Dr. I. Michael Navon
Professor of Mathematics,
Department of Scientific Computing ,
Florida State University
Optimization and Optimal Control
Office: 483 Dirac Science Library
Phone: (850) 728-5409
Fax: (850) 644-0098
NSF Supported Ensemble Kalman Filter Research Page
Workshop on Predicta- bility, Observations, and Uncertainties in Geosciences
13-15 March 2006
Presentations at Workshop on
Predictability, Observations, and Uncertainties in Geosciences
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1. Advanced 4-D Var Data-Assimilation Methods
The objective of this research effort which has been sponsored by NSF and NASA for many years is to use the mathematical theory of optimal control of partial differential equations for distributed parameter systems.
An application is variational data-assimilation methods which are very important to observationally based geophysical sciences such as dynamic meteorology and oceanography wherein remote sensing satellite data collected over a physical domain and in a finite span of time must be incorporated into a self-consistent set of initial conditions. The basic idea of these methods is to reduce a measure, called a cost functional, of the misfit between the observations and the output of a model. The cost functional is minimized while constrained by the dynamical model by finding an initial conditions control variable vector corresponding to a solution minimizing the cost functional and which satisfies the model strongly/weakly. Each minimization entails a forward integration of the model equations and a backward integration of the adjoint model equation. Computational costs of adjoint method for data assimilation include cost of solution of the forward and adjoint model and storage of intermediate model states for the extent of assimilation window, and large scale minimization of the gradient of the cost functional.
Innovative methods included development of a theory for efficient sensitivity analysis, nonlinear parameter estimation and 4-D variational data assimilation for NASA, NMC/NOAA and FSU-GSM operational 3-D models including a full physical package placing us at the cutting edge of research in this field.
2. Large-Scale Minimization
Methods for large scale constrained and unconstrained minimization are developed designed to mimic the behavior of variable-metric quasi-Newton methods which have an enhanced convergence rate. In these memoryless methods the Hessian matrix is updated but not stored. Current research work on these methods includes tests of the bundle algorithm for minimization of discontinuous functions and work on impact of efficient large-scale minimization algorithms ( L-BFGS, Hessian free methods and hybrid methods applied to multidisciplinary problems).
3. Ensemble Kalman filter methods
In collaboration with the group of Milija Zupanski and Prof Navon, are developing ensemble aspects related to forecast error covariance, balance constraints, , nonlinearity, model errors, computational efficiency, and verification. In particular, the results obtained using a version of Maximum Likelihood Ensemble Filter (MLEF) is considered.