Wind induced sediment resuspension: a lake-wide model

ELSEVIER

Ecological

Modelling

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Wind induced sediment resuspension: a lake-wide model Mark C. Bailey ‘, David P. Hamilton * Crntre

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Accepted

Austrulio.

19 December

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W’A 6907,

‘4 ustralicr

1996

Abstract A lake-wide suspended sediment model has been developed and subsequently coupled with a horizontal circulation model to predict depth-averaged suspended sediment concentrations throughout a lake. Resuspension is induced by shear stresses at the sediment-water interface which are considered to be a result of wave action. These shear stresses are calculated using linear wave theory. The model allows for winds from any direction to generate the waves and associated stresses. Sediment deposition is characterised by a formulation which describes the change in suspended sediment concentration with time rather than relying on one or more representative settling velocities. Sediment resuspension is modelled as being independent of deposition. The processes of advection and diffusion in redistributing resuspended sediments horizontally are accounted for in the hydrodynamic model. The result is a general, process based model for predicting depth-averaged suspended sediment concentrations throughout a shallow lake. The model was tested against data collected during 1993 and 1994 from Thomsons Lake, Western Australia. 0 1997 Elsevier Science B.V. Keywords:

Shallow

lakes; Sediment

transport:

Resuspension

1. Introduction The concentration and distribution of suspended matter is important in determining the quality of a water body. The effect of strong winds on the suspended solids concentration in * Corresponding author. Tel., - 61 9 3803530: fax: + 61 9 3801015; e-mail: hamilton(cLc~~r.uwa.edu.au ’ Present address: c:o Halpern Glick Maunsell. P.0. Box Xl. Leederville. Western Australia 6902. 0304-3800:Y7~$17.00 PI1 SO304-3801.

ccj 1997 Elsevier 97)01955-X

Science

B.V.

All

rights

reserved

model:

Hydrodynamics

shallow lakes has been well documented (e.g., Carper and Bachmann, 1984; Luettich et al., 1990; Bengtsson and Hellstriim, 1992; Arfi et al., 1993). Sediment resuspension events have been shown to alter the concentration of dissolved phosphorus in shallow lakes, with suspended solids acting either as a sink (Gunatilaka. 1982) or a source of phosphorus (e.g., Hamilton and Mitchell. 1988; Scmdergaard et al., 1992). Light attenuation will also change with changing concentration of suspended solids (e.g.. Somly6dy

and Koncsos, 199 1; Kristensen et al., 1992). These effects may be reflected in the phytoplankton and macrophyte species present and their abundance in the lake. The general inter-relationships and effects of sediment resuspension and total suspended solids concentration are outlined in Fig. I. For a lake without significant inflows or outflows, the total concentration of suspended solids in the water column at any time is dependent on the seston concentration and entrainment and deposition rates. Resuspension (or entrainment) of sediments is a function of the bottom shear stresses due to fluid motion and the local sediment characteristics (e.g., Blom et al., 1992). Settling (or deposition) is a continuous process, dependent on the particle and water chemistry (e.g., Lick et al.. 1993). In the past two decades a large number of papers have been devoted to examining and modelling the related mechanisms of sediment resuspension and particle settling in shallow lakes (e.g., Carper and Bachmann, 1984; Hawley and Lesht. 1992; Carrick et al.. 1993; Hamilton and Mitchell, 1996). In shallow lakes the bottom shear stresses associated with horizontal currents are generally too smal1 to influence suspended solids concentrations (Luettich et al., 1990). However. these horizontal circulation currents can have an important effect on the redistribution of particulates resuspended by wave action. Bhowmik and Stall (1978) and Bye (1965) showed that the velocity of surface horizontal currents in a shallow lake is approximately 2 ~~3% of average wind speed. For example in a lake where the surface current boundary layer extends to the bottom of the lake. the magnitude of the mean horizontal current will be approximately l-2% of average wind speed. It then follows that with an average wind speed of 2 m s- ’ from one direction. suspended sediment could be transported up to 1700 m in a 24 h period. This simple scaling is used to illustrate that at any given sampling location, resuspension models which do not include horizontal circulation (Luettich et al.. 1990; Hawley and Lesht, 1992; Hamilton and Mitchell. 1996) will not necessarily reflect the processes by which suspended material arose at that location.

