Multivariate drought prediction analysis is of great significance for drought disaster resistance. In this study, based on the derivation of monthly time-variant drought indicators SPIt, STIt and SSMIt by means of GAMLSS method, the conditional variables and their optimal combination structure were recognized through correlation analysis between targeted agricultural drought prediction variable SSMIti-1 and previous 1–12 monthly drought indicators SPIti-1-n, STIti-1-n and SSMIti-1-n, then the response relationship between combined distribution of conditional variable under different patterns and occurring probability of agricultural drought events was revealed through C-Vine Copulas function and conditional quantile regression method, and finally the CQRM approach based on C-Vine Copulas function of agricultural drought prediction analysis was proposed, which was verified through its application in northern Anhui Province area, China. It can be summarized from the application results that, (1) generally, previous 1–3 monthly-scale drought indicators SPIti-1-n, STIti-1-n and SSMIti-1-n can be utilized as primary conditional variables of agricultural drought prediction analysis, and the response time of drought propagation process to diverse conditional variables in summer and autumn (less than 1 month) is relatively shorter in comparative with that of winter and spring (nearly 3 months). (2) the utilization of more conditional variables is not definitely beneficial for the enhancement of agricultural drought prediction accuracy, and it is crucial to recognize effective monthly conditional variables and also construct its optimal combination structure through correlation analysis to improve the overall fitting performances of agricultural drought prediction analysis.

The implement of water resources spatial equilibrium (WRSE) schemes is fundamental task of integrated water resources management in China, in which, the evaluation and simulation analysis of WRSE system is of great concern for understanding the overall variation and feedback characteristics of WRSE system. Therefore, we utilized the ordered degree, entropy and connection number coupling model to evaluate the variation of WRSE system, and also employed system dynamics (SD) and scenario simulation integrated method to reveal the feedback characteristics between different equilibrium variables and subsystems, and thus the set pair analysis-SD based approach for structure simulation and variation trend evaluation of WRSE system was constructed. The application results in Anhui province, China demonstrated that, the overall variation of provincial spatial equilibrium situation of WRSE system presented obvious improving trend, 2009-2019, the index of ordered degree and connection number entropy in Hefei, increased from the minimum of 0.6434 (Grade 3, unequilibrium) to maximum of 0.9985 (Grade 1, equilibrium). Moreover, the future variation of WRSE system will display stable improving trend during 2020 to 2029, in which, annual water resources availability and water resources utilization efficiency will have significant influence on WRSE system. And the research findings can be favorable to formulate water resources development and utilization strategies.

Coordinated development of water resources-social economy-ecological environment (WSE) system is crucial for global prosperity and stability. However, due to the complex interactions and high uncertainty in the WSE system, there is a lack of effective evaluation and diagnosis methods of WSE system coordinated development. This study presents a quantitative development evaluation model using the connection number value. A mechanical model is proposed to identify the coordination status and uncoordinated orientation. Finally, a coordinated development evaluation model is established by a risk matrix coupling various combinations of the development and coordination states. In addition, this method is applied to 16 cities in Anhui Province, and its spatiotemporal characteristics of coordinated development and uncoordinated reasons for the WSE system from 2011 to 2020 are identified. The results indicate that the average development degrees D in North Anhui, Central Anhui, and South Anhui are 0.422, 0.474, and 0.560, respectively; and those of coordination degrees C are 0.779, 0.804, and 0.737, respectively. Thus, the development of the WSE system in South Anhui is ahead of that in Central Anhui, and that in North Anhui is the most backward. The coordination status in Central Anhui is superior to that in North Anhui, while that in South Anhui is the worst. Consequently, the trends of the development and coordination for the WSE system in Anhui Province are opposite. Furthermore, the coordinated development states of South Anhui, Central Anhui, and North Anhui deteriorate in sequence before 2016, but afterward, the sequence becomes Central Anhui, North Anhui, and South Anhui. Huainan, Wuhu, Bengbu, Tongling, and Suzhou are the most severely uncoordinated development cities, and the 16 cities in Anhui Province are divided into three uncoordinated types. In addition, some practical suggestions are presented for WSE system management in Anhui Province. The results obtained in this study help to elucidate the physical mechanism of WSE system coordinated development and provide policy insights for regional sustainable development.

