Presentation is loading. Please wait.

Presentation is loading. Please wait.

Dusanka Zupanski And Scott Denning Colorado State University Fort Collins, CO 80523-1375 CMDL Workshop on Modeling and Data Analysis of Atmospheric CO.

Published byAlaina O’Connor’ Modified over 9 years ago

Similar presentations

Presentation on theme: "Dusanka Zupanski And Scott Denning Colorado State University Fort Collins, CO 80523-1375 CMDL Workshop on Modeling and Data Analysis of Atmospheric CO."— Presentation transcript:

1 Dusanka Zupanski And Scott Denning Colorado State University Fort Collins, CO 80523-1375 CMDL Workshop on Modeling and Data Analysis of Atmospheric CO 2 Observations in North America 29-30 September 2004 ftp://ftp.cira.colostate.edu/Zupanski/presentations ftp://ftp.cira.colostate.edu/Zupanski/manuscripts Critical issues of ensemble data assimilation in application to carbon cycle studies

2  Introduction: EnsDA approaches  Non-linear processes  Model error and parameter estimation  Uncertainty estimates  Correlated observations  Non-Gaussian PDFs  Conclusions and future work Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu OUTLINE:

3 Probabilistic approach to data assimilation and forecasting or Ensemble Data Assimilation (EnsDA) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu Provides the following: (1) Optimal solution or state estimate (e. g., optimal CO 2 analysis) (2) Optimal estimates of model error and empirical parameters (3) Uncertainty of the analysis (a component of the analysis error covariance P a ) (4) Uncertainty of the estimated model error and parameters (components of the analysis error covariance P a ) (5) Estimate of forecast uncertainty (the forecast error covariance P f )

4 DATA ASSIMILATION (ESTIMATION THEORY) Discrete stochastic-dynamic model Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu Discrete stochastic observation model w k-1 – model error (stochastic forcing) M – non-linear dynamic (NWP) model G – model (matrix) reflecting the state dependence of model error  k – measurement + representativeness error M  D H– non-linear observation operator ( M  D )

5 (1) State estimate (optimal solution): (2) Estimate of the uncertainty of the solution: ENSEMBLE KALMAN FILTER or EnsDA APPROACH In EnsDA solution is defined in ensemble subspace (reduced rank problem) ! KALMAN FILTER APPROACH MAXIMUM LIKELIHOOD ESTIMATE (VARIATIONAL APPROACH ): MINIMUM VARIANCE ESTIMATE (KALMAN FILTER APPROACH ): DATA ASSIMILATION EQUATIONS:

6 Ensemble Data Assimilation (EnsDA) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu (1) Maximum likelihood approach (involves an iterative minimization of a functional)  x mode (MLEF, Zupanski 2004) (2) Minimum variance approach (calculates ensemble mean)  x mean x mode x mean x PDF(x) x mode = x mean x PDF(x) Non-GaussianGaussian

7 Critical issues: Non-linear processes Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu - Use only non-linear models (tangent-linear, adjoint models are not needed) - Iterative minimization is beneficial for non-linear processes Example: KdVB model (M. Zupanski, 2004)

8 Critical issues: Model error and parameter estimation Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu - Estimate and correct all major sources of uncertainty: initial conditions, model error, boundary conditions, empirical parameters - Unified algorithm: EnsDA+state augmentation approach (Zupanski and Zupanski, 2004) Example: KdVB model

9 10 obs101 obs EnsDA experiments with KdVB model (PARAMETER estimation impact)

10 EnsDA experiments with KdVB model (BIAS estimation impact) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

11 Critical issues: Uncertainty estimates Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu - Analysis error covariance P a (analysis uncertainty) - Forecast error covariance P f (forecast uncertainty) - Both defined in ensemble sub-space KdVB model example:

12 Critical issues: Correlated observations Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu Problem: Numerous observations (~10 8 -10 9 ) are being projected onto a small ensemble sub-space (~10 1 -10 3 ) ! Loss of observed information! Remedies:  Process observations one by one (Anderson 2001, Bishop et al. 2001; Hamill et al. 2001). Or  Process observations successively over relatively small local areas (LEKF, Ott et al. 2004). Assumption in both approaches: Observations being processed separately are uncorrelated (independent)! This may not be justified for dense satellite observations.

13 Critical issues: Correlated observations Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu How does the observed information impact the uncertainty estimate of the optimal solution (analysis error covariance P a ) ? - square root of analysis error covariance (N state x N ens ) - square root of forecast error covariance (N state x N ens ) - impact of observations on the optimal solution (N ens x N ens ) The eigenvalue spectrum of (I+A) -1/2 may help understand the impact of observations, and perhaps find a better solution for correlated observations.

