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Article

Spatiotemporal Analysis and Risk Prediction of Water Quality Using Copula Bayesian Networks: A Case in Qilu Lake, China

by
Xiang Cheng
1,2,
Shengrui Wang
1,2,3,
Yue Dong
1,2,*,
Zhaokui Ni
1,2 and
Yan Hong
1,2
1
Guangdong-Hong Kong Joint Laboratory for Water Security, Beijing Normal University, Zhuhai 519087, China
2
Center for Water Research, Advanced Institute of Natural Sciences, Beijing Normal University, Zhuhai 519087, China
3
Yunnan Key Laboratory of Pollution Process and Management of Plateau Lake Watershed, Kunming 650034, China
*
Author to whom correspondence should be addressed.
Processes 2024, 12(12), 2922; https://doi.org/10.3390/pr12122922
Submission received: 14 November 2024 / Revised: 6 December 2024 / Accepted: 12 December 2024 / Published: 20 December 2024
(This article belongs to the Special Issue State-of-the-Art Wastewater Treatment Techniques)
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Abstract

Lake water pollution under anthropogenic influences exhibits characteristics of high uncertainty, rapid evolution, and complex control challenges, presenting substantial threats to ecological systems and human health. Quantitative risk prediction provides crucial support for water quality deterioration prevention and management. This study employed the Copula Bayesian Network model to conduct a comprehensive risk assessment of water quality in Qilu Lake, China (2010–2020), incorporating inter-indicator correlations and multiple uncertainty sources. Analysis revealed generally “worse” water quality conditions (5.10 ± 1.35) according to established index classifications, with predicted probabilities of reaching “deteriorated” status ranging from 11.80% to 47.90%. Significant spatial and temporal variations in water quality and pollution risk were observed, primarily attributed to intensive agricultural non-point source loading and water resource deficiency. The study established early warning thresholds through key indicator concentration predictions, particularly for the southern region where “deteriorated” risk levels corresponded to specific ranges: TN (3.42–8.43 mg/L), TP (0.07–1.29 mg/L), and CODCr (27.75–67.19 mg/L). This methodology effectively characterizes lake water quality evolution while enabling risk prediction through key indicator monitoring. The findings provide substantial support for water pollution control strategies, risk management protocols, and regulatory decision-making for lake ecosystem administrators.

Graphical Abstract

1. Introduction

Lakes constitute essential freshwater ecosystems on Earth, serving critical functions in water purification, climate regulation, and biodiversity maintenance while fundamentally supporting human society and economic development [1]. However, intensifying anthropogenic activities and continuous socioeconomic development have significantly compromised lake ecosystem health [2]. Contemporary lakes face numerous ecological challenges, particularly eutrophication and recurring cyanobacterial blooms, which substantially impact regional ecological security and socioeconomic development [3]. A comprehensive analysis of lake water pollution enables the thorough assessment of ecological environments and associated risks, facilitating the precise identification of water quality issues and the effective implementation of water quality management strategies.
Water quality assessment serves as a fundamental prerequisite for pollution control and water resource management [4]. While single-factor water quality assessment methods offer computational simplicity, they provide limited unilateral results that inadequately represent comprehensive water quality conditions [5]. Consequently, comprehensive evaluation methodologies have gained widespread adoption in surface water quality assessments [6]. Notable applications include the Water Pollution Index (WPI) for Fuxian Lake evaluation [7], Water Quality Index (WQI) for Taihu Lake assessment, Canadian Council of Ministers of the Environment Water Quality Index (CCME-WQI) for Three Gorges Reservoir analysis, and Nemerow Pollution Index (NPI) for urban surface runoff evaluation [8]. This study employs the NPI methodology, which effectively emphasizes severely polluted parameters while accounting for better-quality indicators, thus avoiding arbitrary parameter weighting in computations.
Risk assessment provides an effective framework for environmental management, enabling the identification of critical risk sources [9], outcome prediction [10], and streamlined decision-making processes. Traditional water environmental risk assessment approaches encompass artificial neural networks [11], hierarchical analysis [12], fuzzy integrated evaluation models [13], and gray clustering assessment models [14]. However, these non-probabilistic methods potentially generate ambiguous results, understating the overall risk levels. Probabilistic approaches, particularly Bayesian network (BN) models, offer superior uncertainty quantification through probabilistic causality representation [15]. BN models have demonstrated increasing utility in ecological risk analysis [16], water quality risk assessment [17], and human health risk assessment [18]. These models effectively address high-variability, complex, and uncertain scenarios [19] through directed acyclic graphs (DAGs) and conditional probability tables (CPTs), integrating expert knowledge bases [20] with empirical datasets [21] for comprehensive modeling analyses [22]. To address BN limitations in high-dimensional joint probability distribution construction, Copula functions are introduced, enabling the direct representation of key indicators’ joint distributions for multifactor risk analysis.
Qilu Lake, among Yunnan Province’s nine plateau lakes, exhibits severe contamination levels. Rapid socioeconomic development and improper water resource utilization within the basin have exacerbated ecosystem degradation, water quality deterioration, and eutrophication [23]. Post-2012, the lake has experienced significant water quality degradation and water volume reduction, with total nitrogen (TN) and chemical oxygen demand (CODCr) exceeding Class V surface water standards. This study addresses these challenges through the following three primary objectives: (1) the evaluation of water pollution status and spatiotemporal variations using the Nemerow Pollution Index; (2) the implementation of an integrated Copula–Bayesian network model for comprehensive water quality risk assessment, accounting for inter-indicator correlations and multiple uncertainty sources; and (3) the prediction of water quality risk levels and critical indicator concentration ranges through the Bayesian network model to establish effective early warning mechanisms for lake protection and management.

