R. P. Canale S. Nachiappan D. J. Hineman H. E. Allen

Canale, R. P. MICHIGAN SEA GRANT REPRINT---- --------- MICHU-SG-75-304 A DYNAMIC MODEL FOR PHYTOPLANKTON PRODUCTION IN GRAND TRAVERSE RAY R. P. Canale S. Nachiappan D. J. Hineman H. E. Allen Reprinted from Proceedings 16th Conference on Great Lakes Research 1973:21-23. International Association for G reat Lakes Research K. -------- ^O R \ SV*

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Proc. 16th Conf. Great Lakes Res. 1973: 21-33. Internat. Assoc. Great Lakes Res. A DYNAMIC MODEL FOR PHYTOPLANKTON PRODUCTION IN GRAND TRAVERSE BAY R. P. C anale, S. N achiappan, D. J. H inem an and H. E. A llen D ep a rtm e n t o f C ivil E n g in e erin g, Sea G rant P ro g ra m and In stitu te o f E n v iro n m en ta l and In d u stria l H ealth, U n iversity o f M ichigan, A n n A r b o r, M ichigan A b s tr a c t. The seasonal dynamics of dissolved and particulate phosphorus, particulate nitrogen and organic nitrogen, ammonia, nitrate, silica, chlorophyll a and total zooplankton have been modeled in the lower part of the west arm of Grand Traverse Bay. The models are based on mass continuity equations and account for water movements, chemical and biological reactions and outside nutrient inputs. The model predictions compare favorably with data obtained during 50 separate Sea Grant field surveys. The model has been used to forecast the water quality in the Bay which will result from likely patterns of residential, commercial and industrial growth and varying degrees of phosphorus control in the Traverse City area. (Key words: Phytoplankton; seasonal dynamics; mass continuity equations; Grand Traverse Bay). INTRODUCTION F o r the p a s t th re e y e a r s r e s e a r c h e r s su p p o rted by the U n iv ersity of M ich i gan S ea G rant P ro g ra m have conducted ex ten siv e lim n o lo g ical fie ld su rv e y s in both a r m s of G rand T ra v e r s e B ay. T h ese su rv e y s have included o b se rv a tio n s of s e v e ra l p h y sic al, ch e m ic al and b io lo g ica l c h a r a c te r is tic s of th e B ay. The m a jo r goal of th is fie ld -sa m p lin g p ro g ra m h as been to pro v id e d a ta w hich can be u se d to guide the c o n stru c tio n of m a th e m a tic a l m odels w hich quantify the in te ra c tio n s am ong the v a ria b le s. Subsequent to v e rific a tio n, th e m odels a r e in tended to be used to p re d ic t th e w a te r q u ality w hich r e s u lts fro m d iffe re n t p o l lution co n tro l sc h e m e s and a lte rn a te p a tte rn s of land use in the T ra v e r s e C ity a re a. T h is p re d ic tiv e cap ab ility w ill fa c ilita te the adaption of ra tio n a l w a te r q u ality co n tro l p ro g ra m s desig n ed to m ain tain the re la tiv e ly high q u ality of Bay w a te rs. O th er e ffo rts in th e p ro g ra m have re s u lte d in h y d ro lo g ical m odels (B ra te r 1972), m odels fo r w a te r c irc u la tio n (Sm ith 1973)1 and m odels fo r co lifo rm b a c te ria (C anale and G reen 1972; C anale 1973). T h is p a p e r r e p o r ts on the u tilizatio n of Sea G ran t field d a ta fo r th e c o n stru c tio n, v e rific a tio n and ap p lic a tio n of a dynam ic m odel fo r phytoplankton, n u trie n ts and zooplankton in th e lo w er w est a rm of G rand T ra v e r s e Bay. SAMPLING PROGRAM D ata g a th e re d through the fie ld sa m p lin g p ro g ra m have been co lle c te d on m o re than 50 c ru is e s sin c e in itiatio n of the p ro g ra m in Ju ly 1970. D uring the f ir s t sta g e s of the p ro g ra m 13 o p e n -w a te r sta tio n s w ere sam p led on a ro u tin e b a s is and 18 of the c r u is e s w ere m ade to sam p le ch em ical c h a r a c te r is tic s of Bay tr ib u ta rie s. A m odified sam p lin g schem e w as in stitu te d in Ja n u a ry 1972 to p ro v id e g r e a te r focus on th e w est a rm of the Bay. F ig u re 1 d isp la y s the lo c a tio n of th e sam pling sta tio n s c u rre n tly u sed a s w ell a s th e co n figuration of the s ix - c e ll m odel. The m e a su re d p a r a m e te r s w hich a r e d ire c tly co m p ared w ith m odel r e s u lts a re lis te d in T able 1, along w ith m ethods of a n a ly sis and e r r o r e s tim a te s. A dditional d e ta ils re g a rd in g the handling and sto ra g e of sa m p le s 1Smith, E. B. "Dissertation in progress" (Ph.D. thesis, University of Michigan, Ann Arbor, Michigan, 1973).

