Log-Linear Model and Delivery Load Analysis for Improvements in Water Quality through TMDL in the Gyeongan Stream Watershed, Republic of Korea

Abstract

The effectiveness of implementing the total maximum daily load (TMDL) in the Gyeongan stream watershed was evaluated to assess its impact on water quality. The relationships between water quality and flow rate and load and water quality were reinterpreted using a log-linear model and the delivery load, respectively. To estimate annual water quality trends and analyze the effects of water quality improvement in each parameter, an improved multivariable log-linear model addressing the limitations of the traditional L-Q equation was applied to analyze the relationship between water quality and flow rate, excluding the effects of flow rate and seasonality. The effect of total phosphorus (T-P) was particularly prominent. A new delivery load was developed and applied to address the limitations of the original unit-based delivery load. Evaluations showed that water quality continuously improved across all parameters, and all methods (excluding the influence of flow rate on water quality fluctuations) were highly effective in estimating water quality changes attributable to anthropogenic pollution sources. The analysis of pollutant contributions revealed that managing point sources is necessary for controlling the biochemical oxygen demand and total nitrogen, while point and non-point sources require T-P management. Future policy development should consider this when formulating management strategies.

1. Introduction

The Republic of Korea has legislated discharge standards for sewage and wastewater to prevent water pollution. However, owing to urbanization and industrialization, regulating the total amount of pollutants discharged into streams and lakes is challenging, even when they meet permissible limits [1,2], and this has exacerbated environmental issues and resulted in ongoing disputes over fairness among polluters. To address these issues, the “Comprehensive Water Management Plan for the Four Major Rivers” was established in 1998–2000 [3]. In accordance with the Four Major Rivers Act, the concept of a total maximum daily load (TMDL) was introduced to the water quality management of three major rivers (Nakdong, Yeongsan-Seomjin, and Geum) in 2005, and this was then expanded to the Han River in 2013, which transitioned from concentration to load-based water quality management [3,4,5].

The United States implemented point source pollution management (NPDES; National Pollutant Discharge Elimination System) but has implemented TMDL, which includes non-point source pollution management, to address impaired water bodies since 1992 [3,6]. They select and manage target substances necessary for water quality improvement in each water system, and there has been 80 percent progress in implementing these plans by 2022. The final report noted that at least 26 states out of 87 states have pursued advanced restoration approaches and 9 states out of 70 states have pursued protection plans [7].

With respect to the TMDL, water quality level targets are set for each water system segment, the allowable load is calculated, and the total amount of pollutants discharged within each watershed is managed to maintain these levels. If the discharge amount falls below the set pollutant load, additional regional development projects can be permitted, enabling sustainable development in conjunction with environmental conservation [8]. Pollution source management plans were established and evaluated following the introduction of the TMDL concept in the Republic of Korea, and to prevent uncontrolled development and encourage the minimization of pollutants and eco-friendly development practices, development was permitted based on the principle of “first reduce, then develop”. However, land use has been continuously shifting toward urbanization [2,9,10].

To manage the water quality in urbanizing watersheds, it is necessary to identify the efflux characteristics of pollutants; however, this is challenging because they typically occur with rainfall [11]. Therefore, to enable the effective management of water quality in a watershed, it is critical to identify the amount (load) and characteristics of pollutant efflux. The related factors that need to be considered are the pollutant efflux pathways and topographical and hydrological conditions. However, investigating all these conditions is challenging owing to financial constraints and uncertainties in simulation results. Therefore, the use of empirical formulas is reasonable [12].

To manage the target water quality, load duration curves calculated from the daily flow rate and water quality data at key stream points are used to establish the TMDL [13]. However, despite the reduction in pollutant discharge, there have been instances of water quality degradation [14]. Hence, further detailed evaluations are necessary. In this study, we aimed to reinterpret the relationship between the water quality and flow rate using the multivariate log-linear model (MLM). Additionally, we sought to improve the currently applied delivery load and identify the contribution of pollution sources by discharge pathways. Our ultimate aim was to evaluate the water quality improvement effects achieved through the implementation of the TMDL.

2. Materials and Methods

2.1. Research Area

The Gyeongan stream originates from Munsu Mountain between Yongin city and Ho-dong and flows northwest. It changes its course downstream of Yongin city and heads north, where it is joined by several tributaries, including the Yangji stream, Geumeo stream, Osan stream, Mokhyeon stream, Gonjiam stream, Nogok stream, Beon stream, and Usan stream, before ultimately draining into the Han River [15]. Although it accounts for only ~1.6% of the total inflow to Paldang Reservoir, its short flow distance significantly impacts pollution in the reservoir. Therefore, pollution source management has often focused on the Gyeongan stream [16].

The study area is shown in Figure 1.

Paldang Reservoir is a critical water source, and it is crucial to manage the quality of the water draining into it. Despite the numerous studies conducted in this regard [17,18,19,20,21,22,23] and certain improvements in water quality, the area continues to suffer from severe eutrophication [24]. The Gyeongan stream watershed has undergone continuous urbanization; therefore, changes in the water quality can effectively reveal pollutant efflux characteristics. As such, it was selected as the research area.

