# 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
The second network we have implemented is the baseline Enhanced Deep Residual network for Super-Resolution (EDSR) proposed by [55]. EDSR was designed to exploit the possibility to significantly deepen the networks (i.e., to increase the number of layers) opened by residual learning frameworks. Instead of learning fully unreferenced functions, residual networks (ResNet) define the layers as residual functions (actually they are based on residual blocks, including different convolutional and batch normalization layers, and activation functions, where the residual is referenced to the block input) and have been proven much easier to optimize than conventional networks, allowing users to train considerably deeper networks and obtain significantly better accuracies [56]. EDSR simplified the network architecture with respect to models based on original ResNet by reducing the number of parameters employed in each residual block (Figure 2A). In its baseline formulation, it includes a first 2D convolutional layer made up of 64 filters with 3 \(\times\) 3  
Figure 1: Super-Resolution Convolutional Neural Network (SRCNN) adapted to the reconstruction of absolute dynamic topography from multiple channel inputs. (**A**) SRCNN network architecture. (**B–E**) Relative performance of the SRCNN reconstructions, assessed on the independent test data as the difference between the RMSD between the altimeter-like and original model output and the RMSD between the super-resolved absolute dynamic topography (ADT) and the original model ADT (red indicates smaller RMSD from model predictions). The panels show the performance of the models trained/tested considering: (**B**) the full set of predictor variables; (**C**) removing \(\partial\)SST\(\partial\)t from the predictors; (**D**) removing \(\Delta\)ADT from the predictors; (**E**) removing both \(\partial\)SST\(\partial\)t and \(\Delta\)ADT. ADT and related RMSD values are expressed in m.  
kernel size, followed by 16 residual blocks, increasing the number of trainable parameters to approximately 1.2 M, one order of magnitude higher than SRCNN. The first layer output and the output of the last residual block in the sequence are also summed up (skip connection) before entering the output convolutional layer (including a single 3 \(\times\) 3 filter), which connects to the target image. Residual blocks include two convolutional layers with the number of filters equal to the input channels (64) and a 3 \(\times\) 3 kernel size. These two layers are connected through a non-linear activation (ReLU). The outputs of the second convolutional layer within the residual block are summed to the input channels to obtain the residual, after applying them a fixed scaling factor of 0.1. Notably, the scaling strategy applied within the EDSR residual block was formerly proven to stabilize the training of complex networks, allowing users to safely increase the number of filters [57]. The minimum of the loss function reached during the model training was around ~4.5 \(\times\) 10\({}^{-3}\) for SRCNN, whatever the configuration, with small differences between hindcast and validation. The same numbers would indicate a much better performance of ESDR, with validation loss values of around 1.8 \(\times\) 10\({}^{-3}\) for the configuration excluding the ADT error from the predictors and values close to 1.6 \(\times\) 10\({}^{-3}\) for the full predictors set. The minimum hindcast loss got close to 1.1 \(\times\) 10\({}^{-3}\) in both EDSR configurations. However, the test run on the independent data clearly indicated that the improvement only occurred in some parts of the domain, while worse reconstructions can be obtained in dynamically relevant areas, both including the ADT error or not in the predictor list (Figure 2B,C).