Estuarine, Coastal and Shelf Science (1998) 47, 695–706Article No. ec980393

Modelling Salt Intrusion and Nitrate Concentrations inthe Ythan Estuary

P. A. Gillibrand and P. W. Balls

FRS Marine Laboratory, PO Box 101, Aberdeen AB11 9DB, U.K.

Received 6 March 1998 and accepted in revised form 9 July 1998

A one-dimensional salt intrusion model is used to investigate the hydrography of the Ythan estuary, a small shallowmacrotidal estuary in the north-east of Scotland. The model simulates the longitudinal distributions of water level, salinityand total oxidized nitrogen (TON) in the estuary. The model employs upstream differencing and the Smolarkiewiczanti-diffusion scheme to avoid the numerical difficulties typically encountered when modelling strong tidal flows usingcentred differences. The physical mechanisms driving the simulations are the tide at the entrance to the estuary andfreshwater discharge at the head. The model was calibrated against measurements of water level made at three locationsin the estuary, salinity observations made at a central platform and axial salinity distributions. At both spring and neaptides, the full range of salinity observed at the central platform was simulated. However, at the midway stage betweensprings and neaps, the simulated peak salinity was less than that observed. This was probably due to the sensitivity of themodel to the digitisation of the estuarine bathymetry.

The model successfully simulated salinity distributions for periods of high and low river flow, and was used to illustratehow TON concentrations fluctuated in response to variations in river flow. The potential implications of variations in thebathymetry of the estuary on salinity and nutrient distributions were predicted to be slight. However, the four foldincrease in riverine TON concentrations that has occurred over the past 30 years was shown to increase TONdistributions along the entire length of the estuary. The calculated estuary flushing time was strongly dependent on riverflow and varied between 11–60 h.

Keywords: estuaries; one-dimensional model; salt intrusion; nutrients; flushing time; Scotland coast

Introduction

Several recent studies have examined nutrient levels inthe Ythan river and its estuary in the north-east ofScotland. The River Ythan contains some of thehighest concentrations of nitrate found in any Scottishriver (Lyons et al., 1993), and these have been linkedto the highly agricultural nature of the surroundingcatchment area (Edwards et al., 1990; MacDonaldet al., 1994). (Some publications have reported nitrateconcentrations and others TON (nitrate+nitrite), butthe two terms are in practice interchangeable sincenitrite concentrations are insignificant.) Increasinglevels of nitrate in the river since the late 1960s arethought to be due to changing land-use and theintensification of agriculture over the same period(Raffaelli et al., 1989). These long-term increases innitrate concentration have been reflected in theestuary itself (Balls et al., 1995) and have led to theYthan estuary being recognized as a eutrophi-cation problem area by the Paris Commission(OSPARCOM, 1992). Balls et al. (1995) showed thattotal oxidized nitrogen (TON) concentrations have

0272–7714/98/120695+12 $30.00/0

increased in the River Ythan from c. 100–150 ìM inthe late sixties to c. 500–550 ìM in the early 1990s.Concentrations in the estuary have increasedproportionately.

The increasing nutrient supply to the estuary hascoincided with the development of extensive weedmats of macroalgae on intertidal mud flats in the lowerestuary. Long-term datasets have shown that theextent of these mats has increased over the last 30years. The weed mats have produced anoxic con-ditions in the underlying sediments, which has hadsevere effects on invertebrate populations, some ofwhich form the main prey for wading shorebirds(Raffaelli et al., 1989, 1991).

Short-term changes in estuarine nutrientconcentrations, and in particular the response to rain-fall events, were examined by Balls et al. (1997).During rainfall events, the riverine TON concen-tration decreases as the terrestrially derived nitratesare diluted by the increased precipitation. This effectpotentially offsets the general increase in estuarinenitrate concentration that is associated with thedecrease in salinity. Thus the increase in TON

696 P. A. Gillibrand and P. W. Balls

expected in the estuary following a heavy rainfall eventmay not be of the magnitude anticipated. Althoughthis effect was qualitatively observed, a quantitativeestimate of the two opposing effects could not beestimated (Balls et al., 1997).

