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

Abstract

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.

Reproducibility of Equatorial Kelvin Waves in a Superparameterized MIROC: 1. Implementation and Verification of Blockwise‐Coupled SP‐MIROC

“…However, we identified a bias of excessive ice clouds. As discussed in Yamazaki and Miura (2024b) of this study, the amplitude boost of EKWs was enabled by a top-heavy heating in SP-MIROC. No notable artifact was identified in the fields simulated by the 4 × 4-bundled SP-MIROC and the mean states were found to be similar between nonbundled and 4 × 4-bundled SP-MIROC.…”

“…In contrast, the amplitude of SP-MIROC waves is stronger and closer to that of the analyses. As discussed in Yamazaki and Miura (2024b), top-heavy heating in SP-MIROC, compared to CTL-MIROC, is responsible for the intensified EKWs. Organized precipitating systems in the tropics consist of convective cores and stratiform areas, which have a top-heavy heating profile favorable for EKW growth (Fuchs et al, 2012).…”

“…In our companion paper Yamazaki and Miura (2024b), the mechanism responsible for intensified EKWs in SP-GCMs are explored using linear stability analyses with the basic states taken from the MIROC and SP-MIROC experiments described in this paper.…”

“…used in this study are listed in Table1. To avoid complexities arising from potentially wavenumber-dependent excitation mechanisms, a narrow window employed by Nakamura and Takayabu (2022) was adopted for the EKW; the mechanisms are explored in details inYamazaki and Miura (2024b) of our work. Because the excitation mechanisms of other waves are beyond the scope of this work, broadband windows employed by…”