Adaptive Simplified Calculation of Algal Bloom Risk Index for Reservoir-Type Drinking Water Sources Based on Improved TOPSIS and Identification of Risk Areas

Abstract

As a result of global climate change and human production activities, algal blooms are occurring in aquatic environments. The problem of eutrophication in water bodies is becoming increasingly severe, affecting the safety of drinking water sources. In this study, an algal bloom risk index model combining the Improved Fuzzy Analytic Hierarchy Process (IFAHP), Entropy Weight Method (EWM), and Game Theory (GT) was proposed for the Shanxi Reservoir based on the TOPSIS method. After the seasonal and spatial variability in algal bloom risk from 2022 to 2023 was analyzed, an adaptive simplification of the algal bloom risk index calculation was proposed to optimize the model. To enhance its practical applicability, this study proposed an adaptive simplification of the algal bloom risk index calculation based on an improved TOPSIS approach. The error indexes R² for the four seasons and the annual analysis were 0.9884, 0.9968, 0.9906, 0.9946, and 0.9972, respectively. Additionally, the RMSE, MAE, and MRE values were all below 0.035, indicating the method’s high accuracy. Using the adaptively simplified risk index, a risk grading and a spatial delineation of risk areas in Shanxi Reservoir were conducted. A comparison with traditional risk classification methods showed that the error in the risk levels did not exceed one grade, demonstrating the effectiveness of the proposed calculation model and risk grading approach. This study provides valuable guidance for the prevention and control of algal blooms in reservoir-type drinking water sources, contributing to the protection of drinking water sources and public health.

1. Introduction

Algal blooms are rapid increases or accumulations of algal populations that occur in freshwater or marine water systems [1]. Such blooms are dangerous when specific microalgae (especially cyanobacteria) reach high levels of enrichment in the bloom [2]. Changes in environmental conditions, such as favorable temperatures (25 °C or above) [3], adequate sunlight [4], and reduced water flow [5], are key factors influencing the occurrence of algal blooms. As a result, algal blooms frequently develop in lakes, reservoirs, and other stagnant water environments [6]. The eutrophication of water bodies supplies excess nutrients, such as nitrogen and phosphorus, that promote rapid algal growth and serve as the primary drivers of algal bloom outbreaks [7,8,9]. Furthermore, the extensive die-off that occurs among organisms following algal bloom exacerbates water eutrophication, perpetuating a self-reinforcing, detrimental cycle [10].

Research by numerous scholars has demonstrated that eutrophication in water source reservoirs is a widespread issue in many countries, including the United States [11], Russia [12], France [13], and Brazil [14]. In China, monitoring data from 395 centralized water source reservoirs indicate that less than 80% comply with water quality standards [15]. In reservoir-based drinking water sources, elevated concentrations of nitrogen and phosphorus directly enhance the photosynthesis and reproduction of algae. The resulting nutrient surplus allows previously limited algal populations to expand rapidly, leading to large-scale algal blooms [16]. These harmful algal blooms significantly diminish the functionality of reservoirs in providing drinking water, irrigation, and ecosystem services. Specifically, they threaten drinking water safety, reduce ecosystem biodiversity, and increase the complexity of water supply management [17].

Researchers typically use a technical approach that combines exogenous and endogenous management to manage in situ algal bloom in reservoir areas. Endogenous control is based on physical, chemical, and biological algal control [18,19]. Exogenous control aims to decrease the amount of nutrients that enter the water body from outside sources in the catchment area, such as runoff from cities and farms and wastewater discharge from chemical factories [20,21]. However, these algal bloom control techniques are constrained in reality by their high cost, poor effectiveness, and potential to cause secondary pollution [22]. Thus, creating an assessment system for algal bloom risk and developing effective and eco-friendly methods for the prevention and control of algal bloom is crucial. Developing a mathematical model that offers a fresh perspective on managing algal blooms in drinking water reservoirs is a significant research area and potentially has valuable practical applications.

TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) is an evaluation method that ranks a limited number of evaluation targets according to their proximity to an idealized target, thus reflecting the relative value of available objects [23]. It has no special requirements regarding sample size and is not affected by the selection of reference sequences, ensuring robustness in its evaluations. The application of TOPSIS in water environment science mainly focuses on evaluating water bodies’ quality and carrying capacity, analyzing the security of water resources security, etc. [24,25]. Majumder et al. [26] present a hybrid decision-making technique combining trapezoidal fuzzy BWM with trapezoidal fuzzy TOPSIS and determine the most beneficial option to improve the effectiveness of a water treatment plant (WTP). Wei et al. [27] investigate the water resource carrying capacity (WRCC) of Henan Province, identify the main obstacles, and provide suggestions for optimizing the WRCC. To quantify the WRCC of Shihezi, Gulishengmu et al. [28] select an oasis city in the Manas River Basin (MRB), Northwest China, and use a total of 21 indicators from three subsystems to construct an evaluation index system based on the theory of the water resource–socio-economic–ecological complex system.

In a multi-factor evaluation system such as TOPSIS, confirming the indicators’ weights is the key to ensuring the accuracy of the comprehensive evaluation results. Many scholars have proposed various index weight calculation models based on relevant mathematical theories, such as the expert scoring method, weight method, entropy value method, and standard deviation method. [29]. However, studies based on a single evaluation method have defects such as apparent fluctuations in the data and difficulty finding typical distribution patterns, which significantly limit the accuracy of the evaluation results. Huang et al. [30] combined the entropy weight method (EWM) and the analytic hierarchy process (AHP) to eliminate the subjective or objective bias generated by the use of a single evaluation method. They established a collapse risk evaluation system at Qianjin West Road, by the S1 line of the Kunshan metro in China. Through a regional study of water resources in Huizhou, Deng et al. [31] selected 24 indicators in five dimensions of the DPSIR theory, such as “driving force-pressure-state-impact-response”, and constructed an ecological evaluation index system of the water environment. Liang et al. [32] used the combined weight method of game theory (GT) to unify the subjective and objective weights of multiple information sources. They also established a comprehensive benefit evaluation model for maize with the help of TOPSIS to determine the optimal drought-resistance measures for maize seed production.

Therefore, taking Shanxi Reservoir in Wenzhou City, Zhejiang Province, as the study area, this study aims to improve the traditional TOPSIS by adopting a combination of the Improved Fuzzy Analytic Hierarchy Process (IFAHP), Entropy Weighting Method (EWM), and Game Theory (GT) weighting method and adaptively simplify it to realize the more direct, faster, and efficient prevention and control of algal bloom risk. To achieve this goal, based on the existing research, this paper puts forward the following hypotheses: (1) the limitations of the traditional TOPSIS can be effectively solved by adjusting the weighting scheme of the indicators; (2) TOPSIS’ computational amount in the presence of multiple indicators can be reduced by establishing an adaptive simplification of the calculation equations; and (3) the quality of water resources management in reservoir-type drinking water sources can be improved by proposing a more practical method of grading algal bloom risk areas and efficiency can be increased.

