Advection errors in an orthogonal terrain-following coordinate: Idealized experiments

Abstract

The orthogonal curvilinear terrain-following coordinate (OS-coordinate) can create smooth vertical layers and orthogonal vertical computational grids, therefore reducing the advection errors in the classic terrain-following coordinate. The reduction of advection errors by the OS-coordinate had been validated by the idealized experiments using one kind of terrain and one kind of resolution. We have implemented two more types of 2D linear advection experiments to further analyze the advection errors of the OS-coordinate. The first experiment is to use three kinds of terrain which are one-crest, three-crest, and five-crest wavelike terrain (multi-mountain experiment). And the second experiment is to use five different horizontal (vertical) resolutions (multi-resolution experiment). In both types of the experiments, we compare the advection errors in the OS-coordinate with those in the corresponding hybrid terrainfollowing coordinate (HS-coordinate) to investigate the effect of the OS-coordinate on reducing the advection errors. For the multimountain experiment, the advection errors in the OS-coordinate and those in the HS-coordinate are almost the same in one-crest terrain experiments. And in the three-crest terrain experiments, the advection errors in the OS-coordinate are slightly smaller than those in the HS-coordinate. However, in the five-crest terrain experiment (complex terrain), the advection errors in the OS-coordinate are much reduced comparing with those in the HS-coordinate. This reason is that the OS-coordinate creates the orthogonal computational grids while the HS-coordinate creates the non-orthogonal computational grids. And the differences between these two grids are most significant in the five-crest terrain experiments. Moreover, the differences between these two grids actually represent the different quality of them. This indicates that the OS-coordinate can reduce the advection errors comparing with the corresponding hybrid terrain-following coordinate above the complex terrain, through improving the quality of the vertical computational grids. For the multi-resolution experiments, the advection errors in the OS-coordinate are always smaller than those in the HS-coordinate, and more importantly, the higher the vertical resolution is, the greater the reduction of the advection errors by the OS-coordinate is. All the results obtained by the idealized experiments in this paper indicate that the OS-coordinate may reduce the advection errors near the complex terrain in a high-resolution model.