Numerical models can quantify such processes overa wider range of river flow conditions than might bepossible with a field programme. In addition, a prop-erly calibrated model provides information on salinityand nutrient concentrations throughout the full lengthof the estuary, rather than at necessarily limited andselective sampling locations. In recent years, variousone-dimensional mathematical models have beenapplied to a number of British estuaries (e.g. Uncles& Jordan, 1980; Wallis & Knight, 1984; Nassehi &Williams, 1987; Uncles & Stephens, 1990). In thispaper, the modification and application of a one-dimensional transient salt-intrusion model, first devel-oped by Thatcher and Harleman (1972, 1981), isdescribed. The model is used to examine salinity andTON distributions along the length of the Ythanestuary under a range of river flows. Responses in theestuary to fluctuations in river flow are examined.Finally, the implications of variations in estuary depthare considered and the flushing time of the estuary isestimated. The potential influence of estuarinebathymetry is of particular importance in the shallowwaters of the Ythan estuary. It has been suggested thatlong-term depth changes have the potential to favourthe development of weed mats.

Description of study area

The Ythan estuary is approximately 11 km long fromthe tidal limit at the town of Ellon to the mouth at theNorth Sea about 20 km north of Aberdeen (Figure 1).The estuary is typically 300 m wide, with a maximumwidth of 620 m at Sleek of Tarty, and has a meanwater depth along the thalweg of 2·2 m. Mid-tidewater depths in the estuary range from 4·0 m at themouth to about 1·0 m at the Snub. The tidal range atthe mouth ranges from 1 m at neap tides to almost3 m at springs, and the intertidal area of the estuaryhas been estimated at 1·85 km2 (Leach, 1971). Themain freshwater input is from the River Ythan whichhas a catchment of 680 km2 and a long-term meanannual flow of 6·96 m3 s"1 (Balls et al., 1997).

The flushing time of the estuary, which dependsstrongly on the river flow, has been estimated as beingbetween one tidal cycle (Leach, 1971) and 5–12 days(Balls, 1994). The estuary is generally well-mixed,although some limited stratification can develop in thecentral region from the Snub to the Logie Buchanbridge (Raffaelli et al., 1997).

4°W

Ellon

GaugingStation

STWInput A92

J

The Snub

Sleek ofTarty

A975CatamaranMooring

Newburgh

58°N

2°W

57°N

56°N

IH

G

E

C

A

NorthSea

LogieBuchan

0

km

1 2

Aberdeen

F 1. Map of the Ythan estuary showing the locationsof the catamaran mooring, water level measurements,gauging station and relevant bathymetric and modelcross-sections.

Observations

Over the period June 1994 to June 1995, a series ofcontinuous measurements was made in the Ythanestuary. At a central location (Figure 1), a mooredcatamaran supported an Aanderaa current meter(RCM-7) which measured temperature and conduc-tivity every 10 min over the course of the year. Fromthese parameters, salinity was calculated using thePractical Salinity Scale 1978. From November 1994–June 1995, measurements of water depth were madeevery 15 min at the same location using an AanderaaWLR-5. The instrument was moored on the seabedand measured seabed pressure, from which variationsin water depth were determined. River flow dataduring this period were obtained from the ScottishEnvironment Protection Agency (North region).During September–October 1994, nutrient concen-trations were measured in the River Ythan severaltimes daily. Some of these data have been describedby Balls et al. (1997).

A sample of the water level and salinity data,measured in March 1995 at the catamaran, is pre-sented in Figure 2. The data from this period wereused to calibrate the model. The water level data

i1ofa(esirie

Modelling salt intrusion and nitrate concentrations 697

llustrate the variation in the tidal range, from aboutm at neap tides to about 2·5 m at springs. Thebserved salinity over a tidal cycle regularly oscillatedrom almost wholly fresh water (salinity less than 5)t low tide to almost wholly seawater at high tidesalinity greater than 33). During the period of small-st tidal ranges, on 9–12 March, the high wateralinity dropped sharply. However, the slight increasen the height of high water on 13 March quicklyestored the maximum salinity to 33·5. This is anndication of the sharp definition of the front whichxists in the estuary; only a slight change in tidal

height was required for the front to traverse thecatamaran location and transform the maximumsalinity observed there from brackish to salt water.

During the summer of 1995, a series of hydro-graphic surveys of the Ythan was carried out (Raffaelliet al., 1997). These included measurements of con-ductivity and temperature along the axis of the estuaryfrom the mouth to section ‘ J ’ (Figure 1) using a YSIconductivity, temperature and depth (CTD) probe.These data were used to calculate salinity (UNESCO,1978) and the salinity distributions were used tocalibrate the model. Further measurements of waterlevel were made at the Logie Buchan bridge (samplinglocation ‘ H ’), the catamaran position (‘ E ’) andsampling location ‘ C ’ (Figure 1) at various timesduring 1997. Full details of the observed time seriesdata used to develop and test the model are given inTable 1.

