J. Piantadosi, P.G. Howlett, and J.W. Boland (Australia)
Daily rainfall, Copulas, correlation, Spearman’s ρ
We present a model for the generation of synthetic daily rainfall data which we demonstrate for Parafield in Ade laide, South Australia. The daily rainfall is modelled as a non-negative random variable from a mixed distribution with either a zero outcome or a strictly positive outcome. We use the method of maximum likelihood to find the gamma distribution that best matches the observed proba bility density for the strictly positive outcomes. To generate rainfall data we use a uniformly distributed random vari able to choose the cumulative probability and hence spec ify the corresponding daily rainfall. If the synthetic data is generated from a sequence of independent random vari ables then the monthly standard deviations are too low. To overcome this problem we describe a new model that gen erates a sequence of correlated random numbers using a joint density for successive days given by a generalised di agonal band copula. The new model preserves the marginal daily distributions and hence also preserves the monthly means. We show that by adjusting the width of the diagonal band copula we can match the observed monthly standard deviations. Finally we discuss the results from 1000 years of simulated rainfall with various choices of daily Spear man’s ρ and compare the values with the observed statistics from 104 years of official rainfall records.
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