madenjian 1987 aquacultural-engineering 1

7/28/2019 Madenjian 1987 Aquacultural-Engineering 1

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Aquacultural Engineering 6 (1987) 209-22 5

P r e d i c ti n g N i g h t T i m e D i s s o lv e d O x y g e n L o s s i nP r a w n P o n d s o f H a w a i i: P a r t I I. A N e w M e t h o d

Ch arles P. M adenjian, G ary L. R ogers an d A rlo W. FastHawaii Institute of Marine Biology, U niversity of Hawaii ,PO B ox 1346, Honolulu, Haw aii 96744, U SA

A B S T R A C TDisso lved oxygen concen t ra t ion (DO) , water t empera ture and win d speedwere m o n i t o r ed o ver n ig h t a t p r a w n ( M a c r o b r a c h i u m r o se n b e rg i i) p o n d so f A m o r i e n t A q u a f a r m I n c. ( K a h u k u , O a h u ) a n d a t B r ig h a m Y o u n gUnivers it y -Hawai i (Laie , Oahu) f ro m Ju ne to N ove m ber 1985 . A ne wm o d e l , t h e w h o l e p o n d r e s p ir a t io n -d i ff u s io n (W P R D ) m o d e l , wa sd eve l o p ed t o p r ed i c t p o n d D O a t d a wn . Th e two co m p o n en t s co m p r i s i n gthe mod el were w hole po n d resp iration an d d if fus ion . M od el inpu t si n c lu d e d a m e a s u r e m e n t o f p o n d D O a n d w a t er t em p e r at ur e a t d u sk ,a n o t h er D O a n d t em p er a tu r e m ea s u r em en t m a d e s ever al h o u r s a ft er t h ed u s k m ea s u r em en t , a n d a n e s t im a t e o f t h e aver ag e w i n d s p eed f o r t h en igh t. Fo r a lag o f 3 h be tween the dusk a nd secon d D O measurem ent , them ea n a b s o l u te d ev i a ti o n o f t h e p r ed i c t ed d a w n D O f r o m t h e o b ser vedd a wn D O wa s 0 .4 0 m g 0 2 l i te r - i ( s ta n d a rd er ro r o f m ea n = 0 .8 m g 0 2l iter-1) , bas ed on 40 veri ficat ion trials. The W PR D m od el pe r fo rm edequal ly w el l for bo th ca lm n igh ts (w ind speed < 0"3 m s -1) a nd fo r re la -t ively w indy nights (wind spee d > 7 m s- i ).

I N T R O D U C T I O NT h e a b il it y t o p r e d i c t t h e d i s s o lv e d o x y g e n c o n c e n t r a t i o n ( D O ) a t d a w nin a q u a c u l t u r e p o n d s m a y s e r v e as a v a lu a b l e to o l t o th e f a r m m a n a g e r .B a s e d o n t h e p r e d i c t io n , t h e f a r m e r c a n d e c i d e w h e t h e r o r n o t to e m p l o ye m e r g e n c y a e r a ti o n . C o n s e q u e n t l y , th e m a n a g e r w o u l d a e r a t e o n l y w h e nn e e d e d a n d t h u s r e d u c e t h e f a rm o p e r a t i o n e x p e n s e s w h i l e a t t h e s a m et im e a c h i e v i n g i n te n s iv e p r o d u c t i o n l e v e l s .D e s p i t e c l a i m s o f u n i v e r s a l a p p l i c a b i l i t y ( B o y d et a l . , 1 9 7 8 ; R o m a i r eet a l . , 1 97 8) , t he B o y d - R o m a i r e - J o h n s t o n m o d e l w a s n o t a n a c c u r a te

209Aq.acu lmra l Eng ineer ing 014 4-86 09/8 7/S0 3.50-- Elsevier Applied SciencePublishers Ltd. England. 1 987. Printed in Great B ritain


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21 0 C. P. M adenjian, G. L. Rogers, A . W. Fastd e p i c t i o n o f th e n i g h t t im e D O d e c l in e in p r a w n ( M a c r o b r a c h i u m r o s e n -berg i i ) p o n d s o f H a w a i i ( M a d e n j i a n e t a l ., 1987) . Fu r the rmore , t he l i nea re x t r a p o l a t io n te c h n i q u e e m p l o y e d b y B o y d e t a l . (1978) was unsuccess -f u l a t a c c u r a t e l y f o r e c a s t i n g d a w n D O i n H a w a i i a n p r a w n p o n d s .M a d e n j i a n e t a l . , ( 1 9 8 7 ) p r o p o s e d t h a t a l t h o u g h t h e l o g - li n e a r e x t r a p o l a -t i o n t e c h n i q u e y i e l d e d s u b s t a n t ia l ly m o r e a c c u r a t e p r e d i c t i o n s o f d a w nD O o f p o n d s a t A m o r i e n t A q u a f a r m I nc . ( K a h u ku , O a h u ) t h a n t h e l in e a re x t r a p o l a t i o n p r o c e d u r e , t h e u s e f u l n e s s o f t h e l o g - l i n e a r e x t r a p o l a t i o nt e c h n i q u e w o u l d b e l i m i t e d d u e t o i n s e n s it iv i ty t o w i n d s p e e d . S o m e s it esi n H a w a i i , s u c h a s A m o r i e n t , e x h i b i te d a w i d e r a n g e i n w i n d s p e e d ( f ro mne a r 0 to ov e r 10 m s - i a t 10 m e l eva t ion ) .M e y e r a n d B r u n e ( 1 9 8 2 ) , t h r o u g h s e n si ti v it y a n a ly s is o f a g e n e r a ls i m u l a t i o n m o d e l f o r d i u r n a l o x y g e n f l u c tu a t i o n s i n a q u a c u l t u r e p o n d s ,o b s e r v e d t h a t p h y t o p l a n k t o n b i o m a s s, p o n d B O D ( bi ol og ic a l o x y g e nd e m a n d ) , a n d w i n d s p e e d a p p e a r e d t o h a v e th e g r e a te s t e f fe c t o n p o n dD O . T h e o x y g e n t r a n s f e r c o e ff i ci e n t is d e f in e d a s t h e s p e e d a t w h i c ho x y g e n m o v e s t h r o u g h t h e w a t e r c o l u m n . M e y e r a n d B r u n e u s e d t h ee m p i r i c a l r e l a t io n s h i p e s t a b 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 ) t oes t ima te t he oxyg en t r ans fe r coe f f i c i en t (KL, m h - 1) a s a func t ion o f windspeed (W, m s -a ) . As wind speed inc reases , t he oxygen t r ans fe r coe f f i -c i e n t i n c r e as e s m a n y f o ld . C o n s e q u e n t l y , a g e n e r a l m o d e l f o r p r e d i c t i n gd a w n D O f o r p r a w n p o n d s i n H a w a i i s h o u l d i n c o r p o r a t e a d i f f u s i o nc o m p o n e n t b as e d o n w i n d s p e ed .T h e p u r p o s e o f t h is p a p e r w a s t o p r e s e n t a n e w m o d e l f o r f o r e c a st in gd a w n D O i n H a w a i i a n p r a w n p o n d s a n d t o e v a l u a t e t h e m o d e l ' s p e r -f o r m a n c e . T h e d a t a n e e d e d t o p r e d i c t t h e d a w n D O u s i n g t h i s m o d e li n c l u d e d : ( 1 ) m e a s u r e m e n t o f p o n d D O a n d t e m p e r a t u r e a t d u s k a n dseve ra l hour s a f t e r dusk and (2 ) an e s t ima te o f t he ave rage wind speedf o r t h e n ig h t. T h e p r a w n p o n d m a n a g e r s h o u l d b e a b le t o o b t a i n t h em o d e l i n p u t i n f o r m a t i o n w i t h o u t e x c e ss iv e t im e , e f f o rt , o r e x p e n se . T h u s ,t h e m o d e l s h o u l d s e r v e a s a u s e fu l t o o l to t h e p r a w n p o n d m a n a g e r .