12-Mar

20.0

0.02-Mar

1995

Riv

er f

low

(m

3 /s)

12.0

4.0

36.0

0.0

Sal

init

y 27.0

9.0

1.0

–1.0Wat

er le

vel (

m)

0.0

8.0

7-Mar 17-Mar 22-Mar 27-Mar

18.0

16.0

F 2. Sample of data collected at the catamaran moor-ing from March 1995. The data consist of (a) water level(m) and (b) salinity measurements. The river flow measuredat the gauging station is also shown (c).

T 1. The location, recording period and measured parameters (temperature, salinity andpressure) of the current meter and water level recorded deployments in the Ythan estuary. The labels‘ C ’, ‘ E ’ and ‘ H ’ refer to Figure 1

Record No Position Duration Parameters

5211 57)20.28*N 2)00.02*W ‘ E ’ 15 09–18 10 1994 T, S5341 57)20.28*N 2)00.02*W ‘ E ’ 01 02–01 03 1995 T, S5351 57)20.28*N 2)00.02*W ‘ E ’ 01 03–29 03 1995 T, S533W 57)20.28*N 2)00.02*W ‘ E ’ 01 02–29 03 1995 P554W 57)20.28*N 2)00.02*W ‘ E ’ 12 03–12 04 1997 P565W 57)20.28*N 2)00.02*W ‘ E ’ 14 05–12 06 1997 P553W 57)19.02*N 1)59.22*W ‘ C ’ 11 03–09 04 1997 P566W 57)21.64*N 2)00.99*W ‘ H ’ 08 09–13 10 1997 P

Description of the model

The model employed in this study is the one-dimensional, transient, salt intrusion model developedby Thatcher and Harleman (1972, 1981). The Ythanis largely vertically well-mixed and the principalgradients are along the longitudinal axis of the estuary.Therefore, a one-dimensional model was sufficient tosimulate the features of interest in this study withoutintroducing the complexities and data requirements oftwo- and three-dimensional models.

The model solves the following standard set ofdifferential equations, which describe the conservationof volume, momentum and mass:

the continuity equation

698 P. A. Gillibrand and P. W. Balls

the longitudinal momentum balance equation

the salt balance equation

where b is the channel width (m), ç the surfaceelevation above mean water level (m), Q the cross-sectional discharge (m3 s"1), q the freshwater inputper unit length (m2 s"1), u the cross-sectional velocity(ms"1), g the acceleration due to gravity (ms"2), Athe instantaneous cross-sectional area (m2), dc thedistance from the water surface to the centroid of thecross section (m), ñ the water density (kg m"3), Cthe Chezy coefficient, Rh the hydraulic radius (m), Sthe cross-sectional salinity and Kx the longitudinaldispersion coefficient (m2 s"1). The Chezy coefficientis specified by:

where n is the Manning roughness coefficient.The water density, ñ, was calculated from salinity

and temperature using the equation of state ofFofonoff (1962). For the results described in thispaper, temperature was not simulated by the model,but the mean value measured during each simulatedperiod was used in the density calculation.

Solution of equations

Equations 1–3 were solved using finite differenceapproximations. The scheme is explicit and stepsforward in time. Initial tests, using the original modelcode, showed promising results, but the predictedsalinities were distorted by physically spurious short-waves, whereby predicted salinities in the estuary werehigher than those in the ocean or lower than rivervalues and were therefore physically unrealistic. Thegeneration of such waves is a problem which iscommonly encountered when modelling scalarparameters in strong tidal flows using centred,second-order spatial differences. In a modelling studyof the Tamar estuary, Uncles and Stephens (1990)developed a moving-element numerical model whichsuccessfully prevented generation of short-waves. It isalso possible to avoid the problem by using first-orderupstream differencing, but this method has thewell-known disadvantage of introducing numericaldiffusion into the solution, whereby the results areexcessively smoothed. However, anti-diffusion

schemes are available that remove the diffusion associ-ated with upstream differencing from the solution.In the present model, the anti-diffusion schemedescribed by Smolarkiewicz (1983) is employed. Thisscheme takes advantage of the fact that numericaldiffusion is analogous to an advective term and byreversing the effect of the term removes the diffusiveeffect. The scheme is applied in the present modelexactly as described by Smolarkiewicz (1983) andis implemented immediately after the advectioncomponent of (3) has been calculated.

