## 4 Results and Discussion  
### Validation Using SSH of DTU18 Verification Model  
In this section, the retrieval performance of the MHL, CMDL (CNN Multimodal Deep Learning), RMDL (Residual Multimodal Deep Learning), and MRMDL models are compared and analyzed to identify the refinements of the suggested model. Among them, CMDL, RMDL, and MRMDL represent the multimodal deep learning methods comprised of CNN, ResNet, and MResNet feature extraction with MHL, respectively. The models MHL, CMDL, RMDL, and MRMDL are trained on the training set and the hyperparameters of the models are optimized on the validation set. The models' performances are evaluated by the test set. All models were implemented in PyTorch [24] and trained on a single NVIDIA GeForce RTX2060 GPU. Table 3 summarizes the number of input and output channels for each layer of all models used in this paper. In the feature extraction stage, RMDL adopts the original structural design of ResNet 50, while CMDL and MRMDL adopt the same channel design solutions. In the SSH retrieval phase, all models used the same MHL design structure with four hidden layers and 200 neurons per layer. The performance metrics of the four models are statistically illustrated in Table 4. It is evident that the MRMDL model achieves the best retrieval results among the four models. Compared to the DTU18 validation model, the _MAD_, _RMSE_, and _PCC_ equal 3.92 m, 6.19 m, and 0.98, respectively. It means that the proposed MRMDL model based on MResNet residual structure can extract the data features of DDM more comprehensively and effectively. Meanwhile, the retrieval results of the CMDL, RMDL, and MRMDL models are better than the MHL model. This demonstrates that the multimodal deep learning models effectively enhance the accuracy of the SSH retrieval when compared to the single model. In addition, the retrieval results from the CMDL, RMDL, and MRMDL models show that the RMDL and MRMDL models can realize a deeper network structure and obtain better retrieval results when compared to the CNN model. Furthermore, the retrieval results from the RMDL and MRMDL models show that the MRMDL model optimized for the DDM \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layer Name** & **RMDL** & **CMDL** & **MRMDL** & **MHL** \\ \hline Conv1 & (2, 64) & (2, 64) & (2, 64) & - \\ \hline Conv2 & (64, 256) & (64, 32) & (64, 32) & - \\ \hline Conv3 & (256, 512) & (32, 16) & (32, 16) & - \\ \hline Conv4 & (512, 1024) & (16, 8) & (16, 8) & - \\ \hline Conv5 & (1024, 2048) & (8, 4) & (8, 4) & - \\ \hline FC1 & 200 & 200 & 200 & 200 \\ \hline FC2 & 200 & 200 & 200 & 200 \\ \hline FC3 & 200 & 200 & 200 & 200 \\ \hline FC4 & 200 & 200 & 200 & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The number of input and output channels of each layer of the neural network model. data structure can retain more DDM information, resulting in superior retrieval results. Table 3 also gives the average running times of the four models in one epoch. MRMDL, CMDL, and MHL running times are relatively close and much shorter than RMDL. Figure 5 shows the scatter density plots of the retrieval results for the MRMDL (a), CMDL (b), RMDL (c), and MHL (d) models in relation to the SSH DTU18 validation model. MRMDL retrieval results outperform other models in terms of overall performance and correlated more strongly with the DTU18 validation model, with a _PCC_ of 0.98. However, as the primary purpose of CYGNSS satellites is not ocean altimetry, the satellite receiver is not optimized for SSH retrieval. Its retrieval error is significant, with _MAD_ about 3.92 m and _RMSE_ about 6.19 m. Figure 6a shows the statistical histogram of the error distribution of the four model SSH retrieval results compared to the DTU18 validation model. The statistical results demonstrate that the errors of the four models MRMDL, RMDL, CMDL, and MHL are between \(-5\) and \(5\) m are 77.33%, 76.92%, 72.34%, and 68.97%, respectively. The retrieval errors between \(-10\) and \(10\) m are 89.72%, 89.68%, 86.58% and 82.91%, respectively.