A continuous rainfall model based on vine copulas

Abstract

Abstract. Copulas have already proven their flexibility in rainfall modelling. Yet, their use is generally restricted to the description of bivariate dependence. Recently, vine copulas have been introduced, allowing multi-dimensional dependence structures to be described on the basis of a stage by stage mixing of two-dimensional copulas. This paper explores the use of such vine copulas in order to incorporate all relevant dependencies between the storm variables of interest. On the basis of such fitted vine copulas, an external storm structure is modeled. An internal storm structure is superimposed based on Huff curves, such that a continuous time series of rainfall is generated. The performance of the rainfall model is evaluated through a statistical comparison between an ensemble of synthetical rainfall series and the observed rainfall series and through the comparison of the annual maxima.

Critical rainfall statistics for predicting watershed flood responses: rethinking the design storm concept

“…The increased complexity of considering event duration in stochastic rainfall generation (e.g. Vernieuwe et al , ) is not necessarily justified in all cases. Researchers may be able to take a more parsimonious approach to estimating probable future rainfall runoff responses by removing this event statistic from consideration if it proves non‐sensitive.…”

“…We think some of these studies may have imposed an artificial restraint on the development of design storms or stochastically generated precipitation records by considering limited sets of possible event statistics to describe precipitation events. For example, Nguyen et al (), Watt and Marsalek (), Paschalis et al (), Terranova et al () and Vernieuwe et al () discuss the importance of considering the temporal distribution of a precipitation event for design hyetograph construction or runoff response, yet not all studies consider the temporal distribution as a random variable (or variables) with a probability of occurrence less than unity. We propose that recent studies may potentially underestimate or overestimate the aleatory uncertainties of precipitation and system response return frequencies to extreme precipitation because of a constricted set of rainfall statistics.…”

Multivariate Copula Analysis Toolbox (MvCAT): Describing dependence and underlying uncertainty using a Bayesian framework

“…[]. Multivariate methods and copulas have been used in many fields of study including finance [ Rachev , ], insurance [ Charpentier and Segers , ], integrated risk management [ Embrechts et al ., ], drought monitoring [ Hao and AghaKouchak , ], flood risk analysis [ Jongman et al ., ], frequency analysis [ Parent et al ., ], rainfall simulation and analysis [ Li et al ., ; Vernieuwe et al ., ], dependence analysis of hyetographs and hydrographs [ Serinaldi and Kilsby , ], and extreme value analysis [ Renard and Lang , ; Ribatet and Sedki , ]. Recent studies have striven to open new frontiers to address real‐world problems using copulas.…”

Stochastic simulation of precipitation-consistent daily reference evapotranspiration using vine copulas

“…Gräler et al 2011;Vernieuwe et al 2015). The advantage of the method is that it allows for constructing a multivariate copula based on the mixing of (conditional) bivariate copulas.…”

“…Copulas have already proven their usefulness in hydrology. They have been employed in, for instance, the analysis of the dependence structure between storm characteristics (Vandenberge et al 2010a), in a statistical analysis of (extreme) rainfall events (Gräler et al 2011;Vandenberghe et al 2011;Kao and Govindaraju 2008) and in the development of stochastic rainfall models (Serinaldi 2009;Evin and Favre 2008;Salvadori and De Michele 2006;Vernieuwe et al 2015). As copulas describe the dependence structure between stochastic variables, regardless of their marginal distributions, they are very useful for describing the dependences between evapotranspiration, rainfall characteristics, and other climatological variables such as net radiation or temperature.…”