l a r i f i e dt h r o u g h e x p e r i m e n t s . A n o t h e r o p t i o n w o u l d b e t o a p p r o a c h th e q u e s t i o n o f d e t r it a lBOD b y s i m u l at in g t h e b a c t e ri a l p o p u l a t i o n f l u c t u a t i o n s i n s t ea d o f a s s u m i n g t h a t t h er a te o f d e c a y r e s p o n d e d o n l y t o t e m p e r a t u r e . T h e p r e s e n c e o f b a c t e r i a a c ti v e i nd e t r i t a l d e c a y p r o c e s s e s is i m p l i c i t i n t h e d e c a y f u n c t i o n .

T h e m o d e l d o e s n o t a c c o u n t f o r t h e l o c a t i o n o f t h e d e t r i ta l m a t e r i a l i n t h e w a t e rc o l u m n , a s w o u l d b e r e qu i r e d t o s t i m u l a t e a s t r a t i fi e d p o n d o r a n o l d e r p o n d w i t hh e a v y s e d i m e n t b u i l d - u p .

D I S C U S S I O N

T h e m o d e l a s p r e s e n t e d u t i li z e s b a s i c p r in c i p l e s c o n c e r n i n g o x y g e n tr a n s f e r , b io l o g i c a lo x y g e n p r o d u c t i o n a n d c o n s u m p t i o n a n d d e g r a d a t i o n o f o r g a n ic m a t t e r . I t c a n b e u s e dw i t h e x p e r i m e n t a l d a t a a n d i n h y p o t h e s i s t e st in g . I t s c o n s t r u c t i o n a n d o p e r a t i o n h a se l u c i d a t e d ke y a r e a s f o r f u t u r e r e s e a r c h , w i t h t h e g o a l o f i n c r ea s i n g i t s a p p l i c a b i l i t y f o ra q u a c u l t u ri s ts , a n d d e v e l op i n g a co h e s iv e m o d e l o f s h o r t t e r m o x y g e n p r o d u c t i o n a sa t o o l f o r s c i e n ti f ic s t u d y . T h e m a j o r c o n s t r u c t s i n t h e m o d e l h a v e b e e n f o r m a l i z e d i no t h e r s t ud i e s o f a q u a t ic s y s t e m s in li m n o l o g y a n d a e r o b ic w a s t e t r e a t m e n t p o n d s i ns a n i t a r y e n g i n e e ri n g . T h i s m o d e l i s a n i n c o r p o r a t i o n a n d s y n t h e s i s o f th e s e c o n s t r u c t s ,a p p l i c a b l e t o a qu a c u l t u r e p o n d s . A r e a s w h e r e a v a i la b l e i n f o r m a t i o n i s t e n t a t i v e h a v eb e c o m e a p p a r e n t , a s e v a l u at e d in t h e p r e v io u s se c t io n . A s h o r t te r m m o d e l e m p h a s i z e sc h a n g e s o c c u r r i n g i n s h o r t t i m e p e r i o d s m i n i m i z i n g t h e s e a s o n a l e f f e c t s o f c h a n g in gc o m p o s i t i o n o f p h y t o p l a n k t o n s p e ci e s, fi sh o x y g e n r e q u i r e m e n t s , s e d i m e n t b u il d -u pa n d w a t e r b a l a n c e .

