The GSI Analysis System Implementation at GMAO

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The GSI Analysis System Implementation at GMAO
Ricardo Todling
Global Modeling and Assimilation Office
Contributions from J. Derber(), R. Treadon(),
A. da Silva, C. Cruz, G. Gaspari, W. Gu, J.
Guo, and B. Zhang.
First LNCC Meeting on Computational Modeling
Brazilian Laboratory for Scientific Computation
Petropolis, Brazil, 9-13
August 2004
Contact todling_at_gmao.gsfc.nasa.gov
NCEP/NOAA
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OUTLINE

• Overview why replace PSAS?
• Implementation of GSI-based DAS
• More on PSAS vs GSI
• Preliminary results with GSI-based DAS
• Where do we go from here?
• Personal account of lessons learned

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A Word of Caution
Throughout this presentation I refer to the
replacement of NASAs Physical-space Statistical
Analysis System (PSAS) as if it were only PSAS
being replaced. In actuality we are replacing the
entire Analysis System since the issues with the
PSAS-based DAS can be traced back to various
aspects within the Analysis System and not only
to PSAS.
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Why NOAAs GSI and not NASAs PSAS?

• NASA desire to directly contribute to NOAA
  efforts
• NOAA DAS capability to handle various observation
  operators
• NOAA DAS better handle on off-synoptic hour data
  ()
• GSI handle on significant level data ()
• NASA IRETs poor coverage at SH high latitudes
  ()
• NASA IRETs poor horizontal resolution ()
• NOAA DAS assimilation of direct radiances instead
  of retrievals
• GSI similar promises to PSAS wrt background error
  covariance model development
• NOAA DAS superior product quality

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Whats lost by abandoning PSAS?

• Readiness to work on observation sensitivity
  issues
• Readiness to develop advanced schemes for data
  assimilation, such as retrospective data
  assimilation
• Efforts related to forecast moisture bias
  correction
• Tuning of error statistics
• Some operational procedures related to the
  addition of new data-streams
• Lots of work done in the past few years obs
  operator temp. cov.
• Software familiarity on the NASA side

Do I think the list of PSAS difficulties can be
solved?
ABSOLUTELY
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GMAO vs NCEP Typical H500 difference
Courtesy of GMAO Monitoring Team
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Forecast Skills Anomaly Correlations RMS Errors
FVDAS
NCEP
FVNCEP
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Forecast Skills Anomaly Correlations
NCEP
FVDAS
NAVY
FVNCEP
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Structure of the PSAS-based DAS
Superstructure fvSetup, scripts
Analysis
PAQC
fvGCM
Hermes
IRet
PSAS
Infrastructure ODS, GFIO, Buffer, etc
Base Libraries HDF, MPI, LAPACK, BLAS, etc
Operating System
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Structure of the GSI-based DAS
Superstructure fvSetup, scripts
Analysis
PAQC
fvGCM
Hermes
IRet
GSI
Infrastructure ODS, GFIO, Buffer, etc
Base Libraries HDF, MPI, LAPACK, BLAS, etc
Operating System
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Steps to replace PSAS with GSI

• Modifications to Hermes (O3,Surf,Spec)
• Use NCEPs QC-ed observation files
• Use NCEPs SSI as initial prototype
• Low resolution (T62L28)
• Full vertical SSI resolution (T62L64)
• Replace SSI with GSI

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Hermes changes no-data, no-harm
SSI/GSI
fv grid
spectral
spectral
fv grid
W_f
X_f
X_a
Z_a
fv grid
Z_f
W_a W_f (Z_a - Z_f)
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The Physical-space Statistical Analysis System
(PSAS)
PSAS is an observation-space based algorithm
designed to solve the classical analysis update
equation of estimation problems without requiring
the inversion of the residual error covariance
matrix. Thats PSAS solves the analysis eq.
xa xf B HT ( H B HT R )-1 ( y H xf )
in the following two steps
( H B HT R ) z y H xf
(1) CG Solution of
xa xf B HT z
(2) Final solution as
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The Variational Formulation of the Analysis
Problem
Alternatively, the analysis problem can be posed
in the variational framework of minimizing a cost
function of the form
J(x) ( x xf )T B-1 ( x xf ) ( y h(x)
)T R-1 ( y h(x) )
The analysis xa min J(x). Methods for
minimizing this cost function J usually require
the availability of its gradient
dJ B-1 ( x xf ) HT(x) R-1 ( y h(x) )
SSI formulation
GSI formulation

