Yunnan Province lies on the border of southwest China, Figure 1, with a total area of 394,100 square kilometers, accounting for 4.1% of the country’s total land area, ranking eighth in China. Yunnan Province is rich in water resources. In 2014, the total amount of water resources in the province was 172.7 billion cubic meters, ranking the third in China. It has more than 900 rivers and more than 40 natural lakes each of whose catchment area is over 100 square kilometers. The per capita water resource in Yunnan is 1.83 times of that in China (2014 water resources bulletin of Yunnan Province). In spite of that, water resources in Yunnan Province are distributed unevenly in terms of time and space, from May to October, the precipitation is large, reaching more than 80% of the annual precipitation, while from November to April, the precipitation is less than 20% of the annual precipitation, Yunnan is inflicted with severe seasonal water shortage. In addition, Yunnan Province belongs to mountainous and plateau terrain, with a mountainous area of 331,100 square kilometers, accounting for 84% of the total area of the province, and various types of karst landforms are developed. The population, cultivated land, and water resources do not match. The dam area, which accounts for less than 7% of the land area of the province, concentrates about one-third of the population and two-thirds of the cultivated land, but the amount of water resources is only 5% of the province, the development and use of water resource impose a great difficulty and require a high cost; as a result, the available water resource is quite limited. In this context, it is of great urgency to study the comprehensive development level of reclaimed water in Yunnan Province.

The catastrophe theory can be adopted to directly address discontinuity independent of any special internal mechanism, in particular to systems whose internal forces are yet to be determined (Ather, 2021). The theoretical mathematical model is simple, and can solve the unknown problems that cannot be solved by traditional mathematical methods, so it is widely used in many fields. Common catastrophe models are described in Table 1.

The criterion for selecting different catastrophe models given in Table 1 is the number of control variables. When the control variable is 1, it corresponds to the fold catastrophe. When the number of control variables is 2, it corresponds to the cusp catastrophe. When the number of control variables is 3, it corresponds to the swallowtail catastrophe. When the number of control variables is 4, it corresponds to the butterfly catastrophe. The control variables here are the evaluation indexes of each layer.

The catastrophe theory-based assessment method (Zhang et al., 2013; Lv et al., 2020) is a multi-criterion approach and includes the following steps:

1) Development of an assessment matrix system. Indicators are selected according to the internal mechanism of the system to develop a multi-layer tree structure matrix which is able to reflect the importance sequence of these indicators.

For indicators concerning which higher values are preferred:     x = ( x i − x m i n ) / ( x m a x − x m i n ) . (1)

For indicators concerning which lower values are preferred: x = ( x m a x − x i ) / ( x m a x − x m i n ) . (2)

3) Normalization. A normalization formula is used to perform recurrence qualification analysis-based calculation to obtain the initial comprehensive assessment value R_i . According to the order from the bottom to the top, different potential functions of catastrophe model are selected according to the number of control variables (indicators), and the recursive calculation is carried out layer by layer. Finally, the catastrophe assessment value R_i can be obtained. Given the nature of the practical problem, “complementary” or “non-complementary” criterion applies. ① Non-complementary criterion: when the effects of control variables on the state variables are not interchangeable, the final value of these control variables is determined according to minimal principle; ②complementary criterion: when the effects of control variables on the state variables can compensate each other, the final value is the mean of these control variables.

Given the fact that normalization formulas for catastrophe assessment methods feature with convergence results, the final assessment results are often high (approach to 1, in Table 4), and the gaps between assessment values are often small. Although the quality of the evaluation object can be determined by the size order of the comprehensive evaluation value, it is not as intuitive as the evaluation value obtained by other comprehensive evaluation methods. 1. The year with relatively low comprehensive development level (2013) has a very high comprehensive evaluation value ( R i = 0.941), which is not in line with people’s habit of evaluating f objects according to the absolute size of evaluation value, and easily leads to misunderstanding (Dou and Ghose, 2006; Huderek et al., 2019). 2. The gaps between assessment values are often small. This is not convincing enough nor conducive to the follow-up utilization of evaluation results. For example, the year with a relatively low comprehensive development level (2013, R i = 0.941), although it is smaller than the year with a high comprehensive development level (2015, R i = 0.971), the gap is only 0.03, which is not conducive to intuitively seeing the dynamic change range and characteristics of comprehensive development level of reclaimed water through evaluation.

