An Improved Model for Water Quality Management Accounting for the Spatiotemporal Benthic Flux Rate

Abstract

Although water quality models provide useful interpretations for water quality management, it is critical to accurately input and simulate the flux rate, which varies with space and time. In the Environmental Fluid Dynamics Code model, the flux rate value set does not consider spatiotemporal variability. The water quality of the Saemangeum freshwater lake in Korea is poor despite quality improvement measures. In this study, the model was improved by considering the characteristics of flux rates that change spatiotemporally based on environmental conditions and factors influencing the benthic layer. An exponential relational expression was generated and applied to the model while considering the aerobic, anaerobic, and influencing factors. Results from four important sites in the Saemangeum Reservoir were compared with the RSR, %Difference, and AME results of the previous model for evaluating the reproducibility of the improved model. Calibration and verification of the model were performed in 2013 and 2016, respectively. The improved model yielded values close to the optimal value after computing the evaluation functions of both models. It had excellent reproducibility and simulated water quality by reflecting a reasonable value for the benthic flux rate. The improved model can be extended to evaluate other water bodies in the future.

1. Introduction

Onshore and marine development, urbanization, and industrialization have resulted in population concentration and an increase in impervious surfaces. The manner in which this affects water quality and quantifying the impact on water quality are critical issues to be addressed. Consequently, research on water quality prediction models in both terrestrial and marine systems is a topic of great interest worldwide [1].

Man-made estuarine pollution is a direct or potential source of pollution in coastal regions. Its primary cause is the increase in pollutants caused by watershed development associated with the development of estuarine freshwater lakes [2]. Even if this cause is excluded, the watershed endpoint is extremely vulnerable to pollutant influx because of its geographical location [3]. Furthermore, sea dikes and reclamation reduce seawater flow, thereby promoting stratification, an excessive supply of nutrients, and organic matter accumulation. Eutrophication occurs due to the overgrowth of phytoplankton caused by the breakdown of excessive organic waste, creating conditions for the emergence of anoxic and hypoxic (anaerobic) habitats [4].

In particular, it is expected that a large portion of the sediment inflow from upstream or that generated within the lake will sink inside the Saemangeum Reservoir because of the built sea dike, dredging, and filling of the lake in South Korea. Pollutants settled as particles and accumulated on the riverbed for a period of time before being released back into the water through processes such as decomposition, diffusion, resuspension, and bioturbation. Thus, they are likely to act as internal pollutants, exacerbating water pollution [5].

Therefore, it is difficult to effectively manage water quality within the lake, unless measures are taken to reduce the internal pollution load, even if the inflow of pollutants from point or non-point sources associated with the watershed flowing into the lake is controlled [6]. In Saemangeum Lake, which is under development in Korea, it is expected that much of the sediment that flows from upstream or occurs within the lake will sink within the lake because of the built seawall, dredging, and embankment [7]. Despite the implementation of continuous water quality improvement measures in Saemangeum Lake, its effects are not clearly visible [8].

Formation of the Saemangeum freshwater lake has been linked to issues such as density stratification between seawater and freshwater, sedimentation in the water system, nutrient release from sediments, and algal blooms [9]. In the lower layers, where the oxygen supply from the surface layer is limited due to eutrophication and stratification in the summer, a hypoxic layer is formed under anaerobic conditions, increasing the possibility of increased release of low-quality pollution sources from sediments [10]. Moreover, even if the water quality is improved through the Ministry of Environment’s Saemangeum water quality improvement project when a large amount of sediment has accumulated over several years, the pollution load from these acts as an internal load and has an adverse effect on ensuring proper water quality [11]. Water quality numerical models provide useful interpretations and management options. Numerical models are useful for assessing and managing water quality in water bodies. The Environmental Fluid Dynamics Code (EFDC) model has been applied in several studies and has proven to be very useful; however, it cannot reproduce the spatiotemporally changing dissolution phenomenon.

Many studies have investigated the release of phosphorus among nutrients from sediment. Phosphorus release is highly dependent on dissolved oxygen (DO) and actively occurs under anaerobic and high pH conditions [12]. These release characteristics indicate that the predicted water quality may vary depending on the flux rate value used when numerically simulating the water quality of the Saemangeum Reservoir. Therefore, an accurate representation of the flux rate and release environment in the benthic layer in numerical modeling is critical [13].

Nutrient release from sediments in brackish waters, such as the Saemangeum Reservoir, is controlled by the temperature and salinity of the water column and occurs at the interface between the sediment and water layers. When oxygen is consumed in the benthic layer of the water column to produce a hypoxic layer, the nutrient flux rate increases, causing lake eutrophication and affecting water quality management [14]. Therefore, the benthic flux phenomenon must be sufficiently reproduced to comprehensively include it in the model.

Based on the results of water quality modeling, the PO₄-P benthic flux rate applied to Saemangeum Lake by the National Institute of Environmental Research of Korea (2014) [15] and the Korea Rural Community Corporation (2015) [9] is 0.001 g/m²/day. This benthic flux rate was considered temporally and spatially constant and was calculated by referring to research cases applied to artificial lakes similar to Saemangeum Lake. In a study on Ganwol Lake, rates of 0.0001, 0.001, and 0.002 g/m²/day were applied. The benthic flux rate test of PO₄-P was conducted at three representative points, and it was applied uniformly for each zone. In other studies, the rates applied were 0.001 g/m²/day for Okeechobee Lake [16] and 0.0023 g/m²/day for Falls Lake [17] in the United States, and 0.0015 g/m²/day for Chaohu Lake in China [18]. Because there were no PO₄-P benthic flux rate data for these lakes, they were calculated through model calibration and reflected to be spatially and temporally constant. However, reflecting the benthic flux of PO₄-P, as in the case study mentioned above, is inconsistent with the theory of phosphorus elution, which changes according to dissolved oxygen (DO) and pH conditions in the natural state [5,9,10,12]. This represents a limitation of the current model.

