Workshop on the
USE OF ENSEMBLES IN DATA ASSIMILATION
April 13-14, 1999, NCEP, Camp Springs, MD
Data assimilation plans at NCEP (20 mins)
Recent developments in the ECMWF Ensemble Prediction System (30 mins)
Estimating analysis uncertainty using the NCEP global ensemble (30 mins)
The Specification and Use of Synoptically-Dependent Background Errors in 3DVAR using information from an Error Breeding Cycle
Preliminary experiments on applications of ensembles to data assimilation
Prospects for an operational ensemble Kalman filter (30 mins)
Martin Ehrendorfer (Presented by J. Barkmeijer,
The Ensemble Transform Kalman Filter (30 mins)
Spread/Analysis Error relationships in a simple model (20 mins)
Dynamics and statistics of forecast errors in a quasi-geostrophic model (10-30 mins)
Analysis and Forecast Errors and the Ensemble Kalman Filter (30 mins)
Estimates of flow dependent covariance structures (20 mins)
Lars Peter Riishojgaard:
Anisotropic flow-dependent modeling of the forecast error correlations
Jeff Anderson, GFDL
Dale Barker, UK Met. Office, Bracknell, UK
Jan Barkmeijer, ECMWF, Reading, England
Craig Bishop, Pennsylvania State University, State College, PA
Kerry Emanuel, MIT, Boston, MA
Brian Etherton, Pennsylvania State University, State College, PA
Peter Houtekamer, AES, Dorval, Canada
Tom Hamill, NCAR, Boulder, CO
Eugenia Kalnay, University of Oklahoma, Norman, OK
Sharan Majumdar, Pennsylvania State University, State College, PA
Lars Peter Riishojgaard, NASA GSFC, Greenbelt, MD
Chris Snyder, NCAR, Boulder, CO
Jeff Whitaker, CDC, Boulder, CO
The Specification and Use of Synoptically-Dependent
in 3DVAR using information from an Error Breeding Cycle
A study is currently under way at the UKMO to
use 3D synoptically-dependent
background error modes (SBEMs) within 3DVAR. Current background errors are
`static', derived via the `NMC' method. An error-breeding cycle is used to
provide SBEMs which are used in 3DVAR via a new control variable and cost
function. Details of the methodology and early results will be presented.
Recent developments in the ECMWF Ensemble Prediction System\\
Perturbations used in ensemble forecasting ask
for a careful computation.
One of the conditions they should satisfy is that their statistics
resemble what is known of the analysis error. Prelimenary results on the
EPS performance will be presented of singular vectors computed
with a Reduced Rank Kalman Filter. Such singular vectors are constrained
by the analysis error covariance matrix at initial time. This is achieved
by using the Hessian of the full 4D-Var costfunction. Also the use of different
analyses in the EPS or the construction a so-called consensus analysis
will be discussed.
Prospects for an operational ensemble Kalman filter
An ensemble of short-range forecasts can provide
covariances of the forecast error, needed by the Kalman filter.
The finite ensemble size causes the estimated correlations to be noisy.
To filter small forecast-error correlations associated with remote
observations, a Schur (termwise) product of the covariances of the
forecast error and a correlation function with local support is used.
To solve the Kalman filter equations, the observations
into batches which are assimilated sequentially. The ensemble of
background fields is updated at each step, and thus provides a measure
of the improving quality of the background fields as more and more
batches of observations are assimilated. For each batch, a Cholesky
decomposition method is used to solve the linear system of equations.
Observations from several regions of the globe may be selected for a
single batch, such that information from different regions
has zero correlation due to the Schur product. The linear system
then becomes block diagonal.
A prototype sequential filter has been developed
data assimilation. Application in real time would appear to be
Dynamics and statistics of forecast errors in a quasi-geostrophic model.
Results from QG model. Time scale
of specified initial ensemble to "the attractor", characteristics
of perturbations on the attractor. Instantaneous statistics of
analysis and forecast errors for 3DVAR, in particular influence of
past dynamics through projection of errors onto leading Lyapnov
subspace. Singular vectors for approximate "analysis error covariance
norm" and their differences from energy SV's.