by

E.S. Millard^*, E. Halfon^**, C.K. Minns^*, and C.C. Charlton^*

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MODEL FRAMEWORK

Contaminant Fate Model (TOXFATE)

TOXFATE (Fig. 1) is a contaminant fate model which integrates information on the properties of a chemical with the environment where the chemical is found, such as wind speed, the amount of particulate matter, etc.

TOXFATE simulates the time-varying concentrations of a toxic contaminant in the water column. The model is formalized as a system of ordinary differential equations and the equations can be parameterized to represent a variety of contaminants. In this effort the state variables are organic contaminant concentrations in particulate matter and water. The physical-chemical properties of the toxic contaminants, such as molecular weight, solubility, octanol-water partition coefficient (K_ow), Henry's Law constant are used as input data to the model (Table 1). The transport processes of sedimentation are handled by a box model. The pollutant is assumed to be immediately and completely mixed within each spatial cell (epilimnion and hypolimnion).

Two mass balance equations describe the fate of a toxic contaminant. The equations are solved numerically. These equations describe the movement of the contaminants across different phases. For example Eq. 1 has the following meaning: The change in time of the amount of toxic contaminants in the water column is a function of several processes including loadings losses to the atmosphere and internal redistribution of the toxic contaminant in different phases, thus

dx

V -- = loading - sorption to particulate

dt

+ desorption from particulate - volatilization

In mathematical terms the fate model has the following form:

dx₁

V -- = L - V S k₁ K_oc foc_ss x₁ + V S k₂ x₂ - V k₄ x₁

dt

where:

x₁ = toxicant concentration in water [mg m^-3]

x₂ = concentration of toxicant in particulate [mg kg^-1]

k₁ = sorption from water [m³ h^-1 L^-1)]

k₂ = desorption from particulate matter [h^-1]

k₃ = sedimentation velocity of particulate matter [cm d^-1]

k₄ = volatilization [h^-1]

The volatilization model in TOXFATE is the standard two-layer representation of the water surface (Liss, 1973); the volatilization rate is modeled using the well known two-film representation of the water surface (Liss, 1973). Thus the volatilization parameter, k₄ [h^-1] is computed a

s

1 A

k₄ = ----------- - (2)

K_liq + K_gas V

where, K_liq [h m^-1] is the inverse of the liquid phase mass transfer coefficient, K_gas [h m^-1] is the inverse of the gas-phase mass transfer coefficient, and A [m²] and V [m³] are the areas and volumes of the microcosm. The parameter K_liq is computed as:

1

K_liq = --------------- (3)

k_O2 (32/MWT)^.5

where k_O2 is the oxygen (molecular weight 32) exchange constant [m h^-1] computed according to measured wind speeds (u) at 10 m over the water surface (Banks, 1975).

k_O2 = 1.51 x 10^-2 u^.5 for u < 5.5 m/s

(4)

k_O2 = 1.15 x 10^-3 u² for u > 5.5 m/s.

In this model the effects of intermittent turbulent and advective transport events are not included since, as Burns et al. (1981) noted, Whitman models usually differ very little from the predictions of more complex (e.g., surface renewal) models (Danckwerts, 1970). The k_O2 factor is adjusted for water temperature with the following formula,

k_O2 = k_O2 * 1.024 ^{(Temperature-20)} (5)

The gas resistance, K_gas, is computed as follows:

1

K_gas = -------------- (6)

W H (18/MWT)^.5

R TKEL

where W [cm h^-1] = 0.1857 + 11.36 u [m/s] at 10 m over the water surface (Liss, 1973), H [m³-atm/mol] is Henry's Law constant, 18 is the molecular weight (mw) of water, R is the gas constant and TKEL is the water temperature (^oK). If H is not known, it can be computed using information on the vapour pressure VAPR (in mm Hg) and the contaminant solubility SOLL (mole m^-3), then

VAPR

H = -------- (7)

760 SOLL

The factor 760 in Eq. 7 converts the vapour pressure from mm Hg to atmospheres.

The sorption rate on particulate matter depends on the K_oc of the chemical and on the organic content of the compartment. Sorption is modeled assuming nonequilibrium between water and particulate matter.

dx₂

V S -- = V S k₁ K_oc foc_ss x₁ - V S k₂ x₂ - S k₃ A x₂

dt

where x₂ is the concentration of contaminants in particulate matter [mg_contaminant/kg_{particulate matter}], k₁, k₂ and k₃ are parameters whose respective values were obtained by calibration, K_oc is the affinity of the contaminant for organic matter [(mg_contaminant/kg _{particulate matter}) / (mg_contaminant / L_water)], foc_ss is the fraction of organic carbon in particulate matter, about 0.12, x₁ is the concentration of the contaminant in water [mg_contaminant/m³_water], V is the volume of water [m³] and S is the concentration of particulate matter [kg m^-3].

As mentioned above four parameters were calibrated,

k₁ to k₄. Parameters k₁ and k₂ describe the affinity of toxic contaminants for particulate matter. The rate constants, however, are controlled by other measured quantities, such as K_oc and f_oc. Thus k₁ and k₂ are scaling constants.

