Stochastic simulation of periodic processes with arbitrary marginal distributions

Stochastic simulation of hydrological processes has a key role in water resources planning and management due to its ability to incorporate hydrological uncertainty within decision-making. Due to seasonality, the statistical characteristics of such processes are considered periodic functions, thus implying the use of cyclostationary stochastic models, typically using a common statistical distribution. Yet, this may not be representative of the statistical structure of such processes across all seasons. In this context, we introduce a novel model suitable for the simulation of periodic processes with arbitrary marginal distributions, called Stochastic Periodic AutoRegressive To Anything (SPARTA). Apart from capturing the periodic correlation structure of the underlying processes, its major advantages are a) the accurate preservation of seasonally-varying marginal distributions; b) the explicit generation of non-negative values; and c) the parsimonious model structure. Finally, the performance of the model is demonstrated through a theoretical (artificial) case study.