The research investigates and advances strategies how to bridge the scale discrepancies between local, regional and global phenomena in climate models without the prohibitive computational costs of global cloud-resolving simulations. In particular, the research explores new frontiers in computational geoscience by introducing high-order Adaptive Mesh Refinement (AMR) techniques into climate research. AMR and statically-adapted variable-resolution approaches represent an emerging trend for atmospheric models and are likely to become the new norm in future-generation weather and climate models. The research advances the understanding of multi-scale interactions in the climate system and showcases a pathway how to model these interactions effectively with advanced computational tools, like the Chombo AMR library developed at the Lawrence Berkeley National Laboratory. The research is interdisciplinary and combines applied mathematics, scientific computing and the atmospheric sciences. In this research project, a hierarchy of high-order atmospheric models on cubed-sphere computational grids have been developed that serve as an algorithmic prototype for the finite-volume solution-adaptive Chombo-AMR approach. The foci of the investigations have lied on the characteristics of both static mesh adaptations and dynamically-adaptive grids that can capture flow fields of interest like tropical cyclones. Six research themes have been chosen. These are (1) the introduction of adaptive mesh refinement techniques into the climate sciences, (2) advanced algorithms for nonhydrostatic atmospheric dynamical cores, (3) an assessment of the interplay between resolved-scale dynamical motions and subgrid-scale physical parameterizations, (4) evaluation techniques for atmospheric model hierarchies, (5) the comparison of AMR refinement strategies and (6) tropical cyclone studies with a focus on multi-scale interactions and variable-resolution modeling. The results of this research project demonstrate significant advances in all six research areas. The major conclusions are that statically-adaptive variable-resolution modeling is currently becoming mature in the climate sciences, and that AMR holds outstanding promise for future-generation weather and climate models on high-performance computing architectures.

This is an overview of the development of adaptive techniques for atmospheric modeling. Written in an educational style, it functions as a starting point for readers interested in adaptive modeling, in atmospheric sciences and beyond. Coverage includes paradigms of adaptive techniques, such as error estimation and adaptation criteria. Mesh generation methods are presented for triangular/tetrahedral and quadrilateral/hexahedral meshes, with a special section on initial meshes for the sphere.

Downscaling is a widely used technique for translating information from large-scale climate models to the spatial and temporal scales needed to assess local and regional climate impacts, vulnerability, risk and resilience. This book is a comprehensive guide to the downscaling techniques used for climate data. A general introduction of the science of climate modeling is followed by a discussion of techniques, models and methodologies used for producing downscaled projections, and the advantages, disadvantages and uncertainties of each. The book provides detailed information on dynamic and statistical downscaling techniques in non-technical language, as well as recommendations for selecting suitable downscaled datasets for different applications. The use of downscaled climate data in national and international assessments is also discussed using global examples. This is a practical guide for graduate students and researchers working on climate impacts and adaptation, as well as for policy makers and practitioners interested in climate risk and resilience.

Numerical modeling of conserved atmospheric fields is critical to weather prediction and climate simulation. Atmospheric dynamics often distort these fields into long filamentary structures that are difficult to model, because the extreme aspect ratios of the filaments present a wide range of spatial scales that need to be resolved. A method of dealing with these differing spatial scales is to use a dynamic adaptive grid (DAG) technique, which continuously moves grid points in response to changes in the tracer field to give higher resolution where small spatial scales are prominent. The Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) of Smolarkiewicz is used to solve the advection equation on a moving grid. As the number of grid points increases, instabilities in MPDATA with an adaptive grid occur due to violation of the CFL condition. Analysis of the problem leads to a method of limiting grid point movement to maintain stability.

The topics of climate change, weather prediction, atmospheric sciences and other related fields are gaining increased attention due to the possible impacts of changes in climate and weather upon the planet. Concurrently, the increasing ability to computationally model the governing partial differential equations that describe these various topics of climate has gained a great deal of attention as well. In the current book, several aspects of these topics are examined to provide another stepping stone in recent advances in the fields of study and also focal points of endeavor in the evolving technology.