2. Materials and Methods

2.1. Study Area

Qilu Lake is located in Yuxi city, Yunnan Province, on the Yunnan–Guizhou Plateau (24°4′~24°14′ N, 102°33′~102°52′ E; Figure 1). The lake surface elevation is 1796.62 m (highest water level), the surface area is 36.95 km2, the average depth is 4.0 m, and the residence time is 1.53 years [24]. From 2010 to 2020, the average water level was 1794.65 m, corresponding to an annual storage volume of 110 million m3 and a water resource volume of 37.24 million m3. Seasonally, water levels peak between July and September, driven by the summer monsoon’s concentrated rainfall, and reach their lowest between March and April due to the dry season’s limited precipitation and high evaporation. The region experiences a subtropical southwestern monsoon climate, characterized by a mean annual precipitation of 881 mm and an average temperature of 15.6 °C. As a closed plateau shallow lake, Qilu Lake receives inflow from four tributaries without natural outflow channels. The watershed, supporting a population exceeding 300,000, plays a crucial role in Tonghai County’s socioeconomic development through multiple ecosystem services.
To capture the spatial heterogeneity of water quality in Qilu Lake, three sampling sites were established. Site S is located in the shallow western region (1–3 m depth), adjacent to intensive agricultural land. Site C is situated in the central–eastern mid-depth zone (3–5 m depth), primarily influenced by urban and rural development. Site N lies in the deep eastern region (5–7 m depth), surrounded by forest and grassland buffers. This distribution enables a comprehensive analysis of the interactions between water depth, adjacent land use, and water quality parameters across environmental gradients, contributing to a thorough understanding of lake dynamics.

2.2. Analysis Methods

2.2.1. Water Quality Comprehensive Assessment Method

Water quality data from three routine monitoring stations in Qilu Lake were collected, preserved, and analyzed monthly over an 11-year period (2010–2020). Climatic parameters included precipitation (PP) and air temperature (AT), with observation periods divided seasonally, as follows: spring (March–May), summer (June–August), autumn (September–November), and winter (December–February).
The Nemerow Pollution Index (NPI) was employed for comprehensive water quality evaluation [25]. This method effectively combines average and maximum pollutant values, which are particularly suitable for scenarios where individual contaminant concentrations exceed thresholds while mean values remain compliant. Eight parameters were selected to comprehensively represent surface water quality—physical–chemical indicators (pH and dissolved oxygen), nutrient parameters (total nitrogen, total phosphorus, and ammonia nitrogen), and organic pollution indicators (chemical oxygen demand, permanganate index, and five-day biochemical oxygen demand). These parameters were evaluated against Class I–V standards (the national surface water quality standards GB3838-2002) [26], establishing six water quality grades (Table 1). The NPI was calculated using the following equations:
P i = C i S i ,
N P I = P i a v e 2 + P i m a x 2 2
where Ci represents the measured concentration of water quality indicators, Si denotes the standard concentration for each indicator, Piave is the average value of Pi, and Pimax is the maximum value of Pi.

2.2.2. Mann–Kendall Test

The Mann–Kendall (M–K) test, a nonparametric statistical method, was implemented to quantify temporal trends in water quality parameters. This distribution-free approach demonstrates a robust performance with outliers. Mutation points were identified at UF and UB curve intersections within ±1.96 confidence intervals. Significant trend changes were indicated by |UFi| > 1.96 [27].