Water quality models provide useful interpretations and effective evaluation and management alternatives using numerical models. The EFDC model was shown to have excellent applicability in many studies [19,20,21,22,23,24]. However, they cannot reproduce the benthic flux phenomenon that changes over space and time.

The objectives of this study were to (1) improve the water quality model to accurately reflect the water body environment with respect to its benthic flux rate, which acts as an internal load when simulating long-term water quality, and (2) examine the reproducibility of the improved model by reflecting the spatiotemporal change in the benthic flux rate while considering influencing factors such as anaerobic and aerobic conditions in the water layer. Calibration and verification of the model were performed in 2013 and 2016, respectively. The established model can be easily used for developing water quality improvement strategies.

2. Materials and Methods

2.1. Study Area

In November 1991, a sea dike was built as part of the Saemangeum project. The Saemangeum sea dike was completed in April 2010, and its final water-barrier work was completed in April 2006. This sea dike spans 33.9 km from Daehang-ri, Byeonsan-myeon, Buan-gun to Bieung-do, Gunsan, and includes estuaries of the Mangyeong (north side) and Dongjin (south side) rivers. It consists of four waterproof dikes and two drainage sluice gates (Shinsi, Gayeok) (Figure 1). The Saemnageum sea dike’s interior has a topographic range of 0–40 m, while the seabed is typically flat. The total area of the Saemangeum project is 401 km². Based on the management water level elevation of (−) 1.5 m during the completion of the Saemangeum Reservoir waterproof dike construction, the amount of land exposed to the natural elements was 180 km² or 45% of the total area and 64% of the land area (282.9 km²) [25].

The Saemangeum watershed is further divided into the Mangyeong and Dongjin River watersheds, part of a watershed on the nearby west coast, the Jikso Stream watershed, and the Saemangeum reclamation area. These watersheds have a combined area of 3319 km², of which the Mangyeong and Dongjin rivers have a watershed area of 1571 km² and 1034 km², respectively, accounting for 78.5% of the total water area [26].

2.2. Model Description

The EFDC is a three-dimensional numerical model for simulating the hydraulic and material transport of coasts, estuaries, lakes, wetlands, and rivers. It was developed by the Virginia Institute of Marine Science in the United States in the early 1990s and is currently managed by the U.S. Environmental Protection Agency [27]. The EFDC model comprises four modules: Hydrodynamics, water quality, sediment transport, and toxicity. It can simulate fluid transport and diffusion, suspended solids behavior, salinity and water temperature changes, water quality and eutrophication mechanisms, and the behavior of toxic contaminants [28]. The governing equations for the flow analysis of the EFDC model consist of continuity, horizontal and vertical momentum, density state, and mass conservation equations. Details about these can be found in Tetra Tech, Inc. (Pasadena, CA, USA) (2007) [28,29]. The three-dimensional continuous equations, motion, and static equations of the EFDC model are as follows:

$$\frac{\partial \left(m\zeta \right)}{\partial t}+\frac{\partial \left(m_x{H}_u\right)}{\partial x}+\frac{\partial \left(m_x{H}_v\right)}{\partial y}+\frac{\partial \left(mw\right)}{\partial z}=0$$

(1)

$$\frac{\partial \left(m\zeta \right)}{\partial t}+\frac{\partial \left(m_{y}H{\int }_0^{1}udz\right)}{\partial x}+\frac{\partial \left(m_{x}H{\int }_0^{1}vdz\right)}{\partial x}=0$$

(2)

$$\begin{gathered} \frac{\partial \left(mHu\right)}{\partial t}+\frac{\partial \left(m_{y}Huu\right)}{\partial x}+\frac{\partial \left(m_{y}Hvu\right)}{\partial y}+\frac{\partial \left(mwu\right)}{\partial z}-\left(mf+v\frac{\partial m_y}{\partial x}-u\frac{\partial m_y}{\partial y}\right)H_v \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=-m_{y}H\frac{\partial \left(g\zeta +p\right)}{\partial x}-m_y\left(\frac{\partial h}{\partial x}-z\frac{\partial H}{\partial x}\right)\frac{\partial p}{\partial z}+\frac{\partial }{\partial z}\left(m\frac{1}{H}Av\frac{\partial u}{\partial z}\right)+Q_u \end{gathered}$$

(3)

$$\begin{gathered} \frac{\partial \left(mHv\right)}{\partial t}+\frac{\partial \left(m_{y}Huv\right)}{\partial x}+\frac{\partial \left(m_{y}Hvv\right)}{\partial y}+\frac{\partial \left(mwv\right)}{\partial z}+\left(mf+v\frac{\partial m_y}{\partial x}-u\frac{\partial m_y}{\partial y}\right)H_u \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=-m_{x}H\frac{\partial \left(g\zeta +p\right)}{\partial y}-m_x\left(\frac{\partial h}{\partial y}-z\frac{\partial H}{\partial y}\right)\frac{\partial p}{\partial z}+\frac{\partial }{\partial z}\left(m\frac{1}{H}Av\frac{\partial v}{\partial z}\right)+Q_v \end{gathered}$$

(4)

$$\frac{\partial p}{\partial z}=gH\frac{\rho -{\rho }_0}{{\rho }_0}=-gHb$$

(5)

where u and v are horizontal velocity components (m/s) in the x and y directions, and w is a vertical velocity component (m/s) in the converted dimensionless vertical coordinate system z. H is the water depth below the u reference surface (m), ζ is the water surface displacement (m) from the reference surface, and H is the total water depth, which is the value of h + ζ. m_x, m_y is the square root of the diagonal component of the Metric Tensor that satisfies the arbitrary distance $d{s}^2={m_x}^2{d_x}^2+{m_y}^2{d_y}^2$ in the curvilinear coordinate system. Q_u and Q_v are the Momentum Source-Sink terms (kg·m/s), p represents the pressure (Pa), f is the Coriolis parameter, Av is the vertical turbulence viscosity coefficient, ρ is density (kg/m³), b is buoyancy (m/s²), and g is the gravitational acceleration (m/s²) (Tetra Tech Inc., 2007).