Longitudinal dispersion

The longitudinal dispersion coefficient, Kx, variestemporally and spatially and is dependent on thedynamical characteristics of the estuary. FollowingThatcher and Harleman (1981) and Lepage andIngram (1986), Kx was specified as a function of thetidal prism/fresh water ratio, RP, and appropriatevelocity and length scales, i.e.

Kx=K0U maxLRP"0·25 (5)

where K0 is a constant. The length scale, L, wasspecified as the estuary length, and the velocity scale,Umax, was calculated each tidal cycle as the maximumflood velocity at the estuary mouth. The prism ratiowas specified as RP=P/(QfT) where P is theintegrated tidal prism, Qf the freshwater flow and Tthe tidal period. The ratio is calculated at the start ofevery tidal cycle.

Digitization of the Ythan estuary and boundary conditions

The estuary was divided into 27 segments (28sections) of length 0·4 km. The first section waslocated at sampling position A (Figure 1) and the finalsection at the Ellon gauging station. For reasons ofclarity, only those model sections specifically referredto in the text are shown in Figure 1. Bathymetric data,in the form of cross-sections levelled to a commondatum, were available for sampling locations A–J(Raffaelli et al., 1997) and these data were interpo-lated to provide channel widths and depths at themodel sections. The model used a ‘ storage ’ represen-tation of the estuary channel (Thatcher & Harleman,1981), which allows for the full cross-sectional area ofthe estuary to be included for salinity conservation butrestricts the current flow to a main channel. Aroundthe Sleek of Tarty and The Snub, where flow overthe intertidal areas is weak, this schematizationadequately represents the dynamical reality of the

Modelling salt intrusion and nitrate concentrations 699

Ythan. Upstream of Logie Buchan storage areas arenot used in the model, and downstream of theA975 bridge storage areas constitute only a minorproportion of the total cross-sectional area.

River flow data, obtained from the ScottishEnvironmental Protection Agency (North region),provide the boundary condition at the uppermostsection. At the mouth, tidal elevations were specified.Times and heights of high and low water for thesimulated periods were obtained from the AdmiraltyTide Tables for Aberdeen. By regressing the observedtidal data from location ‘ C ’ (Table 1) against pre-dicted levels from the Aberdeen tables, a regressioncoefficient of 0·8235 was obtained and applied to thewater level calculated at the mouth of the Ythan.Times of high and low water at Aberdeen werecorrected (typically advanced by 20 min) for theestuary mouth. The ocean salinity was specified as33·5–34·6 depending on the simulation period. Onthe ebb tide, a forward difference scheme at themouth allows lower salinity water to escape theestuary. On the flood tide, the salinity at the mouthreturns gradually to the ocean value over a period of1·2 h (one-tenth of a tidal cycle). No data wereavailable to justify or test this last assumption.No wind forcing was included in the simulationsdescribed.

TON simulation

Concentrations of total oxidized nitrogen (TON)were calculated using a routine exactly analogous tothe salt balance equation (3). This approach assumesthat nitrogen is conservative over the times scalesassociated with the flushing of the estuary, typically afew days. Available data support the assumption ofconservative behaviour (Balls, 1994; Balls et al.,1995). The only difference between the two routineslies in the boundary concentrations. At the oceanboundary, TON concentrations were constant foreach simulation and varied from 1·0 ìM for summersimulations to 8·0 ìM for winter/spring simulations(Turrell & Slesser, 1992). At the head, a largequantity of data for river concentrations was availablefor the period September–October 1994 (Balls et al.,1997) and these values were used for the autumnsimulation. For the February 1995 simulation, TONconcentrations were simulated simply to illustrate thepotential for higher values to be present throughoutthe estuary during periods of high runoff. The riverTON concentration of 525 ìM estimated by Ballset al. (1995) for data obtained in 1991/1992 wasused.

Model calibration

The model was calibrated against tidal heightdata (Table 1) obtained at three locations along theestuary. Because of the shortage of hydrodynamic datafrom the Ythan, an accurate calibration using themethods described by, for example, Fread and Smith(1978) and Davidson et al. (1978) was not possible.The model was calibrated by adjusting the Manning’sn in Equation 4 until a best fit between predicted andobserved tidal ranges along the estuary was obtained.The selected distribution of Manning’s n and theobserved and predicted tidal ranges along the estuaryare presented in Figure 3.

