Abstract It is vital to identify drought events and to evaluate multivariate drought characteristics based on a composite drought index for better drought risk assessment and sustainable development of water resources. However, most composite drought indices are constructed by the linear combination, principal component analysis and entropy weight method assuming a linear relationship among different drought indices. In this study, the multidimensional copulas function was applied to construct a nonlinear multivariate drought index (NMDI) to solve the complicated and nonlinear relationship due to its dependence structure and flexibility. The NMDI was constructed by combining meteorological, hydrological, and agricultural variables (precipitation, runoff, and soil moisture) to better reflect the multivariate variables simultaneously. Based on the constructed NMDI and runs theory, drought events for a particular area regarding three drought characteristics: duration, peak, and severity were identified. Finally, multivariate drought risk was analyzed as a tool for providing reliable support in drought decision-making. The results indicate that: (1) multidimensional copulas can effectively solve the complicated and nonlinear relationship among multivariate variables; (2) compared with single and other composite drought indices, the NMDI is slightly more sensitive in capturing recorded drought events; and (3) drought risk shows a spatial variation; out of the five partitions studied, the Jing River Basin as well as the upstream and midstream of the Wei River Basin are characterized by a higher multivariate drought risk. In general, multidimensional copulas provides a reliable way to solve the nonlinear relationship when constructing a comprehensive drought index and evaluating multivariate drought characteristics.

中文翻译：

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基于非线性多元干旱指数的综合干旱特征分析

摘要 基于综合干旱指数识别干旱事件并评估多变量干旱特征对于更好地评估干旱风险和水资源可持续发展至关重要。然而，大多数复合干旱指数是通过线性组合、主成分分析和熵权法构建的，假设不同干旱指数之间存在线性关系。本研究应用多维Copulas函数构建非线性多元干旱指数(NMDI)，以解决其依赖结构和灵活性带来的复杂非线性关系。NMDI 是通过结合气象、水文和农业变量（降水、径流和土壤水分）构建的，以更好地同时反映多变量变量。基于构建的 NMDI 和运行理论，确定了特定区域的干旱事件关于三个干旱特征：持续时间、峰值和严重程度。最后，分析了多变量干旱风险，作为为干旱决策提供可靠支持的工具。结果表明：（1）多维Copulas可以有效解决多元变量之间复杂的非线性关系；(2) 与单一干旱指数和其他综合干旱指数相比，NMDI 在捕捉记录干旱事件方面略敏感；(3) 干旱风险呈现空间变异性；在研究的五个分区中，荆河流域以及渭河流域的上中游具有较高的多元干旱风险。一般来说，