Identification of varying time scales in sediment transport using the Hilbert–Huang Transform method

Abstract

Summary Sediment transport processes vary at a variety of time scales – from seconds, hours, days to months and years. Multiple time scales exist in the system of flow, sediment transport and bed elevation change processes. As such, identification and selection of appropriate time scales for flow and sediment processes can assist in formulating a system of flow and sediment governing equations representative of the dynamic interaction of flow and particles at the desired details. Recognizing the importance of different varying time scales in the fluvial processes of sediment transport, we introduce the Hilbert–Huang Transform method (HHT) to the field of sediment transport for the time scale analysis. The HHT uses the Empirical Mode Decomposition (EMD) method to decompose a time series into a collection of the Intrinsic Mode Functions (IMFs), and uses the Hilbert Spectral Analysis (HSA) to obtain instantaneous frequency data. The EMD extracts the variability of data with different time scales, and improves the analysis of data series. The HSA can display the succession of time varying time scales, which cannot be captured by the often-used Fast Fourier Transform (FFT) method. This study is one of the earlier attempts to introduce the state-of-the-art technique for the multiple time sales analysis of sediment transport processes. Three practical applications of the HHT method for data analysis of both suspended sediment and bedload transport time series are presented. The analysis results show the strong impact of flood waves on the variations of flow and sediment time scales at a large sampling time scale, as well as the impact of flow turbulence on those time scales at a smaller sampling time scale. Our analysis reveals that the existence of multiple time scales in sediment transport processes may be attributed to the fractal nature in sediment transport. It can be demonstrated by the HHT analysis that the bedload motion time scale is better represented by the ratio of the water depth to the settling velocity, h/w. In the final part, HHT results are compared with an available time scale formula in literature.