Fig 1.
Schematic diagram of the fusion model this model integrates WaveNet network, LSTM network and GCN network.
The data are first processed using convolution in the temporal dimension, followed by a spatial convolutional network in the spatial dimension, and finally reinforced by an LSTM network to correlate the front-to-back dependencies of the data.
Fig 2.
The geographical position and site distribution of section A.
Table 1.
Data statistics of each water pollution factor in section A.
Table 2.
Data statistics of each water pollution factor in section B.
Fig 3.
Framework of the adaptive graph convolution.
It contains 3 components Aα, Bα, and Cα. Aα is used to represent the geographical information of the nodes, Bα is a random initialization matrix to enhance the flexibility of the model, and Cα is used to represent the learnable node embeddings.
Fig 4.
Framework of the WaveNet block.
It employs dilated causal convolution as a foundation and includes a gated mechanism and a residual connection.
Fig 5.
Framework of the CNN-LSTM hybrid model.
It contains multiple convolution layers, which are finally output through an LSTM and a full connection layer.
Fig 6.
Schematic representation of spatio-temporal network fusion strategy.
The GCN network immediately follows the CNN to form a spatio-temporal processing module, which is stacked to handle spatial dependencies of different spans, and finally, the LSTM network outputs the results.
Fig 7.
Framework of a single spatio-temporal network (ST-Block).
Creating a spatio-temporal block by combining the WaveNet Network and Adaptive Graph Convolution Network previously described. Added residual network to AGCN.
Fig 8.
It combines the skip result of each spatio-temporal block with the stacked output, and finally compute the result through the LSTM network. All space-time blocks are connected to each other by skip connections.
Fig 9.
Correlation heatmap of muti-site water quality data.
(A) Correlation heatmap among sites. The correlation between sites varies, some sites can be correlated up to 0.75. while some sites correlation is 0. (B) Correlation heatmap with site 4 time point 7 at different times and different site. The correlation between the same site and site 4 time point 7 reaches its maximum at a certain point, which is related to the distance between the site and site 4.
Fig 10.
Average number of correlated sites for each factor in Sections A and B.
This graph demonstrates the different site correlations that exist for the different factor data. Some of these data with low correlations may affect the results.
Table 3.
The overall performance of each model in section A.
Table 4.
The overall performance of each model in section B.
Fig 11.
Training error and validation error curves of W-WaveNet model under all factors of section A.
Table 5.
MAE, RMSE and r2 for each model at pH and NH3 in section A.
Table 6.
MAE, RMSE and r2 for each model at TP and TN in section A.
Fig 12.
Histogram of MAPE and RMSPE for each model under all factors of section A.
With all factor data, the figure demonstrates that W-WaveNet produces the best results or outcomes that are close to the best results.
Fig 13.
Scatter plot of TN of each model in section A.
This plot shows that the predicted scatter plot of W-WaveNet is closer to the straight line compared to the other models.
Fig 14.
Time-series plots of NH3 at section A predicted by each model.
This plot shows that the prediction curve of W-WaveNet is closer to the observed curve than other models.