MODEL ERROR ESTIMATIONCooperative Institute for Research in the Atmosphere Research Benefits to NOAA:This is a novel research approach, providing an optimal estimate of the atmospheric state, model error estimation and the uncertainty of simulated/forecasted atmospheric processes. The knowledge about model error gained as a result of this research could be used to improve NOAA forecast models and observation operators.

Theoretical basisTheoretical framework for model error estimation is provided by the estimation theory. Model error estimate is obtained as a solution of an optimization problem, where discrepancies between the model and the data are minimized. This approach is a generalization of standard data assimilation methodologies, since observations are used not only to correct the errors in the initial conditions (IC) but the model errors (ME), as well.

Goals•Develop a general model error estimation methodology, applicable to any mathematical model•Employ all available observations (conventional surface and upper-air, satellite, radar, GPS, raingage)• Estimate and correct model errors in:

- forecast models (Eta, RAMS, WRF, GEOS)- observation operators (satellite radiative transfer models, radar reflectivity

models)

• Determine uncertainty of the model error estimate in the form of model error cross-covariance

MethodologySTATE AUGMENTATION APPROACH used in the frameworks of:• 4-DIMENSIONAL VARIATIONAL (4DVAR) data assimilation method (provides model error estimate only)• ENSEMBLE DATA ASSIMILATION (EnsDA) method (provides model error estimate and uncertainty of the estimate)

Types of model error• Serially correlated error (bias)• Lateral boundary conditions error• Parameter error (error in the model’s empirical parameters)

PublicationsVukicevic, T., T. Greenwald, M. Zupanski, D. Zupanski, T. Vonder Haar

and A. Jones, 2003: Mesoscale cloud state estimation from visible and infrared satellite radiances. Submitted to Mon. Wea. Rev.Zupanski D., M. Zupanski, E. Rogers, D. F. Parrish and G. J. DiMego,

2002: Fine resolution 4DVAR data assimilation for the Great Plains tornado outbreak of May 3rd 1999. Wea. Forecasting, 17, 506-525.

Zupanski D. and M. Zupanski, 2003: Maximum likelihood ensemble filter. Part II: Model error estimation. Submitted to Mon. Wea. Rev. (also available at

ftp://ftp.cira.colostate.edu/Zupanski/manuscripts/MLEF_model_err.pdf)Zupanski, D., M. Zupanski, T. Vukicevic, T. Vonder Haar, D. S. Ojima,

W.-S. Wu and D. M. Barker, 2003: Model error estimation using advanced data assimilation systems. Submitted to Mon. Wea. Rev. (also available at ftp://ftp.cira.colostate.edu/Zupanski/manuscripts/RAMDAS_paper.pdf)Zupanski M., D. Zupanski, D. Parrish, E. Rogers and G. J. DiMego,

2002: Four-dimensional variational data assimilation for the blizzard of 2000. Mon. Wea. Rev., 130, 1967-1988.

Collaborations NOAA/NCEP/EMC NOAA/NESDIS/RAMM Team NOAA/OGP/PACS/GAPP

Dusanka Zupanski NOAA Measurement Themes:CIRA Research Themes/Priorities

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Forecast error covariance

Data assimilation(Init. Cond. and Model Error adjust.)

Observations First guess

Init. Cond. and Model Error opt. estimates

Ens. forecasting

Analysis error Covariance

(in ensemble subspace)

EnsDA framework

State augmentation approach (a model bias example)

1-n1-n

1-n

k1-n

n1-n

n

nn FF

Mw

Φ

x

bΦ

Φx

Φ

xw

)1(

bias model ; conditions initial ; , k0k0k bxbxz

Control variable for the analysis cycle k:

4DVAR framework

Forecast error covariance

Data assimilation(Init. Cond. and Model Error adjust.)

Observations First guess

Init. Cond. and Model Error opt. estimates

Eta model: surface pressure model error time evolution (4DVAR)

RAMS model: Exner function (level=5000m) model error time evolution (4DVAR)

Vertical cross-section

KdVB model: Analysis error covariance matrix (EnsDA)