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.