2.2.3. Copula-Based Bayesian Network (CBN)

This study implemented a nonparametric Bayesian network model incorporating Copula functions to conduct a comprehensive, dynamic risk assessment of water quality indicator interactions. The Copula-based Bayesian Network (CBN) model demonstrates superior capabilities in handling nonlinear environmental data compared to conventional regression models, effectively capturing and modeling complex interdependencies among environmental variables. The graphical architecture of CBN facilitates a visual representation of variable relationships, enhancing the interpretability of environmental interactions.
The Bayesian network structure was optimized through an integrated approach combining mutual information and hill-climbing algorithms (MI&HC). This methodology initially establishes the network structure through mutual information analysis, followed by optimization via the hill-climbing algorithm, thereby addressing fundamental limitations of traditional hill-climbing approaches. While mutual information serves as a conventional metric for variable correlation assessment, the computation of joint probability density functions presents significant complexity. The implementation of Copula entropy-based mutual information estimation substantially enhances both computational accuracy and efficiency. This approach leverages the intrinsic relationship between Copula entropy and mutual information, transforming the mutual information estimation challenge into a Copula entropy calculation, thus enabling rapid and precise computation. Detailed operational procedures and mathematical formulations are provided in the Supplementary Materials.

2.3. Data Processing

Data processing and statistical analyses were conducted using multiple specialized software platforms. Primary data management was performed using MS Office 2016, while statistical analyses, including Mann–Kendall trend tests and correlation analyses [28], were executed in R software (version 4.2.0). The Copula-based Bayesian Network (CBN) modeling was implemented through R (version 4.2.0) and UNINET (version 3.1.3), an uncertainty analysis software package developed by Delft University of Technology [29,30]. All statistical analyses maintained a significance threshold of p < 0.05.

3. Results

3.1. Comprehensive Characterization of the Water Quality in Qilu Lake

3.1.1. Water Quality Analysis in Qilu Lake

Qilu Lake exhibited severe water quality degradation, with classification inferior to Class V primarily due to elevated CODCr and TN concentrations. While other parameters remained within Class V standards, TP levels showed an increasing trend in recent years. The annual mean TN concentration was 3.33 mg/L, reaching a maximum of 5.03 mg/L in 2013 (2.5 times the Class V standard). A significant mutation point occurred in 2015, with pre-mutation concentrations increasing from 3.40 mg/L to 4.90 mg/L, followed by a 40.2% post-mutation reduction (Figure 2). Seasonal variations showed maximum concentrations in summer (3.66 mg/L) and minimum in spring (3.07 mg/L), exceeding Class V standards by 3.1 and 2.8 times, respectively. Spatial distribution followed the following pattern: southern (3.83 mg/L) > northern (3.14 mg/L) > central region (3.03 mg/L).
CODCr exhibited an annual mean concentration of 44.33 mg/L, with peak values (56.08 mg/L) in 2013 exceeding Class V standards by 1.4 times. A mutation point occurred in 2016, followed by a 31.5% decrease, though concentrations increased significantly from 32.6 mg/L to 49.42 mg/L between 2017 and 2020 (Figure 2). Seasonal variations showed elevated levels in spring and summer, with summer maxima exceeding Class V standards by 1.9 times. Regional variations were minimal, though all areas exceeded Class V standards by up to 1.4 times.
NH3-N concentrations maintained Class II-III levels, averaging 0.45 mg/L with peak concentrations of 0.94 mg/L in 2014 (Figure 2). Seasonal patterns showed the following pattern: autumn (0.53 mg/L) > winter (0.48 mg/L) > summer (0.41 mg/L) > spring (0.40 mg/L). Spatially, concentrations varied, as follows: southern (0.51 mg/L) > northern (0.46 mg/L) > central region (0.40 mg/L); the southern region met Class III standards and others achieved Class II standards.
TP concentrations, while below Class V thresholds, showed an increasing trend, averaging 0.08 mg/L. Concentrations decreased from 0.11 mg/L to 0.05 mg/L (2011–2015) before increasing to 0.12 mg/L by 2020 (Figure 2), reaching Class V classification in 2019–2020. Seasonal variations were minimal (approximately 0.09 mg/L; Class III level), while spatial distribution showed the following pattern: southern (0.10 mg/L) > northern (0.08 mg/L) > central region (0.07 mg/L).

