Enhancing intensity-duration-frequency curves estimation: a Markov dependence approach

The accurate estimation of the probabilities of rainfall events exceeding given (typically high) intensities is a fundamental challenge in hydrological risk assessment. Since the design of infrastructures must take into account rainfall extremes at different temporal scales, coherence between estimated exceedance probabilities across different durations is desirable. Intensity duration frequency (IDF) curves, describing the expected frequency of extreme rainfall intensities measured at different durations, are an important tool in this context. Most existing methods for IDF estimation introduce adequate shape constraints through duration-dependent Generalized Extreme Value (dGEV) distributions, but assume that extreme rainfall intensities over different durations are independent of each other, which does not seem realistic. Proposed models to introduce dependence come at a heavy computational burden and often resort to approximate inference. We propose an alternative model, based on a first-order Markov assumption, which incorporates dependence between intensities at consecutive (discretely defined) durations via bivariate extreme distributions, while the marginal distributions are dGEV, thus satisfying the shape constraints. We investigate the usefulness of the proposed model via a simulation study. Results show that ignoring dependence across durations can result in overdispersed estimates. Finally, the proposed methods are showcased with an application to four stations in the German state of Brandenburg.