This study focuses on the development and application of a model suitable for describing the relationships enclosed in the dashed box of Fig. 1. The model was developed to allow predictions of the suspended solids concentrations due to wave action over the entire area of a shallow lake for any given wind speed and direction. This model has been coupled with a depth-averaged, two-dimensional hydrodynamic model. Both the suspended sediment model and the combined suspended sediment and hydrodynamic model have been tested against suspended solids data collected on windy days in a shallow lake.

2. Study

site and background

Thomsons Lake (Fig. 2) is a shallow, flat-bottomed lake with a maximum depth of approximately 1.5 m, it is circular with a diameter of approximately 1600 m. The lake is 20 km south of Perth, Western Australia, and 7 km inland from the Indian Ocean. Primarily, it is a surface expression of the ground water table (Arnold, 1990), however it is also fed by small flows that enter the lake through the surrounding rush beds. Thomsons Lake has become meso-eutrophic in recent years as a result of increased urbanisation in the catchment (Cheal and Davis, 1994). The lake was chosen for this study after an initial survey showed that sediment resuspension occurred regularly at typical local wind speeds. Sediment loadings from the immediate lake catchment area are negligible due to extensive fringing native bushland and reeds. These reeds extend out into the lake to a water depth of approximately 0.9 m, buffering the shoreline from direct wave action.

Fig. 1. A summary of the water quality variables potentially affected by the resuspension of sediments in a shallow lake. The dashed box indicates the processes modelled in this study.

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Hamilton

; Ecological

Fig. 2. The bathymetry of Thomsons Lake, Perth, Western Australia. The sampling stations used in this study are numbered (I - 5). The meteorological station was located at station I.

The lake sediments are cohesive and comprised of over 50% organic material (Bailey, unpublished data). The phytoplankton population of Thomsons Lake between August and November 1994 was dominated by two blooms of cyanobacteria, Microcystis ueruginosu Kiitz. emend. Elenkin and Anabaena circinulis Raben. ex Born. et Flah. (Bailey and Hamilton, in press). Over the same period, the thermal stratification in the lake was broken down by either wind stirring when wind speeds exceeded 2 m s ’ for more than 3 h or convective overturn due to overnight cooling (Bailey and Hamilton, in press).

3. Methods Suspended solids data were collected from five stations around Thomsons Lake between July and

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September in 1993 and between August and November in 1994. The stations were located at buoys in positions surveyed by the Water Authority of Western Australia (Fig. 2). In 1993, 106 lake water samples were collected over four windy days and one calm day. The samples comprised of pairs of 250 ml samples, simultaneously collected 0.3 m above the sediment bed and 0.3 m below the water surface at each station. As no gradients in suspended solids concentration were apparent between pairs of surface and bottom samples (Fig. 3), subsequent samples were taken at mid-depth. In 1994, a total of 195 suspended solids samples were collected hourly during wind events on 19 days using a single, mid-depth sample taken at each station. At the completion of each day of sampling in 1993 and 1994, the water samples were returned to the laboratory for analysis of suspended solids ( + 1 mg l- ‘), using filtration through pre-weighed Whatman GF/C filters and subsequent drying and weighing of filters (APHA, 1992). The high organic content of the sediments precluded the use of ashing as a technique for distinguishing between resuspended material and buoyant phytoplankton. In 1993, hourly wind speeds were collected from Murdoch University Meteorological Station

0

80 Suspende2dO sedimen+?q+x?r

scan$es

(mg I ‘)

Fig. 3. Suspended sediment concentration measured in the upper 30 cm of the water column versus the concentration measured simultaneously in the lower 30 cm of the water column in Thomsons Lake in 1993. The slope of the solid line is I:].