3.1.2. Comprehensive Evaluation of Water Pollution in Qilu Lake

The Nemerow Pollution Index (NPI) of Qilu Lake demonstrated a fluctuating pattern from 2010 to 2020, with maximum (7.79) and minimum (3.33) values in 2013 and 2017, respectively (Figure 3). A significant mutation point occurred in 2015, marking distinct pre- and post-change periods. Pre-mutation water quality deteriorated from “worse” to “deteriorated”, primarily due to reduced precipitation, accelerated agricultural development, and increased endogenous pollution. Post-mutation NPI decreased from 7.31 to 4.49, which was attributed to increased precipitation and engineering controls, though water quality began deteriorating again in 2018 due to declining precipitation, inadequate project management, and high agricultural pollution loads.
Seasonal NPI values averaged 4.82, 5.58, 5.16, and 5.09 for spring, summer, autumn, and winter, respectively. Spatial variation showed annual averages of 4.88, 4.71, and 5.89 for northern, central, and southern regions, respectively, with superior water quality in the central region. These variations primarily resulted from uneven seasonal precipitation and regional development patterns, with particularly severe agricultural non-point source pollution in the southern region’s primary vegetable cultivation areas.

3.2. Water Quality Risk Prediction in Qilu Lake

The CBN model was employed to conduct prospective risk analysis for predicting water quality risks across various spatial and temporal scales. Results indicated severe water quality issues in Qilu Lake, predominantly characterized by “worse” grade risks (occurrence probability: 45.3–76.5%). The “deteriorated” grade, representing the most critical risk condition, exhibited occurrence probabilities ranging from 11.80% to 47.90% (Figure 4). Temporal analysis revealed significant seasonal variations in water quality degradation risk. Summer demonstrated the highest risk occurrence (mean: 29.3%; range: 17.4–47.9%), while spring exhibited the lowest (mean: 16.7%; range: 11.8–25.7%). The peak summer risk (47.9%) exceeded the spring maximum by 22.2%. Autumn and winter displayed comparable risk profiles. Spatial analysis indicated substantially elevated risks in the southern region (mean: 38.05%; range: 25.7–47.9%) compared to the central region, which exhibited the lowest risk levels (mean: 14.83%; range: 12.6–17.4%). The maximum risk probability in the southern region (47.9%) exceeded the central region’s peak by 30.5%, demonstrating significant spatial heterogeneity primarily attributed to seasonal and regional water quality variations.
Reverse risk analysis utilizing the CBN model was implemented to estimate probability density distributions of specific water quality indicators. Analysis revealed that increasing water quality risk levels corresponded to expanded probability density distribution ranges and elevated mean values. Particular attention was directed toward the “deteriorated” grade risk due to its severe implications. Under “deteriorated” risk conditions in the southern region, water quality parameters exhibited the following ranges: TN (3.42–8.43 mg/L), TP (0.04–0.31 mg/L), NH3-N (0.07–1.29 mg/L), CODCr (27.75–67.19 mg/L), CODMn (7.49–20.16 mg/L), and BOD5 (4.05–13.04 mg/L) (Figure 5). pH and DO maintained acceptable ranges within their probability densities.
The central and northern regions demonstrated more constrained probability density distributions with lower mean values compared to the southern region. Under “deteriorated” risk conditions, the central region exhibited concentrations of TN (4.17–4.26 mg/L), TP (0.04–0.17 mg/L), NH3-N (0.11–1.38 mg/L), CODCr (39.79–70.54 mg/L), CODMn (9.16–23.93 mg/L), and BOD5 (3.78–12.85 mg/L). The northern region showed similar patterns, as follows: TN (4.19–6.91 mg/L), TP (0.03–0.15 mg/L), NH3-N (0.11–1.38 mg/L), CODCr (40.35–73.11 mg/L), CODMn (8.82–23.46 mg/L), and BOD5 (4.14–13.07 mg/L). System complexity correlates positively with uncertainty introduction [31], wherein larger standard deviations indicate enhanced risk indicator volatility. The southern region consistently demonstrated higher standard deviations across water quality indicators compared to other regions. These probability density distributions under varying risk scenarios provide essential early warning indicators, enabling lake managers to maintain water quality parameters within acceptable ranges, thereby mitigating potential water quality deterioration risks.

