A Comparison of Semi-Lagrangian and Eulerian Tropical Climate Simulations

Abstract

At the modest vertical resolutions typical of climate models, simulations produced by models based on semi-Lagrangian approximations tend to develop a colder tropical tropopause than matching simulations from models with Eulerian approximations, all other components of the model being the same. The authors examine the source of this relative cold bias in the context of the NCAR CCM3 and show that it is primarily due to insufficient vertical resolution in the standard 18-level model, which has 3-km spacing near the tropopause. The difference is first diagnosed with the Held and Suarez idealized forcing to eliminate the complex radiative?convective feedback that affects the tropopause formation in the complete model. In the Held and Suarez case, the tropical simulations converge as the vertical grid layers are halved to produce 36 layers and halved again to produce 72 layers. The semi-Lagrangian approximations require extra resolution above the original 18 to capture the converged tropical tropopause. The Eulerian approximations also need the increased resolution to capture the single-level tropopause implied by the 36- and 72-level simulations, although with 18 layers it does not produce a colder tropopause, just a thicker multilevel tropopause. The authors establish a minimal grid of around 25 levels needed to capture the structure of the converged simulation with the Held and Suarez forcing. The additional resolution is added between 200 and 50 mb, giving a grid spacing of about 1.3 km near the tropopause. With this grid the semi-Lagrangian and Eulerian approximations also create the same tropical structure in the complete model. With both approximations the convective parameterization is better behaved with the extra upper-tropospheric resolution. A benefit to both approximations of the additional vertical resolution is a reduction of the tropical temperature bias compared to the NCEP reanalysis. The authors also show that the Eulerian approximations are prone to stationary grid-scale noise if the vertical grid is not carefully defined. The semi-Lagrangian shows no indication of stationary vertical-grid-scale noise. In addition, the Eulerian simulation exhibits significantly greater transient vertical-grid-scale noise than the semi-Lagrangian.