Workshop on the


April 13-14, 1999, NCEP, Camp Springs, MD







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The workshop is to provide a forum for discussions on improving data assimilation techniques via the use of ensemble forecasts, and to provide specific recommendations to NCEP on same.


A concise (5-page) set of recommendations for short (1-2 years) and longer term development program for improvements in data assimilation using ensembles, including suggestions for continued interaction amongst workshop participants.


Tuesday, April 13

8:30-9:00    Refreshments


9:00    Louis Uccellini, Director, NCEP:
    Welcoming Remarks

9:05    Steve Lord, Acting Director, EMC:
    Purpose and expectations of the workshop

9:15    John Derber:
    Basic requirements for the use of ensembles to define background error covariances

9:45    Discussion

Chair:    Dale Barker

10:00    Peter Houtekamer:
    Prospects for an operational ensemble Kalman filter

10:30    Break

10:45    Jeff Anderson:
Application of a fully non-linear filter and Monte Carlo techniques to ensemble data assimilation in intermediate models

11:15    Craig Bishop:

A Survey of Ensemble Kalman Filters

11:45    Discussion

12:00    Lunch brought in

13:00    Jan Barkmeijer:
    Recent developments in the ECMWF Ensemble Prediction System

13:30    Martin Ehrendorfer (Presented by J. Barkmeijer):
    Kalman filtering and ensemble prediction

13:45    Chris Snyder:
    Dynamics and statistics of forecast errors in a quasi-geostrophic model

14:00    Tom Hamill:
    A Combination 3DVAR-Ensemble Kalman Filter Approach to Data Assimilation

   14:15    Discussion

14:30    Break

Chair:    Jeff Anderson

14:45    Dale Barker:
    The specification and use of synoptically-dependent background errors in 3DVAR using information from an Error Breeding Cycle

15:15    Eugenia Kalnay:
    Some ideas on the possible use of bred vectors in data assimilation

15:45    Jeff Whitaker:
    Spread/analysis error relationships in a simple model

16:05    Zoltan Toth:
    Estimating analysis uncertainty using the NCEP global ensemble

16:35    Discussion

17:00    Workshop Report Structure - Discussion/Report leader: Kerry Emanuel
    Suggested topics                                                                                                          Working group leaders                                                   Rapporteurs
    a)    Required ensemble characteristics                                                                Jan Barkmeijer                                                                  Istvan Szunyogh
    b)    Use of ensembles with existing analysis schemes                                                                                                                                  Wan-Shu Wu
    c)    Ensemble-based analysis schemes                                                              Craig Bishop                                                                      Milija Zupanski

17:30    Adjourn for day

18:30    Optional dinner

Wednesday, April 14

8:00    Refreshments

Chair:    Eugenia Kalnay

8:30    Jim Purser:
    Ensemble guidance in defining adaptive covariances

8:50    Milija Zupanski
    Plans for using fully flow-dependent background error covariance information in the NCEP regional 4DVAR data assimilation system

9:10    Discussion

9:30    Break

10:00    Summary of  presented material (Report Leader and Rapporteurs)
                Writing assignments established

11:00    Writing (In 2-3 groups)

12:00    Lunch brought in

13:00    Writing continues (In 2-3 groups)

14:00    Break

14:30    Discussion: Review and Revise Group Reports; Finalize Workshop Report

16:00    Adjourn


Jeff Anderson, GFDL, Princeton, NJ
Stephen Anderson, Metron, Reston, VA
Dale Barker, UK Met. Office, Bracknell, UK
Jan Barkmeijer, ECMWF, Reading, England
Craig Bishop, Pennsylvania State University, State College, PA
Steve Cohn, NASA GSFC, Greenbelt, MD
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
Zhao-Xia Pu,  USRA - NASA GSFC, Greenbelt, MD
Chris Snyder, NCAR, Boulder, CO
Jeff Whitaker, CDC, Boulder, CO