为合理评价区域水资源分布与经济社会发展的空间均衡问题,在已有方法的基础上,提出了子区域基尼匹配系数与减法集对势相结合的水资源空间均衡评价模型.以水资源总量为基础,与人口数量、第二产业GDP 和耕地面积 3 项指标构建一一对应的匹配关系,利用洛伦兹曲线围成的单个子区域面积比来计算子区域基尼匹配系数,进而计算五元减法集对势,最终得到相应的评价等级,并对安徽省 2011-2018 年 16 个地级市的水资源空间均衡状态进行了评价.结果表明:在 3 组匹配关系中,空间均衡状态最好的为水资源总量-耕地面积,次之为水资源总量-人口数量,最差的一组为水资源总量-第二产业 GDP;3 对匹配关系空间均衡等级的多年均值表现为Ⅴ(反势)级,其中 2012 年和 2015 年的空间均衡状态最差,2018 年的空间均衡状态最佳.

Drought propagation analysis is of great significance to develop reliable drought-resistant schemes. In this study, based on the construction of time-variant meteorological and agricultural drought indicators SPI t and SSMI t through Generalized Additive Models for Location, Scale and Shape (GAMLSS) method, the static and dynamic drought propagation time were defined and determined by Five-element Subtraction Set Pair Potential (FSSPP) and Copula function methods. Then, the driving factors resulted in meteorological to agricultural drought propagation were recognized through Pearson Correlation Coefficient (PCC) indicator. And finally, the application results of the proposed approach in Anhui province, China indicated that, (1) the static propagation time of meteorological to agricultural drought process varied within 1 to 4 months, and differed slightly in different seasons. And drought propagation time in spring and summer was noticeably longer than that of autumn and winter. (2) the dynamic drought propagation time presented decreasing trend in winter, spring and summer but displayed slight increasing trend in autumn in Anhui province. On the whole, the research findings are beneficial for theoretical and practical research of drought propagation system.

对于水资源主要消耗用户和粮食重要生产基地的大型灌区,进行供需双侧调控是缓解灌区水资源供需矛盾、提高区域高质量可持续发展的重要途径之一.为了揭示灌区水-能源-粮食复杂的协调关系,针对性地开展系统优化调控.首先基于系统评价理论构建大型灌区水-能源-粮食系统耦合协调度评价模型,再基于灌区水资源系统模拟模型,以灌区水-能源-粮食耦合协调度最大为目标,以灌区主要作物水稻种植比例、水库分级分期旱限水位、水稻需水关键期限制供水比例作为优化调控变量,结合加速遗传算法,开展基于水资源供需双侧优化调控的灌区水-能源-粮食系统耦合协调评价与优化调控研究.杭埠河灌区应用结果显示:优化调控确定的灌区水稻种植比例、水库分级分期旱限水位、水稻需水关键期限供比例,相较于灌区运行现状能提高水-能源-粮食系统耦合协调水平,双季稻种植面积一定程度恢复使粮食产量明显提高,优化的水库旱限水位及水稻需水关键期水库限供比例,可在提升灌区干旱年份水资源利用效率的同时,较好地降低粮食作物因旱减产损失.可见,开展灌区供需双侧优化调控能显著提高灌区水-能源-粮食系统耦合协调性和适配性,可为提高水资源利用效率、布局主要粮食作物生产以及落实灌区水利高质量发展实施途径提供参考.

