Coupling Monte Carlo simulation with CRITIC-enhanced water quality assessment for the Weishui Reservoir

Water resources are a crucial asset for the economic development of human society and constitute one of the controlling factors in the ecological environment (Wei et al. 2020; Tang et al. 2022). As important surface water components, reservoirs play a vital role in flood control, irrigation, water storage, power generation, and water supply for urban use (Ji et al. 2020). In recent years, with the rapid growth of the population and the swift development of industry and agriculture, a significant amount of wastewater has been discharged into reservoirs, leading to frequent water pollution incidents in reservoirs (Xu et al. 2019; Su et al. 2022). This severely threatens the ecological health of reservoir ecosystems and the safety of water supplies for people. Water quality assessment is a crucial pillar of watershed water environmental management and holds significant importance in the context of water pollution control (Yang et al. 2020).

Commonly used water quality assessment methods include the single pollution index method, principal component analysis method, fuzzy evaluation method, and comprehensive water quality index (CWQI) method (Wang et al. 2021; Zhang et al. 2021; Zhao et al. 2021). These methods each possess distinct characteristics. For instance, the single pollution index method entails comparing the measured values of evaluation indicators with their respective standard values to ascertain the pollution status of individual indicators (An et al. 2023). The principal component analysis method involves statistically analyzing data and assigning values rationally to evaluation indicators for comparative water quality analysis (Li et al. 2012). They calculate the degree of proximity between the actual concentrations of evaluation indicators and the water quality standards, utilizing fuzzy operators for computation (Liu & Zou 2012). The CWQI method involves the arithmetic mean of the single-factor pollution indices of various evaluation indicators to provide a comprehensive assessment of water quality (Jin et al. 2022). The CWQI method is a simple calculation process that reflects the overall pollution status of a water body and is a widely used water quality assessment method worldwide (Xue et al. 2023). However, the traditional CWQI method handles the weighting of various evaluation indicators relatively simplistically, failing to emphasize the distinctions among indicators. Furthermore, it assesses water quality from a deterministic perspective based on known sampling data without accounting for variations in natural conditions (such as rainfall) and errors in human operations during the sampling process (Huang et al. 2019). This results in uncertainty in the measured indicator concentrations and an inability to accurately reflect the pollution status of the water body. Therefore, it is essential to calculate weights sensibly and thoroughly consider uncertainties in the evaluation process to manage water quality effectively.

The Monte Carlo method is a numerical computation technique based on random numbers and grounded in probability and statistical theory (Seifi et al. 2020). It is one of the effective tools for addressing problems involving uncertainty. In recent years, the Monte Carlo method has gradually gained widespread application in the uncertain analysis research of traditional water quality assessment methods. For example, Lin et al. (2020) proposed a water quality eutrophication evaluation method based on the preference by similarity to an ideal solution (TOPSIS) method and Monte Carlo simulation (MCS) and identified the most sensitive factors of the method through a global sensitivity analysis. Xi & Zhihe (2023) constructed a water quality evaluation method that combines the Monte Carlo method (MC), criteria importance through intercriteria correlation (CRITIC), and vIseKriterijumska optimizacija i kompromisno resenje (VIKOR) methods. The results indicate the accuracy and reliability of the method and its ability to overcome the uncertainty caused by sampling errors.

Therefore, to understand the current situation and trends of water quality in the Weishui Reservoir, this paper selects the comprehensive pollution index method (CWQI) and the comprehensive pollution index (CWQI) method improved based on the CRITIC method, coupled with the Monte Carlo method, to analyze the spatiotemporal changes of water quality in the Weishui Reservoir. The aim is to provide a certain scientific basis for the water quality management of the Weishui Reservoir.

Select two monitoring points within the watershed as the evaluation objects. One of the sampling points is located at the inflow point of Shaxiping (111°24′13.2″E, 29°54′13.2″N) in the Weshui Reservoir. Another sampling point is situated at Dayanzui (111°34′55.9″E, 29°57′41.3″N) within the Weishui Reservoir, serving to monitor the water quality within the reservoir.

