An unsupervised method for extracting coherent spatiotemporal patterns in multi-scale data

The unsupervised and principled diagnosis of multi-scale data is a fundamental obstacle in earth sciences. Here we explicitly define multi-scale data as being characterized by spatiotemporal processes (i.e. processes acting along time and space simultaneously) with process scales acting across orders of magnitude, non-stationarity, and/or invariances such as translation and rotation. Existing methods, such as traditional analytic approaches, data-driven modeling like Dynamic Mode Decomposition (DMD), and even deep learning, are not well-suited to diagnosing multi-scale data, usually requiring supervised strategies such as human intervention, extensive tuning, or selection of ideal time periods.We present the multi-resolution Coherent Spatio-Temporal Scale Separation (mrCOSTS), a data-driven method capable of overcoming the challenges of multi-scale data. It is a hierarchical variant of Dynamic Mode Decomposition (DMD) that enables the unsupervised extraction of spatiotemporal features in multi-scale data. It operates by decomposing the data into bands of temporal frequencies associated with coherent spatial modes. The method requires no training and functions with little to no hyperparameter tuning by instead taking advantage of the hierarchical nature of multi-scale systems.We demonstrate mrCOSTS on multi-scale data from a range of disciplines and scales: 1) sea surface temperature of the El-Nino Southern Oscillation (ENSO), 2) Antartic sea ice concentration, and 3) directly evaluating a numerical weather model against LIDAR observations of wind speed. In each example we demonstrate how mrCOSTS can be used to gain insights into the underlying dynamics of each system, revealing missing components in the description of each system's variability, diagnosing extreme events, and provide a pathway forward for building better physical representations in models.Using mrCOSTS, we show that ENSO is the result of 6 coherent spatio-temporal bands and use these results to explain the difference in intensity and spatial pattern of extreme 2015-2016 ENSO event relative to other extreme ENSO events. In the second example, we show that the dynamics of Antarctic sea ice concentration were found to have a negligible interannual component until 2012 when a long-term decline initiated and interannual dynamics at a decadal-scale started contributing. The large decline in sea ice concentration between 2014-2017 was almost entirely the result of the new interannual dynamics while the recent record low sea ice concentrations had a strong climate change signal. Finally, we demonstrate how mrCOSTS enables the evaluation of models directly against spatially-explicit observations. We evaluated an eddy-resolving numerical model against LIDAR observations of wind speed. The scale-aware model evaluation allowed us to easily reveal that errors at the largest scales dominated the system despite the agreement of lower order statistical moments. In each case using mrCOSTS we trivially retrieved complex dynamics that were previously difficult to resolve while additionally extracting previously unknown patterns or complexities of systems characterized by multi-scale processes.