The basic equation used for water quality analysis is as follows:

$$\begin{gathered} \frac{\partial }{\partial t}\left(m_x{m}_{y}HC\right)+\frac{\partial }{\partial t}\left(m_{y}HuC\right)+\frac{\partial }{\partial y}\left(m_{x}HvC\right)+\frac{\partial }{\partial z}\left(m_x{m}_{y}wC\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\frac{\partial }{\partial x}\left(\frac{m_{y}H{A}_x}{m_x}\frac{\partial C}{\partial x}\right)+\frac{\partial }{\partial y}\left(\frac{m_{x}H{A}_y}{m_y}\frac{\partial C}{\partial y}\right)+\frac{\partial }{\partial z}\left(m_x{m}_y\frac{A_z}{H}\frac{\partial C}{\partial z}\right)+m_x{m}_{y}H{S}_c \end{gathered}$$

(6)

where C represents the concentration of each water quality factor; A_x, A_y, and A_z are the turbulent diffusion coefficients in the x, y, and z directions, respectively; and S_c is the source-sink term per unit volume.

2.3. Model Construction

To reproduce the hydraulic and water quality characteristics of the Saemangeum Reservoir, the model application range was chosen as 64 km in the east–west and 54 km north–south directions. The open sea was included on the Mangyeon River’s side via the Sichuan drainage sluice from the Mangyeong River sluice gate. The open sea was included in the Dongjin River, through the Garyeok drainage sluice from the Dongjin River sluice gate. This was confirmed in 2016.

The water depth and terrain data for each grid reflected the internal work by referring to waterproof dike and dredging construction data obtained from a survey conducted in 2008 by the Korea Rural Community Corporation’s Saemangeum project group [30].

The orthogonal curvilinear and sigma stretching coordinate systems were used for the horizontal and vertical directions, respectively. For 2013, the calibration year, and for 2016, the verification year, there were 5897 active grids, with the longitudinal and transverse lengths ranging from 68.3 to 627.2 m. Furthermore, the waterproof dike was masked to simulate a waterway with flow that was interrupted during the waterproof dike construction.

The system is comprised of 10 σ-levels in the vertical direction, with each layer receiving 10% of the height to reproduce topography, water depth, and hydraulic phenomena.

The flow rate and water quality boundary conditions inflow into the lake were calculated using the soil and water assessment tool (SWAT). The inflow and outflow from the open sea were simulated by setting open boundary conditions. At each calculation time, the inflow and outflow data at the open boundary were input by synthesizing four tides from the results of NAO99.JB [31], a marine tidal model. Calibration and verification were performed in 2013 and 2016, respectively.

Water quality simulation must be preceded by temperature and DO correction. Water temperature affects various physical and chemical properties of water and directly affects the water quality in rivers and lakes by interacting with DO, pH, chemical toxicity, ammonia, and metals [32,33]. Therefore, it is essential to address it during the initial stage of water quality correction [34]. Bottom benthic flux or sediment oxygen demand (SOD) is a reaction that occurs only in the sedimentary and bottom layers of water, affecting the surface layer via advection and diffusion [35]. However, in a water area with a weak flow, such as the Saemangeum Lake, vertical effects such as bottom elution or SOD may be sensitive, but the effect may not propagate to the surface layer and continue to affect the bottom layer.

Therefore, since the results of the model can be sensitive to the effects of SOD and bottom elution, appropriate input is required [36]. The related variables were entered in Card image 47 and applied to six variables: PO₄, NH₄, NO₃, Silica, chemical oxygen demand (COD), and SOD. In addition, variables related to algae, organic carbon, phosphorus, nitrogen, and COD were entered through a trial-and-error method (

Table 1. Water quality parameters used in the EFDC model.

Parameters	Unit	Definition	Calibration
PMc, PMd, PMs	/day	maximum growth rate under optimal conditions for algal group x	2.8
KHNx	/gNm3	half-saturation constant for nitrogen uptake for algal group x	0.01
KHPx	/gPm3	half-saturation constant for phosphorus uptake for algal group x	0.001
KHS	/gSim3	half-saturation constant for silica uptake for diatoms	0.05
CCHlx	gC/mgChl	carbon-to-chlorophyll ratio in algal group x	0.03
TMc1, TMd1, TMg1	°C	optimal temperature for algal growth for algal group x	20.0
TMc2	°C	optimal temperature for algal growth for algal group x	27.5
TMd2, TMg2			25.0
BFPO4d	-	sediment-water exchange flux of phosphate (g P/m2/day)	0.009
WSS	m/day	settling velocity of particulate metal	1.0
KRP	/day	minimum hydrolysis rate of refractory particulate organic phosphorus	0.15
KLP	/day	minimum hydrolysis rate of labile particulate organic phosphorus	0.0175
KDP	/day	minimum mineralization rate of dissolved organic phosphorus	0.001
Kcd	/day	oxidation rate of chemical oxygen demand at TRCOD	20
BFCOD	-	benthic flux rate of chemical oxygen demand	0.12
KRN	/day	minimum hydrolysis rate of refractory particulate organic nitrogen	0.075
KLN	/day	minimum hydrolysis rate of labile particulate organic nitrogen	0.175
KDN	/day	minimum mineralization rate of dissolved organic nitrogen	0.001
BFNH4	-	benthic flux rate of ammonia nitrogen	0.009
WSRP	m/day	settling velocity of refractory particulate organic matter	0.55
WSLP	m/day	settling velocity of labile particulate organic matter	0.55
KRC	/day	minimum dissolution rate of refractory particulate organic carbon	0.075
KLC	/day	minimum dissolution rate of labile particulate organic carbon	0.175
KDC	/day	minimum respiration rate of dissolved organic carbon	0.01
ASCd	gSi/gC	silica-to-carbon ratio of diatoms	0.05
KSU	/day	dissolution rate of particulate biogenic silica	0.05

).

