AI 中文总结
本文提出一种调整后的替代差异度量方法，通过秩变换与摩尔邻域插补改进全局敏感性分析，经多基准测试，该方法在非光滑水文输出上实现完美秩一致性，且网格分辨率是性能变异性的核心驱动因素。
AI 中文摘要
基于Sobol'总阶指数（$T_i$）的敏感性分析方法具有良好的理论基础，但计算成本高昂。最近提出的一种替代差异度量通过量化输入-输出散点图与均匀性的偏差，提供了一种更廉价的替代方案，但缺乏理论依据，且未针对其他基于数据的估计量进行基准测试。我们引入了一种调整后的替代差异度量，该方法在网格化前对输出进行秩变换，并通过摩尔邻域规则对孤立空单元格进行插补，大幅提升了与$T_i$的一致性。我们通过copula理论论证证明，该调整是具有零条件的一致筛选统计量，存在明确的全支撑上限以限制其作为幅度估计量的使用，且存在仅由交互作用介导的依赖关系的失效模式。我们在7个基准函数和一个真实世界水文模型上，将调整后的替代差异度量与三种零额外成本的对比方法——多项式混沌展开（PCE）、PCE衍生的Shapley效应以及PAWN型最大柯尔莫哥洛夫-斯米尔诺夫指数——进行基准测试。调整后的替代差异度量是唯一在非光滑水文输出上实现完美秩一致性的估计量，而PCE在此场景下存在模型误设问题。对5个算法参数的联合敏感性分析显示，网格分辨率而非插补阈值或采样方法是导致性能变异性的驱动因素。
英文摘要
Sensitivity analysis methods based on Sobol' total-order indices ($T_i$) are well-founded but computationally demanding. A recently proposed ersatz discrepancy measure offers a cheaper alternative by quantifying deviations from uniformity in input--output scatterplots, yet lacks theoretical grounding and has not been benchmarked against other data-given estimators. We introduce an adjusted ersatz discrepancy that rank-transforms the output before gridding and imputes isolated empty cells via a Moore-neighbourhood rule, substantially improving agreement with $T_i$. We prove, via a copula-theoretic argument, that the adjustment is a consistent screening statistic with a zero condition, an explicit full-support ceiling bounding its use as a magnitude estimator, and a documented failure mode for purely interaction-mediated dependencies. We benchmark the adjusted ersatz against three zero-extra-cost comparators -- polynomial chaos expansion (PCE), PCE-derived Shapley effects, and a PAWN-type maximum Kolmogorov--Smirnov index -- across seven benchmark functions and a real-world hydrological model. The adjusted ersatz is the only estimator achieving perfect rank agreement on a non-smooth hydrological output where PCE is misspecified. A joint sensitivity analysis of five algorithmic parameters shows grid resolution, not the imputation threshold or sampling method, drives performance variability.
Comments25 pages, 9 figures, 11 tables, two supplementary files
