Stochastic modeling of variations in stream flow discharge induced by random spatiotemporal fluctuations in lateral inflow rate

Due to natural heterogeneity in runoff processes, the analysis of response of stream channels to the variation of lateral inflow is therefore viewed in terms of stochastic spatiotemporal processes. Based on the representation theorem, a closed-form expression is derived to describe the spectral response characteristic of stream subject to spatiotemporal fluctuations in lateral inflow. It provides a basis for evaluating the induced discharge variability in stream channels. It is found that the evolutionary power spectrum of the stream flow discharge process and therefore the variance is increased with the distance from the upstream boundary and the characteristic length scale of the lateral inflow process. Flow discharge prediction in the downstream region has a high degree of uncertainty by solving the deterministic partial differential equation.