Impact of time’s arrow on streamflow and its stochastic modelling

We investigate the impact of time’s arrow on hydrological processes. The role of stochastic simulation and uncertainty is first investigated. Uncertainty is a major factor in physical sciences and engineering. The probabilistic behavior of an engineering system is essential considering that uncertainty issues are important and must be managed. The true distribution for the system response is subject to parameter uncertainty and is in most of the times difficult or even impossible to calculate. This is due to the complexity of the hydrosystems. In such cases, stochastic simulation else known as Monte Carlo simulation is a viable tool to provide numerical estimations of the stochastic features of the system response. Long range dependence is a feature connected to uncertainty and is very important in hydrology. Itis being discussed through relevant literature and models. Time’s arrow or temporal asymmetry is also related to uncertainty and randomness and has an important role in science. It has been implemented in stochastics for some time but it has recently attracted attention in relevant publications in hydrology. Studies have shown that the temporal asymmetry of the streamflow process is marked for scales up to several days and this highlights the need to reproduce it in flood simulations. After a review of the relevant literature, an analytical method based on an asymmetric moving average (AMA) scheme is being used to simulate time series with temporal asymmetry. The temporal asymmetry of real world streamflow time series is being investigated at hourly scale from the large USGS database. Finally, a modification of the method that can simulate time asymmetry at two timescales simultaneously is proposed. The method is successfully tested in the physical world through a case study.