Multi-scale systems, such as the climate system, the atmosphere, and the ocean, are hard to understand and predict due to their intrinsic nonlinearities and chaotic behavior. Here, we apply a physics-consistent machine learning method, the multi-resolution dynamic mode decomposition (mrDMD), to oceanographic data. mrDMD allows a systematic decomposition of high-dimensional data sets into time-scale dependent modes of variability. We find that mrDMD is able to systematically decompose sea surface temperature and sea surface height fields into dynamically meaningful patterns on different time scales. In particular, we find that mrDMD is able to identify varying annual cycle modes and is able to extract El Nino-Southern Oscillation events as transient phenomena. mrDMD is also able to extract propagating meanders related to the intensity and position of the Gulf Stream and Kuroshio currents. While mrDMD systematically identifies mean state changes similarly well compared to other methods, such as empirical orthogonal function decomposition, it also provides information about the dynamically propagating eddy component of the flow. Furthermore, these dynamical modes can also become progressively less important as time progresses in a specific time period, making them also state dependent. (C) 2022 Author(s).