Gwangju city is located downstream of the Gyeongan stream watershed, and it was the first city in the country to voluntarily implement the TMDL in 2004. Yongin city is located upstream of the watershed, and it also voluntarily initiated this system in 2007 [25]. These cities voluntarily set the target water quality and established the TMDL before the mandatory implementation in 2013. Other local governments that have implemented this voluntary system include those of seven cities around Paldang Reservoir (Gapyeong-gun, Gwangju-si, Namyangju-si, Yangpyeong-gun, Yeoju-si, Yongin-si, and Icheon-si). The effects of voluntary and mandatory measures on water quality improvement are discussed in Section Improvement in Water Quality.

2.2. Research Method

2.2.1. Log-Linear Model

Simple Log-Linear Model

Managing the water quality of urbanizing watersheds requires identifying the pollutant efflux characteristics. However, because pollutants are typically discharged with rainwater, they are difficult to quantify. Therefore, developing empirical formulas is considered an efficient approach.

The log-linear model can be simply represented by the equation initially developed by Gunnerson (1967) [26]. We refer to this as the simple log-linear model (SLM),

$$L=a{Q}^b$$

(1)

where L is the load (kg/d), Q is the flow rate (m³/s), and a and b are constants.

The SLM establishes a linear (log) relationship between Q and water quality (load) [12,27,28,29,30], which can be expressed in terms of concentration, as shown in the following equation (Equation (2)),

$$C=a{Q}^b$$

(2)

where C is the concentration (mg/L).

However, the SLM struggles to predict changes based on variations in pollution sources.

Park (2007) applied the watershed slope and flow rate per unit area of the watershed, but the parameter calculation was too complicated [12]. Lee (2002) considered the ratio of daily runoff to the annual average runoff, but there were limitations in applying it to unmeasured watersheds [31]. Ha et al. (1998) applied the distance ratio reduction factor to the emission load [32]. Eom (2004) applied area ratio discharge and shape coefficient, but there were limitations in predicting changes according to discharge type (point/non-point) [33]. Despite several studies being conducted to improve it, interpreting the changes in the water quality as a function of the flow rate remains difficult (Figure 2).

MLM

The MLM was initially developed by Cohn et al. [34], and it helps to interpret water quality changes over time as a function of flow rate variations. It is more effective than the SLM at explaining variations in water quality data. Using the model coefficients, we can examine the trends and seasonality in water quality [34,35,36].

The MLM is expressed in the following equation,

$$\ln \left[C\right]={\beta }_0+{\beta }_{1}ln\left[\frac{Q}{\tilde{Q}}\right]+{\beta }_2{\left\{ln\left[\frac{Q}{\tilde{Q}}\right]\right\}}^2+{\beta }_3\left[T-\tilde{T}\right]+{\beta }_4{\left[T-\tilde{T}\right]}^2+{\beta }_{5}sin\left[2\pi T\right]+{\beta }_{6}cos\left[2\pi T\right]$$

(3)

where ${\beta }_0$ is a constant, ${\beta }_1$ and ${\beta }_2$ are discharge parameters, ${\beta }_3$ and ${\beta }_4$ represent time parameters, and ${\beta }_5$ and ${\beta }_6$ remove the effects parameter of seasonality (first-order Fourier).

Seven parameters were used in this study: one constant, two coefficients related to flow rate, two coefficients related to time, and two coefficients to account for seasonal variations via a sine wave function (the first-order Fourier). Here, Q represents the flow rate (m³/s), T represents the time, and $\beta$ represents the model’s coefficient. $\overline{Q}$ and $\overline{T}$ are the centering variables that simplify numerical operations and do not affect model convergence:

$$\tilde{T}=\overline{T}+\frac{{\sum }_{i=1}^N{\left(T_i-\overline{T}\right)}^3}{2{\sum }_{i=1}^N{\left(T_i-\overline{T}\right)}^2}$$

(4)

$$\overline{T}=\frac{1}{N}\sum _{i=1}^N{T}_i$$

(5)

However, long-term water quality variations are often characterized by a quadratic function, and reproducing the patterns of re-decrease or re-increase in water quality is challenging. In such cases, it is necessary to apply this term in the form of a cubic function to better represent the overall trend of water quality changes and prevent distortion (Equation (6)),

$$\ln \left[C\right]={\beta }_0+{\beta }_{1}ln\left[\frac{Q}{\tilde{Q}}\right]+{\beta }_2{\left\{ln\left[\frac{Q}{\tilde{Q}}\right]\right\}}^2+{\beta }_3\left[T-\tilde{T}\right]+{\beta }_4{\left[T-\tilde{T}\right]}^2+{\beta }_5{[T-\tilde{T}]}^3+{\beta }_{6}sin\left[2\pi T\right]+{\beta }_{7}cos\left[2\pi T\right]$$

(6)

Among the coefficients, ${\beta }_1$ and ${\beta }_2$ are the parameters related to the flow rate, but ${\beta }_1$ is the parameter that primarily indicates the cause of the target substance concentration in relation to flow rate. A negative value indicates that the dissolved components are derived from point sources of pollution, whereas a positive value indicates that they are related to non-point sources associated with sediment. Furthermore, a value closer to zero signifies a lack of an effect on the flow rate, suggesting that the surface runoff and rainfall are compositionally similar. ${\beta }_3$, ${\beta }_4$, and ${\beta }_5$ are the parameters relating to the trend of the concentration over time. Each coefficient indicates changes in concentration: a positive value signifies an increase and a negative value indicates a decrease. ${\beta }_6$ and ${\beta }_7$ are the parameters used to eliminate the effects of seasonality, represented by a Fourier transformation of the seasonal changes, where Fourier transformation refers to the conversion of a function of time or space into a function of frequency. In the time domain, it means dispersing localized functions into the frequency domain [37]. It is also plausible that the amplitude, phase, and frequency patterns may be similar every year under the same flow rate conditions. Even if multiple factors are involved, up until the time they show periodicity, they can be expressed through a sine wave function.

