A Conservative Harmonic Method for Commutative Coarse-graining of Tracers in the Global Ocean

Spatial coarse-graining is a powerful methodology for extracting space-local information about multiscale processes. Filtering using homogeneous kernels guarantees commutativity with derivatives and conserves spatial means. In the case of the global ocean, a choice for treating land boundaries is needed. The simple choice to deform the kernel to avoid land results in non-conservative behavior (modifies the spatial mean) and breaks commutativity. Another choice is 'land-filling' in a manner that is physically consistent with the underlying boundary conditions of the dynamics. Here we present a physically consistent method for land-filling oceanic tracers, such as temperature, salinity, and density. We present the application of this method to sea-surface temperature (SST) and compare with results using the simple deforming-kernel approach.