Atmospheric Dynamics Modeling Group / Projects

The research projects in our group are focused on the overarching themes of atmospheric modeling and dynamics. Our group is highly interdisciplinary with diverse interests in atmospheric science, applied mathematics and computational science / scientific computing.
In particular, we develop new numerical methods and variable-resolution computational grids for the dynamical cores of atmospheric General Circulation Models (GCMs), analyze and compare existing dynamical cores (especially their behavior at the subgrid-scale), develop test cases for dynamical cores that get utilized in community-wide model intercomparison projects, analyze and improve the respresentation of tropical cyclones in global climate models, investigate stratospheric dynamics with a focus on the Quasi-Biennial Osciillation (QBO) and Sudden Stratospheric Warmings (SSWs), and design cyber-infrastructure tools for the climate sciences. All of our research projects utilize parallel and high-performance computing architectures.

DCMIP Summer School on Future-Generation Non-Hydrostatic Weather and Climate Models

Boulder, CO, July, 30 - August, 10 2012

We (Christiane Jablonowski, Peter Lauritzen, Paul Ullrich, Mark Taylor, Ram Nair) are organizing a summer school and model intercomparison workshop with special focus on non-hydrostatic global models which are under development right now. We are inviting students, postdoctoral researchers and the international dynamical core modeling community to join us at the National Center for Atmospheric Resaearch (NCAR, Boulder, CO) for 2 weeks from July/30-August/10/2012 for an exciting student-focused and research-driven event that will lead to an unprecedented dynamical core intercomparison project, even broader in scale than our 2008 workshop. The event is endorsed by the WMO Working Group on Numerical Experimentation (WGNE). The summer school and model intercomparison workshop will be supported by newly developed cyberinfrastucture tools like shared workspaces that we develop in collaboration with NOAA and NCAR under an NSF grant.

We suggest exploring new test techniques for non-hydrostatic models that are also applicable at hydrostatic scales. Examples are our newly developed tropical cyclone test case of intermediate complexity that not only assesses the dynamical core but also includes a 'simple physics' package. It lets us investigate non-linear interactions and the physics-dynamics coupling. Other test cases might include 'small Earth' experiments that give insight into non-hydrostatic motions at low computational cost. Please contact me (Christiane Jablonowski) if you would like to get more information. The application period for students and postdocs is now open until 3/31/2012.

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.

We have published a book that is based on the lectures from the 2008 Summer Colloquium:
Lauritzen, P. H., C. Jablonowski, M. A. Taylor and R. D. Nair (Eds.) (2011), Numerical Techniques for Global Atmospheric Models, Lecture Notes in Computational Science and Engineering, Springer, Vol. 80, 572 pp.

Figure: Selected results of the dynamical core intercomparison project conducted during the 2008 NCAR ASP summer school. The figure shows a cross section of an advected slotted ellipse after 12 days that was transported up and down and around the sphere via an analytically prescribed 3D wind field. The initial condition and reference solution can be used to assess the characteristics of the advection schemes in the participating models denoted by the acronyms. The horizontal grid spacings are approximately 110 km with 60 levels in the vertical direction (vertical grid spacing is 250 m).

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.

The climate system is characterized by complex nonlinear interactions over a broad range of temporal and spatial scales. Our research objective is to determine how these multi-scales interact and how to use enabling computational tools to mathematically represent scale interactions in climate models. The research focuses in particular on scale interactions in the so-called dynamical core of Atmospheric General Circulation Models (GCM). The dynamical core refers to the fluid dynamics component of a GCM and encompasses the numerical methods used to solve the equations of motion on the resolved scales. The research explores how Adaptive Mesh Refinement (AMR) and other variable resolution grid techniques allow high resolution meshes in regions of interest like the eye of a tropical cyclone or over mountainous terrain. It thereby suggests pathways how to bridge the scale discrepancies between local, regional and global phenomena, a key frontier in climate modeling.