Therefore, the MLM is more conducive to predicting changes based on discharge patterns than the SLM, and it can be used to examine flow rate variations.

2.2.2. Delivery Load

While the MLM is useful for simulating temporal variations in water quality, it treats factors other than the flow rate and seasonality as lumped parameters over time. Consequently, it cannot directly interpret the relationship between changes in pollutant sources or loads and water quality. In water quality management, the primary concern is understanding how water quality changes in response to variations in pollutant sources or loads rather than fluctuations caused by weather and seasonal factors. Therefore, to address this issue and facilitate the interpretation of water quality changes in relation to pollutant sources or loads, we developed a new empirical load delivery equation. We then evaluated its applicability.

Problems Associated with Calculating the Existing Delivery Ratio

Pollutants originating from a watershed are discharged through reduction facilities and undergo an increase or decrease in transport before reaching specific points in the receiving waterbody. The delivery ratio is defined as the ratio of the pollutant load at a specific point to the total discharge load from the watershed. The behavior of pollutants varies depending on their characteristics, and the types of pollutant sources are influenced by various physical, chemical, and biological factors (such as weather and terrain). While watershed models considering various factors can be used to interpret such behavior, constructing and operating these models typically require significant time. Moreover, the accuracy of the interpretation of pollutant delivery from point sources significantly impacts the model results.

With respect to the TMDL of the Republic of Korea, the estimation of pollutant quantities discharged from individual point and non-point pollution sources, excluding environmental infrastructure, has traditionally been based on the unit-area method (Equation (7)),

$$L_d=R\left(L_t+L_p+\alpha L_n\right)$$

(7)

where $L_{\mathrm{d}}$ is the pollutant delivery load (kg/d), $\mathrm{R}$ is delivery ratio, $L_{\mathrm{t}}$ is the discharge load from the sewage treatment plant (STP; kg/d), $L_{\mathrm{p}}$ is the discharge load from an individual point source (kg/d), $\alpha$ is the discharge rate from a non-point source, $L_{\mathrm{n}}$ is pollutant load from non-point sources estimated by the unit-area method.

The pollutant load estimated by the unit-area method is multiplied by the non-point source discharge rate. This value is then added to the point source discharge load to obtain the total discharge load. Subsequently, the delivery ratio was calculated considering the watershed area and flow rate (Equation (8)),

$$R=\sigma \frac{Q^{\beta }}{A^{\gamma }}$$

(8)

where $R$ is the delivery ratio, $\mathsf{\sigma }$ is the delivery coefficient, $Q$ is the flow rate (m³/s), $A$ is the area of the watershed (km²), and $\beta$ and $\gamma$ are multipliers. This equation is multiplied by this total discharge load to determine the delivery load.

This method is used to calculate average annual values obtained from various watersheds, and it is thus limited when considering the individual characteristics of each watershed. However, if the watershed size is sufficiently large, spatial representativeness can be acknowledged to some extent. Nonetheless, pollutant discharge from non-point sources heavily depends on rainfall and seasonal factors, making it difficult to directly apply average annual unit values to real-time discharge analysis. Similarly, individually dispersed point sources also exhibit such tendencies.

Development of the Delivery Load

The MLM is not related to load; therefore, to identify the relationship between water quality and pollutant loads, we modified the MLM to include seasonality in the delivery load equation (Equation (9)):

$$L_{dd}=R_t{L}_t+f\left({L_p}^k+\alpha L_n{q_n}^{\beta }\right)$$

(9)

where $L_{dd}$ is the pollutant delivery load (kg/d), $R_t$ is the effluent delivery ratio from STP, $L_t$ is the effluent load from STP (kg/d), $L_p$ is the discharge load from an individual point source (kg/d), $k$ is the delivery coefficient for an individual point source discharge load, $L_n$ is the annual average discharge load from a non-point source (kg/d), and $q_n$ is the efflux height from a non-point source (mm/d).

Assuming that the discharge load from STP and individual point sources were delivered at a constant delivery ratio (R), that from individual non-point sources was calculated considering the efflux height. Generally, there is a distinct difference between the water quality before and after the summer rainy season. Before the rainy season, pollutants accumulate from non-point sources and scattered individual point sources, and they are washed away during the summer rains, resulting in poorer water quality in spring compared to autumn, even under the same flow rate conditions. The seasonal correction parameter corrects for this phenomenon:

$$f=e^{a\sin \left[2\pi T\right]+b\cos \left[2\pi T\right]}$$

(10)

$$q_n=\frac{Q-Q_t-Q_p}{A}\times 86.4$$

(11)

where $f$ is the seasonal correction parameter, $Q_t$ is the flow rate from STP (m³/d), $Q_p$ is the flow rate from an individual point source (m³/d), and $A$ is the area (km²).

