Improving the Dynamic Core of a Pseudo-incompressible Model in the η Coordinate

The development of high-resolution mesoscale weather forecast numerical models is an important way to improve torrential rain forecasts. Regional mesoscale models with a spatial resolution of 100 m pose great challenges to current computational resources. A feasible solution to overcome this issue is developing soundproof models to replace fully compressible models. The soundproof models permit relatively larger time steps, considerably improving the integration efficiency. In 2018, the authors developed a test version of a pseudo-incompressible model in a terrain-following mass-based coordinate (η coordinate) based on a soundproof theory, namely the pseudo-incompressible theory. Numerical tests indicate the reliability of the model. However, a key issue of the proposed model is that it does not exclude acoustic waves. In this paper, the authors improve the previously reported pseudo-incompressible model and establish a new dry-air dynamic core for the model. A key improvement in the governing equations of the new dynamic core is that it solves an elliptic equation for perturbation pressure, which theoretically ensures the exclusion of acoustic waves. The time-integration scheme of the new dynamic core is more concise, removing the time-split algorithm. The authors compare the simulation results of the improved pseudo-incompressible model with those of the WRF (weather research and forecasting) model for a dry, hot bubble numerical test. The results show that the dynamic and thermodynamic field distributions obtained by the improved pseudo-incompressible model are similar to those of the WRF model, and the simulated perturbation pressure–time series is smooth, indicating that acoustic waves are indeed removed by the improved version of the model. This is a remarkable improvement over the 2018 version of the model.