2. Materials and Methods

2.1. Study Area

Shanxi Reservoir (27°36′~27°50′ N, 119°47′~120°15′ E) is located in the middle reaches of the mainstream of the Feiyun River in Wenzhou City, Zhejiang Province, which has a typical subtropical humid monsoon climate, with an annual average temperature and precipitation of 18 °C and 1876.9 mm. The dam of Shanxi Reservoir was completed in 2000, and its main areas include the dam, open spillway, spillway, diversion tunnel, and powerhouse [33]. It is a secondary protection zone for water sources and has a total catchment area of 2026.48 km², a standard storage level of 142 m, and a total capacity of 12.91 × 108 m³. It has various functions, such as providing an urban water supply, flood control, power generation, and irrigation. The basin topography of the reservoir area is high in the west and low in the east. The reservoir’s upper and middle reaches are relatively flat mountainous areas, while the lower reaches are low hills and valley plains. The main rainfall period in the basin is from April to September, accounting for three-quarters of the year [34]. Its land use is dominated by forested land and cropland, of which 70% is forested, dominated by plantation forests, and 21% is cropland, dominated by dry crops.

2.2. Sampling Positions and Methods

2.2.1. Sampling Positions

In this study, based on the ecological areas concept, Shanxi Reservoir was divided into two areas for sampling based on topographic and environmental characteristics, including the main area, dominated by the Shanxi branch, and the branch area, consisting of Sanchaxi, Huangtankeng, Xuezuokou, and Jujiangxi Branch together [18]. Based on natural geography, hydrological characteristics, riparian land use, and other relevant factors, 23 sampling positions were strategically determined; their specific locations are shown in Figure 1. The sampling positions were distributed as follows: nine in the main area (SXR1–SXR9), three in the Sanchaxi Branch (SCXS1–SCXS3), three in the Huangtankeng Branch (HTK1, HTKS2, HTKS3), three in the Xuezuokou Branch (XZKS1–XZKS3), and five in the Jujiangxi Branch (JJXS1–JJXS5).

From July 2022 to April 2023, samples were collected quarterly. At each sampling position, water and phytoplankton samples were collected three times at different depths, resulting in 69 water samples and 69 phytoplankton samples per quarter.

2.2.2. Sampling Methods

Water samples were collected using a water sampler with two mixed water samples of 1.5 L each from the upper, middle, and lower layers at depths of 1 m, 4 m, and 7 m, respectively. One water sample was fixed with 15 mL of Lugol’s iodine for phytoplankton analysis [35]. The other sample was measured in the field using a multifunctional water quality meter (HACH HYDROLAB DS5X, Loveland, CO, USA) to determine dissolved oxygen (DO), pH, and water temperature (Tem). This sample was then sent to the laboratory for the analysis of other water quality indicators, such as permanganate index (COD_Mn), total nitrogen (TN), total phosphorus (TP), etc., following the standardized methods recommended by the National Water Monitoring Protocol [36].

2.3. Phytoplankton Identification

In this study, the identification of phytoplankton samples was optimized based on the principles of the Utermöhl method, reducing the labor and material costs of algal sample analysis while maintaining accuracy [37]. The phytoplankton samples were placed in a dark environment for at least 24 h for stabilization. Then, each sample was concentrated to 30 mL at the end of the stationary period through aspirating the supernatant with a siphon. The concentrated samples were centrifuged at 3000–5000 rpm for 10 min and allowed to stand again for at least 24 h after centrifugation. Upon completion of the resting period, the supernatant was skimmed from the samples to produce 5 mL of the phytoplankton sample concentrate. Before identification, 0.1 mL of the concentrated sample was shaken well, and the phytoplankton were identified and counted using a 40×/10×optical microscope (Olympus BX51, Tokyo, Japan) to determine the number of phytoplankton per unit volume. Their length, width, and thickness were then measured based on approximate geometric shapes. The biovolume was calculated using the product summation formula, which was then converted into biomass per unit volume. The primary methods used to identify the phytoplankton and the biomass calculation methods were chosen with reference to the relevant literature [38,39,40]. This optimized method was validated for phytoplankton identification in the Shanxi Reservoir [35].

2.4. Methodology for Calculating the Algal Bloom Risk Index

2.4.1. Process of Calculating the Algal Bloom Risk Index

In multi-objective decision analysis, TOPSIS—also referred to as the distance between superiority and inferiority method—is frequently employed. Based on how close a small number of examined objects are to the intended objective, this approach assesses the benefits and drawbacks of the current objects [41]. This study proposes integrating teh weights of the risk indicators to compute the risk index of algal bloom through combining three single-weight determination methods (Figure 2). The following steps were used to incorporate the integrated weights into the computation problem’s matrix, based on the conventional TOPSIS method:

(a)

Weighted normalized matrix construction

To create the weighted normalized matrix $R^{*}$, each column of matrix R is multiplied by its corresponding game theory composite weights $s_j^{*}$ based on the original data matrix R = (r_ij)_m×n and the composite weights $s^{*}$, determined using the combined assignment method (refer to Equation (c12) for the operation procedure):

$$R^{*}={\left(r_{\mathit{ij}}^{*}\right)}_{\mathrm{m}\times \mathrm{n}}={\left(s^{*}\overline{r_{\mathit{ij}}}\right)}_{\mathrm{m}\times \mathrm{n}}$$

(a1)

$$\overline{r_{\mathit{ij}}}={\displaystyle \frac{r_{\mathit{ij}}-\min (r_{\mathit{ij}})}{\max (r_{\mathit{ij}})-\min (r_{\mathit{ij}})}}$$

(a2)

where i = 1, …, m; j = 1, …, n; m is the total number of evaluation indicators, with a value of 8; n is the number of objects to be evaluated, i.e., the number of sampling positions, with a value of 23; $r_{\mathit{ij}}$ is the original data of each algal bloom risk indicator; $\overline{r_{\mathit{ij}}}$ is the normalized data of each algal bloom risk indicator; $\max (r_{\mathit{ij}})$ and $\min (r_{\mathit{ij}})$ are the maximum and minimum values of each algal bloom risk indicator, respectively.

(b)

Algal bloom risk index definitions for positive and negative optimum solutions

The level of danger of algal bloom in the reservoir is correlated with the algal bloom risk index indicator chosen for this investigation. The degree of algal bloom risk decreases with an increase in the negative correlation index value and increases with an increase in the positive correlation index value. Consequently, the lowest value of the positive correlation index or the highest value of the negative correlation index is the negative optimum solution for the level of algal bloom risk. The exact opposite, however, is the positive optimal solution for the level of algal bloom risk. Consequently, the following formula can be obtained:

$$V^{-}=\left\{\left(\max r_{\mathit{ij}}^{*}|j\in {\beta }_1\right),\left(\min r_{\mathit{ij}}^{*}|j\in {\beta }_2\right)\right\}$$

(a3)

$$V^{+}=\left\{\left(\min r_{\mathit{ij}}^{*}|j\in {\beta }_1\right),\left(\max r_{\mathit{ij}}^{*}|j\in {\beta }_2\right)\right\}$$

(a4)

where $V^{-}$ is the negative ideal solution for the calculation of the risk level of algal bloom, $V^{+}$ is the positive ideal solution for the calculation of the risk level of algal bloom, ${\beta }_1$ is the set of negatively correlated indicators used in the calculation of the risk index, and ${\beta }_2$ is the set of positively correlated indicators in the calculation of the risk index.

