Stochastic generation of rainfall and streamflow time series at multiple sites using independent component analysis

Abstract

An important objective in stochastic hydrology is to generate synthetic rainfall and/or stream-flow sequences that have similar statistics and dependence structures to those of the historical record. The generation of these sequences can be particularly challenging in the multivariate setting, where it is necessary to simulate both the spatial and temporal dependence of the original multivariate time series. The approaches that are currently available, such as the multivariate autoregressive models, commonly assume gaussian dependence and, due to the large number of parameters that need to be estimated from relatively short historical records, typically only consider lag-one temporal dependence. Proposed here is a two-step approach to developing synthetic multivariate time series at monthly or longer time scales, which involves firstly applying a transformation to the multivariate data in order to generate a set of statistically independent univariate time series, followed by the application of a univariate time series model to the transformed series. The benefits of the two step approach is that, because the time series models are applied to the univariate case, it is possible to consider a much broader class of parametric or non-parametric autoregressive models. To transform the data, we use a technique known as independent component analysis (ICA), which uses an approximation of mutual information to maximise the independence of the transformed time series, and we compare this with the better-known method of principal components analysis (PCA), which minimises the covariance of the multivariate data. These approaches are evaluated on a monthly multivariate dataset from Colombia, and it is shown that the discrepancy between the synthetically generated multivariate dataset and the original dataset, measured as the mean integrated squared bias (MISB), is reduced by 25% when using ICA for the transformation to univariate series, compared with using PCA. Interestingly, this improvement was not limited to the representation of the joint dependence, with an improvement of 28% observed when considering marginal densities in isolation. These results suggest that when developing models for the synthetic generation of multivariate time series, more emphasis should be placed on higher order statistics so that spatial and temporal dependence is correctly simulated.