2.4. Water Body-Benthic Sediment Reaction Simulation Method

The phosphorus flux rate is reflected in the concentration calculation of the EFDC model’s sedimentation model and nutrient diffusion equation; however, only the preset flux rate can be specified without considering the influencing factors. Thus, the benthic layer (K = 1), which changes with calculation time, cannot be considered the flux rate change due to aerobic and anaerobic conditions, water temperature, and salinity simulation. Aerobic and anaerobic conditions, water temperature, and salinity, which are affected by the DO concentration calculated in the grid’s benthic layer, must be considered in the model because they are closely related to the flux rate.

$$\frac{{\partial \mathrm{P}\mathrm{O}}_{4}t}{\partial t}={\sum }_{x=c,d,g}({FPI}_x·{BM}_x+{FPIP}_x·{PR}_x-P_x)APC·B_x+K_{DOP}·DOP+\frac{\partial \left({WS}_{TSS}·{\mathrm{P}\mathrm{O}}_{4}p\right)}{\partial Z}+\frac{{\mathrm{B}\mathrm{F}\mathrm{P}\mathrm{O}}_{4}d}{∆Z}+\frac{{\mathrm{W}\mathrm{P}\mathrm{O}}_{4}p}{V}+\frac{{\mathrm{W}\mathrm{P}\mathrm{O}}_{4}d}{V}$$

(7)

where PO₄t = (PO₄d + PO₄p) is the total phosphate concentration (g P m⁻³); PO₄d and PO₄p are dissolved and particulate (adsorbed) phosphate concentrations (g P m⁻³), respectively; ${FPI}_x$ is the fraction of inorganic phosphorus in metabolized phosphorus of algae group x; ${FPIP}_x$ is the fraction of inorganic phosphorus in predated vegetable algae; ${WS}_{TSS}$ is the sedimentation rate of suspended solids (m day⁻¹); BFPO₄d is the phosphate exchange flux at the sediment-water layer interface (g P m⁻² day⁻¹); and WPO₄t is the external load of the total phosphate (g P day⁻¹) [20]. The total phosphate concentration was equal to the sum of the concentrations of dissolved and particulate phosphates. The first term on the right-hand side represents the basal metabolism, predation, and intake of algae; the second term represents mineralization from dissolved organic phosphorus; the third term represents the sedimentation of adsorbed phosphate; the fourth term represents the exchange of dissolved phosphate at the sediment–water column interface; and the fifth term represents the external load.

The factors influencing the phosphorus flux rate considered in this study were water temperature and salinity. An increase in water temperature promotes the activity of microorganisms and benthic organisms reducing DO in sediments due to the increased respiration of microorganisms in sediments [37,38]. A decrease in sediment DO causes a low oxidation/reduction potential and a decrease in Fe(III), ultimately increasing phosphorus concentrations, such as dissolved total phosphorus (DTP), in water bodies by releasing Fe/Al-P [39,40]. Furthermore, because of higher oxygen demand, higher water temperatures increase the mineralization ratio of sediment organic matter and decrease the total amount of DO on the sediment surface. This further increases the phosphorus release [41,42]. Increased salinity in the water body raises the pH, inhibiting phosphorus absorption onto iron oxide [43,44]. The adsorption of phosphorus and iron oxide is limited in salty marine environments compared to freshwater environments. As the ocean is sulfate-rich, Fe(II) in sediments combines with hydrosulfide (HS⁻) [45,46,47]. Thus, if the concentration of phosphorus in pore water is relatively high without iron, its release into the water layer increases [48,49,50]. The relationships between the flux rate and its influencing factors have been extensively researched.

In the model, a relational expression was developed to represent the phosphorus flux rate based on water temperature and salinity. Phosphorus flux rate data [51] obtained by testing the sediments of the Saemangeum Reservoir from 2016 to 2018 were used as basic data (

Table 2. Result of flux rate tests at five main stations of the Saemangeum Reservoir.

Classification	Station	$\mathbf{T}-\mathbf{P} \mathbf{Flux} \mathbf{Rate} (\mathbf{g}/{\mathbf{m}}^2·\mathbf{d})$		Water Temperature (°C)	Salinity (psu)
		Aerobic	Anaerobic
1st	ME2	0.1317	0.1528	26.5	2.80
	ML3	0.0191	0.0216	23.8	23.8
	MK7	0.1311	0.1884	21.2	21.2
	DE2	0.0561	0.0504	26.9	1.20
	DL2	0.0178	0.0302	19.5	19.5
2nd	ME2	0.0280	0.0382	15.3	9.40
	ML3	0.0176	0.0270	15.2	25.5
	MK7	0.0048	0.0230	14.0	24.0
	DE2	0.0115	0.0053	16.7	6.6
	DL2	0.0433	0.0744	14.7	22.8
3rd	ME2	0.047	0.0332	15.5	12.1
	ML3	0.1273	0.0248	12.6	30.5
	MK7	0.0069	0.0346	12.1	30.7
	DE2	0.0145	0.0247	15.6	17.0
	DL2	0.0112	0.0491	12.9	22.6
4th	ME2	0.0458	0.0710	28.1	3.4
	ML3	0.0223	0.0223	28.1	17.3
	MK7	0.0119	0.0159	29.6	12.1
	DE2	0.0178	0.0601	27.7	0.8
	DL2	0.0046	0.0178	28.0	19.4
5th	ME2	0.1589	0.330	9.6	7.4
	ML3	0.0244	0.06898	4.8	30.7
	MK7	0.0344	0.0447	4.8	30.7
	DE2	0.0009	0.0285	5.8	18.3
	DL2	0.1635	0.1184	4.8	29.2

). Monthly water temperature and salinity data from the Ministry of Environment’s measurement network were used. The surveys were conducted in September, during the transition from summer to autumn; November, when the algae that proliferate in autumn auto-flocculated and settled; and April, during spring farming season, when there was a high influx of agricultural non-point pollutants. A total of five surveys were conducted in September and November 2016, April and November 2017, and April 2018.

