Integration of Photodegradation Process of Organic Micropollutants to a Vertically One-Dimensional Lake Model

Abstract

Photochemical reactions in the water environments are essential for understanding the fate of organic pollutants, which exist widely in aquatic environments causing potential risks. Therefore, this study aimed to integrate a module of the photodegradation process into a vertically one-dimensional model of the lake to quantify the influence of phytoplankton on the photodegradation process for the first time. After adjusting the code of the APEX (Aqueous Photochemistry of Environmentally occurring Xenobiotics), the suite of photochemical reactions was integrated into the pollutant module of MyLake (Multi-year Lake simulation), as MyLake-Photo. This integrated model was then applied to calculate the concentration of four organic micropollutants under the ranges of solar radiation conditions (0–390 W/m²), phytoplankton biomass (0.01–20 mg/m³ of chlorophyll), and water temperature (1–25 °C). These scenario analyses revealed that phytoplankton biomass and pollutant photodegradation are negatively correlated owing to the light absorption by chlorophyll. Thermal stratification also significantly influenced the vertical distribution of organic micropollutants. Then, the model was applied for calculating a temporal distribution of ibuprofen concentration in Lake Giles (PA, USA) with a simple but realistic assumption. The concentration of organic micropollutants varies with seasons, which was mainly affected by the changes in irradiance and water temperature. In this manner, the integrated model is capable of estimating the temporal and vertical shifts of the concentration of organic micropollutants in lakes, allowing us to investigate the fate of organic micropollutants in lakes. The integrated model also allows us to investigate the effect of phytoplankton and CDOM on the photodegradation of organic micropollutants, which should be combined with field surveys and experimental studies for further improvement.

1. Introduction

Photochemical reactions are essential in aquatic environments, specifically in photolysis, photosynthesis, chemical speciation of iron, formation of reactive oxygen species, and some others [1,2,3]. For instance, the sunlight-induced photochemical reduction of ferric iron is an important source of dissolved ferrous iron in aqueous and sedimentary environments which provides dissolved ferrous iron for the primary productivity of marine systems [4]. Moreover, photochemical processes are critically important in driving biogeochemical element cycling and in the breakdown of contaminants in surface waters [5]. Among the contaminants, organic micropollutants (OMPs) are present widely in aquatic ecosystems and cause a threat to the environment and human health [6]. For instance, pesticides, pharmaceuticals and personal care products, ultraviolet (UV) absorbers, ionic liquids, antioxidants, and phytotoxins have been detected in a number of water bodies worldwide [7,8,9,10]. Organic products of those photochemical reactions of OMPs and natural organic matter also play a major role in redox chemistry and the biogeochemical cycling of carbon in the aquatic environment [11,12]. For treatment technologies of OMPs, adsorption, photocatalysis, and microwave catalysis have been widely used in wastewater and new technologies are constantly being developed [13,14,15]. For developing, designing, and implementing proper treatment processes, it is required to understand the photochemical processes and self-purification capacity of OMPs in natural environments.

To properly understand and manage micropollutants in aquatic environments, it is necessary to understand their origins, fate, and transport [16]. For this purpose, sampling campaigns and laboratory analysis are essential and convincing [17,18,19]. Such investigations have found that photodegradation is an important degradation mechanism for a number of OMPs in surface water [20,21]. For instance, diclofenac entering Lake Greifensee (Switzerland) has been reported to be eliminated by 90% owing to photochemical degradation [22]. Another study has shown that two types of fluorescent whitening agents flowing into Lake Biwa (Japan) were photodegraded by 95% and 55% in the lake [23].

However, those methods are costly, time-consuming, and thus difficult to repeat regularly [24]. Moreover, it is generally not feasible to extrapolate results obtained in a lab photochemical experiment, for instance, using a centimeters-deep-water column of photoreactors, to a depth of several meters of natural water bodies [25]. To overcome such cost and scale issues, numerical simulation is one of the useful approaches [24]. Some hydrodynamic models have been developed for being coupled with chemical and ecological processes [26,27,28]. Photodegradation rate constants of OMPs in environmental water can be predicted on the basis of simulated irradiance, type of OMPs, and parameters of photosensitizers and photochemically produced reactive intermediates (PPRIs) [29]. For example, the APEX (Aqueous Photochemistry of Environmentally occurring Xenobiotics) model has been developed to predict photochemical reactions and photo-transformation of OMPs [30]. Such models allow us to predict light-induced degradation of some pollutants based on photochemical transformation kinetics, with photo-reactivity parameters and assuming water depth and concentration of nitrate, nitrite and carbonate [31,32,33,34].

