DATA ASSIMILATION AND MODEL ERROR ESTIMATION Dusanka Zupanski Cooperative Institute for Research in the Atmosphere Colorado State University Fort Collins, CO Oregon State University Physical Oceanography Seminar Series 27 April 2004 ftp://ftp.cira.colostate.edu/Zupanski/presentations ftp://ftp.cira.colostate.edu/Zupanski/manuscripts

OUTLINE:  Data assimilation research pursued at CIRA  Approaches: variational and ensemble (EnsDA)  Model error estimation  Experimental results  Summary and future work Dusanka Zupanski, CIRA/CSU

DATA ASSIMILATION RELATED RESEARCH  Basic development of data assimilation - Variational methods (T.Vukicevic, M. Zupanski, D. Zupanski) - Ensemble (EnsDA) methods (M. Zupanski, D. Zupanski) - Non-Gaussian probability distributions (M. Zupanski) - Model error estimation (D. Zupanski)  Specific applications - 4DVAR cloud state estimation (T.Vukicevic, M. Sengupta) - 4DVAR soil moisture estimation (A. Jones, T. Vukicevic) - 4DVAR carbon cycle studies (T. Vukicevic; D. Ojima – CSU/NREL; D. Schimel – NCAR; S. Denning – CSU/ATS; D. Zupanski) CSU/NREL; D. Schimel – NCAR; S. Denning – CSU/ATS; D. Zupanski) - EnsDA application to NCEP’s global (GFS) model (M. Zupanski) - EnsDA application in GOES-R risk reduction (M. DeMaria, D. Zupanski) - EnsDA application to NASA’s GEOS model (D. Zupanski) Dusanka Zupanski, CIRA/CSU

DATA ASSIMILATION RELATED RESEARCH  Research funding - DoD (CG/AR), NOAA (NESDIS, JCSDA, THORPEX), NSF, NASA NSF, NASA  Data assimilation research at CIOSS and COAS - (A. Bennett, R. Miller, G. Egbert, B. Chua, A. Kurapov) Dusanka Zupanski, CIRA/CSU

OUTLINE:  Data assimilation research pursued at CIRA  Approaches: variational and ensemble (EnsDA)  Model error estimation  Experimental results  Summary and future work Dusanka Zupanski, CIRA/CSU

DATA ASSIMILATION APPROACHES  Variational - Weak constraint 4DVAR (including model bias estimation) - RAMS mesoscale atmospheric model - Developed after NCEP’s Eta model 4DVAR - WRF 3DVAR observation operators for conventional atmospheric observations atmospheric observations - GOES visible and IR radiances (all weather) - Non-linear operators (M, H) are used  EnsDA - Maximum Likelihood Ensemble Filter (MLEF) - Model error estimation (model bias, empirical parameters) - Optimal solution obtained by minimizing a cost function - KdVB model, NASA’s GEOS column model - Adjoint model not needed (non-linear and discontinuous processes handled well) - Non-linear operators (M, H) are used Dusanka Zupanski, CIRA/CSU (MLEF is described in M. Zupanski, submitted to MWR, 2004)

4DVAR framework Forecast error covariance Data assimilation: (IC, Model Error, and BC adjustment) Observations First guess Optimal estimates Forecast error covariance Data assimilation: (IC, Model Error, and BC adjustment) Observations First guess Optimal estimates Ens. forecasting Analysis error Covariance (in ensemble subspace) EnsDA (MLEF) framework (KF) (MLEF) (4DVAR and MLEF)

OUTLINE:  Data assimilation research pursued at CIRA  Approaches: variational and ensemble (EnsDA)  Model error estimation  Experimental results  Summary and future work Dusanka Zupanski, CIRA/CSU

Dusanka Zupanski, CIRA/CSU Parameter estimation is a special case of state augmentation approach! Model error estimation x 0 – initial conditions ; b k – model bias n – model time step; k – analysis cycle;  - constant  State augmentation approach (following Zupanski, MWR 1997) - model state (x ) augmented to include model error (  ) - estimate optimal initial conditions and a serially correlated model error (boundary conditions error is a part of model error)  Assimilation of real observations - model error cannot be neglected - use information from observations to learn about model error (Assumption:  0 = b k-1 )

Relation between  of first order Markov process variable and the time decorrelation length L*  t, for time separation k*  t For  =0.80: k=10  L=22.6 k=20  L=60 k=30  L=101.2 For  =0.70: k=10  L=18.86 k=20  L=45.1 k=30  L=72.38 With assuming n  1:

