The Earth and Environmental Systems Sciences Division (EESSD) has recently emphasized the need for continued development of Earth system models to strengthen our understanding and predictive skill of weather and climate. Progress toward accurate climate simulations is impeded by known model biases linked to parameterized processes, particularly those in the tropical atmosphere-ocean system. Climate simulations improve when model grid resolutions approach the characteristic scales of key phenomena such as clouds and ocean eddies. However, simulations with enhanced, globally uniform resolution can require extreme computational resources. Models that utilize variable-resolution global grids balance the benefits of fine-scale resolution in targeted areas with the burden of increased computational demand. As part of the Multiscale Methods for Accurate Efficient and Scale-Aware Models of the Earth System"" project variable-resolution climate models are being used to develop test and implement ""scale-aware"" parameterization schemes and advanced numerical methods and prepare these dynamical cores for future many-core computing architectures providing greater resolution. We review recent progress in our effort to advance a variable-resolution climate model with dynamic adaptive mesh refinement (AMR) capabilites called Chombo-AMR. Chombo-AMR has a numerical integration accuracy and computational scalability that permit refined-grid patches to migrate with an unlimited number of targeted evolving features of interest rather than requiring enhanced resolution over the entire space-time domain. Preliminary simulations reveal Chombo-AMR's ability to preserve sharp gradients in increasingly complex dynamical test settings. Additionally version 5 of NCAR's Community Atmosphere Model physics parameterization package is being incorporated into Chombo-AMR to more accurately account for unresolved physical processes. The model will soon be utilized to explore several computational and scientific multiscale climate modeling issues including physical processes coupling both in the temporal domain and in the nonhydrostatic regime (for grid meshes <10 km) the scale-awareness of physical parameterizations and the simulation of complex flows associated with orography and coastal boundaries. The strengths of AMR are also optimally aligned to examine key climatic phenomena such as the Madden-Julian oscillation and tropical cyclones which feature nonstationary and intermittent dynamics fueled by small-scale latent heat release within cumulus convection and characterized by multiscale interactions.