Nevertheless, to date, there is no available model simulating hydrodynamics and the photodegradation kinetics of OMPs simultaneously. The former process includes diffusion and convective mixing of OMPs while the latter accounts for their degradation. The interactions between the two remain unexplored and elucidated [35]. The convection-dispersion equation is the basic equation used in the mechanistic model for the dissolved substance in water [28]. The open-source models and environmental dataset can provide a feasible pathway for model intergradation. For the degradation of OMPs, it is generally sufficient to use first-order kinetics to describe their decay processes [36]. Thus, the concentration of natural components and pollutants in natural water bodies changes temporally with hydrodynamic, thermodynamic, and biochemical reactions and cycles. In those processes, solar irradiance and water temperature are critical factors, which vary over seasons [6]. Incident light, including ultraviolet radiation (UV) and visible light, generally attenuates with increasing water depth due to absorption by components such as chromophoric dissolved organic matter (CDOM), phytoplankton, particles, and water itself [37]. Moreover, the phytoplankton biomass is an important factor in the attenuation of UV and visible light, considering the potential inhibition of photodegradation processes. Nevertheless, such role of phytoplankton has not been integrated into currently available photodegradation models. Water matrix, specifically CDOM, nitrate, nitrite, and dissolved oxygen, also directly affects the photochemical reaction [6].

In the epilimnion layer, where the photochemical reaction is active, light irradiance is determined by incident sunlight and influenced by water, phytoplankton, and inorganic particles [37,38]. Regarding the influence of aquatic plants on photochemistry, a study has demonstrated that macrophyte removal enhanced the photolysis of hydrochlorothiazide and diclofenac in the river [39]. The shading effects of aquatic plants on light availability and photochemical degradation of pollutants have been qualitatively addressed in subsequent studies. The seasonal variation of pollutant photodegradation and concentration has been observed and illustrated together with the influence of aquatic plants [40,41]. However, no existing studies have quantitatively explored the effects of phytoplankton on the degradation and concentration of organic micropollutants, although phytoplankton is the dominant primary producer in open water bodies. Therefore, it is important to develop a model to simulate the dynamics of OMPs in natural water bodies, integrating the effects of phytoplankton and other seasonal variables. We hypothesized that the presence of phytoplankton poses a major inhibitory effect on the photodegradation of OMPs, and thus we intended to describe it quantitatively by using a model.

Considering those limitations in the model simulation, we aimed to develop a model integrating photochemical kinetics and water quality dynamics. Then the model was applied to quantify the potential influence of phytoplankton on the photodegradation of OMPs. To be specific, we integrated MyLake (Multi-year Lake simulation, the one-dimensional water quality model, [42]) and APEX (a kinetics model for photodegradation in natural water [30]) as MyLake-Photo. Then, the integrated model was applied to calculate photodegradation rates and concentration of OMPs under various environmental conditions.

2. Materials and Methods

2.1. Integration of MyLake and APEX

MyLake model and APEX were integrated as MyLake-Photo, one of MyLake model series as the one-dimensional water quality model. As shown in Figure 1, the modified MyLake version 2 [43] and APEX version 1.0 [30] were integrated to calculate the concentration of the OMPs on the MATLAB platform. Full details of the original MyLake may be found in the journal and its user manual [42]. The modified APEX includes the automatic input and the new adsorption spectrum of solar irradiance. For this integration, we introduced new variables, which are pollutant concentration and photodegradation rate constant of an OMP.

2.1.1. The Modified APEX Module

APEX 1.0 is an open-source and freely available mathematics software, which can be executed on Octave [30]. It computes the photo-transformation kinetics of compounds that occur in sunlit surface waters. To implement the model integration, we modified APEX to be executed on MATLAB. An automatic input module was also added to APEX. This module enables us to (1) automatically select the photo-reactivity parameters of OMP once a focused OMP is given, and (2) automatically change the solar zenith angle according to latitude and day of the year as the model runs over time.

