Simplified Process to Determine Rate Constants for Sunlight-Mediated Removal of Trace Organic and Microbial Contaminants in Unit Process Open-Water Treatment Wetlands

Overall decay rate equations for TrOC and microorganisms

TrOCs in UPOW wetlands are transformed through photolysis, biotransformation, or a combination of the two (Jasper and Sedlak, 2013; Jasper et al., 2014a; Prasse et al., 2015; Bear et al., 2017); sorption was not found to be an important removal mechanism when not coupled with biotransformation (Jasper et al., 2014a). Photolysis can occur through direct and indirect processes (Schwarzenbach et al., 2003). Direct photolysis is caused when compounds absorb photons of light directly, resulting in cleavage of chemical bonds. Indirect photolysis differs from direct photolysis in that photons are first absorbed by sensitizer molecules [such as dissolved organic matter (DOM)], which then produce photochemically produced reactive intermediates (PPRI) that can oxidize target compounds. Important PPRI include hydroxyl radical ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet { \rm{OH}}$$ \end{document} ), carbonate radical ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet { \rm{CO}}_3^{ - }$$ \end{document} ), singlet oxygen (¹O₂), and excited triplet state dissolved organic matter (³DOM*) (Hoigne et al., 1988; Zepp, 1988; Blough and Zepp, 1995; Jasper and Sedlak, 2013).

TrOC decay rates were estimated based on the numeric models created by Jasper and Sedlak (2013) and Jasper et al. (2014a), which have already been validated at the Discovery Bay (Jasper et al., 2014a) and Prado (Bear et al., 2017) UPOW wetlands. Given that TrOC removal in open-water wetlands occurs through photolysis and biotransformation, the total transformation rate of a particular contaminant i ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^i$$ \end{document} ; day⁻¹) was modeled as the sum of the photolysis rate ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{photo}}}^i$$ \end{document} ; day⁻¹) and the biotransformation rate ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{bio}}}^i$$ \end{document} ; day⁻¹). \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} k_{{ \rm{TrOC}}}^i = k_{{ \rm{photo}}}^i + k_{{ \rm{bio}}}^i \tag{1} \end{align*} \end{document}

Equations used to estimate \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{photo}}}^i$$ \end{document} are described in a subsequent section, and sample calculations are provided in a spreadsheet included in the Supplementary Data. Biotransformation rates vary seasonally due to reduced microbial activity at lower temperatures. Consequently, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{bio}}}^i$$ \end{document} (day⁻¹) was modeled as a function of air temperature (T; Kelvin) using a modified Arrhenius equation (Jasper et al., 2014a): \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} k_{{ \rm{bio}}}^i = k_{{ \rm{bio , ref}}}^i{ \rm{ \;}}{{ \rm{e}}^{ - { \rm{ {\upkappa} }} \left( {{T_{{ \rm{ref}}}} - T} \right) }} \tag{2} \end{align*} \end{document}

where \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{bio , ref}}}^i$$ \end{document} (day⁻¹; values provided in Supplementary Table S2) is the biotransformation rate at reference temperature T_ref (300.15 K = 27°C), and κ (K⁻¹) is the temperature coefficient. Typical κ values for TrOC range between 0.03 and 0.09 K⁻¹; Jasper et al. (2014a) used an average value of 0.06 K⁻¹. A limitation of the biotransformation model is that the effect of the biomat thickness on TrOC biotransformation rates is not fully understood, and is therefore not reflected in the biotransformation rate equation (i.e., biotransformation rates are assumed to stay constant for different biomat thicknesses). However, variations in biomat thickness can affect the redox gradient within the biomat, which could thereby affect the microorganism community composition and, subsequently, biotransformation rates.

Sunlight inactivation is an important mode of disinfection of bacteria and viruses in UPOW wetlands, and has been found to be as or more important than sedimentation or other dark removal processes (Davies-Colley, 2005). Sunlight inactivation of waterborne bacteria and viruses occurs through two main mechanisms: endogenous photoinactivation and exogenous photoinactivation (Davies-Colley et al., 1999, 2000). Endogenous photoinactivation occurs through damage to biomolecules within the microorganism (i.e., nucleic acids and amino acids) when sunlight is absorbed by the microorganism itself (Cunningham et al., 1985; Jagger, 1985). The exogenous photoinactivation mechanism is similar to indirect photolysis of TrOC in that damage is caused by PPRI produced by sensitizers that reside in the water column outside the cell or virion. ¹O₂ is often the most important PPRI for exogenous inactivation of bacteria (Kadir and Nelson, 2014) and viruses (Kohn and Nelson, 2007; Mattle et al., 2015).

Susceptibilities to each sunlight inactivation mechanism differ among microorganisms. In general, viruses have slower photoinactivation rates than bacteria (Sinton et al., 1999, 2002), and within the viruses, bacteriophage MS2 has a slower endogenous photoinactivation rate than many other human viruses and bacteriophage (Love et al., 2010; Romero et al., 2011; Silverman et al., 2013; Mattle et al., 2015). Therefore, while the general framework of the bacteria and virus inactivation rate equations are the same across microorganisms, they contain species-specific parameters. Sunlight inactivation rates were estimated based on the numeric models created by Fisher et al. (2011), Silverman et al. (2015), Nguyen et al. (2015), and Silverman and Nelson (2016), and were previously validated at the Discovery Bay UPOW wetland. The total sunlight inactivation rate of a bacterium or virus i ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{microbial}}}^i$$ \end{document} ; day⁻¹) was estimated as the sum of the first-order endogenous ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^i$$ \end{document} ; day⁻¹), exogenous ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{exo}}}^i$$ \end{document} ; day⁻¹), and dark ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{dark}}}^i$$ \end{document} ; day⁻¹) inactivation rates. All inactivation rates were calculated assuming a well-mixed water column. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} k_{{ \rm{microbial}}}^i = k_{{ \rm{endo}}}^i + k_{{ \rm{exo}}}^i + k_{{ \rm{dark}}}^i \tag{3} \end{align*} \end{document}

Equations used to estimate \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^i$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{exo}}}^i$$ \end{document} are described in a subsequent section, and sample calculations are provided in a spreadsheet in the Supplementary Data. Based on studies conducted in the laboratory using water from the Discovery Bay UPOW wetland, E. coli had an average \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{dark}}}^{E. \;coli}$$ \end{document} of 0.86 day⁻¹ (Nguyen et al., 2015), whereas MS2 was not significantly inactivated by dark mechanisms (i.e., \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{dark}}}^{{ \rm{MS}}2}$$ \end{document}  = 0) (Kohn and Nelson, 2007; Love et al., 2010; Silverman et al., 2013, 2015).

Choice of indicator compounds and microorganisms

There are hundreds of potential contaminants of concern in municipal wastewater effluent—it is not possible to monitor or model decay of every one. As an alternative, indicator compounds can provide insight into the behavior of a suite of contaminants (Dickenson et al., 2009, 2011). Therefore, four compounds that are regularly detected in municipal wastewater were selected as indicator compounds to represent a range of TrOC transformation behaviors, based on the findings of Jasper and Sedlak (2013) and Jasper et al. (2014a) (Fig. 2):

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FIG. 2.

