On the chemical mass-balance in estuaries

On the chemical mass-balance in estuaries

freo&imicaet ~o~noc~mic~Acts, 197%Vol. 88, pp. 1710to 1728. Pergamon Press. Printedin Nort&?rn Ireland On the chemical mass-balance in estuaries E. ...

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freo&imicaet ~o~noc~mic~Acts, 197%Vol. 88, pp. 1710to 1728. Pergamon Press. Printedin Nort&?rn Ireland

On the chemical mass-balance in estuaries E.







J. M. EDMOND, A. C. N0 and R. F. STALLARD Department of Earth and Planetary Sciences, M~s~husetts Institute of Technology, Cambridge, ~~s&ehusetts 02139, U.S.A. (Received 2 Jaozuary 1974; accepted in, revised form 16 May 1974) Abstract--A general model is presented for mixing processes between river and ocean water in which are established criteria for the identification of any non-conservative behavior of the dissolved constituents involved. A review of previous data shows that in no case has removal of silica been demonstrated unambiguously in estuarine regimes. New data for iron which show highly non-conservative behavior are used in an example of the application of the model.

CONSTRUCTION of precise mass-balances is of fundamental conceptual importance in geochemistry. The primary oceanic input of dissolved constituents derived from continental weathering is generally regarded as the best characterized component. It is implicitly assumed in this connection that there is chemical continuity between the river and ocean waters; that mixing processes in estuaries and fresh water plumes are chemically conservative. Beginning with MAEDA (1952) numerous attempts have been made to validate this assumption (see Table 1). The emphasis has been on silica due to its fundamental i.mportance in the ‘reverse weathering’ process (SILLEN, 1961; MACKENZIE and GARRELS, 1966). Individual studies have been reported for other species. It is seen that there is no obvious generality in the reported interpretations either in the extent of removal or the mechanisms. In an effort to clarify this situation repeated detailed surveys have been made of the Merrimack River in Massachusetts. This estuary is stratified (a typical vertical salt gradient is 23&,fm ) with no secondary tributaries and a residence time of water in the mixing zone of approximately 1 day (HARTWELL, 1970). For silica linear relationships with salinity were observed over the range measured (Fig. 1). The standard deviation of points from a straight line was always less than 2 pm/l. However, the end-member values and hence the slopes of the lines varied considerably. Extended time series measurements (2 yr) for silica along the river itself made by this laboratory had shown that the shop-term variations in silica concentrations were entirely a function of flow. At many locations along the river, there are digitally recording guaging stations which can be interrogated directly by telephone. The flow, and hence the river end-member value, was quite constant during the days preceeding each sampling trip. In order to establish a representative oceanic end-member, sampling was extended several miles offshore. The Merrimack plume is swept southwards in the longshore drift towards Massachusetts Bay (M~OHAR-MAJARAJ and BEARDSLEY, 1973). Water coming from

* NOWat Scripps Institution of Oceanography, La Jolla, California 92037, U.S.A. 1719


1720 Table

1. Summary


et al.

of previous work on chemical mass bdtmces in estuaries





MAEDA (1952, 1953) MAKIMOTOet al. (1956) MAEDA and TSUEAMOTO (1969) MAE~A and TAKESNE (1961) &EN et Ul. (1958)

Various: Japan restricted salinity range





STE~ANSSONand RICHARDS (1963) PARK et al. (1970)


Si, N, P

FG% et al. (1964) KOBAYASIZI (1967)

Si Si, N

STJRTON et al. (1970) BWRTON (1970)

&n-long Kiso and Nagara over restricted range Southampton Water Vellar

Complete removal by inorganic processes Conservative in winter minor biological removal in summer No interpretation Conservative

Lrss and SPENSSER (1970)



HOSOKAWA et aE. (1970)


WOLLAST and DE BROE~ (1971)

Mullica Scheldt

WINDOX et 62. (1971)



et al. (1971)

Si Si

Conservative Mixing of two fresh water components of differing composition with sea water 1 O-20 y0 inorganic removal

S, B, Mg, Ca, F, Si, Al Fe Si


Zn, Cu, Ni rvfn

LISS aud POINTON (1973)


DEN~LER (1973) FANNINU and PILSON (1973)

