A comparative copula-based bivariate frequency analysis of observed and simulated storm events: A case study on Bartlett-Lewis modeled rainfall

Because of a lack of historical rainfall time series of considerable length, one often has to rely on simulated rainfall time series, e. g., in the design of hydraulic structures. One way to simulate such time series is by means of stochastic point process rainfall models, such as the Bartlett-Lewis type of model. For the evaluation of model performance, with a focus on the reproduction of extreme rainfall events, often a univariate extreme value analysis is performed. Recently developed concepts in statistical hydrology now offer other means of evaluating the overall performance of such models. In this study, a copula-based frequency analysis of storms is proposed as a tool to evaluate differences between the return periods of several types of observed and modeled storms. First, this study performs an analysis of several storm variables, which indicates a problem with the modeling of the temporal structure of rainfall by the models. Thereafter, the bivariate frequency analysis of storms, defined by their duration and volume, illustrates the underestimation and overestimation of the return period of the storms simulated by the models, which is partially explained by a large difference in the marginal distribution functions of the storm duration and storm volume, the difference in the degree of association between the latter, and a different mean storm interarrival time. The proposed methodology allows for the identification of some problems with the rainfall simulations from which recommendations for possible improvements to rainfall models can be made.