A Study of the Effect of Lake Shape on Hydrodynamics and Eutrophication

Abstract

As an important part of the urban landscape, lakes not only enhance the overall environmental quality of a city, but also strengthen the residents’ sense of well-being and cultural identity. With the acceleration of urbanization, the water quality and ecological health of urban lakes have become increasingly prominent issues. However, there is a lack of quantitative research on the effects of lake shape on the spatial and temporal distribution of hydrodynamics and water quality. Using the Environmental Fluid Dynamics Code (EFDC) model, this study simulates the hydrodynamic characteristics and water quality responses of an urban lake in Tianjin, focusing on the critical role of lake shape in regulating hydrodynamics and water quality. By quantifying the relationship between lake landscape indices (e.g., shape index, Fractal Dimension) and hydrodynamic parameters, this study reveals how lake shape regulates water flow characteristics and nutrient distribution, thereby influencing eutrophication risk. The results show that regular lakes (e.g., Lake B) exhibit higher flow velocities (0.027 m/s) and significantly lower chlorophyll-a concentrations (6–9 μg/L), reducing eutrophication risk, whereas complex-shaped lakes (e.g., Lake X) have lower flow velocities (0.0087 m/s) and higher localized chlorophyll-a concentrations (13–15 μg/L), increasing the risk of eutrophication. This study systematically quantifies the impact of lake shape on hydrodynamic characteristics and water quality distribution, providing a scientific reference for lake shape optimization, precise water replenishment, and water quality management.

1. Introduction

Urban lakes are an important part of the ecosystem, assuming a variety of functions such as biodiversity protection, climate regulation, and mitigation of the urban heat island effect [1,2]. As an important part of the urban landscape, lakes not only improve the overall environmental quality of a city but also enhance the residents’ sense of well-being and cultural identity [3]. For example, many lake parks have become important places for urban residents’ leisure, fitness, socialization, and cultural activities, providing space for walking, viewing, fishing, boating, and other activities. In addition, some historic urban lakes carry local cultural memories and are closely related to regional cultural development, becoming part of citizens’ collective memory and local cultural symbols [4,5]. Therefore, when exploring the impact of lake morphology on water quality, attention should also be paid to its cultural ecosystem services to ensure that the ecological functions and social values of lakes can be synergistically optimized.

However, with the rapid advancement of industrialization and urbanization, the water quality and the eutrophication of urban lakes have become increasingly serious. This not only affects the quality of life of residents, but also poses a threat to urban ecological health [6,7]. The problem of eutrophication is prevalent in lakes globally, and its nature is due to the excessive input of nutrients such as nitrogen and phosphorus, leading to abnormal algal growth and frequent blooms [8]. Studies have shown that algal blooms are driven by a combination of multiple factors, among which hydrodynamic conditions such as flow velocity and water disturbance play a key role in nutrient transport and distribution [9,10,11,12]; water environmental factors, including nutrient concentration, water temperature, dissolved oxygen, and acidity/base, provide suitable conditions for phytoplankton growth [13]; and meteorological conditions such as temperature and precipitation indirectly influence phytoplankton growth and bloom by altering the physical and chemical properties of the water body [14]. For example, hydrodynamic environments with low to moderate flow rates are thought to be favorable for rapid cyanobacterial and green algal blooms, whereas excessively high flow rates may inhibit algal aggregation [15]. In addition, it has been shown that extreme temperature increases or decreases in precipitation may increase the risk of blooms by exacerbating the stratification stability of the water column [16,17,18]. Despite the large number of studies on hydrodynamic, hydrometeorological, and meteorological factors, there is still a lack of research on how lake morphology regulates the combined effects of these drivers [19,20,21].

Numerical models have been widely used in the study of lake ecosystems to simulate the complex mechanisms of physical, chemical, and biological processes in water bodies. Currently, models such as WASP, RCA, and MIKE have achieved remarkable results in the field of water quality simulation [22]. For example, Hernandez et al. used the WASP5 model to study the interactions of environmental factors in reservoirs [23]; the RCA model integrates modules such as eutrophication and sediment fluxes to simulate water quality changes in bays and lakes [24,25]; and the MIKE model can comprehensively simulate hydrological and water quality processes [26]. However, the EFDC model has a significant advantage in the study of complex water body environments due to its ability to simulate lake hydrodynamics and spatial and temporal distribution of pollutants simultaneously [27]. Although the EFDC model has been successfully applied to several lake systems, its application in the context of urban lakes is still insufficient [28,29].