220

(MUMS), 10 km north-east of the lake. The MUMS wind speed data were checked against readings taken at the lake surface and adjusted to give 10 m values (CERC, 1984) above the lake surface. However, it was considered inappropriate to use wind direction data from the MUMS as this could not be checked at the lake. Because of this we sampled only during strong wind events from the south-west quarter in 1993 (strong south-westerly winds are very common in this region). In 1994, wind speed and direction were measured at a height of 2.5 m above the water level from a platform at station 1, these wind speeds were also converted to 10 m values (CERC, 1984) and sampling was performed irrespective of wind direction. Water levels were recorded at two gauges: one close to station 3 and another close to station 5.

4. Suspended solids settling characteristics The sediment settling characteristics were determined using settling column analyses based on the description given by Fukuda and Lick (1980). This simple technique allows the change in suspended sediment concentration with time to be determined. In 1993 we performed settling column analyses on two types of samples. Firstly, in light of previous work (e.g., Fukuda and Lick, 1980; Luettich et al., 1990; Blom et al., 1992; Hawley and Lesht. 1992; Kristensen et al., 1992: Vlag, 1992; Hamilton and Mitchell, 1996) we examined the settling characteristics of sediments taken from the top 5 mm of undisturbed sediment cores, which were then resuspended in filtered lake water. Secondly, we performed settling column analysis on the suspended sediment present in unfiltered 1 1 water samples collected at station 1 during a storm event on 30 August, 1993. The concentration versus time characteristics of the two types of samples was markedly different. For example, the samples containing ‘naturally’ resuspended sediments had a median settling velocity of 0.006 cm S -’ while the median settling velocity of the bottom sediments collected from cores was 0.358 cm S -I. Given this difference between the results of

Fig. 4. The change in suspended sediment concentration with time during settling column analyses of water samples taken from all stations in Thomsons Lake. The solid line is the best exponential fit of the average values at each measured interval given by: Suspended sediment concentration = 43.37 exp( 3 x 10-2x I).

the two types of sampling strategies we only examined concentration versus time histories of sediments found resuspended in the water column by storm events in further settling analyses. This approach is consistent with the aim to model the deposition of suspended sediments found naturally in the water column. In 1994, settling column analyses of naturally occurring resuspended sediments were performed on a further ten water samples taken from each station during two storm events. Fig. 4 shows the changes in concentration over time for all of the naturally resuspended sediment samples, where the line denotes the function which best fits the mean concentration at each time interval. This function is the exponential, C = 43.37 exp( 3.0 x 10di x t), with r2 = 0.85 (P< 0.01). We have considered this function to be analogous to a deposition model for the suspended sediments in Thomsons Lake and it can be written in a general depth averaged form.

(1) Where b is defined as the deposition parameter, C,, is the initial concentration and 11is the depth. The settling column was 1 m deep, implying that h = 1.0 m, and with t measured in seconds then /I can be set as 3.0 x 10 5 m s ’ for Thomsons Lake suspended sediments. In using Eq. (1) as a

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general model for the deposition of resuspended sediments in Thomsons Lake, h is set to the water depth at the location where deposition is occurring. Lick (1982), Ssndergaard et al. (1992) and Hamilton and Mitchell (1996) also suggested that the change in concentration with time due to settling may be characterised by an exponential decay function. However, they did not use the function directly in their models, and like Blom et al. (1992) and Vlag (1992) they used a simpler model for deposition based on the form; Cdep= IV,C,,. The parameter M’, is then either a settling velocity assigned to the entire suspended sediment concentration or an array of settling velocities with each component assigned to a different sediment fraction. By directly using the function describing the change in concentration with time as the deposition model, the requirement to assign a single settling velocity or range of settling velocities to the suspended sediment is circumvented.

5. Sediment entrainment

and deposition model

Sediment resuspension occurs when bottom stresses are sufficient to entrain material from the lake bed (Hawley and Lesht, 1992; Vlag, 1992). It should be noted here that there will be important differences between the processes observed in lakes and those observed in the laboratory. Lau and Krishnappan (1992) showed in flume experiments that deposition did not occur at the same time as entrainment, thus in a manner deposition was related to entrainment. These results were based on resuspension and deposition in a near-uniform turbulent stress field over the sediment bed. By contrast, the bottom shear stresses due to wave action in a lake will be highly variable (Best, 1992; Nielsen, 1992). Accordingly. we have modelled deposition as being independent of entrainment; lake-wide, deposition will occur simultaneously with entrainment. We used a depth-averaged model to describe the resuspension and deposition processes. This approach is justified by the observed lack of vertical variation in suspended solids concentration (Fig. 3), and the breakdown of thermal stratification at low wind speeds (Bailey and Hamilton, in press).

