A Rapid Method for Modeling Transient River Response Under Stochastic Controls With Applications to Sea Level Rise and Sediment Nourishment

Recent analysis of equilibrium and quasi-equilibrium channel geometry in engineered (fixed-width) rivers has successfully shown that two temporal scales can be distinguished, with quasi-static (long-term) and dynamic (short-term) components. This distinction is based on the fact that channel slope cannot keep pace with short-term fluctuations of the controls. Here we exploit the distinction between the two temporal scales to model the transient (so time-dependent) phase of channel response, which is the phase wherein the channel approaches its new equilibrium. We show that: (a) besides channel slope, also the bed surface texture cannot keep pace with short-term fluctuations of the controls, and (b) mean transient channel response is determined by the probability distributions of the controls (e.g., flow duration curve rather than flow rate sequence). These findings allow us to set up a rapid numerical method that determines the mean transient channel response under stochastic controls. The method is based on distinguishing modes (i.e., sets of controls) and takes the probability density of each mode into account. At each time step, we compute the mode-specific flow, sediment transport rate, and corresponding change in bed level and surface texture. The net change within the time step is computed by weighting the mode-specific changes in bed level and surface texture with the probability density of each mode. The resulting mean transient channel response is a deterministic one, despite the controls being stochastic variables. We show that the proposed method provides a rapid alternative to Monte Carlo analysis regarding the mean time-dependent channel response.