In this study, a coupled hydrodynamic and water quality model of an urban lake in Tianjin was constructed based on the EFDC model, and an in-depth study was carried out around the lake morphology, aiming to (1) reveal the hydrodynamic characteristics of different lake morphologies and quantify the effects of lake shape on the distribution of flow velocity and flow field; (2) assess the effects of lake morphology on the spatial and temporal distribution of water quality parameters (e.g., dissolved oxygen (DO), chemical oxygen demand (COD), total nitrogen (TN), total phosphorus (TP), and chlorophyll-a (Chl-a)); (3) analyze the response relationship between the lake flow field and water quality parameters by simulating different recharge conditions (see Section 4.2), providing a scientific basis for water quality management and control of eutrophication; and (4) analyze the main influences on the water quality of the water body, and further screen out the features that are the most critical for the prediction of chlorophyll-a content.

2. Methodology

2.1. Study Region

This study takes the MJ Lake system in Tianjin as the research object. Located in the southwestern part of Tianjin city, it is an important ecological and recreational scenic area with a total water surface area of 1.7 million square meters. The MJ Lake system comprises three interconnected sub-lakes (Lake B, Lake N, and Lake X), linked by connecting gates to form a unified lake system. Lake B has a regular shape and a high flow rate, Lake N has an intermediate shape between regular and complex, and Lake X has a complex shape and a low flow rate (Figure 1). The lake system has only one recharge inlet, located on the southern side of Lake B, with the recharge water flowing into Lakes N and X through the connecting gates.

2.2. Calculation of the Landscape Indices

To quantify the effects of lake shape on hydrodynamics and water quality, the following landscape indices were calculated:

(1)

The shape index (SI) measures how compact the shape of the lake is with respect to a circle of the same area, with the following formula:

$$SI={\displaystyle \frac{P}{2\sqrt{\pi A}}}$$

(1)

where $P$ is the perimeter of the lake and $A$ is the area of the lake.

(2)

Fractional dimension (FD): Reflecting the complexity of lake morphology, the closer the fractional dimension is to 2, the more complex the shape. The formula is as follows:

$$FD={\displaystyle \frac{2\ln P/4}{\ln A}}$$

(2)

(3)

Near-circularity index (RCC): This assesses the degree of narrowness of a lake’s shape, where the larger the value, the narrower the shape. The formula is as follows:

$$RCC=1-{\displaystyle \frac{A}{A_S}}$$

(3)

where $A$ is the area of the lake and $A_S$ is the area of the smallest outer circle of the lake.

2.3. Model Construction and Data Sources

In this study, the EFDC (Environmental Fluid Dynamics Code) model recommended by the U.S. Environmental Protection Agency (EPA) was used to construct a coupled lake hydrodynamic and water quality model [30,31]. The model is based on the turbulent equations of motion of incompressible, variable-density fluids, and combines momentum equations, continuity equations, and equilibrium equations of water quality components, which can accurately simulate the physical, chemical, and biological processes in lakes. The specific settings of the model are as follows:

(1)

Model boundary conditions: these include lake topographic data, recharge flow, meteorological conditions (wind speed, wind direction, temperature, etc.), and initial pollutant concentrations.

(2)

Initial conditions: based on the summer monitoring data in 2020, initial water level, water temperature, DO, TN, TP, and Chl-a concentrations were set.

(3)

Grid division: a two-dimensional orthogonal grid was used, with a total of 8837 cells, in which the grid was refined in key areas such as the connecting gates to improve the simulation accuracy.

The data required for this study mainly came from the following two types of data:

(1)

Water quality monitoring data: collected according to the Environmental Quality Standard for Surface Water (GB3838-2002) [32], including water temperature, dissolved oxygen (DO), TN, TP, and Chl-a concentrations from July to September 2020, with a sampling frequency of every 15 days.

(2)

Meteorological data: provided by the China Meteorological Data Service Center, including wind speed, wind direction, rainfall, temperature, etc., with a data interval of 1 h.

3. Modeling and Validation

3.1. Model Building

The scope of the mathematical model included the entire lake watershed, a total of 8837 grid cells were set up using 2D orthogonal grid division, and the grid was encrypted in key areas such as the connecting gates to enhance the simulation accuracy (Figure 2). The initial conditions were based on the measured data from 1 July to 30 September 2018, including an initial water level of 6 m, a water temperature of 25 °C, a DO concentration of 5 mg/L, and a Chl-a concentration of 8 μg/L. Boundary conditions were set up in conjunction with the actual recharge flow rate and the meteorological conditions (e.g., wind speed and wind direction).

