Diffusion‐Based Smoothers for Spatial Filtering of Gridded Geophysical Data

We describe a new way to apply a spatial filter to gridded data from 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. An open‐source Python package implementing this algorithm, called gcm‐filters, is currently under development. Plain Language Summary “The large scale part” and “the small scale part” of quantities like velocity, temperature, and pressure fluctuations are important for a range of questions in Earth system science. This study describes a precise way of defining these quantities, as well as an efficient method for diagnosing them from gridded data, especially the data produced by Earth system models. Key Points A new way to apply a spatial low‐pass filter to gridded data is developed The new method can be applied in any geometry since it only requires a discrete Laplacian operator The algorithm's flexibility is illustrated using a range of examples from simulation and observation data