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This is the web page of a Research Project funded by the National Science Foundation - Collaboration in Mathematical Geosciences under Grant No. 0327651, entitled "Ensemble Data Assimilation Based on Control Theory". This is a collaborative effort between Colorado State University (CSU) and Florida State University (FSU).
Principal Investigators: Dr Milija Zupanski (CSU) and Prof I. Michael Navon (FSU)
Co-Principal Investigators: Prof David Randall (CSU) and Prof Dacian Daescu (FSU)
Postdoctoral and other Investigators: Steven Fletcher, Bahri Uzunoglu, Xiaozhen Xiong and Mohamed Jardak
Project duration: 1 September 2003 - 31 August 2008
Goals and objectives:
1. Develop and test new Ensemble data assimilation (EnsDA) methodology based on control theory, with capability to assimilate nonlinear observations and employ a non-Gaussian Probability Density Function (PDF) assumption.
2. Evaluate the new methodology in assimilation of nonlinear observations. Pay special attention to Hessian preconditioning in highly nonlinear applications.
3. Compare Bayesian particle filter with EnKF and MLEF methods.
4. Compare forecast error covariances from the second-order 4D-Var and from EnsDA.
5. Assess the impact of nonlinear observation operators on particle filter, EnKF and MLEF methods.
Summary: This research project has produced a novel methodology for ensemble data assimilation (EnsDA) based on control theory, named the Maximum Likelihood Ensemble Filter (MLEF). This methodology extends the applicability of current nonlinear filters to arbitrary nonlinear observation operators, with important implications to remote sensing and other nonlinear observations. In addition to the main goal of developing an ensemble data assimilation system based on control theory, at least two major new results were produced by this research: (1) non-Gaussian framework for data assimilation was first formulated within this project, and is now gaining a worldwide recognition, and (2) new non-differentiable unconstrained minimizations algorithms are formulated and tested within this project. In addition, the issue of insufficient number of degrees of freedom was addressed during last year (2007-2008), resulting in an improvement of currently used error covariance localization techniques. To date, this project produced 13 papers(10 published, 2 submitted, 1 to be submitted).
Educational Impact:
- A course entitled : ISC-5935-02: Computational Aspects of Data Assimilation, Fall 2007, that was taught at Florida State University used the MLEF as an illustration of advanced ensemble data assimilation methods.
Selected Accomplishments:
- The MLEF system has been developed and tested in numerous applications. The MLEF algorithmic structure is shown in Fig.1. A detailed documentation of the MLEF algorithm is also available.
- A novel non-Gaussian EnsDA framework has been developed under this project. The approach includes a minimization of the non-Gaussian cost function, with an efficient implicit Hessian preconditioning [1, 2, 3].
- The MLEF includes an iterative minimization, which allows a consistent and efficient solution of the nonlinear analysis problem. An illustration of the MLEF performance with a nonlinear observation operator is shown in Fig.2.
- High-dimensional applications of the MLEF are improved with error covariance localization. An example of the MLEF in hurricane Katrina case, using the Weather Research and Forecasting (WRF) model, is shown in Fig.3.
A detailed project overview is given in the Final Report.