In addition, to assess the influence of the phytoplankton on photochemical processes, the modified APEX model includes a module of the light attenuation formula for the wavelength of 290–800 nm, describing the relationship between light attenuation and components such as CDOM and phytoplankton. The absorption coefficient for a specific wavelength at a certain chlorophyll concentration was determined on the assumption that the increment of absorption spectra is proportional to the concentration of chlorophyll. Equation (1) expresses that the total absorption spectrum is the sum of CDOM, chlorophyll, nitrite, and nitrate spectra. Equation (2) is the empirical equation estimating the absorption of CDOM based on the concentration of dissolved organic carbon (DOC) in the water, following the relevant equation of the APEX 1.0 model [30,44,45,46]. Equation (3) describes the relations between absorption and concentrations of each substance except for CDOM. In addition, we assumed that the total absorption spectrum of chlorophylls was the same as the absorption spectrum of chlorophyll-a because chlorophyll-a is contained by all the phytoplankton species [47] and the absorption spectrum of chlorophyll-a represents the total absorption spectrum of chlorophyll in lakes [48]. Specifically, the absorption spectrum of chlorophyll-a in diethyl ether [49] (Figures S1 and S2) was added to the module.

$$A_{tot}\left(\lambda \right)=A_{CDOM}\left(\lambda \right)+A_{Chl}\left(\lambda \right)+A_{N{O}_2^{-}}\left(\lambda \right)+A_{N{O}_3^{-}}\left(\lambda \right)$$

(1)

$$A_{CDOM}\left(\lambda \right)=a_0\times DOC\times e^{-S\ast \left(\lambda -{\lambda }_0\right)}\times d$$

(2)

$$A_X\left(\lambda \right)=100\times {\epsilon }_x\left(\lambda \right)·d·\left[X\right]$$

(3)

where the $A_{CDOM}\left(\lambda \right)$ is the absorbance of the surface water layer by CDOM, $a_0$ is the absorption coefficient at a reference wavelength ${\lambda }_0$, the value of $a_0$ and ${\lambda }_0$ could be determined according to the condition of the water. The reference wavelength is 370 nm following the literature on CDOM adsorption [50,51,52]. S is the spectral slope of adsorption, DOC is the concentration of DOC, unit (mg C/m³), λ is the wavelength of the light, unit (nm), d is the path length of light, and unit (m). $A_{tot}\left(\lambda \right)$ is total absorbance of the surface water layer which is the summation of absorbance based on CDOM ($A_{CDOM}\left(\lambda \right)$), chlorophyll ($A_{Chl}\left(\lambda \right)$), nitrite ($A_{N{O}_2^{-}}\left(\lambda \right)$), nitrate ($A_{N{O}_3^{-}}\left(\lambda \right)$). $A_X\left(\lambda \right)$ is the absorbance of substance X (i.e., chlorophyll, nitrite, and nitrate), ${\epsilon }_x\left(\lambda \right)$ is the molar absorption coefficient of X (M⁻¹ cm⁻¹), and $\left[X\right]$ is the molar concentration of X (M).

2.1.2. The Integrated Model: MyLake-Photo

To investigate the fate of OMPs including photodegradation reaction, the MyLake-Photo model was developed based on MyLake version 2 [34] by adding the photodegradation module and the advection-diffusion equation of the OMPs (Equation (4)):

$$A\frac{\partial C}{\partial t}=\frac{\partial }{\partial z}\left[DA\frac{\partial C}{\partial z}\right]-A\frac{\partial \left(wC\right)}{\partial z}-k_p+k_b AC$$

(4)

where C is the target concentration of dissolved OMPs (mg/m³), A is the area of the layer (m²), t is time (day), z is depth (meter), D is the vertical diffusion coefficient (m² day⁻¹) and $w$ is downward vertical velocity. In addition, the MyLake version 2.0 used the convective mixing module to measure the exchange of water between the layers, due to the unstable density profile of the water. K_p (day⁻¹) and k_b (day⁻¹) are photodegradation and biodegradation rate constants, respectively. Biodegradation rate constant is a function of water temperature following the Arrhenius equation: $k_b=A\exp \left(-\frac{E_a}{RT}\right)$, where A is the Arrhenius constant, $E_a$ is the activation energy, R is the universal gas constant (8.314 kJ/mol K) and T is the temperature (K).

