2. Numerical Model
2.b. Simulation setup Computational domain and spacial resolution of the model (Figure 1) The computational domain of model atmosphere extends to 51.2 km horizontally and 20 km hight vertically. In order to calculate solar and infrared radiative flux at the top of model atmosphere, radiation layer where temperature field associated with radiation process is only calculated extends from 20 km hight to the top of atmosphere. Both horizontal and vertical grid interval are 100 m except in the lowermost 100 m hight, where the vertical grid points are at z = 50, 25, 12.5, 6.25, and 3.125 m. The lowest level horizontal wind is calculated at about 1.5 m hight. The grid interval and vertical grid point below 100 m hight are determined by some preliminary numerical experiments. The verical computational domain of model grand surface extends to 6 times of diurnal skin depth δd. The value of δd is about 8 cm (appendix A.e ). The vertical grid interval increases with depth and the vertical grid point normalized by δd are at -0.1, -0.2, -0.35, -0.53, -0.79. -1.2, -1.8, -2.7, -4.0, and -6.0. Boundary conditions The model horizontal boundary is cyclic. The vertical wind velocity is set to be 0 at the surface and upper boundary. Above 17 km hight, the numerical diffusion is introduced to the horizontal and vertical momentum equations in order to attenuate gravity wave excited by the thermal convection. The value of numerical diffusion coefficient linearly increases from 0 to 1000 m2sec-1 between 17 and 19 km hight. The lower boundary of the grand surface is given as a insulation boundary. The solar flux at the top of model atmosphere diurnally changes under the condition of Ls = 100° at 20°N. It is the same as that used by Pollack et al. (1979). The seasonal condition is around the summer solstice of northern hemisphere (Ls = 90°). The latitudinal condition is close to that of Viking Lander 1 site (22.4°N). Basic state and initial condition The vertical temperature profile at local time (LT) 6:00 calculated by using 1D radiative convective model, which has same representation of radiative and grand surface process as that of 2D model, is adapted to that of basic state atmosphere (Figure C1). The basic state pressure and density are obtained by using hydrostatic equation and equation of state for ideal gas (appendix A.a, appendix B.a.iv). Detail mathematical expressions of the 1D model and its finite differential form are shown in appendix C. Initial condition in dust-free case is motionless atmosphere which has horizontally uniform temperature. The vertical profile of initial atmospheric temperature is same as that of basic state. In order to generate the thermal convection with ease, potential temperature perturbation is randomly imposed on at lowest level (z = 3.125 m). The amplitude of the potential temperature perturbation is ranged between ± 3 K. The vertical profile of initial grand temperature is calculated by using the 1D model which is used for calculation of the atmospheric basic state (Figure C2). Initial condition in dusty case is described in section 4. Time step and computational resources The time interval is 0.5 or 1 second except for radiation process. These values are evaluated by using CFL condition and phase velocity of fast internal gravity wave in the model atmoshpere. The phase velocity of fast internal gravity wave is described as follows; where is Burunt-Vaisara frequency and is the depth of model atmosphere. The time interval using in radiation process is 60 seconds, which is smaller than the time scale of temperature change associated with the thermal convection. If it is assumed that the order of convective wind velocity is 10 msec-1 and depth of convection layer is 1 to 10 km, the time scale of temperature change associated with the thermal convection can be estimated 100 to 1000 sec. The numerical integrations are performed by using Fujitsu VPP 800 at Kyoto University Data Processing Center and Center for PLAnning and INformation Systems, Institute of Space and Astronautical Science. Required CPU time in executing 24 hours integration is about 8 hours.
A numerical simulation of thermal convection in the Martian lower atmosphere.