In fluid mechanics two ways can be used to describe the behavior of a flow field. One is the Lagrangian method which describes the time rate of change in the flow properties along the traces of identifiable flow parcels. The other is the Eulerian method which observes the properties of flow at a fixed position over time.

In this talk, I will discuss the analogies of Lagrangian and Eulerian methods in visualization of time-varying scalar data. I will briefly overview some traditional visualization methods for time-varying data, which I will argue are mostly Lagrangian. Then I will describe our recent research in analyzing time-varying scientific data with Eulerian approaches. The new approaches allow us to obtain more accurate spatio-temporal information about the features in time-varying data sets. I will discuss the essential components of our analysis environment including multiscale data representations, distance metrics and classification schemes, and a method for multivariate data visualization. Our goal is to complement the existing visualization techniques, and provide the scientists with better quantitative data analysis tools.