Effect of water residence time on annual export and ...klinck/Reprints/PDF/dettmannEst2001.pdf · tions for annual net export of nitrogen to the sea, internal losses (e.g., denitrification

Estuaries Vol. 24, No. 4, p. 481-490 August 2001

Effect of Water Residence Time on Annual Export and

Denitrification of Nitrogen in Estuaries: A Model Analysis

EDWARD U . DETFM_&NN*

U.S. Environ,mental Protection Agene~, Office of Research and Dec,elop,ment, National Health and Environmental Effects Research Laboratory, Atlantic Ecology Division, 27 Tarzwell Drive, Nar'ragansett, Rhode Island 02882

ABSTRACT: A simple model of annual average response of an estuary to mean nitrogen loading rate and freshwater res idence time was d e v e l o p e d and tested. It uses nitrogen inputs f rom land, depos i t ion f r o m die a tmosphere , and first- order calculadmts of internal lo~s rate and net expor t to pe r f o r m a steady-state analysis over a yearly cycle. The m o d e l calculates the fract ion of total nitrogen input f rom land and the a tmosphere that is e x p o r t e d and the f racdon that is denitrified or lost to other proc~,~s~s within file estuary. The model was tes ted against data f rom file l i terature for 11 North American and E u r o p e a n estuaries having a wide range of physical characteristics~ nitrogen loading rates, and geographical and climatic settings. The model shows that die fract ion of nitrogen entering an estuary that is expor ted or denitrified can be predicted from the freshwater residence time. The first-order rate cm~tant for nitrogen loss within an estuary, at a fract ion of total nitrogen in the water colunm, is 0.30 mo -~. Denitrificadon typically accounts for 69- 75% of the total annual net nitrogen removal f rom die water cohunn by p r o c u r e s within the ~stnar); The model makes expl ic i t file d e p e n d e n c e of ni trogen concentrat ion in the water column on file l oad ing rate of nitrog'en, water r~sidence time, ~stuary volume, and the rate constant for lo~s wifliin the estuary.

I n t r o d u c t i o n

Water quality in man)" estuaries, bays, and other coastal mar ine systems has progressively declined, and the structure of their ecological communi t ies has changed in undesirable ways. These effects often appear to be related to eutrophicat ion; increases in organic mat ter usually caused by increases in nutrients. Symptoms of excess nutr ients include seasonal reduct ions of dissolved oxygen, increases in turbidity, nuisance or hazardous algal blooms, loss of biodiversity, declines in the abundance of desirable species of submerged vegetation, and losses of fish and shellfish (Vitousek et al. 1997; Carpenter et al. 1998).

Eutrophicat ion of coastal waters is a widespread problem that appears to be intensifying (Nixon 1995; Pelley 1998). It is one of the leading impair- ments of water quality in estuaries in the United States (USEPA 1998a). As a result, the U.S. Envi- ronmenta l Protect ion Agency (USEPA) has developed a National Nutr ient Strategy (USEPA 1998b) that the agency is following to develop criteria and standards for nutrients. Trends of eut rophicat ion elsewhere in the world and some regulatory responses of the European communi ty have been summarized by Pelley (1998).

Researchers and environmenta l managers must unders tand how coastal systems respond to nutri-

* Tele: 401/'782-3039; fax: 401/782-3030; e-mail: dettma.nn. [email protected].

ent loading if the)" are to proper ly design programs to limit eut rophicat ion and predict their results. In addit ion to knowing the critical nutrients, their sources, and their input rates, it is impor tan t to unders tand the factors that de te rmine how sensitive these systems are to nu t r ien t loading. Even though phosphorus is usually the principal limit- ing nut r ien t in fi-eshwater, substantial evidence in- dicates that n i t rogen is the nu t r ien t that most fi-e- quently limits pr imary produc t ion in marine systems, including saline por t ions of estuaries (e.g., goyn ton et al. 1989; Howarth 1988; Oviatt et al. 1995). Concern over the role of excess n i t rogen in eut rophicat ion has created great interest in questions such as the following: What fraction of nitrogen input is expor ted from estuaries and other marine embayments? What is the fate of n i t rogen within these systems? What is the relationship between the loading rate and the concent ra t ion of n i t rogen in these systems, and what factors influ- ence this relationship? These questions are the fo- cus of this paper.

Ahhough short- term relationships (e.g., dail)r weekly, or seasonal) between inputs of n i t rogen and responses by the system are complex, these relationships can be much simpler over longer times. Numerous researchers have found relatwely simple correlat ions between annual inputs of nutrients and the responses of estuaries and marine mesocosms. Oviatt et al. (1986) presented empirical log-linear relationships between nutr ient inputs

�9 2001 Estuarine Research Federation 481

482 E.H. Oettrnann

to marine mesocosms and various mea, sures of their yearly p roduc t ion and respiration. Nixon (1983) and Nixon et al. (1986) demonstrated log- log relationships between annual inputs of dissolved inorganic ni t rogen (DIN) and concentra- tions of DIN and chlorophyll ca in estuaries and marine mesocosms. Recently, Nixon et al. (1996) found correlations between residence times of water and rates at which ni t rogen in estuaries is denitrified or exported. These simple empirical relationships suggest that it may be possible to ex- press and refine them in terms of the mechanisms underlying the ni t rogen cycle. The purpose of this work was to determine whether a simple semi- mechanistic model can explain some of these empirical correlations, in particular those that relate water residence time to net export and denitrification.