The development of social economy often requires a large consumption of water resources, and will also discharge a large amount of pollutants to the environment. Currently, the rapid development of regional water resources, social economy and ecological environment (WSE) complex system encounters significant challenges, and the coordination development of WSE complex system becomes important and necessary condition of regional sustainable development. Therefore, to scientifically evaluate the coordination development state of WSE system, based on the establishment of evaluation index system, the connection number and distance coordination model coupling approach for the coordination development evaluation of WSE complex system was proposed in this manuscript. The application results of the proposed method in Anhui Province, China indicate that, during 2011-2020, the coordination level of Anhui province is relatively high, and the coordination grade of most cities are in grade I or II. The coordination development degree of Anhui province presented a distinct improving trend with time, from most cities in grade IV or V in 2011 to most cities in grade II in 2020, from the worst 0.0580 in 2011 to the best 0.9200 in 2020. In terms of space, the coordinated development level of southern Anhui is higher than that of northern Anhui. Meanwhile, the coordination development status of the 16 cities in Anhui province can be divided into three patterns according to its historical variation characteristics, i.e., coordination development mode, ecological environment backward mode, and social and economic backward mode. Compared with the commonly used coordination evaluation method, the method of this paper can solve the problem of homogenization, and its calculation results are more reasonable and practical.

Construction of an integrated drought index is a fundamental task to conducting drought disaster risk management and developing drought resistance planning strategies. Given the evident non-consistent features during the drought evolution process, firstly, the GAMLSS approach was utilized to construct multiple combination scenarios of time-variant parameters and corresponding probability distribution functions. Then, the time-variant comprehensive drought index integrating the variable characteristics of precipitation and soil moisture was established by means of the copula function. Finally, the reliability of the time-variant comprehensive drought index was verified through its application in frequency analysis and return period determination of drought hazard system in Huaibei Plain, China. The application results demonstrated that: (1) The variation of the time-variant integrated drought indicator presented strong consistency with both soil moisture and precipitation during historical years in Huaibei Plain. (2) The overall variation of the drought hazard system characterized by drought duration and severity presented a gradual mitigation trend from west to east and north to south in Huaibei Plain, which agrees with the geographic differences and water resources availability distribution features. (3) Drought recognition results, including the frequency of drought events and typical drought processes with extreme grades, are in agreement with the practical statistics and observed data series. On the whole, the proposed time-variant integrated drought indicator is capable of extracting complex variation characteristics within the drought hazard evolution process, and can be further applied in drought monitoring, recognition and assessment research fields.

Currently, the implementation of water resource spatial equilibrium strategy is a fundamental policy of water resource integrated management in China; it is also a considerable challenge to explore the relationship structure features of water resources, society, economy and ecological environment (WSEE) complex system. For this purpose, firstly, we applied information entropy, ordered degree and connection number coupling method to reveal the membership characteristics between different evaluation indicators and grade criterion. Secondly, the system dynamics approach was introduced to describe the relationship features among different equilibrium subsystems. Finally, the ordered degree, connection number, information entropy and system dynamics integrated model was established to conduct relationship structure simulation and evolution trend evaluation of the WSEE system. The application results in Hefei city, Anhui Province, China, demonstrated that: (1) the variation of overall equilibrium conditions of WSEE system in Hefei city, 2020–2029 was higher compared to that of 2010–2019, though the increasing rate of ordered degree and connection number entropy (ODCNE) became slower after 2019; and (2) the annual ODCNE value from 2020 to 2029 of WSEE system under dry year scenarios increased about 0.0812, which indicated that the construction of Yangtze-Huaihe Diversion (YHD) project could play significant positive role in mitigating the equilibrium situation of WSEE system in Hefei city in the future. On the whole, this study is capable of providing the guidance basis for constructing a theoretical framework of structure simulation and equilibrium evaluation analysis of WSEE complex system.

Agricultural water consumption security is crucial for maintaining food production stability. Aiming to investigate water consumption efficiency and objectives in agricultural and non-agricultural sectors, we adopted a Budyko-analogous framework to establish an optimal water allocation model based on the maximum water utilization benefits principle. The proposed Budyko framework was verified through its application in Anhui Province, China, and the difference in water utilization efficiencies among different regions was discussed. The research findings can be concluded as follows: (1) during 2011-2020, the provincial agricultural productive loss caused by per-unit water shortage was lower compared to non-agricultural sectors, and this trend was adaptive in the south but totally opposite in the north; (2) the guaranteed level of agricultural water consumption was higher compared to non-agricultural sectors in the north due to the predominance of agricultural production but totally contrary in the south. Overall, the above findings are consistent with the actual industrial structure of Anhui Province.

