Atmospheric Dynamics Modeling Group / Projects

Numerical Techniques for Global Atmospheric Models

Boulder, CO, June 1-13, 2008

Organized by Peter H. Lauritzen (NCAR), Christiane Jablonowski (University of Michigan), Mark Taylor (Sandia National Laboratories) and Ramachandran D. Nair (NCAR)

The 2-week summer colloquium titled "Numerical Techniques for Global Atmospheric Models" surveyed the latest developments in numerical methods for the dynamical cores of Atmospheric General Circulation Models. The objectives of the colloquium were (1) to teach a large group of about 40 graduate students in atmospheric science and mathematics how today's and future dynamical cores are or need to be built, (2) to invite over 10 dynamical core modeling groups to NCAR for an unprecedented student-run dynamical core intercomparison project, (3) to establish new dynamical core test cases in the community and (4) to invite keynote speakers to NCAR that give lectures on modern numerical techniques and innovative computational meshes.

Adaptive Mesh Refinement (AMR) techniques provide an attractive framework for atmospheric flows since they allow an improved resolution in limited regions without requiring a fine grid resolution throughout the entire model domain. The model regions at high resolution are kept at a minimum and can be individually tailored towards the research problem associated with atmospheric model simulations.

An adaptive grid is a virtual necessity for resolving a problem with different and varying length scales. In order to avoid under-resolving high-gradient regions in the problem, or conversely, over-resolving low-gradient regions at the expense of more critical regions, a model instead adapts to resolve regions with the requisite detail. Climate and weather models, or generally speaking computational fluid dynamics (CFD) codes, are among the many applications that are characterized by multiscale phenomena and their resulting interactions. For instance, large-scale weather systems such as midlatitude cyclones drive small-scale frontal zones, thunderstorms or rain events. These small-scale features may then influence the larger scale if, as an example, evaporation processes and turbulence at the surface trigger sensible and latent heat fluxes.

Our research focuses on the development of AMR techniques for the dynamical cores of atmospheric General Circulation Models and their 2D shallow water counterparts. In particular, we investigate block-structured adaptive meshes on the sphere in both latitude-longitude and so-called cubed-sphere grid geometries. Our numerical schemes of choice are conservative and monotonic Finite-Volume methods that are free of spurious numerical oscillations. Furthermore, we assess grid reflection and wave propagation properties on adapted meshes, and investigate optimal remapping techniques for cubed-spheres and latitude-longitude grids.

 

Figure: Examples of the adaptive mesh refinement technique applied to a block-structured Finite-Volume shallow water model. All blocks are self-similar and contain 9x6 additional grid points. The figures show how the refined regions track the relative vorticity fields of a barotropic instability (left) and an idealized tropical cyclone in the Southern Hemisphere (right).

There are many factors that influence the formation anddevelopment of tropical cyclones in the Atlantic Ocean Basin. Among them are variations in sea surface temperatures, dust aerosol loading of the air, wind distributions, and convection. These variations contribute significantly to the annual and decadal fluctuations of tropical cyclone activity, but with various strengths. Today, one of the most uncertain questions in hurricane research is the impact of African dust and the Saharan Air Layer on tropical cyclogenesis. The triggering mechanisms for the formation of hurricanes greatly depend on the conditions in the Atlantic basin, and in particular on the interaction between dust, the Saharan Air Layer, and African Easterly Waves.

The goal of this research is to model the influences of African dust and the Saharan Air Layer on the development of tropical cyclones. For these model studies an idealized initial cyclonic vortex is introduced into a general circulation models under idealized environment conditions, including the National Center for Atmospheric Research's (NCAR) Community Atmospheric Model (CAM) and in the future NASA's Goddard Earth Observing System Model, version 5 (GEOS-5). Additionally, this method will be implemented in NCAR's Weather Research and Forecasting (WRF) Model. WRF will be modified to inject African dust into the atmosphere over the Atlantic Ocean to study the impact of African dust and the Saharan Air Layer on tropical Cyclogenesis. Understanding these processes and correlations will better help the United States and other countries prepare for future hurricane seasons.

Figure: Idealized cyclone simulations with NCAR's CAM 3.1 model in aqua-planet configuration (using the Finite Volume (FV) dynamical core). The top row displays the magnitude of the wind near the surface at the resolution 0.25 x 0.25 degrees with an initial maximum wind of 17.8 m/s. The initial radius of maximum wind is 200 km. Results for the initial vortex (day 0), and the vortex after 5 and 10 days are shown. The bottom row displays the wind magnitude for a vertical cross section through the center latitude of the vortex as a function of the radius from the center of the vortex [Reed and Jablonowski, 2008].