    From NCEP:
John Derber
Geoff Dimego
Steve Lord
Hua-Lu Pan
Dave Parrish
Jim Purser
Istvan Szunyogh
Zoltan Toth
Steve Tracton
Wan-Shu Wu
Dusanka Zupanski
Milija Zupanski


Application of a Fully Non-Linear Filter and Monte Carlo Techniques
to Ensemble Data Assimilation in Intermediate Models

Jeff Anderson

A probabilistic approach to the fully non-linear filtering problem is
developed in the context of the problem of data assimilation for
atmospheric and oceanic models. The goal of this method is to produce a
probability sample of the state of a dynamical system that is
consistent with a set of temporally discrete observations. This sample
can then be used as initial conditions for ensemble forecasts which
themselves approximate probability samples of the forecast state of the
system. Both the state of the assimilating model and the set of
observations available at a given instant of time are treated formally
as random variables. The state of the system given a new set of
observations can then be computed, after an application of Bayes' rule,
as a convolution of the conditional probability densities associated
with the new observations and the prior density generated from a
knowledge of the model's dynamics and all previous observations.
Traditionally, this problem has been simplified through linearization
leading to the Kalman-Bucy filter. However, in the approach discussed
here, a Monte Carlo (ensemble) approach is used to sample the prior
density and an expanded Monte Carlo sample is generated. This expanded
Monte Carlo sample can then be convolved with the conditional
distribution from the new observations. An updated probability sample
of the state of the system is then generated by subsampling the
convolution of the expanded Monte Carlo sample. A number of interesting
issues related to applying Monte Carlo methods in this context are

Presentations at previous meetings have shown results in low order models.
This talk will quickly review the method and its use of ensembles. The
method will then be extended for application in models with many degrees
of freedom and results presented for a spectral barotropic vorticity
model on the sphere and a grid-point PE model.
The Specification and Use of Synoptically-Dependent Background Errors
in 3DVAR using information from an Error Breeding Cycle

The specification and use of synoptically-dependent background errors in 3DVAR using information from an Error Breeding Cycle

Dale Barker

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

J. Barkmeijer

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.

A Survey of Ensemble Kalman Filters

Craig Bishop

A variety of ensemble Kalman filters are tested by performing
OSSEs on an idealized barotropic vorticity equation model.
For fixed (non-adaptive) observational networks, the effectiveness of
the schemes is sensitive to the manner in which the ensemble perturbations
are generated. Important issues that one must consider when creating
an ensemble for data assimilation include the following:

(a) the ensemble perturbations need to be
well resolved by the observational network
in order to avoid spurious representations
of the part of the vector subspace
not represented in the ensemble;

(b) spurious long distance correlations need to be avoided; and

(c) perturbations which obey linear dynamics at the assimilation time
may linearly combine into a likely prediction error more readily than
perturbations which are profoundly non-linear at the assimilation time.

Interestingly, ensemble generation schemes such as those that accurately sample
the PDF or those that "optimally" estimate the leading eigenvectors and
eigenvalues of the prediction error covariance matrix do not necessarily
have the desirable characteristics mentioned above. In our particular OSSEs,
ensemble generation techniques optimized for the PDF or prediction error
variance perform badly as a basis for data assimilation.
We found that the most effective ensemble Kalman filter is one in which the
initial perturbations are
based on the eiegnvectors of an isotropic correlation matrix scaled by
the square root of their eigenvalues. This choice of initial perturbations
yields evolved perturbations with the three desirable characteristics mentioned
above. This Kalman filter significantly out performs 3-D Var with isotropic
error covariances.

In order to avoid the problem of diminishing ensemble spread,
all of our Kalman filters (except that which is based
on the Houtekamer and Mitchell (1998) scheme) include some sort
of on-line estimation of prediction error covariance parameters
(cf Dee 1995, MWR). This on-line estimation is made easier by an ensemble
transformation approach that also obviates the need to invert large matrices.

