Research in Computational Science and Math Applied to Geophysics: IMAGe and SCD

This figure represents the partitioning technique based on space-filling curves that we applied to the Parallel Ocean Program (POP). We were able to evenly distribute the workload within POP, which enables us to increase its simulation rate. The colored boxes in the figure represent a partitioning of POP across eight processors. The missing boxes correspond to land areas which are discarded. The black serpentine curve is the space-filling curve used for the partitioning. The improved partitioning technique allows POP to efficiently utilize 30,000 processors and enables the use of very high-resolution simulations for climatological research. This is an excellent example of how CISL research is improving modeling in the geosciences.

The research activity within CISL enhances the computational infrastructure at NCAR and supports more efficient scientific computation and simulation. This research is acknowledged to be necessary to maintain an innovative computational facility and to lead the geophysics community in incorporating new numerical methods and models. This mission is aligned with NCAR's strategic priority of "Conducting research in computer science, applied mathematics, statistics, and numerical methods."

Given this broad priority, the research in CISL must span several disciplines and address computational science at many levels. These include improvements to network flow and scalability of existing codes to different numerical methods for simulating the flow of geophysical fluids. Integrated with the computational science are areas of applied mathematics that include data analysis, models for multiscale processes, and techniques for assimilating data into numerical models. Because these different elements are coordinated through a single Lab, there is an easy transfer of technology and ideas from prototypes and theoretical results in IMAGe, to issues of implementation and workflow in SCD, and finally into incorporation as tools and models for the communities served by CISL. There is also a valuable reverse transfer whereby emerging computational capability and data storage spur particular research that takes advantage of these features.

For 2006, the IMAGE program on multiscale modeling provided a focus for computational and mathematical activities in CISL that address the problems of representing complex geophysical processes, such as the atmosphere at different scales. In addition, significant results were produced outside this program that were still aligned with the CISL mission. The scalability of the ocean component of the NCAR climate model (POP) was significantly improved by applying some general techniques based on changing how physical variables are referenced in the code and how the computations are divided among many processors.

There were also advances in numerical methods that increase the accuracy of geophysical simulations by adapting to the structure of the flow. Other research tackled a more fundemental problem of efficient representions of a surface by expansion in nonstandard basis such as wavelets or radial basis function or through a statistical formulation. This work supports the analysis and visualization of spatial fields and provides an intriguing basis for new numerical methods. Another research component is on the boundary between computational science and numerical models for geophysical processes. Robust methods were developed to adjust for model errors when assimilating data into a numerical model.

Also during FY 2006, several large numerical experiments were completed to study the complex structures of magnetic fields under turbulent flow of charged particles. These simulations not only contribute to the understanding of magnetohydrodynamics but also represent an activity driven in part by the computational capacity at NCAR. The simulations also served as a benchmark for the facility.

Our plans for FY 2007 are continuations of these activities. Some important milestones are incorporating higher order numerics into components of the NCAR community models and further improvements in the scalability of the full NCAR climate model. Several of the research projects are expected to be cross linked including the connections between adaptive radial bases and covariance functions and the statistical analysis and visualization of coherent structures in turbulent flows. The IMAGe Theme-of-the-Year program for FY 2007 will be on statistical methods for the design and analysis of geophysical simulation experiments, and it will be useful for improving the numerical models at NCAR and interpreting their output.

Support by funding agencies other than the NSF are indicated in the individual reports.