3.2. Design for Simulated Working Conditions

In order to investigate the role of lake shape in regulating the hydrodynamic characteristics and water quality distribution, simulation conditions for hydrodynamics and water quality were designed in this study, respectively.

3.2.1. Hydrodynamic Analysis Conditions

The lake flow field distribution is mainly affected by lake shape and recharge flow. In order to simplify the analysis and highlight the role of lake shape, a typical recharge condition of 1.0 m³/s (lasting for 10 days) was selected for hydrodynamic simulation. This flow rate is moderate and can reflect the main characteristics of the lake hydrodynamic changes, which helps to reveal the flow rate differences and circulation characteristics between regular and complex lakes.

3.2.2. Water Quality Analysis Conditions

To evaluate the effect of different recharge flow rates on water quality improvement, the following three working conditions were designed:

Low flow condition (0.5 m³/s): recharge lasted for 20 days to simulate the effect of slow recharge on nutrient diffusion and the risk of eutrophication in the retention area.

Medium flow condition (1.0 m³/s): recharge lasts for 10 days as a typical condition to assess the combined effect of lake shape on nutrient dispersion and Chl-a concentration distribution.

High flow condition (2.0 m³/s): recharge lasts for 5 days to analyze the response of rapid recharge to dynamic changes in lake water quality and the short-term flushing effect in complex lake areas.

3.3. Model Rate Determination

This study utilized measured data from 1 July to 10 August 2018 for model calibration. A typical recharge condition was chosen for the validation: during the period from 1 July to 10 July (days 1–10), the Lake B pumping station was turned on for recharge at a flow rate of 1.0 m³/s; then, it entered the quiescent phase (days 11–40) without further recharge. The water level of the lakes gradually decreased during the resting phase due to natural depletion such as evaporation.

Three monitoring points were set up in Lake B, mainly because of its more regular shape and larger area, in order to more comprehensively reflect the characteristics of water quality and flow rate distribution in the lake. Lake N and Lake X, due to their complex shapes and small areas, each had two monitoring points set up to cover the areas of significant hydrodynamic changes and eutrophication-sensitive areas, respectively. When analyzing, because of the high consistency of data between monitoring points, we selected the most representative monitoring point data in each lake for model validation and result analysis, and the specific locations are shown in Figure 1: Lake B takes the No. 2 monitoring point, Lake X takes the No. 5 monitoring point, and Lake N takes the No. 6 monitoring point. Three parameters of flow rate, TN, and TP were selected for validation and a comparison between the simulated and measured values is shown in Figure 3 and Figure 4.

As can be seen from the figure, the EFDC model shows high simulation accuracy in regular lakes (Lakes B and N), with the simulated values of flow rate, total nitrogen (TN), and total phosphorus (TP) having an error of less than 10% from the measured values; Nash-Sutcliffe Efficiency (NSE) is generally higher than 0.8, which reflects the characteristics of uniform flow rate and the easily captured distribution of water quality in regular lakes. In contrast, the complex lake (Lake X) has a complex shape and weak hydrodynamics in the local stagnation zone, resulting in slightly higher local errors in the model in the simulation of flow velocity and nutrient distribution, but the overall trend is still consistent with the measured values.

4. Analysis of Lake Flow Fields and Factors Affecting the Water Environment

This section focuses on analyzing the mechanism of lake shape on flow field distribution and eutrophication. By calculating the relationship between lake shape indices (e.g., shape index, fractional dimension number) and flow velocity distribution, it reveals how different lake shapes regulate hydrodynamic characteristics and water quality responses [33,34]. Based on this, the simulation analyses of different recharge conditions and stationary phases were combined to further verify the regulation of lake shape on the distribution of key water quality parameters (e.g., Chl-a concentration, TP concentration) and the risk of eutrophication. This study focuses on the differences in hydrodynamic characteristics and eutrophication risk between lakes with complex shapes and regular lakes and provides theoretical support for scientific water replenishment strategies and lake management.

4.1. Impact of Lake Landscape Indices on Lake Eutrophication

Lake shape further affects water quality conditions and eutrophication risk by influencing the flow characteristics of water bodies. To quantify the potential influence of lake shape on eutrophication, landscape indices, including the near-circularity index, shape index, and subdimensionality, were calculated for Lakes X, N, and B in this section, as shown in

Table 1. Table of lake landscape indices.

