# Super-Resolving Ocean Dynamics from Space with Computer Vision Algorithms
## 3 Results
### Testing Single-Image, Super-Resolution Configurations and Designing a Multi-Scale Adaptive Model
ADR-SR performance assessed on the test dataset significantly improved with respect to that of the other networks, and, for the first time, including the information on the low-resolution ADT interpolation error leads to a tangible reduction of the RMSD over most of the basin (Figure 3B,C). Still, a lower accuracy is found close to some of the altimeter repeated tracks (visible as diamond shapes), which might be due to the limited ability either of ADR-SR and of the previously tested networks to correctly handle the information provided at different spatial scales by the input predictor variables. This specifically reflects the larger scale of ADT mapping error patterns with respect to the geophysical variables. To overcome this issue, we have developed here a novel deep convolutional architecture, which combines the successful developments of previously tested super-resolution models with the dilated-convolution-based multi-scale information learning inception module proposed by [60]. Dilated convolution allows users to extract information at different scales and significantly expands the network's receptive field even without enlarging the kernel size [61]. Choosing a dilation rate, r, r-adjacent pixels are skipped by the convolution kernel, so that related weights refer to samples taken at tuneable distances. In the inception module designed by [60], the channels input to each module first pass through three parallel dilated convolution layers with kernel size 3 \(\times\) 3 and dilation factor of 1, 2 and 3, respectively. Then, all convolution outputs are concatenated and passed to the successive layers. We have named the new model \"dilated Adaptive Deep Residual Network for Super-Resolution (dADR-SR)\". Its architecture is depicted in Figure 4. In the first step, dADR-SR input channels are passed to three parallel convolutional layers, each one with ten filters and a 3 \(\times\) 3 kernel size, but with an increasing dilation factor of 1, 3 and 5, respectively. The output of the three convolutional layers is then concatenated into a single multiscale feature tensor, which represents the input to a sequence of multiscale adaptive residual blocks. Indeed, within each residual block, the same multiscale parallel feature extraction is carried out, thus defining a multiscale adaptive residual block (M-ARB). To avoid excessively increasing the number of parameters to train, the number of residual blocks is here kept to 12 (four fewer than in the EDSR/ADR-SR baseline), and the number of filters included in the two sets of convolutional layers inside each M-ARB is chosen as 120 and 10, respectively. Within the M-ARB, after concatenating the learned multiscale features, a SE module is included (with a predefined dimensionality reduction factor of 10 instead of 16, so that the bottleneck in dADR-SR is shaped 30-3-30, instead of 32-2-32). The final number of trainable parameters in the dADR-SR model is slightly below 1.6 M.  
The dADR-SR model outperforms any of the previous networks when tested on the independent dataset, displaying a marked reduction of the RMSD over the entire basin (Figure 5), with only extremely few and very small spots showing a minimal degradation (Figure 4B,C). The information captured at the different scales by including all predictors thus further enhances the accuracy of the reconstruction with respect to the model that does not consider the low-resolution ADT interpolation error. Figure 4: The dilated Adaptive Super-Resolution (dADR-SR) model developed to reconstruct high-resolution absolute dynamic topography from multiple channel inputs.