Stochastic modelling of periodicity and trend for multisite daily rainfall simulation

Periodicity and trend, modelled with emphasis on stochastic aspects using the Gibbs procedure in Markov chain Monte Carlo sampling, are incorporated in multisite daily rainfall simulation. In particular, this gives realistic results for the timing of annual maximums within an annual cycle. A truncated Fourier series of two harmonics is used to model the deterministic part of the periodicity component. A reduced-parameter two-station model is extended for multisite simulation. Results show that depth–duration curves and characteristics such as cross-correlations are adequately represented. Projections are made, after applying the Gibbs procedure to sub-samples of 25 years, to form enveloping trend curves of possible future rainfalls. These are augmented by extending a trend line back in time previous to a historic record, using the relationship with a longer series of rainfall data from a homogeneous zone.