Factors affecting the mixed-layer concentrations of singlet oxygen in sunlit lakes

The steady-state concentration of singlet oxygen within a lake ([1O2]SS) is an important parameter that can affect the environmental half-life of pollutants and environmental fate modelling. However, values of [1O2]SS are often determined for the near-surface of a lake, and these values typically do not represent the average over the epilimnia of lakes. In this work, the environmental and physical factors that have the largest impact on [1O2]SS within lake epilimnia were identified. It was found that the depth of the epilimnion has the largest impact on depth-averaged [1O2]SS, with a factor of 8.8 decrease in [1O2]SS when epilimnion depth increases from 2 m to 20 m. The next most important factors are the wavelength-dependent singlet oxygen quantum yield relationship and the latitude of the lake, causing variations in [1O2]SS by factors of 3.2 and 2.5 respectively, over ranges of representative values. For a set of representative parameters, the depth-averaged value of [1O2]SS within an average epilimnion depth of 9.0 m was found to be 5.8 × 10−16 M and the near-surface value of [1O2]SS was found to be 1.9 × 10−14 M. We recommend a range of 6 × 10−17 to 5 × 10−15 M as being more representative of [1O2]SS values within the epilimnia of lakes globally and potentially more useful for estimating pollutant lifetimes than those calculated using [1O2]SS values that correspond to near-surface, summer midday values. This work advances our understanding of [1O2]SS inter-lake variability in the environment, and provides estimates of [1O2]SS for practitioners and researchers to assess environmental half-lives of pollutants due to reaction with singlet oxygen.


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. Statistics Table 1 in the main text). Note that the [ 1 O 2 ] SS is a constant value over the depth of the epilimnion, and below the epilimnion varies as a function of water depth.

Quantum yield relationships
Φ ∆, relationships were modelled by fitting experimental data from Partanen et al. 2 to a bi-exponential model, shown in equation S1) Where Φ ∆, is the modelled singlet oxygen quantum yield at a given wavelength ( , nm), and 1 , 2 , 1 , and 2 are fitting parameters.
The upper and lower bounds of the range of Φ ∆, values used in this work were obtained by adjusting the fitting parameters so that the experimental data was enclosed within the bounds of the modelled curves. The representative Φ ∆, curve was taken as the average of these upper and lower bounds. Figure S3 shows the experimental data overlaid on the modelled range of Φ ∆, values used in this work.

Figure S3
Modelled range of ∆, values used in this work (as presented in the main text Figure  1A) along with points representing experimental ∆, data measured in Partanen et al. 2

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Biexponential fits of SRNOM and PLFA Figure S4. Biexponential fits to experimental wavelength-dependent ∆ data. PLFA is shown in red, and SRNOM is shown in blue.

Reflectance calculations
To calculate the fraction of light transmitted into a water body, Fresnel's equations were used (eq. S2-S4).
Where t is the fraction of light transmitted, rs is the fraction of s-polarized light reflected, rp is the fraction of p-polarized light reflected, is the angle of incident light, and is the angle of transmitted light.
was calculated using Snell's Law: where is the index of refraction of water, and is the index of refraction in air. where lat. is the latitude (° N or S), is the solar declination angle, and ℎ is the hour angle.
The solar declination angle, , varies as a function of time of year, as seen in table S3.  Figure S6.

Diffuse attenuation coefficients and absorbance
The impact of DOC concentration on [ 1 O2]SS Figure S7. The modelled fraction of light attenuated as a function of water column depth for multiple DOC concentrations and wavelengths of light. These values were calcuated using an empirical relationship for K d that takes DOC concentrations as the input variable. 4

Equation for Rf using absorbance spectra
Since absorbance is measured in decadic log units, it is important to use the correct form of the main text equation 2. The equation shown below should be used when decadic absorbance is the input parameter rather than diffuse attenuation coefficients.
where is the decadic absorbance of the water (cm -1 ), and the other parameters are as defined in the main text.