S A M P L I N G M E T H O D SF r o m J u n e t o S e p t e m b e r 1 9 8 5 , 1 5 o v e r n i g h t m o n i t o r i n g t ri p s w e r et r a n s a c t e d a t A m o r i e n t A q u a f a r m I n c. i n K a h u k u . D u r i n g e a c h t ri p , D Oa n d w a t e r t e m p e r a t u r e w e r e m e a s u r e d a t h o u r l y in t e rv a l s f r o m s u n s e tun t i l a f t e r sun r ise (un t il D O s t a r t ed to i nc rease ) a t two s t a t i ons (wes t ande a s t s id e s o f p o n d ) a t e a c h o f t h e t w o p o n d s m o n i t o r e d . T e m p e r a t u r e a n dD O w e r e m e a s u r e d a t t h e s u r f ac e ( a p p r o x im a t e l y 1 0 c m b e l o w s u r fa c e)a n d t h e b o t t o m ( w i t h i n 1 0 c m a b o v e b o t t o m ) a t e a c h s i t e u s i n g a Y S I


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Predicting night t im e D O loss: Part H 211m o d e l 5 4 o x y g e n m e t e r w i t h a f i e l d p r o b e a n d s t i r r e r . S e v e n d i f f e r e n tpo nd s w e re m on i t o red (A 18 , A 19 , D 11 , D 12 , D 13 , D 17 , and D 18 ).

O v e r n i g h t w i n d s p e e d d a t a c o i n c i d i n g w i t h t h e s a m p l i n g t r i p s a tA m o r i e n t w e r e f u r n i s h e d b y t h e H a w a i i N a t u r a l E n e r g y I n s ti tu t e. W i n ds p e e d w a s m e a s u r e d o n c e e v e r y 6 m i n a t a h e ig h t o f 2 4 . 4 m ( at t h eK a h u k u t o w e r ) a b o v e t h e K a h u k u f l a t a p p r o x i m a t e l y 2 k m f r o m t h eA m o r i e n t p o n d s . A n a v e r ag e w i n d s p e e d f o r e a c h s a m p l in g n i g h t w a sc a l cu l a te d . T h e a v e r a g e w i n d s p e e d w a s a d j u s t e d f o r a h e i g h t o f 1 0 ma b o v e t h e p o n d s u r f a ce u s i n g th e f o l lo w i n g r e la t i o n s h i p s u g g e s te d b y T .S c h r o e d e r ( p e r s . c o m m . , M e t e o r o l o g y D e p t . , U n i v . H a w a i i , H o n o l u l u ,HI) :

- = ( 1 )vbw he re va - - w ind ve lo c i ty a t he ig ht a , vb = win d ve loc i ty a t he igh t b , a n d aand b a re t he t w o e l eva t i ons . Th e w i nd ve l oc i ty w as ad j us t ed fo r a he i gh to f 10 m b ecau se t he r e l a t i ons h i p o f the ox ygen t r ans fe r coe f f i c i en t t ow i n d s p e e d w a s e s t a b l is h e d b a s e d o n w i n d s p e e d f o r a 1 0 m e l e v a t i o na b o v e p o n d s u r f a c e .T h e m o d e l w a s a l s o t e s t e d a t a n e n t i r e ly d if f e r e n t l o c a ti o n : t h e p r a w np o n d s a t t h e f a r m o p e r a t e d b y B r i g h a m Y o u n g U n i v e r s i t y - H a w a i iC a m p u s a t L a i e o n O a h u , f r o m O c t o b e r t o N o v e m b e r 1 9 8 5 . F i v es a m p l in g tr ip s w e r e u n d e r t a k e n a n d d u r i n g e a ch t rip , D O a n d t e m p e r a -t u r e w e r e m e a s u r e d a t p o n d s B Y 2 a n d B Y 3 . T w o o r t h r e e s t a t i o n s w e r es a m p l e d a t e a c h o f t h e tw o p o n d s a n d s u rf a ce a n d b o t t o m m e a s u r e m e n t sw e r e p e r f o r m e d . P o n d s w e r e s a m p l e d a t d u s k , a p p r o x i m a t e l y 3 h a f t e rt he dus k sam p l ing , and aga i n j u s t p r i o r t o (w i t h in 30 m i n ) sun r i se . A na v e ra g e D O f o r t h e p o n d w a s a rr iv e d a t b y c o m p u t i n g th e m e a n D O f o re a c h s t a t i o n (b y a v e r a g i n g t h e s u r f ac e a n d b o t t o m o b s e r v a t io n s ) a n d t h e na v e r a g i n g t h e m e a n D O f o r a ll t h e s t at io n s s a m p l e d . A v e r a g e p o n d t e m -p e r a t u r e w a s c a l c u la t e d i n a n a n a l o g o u s m a n n e r t o t h a t f o r a v e r a g e D O .

T h e r e w a s n o w i n d t o w e r c l o s e e n o u g h t o t h e B Y U f a r m p o n d s t op r o v i d e w i n d s p e e d e s t i m a t e s a p p l i c a b l e t o t h e B Y U p o n d s . W e m o n i -t o r e d w i n d s p e e d d u r i n g t h e s a m p l i n g n i g h t s a p p r o x i m a t e l y e v e r y h o u ru s in g a w i n d t u r b i n e m e t er . W i n d s p e e d w a s m e a s u r e d a t a n e l e v a t io n o f2 .5 m a b o v e t h e p o n d s u rf a ce . R e v o l u t i o n s o f th e m e t e r w h e e l w e r er e c o r d e d f o r a m e a s u r e d t im e p e r i o d ( b e t w e e n 5 a n d 1 0 m i n ) a n d w i n dspeed w as ca l cu l a t ed us i ng a ca l i b ra t i on f ac t o r (100 r evo l u t i ons pe r6 8 s = 0 . 4 4 7 m s -~ ) . T h e a v e r a g e w i n d s p e e d w a s t h e n a d j u s te d f o r a ne l eva t i on o f 10 m abov e w a t e r l eve l u s i ng the sam e re l a t i onsh i p p re -sen t ed above .


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21 2 C. P. Ma denf ian , G . L . Rogers , A . W. Fas tT H E M O D E L

T h e m o d e l d e v e l o p e d f o r p r e d i c t i n g n i g h t t i m e D O l o s s i n H a w a i i a np r a w n p o n d s h a s t w o c o m p o n e n t s : t h e w h o l e p o n d r e s p ir a ti o n c o m p o -n e n t a n d t h e d i f f u s io n c o m p o n e n t . W e s h a l l r e f e r to t h e m o d e l a s t h ew h o l e p o n d r e s p i r a ti o n - d i f f u s io n ( o r W P R D ) m o d e l .B o t h c o m p o n e n t s o f t h e m o d e l d e p e n d e d o n t e m p e r a t u r e . W em o d e l e d o v e r n i g h t w a t e r t e m p e r a t u r e a s a n e x p o n e n t i a l d e c a y f u n c t i o nwi th t ime :

T = a e b t (2)wh ere T i s w a te r t em pera tu re ( C), t i s t ime (h ), and a and b a r e cons t an t s( b w a s n e g at iv e ). T h e t e m p e r a t u r e m o n i t o r i n g d a t a f o r A m o r i e n t i n d i-c a t e d t h a t t h e e x p o n e n t i a l d e c a y f u n c t i o n f i t s t h e o b s e r v e d o v e r n i g h tt e m p e r a t u r e c u r v e w e ll. T h e a a n d b c o n s t a n t s c o u l d b e e s t im a t e d f r o mo b s e r v a t i o n s o f t h e p o n d t e m p e r a t u r e a t d u s k a n d s e v e r a l h o u r s l a t e ra n d f r o m t h e t im e s a t w h i c h t h e t e m p e r a t u r e s w e r e o b s e r v e d . S u b st it u t-i n g f o r t i m e a n d t e m p e r a t u r e i n e q n ( 2 ) f o r b o t h t h e d u s k o b s e r v a t i o na n d t h e s e c o n d o b s e r v a t i o n y i e l d e d t w o e q u a t i o n s a n d t w o u n k n o w n s ;thus , a and b cou ld be ca l cu l a t ed .I n a l l o u r a p p l i c a t i o n s o f t h e m o d e l , w a t e r t e m p e r a t u r e d e c r e a s e dm o n o t o n i c a l l y f r o m d u s k t o d a w n . I f t e m p e r a t u r es w e r e t o s o m e h o winc rease (pe rh aps due to f i ll ing o f t he po nd wi th warm wa te r) , the r e l a -t io n s h i p b e t w e e n t e m p e r a t u r e a n d t im e d e s c r i b ed a b o v e w o u l d n o t b eapp ropr i a t e . In such a case , pe rhaps a be t t e r r e l a t i onsh ip wo u ld be :

T = a + b ~ tw h e r e a a n d b a r e c o n s t a n ts .

