Abstract.As far as the representation of deep moist convection is concerned, only two kinds of model physics are used at present: highly parameterized as in the conventional general circulation models (GCMs) and explicitly simulated as in the cloud-resolving models (CRMs). Ideally, these two kinds of model physics should be unified so that a continuous transition of model physics from one kind to the other takes place as the resolution changes. With such unification, the GCM can converge to a global CRM (GCRM) as the grid size is refined. This paper suggests two possible routes to achieve the unification. ROUTE I continues to follow the parameterization approach, but uses a unified parameterization that is applicable to any horizontal resolutions between those typically used by GCMs and CRMs. It is shown that a key to construct such a unified parameterization is to eliminate the assumption of small fractional area covered by convective clouds, which is commonly used in the conventional cumulus parameterizations either explicitly or implicitly. A preliminary design of the unified parameterization is presented, which demonstrates that such an assumption can be eliminated through a relatively minor modification of the existing mass-flux based parameterizations. Partial evaluations of the unified parameterization are also presented. ROUTE II follows the "multi-scale modeling framework (MMF)" approach, which takes advantage of explicit representation of deep moist convection and associated cloud-scale processes by CRMs. The Quasi-3-D (Q3-D) MMF is an attempt to broaden the applicability of MMF without necessarily using a fully three-dimensional CRM. This is accomplished using a network of cloud-resolving grids with large gaps. An outline of the Q3-D algorithm and highlights of preliminary results are reviewed.

This paper suggests two possible routes to achieve the unification of model physics in coarse- and fine-resolution atmospheric models. As far as representation of deep moist convection is concerned, only two kinds of model physics are used at present: highly parameterized as in the conventional general circulation models (GCMs) and explicitly simulated as in the cloud-resolving models (CRMs). Ideally, these two kinds of model physics should be unified so that a continuous transition of model physics from one kind to the other takes place as the resolution changes. With such unification, the GCM can converge to a global CRM (GCRM) as the grid size is refined. ROUTE I for unification continues to follow the parameterization approach, but uses a unified parameterization that is applicable to any horizontal resolutions between those typically used by GCMs and CRMs. It is shown that a key to construct such a unified parameterization is to eliminate the assumption of small fractional area covered by convective clouds, which is commonly used in the conventional cumulus parameterizations either explicitly or implicitly. A preliminary design of the unified parameterization is presented, which demonstrates that such an assumption can be eliminated through a relatively minor modification of the existing mass-flux based parameterizations. Partial evaluations of the unified parameterization are also presented. ROUTE II for unification follows the "multi-scale modeling framework (MMF)" approach, which takes advantage of explicit representation of deep moist convection and associated cloud-scale processes by CRMs. The Quasi-3-D (Q3-D) MMF is an attempt to broaden the applicability of MMF without necessarily using a fully three-dimensional CRM. This is accomplished using a network of cloud-resolving grids with gaps. An outline of the Q3-D algorithm and highlights of preliminary results are reviewed

A three-dimensional anelastic model has been developed using the vorticity equation, in which the pressure gradient force is eliminated. The prognostic variables of the model dynamics are the horizontal components of vorticity at all heights and the vertical component of vorticity and the horizontally uniform part of the horizontal velocity at a selected height. To implement the anelastic approximation, vertical velocity is diagnostically determined from the predicted horizontal components of vorticity by solving an elliptic equation. This procedure replaces solving the elliptic equation for pressure in anelastic models based on the momentum equation. Discretization of the advection terms uses an upstream-weighted partially third-order scheme. When time is continuous, the solution of this scheme is quadratically bounded. As an application of the model, interactions between convection and its environment with vertical shear are studied without and with model physics from the viewpoint of vorticity dynamics, that is, the deceleration/acceleration process of the basic flow in particular. The authors point out that the process is purely three-dimensional, especially when the convection is relatively localized, involving the twisting terms and the horizontal as well as vertical transports of vorticity. Finally, it is emphasized that parameterization of cumulus friction is a resolution-dependent problem of vorticity dynamics associated with cumulus convection.

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A new framework for modeling the atmosphere, which we call the quasi-3D (Q3D) multi-scale modeling framework (MMF), is developed with the objective of including cloud-scale three-dimensional effects in a GCM without necessarily using a global cloud-resolving model (CRM). It combines a GCM with a Q3D CRM that has the horizontal domain consisting of two perpendicular sets of channels, each of which contains a locally 3D grid-point array. For computing efficiency, the widths of the channels are chosen to be narrow. Thus, it is crucial to select a proper lateral boundary condition to realistically simulate the statistics of cloud and cloud-associated processes. Among the various possibilities, a periodic lateral boundary condition is chosen for the deviations from background fields that are obtained by interpolations from the GCM grid points. Since the deviations tend to vanish as the GCM grid size approaches that of the CRM, the whole system of the Q3D MMF can converge to a fully 3D global CRM. Consequently, the horizontal resolution of the GCM can be freely chosen depending on the objective of application, without changing the formulation of model physics.To evaluate the newly developed Q3D CRM in an efficient way, idealized experiments have been performed using a small horizontal domain. In these tests, the Q3D CRM uses only one pair of perpendicular channels with only two grid points across each channel. Comparing the simulation results with those of a fully 3D CRM, it is concluded that the Q3D CRM can reproduce most of the important statistics of the 3D solutions, including the vertical distributions of cloud water and precipitants, vertical transports of potential temperature and water vapor, and the variances and covariances of dynamical variables. The main improvement from a corresponding 2D simulation appears in the surface fluxes and the vorticity transports that cause the mean wind to change. A comparison with a simulation using a coarse-resolution 3D CRM is also made.