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For the sediment entrainment-deposition model (SEDM), Thomsons Lake was represented by a grid of 100 x 100 m cells, For a cell with an initial concentration, C,(kg m - ‘) (kg m - ‘), the concentration following a time step of At (seconds) will be given by, C (n+ 1)= Ccn,+ ACento~+ 1)- AGrp,,> - I)

(2)

where ACentcn+ I, (kg m ~ ‘) is the change in concentration due to entrainment over At and ACdrpfn + I) (kg m -‘) is the change in concentration due to deposition over At. We used a parameterisation of Du Boys’ relationship (Vanoni, 1975) between the change in depth-averaged concentration due to entrainment, and the bottom stress. Our formulation is based on the work of Lavelle and Mofjeld (1987), who argued, via a review of previous work, that in many cases the critical shear stress for entrainment may be set to zero, and Hawley and Lesht (1992), who used parametric analysis to show that entrainment may be modelled as linear function of the bottom shear stress. The formulation for the change in concentration due to entrainment is given by; Ac,,,=;K,

2 At ( Tret1

(3)

where T (N m -2) is the bottom shear stress due to fluid motion, TV,,-is defined as a unit stress (Hawley and Lesht, 1992) to maintain a non-dimensional stress term, the depth of the water column is given by h (m). and K, (kg m -’ s ‘) is the sediment entrainment parameter. From Eq. (1) the change in depth-averaged concentration due to deposition (Cdrp) over time step At is.

AGep,,, +I,= C,,,,(l -xp( -yjj In Eq. (4) we assume that the particle deposition rate will not be altered by turbulence, that the deposition rate is constant with depth and that the deposition parameter, p, is independent of SUSpended solids concentration. Van Rijn (1989) suggests that this final assumption is valid for concentrations less than 300 mg 1~ ‘.

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Eq. (2) therefore becomes;

To solve Eq. (5) a bottom stress is computed for each 100 x 100 m cell of the lake. A combination of three forms of bottom shear stress act on the bed; current induced stresses, turbulent eddy stresses and wave induced stresses. Carper and Bachmann (1984), Gabrielson and Lukatelich (1985), Luettich et al. (1990), Hawley and Lesht (1992) and Hamilton and Mitchell (1996) have shown that for shallow lakes, sediment resuspension is primarily a result of wave action. Scaling analyses show that current induced velocities can attain the same order of magnitude as wave orbital velocities but, as explained by Nielsen (1992) the thinner bottom boundary layer associated with wave action means that the sediment entrainment stress due to currents will be negligible compared with wave generated stresses. Each computational cell was assigned a depth and straight line fetch (CERC, 1984). The fetch for each cell was computed for each octant of wind direction (i.e., north, north-west, west, etc.). The lake was thus described by the bathymetry matrix and eight arrays of fetch values. Given hourly input values of wind speed at 10 m and direction, the SverdruppMunk-Bretschneider shallow-water wave equations (CERC, 1984) were then used to compute surface wave height (H), wavelength (i), and period (T) for each cell. The short period of the surface waves in shallow lakes ( * 1 s) means that the associated bottom boundary layer is thin (Nielsen, 1992) and it is reasonable to model the bottom shear stresses using the following formulation from laminar wave theory (Luettich et al., 1990).

