Coupling stochastic models of different timescales

A methodology is proposed for coupling stochastic models of hydrologic processes applying to different timescales so that time series generated by the different models be consistent. Given two multivariate time series, generated by two separate (unrelated) stochastic models of the same hydrologic process, each applying to a different timescale, a transformation is developed (referred to as a coupling transformation) that appropriately modifies the time series of the lower-level (finer) timescale so that this series becomes consistent with the time series of the higher-level (coarser) timescale without affecting the second-order stochastic structure of the former and also establishes appropriate correlations between the two time series. The coupling transformation is based on a developed generalized mathematical proposition, which ensures preservation of marginal and joint second-order statistics and of linear relationships between lower- and higher-level processes. Several specific forms of the coupling transformation are studied, from the simplest single variate to the full multivariate. In addition, techniques for evaluating parameters of the coupling transformation based on second-order moments of the lower-level process are studied. Furthermore, two methods are proposed to enable preservation of the skewness of the processes in addition to that of second-order statistics. The overall methodology can be applied to problems involving disaggregation of annual to seasonal and seasonal to subseasonal timescales, as well as problems involving finer timescales (e.g., daily to hourly), with the only requirement that a specific stochastic model is available for each involved timescale. The performance of the methodology is demonstrated by means of a detailed numerical example.