Coupling stochastic models of different timescales

A methodology is proposed for coupling stochastic models of hydrologic proc esses applying to different timescales so that time series generated by the different models be consistent. Given two multivariate time series, genera ted by two separate (unrelated) stochastic models of the same hydrologic pr ocess, each applying to a different timescale, a transformation is develope d (referred to as a coupling transformation) that appropriately modifies th e time series of the lower-level (finer) timescale so that this series beco mes 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 pr oposition, which ensures preservation of marginal and joint second-order st atistics and of linear relationships between lower- and higher-level proces ses. Several specific forms of the coupling transformation are studied, fro m the simplest single variate to the full multivariate. In addition, techni ques for evaluating parameters of the coupling transformation based on seco nd-order moments of the lower-level process are studied. Furthermore, two m ethods are proposed to enable preservation of the skewness of the processes in addition to that of second-order statistics. The overall methodology ca n be applied to problems involving disaggregation of annual to seasonal and seasonal to subseasonal timescales, as well as problems involving finer ti mescales (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 exampl e.