The model was then calibrated against the waterlevel and salinity measurements made during March1995, a period of steady river flow (Figure 2). Theonly parameter adjusted to calibrate the salinity wasthe constant K0 (Equation 5). The best fit between theobserved and predicted salinity was produced withK0=10"4. The predicted time series of water leveland salinity from cross-section 9 are shown inFigure 4. At spring and neap tides the full range ofsalinity observed over a tidal cycle is simulated by themodel. However, during intermediate tidal ranges thecalculated peak (high water) salinity drops away,whereas the observed value remains at 33·5[Figure 4(b)]. Some caution must be maintainedwhen comparing point measurements with cross-sectionally averaged model results, but the calibrationexercise suggests that the representation of thebathymetry in the model is not quite correct and thatin reality the saltwater wedge penetrates slightlyfurther up the estuary than is predicted by themodel. The predicted low water salinity comparedwell with that observed throughout the simulation[Figure 4(c)].

In order to compare the salinity (and TON) atvarious locations in the estuary, the data and modelresults were smoothed using a low-pass filter by Godin(1967). This filter suppresses all fluctuations withperiods less than 30 h, thus removing most of the tidaloscillation and revealing any underlying signal. Thesalinity data from March 1995 and predicted salinitiesfrom model cross-sections 3, 9 and 15 (closest tolocations A, E and G, Figure 1) are presented inFigure 4(d). The calculated values at E comparereasonably well with the observed values.

A further test of the model was conducted bycomparing predicted salinity distributions with theobserved axial salinities from summer 1995 obtainedby the University of Aberdeen (Raffaelli et al., 1997).The period 12 May to 12 September was simulated,and salinity distributions at high and low water were

700 P. A. Gillibrand and P. W. Balls

compared with the observations. In Figure 5, theobserved axial salinity distributions from eightsurveys, four each at high and low water, are pre-sented with the corresponding model prediction.The observations indicate the abruptness of thetransition from seawater to fresh water at high tide.The location of the front fluctuates in response totidal range and river flow, but is typically centered4–7 km from the mouth of the estuary. At low water,the entire estuary becomes very brackish when thetidal range is small (6 June) or when runoff is high(11 September).

In general, the model performed reasonably well.Except on 24 May, when the simulated salinity wasconsiderably less than that observed, the high waterprofiles were well simulated. The low water profileswere predicted well on 14 June and 14 July, but less soon 6 June and 11 September. However, these resultsgive confidence that the model was simulating theprincipal hydrographic features of the estuary.

12

2.5

Distance from mouth (km)

Tid

al r

ange

(m

)

2.0

1.5

1.0

0.5

4 80 102 6

(b)

0.08

Man

nin

g's

n

0.06

0.04

0.02

(a)

0.00

F 3. Hydrodynamic calibration of the model. Thelongitudinal distribution of Manning’s n used in all thesimulations (a) and the comparison between model pre-dicted (——) and observed ( ) tidal range (m) along theestuary (b).

12-Mar

36.0

0.02-Mar

1995

18.0

36.0

0.0

Sal

init

y 27.0

9.0

9.0

7-Mar 17-Mar 22-Mar 27-Mar

18.0

27.0

1.0

–1.0Wat

er le

vel (

m)

A

G

E

High water

Low water

36.0

0.0

27.0

9.0

18.0

0.0

(d)

(c)

(a)

(b)

F 4. Salinity calibration of the model, March 1995.Solid lines indicate model predictions, dashed lines repre-sent observed data. Model-predicted time series of(a) water level (m), (b) salinity at the catamaran location,(c) modelled and observed high and low water salinity at thecatamaran, and (d) low-pass filtered salinities at locations A,E and G.

Results and discussion

Model simulations of two other periods of interestwere performed, representing conditions of low(September–October, 1994) and high (February1995) river flow. These simulations also includedpredictions for total oxidized nitrogen (TON),although in the latter simulation riverine TON datawere not available and the predictions are for illustra-tive purposes only. A series of numerical experiments,designed to examine the potential impact of changes

Modelling salt intrusion and nitrate concentrations 701

in the morphology of the Ythan and to estimate theflushing time of the estuary, are also described.

12

35

Sal

init

y

0

8/9

Distance from mouth (km)

3.1, 19.7

120

11/9

3.2, 41.8

35

0

Sal

init

y

14/8

3.1, 1.5

14/7

3.5, 2.3

35

0

Sal

init

y

24/5

2.1, 4.7

14/6

3.4, 3.8

35

0

Sal

init

y

16/5

3.4, 5.5

6/6

1.9, 4.2

F 5. Comparison between observed (solid line) and modelled (dashed line) axial salinity distributions, May–September1995. Distributions at high tide are on the left hand side, those at low tide on the right. The day/month are shown in the upperright of each diagram, and the tidal range (m) and river flow (m3 s"1) in the bottom right.

