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Hydroclimatic processes are characterized by heterogeneous spatiotemporalcorrelation structures and marginal distributions that can be continuous,mixed-type, discrete or even binary. Simulating exactly such processes cangreatly improve hydrological analysis and design. Yet this challenging task isaccomplished often by ad hoc and approximate methodologies that are devised forspecific variables and purposes. In this study, a single framework is proposedallowing the exact simulation of processes with any marginal and anycorrelation structure. We unify, extent, and improve of a general-purposemodelling strategy based on the assumption that any process can emerge bytransforming a parent Gaussian process with a specific correlation structure. Anovel mathematical representation of the parent-Gaussian scheme provides aconsistent and fully general description that supersedes previous specificparameterizations, resulting in a simple, fast and efficient simulationprocedure for every spatiotemporal process. In particular, introducing a simplebut flexible procedure we obtain a parametric expression of the correlationtransformation function, allowing to assess the correlation structure of theparent-Gaussian process that yields the prescribed correlation of the targetprocess after marginal back transformation. The same framework is alsoapplicable for cyclostationary and multivariate modelling. The simulation of avariety of hydroclimatic variables with very different correlation structuresand marginals, such as precipitation, stream flow, wind speed, humidity,extreme events per year, etc., as well as a multivariate application,highlights the flexibility, advantages, and complete generality of the proposedmethodology.

A unified theory for exact stochastic modelling of univariate and  multivariate processes with continuous, mixed type, or discrete marginal  distributions and any correlation structure