The surveys were conducted at five stations: ME2 and DE2 in the agricultural district, ML3 and DL2 in the urban district, and MK7 in the environmental and ecological districts, which were the main targets for water quality management of the Saemangeum Reservoir (Figure 2).

It is a general theory that the phosphorus flux rate increases with water temperature and salinity, as has been previously reported in several studies [37,38,39,40,41,42,43,44,45,46,47,48,49,50]. The maximum and minimum ranges of the measured water temperature, salinity, and phosphorus flux rate data and the relationship between water temperature and salinity variables in previous studies were considered and reflected in this model.

The log (Figure 3), linear (Figure 4), and exponential functions (Figure 5) were applied to determine the relational expression for the formulated data, and the exponential function with the highest coefficient of determination was selected.

The flux rate was calculated by applying an exponential function to the relational expressions (8)–(10). Figure 5 depicts the trend line, and the relational expressions obtained through trend analysis are as follows:

$$B_{flux1}={0.0009e}^{0.1491·S}$$

(8)

$$B_{flux2}={0.0065e}^{0.0825·S}$$

(9)

$$B_{flux3}={0.0020e}^{0.1445·T}$$

(10)

$$B_{flux4}={0.0097e}^{0.0813·T}$$

(11)

where $B_{flux1}$ is the flux rate according to salinity in aerobic condition, $B_{flux2}$ = is the flux rate according to salinity in anaerobic condition, $B_{flux3}$ is the flux rate according to temperature in aerobic condition, $B_{flux4}$ is the flux rate according to temperature in anaerobic conditions, S is salinity (psu), and T is the temperature (°C).

For the relationship with salinity, R² = 0.93 and R² = 0.71 under aerobic and anaerobic conditions were used, respectively. For the relationship with water temperature, R² = 0.90 and R² = 0.70 under aerobic and anaerobic conditions were used, respectively. Thus, the calculated results were statistically significant.

Equations for calculating the flux rate according to the water temperature and salinity under aerobic or anaerobic conditions were combined, and the flux rate for the final calculation was proposed as follows:

$$B_{flux}=min\left\{{B_{flux}}^{\prime },max\left(B_{flux1},B_{flux2},B_{flux3},B_{flux4}\right)\right\}$$

(12)

where ${B_{flux}}^{\prime }$ is the user-defined upper limit of the flux rate and $B_{flux1–4}$ is the flux rate that is finally applied to the calculations. A reasonable value must be entered for the user-defined upper limit of the flux rate (${B_{flux}}^{\prime }$) through experiments and a literature review on the release range of the study area. Finally, if the flux rate calculated for each condition ($B_{flux1},B_{flu2},B_{flux3},B_{flux4}$) exceeded the user-defined upper limit of the flux rate (${B_{flux}}^{\prime }$), the value predefined by the user was entered. Furthermore, based on the critical concentration in the benthic layer of the water body, it was calculated to be anaerobic if DO < 2 mg/L, and aerobic if DO > 2 mg/L.

The variables were declared in the Var_Global_Mod.f90 file to add them according to the DO concentration in the variable state of the existing constant-input condition. In addition, the array size of the variables was specified in the VARALLOC.for file, and the variables were initialized in the VARZEROReal.for file. Then, the variables to be calculated in RWQC1.for were added. Biogeochemical reactions were placed in WQSKE3.for since the term reflecting the flux rate term was calculated in RWQBEN2.for Calculations were performed for each condition in the linked file.

2.5. Model Assessment

The measured and simulated values were compared to determine the reproducibility of the model. For the evaluation functions, the RMSE-observation standard deviation ratio (RSR), % difference (%diff.), and the absolute mean error (AME) were used.

Table 3. Statistical indicators used to evaluate model accuracy.

Criteria	Equation	Optimal Value
RSR	$\mathrm{RSR}=\frac{RMSE}{O_{STDEV}}=\frac{\sqrt{{\sum _{i=1}^n(O_i-P_i)}^2}}{\sqrt{{\sum _{i=1}^n(O_i-{\stackrel{-}{O}}_i)}^2}}$	0
% Difference	$\%\mathrm{diff}.=\frac{\sum _{i=1}^n{O}_i-\sum _{i=1}^n{P}_i}{\sum _{i=1}^n{O}_i}\times 100$	0
AME	$\mathrm{AME}=\frac{1}{N}\sum _{i=1}^n\left|O_i-P_i\right|$	0

lists the evaluation functions and their optimal values (Table 3) [52].

2.6. Model Validation

Before running the water quality simulation, the measured and simulated water levels at the drainage gate were compared to check whether the hydraulic simulation was reasonable. The water level simulation yielded an RMSE-observation standard deviation ratio (RSR) of 0.02, a difference of 2.02%, and an AME of 0.188 in the test year 2016. Thus, the model accurately predicted the lake water level. According to the time series simulation results, errors occurred during several periods in 2016, from 11 July to 15 August. This period corresponded with the flood season, and it is thought that these errors were caused by the phenomenon of a large volume of flow in and out of the drainage sluice and the flow gathered in the watershed flowing in simultaneously (Figure 6).