14 RAMS model example Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu A safe approach to prevent loss of observed information, assuming independent observations: N obs  N ens. If eigenvalues of (I+A) -1/2 spread over the entire interval [0,1], ensemble size (N ens ) is appropriate for a given observation number (N obs ).

15 CSU shallow-water model on geodesic grid When system can learn from its past, less information from observations is needed ! Smooth start (in cycle 1) can improve the performance of EnsDA Milija Zupanski, CIRA/CSU ZupanskiM@CIRA.colostate.edu Analysis error smaller than obs error (Results from M. Zupanski et al.)

16 Non-Gaussian PDFs Non-linear Atmospheric- Hydrology- Carbon state variables and observations are likely to have non-Gaussian PDFs.  MLEF, as a maximum likelihood estimate, is a suitable tool for examining the impact of different PDFs.  Develop a non-Gaussian PDF framework (M. Zupanski) - allow for non-Gaussian observation errors - apply the Bayes theorem for multiple events Milija Zupanski, CIRA/CSU ZupanskiM@CIRA.colostate.edu

17 CSU EnsDA algorithm is currently being examined in application to NASA’s GEOS column model in collaboration with: -A. Hou and S. Zhang (NASA/GMAO) -C. Kummerow (CSU/Atmos. Sci.) NASA’s GEOS column model example R 1/2 =  R 1/2 = 2  Prescribed observation errors directly impact innovation statistics. Since the observation error covariance R is the only input required by the system, it could be tuned! Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu In case we solved all critical issues, one problem remains: How to define observation error covariance matrix R, if it is not known?

18  EnsDA approaches are very promising since they can provide not only optimal estimate of the state, but also the uncertainty of the optimal estimate.  The experience gained so far indicates that the EnsDA approach is suitable for addressing critical issues of data assimilation in Carbon cycle studies.  Model error and parameter estimation are necessary ingredients of a data assimilation algorithm.  Problems involved in Carbon data assimilation require a state-of- the art approach. We anticipate findings from different scientific disciplines (e. g., atmospheric science, ecology, hydrology) to be of mutual benefits.  It is especially important to gain experience with complex coupled models (e. g., RAMS-SiB-CASA), correlated (satellite) observations, and non-Gaussian PDFs in the future. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.eduCONCLUSIONS

19 Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

Download ppt "Dusanka Zupanski And Scott Denning Colorado State University Fort Collins, CO 80523-1375 CMDL Workshop on Modeling and Data Analysis of Atmospheric CO."

Similar presentations

Data-Assimilation Research Centre

Data-Assimilation Research Centre
Introduction to Data Assimilation NCEO Data-assimilation training days 5-7 July 2010 Peter Jan van Leeuwen Data Assimilation Research Center (DARC) University.

Introduction to Data Assimilation NCEO Data-assimilation training days 5-7 July 2010 Peter Jan van Leeuwen Data Assimilation Research Center (DARC) University.
Modeling of Data. Basic Bayes theorem Bayes theorem relates the conditional probabilities of two events A, and B: A might be a hypothesis and B might.

Modeling of Data. Basic Bayes theorem Bayes theorem relates the conditional probabilities of two events A, and B: A might be a hypothesis and B might.
Introduction to Data Assimilation Peter Jan van Leeuwen IMAU.

Introduction to Data Assimilation Peter Jan van Leeuwen IMAU.
Ensemble data assimilation (EnsDA) activities of the GOES-R project Progress report Dusanka Zupanski CIRA/CSU GOES-R meeting 8 September 2004 Dusanka Zupanski,

Ensemble data assimilation (EnsDA) activities of the GOES-R project Progress report Dusanka Zupanski CIRA/CSU GOES-R meeting 8 September 2004 Dusanka Zupanski,
P2.1 ENSEMBLE DATA ASSIMILATION: EXPERIMENTS USING NASA’S GEOS COLUMN PRECIPITATION MODEL D. Zupanski 1, A. Y. Hou 2, S. Zhang 2, M. Zupanski 1, C. D.

P2.1 ENSEMBLE DATA ASSIMILATION: EXPERIMENTS USING NASA’S GEOS COLUMN PRECIPITATION MODEL D. Zupanski 1, A. Y. Hou 2, S. Zhang 2, M. Zupanski 1, C. D.
Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado Model Error and Parameter Estimation Joint NCAR/MMM CSU/CIRA Data Assimilation Workshop.

Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado Model Error and Parameter Estimation Joint NCAR/MMM CSU/CIRA Data Assimilation Workshop.
Critical issues of ensemble data assimilation in application to GOES-R risk reduction program D. Zupanski 1, M. Zupanski 1, M. DeMaria 2, and L. Grasso.

Critical issues of ensemble data assimilation in application to GOES-R risk reduction program D. Zupanski 1, M. Zupanski 1, M. DeMaria 2, and L. Grasso.
1B.17 ASSESSING THE IMPACT OF OBSERVATIONS AND MODEL ERRORS IN THE ENSEMBLE DATA ASSIMILATION FRAMEWORK D. Zupanski 1, A. Y. Hou 2, S. Zhang 2, M. Zupanski.

1B.17 ASSESSING THE IMPACT OF OBSERVATIONS AND MODEL ERRORS IN THE ENSEMBLE DATA ASSIMILATION FRAMEWORK D. Zupanski 1, A. Y. Hou 2, S. Zhang 2, M. Zupanski.
Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado A General Ensemble-Based Approach to Data Assimilation Model Error and Parameter.

Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado A General Ensemble-Based Approach to Data Assimilation Model Error and Parameter.
Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado Ensemble Kalman Filter Guest Lecture at AT 753: Atmospheric Water Cycle 21 April.

Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado Ensemble Kalman Filter Guest Lecture at AT 753: Atmospheric Water Cycle 21 April.
P1.8 QUANTIFYING AND REDUCING UNCERTAINTY BY EMPLOYING MODEL ERROR ESTIMATION METHODS Dusanka Zupanski Cooperative Institute for Research in the Atmosphere.

P1.8 QUANTIFYING AND REDUCING UNCERTAINTY BY EMPLOYING MODEL ERROR ESTIMATION METHODS Dusanka Zupanski Cooperative Institute for Research in the Atmosphere.
Model error estimation employing ensemble data assimilation Dusanka Zupanski and Milija Zupanski CIRA/Colorado State University, Fort Collins, CO, U.S.A.

Model error estimation employing ensemble data assimilation Dusanka Zupanski and Milija Zupanski CIRA/Colorado State University, Fort Collins, CO, U.S.A.
Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado Ensemble Data Assimilation and Prediction: Applications to Environmental Science.

Dusanka Zupanski CIRA/Colorado State University Fort Collins, Colorado Ensemble Data Assimilation and Prediction: Applications to Environmental Science.
MODEL ERROR ESTIMATION Cooperative Institute for Research in the Atmosphere Research Benefits to NOAA:This is a novel research approach, providing an optimal.

MODEL ERROR ESTIMATION Cooperative Institute for Research in the Atmosphere Research Benefits to NOAA:This is a novel research approach, providing an optimal.
Hou/JTST2000 - 1 Exploring new pathways in precipitation assimilation Arthur Hou and Sara Zhang NASA Goddard Space Flight Center Symposium on the 50 th.

Hou/JTST Exploring new pathways in precipitation assimilation Arthur Hou and Sara Zhang NASA Goddard Space Flight Center Symposium on the 50 th.
1 アンサンブルカルマンフィルターによ る大気海洋結合モデルへのデータ同化 On-line estimation of observation error covariance for ensemble-based filters Genta Ueno The Institute of Statistical.

1 アンサンブルカルマンフィルターによ る大気海洋結合モデルへのデータ同化 On-line estimation of observation error covariance for ensemble-based filters Genta Ueno The Institute of Statistical.
Ibrahim Hoteit KAUST, CSIM, May 2010 Should we be using Data Assimilation to Combine Seismic Imaging and Reservoir Modeling? Earth Sciences and Engineering.

Ibrahim Hoteit KAUST, CSIM, May 2010 Should we be using Data Assimilation to Combine Seismic Imaging and Reservoir Modeling? Earth Sciences and Engineering.
Parameter Estimation and Data Assimilation Techniques for Land Surface Modeling Qingyun Duan Lawrence Livermore National Laboratory Livermore, California.

Parameter Estimation and Data Assimilation Techniques for Land Surface Modeling Qingyun Duan Lawrence Livermore National Laboratory Livermore, California.
Carbon Flux Bias Estimation at Regional Scale using Coupled MLEF-PCTM model Ravindra Lokupitiya Department of Atmospheric Science Colorado State University.

Carbon Flux Bias Estimation at Regional Scale using Coupled MLEF-PCTM model Ravindra Lokupitiya Department of Atmospheric Science Colorado State University.

Similar presentations

Ads by Google