4. Discussion

4.1. Driving Factors of Water Quality Changes in Qilu Lake

The dynamics of water quality indicators effectively reflect variations in lake ecosystem conditions, which are primarily influenced by natural factors and anthropogenic activities [32]. Pearson’s correlation analysis revealed significant negative correlations between water volume (WV) and key parameters including NPI, TN, and CODCr (Figure 6). The Qilu Lake Basin, lacking transit rivers, depends entirely on precipitation for water resources, resulting in constrained water availability and temporal distribution irregularities. Water volume in Qilu Lake showed considerable fluctuations, with a notable minimum in 2013 (approximately 0.5 × 108 m3) and reaching its peak in 2017 (1.6 × 108 m3). This variation pattern primarily reflected the precipitation-dependent nature of the lake’s water resources, characterized by distinct wet and dry periods throughout the decade. The water quality parameters demonstrated synchronized responses to water volume changes, albeit with varying intensities. CODCr, TN, and NPI exhibited similar temporal patterns, reaching their maximum values in 2013–2014 (CODCr = 56 mg/L, TN = 5 mg/L, NPI = 7.5), which was coincident with minimum water volume, followed by a gradual decline during subsequent years. TP showed a different pattern, with an initial peak in 2012 (0.10 mg/L), followed by a significant decrease in 2014 (0.05 mg/L), and a subsequent increasing trend through 2020. NH3-N maintained relatively stable concentrations with minor fluctuations throughout the study period. Conversely, the improved water quality observed in 2017 coincided with maximum water volume, illustrating the dilution effect during wet periods. This pattern supports the significant negative correlations revealed by Pearson’s analysis between water volume and key water quality parameters (NPI, TN, and CODCr). Furthermore, the basin’s water resource development rate exceeds 90%, surpassing 150% during drought periods. Tonghai County, a major vegetable production area, demonstrates continuous increases in cultivation area and yield. Vegetable cultivation demands substantially higher water consumption (16.93 m3/hm2) compared to grain crops (approximately seven times greater). During drought periods, reduced precipitation coupled with extensive agricultural irrigation exacerbates water scarcity, accelerating quality deterioration. Conversely, during wet years, reduced human irrigation using lake water led to improved water quality due to greater water availability.
Pollutant discharge significantly influences lake water quality [33,34], with pollution loads identified as primary drivers of quality degradation [35]. Agricultural non-point source pollution emerges as a critical contributor to surface water eutrophication [36]; this is particularly evident in the Qilu Lake watershed, where agricultural activities constitute the predominant pollution source. The watershed is characterized by extensive crop cultivation areas, intensive rotation practices, elevated multiple cropping indices, and substantial chemical fertilizer applications. Chemical fertilizer application intensity in the Qilu Lake Basin reached 516.69 kg/hm2 in 2017, significantly exceeding the national ecological township standard of 250 kg/hm2, with persistently high application rates maintained over extended periods. An analysis of agricultural fertilizer runoff revealed significant contributions to total pollutant loads—CODCr (12.43%), NH3-N (57.01%), TN (43.05%), and TP (73.98%)—demonstrating the intrinsic relationship between agricultural intensification and lake water quality deterioration. This presents a fundamental conflict between intensive agricultural practices dependent on excessive fertilization and the lake’s limited environmental carrying capacity, necessitating urgent modifications to current agricultural methods, particularly regarding fertilization practices and irrigation systems.
Lakes, reservoirs, and rivers typically exhibit pronounced seasonal variations in hydrology and water quality [37]. Lake ecosystems demonstrate particular sensitivity to climate change, establishing strong correlations with nutrient loading patterns [38]. Climate change manifests primarily through alterations in precipitation and temperature [39], with rainfall patterns significantly influencing surface and subsurface runoff volumes and subsequent non-point source pollution loads [40]. Our correlation analysis provides robust evidence for the influence of meteorological variables on water quality parameters. The correlation matrix reveals a significant positive correlation between air temperature and water temperature (r = 0.87), demonstrating strong thermal coupling between atmospheric and aquatic environments. Furthermore, air temperature exhibits significant positive correlations with key water quality indicators, including CODMn (r = 0.31) and CODCr (r = 0.23), while water temperature shows positive correlations with CODMn (r = 0.43) and CODCr (r = 0.19). These findings suggest that water quality deteriorates during warmer seasons. Precipitation patterns show complex relationships with water quality parameters. The correlation analysis indicates that rainfall has positive correlations with CODMn (r = 0.18) and total nitrogen (r = 0.094)—albeit modest—supporting the hypothesis that increased precipitation may facilitate nutrient loading through surface runoff. The results indicate that water quality reaches its lowest levels and risks peak during summer, characterized by high precipitation and elevated temperatures, while spring demonstrates contrasting conditions, which is consistent with previous research findings [41,42]. The southern region of Qilu Lake, serving as the primary collection area for vegetable cultivation and rural non-point source pollutants, experiences significant water quality challenges. Summer rainfall generates surface runoff, transporting concentrated pollutants into the lake. Direct discharge of agricultural wastewater and domestic sewage through pumping stations, combined with multiple rivers inputs, contributes to sustained poor water quality in the southern region. While external pollution loads can be managed through anthropogenic interventions, persistent eutrophication often results from endogenous pollution in lake sediments [43]. Studies of Dianchi Lake demonstrated high endogenous nitrogen and phosphorus load contributions (72–77%) [44], while Lake Tai research highlighted the role of wind-induced sediment resuspension in enhancing eutrophication through nutrient release [45]. Systematic analysis of sediment pollution in Qilu Lake reveals significant internal loading dynamics, with sediment release contributing 17.64% and 2% of total nitrogen (TN) and phosphorus (TP) loads, respectively. Surface sediment TN concentrations range from 1992 to 7019 mg/kg (mean 3597 mg/kg), with elevated levels (4000–5000 mg/kg) in southern and eastern areas. TP concentrations vary between 981 and 4926 mg/kg (mean 2166 mg/kg), occasionally exceeding TN values. Both nutrients peak at the Hongqi River entrance. Organic matter content (51–143 g/kg; mean 94 g/kg) exceeds national first-class soil fertility standards. Annual sediment release in 2017 reached 339.07 t TN and 3.74 t TP. Effective eutrophication management necessitates addressing internal pollution sources through permanent burial or excavation.