September–October 1994 simulation

The data set obtained from 15 September–19 Octoberincluded the only measurements made (during the

present study period) of nutrient concentrations in theRiver Ythan (Balls et al., 1997). The results from themodel simulation are presented in Figure 6. Thefigure confirms that the high water salinity was wellpredicted by the model at spring tides, but less so atintermediate and neap tides. The low water salinitywas reproduced reasonably accurately throughout the

702 P. A. Gillibrand and P. W. Balls

simulation as was the filtered salinity. Figure 6(b)illustrates the gradient of smoothed salinity along theestuary. At ‘ A ’, the smoothed salinity was typically33·0. Further upstream at locations ‘ E ’ and ‘ G ’, thesalinity gradually reduced until fresh river waterdominated at ‘ I ’. At the extremes of the estuary, thespring-neap cycle was not reflected in the filteredsalinity because it had only minor effects on theobserved salinity at the mouth and head. Inthe intermediate reaches ‘ E ’ and ‘ G ’ however, thefiltered salinity increased during spring tides(21–22 September and 6–7 October) and decreasedduring neaps (28–29 September and 13–14 October).The predicted filtered salinity compared closely withthe observed times series at location ‘ E ’.

The filtered TON results were generally aninversion of the calculated salinity. At ‘ I ’, the TONconcentration reflected exactly the prescribed riverconcentration. Balls et al. (1997) highlighted the dropin river TON concentration immediately following

increased runoff events, such as on 20 September and4 October [Figure 6(c,d)], and speculated whetherthis lowering of river concentrations would offset therise in estuarine TON levels caused by the enhancedriver flow. These results suggest that although theresponse was weakened the increased river flow stillproduced a significant increase in TON levels in theestuary at and below position ‘ G ’ [Figure 6(c,d)].Daily mean values of predicted TON from theextremes of the estuary, at ‘ A ’ and ‘ I ’, were calcu-lated and plotted against river flow (Figure 7). Thedata from ‘ I ’ illustrate how the riverine TON con-centration was inversely proportional to river flow asdilution increased (Balls et al., 1997). The modelpredictions for ‘ A ’ show that, despite this dilutioneffect, the estuarine TON concentrations weredirectly proportional to river flow. Thus the increasein the estuary freshwater fraction following runoff

events caused elevated TON concentrations that werenot offset by the reduced riverine concentrations.

E

2-Oct

40.0

0.017-Sep

1994

TO

N (

µM) 30.0

10.0

5.0R

un

off

(m3 /s

)

0

(d)4.0

A

1.02.0

A

G

600

0

TO

N (

µM)

400

200

(c)

36.0

0.0

Sal

init

y 27.0

9.0(b)

36.0

0.0

Sal

init

y 27.0

18.0

(a)

18.0

9.0

II

G

E

A

20.0

22-Sep 27-Sep 7-Oct 12-Oct 17-Oct

3.0

F 6. Simulation of the September–October 1994period. Solid lines indicate model predictions, dashed linesrepresent observed data. (a) observed and predicted timeseries of high and low water salinity at the catamaran, (b)low-pass filtered salinity at locations A, E, G, I, (c) predictedlow-pass filtered TON concentrations (ìM) at A, E, G, I,(d) predicted low-pass filtered TON concentration (ìM) atA (solid line) and river flow data (dashed line).

Dai

ly m

ean

TO

N a

t 'A

' (+,

µM

)

4.0

32.0

12.01.0

River flow (m3/s)

28.0

24.0

20.0

16.0

2.0 3.0

440

Dai

ly m

ean

TO

N a

t 'I

' (∆,

µM

)

400

480

520

F 7. Daily mean values of model-predicted TONconcentrations (ìM) at A (crosses) and I (triangles) againstriver flow data (m3 s"1) for the September 1994 simulation.Due to the different ranges of TON involved, values from Aand I are plotted against the left-hand and right-hand axesrespectively.

February 1995 simulation

The second simulation performed was for 1–28February 1995, a period of sustained high river flowwith a marked rainfall event when the flow peaked at20 m3s"1. The results of this simulation are shown

Modelling salt intrusion and nitrate concentrations 703

in Figure 8. This model simulation shows featuressimilar to those previously shown. High water salinitywas reproduced reasonably well at springs andneaps but less so at intermediate tides. The low waterand filtered salinity time series were accuratelysimulated throughout and the spring-neap cycle wasagain clearly visible in the observed and calculatedsalinity time series. With the higher river flow, theestuary at neap tides (8–10 February) was verybrackish as far down as the catamaran location ‘ E ’[Figure 8(b)].