W ho le pond respirationT h e w h o l e p o n d r e s p i r a t i o n r a t e i n c l u d e d a l l r e s p i r a t i o n o f o r g a n i s m s( in c l u d in g p l a n k t o n , o r g a n i s m s o n s e d i m e n t s , a n d p r a w n s ) a n d c h e m i c a lo x i d a t io n s o c c u rr in g . W e m o d e l e d t h e w h o l e p o n d r e s p i ra t i o n r a te a s a ne x p o n e n t i a l fu n c t i o n o f t e m p e r a t u r e :

W P R = c e k T. (3 )wh ere W PR -- wh o le pon d r e sp i r a t i on r a t e (mg 02 l i t e r - ~h - ~), c= r e sp i r a -t i o n c o n s t a n t ( m g 0 2 l it er -~ h - ~ ), k = i n s t a n t a n e o u s r a te o f i n c r e a se o fr e s p i r a ti o n w i th t e m p e r a t u r e ( C - i ) , T = w a t e r t e m p e r a t u r e ( C ) . k , t h eins t an t an eou s r a t e o f inc rease o f r e sp i r a t i on wi th tem pera tu re , was e s ti -m a t e d f o r p l a n k t o n r e s p i r a ti o n t o b e 0 . 0 5 4 2 f r o m t h e i n c u b a t i o n e x p e r i-


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Pred ic t ing n igh t t ime D O loss: Par t H 213m e n t s ( a t c o n s t a n t t e m p e r a t u r e ) c o n d u c t e d i n e a r li e r s tu d i e s ( M a d e n j i a ne t a L , 1 9 8 7 ). W e a s s u m e d t h a t t h is r a t e o f in c r e a s e w o u l d a p p l y t o t h es e d i m e n t r e s p i r a t i o n r a te . O u r e s t im a t e o f k fo r p l a n k t o n r e s p i r a ti o n f el lw i t h i n t h e r a n g e o f k r e p o r t e d b y E d b e r g a n d H o f s t e n ( 1 9 7 3 ) f o r s e d i -m e n t s a t t e m p e r a t u r e s b e t w e e n 1 5 a n d 3 0 C .N o t e t h a t t h e p r a w n r e s p i r a t i o n w a s a ls o i n c l u d e d i n t h e w h o l e p o n dr e s p i r a t i o n r a t e . C o n s i d e r i n g t h e d e n s i t y o f p r a w n s a t t h e A m o r i e n tp o n d s a n d t h e r e s p i r a t i o n r a t e s r e p o r t e d b y I w a i ( 1 9 7 6 ) a n d S h a r p( 1 9 7 6) , t h e p r a w n c o n t r i b u t i o n t o t h e w h o l e p o n d r e s p i r a ti o n r a te a t t h eA m o r i e n t p o n d s w a s r el at iv e ly u n i m p o r t a n t c o m p a r e d t o s e d i m e n t o rw a t e r r e s p i r a t i o n . N o t e t h a t t h e m o d e l m a y b e a d j u s t e d i n t h e c a s e o fc u l t u r e d o r g a n i s m s f o r w h i c h t h e r e i s a s t r o n g r e l a t i o n s h i p o f r e s p i r a t io nt o b i o m a s s a n d t e m p e r a t u r e a n d w h o s e r e s p i r a ti o n c o n t r i b u t e d s u b s t a n -t ia l ly t o t he w ho le p on d r e sp i r a t i on r a t e . In such a ca se , t he r e sp i r a t i onr a t e o f t h e c u l t u r e d o r g a n is m s c o u l d b e m o d e l e d a s a s e p a r a t e s u b c o m -p o n e n t a n d t h e r e m a i n d e r o f th e w h o l e p o n d r e s p ir a ti o n (t he p l a n k t o na n d s e d i m e n t r e s p i r a t i o n ) w o u l d b e m o d e l e d a s s h o w n i n e q n ( 3 ) . A ne s t im a t e o f t h e p o n d b i o m a s s o f t h e c u l tu r e d o r g a n i s m s w o u l d h a v e t o b efu rn i she d to c a l cu l a t e t he fo recas t s.T h e a p p r o a c h o f m o d e l i n g t h e p o n d r e s p i r a t io n r a t e a s a s in g le e n t it ywas c rude . Ho we ver , a ccu ra t e ( and eas i ly m easu red ) i nd i ca to r s o f p l ank -t o n r e s p i r at io n r a t e w e r e n o t f o u n d f o r H a w a i i a n p ra w n p o n d s ( M a d e n -j i an e t a l . , 1987) . To ou r knowledge , t he re was no r e l i ab l e and eas i lymeasu red ind i ca to r o f s ed imen t r e sp i r a t i on . We used th i s s imp l i f i eda p p r o a c h a n d e v a lu a t ed t h e m o d e l p e r f o r m a n c e .Di f fus i on

T he oxygen t r ans fe r coe f f ic i en t was e s t im a ted by subs t i t u ti ng the ave ragen igh t ly wind speed ( ad jus t ed fo r e l eva t ion o f 10 m) in the r e l a t i onsh ipr e p o r t e d b y B a n k s a n d H e r r e r a ( 1 97 7 ) :

K L = 0 .003 6(8 .43 W t)5 - 3 .67 W + 0 .43 W 2) (4)wh ere K L = oxyg en t r ans fe r coe f f i c ien t (m h -~ ) and W = ave rage n igh t lywind speed a t e l eva t ion o f 10 m a bov e pon d su r f ace (m s - ~).T h e o x y g e n t r a n s f e r c o e ff ic i e n t w a s k e p t c o n s t a n t f o r t h e e n t i re n i g h ta n d c o r r e s p o n d e d t o t h e n ig h t t im e a v e r a g e o f w i n d s p e e d . T h e d i f fu s i o nr a te o f D O i n t o o r o u t o f t h e p o n d w a s a f u n c t i o n o f th e o x y g e n tr a n s f e rc o e f fi c ie n t a n d t h e d e v i a t i o n o f th e p o n d D O f r o m t h e D O l e v el a ts a tu ra t ion . Th e oxygen sa tu ra t ion l eve l fo r f r e shw a te r was a func t ion o fw a t e r t e m p e r a t u r e a n d t h e r e f o r e w e d e s i g n a t e d t h e s a t u r a t i o n l e v e l a sSAT( T ). T he h ighe r t he po nd D O was abo ve the sa tu ra t ion l eve l , t he


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21 4 C. P. Maden]ian, G. L. Rogers, A . W. Fastf a s te r th e r a t e o f d e c l in e i n D O d u e t o d i f f u s io n to w a r d s t h e s a t u r a t io nl ev e l. T h e l o w e r t h e p o n d D O w a s b e l o w s a t u r a t io n , t h e f a s te r th e r a t e o finc rease i n D O du e to d i f fus ion tow ards t he sa tu ra t ion leve l. T he d i ffu -s ion e f f ec t (o r r e - a e ra t ion e f fec t) was desc r ibed a s:

K LD I F = ~-~(~S A T ( T ) - D O ) ( 5 )w h e r e D I F = o x y g e n d i f fu s io n r a te (rag 0 2 l i te r -1 h - l ) , K L = o x y g e nt r ans fe r coe f f i c i en t (m h - 1), PD = ave rage po nd dep th (m) ,SAT( T ) = oxyg en sa tu ra t ion l eve l (mg 02 l i t e r - ~ a t w a te r t em pera tu re , T(*C) an d D O = d i s so lved oxyg en co nc en t r a t i o n (rag 02 l i t e r - 1) o f pond .S a t u r a t i o n l ev e l w a s f o u n d , b a s e d o n w a t e r t e m p e r a t u r e , u s i n g t h e r e l a -t i o n s h i p r e p o r t e d b y t h e A m e r i c a n P u b l i c H e a l t h A s s o c i a t i o n ( 1 9 8 3 ) .A v e r a g e p o n d d e p t h w a s e st i m a t e d to b e 0 . 75 m .C o m p l e t e m o d e lC o m b i n i n g th e w h o l e p o n d r e s p ir a t io n a n d d i ff u si o n c o m p o n e n t s , w ec a n w r i t e th e r a t e o f c h a n g e i n p o n d D O w i t h t i m e (d ( D O ) / d t ) , in m g 0 2l i te r - l h - l) as :

d (D O ) = _ c e ~ r + K L ( S A T ( T ) - D O ) (6)d t P DU s i n g t h e r e l a t i o n s h i p o f t e m p e r a t u r e a s a f u n c t i o n o f t im e , w e h a v e :

