Stochastic Watershed Models (SWMs) are emerging tools in hydrologic modeling used to propagate uncertainty into model predictions by adding samples of model error to deterministic simulations. One of the most promising uses of SWMs is uncertainty propagation for hydrologic simulations under climate change. However, a core challenge is that the historical predictive uncertainty may not correctly characterize the error distribution under future climate. For example, the frequency of physical processes (e.g., snow accumulation and melt) may change under climate change, and so too may the frequency of errors associated with those processes. In this work, we explore for the first time non-stationarity in hydrologic model errors under climate change in an idealized experimental design. We fit one hydrologic model to historical observations, and then fit a second model to the simulations of the first, treating the first model as the true hydrologic system. We then force both models with climate change impacted meteorology and investigate changes to the error distribution between the models. We develop a hybrid machine learning method that maps model state variables to predictive errors, allowing for non-stationary error distributions based on changes in the frequency of model states. We find that this procedure provides an internally consistent methodology to overcome stationarity assumptions in error modeling and offers an important advance for implementing SWMs under climate change. We test this method on three hydrologically distinct watersheds in California (Feather River, Sacramento River, Calaveras River), finding that the hybrid model performs best in larger and less flashy basins.

中文翻译：

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用于气候变化下不确定水文模拟的混合非平稳随机流域模型 (SWM)

随机流域模型 (SWM) 是水文建模中的新兴工具，用于通过将模型误差样本添加到确定性模拟中，将不确定性传播到模型预测中。 SWM 最有前途的用途之一是气候变化下水文模拟的不确定性传播。然而，一个核心挑战是历史预测的不确定性可能无法正确表征未来气候下的误差分布。例如，物理过程（例如积雪和融化）的频率可能会因气候变化而发生变化，与这些过程相关的错误频率也可能会发生变化。在这项工作中，我们首次在理想化的实验设计中探讨了气候变化下水文模型误差的非平稳性。我们将一个水文模型拟合到历史观测中，然后将第二个模型拟合到第一个模型的模拟中，将第一个模型视为真实的水文系统。然后，我们用气候变化影响气象学来强制这两个模型，并研究模型之间误差分布的变化。我们开发了一种混合机器学习方法，将模型状态变量映射到预测误差，从而允许基于模型状态频率变化的非平稳误差分布。我们发现该程序提供了一种内部一致的方法来克服误差建模中的平稳性假设，并为在气候变化下实施 SWM 提供了重要的进步。我们在加利福尼亚州三个水文不同的流域（羽毛河、萨克拉门托河、卡拉维拉斯河）上测试了这种方法，发现混合模型在较大且不那么华丽的流域中表现最佳。