How to parsimoniously disaggregate rainfall in time

Generating finer scale time series of rainfall that are fully consistent with any given coarse-scale totals is still an important and open issue in hydrology. This is commonly tackled by disaggregation models. We focus on a simple and parsimonious model based on a particular nonlinear transformation of the variables obtained by a stepwise disaggregation approach, which generates time series with Hurst-Kolmogorov dependence structure. Unfortunately, nonlinear transformations of the variables do not preserve the additive property, which is one of the main attributes of the original disaggregation scheme. To overcome this problem, an empirical adjusting procedure is suggested in order to restore consistency, but such a procedure may, in turn, introduce bias in all statistics that are to be preserved. We modify the time series generated by our model in a way to be consistent with a given higher-level time series, without affecting the stochastic structure implied by our model.