This approach helps to interpret the changes in delivery loads based on flow rates and types of pollution sources. Specifically, dividing the delivery loads from each pollution source by the flow rate yielded their partial concentrations, enabling us to identify the contributions of each pollution source to water quality and delivery loads:

$$C_{pt}=\frac{R_t{L}_t}{Q}$$

(12)

where $C_{pt}$ is the partial concentration from STP (mg/L);

$$C_{pp}=\frac{f{L_p}^k}{Q}$$

(13)

where $C_{pp}$ is the partial concentration from an individual point source (mg/L);

$$C_{pn}=\frac{c{L}_n{q_n}^d}{Q}$$

(14)

where $C_{pn}$ is the partial concentration from a non-point source (mg/L).

The composition ratios of discharge loads for each pollution source group and the composition ratios of concentrations delivered to specific points in public water bodies are not identical. In other words, the loads discharged from STP remain relatively constant annually, while the non-point source discharge loads exert their influence only during specific periods of increased flow rate due to rainfall.

2.3. Water Quality and Load Data

Flow rate and water quality data were sourced from the Water Environment Information System, measured over 36 times a year at approximately 8-day intervals. Dates with missing values for flow rate and water quality were excluded. The data spanned from 2005 to 2022. Additionally, four water quality parameters were considered: BOD₅, T-N, T-P, and TOC (TOC has been measured since 2008).

The load date was determined using annual implementation evaluation data in the Gyeongan stream watershed.

3. Results and Discussion

3.1. Assessment of Application for Water Quality and Flow Rate

3.1.1. Coefficient Adjustment

A regression analysis for the eight coefficients of the MLM was conducted using Microsoft Excel (version 2019), employing monthly data for water quality and flow rate. The p-value based on the analysis is presented in

Table 1. Comparison of p-value by MLM category.

Category	p-Value
	${\mathit{\beta }}_0$	${\mathit{\beta }}_1$	${\mathit{\beta }}_2$	${\mathit{\beta }}_3$	${\mathit{\beta }}_4$	${\mathit{\beta }}_5$	${\mathit{\beta }}_6$	${\mathit{\beta }}_7$
BOD5	*	*	0.002	0.004	0.057	0.001	*	*
T-N	*	*	0.375	0.827	0.980	*	*	*
T-P	*	0.759	0.015	*	*	0.098	*	*
TOC	*	*	*	*	0.048	0.001	*	*

* p-value < 0.001.

. Figure 3 interprets the water quality variations in the Gyeongan stream watershed using the MLM. Excluding periods of unusually high or low measured values, the calculated results generally adequately reproduce the seasonal variations and annual changes observed in the measured data.

For the water quality parameter total nitrogen (T-N), the parameters ${\beta }_3$ and ${\beta }_4$, which indicates the trends in concentration over time, were statistically insignificant. Similarly, for the water quality parameter total phosphorus (T-P), the parameter ${\beta }_2$, which serves as a secondary cause for the concentration of the water quality parameters relative to flow rate, was also statistically insignificant. However, the ${\beta }_5$ value, a parameter in the cubic equation, was statistically significant for all water quality parameters except T-P, suggesting that Cohn’s formula was appropriately modified.

3.1.2. Application of MLM

Flow Regime Analysis

Assuming constant terms for annual flow rate-related and seasonal-related factors (Equation (3)) enables the trend of annual water quality changes to be evaluated while excluding the effects of flow rate and seasonality. In this study, the time for the seasonal term was set to the 15th day of each month, and water quality was applied as the monthly average, while the flow rate was tracked using monthly flow rate data from a representative year with typical flow rate conditions over a long period. The representative year was selected as the year closest to the median value of the monthly average flow rate and the median value of the standard deviation of the monthly average flow rate for each year, and the year 2022 was therefore determined as the representative year in the Gyeongan stream watershed (Figure 4).

Coefficient Input

The flow rate and water quality data from 2005 to 2022 were input into the MLM (Equation (6)). The coefficients are presented in

Table 2. Comparison of MLM coefficients.

Category	${\mathit{\beta }}_0$	${\mathit{\beta }}_1$	${\mathit{\beta }}_2$	${\mathit{\beta }}_3$	${\mathit{\beta }}_4$	${\mathit{\beta }}_5$	${\mathit{\beta }}_6$	${\mathit{\beta }}_7$
BOD5	0.623	−0.236	−0.004	−0.023	0.001	−0.001	0.307	−0.486
T-N	1.537	0.053	0.024	0.001	0.000	0.000	0.185	0.482
T-P	−2.653	−0.043	−0.012	−0.122	0.011	0.000	0.147	−0.168
TOC	1.128	−0.138	0.065	−0.031	−0.002	0.000	0.090	−0.213

.

Except for the T-N concentration, the ${\beta }_1$ values of all water quality parameters were negative, suggesting that most pollutants discharged into the Gyeongan stream watershed were from point sources. This is due to the specific characteristics of the watershed, which has 12 STPs (6 in Gwangju city and 6 in Yongin city) [38,39]. However, the ${\beta }_1$ and ${\beta }_2$ values of the T-P concentration, a target substance for the TMDL, converged to zero, implying that most T-P was discharged from environmental infrastructure.