To validate the results of the water quality simulation for the Saemangeum Reservoir, the measured and simulated values were compared at stations ME2, ML3, DE2, and DL2. High concentrations were observed for all items at stations ME2 and DJ2, which are the midstream and upstream points of the Mangyeong and Dongjin waterways, respectively. The concentration gradually decreased and stabilized as it flowed down to stations ML3 and DL2. This was considered to be due to the mid-upstream locations of the lake being vulnerable to the pollution from the upstream watershed, and the flow of the water body not being smooth due to the ongoing waterproof dike construction. Furthermore, because the downstream locations were close to the drainage sluice gate, the water quality concentration was simulated to be lower than that of the upstream locations because the freshwater environment was changed to brackish water or seawater as a result of seawater circulation. According to the water quality modeling, the DO items showed an RSR of 0.003–0.204%, a diff. of 0.3–18.7, and an AME of 0.022–1.491; the Chl-a items showed an RSR of 0.017–1.596, a %diff. of 1.5–146.3, and an AME of 0.146–22.549; the T-N items showed an RSR of 0.025–0.295, a %diff. of 2.3–27.0, and an AME of 0.016–0.353; and the T-P items showed an RSR of 0.013–0.471, a %diff. of 0.1–13, and an AME of 0.008 to 0.833. As a result, the model was evaluated for its ability to accurately reflect changes in the lake’s water quality (

Table 4. Summary of statistics regarding water quality concentrations simulated and measured by each station.

Validation Stations		RSR	%diff.	AME
DO	ME2	0.029	2.7	0.241
	ML3	0.066	6.0	0.501
	DE2	0.204	18.7	1.491
	DL2	0.003	0.3	0.022
Chl-a	ME2	0.123	11.2	3.955
	ML3	0.480	44.0	5.909
	DE2	0.361	33.1	9.697
	DL2	1.596	146.3	22.549
T-N	ME2	0.134	12.3	0.353
	ML3	0.295	27.0	0.214
	DE2	0.139	12.7	0.209
	DL2	0.115	10.6	0.101
T-P	ME2	0.027	2.5	0.003
	ML3	0.471	43.2	0.020
	DE2	0.157	14.4	0.013
	DL2	0.083	7.6	0.004
COD	ME2	0.118	10.9	0.773
	ML3	0.110	10.1	0.394
	DE2	0.146	13.4	0.833
	DL2	0.009	0.8	0.035

and Figure 7).

DO exhibited a seasonal pattern of low concentrations in summer and high concentrations in winter. However, the calculation results for the ME2 station did not include its summer concentration values. It appears that the water quality results did not reflect the measured values because the water level of the Saemangeum Reservoir is currently maintained at an elevation of −1.5 m. Hence, the water flow upstream does not always occur, but wet–dry cycles occur repeatedly. In the case of COD, the simulated values reflected the trend of the measured values.

Chl-a, the maximum percentage difference, was calculated to be 146.3% (average: 31.05%), indicating an overestimation of the measured values. However, the results of the annual time-series simulation accurately reflected the effects of algae that occurred from late autumn to spring under the influence of seasonal solar radiation and water temperature. The current EFDC algal simulation option allows for the simulation of three types of planktonic algal communities (cyanobacteria, diatoms, and green algae), excluding macroalgae [53]. However, in the case of other algae that are not included in these three communities, such as flagellar algae commonly observed in rivers and lakes in Korea, including Cryptomonas spp., it was assumed that they exhibited similar behavior to that of green algae for convenience in this study, while considering the limitations of algal communities that can be simulated, major occurrences, and dominant periods.

The upstream portion of the Saemangeum Reservoir is freshwater, the middle portion is brackish water, and the downstream part is seawater. Therefore, adequate algae observation data should be collected, and the EFDC source code should be modified to increase the number of algal communities that can be simulated in future studies.

2.7. Validation of Water Body-Benthic Sediment Reaction Simulation Method

A test using the ideal grid was performed to validate the model’s improved phosphorus benthic flux rate. The terrain and grid were 3 km east–west and 1 km north–south, with a water depth of 3 m (Figure 8). The horizontal grid was 100 m in both the north–south and north–south directions, and vertically, 10 layers of equal proportions were configured. The initial water level was set to 0 m for the initial and boundary conditions, and the initial DO concentration was set to 10 mg/L. The initial temperature and salinity were set to 4 °C and 27.1 psu, respectively. The other parameters of water quality were set at 0 mg/L. It was assumed that there was no inflow or outflow from external sources.

The scenario for validating the phosphorus flux rate improvement model was as follows. In Case 1, the existing model was applied. In Case 2, an improved model was applied. In Case 3, typhoon invasion from the 228th day was reflected such that vertical mixing occurred between the upper and lower layers of the water body. The flux rate changes were simulated and reviewed when DO in the surface layer was transferred to the bottom layer, and the anaerobic conditions in the bottom layer were converted to aerobic conditions. In Case 4, it was determined whether the simulation was normally performed when the release zones were separated, and the experimental conditions were the same as those in Case 3. The initial temperature and salinity were set at 4 °C and 27.1 psu, respectively. The experimental conditions are listed in

Table 5. Experimental conditions for validating the improved model.

Experiment Cases	Applied Model	Vertical Mixing	Release Zone	Flux Rate (g/m2/day)
				SOD	PO4
					Aerobic (Oxidized)	Anaerobic (Reduced)
Case 1	Existing	×	×	−2.0	0.02
Case 2	Improved	×	×	−2.0	0.02	0.10
Case 3	Improved	○	×	−2.0	0.02	0.10
Case 4-1 Case 4-2	Improved	○	○	−2.0	(Zone 1) 0.02 (Zone 2) 0.00	(Zone 1) 0.10 (Zone 2) 0.10

.

According to the experimental results for Case 1, the DO concentration in the bottom layer decreased linearly. After 227 day, low concentrations were simulated, and the water body changed from aerobic to anaerobic. The PO₄-P concentration increased linearly. In addition, the DO concentration in the bottom layer increased in the same pattern, even after reaching a critical concentration of 2 mg/L or less. This was consistent with the conditions of the existing model where a constant value of 0.02 g/m²/day is specified for the flux rate.

