η坐标系下假不可压大气模式动力框架改进

Improving the Dynamic Core of a Pseudo-incompressible Model in theηCoordinate

发展高分辨区域中尺度天气预报模式是改进暴雨落区预报的一个重要途径。区域中尺度模式空间分辨率达到100 m,对当前计算资源提出了严峻挑战。一种可行的解决方案是发展滤除声波的模式替代全弹性模式。滤除声波的模式可以使用较大的时间步长积分,能显著提高积分效率。作者在2018年利用一种声波滤除理论——假不可压理论,初步在地形追随质量坐标系(η坐标系)下建立了假不可压模式。数值试验表明模式的结果是合理可信的,然而关键问题是没有滤除声波。本文改进了假不可压模式,建立新的假不可压模式干动力框架。新动力框架控制方程的关键改进是使用椭圆方程求解扰动气压,理论上保证了声波的滤除。新动力框架的时间积分方案更简洁,不使用时步分裂算法。对比改进的假不可压模式和WRF(Weather Research and Forecasting)模式的干热泡对流数值试验结果,发现假不可压模式获得了与WRF模式相似的动力场和热力场分布,且模拟的气压扰动时间序列平滑,说明声波已被滤除,相比2018版本的假不可压模式,这是较大的改进。

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(ηcoordinate)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.