Arctic Ocean surface energy budget parameterizations are evaluated from a large-scale perspective, through the lenses of three theoretical frameworks, the "similar-behavior," "ensemble-average," and "quasi-equilibrium" frameworks, for understanding how the sub-grid and grid-scales interact with each other. The present study uses local point measurements and values derived from the European Center for Medium Range Weather Forecasts forecast model, both taken as part of the Surface Heat Budget of the Arctic Ocean Experiment (SHEBA).

The similar-behavior framework assumes that relationships between grid-scale variables are similar to relationships between sub-grid variables, the ensemble-average framework assumes that the sub-grid scale communicates with the grid-scale through the ensemble average of sub-grid realizations, and the quasi-equilibrium framework assumes that the parameterization is fundamentally controlled by the grid-scale evolution. Although the first two frameworks are intuitive and commonly assumed, they have no a priori justification. The quasi-equilibrium framework, on the other hand, flows logically from the nature of parameterization, and constraints derived from that framework can provide tests that all parameterizations should pass.

Lag-correlation and variance structure analysis suggests that for a number of Arctic Ocean surface energy budget terms, especially for some months during northern winter, current parameterizations do not exhibit structures that would be expected if a simple upscaling of small-scale behavior is valid. Analysis using the quasi-equilibrium framework suggests that while the parameterizations for a few terms in the surface energy budget (ice conduction and latent heat) exhibit evidence of large-scale control, other terms (net radiation and sensible heat) do not. Those parameterizations not exhibiting large-scale control may fundamentally misrepresent the connection between small and large-scales.