Calculation method for sediment load in flood and non-flood seasons in the Inner Mongolia reach of the Yellow River

Based on an empirical sediment transport equation that reflects the characteristics of ＂more input, more output＂ for sediment-laden flow in rivers, a general sediment transport expression was developed, which can take into account the effects of upstream sediment input, previous cumulative sediment deposition, critical runoff for sediment initiation, and the differences in sediment particle sizes between the mainstream and tributaries. Then, sedi- ment load equations for non-flood and flood seasons for the sub-reaches from Bayangaole to Sanhuhekou and from Sanhuhekou to Toudaoguai, as well as the whole Inner Mongolia reach from Bayangaole to Toudaoguai, were formulated based on data collected between 1952 and 2010. The corresponding sediment deposition and the cumulative values at each river reach were calculated using the proposed sediment transport equations for the period 1952 to 2010 according to the principle of sediment conservation. Comparisons between the calculated and measured values using the proposed sediment load equations for the sub-reaches and the entire reach showed that the calculated sediment load and sediment deposition and the cor- responding cumulative values in the flood and non-flood seasons were in good agreement with the measured values. These results indicated that the proposed methods can be applied to calculate the sediment load and the associated sediment deposition in the flood and non-flood seasons for long-term trend analysis of sediment deposition in the Inner Mongolia reach of the Yellow River.

Accumulation phenomena in fluvial processes and the corresponding stochastic model

Accumulation occurs widely in fluvial processes.Accurately accounting for the effects of previous water and sediment conditions on accumulation is essential for studying riverbed evolution.In this study,to reveal the physical mechanisms of accumulation,various geometric observations of both the upstream and downstream reaches of dams on several typical fluvial channels were analyzed.The changes in water and sediment conditions were defined as external disturbances.Assuming that the probability of an external disturbance conforms to a Poisson distribution,and that the response intensity induced by an individual disturbance decays exponentially over time,a mathematical description of the accumulation of internal responses to external disturbances is given.Furthermore,a corresponding theoretical model for simulating the spatiotemporal readjustments of characteristic river variables is proposed based on stochastic theory.The proposed models are then applied to investigate spatiotemporal readjustment in the upper and lower reaches of dams following their construction.The results indicate that temporally,the vertical,lateral,and overall readjustment rates of the reaches are relatively fast in the early period following dam construction but then decrease rapidly over time.Accumulated riverbed degradation,channel width,and sedimentation continuously increase until a new dynamic equilibrium is reached.These phenomena reflect the representative accumulation characteristics of fluvial processes.Spatially,the erosion intensities in downstream reaches decrease nonlinearly along the channel until eventually diminishing.The unbalanced spatial distribution of erosion intensity arises from the system response characterized by propagation in space but decay over time,which is characteristic of accumulation phenomena after disturbances.The results of the developed model show that the spatiotemporal readjustments of the studied cross-sections and channel reaches can be accurately described by the unified theoretical formula derived herein.The model predictions show good agreement with observed field data with determination coefficients of 0.92,0.93,0.76,and 0.95 for vertical,lateral,longitudinal,and overall readjustments,respectively.The proposed theoretical models account for both the accumulation characteristics of fluvial processes and their spatial distributions.In demonstrating the proposed ap-proach,this study provides a theoretical basis and new calculation method for quantitatively describing the spatiotemporal readjustments of non-equilibrium fluvial channels following external disturbances.

A Partial Differential Inequality in Geological Models

Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation. This limiter happens to satisfy a stationary scalar hyperbolic inequality, within a constraint, for which the authors prove the existence and the uniqueness of the solution. Actually, this solution is shown to be the maximal element of a convenient convex set of functions. The existence proof is obtained thanks to the use of a numerical scheme.