Collaborative Research: A Coordinate-Free Framework for Improving Eddy Parameterizations

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This project is to create and apply a new theoretical framework for developing and assessing parameterizations of eddy transport in numerical models. The framework constitutes a set of principles linking physical meaning to parameterization form, including extant as well as yet-unformulated variations. This work will provide an avenue for the cross-evaluation of existing or proposed parameterizations from first principles. Two significant software packages that will result from this work are (i) symbolic algebra software for implementing eddy parameterizations in an arbitary model coordinate system and choice of discretization, and (ii) numerical code for error diagnostics in model implementation.The Explicit, Stochastic, Coordinate-independent (ESC) framework will incorporate: (i) explicit and rigorous definitions for filtering and averaging operations; (ii) a flexible approach to stochastic modeling that relaxes the unrealistic constraints implicit in existing parameterizations on eddy path smoothness and dependence on local conditions; and (iii) the use of coordinate-independent representations to express the physical essence of parameterizations free from choice of model geometry. This work will clarify the link between parameterization forms and conserved properties (energy, enstrophy, etc.); speed the identification and assessment of discretization errors in multiple model systems; uniquely identify the advective and diffusive components of parameterized fluxes across implementations; and account for the impact of the observed range of high-frequency trajectory behavior on parameterization structure.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.