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A semi-Lagrangian version of the National Center for Atmospheric Research Community Climate Model is developed. Special consideration is given to energy consistency aspects. In particular, approximations are developed in which the pressure gradient in the momentum equations is consistent with the energy conversion term in the thermodynamic equation. In addition, consistency between the discrete continuity equation and the vertical velocity ω in the energy conversion term of the thermodynamic equation is obtained. Simulated states from multiple-year simulations from the semi-Lagrangian and Eulerian versions are compared. The principal difference in the simulated climate appears in the zonal average temperature. The semi-Lagrangian simulation is colder than the Eulerian at and above the tropical tropopause. The terms producing the thermodynamic balance are examined. It is argued that the semi-Lagrangian scheme produces less computational smoothing of the temperature at the tropopause than the first-order finite-difference vertical advection approximations in the Eulerian version. Thus, by decreasing this particular computational error, the semi-Lagrangian produces less computational warming at the tropical tropopause. The net result is a colder tropical tropopause.
Williamson et al. (Fri,) studied this question.