When TOXFATE is used to predict the fate of a toxic contaminant in a lake one of the parameters needed to correctly predict the fate of a contaminant is the wind speed at one metre from the water surface. This information is usually collected either on site or obtained from airports nearby. In the case of the microcosm experiments the wind was provided by a fan mounted on top of the microcosms. Measurements with an anemometer showed that it was impossible to correctly quantify the wind speed at the microcosm surface since the measurement varied widely across the surface. For this purpose an optimization method was used to estimate a nominal wind speed from the data. The calculation of this wind speed allows us to understand whether a contaminant is more or less volatile. For example, if a high wind speed is estimated, then the interpretation is that a large amount of PCBs was lost from the microcosm to the atmosphere. Conversely, a low wind speed indicates that most of the contaminant is still found in the microcosm. The computed wind speed is therefore an estimate of the volatilization capability of the contaminant.

Model and simulation were compared and parameters were calibrated accordingly. Table xxx shows the predicted and observed concentrations of PCBs.

A mass balance of contaminants is important to assess the fate of the chemicals once they enter the microcosm.

Contaminants fate

The fact that only a low percentage of the contaminants is found in the microcosm confirms our estimate that volatilization is the most important route of removal. The model suggests that volatilization is as important as sedimentation as a removal process for PCBs.

A simulation model, TOXFATE, has been employed to quantify the behaviour of PCBs in microcosms. The main purpose of this research is to quantify the fate of PCBs.

In the calibration stage TOXFATE has quantified the behaviour of PCBs in microcosms. The predicted and observed concentrations in the different components of the ecosystem agree within xxx for averages and are completely indistinguishable if standard deviations are considered.

Danckwerts, P.V., 1970. Gas-liquid reactions. McGraw-Hill Book Co., New York, 276 pp.

Halfon, E. 1984a. Modeling the fate of toxic contaminants in the Niagara River and Lake Ontario. Part I and Part II, Environment Canada, NWRI report No. 84-39.

Halfon, E.H. and Oliver, B.G. 1990. Simulation and data analysis of four chlorobenzenes in a large system, Lake Ontario, with TOXFATE, a contaminant fate model, S.E. Jorgensen (Ed.) Ecological Modelling in the 1990's, Elsevier (in press).

Liss, P.S., 1973. Processes of gas exchange across an air-water interface. Deep-Sea Res., 20:221-238.

The processes of sedimentation and volatilization are dominant pathways in determining the fate of PCBs in natural systems such as the Great Lakes (MacKay, 1989). The two processes compete for a portion of the total PCBs pool in the water; their relative success is influenced in part by particulate- and water-phase partitioning. Both density of adsorbent particles and their organic carbon content are responsible for the partitioning between the soluble and particulate pools. These factors determine the size of pool available for either process. Volatilization occurs from the soluble pool while sedimentation is from that part of the total PCBs pool attached to particulates. The degree of mixing, in terms of strength of turbulence and depth of the mixed layer, influences volatilization. All these processes affect the fate and transport of radio-tracer labelled PCBs in large model ecosystems.

Our study has four main goals:

a) To verify Millard et al.'s (1983) suggestion that PCBs unaccounted for (in a mass balance) are lost by volatilization;

b) To determine the relative importance of mixing and algal productivity on volatilization and sedimentation; c) To determine whether a soluble or particle-bound mode of entry of PCBs into a system has an influence on fate and whether mode of entry affect the relative importance of volatilization and sedimentation; and

d) The last, but perhaps most important goal, is to build a fate model that would allow us to describe mathematically the trends over time of PCBs concentrations in the model ecosystems and thus determine the dominant removal process under various scenarios of mixing and productivity.

Three experiments were carried out. The first experiement is conducted to test the assumption that, if we cut off the access to an air-water interface, volatilization would be low. A high proportion of added PCBs would be recovered confirming the hypothesis that the losses had been due to volatilization.

The second part of the study consists of two experiments to investigate the importance of mixing and productivity on fate of PCBs in the same model ecosystems. Our a priori hypothesis is that high productivity should reduce volatilization losses and enhance the transfer of PCBs to the bottom through sedimentation. We assume that higher particle density from algal biomass would reduce the size of the soluble pool and therefore the amount of PCBs available for transfer to the atmosphere. In contrast, we hypothesize that high mixing would promote volatilization because of the rapid renewal rate of the bulk water at the air-water interface and thus increase the opportunity for transfer to the atmosphere. The synergistic and antagonistic effects of the various combined treatments were not known. However, expectations for additive treatment effects were probably realistic. As an example, since we expected sedimentation to be enhanced by productivity and volatilization to be lower with lower mixing, we therefore expected the highest sedimentation when productivity was high and mixing low. Likewise the highest volatilization was anticipated where mixing was high and productivity low.

The experiments are carried out in microcosms referred to as Lake Column Simulators (LCS). The columns, 4.5 metres high and one metre in diameter, are filled to 4.35 m for a total volume of 3417 L. A refrigerating system cools the lower portion of each column producing a thermocline between 2.0 and 2.5 m. The epilimnion average 2.15 m depth (1689 L) and the hypolimnion 2.2 m (1728 L). Temperature differences between the two layers are pronounced and the thin metalimnion is considered to be part of the hypolimnion in terns of mass balance calculations. A complete description of the LCS is given in Millard et al. (1982). Magnetic drive pumps replace the smaller pumps used for vertical mixing in the earlier study (Reference). These pumps are better suited to continuous operation and pumping speed could be varied so that mixing regimes and turbulence at the air-water interface could also be varied quantitatively.

