The Budyko framework, widely regarded as a simple and convenient tool to synthesize catchment water balance, is often employed with the atmospheric evaporative potential (E_p) that responds to water availability over a land surface. In this study, we demonstrated how the responsiveness of E_p to soil moisture deficiency affects outcomes from a conventional Budyko equation. We combined a two-parameter Budyko equation with the state-of-the-art complementary relationship (CR) of evaporation (E), and analytically showed that the two-parameter Budyko equation corrects E_p to the wet environment E (E_w) of the CR. Using the Budyko equation combined with the CR, we assessed runoff sensitivity to climatic and land surface changes. Results showed that the CR could become a constraint for calibrating the implicit parameter of the Budyko equation. When compared to the Turc-Mezentsev equation with E_p, the shape parameters of the two-parameter Budyko equation increased to regenerate an ensemble of global E data sets. Correcting E_p to E_w via the Budyko equation with CR reduced runoff elasticities to land property changes, suggesting that climatic changes are more important to changes in runoff than a prior sensitivity assessment would suggest. This study also suggests that the two-parameter Budyko equation isolates the effect of the E_p adjustment from the shape parameter, allowing it to more properly account for surface energy availability.

中文翻译：

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用互补蒸发原理重新审视二参数 Budyko 方程以适当考虑表面能平衡

Budyko 框架被广泛认为是合成集水区水平衡的简单方便的工具，通常与响应陆地表面可用水量的大气蒸发势 (E _p ) 一起使用。在这项研究中，我们展示了 E _p对土壤水分缺乏的反应如何影响传统 Budyko 方程的结果。我们将双参数 Budyko 方程与蒸发 (E) 的最新互补关系 (CR) 相结合，并通过分析表明，双参数 Budyko 方程将 E _p校正到潮湿环境 E (E _w) 的 CR。使用 Budyko 方程结合 CR，我们评估了径流对气候和地表变化的敏感性。结果表明，CR 可以成为校准 Budyko 方程隐式参数的约束条件。与具有 E _p的 Turc- Mezentsev 方程相比，双参数 Budyko 方程的形状参数增加以重新生成全局 E 数据集的集合。通过带有 CR 的 Budyko 方程将E _p校正为 E _w降低了土地财产变化的径流弹性，这表明气候变化对径流变化的影响比先前的敏感性评估所表明的更为重要。该研究还表明，双参数 Budyko 方程隔离了 E _p 从形状参数调整，使其能够更恰当地考虑表面能可用性。