A m a j o r g o a l i s t o s i m u l a t e p o n d DO d u r i n g i n f r e qu e n t , y e t c r i t i c a l e v e n t s , su c h a sc l o u d y d a y s i n t h e s u m m e r , b l u e - g r e e n al g ae d i e -o f f s a n d w i n d y o r s til l d a y s . O n ec o n d i t i o n w h i c h c a n n o t b e s i m u l a te d p r e s e n t l y i s p o n d d e s t r a ti f ic a t i o n f r o m w i n d a n dt e m p e r a t u r e c h a n g e s. T h e a s s u m p t i o n t h a t t h e h o r i z o n t a l s e c t o r b e in g s i m u l a t e d is w e l lm i x e d l im i t s th e r e p r e s e n t a t i o n o f t h is c o n d i t i o n , b e c a u s e i n fl u e n c e f r o m o t h e r h o r i -z o n t a l s e c t o r s is i g n o r e d . M o d e l i n g a s t ra t i f ie d p o n d a s a s e t o f h o r i z o n t a l s e c t o r s ,w h e r e e a c h s e c t o r i s a s s u m e d w e l l m i x e d a n d w h e r e o n e s e c t o r m a y i n f l u e n c e t h e o t h e r ,m a y c o n t r i b u t e t o a n a c c u r a t e r e p r e s e n t a t i o n o f t h is s y s t e m . M i x in g o f w a t e r i n a p o n dis c a u s e d b y v a r i o u s a d v e c t i o n , d i s p e r s i o n a n d d i f f u s i o n p r o c e s s e s a s w e l l a s c i r c u l a t i o np a t t e r n s . T h e t u r b u l e n c e m a y s t ir u p a n d a e r a t e t h e s u s p e n d e d m a t e r i a l s n e a r t h e s ed i-m e n t - w a t e r i n t e r f a c e i n c r e a s i n g p o n d BOD a n d e n h a n c i n g l i g h t a t t e n u a t i o n . Wi t h t h ei n c o r p o r a t i o n o f a h y d r o d y n a m i c o r m i x i n g s u b m o d e l , th e f o l lo w i n g q u e s ti o n s m a y b ea d d r e s s e d : I s t h e s e d i m e n t l a y e r o f t e n r e s u s p e n d e d i n a p o n d , a e r a t in g th e b e n t h o s ?H o w d o e s t h e c i r c u la t i o n o f a p o n d v a r y w i t h i ts d e p t h ? H o w d o v ar i o u s s t o r m e v e n t so f k n o w n h y d r o d y n a m i c c h a r a c t e r i s t i c s a f f e c t a p o n d ? M o d e l s o f w i n d - g e n e r a t e dc i r c u la t io n h a v e b e e n r e v ie w e d b y B a n k s ( 1 9 7 5 ) .

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2 6 0 D . I . M E Y E R , D . E . B R U N E

W h e n e v a l u a t e d a s a t o o l t o b e u s ed b y t h e f i sh f a r m e r , t h e D O f l u x m o d e l i s i na d e v e l o p m e n t a l s t a g e. T h e la r ge n u m b e r o f i n p u t p a r a m e t e r s c o n t r i b u t e t o t h e f le x i-b i l i t y o f p o n d c o n d i t i o n s , b u t m a k e i t c u m b e r s o m e t o u s e as a d a i ly i n d i c a t o r . H o w -e v e r , m o s t i n p u t s w i l l n o t v a r y w i t h i n a p o n d a n d c o u l d b e s e t a s c o n s t a n t i n p u tv a l u e s t o d e t e r m i n e c o n d i t i o n s w h i c h c o u l d l e a d to c r i t ic a l D O l e v e l s . I m p l i c i t i n t h eu s e o f t h i s m o d e l is a n e e d f o r m o r e e x t e n s i v e f ie l d v e r i f i c a t i o n . A s a r e s e a r c h t o o l ,t h e m o d e l h a s i m p o s e d a m a t h e m a t i c a l f r a m e w o r k f o r c u r r e n t t h e o r i e s a p p l i c ab l e t oD O f l u x . G i v e n t h a t B O D , p h y t o p l a n k t o n a n d w i n d s p e e d h a v e a m a j o r ef f e c t o n t h ep o n d D O . L a b o r a t o r y s t u d ie s w h i c h w i l l s u p p o r t a b e t t e r u n d e r s t a n d i n g o f t h e s ec o m p o n e n t s i s r e c o m m e n d e d .

R E F E R E N C E SAndre w s , G . & B oyd , C . E . (1978) . An e va l ua t i on o f s e c c h i d i sk v is i b i li t y fo r e s t ima t i ng p l a nk t onde ns i t y i n f i sh ponds . H y d r o b i o l o g i a , 6 5 , 6 0 1 , 6 0 8 .Andre ws , J . W. & Ma t suda , Y . (1975) . The i n f l ue nc e o f va r i ous c u l t u re c ond i t i ons on t he oxyge nc onsum pt i on o f C ha nne l c a t f ish . T r a n s . A m e r . F i s h . S o c . , 104 (2 ) , 322 -7 .Aruga , Y . (1965) . Ec o l og i c a l s t ud ie s o f pho t osyn t he s i s a nd ma t t e r p rodu c t i on o f phy t op l a nk t on .I I . P ho t osyn t he s i s o f a l gae i n r e la t i on t o l i gh t i n t e ns i t y a nd t e m pe ra t u re . B o t . M a g ., T o k y o , 78,3 6 0 - 6 5 .Augu s t o , J . A . F . (1975) . E f fe c t s o f i no rga n i c fe r t i l iz a t i on on ph y t op l a nk t o n i n f e d ca t f ish pond .M a s t e r ' s T h e s i s , Aub urn Un i ve r s it y , A l a ba ma .B a nks , R . B . (1975) . S ome fe a t u re s o f wi nd a c t i on on sha l low l a kes . A S C E , E E 5 , 8 1 3 - 2 7 .B a nks , R . B . & H e r re ra , F . F . (1977) . E f fe c t o f wi nd a nd ra i n on su r fa c e r e a e ra t i on . A S C E , E E 3 ,