22 CANALE, NACHIAPPAN, HINEMAN and A LLEN TABLE 1. M easured param eters during field and modeling study of T raverse Bay, analytical methods and estim ated e rro r by analysis. P aram eter Number of Stations Number of Observations Analytical Method' Ammonia 18 142 Phenolhypochlorite n o 2- no3 18 146 Copperized Cadmium Reduction Total Dissolved P 18 130 Ascorbic Acid (persulfate digestion) Particulate P 18 130 Ascorbic Acid (persulfate digestion) Silica - Sj 18 146 Silicomolybdenum Blue 95% Confidence Limit on Analytical E rro r ± 15% ± 20% ± 10% ± 20% ± 10% Chlorophyll a 18 117 Fluorom etric ± 10% Zooplankton 9 36 D irect Count ± 5% FIG. 1. Circulation pattern, sampling stations and segmentation of the six-cell model. p r io r to a n a ly sis and the an a ly tic tech n iq u es a re d is cu sse d in a U n iv ersity of M ichigan S ea G rant R ep o rt (1973). P a r a m e te r s sam pled a t so m e point in the field p ro g ra m, but not u sed d ire c tly in the c u rre n t m odel, include co n serv ativ e ions, heavy m e ta ls, D.O., ph, alk alin ity, conductivity, b enthos o rg a n ism s and s u rfic ia l sed im en t c h e m is try. The r e s u lts of th e se a n a ly se s a re m ain tain ed in a co m p u ter file fo r convenient re tr ie v a l. The d ata obtained d u rin g th is p ro g ra m have supported the m odeling activ ity in th re e d iffe ren t w ays. The f ir s t use h a s been to aid in m odel constru c tio n through th e q u an tification of co efficien ts in the m odel. An exam ple is the u se of light m e a su re m e n ts at v a rio u s d epths to obtain r e g re s s io n e s tim a te s of the light in te n sity extinction coe fficien t. T he second u se of the d a ta h a s been to p ro v id e in p u ts to the model,- sp e c ific a lly sy ste m loadings and in itia l conditions. It h as been d e te rm in e d fro m the d a ta th a t th e B o ard m an R iv er and th e u p p er Bay a re the m a jo r c o n trib u to rs

MODEL FOR PHYTOPLANKTON PRODUCTION 23 to the low er w est a rm. B oardm an loadings have b een e stim a te d u sing U. S. G eological S urvey d isc h a rg e d ata and c o n c e n tra tio n s at the R iv er m outh. Conc e n tra tio n s at the upper boundary of the s ix - c e ll sy ste m have been a ssu m e d to be re p re s e n ta tiv e of the u pper B ay. The fie ld d a ta have also been u tiliz e d in v e rific a tio n of the m odel. By co m p arin g m o d e l-g e n e ra te d co n c e n tra tio n s with c o n c e n tra tio n s at sta tio n s in the in te r io r of the s ix - c e ll m odel, it is p o ssib le to a s s e s s th e ability of the m odel to p re d ic t re a l-w o rld conditions. In all c a s e s the d a ta p re s e n te d h e re a r e c o m p o site s of all ap p licab le d ata co llecte d d u ring the two and o n e-h a lf y e a r s of the sam p lin g p ro g ra m. F u rth e r m o re, sin ce it h as been assu m ed in th e p re s e n t m odel th a t each of the six se g m en ts is u n ifo rm, it is n e c e s s a ry to u se d e p th -a v e ra g e d d ata fo r input and v e r i fic a tio n p u rp o ses fo r a ll v a ria b le s except p rim a ry p ro d u ctiv ity. T h is does not a p p e a r to be a se rio u s lim ita tio n sin c e s ta tis tic a l a n a ly sis of the fie ld d a ta a s re p o rte d by C anale et al. (1973) fa ile d to show sig n ific an t v a ria tio n s o v e r depth fo r the o th e r p a r a m e te r s of in te re s t. MODELING METHODOLOGY A m odel is d e s ire d w hich can be u se d to c a lc u la te th e sp a tia l and te m p o ra l d istrib u tio n of d isso lv ed and p a rtic u la te p h o sp h o ru s, p a rtic u la te n itro g e n, d is solved o rg