The formulation of CReSS is based on the nonhydrostatic and compressible equation using terrainfollowing coordinates. Prognostic variables are 3dimensional velocity components, perturbations of pressure and potential temperature, water vapor mixing ratio, subgrid scale turbulent kinetic energy (TKE), and cloud physical variables. A finite difference method is used for the spatial discretization. The horizontal domain is rectangular, and variables are set on a staggered grid: the ArakawaC grid in the horizontal and the Lorenz grid in the vertical. For time integration, the modesplitting technique (Klemp and Wilhelmson 1978) is used. Terms related to sound waves of the basic equation are integrated with a small time step, and other terms with a large time step. Cloud physical processes are formulated by a bulk method of cold rain, which is based on Lin et al. (1983), Cotton et al. (1986), Murakami (1990), Ikawa and Saito (1991), and Murakami et al. (1994). The bulk parameterization of cold rain considers water vapor, rain, cloud, ice, snow, and graupel. The microphysical processes implemented in the model are described in Fig.1. 
Figure 1: Diagram describing water substances and cloud microphysical processes in the bulk scheme of CReSS. (Tsuboki and Sakakibara, 2002) 
Parameterizations of the subgrid scale eddy motions in CReSS are oneorder closure of Smagorinsky (1963) or the 1.5order closure of turbulent kinetic energy (TKE). In the latter parameterization, the prognostic equation of TKE is used. All numerical experiments in this textbook use threedimensional 1.5order closure scheme. The surface process of CReSS is formulated by a bulk method, whose bulk coefficients are taken from Louis et al. (1981). Several types of initial and boundary conditions are available. For a numerical experiment, a horizontally uniform initial field provided by a sounding profile will be used with an initial disturbance of a thermal bubble or random temperature perturbation. The boundary conditions are one of the following types; rigid wall, periodic, zero normalgradient, and waveradiation types. CReSS can be nested within a coarsegrid model for a prediction experiment. In such an experiment, the initial field is provided by interpolating gridpoint values and the boundary condition is provided by the coarsegrid model. For a computation within a large domain, conformal map projections are available, which include the Lambert conformal projection, the polar stereographic projection, and the Mercator projection. For parallel computing of a large computation, CReSS provides twodimensional domain decomposition in the horizontal direction (Fig.2). Parallel processing is performed using the Massage Passing Interface (MPI). Communications between individual processing elements (PEs) are performed by exchanging data of the two outermost grids. The OpenMP is also available. 
Figure 2: Schematic representation of twodimensional domain decomposition and the communication strategy for parallel computations using MPI. 
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