A high-precision calculation formula for the sediment carrying capacity of Weihe River based on incomplete self-similarity principle combined with dimensional analysis

The capacity of water flow to transport sediment is one of the most fundamental indicators of river dynamics. Previous studies often use the measured data to determine the part of the coefficient, due to the complexity of the sediment-bearing flow movement. It is often required to consider the hydraulic sediment characteristics. The accuracy and universality of the model also need to be further improved in recent years. This study aims to predict the high-resolution sediment-carrying capacity of the Weihe River using incomplete self-similarity with dimensional analysis. A total of 746 sets of quasi-equilibrium observation data were gathered from three hydrological stations in the lower sections of the Weihe River from 2006 to 2023. Specifically, the flood data was measured from three hydrological stations in Xianyang, Lintong, and Huaxian City. The simple processing was carried out to obtain the characteristic parameters, such as the water depth, velocity, sediment content, median particle size, and settling velocity. A precise formula was developed to calculate the sediment transport capacity considering the specific water and sediment properties of the river. The sediment transport capacity was derived using dimensional analysis. An expression was also involved using nondimensional parameters. The relationship between the dimensionless parameter and sediment transport capacity was explained using ideal assumptions. The incomplete self-similarity was also highlighted. Additionally, several undetermined constants were determined to refine the calculation formula, according to measured data. Given the current performance of the calculation, the model was adjusted to incorporate the sediment content. The results indicate that the Velikanov parameter was more suitable for the prediction model, compared with the Froude number Fr. The sediment transport capacity was obtained using the Velikanov parameter, indicating the strong prediction under the fundamental principles of water flow dynamics; Specifically, the rougher river bed was, the smaller sediment carrying capacity of the water flow was. The multi-factor incomplete self-similar relationship was dominated by the interaction of variables. The exponential term of the incomplete self-similar model was the interaction of dimensionless parameters in the formula structure. The complex sediment transport was then simulated to enhance the performance of the model using conventional regression. The sediment content was one of the crucial influencing factors on the capacity of the water flow to transfer sediment. However, the mathematical derivation was used to define the incomplete self-similar relationship between sediment content and sediment carrying capacity; Once the sediment content approached 0, the sediment carrying capacity was converged at the same time. The prediction error substantially decreased to consider this variation. Three components were considered for the highest performance, with a correlation coefficient of 0.98 and a relative error of only 0.07. The concentration coefficient and deviation coefficient were 1.01 and 0.07, respectively. This model also surpassed the several prior formulas after river test data, due to the variations in the features of different rivers. Excellent prediction accuracy was achieved at both high and low sediment content. Thus, the model can be utilized to forecast the sediment-transport capacity of the lower Weihe River, which is characterized as a sediment-laden river. Due to the clarity of the formula structure, the coefficients of the other types of rivers can still be re-calibrated by the measured data for the feasible calculation of sediment carrying capacity. At the same time, this finding can also provide some research examples for the sediment carrying capacity on the estuary flow slope.