I have adapted the approach by which Vollen- weider (1969, 1975) analyzed the fate of phosphorus in lakes, and hmre tested whether it can be ap- plied to ni t rogen in estuaries. Vollenweider and others (e.g., Dillon and Rigler 1974) used a simple model to quantify some aspects of how freshwater lakes respond to phosphorus . They expressed the rate of outflow of phosphorus in terms of the residence time of water in a lake and assumed that phosphorus is lost to sediments at an average rate that is propor t ional to total phosphorus in the water column. The model is the foundat ion of an analytical approach used widely to manage water quality in lakes threatened by eutrophicat ion.

I used mass balance to construct simple equations for annual net export of ni t rogen to the sea, internal losses (e.g., denitrification and burial in sediments), and concentra t ion in the water colun-m. The model is based on the hypothesis that the average rate of ni t rogen loss from the water colun-m is propor t ional to total n i t rogen in the water column. Net export is calculated from the water's residence time. I used these equations to explore how the extent of removal depends on the loading rate of ni trogen, the residence time of fi-eshwater, and the estuary's volume. The method uses annual budgets for total ni trogen; it does not address seasonal dynamics.

T h e M o d e l

BACKGROUND

Model equations are based on annual mass balance of the total of all biologically active forms of ni t rogen in an estuary, including dissolved inorganic and dissolved and particulate organic forms. Budgetary terms include ni t rogen loading, losses within the estuary, and export across the seaward boundary. There are two loading terms: upland in-

puts and inflows across the seaward boundary. Up- land inputs include streams, groundwater, runoff, direct discharges (e.g., municipal wastewater and industrial discharges), and atmospheric deposition directly onto the estuary. Losses within the estuary include all ni t rogen lost annually from the water column by processes such as denitrification, loss to sediments, and incorporat ion into fish biomass later removed by fisheries. This term does not include temporary (seasonal) loss from the water (e.g., organic ni t rogen that is incorporated into sediments but later remineralized and re turned to the water column).

DERIVATION OF EQUATIONS

The rate of change of the total mass of ni t rogen (N) in the water co lumn is the difference between the rate of input from all sources (L) and the sum of all rates of removah

dN - L - E - R ( 1 )

dt

where E is the rate of export across the seaward boundary and R is the net annual rate of removal from the water co lumn ~dthin the estuary. The total rate of input is L - L 1 + L s , where g 1 is the input rate fi-om upland sources, and L~ is the input rate across the seaward boundary.

While the ni t rogen content of the water column may change over seasons or shorter periods, differences between the beginning and end of a yearly cycle are generally small. To a first approxima- tion over an annual cycle,

dN - - ~ 0 (2) at

so that Eq. 1 may be written

L - L1 + L~ - E + R. (S)

Defining the net rate of export (E,,) as total export minus input across the seaward bounda ry (E n - E

L~) reduces Eq. S to

h I - - ]7 n + R. ( 4 )

The total mass of ni t rogen in the water column includes two components : that which has entered across the seaward boundary (N,) and that from upland sources (Nl), i.e.,

N - N 1 + N,. (5)

I hypothesized that, on an annual mrerage, long- term ni t rogen loss from the water c o h m n as a net result of all internal processes occurs at a rate that is propor t ional to the average mass of ni t rogen in

the water co lumn, i.e., R = c~N = oL(N 1 + N,), where oL is a first-order rate coefficient, with units t ime-k

N e t e x p o r t of n i t r o g e n across the seaward b o u n d a r y can be expressed in terms of the freshwater r e p l a c e m e n t t ime ('rfw), which gives the average transit t ime th rough the estuary for inflow- ing freshwater and is often re fe r red to as the mean f r e s h w a t e r r e s i d e n c e t ime ( g o l i n a n d R o d h e 197.3). Most seawater and n i t rogen that enter on a flood tide leave on the following ebb, while bo th freshwater and n i t rogen f rom upland sources mus t often traverse m u c h of the estuary 's length before exiting. There fo re , E n can be a p p r o x i m a t e d as Nl/ ' r fw , ana logous to the expression Q,,~ - V~,~/'r~ for outflow of freshwater (where V~w and Q,w are the v o h m e and through-f low rate of freshwater in the estuary, respectively).

Substi tuting R - ot(N 1 + N~) and E n - Nl/'r~w into Eq. 4 gives

Be N 1 ( 1 (N1 + Ns) ) - - + o ~ N + ov N 1. ( 6 ) "rf,~ N 1

Net expor t of n i t rogen, expressed as a fract ion of up land loading, is

En FE(1) L1. (7)

Substi tuting En = Nl /q fw and L 1 fi-om Eq. 6 into Eq. 7 gives

FE (1) 1 1

NI+N (N<) 1 + ot'rfw N1 1 + o~"rfw 1 +

(s)

If N~ << N1, the case for many estuaries, the value of 1 + N J N 1 app roaches 1, and one may approx- imate FE(1) as follows:

1 - . ( 9 )

F~z(1) 1 + o~q'fw

This expresses net annual expor t of n i t rogen as a funct ion of only o~ and "rt-,~. T h e value of FE(1) for a given estuary est imated f rom Eq. 9 will depar t f rom that given by Eq. 8 by an a m o u n t that depends on the ratio of N~ to N~.

T h e fraction of up land N loading that is lost fi-om the water c o h m n within the estuary is F~(I) = 1 - FE0 ~. From Eq. 9, this may be written

cere,,. (10) FR(I) -- 1 + ot"rfw'

Model of Nitrogen in Estuaries 4 8 3

Equat ion 6 may also be used to derive an equation for the mean concen t ra t ion IN] of n i t rogen in the estuary (see Appendix) .

DATA AND ANALYSIS METHODS

Data are analyzed for 11 estuaries in Nor th Amer ica and Europe. Data for these estuaries were originally compi led f rom the l i terature by Nixon et al. (1996). These data have been recompi led , sup- p l emen ted w-ith addi t ional data f rom the l i terature, and used to fit and evaluate the equat ions de- scribed above.