Location	Perimeter (m)	Area (10,000 m2)	Roundness Compactness Coefficient (RCC)	Shape Index (SI)	Fractal Dimension (FD)
Lake B	3407	20	2.15	0.61	0.67
Lake X	6700	16	4.72	1.24	0.88
Lake N	4126	37	1.91	1.08	0.80

.

From the table, it can be seen that the shape of Lake B is relatively regular, with lower values of the Roundness Compactness Coefficient (RCC) and Fractal Dimension (FD), indicating that its shoreline is relatively flat and the water body is more mobile, and therefore the risk of eutrophication is relatively low. The shape of Lake N is between regular and complex, and its shape index (1.91) and subdimension (1.08) indicate that the hydrodynamic characteristics are moderate, and the stability of the water quality is high, but there is still a certain risk. Lake X has the highest shape index (4.72), the largest number of dimensions (1.24), and a complex shoreline, which indicates that its shape may impede the flow of the water body, leading to localized nutrient accumulation and increasing the risk of eutrophication.

4.2. Characterization of Lake Flow Field Distribution

In this section, the flow field distribution characteristics of the lake are analyzed under a single recharge condition (1 m³/s), focusing on the flow velocity and flow rate changes in the connecting gates of Lake B and Lake N (connecting gate # 1) and Lake B and Lake X (connecting gate # 2), and revealing the influence of the lake morphology on the hydrodynamic characteristics.

4.2.1. Characteristics of Lake Flow Field Distribution During Recharge Phase

As shown in Figure 5, the average flow rate at the 1# connecting gate during the recharge phase (days 1–10) was 0.027 m/s, which was significantly higher than that at the 2# connecting gate (0.0087 m/s), while the average flow rate at the 1# connecting gate was 0.5 m³/s, which was also significantly higher than that at the 2# connecting gate (0.17 m³/s). This suggests that the connectivity of the water body between Lakes B and N is relatively strong, whereas the connectivity between Lakes B and X is relatively poor. The distribution of flow velocity and flow rate reflects the significant influence of lake morphology on hydrodynamics: Lake N is more open and regular in shape, which helps the water flow to enter quickly and spread evenly; in contrast, Lake X has a complex shape and poor connectivity, which leads to a significant reduction in water flow velocity and flow rate.

Due to its regular shape and high connectivity, Lake N has a uniform spreading path, high flow rate, and rapid velocity, which help to promote water mixing and reduce the risk of eutrophication. In contrast, Lake X has a complex shape and poor connectivity, and the diffusion of water flow in the recharge outlet is limited, leading to prolonged retention time in the low-flow region and further increasing the risk of nutrient accumulation. To improve the hydrodynamic characteristics of Lake X and mitigate the risk of eutrophication in localized areas, engineering optimization measures can be implemented near the recharge inlet, such as adjusting the geometric design of the connecting gates to enhance mobility or installing additional auxiliary pumping stations to improve the mixing efficiency of the water body.

During the recharge phase (days 1 to 10), the flow characteristics of the water body in Lake B were analyzed (as shown in Figure 6). Taking the fifth day as an example, the water body at the inlet (arrows) flowed northward along the main stream with a narrow initial range, but with the gradual expansion of the lake surface, significant circulation was formed in the center of Lake B (blue dotted frames). Circulation enhances the mixing capacity of the water column, but may also lead to localized areas of nutrient accumulation. In the southern part of Lake B, water flows rapidly into Lake N through the connecting gate # 1. Due to the regular shape and good connectivity of Lake N, the flow velocity is significantly accelerated and the spreading path of the water is more uniform (red frame).

In contrast, Lake X, due to its complex shape and poor connectivity, has a slow flow rate through the connecting gate # 2 and lacks significant circulation in most areas of the lake, especially in the southern and western areas of the complex shape, where mobility is significantly reduced. This hydrodynamic characteristic leads to insufficient renewal capacity of the water body and accumulation of pollutants and nutrients in the low-flow area, which significantly increases the risk of eutrophication.

