Joint modeling of annual maximum precipitation across different duration levels

Abstract

Summarizing a series of rainfall events for different duration levels by their annual maxima provides valuable information. These statistics are e.g. the design base of urban drainage systems. Investigating an entire set of duration levels, the dependence among them has to be taken into account. We propose an approach where a set of generalized extreme value distributions and a D-vine copula are exibly parameterized by the set of duration levels of interest. A priori, it is not necessary to fix the duration levels nor the number of duration levels. This joint model produces increasing values for both, longer duration levels and larger return periods. In a sample application, we show that this model is exible enough to capture variations across the duration levels while reproducing the correlation structure of the data. A joint probabilistic model allows to study a new set of design questions where conditional probabilities or joint return periods are of interest. This is for instance the case when nested sub- basins are studied. An urban area within a larger catchment will be sensitive to annual maxima of shorter durations due to high intensities while the enclosing catchment is prone to annual maxima of long durations due to huge volumes. A risk analysis of the entire catchment requires a joint study of both and an approach where the duration levels' dependence is taken into account.