The MyLake model and the modified APEX model have consistent temporal and spatial units for the variables, which are in meter and day. The modified APEX module receives the physical conditions relevant to photochemistry from the MyLake module. Then, the photodegradation constant (k_p) of the organic micropollutants is calculated in the modified APEX module, as the function of depth(z), and time(t), by the following equation:

$$k_p\left(z,t\right)=f\left[P_{Chl}\left(z,t\right), DOC\left(z,t\right),I\left(z,t\right),{\theta }_s\left(t\right)\right]$$

(5)

in which $P_{Chl}\left(z,t\right)$ is the total concentration of chlorophylls, representing phytoplankton biomass (mg/m³), $DOC\left(z,t\right)$ is the concentration of DOC (mg/m³), $I\left(z,t\right)$ is irradiance (W/m²). They are the function of depth and time and are calculated by the MyLake model. ${\theta }_s\left(t\right)$ is the solar zenith angle that changes with time. Then, they are used for updating $k_p\left(z, t\right)$ in the modified APEX module, and the target concentration of OMPs is calculated in MyLake by the finite differential method. After updating the distribution of concentration based on Equation (4), convective mixing is calculated based on temperature profile and wind force

2.1.3. Validation of the Model Integration

To ensure the proper model integration, we conducted two performance tests: verifications of (1) the modification of the APEX module and (2) the integration of two models. First, the results from the modified APEX module and APEX 1.0 [30] were compared with same conditions focusing on photochemical parameters and solar zenith angle on the assumption that chlorophyll concentration is zero. The results confirmed that the modified APEX and APEX 1.0 are identical (refer to Figure S3). Second, the integrated model was validated by comparing the output from MyLake 2.0 [43] and MyLake-Photo. The simulation results of the substance from MyLake 2.0 and MyLake-Photo were the same under the long-year simulation (refer to Figure S4 [43]). Moreover, the total mass of the OMPs was confirmed to be conserved when degradation rate is assumed to be zero.

2.2. Model Applications

To investigate the photodegradation process and concentration of the OMPs in the lake, the integrated model was applied to quantify the potential influence of phytoplankton on the photodegradation of OMPs by taking Lake Giles (PA, USA) as an example. For this lake, a long-term dataset on water quality and light attenuation from 1997 is available [53,54,55]. This simulation was divided into (1) the model sensitivity analysis assuming no inflow condition and (2) the two-year calculation of a chosen OMP in this lake. The integrated model was validated by the data that we obtained from the original MyLake model and APEX model under the same condition as MyLake-Photo.

2.2.1. Study Site

Lake Giles is located in northeastern Pennsylvania (41°22′ N, 75°5′ W). The catchment area is 1.83 km², the lake surface area is 0.48 km², the maximum depth is 24.1 m, the volume is 4.9 × 10⁶ m³, and the estimated hydraulic retention time is 5.2 years [56]. Lake Giles is a small lake in North America with significant seasonal variability in water temperature, phytoplankton biomass, and solar irradiance, which are essential variables for our study [53]. It represents the small oligotrophic lakes that are widely distributed in the temperate regions of North America and northeastern Europe [57]. The shortwave radiation (280–3000 nm) showed a clear seasonal variation, which varied from 0.1 W/m² to 390 W/m² during the past twenty years. The average 1% PAR (photosynthetically active radiation) depth is 14.4 m, and the average 1% UV (320 nm) depth is 2.0 m from 2015 to 2016 in Giles [55]. The surface water temperature was as high as 25 °C in summer and close to 0 °C in winter (with ice). The deep-water temperature was as high as 9 °C in summer and close to 4 °C in winter. The total chlorophyll concentration varied from 0.01 to 20 mg/m³ with an average of 2 mg/m³. The average DOC concentration increased from 0.96 mg/L in 1993 to 2.48 mg/L in 2019 [53,54]. In addition, it has been successfully modeled based on MyLake version 2 [58].

2.2.2. Sensitivity of Vertical OMPs Distribution to Water Conditions

The analysis was designed to elucidate the sensitivity of the photodegradation rate and concentration of the OMPs to the physical conditions of solar radiation, phytoplankton biomass, and water temperature. The photodegradation rate and concentration of OMPs were calculated using the Mylake-Photo under the condition defined by four variables, which were the type of OMPs, solar irradiance, water temperature regime, and chlorophyll (refer to

Table 1. The value of investigated variables in MyLake-Photo. Surface refers to depth 0–1 m; Bottom refers to depth 24–25 m.

