Data assimilation of coherent structures in parametric and gridded spaces: an idealized ocean eddy study

Data assimilation (DA) combines observations and model background to estimate the state of geophysical systems. Coherent structures, such as ocean eddies, are localized geophysical features characterized by a small set of properties: position, amplitude, and shape for instance. When linear and gaussian DA is applied directly to a gridded field without prior structural adjustment, the linear combination of background and observation can distort these properties, particularly when displacement uncertainty dominates. In this work, we explore a DA framework of coherent structures in a reduced parametric space, where the state is defined by a set of parameters describing the structure. Using an idealized one-dimensional ocean eddy, we compare single-step analyses performed both in gridded and parametric spaces. Three tutorial experiments with prescribed parametric uncertainties illustrate this distortion mechanism directly. A fourth experiment, starting from noisy gridded observations, provides a more balanced evaluation using the inverse nonlinear mapping from grid to parameter space. In these idealized experiments, the parametric approach maintains a physically consistent shape after assimilation. The parametric DA requires reliable parameter extraction, and its benefits depend on the number of structures relative to grid resolution.