Located in the hinterland of the Beijing-Tianjin-Hebei region, the BYD wetlands are important sources of water regulation, flood control, pollution mitigation and ecological protection for the region. As the largest freshwater wetland area in the North China Plain, the BYD wetlands consist of more than 3700 streams and canals, and 143 lakes and ponds, whose bottom elevation ranges from 5.5 to 6.5 m (Zhuang et al., 2011). The BYD wetlands are bounded by 38°45′-39°02′N, 115°38′-116°07′E, with a total area of 366 km² when the water level is 10.5m in Shifangyuan station above the Dagu sea level (Zhang et al., 2007). As a part of the ancient lake basin, the BYD wetlands lie in the low-lying area between Yongding River alluvial fan and Hutuo River alluvial fan, forming a large depression which catches eight main tributaries of the Daqing River system from Taihang Mountain (Fig. 1). On the basis of Quaternary alluvium, the soil developed mainly into swamp soil, cinnamon soil, fluvo-aquic soil and paddy soil. The vegetation consists of four subtypes including emergent, submerged, floating-leaved, and freely-floating aquatic vegetation. The region is characterized by a warm temperate and continental monsoon climate with an annual average temperature of 12.0 ℃, and annual average precipitation of 550-600 mm which varies greatly each year (Jiang et al., 2018). Within the wetlands, there are 39 pure water villages and 89 semi-water villages, with about 220000 residents (Yi et al., 2019). Around the wetlands, the dominant land use is farmland and the landscape structure is simple. Environmental pollution and ecological degradation in this region have been accelerating in the past several decades due to the continued pressures from rapid economic growth, industrialization and urbanization.

Due to the complexity of study objects, the diversity of evaluation targets, and the uncertainty of the mechanisms influencing ecological vulnerability, there is no uniform indicator or standard system for vulnerability assessment or evaluation at present (Shang and Bai, 2012; Wang and Zhong, 2020). Every ecosystem is composed of the organisms and their environment. Considering that the environment is composed of air, water and soil, and is filled with a large number of spores and seeds which can germinate and grow once the conditions are suitable, we did not choose organisms as the indicators in our assessment model, but only evaluated the environmental elements, so it may also be called an environmental vulnerability assessment. However, it is difficult to separate environmental vulnerability from ecological vulnerability (Beroya-Eitner, 2016). The environmental limiting factors of the BYD wetlands are water shortage and pollution, so the selection of the evaluation indicators was mainly based on these two factors. By on-site surveys of the BYD wetlands during 2010-2017, with reference to the indicators commonly used in previous studies (Li et al., 2010; Yuan et al., 2011; Liu et al., 2014), and following the principles of representativeness, comprehensiveness, systematics and suitability (Li et al., 2010; Jin and Meng, 2011), an evaluation indicator system of ecological vulnerability for the BYD wetlands was finally constructed (Table 1). In this system, the vulnerability evaluation indicators are divided into two categories: cause and result. The cause is divided into natural cause and social cause, which represents the sensibility or influence of the system. The result includes sci-tech and economic elements, which represents its adaptive/recovery capacity or resilience (Li et al., 2010; Liu et al., 2014). The evaluation indicator set C = {c₁, c₂, …, c_m}, and m = 23 (Table 1).

According to the actual data of each evaluation indicator, an evaluation criteria set S is determined (modified according to the literature of Yuan et al. (2011)). This method involves first calculating the average of each year as S₃. Then, taking S₃ as a standard, the value is increased and decreased by 10% and 30%, respectively, dividing the ecological vulnerability assessment criteria into five grades. For S = {S₁, S₂, …, S_n} (n=5), their meanings correspond to: Grade I, not fragile; Grade II, low fragile; Grade III, generally fragile; Grade IV, high fragile; and Grade V, severely fragile.

All of the data for the evaluation indicator set are primarily normalized, and a fuzzy relation matrix R is constructed.

where r_jk is the membership degree of the j^th indicator in the evaluation indicator set C to the k^th grade in the evaluation criteria set S. In the formula, 0≤r_jk≤1 ( j=1, 2, …, m; k=1, 2, …, n).

According to the maximum and minimum membership function from fuzzy set theory, whose membership function represents the degree to which the specified value belongs to the set in the fuzzy evaluation model (Wang et al., 2009), the membership degrees of the five grades of ecological vulnerability under the influence of a single factor are determined quantitatively.

