| 
| B.a.ii. Thermodynamic equation |  
The advection terms
 of Equation (A.4)
(see Appendix A.a)
are evaluated by a fourth-order centered scheme. For time integration,
the forward scheme is adopted for the friction terms,  and  ,
the radiative heating term,  ,
and the dissipative heating term,  .
The calculation method for the radiative heating term is shown in 
Appendix B.d.. 
 
|  | (B.13) |  
 
|  | (B.14) |  
 
 
 
 
 
 
 
|  | (B.18) |  
 
 
 |