A positive ${\beta }_3$ value indicates an increase in concentration and vice versa, and it is thus possible to predict from the coefficients that the concentrations for all water quality parameters, except for T-N, will decrease over time.

Improvement in Water Quality

We applied the coefficients derived through regression analysis (Table 2) to the MLM (Equation (6)) to assess the changes in water quality over time from 2005 to 2022 (Figure 5).

The TMDL was voluntarily implemented before 2013 and became mandatory from 2013 onwards. The concentration changes (slopes) of target substances, such as biochemical oxygen demand (BOD₅) and T-P, showed negative slopes, indicating improved water quality. The larger slope during the voluntary phase compared with that during the mandatory phase can be attributed to the expansion of the environmental infrastructure, which was facilitated by prioritized financial support. Notably, the T-P concentration drastically improved, likely owing to the execution of reduction plans (advanced treatment) under the TMDL. This supports the results of previous studies that showed the expansion of STPs in the watershed following implementation of the TMDL: the construction of public STPs and the installation of T-P treatment facilities have strengthened discharge water quality standards [20].

Before the TMDL was implemented, substances such as BOD₅ and T-P were primarily discharged into streams by private STPs (BOD₅ discharge concentration < 20.0 mg/L). However, since the implementation of the TMDL, they have mainly been discharged by public STPs (BOD₅ and T-P discharge concentrations < 5.0 and <0.200 mg/L), resulting in reductions. Although the slope was larger during the voluntary phase owing to the discharge of high-concentration wastewater, the concentration has been either maintained or levels have improved consistently since the mandatory phase of the TMDL.

The T-N concentrations also decreased, despite not being a target TMDL substance. This is likely because they were not discharged by individual treatment facilities, but by public STPs which have a discharge concentration of <20.000 mg/L (as private STPs < 50 m³ have a discharge concentration of <40.000 mg/L). There were no considerable changes in the total organic carbon (TOC) concentration.

Water quality is highly dependent on the flow rate, which makes it difficult to draw conclusions when making simple comparisons; therefore, it is necessary to exclude the flow rate. The changes in water quality, while excluding the flow rate, were obtained by applying the coefficients derived from regression analysis to the MLM and using the median values obtained from the flow regime analysis (

Table 3. Annual change in the concentrations using the MLM.

Year	BOD5						T-N
	Observed		Calculated		Simulated		Observed		Calculated		Simulated
	AC *	SD **	AC *	SD **	AC *	SD **	AC *	SD **	AC *	SD **	AC *	SD **
2005	3.7	1.79	4.0	1.84	4.2	1.96	6.5	3.32	6.4	2.12	6.3	2.17
2006	4.3	1.73	3.4	1.20	3.6	1.69	5.9	1.70	5.8	2.00	5.8	1.99
2007	3.4	2.19	3.0	1.17	3.2	1.50	5.8	2.30	5.5	1.85	5.5	1.85
2008	2.7	1.46	2.8	1.06	2.9	1.36	5.3	1.94	5.2	1.75	5.2	1.76
2009	3.1	1.60	2.8	1.13	2.7	1.25	5.2	2.12	5.1	1.71	5.1	1.70
2010	2.2	1.28	2.4	0.95	2.6	1.18	5.1	1.60	5.0	1.69	5.0	1.66
2011	2.4	1.36	2.2	0.71	2.4	1.12	5.5	2.46	5.0	1.54	4.9	1.64
2012	2.6	1.58	2.3	1.14	2.4	1.08	5.3	2.42	5.0	1.62	4.9	1.63
2013	2.0	0.80	2.1	0.82	2.3	1.05	4.4	1.46	4.9	1.65	4.9	1.63
2014	3.2	2.00	2.4	1.09	2.2	1.02	4.6	1.94	4.9	1.70	4.9	1.63
2015	2.5	1.11	2.4	1.03	2.2	1.00	4.7	2.14	4.9	1.73	4.9	1.63
2016	2.5	1.03	2.2	0.84	2.1	0.98	4.8	1.72	4.9	1.74	4.9	1.63
2017	2.1	1.24	2.3	1.08	2.1	0.95	5.8	1.94	4.8	1.64	4.9	1.62
2018	2.2	1.13	1.9	0.66	2.0	0.92	5.2	1.82	4.8	1.65	4.8	1.59
2019	2.1	1.08	2.1	1.00	1.9	0.88	4.5	1.48	4.6	1.62	4.6	1.55
2020	1.6	0.52	1.7	0.80	1.8	0.83	4.2	1.16	4.4	1.51	4.4	1.49
2021	1.5	0.59	1.7	0.61	1.7	0.77	3.8	1.32	4.1	1.47	4.2	1.41
2022	1.7	0.87	1.5	0.70	1.5	0.70	3.9	1.26	3.8	1.31	3.8	1.32
Year	T-P						TOC
	Observed		Calculated		Simulated		Observed		Calculated		Simulated
	AC *	SD **	AC *	SD **	AC *	SD **	AC *	SD **	AC *	SD **	AC *	SD **
2005	0.264	0.10	0.339	0.07	0.343	0.07	-	-	3.1	0.49	3.1	0.58
2006	0.315	0.08	0.276	0.05	0.277	0.05	-	-	3.3	0.32	3.4	0.64
2007	0.245	0.09	0.222	0.04	0.224	0.04	-	-	3.5	0.44	3.6	0.69
2008	0.223	0.06	0.182	0.03	0.182	0.04	3.7	0.82	3.7	0.45	3.7	0.73
2009	0.213	0.07	0.150	0.03	0.150	0.03	4.5	1.16	3.9	0.53	3.8	0.75
2010	0.127	0.04	0.123	0.02	0.124	0.02	3.4	0.89	3.5	0.49	3.8	0.76
2011	0.124	0.04	0.102	0.02	0.104	0.02	3.7	0.95	3.7	0.39	3.8	0.76
2012	0.067	0.01	0.088	0.02	0.089	0.02	3.8	1.44	3.7	0.85	3.7	0.75
2013	0.062	0.02	0.077	0.01	0.077	0.01	2.9	0.40	3.4	0.45	3.6	0.73
2014	0.066	0.03	0.069	0.01	0.068	0.01	4.1	1.04	3.7	0.78	3.5	0.71
2015	0.049	0.02	0.063	0.01	0.062	0.01	3.9	0.93	3.6	0.79	3.4	0.69
2016	0.065	0.03	0.058	0.01	0.057	0.01	4.1	0.90	3.3	0.53	3.3	0.67
2017	0.058	0.02	0.055	0.01	0.054	0.01	3.3	0.68	3.5	0.83	3.2	0.64
2018	0.076	0.04	0.053	0.01	0.053	0.01	2.8	0.46	3.0	0.44	3.1	0.62
2019	0.075	0.02	0.055	0.01	0.054	0.01	3.1	0.61	3.2	0.78	3.0	0.61
2020	0.067	0.03	0.056	0.01	0.057	0.01	2.7	0.44	2.9	0.53	3.0	0.60
2021	0.067	0.03	0.062	0.01	0.061	0.01	2.9	0.37	3.0	0.38	3.1	0.60
2022	0.058	0.02	0.069	0.01	0.069	0.01	3.3	0.77	3.1	0.60	3.1	0.60