= K Ld ( D O ) - ce ~ b ') + - - ( SA T (a e b ' ) - D O )d t P D ( 7 )We de f ine d the r e sp i r a t i on coe f f i c i en t a s a pos i t i ve num ber ; t hus , t henega t ive s ign p re f ixed the who le pond r e sp i r a t i on t e rm in eqns (6 ) and( 7) s in c e t h e w h o l e p o n d r e s p i r a t io n e f fe c t w a s t o d e c r e a s e p o n d D O .M o d e l v e r i f i c a t i o nT h e W P R D m o d e l w a s f i r s t v e r i f i e d u s i n g t h e A m o r i e n t d a t a . P r e d i c -t i o n s o f t h e m o d e l w e r e p r o d u c e d b a s e d o n : ( 1 ) o b s e r v a t i o n s f r o m t h eeas t s ide o f t he pond on ly , (2 ) obse rva t ions f rom the wes t s ide o f t hepond on ly , and (3 ) ave rage o f t he obse rva t ions f rom the wes t and eas ts ides o f po nd ( an ave rage fo r t he pon d ; we wi ll des igna t e t h is s e t as t hep o n d se t). T h e s u r fa c e a n d b o t t o m D O v a l ue s w e r e a v e r a g e d fo r e a c h o ft h e t h r e e se ts o f d at a . F o r e c a st s w e r e p r o d u c e d u s in g t h e d u s k D O a n d


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Predicting night t im e D O loss: Part H 215t e m p e r a t u r e m e a s u r e m e n t s a n d th e D O a n d t e m p e r a t u r e m e a s u r e m e n t sc o n d u c t e d s e v e r a l h o u r s a f t e r d u s k . N o t e t h a t t h e r e s p i r a ti o n c o e f f ic i e n tw as e s t i m a t ed us i ng a num er i ca l ana l ys i s t e chn i que (u s i ng t he secan tm e t h o d , s e e C o n t e a n d d e B o o r , 1 9 7 2 ) , s u c h t h a t t h e p r e d i c t i o n c u r v ew a s f i t t e d t h r o u g h t h e s e c o n d D O o b s e r v a t i o n ( t h e D O m e a s u r e m e n tm a d e s e v e r a l h o u r s a f t e r t h e d u s k D O w a s o b s e r v e d ) . W i t h t h e r e s p i r a -t i on coe f f i c i en t e s t i m a t ed , t he i n t eg ra l o f t he r i gh t -hand s i de o f eqn (7 )w a s t h e n e v a l u a t ed f r o m d u s k t o d a w n ; t h e v a l u e o f t h e i n t e g ra l w a sa d d e d to t h e d u s k D O m e a s u r e m e n t t o y i el d t h e f o r ec a s t of d a w n D O :[ aaw~ d (D O )D O d a w n - - - -D O du s k + - - dt (8)j a~k d tA F O R T R A N c o m p u t e r p r o gr a m , us in g a R u n g e - K u t t a r o u ti n e f ro mt he IM SL L i b ra ry (1982) , w as w r i t t en t o eva l ua t e t he i n t eg ra l i n eqn (8 )a n d p r o d u c e t h e fo r e c a st s . I n a d d i t io n t o t h e fo r e c a s ts o f d a w n D O i n t h ep o n d s , h o u r l y p r e d i c t i o n s w e r e g e n e r a t e d f o r th e n i g h t t im e p e r i o d a n dt h e p r e d i c te d D O c u r v e f o r o v e r n i g h t d e c l in e w a s c o m p a r e d w i t h t h eo b s e r v e d D O c u rv e .S t a t i s t i c s fo r t he abso l u t e va l ues o f t he r e s i dua l s ( t he d i f f e renceb e t w e e n t h e o b s e r v e d a n d p r e d i c t e d d a w n D O ) f r o m t h e a p p li c a ti o n o ft h e W P R D m o d e l t o th e A m o r i e n t d a t a w e r e e x a m i n e d . A t -t es t f o rp a i r e d c o m p a r i s o n w a s p e r f o r m e d o n t h e a b s o l u t e v a l u e o f t h e re s id u a l sf o r t h e W P R D m o d e l a n d t h o s e f o r t h e l o g - l i n e a r e x t r a p o l a t i o n t e c h -n i q u e ( M a d e n j i a n e t a l . , 1987) . A dd i t i ona l l y , t he p red i c t i ons o f daw nD O (f or A m o r i e n t p o n d s ) b y th e W P R D m o d e l w e re re g re ss e d u p o n t h eo b s e r v e d d a w n D O v a lu e s t o s e e h o w c l o se th e s l o p e o f s u c h a li n e w a sc l ose to 1 and ho w c l ose t he i n t e rcep t w as t o 0 .T h e n e t e f f e c t o f d i f f u s i o n o n t h e D O d e c l i n e o b s e r v e d i n t h eA m o r i e n t p o n d s w a s e s t im a t e d i n t h e fo l lo w i n g m a n n e r . T h e d i f f u s io nc o m p o n e n t w a s r e m o v e d f r o m t h e fu l l m o d e l ( t h e f u ll m o d e l w a s g iv e nb~ eqn (7 )) and t he d aw n D O p red i c t i ons w ere g ene ra t ed us i ng the e s t i-m a t e o f t he r e sp i r a t i on coe f f i c i en t f rom t he fu l l m ode l app l i ca t i on . N o t et ha t i n t he fu l l m ode l app l i ca t i on t o e s t i m a t e t he r e sp i r a t i on coe f f i c i en tt h e p r e d i c t i o n c u r v e w a s f i t t e d t h r o u g h t h e o b s e r v e d d a w n D O . T h eo v e r n i g h t n e t e f f e ct o f d if f u s io n w a s d e f i n e d a s t h e p r e d i c t e d d a w n D Of o r t h e d i f f u s i o n l e s s m o d e l s u b t r a c t e d f r o m t h e o b s e r v e d d a w n D O . I fpos i t i ve , t he ne t ove rn i gh t e f f ec t o f d i f fu s i on w as an add i t i on o f D O t ot he pond ; i f nega t i ve , the n e t e f f ec t o f d i ffu s i on w as a l o s s o f D O f romt h e p o n d d u r i n g t h e n i g h t.F o r th e B Y U d a ta , f o re c a st s o f d a w n D O w e r e b a s e d o n p o n d a v e ra g eD O a n d p o n d a v e r a g e t e m p e r a t u r e . P r e d i c t i o n s w e r e c a l c u l a t e d u s i n g


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216 c . P . M adenf ian , G. L . Rogers, A . W. Fas tt h e o b s e r v e d p o n d D O a n d t e m p e r a t u r e a t d u s k a n d t h e p o n d D O a n dt e m p e r a t u r e m e a s u r e d a p p r o x i m a t e l y 3 h la te r , a l o n g w i th t h e a v e r a g en ig h t l y w i n d s p e e d . D a t a w e r e e n t e r e d in to th e F O R T R A N p r o g r a m ,e q n ( 8) w a s s o l v ed , a n d t h e f o r e c a s t s w e r e c o m p u t e d . S t a t i st ic s f o r a b s o -l u te v a lu e s o f t h e r e s id u a l w e r e e x a m i n e d .