OUTLINE:  Data assimilation research pursued at CIRA  Approaches: variational and ensemble (EnsDA)  Model error estimation  Experimental results (4DVAR method)  Summary and future work Dusanka Zupanski, CIRA/CSU

DATA ASSIMILATION APPROACHES  Variational - Weak constraint 4DVAR (including model bias estimation) - RAMS mesoscale atmospheric model - Developed after NCEP’s Eta model 4DVAR - WRF 3DVAR observation operators for conventional atmospheric observations atmospheric observations - GOES visible and IR radiances (all weather) - Non-linear operators (M, H) are used  EnsDA - Maximum Likelihood Ensemble Filter (MLEF) - Model error estimation (model bias, empirical parameters) - Optimal solution obtained by minimizing a cost function - KdVB model, NASA’s GEOS column model - Adjoint model not needed (non-linear and discontinuous processes handled well) - Non-linear operators (M, H) are used Dusanka Zupanski, CIRA/CSU (MLEF is described in M. Zupanski, submitted to MWR, 2004)

Dusanka Zupanski, CIRA/CSU ETA 4DVAR: Surface pressure model error time evolution (every 2-h over a 12-h data assimilation interval) From Zupanski et al (submitted to QJRMS)

Dusanka Zupanski, CIRA/CSU RAMS 4DVAR: Exner function model error time evolution (lev=5km), every 2-h From Zupanski et al (submitted to QJRMS)

Sample of results from 4DVAR cirrus cloud study (21 March 2000, RAMS model resolution 6km/84layers, 1-h assimilation window) Tomislava Vukicevic, CIRA/CSU (Vukicevic et al., submitted to MWR 2004)

Comparison with independent data: ARM sounding of T Good convergence Model domain bias eliminated Error variance significantly reduced Temperature Iteration number Tomislava Vukicevic, CIRA/CSU

Vertical extent of cirrus cloud and radar reflectivity values in good agreement with the observations within 1 h window of assimilation Tomislava Vukicevic, CIRA/CSU

Andy Jones, CIRA/CSU (Jones et al., J. Hydrometeor., 2004)

Andy Jones, CIRA/CSU (Jones et al., J. Hydrometeor., 2004)

OUTLINE:  Data assimilation research pursued at CIRA  Approaches: variational and ensemble (EnsDA)  Model error estimation  Experimental results (EnsDA method)  Summary and future work Dusanka Zupanski, CIRA/CSU

DATA ASSIMILATION APPROACHES  Variational - Weak constraint 4DVAR (including model bias estimation) - RAMS mesoscale atmospheric model - Developed after NCEP’s Eta model 4DVAR - WRF 3DVAR observation operators for conventional atmospheric observations atmospheric observations - GOES visible and IR radiances (all weather) - Non-linear operators (M, H) are used  EnsDA - Maximum Likelihood Ensemble Filter (MLEF) - Model error estimation (model bias, empirical parameters) - Optimal solution obtained by minimizing a cost function - KdVB model, NASA’s GEOS column model - Adjoint model not needed (non-linear and discontinuous processes handled well) - Non-linear operators (M, H) are used Dusanka Zupanski, CIRA/CSU (MLEF is described in M. Zupanski, submitted to MWR, 2004)

Maximum Likelihood Ensemble Filter (MLEF) Data assimilation with KdVB model (quadratic obs operator, 10 ensembles, 10 obs) Impact of assimilationAnalysis error covariance NO OBS MLEF Model dynamics helps in localization of analysis error covariance ! H(x)=x 2 (M. Zupanski, submitted to MWR, 2004)

MLEF data assimilation with KdVB model Impact of minimization Cost function minimization reduces RMS error NO MINIMIZATION MLEF Analysis statistics is adequate in both algorithms, analysis quality differs

EnsDA Experiments with KdVB model (PARAMETER estimation impact) 10 obs101 obs INCORRECT DIFFUSION CORRECT DIFFUSION PARAMETER ESTIMATION

EnsDA Experiments with KdVB model (Model BIAS estimation impact) Dusanka Zupanski, CIRA/CSU (Zupanski and Zupanski, submitted to MWR, 2004) NEGLECT BIASBIAS ESTIMATION (vector size=101) BIAS ESTIMATION (vector size=10)NON-BIASED MODEL

