A Knowledge-Aided Robust Ensemble Kalman Filter Algorithm for Non-Linear and Non-Gaussian Large Systems

A Knowledge-Aided Robust Ensemble Kalman Filter Algorithm for Non-Linear and Non-Gaussian Large Systems

Lopez Restrepo, S. (TU Delft Mathematical Physics; Universidad EAFIT; SimpleSpace)
Yarce Botero, A. (TU Delft Mathematical Physics; Universidad EAFIT; SimpleSpace)
Pinel, Nicolás (Universidad EAFIT)
Quintero, O. L. (Universidad EAFIT)
Segers, Arjo (TNO)
Heemink, A.W. (TU Delft Mathematical Physics)

2022

This work proposes a robust and non-Gaussian version of the shrinkage-based knowledge-aided EnKF implementation called Ensemble Time Local H_∞ Filter Knowledge-Aided (EnTLHF-KA). The EnTLHF-KA requires a target covariance matrix to integrate previously obtained information and knowledge directly into the data assimilation (DA). The proposed method is based on the robust H_∞ filter and on its ensemble time-local version the EnTLHF, using an adaptive inflation factor depending on the shrinkage covariance estimated matrix. This implies a theoretical and solid background to construct robust filters from the well-known covariance inflation technique. The proposed technique is implemented in a synthetic assimilation experiment, and in an air quality application using the LOTOS-EUROS model over the Aburrá Valley to evaluate its potential for non-linear and non-Gaussian large systems. In the spatial distribution of the PM_2.5 concentrations along the valley, the method outperforms the well-known Local Ensemble Transform Kalman Filter (LETKF), and the non-robust knowledge-aided Ensemble Kalman filter (EnKF-KA). In contrast to the other simulations, the ability to issue warnings for high concentration events is also increased. Finally, the simulation using EnTLHF-KA has lower error values than using EnKF-KA, indicating the advantages of robust approaches in high uncertainty systems.

data assimilation
air quality modeling
robust estimation
Ensemble Kalman filter
covariance estimation

http://resolver.tudelft.nl/uuid:1e5dc610-f5b3-4263-8750-441f24c9a314

https://doi.org/10.3389/fams.2022.830116

2297-4687

Frontiers in Applied Mathematics an Statistics, 8, 1-19

Institutional Repository

journal article

© 2022 S. Lopez Restrepo, A. Yarce Botero, Nicolás Pinel, O. L. Quintero, Arjo Segers, A.W. Heemink