Elimination of spectral blocking by ensuring rotation‐free property of discretized pressure gradient within a spectral semi‐implicit semi‐Lagrangian global atmospheric model

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 145; no. 724; pp. 3351 - 3358
• Main Authors: Ujiie, Masashi, Hotta, Daisuke
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.10.2019; Wiley Subscription Services, Inc
• Subjects: Atmospheric models; Isobaric surfaces; mimetic discretization; Prediction models; Pressure; pressure gradient; Pressure gradients; Primitive equations; Rotation; spectral blocking; spectral method; Weather forecasting
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.3636

The widely‐adopted discretization of the horizontal pressure gradient term formulated by Simmons and Burridge for atmospheric models on σ‐p hybrid vertical coordinate is found to incur spectral blocking for rotational wind components at high vertical levels when used in a spectral semi‐Lagrangian model run on a linear grid. A remedy to this issue is proposed and tested using a spectral semi‐implicit semi‐Lagrangian hydrostatic primitive equations model. The proposed method removes aliasing errors at high wave‐numbers by ensuring that the rotation‐free property of the pressure gradient term on the isobaric surface, a feature possessed by the continuous system, is preserved in the discretized system, which highlights the significance of mimetic discretization within the context of numerical weather prediction models. Kinetic energy spectra of 48 h forecasts produced by JMA‐GSM with (a,c) previous and (b,d) new pressure gradient discretization schemes, for (a,b) an upper‐level (81st model level, ∼11 hPa) and (c,d) a middle level (51st model level, ∼180 hPa). On each panel, the rotational and divergent components are plotted, respectively, with thick and thin lines. Units are m2/s2. Note the log scale on both axes. The forecasts are initialised with JMA's operational deterministic analysis valid at 25 December 2018, 1200 UTC.