Trace organic contaminant removal rates attributed to each removal mechanism (i.e., biotransformation, direct photolysis, indirect photolysis). Transformation rates were estimated with pH = 8; [DOC] = 7.5 mg-C L⁻¹; a 30-cm-deep, well-mixed water column; irradiance estimated for 35°N latitude in June; and air temperature = 22°C. [DOC], dissolved organic carbon concentration.

Similarly, wastewater can contain a broad range of microbial contaminants, requiring the use of indicator microorganisms to represent disinfection behavior. The fecal indicator bacteria E. coli was chosen to represent bacteria inactivation, and bacteriophage MS2 was used to model virus inactivation. E. coli is susceptible to endogenous, but not exogenous, photoinactivation (Nguyen et al., 2015). MS2 is susceptible to both endogenous and exogenous photoinactivation, although it is more resistant to the endogenous mechanism than E. coli (Silverman et al., 2015).

Inputs to photolysis and photoinactivation models: environmental and water quality conditions

Subsequent sections outline the equations used to model photolysis and photoinactivation rates in UPOW wetlands, which have a strong dependence on environmental and water quality conditions. These factors include (1) the solar intensity incident on the water surface (which depends on latitude, season, cloud cover, and time of day); (2) [DOC] (which influences light attenuation in the water column and formation of PPRI); and, (3) pH, which affects formation rates of PPRI and reaction rates between TrOC and PPRI. Photolysis and photoinactivation rates are not expected to depend on temperature within the range observed in UPOW wetlands.

Photolysis and photoinactivation rates were determined for well-mixed water columns with depths of 20, 30, and 40 cm; a 5-cm-thick biomat was assumed for all depths. The following representative values were used as inputs for environmental and water quality variables:

Time of year—photolysis and photoinactivation rates were determined for three representative dates: December 21, March (or September) 21, and June 21; these dates correspond to the winter solstice, the March (and September) equinoxes, and the summer solstice for the northern hemisphere.

Irradiance spectra used to estimate photolysis and photoinactivation rates were predicted using the Simple Model of the Atmospheric Radiative Transfer of Sunshine (SMARTS) (Gueymard, 1995, 2001). SMARTS is a computational model hosted by NREL (www.nrel.gov/rredc/smarts/) that can estimate sunlight irradiance at any location, day of year, time, or elevation. Therefore, SMARTS can account for diurnal and seasonal changes in irradiance. However, an important limitation of SMARTS is that the model assumes clear-sky conditions and does not account for variations in atmospheric conditions or cloud cover that could decrease irradiance. The impact of cloud cover on irradiance spectra depends on the extent of coverage, cloud thickness, and the type of cloud (Bartlett et al., 1998). Therefore, the effect of cloud cover on photolysis rates is difficult to generalize and is the subject of ongoing work. Inputs to SMARTS are provided in the Supplementary Data (Supplementary Table S1) and modeled irradiance spectra are presented in Supplementary Fig. S1 of the Supplementary Data.

Determination of TrOC k ⁱ _photo

The framework and equations for calculating TrOC photolysis are summarized in this section and come from Jasper and Sedlak (2013). As discussed above, photolysis can occur through direct and indirect processes (Schwarzenbach et al., 2003). Depending on the compound, both photolysis processes can be important; therefore, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{photo}}}^i$$ \end{document} (day⁻¹) of a particular compound i was modeled as the sum of the two processes, using the following equation (Jasper and Sedlak, 2013): \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} k_ { { \rm { photo } } } ^i = \frac { { \left( { z - { d_ { { \rm { biomat } } } } } \right) } } { z } \cdot \left( { k_ { { \rm { direct } } } ^i + k_ { { \rm { indirect } } } ^i } \right) \tag { 4 } \end{align*} \end{document}

\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{direct}}}^i$$ \end{document} [day⁻¹; Eq. (5)] is the first-order direct photolysis rate constant, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{indirect}}}^i$$ \end{document} [day⁻¹; Eq. (10)] is the first-order indirect photolysis rate constant, z (cm) is the total depth of the water column, and d_biomat (cm) is the thickness of the biomat. Given that sunlight is required for photolysis to occur, and assuming that the water column is well mixed across the depth (including the volume occupied by the biomat), the photolysis rate was corrected for time the water spends shaded within the biomat by using the term \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${{ \left( {z - {d_{{ \rm{biomat}}}}} \right) } / z} $$ \end{document} (Jasper et al., 2014a; Silverman et al., 2015).

\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{direct}}}^i$$ \end{document} was estimated using Equation (5) with the following inputs: the quantum yields specific to compound i ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{ \Phi }}_{{ \rm{prot}}}^i$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{ \Phi }}_{{ \rm{unprot}}}^i$$ \end{document} ; mol molecules transformed/mol photons absorbed; Supplementary Table S4), the 24 h-averaged photon fluence rate incident on the water surface [Z_{24h avg}(λ); Einstein (cm² day)⁻¹ Eq. (7)], a light screening factor that corrects the incident light spectrum for attenuation in a well-mixed water column [S(λ, z); Eq. (8)] (Schwarzenbach et al., 2003), and the molar absorption coefficient spectrum (ɛ ⁱ (λ); M⁻¹ cm⁻¹; Supplementary Table S3). The term \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{ \alpha }}_0^i$$ \end{document} describes the acid–base speciation of compound i, given that the quantum yield can differ depending on whether the compound is in its protonated ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{ \Phi }}_{{ \rm{prot}}}^i$$ \end{document} ) or unprotonated ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{ \Phi }}_{{ \rm{unprot}}}^i$$ \end{document} ) form. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{ \alpha }}_0^i$$ \end{document} is computed in Equation (6), and pKa ⁱ are provided in Supplementary Table S4.

\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \ & k_{{ \rm{direct}}}^i = 2.303 [ {{ \rm{ \alpha }}_0^{ \rm{i}} \cdot { \rm{ \Phi }}_{{ \rm{prot}}}^{ \rm{i}} + ( {1 - { \rm{ \alpha }}_0^i }) \cdot { \rm{ \Phi }}_{{ \rm{unprot}}}^i} . ] \\ \ & \qquad\qquad\qquad \mathop \cdot \sum \limits_ \lambda {Z_{24{ \rm{h \;avg}}}} \left( { \rm{ \lambda }} \right) \cdot S \left( { \lambda , \;z} \right) \cdot {{ \rm{ \varepsilon }}^i} \left( { \rm{ \lambda }} \right) \quad\quad\quad ( 5 ) \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} { \rm { \alpha } } _0^i = { \frac { { { 10 } ^ { - { \rm { pH } } } } } { { { 10 } ^ { - { \rm { pK } } { { \rm { a } } ^i } { \rm { } } } } + { { 10 } ^ { - { \rm { pH } } } } { \rm { \; \; } } } } \tag { 6 } \end{align*} \end{document}