R E S U L T ST h e p r e d i c t i o n s o f t h e W P R D m o d e l f o r t h e A m o r i e n t d a t a i m p r o v e d a st h e t im e l a g b e t w e e n t h e d u s k a n d t h e s e c o n d D O m e a s u r e m e n ti n c r e a s e d ( T a b l e 1). A t a l ag o f 3 h o r g r e a t e r , t h e m o d e l p r e d i c t i o n s

T A B L E 1M inimum (Min), M aximum (Max), and M ean Ab solute Value of the Residuals from theW hole Pond Respirat ion-D iffusion (WPRD ) M odel , Using a Dissolved O xygen Con cen-t ra tion (DO) Measurem ent a t Dusk and a D O M easuremen t Approx imate ly 3 h A f te rDusk, Applied to Amorient (Kahuku, Oahu) Data, June to September 1985 (The res i-dual was the obse rved D O minus the pre dicted D O ( in mg O~ l i ter- 1). Lag referred tothe num ber o f hours be tween the t ime o f the D O mea surement at dusk and the t ime o fthe second DO measurement . DO was measured f rom bo th the east and wes t s ides o f thepond; pon d D O was the average D O of the west and east s ide observat ions . S tandarderro r of m ean enclosed in parentheses)

Residu als (m g 02 l i ter - ~)W e s t E a s t P o n d

L a g M i n M a x M e a n M i n M a x M e a n M i n M a x M e a n1 0-0 0 4 .46 1 .12(0.22) 0 .07 5 . 2 8 1 .55(0-31) 0 - 0 3 3 .2 5 1 .01(0.17)2 0-01 3 . 7 2 0 .66(0-15) 0 .0 1 4 .08 0 .93(0.15) 0 .0 1 2 .64 0-68(0.12)3 0 -01 3 .10 0 .39(0 .11) 0 -0 1 3 .3 2 0 .75(0 .15) 0 .00 1 .7 0 0 .41(0-08)4 0 .0 1 2 .08 0 .37(0.08) 0 .07 3 . 7 2 0 .68(0.14) 0 .0 1 1 .7 4 0 .33(0.07)5 0 .0 1 1 .3 3 0 .27(0.05) 0 .02 2 .59 0 .48(0.11) 0 . 0 1 1 .6 3 0 .28(0.06)6 0 .0 2 0 .7 5 0 -2 0(0.0 3) 0 . 0 1 1 . 4 5 0 . 3 4 ( 0 - 0 6 )0 . 0 1 0 -9 2 0 .1 9(0.0 4)

d e v i a t e d f r o m t h e a c t u a l D O , o n a v e r a g e , b y le ss t h a n 0 .5 m g 0 2 l i t e r - t( fo r p o n d D O b a s e d o n a v e r a g e o f D O m e a s u r e d a t e a s t a n d w e s ts t a t i o n s ) .C o n s i d e r t h e ca s e o f p r e d i c t i n g d a w n D O u s in g th e A m o r i e n t d a t ab a s e d o n a d u s k D O ( a n d t e m p e r a t u re ) m e a s u r e m e n t a n d a D O ( an dt e m p e r a t u r e ) m e a s u r e m e n t 3 h a f t e r th e d u s k m e a s u r e m e n t w a s m a d e .


9/17

Predicting night t ime D O loss: Part H 217F o r a la g o f 3 h b e t w e e n D O m e a s u r e m e n t s , t h e W P R D m o d e l , b a s e d o np o n d a v e r a g e D O ( e as t a n d w e s t o b s e r v a t i o n s a v er a g ed ) , u n d e r e s t i m a t e dthe dawn DO in 17 o f 30 t r i a l s (Tab le 2 ) . The ave rage abso lu t e d i f f e r -e n c e b e t w e e n t h e p r e d i c t e d a n d o b s e r v e d D O w a s 0 " 4 1 ; t h e m o d e l , a tw o r st , u n d e r e s t i m a t e d d a w n D O b y 1 .7 0 m g 0 2 l it e r- 1 ( p o n d D 1 2 o n 2 5Ju ly 1985) a nd a t be s t y i e lded a p red i c t i on tha t was e s sen t i a ll y equa l tot h e o b s e r v e d d a w n D O ( p o n d D 1 8 o n 1 4 J u n e 1 9 8 5 ) ( T ab le s 1 a n d 2 ).T h e s l o p e o f t h e r e g r e s s io n li n e f o r p r e d i c t e d D O ( b a se d o n a v e r a g ep o n d D O a n d a 3 h l ag in D O o b s e r v a t i o n s ) a s a f u n c t i o n o f o b s e r v e dD O was no t s ign i f i can tly d i f f e r en t f rom 1 ( s lope - - 1. 04 , s am ple t -s ta ti s-t ic -- 0 . 477 , p = 0 . 6196 ) and the i n t e r cep t was s ign i fi can t ly d i f f e r en t f rom0 in te rce pt = - 0 .44 , sam ple t - sta ti s tic = - 1 .07 , p - - 0 .2941 ) . H enc e ,t h e r e w a s a 1 : 1 c o r r e s p o n d e n c e b e t w e e n p r e d i c t e d a n d o b s e r v e d d a w nD O (no de t ec t ab l e b i a s i n t he p red ic to r ) (F ig . 1 ). T he p red ic t ion s o f theW P R D m o d e l , b a s e d o n p o n d a v e r a g e D O ( a v e r a g e d e a s t a n d w e s to b s e r v a t io n s ) a n d t i m e l ag o f 3 h b e t w e e n t h e d u s k a n d s e c o n d D Oo b s e r v a t i o n , w e r e m o r e a c c u r a t e t h a n t h a t o f th e l o g - l in e a r e x t r a p o l a t i o np r o c e d u r e , a s d e t e r m i n e d b y a t - t e s t f o r p a i r e d c o m p a r i s o n s ( t = 2 . 6 7 ,p - 0 - 0 1 2 4 ) .T h e d i ff u si o n c o m p o n e n t e v a l u a te d f o r p o n d a v e ra g e D O ( fo r la g o f3 h b e t w e e n t h e d u s k a n d s e c o n d D O m e a s u r e m e n t s ) r a n g e d , i n n e te f fec t , f rom a s l igh t overn ight loss of 0"28 mg Oz l i t e r -1 to a ne t over -n igh t ga in o f 5 . 10 m g 0 2 l i te r -1 (Tab le 2 ). O n ave rage fo r t he Am or i en tp o n d s , t h e d i f fu s i o n c o m p o n e n t w a s e s t im a t e d to b e r e s p o n s i b l e f o r a n e tove rn igh t ga in i n D O of 1 . 27 m g 02 l i t e r - 1. In gene ra l , t he ov e rn igh t ga ini n D O d u e t o d i f f u s io n i n c r e a s e d w i th i n c re a s i n g w i n d s p e e d . O v e r n i g h ta v e r a g e w i n d s p e e d a d j u s t e d f o r a n e l e v a t io n o f 1 0 m a b o v e t h e p o n dsur face r anged f rom 4 . 65 to 9"73 m s -~ fo r t he s am pl ing pe r iods a tA m o r i e n t . H o w e v e r , t h e n e t d i f f u s i o n e f fe c t w a s a l so d e p e n d e n t o n t h ed r o p i n D O b e t w e e n t h e t w o D O m e a s u r e m e n t s as w ell a s t h e D O a td u s k . O t h e r f a c t o r s c o n s i d e r e d c o n s t a n t , t h e o v e r n i g h t g a i n i n p o n d D O ,a t t ri b u t a b l e t o d i ff u s io n , i n c r e a s e d a s t h e d e c l i n e i n p o n d D O b e t w e e nd u s k a n d t h e t i m e o f t h e s e c o n d D O o b s e r v a t i o n i n c re a s e d . O t h e r f a c -t o r s c o n s i d e r e d c o n s t a n t, a s D O a t d u s k d e c r e a s e d , t h e o v e r n i g h t g a i n i np o n d D O d u e t o d i ff u s io n i n c r e as e d .T h e p r e d i c t e d D O c u r v e (a v e r ag e p o n d D O b a s e d o n a 3 h la g) f o rp o n d D 17 ( 6 J u n e 1 9 8 5 ) a n d t h e o b s e r v e d D O c u r v e w e r e w e.ll m a t c h e d ;a l t h o u g h t h e r e w e r e s o m e r a n d o m f l u c t u a t i o n s i n t h e o b s e r v e d c u r v ef rom the p red ic t ed cu rve (Fig . 2). D ev ia t ion s f rom the p red ic t ed cu rvew e r e g r e a te s t b e t w e e n 2 0 . 0 0 a n d 2 3 . 0 0 h .F o r t h e B Y U s tu d y , t h e a v e r a g e n ig h t l y w i n d s p e e d e s t im a t e d f o r a ne l e v a t i o n o f 1 0 m a b o v e p o n d s u r f a c e r a n g e d f r o m a p p r o x i m a t e l y 0 t o


