Scheme using a finite‐volume method for local horizontal derivatives in the spectral model: The non‐hydrostatic case

• Published in: Quarterly journal of the Royal Meteorological Society 2024-10, Vol.150 (765), p.4987-4999
• Main Authors: Yang, Jinhui, Wu, Jianping, Song, Junqiang, Peng, Jun, Yin, Fukang, Leng, Hongze, Ren, Kaijun, Yang, Xiangrong
• Format: Article
• Language: English
• Subjects: Divergence; finite‐volume method; Gradients; idealized tropical cyclone; non‐hydrostatic spectral model; spectral transform; Weather forecasting
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.4852

In a typical non‐hydrostatic spectral dynamic numerical weather prediction (NWP) kernel, all forecast variables are transformed between grid point and spectral spaces to compute their gradients and solve the implicit problem. This kernel requires numerous spectral transformations, which depend heavily on extensive global communication and significantly hinder parallel computing efficiency. This paper introduces an innovative non‐hydrostatic spectral kernel that incorporates a finite‐volume method within the spectral framework. We have developed a horizontal divergence (D)‐based structure equation, allowing direct computation of most prognostic variables and their horizontal gradients at grid point space. By doing so, the need for spectral transformations is substantially decreased. Our experiments demonstrate that this new approach reduces the cost of spectral transformations by up to 40%, enhancing the overall model efficiency by 15%–22%. Additionally, a series of tests confirmed the accuracy and stability of this new solver. This paper proposes a new non‐hydrostatic spectral solver by applying a finite‐volume method (FVM) into the spectral framework, where a horizontal divergence (D)‐ based structure equation is constructed and most of the prognostic variables as well as their horizontal gradients are calculated in grid point space directly. The number of spectral transforms is dramatically reduced. In practice, the cost of spectral transform with the proposed solver is reduced up to 40%.