Estimation of Uncertainty in Air-Water Exchange Flux 2 and Gross Volatilization Loss of PCBs: a Case Study 3 based on Passive Sampling in the Lower Great Lakes

Compared with dry and wet deposition fluxes, air-water exchange flux cannot be directly measured experimentally. Its model-based calculation contains considerable uncertainty because of the uncertainties in input parameters. To capture the inherent variability of air-water exchange flux of PCBs across the lower Great Lakes and to calculate their annual gross volatilization loss, 57 pairs of air and water samples from 19 sites across Lakes Erie and Ontario were collected using passive sampling technology during 2011-2012. Error propagation analysis and Monte Carlo simulation were applied to estimate uncertainty in the air-water exchange fluxes. Results from both methods were similar, but error propagation analysis estimated a smaller uncertainty than Monte Carlo simulation in cases of net deposition. Maximum likelihood estimations (MLE) of wind speed and air temperature were recommended to quantify the site-specific air-water exchange flux. An assumed 30-40% of relative uncertainty in overall air-water mass transfer velocity was confirmed. MLEs of volatilization fluxes of total PCBs across Lakes Erie and Ontario were 0.78 and 0.53 ng m-2 day-1, respectively, and gross volatilization losses of total PCBs over the whole lakes were 74 kg year-1 for Lake Erie and 63 kg year-1 for Lake Ontario. Mass balance analysis across Lake Ontario indicated that volatilization was the uppermost loss process of aqueous PCBs.


INTRODUCTION 41
Polychlorinated biphenyls (PCBs) are a class of persistent toxic chemical 42 substances of concern in the Great Lakes. 1--3Atmospheric deposition was 43 considered as a significant source of PCBs to the lower Great Lakes, including dry 44 deposition, wet deposition and air--water diffusive fluxes. 4,5 tmospheric 45 processes accounted for 80--90% of total loadings of PCBs to the oceans and 65% 46 of total atmospheric deposition of PCBs was attributed to gas transfer. 6Results 47 from Lake Superior revealed that volatilization was a major loss process of PCBs 48 from water column and gross volatilization loss of PCBs was 250 kg year --1 for 49 1992. 7Across Lakes Erie and Ontario, net volatilization from lake waters was 50 still a primary trend of PCB gas exchange process in our previous work. 8In 51 previous publications, air--water exchange fluxes of PCBs had been estimated, but 52 with limited knowledge on its uncertainty, 6, 7, 9--11 especially involving variations 53 of the flux over time and space.

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Compared with dry and wet deposition fluxes, air--water (diffusive) exchange 55 flux cannot be directly measured experimentally and its calculation (based on a 56 two--film diffusion model) involves air vapor and freely--dissolved water 57 concentrations, air--water partitioning and air--water mass transfer coefficients of 58 PCBs. 10,12,13 Te gaseous and freely--dissolved PCBs are not bound to particulates 59 by definition, and the filtered air or water in active sampling is only operationally 60 defined as gaseous or dissolved, as any particles penetrating the filters are also 61 included. 14,15 y contrast, passive sampling is an ideal technology for air--water where %equ is the predicted percent equilibrium (for more detail see the SI).where Kaw is air--water partitioning coefficient corrected by (air) temperature. 138 Kaw is determined as Equation 5, where Hc is Henry's law constant (in atm L 140 mol --1 ), R is the gas constant (0.08206 in atm L mol --1 K --1 ), and T is the absolute 141 temperature in Kelvin.Hc values were obtained from Khairy et al. 25 142 Overall mass transfer velocity (va/w) was calculated based on a modified 144 two--film air--water exchange model, 10 equated as follows,  S2), Error propagation analysis was applied to the air--water exchange flux given by 164 Equation 4 and 5, yielding the following: The relative standard deviations (RSD) of atmospheric and aqueous 167 concentrations ( ) are associated with the analysis and obtained from 168 Table S2.A value of 30% and 50% was assumed for RSDs in  !/! and  !, 169 respectively, after Rowe and Perlinger. 17   For most samples in this study, probability distribution patterns of 298 meteorological data are similar to the above case (see Table S1).Briefly, 299 temperature data followed a Weibull, Beta, or normal distribution, and in most 300 cases MLE was close to its arithmetic mean.In contrast, wind speed data 301 followed a lognormal distribution; the arithmetic mean likely overestimated 302 wind speed and hence the air--water exchange flux.This applies both to daily 303 sampling (as in active) as well as monthly samples (as in passive sampling).S3).Histograms of site--specific air--water 403 exchange fluxes across Lakes Erie and Ontario are also illustrated in Figure 4.In 404 both lakes, the calculated probability distributions via Monte Carlo simulation 405 agreed well with the histograms.Across the whole Lake Erie, the calculated 406 fluxes of total PCBs within a confidence level of 90% ranged from --5.1 ng m --2 407 day --1 (net deposition) to 52 ng m --2 day --1 (net volatilization), and MLE, median 408 and mean values were 0.78 ng m --2 day --1 , 3.4 ng m --2 day --1 and 11.7ng m --2 day --1 ,