A total of 25 biochemical indicators were detected at both sampling points (pH, DO, COD_Mn, -N, BOD₅, CN, As, VOC, Cr, Hg, Cd, Pb, Cu, Zn, Se, TP, TN, F⁻, Petrol, ⁠, Fe, Mn, SD, Chl.a, linear alkylbenzene sulfonates (LAS)). Due to the Shaxiping sampling point being located on the inflow river of the reservoir and the Dayanzui sampling point within the reservoir, there exist differences in the water quality indicators monitored at each location. Moreover, many indicators exhibit a lack of data continuity as their concentrations have consistently remained below the detection limit over an extended period. Therefore, in this study, different biochemical indicators were employed for water quality assessment at the Shaxiping and Dayanzui sampling points. The biochemical indicators used for the Shaxiping sampling point include DO, COD_Mn, -N, BOD₅, TP, and F⁻. The biochemical indicators used for the Dayanzui sampling point include DO, COD_Mn, -N, BOD₅, TP, and TN.

Water samples were collected 0.5 m below the surface using a 5 L plexiglass water collector. After collection, the samples were stored in polyethylene plastic bottles and rinsed thrice with distilled water. Subsequently, the samples were refrigerated at 4 °C in insulated boxes until the analysis of water quality parameters. Parameters like DO were examined using a multi-parametric probe with calibrated sensors during field measurements. In the laboratory, COD_Mn was analyzed through permanganate titration, BOD₅ was measured via the reduction of DO in the raw water samples after 5 days, total phosphorus (TP) was determined using potassium persulfate molybdenum antimony spectrophotometry, -N was measured through Nessler's reagent spectrophotometry and F⁻ concentrations were determined using ion chromatography, TN was determined using a HACH DR6000 UV–VIS spectrophotometer.

According to the Chinese Surface Water Environmental Standards (GB3838-2002), when formulating water quality assessment standards, the standards for Class III water are often used as reference values for evaluation indicators. The water quality grading table using the CWQI method is shown in Table 1.

The traditional CWQI method can quantitatively analyze the overall pollution level in a particular area. Still, it does not consider the weights of various evaluation indicators during the calculation and cannot classify water quality. Therefore, we chose to improve the CWQI method using the CRITIC method in this study. The CRITIC method is an objective weighting method that comprehensively measures the weights of indicators based on the contrast and conflict between evaluation indicators. Contrast is represented by the standard deviation and is used to indicate the differences in the same indicator among different scenarios. The correlation coefficient represents conflict, and when two indicators have a high positive correlation, their conflict is low, resulting in lower weights (Xi & Zhihe 2023). The CRITIC method considers both the variability of indicators and the correlation between them, making it more comprehensive than entropy weighting and standard deviation weighting methods. The specific calculation process of the CRITIC method is as follows (Li et al. 2022):

• (1)
  Constructing an assessment matrix.

  

  (3)

  where m is the number of influencing factors, n is the number of evaluation indicators, and x_ij denotes the j indicator under the i influencing factor.
• (2)

  Normalization

Normalization is required to eliminate the effect of different magnitudes of the data, and the specific formula for normalization is as follows.

The weights of the five pollutants calculated based on Equations (1)–(9) are shown in Table 2.

Table 2

Weight of various pollutants in the Weishui Reservoir

Monitoring stations .	DO .	CODMn .	-N .	BOD5 .	TP .	F− .	TN .
Shaxiping	0.138	0.132	0.289	0.174	0.140	0.127	–
Dayanzui	0.182	0.164	0.159	0.160	0.191	–	0.144

Monitoring stations .	DO .	CODMn .	-N .	BOD5 .	TP .	F− .	TN .
Shaxiping	0.138	0.132	0.289	0.174	0.140	0.127	–
Dayanzui	0.182	0.164	0.159	0.160	0.191	–	0.144

View Large

The water quality classification standards for the improved CWQI method based on the CRITIC method are shown in Table 3.

The Monte Carlo method in this study was conducted using an Oracle Crystal Ball. The main steps involved two phases: determining the distribution functions and distribution parameters of variables and defining variables and conducting sampling. The specific process is as follows:

• (1)

  The Anderson–Darling test in Oracle Crystal Ball was used to determine the best-fitting distribution for the assumed variables and set distribution parameters accordingly.