(6)

6. Circulation model In shallow lakes (i.e.. depth < 2.5 m), Hunter and Hearn (1987) showed that the dominant force

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balance is between the surface wind stress and bottom friction, and thus the wind-induced current velocity boundary layer will generally occupy the full depth of the lake. Therefore in shallow lakes, horizontal topographic gyres will dominate the overall circulation. To examine the effect of imposing a depth-averaged horizontal circulation pattern on the distribution of sediments resuspended by wave action, we used the Tidal Residual Intertidal Mudllat model (TRIM-2D), a two dimensional, depth-averaged, semi-implicit hydrodynamic model developed by Cheng et al. (1993) for shallow water applications. The model was initially used to simulate the hydrodynamics of San Francisco Bay, and has since been applied in modelling suspended solids transport (McDonald and Cheng, 1994). Each 100 x 100 m cell was defined by nine depths; a depth at each corner, a depth at the centre of each side and depth at the cell centre. These nine points were used to calculate the average cell depth and the cross-sectional areas for fluxes in the north and south directions (refer to Fig. 1 in Cheng et al., 1993). The grid size selected for Thomsons Lake was considered appropriate to account for the relatively gradual changes in bathymetry over the lake (Fig. 2), whilst giving adequate horizontal resolution. TRIM utilises the Chezy-Manning formulation for bottom stresses based on the frictional dissipation of momentum at the sediment-water intercoefficient, The bottom roughness face. Manning’s Number, was set to 0.025 (Streeter and Wylie, 1983). The model was forced with surface stresses computed from wind speed and direction. The surface stress in the x and I: direction (z, and r,.) is related to the x and y components of wind velocity (u., and u,) by the formulation; (7)

where C,= 1.25 x 10 3 is the drag coefficient between air of density 1.25 kg m ~ 3 (p,) and water of density 1000 kg m ~’ (p,). The total suspended solids concentration (C) was modelled as a single conservative tracer in the transport equation, using the computed depth-averaged velocities, o’, and U,.;

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Buiky.

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Hamilton

Ecological

In a shallow lake the horizontal turbulent diffusivity, K,,, may vary over two orders of magnitude depending on the type of forcing and location (Maiss et al., 1994). We used a lakewide value of 1 m2 s-’ based on a range proposed by Lemmin (1989) for wind-induced mixing in a small lake. To combine SEDM, which calculated concentrations on a 3600 s time step, and TRIM, in which a 600 s time step was used, concentrations were passed between the models at the end of each hour. The concentrations predicted from SEDM were based on the average wind speed and direction for the previous hour and the initial concentrations in each cell which were derived from the TRIM calculations from the end of the previous hour.

7. Model calibration The calibration and validation process utilised data from days 210, 224, 242 and 247 in 1993 and days 223, 243, 245 and 264 in 1994; a total of 140 measurements at five stations on the lake. For each of these sample days the model was run over 24 h; from midnight to midnight. We excluded suspended sediment data from many other days of sampling in 1994 due to the elevated suspended biomass associated with two blooms of buoyant cyanobacteria (Bailey and Hamilton, in press). Using the parameter values given in Table 1, the maximum computed horizontal current velocities from TRIM were + l-2% of the wind velocities. There were no current meter data to validate the computed velocities, however, based on the work of Bhowmik and Stall (1978) the modelled velocities are of the correct order of magnitude. The sediment deposition parameter (p) in SEDM was set according to the fitted exponential curve in Fig. 4. Therefore the sediment entrainment parameter, K,, was the only

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non-fixed parameter in the SEDM and the SEDM + TRIM models and as such calibration of the models was achieved by adjusting K,. The entrainment parameter may potentially be assigned different values for each computational cell in the models, however, in this study K, was assigned the same value for each computational cell. This assumption was based on core samples taken at each site which showed that sediment type and water content were relatively uniform horizontally and that there were no obvious factors affecting entrainment, such as the presence of benthic macrophytes or algae (Bailey, unpublished data). The calibration criterion was to achieve the best fit against suspended solids concentrations measured at station 2. This station was the furthest downwind from the majority of the wind events and measured concentrations at this site thus showed the greatest wind induced response (Fig. 5). Calibration was considered to be satisfactory when the sum of the squares of the residuals between measured and modelled concentrations for a 24 h period was minimised. For both SEDM and SEDM + TRIM, the values of the entrainment parameter required to calibrate the models did not differ significantly between calibrations using the 1993 and the 1994 data. The values of the initial conditions and the various parameters used for the models are given in Table 1. Table 1 Parameter values for the SEDM tions used in this study Model

parameter

Deposition parameter, p(ms ‘) Background suspended solids concentration (mg IF’) Horizontal diffusion coefficient. K, (m’ s-‘) Manning’s number. n Entrainment parameter. K, (mg m -’ SC’)

and SEDMfTRIM

SEDM+TRIM

SEDM 3.0x

10 -5

3.0 x IO-’ 2.0

2.0

Not

required

1.0

Not 35

required

0.025 23

simula-

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1607

-c

140

B120 L 5100 .-E ; 80

1

2

5

Station Fig. 5. Plot of suspended sediment concentrations measured (‘-2) and average of 1994 data at each station (0).

