Kalman filtering algorithms for data assimilation



Arnold Heemink
Martin Verlaan

Delft University of Technology

Overview

State space model

Kalman filtering

Large scale models

SQRT formulation of the covariance P

Ensemble Kalman filter (EnKF)

Ensemble Kalman filter

Reduced Rank filter (RRSQRT)

Reduced Rank filter

Partial Orthogonal Ensemble Kalman filter (POEnKF)

Complementary Orthogonal sub space Filter For Efficient Ensembles (COFFEE)

Application to a two dimensional transport
transport model based on the advection diffusion equation

"Velocity field"

"Simulation results used for generating..."

"Eigenvalues of the covariance matrix"

"Filter results compared with the..."

"Filter results compared with the..."

"Filter results compared with the..."

"RMS errors for the various..."

"RMS error of the Ensemble..."

"RMS error of the RRSQRT..."

"RMS error of the POEnKF..."

Application to the Lorenz model

"Ensemble Kalman filter results for..."

"Ensemble Kalman filter results for..."

"Ensemble Kalman filter results for..."

"Results of POEnKF with q..."

"RMS error for the various..."

Nonlinearity in data assimilation problems

A measure for nonlinearity

Conclusions