Space-time continuous rainfall modeling - a copula approach

To aid in the simulation of runoff for Lake Michigan diversion accounting, a dense network of 25 rainfall gages has been operated by the Illinois State Water Survey since 1989. About 2000 storm events have been identified from the 21 years of space-time continuous rainfall data recorded at a one hour timescale. The space-time dependence structure of storm event total amount, maximum wet period amount, total duration of wet periods, and inter-storm time interval are being modeled using copulas. For computational tractability vine copulas are used to decompose the multivariate densities into bivariate linking copulas, thus, involving lower-dimensional integrals. An additional advantage is that the vine copula offers the flexibility of selecting different bivariate family copulas for each section. After generation of the storm event characteristics by the copulas, the wet-dry sequence is modeled by the simpler Poisson model while the distribution of the total storm event amount over the wet periods is achieved by a lag-1 autoregressive model. Initial results indicate that the storm characteristics are being well captured by the proposed model.