an ic n itro g en, am m onia, n itra te, s ilic a, to ta l alg ae and to ta l zooplankton. T he assu m ed in te ra c tio n s am ong th e se v a ria b le s a s in c o rp o ra te d into the m a th e m a tic a l m odel a re illu s tr a te d in F ig. 2. T he se a so n a l dynam ics of each of th e se v a ria b le s can be d e te rm in e d at a num b er of lo c atio n s w ithin the Bay by the in te g ra tio n of m a ss continuity equatio n s w hich account fo r changes due to tr a n s p o rt by w a te r m ovem en ts, grow th, d ecom p o sitio n, b io lo g ical uptake, ex change w ith Lake M ichigan and d ire c t input fro m th e B o ard m an R iv e r. The b a s ic eq u atio n s w hich c o m p rise the m odel a re developed by tak in g m a ss b a la n c e s fo r the v a rio u s m odel c o n stitu e n ts about u n ifo rm c e lls. A sy ste m of c e lls coupled by ad v ectiv e and d is p e rs iv e flow s s im u la te s the e ffe c ts of w ate r c irc u la tio n, w hile s o u rc e s and sin k s w ithin a c e ll r e p r e s e n t th e effe c ts of ch e m ic al and b io lo g ical re a c tio n. A m a te ria l b alan ce eq u atio n fo r the ith ch em ical o r b io lo g ical FIG. 2. Environmental inputs and system interactions.

24 CANALE, NACHIAPPAN, HINEMAN and A LLEN sp e c ie s about the j th volum e elem en t can be w ritte n as: dcij Vj - 5T = + V5Si j Wij (1) w h ere C y is the co n c en tra tio n of sp e c ie s i in segm en t j, w here Vj is th e volum e of se g m en t j, w h ere Jjj is the net flux of sp e c ie s i into seg m en t j, w here A j is the in te rfa c ia l a r e a of the j 1-11 segm en t, w h ere S ^ is the su m m atio n of s o u rc e s and sin k s of sp e c ie s i in seg m en t j w hich a re a sso c ia te d w ith v a rio u s b io lo g ical, ch e m ic al, and p h y sic al re a c tio n s, w h ere Wtj r e p r e s e n ts the d ire c t input of sp e c ie s i into seg m en t j and w here t is tim e. Fluid. T ra n sp o rt The p h y sic a l tr a n s p o r t of sp e c ie s due to flu id m ovem ents is re p re s e n te d by flux te rm s in Eq. 1. Sm ith (1973)1 h a s developed a n u m e ric a l m odel fo r w a te r c irc u la tio n in G rand T ra v e r s e Bay by n u m e ric a lly in te g ra tin g lin e a riz e d eq u atio n s of m otion fo r th is sy ste m. T h is c irc u la tio n m odel g iv es tra n s ie n t, depth a v e rag ed flow s in re sp o n se to fo rc in g fro m w inds. The g e n e ra l fe a tu re s of th is m odel have b een te s te d a g a in st fie ld o b se rv a tio n s by M onahan e t al. (1973). The r e s u lts of the n u m e ric a l c irc u la tio n m odel have been adapted to d e fine ty p ic a l ad v ectiv e and d is p e rs iv e flux te r m s in Eq. 1. The m agnitude and d ire c tio n of th e se te rm s a re shown in F ig. 1 and re p re s e n t the c irc u la tio n p a t te rn s w hich develop in the Bay a fte r th re e h o u rs of fo rc in g by 1 0 -m ile s -p e r- hour southw est w inds. E x ten siv e field o b se rv a tio n s and n u m e ric a l calc u latio n s of w a te r m ovem ents su g g est th at th is c irc u la tio n is roughly s im ila r to the r e sp o n se of th e low er w est a rm of the Bay u n d er a v a rie ty of ty p ical wind fo rc in g s. P hytoplankton The accu m u latio n o r d epletion of phytoplankton is governed by the m ech a n ism s of fluid tra n s p o r t, grow th, r e s p ira tio n, p re d a tio n by zooplankton, sinking and input fro m e ith e r the u p p er Bay o r th e B o ard m an R iv e r. Although the actu al phytoplankton population can be re p re s e n te d by n u m e ro u s m e a su re s, it h a s been convenient to ap p ro x im ate the population