4.2. Implications for Qilu Lake Management Based on Water Quality Risk Prediction

The effective protection of Qilu Lake requires comprehensive water resource management, integrating rational resource allocation, supply–demand optimization, and advanced water conservation and recycling strategies. The hydrochemical dynamics of Qilu Lake, including pollutant dilution and concentration patterns, are intrinsically linked to land use practices and water resource availability within the basin. During wet periods, agricultural runoff and increased surface water transport contribute to elevated concentrations of total nitrogen (TN) and total phosphorus (TP) in the lake, exacerbating eutrophication risks. In contrast, dry periods promote the concentration and sedimentation of pollutants, intensifying chemical oxygen demand (CODCr) levels and altering nutrient transformation processes. These dynamics underscore the critical need for targeted interventions to mitigate the impacts of basin activities on the lake’s water quality.
Agricultural enhancement strategies within the basin play a pivotal role in addressing these challenges, emphasizing the adoption of high-efficiency irrigation technologies and integrated water–fertilizer management systems. Transitioning from conventional flood irrigation to advanced methods such as sprinkler, drip, and micro-irrigation systems directly reduces agricultural water wastage and minimizes nutrient leaching into the lake, thereby lowering TN and TP inputs. Automated operations and precision irrigation protocols further optimize water utilization, ensuring sustainable agricultural productivity while mitigating non-point source pollution. Critical infrastructure improvements, such as the interception of low-pollution surface runoff during rainfall and the prevention of direct sewage discharge, are essential for reducing CODCr concentrations in the lake. Additionally, water recycling systems for irrigation, combined with subsequent treatment at reclamation facilities, significantly reduce pollutant loads entering Qilu Lake. Enhancing natural purification processes through sedimentation, multi-pond systems, and aquatic vegetation further supports the absorption and degradation of TN and TP, contributing to improved water quality.
The governance framework for Qilu Lake incorporates “source control, emission reduction, pollution interception, and remediation” strategies, explicitly addressing spatial and temporal variations in pollutant distribution and their measurable impacts on lake water quality. In the southern region, where agricultural activities dominate, source control measures focus on reducing chemical fertilizer application and improving nutrient utilization efficiency to mitigate TN and TP inputs, which are strongly correlated with the lake’s Nutrient Pollution Index (NPI) [46]. Systematic agricultural transformation, including the replacement of low-efficiency crops and the optimization of fertilizer application protocols, ensures the dual objectives of maintaining crop yields and reducing eutrophication risks [47]. Farmland water management infrastructure, such as comprehensive collection and drainage systems, prevents pollutant leaching during precipitation events, directly reducing TN, TP, and CODCr levels in the lake. Pollutant interception measures follow a hierarchical approach aligned with contaminant migration pathways, ensuring maximum retention and purification before pollutants reach the lake. Near-source interception systems, such as sedimentation-promoting purification systems within farmland drainage networks, reduce TN and TP loads at their origin. Transportation control through ecological ditch networks further minimizes pollutant transport, while terminal purification via integrated ecological ponds, wetlands, and riparian zones enhances pollutant retention and degradation. This multi-stage system significantly reduces TN and TP concentrations in the lake, mitigating eutrophication risks and improving overall water quality.
The effective management of Qilu Lake necessitates prioritizing the prevention and control of key pollutants, particularly TN, TP, and CODCr, while implementing early warning systems based on concentration ranges across different water quality risk levels. This approach is especially critical for mitigating water quality risks in vulnerable areas, notably the southern region during summer months, and preventing large-scale pollution events such as algal blooms. Research indicates that recurring cyanobacterial blooms maintain elevated nutrient concentrations [48], enhancing heterotrophic bacterial activity [49] and accelerating nutrient transformation between organic and inorganic states [49,50], thus perpetuating bloom conditions through efficient nutrient cycling. This process establishes a self-reinforcing cycle where increased pollution accelerates nutrient cycling rates, exacerbating eutrophication through continuous nutrient availability. Water quality deterioration typically results from multiple interacting risk factors, with simultaneous exceedance of multiple water quality parameters presenting more significant challenges than single-parameter violations. Spatial analysis reveals strong positive correlations between the NPI and both TN and TP concentrations in the southern region, with diminishing correlations in northern and central regions, reflecting spatial heterogeneity in water quality (Figure 7). Conditional Bayesian Network (CBN) analysis demonstrates weak correlation between NPI and CODCr, attributed to limited data sensitivity, which is corroborated by minimal variations in CODCr probability density distributions across risk levels (Figure 6). However, CODCr exceedance of Class V standards has intensified since 2019, warranting its inclusion alongside TN and TP as critical risk indicators for comprehensive water quality management.