Z_{24h avg}(λ) was calculated from the 24-h averaged global horizontal irradiance incident on the water surface (E_{24h avg}(λ); W m⁻²) using Equation (7), where h is Planck's constant (h = 6.626 × 10⁻³⁴ J·s), c is the speed of light (c = 3.0 × 10⁸ m s⁻¹), λ is the wavelength (nm), and u is a unit conversion factor (u = 1.435 × 10⁻³² Einstein s m³ (photon day nm cm²)⁻¹. E_{24h avg}(λ) was estimated using SMARTS (Gueymard, 1995, 2001). Global horizontal irradiance spectra were predicted for each hour of the 21st day of the month and averaged over 24 h to calculate the daily average. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} { Z_ { 24 { \rm { h \;avg } } } } \left( { \rm { \lambda } } \right) = \left( { { \frac { { \rm { \lambda } } \cdot u } { h \cdot c } } } \right) { E_ { 24 { \rm { h \;avg } } } } \left( { \rm { \lambda } } \right) \tag { 7 } \end{align*} \end{document}

The light screening factor, S(λ, z), is wavelength dependent and was calculated for a well-mixed water column using Equation (8) (Schwarzenbach et al., 2003); inputs are the depth of the light-exposed water column (z − d_biomat; cm), the wavelength-specific decadic light absorption coefficient [α(λ); cm⁻¹; Eq. (9)], and a path length correction factor (ψ) used to correct the depth for light path geometry. The value of ψ was assumed to be 1.2, which is an average path length correction factor calculated based on light refraction at the water surface (Zepp and Cline, 1977). \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} S \left( { { \rm { \lambda } } , { \rm { \;z } } } \right) = \left( { { \frac { 1 - { { 10 } ^ { - { \rm { { \uppsi } } } \cdot { \rm { \alpha } } \left( { \rm { \lambda } } \right) \cdot ( z - { d_ { { \rm { biomat } } } } ) } } } { 2.303 \cdot { \rm { { \uppsi } } } \cdot { \rm { \alpha } } \left( { \rm { \lambda } } \right) \cdot ( z - { d_ { biomat } } ) } } } \right) \tag { 8 } \end{align*} \end{document}

α(λ) was estimated based on the [DOC] in the water ([DOC]; mg-C L⁻¹) using Equation (9). Values for m(λ) and b(λ) (Supplementary Table S6) come from Jasper and Sedlak (2013) and were derived from absorbance data for over 15 samples collected from the Discovery Bay UPOW wetland on different days with a range of [DOC]. Equation (9) was previously used to model TrOC photolysis rates in the Discovery Bay UPOW wetland that received clarified secondary effluent, as well as the Prado UPOW wetland that received water from the effluent-dominated Santa Ana River. If photolysis rates are to be estimated in water sources with optical properties that may differ from the Discovery Bay and Prado UPOW wetlands, one could compare the measured absorption spectrum with that estimated by Equation (9) to determine whether photolysis rates predicted herein will apply in their context. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} { \rm{ \alpha }} \left( { \rm{ \lambda }} \right) = m \left( { \rm{ \lambda }} \right) \left[ {{ \rm{DOC}}} \right] + b \left( { \rm{ \lambda }} \right) \tag{9} \end{align*} \end{document}

\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{indirect}}}^i$$ \end{document} (day⁻¹) was estimated using Equation (10), where \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{ \bullet { \rm{OH}}}^i$$ \end{document} , \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{ \bullet { \rm{CO}}_3^ - }^i$$ \end{document} , and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{}_{}^1{{ \rm{O}}_2}}^i$$ \end{document} (M⁻¹day⁻¹) are the second-order reaction rate constants between contaminant i and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet { \rm{OH}}$$ \end{document} , \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet { \rm{CO}}_3^{ - { \rm{ \;}}}$$ \end{document} , and ¹O₂, respectively; these values differ depending on whether contaminant i is in its protonated or unprotonated form (i.e., depending on the pH and pKa ⁱ ), and are provided in Supplementary Table S4. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \left[ { \bullet { \rm{OH}}} \right] _{{ \rm{ss}}}}$$ \end{document} , \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \left[ { \bullet { \rm{CO}}_3^{ - { \rm{ \;}}}} \right] _{{ \rm{ss}}}}$$ \end{document} , and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \left[ {{}_{}^1{{ \rm{O}}_2}} \right] _{{ \rm{ss}}}}$$ \end{document} (M) are the steady-state concentrations of each PPRI; these steady-state concentrations were estimated using Equations (11) through (17). \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{}_{}^3{ \rm{DO}}{{ \rm{M}}^{ \rm{*}}}}^i$$ \end{document} (day⁻¹) is the pseudo first-order reaction rate constant between ³DOM* and contaminant i, and was estimated using Equation (18).

\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \left[ { \bullet { \rm{OH}}} \right] _{{ \rm{ss}}}}$$ \end{document} was estimated using Equation (11) (Jasper and Sedlak, 2013), which accounts for the rates of •OH formation by nitrate [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${R_{{ \rm{form}} , \bullet { \rm{OH}} , { \rm{ \;NO}}_3^ - }}$$ \end{document} ; M day⁻¹; Eq. (14)] and DOM [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${R_{{ \rm{form}} , \bullet { \rm{OH}} , { \rm{ \;DOM}}}}$$ \end{document} ; M day⁻¹; Eq. (15)], as well as the second-order rates of •OH scavenging by carbonate species ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{ \bullet { \rm{OH}} , { \rm{HCO}}_3^ - }}$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{ \bullet { \rm{OH}} , { \rm{CO}}_3^{2 - }}}$$ \end{document} ; M⁻¹ day⁻¹; Supplementary Table S5) and DOM ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{ \bullet { \rm{OH}} , { \rm{DOM}}}}$$ \end{document} ; (mg L⁻¹-C)⁻¹ day⁻¹; Supplementary Table S5).

DOM was approximated as [DOC]. The concentrations of bicarbonate ([ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$ {{ \rm{HCO}}_3^ - }$$ \end{document} ]) and carbonate ([ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${{ \rm{CO}}_3^{2 - }}$$ \end{document} ]) in the water depend on the pH-regulated speciation of carbonate molecules, and were calculated as described in Equations (12) and (13). Total carbonate concentration was approximated as the total dissolved inorganic carbon concentration ([DIC]), which was assumed to be 60 mg-C L⁻¹, based on measured [DIC] in the Discovery Bay UPOW wetland (Jasper and Sedlak, 2013). \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \left[ { { \rm { HCO } } _3^ - } \right] = \left[ { { \rm { DIC } } } \right] \cdot { \left( { 1 + { \frac { { { 10 } ^ { - { \rm { pH } } } } } { { { 10 } ^ { - { \rm { pK } } { { \rm { a } } _1 } } } } } + { \frac { { { 10 } ^ { - { \rm { pK } } { { \rm { a } } _2 } } } } { { { 10 } ^ { - { \rm { pH } } } } } } } \right) ^ { - 1 } } \tag { 12 } \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \left[ { { \rm { CO } } _3^ { 2 - } } \right] = \left[ { { \rm { DIC } } } \right] \cdot { \left( { 1 + { \frac { ( { { 10 } ^ { - 2 { \rm { \;pH } } } } ) } { { { 10 } ^ { - \left( { { \rm { pK } } { { \rm { a } } _1 } + { \rm { pK } } { { \rm { a } } _2 } } \right) } } } } + { \frac { { { 10 } ^ { - { \rm { pH } } } } } { { { 10 } ^ { - { \rm { pK } } { { \rm { a } } _2 } } } } } } \right) ^ { - 1 } } \tag { 13 } \end{align*} \end{document}

