Bridging Scales in 2- and 3-Dimensional Atmospheric Modeling with Adaptive Mesh Refinement

Abstract

Complex multi-scale atmospheric phenomena, like tropical cyclones, challenge conventional weather and climate models, which use relatively coarse uniform-grid resolutions to cope with computational costs. Adaptive Mesh Refinement (AMR) techniques mitigate these challenges by dynamically and transiently placing high-resolution grids over salient features, thus providing sufficient local resolution while limiting the computational burden.

This thesis explores the development of AMR, a technique that has been featured only sporadically in the atmospheric science literature, within a new nonhydrostatic, finite-volume dynamical core and demonstrates AMR's effectiveness in improving model accuracy and ability to resolve multi-scale features. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique developed with the Chombo AMR library. The AMR dynamical core is implemented in a hierarchy of models of increasing complexity, from an idealized 2D shallow water configuration to the nonhydrostatic 3D equation set with subgrid-scale parameterizations schemes. AMR's numerical accuracy, computational efficiency, and ability to track and resolve multifaceted and evolving features are assessed with a variety of existing and new test cases, implemented within each model iteration.

Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity, or minimum pressure based thresholds, in order to achieve the best accuracy for cost. Simulations show that the model's AMR can accurately resolve key local features in both shallow water and 3D test cases without requiring global high-resolution grids, as the adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse-fine interfaces. Furthermore, the AMR grids keep degradation of the large-scale smooth flows to a minimum. 2D and 3D physics parameterizations are able to function effectively over multiple levels of refinement, though the parameterizations are sensitive to grid resolution.

AMR is most effective when refinement is triggered early or when the base uniform resolution can partially resolve the features of interests. Very coarse base resolutions lead to large initial errors that cannot be overcome by AMR. However, the addition of refinement later in the simulation still results in significant improvements, especially in resolving small-scale features. The research showed that flow properties, such as strong gradients or rainbands, can be sensitive to small changes in AMR criteria. These may delay the onset of the refinement or alter the shape of the refined area, which impacts the evolution of the flow. With coarse base resolutions, the tagging criteria must therefore be uniquely tailored to capture the early growth phases of the feature of interest. A promising refinement technique is a combination of some initial refinement and AMR. The initial refinement limits error growth at the base resolution and ensures that the model can resolve the feature of interest. Overall, AMR is shown to be a powerful modeling approach that bridges the resolution gap for extreme weather events.