Prediction of discharge in a tidal river using the LSTM-based sequence-to-sequence models
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Abstract: The complexity of river-tide interaction poses a significant challenge in predicting discharge in tidal rivers. Long short-term memory (LSTM) networks excel in processing and predicting crucial events with extended intervals and time delays in time series data. Additionally, the sequence-to-sequence (Seq2Seq) model, known for handling temporal relationships, adapting to variable-length sequences, effectively capturing historical information, and accommodating various influencing factors, emerges as a robust and flexible tool in discharge forecasting. In this study, we introduce the application of LSTM-based Seq2Seq models for the first time in forecasting the discharge of a tidal reach of the Changjiang River (Yangtze River) Estuary. This study focuses on discharge forecasting using three key input characteristics: flow velocity, water level, and discharge, which means the structure of multiple input and single output is adopted. The experiment used the discharge data of the whole year of 2020, of which the first 80% is used as the training set, and the last 20% is used as the test set. This means that the data covers different tidal cycles, which helps to test the forecasting effect of different models in different tidal cycles and different runoff. The experimental results indicate that the proposed models demonstrate advantages in long-term, mid-term, and short-term discharge forecasting. The Seq2Seq models improved by 6%–60% and 5%–20% of the relative standard deviation compared to the harmonic analysis models and improved back propagation neural network models in discharge prediction, respectively. In addition, the relative accuracy of the Seq2Seq model is 1% to 3% higher than that of the LSTM model. Analytical assessment of the prediction errors shows that the Seq2Seq models are insensitive to the forecast lead time and they can capture characteristic values such as maximum flood tide flow and maximum ebb tide flow in the tidal cycle well. This indicates the significance of the Seq2Seq models.
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Figure 3. Schematic diagram for the Longshort-term memory (LSTM) recurrent cell, adapted and reproduced from (Olah, 2015; Lees et al., 2022). These cells are repeated from the first timestep to the last one of the sequence. From one timestep to the next, ct captures the state of the system at time t. A series of gates, such as the forget gate (ft), the input gate (it), and the output gate (ot), protect and control the information flow from the input data xt to the cell state ct.
$c't $ is the candidate cell-state value, which transformed through the tanh layer that are passed into ct base on the output of ot. The layers of neural networks: weights (w), biases (b), and activation functions (σ, tanh) correspond to the yellow layers are also shown in the diagram. The subscripts of σ indicate the three different gates in LSTM, which are a way to optionally let information through.
Figure 4. Schematic diagram for Seq2Seq model employed in this study. LSTM, Longshort-term memory
Figure 5. Area of study. Red circles indicate (C1, C2, and C3) the deploy locations of the Acoustic Doppler Current Profilers, and the dashed blue line represents the Xuliujing Section.
Figure 6. Time series of the discharges at Datong Station (a) and shapes of the Xuliujing Section on two dates in 2019 and 2020 (b). The discharge in Xuliujing Station is difficult to observe or estimate due to the large section and tide influence, so the discharge in Datong Station (shown in Fig. 5) is commonly regarded as the net discharge into the East China Sea. A boat-mounted single-beam echo sounder transducer (sonar) was used for bathymetric surveying at Xuliujing Section (Fig. 5) once a month.
Figure 7. The short-term discharge prediction by means of the four different models. Here discharge values of 12 h are used as input data and another 3 h ones are used as output data. The blue dotted line is the predicted discharge by harmonic analysis, the green dotted line is the predicted discharge by harmonic analysis PSO-BP neural network, the black dotted line is the predicted discharge by LSTM, the red dotted line is the predicted discharge by Seq2Seq, and the black line is the measured data.
Figure 8. Estimation error of four different models in short-term discharge prediction.
Figure 9. The middle-term discharge prediction. Here discharge values of 24 h are used as input data and another 6 h ones are used as output data.
Figure 10. Estimation error of four different models in middle-term discharge prediction.
Figure 11. The long-term discharge prediction. Here discharge values of 72 h are used as input data and another 24 h ones are used as output data.
Figure 12. Estimation error of four different models in long-term discharge prediction.
Figure 13. The correlation coefficient between the estimated tidal discharge and the measured values using the three different models. The data in a, b, and c are corresponding to the data in Figs 7, 9 and 11, respectively.
Table 1. The starting and ending time of the datasets
Forecast duration (lead time) Starting and ending time (YYYY/MM/DD) Neap tide Spring tide Middle tide Short term (3 h) 2020/10/01–2020/11/10 2020/10/01–2020/11/18 2020/10/01–2020/11/29 Middle term (6 h) 2020/08/01–2020/11/10 2020/08/01–2020/11/18 2020/08/01–2020/11/29 Long term (24 h) 2020/01/01–2020/11/10 2020/01/01–2020/11/18 2020/01/01–2020/11/29 Note: All datasets are sampled at half-hour intervals. 
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Table 2. Tidal constituents at Xuliujing with amplitudes greater than 8000 m3/s
Tide
constituentFrequency/
(cycle·h–1)Amplitude
(m3·s–1)Phase/(°) Signal-to-noise
ratioM2 0.080511 63408 216.67 220 S2 0.083333 28935 267.85 46 M4 0.161023 15747 233.32 36 MS4 0.163845 12991 298.97 25 K1 0.041781 8642 24.510 330
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Table 3. Parameter setting of PSO algorithm
Parameters Setting Swarm size 30 Inertia weight 0.5 Personal learning factor 4.494 Social learning factor 4.494 Maximum velocity 1.0 Number of iterations 200 Fitness function root mean square error
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Table 4. Parameter Setting of LSTM model
Parameters Setting Short term Middle term Long term Hidden size / 128 / Num layers / 1 / Input dimension / 3 / Input length 24 48 144 Output dimension / 1 / Output length 6 12 48 Learning rate / 0.01 / Target error / 0.001 / Batch size / 256 / Epochs / 200 / Regularization / 0.001 / Activation / ReLU / Optimizer / Adam / Note: For different forecast durations, only the length of the input and output length is different. / indicats xxx.
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