\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet { \rm{OH}}$$ \end{document} formation rates were estimated using Equations (14) and (15), assuming that the nitrate concentration ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\left[ {{ \rm{NO}}_3^ - } \right]$$ \end{document} ) remains constant throughout the system. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${{ \rm{ \varepsilon }}_{{ \rm{NO}}_3^ - }} \left( { \rm{ \lambda }} \right)$$ \end{document} is provided in Supplementary Table S3; \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\left[ {{ \rm{NO}}_3^ - } \right]$$ \end{document} was assumed to be 10 mg-N L⁻¹, based on observations at the Discovery Bay UPOW wetland (Jasper and Sedlak, 2013). Greater nitrate concentrations would increase TrOC decay rates due to increased production of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet$$ \end{document} OH. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \ & {R_{{ \rm{form}} , \bullet { \rm{OH}} , { \rm{ NO}}_3^ - }} = 2.303\ {{ \rm{ \Phi }}_{ \bullet { \rm{OH}} , { \rm{NO}}_3^ - }} \left[ {{ \rm{NO}}_3^ - } \right] \\ \ & \quad\quad\quad\quad\quad\quad\quad \mathop \cdot \sum \limits_{ \rm{ \lambda }} {Z_{24{ \rm{h avg}}}} \left( { \rm{ \lambda }} \right) \cdot S \left( {{ \rm{ \lambda }} , \ z} \right) \cdot {{ \rm{ \varepsilon }}_{{ \rm{NO}}_3^ - }} \left( { \rm{ \lambda }} \right) \quad\quad\quad ( 14 ) \end{align*} \end{document}

\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \left[ { \bullet { \rm{CO}}_3^ - } \right] _{{ \rm{ss}}}}$$ \end{document} was estimated using Equation (16), which accounts for \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet { \rm{CO}}_3^ -$$ \end{document} formation through reaction of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet$$ \end{document} OH with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{HCO}}_3^ -$$ \end{document} or \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \rm{CO}}_3^{2 - }$$ \end{document} ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{ \bullet { \rm{OH}} , { \rm{HCO}}_3^ - }}$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{ \bullet { \rm{OH}} , { \rm{CO}}_3^{2 - }}}$$ \end{document} ; M⁻¹ day⁻¹; Supplementary Table S5), as well as the rate of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet { \rm{CO}}_3^ -$$ \end{document} scavenging by DOM [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{ \bullet { \rm{CO}}_3^ - , { \rm{DOM}}}}$$ \end{document} ; (mg L⁻¹-C)⁻¹ day⁻¹; Supplementary Table S5].

\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} { \left[ { \bullet { \rm { CO } } _3^ - } \right] _ { { \rm { ss } } } } = { \frac { { k_ { \bullet { \rm { OH , HCO } } _3^ - } } \left[ { { \rm { HCO } } _3^ - } \right] { { \left[ { \bullet { \rm { OH } } } \right] } _ { { \rm { ss } } } } + { k_ { \bullet { \rm { OH } } , { \rm { CO } } _3^ { 2 - } } } \left[ { { \rm { CO } } _3^ { 2 - } } \right] { { \left[ { \bullet { \rm { OH } } } \right] } _ { { \rm { ss } } } } } { { k_ { \bullet { \rm { CO } } _3^ - , { \rm { DOM } } } } \left[ { { \rm { DOC } } } \right] } } \tag { 16 } \end{align*} \end{document}

The equation used to calculate [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${^1{{\rm{O}}_2}}$$ \end{document} ]_ss was based on [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${^1{{\rm{O}}_2}}$$ \end{document} ]_ss observed in effluent-dominated water by Haag and Hoigné (Haag and Hoigné, 1986; Jasper and Sedlak, 2013). These observations were made in near-surface water in summer with exposure to sunlight at noon (E(λ)∼1.22 W/m²). Values of [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${^1{{\rm{O}}_2}}$$ \end{document} ]_ss measured by Haag and Hoigné were normalized by the concentration of dissolved organic carbon in that particular water body (i.e., [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${^1{{\rm{O}}_2}}$$ \end{document} ]_ss/[DOC]) and averaged, with a resulting value of 1 × 10^–14 M/(mg/L-C) (Haag and Hoigné, 1986; Jasper and Sedlak, 2013). To calculate [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${^1{{\rm{O}}_2}}$$ \end{document} ]_ss using Equation (17), the normalized value of [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${^1{{\rm{O}}_2}}$$ \end{document} ]_ss/[DOC] was multiplied by [DOC] and corrected for incident light intensity and light attenuation in the water column (Haag and Hoigne, 1986; Jasper and Sedlak, 2013). Corrections were made based on light at 410 nm, given that this wavelength was previously determined to best describe \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \left[ {{}_{}^1{{ \rm{O}}_2}} \right] _{{ \rm{ss}}}}$$ \end{document} (Haag and Hoigné, 1986). \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \ & { \left[ {{}_{}^1{{ \rm{O}}_2}} \right] _{{ \rm{ss}}}} = 1 \times {10^{ - 14}}{{ \rm{M}} \over {{ \rm{mg / L}} - { \rm{C}}}} \cdot \left[ {{ \rm{DOC}}} \right] \\ \ & \quad\quad\quad \cdot {{{E_{24{ \rm{h avg}}}} \left( {410 { \rm{nm}}} \right) \cdot S \left( {410 { \rm{nm}} , \ z} \right) } \over { \begin{matrix} {1.22 { \rm{W / }} {{ \rm{m}}^2}} \\ \end{matrix} }} \quad\quad\quad\quad ( 17 ) \end{align*} \end{document}

The reaction rate between ³DOM* and compound i ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{}_{}^3{ \rm{DO}}{{ \rm{M}}^*}}^i$$ \end{document} ) was estimated using Equation (18), which was proposed by Jasper and Sedlak (2013). This equation includes a wavelength-dependent quantum yield coefficient, fⁱ(λ) L Einstein⁻¹; Supplementary Table S4), which accounts for the efficiency of light absorption by DOM, and the reactivity between ³DOM* and contaminant i. Of the TrOC evaluated herein, only propranolol photolysis included a contribution from reaction with ³DOM*. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} k_{{}_{}^3{ \rm{DO}}{{ \rm{M}}^*}}^i = 2.303 \mathop \sum \limits_{ \rm{ \lambda }} {f^i} \left( { \rm{ \lambda }} \right) \cdot {Z_{24{ \rm{h \;avg}}}} \left( { \rm{ \lambda }} \right) \cdot S \left( {{ \rm{ \lambda }} , z} \right) \cdot { \rm{ \alpha }} \left( { \rm{ \lambda }} \right) \tag{18} \end{align*} \end{document}

Determination of microbial k ⁱ _endo and k ⁱ _exo

The framework and equations for calculating photoinactivation rates of microbial contaminants are summarized in this section, and come from Fisher et al. (2011), Nguyen et al. (2015), Silverman et al. (2015), and Silverman and Nelson (2016).

