水、土、能是人类生存和发展的重要自然资源。基于稳定性(S)、协调性(H)、可持续性(F)构建安徽省"水-土-能"系统安全评价指标体系，利用"单指标量化-多指标综合-多准则集成"(Single index quantification-multi-index comprehensive-multi-criteria integration，SMI-P)法测算各子系统指数及其系统安全水平，引入Copula函数分别探究S-H、S-F、H-F和S-H-F等不同组合的联合概率分布，测算其联合风险概率。结果显示:2012-2021年，安徽省"水-土-能"("Water-Land-Energy"，WLE)系统安全水平波动上升，均值为0。568 5，其中稳定性对系统安全水平影响最大;S-H、S-F、H-F分别呈弱正相关、强正相关、较强负相关关系，S-F联合风险概率最大，为0。280 7;S-H-F系统联合风险概率为0。071 2。当S、H、F其中一个固定时，另外两个的值越大，相应的联合风险概率越大。探究"水-土-能"系统安全水平及风险发生频率，有利于保障区域可持续发展，提高风险分析精度，为决策部门提供有效信息。
Safety evaluation and joint risk probability calculation of Water-Land-Energy systems in Anhui Province
This study establishes an evaluation index system for the safety of the Water-Land-Energy(WLE)system in Anhui Province,focusing on stability(S),harmony(H),and sustainability(F).The Single index quantification-multi-index comprehensive-multi-criteria integration(SMI-P)method is utilized to quantify the indexes,and the weight weighting method is employed to determine the index of each subsystem.Subsequently,the safety level of the WLE system is computed based on these indices.To model the joint probability distribution of each subsystem's index,the Copula function is applied to fit their marginal distribution functions.Based on the aforementioned steps,joint distribution functions for various combinations(S-H,S-F,H-F,and S-H-F)were constructed.Subsequently,the optimal joint distribution function was determined using Euclidean distance,and the joint risk probability associated with each combination was assessed.The results indicate that from 2012 to 2021,the safety level of the WLE system in Anhui Province fluctuated between 0.511 5 and 0.594 6,with an average value of 0.568 5.Throughout this period,it consistently remained in the critical safety stage.The mean safety levels of each subsystem are as follows:S(0.587 2)＞H(0.562 6)＞F(0.555 6).The correlation between the safety level of the Stability subsystem and the overall system is the highest at 0.859 9.Additionally,the safety levels of S-H,S-F,and H-F show weak positive correlation,strong positive correlation,and strong negative correlation,respectively.The probability density plots fitted for S-H and S-F exhibit asymmetry.S-F displays greater sensitivity to changes in the low-value region,whereas H-F demonstrates characteristics of negative symmetry.Additionally,there is a degree of precedence in the development of these two combinations.The joint risk probability of S-F is the highest at 0.280 7,whereas S-H-F stands at 0.071 2.Notably,when one of S,H,or F is fixed,an increase in the values of the remaining two corresponds to a higher joint risk probability.
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