# Data Assimilation For Fluid Dynamic Models

**Mentor:** Elaine Spiller

**Approach:** Implement and evaluate numerical methods to solve stochastic differential equations modeling
atmospheric and oceanographic fluid flows.

**Summary:** Data assimilation is a broad term for techniques that combine noisy observations with dynamic
model based predictions. Applications vary widely; some interesting examples are weather prediction/storm
tracking, ecological population studies, and real-time traffic flow. Many data assimilation schemes are based
on assumptions that models are approximately linear and that the uncertainty of a system follows a Gaussian
distribution, both of which are often invalid assumptions. This project is concerned with applications
where data is (spatially) sparse and obtaining data on a grid is challenging – as is typical of atmospheric and
oceanographic problems. This is an exciting area of study since the applications are diverse and important
to help us understand the current and future state of our planet. Scientifically, it is important to develop
methods that can deal with the available data (often from weather balloons, ocean drifters or ocean gliders
in cases of environmental science). Since data in such problems comes to us in the Lagrangian frame, or
semi-Lagrangian frame in the case of gliders, it is useful to establish data assimilation methods that work in
different frames of reference. The ultimate scientific goal is to establish methods in the Lagrangian frame that
can also naturally deal with nonlinearity. The project will combine techniques from dynamical systems
theory with traditional, statistically based data assimilation methods to accomplish this task. Students involved
in this project will learn about data assimilation and fluid dynamic models, implement numerical methods
to solve stochastic differential equations, learn about and implement filtering methods (i.e., updating models
with data), and learn about flow behavior from a dynamical systems perspective.