Principal Investigator: P.M. Lyster
Earth System Science Interdisciplinary Center
Department of Meteorology
University of Maryland College Park
and NASA/GSFC Data Assimilation Office
This is the documentation which is being
provided in support of the following milestone
submission for the project:
Milestone 10: 200-fold speedup for the
Lagrangian filter over the equivalent problem solved using an Eulerian filter on
a single node of a Cray C90 (delivered with scaling analysis).
We have developed a new numerical algorithm, the Lagrangian filter,
for solving the Kalman filter
equations for constituent assimilation of observations using a direct
solution on trajectories that propagate with the wind flow.
This is a finite dimensional approximation of the solution by
characteristics of the estimation problem and may be thought
of as an extension of the well known method of trajectory
mapping.
We assert that the Lagrangian
filter is a more natural framework for the study of
the constituent problem with data assimilation than the equivalent
Eulerian filter because of the
conservative properties of field, error variance, and error covariance
dynamics. Considerable insight in the behavior of the filters was gained
as a result of these properties.
The Lagrangian filter also requires fewer floating point operations
than the Eulerian filter
because of the simple forecast error propagation step.
However it is still computationally expensive and
we implemented it for two-dimensional flow in
the stratosphere and validated it against the
Eulerian filter.
This code was developed using the distributed-memory
parallel methodology -- in particular it uses the Message-Passing Interface (MPI)
library.
This work was enabled by the use of
parallel computers under NASA's High Performance Computing
and Communications (HPCC) program, and we have achieved
on an SGI/Cray T3E-1200 computer a 200-fold speedup over the
equivalent problem solved using
the Eulerian filter on a single processor of a Cray C90.
The following is a link to a paper
A Lagrangian Trajectory Filter for Constituent Data Assimilation
by Lyster et al.
ftp://dao.gsfc.nasa.gov/pub/papers/lyster/lagrangian.ps
Contents:
1. Introduction
2. The Lagranian filter
3. Interpolation and Trajectory Generation Algorithms
4. Parallelization and Performance Issues: including the
HPCC Milestone and Speedup Curves
5. Behavior of the Lagrangian filter with the Baseline Data Set
for September 1992
6. Summary and Conclusions
Download the source code:
ftp://dao.gsfc.nasa.gov/pub/papers/lyster/lagn_euln_hpcc_r_1_0_0.tar.gz You
can gunzip and untar this file and read lagn_euln/README for instructions
on how to run it (specifically on an Origin 2000, but it is portable
to other machines with the parallel MPI library).
Contact:
Peter Lyster: lys@dao.gsfc.nasa.gov