Various: Orinoco

Fe Si, New England

Savannah Mississippi

Si Si

Si Si


Conservative Chemical process important Extensive removal Complete removal by diatoms Conservative or unresolved Kay be nonconservative Extensive removal 2530% removal by unspecified mechanisms Conservative Ambiguous due to lack of value for fresh water end-member Conservative ~7 0/0 removal: mechanism unresolved

the north in this drift was sampled well offshore and several miles north of the

mouth of the river. The high salinity points are therefore representative of the oceanic end-member actually mixing with the river water. In no case did the highest measured sea water value exceed 29x, or the extrapolated value at zero silica 31x,. If the virtual end-member is assumed at an average open ocean value e.g. 35x,, following previous authors (BIEN et cd., 1957; WOLLAST and DE BROEU, 1971), then these profiles would be interpreted as indicating complete removal; however, given the close linearity of the Si-S curve, mixing is conservative within the region studied. For iron, on the other hand, it is apparent from the profile (Fig. 2) that sig~ficant removal occurs.

On the chemical mass-balance


in estuaries



Fig. 1. Silica-salinity diagrams for the Merrimack Estuary (Massachusetts). Unfiltered surface samples were collected from a boat over a single tidal cycle, stored on ice and run within 24 hr (MULLIN and RILEY, 1956). Duplicate runs had shown that filtered and unfiltered samples gave identical results for silica. Salinity was determined with a Hytech Lab Salinometer: for values less than 5x,, a chloride specific ion electrode (Orion) was used. The two techniques were carefully intercalibrated.

Since it appears from this situation that much of the diversity in previous conclusions is due to a lack of specific criteria for the choice of end-members relative to which non-conservative mixing can be identified and quantified, it is instructive to consider a simple analytical model. Model We wish to model the mixing processes between river and ocean water in estuaries. Since this model should be applicable over the entire mixing zone and since, experimentally, it may not happen that the absolute end-members, ‘pure’ river water and ‘pure’ ocean water, are in fact sampled, i.e. that all samples are from within the mixing zone, let the end-members be designated as ‘riverine’ and ‘oceanic’. As a trsoer of the degree of mixing it is most direct to use dissolved constituents of known or assumed conservative behavior and characteristic of the In practice it is more convenient to use salinity; although this is not defined oceanic component. in rivers, the levels of total salts are sufficiently low in most instances as to make negligible the uncertainty thus introduced. An ideal tracer might be the lsO/lsO ratio in the water. The net flux of water across a given iso-saline surface is equal to the flux of primary river water Q,. The advective flux of ocean salt

A,, = (8 - 4, s&Q,, 0

where 9 is the salinity


on the chosen surface, 8, is the salinity

of the oceanic end-member,






et ai.


Fig. 2. Data from the Merrimtaek Estuary, 1~~30~~3,(Table 2). (a-f Total dissolved iron vs salinity. Samples were filtered through a glass fiber &her (nominal pore size 045,um) and acidified with 3 ml of 3 NIX%. Determination of iron was by the calorimetric method of STCIOHIGY (1970). Data points s,re numbered in order of increasing salinity. Dashed line indicates conservative mixing between observed end-members. (b) Silicate vs salinity. (c) Iron data fitted to two arbitrary functions, together with the corresponding relative removal QJQ,. Solid line crossing removal curves indicates minimmn removal as discussed in text. {d) Iron data Wed to consecutive straight line segments. Insert illuetr&es standard deviations of progressive Ats; arrow indicates ohosen cutoff. 8, is the salinity of the riverine end-member. The diffusive flux D is determined by the oon~ centration gradient for the species considered tmd by the turbulent eddy diffusion coefficient normal to the surface, .I& which is common to all species. Roth the concentration gradients and K, vary in space and time. Integrating over the area o of the iso-saline surface, the diffusive Aux of salt

where ?%is in the diredion normal to the iso-saline surface. From the d~ution reltation

On the chemical



in estuaries

Since sea salt does not accumulate

where D,, is the diffusive flux of sea salt. its net flux over time must be zero.

in the mixing


Q,, = A,, + D,, = 0 = Q,S, + D,


For a dissolved is


C of unknown


the flux of material


by the river

Q, = CTQ,, the advoctive

flux across an iso-saline

surface is A,

where C is the concentration at the surface, function of salinity, the diffusive flux is

D, =



and assuming

that C is a continuous


s IA

= s lr


cda n dP,


S -SdC =o--.D S, dS


(‘$- “) g



- S,) cs,s~ s ) r


Q,(S - S,).

