An uncertainty partition approach for inferring interactive hydrologic risks

Abstract

Abstract. Extensive uncertainties exist in hydrologic risk analysis. Particularly for interdependent hydrometeorological extremes, the random features in individual variables and their dependence structures may lead to bias and uncertainty in future risk inferences. In this study, an iterative factorial copula (IFC) approach is proposed to quantify parameter uncertainties and further reveal their contributions to predictive uncertainties in risk inferences. Specifically, an iterative factorial analysis (IFA) approach is developed to diminish the effect of the sample size and provide reliable characterization for parameters' contributions to the resulting risk inferences. The proposed approach is applied to multivariate flood risk inference for the Wei River basin to demonstrate the applicability of IFC for tracking the major contributors to resulting uncertainty in a multivariate risk analysis framework. In detail, the multivariate risk model associated with flood peak and volume will be established and further introduced into the proposed iterative factorial analysis framework to reveal the individual and interactive effects of parameter uncertainties on the predictive uncertainties in the resulting risk inferences. The results suggest that uncertainties in risk inferences would mainly be attributed to some parameters of the marginal distributions, while the parameter of the dependence structure (i.e. copula function) would not produce noticeable effects. Moreover, compared with traditional factorial analysis (FA), the proposed IFA approach would produce a more reliable visualization for parameters' impacts on risk inferences, while the traditional FA would remarkably overestimate the contribution of parameters' interaction to the failure probability in AND (i.e. all variables would exceed the corresponding thresholds) and at the same time underestimate the contribution of parameters' interaction to the failure probabilities in OR (i.e. one variable would exceed its corresponding threshold) and Kendall (i.e. the correlated variables would exceed a critical multivariate threshold).

Tracing Uncertainty Contributors in the Multi‐Hazard Risk Analysis for Compound Extremes

“…In this study, the model parameters are considered as the component of random error in IFA, which implies the overall contribution from all parameters in marginals and copula function. For the contributions from different parameters, the parametric uncertainties in marginals (especially for the shape parameter in a distribution) would tend to have much higher contributions than the uncertainty in copula parameter (Fan, Huang, Huang, Li, & Wang, 2020). For the marginal distributions for individual variables, they are also likely to have visible effects on the predictions of $${p}_{T}^{\text{AND}}$$ for a specific design threshold.…”

“…Once the copula model has been formulated with pre‐specified marginal and dependence structures, the parameter uncertainties (i.e., γ i and θ in Equation 1) would also produce noticeable impacts on the predictive variabilities for the resulting risk analyses of compound extremes (e.g., Fan et al., 2018; Guo et al., 2020; Sarhadi et al., 2016). There are several methods for quantifying parameter uncertainties in copula models, such as Monte Carlo simulation (e.g., Montes‐Iturrizaga & Heredia‐Zavoni, 2017), bootstrapping methods (e.g., Dung et al., 2015; Fan, Huang, Huang, Li, & Wang, 2020) and Bayesian inferences (e.g., Fan et al., 2018; Guo et al., 2020; Sadegh et al., 2017).…”

“…For example, a Bayesian information-theoretical approach has been developed by Guo et al (2020) to explore uncertainty propagation from model parameters to design flood estimations. The effects of parameter uncertainties on multivariate risk analyses have also been addressed by and Fan, Huang, Huang, Li, and Wang (2020). However, most previous studies merely focused on parameter uncertainties whilst uncertainties in model structures are somewhat overlooked possibly due to some technical difficulties.…”

A Statistical Hydrological Model for Yangtze River Watershed Based on Stepwise Cluster Analysis

“…A number of statistic models such as multiple linear regression, autoregressive, and autoregressive integrated moving average cannot reflect nonlinear relationships between predictors (e.g., climatic factors) and responses (e.g., streamflow) (Solomatine and Ostfeld, 2008;Ordieres-Meré et al, 2020). Besides, it can hardly fit the observations very well with nonlinear relationships in the water cycle (Fan et al, 2020;Li et al, 2020). The artificial intelligence-based models may suffer from a few deficiencies such as getting trapped in local optimum, overfitting, subjectivity in the choice of model parameters, and the components of its complex structure (Wang et al, 2020).…”

Data‐driven model for river flood forecasting based on a Bayesian network approach

“…With the aim of assessing the flow discharge at a given location, they can take into account individual gauge uncertainties in the form of probabilistic distributions. More importantly, they allow the decomposition of uncertainty components related to the model of the gauging curve ("structural error"), parameter estimation ("parametric error") and potentially systematic and non-systematic errors in the water level series ("propagation error") (Boutkhamouine, Roux, & Pérès, 2017, Boutkhamouine, Roux, Pérès, & Vervoort, 2018, Fan, 2019, Dittes, Špačková, & Straub, 2019.…”