at each station

8. Results and discussion The use of a depth-averaged approach to modelling (Luettich et al., 1990; Hawley and Lesht, 1992) is justified as the water column was found to be generally well mixed (Bailey and Hamilton, 1997) and no vertical gradient in suspended solids concentration was observed in samples taken simultaneously from the top and the bottom of the water column (Fig. 3). In Fig. 5 all the measured suspended solids concentrations are plotted according to location. The sampling was generally performed during afternoon sea-breeze events from the south-west and as such, stations 2 and 3 were consistently furthest downwind. This is reflected in the higher average concentrations at these stations for both the 1993 and 1994 data. This general observation that suspended solids concentrations increase with fetch length is in agreement with the observations of Carper and Bachmann (1984) and Hamilton and Mitchell (1996). The significant variation between the settling characteristics of the resuspended core sediments and the sediments naturally present in the water column during strong wind events is important to note for further studies, especially if cohesive sediments are involved.

in 1993 and

1994, average

of 1993 data

at each

station

The settling column technique does not recreate the turbulent conditions under which the particles settle in the lake, and as such, the flocculative behaviour of particles may be changed by removing the dispersive effect of the stresses imposed by turbulence (Lau and Krishnappan, 1992; Lick et al., 1993). Also, the hydrodynamic effects of turbulence on settling are not incorporated, whereby the inertia of the particles has been shown to result in different settling rates in environments of differing turbulent energy (Wang and Maxworthy, 1993; Hoyal et al., 1995). At present there are no criteria for incorporating these effects and perhaps one shortcoming of deposition models to date (including this one) is that they have been ignored. The influence of advection and diffusion, and the effects of including changes in wind direction, and hence the fetch length for each cell, are illustrated by Fig. 6(a-d). In the sediment resuspension model without circulation, SEDM, output generated from wind data collected on day 243 in 1994 shows the effects of changing wind direction in the model. At 18:00 h (Fig. 6(a)) the wind is from the south with the peak concentrations at the northern edge. Prior to 18:OO h the wind was south-easterly, leaving a residual record of resuspended sediments on the western edge. At

M.C.

Fig. 6. Suspended sediment 1994. Plots are a snapshot IS:00 h and (d) 20:00 h.

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concentration contours (mgl~ ‘) computed with 24 h of wind speed and direction data from day 243. at (a) 18:00 h and (b) 20:00 h. computed using SEDM. Plots using SEDM + TRIM are shown for (c)

20:00 h (Fig. 6(b)) the wind is from the south-west and the peak has moved towards the north-east corner. As the wind swings to the south-west, residual concentrations remain in the north-western corner of the lake. In SEDM simulations, the horizontal distribution of the suspended solids is linked to the value assigned to the sediment deposition parameter; a smaller deposition parameter would result in larger residual concentrations following a change in wind direction. In Fig. 6(c,d), examples of the SEDM + TRIM simulations using the same input data from day 243 in 1994 are shown. The effect of circulation is evident in the characteristic bow shape of the concentration contours in Fig. 6(d). Circulation has dispersed concentrations along stream lines around the edge of the lake and diffusion has dissipated concentrations down local concentra-

tion gradients against the mean current into the centre of the lake. The overall effect of including changes in wind direction and the processes of diffusion and circulation in the resuspension and deposition model is to reduce the peak concentrations in the high energy downwind locations and to increase the concentrations in the low energy upwind regions of the lake. The result is that modelled horizontal gradients of suspended solids concentration match more closely with the observed gradients. To best visualise this overall improvement, the means of all the measured concentrations and the means of all the corresponding modelled concentrations at each station around the lake for each year have been plotted in Fig. 7(a,b). In the plots of the 1993 data and simulations in Fig. 7(a), the SEDM results mirror the general trend seen in the mea-

