Many studies have examined how runoff (Q) responds to long‐term changes in precipitation (P) and temperature (T), but the effects of potential evapotranspiration (PET) have received less attention. We examine observational data sets for P, T, and Q, along with PET estimated from observations, to determine the extent to which derived P and PET runoff elasticities (𝜀_𝑃 and 𝜀_𝑃𝐸𝑇, the fractional changes in runoff associated with given fractional changes in precipitation and PET, respectively) meet Dooge's complementary relationship (under certain conditions, 𝜀_𝑃 + 𝜀_𝑃𝐸𝑇 = 1). We apply three statistical methods and two hydrologic models to estimate 𝜀_𝑃 and 𝜀_𝑃𝐸𝑇 in 84 headwater river basins in California, Oregon, and Washington. We find that while the estimates of 𝜀_𝑃 are generally consistent across two statistical estimators and one model‐based estimator, the estimates of 𝜀_𝑃𝐸𝑇 using the statistical methods differ considerably (generally, they are much more negative) from the model‐based estimates, and some appear to be implausible. The model‐based estimates show better conformance to the complementary relationship (and in the median across sites, they sum to close to 1.0). We explore several factors that might explain the failure of the observation‐based estimators, including interaction between P and PET and nonclosure of the water budget at annual time scales.

中文翻译：

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美国西部的径流和蒸散弹性：它们与杜奇的互补关系一致吗？

许多研究已经研究了径流（Q）如何响应降水（P）和温度（T）的长期变化，但是潜在蒸散量（PET）的影响受到的关注较少。我们研究的观测数据集为P，T和Q，随着PET从观测估计，以确定在何种程度上衍生的P和PET径流弹性（ε _𝑃和ε _𝑃𝐸𝑇，在径流与在给定的分数变化相关的分数的变化沉淀和PET分别满足Dooge的互补关系（在某些条件下，_𝑃  + _𝑃𝐸𝑇  = 1）。我们使用3个统计方法和两个水文模型ε估计_𝑃和ε _𝑃𝐸𝑇位于加利福尼亚，俄勒冈和华盛顿的84个源头流域。我们发现，虽然_{two estimates}的估计值在两个统计估计值和一个基于模型的估计值之间通常是一致的，_但是使用统计方法_得出的𝜀 _estimates估计值与基于模型的估计值之间存在很大差异（通常是负数），有些似乎难以置信。基于模型的估计值显示出与互补关系更好的一致性（在各个站点的中位数中，它们的总和接近1.0）。我们探索了可能解释基于观测的估算器失败的几个因素，包括P和PET之间的相互作用以及年度时间尺度上水预算的不公开。