Kd vs. absorbance in calculations of [ 1 O2]SS
To compare the impact of using modeled Kd values and measured absorbance spectra on calculated values of [ 1 O2]SS, measured absorbance spectra for surface waters and organic matter isolates containing a range of DOC concentrations were used ( Figure   S8). Some of the surface waters were also used in the test tube validation (see below).
The rest of the waters used in this analysis were collected from lakes and streams across northern and western Switzerland on July 2 nd and 25 th , 2019. These samples S11 were collected approximately 5 -10 cm below the surface of the lake or stream and stored on ice until they could be refrigerated. Samples were passed sequentially through two filters (glass-fiber filter, pore size 0.7 μm, followed by Omnipore PTFE, pore size 0.2 µm), and stored in HDPE bottles (acid-washed, autoclaved, and wrapped in aluminum foil) at 3 o C.

Modelled absorbance spectra
It is advantageous to be able to model the absorbance spectra of surface waters, both in case it is not feasible to experimentally determine the absorbance spectra, or when a range of surface waters are of interest, not only a specific lake or river. The APEX model, for example, allows for user-input absorbance spectra as well as for approximated spectra based on the concentration of non-purgeable organic carbon (NPOC) and wavelength. This empirical relationship was developed by fitting exponential curves to experimentally obtained absorbance data for 9 lakes in northwest Italy, and is shown in equation S10 below. 5 = • (0.45 ± 0.04) • −(0.015 ± 0.002) (S10) where is the absorbance (cm -1 ), NPOC is the concentration of non-purgeable organic carbon (mgC/L), is the wavelength (nm), and DOC is the concentration of dissolved organic carbon (mgC/L).
As seen in Figure S10, we find that absorbance spectra collected from surface waters from Switzerland and the U.S. (Figure S8) do not well match the absorbance spectra generated using the empirical relationship in equation S10. This may be

Test tube validation using natural water samples and organic matter isolates Natural water sample collection and preservation
Natural water grab samples were obtained from Lake Bradford (Tallahassee,

Sample characterization
Samples were characterized by measuring their absorbance spectra using a Cary 100 Biospec UV-Vis spectrophotometer, and by measuring their DOC concentration using a Shimadzu TOC-L analyzer. Φ ∆ values for each of the samples were taken from Partanen et al. 2 The DOC concentration (natural water samples) or DOM concentration (organic matter isolates) and the Φ ∆ values can be seen in Table S4, and the absorbance spectra of the samples can be seen in Figure S13.  Figure S13. Absorbance spectra for surface water samples and organic matter isolates used in the test-tube validation. Note that Dismal Swamp and Suwannee River water were diluted three-fold for the absorbance measurement. The spectra presented here are corrected for this dilution. � versus time for the natural water samples, organic matter isolates, and reference sensitizers can be seen in Figure S14. and Φ ∆ must be known. The measured sample absorbances shown in Figure S13 were used, as were the Φ ∆ values in Table S4, as described above. Note that these quantum yields are not wavelength dependent but are valid for the irradiance spectrum of the UVA lamp used in this validation. To calculate 0, , the irradiance spectrum of the UVA bulbs used to irradiate the samples ( Figure S15) needed to be converted from the arbitrary units obtained by an uncalibrated radiometer (Ocean Optics Jaz Radiometer) to absolute irradiance (mmol photons cm -2 s -1 nm -1 ) using a chemical actinometer that was irradiated alongside the surface water samples. The following equations were used:

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where is a wavelength-independent scaling factor, and , is the relative irradiance (unitless).
The relative irradiance is calculated according to equation S14: 18 where , is the irradiance spectrum collected from an uncalibrated radiometer.
is calculated according to equation S15: where , is the observed PNA degradation rate constant (s -1 ), Φ is the direct photolysis quantum yield of PNA 18 , are literature values for the molar extinction coefficient of PNA 18 , and is the PNA solution screening factor.
The screening factor, , is defined as: where is the absorbance of the experimental PNA solution (cm -1 ), and ℓ is the pathlength (cm).