p re s e n t by the co n cen tratio n of chloro p h y ll a, w hich is denoted by P. The continuity of phytoplankton chlorophyll a in the jth se g m en t is defined by: dp j V3 ^ r = JP 3A J + Vj [G PJ (T,I,N j) - D pj (T) - Cg (T.P j JZj JPj + Wpj (2) In Eq. 2 the grow th of the phytoplankton is a ssu m e d p ro p o rtio n a l to the concentra tio n of phytoplankton and an o v e ra ll grow th co efficient, G pj. The grow th coe fficien t is a function of the te m p e ra tu re, T; sunlight in te n sity, I; photoperiod; and n u trie n t co n c e n tra tio n s, N<. T he influence of light on the grow th of the phytoplankton is f u rth e r dependent on v e rtic a l light ex tin ctio n and se lf-sh a d in g e ffe c ts. The d isa p p e a ra n c e of phytoplankton due to ex c re tio n, re s p ira tio n and sinking is also c o n sid e re d p ro p o rtio n a l to the c o n c en tra tio n of phytoplankton and is re p re s e n te d by a te m p e ra tu re -d e p e n d e n t o v e ra ll death coefficient, D p j. The r a te of phytoplankton d ep letio n due to zooplankton p red a tio n is assu m ed to be p ro p o rtio n a l to th e p ro d u ct of the phytoplankton co n cen tratio n, the zooplankton c o n c e n tra tio n and the g ra z in g r a te, C g. The g ra z in g r a te is a function of te m p e ra tu re and th e phytoplankton co n cen tratio n. T he rem a in in g te rm s in Eq. 2,

MODEL FOR PHYTOPLANKTON PRODUCTION 25 Jp- and W p j, r e p re s e n t th e phytoplankton flux and input c o n trib u tio n s to the r a te of change of the phytoplankton c o n c en tra tio n. Z ooplankton C hanges in the zooplankton c o n c en tra tio n can be d e s c rib e d by a s im ila r m a s s b alan c e equation fo r the j th segm en t: dzj d T = JZ ja j + Vj [GZj (T >p P - D Zj (T )]Z j + W Zj (3) w here the zooplankton population is m e a su re d a s the n u m b e r of individual o r g a n is m s /lite r. The o v e ra ll grow th r a te of th e zooplankton is p ro p o rtio n a l to th e c o n c en tra tio n of zooplankton and an o v e ra ll grow th ra te co efficient, GZj. The grow th r a te co efficient is dependent on th e zooplankton g ra z in g r a te and the phytoplankton ab so rp tio n efficien cy of th e zooplankton, a s w ell a s on the te m p e r a tu re and th e c o n c en tra tio n of phytoplankton. The d ep letio n of zooplankton is a ssu m e d p ro p o rtio n a l to th e c o n c en tra tio n of zooplankton and an o v e ra ll te m p e r a tu re dependent death r a te co e ffic ie n t, DZj, w hich acco u n ts fo r re s p ira tio n and p re d a tio n by o th e r e le m e n ts in the food w eb. The zooplankton flux and input te rm s a re given by J Zj and W Zj in Eq. 3. N u trie n ts T he im p o rta n t algal n u trie n ts in T ra v e r s e B ay a re b eliev e d to b e s ilic a, n itro g e n and p h o sp h o ru s. T h ese e le m e n ts m ay o c c u r in in o rg an ic, o rg an ic, soluble o r p a rtic u la te fo rm. F u rth e rm o re, in o rg an ic fo rm s m ay a p p e a r w ith a l te rn a te s ta te s of oxidation; fo r ex am p le, in o rg an ic n itro g e n m ay o ccur a s a m - m onia, n itr ite o r n itra te. The m a s s b alan c e eq u atio n s fo r each of th e se nutr ie n ts in v o lv es th e th re e m e ch a n ism s a s d is c u s s e d in Eq. 1. A m a ss b alan ce eq u atio n fo r the in o rg an ic fo rm of each of th e n u trie n ts in segm en t j can be w ritte n a s : dnj v! S T ' J NjA l -»HPGPjP i v) * r on m ONjVj + W, (4) w h ere Nj is th e c o n c e n tra tio n of in o rg an ic n u trie n t and ONj is the c o n c en tra tio n of the soluble o rg a n ic fo rm of the n u trie n t. In Eq. 4 n u trie n t