Variable	Moderate Condition	Range
Solar irradiance	284 W/m2	0.100–390 W/m2
Water temperature	Surface 23 °C	Surface 0.0–25 °C
	Bottom 5.0 °C	Bottom 4.0–9.0 °C
Chlorophyll	2.0 mg/m3	0.010–20 mg/m3

for their ranges). When the sensitivity to one certain variable was analyzed, the other variables were controlled as a moderate condition. The targeted OMP was ibuprofen (IBP) when investigating the sensitivity of the vertical distribution of OMP (i.e., ibuprofen) to each of the four variables. In addition, the sensitivity analysis of chlorophyll concentration was also applied to the other three OMPs: carbamazepine (CBZ), benzophenone-3 (BP), and 1-ethyl-3-methylimidazolium hydrogen sulfate (EMIM). Among them, IBP and CBZ are common pharmaceutical and personal care products, while BP and EMIM are UV filters and ionic liquids, respectively. Refer to Table S1 [30] and Figure S5 for their details.

The sensitivity analysis covered the wide ranges of environmental conditions, which were 0.1–390 W/m² for irradiance (the maximum refers to the maximum daily solar irradiance in summer at 41°38′ N), 0–25 °C for water temperature regime, and 0.01–20 mg/m³ for chlorophyll concentration. As for water temperature regime, we adopted five different vertical distribution: (1) constant at 10 °C, (2) linear shift, (3) moderate shift, (4) typical summer condition, and (5) typical winter condition (Refer Figure S6 for their detailed distribution). Other relevant variables were set as constants: DOC at 1000 mg/m³, wind force at 0.01 N/m² and biodegradation rate at zero. The photo-reactivity parameters of OMPs (i.e., direct photolysis quantum yield and second-order reaction rate constant) were set based on the manual of the APEX 1.0 [30] (refer to Table S1 [30] for the details).

2.2.3. Temporal Distribution of IBP in Lake Giles

We demonstrated how the integrated model is applied to describe the photodegradation behavior and concentration distribution of typical OMPs such as IBP in Lake Giles (Pennsylvania). IBP is the third most popular and marketable over-the-counter drug in the world and is widely available in water bodies [59,60]. In this model application, the changes in water temperature, DOC concentration, total chlorophyll concentration, and IBP concentration at Lake Giles over the period from 17 May 2016 to 23 May 2018 were simulated based on the historical conditions (Table S2, [21,54,58,60,61]).

The initial concentration of IBP in the lake was set as 0.4 mg/m³ at each depth, which was one-third the inflow condition of the river (1.2 mg/m³). We assumed the outflow and inflow volumes were equal and the total volume of the lake was constant. The average daily inflow volume during 2015–2020 was assumed to be 12,500 m³ day⁻¹ based on the retention time, total volume, and inflow scale factor of Lake Giles [47]. The IBP concentration in the river was determined by one survey for selected pharmaceuticals in an agricultural area on the coastline of Lake Erie, USA [61]. For IBP, photodegradation and biodegradation were calculated, as well as changes in concentration under the influence of pollutants from the inflow river. This calculation employed general parameter values, meaning that the biodegradation rate of IBP is 0.012 day⁻¹ at 19 °C [21], the Arrhenius constant is 57.2 kJ/mol, and the activation energy is 168 kJ/mol (refer to Figure S7 [21,62]). In addition, no diffusion or exchange at the water-air and water-sediment interface was assumed in this model application.

3. Results

3.1. Sensitivity of Vertical OMPs Distribution to Physical Conditions

The results under the different solar irradiance showed that the photodegradation rate constant was dependent on irradiance at the water surface (Figure 2a). Thus, the photo degradation rate and concentration of IBP shifted with irradiance (Figure 2b). The rate constants of photodegradation were 0.23, 0.17, 0.12, 0.06, and 0.00 day⁻¹ in the epilimnion layer under 100%, 75%, 50%, 25%, and 0% of the daily maximum (i.e., 390 w/m²), respectively (Figure 2a). Correspondingly, the concentration of IBP was changed to 0.23, 0.32, 0.47, 0.68, 1.00 mg/m³ in the epilimnion layer after 10 days from the initial condition of 1.00 mg/m³ (the vertically uniform distribution) (Figure 2b). The reduction in IBP concentration was confirmed above the layer where the irradiance approaches zero (i.e., approximately 7 m deep).

