Copula autoregressive methodology for multi-lag,multi-site simulation of rainfall

Abstract

This work presents a methodology for the synthetic generation of rainfall time series based on the copula autoregressive methodology with multiple lags and for multiple sites. In this model, the multivariate time series is decomposed using pairwise copula functions to represent the whole cross-dependence, spatial and temporal structure of the data. We explore the advantages of using this nonlinear method over more traditional approaches that as an intermediate step transform the data to a normal distribution or usually omit the zero mass characteristics of the data. The use of copulas gives flexibility to represent the serial variability of the observed data on the simulation and allows for more control of the desired properties. We use discrete zero mass density distributions to assess the nature of rainfall, alongside a vector generalized linear model for the evaluation of time series distributions and their time dependence in multiple locations. We found that the copula autoregressive methodology models in a satisfactory manner the characteristics of the data, including its zero mass characteristics. These results will help to better understand the fluctuating nature of rainfall and also help to understand the underlying stochastic process.