The normalized expression of the membership degree r_jk (Liu et al., 2017; Zhao et al., 2018) is:

For a positive indicator,

For a negative indicator,

where X_jk is the original value; and X_max and X_min are the maximum and minimum of the j^th indicator, respectively.

Finally, the five-grade membership function of each evaluation indicator is constructed in turn, the membership degree is obtained by substituting the evaluation factor data into the five-grade membership function, and ultimately 23 groups are obtained. Five numbers in each group are obtained to form a 5×23 fuzzy matrix.

The weight represents the importance of each evaluation indicator. The entropy weight method, which has been confirmed as an objective method for weight determination by previous studies (Zou et al., 2006; Zhao et al., 2018), is adopted in this evaluation to determine the weights. If the value of the evaluation indicator fluctuates greatly, then the calculated entropy value is small, indicating that the evaluation indicator has more information and the corresponding weight assigned to the evaluation indicator is large. On the contrary, if the differences between the values of a certain evaluation indicator are small, then the calculated entropy value is large, inferring that the indicator has less information and the weight assigned to the evaluation indicator is correspondingly small. By analogy, the weight of each evaluation indicator is determined according to the amount of information represented by that evaluation indicator. There are m evaluation indicators and n evaluation objects, and the information entropy of the j^th indicator (Zou et al., 2006; Liu et al., 2014) can be defined as:

where K is a coefficient, and f_jk is the ratio of the k^th evaluation object value to the total evaluation object value of the j^th indicator. In the formula, ${{f}_{jk}}=\tfrac{{{r}_{jk}}}{\underset{k=1}{\overset{n}{\mathop{\mathop{\sum }^{}}}}\,{{r}_{jk}}},\begin{matrix} {} \\ \end{matrix}K=\frac{1}{\ln n}$, and suppose when ${{f}_{jk}}=0,{{f}_{jk}}\ln {{f}_{jk}}=0$.

The entropy weight of the j^th indicator can be defined as:

where H_j is the information entropy of the j^th indicator, and m is the number of evaluation indicators. In the formula, 0≤Wj≤1, $\underset{j=1}{\overset{m}{\mathop \sum }}\,{{w}_{j}}$ ≤1.

Using this formula, the weight matrix W, for W = {Wj} (j=1, 2, …, m) can be obtained.

Finally, the weight matrix W and the fuzzy relation matrix R are combined to produce the fuzzy comprehensive evaluation index matrix V.

In the formula (6), “Ô” represents the fuzzy composite operator, and the calculation is similar to the ordinary matrix calculation. There are two fuzzy composite operators which are used more widely: one is the “×” and “+”, the other is the “∧”and “∨”. They can be expressed as Ô (×, +) and Ô (∧,∨), respectively. According to our previous studies, a fuzzy evaluation model using the operator Ô (∧,∨) may lose more information than one using the operator Ô (×, +) (Wang et al., 2009). Therefore, the operator Ô (×, +) was finally chosen to carry out the matrix composite operation.

The evaluation indicator data are mainly collected from four sources: 1) The annual average temperature and summer precipitation data from Hebei Meteorological Service; 2) The wetland water area, average water level, and shallow groundwater depth data from Anxin County Water Conservancy Bureau; 3) The overall assessment of water quality, permanganate index, chemical oxygen demand, ammonia nitrogen, total phosphorus, and mean composite pollution index data from our field survey; 4) The relevant social and economic data from Hebei Economic Yearbook (2011‒2018) and the National Economic and Social Development Statistical Bulletin of Baoding City in 2010-2017. All of the data for the 23 indicators must be examined by the parameter correlation analysis (Wang et al., 2008) before the fuzzy evaluation calculation. Based on the entropy weight values, the data for 20 indicators are determined to participate in the computation of the final fuzzy comprehensive evaluation index. The land use data is provided by the Data Center for Resources and Environmental Sciences, Chinese Academy of Sciences (RESDC) (http://www.resdc.cn).

The weight of each evaluation indicator has been calculated by substituting the evaluation indicator data into formula (4) and formula (5) to obtain the weight matrix W (Table 2).

