# Prediction of River Sediment Transport Based on Wavelet Transform and Neural Network Model
## 3 Results and Discussion  
The real contour of wavelet transform coefficient is shown in Figure 2a,c in which various color areas mean the positive and negative values of wavelet transform coefficients, respectively, representing the abundant and depleted periods, which can analyze the rainfall and runoff characteristics of hydrological stations at the time scale [21]. The module square of wavelet transform coefficient shown in Figure 2b,d reflects the energy density corresponding to the period of time-scale variations, where a larger value of the coefficient modulo square indicates a stronger periodicity of the corresponding time period [25; 26]. Wavelet variance plots of wavelet energy with intensity in the frequency domain are shown in Figures 3 and 4, where the red points indicate the extremes and the time periods of the main time scales can be identified. It is clear from Figure 2 that there is an obvious interannual variation in the rainfall and runoff series, and both of them are nearly the same, indicating that runoff is mainly controlled by rainfall in the region. Additionally, it can be found that there are four main cycle variations about rainfall and runoff, which are 3-6 years, 8-12 years, 15-20 years and 25-30 years, respectively. The annual rainfall and runoff period, mainly on the 3-6 years, was more significant from 1972 to 1980, accompanied by relatively ambiguous abundance and depletion variations. The variation of annual runoff series with 8-12 years is mainly shown in 1965-1975 and 1998-2008, showing regional oscillations of alternating abundance  
Figure 1: Neural network structure. Figure 2: (a) Real part of rainfall wavelet transform coefficients; (b) Square of rainfall wavelet transform coefficient mode; (c) Real part of runoff wavelet transform coefficients; (d) Square of rainfall wavelet transform coefficient mode. and depletion. In main cycle variation of 15-20 years, annual rainfall mainly occurred in 1965-1975 and annual runoff mostly in 1965-1980. In main cycle variation of 15-20 years, annual rainfall mainly occurred in 1965-1975 and annual runoff mostly in 1965-1980. The variation of hydrological time series with a period of 25-30 years is relatively stable in the whole-time domain and combined with the results of wavelet mode squared contours and variograms, the first main cycle of rainfall and runoff has a consistent performance of 28 years. In this paper, Figures 5 and 6 show the discrete wavelet transform is applied to the monthly average runoff and rainfall information of 28-year main cycle, and the high frequency and low frequency parts of the information are extracted respectively, then the runoff and rainfall wavelet coefficients are used as the input layer to make predictions. In essence, the main cycle runoff and rainfall information is used as a training set for the prediction of wavelet coefficients in addition to the prediction of the original data. The advantage is that the magnitude and structure of the weights of the high frequency and low frequency components of the prediction model reflect the relationship between the constituent components of the hydrological time series. Meanwhile, the periodic runoff and rainfall data are used as the training set to improve the accuracy of predicting sediment load. The sequence after discrete wavelet decomposition for data of rainfall and runoff is shown from Figures 7-10, in which the detail signals (D1, D2... D4, D5 and D6) are high-frequency components and approximate signal (A) can be included in the trend term. As seen in Figures 9 and 10, the fluctuations of D3, D4, D5 and D6 are slight, while the D1  
Figure 4: Runoff wavelet variogram. Figure 5: Original sequence of rainfall. Figure 3: Rainfall wavelet variogram. The data from 1982-2010 were collected to build a three-layer neural network, in which 2 units of monthly average rainfall and runoff were taken as the input layer and monthly average sediment load is used as the output layer.