According to the experimental results for Case 2, the DO concentration in the bottom layer decreased linearly, as in Case 1. However, the concentration of PO₄-P increased gradually, and the slope became steeper from the critical concentration of 2 mg/L under anaerobic conditions. This indicated that the model reflected the change from aerobic to anaerobic conditions as the DO concentration in the bottom layer of the water body decreased to 2 mg/L or less. Furthermore, unlike in Case 1, the concentration increased during the oscillation because the calculation results were less than the maximum value during the numerical simulation. According to the experimental results for Case 3, the DO concentration in the bottom layer decreased linearly, as in Case 2. When a critical concentration of 2 mg/L or less was maintained, the concentration of PO₄-P increased rapidly, as in Case 2. From day 228, when vertical mixing was applied, the concentration gradually decreased and then stabilized at an average concentration of 0.149 mg/L. This was because oxygen from the surface layer was transferred to the bottom layer via vertical mixing, and the flux rate decreased as the anaerobic conditions of the bottom layer changed to aerobic conditions. This suggested that the simulation accurately reflected the aerobic and anaerobic conditions of the bottom layer, which were affected by time and external forces.

According to the experimental results of Cases 4-1 and 4-2, release zone 1 showed the same increasing pattern as that in Case 3 when 0.02 g/m²/day was applied in aerobic conditions. However, release zone 2 did not show an increase or decrease when the flux rate was 0.1 g/m²/day. After 226 days, the DO concentration in the bottom layer fell below the critical concentration of 2 mg/L, changing from aerobic to anaerobic condition. Accordingly, the concentration of PO₄-P increased. After 228 day, the DO from the surface layer was transferred to the bottom layer by vertical mixing, which increased the DO concentration and changed the environment of the bottom layer from anaerobic to aerobic conditions. Consequently, the concentration of PO₄-P decreased and then gradually stabilized.

The experimental results for Case 4-1 and Case 4-2 confirmed that the changing concentrations were calculated depending on the aerobic and anaerobic conditions of the bottom layer, as verified in Case 3. Moreover, the flux rate in each zone was accurately reflected, indicating that the simulations were accurate. Therefore, the improved model reproduced the flux rate by distinguishing between aerobic and anaerobic conditions according to the oxidation-reduction reaction of the bottom layer and by considering the effects of water temperature and salinity (Figure 9).

3. Results and Discussion

Application of the Model

Using the improved model, of which the reproducibility was reviewed, we examined the change in phosphorus concentration in the lake according to the benthic flux rate of PO₄-P, calculated using water temperature and salinity. The experimental period was 2016 and the flux rate of PO₄-P was designated as 0.003 for the entire calculation area of the existing model. The maximum value among the release values tested for Saemangeum Reservoir was used to set the maximum value of the flux rate in the improved model. The flux rate was reflected temporally and spatially according to water temperature and salinity conditions by entering 0.16 g/m²/day for aerobic conditions and 0.33 g/m²/day for anaerobic conditions. The results of the numerical experiments are listed in

Table 6. Outline of the numerical simulation for phosphorus concentration change according to the improved model.

Item		Description
Purpose of experiment		Simulation of total phosphorus changes according to improved method of applying the flux rate
Scope of the model		64 km in the east-west direction, and 54 km in the south-north direction
Model configuration	Grid configuration	Orthogonal Curvilinear Coordinate
	Number of grids	5897
Experimental conditions	Open boundary	Composite tides of the four main sub-tidal currents (M2, S2, K1, O1)
	Calculation interval	△t = 6 s
	Experiment period	1 January 2016–31 December 2016
Experimental condition		(Existing model) flux rate: 0.003 g/m2/day(Improved model) flux rate: spatiotemporal flux rate according to water temperature-salinity changes

.

The statistical evaluation function values of the T-P simulation results for the ME2 station upstream of the Saemangeum Reservoir Mangyeong waterway were R² = 0.87, RSR = 0.321, %diff. = 29.4, and AME = 0.064 for the existing model and R² = 0.97, RSR = 0.106, %diff. = 9.68, and AME = 0.021 for the improved model. Thus, the reproducibility of the improved model for the simulation of TP concentration at a given station was higher than that of the existing model (Figure 10).

According to the time-series distribution of the existing model, the concentration of pollutants gradually increased from day 150, showing the highest concentration in July, and then gradually decreased during the oscillation. The improved model showed lower concentrations than the existing model for up to 70 days owing to the relatively low water temperature and high salinity throughout the year. It then gradually increased, peaked at 280 days, and then decreased. The shape of the concentration curve was unstable and oscillated because the station located in the upstream area was directly affected by changes in the pollutant load flowing in the Saemangeum watershed. Moreover, the Saemangeum Reservoir is in a transition zone between seawater and freshwater where the management water level is maintained at an elevation of −1.5 m. This is considered to be due to the fact that the salinity, which was maintained at 5 psu, increased to 14 psu from day 220 when a large difference in concentration occurred.

When the shape of the overall concentration curve was compared to those of the measured values in the existing model after 150 days, it was found that it gradually increased with the increasing TP concentration. However, it did not reach its peak concentration until day 270 and gradually decreased thereafter. From day 120, the concentration value in the improved model was higher than that in the existing model and gradually increased. Therefore, in addition to reproducing the peak concentration on day 270, the concentration that gradually decreased as the dry season approached was also reproduced.

The statistical evaluation function values of the T-P simulation results for the ML3 station downstream of the Saemangeum Reservoir Mangyeong waterway were R² = 0.98, RSR = 0.075, %diff. = 6.95, and AME = 0.013 for the existing model, and R² = 0.98, RSR = 0.095, %diff. = 8.69, and AME = 0.016 for the improved model. Thus, the reproducibility of the improved model for the simulation of TP concentration at a given station was lower than that of the existing model (Figure 11).

