IMAGe Theme for 2006: Emerging Mathematical Strategies for Multi-Scale and Stochastic Modeling of the Atmosphere and Climate

This satellite view of cumulus clouds rapidly developing into cumulonimbus formations indicates the importance of small-scale atmospheric phenomena. The reflective and convective qualities of the merging cumulonimbus formations make a significantly greater impact on the atmosphere than that of the cumulus clouds at the bottom of the photo. Techniques that allow long-term global models to resolve dynamic processes at this scale are improving our ability to accurately simulate climate and weather.

IMAGe's vision is to bring mathematical models and tools to bear on fundamental problems in the geosciences and be a center of activity for the mathematical and geophysical communities. A central activity in IMAGe is the Theme-of-the-Year (TOY)—an annual focus on a particular area of the geosciences or applied mathematics—that has an impact on NCAR's scientific mission. In FY 2006, the first full TOY sponsored by IMAGe consisted of four workshops held at NCAR in a series that blended tutorial lectures with presentations of recent research. This effort supports the NCAR strategic priority of "Engaging a broader and more diverse community," and it leverages three others being advanced by IMAGe: "Improving prediction of weather, climate, and other atmospheric phenomena;" "Conducting research in computer science, applied mathematics, statistics, and numerical methods;" and "Developing and providing advanced services and tools."

A grand challenge in modeling the Earth system is understanding how geophysical processes interact across many different scales. Many important processes occur at scales that are too fine for the broad-scale grids of climate models to resolve. However, subgrid processes such as convection and cloud formation have significant impacts on the circulation of the atmosphere. Resolving the interactions between scales will lead to improved understanding of climate and improved weather forecasting. Besides supporting the Earth system modeling component of NCAR science, this acitivity was also intended to build intellectual bridges between two distinct communities. This TOY was codirected by Andrew Majda, Morse Professor of Arts and Sciences, Courant Institute of Mathematical Sciences, NYU and Joseph Tribbia, Senior Scientist, Climate and Global Dynamics Division, NCAR. Securing an external eminent faculty member in applied mathematics was an important component in this TOY.

The FY 2006 TOY workshop series was spread over the academic calendar and covered:

1. Multi-scale Interactions in the Tropics to Midlatitudes: Mathematical Theory, Observations and Numerical Models
2. Multi-Scale Interactions in a GCM Grid Box: Mathematical Theory, Numerics, and Parameterization
3. Stochastic and Statistical Parameterization of Unresolved Features in the Atmosphere and Upper Ocean
4. Multi-Scale Processes for Low Frequency Variability, Climate, and Climate Change Response

Consistent with TOY goals, the participants had broad backgrounds from graduate students to faculty and from atmospheric scientists to applied mathematicians and statisticians. The FY 2006 TOY involved over 100 different researchers and students. Each five-day workshop included three days of tutorials and two days of technical presentations, with plenty of time for discussion and interaction. The workshops were successful in establishing a two-way communication between the university mathematics community and the scientific community at NCAR, focusing on specific areas of research that will benefit from intense collaboration. Another benefit was to expose Ph.D. students, post-docs, and junior faculty in applied mathematics and statistics to the scientific issues and principles in modeling the atmosphere. Based on this activity, IMAGe was successful in recruiting a young researcher at the Courant Institute, NYU, Christian Franzke, to complete a year of his postdoctoral fellowship at NCAR.

The four workshops of the FY 2007 TOY will explore:

1. Some outstanding challenges in geophysical modeling and a catalog of statistical tools; identifying concrete problems to help structure statistical working groups
2. Application of random matrices theory and methods; a blend of tutorial and research talks with discussions and updates on progress from the first workshop
3. Statistical methods for complex numerical models in the goesciences; a blend of tutorial and research talks with discussions and updates on progress from the first workshop
4. Models and methods for tracking carbon sources; focusing on mathematical tools to estimate the surface sources of carbon dioxides

This project is made possible through NSF Core funding through the NSF Division of Mathematical Sciences.

Project Origin Details

Numerical models are vital to simulate geophysical, chemical and ecological processes and to understand the relationship among components in the Earth system. As models have become larger and more complex, their construction, validation, and analysis are no longer amenable to simple approaches and statistical summaries. Statistical science in the past 20 years has advanced to handle the interpretation of complicated multivariate, spatial and temporal data sets, and it is well suited to tackle large numerical model output that is now the norm in the geosciences. The TOY is undertaken with the goal of matching cutting-edge statistical methods to the needs of geophysical model development and to make statisticial scientists aware of the particular scientific issues and research in the geophysical modeling community.

The TOY is pursued in partnership with the Statistical and Applied Mathematical Sciences Institute (SAMSI), located in Research Triangle Park, North Carolina and the Mathematical Sciences Research Instititute (MSRI) in Berkeley, California. Both SAMSI and MSRI are NSF mathematics institutes with an international stature in the mathemaitcs community. The main acitivites will be a series of three workshops and a summer school, all held at NCAR, that dovetail with SAMSI activities on its programs on random matrices and on computer models and with MSRI's summer school program. IMAGe participation will be valuable in representing a suite of geophysical models within the SAMSI program.