In this project we are looking to assess the QBO behavior in both modeled data (CAM) as well as the ERA40 Reanalysis data, which will allow us to compare observational data to modeled QBO-like mechanisms. The QBO is a phenomenon taking place in the equatorial stratosphere where the zonal wind oscillates between westward and eastward phase with a period of about 28 months. The QBO is believed to be driven by equatorially trapped vertically propagating waves, in particular Kelvin and Mixed Rossby-Gravity waves, which would act as momentum sources. These waves are thought to originate from tropical convection.

In order to evaluate the QBO behavior and the phenomena that triggers it we make use of the following concepts: the Transformed Eularian Mean (TEM) equations as well as wavenumber-frequency diagrams (Wheeler-Kiladis) -- all this with the aid of National Center for Atmospheric Research's (NCAR) command language NCL. The wavenumber-frequency diagrams can tell us if certain wave types are present in the data, such as Kelvin or Rossby-Gravity waves. Kelvin waves are expected to have periods of about 15 days, with zonal wavenumber of about 1-2, and usually observed when mean zonal flow is easterly. Rossby-Gravity waves are expected to have 4-5 days period, with zonal wavenumber about 4, and usually observed hen mean zonal flow is westerly. Figures 1-3 illustrate such diagrams, derived from both model data, as well as reanalysis data (ERA40).

Fig 1 (Left): Wheeler-Kiladis wavenumber-frequency diagram for temperature during Jan-Jun 1980 (easterly regime), at 50mb altitude, between 10S-10N. Kelvin wave stands out, with wavenumber of about 1 and period of 15-20 days. Fig 2 (Right): Wheeler-Kiladis wavenumber-frequency diagram for temperature during Jun-Nov 1980 (westerly regime), at 30mb altitude, between 10S-10N. A Rossby-Gravity wave signal can be picked out at about wavenumber 4-5, with a frequency of about 3-5 days.

Tests of atmospheric General Circulation Models (GCMs) and, in particular, tests of their dynamical cores are important steps towards future model improvements. They reveal the influence of an individual model design on climate and weather simulations and indicate whether the circulation is described representatively by the numerical approach. However, testing a global 3D atmospheric model and it dynamical core is not straightforward.

In the absence of non-trivial analytic solutions, the model evaluations most commonly rely on intuition, experience and model intercomparisons. The dynamical core describes the fluid flow component of GCMs.

We develop idealized test cases for dynamical cores and conduct international dynamical model intercomparisons. An example of a dynamical core test is the evolution of a baroclinic wave that is also depicted in the figure below. In addition, we work on test cases with intermediate complexity that include simple moisture feedbacks, e.g. for tropical cyclone-like simulations.

Figure: Surface pressure field at day 9 of the baroclinic instability test case simulated with 9 different dynamical cores. The tests starts with balanced initial conditions that are overlaid by a Gaussian hill perturbation. The grid imprint of the cubed-sphere and icosahedral grids can be seen in the Southern Hemisphere (GEOS-FVCUBE, GME, ICON, OLAM). Spectral ringing appears in CAM-EUL and HOMME. The baroclinic wave test is documented in Jablonowski and Williamson (QJ, 2006) and in the Jablonowski and Williamson NCAR Technical Report TN-469+STR (2006).

The goal of this research project is to assess and quantify the role of unresolved subgrid-scale mixing processes in the dynamical cores of state-of-the-art General Circulation Models (GCMs). The representation of the subgrid scale in GCMs is complex. Besides physical processes to be represented, numerical errors manifest themselves as subgrid-scale diffusion, and mixing is used to assure numerical stability and to compensate for numerical dispersion errors. The quantitative effect of physical mixing is therefore conflated with mixing processes associated with filtering, implicit and explicit diffusion and numerical errors. This raises new questions concerning the accuracy, stability and climate sensitivity of today's climate modeling approaches.

We focus our research on the numerical schemes used in NCAR's Community Atmosphere Model, version 3 (CAM3.x). This model has options for three (soon five) very different dynamical cores. These are the spectral-transform Eulerian and semi-Lagrangian dynamical cores as well as the Finite Volume dynamics package. All three are well established to propagate resolved, long-scale, structures with credible accuracy. However, they all treat small-scales differently, from the point of view of both physical processes and numerical construction. We perform a set of numerical experiments with increasing complexity. In particular, we analyze the subgrid-scale characteristics of idealized dynamical core experiments like baroclinic instability studies, perform long-term Held-Suarez climate runs with idealized forcing functions and assess aqua-planet simulations with intermediate complexity. In addition, the subgrid-scale mixing in tracer transport experiments are investigated. The goal is to develop evaluation techniques that can be determined in simple tests and used as predictors of the performance in climate models.

Figure: Results of the Held-Suarez test (Held and Suarez, BAMS (1994)) simulated with the Finite-Volume dynamical core of NCAR's CAM3.5 model. The model resolution is 1 x 1 degrees with 26 vertical levels. Left: Snapshot of the 800 hPa relative vorticity field at day 1220, right: 900-day-mean zonal-mean Eddy temperature variance.