Quantifying Uncertainty for Coherent Structures

Field Alignment is a useful and often necessary preprocessing step in contemporary geophysical state and parameter estimation of coherent structures. In an advance, we introduce a new framework for using Field Alignment to quantify uncertainty from an ensemble of coherent structures. Our method, called Coalescence, discovers the mean field under non-trivial misalignments of fields with complex shapes, which is especially difficult to calculate in the presence of sparse observations. We solve the associated Field Alignment problem using novel constraints derived from turbulent displacement spectra. In conjunction with a continuation method called Scale Cascaded Alignment (SCA), we are able to extract simpler explanations of the error between fields before cascading to more complex deformation solutions. For coherent structures, SCA and Coalescence have the potential to change the way uncertainty is quantified and data is assimilated. We illustrate utility here in a Nowcasting application.