Time's arrow in stochastic characterization and simulation of atmospheric and hydrological processes

Time's arrow has important philosophical, scientific and technical connotations and is closely related to randomness as well as to causality. Stochastics offers a frame to explore, characterize and simulate irreversibility in natural processes. Indicators of irreversibility are different if we study a single process alone, or more processes simultaneously. In the former case, description of irreversibility requires at least third-order properties, while in the latter lagged second-order properties may suffice to reveal causal relations. Several examined data sets indicate that in atmospheric processes irreversibility is negligible at hydrologically relevant time scales, but may appear at the finest scales. However, the irreversibility of streamflow is marked for scales of several days and this highlights the need to reproduce it in flood simulations. For this reason, two methods of generating time series with irreversibility are developed, from which one, based on an asymmetric moving average scheme, proves to be satisfactory.