u tiliz a tio n by the phytoplankton is r e la te d to the phytoplankton grow th by a sto ic h io m e tric c o n v e r sio n fa c to r, a N P, w h ere a NP is the g ra m s of n u trie n t re q u ire d p e r g ra m of new phytoplankton p ro d u ced. N u trien t re g e n e ra tio n is a ssu m e d to be p ro p o rtio n a l to th e c o n c en tra tio n of the soluble o rg a n ic fo rm and a te m p e ra tu re dependent re g e n e ra tio n r a te co efficient, R ON (T). T he flux and input of n u trie n ts a re in -. eluded th rough the J Nj and WNj te rm s. In th is c a s e the input te rm s include p o ssib le e ffe c ts of sed im e n t re g e n e ra tio n. E quation 4 h a s been m odified to account fo r lo s s e s o r g ain s due to th e oxidation and red u c tio n fo r the c a s e of am m o n ia and n itra te. A m a s s b alan c e fo r th e soluble o rg an ic fo rm of th e n u trie n ts in the j 1*1 se g m en t can be w ritte n in the fo rm : don. VJ "dt - W ) - r o n W O N jv, * E j (T.Pj, z p v j * W0N 1. (5) In Eq. 5 the s o u rc e s of soluble o rg an ic n u trie n ts due to e x c re tio n, zooplankton g ra z in g and h y d ro ly sis of p a rtic u la te n u trie n t fo rm s a r e ex p licitly included in

26 CANALE, NACHIAPPAN, HINEMAN and A LLEN the te rm E j w hich is a function of te m p e ra tu re and the phytoplankton and zooplankton co n c en tra tio n. A d e ta ile d d is c u ssio n and d eriv a tio n of th e se and o th e r equatio n s and a s su m p tio n s im p lic it in the m odel is given by C anale e t al. (1973). The developm ent of s im ila r eq u atio n s w as f ir s t d e s c rib e d by D it oro et al. (1971). The d y n am ics of the b eh av io r of the c h e m ic al and b io lo g ical s p e c ie s in the m odel a re obtained by u sing m e a su re d p a tte rn s of n u trie n t inputs fro m the B o ard m an R iv er and the u p p er Bay and o b se rv e d c y c le s of te m p e ra tu re, s o la r ra d ia tio n, p h o to p erio d and v e rtic a l light ex tin ctio n in the m odel. F o rty -e ig h t n o n lin e ar d iffe re n tia l equatio n s w ith tim e v a ria b le coefficients, re p re s e n tin g the continuity of eight sp e c ie s in six se g m en ts a r e c o n stru c te d s im ila r to Eq. 2, 3, 4 and 5. T h ese m a s s continuity equatio n s can th en be in te g ra te d n u m e rically u sin g a n u m b er of d iffe re n t n u m e ric a l in te g ra tio n a lg o rith m s. T h ese m ethods include f o u rth -o rd e r v a ria b le s te p -s iz e R u n g e-k u tta sc h em e s and v a ria b le ste p - s iz e, v a ria b le o r d e r p r e d ic to r - c o r r e c to r sc h e m e s of the A dam s type. T h is la tte r m ethod h a s p ro v en to be v ery efficien t and re lia b le and has been u sed to obtain th e r e s u lts p re s e n te d in the next se ctio n. MODEL VERIFICATION AND DISCUSSION The k in e tic and sto ic h io m e tric co e ffic ie n ts in th e phytoplankton m odel have b ee n obtained by exam ination of the r e s u lts of co n tro lled la b o ra to ry and field in v e stig a tio n s a s re p o rte d in the sc ie n tific lite r a tu r e. T he d eriv a tio n of th e se co efficient v alu es have been d is cu sse d in d e tail by C anale e t al. g (1973). F ig u re 3 show s the m odelp re d ic te d se a so n a l cycle of phytoplankton, zooplankton and n u trie n ts ^ 3 in c e ll no. 3 b ased on av e rag e ^.o v a lu e s of m odel co efficien ts and a v e ra g e n u trie n t loading. A ll the 5 _ c u rv e s show n in F ig. 3 r e p r e s e n t th e ex p ected d e p th -a v e ra g e d r e s u lts ex cep t fo r the p rim a ry p ro d u ctiv ity w hich h a s been ca lc u lated