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exchange flux measurements, because it specifically captures the gaseous and 63 freely--dissolved fractions, avoiding the filter bias. 11Nonetheless, passive 64 sampling contains uncertainties from PCB analysis and model coefficients, which 65 transfer loadings of PCBs.This prompted us to comprehensively estimate overall 91 uncertainty in air--water exchange flux of PCBs across the lakes.92 To capture the inherent variation in air--water exchange of PCBs, a case study 93 across Lakes Erie (31 pair air and water samples from 9 sampling sites) and 94 Ontario (26 pairs from 10 sites) was performed based on passive sampling 95 during 2011--2012. 8, 23Error propagation analysis and Monte Carlo simulation 96 were conducted to estimate uncertainty in air--water exchange flux of PCBs.The 97 aim of this study includes 1) estimating uncertainty in air--water exchange 98 equilibrium of PCBs, 2) comparing results from both methods, and 3) evaluating 99 uncertainty in air--water exchange fluxes and annual gross volatilization loss of 100 PCBs across both lakes.chemical analysis.The information on sampling sites, 104 low density polyethylene (LDPE) deployment in air and water, chemical analysis 105 methodologies and preparation of the LDPE passive samplers, quality assurance 106 and quality control were described elsewhere. 8Briefly, the LDPE membranes 107 were spiked with performance reference compounds, and deployed in the air 108 and water of Lakes Erie and Ontario.In this study, uncertainty in air--water 109 exchange flux of PCBs was estimated based on 57 pair samples (air and water) 110 collected during 2011--2012, nine sites from Lake Erie and ten sites from Lake 111 Ontario, as shown in Figure S1.After collection

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Air--water fugacity ratio.The fugacity ratio (fa/fw) is normally calculated 120 from atmospheric and aqueous concentrations of PCBs (Ca and Cw, both in pg m --3 ) (1) 124 Based on the LDPE passive sampling technology, 24 the atmospheric and 125 aqueous concentrations (Ca and Cw) can be calculated according to equilibrium 126 concentrations of PCBs measured in the deployed LDPE sheets (based on LDPE 127 volume) and partitioning coefficients between LDPE and air or water (KPE-a(w)), 128 as presented in Equation 2. Hence, the fugacity ratio depends only on the 129 equilibrium concentrations of PCBs in LDPE matrix (deployed in air and water), 130 as shown in Equation 3. 131