• Tied up to isotropic and homogeneous B
• Convenient of spectral model
• Easy to handle pole
• application of B is low-cost

• Allows for non-homogeneous and anisotropic B
  formulation
• Allows distinguishing land-sea, tropics-midlats,
  etc
• Easy to use in both global and regional
  applications

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The Physical-space Statistical Analysis System
(PSAS)
Pros
Cons

• Adequate for when p ltlt n
• Allows for B formulation on physical-space,
  therefore open to inhomogeneous and anisotropic B
  formulation
• In theory, allows for modeling model error cov
  easily
• No pole issues
• Same code for global and regional applications
  (CPTEC)
• Observation sensitivity operators readily
  available

• Not as suitable for large p
• GMAO-specific implementation
• As formulated, does not readily provide analysis
  errors (alt. NAVDAS)
• Lack non-linear obs operators (alt. NAVDAS)

n dim(x) p dim(y)
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GSI Formulation of Background Error Cov

• Initially assumes background error covariance of
  the form
• B (Bv)T/2 ( Bh1 Bh2 Bh3 )
  (Bv)1/2
• where Bv includes the vertical component of the
  recursive filter and the balance relationships.
  This part of the background term is incorporated
  into the definition of the analysis variables
• and ( Bh1 Bh2 Bh3 ) represents three
  horizontal applications of the recursive filters
• The length scales used in Bv and Bh1 are
  calculated using the NMC method
• The length scales used in Bh2 and Bh3 amount to
  representing the fat tail in the covariance as
  well as its negative lobes

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GSI Background Error Cov Formulations
Isotropic model
Anisotropic model qfl20
Courtesy of J. Derber
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Illustration from Single Aircraft Obs Analysis
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Illustration from Single Ship Obs Analysis
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Illustration from Profiler Observations Analyses
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PSAS vs GSI Increments
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PSAS vs GSI Increments
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Residual Statistics GSI- vs PSAS-based DAS
PSAS-DAS
GSI-DAS
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Residual Statistics GSI- vs PSAS-based DAS
GSI-DAS
PSAS-DAS
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Residual Statistics GSI- vs PSAS-based DAS
GSI-DAS
PSAS-DAS
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Forecast Skill Scores Anomaly Correlations
NCEP DAS
PSAS fvDAS
GSI fvDAS
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Where do we go from here?
Short-term (2yrs)
Long-term (5yrs)

• Bring in NCEPs QC to allow adding to obs data
  stream
• Bypass some of Hermes transformations
• Replace FVGCM with GEOS-5 GCM
• Tackle moisture assimilation issues including
  fcst bias
• Cloud assimilation
• Fully interactive O3
• Land-surface analysis T-skin

• Observation bias removal
• Forecast bias removal
• Land-surface analysis soil moisture, snow,
  others
• Inhomogeneous and anisotropic background err
  covariances
• 4D-Var
• Coupled-chemistry

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Personal Account of Lessons Learned

• Invest strongly in making what you have work
• Decide on the next DA strategy and stick with it
• Place all your efforts in making the strategy
  work
• Rely on other peoples experiences
• Have one or at most two people lead the effort
• Have the leader(s) be single-tasked (w/ a view)
• Make sure that modelers and assimilators talk

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Quick Reference List
Cohn, S. E., A. da Silva, J. Guo, M. Sienkiewicz,
and D. Lamich, 1998 Assessing the effects of
data selection with the DAO physical-space
statistical analysis system. Mon. Wea. Rev.,
126, 2913-2926.
Derber,. J., A. Rosati, 1989 A Global oceanic
data assimilation system. J. Phys. Oceangr. 19,
1333-1347.
Purser, R.J., W.S Wu WS, D.F. Parrish, N.M.
Roberts, 2003umerical aspects of the application
of recursive filters to variational statistical
analysis. Part I Spatially homogeneous and
isotropic Gaussian covariances. Mon. Wea. Rev.,
131, 1524-1535.
Purser, R.J., W.S Wu WS, D.F. Parrish, N.M.
Roberts, 2003umerical aspects of the application
of recursive filters to variational statistical
analysis. Part II Spatially inhomogeneous and
anisotropic general covariances. Mon. Wea.
Rev., 131, 1536-1548.
Wu, W.S., R.J. Purser, D.F. Parrish, 2002
Three-dimensional variational analysis with
spatially inhomogeneous covariances Mon. Wea.
Rev., 130, 2905-2916.