Data for Est,~a,ries

Five of the Nor th Amer ican estuaries are located a long the Atlantic Coast (Boston Harbor , Narra- ganset t Bay, the Delaware Estuary, Chesapeake Bay, and the Po tomac Estuary), and 2 discharge to the Gulf of Mexico (Och lockonee Bay and the Gua- d a h p e Estuary). T h e European systems are the Baltic Sea, N o r s m i n d e Fjord (Denmark) , the Wes- t e r s c h e l d e E s t u a r y (Be lg ium a n d the N e t h e r - lands), and the n o r t h e r n Adriatic Sea.

These estuaries are highly diverse (Tables 1 and 9), with large differences in surface area (1.86- 375,000 kin2), m e a n dep th (0.6-55.3 m) , water residence times (S d-22 yr), up land loading rates of n i t rogen (212-17,600 m m o l m ~ yr 1), and geographical location. Data for a given estuary are often derived f rom m o r e than one study; some cited sources summar ize data fi-om mult iple studies.

Residence times for freshwater were measured or calculated by various techniques, including the f reshwater - replacement m e t h o d (using field data), or o ther me thods that give similar results, such as mode l calculations of e-folding times of tracers (see footnotes to Table 1)�9 T h e values for Och- lockonee Bay, Guada lupe Estuary, and N o r s m i n d e Fjord refer to specific per iods dur ing which data for n i t rogen budgets were obtained; the o ther values are averages.

T h e rates of input , s torage in the water c o h m n , and loss of n i t rogen in Table 9 are annua l averages. Because these rates were mea~sured by various methods , the interested reader should consult the original publ icat ions and the compi la t ion by Nix- on et al. (1996) for details�9 For instance, total upland n i t rogen input to the Delaware Estuary was available, but not listed by individual source cate- gory. Likewise, losses of n i t rogen f rom the water within N o r s m i n d e Fjord by processes other than denitr if lcat ion were calculated by difference, and are listed in the aggregate unde r O t h e r in Table 9.

Denitr if ication losses in Table 9 were deter- mined with various techniques. Losses in Boston Harbor , Nar raganse t t Bay, Delaware Estuary, Och-

484 E.H. Dettmann

TABLE 1. Physica l cha rac t e r i s t i c s o f 7 N o r t h A m e r i c a n estu- m-ies a n d 4 E m ' o p e a n es tuar ies .

Mean Depth Freshwater Surface .~n'ea at Half-tide Residence Time

(m ~ x 10 ~) (m) (too)

Bos ton H a r b o r 195 ~ 4.9 ~ 0.33 ~ N a r r a g a n s e t t Bay 328 b 8.3 b 0.85 b De laware Es tua ry 1,989 r 7.4 ~ 3.3 ~ C h e s a p e a k e Bay 11,549 e,e 6.8 f 7.6 ~ P o t o m a c E s t u a r y 1,210s 6.1 h 5 ~ O c h l o c k o n e e Bay 24J 1.3a 0.1J

G u a d a l u p e Es tua ry

1984 695 k 1.3 k 10.7 k 1987 625 k 1.8 k 1.07 k

Balt ic Sea 874,6001 55.31 2621 N o r s m i n d e F jo rd 1.86'" 0.6 ..... 0.98" W e s t e r s c h e l d e 259 ~ 10.7 ~ 2 ~ Norfla Ach-iatic Sea 18,930P 33.5P 2.4P

R e s i d e n c e tr ine d e t e r m i n e d as e - fo ld ing t i m e in m o d e l i n g s tudy (S igne l l 1999; S igne l l a n d Bu t rnan 1999).

b F r e s h w a t e r r e s i d e n c e tr ine is f r e s h w a t e r r e p l a c e m e n t tr ine (Pi lson 1985).

~ a n d d e p t h a t h a l f t ide a re f r o m NOA~AA (1985) . Note : da t a of Polls a n d K u p f e r m a n (1973) i m p l y a d e p t h of app rox i - m a t e l y 9 m.

a Pol ls a n d K u p f e n n a n (1973) . R e s i d e n c e tr ine is ave rage of two values: f r e shwa te r r ep l ace -

m e n t t i m e a n d e 4 o l d i n g t i m e e s t i m a t e d wi th a s i m u l a t i o n m o d e l (NLxon e t al. 1996).

e L i p p s o n (1973) . s Boyn ton e t al. (1995) . h C a l c u l a t e d f l 'om d e p t h a t h i g h t ide u s i n g ~/2 t ida l r a n g e f l 'om

Lipp son (1978) . i Estin~ate by Boicom-t ( p e r s o n a l c o r m ~ u n i c a t i o n ) . J R e s i d e n c e t i m e c a l c u l a t e d as f r e s h w a t e r r e p l a c e m e n t tr ine

(Se i t z inge r 1987). k Brock ( p e r s o n a l c o m m u n i c a t i o n ) . I W a t e r r e s i d e n c e t i m e c a l c u l a t e d as e - fo ld ing t i m e (Wulf f a n d

S t i g e b r a n d t 1989). '" N ie l sen e t al. (1995) .

F r e s h w a t e r r e s i d e n c e t i m e m o d e l - c a l c u l a t e d as m e a n resi- d e n c e t i m e of f l ' e shwate r pm-cel e n t e r i n g at h e a d of e s t u a r y (Nie l sen p e r s o n a l c o m m u n i c a t i o n ) .

o F r e s h w a t e r r e s i d e n c e tfl~e c a l c u l a t e d by a m o d e l as the m e a n r e s i d e n c e tr ine of a f r e shwa te r p a r c e l e n t e r i n g the u p s t r e a m e n d of the e s tua ry ( S o e t a e r t a n d H e r m a n 1995a) .

