## a. Basic Equations

For the basic equations, a 3D spherical primitive system is used (refer to Numaguti and Hayashi, 1991, and Numaguti, 1992, for details). For the horizontal and vertical directions, a latitude and longitude coordinate (

λ,φ) system and aσ-coordinate system are adopted, respectively. The equations of motion, the continuity equation, the hydrostatic equation, the equation of water vapor, the thermodynamic equation, and the surface energy balance equation are as follows:where

u,vare horizontal wind velocities, is vertical wind velocity inσ-coordinates,Tis temperature,qis specific humidity,pis surface air pressure,_{s}Tis surface temperature, is geopotential,_{g}fis the Coriolis parameter,ais the radius of a planet,gis the gravitational acceleration,Ris the gas constant of the atmosphere,cis specific heat at constant pressure, and_{p}Ls the latent heat of water vapor. , , , and are horizontal diffusion terms andF,_{u}^{vdf}F,_{v}^{vdf}F,_{T}^{vdf}Fare vertical diffusion flux terms._{q}^{vdf}Sis the specific humidity source term associated with condensation,_{q}^{cond}Cis the specific heat of the surface, which is set to 0 in practice._{g}q,_{rad}q, and_{vdfT}qare net radiative flux, sensible heat flux, and latent heat flux terms, respectively._{vdfq}Table 1 shows the values that are used for the parameters in the model. The value of the water vapor absorption coefficient, , was determined using that at 1000 cm

^{-1}in Figure 2 of Yamamoto (1952). The values ofLandp_{0}^{*}are set identical to those in Nakajimaet al. (1992).

Physical constants Universal gas constant R= 8.314 J mol^{*}^{-1}K^{-1}Gravitational acceleration g= 9.8 m s^{-2}Stefan-Boltzman constant σ= 5.67 × 10^{8}W m^{-2}K^{-4}

Model parameters Molecular weight of dry air m= 18 × 10_{n}^{-3}kg mol^{-1}Molecular weight of water vapor m= 18 × 10_{v}^{-3}kg mol^{-1}Gas constant of dry air R= 461.9 J kg_{n}^{-1}K^{-1}Gas constant of water vapor R= 461.9 J kg_{v}^{-1}K^{-1}Specific heat of dry air at constant pressure c= 4_{pn}R= 1616.6 J kg_{n}^{-1}K^{-1}Specific heat of water vapor at constant pressure c= 4_{pv}R= 1616.6 J kg_{v}^{-1}K^{-1}Latent heat of water vapor L= 2.4253 × 10^{6}J kg^{-1}Constant used in the saturated water vapor pressure equation p= 1.4 × 10_{0}^{*}^{11}PaMass of the non-condensable constituents in the atmosphere p= 10_{n0}^{5}PaWater vapor absorption coefficient κ= 0.01 m_{v}^{2}Kg^{-1}Dry air absorption coefficient κ= 0.0 m_{n}^{2}Kg^{-1}Radius of planet a= 6.37 × 10^{6}mTable 1:Values of various constants and parameters used in model calculations.

It is assumed that saturated water vapor pressure can be given by

as in Nakajima

et al.(1992).