The predicted TON concentrations indicate that,during periods of high runoff, TON levels coulddouble in the central estuary (‘ E ’) and increasefour-fold at the mouth (‘ A ’) compared to the lowrunoff situation (Figure 6). The predicted increase inTON at ‘ A ’ following the rainfall event [Figure 8(d)]shows that such events have the potential to signifi-cantly increase TON concentrations throughout theestuary.

E

28-Feb

200

503-Feb

1995

TO

N (

µM)

23-Feb

150

100

8-Feb 13-Feb 18-Feb

20.0

Ru

nof

f (m

3 /s)

0

(d)15.0

A5.0

10.0

A

G

600

0

TO

N (

µM)

400

200

(c)

36.0

0.0

Sal

init

y 27.0

9.0

(b)

36.0

0.0

Sal

init

y 27.0

18.0

(a)

18.0

9.0

II

GE

A

F 8. Simulation of the February 1995 period. Solidlines indicate model predictions, dashed lines representobserved data. (a) observed and predicted time series of highand low water salinity at the catamaran, (b) low-pass filteredsalinity at locations A, E, G, I, (c) predicted low-pass filteredTON concentrations (ìM) at A, E, G, I, (d) predictedlow-pass filtered TON concentration (ìM) at A (solid line)and river flow data (m3 s"1, dashed line).

24.0

100.0

River flow (m3/s)

Flu

shin

g ti

me

(h)

4.0

80.0

60.0

40.0

20.0

8.0 12.0 16.0 20.00

Rem

oval

tim

e (d

ays)

0.0

10.0

10.0

10.0

10.0

10.0

F 9. Estimates of the flushing time (closed circles)and removal time (solid line) of the estuary calculated usingthe model for a range of river flows.

Flushing time

These simulations were designed to estimate theflushing of the Ythan estuary for a variety of riverflows. The flushing time is defined as the time taken toreplace the existing fresh water in the estuary at a rateequal to the river discharge (Dyer, 1973; Officer,1976). In this section, the flushing time, Tf , is com-pared to the time taken to completely remove afreshwater-borne contaminant from the estuary,which we call the ‘ removal time ’. The former wascalculated daily during the March, February andSeptember simulations by solving the equationTf=F/R where F is the total volume of fresh water inthe estuary at high water and R is the river discharge.The removal time was determined by a separate set ofsimulations. The model was run for a 7 day periodwith an arbitrary riverine tracer concentration of 100.The simulation then continued with the riverinesource switched off until the tracer was completelyremoved from the estuary, the time of which wastaken as the removal time. The oceanic tracer concen-tration was zero throughout. The simulation wasperformed for a range of river flows. The results ofthese simulations are presented in Figure 9.

The flushing time varies between 11–59 h and isinversely related to river flow. For river flows above2 m3s"1, the flushing time is less than 30 h, whichcompares quite well with the estimate given by Leach(1971). For the very lowest river flows, the flushingtime increases sharply. The removal of riverine con-taminants, however, takes much longer. Removal

704 P. A. Gillibrand and P. W. Balls

times varied from 1–8 days, which are similar to theestimates given by Balls (1994). The completeremoval of pollutants from the estuary involvesadvection and diffusion processes which significantlyincrease the time scales involved.

Effects of changes in estuary bathymetry

Balls et al. (1995) have shown that nitrate concen-trations in the Ythan river have increased 3- or 4-foldbetween the late 1960s and the present. Although thisincrease in nitrate concentrations has coincided withthe growth of weed mats in the lower part of theestuary, a direct link has not been established. It hasalso been suggested that changes in the topography ofthe estuary may have had an influence on the devel-opment of the weed mats. Although there is noevidence for any significant change in the extent of themudflats in the estuary over the last 30 years (Raffaelliet al., 1997), it is possible that siltation and/or erosionmay have altered the depth of the main channel. Themodel was used to examine the effects of changes intopography on simulated nitrate levels in the estuary.These were compared to the change associatedwith the established increase in riverine nitrateconcentrations.