P R e s i d e n c e t i m e e s t i m a t e d by g e o s t r o p h i c f low c a l c u l a t i o n s for n o r t h e r n A d r i a t i c Sea ( D e g o b b i s e t al. 1986).

lockonee Bay, Guadalupe Estuary, and Norsminde Fjord are based on measurements of Ne produc- tion rates in sediment cores from these systems. Loss in Chesapeake Bay wa~s de termined in sediment cores using the acetylene block method, which probably underes t imated the actual denitrification rate (Kemp et al. 1990). Denitrification losses in the Baltic Sea and no r the rn Adriatic Sea were calculated by mass balance; those for the Wes- terschelde were calculated by mass balance for the 1970s and by a simulation model for the 1980s. Denitrification estimates for the latter $ estuaries may be affected by uncertainties in other budget

items. The denitrification rate in the Potomac Es- tuary was estimated from measurements in other systems (see footnote in Table 9). For fur ther in- format ion concern ing these mea~surements and methods used to calculate annual estuary-wide los.> es, see the original studies cited in Table 9.

Data for the Guadalupe Estuary are gwen for 9 years with very different flushing rates and inputs of nitrogen. Inflows of freshwater and ni t rogen were lower in 1984, a dry year, than in 1987, a wet year; mean residence time of water wa~s 10 times longer in 1984 than in 1987. Data for these 9 },ears are shown and analyzed separately.

Data for the Westerschelde came fi-om 9 periods (the 1970s and the 1980s) and studies that used different methods and obtained different values for individual componen t s of the ni t rogen budget. I calculated separate mass balances and v a h e s for fractional net export for these 9 periods, and then averaged the 9- values for net export.

Data A,na~ysis Methods

Compar ison of Eq. 9 w-ith data suggested that a single value of ot chm-acterizes well the overall relationship between fractional net export of nitrogen and freshwater residence time of these 11 estuaries. Nonl inear regression was then used to determine the value of oL that optimizes the fit of the equation to the data. Similar methods were used to show the relationship between denitrification losses and fi-eshwater residence time. Model equations were used to explore the constancy of the parameter a among estuaries.

Resu l t s an d D i s c u s s i o n

N E T E X P O R T OF N I T R O G E N FROM ESTUARIES

Fractional net export of ni t rogen from an estu- m-y, Fz(l), was calculated from data in Table 9- as (net expor t ) / ( to ta l upland inputs). Data for those estuaries with residence times up to a year and model predictions (Eq. 9) for selected values of the first-order loss coefficient ot are shown in Fig. 1. The Baltic Sea (FE(1) -- 0.094, %w - 9-69- too) has been omitted to display the other data in more detail. For an}, given residence time, net export decreases as ot increases. Note that most data points lie close to the model line for oL - 0.S mo 1 The value of o~ that best fit Eq. 9 to the data for all 11 systems was calculated by nonl inear regression to be 0.S0 mo 1, "Mth 95% confidence interval (C.I.) 0.9-8-0.$6 mo 1 and r 2 - 0.94 (Fig. 9-). A logarithmic time scale is used in Fig. 2 and subse- quent figures to facilitate display of data over the full range of residence times, which span more than three orders of magnitude.

It is apparen t from Figs. 1 and 9 that the per- centage of n i t rogen input that is exported de-

Model of Nitrogen in Estuaries 485

TABLE 2. Ni t rogen budge ts (nmaol m -2 yr -~) for 7 Nortla Amer ican and 4 European estuaries. For Dela~.~are Estuary, Lnputs fl'om all u p l a n d sources are aggrega ted as total inputs. Entr ies ind ica ted as n o t d e t e r m i n e d (nd) oi" small are assumed to be zero in calculations; na = no t applicable. Net expor t calculated by difference (ne t expo r t = total Lnputs - N storage in water cohmm - total losses).

N Upland lXl Inputs Storage lq Losses

Rivers and Other Total Water Deniu'i- Sedimen- Fish Total ]'let Estuary Atmosphere 1,I Fixation Wastewate r Sources [I~pl.lt8 C~oll.lmi~ fication tanoi~ ga i~,.lii~ga Other Lo~ses Export

Boston Harbor 203 ~ 0J 7,554 ~,b Nar raganse t t Bay 91s nd 1,775s Delawm-e Estuary see total see total see total C,hesapeake Bay 118 ~ nd 826" Potomac Estuary 113 m nd 1,981'" Och lockonee Bay 82 ~ <5.5P 5,910].P

Guada lupe Estuary

1984 7 P 42 ~ 407 ~ 1987 69 ~ 42 Y 1,743 ~

Baltic Sea 60 ~ 26 ~ 126 ~ Norsmin de Fjord 77 " nd 11,795 ~

Westerschelde

1970s n d nd 8,289 ~ 1980s n d nd 9,626r

Nor th A&riatic Sea 46 ~ 8 * 861 *

134 ~,~ 7,891 0J 683 a 187 ~ smalb 150 r 1,020 6,871 122z 1,988 0~ 384 h 215 ~ l~.J na 612 1,376

see total 2,100 k 0J 825 ~ 255J smallJ na 1,080 1,020 nd 989 C~ 245" 326 ~ 83 ~ na 654 285 nd 2,094 0J 331" 836 m 96 m na 1,263 831 nd 5,995 0 639P l15q smallJ na 754 5,241

nd 520 24 ~ 2 8 P P S@ na S12 184 nd 1,854 2D 28D 59 ~ 74 Y na 414 1,411

na 212 14' 162 ~ 1P 5 ~ na 178 20 ~ n a 11,872 115 ~ 207 ~' see off:e:" see otl :e: ~ 125 ~ 880 11,427 TM

5,615 ~ 13,904 nd 5,615 ~ 1,070 ~ nd na 6,685 7,219 ~ 8,022Y 17,648 nd 2,941Y 1,070Y nd na 4,011 18,687Y

na 915 nd 287 �9 77 ~ 14 ~ na 378 537 �9

"Albe r and Chan (1994). b Inc ludes rivers, sewage effluent, CSOs, and sew-age sludge. ~ Runoff and groundwater . a Nowicki et al. (1997).