In all experiments a custom preparation of [¹⁴C] Aroclor ^R 1242 (specific activity = 31.1 m Ci× mmole^-1, New England Nuclear Corp.) is used. PCBs concentrations are reported here as radioactivity ( dpm× L^-1). No carrier is used in the experiments and the only non-labelled PCBs in the systems are the low concentrations in the Burlington municipal water used to fill the LCS.

Experiment 1

Two thermally-stratified, abiotic columns are used in this experiment. No algal inoculum is used, no nutrients are added and the lights are kept off to prevent algal growth.

Two treatments are prepared by injecting 0.625 and 0.750 mL of PCB-methanol solution containing 29.357 uCi and 29.528 uCi of labelled PCBs into clay-water slurries of 10 g finely ground illite clay mixed with 100 mL water. Water used to prepare the slurry in all the experiments is glass distilled and cleaned by passing it through XAD-2 resin. Previous checks have shown that over 95% of the total PCBs in slurries with this adsorbent density are adsorbed to the clay.

In one experiment, one slurry is added directly to the epilimnion of one column just under the surface. In another experiment a slurry is added to the hypolimnion of a second column through a tube extending from the surface. The tube is slowly withdrawn and the hypolimnion is gently mixed with a long paddle. This is the only mixing provided to this treatment. The mixing regime in the epilimnion-spiked column is the same as in (reference).

Experiments 2 and 3

In these experiments both productivity levels and mixing regimes are varied between high and low extremes. Each experiment has a high (HM) and low (LM) mixing regime, combined with high (HP) and low (LP) productivity. The four combined treatments in each experiment are referred to as HMHP, LMHP, HMLP, LMLP.

Productivity levels are maintained by addition of phosphorus (P) at 2.5 mg× day^-1 for the HP treatment and 0.2 mg P× day^-1 for the LP treatment. Nitrogen is added at an N:P ratio of 17:1 and all other essential macro- and micronutrients are added daily. The emphasis is on total algal biomass and not species composition. However, the algal inoculum came from a batch culture of mixed chorophycean algal species (Selanastrum, Coelastrum, Ankistrodesmus, Scenedesmus and Chlorella) which are known to thrive under the growth conditions in the LCS.

Pumps are operated at either full capacity (32 L× min^-1) for the high mixing regime or slowed to a rate similar to that used in the earlier work (6.8 L× min^-1) for the low mixing regime.

In both experiments 2 and 3 the PCBs additions per column varied between 30 and 33 uCi. In experiment 2 slurries of 1.0 g clay in 10 mL of water are spiked with 0.1 mL of a PCB-methanol solution. These slurries are added about 30 cm under the surface of each column and quickly disperse throughout the epilimnion because of the mixing.

In experiment 3 the PCBs are dissolved in 100 mL of methanol and added directly to the column in solution about 1 m under the surface using a glass tube.

Samples are collected within three hours of treatment in experiment 1 and within one hour in experiments 2 and 3. Samples are collected 24h later and every two-four hours from then on except for one seven day interval at the end of experiment 1.

Composite samples are collected from epi- and hypolimnion and vacuum-filtered through glass-fibre filters (Whatman GF/C) for determination of particulate PCBs and seston dry weight.

Sedimentation is measured using simple sediment traps made from 0.5 L glass jars 9 cm diameter at the mouth. Traps are suspended in the hypolimnion at 3m. Trap contents are also sampled for particulate PCBs and seston dry weight.

Filters for particulate PCBs measurement are placed directly into glass scintillation vials with 15-20 mL of PCS liquid scintillation cocktail ( Amersham Co.). The contents are agitated on a vortex mixer until the filters disintegrate and a homogeneous suspension is obtained. Soluble levels of PCBs are collected on the filtrates in clean glass filter-flasks. Each filtrate is extracted twice by mixing 0.1 L petroleum ether with 1 L of filtrate for at least 30 minutes for each extraction. The two solvent extracts for each sample are combined, evaporated to several mL and placed in glass scintillation vials with fluor. All samples are counted on a Beckman LS 8100 liquid scintillation counter, corrected for background and quench-corrected using the sample channel's ratio method. Counting accuracy is to a two sigma level of accuracy of 2 % or a default time of 20 min.

In experiments 2 and 3 an estimate is made of the amount of PCBs adsorbed to the walls of the LCS. Stainless steel plates (0.02 m²) are hung at 1 and 3 m for one two one-week periods. The plates are retrieved, rinsed with distilled water and adsorbed PCBs removed by rinsing repeatedly with petroleum ether. Extracts are treated the same as other soluble extractions.

