A study of the stochastic evolution of hydraulic geometry relationships

Abstract

AbstractUncertainty resulting from climatic and environmental changes creates barriers to the accurate acquisition of information about rivers. In this study, a set of stable stochastic differential equations is developed to simulate the dynamic probability distributions of typical hydraulic geometry variables represented by slope, width, depth, and velocity with variations in bankfull discharge over time for a river system. Random parts of the equations are modelled based on single Gaussian white noise and further on combined Gaussian/fractional white noise with Poisson noise. Consistent estimates of the equation parameters are made using a composite nonparametric maximum likelihood estimation (MLE) method. The proposed models are examined through a Monte Carlo simulation of the lower Yellow River, and the results successfully reveal the potential responses of hydraulic geometries to stochastic disturbance and that average trends largely synchronize with the measured values. Comparisons of the three different models confirm the advantages of fractional jump‐diffusion model, and according to further discussion, stream power on the basis of such a model is concluded to serve as the better systematic measure of river dynamics. The proposed stochastic approach is new to the field of fluvial relationships, and its application could help to design and monitor river systems with specified accuracy requirements.