Generating Synthetic Rainfall on Various Timescales—Daily, Monthly and Yearly

The main objective of this paper is to present a model for generating synthetic rainfall totals on various timescales to be applicable for a variety of uses. Many large-scale ecological and water resource models require daily, monthly and yearly rainfall data as input to the model. As historical data provides only one realisation, synthetic generated rainfall totals are needed to assess the impact of rainfall variability on water resources systems (Srikanthan, In: MODSIM2005, Melbourne, Dec. 2005, pp. 1915–1921, 2005). Thus, our preferred model should simulate rainfall for yearly, monthly and daily periods. We believe that, for water supply issues, no higher resolution is needed, although higher resolution would be useful in models designed to measure the risk of local flooding. The critical factors are daily, monthly and yearly totals and daily, monthly and yearly variation. A model for generating yearly totals will be described using traditional time series methods. This model, along with a similarly constructed daily generation model by Piantadosi et al. (A New Model for Correlated Daily Rainfall, 2008), will be cascaded to start with a synthetic yearly total, then generate a synthetic sequence of monthly totals (through selection from a large number of realisations) that match the yearly total, and subsequently perform a similar operation for sequences of daily totals to match the required monthly totals. We present a new model for the generation of synthetic monthly rainfall data, which we demonstrate for Parafield in Adelaide, South Australia. The rainfall for each month of the year is modelled as a non-negative random variable from a mixed distribution with either a zero outcome or a strictly positive outcome. We use maximum likelihood to find parameters for both the probability of a zero outcome and the gamma distribution that best matches the observed probability density for the strictly positive outcomes. We describe a new model that generates correlated monthly rainfall totals using a diagonal band copula with a single parameter to generate lag-1 correlated random numbers. Our model preserves the marginal monthly distributions and, hence, also preserves the monthly and yearly means. We show that, for Parafield, the correlation between rainfall totals for successive months is not significant, and so, it is reasonable to assume independence. This is, however, not true for daily rainfall. We describe a new model that generates correlated daily rainfall totals using a diagonal band copula with a single parameter to generate lag-1 correlated random numbers.