To promote the application of entropy concepts in uncertainty analysis of water resources complex system, a quantitative evaluation and obstacle factor diagnosis model of agricultural drought disaster risk was proposed using connection number and information entropy. The results applied to Suzhou City showed that the agricultural drought disaster risks in Suzhou during 2007–2017 were all in middle-risk status, while it presented a decreasing trend from 2010. The information entropy values of the difference degree item bI were markedly lower than those of the difference degree b, indicating that bI provided more information in the evaluation process. Furthermore, the status of drought damage sensitivity and drought hazard were improved significantly. Nevertheless, high exposure to drought and weak drought resistance capacity seriously impeded the reduction of risk. Thus, the key to decreasing risk was to maintain the level of damage sensitivity, while the difficulties were to reduce exposure and enhance resistance. In addition, the percentage of the agricultural population, population density, and percentage of effective irrigation area were the main obstacle factors of risk and also the key points of risk control in Suzhou. In short, the results suggest that the evaluation and diagnosis method is effective and conducive to regional drought disaster risk management.

In order to effectively deal with the uncertainty between evaluation samples and evaluation criteria, and quantitatively identify the water resources carrying capacity (WRCC) and its obstacle factors in the Yellow River irrigation district, a calculation method of dynamic difference degree coefficient varying with evaluation sample was proposed, and then an evaluation and diagnosis model of WRCC was established. The results applied to the Dagong irrigation district showed that the overall WRCC of five counties in the irrigation district were improved from 2010 to 2017, especially since 2013. The improvement magnitudes of Changyuan County, Fengqiu County, and Hua County were significantly higher than those of Xun County and Neihuang County. In 2017, Fengqiu County, Changyuan County, Hua County, Xun County, and Neihuang County were in water resources critical overloaded status, and the connection number values were 0.231, 0.163, 0.120, −0.293, and −0.331, respectively, which is consistent with the fact that their distances become farther from the main stream of the Yellow River. In addition, the utilization ratio of water resources, available water resources amount per capita, GDP per capita, and water deficient ratio in each county belonged to the middle or strong obstacle index over a long period of time. They were the crucial obstacle factors of WRCC in the Dagong irrigation district, as well as the core and difficult points of water resources management. In some counties, the effective irrigation area ratio, effective utilization coefficient of irrigation water, and water consumption ratio of the ecological environment gradually developed from strong obstacle to weak or strong promotion index. These were important reasons for the improvement of their carrying situation, reflecting their control of agricultural and ecological water consumption. In short, the results of the case study suggest that the model established in this study is conducive to the identification of water resources’ carrying status and its key obstacle factors in the Yellow River irrigation district, and can be applied to the evaluation and regulation of resources and environment carrying capacity.

为深入探讨减法集对势的物理意义,发掘其不确定性方面的信息,在减法集对势的分析基础上提出改进差异度系数取固定的三角模糊数,采用动态三角模糊数与随机模拟相结合的计算方法进行差异度系数的随机模拟,并将该方法应用于安徽省水资源承载力分析评价的实际问题中.结果表明:改进的动态三角模糊数随机模拟方法在安徽省水资源承载力中的评价结果更为稳健精准,可靠性和精确度方面都有所提高,且该方法的计算结果包含原有减法集对势的计算结果,为集对事件提供了关于评价结果可靠性方面的估计信息;改进的三角模糊数随机模拟方法的计算结果合理可靠,说明该方法在水资源承载力评价问题中具有推广应用价值.

