Probability prediction of peak break‐up water level through vine copulas

Abstract

Prediction of the peak break‐up water level, which is the maximum instantaneous stage during ice break‐up, is desirable to allow effective ice flood mitigation, but traditional hydrologic flood routing techniques are not efficient in addressing the large uncertainties caused by numerous factors driving the peak break‐up water level. This research provides a probability prediction framework based on vine copulas. The predictor variables of the peak break‐up water level are first chosen, the pair copula structure is then constructed by using vine copulas, the conditional density distribution function is derived to perform a probability prediction, and the peak break‐up water level value can then be estimated from the conditional density distribution function given the conditional probability and fixed values of the predictor variables. This approach is exemplified using data from 1957 to 2005 for the Toudaoguai and Sanhuhekou stations, which are located in the Inner Mongolia Reach of the Yellow River, and the calibration and validation periods are divided at 1986. The mean curve of the peak break‐up water level estimated from the conditional distribution function can capture the tendency of the observed series at both the Toudaoguai and Sanhuhekou stations, and more than 90% of the observed values fall within the 90% prediction uncertainty bands, which are approximately twice the standard deviation of the observed series. The probability prediction results for the validation period are consistent with those for the calibration period when the nonstationarity of the marginal distributions for the Sanhuhekou station are considered. Compared with multiple linear regression results, the uncertainty bands from the conditional distribution function are much narrower; moreover, the conditional distribution function is more capable of addressing the nonstationarity of predictor variables, and the conclusions are confirmed by jackknife analysis. Scenario predictions for cases in which the peak break‐up water level is likely to be higher than the bankfull water level can also be conducted based on the conditional distribution function, with good performance for the two stations.

Flood hydrograph coincidence analysis of the upper Yangtze River and Dongting Lake, China

“…The traditional copula functions used in the construction of a multidimensional joint distribution are mainly multidimensional elliptic copula and Archimedean copula, but their structures are relatively fixed, and they require the same correlation structure among variables. Therefore, they cannot accurately describe the dependencies of higher-dimensional variables (Aas et al 2009;Schepsmeier and Czado 2016;Yu et al 2019;Jane et al 2020;Tosunoglu et al 2020;Wu et al 2020;).…”

A Framework of Dependence Modeling and Evaluation System for Compound Flood Events

“…Although vine copula model allows the selection of arbitrary copula functions, existing literature choose optimal copula function from a limited scope of Archimedean and elliptical copulas (Brunner et al., 2019; Chen et al., 2019; Liu et al., 2018; Vernieuwe et al., 2015), which is insufficient to represent diverse dependence structures between variables. In addition, few vine‐based models took sufficient number of variables into account, so without manifesting the ability to characterize dependence profiles among multiple variables (Bevacqua et al., 2017; Shafaei et al., 2017; Sun et al., 2021; Tosunoglu & Singh, 2018; Tosunoglu et al., 2020; Yu et al., 2019).…”

Probabilistic Projections of Multidimensional Flood Risks at a Convection‐Permitting Scale

“…Vine copula (also known as pair‐copula construction), which is a more flexible approach than copulas, has been proven to be a powerful tool for describing the complex interactions of flood characteristics in a dimension of three or higher (Bedford & Cooke, 2002; Bevacqua et al., 2017; Daneshkhah et al., 2016; Jiang et al., 2019; Liu et al., 2018; Min & Czado, 2010; Yu et al., 2019). Previous vine copula studies commonly used local optimization schemes to estimate parameters, which is simple and computationally efficient to implement (Aas et al., 2009; Hobæk Haff & Segers, 2015; Sadegh et al., 2017).…”