Mass-flux subgrid-scale parameterization in analogy with multi-component flows: a formulation towards scale independence
A generalized mass-flux formulation is presented, which no longer takes a limit of vanishing fractional areas for subgrid-scale components. The presented formulation is applicable to a~situation in which the scale separation is still satisfied, but fractional areas occupied by individual subgrid-scale components are no longer small. A self-consistent formulation is presented by generalizing the mass-flux formulation under the segmentally-constant approximation (SCA) to the grid–scale variabilities. The present formulation is expected to alleviate problems arising from increasing resolutions of operational forecast models without invoking more extensive overhaul of parameterizations.
The present formulation leads to an analogy of the large-scale atmospheric flow with multi-component flows. This analogy allows a generality of including any subgrid-scale variability into the mass-flux parameterization under SCA. Those include stratiform clouds as well as cold pools in the boundary layer.
An important finding under the present formulation is that the subgrid-scale quantities are advected by the large-scale velocities characteristic of given subgrid-scale components (large-scale subcomponent flows), rather than by the total large-scale flows as simply defined by grid-box average. In this manner, each subgrid-scale component behaves as if like a component of multi-component flows. This formulation, as a result, ensures the lateral interaction of subgrid-scale variability crossing the grid boxes, which are missing in the current parameterizations based on vertical one-dimensional models, and leading to a reduction of the grid-size dependencies in its performance. It is shown that the large-scale subcomponent flows are driven by large-scale subcomponent pressure gradients. The formulation, as a result, furthermore includes a self-contained description of subgrid-scale momentum transport.
The main purpose of the present paper is to appeal the importance of this new possibility suggested herein to the numerical weather forecast community with implications for the other parameterizations (cloud fraction, mesoscale organization) as well as resolution-dependence of parameterizations.