In FY 2006, the first full program on a theme was sponsored by IMAGe. It consisted of a comprehensive series of workshops. Although this format is common among NSF Mathematics Institutes, typically these centers cycle through a diverse set of topics, rarely returning to a previous program theme. The difference in this IMAGe activity is that the TOY touched on topics and research areas that will have a persistent focus at NCAR and will remain a resource and integrator for researchers and students that have been entrained through this program.

The theme for FY 2006 was initiated by identifying an external codirector (Majda), and this resulted in a written proposal developed by the codirectors. Part of this planning also involved the NCAR Geophysical Turbulence Program since this group is intimately involved in research on multiscale processes.

Timeframe

The timeframe was the 2006-2007 academic year.

Detailed Accomplishments

The FY 2006 plan called for three workshops timed to the academic year. The three original workshops were held, and a fourth workshop was added to address larger-scale climate processes. Around these dates Andrew Majda visited for more extended interaction with NCAR staff and visitors. Also several graduate students were hosted for longer visits, as was planned.

The outputs delivered were the four workshops held as scheduled on these dates that covered these topics:

Workshop I: 26-30 September 2005
Multi-scale Interactions in the Tropics to Midlatitudes: Mathematical Theory, Observations and Numerical Models
Venue: NCAR Mesa Lab, Main Seminar Room

Atmospheric Science Topics:

1. Multi-scale phenomena in the tropics: intraseasonal oscillation, cloud superclusters, clusters, etc.
2. Tropical midlatitude connections
3. Hurricane development
4. Current capablity of Global Circulation Models (GCMs) to capture 1-3.

Applied Math Topics:

1. Systematics multi-scale asymptotic methods for complex PDEs of tropics
2. Analysis of simplified models emerging from atmospheric science topic 1 and application to topics in 1-4, including observations and numerics
3. Balanced wave dynamics for equatorial wave guide, moisture, hurricanes, etc.

Workshop II: 31 October - 4 November 2005
Multi-Scale Interactions in a GCM grid box: Mathematical Theory, Numerics, and Parameterization
Venue: NCAR Mesa Lab, Main Seminar Room

Atmospheric Science Topics:

1. Atmospheric science: Convection, orography moisture, gravity waves
2. Paramterization and numerics for GCMs for weather prediction and climate regimes

Applied Math Topics:

1. Multi-scale asymptotic modeling and systematic numerics and parameterizations
2. Simplified model problems
3. High-resolution numerics

Workshop III: 27 February - 3 March 2006
Stochastic and Statistical Parameterization of Unresolved Features in the Atmosphere and Upper Ocean
Venue: NCAR Mesa Lab, Main Seminar Room

Atmospheric Science Topics:

Applied Math Topics:

1. Systematic strategies for stochastic mode reduction
2. Novel coarse-graining strategies using coupled birth-death processes
3. Bayesian hierarchical statistical models for parameterizations

Workshop IV: 15 - 19 May 2006
Multi-Scale Processes for Low Frequency Variability, Climate, and Climate Change Response
Venue: NCAR Foothills Lab Building 2, Main Seminar Room

Atmospheric Science Topics:

1. Low-frequency atmospheric variabilty and seasonal cycle
2. Coupled GCMs and hierarchy of simplified climate models
3. Observations for climate

Applied Math Topics:

1. Design of optimal bases for low-order models
2. Theories for fluctuation-dissipation relations
3. Analysis of stochastic and deterministic coupled models

In general, the outcomes of this TOY have benefited the modeling community by increasing the interaction between NCAR scientists and the applied mathematics community. The FY 2006 theme has resulted in at least three new collabrations with NCAR scientists on different aspects of multiscale processes. In has also resulted in the recruitment of a scientific visitor (Christian Franzke) for FY 2007 to continue research on multiscale processes. Franzke, as part of his appointment in IMAGe, has set up a series of visits with other mathematical researchers that also reinforce the TOY.

Project Plan Evaluation Measures

Inputs include surveys and interviews of workshop participants. In addition, the IMAGe annual retreat will provide additional evaluation from NCAR staff.

Milestones are set by the TOY workshop schedule listed above.

The TOY is a program carefully designed to address IMAGe's mission. The expected outcomes are new synergies between applied mathematics and geoscience research. One metric is a survey of graduate students and post-docs attending the workshops and other activities to assess the contribution to Ph.D. dissertations and research. One focused goal is to quantify how many geophysical problems have been included into this mathematical research based on the TOY. Another metric is the quality of significant collaborations that have been formed through the TOY, particularly in areas where progress was difficult without new mathematical approaches. In the context of summer schools, an important metric is how many participants have used the Data Assimilation Research Testbed software after the school.

Impact

The long-term nature of this project makes its impacts difficult to predict. IMAGe's improvements to computational fluid dynamics models have already been demonstrated, and they are in the process of being incorporated into production codes at NCAR and elsewhere. The TOY project is designed to disseminate the synergies between applied numerical methods and the simulation of geophysical processes throughout the participating universities and beyond. We intend for this effort to not only increase interdisciplinary collaborations but to spread improved modeling techniques to researchers throughout the community, even if they have not attended a TOY workshop.