2. Numerical Model
2.b. Simulation setup and Computational resources Computational domain and spatial resolution of the model (see Figure 1) As shown in Figure 1, the computational domain of the model atmosphere extends 51.2 km horizontally and 20 km vertically. At the top of the model atmosphere, a layer has been added so only the temperature field is calculated to improve the accuracy of the radiation flux. Both horizontal and vertical grid intervals are 100 m, except for the lowermost 100 m height, in which the vertical levels are located at z = 50, 25, 12.5, 6.25, and 3.125 m. Since a staggered grid is utilized, the lowest level at which horizontal wind is evaluated is located at approximately 1.5 m. The grid interval, 100 m, is determined by preliminary numerical experiments with varying model resolution. The vertical computational domain of the model ground layer extends to a depth six times of diurnal skin depth δd. The vertical grid interval is not constant. The vertical grid points normalized by δd are located at -0.1, -0.2, -0.35, -0.53, -0.79. -1.2, -1.8, -2.7, -4.0, and -6.0 (The value of δd is described in Appendix A.e). Boundary conditions The horizontal boundary condition of the model atmosphere is cyclic. Vertical wind velocity at the surface and upper boundary layer is zero. Above 17 km height, numerical diffusion is introduced to the horizontal and vertical momentum equations in order to attenuate gravity waves excited by thermal convection. The numerical diffusion coefficient linearly increases from 0 to 1000 m2 sec-1 between 17 and 19 km height. Solar flux The solar flux at the top of the model atmosphere changes diurnally under the condition that Ls = 100° at 20°N. The seasonal condition corresponds to the summer solstice of the northern hemisphere (Ls = 90°). The latitudinal condition is close to that of the Viking Lander 1 site (22.4°N). Basic state and initial condition For the basic state of the model atmosphere, the vertical temperature profile is calculated at 6:00 local time (LT) by the 1D radiative convective model that has the same representations of radiative and ground processes as those described in Section 2.a. Pressure and density profiles of the basic state are obtained from the temperature profile via the hydrostatic equation and the equation of state for an ideal gas. Detailed mathematical expressions of the 1D model, calculation procedure of the temperature profile, and the actual profile adapted for the basic state are shown in Appendix C. The initial condition for the dust-free case is a motionless atmosphere with horizontally uniform temperature. The vertical profile of initial atmospheric temperature is the same as that of the basic state mentioned above. In order to facilitate the initial development of thermal convection, a random perturbation of potential temperature with an amplitude less than 3 K is imposed at the lowest level (z = 3.125 m). The vertical profile of initial ground temperature is given as that calculated by the 1D model that is used for determining the temperature profile of the basic state. The initial condition for the dusty case is described in Section 4. Time step and computational resources The time interval of integration is 0.5 or 1 sec. These values are determined by using the Courant-Friedrichs-Lewy (CFL) condition with a phase velocity of the fastest internal gravity wave in the model atmosphere, which is described as where is buoyancy frequency is the depth of the model atmosphere. When integrating the radiation process, the time interval is 60 sec, which is short enough for the radiation field to follow the temperature change associated with thermal convection. This interval is suitable because the temporal scale of temperature change associated with thermal convection can be estimated as 100 to 1000 sec, provided that the magnitude of convective wind velocity is of the order of 10 m sec-1 and the depth of the convection layer ranges from 1 to 10 km. Numerical integrations were performed by using Fujitsu VPP 800 systems at the Kyoto University Data Processing Center and Center for PLAnning and INformation Systems, Institute of Space and Astronautical Science. The required main memory size was approximately 256 Mbytes. CPU time for executing an integration of 24 model hours with a time interval of 0.5 sec was approximately 8 hours.
A Numerical Simulation of Thermal Convection in the Martian Lower Atmosphere with a Two-Dimensional Anelastic Model