A Hybrid, Non-Stationary Stochastic Watershed Model (SWM) for Uncertain Hydrologic Simulations Under Climate Change

Abstract

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.