The presence of phytoplankton reduced the photodegradation rate constant of IBP (Figure 3a,b). Compared to the case of the least chlorophyll concentration (0.01 mg/m³), the rate constant of IBP in the surface layer decreased by 2.0%, 8.7%, and 15.4% under the chlorophyll concentration of 2, 10, and 20 mg/m³, respectively. Consequently, the concentration of IBP after 10 days was higher by 2.1%, 9.6%, and 17.3% in those cases, compared to the case with the least concentration (Figure 3c,d). The effect of phytoplankton biomass on IBP concentration was negligible in 5 m and deeper layers.

Regarding the vertical temperature distribution, the APEX model assumes no direct influence of water temperature on the photodegradation rate constant. However, the vertical distribution of the concentration of IBP after 10 days shifted depending on the temperature regime as the result of convective and wind-forced mixing processes. The concentrations of IBP showed vertical uniformity in the epilimnion layer, where the water temperature and density were uniform (Figure 4b). For IBP concentration in the epilimnion layer (i.e., 0–1 m deep), the fastest reduction in concentration was observed under linear and moderate conditions.

The photodegradation rate constants under the moderate condition differed among the four OMPs (Figure 5a). The photodegradation rate constant of EMIM was 0.56 day^−1, which was much higher than that of the other three OMPs (Figure 5a). Correspondingly, the order of concentrations in any layers was EMIM, BP, IBP, and CBZ, which were 0.04, 0.28, 0.38, and 0.33 mg/m³, respectively (Figure 5b).

The effects of phytoplankton biomass on the photodegradation rate constant were similar among the four pollutants in the chlorophyll concentration, ranging from 0 to 20 mg/m³ (Figure 5c). In the case of chlorophyll concentration at 20 mg/m³, the photodegradation rate constants decreased by 15.4%, 14.8%, 15.5%, and 14.4% for IBP, CBZ, BP, and EMIM, respectively. In those decreases, the part of direct photodegradation rate constants decreased by 17.3%, 10.1%, 15.5%, and 14.1% for IBP, CBZ, BP, and EMIM (Figure 5d).

3.2. Temporal Change of IBP Concentration in Lake Giles

In the simulation of IBP concentration in Lake Giles, its photodegradation rate constants showed a cyclic variation with seasonal changes, which was a similar pattern to solar irradiance (Figure 6). The temperature of the surface lake varies drastically with the seasonal cycle, ranging from 0 °C in winter to 27 °C in summer. The highest degradation rate constant was 0.138 day⁻¹ (in summer), while the lowest degradation rate was 0.051 day⁻¹ (in winter). Consequently, the IBP concentration at the epilimnion layer showed a distinct seasonality. In the depth of 0–1 m, the IBP concentration showed dynamic equilibrium in summer, fluctuating around 0.19 mg/m^3. The concentration of IBP fluctuated sharply in winter, showing a significant overall increase from summer, with a maximum of 0.57 mg/m³ (Figure 6c,d).

The results of the vertical distribution of IBP in the lake varied throughout the year. The simulated IBP concentration showed the reduction toward the lakebed as an overall trend with a vertically constant part in the deep zone in all seasons (Figure 7). In summer, IBP concentration changed rapidly at the 5–8 m layers from 0.20 mg/m³ to approximately 0.03 mg/m³. In winter, IBP concentrations decreased rapidly after the extreme maximum of 0.52 mg/m³ in the epilimnion layer (0 to 1 m), decreasing to about 0.1 mg/m³ after 9 m. The lowest concentration of IBP in surface water was found to be 0.17 mg/m³ in autumn, while the highest concentration occurred in winter. The regions for the drastic shift in the IBP concentrations overlapped with the thermocline, where water temperature vertically shifted significantly (i.e., the shaded gray region). There was the epilimnion layer where the water was well mixed, and the concentration of IBP was vertically uniform in spring, summer, and autumn. In winter, IBP concentration sharply increased from December 2016 to January 2017 in the epilimnion layer (0 to 1 m) of the lake.

