Reproducibility of Equatorial Kelvin Waves in a Super-Parameterized MIROC: 2. Linear Stability Analysis of In-Model Kelvin Waves

While low-resolution climate models at present struggle to appropriately simulate convectively coupled large-scale atmospheric disturbances such as equatorial Kelvin waves (EKWs), superparameterization helps better reproduce such phenomena. To evaluate such model differences based on physical mechanisms, a linearized theoretical framework of convectively coupled EKWs was developed in a form readily applicable to model evaluation by allowing background stability and diabatic heating to have arbitrary vertical profiles rather than assuming simplified ones. A system of linearized equations of convection-coupled gravity waves was derived as a two-dimensional model of the convectively coupled EKWs. In this work, the basic states are taken from observations, CTL-MIROC and SP-MIROC experiments introduced in Part 1. The tendency of convectively coupled gravity waves to grow faster under top-heavy heating is confirmed for realistic stratification profiles, as found in previous studies under constant stratifications. A comparison of linear unstable solutions with basic states taken from SP-MIROC and CTL-MIROC shows that the top-heavy heating profile in SP-MIROC largely contributes to the enhancement of the EKW-like unstable modes, while subtle differences of stratification profiles considerably affect EKW behaviors. The bottom-heavy heating bias in the CTL-MIROC likely originates from insufficient modeling of subgrid stratiform precipitation in tropical organized systems. It is desirable to incorporate such stratiform components in cumulus parameterizations to achieve better EKW reproducibility.