B. Finite difference equations of the model
 B.e. Ground surface

The time integration of 1D thermal conduction equation of ground surface (A.55) in appendix A.e is performed by the Crank-Nicolson scheme. The space differencing in (A.55) is evaluated by the second order centered scheme. The ground temperature and vertical grid interval are evaluated on the grid point and the heat flux is evaluated on the half grid point. The number of vertical grid point is and the suffix varies from the lowest grid point. The is assumed to the surface temperature

 (B.59)

Where . When the terms at are moved to left hand side and the terms at are moved to right hand side, then

 (B.60)

Where . When , this equation can be represented in matrix form as follows.

 (B.61)

The matrix are J'-th order square matrix and these elements are

Considering the upper boundary condition (A.56) and insurate lower boundary, (B.61) is modified as follows.

 (B.62)

Therefore,

 (B.63)

where the first and th diagonal element of are represented as follows.

is a column vector whose dimension is and which elements are represented as follows.

A numerical simulation of thermal convection in the Martian lower atmosphere.
Odaka, Nakajima, Ishiwatari, Hayashi,   Nagare Multimedia 2001