The inactivation rates of bacteria and viruses are wavelength dependent. Both bacteria and viruses are most sensitive to sunlight in the UVB region (i.e., the shortest wavelengths of sunlight that reach the earth's surface), and have decreasing sensitivity to light with increased wavelength (i.e., into the UVA and visible regions of the solar spectrum) (Fisher et al., 2011; Kadir and Nelson, 2014; Silverman and Nelson, 2016). Therefore, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^i$$ \end{document} [Eq. (19)] were estimated using biological weighting functions, Pⁱ(λ) [m² (W h)⁻¹], which are spectra of organism-specific coefficients describing sensitivity to light (Fisher et al., 2011; Nguyen et al., 2014; Silverman et al., 2015; Silverman and Nelson, 2016). Pⁱ(λ) spectra for E. coli (Silverman and Nelson, 2016) and MS2 (Fisher et al., 2011; Nguyen et al., 2014) are provided in Supplementary Table S7. The Pⁱ(λ) spectrum for E. coli was developed specifically for E. coli that are indigenous to wastewater, given that sunlight inactivation rates of wastewater-sourced bacteria have been found to be slower than those of laboratory-grown bacteria of the same species (Fisher et al., 2012; Nguyen et al., 2015; Silverman and Nelson, 2016). Some Pⁱ(λ) spectra have been developed for 1-nm wavelength increments, whereas others have been developed with Pⁱ(λ) values for a bin of wavelengths; Δλ is a term used to take this binning into account. For example, E. coli Pⁱ(λ) was developed with Δλ equal to 1, whereas MS2 Pⁱ(λ) was developed with Δλ equal to 3. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \ & k_{{ \rm{endo}}}^i = {{24 { \rm{h}}} \over { \rm{d}}} \cdot {{ \left( {z - {d_{{ \rm{biomat}}}}} \right) } \over z} \\ \ & \quad\quad\quad\quad \mathop \cdot \sum \limits_{ \rm{ \lambda }} {E_{24{ \rm{h avg}}}} \left( { \rm{ \lambda }} \right) \cdot S \left( {{ \rm{ \lambda }} , z} \right) \cdot {P^i} \left( { \rm{ \lambda }} \right) \cdot \Delta { \rm{ \lambda }} \quad\quad\quad\quad ( 19 ) \end{align*} \end{document}

\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{exo}}}^i$$ \end{document} was estimated based on [¹O₂]_ss [Eqs. (17) and (20)] (Silverman et al., 2015). While additional PPRI are involved in bacteria (Kadir and Nelson, 2014) and virus (Romero-Maraccini et al., 2013; Rosado-Lausell et al., 2013; Mattle et al., 2015) inactivation, singlet oxygen has been found to be the most important PPRI for MS2 inactivation in water collected from wastewater treatment ponds (Kohn and Nelson, 2007; Mattle et al., 2015; Kohn et al., 2016). Additionally, measured MS2 \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{exo}}}^i$$ \end{document} have been observed to scale with measured [¹O₂]_ss (Kohn and Nelson, 2007; Rosado-Lausell et al., 2013; Silverman et al., 2013). Therefore, [¹O₂]_ss was used as an indicator for overall microorganism inactivation by PPRI. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} k_ { { \rm { exo } } } ^i = \frac { { \left( { z - { d_ { { \rm { biomat } } } } } \right) } } { z } \cdot k_2^i \cdot { { [ ^1 } { { \rm { O } } _2 } ] _ { { \rm { ss } } } } \tag { 20 } \end{align*} \end{document}

\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_2^i$$ \end{document} (M⁻¹day⁻¹) is the second-order reaction rate between microorganism i and singlet oxygen. For a given microorganism, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_2^i$$ \end{document} values have been found to differ with exposure to different environmental waters (Silverman et al., 2013, 2015). As a result, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_2^i$$ \end{document} was determined specifically for UPOW wetland water sourced from the pilot-scale UPOW wetland in Discovery Bay, CA, which received nitrified and clarified wastewater effluent (Jasper and Sedlak, 2013; Jasper et al., 2014a, 2014b; Nguyen et al., 2015; Silverman et al., 2015). For MS2, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_2^i$$ \end{document} measured in the Discovery Bay UPOW wetland was 2.6 × 10¹⁴ M⁻¹day⁻¹ (Silverman et al., 2015); this value is greater than \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_2^i$$ \end{document} in other waters (Kohn and Nelson, 2007; Silverman et al., 2013). E. coli is not susceptible to exogenous photoinactivation (Kadir and Nelson, 2014), therefore \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{exo}}}^i$$ \end{document} should not be included in the calculation of total E. coli \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{microbial}}}^i$$ \end{document} (Kadir and Nelson, 2014).

One limitation of the E. coli \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^i$$ \end{document} model is that it does not account for the effect of elevated pH and DO concentration, which can increase sunlight inactivation rates for the bacteria (Kadir, 2010). Observed E. coli \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^i$$ \end{document} could be as much as two or three times greater than predicted due to the high pH and DO encountered in open-water wetlands (Davies-Colley et al., 1999; Kadir, 2010; Kadir and Nelson, 2014; Silverman and Nelson, 2016), meaning that estimated E. coli \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^i$$ \end{document} are conservative values. Ongoing research is being conducted to generate correction factors to adjust estimated E. coli inactivation rates for pH and DO effects. This effect is not as important for viruses, as data on inactivation of MS2 in wastewater treatment pond water demonstrated little effect of pH on inactivation rates over the pH range typically found in open-water natural treatment systems (i.e., pH 7–10) (Davies-Colley et al., 1999; Kohn and Nelson, 2007). DO concentration is not expected to affect photolysis rates of atenolol, sulfamethoxazole, or carbamazepine (Jasper and Sedlak, 2013). Propranolol photolysis rates may decrease at elevated DO, given the importance of ³DOM* for propranolol photolysis, and the role of O₂ as a ³DOM* quencher.

An additional limitation of the sunlight inactivation rate equations is that they do not account for the effect of temperature. Elevated temperatures can have a modest effect of increasing inactivation rates. For example, elevated temperatures were found to increase exogenous inactivation rates of MS2 (Romero et al., 2011; Carratalà et al., 2016), but not endogenous inactivation rates (Romero et al., 2011). If anything, using the models presented in this study to estimate inactivation rates will result in a conservative estimate of inactivation rates at elevated temperatures.

Calculation of nitrate removal rates

Nitrate removal in UPOW wetlands occurs primarily through microbial denitrification within the biomat, with a potential contribution from anaerobic ammonium oxidation (anammox) (Jasper et al., 2014b; Jones et al., 2017, 2018). Jasper et al. (2014b) quantified nitrate removal rates in the Discovery Bay UPOW wetland over a 3-year period. As is typically observed for treatment wetlands (Kadlec, 2012), nitrate removal followed temperature-dependent, first-order areal kinetics, resulting in seasonal variation of removal rates (Jasper et al., 2014b). Given this temperature dependence, Jasper et al. (2014b) used data from the Discovery Bay UPOW wetland to model areal nitrate removal rates ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{{ \rm{NO}}_3^ - }}$$ \end{document} ; m/year) using a modified Arrhenius equation (Kadlec, 2012; Jasper et al., 2014b): \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} {k_{{ \rm{NO}}_3^ - }} = {k_{20 , \;{ \rm{NO}}_3^ - }}{{ \rm{ \theta }}^{ \left( {T - 20{ \rm{^ \circ C}}} \right) }} \tag{21} \end{align*} \end{document}

where \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{{ 20,\rm{NO}}_3^ - }}$$ \end{document} is the areal nitrate removal rate at 20°C ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{{ 20,\rm{NO}}_3^ - }}$$ \end{document}  = 59.4 ± 6.2 m year⁻¹), θ is the temperature coefficient (θ = 1.12 ± 0.02), and T is the air temperature (°C). The nitrate removal rate equation was validated in three UPOW wetland cells at the Prado Wetlands in Southern California (Bear et al., 2017).

