LAUSR

Abstract Hydraulic geometry relations comprise a classic way to understand characteristics of a river. However, environmental changes pose large uncertainties for the reliability of such relations. In the current study, on the basis of the ordinary differential equations (ODEs) formed through linear treatment of the deterministic power-law hydraulic geometry relations, a set of stochastic differential equations (SDEs) driven by Fractional white noise and Poisson noise are developed to simulate the historical dynamic probability distributions of typical hydraulic geometry variables such as slope, width, depth, and velocity with bankfull discharge variation over time in the lower Yellow River of China. One group of possible stochastic average behaviors within the next 50 years are calculated under three different design incoming water-sediment conditions (including 300, 600, and 800 million t of annual average sediment discharge). In each part of the lower reaches, after estimation of the SDE parameters using a nonparametric maximum likelihood estimation (MLE) method, the model is carefully examined using Monte Carlo simulation as compared with the deterministic control models. The results of this comparison reveal the potential responses of hydraulic geometry characteristics to environmental disturbances, and the average trends mainly agree with the measurements. Comparisons among the three different prediction results reveal the stochastic average solution generally is greater than the deterministic solution. The results also confirm the severe negative impacts that result from the condition of 300 million t of incoming sediment, thus, pointing out the need to raise the level of river evolution alert for the lower Yellow River of China in the future. Moreover, with the help of the stochastic computation, the stream power and hydraulic width/depth ratio could be representative of an effective systematic measure for river dynamics. The proposed stochastic approach is not only important to development in the field of fluvial relations, but also beneficial to the practical design and monitoring of a river system according to specified accuracy requirements.