The model simulated the March 1995 period whichexperienced average river flow conditions. The modelwas run for four scenarios: (i) with the present longi-tudinal depth profile and a riverine TON concen-tration of 125 ìM, (ii) with the present longitudinaldepth profile and a riverine TON concentration of525 ìM, (iii) with water depths reduced by 50% and(iv) with water depths increased by 100%. Simulations(iii) and (iv) had a riverine TON concentration of525 ìM. Boundary conditions and the configurationof the model were as specified earlier. The riverineTON concentration of 125 ìM corresponds to valuesmeasured in the late sixties and that of 525 ìM totypical values estimated in the nineties (Balls et al.,1995). The model output, presented in Figure 10,consists of longitudinal distributions of salinity andTON at neap tides, when the lower estuary might bemost vulnerable to increased nutrient levels.

The results suggest that even substantial changes intopography have very little impact on the salinity andTON distributions. The estuary appears to adjusthydrodynamically to reductions or increases in depthand shows only slight modifications to the distribu-tions produced with the present bathymetry. By farthe most noticeable increase in predicted TON con-centrations throughout the estuary is associated withthe increase in riverine levels. The results suggest thatthe increase in riverine TON affects concentrations

12.0

600

Distance from mouth (km)

TO

N (

µM)

100

500

400

300

200

4.0 8.00

36.0

0.0

Sal

init

y

16.0

32.0

28.0

24.0

20.0

12.0

8.0

4.0

River TON = 125River TON = 52550% shallower100% deeper

F 10. Longitudinal salinity and TON distributionsat neap tide in March 1995 with the present estuarybathymetry, a 50% reduction in channel depth, and a 100%increase in channel depth. The simulations used a riverineTON concentration of 525 ìM. Also shown is the TONdistribution with a riverine concentration of 125 ìM,corresponding to the value in the 1960s.

right to the mouth of the estuary at neap tides. Duringspring tides, when seawater intrudes further up theestuary, the increase in TON concentrations in thelower estuary is less.

Summary

The model described in this paper reproducesmany of the salient features of salt intrusion in theYthan estuary. The hydrodynamics were accurately

Modelling salt intrusion and nitrate concentrations 705

simulated, with the measured tidal range reproducedby the model at three locations along the estuary.Simulations of salinity at the catamaran locationshowed that at spring and neap tides, the full range ofobserved salinity was reproduced. At intermediatestages of the cycle, however, the high water salinitypredicted by the model decreased quicker than wasobserved. In all simulations, low water salinity at thecatamaran location was accurately predicted. Themodel performed less well when river flows wererelatively large compared to tidal flows. Predictedaxial salinities compared well with observations exceptduring periods of the smallest tides or periods of veryhigh runoff (Figure 5). These inaccuracies are prob-ably due to shortcomings in the digitization of theestuary channel in the model, a result of the sparsity ofbathymetric data. However, the essential features ofsalt intrusion in the estuary were adequately simulatedand the upstream difference method, with the anti-diffusion scheme of Smolarkiewicz (1983), performedsatisfactorily by preventing the development ofnumerical short waves without introducing excessivenumerical dispersion.

The principal aim of this study was to examinelevels of nitrate in the estuary under various riverflows, and to determine the importance of variationsin the riverine concentration to the estuary. Themodel showed that estuary nutrient concentrationsare predominantly controlled by the river end-member. During strong rainfall events, such asoccurred in February 1995, TON concentrationscould be significantly raised throughout the estuary(Figure 8). The dip in riverine TON concentrationassociated with rainfall events has only a minor effecton the estuarine concentrations and these directlyreflect the peak in river flow.

The observed long-term, four-fold increase inriverine TON concentrations is predicted to havecaused a proportional increase throughout theestuary. However, there is no established causal linkbetween increased nutrient concentrations and thecoincident growth in weed mats. Changes in estuarybathymetry has been previously identified as a poss-ible contributor to increased weed coverage, butmodel simulations also suggest that such changeswould have had no significant effect on nitrate con-centrations, and for this reason, any mechanism con-necting bathymetric changes and weed growth mustact independently of nutrient distributions.

Acknowledgements

The authors thank Dr M. L. Thatcher who providedthe computer code and documentation for the original

model. Dr D. Raffaelli and Ms S. Way from theCulterty Field Station, University of Aberdeen,coordinated and carried out many of the hydrographicand bathymetric surveys, some of the results of whichare described within. SEPA North Region helped withthe analysis of nutrient samples and provided the riverflow data. George Slesser of the Marine Laboratoryprocessed the time series data, and Rodney Payne andRichard Adams, also MLA, assisted with the fieldsampling.? 1998 Crown copyright

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