Where do these two models leave us? F = K ol * ( C w – C a / H) Whitman two film model un-measurable parameters: z w & z a Surface renewal model un-measurable parameters: r w, & r a

Calculation of Flux Figure from Schwarzenbach, Gschwend and Imboden, 1993 Net Flux = k ol * (C w – C a /H*) 1 / k ol = 1 / k w + 1 / k a H* Gross fluxes: Volatilization: Water to air transfer F volatilization = k ol * Cw Absorption: Air to water transfer F absorption = k ol * C a / H*

Processes of Air / Water Exchange “Little” Mixing: Stagnant, 2-film model - “little” wind “More” Mixing: Surface Renewal model – “more” wind Wave Breaking: intense gas transfer ( breaking bubbles) – “even more” wind Figure from Schwarzenbach, Gschwend and Imboden, 1993

Conceptualization of Wind Speed Effects on Air/Water Exchange Figure from Baker, 1996 Aerodynamic Transport Region ~10 3 m Viscous Sublayer ~10 -3 m Transfer to broken surface region Unbroken Surface Broken Surface

Effect of Wind Speed on Flux Figure from Schwarzenbach, Gschwend and Imboden, 1993 Effect of Wind Speed seen only through changes in Mass Transfer Co-efficient Net Flux = k ol * (C w – C a /H*) ---- where 1 / k ol = 1 / k w + 1 / k a H*

Water Side Mass Transfer Coefficient 1 / k ol = 1 / k w + 1 / k a H* Wanninkhof et al. (1991) summarized SF 6 experiments in five North American Lakes and found the gas transfer coefficient to be a power function of Wind Speed. The relationship is normalized to the appropriate Schmidt number to relate to the gas transfer of CO 2 across the water side boundary layer. k w,CO2 = 0.45 u 1.64 where k w,CO2 is the mass transfer coefficient (cm / hr) across the water layer for CO 2 (SC = 600 at 20 o C), and u is the wind speed at a 10 m reference height (m/s).

Addition of Weibull distribution in calculation of K ol from Xhang et al A two parameter Weibull Distribution can be used to describe the cumulative frequency distribution of wind speeds (Livingstone and Imboden, Tellus 45B ). F (u) = e ^ –(u /  )  Where F (u) is the probability of a measured wind speed exceeding a given value, u. the form of the distribution curve is determined by the shape parameter, . The scale of the u-axis is determined by the scale parameter, . the negative derivative of F(u) yields the corresponding probability density function: f(u) = (  / u) ( u /  )  e ^-( u /  )  Thus, the mean transfer coefficient over the whole range of wind speeds is obtained by integrating the product of the transfer velocity and wind speed probability density f(u). k mean,CO2 = 0 to 8 f(u) *k w (u) * du

Weibull distribution - continued Instead of a single mean wind speed value during a sampling period, the wind speed probability density f(u) can be used to account for the effects of a nonlinear wind speed on mass transfer across the water layer over a range of wind speeds during a certain time period. This Weibull distribution can be transformed into a linear form y = ax + b as follows: x = ln u y = ln [ -ln F(u) ] and parameters a & b are determined by linear regression. They are related to the Weibull parameters as follows:  = a  = exp (-b / a) Gas transfer of tracer CO 2 can be up to 50% higher when accounting for the non- linear influence of wind speed. Calculations based on mean wind speeds underestimate the total PCB flux to Lake Michigan by as much as 20 to 40% depending upon wind speed variation. from Xhang et al. 1999

1 / k ol = 1 / k w + 1 / k a H* Wanninkhof et al. (1991) summarized SF 6 experiments in five North American Lakes and found the gas transfer coefficient to be a power function of Wind Speed. The relationship is normalized to the appropriate Schmidt number to relate to the gas transfer of CO 2 across the water side boundary layer. k w,CO2 = 0.45 u 1.64 where k w,CO2 is the mass transfer coefficient (cm / hr) across the water layer for CO 2 (SC = 600 at 20 o C), and u si the wind speed at a 10 m reference height (m/s). Water Side Mass Transfer Coefficient

Water Side Mass Transfer Coefficient - Continued k w,HOC = k w,mean,CO2 (Sc HOC / Sc CO2 ) -0.5 = cm s -1 Where Sc is the Schmidt number, the ratio of kinematic viscosity of water and the molecular diffusivity in water. Diffusivity of Hydrophobic organic contaminants (HOCs) through water are calculated using the emperical method of Wilke and Chang (1955). The Schmidt number for CO 2 ranges from ~1900 to ~500 for temperatures from 0 o C to 25 o C according to the equation: ln Sc CO2 = T where Sc CO2 is the Schmidt number for CO 2 and T is the temperature in K. Sc HOC = Ab. Viscosity / (Water Density * Diffusivity of HOC in Water) (g cm -1 sec -1 ) / ( g cm -3 ) * cm 2 sec -1

Water Side Mass Transfer Coefficient - Continued 2 Viscosity,  g cm -1 s -1 ) Density of Water (g cm -1 ) Diffusivity of PAH in water: D w,PAHs = / ((100 *  1.14 ) * Mol Vol ) = cm 2 sec -1

Air Side Mass Transfer Coefficient – Importance of Density When air temperatures are lower than water temperatures, then air at the water surface is warmer than the ambient air, and thus a density difference exists between the two air layers. The resulting buoyancy can affect the mass transfer at the air/water interface. This influence is not important when average wind speeds are in excess of ~3 m/s at 10 m reference height.