When water flows through connecting gates from a narrow area into a wide body of water, circulation often forms at the outlet (as shown in Figure 7), a phenomenon that significantly affects the mixing and localized deposition of nutrient salts, which increases the risk of eutrophication. The increase in circulation intensity is usually accompanied by an increase in water retention time, which further promotes the release of nutrient salts from the sediments. To mitigate this problem, engineering measures, such as optimizing the geometric design of connecting gates, installing additional diversion gates, or adjusting the location of gates, can be taken, in conjunction with the morphological characteristics of the lake, to weaken the strength of circulation, improve flow field distribution, and reduce nutrient accumulation, thereby enhancing water quality stability.

4.2.2. Characterization of Lake Flow Field Distribution During Stationary Phase

During the stationary phase, the shape of the lake significantly affected the wind-driven water movement, showing the moderating effect of shape differences on circulation characteristics and water quality distribution (shown in Figure 8). Lake B, due to its regular shape, formed a wide circulation under the effect of the wind, which enhanced the water mixing and gas exchange, and effectively improved the uniformity and self-purification capacity of the water quality. The long and narrow morphology of Lake N led to the uneven strength of the circulation in the northern and southern parts of the lake, where the stronger northern circulation helped to maintain the stability of water quality, while the weak southern circulation increased the risk of eutrophication by prolonging retention time.

In contrast, Lake X, with its complex shape and zigzag shoreline, made wind-driven circulation difficult, especially in the southern and western regions of the complex shape, where stagnant flow led to reduced dissolved oxygen and pollutant accumulation, further exacerbating water quality degradation. After a 39-day resting period, the lake flow field stabilized, but the low-flow areas of the complex-shaped lake remain a potential hazard for eutrophication. To reduce the risk, it is recommended to combine the recharge strategy with the optimization of flow field characteristics to enhance water quality stability during the resting phase.

Lake morphology has an important influence on hydrodynamic characteristics and water quality distribution. Because of their regular shape and good connectivity, lakes with regular morphology are usually more likely to form a large-scale stable circulation, which promotes the mixing and flow of water bodies. On the other hand, lakes with complex shapes tend to have restricted circulation and more stagnant areas due to irregular shorelines and uneven flow distribution, which can easily lead to the accumulation of pollutants and deterioration of water quality. However, there is a lack of systematic analysis of how such morphological differences regulate the dynamic response of water quality parameters by influencing flow velocity distribution and retention time.

4.3. Characterization of Spatial and Temporal Distribution of Lake Water Quality

In this study, we systematically analyzed the regulation of lake morphology on the dynamic response of water quality parameters (e.g., DO, COD, TN, TP) by simulating three recharge conditions (0.5 m³/s recharge for 20 days, 1 m³/s recharge for 10 days, and 2 m³/s recharge for 5 days). The results show that different lake morphologies have significant effects on flow velocity distribution and retention time, which in turn regulate the spatial and temporal distribution characteristics of water quality parameters. The simulation results provide an important scientific basis for optimizing the recharge strategy and controlling the risk of eutrophication.

4.3.1. Characterization of Lake Water Quality Response During Recharge Phase

This section analyzes the change characteristics of lake water quality under three recharge conditions (0.5 m³/s recharge for 20 days, 1.0 m³/s recharge for 10 days, and 2.0 m³/s recharge for 5 days), and explores the regulating effect of lake shape on DO, COD, TN, and TP, providing a basis for scientific recharge strategies (shown in Figure 9).

The results showed that the water quality parameters of Lakes B, X, and N changed significantly under different recharge conditions and the shape of the lakes had an important role in regulating the flow rate distribution and water mixing. Under the low flow condition (0.5 m³/s recharge for 20 days), the dilution effect of recharge in Lake B was better, and the DO concentration was slightly increased, but due to the complex shape and low flow velocity in Lake X, the distal area formed an obvious hypoxic zone (DO lower than 3.0 mg/L) and the pollutant retention phenomenon (COD increased to 64.0–80.0 mg/L) occurred at the same time. Medium flow conditions (1.0 m³/s recharge for 10 days) enhanced the dilution effect of Lakes B and N. The DO concentration in the mainstream area locally increased to 14.0–15.0 mg/L, but pollutant accumulation still existed in the stagnant area of Lake X. The DO concentration in the mainstream area locally increased to 14.0–15.0 mg/L, but the pollutant accumulation still existed in the stagnant area of Lake X. The high-flow condition (2.0 m³/s recharge for 5 days) further improved the overall water quality of Lakes B and N and the distal DO concentration was partially increased to 6.0–8.0 mg/L. However, a transient water quality abnormality was observed in the localized area of Lake X due to sediment resuspension effects.

