## 5 Conclusions  
The traditional GNSS-R SSH retrieval method has the problems of complicated error model, low retrieval accuracy, and difficulty utilizing DDM information. To compensate for this deficiency, while considering the heterogeneity of the input data, this paper proposes an end-to-end modified deep learning model. The primary conclusions of this paper can be summed up as follows.  
(1) The MRMDL model suggested in this study is primarily composed of MResNet and MHL-NN. First, MResNet is utilized to identify effective features from the combination of BRCS DDM and Raw DDM. Second, the proposed features are fused with the  
Figure 11: Statistics of global SSH errors retrieved by HALF retracking method and MRMDL model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **MAD (m)** & **RMSE (m)** & **PCC** \\ \hline HALF & 6.05 & 7.48 & 0.96 \\ \hline MRMDL & 3.92 & 6.19 & 0.98 \\ \hline Improve (\%) & 35.21 & 17.25 & 2.08 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of SSH retrieval performance between MRMDL model and HALF re-tracking method.  
auxiliary parameter data in an additional fully connected layer. Final, MHL-NN is used to retrieve the sea surface height.
2. For the DDM reflected signal with low power, high noise, and tiny image size, a residual block applicable to the DDM structure is designed to adaptively identify effective features. The results show that the MResNet can retain more DDM information and produce advantageous retrieval results.
3. The reliability of the model was verified using SSH from tide-corrected DTU18 and spaceborne radar altimeters (Jason3, HY-2C, HY-2B). The results illustrate that the presented MRMDL model provides superior retrieval performance. Compared to the DTU18 validated model, the _MAD_, _RMSE_, and _PCC_ are 3.92 m, 6.19 m, and 0.98, respectively. Compared to the SSH of the radar altimeter, the _MAD_, _RMSE_, and _PCC_ are 4.32 m, 6.50 m, and 0.97, respectively.
4. Compared to the traditional HAL re-tracking approach, the SSH retrieval algorithm based on the MRMDL model can significantly improve SSH retrieval precision. The _MAD_ and _RMSE_ are decreased by about 35.21% and 17.25%, respectively; the _PCC_ is enhanced by about 2.08%.  
The MRMDL method proposed in this paper will provide new ideas for future DDM-based GNSS-R SSH inversion algorithms. Due to the enormous dataset of GNSS-R, more intelligent and effective data quality control methods need to be applied.  
This study was carried out with the help of all the authors; [PERSON]: scientific analysis and manuscript writing. [PERSON], F.W. and H.Z.: experiment design, project management, editing. [PERSON]-X., [PERSON] and Y.Z.: review and editing. [PERSON], W.Z., F.W. and H.Z. made equal contributions to this paper. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Natural Science Foundation of China under Grant (42274119), in part by the Liaoning Revitalization Talents Program under Grant (ALYC2002082), in part by National Key Research and Development Plan Key Special Projects of Science and Technology Military Civil Integration (2022 YFF1400500), and in part by the Key Project of Science and Technology Commission of the Central Military Commission.  
Not applicable.  
The authors declare no conflict of interest.