Based on the time-series simulation results of the existing model, the concentration was initially set at 0.05 mg/L and subsequently stabilized. It was then slightly increased to reproduce the peak concentration in June that occurred on the 150th day. However, it gradually decreased after the error, and a peak concentration value was observed. In the improved model, the concentration was similar to that of the existing model but gradually increased after 120 days, reflecting the peak concentration at day 150, and then gradually decreased. Neither model reproduced the peak concentrations on Day 270. However, while the existing model decreased linearly, the improved model exhibited a slight increase before decreasing. This suggested that the tendency of the measured values was reflected in the long-term water quality simulation.

When compared with the ME2 station in the upstream region, both models showed lower concentrations at the ML3 station downstream and higher concentrations at the upstream site. This was because the pollutant load from the watershed increases the consumption of DO, and a high phosphorus concentration is formed in summer and autumn when the pollutant inflow increases due to the influence of the pollutant load from the watershed. This was consistent with the findings of a previous study [54], which found that total phosphorus concentration decreased downstream, the sediment concentration increased upstream, and sediment and sediment concentrations decreased exponentially downstream. Compared to the upstream locations, the midstream and downstream locations of the lake flow down into the lake as they go downstream and are directly affected by the dilution effect and the operation of the sluice gates. Periodic circulation between the surface water and bottom layer was rather active because of the inflow and outflow that occurred when maintaining water quality and controlling the water level in the lake. Consequently, DO was supplied to form a layer in an aerobic state, and a relatively low concentration of TP was simulated.

The statistical evaluation function values of the TP simulation results for the DE2 station upstream of the Saemangeum Reservoir Mangyeong waterway were R² = 0.90, RSR = 0.30, diffusion = 27.77%, and AME = 0.064 for the existing model, and R² = 0.99, RSR = 0.04, %diff. = 3.61, and AME = 0.008 for the improved model. Thus, the reproducibility of the improved model for the simulation of TP concentration at a given station was higher than that of the existing model (Figure 12).

The time-series distribution of the existing model generally shows stable concentrations with low fluctuations. The concentration gradually increased until day 150 and then gradually decreased. When compared to the measured values, the overall trend was reproduced; however, the concentrations in the lake, which gradually increased after summer, were not accurately simulated. In the improved model, the peak concentration was simulated at day 180, 30 days later than in the existing model, and then gradually decreased. Furthermore, concentrations that gradually increased after summer were reproduced.

The statistical evaluation function values of the T-P simulation results for the DL2 station downstream of the Dongjin waterway in the Saemangeum Reservoir were R² = 0.90, RSR = 0.29, %diff. = 27.27, and AME = 0.049 for the existing model and R² = 0.98, RSR = 0.09, %diff. = 8.381, and AME = 0.015 for the improved model. Thus, it was determined that the reproducibility of the improved model for the simulation of TP concentration was high (Figure 13).

The existing model maintained a stable pattern for 180 days, after which the concentration increased and peaked at 190 days. Subsequently, it gradually decreases and stabilizes. The simulated values tended to be underestimated compared to the measured values. Thus, gradually increasing concentrations or the highest measured concentrations could not be accurately simulated. The improved model maintained a stable pattern for up to 180 d, similar to the existing model; however, the concentration gradually increased. The concentration increased significantly on day 190, and then gradually decreased. The simulated increasing pattern after 190 days was similar to that of the existing model; however, the width of the increase was larger. This was due to the increase in the flux rate caused by the high salinity from the start of the simulation, and it was presumed that the internal pollutants acted during the early stage of the simulation. As a result, the concentration increased gradually and then rapidly owing to the upstream pollutant load.

This pattern was similar to that of DE2, which is an upstream station in the Dongjin waterway. In contrast to the Mangyeong waterway, the pollutant load from upstream affected the downstream station, and the concentration did not decrease downstream owing to the occurrence of internal pollutants, thus showing concentrations similar to those upstream.

4. Conclusions

The phosphorus release characteristics in anaerobic and aerobic environments are quite different because of the oxidation-reduction reactions occurring in the bottom layer of the water body. Consequently, nutrients released as a result of environmental changes may promote algae and bacterial growth and influence water quality. It is essential to accurately enter and simulate the flux rate when forecasting and assessing water quality using a numerical model. The flux rates under aerobic and anaerobic conditions were affected by water temperature and salinity. Consequently, under aerobic and anaerobic conditions, relational expressions of water temperature, salinity, and flux rate were created in this study to describe the flux rate ($B_{flux}$) while accounting for the influencing factors. Furthermore, the critical concentration value of the bottom layer environment was adjusted to 2 mg/L in the flux rate reflection module such that the flux rate was applied differently in time and space. Furthermore, the nutrient release characteristics in relation to the redox conditions were determined. The reproducibility of the improved model was rated higher for both the Mangyeong and Dongjin waterways after assessing the TP concentration simulation results of the existing and improved models by splitting them into the Mangyeong and Dongjin waterways. The improved water quality model takes into account the characteristics of the flux rate, which fluctuates temporally and spatially depending on environmental conditions and influencing factors in the water body’s bottom layer. In addition, when predicting future water quality, it is judged that the changing benthic flux rate can be reasonably reflected through the increase in sea surface temperature and decrease in salinity predicted under climate change scenarios (IPCC, AR6) [55,56]. Therefore, an improved water quality model would be useful for developing lake management plans such as operational measures for seawater circulation and water level management for freshwater lakes. However, because the performance of the model was tested in Saemangeum Lake, additional tests on the model should be performed by applying it to other lakes in the future. To this end, we intend to apply the model in the future to other lake areas in order to assess its reproducibility and improve the model.