EnsDA results with assimilation of PSAS analyses employing NASA’s GEOS column model Work in progress under NASA’s TRMM project - D. Zupanski (CSU/CIRA) and A. Hou (NASA/GMAO) R 1/2 = 1/2  R 1/2 =  Choice of observation errors directly impacts innovation statistics. Observation error covariance R is the only given input to the system! Currently under development: EnsDA for the CSU RAMS model (D. Zupanski, M. Zupanski, M. DeMaria, L. Grasso, NOAA/NESDIS GOES-R project) EnsDA for NOAA/NCEP GSF model (M. Zupanski, THORPEX project)

Summary and future work Summary and future work  Variational and EnsDA methods can address a variety of research problems in atmospheric, oceanic, ecological, hydrological and other similar sciences  To employ full data assimilation power, model error estimation should be included  Model error estimation is an important diagnostic and model development tool (estimate and correct model errors during the model development phase)  EnsDA approaches are very promising since they can provide not only optimal estimate of the atmospheric state, but the uncertainty of the estimate as well  IN THE FUTURE: further development of data assimilation, model error estimation and ensemble prediction methods; applications to atmospheric, oceanic and other similar models; assimilation of various in-situ and remote sensing (satellite, radar, GPS) obs.

Possible collaboration on data assimilation issues Possible collaboration on data assimilation issues  Data assimilation for coupled ocean-atmosphere-land models  Share the experience with various satellite observations and observation operators (radiative transfer models)  Model error estimation (oceanic, atmospheric, land, ecological models, radiative transfer models)  On-line estimation of analysis and forecast error covariances, observation error covariances

Algorithm: Regional Atmospheric Modeling and Data Assimilation System (RAMDAS) developed for RAMS using 4DVAR approach Observational operator developed for assimilation of visible and IR radiance Applications: Assimilation of GOES imager visible and IR observations for a case of continental stratus cloud evolution Sensitivity of visible and IR radiance measurements to cloud parameters Assimilation of GOES imager IR observations for a case of cirrus cloud evolution (sample in this presentation) 4DVAR cloud state estimation Tomislava Vukicevic, CIRA/CSU (Vukicevic et al., submitted to MWR 2004)

Plans to apply EnsDA algorithm to RAMS and WRF models  Use the probabilistic assimilation-prediction system with RAMS and/or WRF to assess GOES-R sounder capabilities using simulated data (identical twin experiments)  Use a similar framework to assimilate AIRS soundings for mesoscale case studies (severe weather, tropical cyclone, lake effect snow)  Continue the mesoscale studies when CrIS soundings become available from the NPP mission.  Uncertainty information provided by ensemble forecasting can be used to gain new knowledge about atmospheric processes  New knowledge about model errors and observation errors can also be obtained Dusanka Zupanski, CIRA/CSU

Probabilistic (ensemble) assimilation-prediction system  Data assimilation and ensemble forecasting fully coupled - optimal perturbations for ensemble forecasting - flow-dependent forecast error covariance for data assimilation  Maximum likelihood approach - cost function minimization in ensemble-spanned subspace - no adjoint needed  Model error estimation - empirical model parameters - serially correlated model error (bias) Zupanski (Submitted to MWR, 2004) Zupanski and Zupanski (Submitted to MWR, 2004)

Andy Jones, CIRA/CSU

DATA ASSIMILATION RELATED RESEARCH  Basic development of data assimilation - Variational methods (T.Vukicevic, M. Zupanski, D. Zupanski) - Ensemble (EnsDA) methods (M. Zupanski, D. Zupanski) - Non-Gaussian probability distributions (M. Zupanski) - Model error estimation (D. Zupanski)  Specific applications - 4DVAR cloud state estimation (T.Vukicevic) - 4DVAR soil moisture estimation (A. Jones, T. Vukicevic) - 4DVAR carbon cycle studies (T. Vukicevic; D. Ojima – CSU/NREL; D. Schimel – NCAR; S. Denning – CSU/ATS; D. Zupanski) CSU/NREL; D. Schimel – NCAR; S. Denning – CSU/ATS; D. Zupanski) - EnsDA application to NCEP’s global model (M. Zupanski) - EnsDA application in GOES-R risk reduction (M. DeMaria, D. Zupanski) - EnsDA application to NASA’s GEOS model (D. Zupanski)  Research funding - DoD (CG/AR), NOAA (NESDIS, JCSDA, TORPEX), NSF, NASA, etc. NSF, NASA, etc  Data assimilation research at CIOSS and COAS - (A. Bennett, R. Miller, G. Egbert, B. Chua)