Data Assimilation of High Dimensional, Nonlinear Dynamic Systems
During the spring semester and summer of 2017, Dr. Spiller and myself have been working on the Data Assimilation of the Lorenz '63 system. The Lorenz '63 system is three-dimensional, nonlinear system that has chaotic solutions depending on the initial conditions and values of its parameters. I first worked to solve this system using MatLab. From there I developed a Particle Filter and a Kalman Filter to be used to assimilate the calculated solutions with some 'observations'. From the calculated solutions, I simulated 'noisy observations' simply by adding normalized error to each point of the solution set for some deviation. Thusly, using the filters, I observe the effects, how well the data matches, and track the error as the standard deviation and period for the filters change.
The next system that will be observed is the Lorenz '96 system which is a higher dimensional, nonlinear system The Lorenz '96 system is known for modeling the atmospheric behavior of equally spaced locations and is commonly used for the forecasting of weather related dynamics. The goal is to first create a program that solves the system, then to apply the filters and again observe the behavior, yet at the higher dimensions.