Calculation of decay rates and sensitivity analysis

The model equations described above were used to calculate decay rates for nitrate, TrOC, and microbial contaminants using Microsoft Excel (v16). Figures were made in GraphPad Prism (v7.0).

A one-at-a-time sensitivity analysis was conducted to determine the importance of each model input to the calculation of TrOC degradation rates ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^i$$ \end{document} ; Hamby, 1994); degradation rates were calculated for March at 30°N. The following inputs were individually varied to values 50% greater and 50% less than a median value: [NO₃⁻] (median: 10 mg/L-N; minimum: 5 mg/L-N; maximum: 15 mg/L-N), [DOC] (median: 10 mg-C L⁻¹; minimum: 5 mg-C L⁻¹; maximum: 15 mg-C L⁻¹), [DIC] (median: 60 mg-C L⁻¹; minimum: 30 mg-C L⁻¹; maximum: 90 mg-C L⁻¹), and depth (median: 30 cm; minimum: 20 cm; maximum: 40 cm). A median pH of 9 was used, with minimum and maximum values equal to 8 and 10, respectively. A median temperature of 21°C was used, with minimum and maximum temperatures equal to 19.4°C and 22.6°C, respectively; selected temperatures reflect the average monthly temperature in Orlando, FL (28.5383°N latitude) in March, and temperatures one standard deviation from the mean.

Decay rate constants determined for a range of environmental conditions

Sunlight-dependent rate constants (i.e., \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{photo}}}^i$$ \end{document} , \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^i$$ \end{document} , and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{exo}}}^i$$ \end{document} ) for decay of TrOC, E. coli, and MS2 in a UPOW wetland with a 30-cm depth are presented in Figs. 3–9. In each figure, a range of decay rates are presented for different latitudes, months, [DOC], and pH. Estimated decay rate constants for UPOW wetlands with depths of 20 and 40 cm are presented in Supplementary Figs. S2–S15 of the Supplementary Data, and estimated [¹O₂]_ss are provided in Supplementary Figs. S16–S18 of the Supplementary Data.

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FIG. 3.

Atenolol phototransformation rates (k_photo; day⁻¹) estimated in an open-water wetland with a 30-cm-deep well-mixed water column. k_photo were estimated for the 21st day of (a, d) June, (b, e) March, and (c, f) December. Choose a [DOC] (mg/L-C), pH, and month to determine k_photo. [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${{ \rm{NO}}_3^ - }$$ \end{document} ] = 10 mg/L-N; [DIC] = 60 mg-C L⁻¹. [DIC], dissolved inorganic carbon concentration.

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FIG. 4.

Propranolol phototransformation rates (k_photo; day⁻¹) estimated in an open-water wetland with a 30-cm-deep well-mixed water column. k_photo were estimated for the 21st day of (a, d) June, (b, e) March, and (c, f) December. Choose a [DOC] (mg/L-C), pH, and month to determine k_photo. [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${{ \rm{NO}}_3^ - }$$ \end{document} ] = 10 mg/L-N; [DIC] = 60 mg-C L⁻¹.

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FIG. 5.

Sulfamethoxazole phototransformation rates (k_photo; day⁻¹) estimated in an open-water wetland with a 30-cm-deep well-mixed water column. k_photo were estimated for the 21st day of (a, d) June, (b, e) March, and (c, f) December. Choose a [DOC] (mg/L-C), pH, and month to determine k_photo. [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${{ \rm{NO}}_3^ - }$$ \end{document} ] = 10 mg/L-N; [DIC] = 60 mg-C L⁻¹.

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FIG. 6.

Carbamazepine phototransformation rates (k_photo; day⁻¹) estimated in an open-water wetland with a 30-cm-deep well-mixed water column. k_photo were estimated for the 21st day of (a, d) June, (b, e) March, and (c, f) December. Choose a [DOC] (mg/L-C), pH, and month to determine k_photo. [ \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${{ \rm{NO}}_3^ - }$$ \end{document} ] = 10 mg/L-N; [DIC] = 60 mg-C L⁻¹.

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FIG. 7.

E. coli endogenous inactivation rates (k_endo; day⁻¹) estimated in an open-water wetland with a 30-cm-deep well-mixed water column. k_endo were estimated for the 21st day of (a) June, (b) March, and (c) December. Choose a [DOC] (mg-C L⁻¹) and month to determine k_endo.

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FIG. 8.

MS2 endogenous inactivation rates (k_endo; day⁻¹) estimated in an open-water wetland with a 30-cm-deep well-mixed water column. k_endo were estimated for the 21st day of (a) June, (b) March, and (c) December. Choose a [DOC] (mg-C L⁻¹) and month to determine k_endo.

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FIG. 9.

MS2 exogenous inactivation rates (k_exo; day⁻¹) estimated in an open-water wetland with a 30-cm-deep well-mixed water column. k_exo were estimated for the 21st day of (a) June, (b) March, and (c) December. Choose a [DOC] (mg-C L⁻¹) and month to determine k_exo.

To calculate total TrOC decay rates, Equation (1) should be used, with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{photo}}}^i$$ \end{document} read from the figures, and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{bio}}}^i$$ \end{document} calculated using Equation (2). pH in UPOW wetlands will follow a diurnal cycle, with greatest pH corresponding with maximum sunlight irradiance, due to photosynthesis. Given that TrOC removal due to photolysis occurs when there is sunlight irradiance, the predominant pH during daylight hours should be used when reading the \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{photo}}}^i$$ \end{document} figures. To determine E. coli decay rates, Equation (3) should be used, with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^i$$ \end{document} read from the figures and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{dark}}}^{E. \; \;coli}$$ \end{document} equal to 0.86 day⁻¹ ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{exo}}}^i$$ \end{document} for E. coli is equal to zero). To determine MS2 decay rates, Equation (3) should be used, with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^i$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{exo}}}^i$$ \end{document} read from the figures ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{dark}}}^i$$ \end{document} for MS2 is equal to zero).