Kelly and Nowicki (1992). r Losses to &'edging.

Nbcon e t al. (1995). h Nowicki (1994). ~Value 215 is the m i d p o i n t of ff:e r ange 134-296 given in the sunm~ary by NLxon (1995). J Nixon et al. (1996). kJaworski persona l con 'anunicat ion. IThe value 825 is at the lower end of the range 825-1,025 given by Nixon et al. (1996). This value was der ived from data on

s e d k n e n t type (Biggs and Beasley 1988), assuming tha t deni t i i f ica t ion occurs only in s e d k n e n t tha t is no t gravel or gravelly sand. '" goynton et al. (1995).

Denitr i f icat ion rates for ff:e u p p e r and lower Potomac Estuary are assmned to be the same as ff:ose for the u p p e r Patmxent and lower Mm-yland m a l n s t e m of Chesapeake Bay, respectively (goyn ton et al. 1995).

o Hench-y and Brezonik (1980). p Seitzinger (1987). qValue 115 is m idd l e of r ange given by Nixon et al. (1996).

Brock et al. u n p u b l i s h e d manusca-ipt; Brock persona l communica t ion . Larsson et al. (1985). Wulff and St igebrandt (1989). Denin-ification calculated by difference.

" Nielsen et al. (1995). ~' Total o ther losses ( sedhnenta t ion and fisheries) , ca lcula ted by difference (Nielsen et al. 1995). "~ Directly d e t e r m i n e d (Nielsen et al. 1995).

Billen et al. (1985). Denitr i f icat ion ca lcula ted by difference. Y Soetaer t and H e r m a n (1995b).

Degobbis e t al. (1986). Denitr i f icat ion calculated by difference.

creases as res idence t ime increases. For "re, ~ - 0.1, S.3, and SO mo, 97%, 50%, and 10% of n i t rogen input , respectively, are expor ted . As res idence t ime grows still larger, this p e r c e n t a g e asymptot i- call?, a p p r o a c h e s zero. No te that the d i f ference in net expor t for the G u a d a l u p e Estuary be tween 2 yr with very di f ferent loads and res idence t imes is a p p r o x i m a t e d by the model , a l t hough the predicted value for the dry year (1984) is less than observed.

DENITKIFIC&TION IN ESTUARIES

R e c e n t l i t e r a t u r e c o n t a i n s s o m e d i s c u s s i o n c o n -

c e r n i n g t h e f r a c t i o n o f u p l a n d n i t r o g e n i n p u t t o

a n e s t u a r y t h a t is d e n i t r i f i e d , a n d t h e a p p a r e n t d e -

p e n d e n c e o f t h i s f r a c t i o n o n w a t e r r e s i d e n c e t i m e

( N i e l s e n e t a l . 1 9 9 5 ; N i x o n e t a l . 1 9 9 6 ; N o w i c k i e t

a l . 1 9 9 7 ) . I n t h e f o l l o w i n g , I e x p l o r e t h i s d e p e n -

d e n c e u s i n g a n a d a p t a t i o n o f t h i s m o d e l i n g a p -

p r o a c h . M a n y f a c t o r s , e . g . , s e d i m e n t o x y g e n a n d

c a r b o n c o n t e n t , t e m p e r a t u r e , w a t e r d e p t h , a n d

486 E.H. Dettmann

1 . . . . . .

�9 0.8 -..

x o.6

," 0.4-' \ ~ - . . . - - ~ _ _ . . . . ,~=o.~

O ~ _ _ ~ ~ ~ . . . . . . . . . . . . . . . . a=0.3 ,~ 0 .2 - I.I. c~=0 5

~x=1.0 0 I . . . . . . , ~ , .

0 2 4 6 8 10 12

Fig. 1.

14

Freshwate r R e s i d e n c e T i m e (me)

The fi'action of upland nitrogen input that is exported versus freshwater residence time: observations and model predictions for selected values of the ftrst-order loss coeffi- dent a. BMtic Sea ('rf~ = 262 too) is not shown (see Fig. 2).

s e d i m e n t d i s t u r b a n c e by b e n t h i c o r g a n i s m s c a n af- f ec t d e n i t r i f i c a t i o n r a t e s in e s t u a r i e s ( K e m p et al. 1990; N o w i c k i et al. 1997) . T h i s ana lys i s is l i m i t e d to t h e e f f e c t o f w a t e r r e s i d e n c e t i m e o n d e n i t r i f l - c a t i o n losses .

S i n c e t h e d e n i t r i f i c a t i o n r a t e in t h e P o t o m a c Es- t u a r y was e s t i m a t e d f r o m m e a s u r e m e n t s in o t h e r sTs tems ( see f o o t n o t e in T a b l e 2 ) , it is n o t u s e d in t h e f o l l o w i n g analysis . T h e p e r c e n t a g e o f to ta l in- t e r n a l n i t r o g e n loss a t t r i b u t a b l e to d e n i t r i f i c a t i o n ( T a b l e S) is S7% fo r C h e s a p e a k e Bay, a n d 6 8 - 9 1 % fo r t h e o t h e r e s t u a r i e s ( m e a n a n d s t a n d a r d dev ia - t i o n 7 2 % a n d 15%, r e spec t i ve ly , i f C h e s a p e a k e Bay is i n c l u d e d , 7 6 % a n d 11% i f i t is e x c l u d e d ) .