A linear fate model was developed and calibrated to simulate the trends in PCB concentrations observed in the LCS. An optimization technique is used to estimate both model structure and parameter values and obtain the best least-squares fit between simulations and data. The model (Fig. 1) simulates the concentrations of PCBs in the water column over time. A mass balance approach is used to budget PCBs in the different pools and the amount removed by volatilization and sedimentation. It is assumed that soluble and particulate PCBs are immediately and completely mixed within each compartment (epilimnion and hypolimnion). The model is formulated as a system of five linear differential equations,

V dx/dt = Ax, x(0) = measured concentrations at first sampling time

where x is the concentration [dpm× m^-3] of PCB in each of the five pools with dimensions dpm× m^-3 (x1 and x3, PCB dissolved in epilimnetic and hypolimnetic waters, respectively), x2 and x4, (PCB adsorbed on particulate matter in epilimnetic and hypolimnetic waters, respectively), and x5, PCB adsorbed to colloidal matter. A is a 5 by 5 matrix that describes the relationship between various pools and parameters and V is the volume of the respective compartment (epilimnion or the hypolimnion) of the column (Table 2). Parameters are designated as K (K1 to K8) in the rest of the paper to simplify discussion. All K parameters have dimensions of h^-1 except for K₃ and K₈ that have dimensions of m× h^-1. The parameters K₁ to K₈ quantify the following processes:

K₁ = desorption from particulate matter [h^-1] in epilimnion

K₂ = sorption from water [h^-1] in epilimnion

K₃ = volatilization [m× h^-1]

K₄ = desorption from particulate matter [h^-1] in hypolimnion

K₅ = sorption from water [h^-1] in hypolimnion

K₆ = desorption from colloidal matter [h^-1] in epilimnion

K₇ = sorption from water [h^-1] in epilimnion

K₈ = sedimentation velocity of particulate matter [m× h^-1]

The equations describe the movement of PCBs between different phases. For example, the first line of matrix A can be interpreted as: the change in the total amount of PCB over time (thus, the presence of the volume on the left side of the equation) of dissolved PCBs in the epilimnion as a function of several processes including losses to the atmosphere (K₃) and internal repartitioning (K₁, K_2, K₆, K₇) of PCBs between different phases. Rows in the matrix correspond to compartments x₁ to x₅ in the model. Thus:

V dx/dt = -(adsorption particulate + volatilization + adsorption colloidal)

+ (desorption particulate + desorption colloidal)

Systems identification: In control theory, the procedure to find the model structure is called systems identification. An optimization algorithm is used to first to determine whether parameter values can be found that would result in close agreement between observed and modelled results. If a good fit is obtained, then both the model structure and parameter values are appropriate to describe the data. Otherwise, the model structure must be changed.

Initially, the same four PCB pools measured in the columns were used in the model. These pools are: PCBs dissolved in water and adsorbed on particulate matter in both the epi- and hypolimnion compartments. However, early runs with the model showed that this simple four-pool model could not accurately replicate the observations. The loss of soluble PCBs due to volatilization was rapid in the first four days and then slowed to a more constant rate. Agreement between simulations and data was good for the first few days but bad in the latter stages of the experiment. On the other hand, with a slow volatilization rate in the model, the fit was poor initially but much better during the last few days. Obviously there was something inherently wrong in the basic premise of the model.

At this point we decided to add a fifth pool to the model that was to mimic the behaviour of PCBs attached to colloidal material in water. Experimental work by others (Voice et al., 1983; Gschwend and Wu, 1985) confirms that this pool exists and may play an important role. PCBs associated with colloidal matter would be measured as dissolved because standard filtration techniques are unable to separate this material. Functionally, the colloidal pool would behave like the particulate pool: PCBs are not actually dissolved but adsorbed and they can not volatilize. Colloidal PCBs can adsorb and desorb from water.

In mathematical terms, model simulations and data are compared through a vector y (of dimensions 4 x 1), computed as

y = Cx,

where C is the 4 x 5 output matrix,

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

1 0 0 0

In this way it is possible to relate the observations to the theoretical model. The inclusion of the colloidal pool proved to be correct from a modelling point of view. A rapid volatilization rate simulates the rapid disappearance of PCBs from the columns in the first few days, but the adsorption of PCBs to colloidal material slows the disappearance of PCBs later in the experiment as observed.

The second process is the calibration of model parameters to let the model fit the data in a least-squares sense. The objective function, used to compare simulations and data, has the following form:

5 6

F = S _i S _j [(Obs_ij - Pred(K)_ij)2 / Obs_ij] (1)

i=1 j=1

where Obs_ij is the observation of the ith (1 to 5) compartment at time j (1 to 6). Pred(K)_ij means that the predictions are a function of the estimated parameters K. To find the parameter values, commercial optimization algorithms (IMSL, 1987) were used. The algorithms numerically compute the gradients of the function (F) to each parameter. Sedimentation, quantified by the parameter [K₈], was not estimated by optimization because measured values for each column were used (Table 1).

Initially, we used the IMSL subroutine UMINF that performs an unconstrained optimization. Unconstrained means that the parameters can take any value. No good set of parameter values was found. The main reason is that parameters are correlated with each other. Most parameter pairs, K4 and K5, and K6 and K7, can take almost any value as long as their ratio remains constant. This is especially true for parameters K6 and K7 since only observations of X1 + X5 are available (see above): these parameters can not be quantified uniquely. The subroutine BCONF, for constrained optimization, performed well because parameters were kept within a given range when no unique values could be found.

However, the use of constrained optimization implies that it is not possible to quantify precisely the effects of mixing and productivity. Table 2 shows the best parameter values. K6 and K7 are not included in this table because their value is always located at the constraint and their numerical value is therefore meaningless, what is important is their ratio. Consequently, the results focus on comparison of PCBs fate among the treatments and not by comparing parameter values. In these experiments, it is possible only to compare patterns of behaviour, for example, within a given experiment, the relative importance of volatilization or sedimentation.

