Thoughts on prognostically modeling an eddying double-gyre ensemble mean

Andrew Poje^1,2*Takaya Uchida^3,4,5Quentin Jamet^6,7Luolin Sun^4,5Thierry Penduff⁴Bruno Deremble⁴Joseph Schoonover⁸Megan Trapanese^2,9Nicolas Wienders⁸William Dewar^4,5

• ¹Department of Physics, The Graduate Center,The City University of New York, New York City, United States
• ²College of Staten Island, New York, United States
• ³Moskovskij fiziko-tehniceskij institut nacional'nyj issledovatel'skij universitet, Dolgoprudny, Russia
• ⁴Centre National de la Recherche Scientifique, Paris, France
• ⁵Florida State University, Tallahassee, United States
• ⁶Service Hydrographique et Oceanographique de la Marine, Brest, France
• ⁷Inria Centre de Recherche Rennes Bretagne Atlantique, Rennes, France
• ⁸Fluid Numerics, North Carolina, United States
• ⁹Cornell University, Ithaca, United States

We address the question of separating the ocean's deterministic response to time-dependent forcing from its intrinsic chaotic variability. Ideally, one could compute the ensemble mean directly without performing numerous realizations, but this requires knowledge or closure of the second-order statistics — the classical turbulent-closure problem, here recast for a non-equilibrium, geophysical setting. Building on the ideas of nonlinear midlatitude ocean adjustment (Dewar 2003), we examine this problem using idealized quasi-geostrophic (QG) double-gyre ensembles subjected to episodic temporal variations in wind forcing. Our objective here is not to develop a subgrid parameterization of unresolved eddies, but rather to construct and test prognostic equations for the ensemble mean itself, using the simplest possible closure assumptions. We find that the performance of ensemble mean closures is highly dependent on the spatiotemporal structure of the forcing. Under slowly varying forcing, approximate closures reproduce the mean evolution reasonably well; under rapidly varying, near-zero-mean forcing, the simplest ensemble-mean closures fail, even at the level of basin-averaged total energy and enstrophy. In both regimes, the ensemble-mean response is not simply the accumulated imprint of the applied forcing, but instead appears as a continuing, non-equilibrated dialogue between the mean and eddy fields.