= -g Hence,

Q, = A, + D, =Q,C

The term at S = S,.

in parenthesis

The variation


gives the intersection

of the flux with salinity

-dQc = -Q,(S ds

In the conservative


of the tangent

to C(S)

at S with the C-axis

is -S$$.

case: dQc _ o = d”c d232’ ds

i.e. C(S) is linear over the mixing varies, then the second derivative

range. If the mixing is non-zero.

process is non-conservative,

i.e. the flux


E. BOYLE et al.

Discussion In the context of previous work, this explicit formulation of the mixing process, ie. of C(S), shows that over straight-line segments of the curve simple two-end-member dilution processes are occurring and that to establish nonconservative behavior, curvature must be demonstrated. In general, of course, the principle constraints of constancy of the end-member values over the mixing time and of the presence of only two significant components, i.e. no tributaries, m.ust be established for the model to be valid in application. Inspection of the data presented by previous authors (Table 1) shows that in no case has it been proved unambiguously that silica exhibits non-conservative behavior during estuarine mixing. The classic instance is that reported by BIEN et aE. (1958) for the Mississippi. Two data sets have an adequate number of samples for interpretation (June, 1953, July, 1955). The suite of June, 1953, can be fit to two straight line segments, one of zero slope from Cl = 20.5 to 16x, at Si = 6 pm/l (a = f 2.6 pm/l) and the other from this point to Cl = O-2%,, the lowest measured and Si = 74 ,um/l (cr = & 7.1 ,um/l). The range of values at 0*2x, is from 70.2 to 82.0 pm/l and appears random with respect to depth and location; the spread is slightly larger than the estimated precision (5 per cent or a possible 8 pm/l, lo range) and there is no obvious explanation for this. Similarly, the data of July, 1955, can be fit to two straight lines; one, again of zero slope from 20.4 to 16.5x, at 3 ,um/l and the other from this point to O-58%, and 114 ,um/l. The low chlorinity data have a range of 10 ,um/l. Since there is no known mechanism by which silica can be removed only at discrete ‘points’ (chlorinity range < lx,,) in chlorinity-concentration space it appears that the Si(C1) curve is generated by mixing of three end-members-the Mississippi River water, shelf water of intermediate chlorinity and low silica and the high chlorinity, low silica waters of the open Gulf. No strong case can be made for silica removal in the main mixing zone. This is in agreement with the recent field observations of FANNINQ and PILSON (1973). WOLLAST and DE BROEU (1971) found, in the estuary of the Scheldt, depletion of silica to less than 10 pm/l by a salinity of 15x,,. The data is again well represented by two straight lines, one of zero slope from 17x,, the highest measured, to 15x0 at about 10 pm/l Si ( N 0.75 ppm SiO,) the other from this point to 1x0, the lowest salinity measured and 210 ,um/l Si (- 14 ppm SiO,). All but three of the data points fall on this latter line. In neither of these cases is there any suggestion of the existence of removal processes characteristic of the estuarine zone. Rather, the data are explained by mixing with sea water of intermediate salinity depleted in silica by the usual biological processes operating in the upper waters of shelf seas and the open ocean. LISS and SPENCER (1970) appear to find appreciable removal of silica in the Conway estuary in North Wales. However, the spread of values at low salinity over a range of 8 pm/l is sufficiently large to suggest that C, may have been varying in time. Also the data can be approximated by two straight-line segments intersecting at about ll%,, and 21 ,umll indicating the possible influence of tributaries as found by BURTON (1970) for the Vellar. In fact, there is a significant

On the chemical mass-balance in estuaries


tributary adjacent to their station no. 2 (see their Fig. 1). In the absence of information about these points this case must be regarded as ambiguous. In the recent work of LISS and POINTON (1973) the very large scatter in the data prevents detailed analysis. It should be pointed out that removal of boron, as claimed by these authors, can only be from the oceanic component, in that the riverine end-member is very small. HOSOKAWA et al, (1970) found conservative behavior for boron. They interpreted their data for silica as showing non-conservative mixing: however, the scatter is too large to substantiate this. Their aluminum-salinity relationship does appear to indicate removal. The published profiles for iron (COONLEY et aZ., 1971; WINDOM et al., 1971) do show large-scale removal. This is also found in the Merrimack estuary (Fig. 2a, Table 2). Since in the discussion so far either conservative processes have been identified or the data has been too scattered for detailed analysis, it is informative to use the Merrimack profile as an example of the application of the model. In Fig. 2a is plotted the primary iron-salinity data. The function dC/dS must be calculated in order to compute the flux. Since a priori there is no mechanistic explanation of the observations which might constrain the functionality of the curve, two quite arbitary functions have been fit to the data (Fig. 2c, Table 2). Although the fits are almost equally good (cl = 0.17 and u, = 0.15) the calculated relative fluxes (&J&J differ significantly. It is clear that the uncertainty in the Table 2. Salinity, silicate, and iron data from the Merrimack Estuary, 10/30/73 Sample

