A low-rank ensemble Kalman filter for elliptic observations

Understand

We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators.

• Commonly used EnKF regularization methods suppress state correlations at long distances.
• For observations described by elliptic partial differential equations, such as the pressure Poisson equation (PPE) in incompressible fluid flows, distance localization cannot be applied, as we cannot disentangle slowly decaying physical interactions from spurious long-range correlations.
• This is particularly true for the PPE, in which distant vortex elements couple nonlinearly to induce pressure.