Application of deep learning technique to the sea surface height prediction in the South China Sea
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Abstract: A deep-learning-based method, called ConvLSTMP3, is developed to predict the sea surface heights (SSHs). ConvLSTMP3 is data-driven by treating the SSH prediction problem as the one of extracting the spatial-temporal features of SSHs, in which the spatial features are “learned” by convolutional operations while the temporal features are tracked by long short term memory (LSTM). Trained by a reanalysis dataset of the South China Sea (SCS), ConvLSTMP3 is applied to the SSH prediction in a region of the SCS east off Vietnam coast featured with eddied and offshore currents in summer. Experimental results show that ConvLSTMP3 achieves a good prediction skill with a mean RMSE of 0.057 m and accuracy of 93.4% averaged over a 15-d prediction period. In particular, ConvLSTMP3 shows a better performance in predicting the temporal evolution of mesoscale eddies in the region than a full-dynamics ocean model. Given the much less computation in the prediction required by ConvLSTMP3, our study suggests that the deep learning technique is very useful and effective in the SSH prediction, and could be an alternative way in the operational prediction for ocean environments in the future.
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Figure 1. A schematic flow chart of ConvLSTM. “Conv” represents the convolution operation. Spatial information is coded as input in LSTM for tracking temporal evolution. The size of convolutional kenel can be 3×3, 5×5 and 7×7. Multiple kennels are denoted by allows.
Figure 2. The topologic structure of ConvLSTMP3 (a) and the adjacent grids (blue) of a target grid (gray) corresponding to the convolution kennelsof size 3×3, 5×5, and 7×7 (b). Vi (i=1, 2, …, n) represents datasets that are used to make the i-th-d SSH prediction for a target grid.
Figure 3. The topologic structures of four models: LSTMS1 (a), ConvLSTMP1 (b), ConvLSTMP2 (c) and ConvLSTMS4 (d). Vi (i=1, 2, …, n) represents datasets that are used to make the i-th-d SSH prediction for a target grid. 1D here means only a time series of SSH data on the target grid, while 2D means multiple time series of SSH data on the target grid as well as its adjacent grids.
Figure 4. A schematic diagram illustrating a 15-d prediction cycle. The squares and circles represent the historical SSHs and predicted SSHs, respectively. The squares or circles behind the arrows represent the input of ConvLSTMP3 and the circles ahead the arrows represent the output (prediction). D0 denotes the current day of the prediction cycle, and N is the length of prediction cycle which is set to 15 (days).
Figure 5. The 5.5°×5.5° region (denoted by A) of the SCS for the deep learning experiments for SSH prediction.
Figure 6. The RMSE and ACC of the 15-d consecutive prediction averaged over the testing period from 6 January 2010 to 31 December 2011 from different schemes.
Figure 7. The ground truth (a–h) and the predicted SSHs by ConvLSTMP3 (i–p) and ROMS (q–x) obtained from August 1 to 15, 2011 in every other day. The black arrows represent the SSH-derived geostrophic currents.
Table 1. The RMSE and ACC of the SSH predictions by ConvLSTMP3 and ROMS during the period of 1–15 August 2011
Period Item RMSE/m ACC/% ConvLSTMP3 ROMS ConvLSTMP3 ROMS Day 1 0.028 0.048 96.4 93.4 Day 2 0.017 0.073 98.0 88.6 Day 3 0.027 0.069 96.2 89.5 Day 4 0.033 0.064 96.3 90.2 Day 5 0.039 0.069 95.0 89.5 Day 6 0.051 0.055 93.0 92.3 Day 7 0.049 0.064 93.9 91.1 Day 8 0.049 0.067 93.8 90.4 Day 9 0.067 0.069 91.6 90.4 Day 10 0.055 0.079 93.5 88.4 Day 11 0.066 0.082 92.2 87.7 Day 12 0.083 0.073 89.4 89.8 Day 13 0.076 0.078 90.3 89.0 Day 14 0.085 0.076 89.5 89.6 Day 15 0.077 0.099 91.3 86.0 15-d mean 0.057 0.072 93.4 89.7 
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Table 2. The configurations of the hardware and software as well as the corresponding CPU time used for the 15-d prediction by ConvLSTMP3 and ROMS
Hardware configuration Software configuration CPU time/s ConvLSTMP3 Intel (R) Core (TM) I7-8750H (2.2 GHz) processor, 32 GB memory (total number used: 1) Python 3.6.0 3.695 ROMS Intel (R) Xeon (R) Gold 6132 (2.60 GHz) processor, 125 GB memory (total number used: 112) Mvapich2 2.2b 5.451
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Table 3. The ACC of the SSH predictions by LSTM, GRU, CNN and ConvLSTMP3 during the period of 1–15 August 2011
Periods Item ACC/%
(LSTM)ACC/%
(GRU)ACC/%
(3D CNN)ACC/%
(ConvLSTM)Day 1 84.53 84.77 94.8 96.4 Day 2 76.33 77.33 95.0 98.0 Day 3 72.10 72.20 94.2 96.2 Day 4 66.63 66.67 95.3 96.3 Day 5 64.71 64.71 94.0 95.0 Day 6 63.17 63.23 93.0 93.0 Day 7 62.27 63.01 93.0 93.9 Day 8 61.71 62.00 92.8 93.8 Day 9 61.03 61.07 90.6 91.6 Day 10 61.45 61.55 91.5 93.5 Day 11 61.24 61.43 92.0 92.2 Day 12 61.24 61.24 89.0 89.4 Day 13 61.22 61.21 89.0 90.3 Day 14 61.03 61.05 89.1 89.5 Day 15 60.92 61.00 88.6 91.3 15-d mean 65.30 65.50 92.1 93.4
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