(c)

Determination of the distance between the algal bloom risk index and the positive and negative ideal solutions

The following formula was used to determine the distance between the algal bloom risk index and the negative and positive ideal solutions for the ith sampling position:

$$H_i^{-}=\sqrt{\sum _{j=1}^{\mathrm{n}}{(r_{\mathit{ij}}^{*}-v_{\mathit{ij}}^{-})}^2}$$

(a5)

$$H_i^{+}=\sqrt{\sum _{j=1}^{\mathrm{n}}{(r_{\mathit{ij}}^{*}-v_{\mathit{ij}}^{+})}^2}$$

(a6)

where $H_i^{-}$ is the distance between the ith sample site’s algal bloom risk index and the negative ideal solution, $H_i^{+}$ is the distance between the ith sampling position’s algal bloom risk index and the positive ideal solution, $r_{\mathit{ij}}^{*}$ is the weighted standardized value of the jth indicator in the ith sampling position, $v_{\mathit{ij}}^{-}$ is the value of the jth indicator in the set of negative ideal solutions, and $v_{\mathit{ij}}^{+}$ is the value of the jth indicator in the set of positive ideal solutions.

(d)

The calculation formula used for the algal bloom risk index:

$${\mathit{RI}}_i={\displaystyle \frac{H_i^{-}}{H_i^{-}+H_i^{+}}}$$

(a7)

where ${\mathit{RI}}_i$ is the sampling position’s algal bloom risk index. The greater its value, the higher the sampling position’s algal bloom risk.

2.4.2. Indicators of Algal Bloom Risk

The selection of evaluation indicators for algal bloom risk was divided into three parts: the fundamental water quality indicators, the integrated water environment indicators, and the algal response indicators.

Through affecting the hydrological and biogeochemical processes in the catchment area, the climatic and hydrological parameter changes that occur over time might indirectly impact the water quality of catchments such as rivers and lakes [42]. Three water quality physicochemical indexes—temperature (Tem), pH, and dissolved oxygen (DO)—were chosen as the fundamental water quality indicators after taking into account the shifting stages of the algal bloom and its main influencing indicators, as well as the actual water quality environment of Shanxi Reservoir.

The Shannon–Wiener diversity index (H′) has been widely used in studies to assess algal diversity and the extent of pollution in water bodies [43,44]. Similarly, the Trophic Level Index (TLI) is effective in evaluating the degree of eutrophication in reservoirs and lakes [45,46]. For the purpose of calculating the algal bloom risk index, the Shannon–Wiener diversity index and the TLI were selected as the integrated water quality and environmental indicators. The methodologies for calculating them are detailed in Equations (b1) and (b2).

$$H^{\prime }=-{\sum }_{i=1}^S{P}_i{\log }_2{P}_i$$

(b1)

where S is the number of species; $P_i$ is the ratio of the number of individuals of species i to the total number of individuals in the sample; a Shannon–Wiener diversity index 0–1 represents severely contaminated water, 1–3 represents moderately contaminated water, and >3 represents mildly contaminated or clean water.

$$\sum TLI={\sum }_{j=1}^{\mathrm{n}}{W}_j·{TLI}_j$$

(b2)

where $W_j$ is the correlation weight of the TLI of the jth parameter; ${TLI}_j$ is the nutrient status index of the jth parameter; n is the number of evaluation parameters; $W_j$ is the correlation weight normalized to the jth parameter.

The dominant algal species play a crucial role in the formation of algal blooms, as their biomass and growth dynamics directly influence the scale and impact of the blooms [18]. Therefore, the three species with the highest average annual biomass were selected as the key algal indicators for this study.

2.4.3. Comprehensive Weight Based on Improved Fuzzy Analytic Hierarchy Process, Entropy Weight Method, and Game Theory

The subjective weight of each assessment component was determined in this study using IFAHP, which overcomes the drawbacks of the conventional FAHP, such as its low calculation accuracy and consistency, leading to repetition. The objective weights of the evaluation elements were determined using the EWM, considering the original data’s objectivity. Furthermore, GT was used to calculate the complete weights to increase the accuracy of the risk assessment analysis and reduce the weight bias of the evaluation elements.

(a)

Improved Fuzzy Analytic Hierarchy Process (IFAHP)

The judgment matrix created by the enhanced three-scale IFAHP employed in this study uses an iterative approach to increase the accuracy of weight calculations [47]. It lacks a consistency test as compared to the conventional hierarchical analysis method. Here are the steps involved in the calculation:

① Comparison matrix $D$ based on each risk indicator’s relative value in determining the algal bloom risk index.

$$D={\left(d_{\mathit{ij}}\right)}_{\mathrm{m}\times \mathrm{n}}=\left(\begin{array}{ccc}{d}_{11}& \dots & d_{1\mathrm{n}}\\ ⋮& \ddots & ⋮\\ d_{\mathrm{m}1}& \dots & d_{\mathrm{mn}}\end{array}\right)$$

(c1)

where $d_{\mathit{ij}}=0$ denotes that the importance of i is less than j; $d_{\mathit{ij}}=0.5$ denotes that the importance of i is equal to j; $d_{\mathit{ij}}=1$ denotes that the importance of i is greater than j.

② Calculation of complementary judgment matrix F = (f_ij)_m×n for algal bloom risk indicators:

$$f_{\mathit{ij}}={\displaystyle \frac{{\mathrm{e}}_i-{\mathrm{e}}_j}{2\mathrm{n}}}+0.5$$

(c2)

where ${\mathrm{e}}_i$ and ${\mathrm{e}}_j$ are the sum of the rows and the sum of the columns of the judgment matrix, ${\mathrm{e}}_i=\sum _{k=1}^{\mathrm{n}}{d}_{\mathit{ik}},{\mathrm{e}}_j=\sum _{k=1}^{\mathrm{n}}{d}_{\mathit{jk}},$ and i,j = 1,2, ……, n, respectively; n is the order of the judgment matrix, i.e., the number of risk indicators, n = 8.

