The Lagrangian filter is an extension of tracer approaches to chemical modeling in the atmosphere. The main advantage is that with the Lagrangian filter the tracers carry not only information about the state (the mixing ratio of, say, methane), but they also dynamically advect the entire error covariance matrix. This is an N^2 problem, where N is the number of tracer points and hence is computationally (FLOPS and memory) very demanding and has never been done before. This scheme is similar to the Kalman filter: it is expected that it will be used to obtain production datasets of atmospheric chemicals and to benchmark so-called suboptimal (i.e., computationally less expensive) filter schemes that are in use around the world and being developed at the GSFC Data Assimilation Office (DAO) and elsewhere.
In the context of HPCC, the Lagrangian filter offers the possibility of reducing the complexity compared with the Kalman filter. This will achieve a speedup of the wall-clock time for an assimilation run. This effort contributes to Milestone 10 of the cooperative agreement with Grand Challenge Investigator Peter Lyster.
Richard Menard (DAO) derived analytical properties for a Lagrangian Kalman filter and found them superior for the data assimilation of trace chemicals. The first step is to implement the scientifically interesting 1-D Lagrangian Kalman filter (C. Mobarry/GSFC). At present, tracer schemes may not be accurate enough for the Lagrangian filter, so we are conducting a comparative study. Thus, the second step is to investigate a suite of known and new algorithms for particle motion constrained to the surface of a sphere (K. Olson/GMU). The third and final step is to implement a highly accurate interpolation scheme from Lagrangian particles to/from scattered observation points (TBD).
We developed a Lagrangian Kalman filter that can be coupled to 1-D dynamics or 2-D dynamics. The 1-D Lagrangian Kalman filter achieving 2 gigaFLOPS on 128 processors of the JPL CRAY T3D (July 1996). Further developments gave 40 megaFLOPS per processor on 64 processors of a CRAY T3D (August 1996). A suite of particle pushers has been written that move particles according to time-varying winds interpolated from a spherical grid. These different techniques are currently being evaluated for their use as part of the Lagrangian Kalman filter. Collaboration has also been established with researchers in GSFC's Atmospheric Chemistry and Dynamics Branch to evaluate these techniques for use in other problems in atmospheric modeling.
This is the first known massively parallel Lagrangian Kalman filter. It will provide a numerical benchmark to study the quality of sub-optimal filters. This code, or the techniques learned from it, may help achieve a performance milestone of the Lyster Grand Challenge team.
Delivered to Lyster a 1-D Lagrangian filter (Mobarry). Lyster and a graduate student are to study the numerical properties of the Lagrangian Kalman filter. Olson has developed a suite of particle pushers for motion constrained to the surface of a sphere. This suite is not yet parallelized. One or more of these particle motion algorithms are to be integrated with the Lagrangian Kalman filter and the interpolation scheme to produce a 2-D filter.
Dr. Clark Mobarry
Goddard Space Flight Center
Clark.Mobarry@gsfc.nasa.gov
301-286-2081
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