There are limitations to the model predictions presented in this article. First, although the photolysis and photoinactivation rate model equations represent well-studied mechanisms, and therefore are broadly applicable across sunlit waters, some of the input parameters for the decay rate equations (i.e., [DIC], \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\left[ {{ \rm{NO}}_3^ - } \right]$$ \end{document} , \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_2^i$$ \end{document} , and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{dark}}}^{E. \; \;coli}$$ \end{document} ) were measured in water from the Discovery Bay UPOW wetland and may differ in systems with different water quality. Second, the Discovery Bay and Prado UPOW wetlands had [DOC] of ∼8 and 4.5 mg-C L⁻¹, respectively (Jasper and Sedlak, 2013; Bear et al., 2017), and the decay rate equations have therefore not been validated for the entire [DOC] range modeled in this article. Additionally, the sunlight spectra predicted by SMARTS as inputs to photodegradation equations do not account for atmospheric conditions that would attenuate light in the atmosphere and are therefore assumed to represent clear-sky (e.g., cloud-, haze- and smog-free) conditions. Previous validation of model estimates was conducted in temperate regions, and the effects of freezing temperatures and ice formation during winter at high latitudes is not accounted for in the decay rate predictions.

Sensitivity analysis to screen for important inputs to TrOC removal equations

A one-at-a-time sensitivity analysis was conducted to determine the importance of each model input (i.e., pH, [DOC], [DIC], depth, [NO₃⁻], and temperature) for the calculation of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^i$$ \end{document} . The importance of each input differed for each TrOC evaluated; these results are summarized in Table 1 and Supplementary Fig. S19. For example, temperature was the most important variable for atenolol removal given the importance of temperature-dependent biotransformation for this compound (i.e., increased temperature resulted in increased \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^{{ \rm{atenolol}}}$$ \end{document} ), whereas depth and [DOC] were important inputs for propranolol and sulfamethoxazole removal given their susceptibility to photolysis (i.e., increasing these values resulted in reduced \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^{{ \rm{propranolol}}}$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^{{ \rm{sulfamethoxazole}}}$$ \end{document} due to a decrease in sunlight available for direct and indirect photolysis). pH was the most important input for carbamazepine transformation given its reliance on steady-state \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet { \rm{OH}}$$ \end{document} concentration for degradation, which is highly pH dependent (i.e., at elevated pH, [•OH]_ss, and therefore \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^{{ \rm{carbamazepine}}}$$ \end{document} , are reduced due to an increase in the concentration of CO₃²⁻ (pK_a2,H2CO3 = 10.33), which quenches \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\bullet { \rm{OH}}$$ \end{document} at a greater rate than is achieved by HCO₃⁻). The pH effect is the opposite for propranolol and sulfamethoxazole, due to their susceptibility to reaction with carbonate radical: propranolol and sulfamethoxazole have faster \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^i$$ \end{document} at elevated pH, given greater CO₃²⁻ concentrations, and therefore greater carbonate radical concentrations, at higher pH.

Design example

The following design example is used to illustrate how the framework for estimating contaminant removal rates described in this article can be utilized in conjunction with the P-k-C* equation [Eq. (22)] to design the area (and subsequent volume) of a UPOW wetland to meet water treatment objectives. The P-k-C* equation describes contaminant decay in surface flow wetlands by modeling wetlands as series of well-mixed tanks and including the term C* to account for the background concentration of a compound of interest in the wetland.

In this example, we consider a UPOW wetland used as a polishing step to remove nitrate from wastewater effluent discharged to a sensitive environment in central Florida (e.g., Orlando, 28.5383°N latitude; additional design assumptions are provided in Table 2). The motivation for constructing this UPOW wetland is that effluents from conventional wastewater treatment systems without biological nitrogen removal have nitrate concentrations that range between 10 and 20 mg/L-N, which can lead to nutrient pollution and eutrophication in aquatic environments (Carey and Migliaccio, 2009). We decided to design the system to achieve 90% nitrate removal during the month with median average monthly temperature in Orlando, which is 21.8°C and occurs in April (data from the World Meteorological Organization). Applying Equation (21) with T = 21.8°C resulted in \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{{ \rm{NO}}_3^ - }}$$ \end{document} equal to 72.8 m year⁻¹ (0.20 m day⁻¹). This estimated \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{{ \rm{NO}}_3^ - }}$$ \end{document} is greater than the 90th percentile of nitrate removal rate coefficients identified by Kadlec and Wallace (2009) in a survey of 72 free water surface wetlands.

To determine the wetland area (A) required to meet the nitrate treatment objective, the P-k-C* model was employed (Kadlec and Wallace, 2009): \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \left[ { { \frac { { C_ { { \rm { out } } } } - { C^* } } { { C_ { { \rm { in } } } } - { C^* } \; } } } \right] = { \left( { 1 + { \frac { { k_A } \;A } { N \;Q } } } \right) ^ { - N } } { \rm { \; \; \;\;OR } } \; \; \; \; \; { \left( { 1 + { \frac { { k_V } \;A \;z } { N \;Q } } } \right) ^ { - N } } \tag { 22 } \end{align*} \end{document}

where,

C_out = contaminant concentration in the effluent

C_in = contaminant concentration in the influent

C* = background concentration of the contaminant in the wetland

k_A = first-order areal removal constant (m day⁻¹; e.g., \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{NO_3^ - }}$$ \end{document} )

k_V = first-order volumetric removal constant (day⁻¹; e.g., \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^i$$ \end{document} , \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{microbial}}}^i$$ \end{document} )

A = wetland area (m²)

N = number of theoretical tanks in series

Q = influent flow rate (m³/day)

z = well-mixed water column depth

For existing systems, tracer tests are used to determine the number of theoretical tanks in series (N) that describes the wetland hydraulics (Kadlec and Wallace, 2009). However, it is not possible to conduct a tracer test in a system that has not yet been designed or constructed. Therefore, for design purposes, N must be estimated. As the flow regime approaches ideal plug flow hydraulics, the number of tanks in series increases. Therefore, treatment system modifications that encourage plug flow—such as using baffles, increasing the length-to-width ratio of the wetland cell or designing the system to have multiple wetland cells in series—will result in a greater value of N. Kadlec and Wallace (2009) surveyed studies that report N values for surface flow vegetated wetlands, and found N to range between 0.3 and 10.7, with a mean of 4.1 (standard error = 0.4). Jasper et al. (2014a, 2014b) found N to equal 6.4 in the highly baffled UPOW wetland in Discovery Bay, CA. The UPOW cells in the Prado wetlands did not contain baffles, but were constructed with a length-to-width ratio of 8.2 to promote channelized flow. However, the system was not as successful in reducing hydraulic inefficiencies, and had an average value of N equal to 2.4 (Bear et al., 2017). In this example, we used a value of 4.4 for N, which is the average of N in the Discovery Bay and Prado UPOW wetlands.

The C* term in the P-k-C* model accounts for the background concentration of a compound of interest in the wetland, which could result from decaying biomass or, in the case of fecal indicator organisms, animal excreta introduced to the wetland. Following recommendations from Kadlec and Wallace (2009), we assumed that the C* value for nitrate is zero. C* for TrOC is also assumed to be zero, as there are no sources for these compounds within the wetland (Kadlec and Wallace, 2009). For fecal coliforms, Kadlec and Wallace (2009) stated that wetland systems with high animal activity have C* values that range between 100 and 500 CFU (100 mL)⁻¹; E. coli C* is assumed to be the same. C* values have not been determined for F+ coliphage (i.e., the family of coliphage that MS2 belongs to), but are assumed to be zero, given that F+ coliphage concentrations of some samples from the Discovery Bay wetland (Silverman et al., 2015) and the Prado wetland (Bear et al., 2017) were found to be below the detection limit.

