Articles | Volume 19, issue 21
https://doi.org/10.5194/gmd-19-10821-2026
https://doi.org/10.5194/gmd-19-10821-2026
Development and technical paper
 | 
13 Nov 2026
Development and technical paper |  | 13 Nov 2026

Development and improvement of a nonhydrostatic spectral model using non-constant coefficient semi-implicit and vertically conservative semi-Lagrangian schemes

Hiromasa Yoshimura

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Cited articles

Bénard, P.: Stability of semi-implicit and iterative centered-implicit time discretizations for various equation systems used in NWP, Mon. Weather Rev., 131, 2479–2491, https://doi.org/10.1175/1520-0493(2003)131<2479:SOSAIC>2.0.CO;2, 2003. 
Bénard, P., Mašek, J., and Smolíková, P.: Stability of Leapfrog Constant-Coefficients Semi-Implicit Schemes for the Fully Elastic System of Euler Equations: Case with Orography, Mon. Weather Rev., 133, 1065–1075, https://doi.org/10.1175/MWR2907.1, 2005. 
Bénard, P., Vivoda, J., Mašek, J., Smolíková, P., Yessad, K., Smith, Ch., Brožková, R., and Geleyn, J.-F.: Dynamical kernel of the Aladin–NH spectral limited-area model: Revised formulation and sensitivity experiments, Q. J. Roy. Meteor. Soc., 136, 155–169, https://doi.org/10.1002/qj.522, 2010. 
Bubnová, R., Hello, G., Bénard, P., and Geleyn, J.-F.: Integration of the fully elastic equations cast in the hydrostatic pressure terrain-following coordinate in the framework of the ARPEGE/Aladin NWP system, Mon. Weather Rev., 123, 515–535, https://doi.org/10.1175/1520-0493(1995)123<0515:IOTFEE>2.0.CO;2, 1995. 
Dueben, P. D., Wedi, N., Saarinen, S., and Zeman, C.: Global simulations of the atmosphere at 1.45 km grid-spacing with the Integrated Forecasting System, J. Meteorol. Soc. Jpn., 98, 551–572, https://doi.org/10.2151/jmsj.2020-016, 2020. 
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Short summary
We have developed a two-dimensional x–z nonhydrostatic spectral model that achieves high computational efficiency by allowing long timesteps. The model incorporates several improvements that enhance numerical stability and accuracy. The model was tested with various cases, and good results were obtained. The model ran stably even in the case of an extremely steep mountain with an average slope of 63.4°. These improvements will be applied to a global atmospheric model in future work.
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