③ The weights $W^{\prime }$ of each algal bloom risk indicator corresponding to each level were calculated as follows:

$$W^{\prime }={(w_1^{\prime },w_2^{\prime },\dots ,w_{\mathrm{n}}^{\prime })}^{\mathrm{T}}={({\displaystyle \frac{\sum _{j=1}^{\mathrm{n}}{f}_{1j}}{\sum _{i=1}^{\mathrm{n}}\sum _{j=1}^{\mathrm{n}}{f}_{\mathit{ij}}}},{\displaystyle \frac{\sum _{j=1}^{\mathrm{n}}{f}_{2j}}{\sum _{i=1}^{\mathrm{n}}\sum _{j=1}^{\mathrm{n}}{f}_{\mathit{ij}}}},\dots ,{\displaystyle \frac{\sum _{j=1}^{\mathrm{n}}{f}_{\mathrm{n}j}}{\sum _{i=1}^{\mathrm{n}}\sum _{j=1}^{\mathrm{n}}{f}_{\mathit{ij}}}})}^{\mathrm{T}}$$

(c3)

④ An iterative method was introduced to improve the accuracy of the numerical calculation of the weights of algal bloom risk indicators, and the iterative steps are as follows:

Calculation: We transform F = (f_ij)_m×n into a mutually inverse judgment matrix G = (g_ij)_m×n using the transformation equation $g_{\mathit{ij}}={\displaystyle \frac{f_{\mathit{ij}}}{f_{\mathit{ji}}}}$. The sets of weights at different levels of hierarchy are used as the initial set of vectors H₀ for the iteration, which is iterated using the equation $H_{k+1}=G{H}_k$ to obtain its infinite norm ${‖H_{k+1}‖}_{\infty }$. The weights of the different hierarchy levels are used as the initial set of vectors H₀ for the iteration.

Judgment: In this paper, inequality ${‖H_{k+1}‖}_{\infty }-{‖H_k‖}_{\infty }<\epsilon$ determines whether or not the iteration is complete. When this condition is met, the algal bloom risk indicator weight value, as estimated by IFAHP, is the outcome.

$$w_j^{\prime }=H_{k+1}={({\displaystyle \frac{h_{k+1,1}}{\sum _{i=1}^{\mathrm{n}}{h}_{k+1,i}}},{\displaystyle \frac{h_{k+1,2}}{\sum _{i=1}^{\mathrm{n}}{h}_{k+1,i}}},\dots ,{\displaystyle \frac{h_{k+1,\mathrm{n}}}{\sum _{i=1}^{\mathrm{n}}{h}_{k+1,i}}})}^{\mathrm{T}}$$

(c4)

If not, use $H_k={\displaystyle \frac{H_{k+1}}{{‖H_{k+1}‖}_{\infty }}}$ as the new starting value and repeat until the condition is met.

(b)

Entropy Weight Method (EWM)

The premise of the EWM is to ascertain objective weights derived from a diverse array of indicators. The entropy value of the indicator is inversely related to the level of unpredictability; thus, a higher entropy value corresponds to a more significant weight [48]. The procedural steps of the approach are as follows:

① Assume that m evaluation objects and n evaluation indicators form the original data matrix R = (r_ij)_m×n and derive the standardized value of each risk component and each sampling location in the computation of the algal bloom risk index:

$$P_{\mathit{ij}}={\displaystyle \raisebox{1ex}{$r_{\mathit{ij}}$}\!\left/ \!\raisebox{-1ex}{$\sum _{i=1}^{\mathrm{m}}{r}_{\mathit{ij}}$}\right.}$$

(c5)

where $P_{\mathit{ij}}$ is the standardized value of each algal bloom risk indicator; $r_{\mathit{ij}}$ is the risk value of the jth risk indicator at the ith sampling position.

② Calculating entropy:

$$s_j=-{\displaystyle \frac{1}{\mathrm{lnm}}}{\sum }_{i=1}^{\mathrm{m}}{P}_{\mathit{ij}}\ln P_{\mathit{ij}}$$

(c6)

where $s_j$ is the entropy value; m is the number of evaluation objects, i.e., the number of sampling positions, m = 23.

③ Define the entropy weights of the algal bloom risk indicators and obtain the objective weights of each one.

$$w_j^{″}={\displaystyle \frac{1-s_j}{{\sum }_{j=1}^{\mathrm{n}}(1-s_j)}}$$

(c7)

(c)

Game Theory (GT)

Game theory aims to amalgamate the weights derived from many methods to minimize the discrepancy between the aggregated weights and those produced from each approach, enhancing the weights’ precision [49]. The precise procedures of the game theory integrated weighting technique are as follows:

① The weights of the algal bloom risk indicators are determined using L distinct assignment procedures, the set of basis weight vectors is denoted as $s_k=\left\{s_{k1},s_{k2},\dots ,s_{k\mathrm{n}}\right\}$ (k = 1, 2, …, L), and every linear combination of these L vectors is expressed as follows:

$$s={\sum }_{k=1}^{\mathrm{L}}{\alpha }_k·s_k^{\mathrm{T}}$$

(c8)

where n is the number of algal bloom risk indicators, n = 8, $s$ is one possible weight vector of the weight set, and ${\alpha }_k$ is the linear combination coefficient, ${\alpha }_k>0$, ${\sum }_{k=1}^{\mathrm{L}}{\alpha }_k=1$. To minimize the deviation of $s$ from each underlying set of weight vectors, the optimization operation on the L linear combination coefficients was performed using the equilibrium idea of game theory:

$$\min {‖{\sum }_{j=1}^{\mathrm{L}}{\alpha }_j{s}_j^{\mathrm{T}}-s_i‖}_2,i=1,2,\dots ,\mathrm{L}$$

(c9)

② According to the optimization first-order derivative condition of Equation (c9), the equivalent system of equations can be transformed as follows:

$$\left[\begin{array}{cc}\begin{array}{ccc}{s}_1·s_1^{\mathrm{T}}& s_1·s_2^{\mathrm{T}}& \dots \\ s_2·s_1^{\mathrm{T}}& s_2·s_2^{\mathrm{T}}& \dots \\ ⋮& ⋮& \ddots \end{array}& \begin{array}{c}{s}_1·s_{\mathrm{L}}^{\mathrm{T}}\\ s_2··s_{\mathrm{L}}^{\mathrm{T}}\\ ⋮\end{array}\\ \begin{array}{ccc}{s}_{\mathrm{L}}·s_1^{\mathrm{T}}& s_{\mathrm{L}}·s_2^{\mathrm{T}}& \dots \end{array}& s_{\mathrm{L}}·s_{\mathrm{L}}^{\mathrm{T}}\end{array}\right]\left[\begin{array}{c}{\alpha }_1\\ \begin{array}{c}{\alpha }_2\\ ⋮\\ {\alpha }_{\mathrm{L}}\end{array}\end{array}\right]=\left[\begin{array}{c}{s}_1·s_1^{\mathrm{T}}\\ \begin{array}{c}{s}_2·s_2^{\mathrm{T}}\\ ⋮\\ s_{\mathrm{L}}·s_{\mathrm{L}}^{\mathrm{T}}\end{array}\end{array}\right]$$

(c10)

③ After obtaining the optimal linear combination coefficients ${(\alpha }_1,{\alpha }_2,\dots ,{\alpha }_{\mathrm{L})}$, they are processed with the improved normalization formula to obtain

$${\alpha }_k^{*}={\displaystyle \frac{\left|{\alpha }_k\right|}{{\sum }_{k=1}^{\mathrm{L}}\left|{\alpha }_k\right|}}$$

(c11)

④ Consequently, the comprehensive weight vector derived from the use of GT, in conjunction with IFAHP and EWM, is

$$s^{*}={\sum }_{k=1}^{\mathrm{L}}{\alpha }_k^{*}{s}_k^{\mathrm{T}}$$

(c12)

2.4.4. Validation of an Adaptive Simplified Algal Bloom Risk Index Calculation

This study employs four characteristic indexs—R-square (${\mathrm{R}}^2$), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Relative Error (MRE)—to assess the accuracy of the calculation results of the adaptive simplified algal bloom risk index.