4.3. Uncertainty Analysis

This investigation encompasses two primary sources of uncertainty—structural uncertainty inherent in Bayesian Network (BN) model construction and uncertainty associated with comprehensive water quality metric implementation. The structural uncertainty in the BN framework stems from its construction methodology, which relies on mutual information and mountain climbing algorithms rather than expert-derived field knowledge, potentially overlooking mechanistic relationships between water quality parameters. To validate the model’s risk assessment outcomes and ensure result credibility, we conducted 10,000 Monte Carlo simulations. The NPI offers advantages through its computational simplicity, capacity to integrate diverse quantitative parameters, and streamlined state assessment capabilities. However, the absence of mechanistic underpinnings introduces challenges in maintaining assessment result stability. Notable limitations include the exclusion of chlorophyll and transparency measurements from the NPI framework due to the absence of corresponding national standards, though incorporation of these parameters could potentially enhance the study’s analytical robustness. These limitations suggest opportunities for methodological refinement in future research.

5. Conclusions

Based on the comprehensive water quality index, M–K test, and the Copula Bayesian Network, this study achieved quantitative water quality pollution identification and risk prediction in Qilu Lake. The results demonstrated that the water quality in Qilu Lake was generally “worse” (NPI, 5.10 ± 1.35), and the continuous deterioration of the water quality led to a surge in risk. The risk probability of reaching the “deteriorated” grade was between 11.80% and 47.90%. The water quality of the lake varied greatly with space, and was observed to be better in the north and center than the south. The southern risk was as high as 38.05% (“deteriorated” grade). Moreover, the water quality presented distinct seasonal variation, with the highest NPI values (5.58) and pollution risk (29.3%, “deteriorated” grade) in summer, followed by autumn (NPI, 5.16), winter (NPI, 5.09), and spring (NPI, 4.82). The water quality and pollution risk were affected closely by high agricultural non-point source load and insufficient water resources. Furthermore, the concentrations of key indicators of different risk levels were predicted as early warning signals. Taking the southern Qilu Lake as an example, when the “deteriorated” level risk occurred, TN (3.42 to 8.43 mg/L), TP (0.07 to 1.29 mg/L), and CODcr (27.75 to 67.19 mg/L) were quantified as early warning intervals for risk control. Based on qualitative cause–effect analysis from anthropogenic influence to water quality risk, the protection of Qilu Lake should reinforce the water resource management and optimize planting mode. Overall, this study demonstrates a more thorough understanding of the characterization of water quality and pollution risk, which could provide help in making decision from the perspective of quantitative risk early warning indicators and associated anthropogenic influences.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/pr12122922/s1, Figure S1: Copula-based Bayesian network (CBN) structures for water quality risk assessment in Lake Qilu at the south (a), the center (b), and the north (c) of Qilu Lake. Figure S2: The flowchart of the CBN.; Table S1: Interannual variation in water quality parameters BOD5, CODMn, pH, and DO. Table S2: Variation in water quality parameters BOD5, CODMn, pH, and DO in different regions. Table S3: Seasonal changes in water quality parameters BOD5, CODMn, pH, and DO. Table S4: The best-fitted distribution of the external and internal risk indicators. References cited in Supplementary Materials [51,52,53,54].