Experiment I

Epilimnion-spiked

Soluble levels of PCBs decline rapidly in the first eight days in the epilimnion-spiked column to about 75% of the 3h levels; later the PCBs level off to a slower but constant decline until the end of the experiment (Fig 2). Soluble levels make up 68.5 % of the total PCBs pool at the first sampling (0.4 h). Particulate PCBs levels are much lower initially (31.5% of the total) but show a similar rate of decline as the soluble phase. Losses of particulate PCBs appear to be more closely related to losses from the soluble pool and not to the decline of seston concentrations that declined at a much slower rate. The rate of decline of seston levels is solely due to sedimentation of the added clay particles since primary production is not a possible mechanism to renew the pool of adsorbent particles.

Seston levels remain at 7-8 mg× L^-1 for the first week. The expected seston dry weight, initially in the epilimnion due to clay addition with the treatment, is almost 6 mg× L^-1. Since algal growth is virtually impossible, the measured seston weight is due almost entirely to the clay added in the treatment. The measured concentrations of seston dry weight on the first two samplings are 6.90 and 7.05 mg× L^-1 at 3 and 24 h, respectively. The close agreement between observed and expected concentrations of the conservative part of the treatment suggests that compartment volumes used in the mass balance and sampling techniques are reasonably accurate. It also suggests that the epilimnion is well mixed in the short interval between PCBs addition and the first sampling.

After 21 days only 16.7% of the added PCBs could be accounted for by the sum of sedimentation and PCBs remaining in the water column (Table 2). Much of this high loss took place in the first few days of the experiment. Even by the time of the first sampling at 3h, the measured total PCBs concentration is only 83% of that expected if the total treatment is evenly dispersed throughout the epilimnion.

The rate of decline and total losses of PCBs in the hypo-spiked column are much less than the epi-spiked treatment. This is particularly notable in the soluble PCBs pool. Total PCBs concentrations at the first sampling indicate no early losses and that the entire treatment must have been in the hypolimnion. Soluble and particulate levels of PCBs showed more similar rates of decline than in the epi-dosed column and these rates are similar to the rate of decline of the seston pool suggesting that losses in this treatment are due to sedimentation of labelled clay particles. PCBs are desorbed from the labelled clay particles but the soluble phase is not subject to volatilization losses because there is no access to an air-water interface. As a result, soluble PCBs are retained in this pool in the hypolimnion. The initial partitioning favoures particulate (54%) compared to the epi-dosed column (31%) although particle density is the same as for the epi-spiked treatment.

Recovery of PCBs in this treatment is much higher (67.4%). Almost 30% of the total treatment is recovered in the sediment trap compared to only 2.5% in the epi-dosed column.

Seston ash-free dry weight is used as an indicator of algal biomass. Seston levels in the high productivity columns are about an order of magnitude higher than in the low productivity treatments in experiment II (Table ###). The difference between high and low productivity columns in experiment III is about six-fold. Ash-free dry weight is about 20 mg× L^-1 at high productivity and 2-4 mg× L^-1 at low productivity in both experiments. At low productivity, seston levels are about 30% higher in experiment III but are still very low compared to the high treatment. Nutrient loadings are identical between the two low productivity columns but slight variations in lighting, inoculum strength or unknown factors may contribute to inherent variability between columns.

Clay added in the experiment II treatment add particles to the total seston pool. The concentration of ash is measured to try to estimate the contribution that these added clay particles make to the seston levels at the start of the experiment. Theoretically, the 1 g of clay from the treatment could have contributed 0.592 mg× L^-1 to the total seston weight and this would have been measured as ash. The high ash level in the high productivity columns is likely the result of calcite (CaCO₃) precipitation from hard waters when photosynthesis is vigorous. The small differences in ash levels between the low productivity treatments in experiments II and III indicate that clay contributions to seston levels are slight at high productivity levels but may have been a substantial part of the adsorbent concentration when productivity is low.

Similar to the epi-dosed column in experiment I, the soluble pool of PCBs in the epilimnion decline rapidly in the early stages of the experiment and then levelled of to a much lower rate of decline in all treatments (Fig 3). Initial repartitioning following treatment addition favoures the particulate slightly in the higher productivity treatments (10-13,000 dpm L^-3) compared to the lower productivity (7800-8800 dpm× L^-3) treatments. Soluble levels start higher in the low productivity columns (23-28,000 dpm× L^-3) compared to the high productivity (18-22,000 dpm× L^-3) columns although levels did not differ by much (3,100-4,000 dpm× L^-3) in the four treatments by the end of the experiment.

Particulate PCBs levels show a similar trend in decline as soluble levels although it is more noticeable in the HP treatment. Also, particulate levels did not start to decline immediately in this treatment but remained steady for 24 hours. *** Remove this sentence, it does not belong here ? All modeling resultys should be grouped together, agree ? [Model results are very close to the observed values for both the soluble and particulate PCBs pools in the epilimnion of all four treatments.]