To e v a l u a t e t h e e f f e c t o f f r e s h w a t e r r e s i d e n c e t i m e o n d e n i t r i f l c a t i o n losses , a s s u m e t h a t to a f i rs t a p p r o x i m a t i o n , d e n i t r i f i c a t i o n a c c o u n t s fo r a c o n - s t a n t f r a c t i o n (7) o f to ta l i n t e r n a l losses in e a c h es tuary . T h e f r a c t i o n o f u p l a n d i n p u t t h a t is d e n i -

1.0

"O �9 0.8 1:: O X 0.6 ILl

Z 0.4

O O

0.2 U.

0.0

~-..._ �9 Norsminde .I~" .~'-.~.~.o st o n ~ Observations

Ochlockonee " " ~ u a d a l u p e ('87) Model

Narragansett �9 "~Westerschelde ct = 0 30 ~.N Adriat ic r2 = 0.94

~il@elaware

C h e s a p e a k e ' ~ . .

" - ~ �9 . . . . . i . . . . . . , . . . . . . ,i , . . . . . ,,,

0.1 1 10 100 1000

F r e s h w a t e r R e s i d e n c e T i m e (mo)

Fig. ~. ~ The fi'action of upland nitrogen input that is exported fi'om 11 estuaries versus fi'eshwater residence rune (logarithmic time scMe).

TABLE S. The fi'action of total annum internal nitrogen loss from the water column that is denitrified (calculated from data in Table 2).

Estuary Fraction Denitrified

Boston Harbor 0.68 Narragansett Bay 0.68 Delawm-e Estuary 0.76 C~lesapeake Bay 0.37 Ochlockonee Bay 0.85 GuadMupe Estuary (1984) 0.90 GuadMupe Estuary (1987) 0.68 Baltic Sea 0.91 Norsmin de Fjord 0.63 Westerschelde (1970s and 1980s) 0.80 North Ach-iatic Sea 0.76

t r i f l ed c a n t h e n b e c a l c u l a t e d a s FD(I) - - ~/Fp.(1), w h e r e Fkd ) is g i v e n by Eq . 10. T h e r e f o r e :

~, otq-tw - . ( 1 1 )

FD(I) 1 + oLq'fw

N o n l i n e a r r e g r e s s i o n was u s e d to f i t Eq . 11 (wi th a - 0.S0 m o -1) to t h e o b s e r v e d d a t a fo r d e n i t r i - f l c a t i o n a n d r e s i d e n c e t i m e , y i e l d i n g 7 - 0.59, w i th 9 5 % C.I. 0 . 5 7 - 0 . 8 0 a n d r ~ - 0.85 (Fig. 3) . W h e n t h e ( p r o b a b l y u n d e r e s t i m a t e d ) d a t a p o i n t f o r C h e s a p e a k e Bay was e x c l u d e d f r o m t h e fit, n o n l i n - e a r r e g r e s s i o n g a v e 7 - 0.75 ( 9 5 % C.I. 0 . 6 9 - 0 . 8 1 , r ~ - 0 .97) .

T h e m o d e l d o e s n o t exp l i c i t l y a d d r e s s v a r i a t i o n s in FD(1) a t t r i b u t a b l e to d i f f e r e n c e s in t h e u n d e r l y i n g d e n i t r i f l c a t i o n r a t e p e r u n i t a r ea . I t d o e s d e m o n - s t r a t e a s t r o n g r e l a t i o n s h i p b e t w e e n f r e s h w a t e r res- i d e n c e t i m e in th is d i v e r s e set o f e s t u a r i e s a n d t h e f l -ac t ion o f u p l a n d n i t r o g e n i n p u t t h a t is d e n i t r i -

1.0 �9 Observations

Model (y= 0 69)

~ t 0.8 Model (7 = 0.80) .- . - - - T~ . . . .

.~ Modo, (.,=o 57> . ..... . - - _ B a ~ - - I

0.6 / . j _ / - / , , . . . . . . . '

e" 0 . 4 - U Adriat ic . " ~ . / / / / o ; . ~

Westersehel

"~O0.2 . l~.-~-/Narragansett OchlocKonee ",r..~.~ ; . LII. .x" ' ~ ' "~";)-~P"Guadalu pe ( '87)

00 ". Bo. on ,noo,_ . . . . . . . . . . . . . . . . . . . . .

0.1 1 10 100 1000

F r e s h w a t e r R e s i d e n c e T i m e (too)

Fig. 3. The fraction of u p l a n d n i t r o g e n i n p u t that is deni- trifled versus freshwater residence time. Tlle solid model line (T = 0.69, r 2 = 0.85) is the fit to all the data. The dashed model lines correspond to the 95% confidence ]hnits for ~/ (0.57 and 0.80). If Chesapeake Bay is exchzded from the fit (see text), the model line (,! = 0.76, r 2 = 0.97) lies between those for - /= 0.69 and ~/ = 0.80.


1.0 "---Z ~-~ 0.14 .......... ~ Data

"1~ ~ " ' . ~ ~ \ - M o d e l ( a = 0 . 1 ) 0 8 - 1 4 " .044 \ \

" " " ~0.29 X - - Mode l ([~.= 0.3)

" " ' , �9 ~Q~ \ - - - Model (a = 1.0)

i 0 . 6 . \\ Z " \ , , ~0 .32 \

0 4 : ' \ ~ 0 . 3 0 \ �9 i ', "\\. � 9

1 "', " I 1 ,...

