Adaptive mesh refinement techniques offer a flexible framework for future variable-resolution climate and weather models since they can focus their computational mesh on certain geographical areas or atmospheric events. Adaptive meshes can also be used to coarsen a latitude-longitude grid in polar regions. This allows for the so-called reduced grid setups. A spherical, block-structured adaptive grid technique is applied to the Lin-Rood finite-volume dynamical core for weather and climate research. This hydrostatic dynamics package is based on a conservative and monotonic finite-volume discretization in flux form with vertically floating Lagrangian layers. The adaptive dynamical core is built upon a flexible latitude-longitude computational grid and tested in two- and three-dimensional model configurations. The discussion is focused on static mesh adaptations and reduced grids. The two-dimensional shallow water setup serves as an ideal testbed and allows the use of shallow water test cases like the advection of a cosine bell, moving vortices, a steady-state flow, the Rossby-Haurwitz wave or cross-polar flows. It is shown that reduced grid configurations are viable candidates for pure advection applications but should be used moderately in nonlinear simulations. In addition, static grid adaptations can be successfully used to resolve three-dimensional baroclinic waves in the storm-track region.

One of the most important advances needed in global climate models is the development of atmospheric General Circulation Models (GCMs) that can reliably treat convection. Such GCMs require high resolution in local convectively active regions, both in the horizontal and vertical directions. During previous research we have developed an Adaptive Mesh Refinement (AMR) dynamical core that can adapt its grid resolution horizontally. Our approach utilizes a finite volume numerical representation of the partial differential equations with floating Lagrangian vertical coordinates and requires resolving dynamical processes on small spatial scales. For the latter it uses a newly developed general-purpose library, which facilitates 3D block-structured AMR on spherical grids. The library manages neighbor information as the blocks adapt, and handles the parallel communication and load balancing, freeing the user to concentrate on the scientific modeling aspects of their code. In particular, this library defines and manages adaptive blocks on the sphere, provides user interfaces for interpolation routines and supports the communication and load-balancing aspects for parallel applications. We have successfully tested the library in a 2-D (longitude-latitude) implementation. During the past year, we have extended the library to treat adaptive mesh refinement in the vertical direction. Preliminary results are discussed. This research project is characterized by an interdisciplinary approach involving atmospheric science, computer science and mathematical/numerical aspects. The work is done in close collaboration between the Atmospheric Science, Computer Science and Aerospace Engineering Departments at the University of Michigan and NOAA GFDL.

Abstract A spherical 2D adaptive mesh refinement (AMR) technique is applied to the so-called Lin–Rood advection algorithm, which is built upon a conservative and oscillation-free finite-volume discretization in flux form. The AMR design is based on two modules: a block-structured data layout and a spherical AMR grid library for parallel computer architectures. The latter defines and manages the adaptive blocks in spherical geometry, provides user interfaces for interpolation routines, and supports the communication and load-balancing aspects for parallel applications. The adaptive grid simulations are guided by user-defined adaptation criteria. Both statically and dynamically adaptive setups that start from a regular block-structured latitude–longitude grid are supported. All blocks are logically rectangular, self-similar, and independent data units that are split into four in the event of refinement requests, thereby doubling the horizontal resolution. Grid coarsenings reverse this refinement principle. ...

We describe a new parallel program for optimizing and analyzing 3-arm Bernoulli bandit problems. Previous researchers had considered this problem computationally intractable, and we know of no previous exact optimizations of 3-arm bandit problems. Despite this, our program is able to solve problems of size 100 or more. We describe the techniques used to achieve this, and indicate various extensions of the program that enable it to solve a wide range of related problems.