Concentrations of PCBs increased in the hypolimnia of all four columns as PCBs adsorbed to particulate matter are sedimented to the bottom. Sedimentation is considered to be the only significant mode of transport of PCBs to the hypolimnion. The hypolimnetic increase is most pronounced in the high productivity columns where particulate concentrations reached over 2 and 3,000 dpm× L^-1 by the end of the experiment in the HMHP and LMHP treatments, respectively. In contrast, by the end of the experiment particulate PCBs concentrations are much lower in the low productivity columns at only 400 dpm× L^-1 in the HMLP column and 1000 dpm× L^-1 in the LMLP column. *** Model observations do not belong here ?? [Modelled values of particulate PCBs followed the same trends as observed values but agreement is poorer than in the epilimnion.] Agreement is best in the two LP columns.

The increase in hypolimnion soluble levels occurs as a result of desorption from sedimented particles since there is no other significant mode of PCBs transport to this compartment. Similar to the partitioning in the epilimnia, soluble levels are lower than particulate levels in the HP columns. Lower particle density because of lower sedimentation rates of particulate matter in the LP columns results in a higher proportion of the total PCBs pool in the dissolved fraction in the LP columns. ** model here again [Agreement between the model and observed results is poorest for the hypolimnion soluble concentrations. This is most notable in the LMLP treatment where observed soluble levels appear to be atypically high. ]

Trends in both PCBs pools are similar to experiment II even though all the PCBs are added in a soluble rather than particulate form in the treatment (Fig 4). Total concentrations right after addition are similar (30,000 dpm× L^-1) to those in experiment II and are similar among the columns in this experiment. Immediate partitionings between particulate and dissolved phases in the epilimnion are similar to the previous experiment and similarly show a higher percentage of PCBs in the particulate phase in the HP treatments where seston levels are higher. The exception is the LMLP treatment where about 91% of the added PCBs are still in the dissolved phase at the first sampling (1h) while in the clay experiment 76% are initially in the dissolved phase.

Initial levels of particulate PCBs and the decline with time are similar to experiment II particularly in the HP treatments. Like the other experiment, particulate levels did not decline immediately in the HP treatments and in the methanol mode of addition they increased slightly over the first 24 hours.

Rapid decline in soluble levels occurr in all treatments up to about day 4 to 6 and then levelled off. This appeared to be most pronounced in the LP treatments since the initial levels in the dissolved phase are higher (27-28,000dpm× L^-1) than in the HP treatments (20-22,000 dpm× L^-1). **** model here again [

Exceptionally good agreement is achieved between modelled and observed results for soluble and particulate phases in the epilimnion.]

Trends over time and final concentrations in particulate and dissolved phases in the hypolimnion are very similar to experiment II. *** Model description of particulate levels is better in this experiment and this is notable in the HP treatment. Observed soluble levels in the hypo of the LMLP treatment appear to be atypically high as in experiment II.

Rapid declines in the total PCBs concentrations in the early stages of both experiments are reflected in the high losses over the first 24 h of the experiment (Table 4). Losses are considered to be the proportion of the original dose of PCBs that could not be accounted for in the water column or the sediment traps. These unaccounted for losses are assumed to be PCBs that have volatilized. There is little influence of the mode of addition (clay versus methanol) to the column on short-term losses with the possible exception of the LMLP treatment in the methanol treatment where losses are about 13% higher than with the clay addition.

Volatilization losses are highest where expected: the high mixing and low productivity treatment. Similarly the highest amount is retained by the column (lowest loss) in the high productivity and low mixing treatment.

In the model, different values for sorption-desorption are used in the epilimnion (k₁, k₂) than in the hypolimnion (k₄, k₅). Millard et al. (1983) have shown that there is a simple log-linear relationship between the percentage of the total PCBs pool in the soluble phase and concentration of particulate organic carbon (POC) in the water column. This work showed that the slope of the relationship in the hypolimnion is steeper than in the epilimnion. Thus, at a given level of organic matter, the proportions of total PCBs that are in the soluble phase are lower. In the experiments reported here, the slope of the relationship for the epilimnion is substantially less (-0.035) compared to the earlier work (-0.091). As an example, the predicted level of soluble PCBs [at a high level of POC typical of the HP treatment (6 mg× L^-1)] would be 54.3% [only 27.1 % in Millard et al. (1983)]. The hypolimnetic relationships are about the same in the two studies.

Partitioning between particulate and soluble phases stay relatively constant during the course of experiments (Table ###). This is likely due to fairly constant levels of algal biomass sustained by regular nutrient additions. The largest fluctuations are in the HP treatments where biomass levels are very high. The only significant difference worth noting is that soluble levels are about 10% higher in the clay HMHP treatment compared to the same treatment in the methanol experiment. At the first sampling time (3h) the amount of PCBs in the dissolved pool tend to be higher than the rest of the experiment in the high productivity columns.

Fate and recovery of PCBs at the end of the experiments conformed well to our a priori hypothesis and agree with the trends seen in the analysis of short-term losses. Overall, recovery is increased by higher productivity and lower mixing and decreased by lower productivity and higher mixing. The additive effect of these two factors on increasing recovery is most noticeable in the LMHP treatment where recovery is highest in both experiments. The biggest single factor effect is the increase in recovery (23 and 25% for experiments II and III respectively) due to increased productivity at low mixing. However, loared mixing at high productivity has almost as much effect (16.6 and 20.5%). The effect of higher productivity is decreased by half at higher mixing (12.0 and 11.0 %). Lowering the mixing at low productivity has the least effect at increasing recovery (2.8 and 8.4%).

