William Edge: Gaussian Process Regression for multi-scale oceanographic observations
We have developed methods to characterise, extract, and map different processes from complete, sparse, spatiotemporal observations. These methods were motivated by the need to analyse a single dynamic regime in the presence of multiple competing processes. Ocean observations contain numerous processes that can overlap in frequency-wavenumber space. We can characterise processes simultaneously from observations by constructing Gaussian Process (GP) kernels tailored to the spectral signature of each process. We used Vecchia’s approximation to a GP to enable the method on much larger datasets than the standard GP approach. From the characterisation we can extract and further analyse our processes of interest. We demonstrate the framework using ocean surface drifters and satellite-based sea surface altimetry on the continental shelf, where the simultaneous presence of eddies and strong internal waves complicate traditional approaches. The characterisations can guide modellers toward better representations of specific processes for data assimilation. More broadly, the method shows promise for producing clean, process-separated mapped outputs from unstructured, multi-platform datasets. These outputs could serve as improved inputs to both climate models and ML-based analysis frameworks. Keywords: oceanography, Gaussian Process, multi-scale decomposition, in-situ, sparse data, submesoscale.