Uncertainty analysis of flood control design under multiple floods

The conventional flood control design analysis usually focuses on a specific aspect like flood peak discharge or the volume of flood, with the development of technology, hydrological analysis tends to be multi-dimensions research. The multivariate frequency analysis of a flood has been widely investigated, while there is lack of literatures about flood control design under multiple floods. In this study, taking the Guiping Shipping Hub as a study case, a Copula-based approach is proposed to investigate the flood control design under multiple floods, comparison between the proposed method and conventional approach is investigated, the sampling uncertainty is analyzed. The results indicate that (1) the joint distribution of main and tributary floods is modeled by Clayton Copula with PE3 as the best-fit marginal distributions. The proposed Flood Control return period (FC-RP) can describe the different role of main and tributary floods in flood control design. (2) flood combinations uncertainty analysis indicates that the uncertainty of the joint design combinations under the effect of multiple floods decreases with the increase of sample size n, but increases with the increase of the design return period. (3) the 95% confidence interval and standard deviation of the design value of flood control design water level calculated by Flood Control RP is smaller than that of OR RP, which means the Flood Control RP can reduce the uncertainty of flood control design under the condition of multiple floods.

Modified Maximum Pseudo Likelihood Method of Copula Parameter Estimation for Skewed Hydrometeorological Data

For multivariate frequency analysis of hydrometeorological data, the copula model is commonly used to construct joint probability distribution due to its flexibility and simplicity. The Maximum Pseudo-Likelihood (MPL) method is one of the most widely used methods for fitting a copula model. The MPL method was derived from the Weibull plotting position formula assuming a uniform distribution. Because extreme hydrometeorological data are often positively skewed, capacity of the MPL method may not be fully utilized. This study proposes the modified MPL (MMPL) method to improve the MPL method by taking into consideration the skewness of the data. In the MMPL method, the Weibull plotting position formula in the original MPL method is replaced with the formulas which can consider the skewness of the data. The Monte-Carlo simulation has been performed under various conditions in order to assess the performance of the proposed method with the Gumbel copula model. The proposed MMPL method provides more precise parameter estimates than does the MPL method for positively skewed hydrometeorological data based on the simulation results. The MMPL method would be a better alternative for fitting the copula model to the skewed data sets. Additionally, applications of the MMPL methods were performed on the two weather stations (Seosan and Yeongwol) in South Korea.

Multivariate frequency analysis of urban rainfall characteristics using three-dimensional copulas

Urban runoff is a major cause of urban flooding and is difficult to monitor in the long term. In contrast, long term continuous rainfall data are generally available for any given region. As a result, it has become customary to use design rainfall depth as a proxy for runoff in urban hydrological analyses, with an assumption of the same frequency for runoff and rainfall. However, this approach has lack of overall coordination and cannot fully reflect the variability of rainfall characteristics. To address this issue, this study presents a three-dimensional copula-based multivariate frequency analysis of rainfall characteristics based on a long term (1961–2012) rainfall data from Guangzhou, China. Firstly, continuous rainfall data were divided into individual rainfall events using the rainfall intensity method. Then the characteristic variables of rainfall (design rainfall depth, DRD; total rainfall depth, TRD; peak rainfall depth, PRD) were sampled using the annual maximum method. Finally, a copula method was used to develop the multivariate joint probability distribution and the conditional probability distribution of rainfall characteristics. The results showed that the copula-based method is easy to implement and can better reflect urban rainstorm characteristics. It can serve a scientific reference for urban flood control and drainage planning.

Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation

Most of the hydrological and hydraulic studies refer to the notion of a return period to quantify design variables. When dealing with multiple design variables, the well-known univariate statistical analysis is no longer satisfactory, and several issues challenge the practitioner. How should one incorporate the dependence between variables? How should a multivariate return period be defined and applied in order to yield a proper design event? In this study an overview of the state of the art for estimating multivariate design events is given and the different approaches are compared. The construction of multivariate distribution functions is done through the use of copulas, given their practicality in multivariate frequency analyses and their ability to model numerous types of dependence structures in a flexible way. A synthetic case study is used to generate a large data set of simulated discharges that is used for illustrating the effect of different modelling choices on the design events. Based on different uni- and multivariate approaches, the design hydrograph characteristics of a 3-D phenomenon composed of annual maximum peak discharge, its volume, and duration are derived. These approaches are based on regression analysis, bivariate conditional distributions, bivariate joint distributions and Kendall distribution functions, highlighting theoretical and practical issues of multivariate frequency analysis. Also an ensemble-based approach is presented. For a given design return period, the approach chosen clearly affects the calculated design event, and much attention should be given to the choice of the approach used as this depends on the real-world problem at hand.

Joint return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation

Most of the hydrological and hydraulic studies refer to the notion of a return period to quantify design variables. When dealing with multiple design variables, the well-known univariate statistical analysis is no longer satisfactory and several issues challenge the practitioner. How should one incorporate the dependence between variables? How should the joint return period be defined and applied? In this study, an overview of the state-of-the-art for defining joint return periods is given. The construction of multivariate distribution functions is done through the use of copulas, given their practicality in multivariate frequency analysis and their ability to model numerous types of dependence structures in a flexible way. A case study focusing on the selection of design hydrograph characteristics is presented and the design values of a three-dimensional phenomenon composed of peak discharge, volume and duration are derived. Joint return period methods based on regression analysis, bivariate conditional distributions, bivariate joint distributions, and Kendal distribution functions are investigated and compared highlighting theoretical and practical issues of multivariate frequency analysis. Also an ensemble-based method is introduced. For a given design return period, the method chosen clearly affects the calculated design event. Eventually, light is shed on the practical implications of a chosen method.