Reliable hydrologic models are essential for planning, designing, and management of water resources. However, predictions by hydrological models are prone to errors due to a variety of sources of uncertainty. More accurate quantification of these uncertainties using a large number of ensembles and model runs is hampered by the high computational burden. In this study, we developed a highly efficient surrogate model constructed by sparse polynomial chaos expansion (SPCE) coupled with the least angle regression method, which enables efficient uncertainty quantifications. Polynomial chaos expansion was employed to surrogate a storage function-based hydrological model (SFM) for nine streamflow events in the Hongcheon watershed of South Korea. The efficiency of SPCE is investigated by comparing it with another surrogate model, full polynomial chaos expansion (FPCE) built by a well-known, ordinary least square regression (OLS) method. This study confirms that (1) the performance of SPCE is superior to that of FPCE because SPCE can build a more accurate surrogate model (i.e., smaller leave-one-out cross-validation error) with one-quarter the size (i.e., 500 versus 2000). (2) SPCE can sufficiently capture the uncertainty of the streamflow, which is comparable to that of SFM. (3) Sensitivity analysis attained through visual inspection and mathematical computation of the Sobol’ index has been of great success for SPCE to capture the parameter sensitivity of SFM, identifying four parameters, , , , and , that are most sensitive to the likelihood function, Nash-Sutcliffe efficiency. (4) The computational power of SPCE is about 200 times faster than that of SFM and about four times faster than that of FPCE. The SPCE approach builds a surrogate model quickly and robustly with a more compact experimental design compared to FPCE. Ultimately, it will benefit ensemble streamflow forecasting studies, which must provide information and alerts in real time.

中文翻译：

---

使用稀疏多项式混沌展开法进行有效的流量预测不确定性量化

可靠的水文模型对于水资源的规划，设计和管理至关重要。但是，由于各种不确定因素，水文模型的预测容易出错。高计算量阻碍了使用大量合奏和模型运行对这些不确定性进行更准确的量化。在这项研究中，我们开发了一种由稀疏多项式混沌扩展（SPCE）结合最小角度回归方法构建的高效替代模型，该模型可以实现有效的不确定性量化。多项式混沌扩展被用来代替基于存储函数的水文模型（SFM），用于韩国洪川流域的九次水流事件。通过与其他代理模型进行比较来研究SPCE的效率，通过众所周知的普通最小二乘回归（OLS）方法构建的全多项式混沌展开（FPCE）。这项研究证实了（1）SPCE的性能优于FPCE，因为SPCE可以构建更精确的替代模型（即较小的留一法交叉验证误差），尺寸只有四分之一（即500）。与2000年相比）。（2）SPCE可以充分捕获流的不确定性，这与SFM相当。（3）通过视觉检查和Sobol指数的数学计算获得的灵敏度分析对于SPCE捕获SFM的参数敏感性，识别对似然函数最敏感的四个参数，，，和取得了巨大的成功，纳什·苏特克利夫效率。（4）SPCE的计算能力比SFM快约200倍，比FPCE快约4倍。与FPCE相比，SPCE方法可通过更紧凑的实验设计快速而稳健地构建替代模型。最终，它将有益于集成流预测研究，该研究必须实时提供信息和警报。