With the rapid economic development and the acceleration of urbanization, the pressure on the water resources system is becoming intense. As an important indicator of water resources security and sustainable development, the water resources carrying capacity has become a hot issue. To overcome the limitation of commonly used methods for weight determination and to evaluate the regional water resources carrying capacity reasonably, the index weight determined by the Analytic Hierarchy Process method was revised by the subtraction set pair potential to calculate the dynamic index weight. Then, the dynamic weight was combined with the set pair analysis method to evaluate the regional water resources carrying capacity dynamically. In addition, the Dagum Gini coefficient and its decomposition method were used to analyze the overall difference of water resources carrying capacity in the whole region and the differences within and between subregions considering the lack of quantitative research in spatial equilibrium. Finally, a case study was carried out in Anhui Province, China. The results showed that from 2011 to 2018, most of the water resources carrying capacity for 16 cities in Anhui Province were in a critical state, with the strongest in the south of Anhui Province and the weakest in the north. The overall spatial difference of carrying capacity in Anhui Province showed an increasing trend from 2011 to 2018. Furthermore, the slightest difference within the subregion was in the north of Anhui Province, while the largest was in the south. The most significant difference between the subregions was between the south and the north of Anhui Province. The primary source of carrying capacity spatial difference in Anhui Province was from the difference between subregions. The results of the case study suggested that the method proposed in this paper are conducive to the early find of possible disadvantages of spatial equilibrium and can effectively identify the main source of regional spatial difference in water resources carrying capacity, which means that the method can be widely applied to similar issues.

随着经济社会发展和气候条件改变,我国区域干旱问题日益突出,水库在抗旱减灾过程中的作用越来越凸显,旱限水位的提出与应用对有效发挥大中型水库在抗旱中的调控作用、缓解流域旱情具有重要意义.针对旱限水位研究现状,本文以史河灌区梅山水库为例,首先考虑城乡供水、农业灌溉、水力发电和生态环境等诸多因素,构建基于模糊集对分析法的水库灌区水资源系统运行效果综合评价模型,并以水资源系统综合运行等级最优为目标,以分期分级旱限水位、灌溉限供措施(基于水库来水特征和作物生长特性)为优化变量,运用免疫遗传算法进行系统优化求解,最后对比有无旱限水位下水库水资源系统综合运行效果,并分析了不同控制方式下水库供水变化和灌区作物因旱减产风险.结果显示:该优化方法相较于以水库供水经济效益为目标旱限水位确定方法,多项年均指标都有较大改善,其中梅山水库经济效益提高了 46万元,充反调节水库水量增加了 555万m3.而水库弃水量减少了 566万m3;史河灌区塘坝供水量增加了 253万m3,而作物减产率下降了 3.32％,同时作物因旱减产风险降低了 3.15％.可见,运用系统综合评估决策方法有利于改善水库灌区系统综合运行效果,提高系统水资源利用效率和水库灌区经济效益;优化的旱限水位控制和与作物生长特性相适应的优化供水策略相对于经验性控制能有效减少灌区中稻因旱减产率,为保障旱限水位的顺利实施和干旱时期农业灌溉抗旱提供有力支撑.

As an important water conservancy engineering project, reservoir regulation plays a crucial role in the insurance of water resources supply and demand balance and sustainable development and utilization, especially during drought seasons. The drought limited water level (DLWL) is the characteristic controlling water level of reservoir regulation operation during dry seasons, and the construction of reliable controlling schemes of DLWL is of great significance for the improvement of regional water resources utilization efficiency. Therefore, basing on the variation analysis of water inflowing series and water resources utilization characteristics among different sectors of Meishan Reservoir in Shihe Irrigation Area of China, firstly, the Hausdorff Dimensional Fractal (HDF) method was applied to divide drought early-warning periods of Meishan reservoir. Then, the initial scheme of DLWL of reservoir was determined through reservoir water inflow and water supply processes analysis during each drought warning periods of different typical hydrological years. And finally, the optimal dynamic controlling scheme of DLWL, described by drought warning water level (DWWL) and drought depleted water level (DDWL) respectively, was eventually proposed in this study based on the establishment of simulation and regulation model of reservoir and irrigation areas system. Moreover, the reliability and effectiveness of the proposed optimal controlling scheme of DLWL was further testified in terms of drought risk analysis of reservoir and irrigation area system under typical consecutive and annual drought scenarios, and meanwhile, the agricultural crop yield loss risk due to drought events corresponding to different controlling schemes of DLWL was also determined. The related research findings of this study could be favorable and beneficial for guiding drought-resistance regulation of reservoir and irrigation area system during drought seasons and providing reasonable decision-making basis of water resources utilization schemes as well.