In the clay experiment, retention in the water (34.4%) and sedimentation (17.1%) are highest in the LMHP treatment while retention is lowest in the HMLP (15.0%) treatment as expected (Table 5). Little difference in the amount of the treatment sedimented (3.6 and 2.9% for HM and LM respectively) is noted between the two low productivity columns regardless of mixing level. A lower volatilization and therefore higher recovery might have been expected in the LMLP compared to the HMLP treatment, but this is not the case. The higher estimate of wall adsorption (8.5%) in the HMLP column offsets the expected lower retention in the water column compared to the LMLP column thus equalizing the recovery in the two LP columns. In the methanol addition, the expected difference in volatilization due to mixing at lower productivity not observed in experiment 2 occurred in this experiment. In both experiments 2 and 3 at high mixing rates, higher productivity (HMHP) reduced volatilization by 11-12% that is attributed to higher retention in the column by adsorption and sedimentation.

No obvious treatment effect could be discerned on the estimates of the wall adsorption except that adsorption is higher overall in the clay mode of addition. This is probably due to actual adherence of small clay particles to the steel plates and not due to actual adsorption from the soluble pool.

The added retention in the water column provide by increased algal biomass (high productivity treatments) is reflected in the higher amount of PCBs in the particulate fraction. It is interesting that higher mixing also affects the amount in the particulate fraction even at high productivity. Obviously the partitioning between pools is dynamic in nature and not just a function of an equilibrium based on adsorbent concentration being established and maintained. PCBs are volatilized from the soluble pool at a higher rate when mixing is high even at high productivity; repartitioning between the particulate and soluble phases occurrs at the expense of PCBs adsorbed to particulates.

Model descriptions of the fate of PCBs conforms well to the hypotheses. Water column retention and partitioning between particulate and dissolved phases agree well with observed values. Exceptions are that column concentrations (low productivity in the clay treatment) are underestimated by 7% in the model. Since recovery within the model is 100%, it is relevant to discuss the effect of treatments on volatilization. In fact, the model accurately predicted the small but consistent (between experiments 2 & 3) difference in volatilization between low and high mixing at the low productivity level.

The one significant difference between model and observed fate is the higher volatilization in the model. One of the main reasons is that there is no error associated with measurements. That is, 100% of the loading is used in the model and channelled into the designated phases and compartments using the allotted parameters. In addition, in the model there are no unknown losses or other competing processes, such as wall adsorption, that occurr in the columns.

There are several reasons for constructing a model to describe the observed trends in fate and PCBs concentrations in our study. In model construction, hypotheses about the interaction between processes and pools are formalized in mathematical terms in an attempt to describe system behaviour. Complexity, due to simultaneous interaction of several processes that would otherwise be difficult to describe, is automatically incorporated into the model. If the formulation of equations is an accurate representation of system behaviour then the model should be successful in its ability to describe the data and to lend credence to the original hypotheses. Our model is consistent in its ability to describe accurately trends in PCBs concentrations as well as the ultimate fate of PCBs added to the columns under varied trophic and mixing regimes. Our basic hypotheses about PCBs dynamics and the relevant factors, such as particle density, sedimentation and volatilization in these systems, must have been reasonably accurate. The success of the model and its simplistic formulation indicates that particle-water interactions in the experiments are simple; transport and fate in the columns are dominated by the few processes included in the model.

Perhaps, more important than confirming our original hypotheses, construction of the model indicates that a pool not measured by us (and not measured by other workers) may have existed in our experiments. The incorporation of the colloidal pool in the epilimnion compartment of the columns allowed us to model accurately PCBs concentrations. Although this pool is not measured, the success of the model lends support for its existence. A non-modeling analysis of the empirical data would not have indicated the presence of this pool. References to other work here.

Experiment I confirm that volatilization is an important loss mechanism for PCBs, even when added in the particulate phase. The rapid and coincident loss of PCBs from the particulate and soluble pools in experiment I is undoubtedly due to volatilization. Removal of the air-water interface in the hypo-spiked column makes this route of transport impossible and results in higher overall recovery, higher sedimentation rate and a loss rate of PCBs coincident with that from the particulate rather than the soluble phase.

Partitioning of PCBs between particle and soluble phases is not static in nature but is dynamic with readily-reversible adsorption-desorption. This is particularly evident in experiment II where most of the PCBs added to the system are adsorbed to clay particles. The fact that the proportion of PCBs in the particulate phase changed after 1 hour in the experimental system and that early loss through volatilization is high indicates how quickly PCBs moved between phases.

A dynamic pathway exists between particle-bound PCBs and the soluble phase and from there, through volatilization, to the atmosphere. Equilibrium between the particulate and soluble phases is unachievable in the early stage of experiment II when high rates of mixing force this pathway toward volatilization. In the case of experiment I, just the presence of an air-water interface and a paucity of particles to adsorb PCBs desorbing from the clay particles.

