Ian Grooms, Department of Applied Mathematics, University of Colorado Boulder

Diffusion-based smoothers for spatial filtering of gridded geophysical data

"The large-scale part" and "the small-scale part" are intuitively meaningful ideas, but it can be hard to give them a precise meaning when dealing with curved geometries and complex boundaries. We describe a new way to apply a spatial filter to gridded data, e.g. from geophysical models or observations, focusing on low-pass filters. The new method is analogous to smoothing via diffusion, and its implementation requires only a discrete Laplacian operator appropriate to the data. The new method can approximate arbitrary filter shapes, including Gaussian filters, and can be extended to spatially-varying and anisotropic filters. The new diffusion-based smoother's properties are illustrated with examples from ocean model data and ocean observational products. A Python package called gcm-filters is available that implements the algorithm.