Building a puzzle to solve a riddle: A multi-scale disaggregation approach for multivariate stochastic processes with any marginal distribution and correlation structure

The generation of hydrometeorological time series that exhibit a given probabilistic and stochastic behavior across multiple temporal levels, traditionally expressed in terms of specific statistical characteristics of the observed data, is a crucial task for risk-based water resources studies, and simultaneously a puzzle for the community of stochastics. The main challenge stems from the fact that the reproduction of a specific behavior at a certain temporal level does not imply the reproduction of the desirable behavior at any other level of aggregation. In this respect, we first introduce a pairwise coupling of Nataf-based stochastic models within a disaggregation scheme, and next we propose their puzzle-type configuration to provide a generic stochastic simulation framework for multivariate processes exhibiting any distribution and any correlation structure. Within case studies we demonstrate two characteristic configurations, i.e., a three-level one, operating at daily, monthly and annual basis, and a two-level one to disaggregate daily to hourly data. The first configuration is applied to generate correlated daily rainfall and runoff data at the river basin of Achelous, Western Greece, which preserves the stochastic behavior of the two processes at the three temporal levels. The second configuration disaggregates daily rainfall, obtained from a meteorological station at Germany, to hourly. The two studies reveal the ability of the proposed framework to represent the peculiar behavior of hydrometeorological processes at multiple temporal resolutions, as well as its flexibility on formulating generic simulation schemes.