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Fig. 7. Average modelled suspended sediment concentrations versus average measured suspended sediment concentrations throughout Thomsons Lake. Modelled values and observed data are shown for (a) days 210. 224, 242 and 247 in 1993 and (b) days 223, 243, 245 and 264 in 1994.

sured data, with increased concentrations at the downwind stations, however there is a marked improvement in the fit against the measured data in using the SEDM + TRIM simulations. In the plot of the 1994 data and simulations in Fig. 7(b), the fit has again been improved with the use of the SEDM + TRIM model. Ward et al. (1984) found that seagrass beds in Chesapeake Bay reduced the amount of sediment resuspended due to wave action. The same effect could be expected to occur in a lake containing beds of benthic macrophytes. Other variations in bottom conditions would also alter the entrainment of sediments, i.e., rock, concrete, clays and sands. These effects can be modelled using the present system by assigning different entrainment parameter values to individual computational cells in the water body. A hypothetical example is presented in a SEDM + TRIM simulation of day 243 in 1994 for times of 18:00 h and 22:00 h (Fig. 8(a,b)), with the entrainment parameter of the dashed region set to 3 mg m ~ ’ s- ’ (an arbitrary value) compared with 23 mg m PI s-’ used for the remainder of the lake. By comparison with Fig. 6(c,d) there is a significant reduction in lakewide suspended solids concentrations. This is a potentially useful lake management tool. If a lake can be successfully modelled and accurate hindcasting achieved, then the effects of changing bottom conditions (e.g., macrophyte beds, sediment remediation) may quickly be approximated by adjusting values of the entrainment parameter array.

9. Conclusions

The sediment entrainment and deposition formulation developed is not site specific. The model contains only one parameter, the sediment entrainment parameter, which cannot readily be calculated or directly measured. Calibration of the model is thus effected through adjustment of the entrainment parameter; previous values for this have been in the range lo-400 mg m - 2 s ~ i (Vlag, 1992). The entrainment parameter will vary according to sediment type, size, consolidation, water chemistry and the presence of benthic flora and it is therefore difficult to make comparisons of values between lakes. As far as possible, the conditions for the settling column analyses remained unchanged from the conditions found during resuspension events. As a result we believe that we were able to accurately determine the settling characteristics of the suspended particles for the purposes of the model. In modelling sediment deposition with an exponential decay curve fitted to the change in concentration with time, which was calculated from the settling column results, the model characterises the natural deposition process simply and accurately. SEDM or similar models based purely on wave action can be calibrated to model down-wind concentrations of resuspended solids in shallow lakes with reasonable accuracy. However, these models in general, will not be useful for modelling

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Fig. 8. A simulation of the effect of altered bottom conditions on sediment resuspension, the region inside the dashed line has been allocated an entrainment coefficient equal to 3 mg m 7 s I, the entrainment parameter in the remainder of the lake is 23 mg m ~’ s -- ‘. The contours (mgl~ ‘) have been modelled with SEDM + TRIM using 24 h of data from day 243 1994. (a) contours for 1800 h. (b) contours at 22:00 h

suspended solids concentrations lake-wide as they do not contain the mechanisms of diffusion and advection. This was highlighted by the overall improvement in modelling made by coupling the resuspension model with a circulation model. Allowing for changes in wind direction, and hence fetch, was an important part of the modelling process. Our work suggests that for lakes in regions of directionally varying strong winds, the effects of changing wind direction may have a greater influence on the distribution of sediment concentration than advection and diffusion.

Acknowledgements The first author was supported through a Centre for Environmental Fluid Dynamics Grant from the Centre for Water Research (University of Western Australia). Access to Thomsons Lake, an ‘A-class conservation reserve’, was granted by the Department of Conservation and Land Management of Western Australia. John Patterson and Carolyn Oldham made valuable comments on the manuscript. We thank Vincenzo Casulli for supply of the TRIM code to the centre for Water Research. This paper was significantly improved by incorporating the constructive criticisms of two anonymous reviewers.

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