Issues surrounding the assimilation of data into models have recently gained prominence in almost all areas of geophysics. The quantity and quality of data have increased dramatically with ever-improving observational technologies. At the same time, the ability to run extensive simulations on ever-faster computers has enhanced the use of models. Data assimilation is the problem of estimating the optimal prediction that combines model output, with its attendant uncertainty,and observations, which will also contain errors.

In this talk I will describe data assimilation techniques applied to a point-vortex fluid model. Owing to small dimensionality and yet complex nonlinear (Lagrangian) dynamics, vortex models are a natural paradigm for the investigation of systems with Lagrangian observations.  The ultimate goal of this investigation is to estimate hidden states of a nonlinear, stochastic dynamical system by combining model predictions and noisy partial observations of the system. Sequential Monte-Carlo (SMC) techniques allow one to approximate posterior distributions of hidden states at an observation instant without making assumptions of linearity on the dynamic model or of Gaussianity on the prior or posterior distributions of the state variables. Particle filters are a way to implement SMC using a large number of random samples, or particles, to obtain discrete approximations of these distributions. I will describe several modifications to particle filters that improve their performance, and I will compare these methods to a standard assimilation method.