Lake shape and hydrodynamic characteristics significantly affect the water quality distribution under recharge conditions. This study shows that Lakes B and N are conducive to rapid diffusion and uniform mixing of recharged water due to their regular shape and good flow connectivity, while Lake X is prone to form low-flow areas due to irregular shoreline and uneven flow distribution, leading to the accumulation of nutrient salts and elevated risk of local eutrophication. In practical management, the recharge flow and timing should be optimized based on the lake’s shape to improve the renewal efficiency of the water body. At the same time, the combination of engineering measures (e.g., aeration or hydrodynamic regulation) improves water body mobility, equalizes the effects of water quality improvement, reduces the risk of eutrophication in distal areas, and enhances the stability of the lake ecosystem.

4.3.2. Characterization of Chl-a Distribution and Its Effects During the Stationary Phase After Recharge

This section analyzes the spatial distribution characteristics of Chl-a and its regulation mechanism after 30 days of resting under three recharge conditions and explores the role of lake shape and flow field characteristics in its distribution.

As can be seen in Figure 10, different flow regimes significantly affected the water quality distribution in the lake area. Under the low-flow condition (0.5 m³/s recharge for 20 days), the dilution effect of recharge was limited, and the concentration of Chl-a slightly decreased in the areas of Lakes B and N. The Chl-a concentration in the mainstream area of Lakes B and N was distributed in the range of 6.0–9.0 μg/L, but in the southern part of Lake X, due to the low flow rate, the Chl-a concentration increased to 10.0–12.0 μg/L, forming an obvious high-concentration accumulation area. Under the medium flow condition (1.0 m³/s recharge for 10 days), the Chl-a concentration in the areas of Lakes B and N was further reduced and uniformly distributed, with a concentration range of 4.0–7.0 μg/L. However, there was still an accumulation in the stagnant area in the western part of Lake X, with a Chl-a concentration of 10.0–12.0 μg/L, highlighting the persistent effect of uneven flow rate distribution. The dilution effect was most significant during the high-flow condition (5 days of 2.0 m³/s recharge), with the overall concentrations in Lakes B and N decreasing to 3.0–6.0 μg/L, which significantly improved water quality. However, short periods of high concentrations near the recharge inlet (9.0–12.0 μg/L) may have been caused by sediment resuspension.

Combined with the distribution characteristics of different conditions, Lake B and Lake N have significant dilution and diffusion effects due to their regular shapes and Chl-a concentrations tend to be uniformly distributed, whereas Lake X has a higher risk of eutrophication due to its complex shape and lower flow rate, as well as the persistence of the accumulation zone. It is recommended to optimize the recharge strategy according to the shape of the lakes in actual management and adopt intermittent recharge for lakes with complex shapes, such as Lake X. This should be combined with sediment management and hydrodynamic regulation measures to improve water quality in stagnant areas and reduce eutrophication risk.

4.3.3. Characterization of Temporal Changes in Chl-a of Lakes in the Stationary Phase

One monitoring point was selected in each of the three lakes to dynamically monitor the temporal change characteristics of Chl-a during the stationary phase. From Figure 11, the initial Chl-a content of the three lakes was about 12 μg/L. As the resting time increased, nutrients gradually accumulated, and Chl-a exhibited a rising trend, indicating that the risk of eutrophication of the water body gradually increased during the resting stage. There were significant differences in the rate of Chl-a rise among different lakes, in which the Chl-a content in Lake X was always higher than that in Lakes B and N, and the rate of increase was faster, eventually exceeding 16 μg/L, while Lakes B and N stabilized at approximately 14 μg/L and 13 μg/L, respectively (as shown in Figure 11).

Figure 12 shows the dynamic characteristics of the mean daily growth rate of Chl-a during the stationary phase in Lakes B, X, and N. The growth rates of Lakes B and N showed obvious positive and negative fluctuations in the ranges of −4% ~ +6% and −3% ~ +7%, respectively, indicating that the regular lake shapes facilitated water column mixing and reduced the risk of unidirectional nutrient accumulation. However, most of the growth rates in Lake X were positive and concentrated in +0.5% ~ +1.5%, indicating that the complex shape resulted in a less mobile water body with significant stagnation effects, providing continued favorable conditions for algal growth.

