On the bas is of re-unders tanding the spatial scope and spatial contents of the Yangtze River Economic Zone (YREZ), applying the usual spatial data analytical methods, the natural characteris tic of spatial divis ion of the YREZ has been attained. The special band-shaped core-periphery-edge s tructure of the YREZ was formed after the four developing periods of independent development, regional concentration and connection, adminis trative economic region and spatial competion and connection and so on. The YREZ has three cores, one main axis, one secondary axis, four locational axises, one peripherical region and one edge region. The bas is of the formation and evolvement of spatial s tructure in the YREZ has been analyzed from complementarity, trans ferability and tervening opportunity and other parts by applying sptial interaction theory. To speed up optimization of spatial s tructure of the YREZ, we should bring forth new ideas in the regional organization of adminis tration. Then the es sential factors of spatial s tructure need to be optimized. One regional organization and adminis tration mis s ion, known as GCT model (G represents government, C s tands for city adminis trators and T is transnational-corporations or trans regional-corporations ), should be the mos t ideal organization model, which is composed of local government, city adminis trators and the mas ter enterprises pos ses s ing transnational-corporations or trans regional-corporations networks. When a mechanism of reaching unanimity through consultation and combination between the three bodies of local government, city and transnational or trans regional-corporations is set up, spatial adminis tration of the YREZ could be mos t efficient. Among the factors of spatial s tructure of the YREZ, the nodes and the pas sageway are the framework as well as the two mos t important factors optimizing spatial s tructure.

针对西北地区水资源严重短缺和水环境污染等问题，为探究五省区水资源承载力状况，基于“水资源-经济-社会-生态环境”框架模型构建了西北五省区水资源承载力评价指标体系，运用熵权TOPSIS模型和耦合协调模型定量评价2004-2019年西北五省区水资源承载力时空演化过程及子系统间的耦合协调性，引入障碍度模型得出西北五省区水资源承载力提升的障碍因素。结果表明：2004-2019年间，西北五省区水资源承载力水平呈缓慢提升态势，由水资源短缺状态转变为水资源合理状态；水资源承载力省际空间上差异性明显，青海和陕西水资源承载力水平较高，但省际间差距呈现逐年缩小的良好趋势；水资源、经济、社会、生态环境子系统承载力发展水平均呈现逐年增长趋势，水资源和生态环境子系统承载力发展水平滞后于经济和社会系统；西北五省区水资源承载力子系统间处于耦合度高、良好协调阶段，五省区发展水平省际空间上表现为比较均衡局面；人均水资源量、产水模数、有效灌溉率、水土流失治理面积、自然保护区面积占比表是阻碍西北五省区水资源承载力提升的主要障碍因素。研究表明西北五省区水资源承载力水平和系统内部协调性目前处于较高水平，整体向着健康、协调均衡的方向不断推进，同时在水资源管理和区域用水方式转变等方面仍有较大的提升空间。

The carrying capacity of water resources is one of the key factors affecting the sustainable development of the region. The evaluation of the carrying capacity of water resources can provide a data basis for the spatial balance of regional water resources. Based on the framework model of “Water Resources-Economy-Society-Ecological Environment”， an evaluation index system for water resources carrying capacity in the five northwestern provinces is constructed， and the entropy TOPSIS model and the coupling coordination model are used to quantitatively evaluate the water resources carrying capacity in the five northwestern provinces from 2004 to 2019. The spatial-temporal evolution process of force and the coupling and coordination between subsystems， the obstacle degree model is introduced to obtain the obstacles to the improvement of the water resources carrying capacity in the five northwestern provinces. The results show that from 2004 to 2019， the water resources carrying capacity of the five northwestern provinces have been slowly increasing， from a water shortage state to a reasonable state of water resources. There is a clear gap in the water resources carrying capacity between Qinghai and Shaanxi. The carrying capacity level is high， but the gap between provinces shows a good trend of shrinking year by year； the carrying capacity of water resources， economy， society， and ecological environment system shows a year-fter-year growth trend， and the development level of the carrying capacity of water resources and ecological environment subsystems lags behind that of the economy. And the social system， the water resources carrying capacity subsystems of the five northwestern provinces are in a stage of high coupling and good coordination. The development level of the five provinces and autonomous regions shows a relatively balanced situation in the inter-provincial space. The amount of water resources per capita， the modulus of water production， and the effective irrigation rate， soil erosion control area， and nature reserve area percentage table are the main obstacles hindering the improvement of water resources carrying capacity in the five northwestern provinces. The research shows that the level of water resources carrying capacity and the internal coordination of the system in the five northwestern provinces and regions are currently at a high level， and the overall direction is advancing towards a healthy， coordinated and balanced direction. At the same time， there is still a lot of room for improvement in water resources management and regional water use transformation.