I , I . 1 ..... " . . . . . . . . " ' - - ' - 2 " : " -- �9 0.037 0 . 0 / - . - - . , . . . . . , . . . . . . . " ," -,-,: ,-, = ---~ ~ ,=:-~:-.~.~

0.1 1 10 100 1000

F r e s h w a t e r R e s i d e n c e T i m e (mo) Fig. 4. The fl'action of upland nitrogen input that is ex-

ported from 11 estum-ies versus fl'eshwater residence time. Mod- el calculations are shown for three values of the first-order rate coefficient for loss within fl~e estum-ies (c 0 . The nmnerical label for each data point gives the value of 0~ calculated for that estum-y.

f led, a n d expla ins a la rge fl-action o f the var iabi l i ty in the data.

NITROGEN LOSSES AND I~,TE COEFFICIENTS IN INDMDUAL ESTUARIES

C o m p a r i s o n of da ta and m o d e l p r e d i c t i o n s in Figs. 1 and 2 ind ica tes tha t Eq. 9, with oL - 0.S0 m o -~, exp la ins the overal l t r end in the data well. To e x p l o r e poss ib le va r i a t i on in the va lue o f this p a r a m e t e r a m o n g estuaries , oL may be ca lcu la ted for a g iven es tuary by r e a r r a n g i n g Eq. 9:

T h e da ta p o i n t for each es tuary is l abe l ed with the va lue o f a ca lcu la ted f r o m Eq. 12 and p lo t t ed with Eq. 9 for oL - 0.1, 0.3, and 1.0 mo 1 in Fig. 4.

T h r e e conc lu s ions are i m m e d i a t e l y a p p a r e n t fl-om this f igure. Whi l e ca lcu la ted values o f a a re close to 0.3 m o 1 for m a n y ind iv idua l es tuar ies , s o m e devia te substant ia l ly f rom this value. T h e s e d e p a r t u r e s t end to be l a rge r for es tuar ies hav ing ve ry shor t or ve ry l o n g r e s i d e n c e t imes than for those hav ing i n t e r m e d i a t e r e s i d e n c e t imes (1 -10 too) . D i f f e r e n c e s a m o n g the values of n e t e x p o r t ca lcu la ted fo r ot - 0.1, 0.g, and 1.0 are l a rge r (i.e., ne t e x p o r t is m o r e sensi t ive to oL) for r e s i d e n c e t imes o f 1-10 mo than fo r va lues subs tant ia l ly h igh- er or lower; this suggests tha t ca lcu la ted values o f c~ are m o r e sensi t ive to e r ro r s in m e a s u r e m e n t o f f r ac t iona l e x p o r t for la rge or smal l r e s i d e n c e t imes than for i n t e r m e d i a t e values,

T h e m o d e l m a k e s it poss ib le to e x p l o r e the sensitivity of the oL ca lcu la ted for an ind iv idua l es tuary

TABLE 4. Sensitivity, of the value of a to net export, calculated for a = 0.3 mo -~ and representative freshwater residence times.

'r~,~ a~/,?FEo) 0 1 (,;~c<./,;~FE(,)) (too) (too- ') (mo-D

0.1 -11 -1.1 1.0 1.7 0.17 3.33 -1.2 -0.19

10 1.6 0.16 100 -9.6 -0.96

1,000 91 9.1

to e r ro r s in m e a s u r i n g ne t expor t . Th i s sensitivity may be ca lcu la ted by d i f f e r e n t i a t i n g Eq. 12 with r e spec t to Fe(ly a n d subs t i tu t ing the e x p r e s s i o n for Fad ) f r o m Eq. 9:

aoL - 1 - ( 1 + oL'r~w)~ (is)

OFe(1) q'fwF~(1) q'~

T h e values o f 0OS//0FE(1) and (0.1) (0OS//0FE(1)) calculated f r o m this e q u a t i o n a re shown in Tab l e 4 for c~ = 0.S m o -1 and a r a n g e o f r e s i d e n c e t imes con> p a r a b l e to those for the es tuar ies in this study. T h e quan t i ty (0.1)(OoL/OFEd)) is the c h a n g e in a for a c h a n g e o f 0.1 in Fe0 ). T h e m i n u s s ign ind ica tes that c~ dec reases as FE(1) increases . It can be shown tha t the m a g n i t u d e of aa/OFs(l) is a m i n i m u m w h e n %,~ - 1 /oc T h e va lues shorn1 in Tab le 4 d e m o n s t r a t e b o t h this m i n i m u m at -rt~ - 1/or (g.g3 m o for oL - 0.g m o 1) a n d the subs tant ia l i nc rease in sensitivity toward the ends of the o b s e r v e d r a n g e o f resi- d e n c e t imes.

T h e r e s i d e n c e t ime for fl-eshwater, the va lue o f oL ca lcu la ted fl-om Eq. 12, a n d the d i f f e r e n c e between o b s e r v e d a n d m o d e l e d f rac t iona l n e t e x p o r t for e a c h es tuary are s u m m a r i z e d in Tab l e 5. Cal- cu la t ed values of ot a re all close to 0.g m o 1 for es tuar ies wi th r e s i d e n c e t imes b e t w e e n 1 and 7.6 too; ou ts ide this r ange , oL deviates cons ide rab ly

TABLE 5. Freshwater residence times ('re,,,,) calculated values for a, and observed minus model-calculated fl'actional net export (AFEu)). Estuaries listed in order of increasing residence time.