4.3.4. Chl-a Impact Factor Analysis

Chl-a is an important indicator of the degree of eutrophication in lakes and its concentration is influenced by a combination of factors, including DO, the concentrations of nitrogen and phosphorus nutrients (e.g., TN and TP), and lake shape characteristics. Lake shape indirectly affects changes in Chl-a concentration by regulating DO levels and the distribution of nitrogen and phosphorus nutrients in the water body. In this section, based on correlation analysis, the regulation of Chl-a concentration by DO and the distribution of nitrogen and phosphorus nutrients was systematically explored using the thermogram data of Lakes B, X, and N. The aim was to reveal the intrinsic relationship between lake shapes and water quality responses, providing a scientific basis for the management of eutrophication (as shown in Figure 13).

The analysis revealed that TP was the main driver of Chl-a concentrations (correlations 0.56 to 0.68), with the role of COD being more significant in Lakes X (0.55) and N (0.50). DO was negatively correlated with Chl-a in both cases (−0.40 to −0.50), suggesting that higher flow rates contribute to mitigating eutrophication. Lake shape indicators (SI and FD) had the highest correlations in Lake X (0.55 to 0.60), indicating that complex shape exacerbated nutrient accumulation with elevated Chl-a. Overall, regular lakes (Lake B) had the lowest risk of eutrophication, complex lakes (Lake X) had the highest risk, and moderately shaped lakes (Lake N) were relatively balanced. This suggests that lake morphology indirectly affects Chl-a concentration by regulating phytoplankton development, DO, and nutrient distribution, providing a scientific basis for water quality management.

5. Discussion

5.1. Accuracy of Hydrodynamic and Water Quality Modeling

In this study, the hydrodynamics and water quality of urban lakes were simulated using the EFDC model, and the results showed that the model has high accuracy in capturing the spatial and temporal distribution characteristics of water quality within the lakes. However, there are limitations in model applicability, such as failure to adequately account for the dynamic inputs of urban surface runoff during rainfall events, which may lead to an underestimation of the short-term impacts of sudden pollution loads. In addition, due to the local water depth of the study lakes being close to 7 m, it is difficult for the two-dimensional model to accurately simulate vertical stratification phenomena such as temperature stratification and dissolved oxygen stratification, which limits the accurate analysis of nutrient cycling and dissolved oxygen distribution.

Compared with other studies, the findings of this study complement theories on the effects of lake shape on hydrodynamics and eutrophication. For example, Seo et al. analyzed the role of hydrodynamics in regulating nitrogen and phosphorus transport using a coupled EFDC-WASP model in a study of the Lodong River, emphasizing the critical effect of hydraulic residence time on water quality [35]. This study further revealed the important role of lake shape in flow regulation and water quality distribution, a result that is complementary to Zhu et al.’s study on lake water quality in the middle and lower reaches of the Yangtze River [36]. In addition, Xu et al.’s study in Hong Kong showed that water bodies with low flow rates and high retention times are more prone to eutrophication, which is consistent with the findings of this study [37].

To improve the applicability of the model, future studies suggest incorporating a three-dimensional model to better capture stratification in the lake water column and dynamic meteorological data (e.g., rainfall intensity and wind speed and direction) to enhance the prediction of water quality changes under extreme climatic conditions. In addition, combining EFDC with other water quality models (e.g., MIKE or SWAT) can provide more layers of simulation results and further expand the understanding of hydrodynamic and water quality interactions.

5.2. Long-Term Effects of Recharge and Wind Action on Lake Water Quality

Water recharge and wind are important tools for water quality regulation in lakes. This study showed that different recharge strategies significantly affected the distribution of dissolved oxygen (DO), total phosphorus (TP), and total nitrogen (TN), while wind further contributed to the homogeneity of water quality parameters by enhancing the circulation of the water column. This is consistent with the study of Huisman et al. (2018), which demonstrated that water column mixing processes play an important role in the vertical distribution and growth of algae, emphasizing the criticality of hydrodynamic conditions in suppressing algal overgrowth [38]. The present study further demonstrated that an improvement in water retention effects due to wind-driven circulation can significantly reduce the risk of eutrophication in localized areas.

In addition, in areas with high Chl-a concentrations (e.g., southern part of Lake X), this study found significant diurnal fluctuations in DO concentrations. Photosynthesis increased DO concentration during the daytime, while respiration caused it to decrease at night. This dynamic change is consistent with the findings of Kim et al. (2021), who used machine learning analysis to point out that DO fluctuation is an important indicator for predicting the risk of cyanobacterial blooms [39]. This study further validated this mechanism with field data and found that areas with significant retention effects were particularly sensitive.

