P1.8 QUANTIFYING AND REDUCING UNCERTAINTY BY EMPLOYING MODEL ERROR ESTIMATION METHODS

1. P1.8 QUANTIFYING AND REDUCING UNCERTAINTY BY EMPLOYING MODEL ERROR ESTIMATION METHODS Dusanka Zupanski Cooperative Institute for Research in the Atmosphere Colorado State University, Fort Collins, CO AMS Ed Lorenz Symposium • Introduction • Data assimilation methods can be effectively used to estimate errors in dynamical models of the atmosphere and ocean. Variational methods have been successfully used for model error estimation. New generation data assimilation techniques, referred as Ensemble Kalman fileter-like methods, are also capable of estimating and correcting model errors of dynamical models. These new methods do not require prescribed background error covariances, since the background error covariances are calculated via ensemble forecasting. Thus, ensemble based data assimilation methods have a potential for quantifying and reducing uncertainty of model simulated atmospheric and oceanic processes. • Methodology Maximum Likelihood Ensemble Filter (MLEF, Zupanski 2005; Zupanski and Zupanski 2005) • Developed using ideas from • Variational data assimilation(3DVAR, 4DVAR) • Iterated Kalman Filters • Ensemble Transform Kalman Filter (ETKF, Bishop et al. 2001) Bias estimation of KdVB model Bias estimation of CSU-RAMS model Analysis error covariance Estimated components of the augmented analysis error covariance matrix Estimated components of the augmented analysis error covariance matrix - experiments with simulated observations - model error created by using erroneous Coriolis force in the model’s equations Forecast error covariance • a non-linear dynamical model • Experiments • Estimate empirical parameters and model errors of a one-dimensional Korteweg-de Vries-Burgers (KdVB) model • Estimate model errors of a 3-dimensional non-hydrostatic model (CSU-RAMS) • Calculate uncertainties of the estimated model errors in terms of analysis error covariance matrix Pa Parameter estimation KdVB model Minimize cost functionJ Acknowledgements This research was partially funded by DoD grant DAAD19-02-2-0005 and NOAA grant NA17RJ1228 . References Bishop, C. H., B. J. Etherton, and S. Majumjar, 2001: Adaptive sampling with the ensemble transform Kalman filter. Part 1: Theoretical aspects. Mon. Wea. Rev.,129, 420–436. Zupanski, D., and M. Zupanski, 2005: Model error estimation employing ensemble data assimilation approach. Submitted to Mon. Wea. Rev. [Available at ftp://ftp.cira.colostate.edu/Zupanski/manuscripts/MLEF_model_err.revised2.pdf] Zupanski, M., 2005: Maximum likelihood ensemble filter: Theoretical aspects. Accepted to Mon. Wea. Rev. [Available at ftp://ftp.cira.colostate.edu/milija/papers/MLEF_MWR.pdf]. Change of variable Cross-covariance between model state and model error is complex for both models. It would be hard to correctly prescribe this cross-covariance, even for simple dynamical models, such as KdVB. Ensemble based approaches, such as the MLEF, can produce complex time evolving covariances for both model state and model error. • augmented control variable of dim Nstate >>Nens • (includes initial conditions, model error, empirical • parameters) “True” diffusion parameters are successfully estimated. Correct innovation statistic (expected to be Gaussian for this experiment) indicates that the estimated Pa is reliable. • control variable in ensemble space of dim Nens