After rearranging the P-k-C* model equation and assuming C* is equal to zero, the following equation was used to solve for the wetland area required for 90% nitrate removal: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} A = { \frac { NQ } { { k_A } } } \left[ { { { \left( { { \frac { { C_ { { \rm { in } } } } } { { C_ { { \rm { out } } } } } } } \right) } ^ { \frac { 1 } { N } } } - 1 } \right] \; \; \;\; OR \; \; \; \; { \frac { NQ } { { k_V } \;z } } \left[ { { { \left( { { \frac { { C_ { { \rm { in } } } } } { { C_ { { \rm { out } } } } } } } \right) } ^ { \frac { 1 } { N } } } - 1 } \right] \tag { 23 } \end{align*} \end{document}

Assuming a design flow rate (Q) of 1 MGD (3785.4 m³ day⁻¹), C_out = 0.1 × C_in (i.e., 90% removal), and k_A =  \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${k_{{ \rm{NO}}_3^ - }}$$ \end{document}  = 0.20 m day⁻¹, the required wetland area was estimated to be 57,400 m² (5.74 ha). Assuming per capita wastewater production of 100 gallons per day, 1 MGD would be the wastewater produced by 10,000 people, and the required wetland area would be 5.74 m² per person served. While the wetland depth was not needed for this calculation, we assumed a design depth of 30 cm for subsequent calculations.

After considering nitrate removal, we evaluated additional water treatment benefits provided through removal of TrOC and microbial contaminants in the UPOW wetland. This was conducted by first calculating \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^i$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{microbial}}}^i$$ \end{document} using Equations (1–3), and the figures provided herein to determine values of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{photo}}}^i$$ \end{document} , \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^i$$ \end{document} , and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{exo}}}^i$$ \end{document} . For these calculations, we assumed a [DOC] of 7.5 mg-C L⁻¹ and pH of 8, both of which are in the range observed in wastewater effluent polishing wetlands (e.g., the Discovery Bay UPOW wetland) (Jasper and Sedlak, 2013; Nguyen et al., 2015; Silverman et al., 2015). Photodegradation rates were estimated for the month of March, to give a median estimate of the extent of TrOC and microbial contaminant removal; alternatively, for the northern hemisphere, one could model photodegradation in December or June to estimate minimum or maximum \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^i$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{microbial}}}^i$$ \end{document} , respectively.

To illustrate the calculation of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^i$$ \end{document} [Eq. (1)], we estimated the degradation rate of propranolol. First, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{photo}}}^{{ \rm{propranolol}}}$$ \end{document} in March in 30-cm-deep water with a pH of 8 was read off of Fig. 4b. This was done by locating the intersection between the line for 30°N (close to Orlando's latitude of 28.5383°N) and the x-axis value of [DOC] = 7.5 mg-C L⁻¹; the corresponding y-axis value of 0.7 day⁻¹ represents \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{photo}}}^{{ \rm{propranolol}}}$$ \end{document} ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^i$$ \end{document} for 20 and 40 cm depths are provided in separate figures in the Supplementary Data). Second, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{bio}}}^i$$ \end{document} was calculated according to Equation (2) using the average air temperature in March in Orlando as an input and was found to be 0.26 day⁻¹. The resulting \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^{{ \rm{propranolol}}}$$ \end{document} (0.96 day⁻¹) was then used as an input to the volumetric P-K-C* model [Eq. (22)]; additional inputs were the surface area calculated above (A = 57,400 m²), the depth (z) equal to 0.3 m, and Q, N, and C* as described above. The resulting C_in/C_out was estimated to be 0.048, which corresponds to a 95.2% reduction in the concentration of propranolol in the proposed UPOW wetland.

To estimate E. coli removal, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{microbial}}}^{E. \;coli}$$ \end{document} was calculated by first reading \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^{E. \;coli}$$ \end{document} off of Fig. 7b; this was done in the same manner as for \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{photo}}}^{{ \rm{propranolol}}}$$ \end{document} . \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{endo}}}^{E. \;coli}$$ \end{document} was estimated to be 1.4 day⁻¹. E. coli is susceptible to dark inactivation, but not to exogenous photoinactivation. Therefore \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{dark}}}^{E.coli}$$ \end{document} was set equal to 0.86 day⁻¹ and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{exo}}}^{E.coli}$$ \end{document} was set equal to zero. These terms were input to the equation for \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{microbial}}}^{E. \;coli}$$ \end{document} [Eq. (3)], which was estimated to be 2.26 day⁻¹. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{microbial}}}^{E. \;coli}$$ \end{document} was used as an input to the volumetric P-K-C* model [Eq. (22)] to estimate C_in/C_out as described above for propranolol, but with C* assumed to be equal to 100 CFU/100 mL. Assuming that the E. coli concentration at the inlet of the wetland is 10⁴ CFU/100 mL (Nguyen et al., 2015), the resulting C_in/C_out was calculated to be 0.015, which corresponds to an estimated 98.5% reduction in the concentration of E. coli in the proposed UPOW wetland.

In the above example, we prioritized nitrate removal for UPOW wetland design, and calculated the resulting extent of propranolol and E. coli reduction (see Table 3 for estimated decay rates of all contaminants). If, however, the treatment needs of the wetland require prioritization of TrOC or microbial removal, the design process could be shifted to first calculate \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{TrOC}}}^i$$ \end{document} or \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$k_{{ \rm{microbial}}}^i$$ \end{document} , then use the volumetric form of Equation (22) to calculate the required wetland area. If greater TrOC or microbial removal is desired, it would require a UPOW wetland with a greater surface area or depth to allow for a longer retention time.

As illustrated above, the simplified modeling approach presented in this study can be used to estimate either the wetland surface area needed to achieve a desired level of contaminant removal or the extent of removal for a given wetland area and hydraulic regime. These estimates should be used as guidance values, because more field data from additional installations are needed to assess variability among UPOW systems. The models presented herein were not formulated to be conservative, but rather attempt to model processes as accurately as possible. Although this approach resulted in relatively good agreement between measured and predicted decay rates, there were some apparent biases in the predictions. For example, carbamazepine decay rates were overpredicted in both the Discovery Bay and Prado UPOW wetlands due to an overestimation of photolysis rates (k_obs/k_predicted ∼0.1 at Discovery Bay; Jasper et al., 2014a); atenolol and propranolol decay rates were either over- or underpredicted in the Discovery Bay and Prado UPOW wetlands depending on the month, but generally were predicted within 30% of measured removal rates (Jasper et al., 2014a). There was ∼1:1 agreement between measured and predicted sulfamethoxazole decay rates in sunlight-exposed mesocosms containing Discovery Bay UPOW wetland water (Jasper et al., 2014a). At the Discovery Bay UPOW wetland, the models generally underpredicted E. coli and F+ coliphage decay rates and had average k_obs/k_predicted of 3.1 (E. coli; Silverman and Nelson, 2016) and 1.2 (F+ coliphage; Silverman et al., 2015). Appropriate safety factors should be employed by design engineers using best judgment, accounting for how much variability and variance is acceptable for the specific context.