• (2)

  Using CWQI and C_R as predictive variables, six hypothetical variables were set for each evaluation indicator, P_i and w_ip_i. After defining the probability distributions for each hypothetical variable, 20,000 Monte Carlo samples were collected. These samples were then substituted into Equations (1) and (10) for simulation, resulting in 20,000 outcomes representing possible results for various scenarios of water quality indicators.

The trophic level classification thresholds for CTSI are shown in Table 4.

The water quality grades are based on China's surface water environmental quality standard GB3838-2002 (Table 5). The water quality objective of the Weishui Reservoir is to achieve Class II.

Table 5

Selected classification criteria for water quality indicators

Index (mg/L) .	Water quality criteria .
	I .	II .	III .	IV .	V .
DO	7.5	6	5	3	2
CODMn	2	4	6	10	15
-N	0.15	0.5	1.0	1.5	2.0
BOD5	3	3	4	6	10
TP	0.01	0.025	0.05	0.1	0.2
F−	1.0	1.0	1.0	1.5	1.5
TN	0.2	0.5	1.0	1.5	2.0

Index (mg/L) .	Water quality criteria .
	I .	II .	III .	IV .	V .
DO	7.5	6	5	3	2
CODMn	2	4	6	10	15
-N	0.15	0.5	1.0	1.5	2.0
BOD5	3	3	4	6	10
TP	0.01	0.025	0.05	0.1	0.2
F−	1.0	1.0	1.0	1.5	1.5
TN	0.2	0.5	1.0	1.5	2.0

View Large

The DO concentration at the Shaxiping (Dayanzui) sampling point ranged from 5.1 to 13.1 mg/L (5.1–11.92 mg/L), with 95% of the samples meeting the Class II. There was no obvious difference in the DO concentrations between the sampling points at Shaxiping and Dayanzui. The COD_Mn levels at the Shaxiping and Dayanzui sampling points were relatively low, with average concentrations of 1.4 and 1.7 mg/L, both meeting Class I standards. There was a noticeable difference in the -N content between the two sampling points. The -N concentration at Dayanzui was significantly higher than that at Shaxiping. The BOD₅ concentration at the Shaxiping (Dayanzui) sampling point ranged from 0.2 to 3 mg/L (0.5–2.9 mg/L), with average concentrations of 1.5 mg/L (1.6 mg/L), both meeting Class I standards. The TP content at the Shaxiping and Dayanzui sampling points was relatively high, with average values of 0.041 and 0.026 mg/L, belonging to Class III water quality. The F⁻ content at Shaxiping was low, ranging from 0.06 to 0.28 mg/L, with all samples meeting Class I water quality standards. The concentration of TN at the Dayanzui sampling point is high, with an average concentration of 1.3 mg/L, 94% of the samples meet the Class III water quality standard. The Secchi disk depth at the Dayanzui sampling point has a depth range of 1–4.6 m, with an average value of approximately 2.2 m. The concentration of Chl.a at the Dayanzui sampling point is low, with an average concentration of 3.5 μg/L.

Overall, the water quality characteristics at the Shaxiping and Dayanzui sampling points were similar. Both TP and TN values exceed the specified water quality standards among the selected parameters.

Seasonal evaluation results of the CWQI method are shown in Table 6. There is evident seasonal variation in water quality at both the Shaxiping and Dayanzui sampling points. The probability of water quality exceeding II standards at the Shaxiping sampling point follows spring > summer > winter > autumn. The probability of water quality exceeding II standards at the Dayanzui sampling point follows the order of summer > spring > winter > autumn.

The probability of water quality reaching Grade II at the Shaxiping sampling point is significantly higher than at the Dayanzui sampling point (Table 7). At the Shaxiping sampling point, the probability of water quality being classified as Grade I is maximized, whereas at the Dayanzui sampling point, the probability of water quality being categorized as Grade III is maximized. This is mainly because the Shaxiping sampling point is located at the reservoir inflow, where the water flow is fast, making it difficult for pollutants to accumulate. The Dayanzui sampling point is located within the reservoir, where the water flow is slow, making accumulating pollutants easier.

