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A hybrid particle-ensemble Kalman filter for problems with medium nonlinearity.

Ian Grooms¹, Gregor Robinson¹

¹Department of Applied Mathematics, University of Colorado, Boulder, CO, United States of America.

|March 11, 2021

Summary

A new hybrid particle ensemble Kalman filter effectively handles medium non-Gaussianity problems. This advanced data assimilation method outperforms traditional filters in complex simulations.

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Area of Science:

Data assimilation
Computational statistics
Applied mathematics

Background:

Many real-world problems exhibit medium non-Gaussianity, where prior states are highly non-Gaussian but posterior states approach Gaussianity.
This occurs in systems with nonlinear dynamics generating non-Gaussian forecasts, yet a strong Gaussian likelihood results in a near-Gaussian posterior.

Purpose of the Study:

To develop and evaluate a hybrid particle ensemble Kalman filter (HPEKF) for data assimilation problems with medium non-Gaussianity.
To address limitations of pure particle filters (PF) and ensemble Kalman filters (EnKF) in such scenarios.

Main Methods:

The HPEKF factors the likelihood, using a particle filter for initial assimilation to achieve a near-Gaussian intermediate prior.
An ensemble Kalman filter then completes assimilation with the remaining likelihood factor.
Likelihood splitting and a mean-preserving orthogonal transformation prevent particle filter collapse and degeneracy.

Main Results:

The HPEKF demonstrated superior performance over pure PF and EnKF in a 2D test case.
In a multiscale Lorenz-'96 model, the HPEKF outperformed the pure EnKF, particularly with a sufficiently large ensemble size.

Conclusions:

The hybrid particle ensemble Kalman filter offers a robust approach for data assimilation in problems with medium non-Gaussianity.
This method enhances accuracy and stability compared to standalone particle filters or ensemble Kalman filters in specific complex systems.