Time-frequency analysis and simulation of the watershed suspended sediment concentration based on the Hilbert-Huang transform (HHT) and artificial neural network (ANN) methods: A case study in the Loess Plateau of China

Abstract

Suspended sediment concentration (SSC) time series are highly nonlinear and nonstationary due to numerous influencing factors that can be characterized by specific time scales, thereby increasing the difficulty of performing SSC simulations. Analyzing the spectral and temporal information of the SSC and its contributing factors can improve the resulting simulation efforts. In this study, the Hilbert-Huang transform (HHT) was used to identify the time scales and change trends of the daily SSC, rainfall, runoff and normalized difference vegetation index (NDVI) of the Kuye River in the Loess Plateau of China. Artificial neural network (ANN), multiple linear regression (MLR), hybrid ensemble empirical mode decomposition (EEMD)-ANN and EEMD-MLR models were chosen to simulate the SSC time series. The periods of the rainfall intrinsic mode functions (IMFs, except IMF9 and 10) were generally consistent with those of the IMFs corresponding to the SSC and runoff. In comparison, the periods of the IMFs corresponding to the NDVI were longer. The minimal period was 3 days for the SSC, rainfall and runoff and 10 days for the NDVI. The minimal period displays the greatest variance contribution and plays the most important role in the SSC, rainfall and runoff changes. The annual cycle has the largest contribution to the NDVI variability. Residual components indicated that the SSC of the Kuye River decreased from 2006 to 2010, while the regional rainfall, runoff and NDVI increased. The R2 values of the ANN and MLR models were 0.34 and 0.39, respectively. Compared with the MLR and ANN models, the R2 values of the EEMD-ANN and EEMD-MLR models increased by 52.9% and 41.0%, respectively, indicating that the ANN model was more robust than the MLR model when simulating nonlinear SSC time series. Compared with EMD, EEMD can alleviate the mode mixing problem and significantly increase the simulation accuracy with the ANN and MLR models. Significance tests were employed to determine the strength of the physical meaning in each IMF component. Taking IMFs with significant (p < 0.05) period oscillations as input data, the EEMD-ANN model had a high R2 of 0.64. Using IMFs having significant (p < 0.05) correlations with the SSC as input variables, the EEMD-ANN model achieved the largest R2 of 0.66. The results of this study supply effective means for simulating and predicting soil erosion. However, it still remains a remarkable challenge to accurately simulate the SSC. Additional factors, such as topographic characteristics and land use, should be considered in future research.