Prediction of discharge in a tidal river using the LSTM-based sequence-to-sequence models

Zhigao Chen Yan Zong Zihao Wu Zhiyu Kuang Shengping Wang

Zhigao Chen, Yan Zong, Zihao Wu, Zhiyu Kuang, Shengping Wang. Prediction of discharge in a tidal river using the LSTM-based sequence-to-sequence models[J]. Acta Oceanologica Sinica. doi: 10.1007/s13131-024-2343-6
Citation: Zhigao Chen, Yan Zong, Zihao Wu, Zhiyu Kuang, Shengping Wang. Prediction of discharge in a tidal river using the LSTM-based sequence-to-sequence models[J]. Acta Oceanologica Sinica. doi: 10.1007/s13131-024-2343-6

doi: 10.1007/s13131-024-2343-6

Prediction of discharge in a tidal river using the LSTM-based sequence-to-sequence models

Funds: The National Natural Science Foundation of China under contract Nos 42266006 and 41806114; the Jiangxi Provincial Natural Science Foundation under contract Nos 20232BAB204089 and 20202ACBL214019.
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  • Figure  1.  The essential structure of BP neural network.

    Figure  2.  Flow chart of PSO-BP algorithm.

    Figure  3.  Schematic diagram for the 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.

    Figure  5.  Area of study. Red circles indicate the deploy location of the Acoustic Doppler Current Profilers (ADCP), 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 (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.

    Figure  14.  The half-hourly discharge estimation by the Seq2Seq models.

    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.

    (cycle · h–1)
    (m3 · s–1)
    Phase/(°) Signal-to-noise
    ratio (SNR)
    M2 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.

    Swarm size30
    Inertia weight0.5
    Personal learning factor4.494
    Social learning factor4.494
    Maximum velocity1.0
    Number of iterations200
    Fitness functionroot mean square error (RMSE)
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    Table  4.   Parameter Setting of LSTM model. For different forecast durations, only the length of the input and output length is different.

    Short termMiddle termLong term
    Hidden size128
    Num layers1
    Input dimension3
    Input length2448144
    Output dimension1
    Output length61248
    Learning rate0.01
    Target error0.001
    Batch size256
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  • 收稿日期:  2024-02-02
  • 录用日期:  2024-04-27
  • 网络出版日期:  2024-05-08