Regarding the fate and transport of IBP in the lake, the inflow is the major source, and the degradation is the decay pathway. In summer, the inflow volume was stable while in winter the inflow volume varied sharply (Figure 8). After a rapid decline (after the first 100 days), the total pollutant mass of the lake was basically maintained at a dynamic equilibrium of about 0.639 kg, with an average daily inflow of 15.0 g/day. The total mass of IBP in the lake ranged from a minimum of 0.479 kg to a maximum of 0.783 kg. The average value of biodegradation was approximately 7.65 g/day. There was a distinct seasonal fluctuation in the daily photodegradation mass, which reached its peak of 12.3 g/day in summer and a minimum of 0.12 g/day in winter, with a mean of 4.23 g/day (Figure 8d). The photochemical degradation accounted for the mass loss of 1.72 kg of IBP in the whole year from January 2017 to December 2017, while the biodegradation accounted for the loss of 2.68 kg in this calculation. In addition, a certain portion of IBP was removed to the outflow (averaged at 12,500 m³/day), and the outflow mass was estimated to be 3.00 g/day on average on the assumption that the outflow IBP concentration was as same as the epilimnion layer (depth 0–1 m) of the lake.

4. Discussion

4.1. Sensitivity of Vertical OMPs Distribution to Physical Conditions

With the two performance tests, we ensured that the model was correctly integrated. The integrated model, MyLake-Photo, clearly showed that the irradiance determines the photodegradation rate. The model output confirmed that the photochemical reaction rate changes proportionally to the irradiance, which agrees with the previous studies. For instance, Diepens and Gijsman have found that when the light intensity is doubled, the photodegradation of bisphenol A polycarbonate is doubled as well [63]. Another study has shown that the rate of photodegradation reactions of riboflavin in phosphate buffer depends on light intensity as well as the wavelengths of irradiation [64]. The MyLake-Photo estimates the photochemical transformation kinetics of OMPs in lakes as a function of photo reactivity parameters (i.e., direct photolysis quantum yield and second-order reaction rate constants with transient species), water components (i.e., DOC, nitrate, nitrite, and phytoplankton), and water depth.

The physical processes of OMPs and other components are related to water temperature and density. The vertical distribution of water temperature determines the difference in density and diffusion coefficient and dramatically affects the mixing process at the epilimnion layer. Thus, the distribution of dissolved constituents is influenced by the thermal stratification of the lake [65,66,67]. The convective mixing process is determined by the water density distribution and is driven by the wind stress on the lake. The concentration of pollutants was vertically uniform in a well-mixed water layer, despite the different rates of photodegradation at different depths (Figure 7). In addition, the photochemical degradation at the epilimnion layer showed different effects on the overall distribution

Among the four pollutants, EMIM showed the highest photodegradation rate constant. This is because its light adsorption capacity and quantum yield for direct photolysis result in the highest direct photodegradation rate among the tested OMPs. In addition, its photodegradation reaction rate with singlet oxygen in indirect photolysis is also the highest, although there was little difference among the four OMPs in terms of the reaction rates to the other reactive intermediates [30,33,68,69,70].

Our results also showed that the presence of phytoplankton inhibits the rate of photodegradation of the four OMPs. Previous studies have indicated that the absorption and scattering of chlorophyll and CDOM contribute to the attenuation of UV and VIS light in lakes [71,72]. Chlorophylls do not participate directly in the photochemical reaction of pollutants, although they compete for light absorption with pollutants, CDOM, nitrate, and nitrite. The wavelengths of light absorbed by chlorophyll partially coincided with the wavelengths involved in the photodegradation of OMPs, mainly in the 350 nm to 450 nm, which is the peak of chlorophyll light absorption. Thus, the increasing chlorophyll concentration leads to a decrease in the light quantum available for photochemical reactions. In subtropical and temperate lakes, the identical pattern that a decrease in UV penetration due to rising phytoplankton biomass in summer has been reported [73,74]. Therefore, such suppressive effect of the presence of phytoplankton on the photodegradation of pollutants cannot be ignored for the fate of OMPs in lakes.

4.2. IBP Concentration in Lake Giles

The simulation showed that the photodegradation rates and concentrations of OMPs in Lake Giles vary over time and space, showing distinct seasonality. It suggests that the photodegradation rate and concentration of OMPs in natural lakes are significantly influenced by solar irradiance, which agrees with a review elucidating the importance of seasonal changes on the photodegradation of pollutants [63]. A survey of various OMPs in a lake in Sweden has also indicated that the concentration of pollutants in the surface lake water is relatively high in spring and low in summer [75,76]. As discussed in the previous section, water temperature significantly affected the vertical distribution of OMP concentrations on top of the property of OMPs also in this simulation. Water temperature is a critical factor influencing diffusion and convective mixing, two physical processes that directly determine the vertical distribution of pollutants. The model results showed that pollutant concentration varies rapidly with depth and water temperature in the layers of the thermocline, and its depth and range shift with the season, as reported in other lakes [77,78].