In particular, an adjusted initial catastrophe assessment was used to overcome the aforementioned problem and improve the catastrophe assessment method in this study. The adjustment process is described as follows:

1) The grade scale is refined to calculate the top-layer catastrophe assessment value r_n when each bottom layer control variable is 0, 0.05, 0.1, 0.15, 0.2,..., 0.9, 0.95, 1. In addition, this scale is used for describing the initial comprehensive value. Each grade corresponds to the following range (r_n ,r_n+1 ) (n = 0, 1, 2, 3,..., 19).

The sensitivity analysis is a crucial approach to analyze uncertain factors in an assessment (Schneeweiss, 2010). In this analysis, correlation to the assessment result is analyzed and predicted by changing each factor within its possible value range. A sensitivity analysis can be based on a single factor or multiple factors.

In a single-factor sensitivity analysis, only one factor is changed to an unfavorable direction (positive indicator is decreased by a certain percent and negative indicator is increased by a certain percent) while other factors remain unchanged; which is used to study the impact of change in such factors on the assessment result. A factor which shows a great impact on the output value is called a sensitive factor, otherwise, a non-sensitive factor. Given the fact that a change in a sensitive factor may impose a great impact on the development level of reclaimed water, all sensitive factors must be strictly controlled.

2012–2016 comprehensive development level of reclaimed water in Yunnan Province is the subject of this study. Quantitative data for this study were obtained from Yunnan Water Resource Reports, Yunnan Provincial Statistical Year Books and other source, and qualitative data were obtained by questionnaires and other methods, as shown in Table 2.

The “Indicator nature” means whether an indicator is positive or negative. An indicator is positive if it is “+” (D₂、D₃、D₅、D₆、D₇、D₈、D₉、D₁₀、D₁₁、D₁₂、D₁₃、D₁₄ ), and negative if it is “-” (D₁、D₄、D₁₅、D₁₆、D₁₇ ).

In indicator layer (D): indicators D ₁∼D ₃, D ₈∼D ₉, and D ₁₅∼D ₁₇ form a complementary swallowtail catastrophe model, and indicators D ₄∼D ₅, D ₆∼D ₇, D ₁₁∼D ₁₂, and D ₁₃∼D ₁₄ a complementary cusp catastrophe model; in element layer (C): C ₁∼C ₂ and C ₆∼C ₇ form a complementary cusp catastrophe model, and C ₃∼C ₅ a complementary swallowtail catastrophe model; in criterion layer: B ₁∼B ₃ form a complementary swallowtail catastrophe model. Layer-by-layer calculations according to the normalization formulas shown in Table 1 are depicted in Figure 3 and result in initial assessment values.

The grade scale is refined to calculate the target layer assessment threshold value r_n when the membership of each indicator in the bottom layer is (0, 0.05, 0.1, 0.15, 0.2,..., 0.9, 0.95, 1). Also, this scale is used for describing the initial comprehensive value. This process is shown in Table 3. If the calculated initial assessment value R _i falls within (r _n ,r _n+1) (n = 0, 1, 2, 3,..., 19), the comprehensive development level of reclaimed water is considered as grade n+1.

The initial assessment value R _i is transformed to the adjusted comprehensive assessment value R′_i according to formula (3), that is, the adjusted comprehensive assessment value obtained with the improved catastrophe method, as shown in Table 4.

It can be seen from Table 4 that the conclusions of catastrophe evaluation method are aggregated, the evaluation results tend to 1, and the differences between the evaluation values are small (0.941, 0.960, 0.971, and 0.955), which is not conducive to people’s intuitive judgment; the improved catastrophe evaluation method overcomes the problem that the comprehensive evaluation value of traditional catastrophe evaluation method is too high and too close, and the results are scattered, so it is easy to draw conclusions and more convincing.