The precision of the adaptive simplified computation outcomes is assessed using ${\mathrm{R}}^2$, which varies from 0 to 1. A value closer to 1 signifies a well-built simplified calculation model, whereas a value further from 1 suggests a badly created model, as expressed in the following formula:

$${\mathrm{R}}^2=1-{\displaystyle \frac{{\mathit{SS}}_{\mathit{res}}}{{\mathit{SS}}_{\mathit{tot}}}}$$

(d1)

$${\mathit{SS}}_{\mathit{res}}={\sum }_{i=1}^{\mathrm{n}}{({\mathit{RI}\text{-}I}_i-{\mathit{RI}\text{-}S}_i)}^2$$

(d2)

$${\mathit{SS}}_{\mathit{tot}}={\sum }_{i=1}^{\mathrm{n}}{({\mathit{RI}\text{-}I}_i-\overline{{\mathit{RI}\text{-}I}_i})}^2$$

(d3)

where ${\mathit{SS}}_{\mathit{res}}$ is the residual sum of the squares, ${\mathit{SS}}_{\mathit{tot}}$ is the total sum of the squares, ${\mathit{RI}\text{-}I}_i$ is the initially computed value of the algal bloom risk index, ${\mathit{RI}\text{-}S}_i$ is the adaptively simplified calculated value of the algal bloom risk index, and $\overline{{\mathit{RI}\text{-}I}_i}$ refers to the mean value of the initial algal bloom risk index. n is the number of samples, with n equaling 23.

The error magnitude of the adaptive simplified calculation results was assessed using RMSE, MAE, and MRE; lower values of these metrics indicate a reduction in error when using the adaptive simplified calculation as opposed to the initial calculation, thereby enhancing the accuracy of the simplified calculation model, as determined by the following formula:

$$\mathrm{RMES}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{i=1}^{\mathrm{n}}{({\mathit{RI}\text{-}S}_i-{\mathit{RI}\text{-}I}_i)}^2}$$

(d4)

$$\mathrm{MAE}={\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{i=1}^{\mathrm{n}}\left|{\mathit{RI}\text{-}S}_i-{\mathit{RI}\text{-}I}_i\right|$$

(d5)

$$\mathrm{MRE}={\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{i=1}^{\mathrm{n}}\left|{\displaystyle \frac{{\mathit{RI}\text{-}I}_i-{\mathit{RI}\text{-}S}_i}{{\mathit{RI}\text{-}I}_i}}\right|$$

(d6)

2.5. Procedural Methods for Data Processing and Analysis

The tables in this paper were created using Microsoft Excel 2021 to ensure accurate data organization and clear presentation. MATLAB R2021a was used to complete the TOPSIS calculation to obtain the calculation results of the risk index of algal bloom [29]. In addition, this study used the Geospatial Data Cloud to obtain the topographic data of the study area and the ArcGIS 10.2 to map the spatial variation in the algal bloom risk index [50]. In this paper, the seasonal variation in the algal bloom risk index, the comparison of the values of the algal bloom risk index before and after the adaptive simplification calculation, and the calculation results of the error index were illustrated using Origin 2016 [51].

3. Results

3.1. Initial Algal Bloom Risk Index (RI-I)

3.1.1. Basic Data of Risk Indicators

In this study, the results of the fundamental water quality indicators—temperature (Tem), pH, and dissolved oxygen (DO)—were obtained through field monitoring. After completing the indoor laboratory tests, the integrated water environment indicators, Shannon–Wiener diversity index (H′) and trophic level index (TLI) were calculated using Equations (b1) and (b2).

Phytoplankton samples from the Shanxi Reservoir were identified, revealing 72 genera in seven phyla. Among them, the Euglenophyta had the most species, totaling 24 genera; the Cyanobacteria followed, totaling 23 genera; the Chlorophyta totaled 15 genera; the Euglenophyta and Dinophyta each had 3 genera; and the Cryptophyta had 2 genera. An analysis of phytoplankton samples from the whole reservoir area showed that the annual mean biomass of the Cyanobacteria was the highest in the total biomass, which was 38.76%, and an individual analysis of each branch showed that the yearly mean biomass of the Cyanobacteria was still the highest in the total biomass. Considering species with a Community Dominance Index (Y) ≥ 0.02 as dominant genera [52], five dominant phytoplankton species were identified in Shanxi Reservoir: Microcystis (0.068), Anabaena (0.043), Navicula (0.031), Gloeocapsa (0.029), and Fragilaria (0.023). Among them, Microcystis, Anabaena, and Gloeocapsa belong to Cyanobacteria. Therefore, Cyanobacteria were selected as a representative algal group responsible for triggering algal blooms in the Shanxi Reservoir. Among Cyanobacteria, Microcystis, Anabaena, and Gloeocapsa were chosen as the algal response indicators for calculating the algal bloom risk index.

In summary, the basic data for the indicators used to calculate the algal bloom risk index were obtained, as shown in

Table 1. Basic data for algal bloom risk indicators in April 2023.

