Stochastic simulation of time irreversible processes

Stochastic simulation is a well-established method for the design, analysis and control of hydrosystems. In particular, it has proved powerful for the management of large reservoir systems, where simulation and optimization are typically performed on a time scale of the order of a month. A basic requirement of the method is a proper technique for stochastic generation of hydrological inputs, respecting characteristic behaviours of hydrological processes, such as seasonality, intermittence, long term persistence and roughness (fractality). However, in several hydrosystem operations, particularly those related to flood control and energy production, the time scales of interest are much finer than monthly, e.g., hourly or even finer. On fine time scales, another behaviour of hydrological processes becomes important and necessary to reproduce: time irreversibility or compliance with time’s arrow. While time’s arrow, with its close relationship to causality, has important philosophical, scientific and technical connotations, it has attracted little attention in hydrological stochastics and even in the entire field of stochastic simulation. On the other hand, stochastics offers a frame to explore, characterize and simulate time irreversibility. As common stochastic techniques produce time series whose properties are symmetric in time, a new stochastic simulation method is presented, which is capable of generating sequences with the required properties related to time irreversibility. The method is generic as it can reproduce any marginal distribution, covariance structure and irreversibility index, and can work both in simulation and forecast mode.