Salinity (%,I

Silicate (pm/l)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

0.07 0.08 0.15 0.34 0.36 0.54 1.17 1.32 1.76 2.73 3.76 4.93 5.94 7.11 7.24 IO.15 12.83 14.13 15.56 16.64 17.06 19.69

63.7 65.1 64.9 66.7 64.6 64.7 66.2 66.4 64.3 63.5 60.4 58.6 55.7 53.4 51.4 46.7 40.3 37.9 36.4 33.3 32.2 30.2

3.73 3.51 3.59 3.29 3.44 3.02 2.99 2.34 2.66 2.19 2.01 1.55 1.70 1.13 1,27 0.96 0.89 0.64 0.64 0.52 0.61 0.36


E. BOYLE et al.

data is magnified in the curve fitting in that this procedure involves implicit assumptions about the derivatives of the iron-salinity relation. In order to determine constraints on the functionality of the relative flux with salinity the data were fit to a series of straight-line segments. A least-squares line was fit to the first five lowest salinity points and extended point by point by recomputation until the standard deviation began to increase significantly (Fig. 2d). The procedure was then repeated and another segment generated. From Fig, 2d it can be seen that the data are fit by three such straight lines with an overall standard deviation (0 = 0.13) comparable to that of the curves. Within the constraints imposed by the scatter in the data no removal can be substantiated above a salinity of 7x0 or below 04%, a straight line and a curve fitting the data equally well. In the region from 0.8 to 7x,, the straight line fit has a standard deviation twice that for the high and low salinity segments. The scatter of the data does not well constrain a curve. The results of this procedure can be interpreted as indicating either removal of iron at the end-points of the intermediate salinity curve, which seems unlikely, in that there is no obvious mechanistic explanation of such a phenomena, or continuous removal in the region between them. If this latter explanation is correct then the increased scatter can be interpreted as indicating that the time scales of iron removal and of mixing are comparable. In this case, parcels of water whose riverine components have different time-salinity histories will show different amounts of iron removal: the basic model assumption that C(S) is continuous and single-valued breaks down. Therefore, the flux cannot be calculated in this region but is constrained only in the linear, conservative and therefore single-valued regions. The removal computed from the straight-line fit

[(l -!?$y

= 56 per cent

is less than that from the curves and is the minimum

] consistent

with the data.

CONCLUSIONS Non-conservative behavior during mixing is characterized by a non-linear relationship of the constituent with salinity. Previous claims of removal of silica in estuaries are based on profiles, which, within the resolution of the data, are in fact composed of straight-line segments and can be explained consistently by the introduction of a third end-member component. In the case of the Conway (LISS and SPENCER, 1970) this is a tributary stream, but more commonly it is depleted coastal or shelf sea water of intermediate salinity. The behavior of silica in the overall mixing of river water with deep ocean surface water is nonconservative but this is not a consequence of the mixing nor is it related to it. The mixing of the fresh and coastal waters in the estuaries themselves or in the vicinity of fresh water plumes is in all reported cases conservative within the uncertainty of the data: the depletion of the coastal waters in silica is presumably caused by processes common to surface water globally. While it is conceivable that, in placid estuaries of long residence time silica could be removed by diatom

On the chemical


in estuaries


growth, the rapid inorganic removal hypothesized by Bien et al. and others with all its implications for geochemical mass balances has not been unambiguously substantiated. Iron shows large-scale removal in the few estuaries studied. However, detailed analysis of the data shows that it is not possible to constrain the functionality of the iron-salinity relationship sufficiently to derive the corresponding salinity Hence, it is not presently practicable to dependence of removal unambiguously. use this indirect approach to identify the mechanisms responsible. This appears to be a result of the fact that any removal process with half-time comparable to the mixing time will generate a range of iron values at a given salinity depending on the mixing history of the sample. The present model does not apply explicity in such a situation and only the overall removal anomaly can be identified. Acknozuledgement+-This is Contribution Number 1 of the Geochemistry Collective at M.I.T. We gratefully acknowledge grants from the Offices of the Provost and the Dean of Science for the purchase of analytical instruments and sustained support of field and laboratory work by the Undergraduate Seminar Office and the Undergraduate Research Opportunities Program, all at M.I.T. A significant pert of the field and laboratory work in summer ‘73 was carried out under cm NSF-Student Originated Studies grant to A. C. Ng. E. Boyle is in receipt of an NSF Graduate Fellowship.

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E. Bon

et al.

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