On the use of Finite-Time Lyapunov Exponents and Vectors for direct assimilation of tracer images into ocean models

Satellite ocean tracer images, of sea surface temperature (SST) and ocean colour images, for example, show patterns like fronts and filaments that characterize the flow dynamics. These patterns can be described using Lagrangian tools such as Finite-Time Lyapunov Exponents (FTLE) or Finite-Time Lyapunov Vectors (FTLV). In recent years, several studies have investigated the possibility of directly assimilating structured data from satellite images into numerical models. In this paper, we exploit specific properties of FTLE and FTLV to define observation operators that can be used in a direct ocean tracer image assimilation scheme. In an idealized context, we show that high-resolution SST and ocean colour images can be exploited to correct velocity fields using FTLE or FTLV.