10/17

OO

TABLE2

OvaPeceDsovO

C

ao(DaDwfoAoePawP

(K

O

JuoS

emb

.~

1(Pecoweb

owep

repaoduo(WPRmounaDmeuemeadkaas

D

"~

meuemeaomaey3haedkDmeuemeuwap

aa(Daafoovoaeaw

sdop

Tduoee(DnmgOe~whongo(deban

vsgognoDdodu

soTrepaoee(Rnmg0e~)whongooDdorepaoDewfosaosmpnpo

~

De

P

Wn

MeauedD(m0e)

Pedced

Rd

D

R

spd

dwD

(ra0e)

(ms)

(mOeI

Dk3haeDw

dk

6Ju8

D1

68

92

69

42

42

-00

14

64

D1

68

91

79

66

66

00

I3

28

8Ju8

D1

54

15

79

44

32

11

02

74

D1

54

i03

87

68

65

02

-01

34

1Ju8

DI7

72

77

59

33

38

-04

25

69

D1

72

10

85

68

68

00

00

33

2Ju8

DI7

77

98

76

49

51

-01

14

63

D1

77

12

86

67

68

-01

02

37

2Ju8

D7

60

86

47

26

16

09

17

78

D1

60

93

74

59

58!

01

03

37


11/17

P r e d i ct i n g n i g h t i m e D O l oss: P a r t H 2 1 9

t t " , t g ", t ~ , t t " , t t ' )


12/17

2 2 0 C. P. M ade nfian , G. L. Rogers, A. W. Fast

8

C- ) ~ 4

0

Y == - 0 . 4 4 + 1 . 0 4 XR 2 == 0 . 8 6N == 3 0 . ~ "

eO o f =

o

l I0 2 4 6 8O B S E R V E D D O ( r a g 0 2 / I )

F ig . I . P r e d i c t e d v s. o b s e r v e d p o n d D O ( o b s e r v e d p o n d D O r e p r e s e n t e d a n a v e r a g eD O f r o m t h e e a s t a n d w e s t s ta t io n s o f th e p o n d ) a t d a w n f o r A m o r i e n t p o n d s ( K a h u k u ,O a h u ) , J u n e t o S e p t e m b e r 1 9 8 5 . P r e d i c t e d d a w n D O w a s b a s e d o n t h e w h o l e p o n dr e sp i r a t i on - d i f f u s i on ( W PRD ) m o de l , u s ing a 3 h l ag be t w een t he dusk and s eco nd D Om e a s u r e m e n t .

10q ~ OBSERVED DO

DOs0t:])E

0 ea

41900 2200 0100 0400 0700H O U R

F ig . 2 . O b s e r v e d a n d p r e d i c t e d p o n d D O ( o b s e r v e d p o n d D O r e p r e s e n t e d a n a v e r a g eD O f r o m t h e e a s t a n d w e s t s ta t io n s o f th e p o n d ) a t A m o r i e n t p o n d D 17 ( K a h u k u , O a h u )dur i ng t he ni gh t beg i nn i ng on 6 June 1985 . P r ed i c t ed D O w as ba sed on t he WP RDm o d e l , u si ng D O o b s e r v a t io n s a t a p p r o x i m a t e ly 2 0 . 0 0 a n d 2 3 . 0 0 h .

5-34 m s-~. The average absolute deviation of the predicted from theobserved dawn DO at the BYU ponds was 0.37 mg 02 l ite r-' ; the maxi-mum deviation was 0-79 and the minimum was 0.09 mg 02 lit er -' (Table3). The absolute value of the deviation of the model prediction from the


13/17

Pr e d i c t in g n i g h t t i me D O l os s: Pa r t H 221o b s e r v e d d a w n D O r a n g e d f r o m 0 . 1 4 t o 0 . 4 2 d u r i n g t h e l as t t w os a m p l i n g t rip s t o th e B Y U f a rm , d u r in g w h i c h w i n d s p e e d w a s b e l o w 0 . 3m s - ~ ( st ill n i gh t , e s se n t i a l l y n o wi n d ) .

T o i l l u s t r a t e t h e e f f e c t o f w i n d , t h e d e c l i n e o f D O w a s s i m u l a t e d f o rw i n d s p e e d s o f 0 a n d 1 0 m s - ~ . W i th w i n d s p e e d s e t a t 1 0 m s - ~ , D O a t2 0 . 0 0 h w a s s e t to 8 .5 m g O ~ l it e r - ~, D O a t 0 6 . 0 0 h (d a w n ) w a s s e t t o 4 . 5m g 0 2 l i t e r - ~ , a v e r a g e p o n d d e p t h w a s 0 - 7 5 m , a n d t e m p e r a t u r e w a s

T A B L E 3Observed and Predicted Dissolved Oxygen Concentration (DO) at Dawn for B Y UPrawn Ponds (Laie, Oahu), October to November 1985 (Predictions were based onwhole pond respirat ion-diffusion (WPRD) model, using a DO measurement at dusk anda second DO measurement made approximately 3 h after dusk. Date is for start of

sampling period)D a t e P o n d W i n d M e a s u r e d D O P r e di ct ed R e s i d ua ls p e e d ( mg O , l i te r - 9 d a w n D O ( ra g 0 2 l i te r - ~)(m s - i ) (mg 02 l i t e r - J)D u s k 3 h a ft er D a w nd u s k

9 Oct 85 BY2 5.34 7.28 6.84 6.36 6.13 0.22BY3 5.34 12.44 9.84 6.28 5.49 0.7920 Oct 85 BY2 1.91 9.62 8.32 6.31 5.66 0.65

BY3 1.91 9.86 8.37 5.47 5'38 0.0930 Oct 85 BY2 3.71 9.47 8.49 6.61 6.75 - 0.14

BY3 3.71 5.62 5"05 4.99 4.22 0-777 Nov 85 BY2 0.20 5.29 4.64 3.09 3.28 - 0.19

BY3 0.20 10.95 9.41 6.17 6.03 0.1413 Nov 85 BY2 0.07 5.77 5"07 3.16 3-41 -0 .25

BY3 0.07 i0.11 9"00 6.08 6'50 - 0.42

28C a t 20 .00 h and 25C a t 06 .00 h . Th en , u s i ng t he sam e re sp i r a -t i on cons t an t ( s ee eqn (3 ) ) a s fo r t he s i m u l a t i on w i t h w i nd speed a t10 m s - j , aga i n se t t i ng D O a t 20 .00 h t o 8 .5 m g 02 l it e r -~, and aga i nse t t i ng w a t e r t em pera t u re t o 28C a t 20 .00 h and 25C a t 06 .00 h , t heD O d e c l in e w a s s i m u l a te d u s in g a w i n d s p e e d o f 0 m s -~ . T h e D Odec l i ne fo r the w i nd l e s s n i gh t w as nea r l y l inea r , w h e reas t he D O dec l i new a s m a r k e d l y c u r v e d d u r i n g t h e w i n d y n i g h t ( w in d s p e e d o f 1 0 m s - ~ )(F i g . 3 ) . The daw n D O fo r t he w i nd l e s s s i m u l a t i on w as 0 .98 m g O zl i t e r - ~; t hus the ne t d i f fus ion e f fec t was 3 .52 m g 02 l i t e r -


14/17

2 2 2 C. P. M aden jian, G. L. Rogers, A. W. Fast

0E

v

0 3Q

01900

% . , %.. 10 m/s% .",~ , . .0...m./.s. . . .

i i2200 0100 0400 0700

HOURFi g . 3 . S i m u l a t ed D O n i gh t t i m e dec l i ne i n a p r aw n pon d f o r w i nd speeds o f 0 and1 0 m s - t. W h o l e p o n d r e s p i ra t i o n r a t e a n d w a t e r t e m p e r a t u r e d u r i n g th e w i n d y n ig h tequa l l ed t he w ho l e pond r e sp i r a t i on r a t e and w a t e r t em pe r a t u r e du r i ng t he w i nd l e s snight. See t ex t for descr ip t io n .

