Priority 3: Conducting Research in Computer Science, Applied Mathematics, Statistics, and Numerical Methods

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

Background

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

Progress

In FY2006, 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 FY2006 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 FY2006 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.

Plans

The four workshops of the FY2007 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.

Outcomes

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 FY2006 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 FY2007 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.

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.

For Further Information & Detail

CISL Annual Report