The results also indicated that the average difference between the inflow and outflow of IBP (net inflow) was 12.00 g/day. Interestingly, the mass loss of IBP by the photodegradation was 4.22 g/day on average, whereas its loss by the biodegradation was 7.65 g/day on average although this biodegradation rate constant in this simulation was not locally confirmed. These two degradation pathways have been confirmed also in previous studies and experiments [21]. Due to the freezing winter period, a large amount of meltwater entered the lake during the winter and spring months, bringing about a large number of OMPs in the lake, which resulted in the increase of the concentration of IBP in the epilimnion layer. Similarly, one research has indicated that the accumulated concentrations during the winter months might explain the high occurrence patterns of OMPs during the spring [76]. In winter and spring, the water quality of lakes tends to be exposed to higher risks caused by the inflow of OMPs than in other seasons [79].

4.3. The Integrated Model: MyLake-Photo

This study developed the MyLake-Photo model as the extension of the MyLake model series, the vertical one-dimensional model, for calculating the photodegradation rate and concentration of OMPs in lakes. For many lakes and reservoirs in the world, data on physical dimensions and inflow are available. Data for model calibration (e.g., DOC concentration and water temperature) can be obtained from regular samples. With such data, MyLake-Photo allows us to calculate the distribution and occurrence of OMPs in lakes (i.e., their vertical distributions over time). Therefore, it is capable of estimating and predicting the concentrations and persistence of OMPs in lakes based on some assumption, which could be scenario analysis. By combining environmental monitoring and experiments, this model is likely to assess the environmental risk of OMPs for human health and ecosystems.

We should also note the major limitations of MyLake-Photo. In this model development, the hydrodynamic modeling was performed assuming the OMPs as dissolved substances, and thus the sedimentation, and suspension/floating processes were neglected. In addition, the concentration near the bottom of the lake might not be accurate, as it was calculated without considering the exchange between sedimentation and water [80]. Moreover, the direct effect of the presence of phytoplankton on photochemical reactions was considered worth to be further investigation, although the actual interaction between phytoplankton and OMPs is complicated. For instance, one study showed that algae-promoted photolysis was the primary process for removing sulfamethoxazole [81]. In addition, CDOM is critical for the kinetics of photodegradation of OMPs. The composition of CDOM is expected to be further added to the integrated model. Those improvements will provide more accurate estimations for the fate of OMPs than our results.

Nevertheless, the integrated model provides a solid basis for investigating the fate of OMPs in lakes, explicitly considering photodegradation. Our results revealed the importance of the photodegradation of pollutants in lakes in a quantitative manner for the first time. We succeeded in quantitatively describing the role of phytoplankton in the photodegradation process. Although the interaction between photodegradation and photosynthesis is significant for aquatic ecosystems and still remains partly unknown, the integrated model could be employed for further investigation of the fate and mechanism of OMPs in lakes.

5. Conclusions

In this study, the integrated model was developed as MyLake-Photo to calculate the photodegradation rate and the concentration of OMPs (i.e., its vertical and temporal distribution) under various environmental conditions in lakes. The integrated model is a one-dimensional hydrodynamic model combined with a photochemical module for OMPs. The model simulation showed that irradiance is the most important factor affecting photodegradation in the lake. In addition, the presence of phytoplankton in the lake would cause the photodegradation rates of the four OMPs to be inhibited by up to 15.5%. The results also revealed that the concentration of IBP in the epilimnion layer of lakes is low in summer and autumn, and high in winter and spring with several folds of the averaged condition. In such a manner, the developed model, MyLake-Photo, can be employed to predict the photodegradation and distribution of various OMPs once the model is calibrated locally in lakes. In combination with sampling, experiments, and other research methods, this model can be used to analyze the environmental risk of OMPs in lakes. Further research is expected to combine experimental and modeling approaches for investigating the effects of phytoplankton and CDOM on the photodegradation and the fate of OMPs.