Branch	Sampling Position	Tem (°C)	pH	DO (mg/L)	H′	TLI	Anabaena (Cells/L)	Gloeocapsa (Cells/L)	Microcystis (Cells/L)
Shanxi Branch	SXR1	16.93	7.76	3	2.14	64	0.01	1.02	7.31
	SXR2	17.27	8.27	3.68	2.3	44.59	0.02	2.13	9.25
	SXR3	17.38	8.34	3.62	2.6	60.59	0.89	1.13	6.86
	SXR4	17.93	8.58	3.5	1.97	61.6	0.05	0.78	10.38
	SXR5	17.91	8.47	3.33	2.94	39.01	0.52	1.88	2.87
	SXR6	19.14	8.69	2.52	2.58	47.2	0.74	0.82	5.51
	SXR7	19.56	9	3.51	3.06	31.78	2.04	5.98	5.33
	SXR8	20.84	8.59	3.33	2.44	54.4	1.67	0.01	4.53
	SXR9	18.37	8.46	3.31	2.5	50.4	0.74	1.72	6.51
Xuezuokou Branch	XZKS1	18.15	8.49	3.4	3.08	63.74	0.65	1.34	1.78
	XZKS2	18.66	8.54	3.43	2.6	60.96	0.03	0.02	7.58
	XZKS3	18.81	8.53	3.35	2.4	27.33	0.01	0.87	2.69
Jujiangxi Branch	JJXS1	19.73	8.51	3.44	2.54	50.88	0.84	1.24	7.87
	JJXS2	19.91	8.59	3.69	3.1	68.02	0.01	0.73	6.02
	JJXS3	19.74	8.66	3.4	2.16	63.85	0.06	1.63	10.88
	JJXS4	20.14	9.8	3.6	2.58	68.11	0.02	22.83	15.58
	JJXS5	19.7	9.72	3.57	1.86	50.78	1.12	8.36	9.88
Sanchaxi Branch	SCXS1	20.07	8.71	3.18	1.95	59.35	1.33	2.64	5.85
	SCXS2	17.77	8.21	5.74	1.63	59.59	0.01	0.02	30.54
	SCXS3	19.42	8.68	3.21	3.52	28.28	0.03	8.86	4.48
Huangtankeng Branch	HTKS1	17.93	8.45	3.29	3.43	66.59	0.04	1.01	2.87
	HTKS2	18.24	8.66	3.18	4.18	66.52	4.17	4.33	4.28
	HTKS3	18.42	9.24	3.5	3.95	69.13	9.88	1.89	6.75

(April 2023 data are used as an example).

3.1.2. Comprehensive Weight

(a)

Weight based on IFAHP (Improved Fuzzy Analytic Hierarchy Process)

A first- and second-level index judgment matrix were developed in this study by progressively assessing the eight algal bloom risk index components using the three-scale method. Subsequently, the initial array of weight vectors was obtained, as delineated in Equation (c3), specifically W(0) = (0.06, 0.12, 0.15, 0.20, 0.05, 0.19, 0.15, 0.08). Four iterations of the data were used to enhance the precision of the weight calculations. The final weights for the eight algal bloom risk assessment criteria C1 to C8 were 0.11, 0.06, 0.20, 0.18, 0.09, 0.15, 0.08, and 0.13, respectively.

(b)

Weight based on EWM (Entropy Weight Method)

In this study, the original data matrix R was established based on the data of various algal bloom risk indicators in the Shanxi Reservoir and was subsequently normalized using Equation (c5).The entropy value can be obtained as $s_1=0.9673,s_2=0.9605,s_3=0.8875,s_4=0.8564,s_5=0.9418,s_6=0.9379,s_7=0.9786,s_8=0.9011$ using Equation (c6), and the entropy weight can be calculated as $w_1^{″}=0.06,w_2^{″}=0.07,w_3^{″}=0.20,w_4^{″}=0.25,w_5^{″}=0.10,w_6^{″}=0.11,w_7^{″}=0.04,w_8^{″}=0.17$ using Equation (c7).

(c)

Weight based on GT (Game Theory)

Equations (c10) and (c11) provide a linear combination of weight coefficients ${\alpha }_1^{*}=0.32$ and ${\alpha }_2^{*}=0.68$ for the risk variables of algal bloom, as derived from game theory. By substituting the two weight coefficients into Equation (c12), the comprehensive weight of each assessment component can be computed; the results aredisplayed in

Table 2. Combined weights for each algal bloom risk indicator.

Indicators	Subjective Weight	Objective Weight	Comprehensive Weight
Tem (C1)	0.11	0.06	0.08
pH (C2)	0.06	0.07	0.07
DO (C3)	0.20	0.20	0.20
H′ (C4)	0.18	0.25	0.23
TLI (C5)	0.16	0.18	0.18
Anabaena (C6)	0.15	0.11	0.12
Gloeocapsa (C7)	0.08	0.04	0.05
Microcystis (C8)	0.06	0.09	0.07

.

3.1.3. Calculation Based on Improved TOPSIS

The algal bloom risk index model’s negative and positive ideal solutions, $V^{-}$ = (0, 0, 0, 0, 0, 0, 0, 0) and $V^{+}$ = (0.08, 0.07, 0.20, 0.23, 0.18, 0.12, 0.05, 0.07), were calculated in combination with the weighted normalized matrix using Equations (a3) and (a4). The initial algal bloom risk index (RI-I) at each sampling position in the Shanxi Reservoir was calculated by substituting the positive and negative ideal solution distances of each sampling position from Equations (a5) and (a6) into Equation (a7).

3.2. Adaptive Simplified Algal Bloom Risk Index (RI-S)

From the improved TOPSIS calculation steps, it can be observed that the process involves a large number of factor indicators, resulting in substantial computational complexity and certain inconveniences. To enhance the model’s practicality and enable an accurate yet straightforward evaluation of algal bloom risk, non-critical indicators were eliminated through the application of an adaptive simplification approach.

The average weight of the risk indicators is defined as the adaptive simplification coefficient $\mathsf{\alpha }$. Risk indicators with comprehensive weight values lower than $\mathsf{\alpha }$ are considered non-critical and are subsequently eliminated. The comprehensive weights of the non-critical indicators are then evenly redistributed among the critical indicators. The calculation formulas for the adaptive simplification coefficient $\mathsf{\alpha }$ and the adaptive simplified, comprehensive weight ${\omega }_x^{*}$ of the critical risk indicators are as follows:

$$\mathrm{m}=\mathrm{p}+\mathrm{q}$$

(e1)

$$\mathsf{\alpha }=\overline{s_i^{*}}={\displaystyle \frac{1}{\mathrm{m}}}$$

(e2)

$$\mathrm{When}{s}_i^{*}\le \mathsf{\alpha }, \mathrm{the} i\mathrm{th} \mathrm{risk} \mathrm{indicator} \mathrm{is} \mathrm{eliminated}$$

(e3)

$$\mathrm{When}{s}_i^{*}>\mathsf{\alpha },{\omega }_x^{*}=s_x^{*}+{\displaystyle \frac{\sum _{h=1}^{\mathrm{p}}{s}_h^{*}}{\mathrm{q}}}$$

(e4)

where i = 1, …, m; j = 1, …, n; x = 1, …, q; h = 1, …, p; m is the total number of risk indicators, and the number is 8; n is the number of sampling positions, and n = 23; q is the number of critical risk indicators; p is the number of non-critical risk indicators; $s_i^{*}$, $s_x^{*}$, and $s_h^{*}$ are the original composite weights of each risk indicator, the original composite weights of critical risk indicators, and the original composite weights of non-critical risk indicators, respectively, calculated from Equation (c12).

