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

Abstract 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.