Estuary (,no) (too -~) AF~b

Ochlokonee Bay 0.1 1.4 0.097 Norsmin de Fjord 0.28 0.14 0.040 Boston Harbor 0.33 0.44 0.037 Narrag>msett Bay 0.85 0.52 -0.105 Cuadalupe Estuary (1987) 1.07 0.29 0.004 Westerschelde 2 0.27 0.021 North Achiatic Sea 2.4 0.29 0.006 Delaw:~re Estu~ry 3.3 0.32 -0.017 Potomac Estuary 5 0.30 -0.003 C~e sapeake Bay 7.6 0.30 -0.001 Guadalupe Estuary (1984) 10.7 0.17 0.116 Baltic Sea 262 0.037 0.082

488 E.H. Dettrnann

more. This pat tern is consistent with min imum sensitivity of ot to the measured value of FE(b at ~rf,~ = 3..3.3 mo (see Table 4), but does not preclude other causes for the observed deviations. The greater deviations in oL reflect larger differences (in absolute magnitude) between observed and modeled net export (IAFe(1)I); t h e maximum IAFe(l)l for 1 ~ ~r,,~ ~ 7.6 mo is 0.021, the m a x i m u m IZXFE(II)I

outside this range is 0.116. The larger deviations in c~ are also partly a result of greater sensitivity of oL to the value of net export for these times. For instance, a for the Westerschelde Estuary ('r~w - 2 too, IAF~I>I = 0.0213 differs from 0.S mo -1 by 10%, while ot for Norsminde Fjord (%w = 0.98 too, IZXF~I>I - 0.04) deviates frolr?. 0 .~ lnO 1 b y 5~/O//0, e v e n

though IAF~r is only twice that for the Wester- schelde. These results indicate that a l though c~ may vary among estuaries, much of the variability in these calculated values may arise from modest er- rors in determinat ion of net export. For estuaries in this study, IzxF~r is always less than 0.12.

Note that while Vollenweider (1976) finds that the first order coefficient for phosphorus removal varies inversely w-ith lake depth, a comparison of values of calculated c~ (Table 5) and mean depth (Table 1) reveals no similar relationship for these estuaries.

S l l n l i n a l * y

This simple steady-state model explains most of the variability found in annual net export of nitrogen and denitrification in estuaries. Considering the simplicity of the model and the wide range of physical characteristics, loading rates, and climatic conditions for estuaries to which it has been ap- plied, it fits the data remarkably well. It gives quan- titative relationships for calculating the fractions of upland inputs of ni t rogen to estuaries that are exported, denitrified within the estuary, or lost to other internal processes, and provides a framework for explaining the causal basis of these relationships.

This analysis shows that the model agrees well with observations of annual net export of ni t rogen and denitrification for 11 estuaries of widely vary- ing characteristics, and that annual denitrification and net ni t rogen export are strongly related to the residence time of freshwater in the estuary.

The model quantifies the net effect of compet- ing biochemical and physical (transport) loss processes. Results show that the transition from export as the more impor tant process for ni t rogen loss fi-om rapidly flushed systems to dominance by internal removal occurs at a freshwater residence time of approximately g.g too.

The fit of model equations to observations shows that a value of 0.g0 mo -1 for the first-order rate

constant for ni t rogen removal (o 0 for all estuaries gives good overall agreement with data for net export. C, alculations for the estuaries in this study give relatively constant values of oL among estuaries with fi'eshwater residence times between approximately 1 and 7.6 mo, and more variable values outside this range. The calculated value of oL for these latter estuaries is relatively sensitive to uncertainties in mass balance calculations. The degree of variability of ot among estuaries merits fur ther in- vestigation.

An equation for the concentra t ion of total biologically active ni t rogen in the water column was also developed (Eq. A4 in Appendix) , but was not tested. Since the concentra t ion of total n i t rogen in the water column of an estuary is often regarded as an indicator of its degree of eutrophicat ion, this equation could provide a potentially useful tool for managing eutrophicat ion in estuaries. Validation of this equation also merits attention.

Relatively few data are needed to apply this model to an estuary. Only the residence time of freshwater is needed to estimate the fiactions of upland inputs of ni t rogen that are exported or denitrified. To estimate the contr ibut ion of upland loading to the annual-average concentra t ion of nitrogen, only the residence time of freshwater, the annual loading of nitrogen, and the estuary's volume are needed. These modest data requirements should make the model particularly suitable for use in estuaries for which there are limited resources for data col- lection.

ACKNOWLEDGMENTS

I t hank Daniel Campbel l , J o h n Kiddon, and H e n r y WaLker for their technical reviews, K e n n e t h Rahn for his editorial review of this manuscr ip t , a n d J a m e s Hel tshe for his gu idance in statistical analysis. Th i s is cont r ibut ion n u m b e r NHEERL-NAR- 20'79 of the U.S. Env i ronmenta l Protection Agency 's Office of Researda and Development , National Hea l th and Envh-onmen- tal Effects Research LaIooratory, Atlantic Ecology Division.

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SOURGES OF UNPUBLISHED IVf2kTERIALS

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BROCK D. A. Personal Communica t ion . Env i romnenta l Section, Texas Water Deve lopmen t Board, RO. Box 13931, Aust in , Texas 78711-3931.

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Received for consideration, A,~g~st 9, 1999 Accepted for p~zblicatioa, Febr.a~a.ry 24, 2001

Appendix Equat ion 6 ma y be used to derive the equa t ion for flae m e a n

concent ra t ion of n i t rogen [N] in an estuary:

(- ) L~ = N~ + (v(N~ + Ns) = + c~N s. (A1)

Solving for Nl

Nl (LI c~N:)'rfw (LfG~ c~Tf,,,,N: )

1 + e ~ 1 + u ~ (Ag)

Since [N] N / V (Nx + N:)/V,

1 + cvrf~, = V \ 1 + o~'r~, j (AS)

and since [N~] N j V ,

[N] = + [N~] 1 + c~'G~ (A4)

where N~ may be calculated as the p r o d u c t of the concent ra t ion o fn in -ogen at the seaward b o u n d a r y and the volume of seawater in the estuary.

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Effect of water residence time on annual export and ...klinck/Reprints/PDF/dettmannEst2001.pdf · tions for annual net export of nitrogen to the sea, internal losses (e.g., denitrification