4 8 9 - 5 0 4 .B oy d , C . E . (1979) . W a t e r Q u a l i t y i n W a r m W a t e r F i s h P o n d s , Craf t Maste r Pr in te rs , Alabama.B oy d , C . E . , R om a i re , R . P . & Johns t on , E . (1978) . P re d i c t ing e ar l y morn i ng d i s so lve d oxyg e nc onc e n t ra t i ons i n c ha nne l c a t fi sh ponds . T r a n s . A m . F i s h S o c . , 1 0 7 , 4 8 4 - 9 2 .B usc h , C . D . , F l oo d , C . A . J r , K oon , J . L . & A l l ison , R . (1977) . M ode l ing c a t fi sh pond n i gh t t imed i s so l ve d oxy ge n l e vel s . T r a n s . A S A E , 20 (2 ) , 394 -6 .C a na l e , R . P ., De P a l m a , L . M. & V oge l , A . H . (1976) . A p l a nk t on -ba se d food w e b mod e l fo r La keMichigan. In: M o d e l i n g B i o c h e m i c a l P r o c e s s e s i n A q u a t i c E c o s y s t e m s , Ann Arbor S c i e nc e ,Mi c h i ga n, pp . 3 3-74 .Da v i s , J. C . (1975) . Mi n i mum d i s so l ve d oxyge n re qu i re me n t s o f a qua t i c l i f e wi t h e mpha s i s onCan adian species: a revie w. J. F i s h . R e s . B o a r d . C a n . , 12 , 2295-333 .De P i n t o , J . W. , B i e rma n , V . J . & V e rho f f , F . H . (1976) . S e a sona l phy t op l a n k t on suc c es s ion as afunc t i on o f spe c i e s c ompe t i t i on fo r phosphorus a nd n i t roge n . In : M o d e l i n g B i o c h e m i c a l P r o-c e ss e s i n A q u a t i c E c o s y s t e m s , Ann Arbor S c i e nc e , Mi c h i gan , pp . 141 -70 .F ry , F . E . J . (1971) . The e f fe c t o f e nv i ronm e n t a l f a c t o r s on t he phys i o l ogy o f f i sh . In : F i s h P h y s i o -l o g y , Ac a de m i c P re ss , Ne w Yo rk , pp . 1 -63 .Grode n , T . W. (1972) . H e a t a n d M a s s T r an sJ er B e t w e e n a W a t e r S u r f a c e a n d t h e A t m o s p h e r e .R e por t No . 0 -6803 , Te nne s se e V a l l e y Au t ho r i t y .Grod e n , T . W. (1977) . M o d e l i n g T e m p e r a t u r e a n d L i g h t A d a p t i o n o f P h y t o p l a n k t o n , R e p o r t N o . 2 ,C e n t e r fo r Ec o l og i c a l Mode l i ng , R e ns sel a er P o l y t e c hn i c In s t i t u t e , N e w York .H e ndr i c ks , D . W. &P o t e , W. D . (1974) . The rm odyn a mi c s a na lys i s o f a p r i ma ry ox i da t i on pond .J . W a t er P o l l u t i o n C o n t r o l F e d e r a t i o n , 46 (2 ) , 333-51 .H u t c h i son , G . E . (1957) . A T r e a ti s e o n L i m n o l o g y , vo t . 1 , John Wi l e y , Ne w York .I c h i mura , S . (1960) , D i u rna l f luc t ua t i ons o f c h l o roph y l l c on t e n t i n la ke wa t e r . B o t . M a g . , T o k y o ,7 3 , 2 1 7 - 2 4 .Je r l ov , N . G . (1968) , O p t i m a l O c e a n o g r a p h y . Elsevie r Ocea nograp hic S er ies , Elsevie r , New York .

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