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Optimized vertical layers for the Hybrid Terrain-Following Coordinate Minimizing Numerical Errors in a 2D Rising Bubble Experiment near Steep Terrain

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Journal of Meteorological Research 2023年第6期37卷 896-907页

作者： Hao YANG Yiyuan LI Bin WANG State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing100029China College of Earth and Planetary Sciences University of Chinese Academy of SciencesBeijing100049China

The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep *** terrain-following(HTF)coordinates with smooth slopes of vertical layers(slopeVL)generally overcome this ***,the HTF coordinate becomes very desirable for atmospheric and oceanic numerical ***,improper vertical layering in HTF coordinates may also increase the incidence of *** for the slopeVL of an HTF coordinate,this study further optimizes the HTF coordinate focusing on the thickness of vertical layers(thickVL).Four HTF coordinates(HTF1–HTF4)with similar slopeVL but different vertical transition methods of thickVL are designed,and the relationship between thickVL and numerical errors in each coordinate is compared in the classic idealized thermal convection[two-dimensional(2D)rising bubble]experiment over steep *** errors of potential temperatureθand vertical velocity w are reduced most,by approximately 70%and 40%,respectively,in the HTF1 coordinate,with a monotonic increase in thickVL according to the increasing height;however,the errors ofθincreased in all the other HTF coordinates,with nonmonotonic ***,analyses of the errors of vertical pressure gradient force(VPGF)show that due to the interpolation errors of thickVL,the inflection points in the vertical transition of thickVL induce the initial VPGF errors;therefore,the HTF1 coordinate with a monotonic increase in thickVL has the smallest errors among all the *** importantly,the temporal evolution of VPGF errors manifests top-type VPGF errors that propagate upward gradually during the time *** the HTF1 and HTF4 coordinates with a monotonic increase in thickVL near the top of the terrain can suppress this *** optimized HTF coordinate(i.e.,HTF1)can be a reference for designing a vertical thickVL in a numerical model.

关键词： hybrid terrain-following coordinate thickness of vertical layer numerical error pressure gradient force two-dimensional(2D)rising bubble experiment steep terrain

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