Although this study revealed significant effects of recharge and wind on lake water quality, there are still some limitations. For example, the wind simulation was based on historical meteorological data, which failed to adequately consider the potential effects of climate change on wind speed and direction. In addition, the long-term regulation of phytoplankton growth and algal bloom risk by recharge frequency and flow rate still needs to be further quantified and analyzed.

Future studies could focus on the combination of dynamic meteorological and hydrodynamic models to optimize recharge strategies and wind management. For example, Zhang et al. (2021) showed that dynamic adjustment of water replenishment frequency can significantly reduce the risk of algal outbreaks by coupling hydrodynamic model and climate model [40]. In addition, the development of a comprehensive model integrating ecological, hydrodynamic, and climate coupling will help to reveal the long-term impacts of the synergistic effects of water replenishment and wind on lake water quality.

6. Conclusions

In this study, through an in-depth analysis of the hydrodynamic characteristics and water environment characteristics of an urban lake in Tianjin, the EFDC model was used to successfully simulate the trend of the lake’s hydrodynamics and water quality changes, including the potential for eutrophication. After modeling, validation, and sensitivity analysis, the following conclusions were drawn, providing a scientific basis and practical guidance for lake water environment management and protection:

(1)

In this study, a two-dimensional coupled hydrodynamic and water quality model using the EFDC framework was successfully developed to simulate the lake’s hydrodynamics and water environment. Model validation shows strong agreement between simulated and measured values, with the Nash-Sutcliffe Efficiency (NSE) generally exceeding 0.80 for parameters such as water level, water temperature, DO, COD, TN, and TP. Among them, Lake N has the highest simulation accuracies in water temperature (NSE = 0.93) and TN (NSE = 0.90). Overall, validation confirms the model’s ability to accurately capture the spatial and temporal distribution characteristics of the lake water body.

(2)

Lake shape had a significant effect on the water quality response. Lake X had poor mobility and prolonged retention time due to its complex shape (shape index of 4.72, fractional dimension of 1.24), leading to significantly higher nutrient accumulation and algal bloom risk; in contrast, lake B had a regular shape (subcircularity index of 0.67) and high flow rate, with a relatively low risk of eutrophication. Correlation analysis showed that TP was the main driver of Chl-a concentration (correlation of 0.56-0.68, p < 0.01), while COD had a more significant effect on Lake X (0.55, p = 0.01) and Lake N (0.50, p = 0.02). Meanwhile, DO was negatively correlated with Chl-a (correlations of −0.40 to −0.50, p < 0.05), suggesting that higher flow rates had a positive effect on mitigating eutrophication. In addition, the correlation between lake shape indicators (SI and FD) and Chl-a reached the highest value in Lake X (0.55–0.60, p < 0.01), further confirming that complex shaped lakes are more likely to exacerbate the accumulation of nutrients and the risk of algal bloom.

(3)

Different recharge conditions had a significant regulatory effect on the water quality distribution of the lake. Under the recharge flow rate of 1.0 m³/s, the DO concentration in the area near the inlet of Lake B was significantly increased to 14.0–15.0 mg/L, while the DO concentration in most of the main body of the lake was maintained at about 3.0 mg/L and the overall water quality condition was improved. In contrast, in Lake X, due to low flow velocities, the DO concentration further decreased to less than 3.0 mg/L in some areas, while the COD concentration rose to more than 80.0 mg/L, indicating a higher risk of nutrient accumulation and water quality deterioration under low-flow conditions. In addition, wind promoted water mixing in the lake to some extent by enhancing water circulation. However, in Lake X, circulation was difficult to form effectively due to the limitations of complex shape and low flow velocities, resulting in the stagnant area remaining a major risk point for eutrophication. This result suggests that an improvement in lake water quality does not only depend on the recharge flow and frequency, but also needs to be considered in combination with the wind effect and the morphological characteristics of the lake.

(4)

In order to reduce the risk of algal bloom in Lake X, the frequency of water replenishment (once every 20 days) should be increased or the flow rate should be adjusted to enhance the dilution effect. This should be combined with engineering optimization measures (e.g., modifying the structure of the connecting gates and installing auxiliary pumping stations) to improve water mobility. For Lakes B and N, the existing replenishment frequency and flow rate can be maintained, while strengthening water quality monitoring during the resting phase. Wind can also be utilized to promote circulation and enhance water mixing, reducing the risk of localized eutrophication.