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Abstract 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. 

Abstract Oceanic mesoscale motions including eddies, meanders, fronts, and filaments comprise a dominant fraction of oceanic kinetic energy and contribute to the redistribution of tracers in the ocean such as heat, salt, and nutrients. This reservoir of mesoscale energy is regulated by the conversion of potential energy and transfers of kinetic energy across spatial scales. Whether and under what circumstances mesoscale turbulence precipitates forward or inverse cascades, and the rates of these cascades, remain difficult to directly observe and quantify despite their impacts on physical and biological processes. Here we use global observations to investigate the seasonality of surface kinetic energy and upper-ocean potential energy. We apply spatial filters to along-track satellite measurements of sea surface height to diagnose surface eddy kinetic energy across 60–300-km scales. A geographic and scale-dependent seasonal cycle appears throughout much of the midlatitudes, with eddy kinetic energy at scales less than 60 km peaking 1–4 months before that at 60–300-km scales. Spatial patterns in this lag align with geographic regions where an Argo-derived estimate of the conversion of potential to kinetic energy is seasonally varying. In midlatitudes, the conversion rate peaks 0–2 months prior to kinetic energy at scales less than 60 km. The consistent geographic patterns between the seasonality of potential energy conversion and kinetic energy across spatial scale provide observational evidence for the inverse cascade and demonstrate that some component of it is seasonally modulated. Implications for mesoscale parameterizations and numerical modeling are discussed. Significance Statement This study investigates the seasonality of upper-ocean potential and kinetic energy in the context of an inverse cascade, consisting of energy transfers to and through the mesoscale. Observations show a scale-dependent cycle in kinetic energy that coincides with temporal variability in mixed layer potential energy and progresses seasonally from smaller to larger scales. This pattern appears dominant over large regions of the ocean. Results are relevant to ocean and climate models, where a large fraction of ocean energy is often parameterized. A customizable code repository and dataset are provided to enable comparisons of model-based resolved and unresolved kinetic energy to observational equivalents. Implications result for a range of processes including mixed layer stratification and vertical structure of ocean currents.