Development of an atmospheric climate model with self-adapting grid and physics

An adaptive grid dynamical core for a global atmospheric climate model has been developed. Adaptations allow a smooth transition from hydrostatic to non-hydrostatic physics at small resolution. The adaptations use a parallel program library for block-wise adaptive grids on the sphere. This library also supports the use of a reduced grid with coarser resolution in the longitudinal direction as the poles are approached. This permits the use of a longer time step since the CFL number restriction (CFL < 1) in a regular longitude-latitude grid is most severe in the zonal direction at high latitudes. Several tests show that our modelling procedures are stable and accurate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49004/2/jpconf5_16_049.pd

Three dimensional adaptive mesh refinement on a spherical shell for atmospheric models with lagrangian coordinates

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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58181/2/jpconf7_78_012072.pd

3D cut-cell modelling for high-resolution atmospheric simulations

Owing to the recent, rapid development of computer technology, the resolution of atmospheric numerical models has increased substantially. With the use of next-generation supercomputers, atmospheric simulations using horizontal grid intervals of O(100) m or less will gain popularity. At such high resolution more of the steep gradients in mountainous terrain will be resolved, which may result in large truncation errors in those models using terrain-following coordinates. In this study, a new 3D Cartesian coordinate non-hydrostatic atmospheric model is developed. A cut-cell representation of topography based on finite-volume discretization is combined with a cell-merging approach, in which small cut-cells are merged with neighboring cells either vertically or horizontally. In addition, a block-structured mesh-refinement technique is introduced to achieve a variable resolution on the model grid with the finest resolution occurring close to the terrain surface. The model successfully reproduces a flow over a 3D bell-shaped hill that shows a good agreement with the flow predicted by the linear theory. The ability of the model to simulate flows over steep terrain is demonstrated using a hemisphere-shaped hill where the maximum slope angle is resolved at 71 degrees. The advantage of a locally refined grid around a 3D hill, with cut-cells at the terrain surface, is also demonstrated using the hemisphere-shaped hill. The model reproduces smooth mountain waves propagating over varying grid resolution without introducing large errors associated with the change of mesh resolution. At the same time, the model shows a good scalability on a locally refined grid with the use of OpenMP.Comment: 19 pages, 16 figures. Revised version, accepted for publication in QJRM

Cascades, backscatter and conservation in numerical models of two‐dimensional turbulence

The equations governing atmospheric flow imply transfers of energy and potential enstrophy between scales. Accurate simulation of turbulent flow requires that numerical models, which have finite resolution and truncation errors, adequately capture these interscale transfers, particularly between resolved and unresolved scales. It is therefore important to understand how accurately these transfers are modelled in the presence of scale‐selective dissipation or other forms of subgrid model. Here, the energy and enstrophy cascades in numerical models of two‐dimensional turbulence are investigated using the barotropic vorticity equation. Energy and enstrophy transfers in spectral space due to truncated scales are calculated for a high‐resolution reference solution and for several explicit and implicit subgrid models at coarser resolution. The reference solution shows that enstrophy and energy are removed from scales very close to the truncation scale and energy is transferred (backscattered) into the large scales. Some subgrid models are able to capture the removal of enstrophy from small scales, though none are scale‐selective enough; however, none are able to capture accurately the energy backscatter. We propose a scheme that perturbs the vorticity field at each time step by the addition of a particular vorticity pattern derived by filtering the predicted vorticity field. Although originally conceived as a parametrization of energy backscatter, this scheme is best interpreted as an energy ‘fixer’ that attempts to repair the damage to the energy spectrum caused by numerical truncation error and an imperfect subgrid model. The proposed scheme improves the energy and enstrophy behaviour of the solution and, in most cases, slightly reduces the root mean square vorticity errors.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106663/1/2166_ftp.pd