D I S C U S S I O NT h e W P R D m o d e l a c c u r at e ly f o r e ca s te d d a w n D O a t A m o r i e n t a n dB Y U p o n d s . T h e m o d e l w a s v a l i d a t e d f o r a w i d e r a n g e o f : w h o l e p o n dr e s p i r a t io n r a t e , d u s k D O , a n d w i n d sp e e d . T h e d i f fu s i o n c o m p o n e n tb a s e d o n w i n d s p e e d w a s a n im p o r t a n t c o m p o n e n t o f t h e m o d el.T h e m o d e l p e r f o r m e d w e l l f o r th e h i g h e r w i n d s p e e d s ( g r e a te r th a n 7m s - t ) a t th e A m o r i e n t p o n d s a n d p e r f o r m e d w e ll f o r th e s ti ll n i g h ts(w i nd speed < 0 .3 m s - t) a t t he B Y U fa rm . O n ave rage , the fo recas t s o ft h e W P R D m o d e l w e r e r e l a ti v e ly a c c u r a t e f o r t h e m o d e r a t e w i n d s p e e d s.T h e t h r e e f o re c a s t s ( b a s e d o n a v e r a g e p o n d D O f o r 3 h s p a n b e t w e e nt h e t w o D O m e a s u r e m e n t s ) w h i c h d e v ia t e d m o r e t h a n 1 m g 0 2 l it e r- 1f r o m t h e o b s er v e d p o n d D O a t d a w n c o r r e s p o n d e d to n ig h ts o f m o d e r -a te w i n d s p e e d ( a v e ra g e w i n d s p e e d b e t w e e n 4 a n d 7 m s - t , f o r 1 0 me l eva t i on ) . Som e o f t he a s sum pt i ons o f t he w ho l e pond re sp i r a t i on com -p o n e n t ( s u ch a s th e e q u a l a n d c o n s t a n t i n s t a n t a n e o u s r a te s o f i n c r e a se o fr e s p i r a t i o n w i t h t e m p e r a t u r e f o r p l a n k t o n , s e d i m e n t , a n d t h e p r a w n s )m a y n o t h a v e b e e n c l o s el y a d h e r e d t o in t h e s e c as e s.

N o t e t h a t t h e m o d e l i n g o f r e s p i r a ti o n r a t e a s so l e ly d e p e n d e n t o nw a t e r t em per a t u re w as a s i m p l i fi ca ti on ; w h o l e pond re sp i r a t i on r a t e m ayh a v e b e e n c h a n g i n g i n r e s p o n s e t o u n a c c o u n t e d f a ct o rs . A n o t h e r e x p la -n a t i o n m a y i n v o l v e t h e r e l a ti o n s h i p o f w i n d s p e e d w i t h t h e p o n d h y d r o -


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Predicting n ight tim e D O loss: Part H 223d y n a m i c s . P e r h a p s t h e p a t t e r n o f c ir c u l a ti o n a n d m i x i n g o f w a t e rt h r o u g h o u t t h e p o n d d e p e n d e d o n w i n d s p e e d . T h e c i r c u l a t i o n p a t t e r n so f m o d e r a t e w i n d s p e e d m a y b e su c h t h a t t h e a v e r a g e p o n d D O e s ti -m a t e d b y m e a s u r i n g D O a t th e s a m p l i n g s t a ti o n s o f th e p o n d m a y t e n d t od e v ia t e m o r e f r o m t h e t ru e a v e r a g e p o n d D O t h a n w h e n w i n d w a s st ro n go r w e a k . T h e l a r g e r t h e d e v i a t i o n o f t h e m e a s u r e d p o n d D O f r o m t h et r u e p o n d D O , t h e g r e a t e r t h e c h a n c e o f r e la t iv e l y l a rg e d e v i a t io n o f th ep r e d i c t e d D O f r o m t h e a c t u a l p o n d D O a t d a w n . A n o t h e r e x p l a n a t i o nm a y b e t h a t t h e u n e x p l a i n e d v a r i a t i o n i n t h e t r a n s f e r c o e f f i c i e n t a b o u tt h e r e g r e ss i o n r e l a ti o n e s ta b 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 ) m a y b eg r e a t e r f o r m o d e r a t e w i n d s p e e d t h a n f o r s t r o n g o r w e a k w i nd s .T h e p o n d w a t e r m i x i n g m a y a l s o h a v e p a r t i a l l y e x p l a i n e d t h er e a s o n f o r i n c r e a s e d a c c u r a c y o f t h e f o r e c a s t w i t h i n c r e a s i n g t i m e l a gb e t w e e n t h e tw o D O m e a s u r e m e n t s . S l ig h t d i s c r e p a n c ie s b e t w e e n t h eo b s e r v e d a v e r a g e D O a n d t h e t r u e a v e r a g e p o n d D O , d u e t o p o n dh y d r o d y n a m i c s , w o u l d h a v e l e d t o g r e a t e r e r r o r i n t h e f o r e c a s t o f d a w nD O a s t h e t i m e s p a n b e t w e e n t h e t w o D O o b s e r v a t i o n s d e c r e a s e d . O fcourse , an i nc rease i n t he t i m e l ag co r re sponded t o a dec rease i n l eadt i m e o f t he fo recas t . Tha t i s , a s t he t i m e span be t w een t he dusk D Oo b s e r v a t i o n a n d t h e s e c o n d D O o b s e r v a t i o n i n c r e a s e d , w e d i d n o t h a v et o fo recas t a s f a r i n t o t he fu t u re t o p red i c t daw n D O . W e expec t ed t ha tt he fu r t he r i n t o t he fu t u re w e p red i c t ed , t he m ore l ike l y an i naccu ra t ep r e d i c ti o n . A n o t h e r f a c t o r t o c o n s i d e r w a s t h a t a s th e t i m e l ag b e t w e e nt h e t w o D O m e a s u r e m e n t s i n c r e a s e d , w e e x p e c t e d a m o r e a c c u r a t ees t i m a t e o f t he r e sp i r a t i on coe f f i c i en t because t he sam pl i ng du ra t i oni nc rease d w i t h i nc reas i ng t im e lag.M o d e l i n g t h e p o n d w a t e r m i x in g w o u l d , in d e e d , b e t e d i o u s a n df a c t o r s s u c h a s w i n d s p e e d a n d p o n d m o r p h o m e t r y w o u l d h a v e t o b econs i de red . Inc l us i on o f po nd w a t e r m i x i ng i n a m ode l t o p red i c td a w n D O w o u l d a l m o s t u n d o u b t e d l y b e i m p r a c t i c a l f o r t h e p r a w n p o n dm a n a g e r .W e r e c o m m e n d e d t h a t t h e s e c o n d D O m e a s u r e m e n t b e t a k e n a b o t i t3 h a f t e r t h e d u s k D O o f t h e p o n d w a s o b s e r v e d . A n e v e n l o n g e r w a i tw o u l d y i e l d m o r e a c c u r a t e f o r e c a s ts o f d a w n D O i n t h e p o n d s . H o w e v e r ,t he t im e d e l a y b e t w e e n u n d e r t a k i n g th e D O m e a s u r e m e n t s m u s t b eb a l a n c e d b y t h e n e e d f o r t im e t o c a r r y o u t r e m e d i a l a c t io n i n th e e v e n t o ffo recas t s o f a po t en t i a l l y ' dange rous l y l ow ' daw n D O . I f t he t im e l agb e t w e e n t h e tw o D O m e a s u r e m e n t s w a s to o l o n g , t h e r e w o u l d b e in s u ff i-c i e n t ti m e t o p l a n f o r o r a p p l y e m e r g e n c y a e r a t i o n p r o c e d u r e s .W e r e c o m m e n d e d t h a t a t le a s t t w o s t a ti o n s o n t h e p o n d ( s uc h as th ee a s t a n d w e s t s i d e s o f t h e p o n d ) b e s a m p l e d f o r D O a n d t e m p e r a t u r e ,w i t h s u r f a c e a n d b o t t o m o b s e r v a t i o n s m a d e . O n a v e r a g e f o r t h e A m o r -


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22 4 C. P. M ade njian , G. L. Rogers, A. W. Fasti e n t p o n d s , t h e f o r e c a s ts b a s e d o n j u s t th e w e s t si d e o f t h e p o n d w e r ere l a ti ve ly accu ra t e ( even s l igh t ly m ore accu ra t e t han fo recas t s based ont h e w e s t a n d e a s t o b s e r v a t i o n s a v e r a g e d ) . H o w e v e r , i t a p p e a r e d t h a tt h e r e w o u l d b e a g r e a t e r r is k o f t h e d a w n D O b e i n g s u b st a n ti a ll y u n d e r -e s t i m a t e d w h e n t h e f o r e c a s t i s b a s e d o n j u s t a n o b s e r v a t i o n f r o m o n es a m p l i n g s t a t io n o n t h e p o n d .

