## 1 Introduction
The model has been proven theoretically. However, the low time accuracy of the model and the high cost of the customized transmitter limit the application of the technology in large mountainous rivers. [PERSON], [PERSON], and [PERSON] [39] used the hydrophone to measure bedload sediment transport at several locations along the Trinity River, California. [PERSON] et al. [40] used a hydrophone positioned beneath a steel plate to quantify bedload sediment transport in a small river. Bedload transport was assessed and compared with that measured using traps, which were utilized to gather bedload transport identified by hydrophone. Bedload transport was assessed and compared with that recorded utilizing traps employed to gather bedload transport identified by hydrophone. [PERSON] et al. [41] observed sand bedload sediment transport in the Loire River, a mild slope river, using an acoustic Doppler current profiler (ADCP), a hydrophone, and the dune tracking method (DTM). Their findings demonstrated that the hydrophone is more effective and precise than ADCP and DTM in measuring sandy bedload transfer. [PERSON] et al. [37] employed hydrophones to measure bedload sediment in the Drau River in Austria. In addition to the hydrophone, they also placed 40 geophones and three slot bedload samplers along the 50 m wide observation section. The analysis of the short-time frequency response of the audio signals of bedload transport gathered by the hydrophone showed that the majority of the frequencies of the audio signals of bedload movement were concentrated at more than 1000 Hz. Simultaneously, the comparison of the hydrophone results with the geophone and slot sampler measured data demonstrated that the hydrophone and geophone signals had a clear correlation. The authors also discovered that the acoustic features of bedload movement were connected to the signal propagation effect in the river environment. Based on this, a theoretical framework for predicting the propagation of acoustic signals in the river was proposed. The application of this model to the Arc-en-Maurienne River revealed that the audio signal affected the spectral components of the acoustic signals generated by the transported bedload. The audio signal's propagation effect had an effect on the spectral components of the acoustic signal [42]. Furthermore, [PERSON] et al. [43; 44] utilized a hydrophone to monitor and estimate bedload transport in five French alpine rivers (with the highest flow discharge of 237 m\({}^{3}\)/s and the deepest median water depth of 2.8 m). They employed the inverse method to assess the bedload sediment size distribution based on the measurements. The hydrophone was also applied to measure bedload sediment transport at 25 locations in 14 rivers in France. From their measurements, they established the relationship between the specific bedload transport flux and the cross-section average acoustic power. Based on the measured data and analyzed results from 14 rivers, [PERSON] et al. [45] combined field observations from 8 rivers with the measured data to fit a power-law relationship between the bedload movement and the mean cross-section sound power. When their results were compared with the results presented by [PERSON] et al. [44], the difference between the two was not significant (at the 95% confidence level). [PERSON] also suggested that the calibration curves of bedload transport and the mean cross-section sound power would fit better if all the field measurements from the two databases were combined. [PERSON] et al. [46] developed a model that considered the bedload movement parameters, the flow conditions, and the acoustic propagation environment. The model was tested using a field data set, and the results showed that the model was sensitive to bed sediment size distribution and to bedload movement. The inverse model based on this model produced good correlation results for estimating the sound power of the audio signals of bedload movement only in the Giffre River [47].