The weighting results of the composite indicators in Table 2 were substituted into the above equation, and it can be concluded that the three risk indicators, namely, water quality factor DO, Shannon–Wiener diversity index (H′), and Trophic Level Index (TLI), are critical risk indicators. Their adaptive simplified comprehensive weighting results, ${\omega }_x^{*}$, are 0.33, 0.36, and 0.31, respectively. After substituting ${\omega }_x^{*}$ into the deformed Equation (a1), the deformed Equation (a1) reads as follows:

$$R^{*}={\left(r_{\mathit{xj}}^{*}\right)}_{\mathrm{q}\times \mathrm{n}}={\left({\omega }_x^{*}\overline{r_{\mathit{xj}}}\right)}_{\mathrm{q}\times \mathrm{n}}$$

(e5)

The subsequent calculation process follows the original steps, and the final result, obtained from Equation (a7), is the adaptively simplified algal bloom risk index RI-S.

3.3. Seasonal and Spatial Variations in RI-S

3.3.1. Seasonal Variations in RI-S

In this study, the seasonal variations in RI-S were investigated from three perspectives: the entire reservoir area, the main area, and the branch area, based on the actual watershed of the Shanxi Reservoir. The four branches within the branch area were analyzed separately. The results are shown in Figure 3.

The analysis of the RI-S across the four branches in various seasons reveals that the seasonal fluctuations are more pronounced in the Jujiangxi Branch, Sanchaxi Branch, and Huangtankeng Branch. The RI-S is highest in spring, followed by autumn, then summer, with winter recording the lowest assessment. The RI-S showed the highest value in the Sanchaxi Branch, followed by the Jujiangxi Branch, with the lowest value recorded in the Huangtankeng Branch. The RI-S in the Xuezuokou Branch exhibited minimal fluctuation across the three seasons of spring, summer, and autumn, predominantly stabilizing between 0.6 and 0.7 without significant cyclical variations.

The RI-S for the branch area is the highest, followed by the risk value for the entire reservoir, while the main area exhibits the lowest risk value. The seasonal trends of the RI-S for these three remained broadly consistent. Spring exhibited the peak RI-S, with the branch area, entire reservoir, and main area ranked from highest to lowest indexes, respectively. The RI-S showed a relative decrease in summer, with the risk values for the branch area and the entire reservoir being comparable and exceeding the risk value of the main area. Algal bloom coverage increased during autumn, leading to a significant increase in the RI-S, which subsequently decreased to its lowest point in winter. All three regions’ algal bloom risk indexes were roughly equivalent in both autumn and winter.

3.3.2. Spatial Variations in RI-S

The spatial distribution of RI-S was analyzed according to the division of the main and branch areas in the study area. The spatial regional distribution is shown in Figure 4. The distribution of the RI-S in the main area showed significant spatial variability, with the RI-S in the central part being higher and that in the tail part being lower. Overall, the annual mean value of RI-S in the northern part of Shanxi Reservoir was higher than that in the southern part, and the annual mean value in the western part was higher than that in the eastern part.

When the RI-S of the main area and the branch areas are compared, it is evident that the main area’s RI-S fluctuates much more than the branch areas throughout the year. However, the RI-S of the branch areas is higher in the spring and summer than that in the main areas. This is primarily because the branch area’s three branches—the Sanchaxi Branch in the northwest, the Xuezuokou Branch in the northeast, and the Jujiangxi Branch in the southeast—have risk indexes that are significantly higher than those of the main area. The RI-S was somewhat higher in the main area than in the branch area during the winter, and it was higher in the main area’s western section and lower in its eastern section during the autumn.

The average annual RI-S of the Sanchaxi Branch was significantly higher than that of the other branches, while the average annual RI-S of the Xuezuokou Branch was significantly lower than that of the other branches, according to a comparison of the RI-S of each branch area. The Xuezuokou Branch had the lowest RI-S in the spring, while the Jujiangxi and Sanchaxi branches had an RI-S that was somewhat higher than the Huangtankeng branch. The RI-S results of the Huangtankeng Branch, Sanchaxi Branch, and Xuezuokou Branch were considerably greater in the summer than those of the other branches. The RI-S results of Sanchaxi, Huangtankeng, and Xuezuokou branches were closer to one another and fluctuated less in the autumn than the RI-S of the other branches, with the Jujiangxi branch having a higher RI-S. All the branches had an extremely low RI-S during the winter, with the Huangtankeng branch’s HTKS2 position having an only slightly higher risk value.

4. Discussion

4.1. Rationalization of Adaptive Simplified Method

A comparison of the results between the adaptive simplified algal bloom risk index (RI-S) and the initial risk index (RI-I) (Figure 5) reveals a high degree of consistency. The associated error of the adaptive simplified model ranges from 0.01 to 0.05, with a maximum deviation of less than 0.06. This minimal deviation underscores the effectiveness of the simplified method in accurately capturing algal bloom risk.

The method’s effectiveness was evaluated using statistical indexs, including the determination coefficient (R²), root mean square error (RMSE), mean absolute error (MAE), and mean relative error (MRE), calculated through Equations (d1)–(d6) (Figure 6). The R² values for the model across four quarters and the annual scale were 0.9884, 0.9968, 0.9906, 0.9946, and 0.9972, respectively, all exceeding 0.98. The RMSE peaked in spring at 0.0228 and reached its lowest annual value at 0.0073. Similarly, the MAE was highest in spring at 0.0187 and lowest for the year at 0.0052. The MRE reached its maximum in summer at 0.0312, with the lowest annual value at 0.0103.

Notably, the adaptive simplified calculation method maintains low error values across different time scales. The error indexs (RMSE and MAE) were the highest in spring, likely due to the increased environmental variability, such as fluctuations in water temperature and nutrient levels. This finding suggests that future research should consider seasonal complexity more comprehensively to further refine the model.

Compared with other studies utilizing simplified TOPSIS calculations [10,26,53], this study’s adaptive simplified method not only preserves the reliability and accuracy of the initial TOPSIS model but also significantly reduces the redundant computational processes involved in multi-factor risk indexs. This approach minimizes the workload and monitoring costs associated with large-scale algal bloom risk assessments, offering a more efficient solution for practical applications. It holds promise as a practical solution for large-scale applications, such as those required for the Shanxi Reservoir, thereby enhancing the feasibility of algal bloom risk assessments in resource-constrained settings.

4.2. Applicability of Adaptive Simplified Method

By integrating existing algal bloom assessment methods, such as the trophic state indices (including Carlson’s Trophic State Index (TSIc), the modified Carlson’s Trophic State Index (TSImc), and the Lake and Reservoir Trophic State Index (EIc)), along with domestic and international trophic state evaluation standards [54], it is evident that the adaptive simplified calculation of the algal bloom risk index proposed in this study is highly applicable to risk area classification and risk area identification. Based on the calculation results, a reliable risk classification standard for algal bloom risk levels is proposed: RI-S ≤ 0.7 corresponds to Level I risk; 0.7 < RI-S ≤ 0.9 corresponds to Level II risk; 0.9 < RI-S ≤ 0.95 corresponds to Level III risk; and 0.95 < RI-S ≤ 1.0 corresponds to Level IV risk. This classification standard not only provides a systematic approach to identify high-risk areas in the Shanxi Reservoir but also offers a practical mechanism for evaluating and managing algal bloom risk. The proposed method serves as a theoretical basis for implementing a more efficient, economical, and safe grading management system.

