IMAGe research: New algorithms, tools, and geophysical models
This image summarizes preliminary results
from an aqua-planet simulation using the HOMME global atmospheric model and
an approximation of atmospheric physics that includes a new method for
representing convection. The Earth's Madden-Julian Oscillation (MJO) is
approximated by a traveling wave of convection in the tropical ocean with
a period of approximately 30-60 days. Convection processes such as tropical
thunderstorms are very important to the Earth's climate because they
distribute heat from the surface into the troposphere. Therefore, accurate
simulation of the MJO helps us understand this fundamental geophysical process.
The figure is a standard summary of the dynamical properties of the
atmosphere where the energy from traveling waves is decomposed into the
spatial size of the waves (horizontal axis in wave number) and their speed
(vertical axis in period). The color scale indicates the kinetic energy
that can be attributed to different combinations of scales and speeds, and
the labeling indicates several well-known atmospheric waves. The MJO is more
difficult to detect as it has a relatively long period. However, preliminary
evidence for its presence appears in this simulation.
This experiment is important because the precise mechanisms of the MJO are
still unknown, and past numerical models have had difficulty simulating
it.
The power of mathematical science is that similar methods and models can
be used to solve problems in very different contexts. The Institute of
Mathematics Applied to Geosciences (IMAGe) was formed in October 2004 to
develop tools, methods, and models that can address some of NCAR's
fundamental science problems. IMAGe is also actively introducing the
mathematics community to new problems that are posed by geophysical
processes and observations. Two important vehicles that support this
interdisciplinary activity are the Theme of the Year workshops and
publically available software for numerical and statistical methods.
IMAGe contributes to the NCAR strategic priorities of "Conducting research
in computer science, applied mathematics, statistics, and numerical methods"
and "Engaging a broader and more diverse community."
Geophysical-Astrophysical Spectral-Element Adaptive Refinement code has been extended to use adaptive three-dimensional grids and has been tested under an advection/diffusion solver. Turbulence was studied in rotating, neutral fluids, and the interactions between rotation, helicity, and transfer of energy between scales was quantified. A promising MHD simulation exploiting Taylor-Green symmetries has produced features in current sheets observed in the solar wind.
The discontinuous Galerkin (DG) method was combined with a state-of-the-art mesh database to produce a code with excellent scaling to many processors. A third-order DG transport scheme was implemented within HOMME with a new monotonic limiter and was shown to eliminate spurious oscillations from the numerical solution.
A design study was completed that indicates the value of including an energy balance model as part of past climate proxy reconstructions. The multivariate, spatial lattice model was completed for interpreting in a joint manner the temperture and precipitation from climate model projections.
The Data Assimilation Research Testbed was successful for real-time forecast of CO concentrations in support for the ARCTUS field program. In addition, DART/CAM was able to produce specific reanalysis fields for the Arctic region for diagnosing mechanisms of sea ice formation and also for improving the filtering at high latitudes in the CAM finite volume dynamical core.
Multiscale modeling plans: A Boussinesq capability is being added in GASpAR to work on atmospheric flows. The FFT libraries in GHOST (Geophysical High Order Suite for Turbulence) are being extended to do pencil (1D) decompositions. Results of the Advanced Science and Discovery experiments on rotating flows with helicity will be compared to a subgrid-scale parameterization for the effect of eddys.
Numerics plans: The DG conservative transport will be tested in CAM/HOMME using the aqua-planet simulations. In addition, a multi-tracer transport algorithm based on conservative remapping will be studied for future implementation. Adaptive mesh refinement algorithms will be developed in the context of a two-dimensional solver for compressible fluids. A multi-grid algorithm will be included. Software infrastructure to perform three-dimensional simulations on general curvilinear domains will be built. Finally, algorithms will be developed for node placement in the context of using radial basis functions (RBF) for the adaptive solution of the shallow water equations.
Statistics plans: Bayesian methods for spatial paleoclimate reconstructions will be completed for North America using multiple proxies. Statistical analysis will be completed for a subset of the NARCCAP experiments for extreme precipitation and a multi-model synthesis that includes the skill in reproducing current climate and interactions among GCM/RCM pairings.
Data Assimilation plans: Development will continue on parallel implementations of DART with WRF and CAM interfaces. Adaptive inflation and localization data algorithms will be refined and applied to improve tropical cyclone analysis and prediction, as well as for organized convective systems over the continental U.S. and contiguous coastal oceans.
IMAGe is supported by NSF Core funding.