农业水土资源作为农业基础性生产要素，明晰其量比关系以及时空上适宜匹配状况，对规范区域内资源的利用方式、促进农业可持续发展以及保障粮食安全，具有重要理论价值与实践意义。陕北地区位于黄土高原核心地带，生态环境脆弱，长期受水土流失问题困扰。农业水土资源有限的承载能力与资源短缺叠加，进一步加剧了该地区水土资源的供需矛盾。同时农业发展受到区域差异显著、农田水利基础设施薄弱以及农产品供给结构失衡等多重因素制约。因此，研究陕北地区农业水土资源及其经济效益匹配特征，并对其进行功能分区，对提升资源利用效率、促进农业可持续发展具有重要现实意义。

本研究通过农业水土资源匹配系数法、基尼系数和泰尔指数等方法，系统评估了2010-2021年陕北地区农业水土资源及其经济效益匹配关系的时空演变格局和差异构成；通过构建多维度分析框架，采用耦合协调度模型和障碍诊断模型，进一步分析陕北地区农业水土资源与农业经济发展的耦合协调关系，揭示了区域农业可持续发展的主要制约因素；采用创新性K-Means++-AHC聚类算法，从资源禀赋、匹配状态、协调发展和空间分异等角度对陕北地区进行农业水土功能分区，并结合标准显性比较优势指数（NRCA）对各区域进行诊断，精准识别各区域在水土地资源、自然禀赋、经济效益、产业发等领域的比较优势，突出区域主导功能。

主要结论：

（1）2010-2021年，陕北地区耕地资源总体呈现上升趋势，表现为“西北高，东南低”分布特征；水资源总量仅占陕西7.8%，呈现“北高南低，西高东低”空间分异特征，榆阳区、神木市等北部县域资源优势显著而东部县域水资源普遍紧缺。区域内农业水土资源存在不同程度的错位现象，米脂、绥德、吴堡、延长、延川和洛川农业水土资源在空间上表现为“土多水少”，而神木、榆阳、黄陵、黄龙、宜川等地农业水土资源在空间上以“土少水多”为特征。2010-2021年，区域内农业水土资源匹配系数（0.24×10⁴ m³·hm^-2）显著低于全省以及全国水平，呈现南高北低、中部最低的格局。研究期内，受水利工程影响，延川县等东部县域匹配度提升，而“工业挤出效应”影响着神木等资源富集区匹配度下降。

（2）2010-2021年陕北地区耕地效益基尼系数0.41（G_S = (0.4, 0.5]）< 农业水土资源匹配基尼系数0.43（G_WS= (0.4, 0.5]）< 农业用水效益基尼系数0.6（G_W = (0.5, 1])。表明区域内农业水土资源与农业产值之间存在匹配差距巨大，且耕地资源和农业产值间的匹配程度优于农业用水资源。通过对泰尔指数进行分解，发现区域内部差异，特别是榆林下辖县（市、区）内部差异是导致陕北地区农业水土资源匹配及其效益总体差异的主要来源。

（3）研究揭示区域农业水土资源与经济发展的耦合协调度长期处于勉强协调状态（0.5-0.6）。耦合协调度呈现出显著的区域差异，表现为南高，北次之，中间低的空间分布特征；濒临失衡区占比从2010年的56%下降至2021年的36%，但其所占比重仍然较大。空间分析显示，耦合协调度有强正向自相关性（Moran's I 0.93-0.97），形成高-高集聚的资源优势区和低-低集聚的中部地区。根据障碍度分析，表明经济效益和土地资源是两大核心制约因素。其中，人均水资源量（C14）、地均生态服务价值（C8）和耕地效益（C5）构成持续性制约，区域内北部受地貌和生态脆弱性约束，南部持续面临水资源短缺。认为陕北农业需进一步加强生态保护与农业用地的协调管理。

（4）构建K-Means++-AHC聚类算法，通过Purity、ARI、AMI和NMI指标，采用Friedman检验和Bonferroni-Dunn检验并综合指标排名，创新算法更具优势。通过该算法将陕北地区划分为4类功能区：I区，资源匹配良好但农业经济发展滞后；II区，利用效率低下；III区，水资源匮乏但农业发达；IV区，协调发展核心区，其水土资源本底优良且协调度最高。研究成果为差异化调控提供理论支撑，建议北部强化生态-农业协同，中部突破资源瓶颈，南部优化水资源配置，整体构建“分区施策、系统协调”的治理体系，推动陕北生态保护与农业高质量发展。