The variable-resolution approach is focused on cubed-sphere computational meshes that have the potential to become a standard in future GCMs. Cubed-sphere grids offer an almost uniform grid point coverage on the sphere. They deliver high performance and almost perfect scaling characteristics on massively parallel computer architectures. The grid is ideally suited for local grid refinements that are based on DoE's AMR software framework Chombo from the Lawrence Berkeley National Laboratory (LBNL). Chombo is under development by DoE's Applied Partial Differential Equations Center (APDEC) under the leadership of our collaborator Dr. Phillip Colella. Both hydrostatic and nonhydrostatic dynamical core designs are developed, implemented and assessed in our team using high-order conservative and oscillation-free finite-volume numerical schemes. In addition, we investigate the numerical schemes in a 2d shallow-water framework that serves as an ideal testbed for 3d model developments. At a later stage our simulations will also involve an in-depth investigation of the validity of physical parameterizations at different spatial scales. The latter will be done in close collaboration with the National Center for Atmospheric Research (NCAR).

   

Figure: Examples of the adaptive mesh refinement and variable-resolution techniques applied to (left, middle) a block-structured Finite-Volume (FV) shallow water model on a latitude-longitude grid and (right) the conformal cubed-sphere grid in NCAR's Spectral Element model. In the model FV all blocks are self-similar and contain 9x6 additional grid points. The figures show (left, middle) how the refined regions track the relative vorticity fields of a barotropic instability and an idealized tropical cyclone in the Southern Hemisphere and (right) a statically-refined mesh over the United States in the model SE (coutesy of our collaborators Mark Taylor and Michael Levy, Sandia National Laboratories).

We develop, implement and test high-order finite-volume methods for the dynamical cores of atmospheric general circulation models. Our computational grid of choice is the cubed-sphere grid that is also depicted above. This project pays special attention to 3rd-order and 4th-order accurate discretizations that perform well at all spatial scales and all aspect ratios between the horizontal and vertical resolution. The methods are promising candidate for future non-hydrostatic dynamical cores with flexible computational grids. Such grids are for example the block-structured AMR grids that overlay the cubed-sphere geometry. We have developed the non-hydrostatic dynamical core 'MCore' in both a Cartesian channel configuration (Ullrich and Jablonowski, Mon. Wea. Rev. 2012) and on a spherical cubed-sphere grid (Ullrich and Jablonowski, 2012, J. Comput. Phys., revised).

Figure: Example simulations with our high-order finite-volume model in a Cartesian channel configuration. The figure depicts 2D and 3D idealized test cases that assess the model performance at small scales (2D thermal bubble), meso-scales (2D mountain waves) and large planetary scales (3D breaking baroclinic wave in a channel). The results are presented in the paper Ullrich and Jablonowski (2012) that is in press in the journal Monthly Weather Review.

This project investigates and improves the representation of tropical cyclones in the National Center for Atmospheric Research (NCAR) Community Earth System Model CESM1. CESM is jointly supported by the Department of Energy (DOE) and the National Science Foundation and contains the Community Atmosphere Model CAM that offers multiple dynamical cores and physics options. In particular, CAM version 5 contains the finite-volume (FV) dynamical core, the High-Order Method Modeling Environment (HOMME), and the spectral transform Eulerian (EUL) and semi-Lagriangian (SLD) dynamical cores.

The objectives of the research are to (1) simulate the evolution of an idealized, initially weak vortex into a tropical cyclone in an aqua-planet configuration of CAM, (2) investigate the sensitivity of tropical cyclone development and structure to varying resolutions and convective parameterizations within CAM, (3) explore the impact of different numerical schemes on the evolution of tropical cyclones through utilization of numerous dynamical cores available in CAM, and (4) use the knowledge gained from these simulations to project the possible effects of climate change on long-term (decadal) tropical cyclone statistics. Such process studies will reveal the impact and relative importance of the physical parameterizations and numerical schemes on the simulations of tropical cyclones in CAM, thereby providing an improved scientific basis for the projections of tropical cyclone activity under changing climate conditions.

We have developed an idealized tropical cyclone test case based on analytic initial conditions that spins up intense (up to category-5) tropical cyclones over the course of 5-10 simulation days. We have also developed a simplified physics package called 'simple physics' for aqua-planet studies that only contains the most basic driving mechanisms for cyclones such as surface fluxes, boundary layer diffusion and large-scale condendation. This physics package lets us define a test case of intermediate complexity.