* AC: Average Concentration. ** SD: Standard Deviation.

, Figure 6).

The BOD₅ concentration (observed) was 3.7 mg/L in 2005, but it reduced to 1.7 mg/L in 2022, showing a 2.2-fold improvement. However, when excluding the flow rate, the concentration (simulated) reduced from 4.2 mg/L in 2005 to 1.5 mg/L in 2022, an approximately 3-fold improvement, suggesting that changes in water quality were more pronounced when the flow rate was excluded. Similarly, the T-P concentration (observed) reduced from 0.264 mg/L in 2005 to 0.058 mg/L in 2022, a 4.5-fold improvement: when excluding the flow rate, it (simulated) improved from 0.343 mg/L in 2005 to 0.069 mg/L in 2022, an approximately 5-fold improvement, indicating an even greater effect. Nevertheless, further studies are required to understand the reasons for any increases in concentration. For T-N, another water quality parameter, the measured and flow rate-independent concentrations showed similar values, with a 1.6-fold improvement. The TOC concentration showed a tendency to either increase or decrease, and no conspicuous change was observed. The application of the improved MLM and representative flow rate shows that it is possible to exclude water quality variations due to meteorological changes and identify the trend of water quality changes.

Indeed, applying the improved MLM with the representative flow rate enabled water quality fluctuations due to meteorological changes to be excluded and also enabled the identification of trends in water quality changes. Therefore, it was possible to conduct a detailed examination of variations in the meteorological flow rate and water quality.

3.2. Assessment of Application for Water Quality and Load

3.2.1. Load

Applying the TMDL involves post-management activities, including calculating the actual loads of various pollutants discharged in the previous year and establishing action plans in case the water quality degrades from the planned targets. The system consistently manages the load to prevent a reduction in the target water quality levels and to achieve the water quality goals of the final year.

Pollutant discharge data for the Gyeongan stream watershed have been accumulated since 2005, but considering initial implementation errors and other factors during the early stages of the program, data from 2007 to 2022 were utilized. Additionally, the discharge loads of TMDL target substances were divided into discharge loads from STP and point/non-point pollution sources (

Table 4. Annual change in discharge load in the Gyeongan stream watershed.

