As far as representation of deep clouds is concerned, we currently have two
families of atmospheric models (besides large eddy simulation): general circulation
models (GCMs), which completely parameterize cloud systems, and cloud-resolving
models (CRMs), which explicitly simulate individual deep clouds. Ideally, these two
families of models should be unified so that GCMs can converge to a global CRM as the
resolution is refined. At present, the families have not been unified and, therefore, we
cannot freely choose intermediate or highly heterogeneous resolutions.
We can think of basically two routes for the unification. One is through
developing a new generation of GCM that converges to a global CRM while using a
simple cloud-system model as in the traditional cumulus parameterizations. One of the
keys to open this route is to reformulate the vertical eddy transport due to subgrid-scale
cloud-induced circulation in such a way that it vanishes when the resolution is
sufficiently high to resolve individual clouds. We will discuss how this can be done
taking the Arakawa-Schubert cumulus parameterization as an example. We will also
emphasize the need for explicitly predicting a measure (or measures) of cloud
organization.
For practical purposes, we should also consider another route: development of a
numerical model that converges to a global CRM while simulating details of cloud
processes. This requires the use of a cloud-resolving resolution at least partially. The
“super-parameterization”, which is now called the “prototype multi-scale modeling
framework (MMF)”, replaces the cumulus parameterization of a GCM by 2D CRMs
embedded in each GCM grid box, taking advantage of the fact that 2D CRMs are
reasonably successful in simulating the thermodynamic effects of deep clouds. While it
has been shown that the prototype MMF can significantly improve simulations of climate
variability, it has important limitations arising from the two-dimensionality of the
embedded CRMs. The Quasi-3D (Q3D) MMF being developed by Jung and Arakawa is
an attempt to overcome these limitations without necessarily using a fully threedimensional
CRM. This is accomplished by coupling a GCM with a CRM applied to a
“gappy” grid, which consists of perpendicular sets of grid-point channels. Unlike the
prototype MMF, the Q3D MMF can converge to a fully 3D global CRM as the GCM’s
resolution is refined. An outline of the Q3D algorithm and highlights of preliminary
results will be presented.
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