Toward an Efficient Uncertainty Quantification of Streamflow Predictions Using Sparse Polynomial Chaos Expansion

Vinh Ngoc Tran,Jongho Kim

doi:10.3390/w13020203

Abstract

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, α, Kbas, Pbas, and Pchn, 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.

Highlights

We investigate the effects of the size of the experimental design on the accuracy of surrogate models constructed by full polynomial chaos expansion (FPCE) and sparse polynomial chaos expansion (SPCE), thereby (i) providing a guideline for choosing the appropriate size of experimental design and (ii) demonstrating the superiority of SPCE to FPCE
This study combined SPCE with least angle regression (LAR) to allow for efficient construction of a surrogate model and fast quantification of its uncertainty for hydrological predictions
The advantages of SPCE were investigated in comparison to the performance of a surrogate model (FPCE) constructed using ordinary least square regression (OLS)

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Hydrological models are tools that convert climate inputs into responses to numerically represent the various physical processes of a watershed [1–5]. These models typically include parameters embodying temporal and spatial variability of watershed characteristics that cannot be measured explicitly [2,6]. The predictive accuracy of hydrologic models is inevitably influenced by the uncertainty of the undetermined parameters, yielding model results that are often mismatched with observations [2,7–11]. Quantifying and reducing uncertainties has been a major challenge for researchers in water planning and supply, sediment management, reservoir operation, and streamflow predictions [12–16]

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