The talk reviews two approaches to high-order variable-resolution modeling that have recently been designed for atmospheric weather and climate models. The first approach is based on the Adaptive Mesh Refinement (AMR) library Chombo that supports fourth-order finite volume methods for block-structured adaptive meshes on cubed-sphere grids. The Chombo-AMR model has been jointly developed by the Lawrence Berkeley National Laboratory and the University of Michigan. The second variable-resolution grid approach is based on the Spectral Element (SE) method that has been implemented on a cubed-sphere grid in the Community Atmosphere Model (CAM). The latter has been jointly developed by the National Center for Atmospheric Research (NCAR) and various Department of Energy laboratories. 

The talk discusses the characteristics of both variable-resolution mesh techniques using a hierarchy of test cases and fluid flow scenarios. In particular, the AMR-Chombo model is evaluated in the 2D shallow-water framework, and various refinement criteria are compared. The CAM-SE model is first assessed in a dry 3D dynamical core mode. In addition, a water-covered Earth (aqua-planet) configuration and realistic model setups with topography are tested. Tropical cyclones serve as the main motivating example and highlight the scientific potential of the variable-resolution mesh approach. Special attention is paid to the flow conditions in the grid-resolution transition regions that have the potential to exhibit grid imprinting. It is shown that the high-order numerical methods successfully suppress spurious noise without the need for special diffusive mechanisms in the grid transition zones.