(COMPLETED) CMG-Ensemble Data Assimilation System Based on Control Theory
Project Period: April 21, 2014 to January 1, 2017
Principal Investigator(s): Milija Zupanski and Michael Navon (FSU)
Co-Principal Investigator(s): David Randall (CSU) and Dacian Daescu (PSU)
Other Investigators: Steven Fletcher, Bahri Uzunoglu (FSU), Xiaozhen Xiong (FSU) and Mohamed Jardak (FSU)
Sponsors: National Science Foundation (NSF)
This is a collaborative effort between Colorado State University (CSU) and Florida State University (FSU).
Goals and Objectives:
- 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.
- Evaluate the new methodology in assimilation of nonlinear observations. Pay special attention to Hessian preconditioning in highly nonlinear applications.
- Make the new methodology available to universities and research institutions. Provide instructions to users.
- Pending the results, develop new Hessian preconditioning / Optimization applicable to highly nonlinear data assimilation (D/A) applications.
A development of fundamentally new EnsDA methodology is proposed, based on innovative use and development of optimization algorithms and Hessian preconditioning applicable to highly nonlinear problems. The uniqueness of the proposed methodology is its capability to: (i) use arbitrary nonlinear observation operators, and (ii) include non-Gaussian probability densities. The anticipated impact of the control theory will be critical for achieving the new quality of EnsDA methodology. In particular, the propsed research consists of three major parts:
- Developing the new EnsDA methodology;
- Evaluating the impact of various optimization algorithms in EnsDA, with special emphasis on the nonlinear aspects of optimization algorithm;
- Evaluating the impact of nonlinear measurements and non-Gaussian assumption on the quality of the probabilistic (e.g., uncertainty) EnsDA output.
It is anticipated that the proposed research will have a substantial impact on the future development and use of probabilistic forecasting and data assimilation in meteorology and oceanography. It is also expected that this research will lay a foundation for qualitative improvement of the present understanding of predictability and nonlinear dynamics, through an optimized use of the Kolmogorov’s equation in low-dimensional dynamical space. Successful ensemble data assimilation will benefit the geosciences and other related fields, since the formalism is general enough to incorporate any dynamical model and any measurements.
Several graduate research assistants and postdoctoral researchers who are contributing in this project, as well as the students attending a graduate course taught at FSU by Prof. Navon will be exposed to state-of-the-art data assimilation and to advanced minimization techniques.