Atmospheric Dynamics Modeling Group / Education

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. More information can also be found on NCAR's CISL webpage.

Photo: Organizers of the NCAR ASP 2008 Colloquium on Numerical Techniques for Global Atmospheric Models. Left to right: Ram Nair, Peter Lauritzen, Mark Taylor, Christiane Jablonowski

This 2-week summer school is in its initial planning phase. We (Christiane Jablonowski, Peter Lauritzen, Mark Taylor, Ram Nair) suggest holding a summer school with special focus on non-hydrostatic global models which are under development right now. We will invite the international dynamical core modeling community to join us for two weeks at NCAR for an exciting student-focused event that will lead to an unprecedented dynamical core intercomparison project, even broader in scale than our 2008 workshop. We will suggest new test techniques for non-hydrostatic models that are also applicable at hydrostatic scales. Please contact me (Christiane Jablonowski) if you would like to get more information. Stay tuned.

The Institute for Pure and Applied Mathematics (IPAM) is an NSF Math Institute on the campus of UCLA in Los Angeles, CA. In the spring next year (March 8 - June 11, 2010) IPAM holds a 13-week long program on Model and Data Hierarchies for Simulating and Understanding Climate. There are four one-week workshops and a week-long tutorial-workshop (first week) embedded into the long program. The themes of the four workshops address (1) the equation sets for climate modeling, (2) the numerical methods and hierarchies, (3) the subgrid-scale physics parameterizations and (4) data analysis and assimilation aspects. We are involved in several of the IPAM events. Prof. Jablonowski is a speaker at the tutorial-workshop, and an organizer (& speaker) of Workshop II: Numerical Hierarchies for Climate Modeling.

Figure: Adaptive Mesh Simulation with a Finite Volume shallow water model (St-Cyr, Jablonowski et al., MWR 2008). The figure shows the relative vorticity field at day 6 of a barotropically unstable wave. Nonuniform resolutions and other topics are discussed at the IPAM Workshop II in April 2010.

For over 9 years Prof. Jablonowski has been collaborating with Prof. Quentin Stout (Computer Science and Engineering, University of Michigan) on the Parallel Computing tutorial 'Parallel Computing 101' which we update substantially every year. This tutorial provides a comprehensive overview of parallel computing, emphasizing those aspects most relevant to the user. It discusses software and hardware, with an emphasis on standards, portability, and systems that are widely available.

The tutorial surveys basic parallel computing concepts, using examples selected from large-scale engineering and scientific problems. These examples illustrate using MPI on distributed memory systems, OpenMP on shared memory systems, and MPI+OpenMP on hybrid systems. It discusses numerous parallelization approaches, and software engineering and performance improvement aspects, including the use of state-of-the-art tools. The tutorial helps attendees make intelligent decisions by covering the primary options that are available, explaining how they are used and what they are most suitable for. Extensive pointers to the literature and web-based resources are provided to facilitate follow-up studies. In recent years, the number of participants has exceeded 100. Among the participants are managers, students, commercial employees, researchers and software engineers from national research centers. We will teach it again at SuperComputing '09 in Portland, OR, in November 2009.

Photo: Christiane Jablonowski and Quentin Stout at SuperComputing '07 in Reno, NV. The photo was taken by Ed Burnette who wrote about the Parallel Computing tutorial in his blog.

The sophomore course Earth System Dynamics gives an introduction to the dynamics of the atmosphere, oceans and the solid earth. The course introduces the equations of motion that govern the motions of the Earth's Systems. We derive the full equation set and then discuss various approximations to study the components of the Earth's system. The first half of the course addresses the dynamics of the atmosphere and climate system. Special attention is paid to the dominant balances in the atmosphere, like the geostrophic balance or hydrostatic balance. The second half of the course focuses on ocean, cryosphere and solid Earth dynamics, and is taught by a faculty member from the UM Department of Geological Sciences. The course is quantitative and based on physical and mathematical principles.

Figure: Satellite image of the NASA Terra satellite, The image shows two spiraling storms, formed simultaneously above Iceland and Scotland on Jan/2/1007. The air in the low pressure systems rotates counterclockwise as expected in the Northern Hemisphere.

The lecture notes (PowerPoint files) for the first half of the course can be downloaded here. These are the lecture notes from the Winter 2009 term:

1 Introduction to the course

2 Characteristics of the atmosphere

3 Ideal gas law, hydrostatic equation, hypsometric equation, mathematical tools

4 Vorticity, divergence, spherical coordinates

5 Material derivative, advection, pressure gradient force (surface force)

6 & 7 Viscous force, gravitational force, introduction to apparent forces

8 Centrifugal force, gravity, Coriolis force

9 Momentum equations, scale analysis, geostrophic balance, hydrostatic balance

10 Continuity equation, thermodynamic equation, total energy equation

11 Potential temperature (Poisson equation), dry adiabatic lapse rate, static stability, Brunt-Vaisala frequency

12 Vertical pressure coordinate, thermal wind relationship

13 Equations of motion in pressure coordinates, pressure tendency equation, evolution of an idealized low

This graduate-level course provides an in-depth discussion of atmospheric motions. We start with a review of the equations of motion and dominant balances, and briefly remind ourselves of the quasi-geostrophic theory. This is our background knowledge. We then discuss waves and instabilities in the atmosphere. This includes the derivation of dispersion relations and a discussion of barotropic, baroclinic, inertial, Kelvin-Helmholtz and static instabilities. The course reviews the general circulation of the atmosphere including the Hadley cells, planetary and equatorial waves and gives an overview of the dynamics of the middle atmosphere. We address the wave-mean flow interaction, the mean and transformed Eulerian mean circulation, tropical meteorology, energy and angular momentum budgets, and atmospheric modeling.

Figure: Example of an idealized dynamical core simulation. The figure shows the zonal-mean monthly-mean zonal wind at the equator. The oscillation resembles the Quasi-Biennial Oscillation (QBO) in the stratosphere.

This is a future graduate-level course that is planned for the Fall 2010 term. It will discuss how atmospheric models are or need to be built, thereby exposing the many choices atmospheric modelers face. The course will both address the dynamical cores of GCMs and selected physical parameterizations. It will be a hands-on class with student projects that lets us assemble a climate model. We will make use of modern software infrastructure like the Earth System Modeling Framework, Earth System Curator and shared workspaces, learn about numerical methods, develop computing skills and deal with data.

 

Figure: Left: Example of an idealized simulation with the NCAR Finite-Volume (FV) dynamical core. The figure shows the 850 hPa temperature field of an idealized baroclinic wave as documented by Jablonowski and Williamson (QJ, 2006) and in the Jablonowski and Williamson NCAR Technical Report TN-469+STR (2006). Right: Example of a model grid (figure taken from David Noone's web page at the University of Colorado, Boulder).