Through a comparative validation with two other widely recognized methods—the integrated trophic state index method (TLIrc) and the scoring method (SM) (

Table 3. Comparison of the adaptive algal bloom risk classification method with two commonly used water eutrophication evaluation methods.

Branch	Sampling Position	Spring			Summer			Autumn			Winter
		RI-S	TLIrc	SM	RI-S	TLIrc	SM	RI-S	TLIrc	SM	RI-S	TLIrc	SM
Shanxi Branch	SXR1	I	I	I	I	I	I	I	I	I	I	I	I
	SXR2	II	II	II	I	I	I	I	I	I	I	I	I
	SXR3	II	II	II	I	I	II	I	I	I	I	I	I
	SXR4	II	I	I	I	I	I	I	I	I	I	I	I
	SXR5	I	II	I	I	I	I	IV	IV	IV	I	I	I
	SXR6	I	I	II	II	III	II	II	II	III	II	II	II
	SXR7	III	IV	III	I	I	I	II	II	II	I	I	I
	SXR8	I	I	I	I	I	I	I	I	II	I	I	I
	SXR9	IV	IV	III	I	I	I	I	I	I	I	I	II
Xuezuokou Branch	XZKS1	II	II	II	II	II	II	I	I	I	I	I	I
	XZKS2	I	I	I	I	I	I	I	I	I	I	II	I
	XZKS3	I	I	II	I	I	I	III	III	III	I	I	I
Jujiangxi Branch	JJXS1	II	II	III	II	II	II	II	II	II	I	I	I
	JJXS2	I	II	I	I	I	I	I	I	I	I	I	I
	JJXS3	II	II	II	I	II	I	II	II	II	I	II	I
	JJXS4	IV	IV	IV	I	I	I	I	I	I	I	I	I
	JJXS5	IV	III	III	I	I	II	I	II	I	I	I	I
Sanchaxi Branch	SCXS1	II	II	III	I	I	I	IV	III	IV	I	I	I
	SCXS2	IV	IV	IV	I	I	I	II	II	II	I	I	II
	SCXS3	III	III	IV	I	I	I	II	II	II	I	I	I
Huangtankeng Branch	HTKS1	I	II	II	I	I	I	I	I	I	I	I	I
	HTKS2	II	III	II	IV	IV	IV	I	I	I	II	II	II
	HTKS3	III	III	III	I	I	I	IV	IV	IV	I	I	I

)—it is evident that, although there are slight differences in the grading results across these evaluation methods, the overall trend remains consistent, with the maximum difference in risk area levels not exceeding one level [55,56]. This consistency supports the credibility of the proposed adaptive simplified algal bloom risk index. Moreover, the results highlight the method’s ability to address certain limitations of traditional approaches. For instance, the integrated trophic state index method relies on fixed evaluation indices and weights, and its correlation coefficients are heavily dependent on individual indices, potentially leading to skewed results. In contrast, the scoring method faces challenges concerning the physical significance of the weights, which can be disproportionately influenced by a single parameter, resulting in deviations from the actual outcomes.

This study adopts a more context-specific approach by considering the Shanxi Reservoir’s role as a drinking water source, along with providing a thorough evaluation of the complexity and ambiguity of the assessment variables. As a result, the proposed method delivers more objective, accurate, and reliable evaluation outcomes, demonstrating its potential as a robust alternative to traditional methods for assessing algal bloom risk.

The mapped distribution of algal bloom risk areas in the Shanxi Reservoir (Figure 7) shows that while higher-risk areas appear in spring and autumn, the overall risk is well managed. This highlights the effective control measures for algal bloom risk in the reservoir. The seasonal variation in algal bloom risk in the Shanxi Reservoir underscores the complex interplay between environmental factors and human activities. Elevated risks in spring, particularly in Level IV areas, are largely attributable to nutrient loading from the surrounding urbanized regions, with increased nitrogen and phosphorus inputs from residential and agricultural runoff. This highlights the crucial role of local human activities, such as improper waste management and agricultural practices, in driving nutrient enrichment and exacerbating water quality issues. In contrast, the summer months saw a decline in risk, with the only remaining high-risk area attributed to improper sewage discharge, further reinforcing the importance of effective waste management in mitigating algal bloom risk. The consistently higher risk in autumn, particularly in the Huangtankeng and Sanchaxi branches, suggests that these areas are particularly sensitive to ongoing human influence, necessitating continuous monitoring and intervention. The reduced risk in winter, linked to lower water temperatures, decreased sunlight, and reduced human activity, points to seasonal dynamics in nutrient cycling and the diminished impact of anthropogenic pollution. These findings emphasize the need for tailored management strategies that account for both environmental conditions and the substantial role of human activities in shaping water quality, particularly in densely populated or agriculturally active regions. Effective monitoring and prevention efforts in high-risk areas are essential for managing algal bloom risk in the long term.

Overall, the algal bloom risk in the Shanxi Reservoir is relatively low; however, there are specific areas where water use management needs to be strengthened. Subsequent studies should explore the inclusion of additional bioindicators as potential risk factors for algal blooms, thereby enabling a more comprehensive evaluation of eutrophication in aquatic ecosystems. It is imperative for management authorities to strictly regulate nitrogen and phosphorus inputs, closely monitor water quality during the mixing of water from various sources, and integrate routine water quality testing with bioremediation strategies. These measures will be essential in effectively mitigating eutrophication and ensuring the long-term protection of the basin’s ecological integrity.

5. Conclusions

The adaptive simplified calculation method for the algal bloom risk index, proposed based on the improved TOPSIS model, demonstrates both scientific validity and practicality. With error indexs all below 0.035, it enables a more accurate assessment of algal bloom risk across different regions of the Shanxi Reservoir. Furthermore, the method is not limited to cyanobacterial blooms and can be applied to various types of algal bloom outbreaks.

The comparison with the actual conditions in the Shanxi Reservoir revealed that the risk area classification method, based on the adaptive simplified algal bloom risk index, is highly rational. The number of high-risk areas in the reservoir increases significantly during the spring and autumn, indicating the need to moderately enhance the frequency or monitoring in future water quality assessments. Additionally, the algal bloom risk levels near residential areas were significantly higher than those in other regions, underscoring the need for enhanced management and control measures to protect drinking water sources and safeguard public health.

This paper’s algal bloom risk indicators are limited to biological and water environment factors, such as cyanobacteria, and have some limitations. For a more thorough analysis, other factors, like zooplankton, could be added, as well as the occurrence of specific emergencies in real situations, such as chemical liquid transportation trucks that dump chemical supplies close to drinking water sources. Relevant studies by subsequent researchers could increase the density of thr sampling positions to make the algal bloom risk index distribution more uniform, make up for the current shortcomings, and improve the accuracy and persuasiveness of the analysis results.