Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado A General Ensemble-Based Approach to Data Assimilation Model Error and Parameter Estimation LSCE Presentation CEA/Saclay, Gif-sur-Yvette, October 19, 2005 Dusanka Zupanski, CIRA/CSU Outline  State augmentation approach  Issues of model error estimation - Degrees of freedom of model error - Information content of available data  Current research projects  Future research directions and collaborations

Major sources of forecast uncertainty Initial conditions Model errors (e.g., errors in dynamical equations, errors due to unresolved scales) Parametric errors (errors in empirical parameters) Forcing errors (e.g., errors in atmospheric forcing in hydrological models) Boundary conditions (e.g., lateral boundaries) All sources of uncertainty should be taken into account simultaneously within a unified mathematical approach.  These uncertainties are not independent!  Verified analysis and forecast uncertainty

Dusanka Zupanski, CIRA/CSU - Dynamical model for standard model state x State Augmentation Approach - Dynamical model for model error (bias) b - Dynamical model for empirical parameters  Define augmented state vector w Find optimal solution (augmented analysis) w a by minimizing J (MLEF method): And augmented dynamical model F ,. (Zupanski and Zupanski 2005, MWR)

Issues of Model Error (and Parameter) Estimation Dusanka Zupanski, CIRA/CSU State augmentation increases the size of the control variable  More Degrees of Freedom (DOF)! Do we need more ensembles? Do we need more observations? What is the number of the effective DOF of an ensemble-based data assimilation and model error estimation system?

Dusanka Zupanski, CIRA/CSU What is the number of the effective DOF? Ensemble Data Assimilation + State Augmentation + Information theory Answer can be obtained by using the following 3 components within a general framework: Shannon information content, or entropy reduction Degrees of freedom (DOF) for signal (Rodgers 2000; Zupanski et al. 2005) C - information matrix in ensemble subspace

Dusanka Zupanski, CIRA/CSU Information Content Analysis GEOS-5 Single Column Model N state =80; N obs =80 d s measures effective DOF of an ensemble-based data assimilation system (e.g., MLEF). Useful for addressing DOF of the model error.

NEGLECT BIASBIAS ESTIMATION (vector size=101) BIAS ESTIMATION (vector size=10)NON-BIASED MODEL BIAS ESTIMATION, KdVB model It is beneficial to reduce degrees of freedom of the model error.

 23 2-h DA cycles: 18UTC 2 May 1998 – 00 UTC 5 May 1998 (Mixed phase Arctic boundary layer cloud at Sheba site)  Experiments initialized with typical clean aerosol concentrations  May 4 was abnormal: high IFN and CCN above the inversion   x= 50m,  z max = 30m (2d domain: 50col, 40lev),  t=2s, Nens=48  Sophisticated microphysics in RAMS/LES  Control variables:  _il, u, v, w, N_x, R_x (8 species), IFN, CCN (dim= 22 variables x 50 columns x 40 levels = 44000)  Radar/lidar observations of IWP, LWP (LWDN, SWDN in future) Acknowledgements Gustavo Carrió, William Cotton, and Milija Zupanski (CSU) MLEF experiments with CSU/RAMS Large Eddy Simulation (LES) model

RAMS/LES Better timing of maxima LWP is also assimilated CONTROL EXP VERIF

RAMS/LES Improved timing and locations of the maxima NO vertical structure is assimilated (LWP) CONTROL VERIF EXP

RAMS/LES Independent observation IFN  above the inversion, as observed IFN  below inversion as cloud forms

More results will be presented by Carrió at the AGU Fall meeting in San Francisco (Arctic clouds session)

SiB-RAMS LPDM meteorological fieldsCO 2 fields and fluxes influence functions influence functions inversion techniques inversion techniques Bayesian MLEF CO 2 observations corrected CO 2 fluxes typically run with several nested grids covering a continental scale run on any subdomain extracted from SiB-RAMS MODELING FRAMEWORK Courtesy of M. Uliasz corrected within each inversion cycle

