below the surface. Also, to avoid
             division by zero, be sure that the underground 
             input temperatures are non-zero and that the pressure 
             thicknesses of the underground layers are non-zero as well.  
               
==========================================================================

 subroutine  gcm_vert_diff(delt, u, v, t, q, tr, diff_m, diff_t,     &
                    p_half, z_full,                                  &
                    dtau_du, dtau_dv, ds