S U M M A R YT h e w h o l e p o n d r e s p i r a ti o n - d i f fu s i o n ( W P R D ) m o d e l y i e ld e d a cc u r at ep r e d i c t i o n s o f d a w n D O a t t h e p o n d s o f A m o r i e n t ( K a h u k u ) a n d t h eB Y U f a r m ( L a ie ) o n O a h u , H a w a i i. T h e m o d e l w as v a l id a t e d f o r a w i d er a n g e o f w i n d s p e e d s f r o m n e a r z e r o t o a p p r o x i m a t e l y 1 0 m s - ~. A p p a r -e n tl y , d i f fu s i o n o f o x y g e n in t o t h e p o n d s a t A m o r i e n t w a s a n i m p o r t a n tf a c t o r f o r t h e n i g h t t i m e D O d e c l i n e o b s e r v e d . F o r e ca s ts w e r e b a s e d o n am e a s u r e m e n t o f d u sk D O a n d t e m p e r a t u r e a n d a d e t e r m i n a t io n o f p o n dD O a n d t e m p e r a t u r e s e v e r al h o u r s a f t e r d u s k . A n e s t im a t e o f t h e a v e r-a g e o v e r n i g h t w i n d s p e e d ( a t e l e v a t i o n o f 1 0 m a b o v e p o n d s u rf a ce ) a ls oh a d t o b e f u r n is h e d . W e r e c o m m e n d e d a d e l a y o f a t le a s t 3 h b e t w e e n t h ed u s k a n d t h e s e c o n d D O d e t e r m i n a t i o n s . W e s u s p e c t e d t h a t s a m p l i n gD O f r o m a t le a s t t w o d i f f e re n t s t a ti o n s o n t h e p o n d w o u l d d e c r e a s e t h ec h a n c e s o f a s u b s ta n t i a l u n d e r - o r o v e r e s t i m a t i o n o f d a w n D O a s c o m -p a r e d t o a f o r e c a s t b a s e d o n D O o b s e r v e d a t j u s t o n e s t a t io n o n t h ep o n d .

A C K N O W L E D G E M E N T SG e r a l d A k i y a m a i s g r a t e f u l l y a c k n o w l e d g e d f o r h i s s a g e a d v i c e o no p e r a t i o n a n d m a i n t e n a n c e o f t h e e q u i p m e n t . D a n M c K e n n a o f t h eM e t e o r o l o g y D e p t , U n i v e r s it y o f H a w a i i , k i n d l y lo a n e d u s a w i n d m e t e r.D a r w i n B o h n e t a ss i st e d w i th fi el d w o r k a t th e B Y U f a r m s it e a n d h e l p e di n t h e m a n u s c r i p t p r e p a r a t i o n . T h a n k s t o K e n K a m i y a , m a n a g e r o f t h eB Y U f ar m , a n d E d M c S w e e n y, m a n a g e r o f th e A m o r i e n t f ar m , f o r th e i rc o o p e r a t i o n . T h i s w o r k i s a r e s u l t o f r e s e a r c h ( ' D e v e l o p m e n t o f P o n dO x y g e n M a n a g e m e n t D e v i c e s a n d P r e d i c ti v e P r o c e d u r e s f o r In c r e a s i n gP r a w n P r o d u c t i o n ' p r o je c t , A / R - 1 9 ) s p o n s o r e d , i n p a rt , b y t h e U n i v e r s i tyo f H a w a i i S e a G r a n t C o l l e g e P r o g r a m u n d e r I n s t i t u ti o n a l G r a n t N o .N A 8 1 A A - D - 0 0 0 7 0 f ro m N O A A , O f fic e o f S ea G r an t , D e p a r t m e n t o fC o m m e r c e ; a n d s p o n s o r e d , i n p a r t , b y t h e A q u a c u l t u r a l D e v e l o p m e n tP r o g r a m o f H a w a i i ( C o n t r a c t N o . 1 7 6 6 3 ) . T h i s i s S e a G r a n t p u b l i c a t io n


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Predicting night time D O loss: Part H 225U N I H I - S E A G R A N T - J C - 8 7 - 0 5 a n d H a w a i i I ns ti tu te o f M a r in e B io lo g yC o n t r i b u t i o n N o . 7 27 .

R E F E R E N C E SA m e r i c a n P u b l ic H e a l t h A s s o c i a t io n ( 1 9 83 ). Standard Me thods f or t he Exam i -nat ion o f W ater an d Wastewater ( 1 6 t h E d n ) , A P H A , A W W A , W P C EW a s h in g to n D C .Ban k s , R . B . & H er r e r a , E E ( 1 9 7 7 ). E f f ec t o f w in d an d r a in o n su r f ace r eae r a -t ion. A S C E , E E 3 , 4 8 9 - 5 0 4 .Bo y d , C . E . , Ro m a i r e , R . E & Jo h n s to n , E . ( 1 9 7 8 ) . P r ed ic t in g ea r ly m o r n in g

d i s so lv ed o x y g en co n cen t r a t io n s in ch an n e l ca t f i sh p o n d s . Trans. A m . Fish.Soc., 1 0 7 , 4 8 4 - 9 2 .Co nte , S . D. & d e B oor , C. (1972) . Elementary Num er icaIAnaly si s: A n A lgor it h -mic Approach , M c G r a w - H i l l, N e w Y o r k .Ed b e r g , N . & Van Ho f s t en , B . ( 1 9 7 3 ) . Ox y g en u p tak e o f b o t to m sed im en t ss tu d ied in situ an d in th e l ab o r a to r y . W ater Res., 7 , 1 2 8 5 - 9 4 .I MSL ( 1 9 8 2 ) . IM SL L ibrary Re fe rence M anua l ( 9 th Ed n ) , I n t e r n a t io n a l M a th e -ma t ica l & Sta t is t ica l L ibrar ies Inc . , H ous ton .Iwai , T . Y. J r . (1976) . Energy t ransformat ion and nu t r ien t ass imi la t ion by thef r e s h w a t e r p r a w n Macrobrachium rosenbergi i u n d e r co n t r o l l ed l ab o r a to r yco n d i t io n s , M Sc . Th es i s , Un iv . Hawa i i .M aden j ian , C. E , R ogers , G . L . & Fast , A. W . (1987) . Pred ic t ing n igh t t im e d is-so lv ed o x y g en loss i n Haw a i i an p r aw n p o n d s : Pa r t I . Ev a lu a t io n o f t rad i t io n a lm e t h o d s . Aquacultural Engineering, 6 , 1 9 1 - 2 0 8 .M ey e r , D . I . & . Br u n e , D . E . ( 1 9 8 2 ). C o m p u te r m o d e l in g o f t h e d iu r n a l o x y g enleve ls in a s t i l lwater aqu acu l tu re po nd . Aquacultural Engineering, 1 , 2 4 5 - 6 1 .Ro m aire , R. E , Boy d , C. E . & Col l i s , W .J . (1978) . Pred ic t ing n igh t t ime d is-so lved oxygen de c l ine in pon ds used fo r t i lap ia cu l tu re . Trans. A m . Fish. Soc.,1 0 7 , 8 0 4 - 8 .Sharp , J . (1976) . S ec t ion I. Ef fec ts o f d isso lved oxygen , tem pera tu re , and we igh to n r e sp i r a t io n o f Macrobrachium rosenbergi i , In : Labora to ry s tud ies on

se lec ted n u t r i t iona l , physica l, and chem ica l fac to rs e f fec t ing the g row th , su r -v iva l , r esp i ra t ion , and b ioenerge t ics o f the g ian t p rawn, Macrobrachiumrosenbergii, A. W . Knigh t , Water Sc i. and Eng . P aper4 501 , U niv. Calif ., D avis.

madenjian 1987 aquacultural-engineering 1

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