Forecasting of surface current velocities using ensemble machine learning algorithms for the Guangdong−Hong Kong−Macao Greater Bay area based on the high frequency radar data
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Abstract: Forecasting of ocean currents is critical for both marine meteorological research and ocean engineering and construction. Timely and accurate forecasting of coastal current velocities offers a scientific foundation and decision support for multiple practices such as search and rescue, disaster avoidance and remediation, and offshore construction. This research established a framework to generate short-term surface current forecasts based on ensemble machine learning trained on high frequency radar observation. Results indicate that an ensemble algorithm that used random forests to filter forecasting features by weighting them, and then used the AdaBoost method to forecast can significantly reduce the model training time, while ensuring the model forecasting effectiveness, with great economic benefits. Model accuracy is a function of surface current variability and the forecasting horizon. In order to improve the forecasting capability and accuracy of the model, the model structure of the ensemble algorithm was optimized, and the random forest algorithm was used to dynamically select model features. The results show that the error variation of the optimized surface current forecasting model has a more regular error variation, and the importance of the features varies with the forecasting time-step. At ten-step ahead forecasting horizon the model reported root mean square error, mean absolute error, and correlation coefficient by 2.84 cm/s, 2.02 cm/s, and 0.96, respectively. The model error is affected by factors such as topography, boundaries, and geometric accuracy of the observation system. This paper demonstrates the potential of ensemble-based machine learning algorithm to improve forecasting of ocean currents.
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Key words:
- forecasting /
- surface currents /
- ensemble machine learning /
- high frequency radar /
- random forest /
- AdaBoost
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Figure 1. Deployment location of HFR stations and observational area. SC: Shangchuan radar station, WS: Wanshan radar station.
Figure 3. Locations of the lepresentative points P1–P5 and sub-areas Z1–Z8, and the observation points with data acquisition rate greater than 90%.
Figure 4. Relative importance of main features in the transition model for single time-step forecasting for surface current zonal component at point P1 (partial).
Figure 5. Surface current synthetic vectors during June 27, 2021 at P1. a. HFR data and b. application model.
Figure 6. Flow chart for single time-step forecasting model of surface current fields.
Figure 7. Surface current fields at 02:10 June 24, 2021. a. Model results and b. HFR data. Time in UCT+8.
Figure 9. RMSE values of surface velocity components for multi time-step forecasting at points P1–P5. a. Zonal component and b. meridional component.
Figure 10. Comparison of surface current vector fields. Model: the reconstruction model; HFR: observation. All times are in UTC+8.
Figure 11. Absolute errors of surface velocity components between forecasting and HFR data under different forecasting windows. Left subfigures are the zonal component; right subfigures are the meridional component.
Table 1. Statistics of tidal ellipticity, tidal type coefficients and shallow water coefficients
Point Tidal ellipticity Tidal type
coefficientShallow water
coefficientO1 K1 M2 S2 P1 –0.4 –0.06 –0.22 0.12 1.51 0.32 P2 –0.10 –0.11 –0.02 0.21 1.11 0.20 P3 –0.07 –0.2 –0.02 0.29 1.09 0.20 P4 0.22 –0.34 –0.05 –0.12 1.27 0.19 P5 –0.37 –0.27 –0.31 0.44 1.68 0.24 
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Table 2. Statistics of the optimal correlation coefficients of surface current components
Point Correlation coefficient Lag time/h Zonal component Meridional component Zonal component Meridional component P1 0.75 0.31 12 11 P2 0.78 0.31 12 8 P3 0.79 0.22 11 9 P4 0.68 0.24 9 9 P5 0.55 –0.09 11 9
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Table 3. Forecasting model set-up
Model Algorithm Feature Feature selection Forecasting model Baseline model \ AdaBoost total observation data Application model random forest AdaBoost observation data whose total variable importance accumulates over 95% Rolling model random forest AdaBoost observation data whose importance accumulates over 95% at the first time-step Reconstruction model random forest AdaBoost observation data whose importance accumulates over 95% at each time-step Note: \ denotes no feature selection.