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 [see also Reed and Jablonowski (Mon. Wea. Rev., 2011), Reed and Jablonowski (JAMES 2011), Reed and Jablonowski (Geophys. Lett., 2011) and Reed and Jablonowski (JAMES 2012)].

In this project we assess the characteristics of the QBO in both model simulations with an idealized version of the Community Atmosphere Model (CAM) as well as the ERA40 Reanalysis data. This allows 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 gravity waves and equatorially trapped vertically propagating waves, in particular Kelvin and Mixed Rossby-Gravity waves, which act as momentum sources. These waves are thought to originate from tropical convection.

In order to evaluate the QBO behavior and the phenomena that trigger it we make use of the following concepts: the Transformed Eularian Mean (TEM) equations as well as wavenumber-frequency diagrams (Wheeler-Kiladis). The wavenumber-frequency diagrams reveal if certain wave types are present in the data, such as Kelvin or mixed 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. Mixed Rossby-Gravity waves are expected to have a 4-5-day period, with zonal wavenumber about 4 They are usually observed when the mean zonal flow is westerly. The figures below illustrate such diagrams, derived from both CAM model data with the semi-Langrian dynamical core, as well as reanalysis data (ERA40). We will also apply our analysis technique to Sudden Stratospheric Warming (SSW) events to shed light on the interplay between waves and the mean flow, and investigate the impact of gravity wave drag parameterizations on the dynamics-physics interaction.

Figure: Example of an idealized dynamical core simulation with NCAR's semi-Lagrangian spectral transform model (driven by the so-called Held-Suarez forcing). The figure shows the zonal-mean monthly-mean zonal wind at the equator. The oscillation resembles the Quasi-Biennial Oscillation (QBO) in the stratosphere.

The dynamical core of atmospheric General Circulation Models (GCMs) comprises the fluid dynamics component of every climate and weather forecasting model. Tests of 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.

We develop idealized test cases for dynamical cores and conduct international Dynamical Core Model Intercomparison Projects (DCMIP) (e.g. at NCAR in 2008 and the forthcoming NCAR summer school and intercomparison workshop in August 2012). 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).

This project assesses and quantifies 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 5 (CAM 5). This model has options for four very different dynamical cores. These are the spectral-transform Eulerian and semi-Lagrangian dynamical cores as well as the Finite Volume (FV) and HOMME spectral element dynamics package. All four 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 is investigated. We develop and apply evaluation techniques and test whether the lessons learned in simplified experiments are predictors of the performance in climate models. In 2011 we published a 113-page Springer book chapter on the pros and cons of diffusion, filters and fixers in GCMs that sheds light on the many subgrid-scale mechannisms in today's weather and climate models.

Figure:Surface pressure (hPa) and 850 hPa meridional velocity (m/s) at day 9 of the growing baroclinic wave test case of Jablonowski and Williamson (2006) from the CAM FV dynamical core at a 1x1 degree resolution (about 110 km) with 26 vertical levels. Simulations with (a,b): default second-order divergence damping, (c,d) fourth-order divergence damping, (e,f) no divergence damping. The unusual contour interval for the v wind emphasizes the very weak oscillations in (d).

Our group is part of an interdisciplinary team (consisting of atmospheric scientists, hydrologists, computer scientists, web application developers and social scientists) at multiple institutions (University of Michigan, NOAA Earth System Research Laboratory, University of Colorado, NOAA Geophysical Fluid Dynamics Laboratory, NCAR). The team designs and builds open-source cyber-infrastructure tools for the Earth System Sciences. We play a key role in the design of collaborative workspaces that combine Wiki and search functionalities with the Earth System Grid (ESG), the Earth System Curator project, Live Access Servers for remote data visualization and analyses purposes, and metadata for models and data sets. The planned 2012 NCAR summer school and model intercomparison project (see above) will serve as a pilot project for this NSF-supported research activity.

Figure: Screenshot of the cyber-infrastructure tool (version 0.4 from September 2011) featured on the Commodity Governance (CoG) web page: http://www.esrl.noaa.gov/cog/cog/ . The CoG workspace lists and links current prototype projects on the right hand side, like our 2008 Dynamical Core Workshop called Dycore-2008.