为实现区域水资源可持续发展,维护社会经济健康。构建了基于可拓云模型的水资源承载力综合评价模型。从水资源、社会、经济和生态环境4个维度建立水资源承载力评价指标体系,运用层次分析法与CRITIC法进行线性组合确定综合权重,对辽宁省2012—2019 年辽宁省水资源承载力状况进行综合评价,并引入障碍度模型探究辽宁省水资源承载力的主要影响因素。结果表明:辽宁省水资源承载力在2012—2015年处于临界状态,2016—2019年水资源承载力水平变化复杂但整体表现下降趋势。通过障碍因子诊断,人均水资源量、供水模数逐渐成为主要影响因素。整体来看辽宁省水资源承载力有所下降,为进一步提高水资源承载能力,必须加强对水资源的综合管理。

To achieve sustainable development of regional water resources and ensure the sound development of social economy, we have established a comprehensive evaluation model for water resources carrying capacity based on the extension cloud model. This model incorporates a well-rounded evaluation index system comprising four dimensions: water resources, society, economy, and ecological environment. By employing a combination of the analytic hierarchy process (AHP) and the CRITIC (Criteria Importance Through Intercriteria Correlation) method, we conducted a comprehensive assessment of the water resources carrying capacity in Liaoning Province from 2012 to 2019. Furthermore, we have introduced an obstacle degree model to identify the main factors influencing water resources carrying capacity in Liaoning Province. Our findings reveal that the water resources carrying capacity of Liaoning Province was in a critical state between 2012 and 2015, with a complex pattern of changes observed from 2016 to 2019, ultimately indicating an overall decline. Specifically, water resources per capita and the water supply modulus, as calculated by the obstacle degree, have emerged as the primary influencing factors. In conclusion, the water resources carrying capacity in Liaoning Province has declined. To enhance the carrying capacity of water resources, it is imperative to reinforce comprehensive water resources management.

根据克鲁格曼的“两个自然”理论,运用空间统计SDE方法,在GIS技术的支持下,基于中国国土空间特征椭圆系列——国土均衡分布椭圆、国土地形分布椭圆、人口分布椭圆等,在空间上定量刻画了中国经济空间分异的基本特征,并为分析经济空间分异提供了新的方法参考。主要结论如下：① 在“两个自然”的分异作用下,中国经济空间分异主要以东-西方向为主。相对于国土均衡分布椭圆,国土地形分布椭圆明显偏西,长、短轴均明显减小,这反映出中国高地势主要集中分布在西部;中国人口空间分布靠近东部地区,其椭圆长、短轴长度均显著减小,充分表现出了经济活动的空间分异特征和空间聚集特征;② 国土地形等“第一自然”要素对社会经济活动的控制作用显著。人口分布椭圆对于地形分布椭圆的空间分异系数为89.55%,其93%的空间展布范围位于胡焕庸线的东南,且分布轴线基本与胡焕庸线平行;③ 在“第二自然”聚集机制的作用下,中国城市体系人口、GDP主体集中在胡焕庸线东南方约20%的大陆国土面积上,且二者之间也存在着明显的空间差异。从“第一自然”要素的空间分异和控制作用来看,胡焕庸线以西地区,特别是西北侧地区发展经济、集聚人口的功能较弱。同时,由于区域发展的内在核心动力聚集机制的空间差异性,区域发展的过程也呈现不平衡的特征。从兼顾效率和公平的角度出发,可通过重点培育人口分布较为集中的成渝城市群、关中城市群等中西部经济增长极拉动中国经济增长和市场空间向中西部发展;可通过制定相关政策吸引人口向GDP分布椭圆北部地区流动、聚集,发挥人口的红利作用,推进经济增长由南向北发展。