C – observed concentration k – index over observations (sampling times and towers) i – index over source grid cell (both respiration & assimilation fluxes) C * R.A – influence function integrated with respiration & assimilation fluxes C IN – background concentration combining effect of the flow across lateral boundaries and initial concentration at the cycle start  R  A – corrections (biases) to be estimated Implementation for a given inversion cycle Courtesy of M. Uliasz

CO 2 flux respiration & assimilation fluxes simulated by SiB-RAMS respiration & assimilation fluxes simulated by SiB-RAMS time independent corrections to be estimated from concentration data for each inversion cycle time independent corrections to be estimated from concentration data for each inversion cycle ASSUMPTION: SiB-RAMS is capable to realistically reproduce diurnal cycle and spatial distribution of CO 2 (assimilation and respiration) fluxes. Therefore, observation data are used to correct those fluxes for errors in atmospheric transport. ASSUMPTION: SiB-RAMS is capable to realistically reproduce diurnal cycle and spatial distribution of CO 2 (assimilation and respiration) fluxes. Therefore, observation data are used to correct those fluxes for errors in atmospheric transport. Courtesy of M. Uliasz

SiB-RAMS simulation: 15 days starting on July 19 th, 2004 on two nested grids (10 km grid spacing on the finer grid) LPDM and influence function domain: 600x600km centered at WLEF tower Concentration pseudo-data were generated for WLEF and the ring of towers from SiB-RAMS assimilation and respiration fluxes using correction values of 1. Model-data mismatch error was assumed to be higher for lower towers:2 ppm for towers>100m, 3 ppm for towers > 50m, and 5 ppm for towers < 50m three 5 day inversion cycles were performed using Bayesian inversion technique with concentration pseudo data (initial corrections = 0.5 and their standard deviations = 0.5) INVERSION EXPERIMENTS

 R : Reduction of uncertainty (  0 -  ) Bayesian MLEF

 A : Reduction of uncertainty (  0 -  ) Bayesian MLEF

Bayesian inversion: reduction of uncertainty  0 -  RR AA

RR AA MLEF (450 ens): reduction of uncertainty  0 - 

Current Research Projects  Precipitation Assimilation (NASA) Apply MLEF to NASA GEOS-5 column precipitation model Address model error and parameter estimation (In collaboration with A. Hou, S. Zhang - NASA/GMAO, C. Kummerow - CSU/Atmos. Sci. Dept.)  GOES-R Risk Reduction (NOAA/NESDIS) Evaluate the impact of GOES-R measurements in applications to severe weather and tropical cyclones Information content of GOES-R measurements (In collaboration with M. DeMaria - CIRA/NOAA/NESDIS, T. Vonder Haar, L. Grasso, M. Zupanski - CSU/CIRA)  Carbon Cycle Data Assimilation (NASA) Apply MLEF to various carbon models (LPDM, SiB3, PCTM, and SiB- CASA-RAMS) Assimilate carbon concentrations globally and locally Address model error and parameter estimation (In collaboration with S. Denning, M. Uliasz, K. Gurney, L. Prihodko, R. Lokupitiya, I. Baker, K. Schaefer - CSU/Atmos. Sci. Dept., M. Zupanski - CSU/CIRA) Dusanka Zupanski, CIRA/CSU

Future Research Directions and Collaborations Information content analysis Quantify value added of new observations (e.g., GPM, CloudSat, GOES-R, OCO) Determine effective DOF of an ensemble-based data assimilation system Model bias and parameter estimation requires collaboration Learning about model errors and uncertainties from different dynamical models Developing diagnostic tools for new model development Discuss issues for collaboration with NCAR/MMM Model errors and parameter estimation for WRF model Information content analysis - effective DOF of WRF data assimilation system Dusanka Zupanski, CIRA/CSU