A Stretched Icosahedral Grid by a New Grid Transformation

This study developed a general grid transformation method for a horizontal grid system on a sphere. The method incorporates the currently used Schmidt transformation method, as well as a new technique that includes intuitive interpretation of the Schmidt transformation. To apply the method, we developed an estimation function that considers both isotropy and homogeneity, and the transformation function uses a governing differential equation to ensure that the function takes the minimum value. Since the proposed transformation method avoids the too-fine grid at the center of the target region, which arises due to the Schmidt transformation method, the new method is superior in terms of computational efficiency. We applied the new transformation to an icosahedral grid. To investigate the stretching effect by this method, we conducted an advection test case using the standard experiment for the shallow water model (Williamson et al. 1992). The error growth rate was minimized over the target region where the fine grid area was distributed. The transition zone between the target region and the coarser grid region exhibited smooth advection, so no spurious error occurred.