Both volatilization and sedimentation processes can be considered detoxifying mechanisms for lakes since both pathways remove hydrophobic contaminants from the open water. However, in the case of sedimentation, decontamination of the water column may have serious implications for the sediment and associated benthic food-chains. Particle density plays a role in modifying the importance of this pathway. This is evident in the higher rates of recovery, the higher sedimentation rate and the higher amount of PCBs retained as particulate in both experiments I and II when the HMHP and LMHP treatments are compared. In the high productivity but low mixing treatments (experiment I) volatilization is less rapid and there is a chance for the high density of adsorbent algal particles to retain PCBs desorbed from the clay treatment. In this case, the loss of soluble PCBs is under liquid phase control. The slower rate of transfer of the bulk liquid phase in the epilimnion limits the rate of volatilization from the soluble pool because rates of desorption from clay and attachment to clay particles are probably quite fast. (Ref. Mention previous work and that of others on rates of adsorption). Turnover time of the epilimnion volume of water is close to one hour at high mixing but is considerably longer (4.5 h) at low mixing rates.

Although PCBs have a high affinity for particles and are easily adsorbed from solution, the proportion of the total PCBspool associated with the particulate is dependent on the density and type of adsorbent particles (ref). PCBs enter aquatic ecosystems through several routes including wet and dry deposition from the atmosphere and in soluble and particulate phases in rivers and sewage effluents.

Physical conditions of the columns promote volatilization compared to situations in many natural bodies of water. We conducted several unpublished experiments where PCBs dissolved in methanol were added to columns with virtually no adsorbent particles present and at varying levels of mixing. Even under quiescent conditions where no circulation is provided, considerable amounts of the added PCBs were lost due to volatilization. The presence of adsorbent particles would have lowered this loss; it is important to note that the physical condition of the water mass in the columns promotes a high background rate of volatilization that is then modified by the addition of adsorbent particles by primary productivity. The shallow depth of the mixed layer of water, a high surface to volume ratio of the epilimnion, warm temperatures, rapid renewal of air at the air-water interface from the cooling fans, and slight turbulence at the water surface even at low mixing are all factors that would promote high rates of volatilization. Use of a lower chlorinated Aroclor with a higher vapour pressure compared to more highly chlorinated PCBs mixtures would also have favoured losses to the atmosphere (Ref.).

In addition to the presence of a separate particulate component or colloidal phase there are also two modes of adsorption to particulates. Earlier work on PCBs dynamics in these experimental systems showed that the relationship between partitioning between particulate and soluble phases differed between the epilimnion and hypolimnion compartments. (ref. Millard et al.). A portion of the epilimnion particulate PCBs fraction contains a labile, readily desorbed fraction. Mackay and (ref. ) have suggested that there are two modes of adsorption of PCBs to particulate matter: a surface and more loosely bound type of adsorption that is easily desorbed and a more tightly bound fraction that is probably associated with the deeper inner physical structure of the particles. The only significant pathway for PCBs to enter the hypo is attached to sedimenting algal and clay particles. The different partitioning relationship in this compartment indicates that these PCBs are part of the more tightly adsorbed particulate pool. However, desorption obviously still occurred or else the pool of soluble PCBs in the hypo would have been virtually non-existent.

Models of PCBs dynamics in large lakes indicate that volatilization and sedimentation are the dominant pathways affecting PCBs in the water column (ref. Mackay, 1989). Determining the importance of processes that affect the concentration of PCBs in the water column could play an important role in predicting the fate of the fate of other hydrophobic contaminants and concentrations in fish. Although our experimental design likely enhanced the volatilization route, the experiments have shown that the level of primary productivity could have a significant influence on PCBs dynamics in natural bodies of water. However, the seston levels in our high productivity treatments are substantially higher than those found in most lakes. In the Laurentian Great Lakes, only very eutrophic bays such as the upper Bay of Quinte would have seston levels as high as our HP treatments (ref. Quinte issue or unpublished data). On the other hand, the seston levels in the LP treatments are in the range of seston levels found in the offshore waters of Lakes Erie and Ontario.

Similar to other workers (reference) we observed a solids concentration effect. At higher seston concentrations, particularly at the start of the experiment, concentrations in the seston are highest in the low productivity treatments. Some PCBs models (reference) have incorporated this phenomenon into the construct of the model; in Lake Michigan solids concentrations are lower than our lowest levels (Rodgers, ). It is difficult to assess the importance of this phenomenon on biomagnification in food chains. Although low productivity systems with low particle concentrations have particles with a higher concentration of PCBs, the proportion of the pool of PCBs in the particulate is less than for more productive systems. It would seem that the potential for biomagnification might be affected more by the total pool of PCBs available than the concentration. On the other hand, sedimentation losses are higher with increased productivity. However, the equilibrium between accumulation and uptake will be the result of several factors including particle concentration, food requirements in terms of particles and particles ingested.

High algal biomass retains PCBs in the water column through adsorption. Binding to suspended sediment has been found (Schrapp and Opperhuizen, 1990) to be effective in reducing the biomagnification of PCBs because of the reduced availability of soluble forms for direct uptake. In lakes, adsorption to algal cells would probably not reduce biomagnification because the algae are an integral part of the food chain. As ecosystem experiments these microcosms are realistic because primary production provides the rapid turnover of an adsorbent particle pool. Many studies (references) on adsorption use either unrealistically high concentrations of sediment or are carried out in small containers over relatively short time periods. The larger size of our model ecosystems make it possible to include two distinct layers with the transport route of sedimentation between them.

REFERENCES

IMSL, Inc. 1987. Math/Library, 2500 ParkWest Tower One, Houston, Texas 77042-3020, U.S.A.