Air Side Mass Transfer Coefficient 1 / k ol = 1 / k w + 1 / k a H* Increasing wind speed increases the air-layer mass transfer coefficient approximately linearly: k a,H2O = 0.2 u +0.3 = cm s -1 where k a,H2O is the mass transfer coefficient across the air layer for the tracer H2O (cm / hr) and u is the wind speed. the tracer is related to HOCs through the ratio of air diffusivities (H 2 O vs. HOC) and can be estimated by the Fuller method: k a,HOC = k a,H2O (D HOC,air / D H2O,air ) 0.61 where k a,H2O is the mass transfer coefficient (cm / hr) across the air layer for H2O, and u is the wind speed at a 10 m reference height (m/s). D a,PAH = (0.001* (Temp 1.75 ) * ( 1/ / mol wgt.) 0.5 ) / ( Mol Vol 0.33 ) 2 = cm 2 s -1 D a,H2O = (0.001* (Temp 1.75 ) * ( 1/ /18) 0.5 ) / ( ) 2 = cm 2 s -1

Effect of Temperature on Flux Net Flux = k ol * (C w – C a /H*) / k ol = 1 / k w + 1 / k a H* ---- Gross fluxes: Volatilization: Water to air transfer F volatilization = k ol * Cw Absorption: Air to water transfer F absorption = k ol * C a / H*

Effect of Temperature on Flux – Kol Net Flux = k ol * (C w – C a /H*) / k ol = 1 / k w + 1 / k a H* Temperature affects on Kol: Viscosity and Density of water Diffusivity of HOC in water Sc of HOC Sc of CO2 Diffusivity of H20 and HOC in air plus Henry’s law associated effects on Kol (via air side)

Effect of Temperature on Flux – Henry’s Law Net Flux = k ol * (C w – C a /H*) / k ol = 1 / k w + 1 / k a H* ---- Gross fluxes: Volatilization: Water to air transfer F volatilization = k ol * Cw Absorption: Air to water transfer F absorption = k ol * C a / H*

Temperature dependence of Henry’s Law

Indirect Effects of Temperature on A/W Flux Net Flux = k ol * (C w – C a / H*) ---- Temperature dependence of ambient atmospheric concentrations (and G/P distributions) Gross fluxes: Volatilization: Water to air transfer F volatilization = k ol * Cw Absorption: Air to water transfer F absorption = k ol * C a / H* log C air =  o +  1 / T +  2 sin(wd) +  3 cos(wd) after Zhang et al Note: possible (and likely) interdependence of T and wind direction

Vapor exchange fluxes and estimated fluxes of HOCs Table from Nelson, 1996 _____________________________________________________________________________ RegionFlux (ng/m 2 day)PeriodReference _____________________________________________________________________________ PCBs Lake Superior+19, +141AugustBaker and Eisenreich, AnnualJeremiason et al., AnnualJeremiason et al., AnnualHornbuckle et al., 1994 Lake Michigan AnnualSwackhamer and Armstrong, AnnualStrachan and Eisenreich,1988 N. Lake Michigan+34 (24-220)AnnualHornbuckle et al., 1995 Lake Ontario+81AnnualMackay, 1989 Green Bay June-OctAchman et al., avgJuneAchman et al., 1993 Open ocean -40June-AugIwata et al., Nov-MarIwata et al., 1993 Nearshore Chicago-32 to +59whole year Zhange et al northern Chesapeak BayNelson et al., 1998 PAHs Baltimore Harbor ( )Bamford et al., 1999 fluorene+2200 phenanthrene -140(-140 to 7500) pyrene+590 Southern Chesapeake Bay fluorene+570FebruaryDickhut and Gustafson, 1995 phenanthrene -570 fluoranthene -140 pyrene -50

Error analysis of Gas Exchange Calculations Bamford et al. (1999) predicted gas exchange in Baltimore Harbor using Temperature dependent Henry’s Law values, and measured air and water concentrations, along with ambient meteorological parameters (wind speed, water Temperature, etc). Using estimated uncertainties of 40%, 20%, 20% and 10% for Kol, Cw, Ca, and H resulted in propagated errors of between 43% and 910% of the calculated fluxes. Errors were larger when the fluxes were smallest (i.e. near equilibrium or nearly 0 ng/m2 day net flux), with average error of 64%. Most of the error associated with the fluxes are related to the estimation of Koldue to the effect of wind speed on the k w.