In everyday life, standards for assessing matters are customary. For example, people tend to use fuzzy words like “outstanding, good, acceptable, pass, and fail” as the assessment scales. However, in the aforesaid improved assessment, 20 scales are used in order to ensure a higher precision, which is inconsistent with people’s habit and presents a challenge for obtaining assessment conclusion.

To more intuitively assess the development of reclaimed water, the grade scales are further restricted to five scales by having the membership degrees of indicators evenly distributed, that is, (0, 0.2), (0.2, 0.4), (0.4, 0.6), (0.6, 0.8), and (0.8,1] and by dividing the target layer into five corresponding ranges, as shown in Table 5.

It is known from calculation results with the improved evaluation method (Table 4) that R′₂₀₁₂ = 0.031 means that the comprehensive development level of reclaimed water in 2012 is “poor” (grade I); R′₂₀₁₃ = 0.334 means that the 2013 level is “pass” (grade II); R′ value from 2014 to 2016 falls within (0.4, 0.6), indicating the 2014–2016 level is “acceptable” (grade III), as shown in Table 6.

According to the evaluation results, the comprehensive development level of reclaimed water was low in 2012 and showed an upward trend from 2012 to 2016. After 2014, the comprehensive development level of reclaimed water tended to be stable. In this study, taking the comprehensive development level of reclaimed water in Yunnan Province in 2015 as the research object, and based on the evaluation model of comprehensive development level of reclaimed water established before, single-factor sensitivity analysis of the model indicators was conducted to study how the assessment value changes when each indicator is changed toward the unfavorable direction by the same percent (5% (Table 8), 10% (Table 9)) and determine the sensitivity of each indicator according to the absolute value of so-caused change in assessment value.

The absolute values of changes in assessment values calculated by changing each of the 17 indicators toward the unfavorable direction according to Table 8 and Table 9 are plotted in Figure 4.When the indicators change 5% toward the unfavorable direction, water deficiency (D₁ ) is the most sensitive factor and grade 1B treatment level (D₁₀ ) and construction impact (D17) are sensitive factors; when the indicators change 10% toward the unfavorable direction, water deficiency (D₁ ) is the most sensitive factor and wastewater discharge (D₄ ) and grade 1B treatment level (D₁₀ ) are sensitive factors. Therefore, water deficiency (D₁ ) is the controlling factor in the assessment of comprehensive development level of reclaimed water, which should be given key monitoring. Wastewater discharge (D₄ ), grade 1B treatment level (D₁₀ ), and construction impact (D₁₇ ) are important factors. When these factors change, they will also have a great influence on the comprehensive development level of reclaimed water, which should be strictly controlled.

The results show that water deficiency (D₁ ) is the most sensitive factor; and wastewater discharge (D₄ ), grade 1B treatment level (D₁₀ ), and construction impact (D₁₇ ) are sensitive factors.

Water deficiency (D₁ ) and wastewater discharge (D₄ ) reflect the demand for reclaimed water in terms of water resources and water environment, that is, the pressure on the development and utilization of reclaimed water. They are the decisive indicators affecting the comprehensive development level of reclaimed water. Grade 1B treatment level (D₁₀ ) is the water quality treatment standard that the sewage treatment plant can meet. It is the technical condition for the development and utilization of reclaimed water at this stage, which determines the process, cost, and the uses of reclaimed water. Therefore, the grade 1B treatment level (D₁₀ ) is a key indicator affecting the comprehensive development level of reclaimed water. In addition, with people’s increasing attention to environmental problems, the implementation of reclaimed water project will inevitably have a certain impact on the surrounding environment. Therefore, the construction impact (D₁₇ ) has also become an important indicator affecting the comprehensive development level of reclaimed water. On the premise of finding out the situation of local water resources, local governments should formulate reclaimed water use planning, adopt reasonable water quality treatment standards, further improve the sewage treatment capacity, and give full play to the advantages of reclaimed water use in the construction and operation cost of water supply system, so as to bring significant environmental benefits and promote the construction of a water-saving society.

These factors should be given key monitoring and strictly controlled because any change in them may cause a great influence on comprehensive development level of reclaimed water.