Kalman filtering and ensemble prediction

Martin Ehrendorfer (Presented by J. Barkmeijer)

A full Kalman filter has been developed in the context of a 3-level
quasi-geostrophic model. Results of 3D-Var cycling experiments with
this full Kalman filter are presented. In particular, the impact of
observations on the structure of singular vectors and error covariance
matrices will be discussed.

A Combination 3DVAR-Ensemble Kalman Filter
Approach to Data Assimilation

Thomas M. Hamill and Chris Snyder

We present an alternative methodology for ensemble-based
data assimilation, based on existing Perturbed Observation
and Ensemble Kalman Filter techniques.  Our technique
assumes forecast error covariances can be modeled to be
a linear combination of time-invariant (3DVAR), spectrally
diagonal covariances and flow-dependent (Ensemble Kalman
Filter) covariances.  This design has several appealing
characteristics.  The 3DVAR term eliminates
rank deficiency problems; no cutoff radius is assumed, so
analyses are spatially smooth; and the technique works even
for limited-size ensembles, as the ratio of the two
background error terms may be adjusted, consistent with
ensemble size.  Results from perfect model simulations
will be presented.

Prospects for an operational ensemble Kalman filter

Peter Houtekamer

An ensemble of short-range forecasts can provide the flow-dependent
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 are organized
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 for atmospheric
data assimilation. Application in real time would appear to be

Some ideas on the possible use of bred vectors in data assimilation

Eugenia Kalnay

I will briefly review several potential uses such as a) minimization of the
distance between observations and the first guess along the space of the bred
vectors (Kalnay and Toth, 1994); b) use of the ensemble spread to increase the
weight of the observations in areas with large short range ensemble spread (Pu
et al, W&F, 1997); c) use of the ensemble and the quasi-inverse of the linear
model to identify "the best regional initial conditions" given the
of a short range ensemble forecast.

Ensemble guidance in defining adaptive covariances

Jim Purser

 By the application of spatial smoothing filters along
generalized grid directions it is possible to synthesize
quite generally anisotropic covariance operators within a
3-dimensional variational analysis. Each is locally characterized
by a symmetric ``aspect tensor'' defining the scale of coherence
in different directions. We speculate on methods by which the
information available in an ensemble may be incorporated into the
process of estimating the aspect tensor in an objective and
dynamically adaptive way.

Dynamics and statistics of forecast errors in a quasi-geostrophic model.

Chris Snyder

 Results from QG model.  Time scale for collapse
 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.

Estimating analysis uncertainty using the NCEP global ensemble

Zoltan Toth

Estimated errors in short-range forecasts and analyses will be compared with variance and covariance information derived from the NCEP global ensemble forecast system at short lead time. Targeted data collected in the FASTEX, NORPEX, CALJET and Winter Storm Reconnaissance 1999 field programs will be used to evaluate the quality of numerical guidance products.

Spread/Analysis error relationships in a simple model

Jeff Whitaker

The relationship between analysis error and analysis spread is examined
in the simple 40 variable model described by Lorenz and Emanuel (Feb 1
1998, JAS).  Two types of analysis ensembles are used: an optimal scheme
based on the ensemble Kalman filter, and a suboptimal scheme with
flow-independent forecast error covariances (similar to 3DVAR).  The
ability of these schemes to estimate the quality of the analysis (as
measured by ensemble spread) is investigated as a function of the number
of observations, the ensemble size, and the size of model and
observation error.

Plans for using fully flow-dependent background error covariance information in the NCEP regional 4DVAR data assimilation system

Milija Zupanski

A fully cycled low rank 4DVAR system will be presented from the theoretical point of view.
The issue of preconditioning in 4DVAR, and its relation to the low rank approximation, will
be addressed in more detail. A "forecast ensemble" formulation of this 4DVAR algorithm,
especially attractive because it does not use the adjoint model, will be shown as well.
Finally, some basic assumptions  involved in the low rank 4DVAR system will be discussed.


Beyond two overhead projectors, the meeting room will also be equipped with a computer supporting electronic presentations (Corel, Microsoft, etc).