u sing m o d e l-p re d ic te d r e s u lts at depths of two and tw enty m e te rs. T he c y c le s show n in F ig. 3 a p p e ar re a so n a b le and a re in g e n e ra l a g re e m e n t with fie ld o b se rv a tio n s. In o rd e r to f u rth e r e v a lu a te th e adequacy of the m odel to re p ro d u c e the se a so n a l v a ria tio n of of the sy ste m v a ria b le s, th e solution of the fo rty -e ig h t d iffe re n tia l eq u a tio n s h a s been co m p ared to depthav e ra g e d field o b se rv a tio n s taken o v e r a p e rio d of two y e a r s. In th is c a se two m odel p re d ic tio n s have been m ade using an upper and low er bound on the m e a su re d inputs fro m the B oardm an R iv er and th e upper FIG. 3. Predicted seasonal cycles of biological chemical species in cell 3. an(j Bay. F ig u re s 4-10 show a co m p a rison of the m odel p re d ic tio n s fo r

M ODEL FO R PHYTOPLANKTON PRODUCTION FIG. 4. Predicted chlorophyll a and field data. FIG. 5. Predicted zooplankton and field data.

CANALE, NACHIAPPAN, HINEMAN and A LLEN FIG. 6. Predicted ammonia and field data. FIG. 7. Predicted nitrate-nitrite and field data.

MODEL FOR PHYTOPLANKTON PRODUCTION FIG. 8. Predicted soluble phosphorus and field data.

CANALE, NACHIAPPAN, HINEMAN and A LLEN FIG. 10. Predicted primary productivity and field data. ch lo ro p h y ll a, zooplankton, am m onia, n itra te, silic a, soluble phosp h o ru s and p rim a ry p ro d u ctiv ity and the field data. Although the m odel does not ex actly fit a ll the d a ta p re se n te d in F ig s. 4, 5, 6, 7, 8, 9 and 10, th e g e n e ra l a g re e m e n t betw een the level and tre n d of the d ata and th e m odel is encouraging. It is not p o ssib le to com pletely explain the d ev iatio n betw een the m odel and c e rta in d a ta p o in ts. Som e of th e d eviation is undoubtedly due to a n a ly tic a l e r r o r s o r the n a tu ra l h etero g en e ity of the sy ste m, s in c e in som e c a s e s s e v e ra l n earb y sta tio n s w ere co m p ared w ith the sa m e m odel output. Som e d ev iatio n betw een the m odel and th e d ata could r e s u lt fro m the adaption of in a p p ro p ria te p a r a m e te r v a lu e s. H ow ever, no attem p t w as m ade to u se fo rm a l s e a rc h te ch n iq u e s fo r optim um p a ra m e te r v alu es. D iffe re n ce s b e tw een the m odel and the d a ta a r is e a s a consequence of the need to tim e a v e ra g e inputs on a se a so n a l b a s is. T hus, s h o r t- te r m flu ctu atio n s due to phenom ena such a s v a ria b le cloud c o v e r, ra in fa lls and c irc u la tio n tra n s ie n ts a re not accounted fo r in the m odel. Although an in itia l v erific a tio n of the m odel has b een achieved, it se e m s obvious th a t m o re c a re fu l te stin g of the m a th em atical p re d ic tio n s w ill re q u ire a m o re ex ten siv e fie ld o b se rv a tio n p ro g ra m. D uring the sp rin g and su m m e r of 1973 it is planned to sa m p le eight Bay w a te r sta tio n s and the input to the Bay e v e ry th re e to fo u r d ay s. T h is expanded fie ld p ro g ra m should guide the addition of fu rth e r re fin e m e n ts to th e m odel. APPLICATION The v e rifie d m odel h a s been used to p re d ic t the effects of population grow th and p h o sp h o ru s re m o v a l on th e q u ality of w a te r in the B ay. F ig u re s 11 and 12 show p ro je c te d le v e ls of phytoplankton ch lo ro p h y ll a, zooplankton, soluble p h o sp h o ru s and s ilic a a s expected u n d er d iffe re n t pollution co n tro l and grow th conditio n s. T h re e c a s e s a re co m p ared w ith p re s e n t conditions in th e se fig u re s.

