Multiscale Temporal Irreversibility of Streamflow and Its Stochastic Modelling

We investigate the impact of time's arrow on the hourly streamflow process. Although time asymmetry, i.e., temporal irreversibility, has been previously implemented in stochastics, it has only recently attracted attention in the hydrological literature. Relevant studies have shown that the time asymmetry of the streamflow process is manifested at scales up to several days and vanishes at larger scales. The latter highlights the need to reproduce it in flood simulations of fine-scale resolution. To this aim, we develop an enhancement of a recently proposed simulation algorithm for irreversible processes, based on an asymmetric moving average (AMA) scheme that allows for the explicit preservation of time asymmetry at two or more time-scales. The method is successfully applied to a large hourly streamflow time series from the United States Geological Survey (USGS) database, with time asymmetry prominent at time scales up to four days.