Mass-flux subgrid-scale parameterization in analogy with multi-component flows: a formulation towards scale independence GAME/CNRM, CNRS-INSU-Météo France, URA1357, Toulouse, France
Model Description Paper
21 Nov 2012
Received: 06 Oct 2011 – Published in Geosci. Model Dev. Discuss.: 24 Nov 2011 Abstract. 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
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.
Revised: 13 May 2012 – Accepted: 26 Oct 2012 – Published: 21 Nov 2012
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
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
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
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
Citation: Yano, J.-I.: Mass-flux subgrid-scale parameterization in analogy with multi-component flows: a formulation towards scale independence, Geosci. Model Dev., 5, 1425-1440, doi:10.5194/gmd-5-1425-2012, 2012.