M ODEL FOR PHY TO PLA N KTO N PRODUCTION 31 FIG. 11. Projected phytoplankton chlorophyll a and zooplankton levels under four alternative loading conditions. The f ir s t exam ple a s su m e s sta b le population, in d u stria l and a g ric u ltu ra l activ ity and a 90% d e c re a s e in p h o sp h o ru s inputs due to m o re strin g e n t c o n tro l. The second and th ird ex a m p le s a ssu m e an in c re a s e in re s id e n tia l population fro m 22,000 to 88,000, a tw o-fold in c re a s e in the r e c re a tio n a l and in d u stria l a c tiv ity, and a sta b le a g ric u ltu ra l p ro d u ctio n. The p o llutional e ffe c ts of th is expansion is exam ined u n d er conditio n s w ith 80% p h o sp h o ru s re m o v a l and w ithout p h osphorus input c o n tro ls. The p re d ic te d populations of phytoplankton and zooplankton u n d er p re s e n t conditio n s and 90% p h o sp h o ru s re m o v a l a r e only slig h tly low er than th e popula tio n s o b se rv e d in the Bay. T h ese r e s u lts r e fle c t the fa c t th at the m a jo r so u rc e of n u trie n ts to the low er p a r t of the w est a rm of the Bay is the U pper Bay r a th e r than the B o ard m an R iv e r. H ow ever, a s the R iv e r loads in c re a s e fo u r-fo ld, th e se inputs becom e m o re sig n ifican t re su ltin g in a p p ro x im ate ly tw o fold in c re a s e s in the peak plankton p o p u latio n s. T his n o n lin e ar re la tio n betw een c u ltu ra l n u trie n t inputs and plankton populations is an u n an ticip ated r e s u lt as su g g e sted by the m odel and is ex p e cted to be a unique c h a r a c te ris tic fo r a given n a tu ra l w ate r body. F ig u re 12 show s the ex p ected se a so n a l p a tte rn s of soluble p h o sp h o ru s and s ilic a. It is in te re s tin g to note th a t a t th e h ig h e st loading the s ilic a b ecom e s grow th lim itin g fo r d ia to m s re s u ltin g in high re s id u a l p h o sp h o ru s le v e ls. T h is situ atio n of c o u rse would not p e r s is t in th e B ay. R a th e r, th e s ilic a lim ita tio n would lead to a sh ift in the sp e c ie s co m p o sitio n of the phytoplankton fro m

32 CANALE, NACHIAPPAN, HINEMAN and A LLEN Present Conditions Projected Conditions Present Conditions with 901fc P Removal Projected Conditions with 8TO P Removal 120 180 240 300 360 TIM E (DAYS) FIG. 12. Projected soluble phosphorus and silica levels under four alternative loading conditions. d ia to m s to g re e n s and b lu e g re e n s. S im ila r s p e c ie s ch an g es due to s ilic a lim i ta tio n have b een re p o rte d by S chelske and S to e rm e r (1972) in low er Lake M ichigan. SUMMARY AND CONCLUSIONS F o r the p a s t th re e y e a r s r e s e a r c h e r s su p p o rted by the U n iv ersity of M ichigan S ea G rant P ro g ra m have conducted ex ten siv e fie ld su rv e y s in both a rm s of G rand T ra v e r s e B ay. T h ese su rv e y s have included o b se rv a tio n s of s e v e ra l p h y sic a l, ch e m ic al and b io lo g ica l c h a r a c te r is tic s of the B ay. A m a jo r goal of th is field sa m p lin g p ro g ra m h as been to p ro v id e d a ta w hich can be u se d to cons tr u c t m a th em atical m o d e ls which specify in te ra c tio n s am ong th e v a ria b le s. S ubsequent to v e rific a tio n, the m odels a r e intended to be used to p re d ic t c e rta in m e a s u re s of w a te r q u ality w hich re s u lt fro m v a rio u s pollution c o n tro l sc h e m e s and a lte rn a te p a tte r n s of la n d -u se zoning. T h is p a p e r h a s re p o rte d on the u tilizatio n of th e se d a ta fo r the co n stru c tio n, v e rific a tio n and ap p licatio n of a dynam ic m odel fo r phytoplankton in th e lo w er w est a rm of G rand T ra v e r s e Bay. T he m odel h a s b een used to calc u la te th e sp a tia l and te m p o ra l d is trib u tio n of d isso lv e d and p a rtic u la te p h o sphorus, p a rtic u la te n itro g e n, am m onia, n itra te, s ilic a, ch lo ro p h y ll a and to ta l zooplankton. The se a so n a l d y n am ics of

