# 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  
A large variety of neural network architectures have been proposed to achieve single-image super-resolution, even considering only those dealing with input-output images of the same size [25]. Comparing all of them is clearly beyond the scope of our work, which is rather to demonstrate whether the super-resolution class of techniques can be efficiently used for quantitatively accurate dynamical retrievals based on multiple variables and observation types. As such, we have implemented here four different models, three of them basically reproducing already published (baseline) networks, and a third one that includes elements from different models but represents an original network architecture. All models are trained considering the mean-squared error as the reference loss function. The first model is the Super-Resolution Convolutional Neural Network (SRCNN) proposed by [26]. It consists of three 2D convolutional layers: the first one includes 128 filters with a 9 \(\times\) 9 kernel size, the second one with 64 filters and a 3 \(\times\) 3 kernel size and the third one with a single \(5\times 5\) filter. The first two layers include a nonlinear activation (rectified linear unit, ReLU), and zero-padding is applied in every layer to keep the original image size end-to-end (Figure 1A). Each layer represents a specific operation in the conceptual explanation of the SRCNN given by [26]: overlapping patches extraction from the low-resolution image (where the patches have the same size as the kernel) and representation into a high-dimensional vector (feature mapping, with vector dimensions equal to the number of filters); non-linear mapping of each high-dimensional vector onto another high-dimensional vector comprising a second set of high-resolution feature maps; these are directly linked to the final image in the third step (reconstruction). We applied SRCNN in four different configurations, namely considering SST, \(\partial\)SST/\(\partial\)t, ADT and \(\Delta\)ADT in input (all together) and alternately removing either \(\partial\)SST/\(\partial\)t, \(\Delta\)ADT or both \(\partial\)SST/\(\partial\)t and \(\Delta\)ADT from the predictor variables. After training the networks (see details in Section 2), we used the fully independent test data to assess the accuracy of the prediction over the entire Mediterranean Basin, comparing the root-mean-squared differences (RMSD) between the altimeter-like ADT and the \"true\" ADT, as well as those between the super-resolved ADT field and our simulated \"ground truth\". SCRNN gave us some first indications (Figure 1B-E): overall, we could not find an improvement in the ADT reconstruction by incorporating all predictors, but what appeared to be actually detrimental was the inclusion of the ADT interpolation error. In fact, excluding \(\Delta\)ADT from the input already improves the accuracy of the simple SRCNN's reconstruction. Conversely, including \(\partial\)SST/\(\partial\)t always appeared beneficial. Even if our initial hypothesis on the relevance of the information on the observing geometry (as provided by the ADT interpolation error) seemed wrong, we must stress that the features that dominate the patterns of \(\Delta\)ADT are much larger than the scales of the dynamical features we want to super-resolve, and SRCNN is plausibly a too shallow/simple network to deal with such different scales due to a very limited ability to learn complex interdependencies between channels (it actually contains only around 110k trainable parameters). Thus, we are still confident that a properly defined network architecture would be able to exploit the information on where the altimeter-like ADT field is expected to be more accurate and where it deserves stronger corrections. As such, we decided to test all successive (and gradually more complex) network architectures with both the configuration with the four predictors and the one without the ADT error.