Knowledge of ocean circulation is important for understanding and predicting weather and climate, and managing the blue economy. This circulation can be estimated through Sea Surface Height (SSH) observations, but requires decomposing the SSH into contributions from balanced and unbalanced motions (BMs and UBMs). This decomposition is particularly pertinent for the novel SWOT satellite, which measures SSH at an unprecedented spatial resolution. Specifically, the requirement, and the goal of this work, is to decompose instantaneous SSH into BMs and UBMs. While a few studies using deep learning (DL) approaches have shown promise in framing this decomposition as an image-to-image translation task, these models struggle to work well across a wide range of spatial scales and require extensive training data, which is scarce in this domain. These challenges are not unique to our task, and pervade many problems requiring multi-scale fidelity. We show that these challenges can be addressed by using zero-phase component analysis (ZCA) whitening and data augmentation; making this a viable option for SSH decomposition across scales.