As fundamental production factors in agriculture, clarifying the quantitative ratio relationships and spatiotemporally suitable matching status of agricultural water and land resources (AWLR) holds significant theoretical value and practical implications for standardizing regional resource utilization patterns, promoting sustainable agricultural development, and ensuring food security. Located in the core area of the Loess Plateau, Northern Shaanxi (NS) features an ecologically fragile environment and has long been plagued by severe soil erosion issues. The limited carrying capacity of AWLR, compounded by resource scarcity, has further intensified the supply-demand conflict of these resources in the region. Meanwhile, agricultural development faces multifaceted constraints including significant regional disparities, inadequate farmland water conservancy infrastructure, and structural imbalances in agricultural product supply. Therefore, investigating the matching characteristics between AWLR and their economic benefits in NS, along with conducting functional zoning, bears crucial practical significance for enhancing resource utilization efficiency and advancing sustainable agricultural development.

This study systematically evaluated the spatiotemporal evolution and disparity composition of AWLR matching and economic benefits in NS from 2010 to 2021 using methods including the AWLR matching coefficient, Gini coefficient, and Theil index. A multidimensional framework incorporating coupling coordination degree and obstacle diagnosis models revealed the coordinated development constraints between agricultural resources and economic growth. An innovative K-Means++-AHC clustering algorithm categorized functional zones based on resource endowment, matching status, coordination level, and spatial heterogeneity. Comparative advantages across WLR, natural endowments, economic benefits, and industrial development were identified using the Normalized Revealed Comparative Advantage (NRCA) index. The main conclusions are as follows:

From 2010 to 2021, arable land resources in NS exhibited an increasing trend with a “high northwest, low southeast” spatial pattern. Total water resources accounted for only 7.8% of Shaanxi Province, displaying a “north-abundant, south-scarce” distribution. Significant resource mismatches were observed: counties including Mizhi, Suide, and Yanchuan demonstrated “land-rich, water-deficient” characteristics, while Shenmu, Yuyang, and Huangling showed “water-abundant, land-deficient” patterns. The regional AWLR matching coefficient (0.24×10⁴ m³·hm^-2) remained substantially below provincial and national averages, presenting a “south-high, north-low” gradient with minimal values in central areas. Hydraulic projects improved matching degrees in eastern counties like Yanchuan, whereas industrial competition reduced matching efficiency in resource-rich areas such as Shenmu.

Gini coefficients ranked as: cultivated land benefit (G_S = (0.4, 0.5]) < AWLR matching (G_WS= (0.4, 0.5]) < agriculture water benefit (G_W = (0.5, 1]), indicating greater mismatches between water resources and agricultural output. This indicates that there is a significant mismatch between AWLR and agricultural output value within the region, and the matching degree between cultivated land resources and agricultural output value is better than that of agricultural water resources. Through the decomposition of the Theil index, it was found that the internal differences within the region, especially within the counties under the jurisdiction of Yulin, are the main sources of the overall differences in AWLR matching and its benefits in NS. Theil index decomposition highlighted intraregional disparities (particularly within Yulin) as the primary source of overall mismatch.

Coupling coordination between AWLR and economic development remained marginally coordinated (0.5-0.6). Spatial heterogeneity manifested as “south-high, north-medium, central-low” patterns. Nearly-imbalanced zones decreased from 56% (2010) to 36% (2021) yet retained significant proportions. Strong positive spatial autocorrelation (Moran's I 0.93-0.97) revealed high-high clusters in resource-rich areas and low-low clusters in central regions. Obstacle diagnosis identified economic benefits and land resources as primary constraints, with per capita water resources (C14), ecological service value per unit land (C8), and cultivated land efficiency (C5) constituting persistent limitations. Northern areas faced ecological vulnerability, while southern regions endured water scarcity, necessitating enhanced eco-agricultural coordination.

The K-Means++-AHC clustering algorithm was developed. By employing the Purity, ARI, AMI, and NMI metrics, the Friedman test and Bonferroni-Dunn test were utilized to comprehensively evaluate and rank the performance of these indicators. This approach highlighted the superiority of the innovative algorithm. Using this algorithm, the northern Shaanxi region was categorized into four functional zones: Zone I, characterized by good resource matching but relatively underdeveloped agricultural economics; Zone II, marked by low resource utilization efficiency; Zone III, featuring scarce water resources yet advanced agricultural development; and Zone IV, identified as the core area for coordinated development, with an excellent WLR foundation and the highest level of coordination. These findings provide theoretical support for differentiated regulation strategies. It is recommended that the northern region enhance the synergy between ecological and agricultural systems, the central region address resource bottlenecks, and the southern region optimize water resource allocation. Overall, a governance framework emphasizing “differentiated policies and systematic coordination” should be established to promote ecological protection and high-quality agricultural development in NS.