M ODEL FOR PHYTOPLANKTON PRODUCTION 33 each of th e se v a ria b le s h a s been d e te rm in e d at a num b er of Locations w ithin th e B ay by the in te g ratio n of m a ss continuity equatio n s w hich account- fo r changes due to tr a n s p o r t by w a te r m ovem en ts, grow th, decom p o sitio n and b io lo g ical uptake. T he dynam ics of the b eh a v io r of the c h e m ic al and b io lo g ical v a ria b le s of in te r e s t have been m odeled in th e low er p a rt of the w est a rm of the Bay using m e a su re d n u trie n t flu x es and o b se rv e d te m p e ra tu re and s o la r ra d ia tio n p a tte rn s. T he m a s s continuity equatio n s w ere in te g ra te d n u m e ric a lly using a n u m b er of so p h is tic a te d n u m e ric a l te ch n iq u e s. M odel p re d ic tio n s co m p are fav o rab ly w ith d a ta obtained durin g 50 s e p a ra te S ea G ran t su rv e y s conducted durin g a p erio d betw een 1970 and 1972. The m odel h a s b een u se d to fo re c a s t th e w a te r q uality in the B ay w hich w ill r e s u lt fro m th e lik e ly p a tte rn s of re sid e n tia l, c o m m e rc ia l and in d u s tria l u se, and v a ry in g d e g re e s of p h o sp h o ru s c o n tro l in the T ra v e r s e C ity a re a. ACKNOWLEDGMENTS The authors are indebted to a number of individuals involved in the University of Michigan Sea Grant program for their contributions to the results reported herein. These contributors include: R. L. Patterson and A. H. Vogel from the School of Natural Resources; T. M. Kelly, P. G. Meier and Mary-Lee G. Sharp from the School of Public Health; D. E. Arnold, E. Callender, E. Stoermer and C. Schelske from the Great Lakes Research Division; A. W. Green, Jr., E. B. Smith and E. C. Monahan from the Department of Atmospheric and Oceanic Sciences; E. F. Brater from the Department of Civil Engineering; and E. D. Rothman from the Department of Statistics. This work is a result of research sponsored by National Oceanic and Atmospheric Administration Office of Sea Grant, Department of Commerce, under Grant No. 04-4-158-23. The U. S. Government is authorized to produce and distribute reprints for governmental purposes notwithstanding any copyright notation that may appear hereon. REFERENCES Brater, E. F. 1972. A hydrological model for estimating the inflows to and outflows from Grand Traverse Bay. Sea Grant Tech. Rpt. No. 32. MICHU-56-72-214, University of Michigan, Ann Arbor, Michigan. Canale, R. P. 1973. Field verification and application of a model for total coliform bacteria in Grand Traverse Bay. J. Water Poll. Control Fed., in press., and Green, A. W., Jr. 1972. Modeling the spatial distribution of coliform in Grand Traverse Bay. Proc. 15th Conf. Great Lakes Res., pp. 719-728. Ann Arbor: Internat. Assoc. Great Lakes Res. ; Vogel, A.; Hineman, D. J.; and Nachiappan, S. 1973. The development of a biological production model for Grand Traverse Bay. Sea Grant Tech. Rpt., University of Michigan, Ann Arbor, Michigan, in press. DiToro, D. M.; O'Connor, D. J.; and Thomann, R. B. 1971. A dynamic model of the phytoplankton population in the Sacramento-San Joaquin delta. Nonequilibrium System in Natural Water Chemistry, Advances in Chemistry, series 106. Monahan, E. C.; Kaye, G. T.; and Michelera, E. D. 1973. Drague measurements of the circulation in Grand Traverse Bay, Lake Michigan. Sea Grant Tech. Rpt. No. 35, MICHU-SG-73-202, University of Michigan, Ann Arbor, Michigan. Sehelske, C. L., and Stoermer, E. F. Phosphorus, silica and eutrophication of Lake Michigan. In Nutrients and eutrophication: The limiting nutrient controverys. American Society of Limnology and Oceanography, Special Symposium, vol. 1. University of Michigan Sea Grant Report. 1973. University of Michigan, Ann Arbor, Michigan, in press.