：This study described the spatial variation in China spatial explicitly through a series of ellipses according to Krugman's "first and second natural" theory. The ellipse of national geometric profile in China was taken as the original state of spatial variation. The first nature variation could be explained through the ellipse of topographical distribution in China, and the second nature variation was represented by the spatial distribution of population. The results are as followings. 1）The spatial variation is mainly between the eastern and the western area in China. The spatial coverage of topographical distribution ellipse is in the west, and it is much smaller than the equilibrium distribution ellipse which is in accordance with the topographical characteristics that the west is higher than the east in China. The population distribution ellipse is mainly covering the North China Plain and the Middle and Lower Yangtze Valley Plain and its spatial coverage is much smaller. It is proved the spatial variation of the first nature and the spatial agglomeration of the second nature. 2）The spatial variation from the first natural factors is significant in China. 93% of the population distribution ellipse range is located in the southeast of Hu's line, and the main axis is almost parallel to Hu's line. The spatial variation index of population distribution ellipse to the topographical distribution ellipse is 89.55%. 3）For the prefectural-level cities, the population ellipse and GDP ellipse are aggregated in the southeast of Hu's line which is 20% of the mainland area in China. There is the spatial disparity between the population and GDP distribution. In general, the natural endowments between the east and west in China resulted in the unbalanced beginning of regional development. It is shown that the regions in the north of Hu's line, especially in the northwest area, is weak to gathering the population. Meanwhile, spatial differences of the agglomeration which is the inner core of the regional developing momentum present the unbalanced process of regional development. From the perspective of both efficiency and equity, the promotion of Chengdu-Chongqing, Guanzhong and other major economic zones which is with the large population is relatively could stimulate the economic growth in central and western China, and to attract the population concentration in the north part of GDP distribution ellipse could promote the economy development from the south to the north. In addition, Standard deviation ellipse method can not only subtly describe the spatial variation of the different features, but also can quantitatively analyze the extent of spatial variation, and it is proved to be a new method for reference to study the economic spatial variation.

水资源承载力研究集综合评价和预测分析为一体。以宜昌市为例,在2005—2015年宜昌市“水资源-社会经济-生态环境”复合系统承载力综合评价基础上,采用GM(1,1)灰色预测模型预测2020年、2025年、2030年水资源承载力;在分析未来水平年预测结果不确定性的基础上,结合最严格水资源管理制度和河长制,探讨4种情景假设下宜昌市社会经济发展模式的可持续性。研究结果表明,未来水平年宜昌市水资源承载力状态良好(2025年左右达到Ⅰ级),建议宜昌市社会经济与生态环境协调可持续发展。

Research on the carrying capacity of water resources involves comprehensive evaluation and prediction and analysis. With Yichang City as a case study, we assessed the comprehensive carrying capacity of a composite system including water resources subsystem, social economy subsystem, and ecology subsystem. Firstly we predicted the carrying capacity of water resources in target years 2020, 2025, and 2030 using GM(1,1) model. Furthermore, we examined the sustainability of social economic development pattern under four scenarios based on analysis of the uncertainty of the prediction results in line with the Most Strict Water Resources Management Policy and the River Chief System. Research findings unveiled that the carrying capacity of water resources in Yichang is good in future, reaching degree Ⅰ around 2025. Under scenario three, in which sewage declines, river water quality improves, eco-environmental water use and forest cover remain increasing, the social economic development is well sustainable. Thus, we propose that social economy development should be coordinate with ecological environment protection.

为切实解决水资源承载力分类评价的高维问题，揭示水资源承载力动态变化规律，提出了改进的投影寻踪聚类模型。对于改进的投影寻踪聚类模型和基于最大信息熵原理的投影寻踪聚类模型，通过分析投影值的负熵变化规律，推导得出了密度窗宽的合理取值范围以及最佳取值；当密度窗宽为最佳取值时，改进的投影寻踪聚类模型比基于最大信息熵原理的投影寻踪聚类模型分类评价效果更好。针对江苏省水资源承载状态，采用改进的投影寻踪聚类模型进行了动态评价，2009年至2020年、2022年水资源承载力等级为Ⅲ级，2021年水资源承载力等级为Ⅱ级。建立灰色GM（1，1） 模型，预测该省2023年至2030年水资源承载力状态为Ⅱ级。改进的投影寻踪聚类模型更加有效地提取了水资源承载力评价指标高维数据的结构特征信息，进一步提升了水资源承载力分类评价模型的精确性，使评价结果更加客观合理。通过2022年与2009年指标贡献率数值比较分析，该省采取的工农业节水、加快社会经济发展、水资源保护等措施，促进了水资源承载力状态持续转好。根据评价指标对江苏省水资源承载力状态以及评价标准的贡献率，深入分析该省水资源承载力存在的短板，提出了提升水资源承载力状态的相关建议，确保江苏省水资源系统承载力状态尽早达到Ⅰ级，实现水资源可持续利用。