A bivariate return period copula application of flood peaks and volumes

Abstract

Flood frequency analysis for the design of hydraulic infrastructures is usually made based on univariate flood peak approaches, using theoretical probability distribution functions of annual maximum peak flood discharges during several years. However, extreme flood events and their associated impacts may be better understood by considering other correlated random variables, such as volume and duration, in a multivariate analysis. For such approach, the Copulas methodology has been applied in several works worldwide, and its results show positive impacts in the analysis of extreme events compared to the traditional univariate methods. In the present work, a methodology is used in a case study to model the joint characteristics of the flood using Copulas concept considering a set of parametric and non-parametric marginal distributions for peak flow, volume, and duration to model the correlated nature among them mathematically. Joint return periods can be easily estimated from Copulas, which represents an additional benefit, as these joint return periods are essential for the analysis of the flood frequency. The selected case study was the Castanhão Reservoir, located in a semi-arid climate area of the state of Ceará, in the Northeast of Brazil (NEB). This semi-arid region's characteristics make NEB a region of high hydrological complexity and highly vulnerable to extreme flood events. In 2004, the Castanhão Reservoir, which has one of the biggest water storage capacity in Latin America, increased to over 70% of its total capacity (6.7 billion m³) after less than two rainy months. Therefore, historical data were collected from the main river gauge stations that flow to Castanhão, located in Jaguaribe River and Salgado River, and the relationship among them was studied. At Jaguaribe river gauge station, the event's joint return period was estimated with Copulas distribuition to almost 1.000 years, which is almost twice as long as the return period of the univariate approach. These results prove that the multivariate analysis can find much greater exceptionalities in flood events, not detected in the univariate approach.