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Air--water exchange flux.The flux (Fa/w, in pg m --2 day --1 ) is commonly 135 calculated from overall air--water mass transfer velocity (va/w, in m day --1 ) and the 136 concentration difference between water and air (Cw--Ca/Kaw) as in Equation 4,10, 17    137 146where va and vw are the air--side and water--side transfer velocities of target 147 compound, respectively.They are a function of the molecular diffusivity of the 148 target compound in air or water and stability--dependent turbulent diffusivity 149 (wind speed). 10150 Error propagation analysis.In order to estimate the uncertainty in air--water 151 fugacity ratio and the calculated diffusive flux using statistical techniques, 152 measured uncertainties in air and water analysis, air--water partitioning 153 coefficients (including Henry's law constant and temperature) and overall mass 154 transfer velocity were considered.155 There are four variables with random uncertainty for the fugacity ratio based 156 on Equations 1 and 5, for which the error propagation is given in Equation 7. 157 With regard to the passive sampling technology, four variables are involved (see 158 Equation 3); its error propagation is detailed in Equation 8. Relative uncertainty 159 of percent equilibrium was estimated in the Supporting Information and ranges 160 from 0% to 51% (Table The standard deviation () in T was 170 calculated based on the NOAA National Data Buoy Center historical archives 171 (www.ndbc.noaa.gov).A detailed description of error propagation analysis is 172 presented in the Supporting Information.173 Monte Carlo simulation.This was performed for the overall air--water mass 174 transfer velocity (va/w) and air--water exchange flux (Fa/w) of PCBs for each 175 sample pair.The general method is to quantifiy uncertainty associated with 176 incomplete data (e.g., wind speed, ambient temperature, atmospheric and 177 aqueous PCB concentrations) by model--fitting probability distribution functions 178 (PDF) of the incomplete data that are used as input to Monte Carlo simulations.179 We fitted fourteen available PDFs to derive the best--fit PDF of site--specific 180 ambient parameters.The best--fit PDFs and probability charts were used to 181 generate a set of random values for input parameters.As variables in the system 182 being modeled are often inter--dependent, we defined correlations between 183 ambient temperature and wind speed based on pairs of measured data.Normal 184 distributions with specified ranges were assumed for other parameters, 185 including atmospheric and aqueous PCB concentrations and Henry's law 186 constants of PCBs.Standard deviation of the PCB concentrations were set to the 187 product of average relative standard deviation and site--specific PCB 188 concentrations.Relative uncertainty in Hc was assumed as 50% after Blanchard 189 et al. and Rowe et al. 17, 26 Finally, Monte Carlo simulations were applied for the 190 estimation of air--water exchange of PCBs across the whole lakes over time and 191 place.Passive sampling data from 2011--2012 was used to construct PDFs of 192 gaseous and freely--dissolved PCB concentrations across Lakes Erie and Ontario.193 Meteorological data from open lake sites were selected as representative air 194 temperatures and wind speeds.Correlations between variables were carefully 195 defined based on the monitoring data, including between atmospheric and 196 aqueous concentrations and between PCB congeners.In each simulation, a total 197 of 10 5 trials were generated to obtain sufficient data to estimate probability 198 distributions of va/w and Fa/w .All simulations were performed using Oracle 199 Crystal Ball R11.1 software packages.More details are presented in the 200 Supporting Information.201 Gross volatilization loss and mass balance of PCBs.Gross volatilization 202 losses of PCBs across Lakes Erie and Ontario were calculated as the product of 203 lake area and arithmetic mean of air--water exchange flux.Input (river inflows 204 and precipitation) and output (river outflow and volatilization loss) of 205 freely--dissolved PCBs into and from Lake Ontario were calculated for 206 construction of whole lake mass balance.(see the Supporting Information for 207 details).
Figure 2.c), and average wind speed (5.14 m s --1 ) was much greater than its MLE 297

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Estimation of uncertainty in air--water exchange flux.The air--water 305 exchange flux was quantified based on the two--film transfer model and relevant 306 monitoring data.Uncertainties are inherent in measured data due to 307 measurement limitations of PCB concentrations in air and water (e.g., sampling 308 uncertainty and instrument precision) and temporal variations of wind speed 309 Air--water fugacity ratios and probabilities of net deposition or volatilization 385 indicate that primary trends of CB 28 and 52 were net deposition, those of CB 386 138 and 153 were net volatilization, and those of CB 101, 118 and 180 387 approached phase equilibrium.The parameter sensitivities were related with 388 air--water exchange situation of PCBs, combining with Equation 4. When 389 air--water exchange was approaching an equilibrium situation, uncertainty in 390 air--water exchange flux was primarily controlled by the uncertainty in Hc, Ca and 391 Cw.Their assumed normal probability distributions would result in symmetrical 392 probability distribution of the flux in Figures S3.c and d.In non--equilibrium 393 situations, uncertainty in wind speed propagated largely to uncertainty in the 394 flux and led to a large tail of its probability distribution (see Figure S3.a, b, e and 395 f).The flux uncertainty was related to uncertainty in Cw in net volatilization 396 situation (e.g.CB 138 and 153), but related to uncertainties in Ca and Hc in net 397 deposition situation (e.g.CB 28 and 52).

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Air--water exchange flux of total PCBs across the whole lakes.After 399 estimating site--specific air--water exchange fluxes of PCBs, we fitted PDFs of 400 atmospheric and aqueous concentrations of PCBs and calculated probability 401 distribution of air--water exchange flux across each entire lakes via Monte Carlo 402 simulation (see Figure 4 and Table

Figure 1 .
624 c , Negative presents for deposition and positive for volatilization, unit: ng m --2 day --1 ; 625 d , Certainty of net deposition or net volatilization, probability distributions of the fluxes are 626 illustrated in Figure S3; 627 628 632 Log--transformed air--water fugacity ratios of selected 7 PCBs.Blue dash line 633 presents equilibrium between air and water theoretically.Red and cyan regions 634 indicate the range that air--water exchange does not significant deviate from 635 equilibrium, based on Equations 7 and 8, respectively.636 637 638

409 617 Table 1 .
Contributions to variation of air--water exchange flux, fugacity ratios, 618 mass fluxes (ng m --2 day --1 ), certainties in deposition or volatilization of , Major contributors to the variance are marked by Bold.622 b , TableS2in the Supporting Information indicated the range of ratios where air water 623 exchange does not significant deviate from equilibrium. a