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Table 4. Assessment statistics of single time-step forecasting (training dataset)
Point Zonal component of surface velocity assessment statistic Meridional component of surface velocity assessment statistic Feature number RMSE/(cm·s–1) R MAE/(cm·s–1) Feature number RMSE/(cm·s–1) R MAE/(cm·s–1) P1 176 0.96 1.00 0.55 176 0.87 1.00 0.40 8 1.04 1.00 0.58 8 0.94 1.00 0.58 P2 176 1.46 1.00 0.82 176 1.31 0.99 0.73 9 1.56 1.00 0.85 8 1.42 0.99 0.76 P3 176 0.96 1.00 0.52 176 1.06 1.00 0.45 8 1.04 1.00 0.55 8 1.14 0.99 0.46 P4 176 2.41 0.99 1.29 176 2.52 0.98 1.35 9 2.60 0.99 1.36 36 2.68 0.98 1.36 P5 176 3.55 0.98 2.11 176 1.69 0.99 0.81 13 4.06 0.98 2.16 13 1.80 0.99 0.85
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Table 5. Assessment statistics of single time-step forecasting (test dataset)
Point Zonal component of surface velocity assessment statistic Meridional component of surface velocity assessment statistic Feature number RMSE/(cm·s–1) R MAE/(cm·s–1) Feature number RMSE/(cm·s–1) R MAE/(cm·s–1) P1 8 0.95 1.00 0.62 8 1.66 0.99 0.67 P2 9 2.41 0.99 1.00 8 2.05 0.98 0.85 P3 8 1.55 1.00 0.71 8 3.68 0.97 1.04 P4 9 5.02 0.98 1.62 36 9.36 0.94 3.29 P5 13 2.97 0.98 1.75 10 1.90 0.99 0.84
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Table 6. Evaluation of multi time-step forecasting (zonal component of surface velocity)
Point Forecasting
stepFeature
numberRMSE/
(cm·s–1)r MAE/
(cm·s–1)P1 2 8 1.82 1.00 1.09 3 8 2.59 1.00 1.61 4 9 3.33 0.99 2.16 5 10 3.93 0.99 2.60 6 12 4.47 0.99 3.02 7 16 4.56 0.99 3.12 8 23 4.60 0.99 3.13 9 32 4.72 0.99 3.27 10 37 4.97 0.99 3.45 P2 2 8 2.51 1.00 1.49 3 9 3.57 0.99 2.16 4 10 4.19 0.99 2.62 5 11 4.69 0.98 3.02 6 16 4.91 0.98 3.17 7 25 4.92 0.98 3.26 8 33 4.81 0.98 3.27 9 39 4.97 0.98 3.40 10 43 5.01 0.98 3.5 P3 2 8 1.70 1.00 0.99 3 8 2.27 1.00 1.40 4 9 2.83 0.99 1.80 5 10 3.29 0.99 2.19 6 13 3.61 0.99 2.45 7 18 3.52 0.99 2.39 8 26 3.67 0.99 2.50 9 34 3.74 0.99 2.62 10 43 3.93 0.99 2.81 P4 2 12 3.84 0.99 2.18 3 22 4.74 0.98 2.78 4 35 5.30 0.97 3.21 5 48 5.60 0.97 3.48 6 58 5.71 0.97 3.65 7 66 5.41 0.97 3.54 8 74 5.58 0.97 3.68 9 80 5.67 0.97 3.79 10 85 5.84 0.97 3.92 P5 2 58 4.48 0.97 2.72 3 85 5.51 0.95 3.46 4 100 5.80 0.95 3.75 5 108 6.08 0.94 4.02 6 114 6.00 0.94 4.04 7 118 6.29 0.94 4.24 8 120 6.39 0.94 4.36 9 122 6.43 0.94 4.40 10 123 6.68 0.93 4.61
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Table 7. Evaluation of multi time-step forecasting (meridional component of surface velocity)
Point Forecasting
stepFeature
numberRMSE/
(cm·s–1)r MAE/
(cm·s–1)P1 2 9 1.58 0.99 0.78 3 25 2.03 0.98 1.08 4 40 2.35 0.97 1.35 5 56 2.53 0.97 1.54 6 74 2.59 0.97 1.67 7 89 2.46 0.97 1.68 8 102 2.67 0.97 1.85 9 111 2.63 0.97 1.87 10 117 2.84 0.96 2.02 P2 2 18 2.12 0.98 1.24 3 46 2.63 0.97 1.66 4 72 2.96 0.96 1.99 5 90 3.44 0.95 2.30 6 102 3.56 0.95 2.54 7 112 3.82 0.94 2.63 8 176 4.12 0.93 2.88 9 126 4.15 0.93 2.90 10 131 4.33 0.92 3.02 P3 2 10 1.78 0.99 0.82 3 19 2.12 0.98 1.08 4 36 2.28 0.98 1.24 5 53 2.44 0.97 1.40 6 65 2.55 0.97 1.54 7 76 2.57 0.97 1.62 8 86 2.64 0.97 1.72 9 93 2.71 0.97 1.79 10 100 2.89 0.96 1.95 P4 2 84 4.99 0.92 3.08 3 109 4.53 0.93 2.82 4 121 4.71 0.93 2.96 5 129 5.17 0.91 3.27 6 134 5.48 0.90 3.55 7 137 5.49 0.90 3.62 8 141 5.71 0.89 3.75 9 143 5.79 0.89 3.85 10 145 6.29 0.87 4.15 P5 2 40 2.46 0.97 1.29 3 67 3.01 0.96 1.67 4 83 3.31 0.95 1.94 5 95 3.97 0.93 2.36 6 104 3.42 0.95 2.18 7 111 3.43 0.95 2.28 8 116 3.50 0.95 2.34 9 121 3.82 0.94 2.60 10 125 4.42 0.91 3.01
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