Among multiple weighting methods for the ecological and environmental vulnerability assessment, the entropy weight method, which determines the weight of each indicator based on the amount of information provided by the observation values of the evaluation indicator, is currently considered to be the most objective weighting method (Zhao et al., 2018). For the wetland ecological vulnerability assessment, we used the entropy method to calculate the weight for each evaluation indicator. By comparing the entropy weight results, we found that the weight values of the evaluation indicators c₁₈, c₃, c₉, c₁₀, c₁₉ and c₂₃ were larger than the others, and the corresponding evaluation indicators were: industrial smoke and dust emission, wetland water area, ammonia nitrogen, total phosphorus, rate of industrial solid wastes disposed, and GDP per capita, respectively. The study showed that the first two indicators, industrial smoke and dust emission and wetland water area, both have weight values above 0.05 and contribute the most to the ecological vulnerability of the BYD wetlands in this period. These two are followed by ammonia nitrogen and total phosphorus content of water body, rate of industrial solid wastes disposed, and GDP per capita, each of which has a weight value of above 0.047. These indicators are considered to be the factors that have a greater impact on the ecological vulnerability of the Baiyangdian wetlands. They are all from social cause except for the wetland water area, which is a natural factor yet is regulated to a certain extent by human activities because of the upstream diversion and downstream gate control. The pollution of air, water and the natural environment will not only cause declining environmental quality, but also make the wetland ecology more fragile. On the contrary, a high-quality regional environment is bound to improve the wetland ecological situation. Therefore, the wetland ecological vulnerability is closely related to regional environmental conditions, and it is an indicator of regional environment quality. In other words, regulation of the wetland ecological vulnerability is a systematic project.

After substitution of the evaluation indicator data into the fuzzy relation matrix R, using formula (6) to combine it with the weight matrix W by the composite operator, the fuzzy comprehensive evaluation index matrix V is obtained. According to the principle of maximum membership degree in the fuzzy set, the grade corresponding to the maximum value by the calculation of V is the final evaluation grade in the fuzzy comprehensive evaluation, which means the vulnerability grade. The membership degrees to Grade I- Grade V of the fuzzy comprehensive evaluation are shown in Table 3.

The distributions of the membership degrees to the five grades of the ecological vulnerability assessment for the BYD wetlands in the eight evaluated years are shown in Fig. 2. The higher the value, the bigger the membership degree to a certain grade. The results showed that the membership degrees of the BYD wetlands to Grade Ⅱ were higher than the other grades in 2010; during 2011-2013, the membership degree to Grade Ⅱ declined gradually, and that to Grade Ⅲ increased; in 2014, the membership degree to Grade Ⅳ increased obviously; and from 2015 to 2017, the membership degree to Grade Ⅳ significantly decreased, while that to Grade Ⅲ increased, which showed a measurable improvement of the ecological situation of the BYD wetlands during the years of 2015, 2016 and 2017. From a comprehensive analysis of the evaluation results above, the ecological vulnerability of the BYD wetlands was assessed as low fragility in 2010, general fragility in 2011-2013, and high fragility in 2014, which turned back into general fragility in the period of 2015-2017. The vulnerability grades for the periods of 2010, 2011-2013, 2014, and 2015-2017 were evaluated as Grade Ⅱ, Grade Ⅲ, Grade Ⅳ, and Grade Ⅲ, respectively.

Many causes exist for the changes in ecological vulnerability of the BYD wetlands in this period, which can be summarized into two aspects. The first is the change in regional environmental quality. The ecological degradation and declining environmental quality in the Beijing-Tianjin-Hebei region has led the government and the public to pay more attention to natural conservation and environmental protection. A series of policies and strategies have been implemented, yet the improvement of environmental quality still objectively needs a process. Second, concrete intervening measures, such as water replenishment and pollution control, were taken to improve the ecological status and environmental quality of the BYD wetlands. For example, during the period from 2006 to 2010, the diversion of the Yellow River to the BYD wetlands occurred a total of four times, with a total amount of water replenishment of 4×10⁸ m³, effectively improving the ecological situation of the BYD wetlands. However, the flood of Daqing River in July 2012 not only increased the amount of water resources, but also brought in pollutants (sewage, garbage, etc.) from along the waterways. At the same time, the diversion of the Yellow River to send replenishing water into the wetlands was cancelled. Thus, the BYD wetlands reached the grade of high fragility in 2014. In 2015, 3.3×10⁷ m³ of water was transferred from the Xidayang Reservoir. In addition, the environmental pollution in the Beijing-Tianjin-Hebei region was briefly contained due to some administrative interventions and environmental protection strategies, which may also be an important reason for the significant improvement in the ecological condition of the BYD wetlands since 2015. However, owing to the regional environmental problems which have not been effectively solved, the overall ecological status of the BYD wetlands is relatively less optimistic.