Year	BOD5				T-N				T-P
	Total	STP *	PS **	NPS ***	Total	STP *	PS **	NPS ***	Total	STP *	PS **	NPS ***
2007	9096	1094	4587	3415	7203	1582	2686	2935	676	130	288	258
2008	10,045	755	5596	3694	7893	1418	3352	3123	731	106	347	277
2009	10,201	631	5860	3711	8626	1364	4138	3124	793	84	436	273
2010	10,993	416	6604	3972	8582	1254	4017	3311	786	81	407	297
2011	8944	411	4384	4149	6731	1273	2344	3114	611	66	255	290
2012	12,342	366	7782	4194	8394	1266	3939	3189	900	65	527	308
2013	6491	344	2321	3826	6400	1538	1984	2878	484	12	208	265
2014	6294	534	2037	3723	5305	1489	980	2836	373	13	101	260
2015	5240	325	1292	3623	4884	1260	830	2794	366	9	103	255
2016	5059	311	974	3775	4876	1328	715	2833	340	8	78	254
2017	5033	293	1039	3701	4805	1291	710	2804	334	8	78	248
2018	5008	275	1104	3628	6472	1194	704	2774	328	9	78	241
2019	4982	258	1169	3555	4570	1127	698	2745	323	9	79	234
2020	5136	372	1234	3529	4508	1085	692	2731	326	11	79	236
2021	4365	269	1155	2940	4343	1158	701	2484	288	8	70	209
2022	4333	228	1148	2957	4357	1149	716	2492	290	11	73	206

* STP: Sewage Treatment Plant. ** PS: Point Source in Individual Sewage treatment System. *** NPS: Non-point Source in Individual Sewage treatment System.

).

We observed a significant decrease in the discharge load starting in 2013, which followed the mandatory implementation of the TMDL. This can be attributed to the successful execution of TMDL reduction plans (improvements in the discharge water quality from STP), and the changes in the STP discharge loads support this.

The point source discharge loads from STP and point sources decreased after the mandatory implementation of the TMDL in 2013, indicating the effectiveness of the system in improving water quality. However, although the 2022 revision to the TMDL Guidelines included additional individual reduction methods for land-based discharge sources, the reduction achieved was insufficient, indicating that improvements (such as the integrated management of non-point sources) are required.

3.2.2. Application of Delivery Load

The coefficients of the delivery load for BOD₅, T-N, and T-P based on water quality and loads from 2007 to 2022 in the Gyeongan stream watershed are presented in

Table 5. Coefficient values derived from the delivery load.

Category	${\mathit{R}}_{\mathit{t}}$	$\mathit{k}$	$\mathit{\alpha }$	$\mathit{\beta }$	a	b
BOD5	0.502	0.693	0.268	0.514	0.343	−0.656
T-N	0.473	0.749	0.937	0.930	0.249	0.586
T-P	0.593	0.324	0.196	1.174	0.278	−0.136

.

The daily variation in the seasonal correction parameters for each water quality parameter is presented in Figure 7. The seasonal correction parameter for BOD₅ peaked in early June and reached its lowest point in early December. The coefficient of variation for the year was approximately 50%, with an average value of 2.03 in May–June before the summer rainfall peak, which was significantly higher than the average value of 0.56 in October–November after the rainfall peak. This reflects the accumulation of pollutants from non-point sources and scattered point sources as well as the flushing effect of rainfall.

The seasonal correction parameter for T-N reached its maximum in January and minimum in July. Unlike BOD₅, T-N showed a more rapid flushing effect from summer rainfall in non-point sources and scattered point sources. This is likely due to N existing primarily in the ion form of nitrate N, which is mainly present in soil pores, making it more susceptible to flushing during summer rainfall. The coefficient of variation for the year was approximately 43%, with an average value of 1.83 in January–February, which was significantly higher than the average value of 0.55 in July–August.

The seasonal correction parameter for T-P peaked in early May and reached its lowest point in early November. Although the seasonal correction parameter for T-P showed a trend similar to that of BOD₅, the coefficient of variation for the year was relatively lower at approximately 22%. The average value in April–May was 1.34, which was higher than the average value of 0.75 in October–November, but the difference was less pronounced compared to BOD₅. The relatively lower variability in the seasonal correction parameter for T-P compared to BOD₅ and T-N can be attributed to the tendency of P to be adsorbed to soil particles, resulting in a smaller flushing effect from rainfall.

The relationship between the efflux height from non-point source ($q_n$) and the discharge coefficient of non-point source ($\mathsf{\alpha }{q_n}^{\beta }$) for each water quality parameter in the Gyeongan stream watershed is depicted in Figure 8, as per Equation (9). The discharge coefficient of non-point source ($\mathsf{\alpha }$) follows the order T-N (0.937) > BOD₅ (0.268) > T-P (0.196), indicating that N has the highest coefficient, followed by BOD₅ and then P. Similarly, the discharge flow rate exponent of non-point source ($\mathsf{\beta }$) is highest for T-P (1.174), followed by T-N (0.930) and BOD₅ (0.514), suggesting that P, with its strong adsorption to soil particles, is more sensitive to changes in flow rates compared to N and BOD₅. Conversely, BOD₅ and N exhibit lower sensitivity to rainfall, leading to relatively higher discharges even during low-flow rate periods and dilution effects during periods of increased flow rates.

According to the existing delivery load, the discharge load of the non-point source can be evaluated for different pollutant types under specific discharge flow rates. For instance, when the discharge flow rates for BOD₅, T-N, and T-P are 12.9 mm/d, 1.1 mm/d, and 4.0 mm/d, respectively, the corresponding values for the discharge load of the non-point source can be determined. Additionally, if the discharge flow rate doubles, the delivery load from non-point sources increases by 1.4 times for BOD₅, 1.9 times for T-N, and 2.3 times for T-P. Therefore, when the flow rate increases, the partial delivery concentration for BOD₅ decreases, while T-N remains relatively stable, and T-P increases. Moreover, the annual delivery load varies depending on the rainfall; it decreases in years with low rainfall and increases in years with high rainfall.