Author Contributions

Conceptualization, methodology, investigation, and writing—original draft: X.C.; validation, resources, and supervision: S.W.; data curation and writing—review and editing: Y.D.; data curation and supervision: Z.N.; data curation: Y.H. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Zhuhai Basic and Applied Basic Research Foundation (No. 2320004002582); the Yunnan Key Laboratory of Pollution Process and Management of Plateau Lake-Watershed, grant number 2020-02-2-W2, 2020-124A-W2; and the National High-level Personnel of Special Support Program People Plan, grant number 312232102.

Data Availability Statement

The original contributions presented in this study are included in the article/Supplementary Materials. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

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Processes 12 02922 g001
Figure 1. Location of Qilu Lake and distribution of sampling points.
Figure 1. Location of Qilu Lake and distribution of sampling points.
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Figure 2. Seasonal and spatial variation characteristics of water quality in Qilu Lake. (a,d,g,j) Interannual variations; (b,e,h,k) spatial distribution; (c,f,i,l) seasonal patterns.
Figure 2. Seasonal and spatial variation characteristics of water quality in Qilu Lake. (a,d,g,j) Interannual variations; (b,e,h,k) spatial distribution; (c,f,i,l) seasonal patterns.
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Figure 3. Temporal (a,c) and spatial (b) changes in the NPI value in Qilu Lake.
Figure 3. Temporal (a,c) and spatial (b) changes in the NPI value in Qilu Lake.
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Figure 4. Probability distribution of the water quality risk grade in different seasons for the three locations of Qilu Lake.
Figure 4. Probability distribution of the water quality risk grade in different seasons for the three locations of Qilu Lake.
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Figure 5. The concentration ranges of TN, TP, NH3-N, CODCr, CODMn, and BOD5 under different water quality risk grades in the north (a), center (b), and south (c) of Lake Qilu.
Figure 5. The concentration ranges of TN, TP, NH3-N, CODCr, CODMn, and BOD5 under different water quality risk grades in the north (a), center (b), and south (c) of Lake Qilu.
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Figure 6. Variation in water volume and water quality index in Qilu Lake from 2010 to 2020 (a). Pearson’s correlation coefficient between water quality parameters and water volume (b).
Figure 6. Variation in water volume and water quality index in Qilu Lake from 2010 to 2020 (a). Pearson’s correlation coefficient between water quality parameters and water volume (b).
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Figure 7. The percentile cobweb plots with high probability values (0.8–1.0, the red lines) of NPI south, center, and north of Qilu Lake. When the NPI has high (or low) probability values, it can be recognized as the key indication if certain other indicators also have high (or low) values.
Figure 7. The percentile cobweb plots with high probability values (0.8–1.0, the red lines) of NPI south, center, and north of Qilu Lake. When the NPI has high (or low) probability values, it can be recognized as the key indication if certain other indicators also have high (or low) values.
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Table 1. Grade classification of the water quality condition.
Table 1. Grade classification of the water quality condition.
NPIFeatureGrade
[0–0.8)The water quality is excellent, and the water environment has not been damaged.Excellent
[0.8–1.0)The water quality is good, and the water environment has been slightly damaged.Good
[1.0–1.8)The water quality is in general and the water environment has been slightly damaged.Moderate
[1.8–3.3)The water quality is poor, and the water environment has been damaged.Poor
[3.3–6.2)The water quality is inferior, and the water environment has been dramatically damaged.Worse
[6.2–+∞)The water environment has been tremendously deteriorated and has basically lost the use of function.Deteriorated
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Cheng, X.; Wang, S.; Dong, Y.; Ni, Z.; Hong, Y. Spatiotemporal Analysis and Risk Prediction of Water Quality Using Copula Bayesian Networks: A Case in Qilu Lake, China. Processes 2024, 12, 2922. https://doi.org/10.3390/pr12122922

AMA Style

Cheng X, Wang S, Dong Y, Ni Z, Hong Y. Spatiotemporal Analysis and Risk Prediction of Water Quality Using Copula Bayesian Networks: A Case in Qilu Lake, China. Processes. 2024; 12(12):2922. https://doi.org/10.3390/pr12122922

Chicago/Turabian Style

Cheng, Xiang, Shengrui Wang, Yue Dong, Zhaokui Ni, and Yan Hong. 2024. "Spatiotemporal Analysis and Risk Prediction of Water Quality Using Copula Bayesian Networks: A Case in Qilu Lake, China" Processes 12, no. 12: 2922. https://doi.org/10.3390/pr12122922

APA Style

Cheng, X., Wang, S., Dong, Y., Ni, Z., & Hong, Y. (2024). Spatiotemporal Analysis and Risk Prediction of Water Quality Using Copula Bayesian Networks: A Case in Qilu Lake, China. Processes, 12(12), 2922. https://doi.org/10.3390/pr12122922

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