The improved method considers the weights of different water quality indicators, balancing the influence of both low-concentration and high-concentration indicators on the results. Therefore, compared to the traditional CWQI method, the evaluation results of the CWQI method based on the CRITIC method show more pronounced seasonal variations (Table 8). The probability of exceeding Class II standards in each season has also changed. The probability of water quality exceeding II standards at the Shaxiping sampling point follows spring > summer > autumn > winter. The probability of water quality exceeding II standards at the Dayanzui sampling point follows the order of summer > winter > spring > autumn.

Overall, the improved method shows similar evaluation results to the traditional method, the probability of Grade I water quality is highest at the Shaxiping sampling point, while the probability of Grade III water quality is highest at the Dayanzui sampling point. Moreover, it is more evident that the probability of the water quality level at the Shaxiping sampling point reaching Class II is higher than at the Dayanzui sampling point (Table 9).

In Figure 5, the SRCC variations for the water quality indicators of CWQI and CR show similarities at the Shaxiping sampling point. Among them, TP has the highest SRCC values, which are 0.49 and 0.68, while the SRCC values for F⁻ are the smallest, being 0.14 and 0.09, respectively. This indicates that at the Shaxiping sampling point, TP is the most influential indicator of water quality, while F⁻ has the least impact.

In Figure 6, the water quality indicators with relatively high SRCC values for CWQI are TN and NH₄⁺-N, with SRCC values of 0.55 and 0.49, respectively. Following them are TP, BOD₅, and DO, with SRCC values of 0.39, 0.13, and 0.11, respectively. The indicator with the least impact is COD_Mn, with an SRCC value of 0.07. For C_R, TN and TP are the indicators with relatively high SRCC values, with SRCC values of 0.62 and 0.48, respectively. -N, BOD₅, and DO are followed, with SRCC values of 0.42, 0.13, and 0.12, respectively. The indicator with the least impact is COD_Mn, with an SRCC value of 0.09.

From the sensitivity analysis results, it can be concluded that the main pollutants affecting the water quality in the Weishui Reservoir basin are TN, TP, and -N. Therefore, controlling TN, TP, and NH₄⁺-N is crucial for improving the water environmental quality of the Weishui Reservoir.

In Figure 7(a), the CWQI and the modified CWQI (CR) were utilized to assess the Shaxiping sampling point. The water quality assessment results for each season were categorized as Class I. In Figure 7(b), the water quality at the Dayanzui sampling point is poorest in the summer, categorized as Class IV, while in the remaining seasons, it is classified as Class III.

Overall, the results of the two evaluation methods are similar. The seasonal variations in the evaluation results of the CWQI are relatively small. In contrast, the modified comprehensive pollution index based on the CRITIC method exhibited significant seasonal variations, better reflecting the diverse pollution levels at different sampling points across seasons. Furthermore, this evaluation method combines the local area's specific pollutants and pollution levels, enabling a targeted analysis of the water quality situation. This facilitates the provision of more targeted environmental management policies and recommendations.

• (1)

  Based on the water quality data from 2010 to 2021, it can be observed that, in the Weishui Reservoir, only the average concentration of TN and TP exceeds the Class III water quality standard, while the concentrations of other water quality indicators meet the Class II water quality standards.

• (2)

  The water quality at the Shaxiping sampling point is excellent, with a water quality classification of Class I consistently across all seasons. The water quality at the Dayanzui sampling point is relatively poor, particularly during the summer, with a water quality classification of Class IV. Therefore, it is necessary to develop specific water quality management plans tailored to different seasons.

• (3)

  This study's water quality assessment method combines the CRITIC, Monte Carlo, and CWQI methods. The evaluation system is rendered more scientifically sound by establishing pollutant weights through the CRITIC method and reducing the uncertainty of water quality data through the Monte Carlo method.

• (4)

  According to the analysis using Spearman's rank correlation coefficient (SRCC), it was found that TN, TP, and -N, are the key indicators affecting the water quality of the Weishui Reservoir. Consequently, it is imperative to implement stringent control measures for these indicators.

The relevant data has been uploaded to the public database, and the link is https://doi.org/10.6084/m9.figshare.25009520.v1.

The authors declare there is no conflict.