The impact of nonlinearity in Lagrangian data assimilation

The focus of this paper is on how two main manifestations of nonlinearity in low-dimensional systems – shear around a center fixed point (nonlinear center) and the differential divergence of trajectories passing by a saddle (nonlinear saddle) – strongly affect data assimilation. The impact is felt through their leading to non-Gaussian distribution functions. The major factors that control the strength of these effects is time between observations, and covariance of the prior relative to covariance of the observational noise. Both these factors – less frequent observations and larger prior covariance – allow the nonlinearity to take hold. To expose these nonlinear effects, we use the comparison between exact posterior distributions conditioned on observations and the ensemble Kalman filter (EnKF) approximation of these posteriors. We discuss the serious limitations of the EnKF in handling these effects

Using flow geometry for drifter deployment in Lagrangian data assimilation

Methods of Lagrangian data assimilation (LaDA) require carefully chosen sites for optimal drifter deployments. In this work, we investigate a directed drifter deployment strategy with a recently developed LaDA method employing an augmented state vector formulation for an Ensemble Kalman filter. We test our directed drifter deployment strategy by targeting Lagrangian coherent flow structures of an unsteady double gyre flow to analyse how different release sites influence the performance of the method. We consider four different launch methods; a uniform launch, a saddle launch in which hyperbolic trajectories are targeted, a vortex centre launch, and a mixed launch targeting both saddles and centres. We show that global errors in the flow field require good dispersion of the drifters which can be realized with the saddle launch. Local errors on the other hand are effectively reduced by targeting specific flow features. In general, we conclude that it is best to target the strongest hyperbolic trajectories for shorter forecasts although vortex centres can produce good drifter dispersion upon bifurcating on longer time-scales

Chlorophyll dispersal by eddy-eddy interactions in the Gulf of Mexico

1] A Lagrangian analysis of the transport and dispersal of plumes observed in satellite-derived ocean color images was conducted using a data-assimilating model of the Gulf of Mexico. The interaction between pervasive cyclonic and anticyclonic eddies in the Gulf generated advective paths that connect remote shelf regions. These paths aligned remarkably well with the plume events recorded with the chlorophyll-a ocean color product from SeaWiFS. Two such events were studied. In one event material was transported in a thin strip between the northern wall of the Loop Current and an adjacent cyclone, connecting the eastern Campheche shelf (off the Yucatan Peninsula) and South Florida shelves. The other event began off the Louisiana shelf break as a small plume traced by chlorophyll and then developed into a long and thin feature which meandered to the shelf break off the northern Yucatan Peninsula, moving between a large anticyclone and several adjacent cyclones. These results indicate that inter-eddy advection plays a crucial role in developing the ocean color patterns observed in the satellite ocean color data