The annual average concentrations for each water quality parameter and the simulated annual average concentrations based on the 2022 baseline flow regime conditions, calculated using Equation (9), are shown in Figure 9. The simulated BOD₅ concentrations for 2022 baseline flow regime conditions can be utilized to estimate water quality changes attributed to artificial pollution sources, excluding the influence of annual variations in water quality due to flow rates and uncertain factors. While the actual annual average BOD₅ concentration showed significant fluctuations over the year, the simulated annual average BOD₅ concentration under the 2022 baseline flow regime conditions demonstrated a continuous decreasing trend annually. This was attributed to the total discharge load of BOD₅, which increased from 2007 to 2010 and then decreased, mainly due to the continuous reduction in discharge loads from environmental infrastructure facilities, which significantly affected the delivery concentration.

The actual annual average T-N concentration showed significant fluctuations over the year, but the simulated annual average T-N concentration under the 2022 baseline flow regime conditions demonstrated a continuous decreasing trend annually. Similar to BOD₅, the total discharge load of T-N increased from 2007 to 2010 and then decreased. However, the continuously decreasing trend in the simulated T-N concentration, as shown in Table 3, was attributed to the continuous reduction in discharge loads from STP, which significantly affected the delivery concentration. The difference between the simulated and actual annual concentrations did not exhibit a specific trend, indicating that the variability in the N delivery concentration from non-point pollution sources depended more on seasonality than flow rates.

The T-P concentration of the actual annual average showed a continuous decreasing trend over the years, and it dropped significantly after the sharp decline in discharge loads from STP after 2012. Similar to BOD₅ and T-N, the total discharge load of T-P increased from 2007 to 2010 and then decreased. However, the continuous decrease in the simulated T-P concentration, as depicted in Table 3, can be interpreted as the result of the continuous reduction in discharge loads from STP, which significantly affected the delivery concentration.

According to prior research by Choi et al. [40], if the coefficient of determination (R²) is 0.5 to 0.6 or higher, it effectively reflects the trend value of the delivery ratio regression analysis. The applicability derived in this study (BOD 0.50, T-N 0.60, T-P 0.91) is judged to be high, as verified in studies by Park [12], Hwang et al. [26], Lee et al. [29], and Kim et al. [41].

For the BOD₅ partial concentration, the discharge load in 2022 predominantly originated from non-point sources, rather than point sources. Although most of the delivery load was due to non-point sources, the concentration was determined by point sources (Figure 10). However, the high contribution ratio of discharge loads from non-point sources did not necessarily indicate a large occurrence of non-point pollution. Instead, it simply indicated that relative to the total discharge load, non-point sources appeared more significant as point sources were managed through the TMDL (the T-N discharge load was the same as BOD).

Similarly, the discharge load for the T-P partial concentration was consistent with that of BOD₅. However, the contribution to water quality from point and non-point sources was ~1:1, with P being released into the Gyeongan stream watershed due to rainfall. It is necessary to address these factors in the TMDL plan. Therefore, it is suggested that managing point sources in the Gyeongan stream watershed is crucial for reducing the BOD₅ concentration, while the T-P concentration from point and non-point sources requires management.

4. Conclusions

This study was conducted to analyze the improvements in water quality following the implementation of the TMDL in the Gyeongan stream watershed. The MLM was applied to reinterpret water quality and flow rate data, and a delivery load was developed to analyze the impact of loads on water quality. The rainfall dependence of specific water quality parameters was effectively analyzed using a log-linear model (L-Q Equation). However, it was challenging to apply this to unmeasured watersheds, highlighting the need to employ the MLM to interpret long-term water quality changes and seasonal variations.

By assuming constant annual and seasonal effects, the influence of flow rate and seasonal variations on water quality changes could be excluded, allowing for the estimation of annual water quality change trends. In particular, a significant decrease in T-P was observed, which can be attributed to the effect of TMDL management (advanced treatment of STP). While annual average concentrations showed significant fluctuations, applying the baseline flow regime criteria helped identify consistent trends in water quality changes, excluding the influence of meteorological variations on flow rate.

While the existing delivery load is excellent for calculating discharge loads by aggregating non-point and point source loads, it may inaccurately reflect the reduction effects of pollution loads from the STP and individual point sources when summed together. Therefore, a new delivery load was developed to address this issue. The developed delivery load incorporates a rational interpretation of the reduction effects of pollution loads from the STP and individual point sources, and it accounts for the flow rate dependency of non-point source loads (adjusted by flow rate and seasonal functions). The continuous improvement in water quality for all parameters was evaluated, demonstrating the utility of excluding the influence of flow rate-related water quality fluctuations and uncertainties to estimate water quality changes due to anthropogenic pollution sources.

The MLM and the delivery load proposed in this study provide a rational relationship between flow rate and water quality, making them valuable tools for assessing TMDL. The results derived from this study can serve as fundamental data for planning purposes and as objective evaluation criteria for analyzing flow rate dependency. It is anticipated that future research will focus on validating the models proposed in this study across various watersheds and integrating them with existing water quality models to enable the effective implementation of TMDL management planning.