Study on Forecasting Break-Up Date of River Ice in Heilongjiang Province Based on LSTM and CEEMDAN
2. Materials and Methods
2.1. Study Area and Data
2.3. LSTM Network
2.4. Fundamental Frameworks of CEEMDAN-LSTM
- Obtain the break-up date series and decompose it into subsequences (multiple IMFs and a residual series) by CEEMDAN.
- Divide the IMFs and residual series into training data and forecast data, and normalize them.
- Calculate the maximum autocorrelation order of each IMF and residual series (shown in Table 3), and build the LSTM to forecast the value of IMFs and residual series.
- Denormalize and evaluate the forecast result.
2.5. Performance Evaluation
3.1. Results of Decomposing the Observed Break-Up Date Series Using CEEMDAN
3.2. Result of LSTM Applied to Forecast the Break-Up Date
3.3. Result of CEEMDAN-LSTM Applied to Forecast the Break-Up Date
4.1. Reasons for the Improvement of the Forecasting Accuracy of Break-Up Date by CEEMDAN-LSTM
4.2. Reasons for the Lower Forecasting Accuracy of BQ and QQHR by LSTM
4.3. The Performance of LSTM in Forecasting the Black Swan Events
- CEEMDAN decomposed the observed break-up date series into subsequences according to different fluctuations and frequencies. The observed break-up date series with a larger standard deviation, compared with a similar break-up date series in length, had relatively more decomposed subsequences. With the decomposition processing, the frequency and fluctuation degree of subsequence decreased, and the sample values of subsequence increased. The residual series had the lowest fluctuation degree and frequency, which was close to linear and varied slightly around the long-term average.
- The subsequence decomposed by CEEMDAN with a lower fluctuation degree or smaller sample values compared with the observed series for LSTM obtained a higher forecasting accuracy. The IMF1 and IMF2 had smaller values, the MAE values for forecasting results of IMF1 and IMF2 were small with the order of magnitude of 10−1. The IMF5, IMF6, and residual series had lower fluctuation degrees, and the MAE values of forecasting results of IMF5, IMF6, and residual series were small with the order of magnitude of 10−2 and 10−3.
- Among the performance evaluation of the LSTM for all seven stations, the absolute error ranged from −13 to 12, the MAE values ranged from 0.80 to 6.40, the QR values were above 60%, the RMSD values ranged from 1.37 to 5.97, the R values ranged from 0.51 to 0.97, and the S values ranged from 0.87 to 0.99.
- The forecasting accuracy was obviously improved by LSTM coupled with CEEMDAN. CEEMDAN-LSTM performed better than LSTM. In the performance evaluation of the CEEMDAN-LSTM for all seven stations, the absolute error ranged from −6 to 4, the MAE values ranged from 0.75 to 3.40, the QR values improved to 100%, the RMSD values ranged from 0.95 to 1.69, the R values ranged from 0.97 to 0.98, and the S values improved to 0.99.
- CEEMDAN can reduce the influence of the few samples on the forecasting accuracy of LSTM. The forecasting accuracy by LSTM was obviously improved after decomposing the observed break-up date series of QQHR with a short length by CEEMDAN. The MAE value of forecasting results for QQHR decreased from 6.33 to 1.83, the QR value was improved from 80% to 100%, and the S value was improved from 0.87 to 0.99.
Data Availability Statement
Conflicts of Interest
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|Series length (year)||69||59||69||62||60||36||47|
|Mean||Day 98||Day 97||Day 107||Day 119||Day 101||Day 98||Day 107|
|Standard deviation (day)||5.14||6.84||5.21||5.07||5.44||6.82||5.20|
|LSTM||Maximum autocorrelation order||14||3||1||16||3||6||2|
|Period||Performance Evaluation Index||HRB||BQ||FJ||MH||MDJ||QQHR||YC|
|Training||Range of AE||[−8, 9]||[−9, 9]||[−6, 5]||[−13, 9]||[−5, 4]||[−11, 12]||[−8, 9]|
|Forecast||Range of AE||[−6, 0]||[−10, 8]||[0, 4]||[−2, 4]||[1, 2]||[−13, −1]||[0, 3]|
|Period||Performance Evaluation Index||HRB||BQ||FJ||MH||MDJ||QQHR||YC|
|Training||Range of AE||[−3, 3]||[−4, 4]||[−3, 4]||[−2, 3]||[−4, 3]||[−3, 3]||[−3, 4]|
|Forecast||Range of AE||[−1, 1]||[−6, −1]||[−2, 1]||[−2, 2]||[−1, 1]||[−4, 2]||[−2, 2]|
|R||0.98||0.97 *||0.98||0.98||0.98||0.97 **||0.97 ***|
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Liu, M.; Wang, Y.; Xing, Z.; Wang, X.; Fu, Q. Study on Forecasting Break-Up Date of River Ice in Heilongjiang Province Based on LSTM and CEEMDAN. Water 2023, 15, 496. https://doi.org/10.3390/w15030496
Liu M, Wang Y, Xing Z, Wang X, Fu Q. Study on Forecasting Break-Up Date of River Ice in Heilongjiang Province Based on LSTM and CEEMDAN. Water. 2023; 15(3):496. https://doi.org/10.3390/w15030496Chicago/Turabian Style
Liu, Mingyang, Yinan Wang, Zhenxiang Xing, Xinlei Wang, and Qiang Fu. 2023. "Study on Forecasting Break-Up Date of River Ice in Heilongjiang Province Based on LSTM and CEEMDAN" Water 15, no. 3: 496. https://doi.org/10.3390/w15030496