为定量分析区域水资源承载力的整体状况及发展趋势,建立关于水资源承载力评价的联系数与三角模糊数随机模拟耦合模型,使用趋势指数定量刻画各相邻年份水资源承载力的变化趋势.将此联系数随机模拟模型与截集三角模糊数计算方法进行实例对比分析,结果表明:在一定的显著性水平和截集水平下,两种计算方法求得的2006年山东省水资源承载力评价结果、长沙市涝灾影响综合评价结果均基本一致,说明联系数随机模拟模型计算方法的可行性,且为置信区间的确定提供了一种可能性.将联系数随机模拟模型应用于安徽省水资源承载力评价中,结果表明:安徽省2005—2018年水资源承载力整体发展趋势逐年缓慢变好;2006年、2011年、2013年和2017年的变化趋势处于恶化状态,其他年份的变化趋势处于改善状态;2010年和2016年的变化趋势呈显著改善,2011年和2017年的变化趋势呈显著恶化.上述评价方法的计算结果合理可靠,说明联系数随机模拟模型在水资源承载力评价中具有推广应用价值.

The comprehensive evaluation analysis of water resource spatial equilibrium (WRSE) system is a fundamental and crucial facet to construct national water resource network system and implement socio-economy equilibrium development strategy in China. To clearly understanding of the structural relationship of WRSE system, we firstly proposed the definition of WRSE system from the perspective of coordination variation between water resource carrying pressure and support force subsystems in this study, then, the multi-dimensional connection cloud and coupling coordination degree approaches were applied to construct integrated evaluation model (MCCD) of WRSE system, and finally, the obstacle degree model was utilized as well to recognize the primary influence factors which resulted in the variation of WRSE system. Eventually, it can be revealed from the application results of MCCD model that, the overall situation of WRSE system in Anhui Province, China was improved obviously during the past 10 years, with the average coupling coordination degree (CCD) increased from 0.58 in 2011 to 0.68 in 2018. In addition, water resources availability per capita (S1) and agricultural irrigation quota (P8) were the two primary indicators causing the variation of water resource carrying support and pressure force subsystems. The above application analysis results were reliable and consistent with the evolution trend of actual historical observed statistics, and could also provide scientific decision-making basis for the implementation of prediction and regulation schemes of WRSE system.

The assessment and diagnosis of agricultural drought vulnerability is the basis for the scientific control and prevention of agricultural drought risk. In order to quantitatively evaluate the regional agricultural drought vulnerability and effectively deal with the fuzziness and randomness between evaluation sample and evaluation grade, the entropy fuzzy pattern recognition model, which was coupled with maximum information entropy principle and fuzzy pattern recognition method, was applied to the evaluation of agricultural drought vulnerability. Furthermore, in order to find methods to reduce drought vulnerability, the subtraction set pair potential method was used to further identify the main influence factors of agricultural drought vulnerability. In addition, a case study was carried out in Bengbu City, China. The results showed that during the period from 2001 to 2010, the evaluation value of agricultural drought vulnerability in Bengbu dropped from grade IV to III, which meant that the tolerance of agricultural system to drought had been improved. Moreover, the main factors that affected the vulnerability in Bengbu were precipitation, water use efficiency and irrigation protection area rate. And the latter two were the main objects of regulation and control. Compared with the other three methods, the physical concept of drought vulnerability assessment model based on entropy fuzzy pattern recognition is more obvious, and the evaluation results are reasonable and credible. The drought vulnerability diagnosis method based on subtraction set pair potential can accurately identify key influence factor and provide measures to reduce drought vulnerability and improve drought risk management.