A flexible additive inflation scheme for treating model error in ensemble Kalman filters

2018 ◽  
Vol 144 (716) ◽  
pp. 2026-2037 ◽  
Author(s):  
Matthias Sommer ◽  
Tijana Janjić
Keyword(s):  
Kalman Filters ◽  
Model Error ◽  
Ensemble Kalman Filters

scholarly journals Accounting for Model Error from Unresolved Scales in Ensemble Kalman Filters by Stochastic Parameterization

2017 ◽  
Vol 145 (9) ◽  
pp. 3709-3723 ◽  
Author(s):  
Fei Lu ◽  
Xuemin Tu ◽  
Alexandre J. Chorin
Keyword(s):  
Kalman Filters ◽  
Numerical Experiments ◽  
Sampling Error ◽  
Forecast Model ◽  
Model Error ◽  
Ensemble Size ◽  
Ensemble Kalman Filters ◽  
Filter Performance ◽  
Performance Results ◽  
Lorenz 96

The use of discrete-time stochastic parameterization to account for model error due to unresolved scales in ensemble Kalman filters is investigated by numerical experiments. The parameterization quantifies the model error and produces an improved non-Markovian forecast model, which generates high quality forecast ensembles and improves filter performance. Results are compared with the methods of dealing with model error through covariance inflation and localization (IL), using as an example the two-layer Lorenz-96 system. The numerical results show that when the ensemble size is sufficiently large, the parameterization is more effective in accounting for the model error than IL; if the ensemble size is small, IL is needed to reduce sampling error, but the parameterization further improves the performance of the filter. This suggests that in real applications where the ensemble size is relatively small, the filter can achieve better performance than pure IL if stochastic parameterization methods are combined with IL.

What Constrains Spread Growth in Forecasts Initialized from Ensemble Kalman Filters?

2011 ◽  
Vol 139 (1) ◽  
pp. 117-131 ◽  
Author(s):  
Thomas M. Hamill ◽  
Jeffrey S. Whitaker
Keyword(s):  
Kalman Filters ◽  
Additive Noise ◽  
Model Error ◽  
Equation Model ◽  
Primitive Equation ◽  
Ensemble Kalman Filters ◽  
Background Error ◽  
Flow Dependency ◽  
Analysis Error ◽  
Filter Analysis

Abstract The spread of an ensemble of weather predictions initialized from an ensemble Kalman filter may grow slowly relative to other methods for initializing ensemble predictions, degrading its skill. Several possible causes of the slow spread growth were evaluated in perfect- and imperfect-model experiments with a two-layer primitive equation spectral model of the atmosphere. The causes examined were the covariance localization, the additive noise used to stabilize the assimilation method and parameterize the system error, and the model error itself. In these experiments, the flow-independent additive noise was the biggest factor in constraining spread growth. Preevolving additive noise perturbations were tested as a way to make the additive noise more flow dependent. This modestly improved the data assimilation and ensemble predictions, both in the two-layer model results and in a brief test of the assimilation of real observations into a global multilevel spectral primitive equation model. More generally, these results suggest that methods for treating model error in ensemble Kalman filters that greatly reduce the flow dependency of the background-error covariances may increase the filter analysis error and decrease the rate of forecast spread growth.

scholarly journals The Square Root Information Increment Ensemble Filter

2016 ◽  
Vol 144 (12) ◽  
pp. 4667-4686
Author(s):  
Mark L. Psiaki
Keyword(s):  
Kalman Filters ◽  
A Priori ◽  
Full Rank ◽  
Forecast Model ◽  
Model Error ◽  
The State ◽  
Low Rank ◽  
Square Root ◽  
Ensemble Kalman Filters ◽  
Lorenz 96

Abstract A new type of ensemble filter is developed, one that stores and updates its state information in an efficient square root information filter form. It addresses two shortcomings of conventional ensemble Kalman filters: the coarse characterization of random forecast model error effects and the overly optimistic approximation of the estimation error statistics. The new filter uses an assumed a priori covariance approximation that is full rank but sparse, possibly with a dense low-rank increment. This matrix can be used to develop a nominal square root information equation for the system state and uncertainty. The measurements are used to develop an additional low-rank square root information equation. New algorithms provide forecasts and analyses of these increments at a computational cost comparable to that of existing ensemble Kalman filters. Model error effects are implicit in the a priori covariance time history, thereby obviating one of the reasons for including an inflation operation. The use of an a priori full-rank covariance allows the analysis operations to improve the state estimate without the need for a localization adjustment. This new filter exhibited worse performance than a typical covariance square root ensemble Kalman filter when operating on the Lorenz-96 problem in a chaotic regime. It excelled on a version of the Lorenz-96 problem where nonlinearities in the forecast model were weak, where the state vector uncertainty lay predominantly in a small subspace, and where the observations were spatially sparse. Such a problem might be representative of ionospheric space weather data assimilation where forcing variability can dominate the state uncertainty and where remote sensing data coverage can be sparse.

scholarly journals A Data-Driven Method for Improving the Correlation Estimation in Serial Ensemble Kalman Filters

2017 ◽  
Vol 145 (3) ◽  
pp. 985-1001 ◽  
Author(s):  
Michèle De La Chevrotière ◽  
John Harlim
Keyword(s):  
Kalman Filters ◽  
Data Driven ◽  
Training Procedure ◽  
Ensemble Kalman Filters ◽  
Regression Problem ◽  
Correlation Estimation ◽  
Sample Correlation ◽  
Correlation Statistics ◽  
Nonlinear Observation ◽  
Lorenz 96

A data-driven method for improving the correlation estimation in serial ensemble Kalman filters is introduced. The method finds a linear map that transforms, at each assimilation cycle, the poorly estimated sample correlation into an improved correlation. This map is obtained from an offline training procedure without any tuning as the solution of a linear regression problem that uses appropriate sample correlation statistics obtained from historical data assimilation outputs. In an idealized OSSE with the Lorenz-96 model and for a range of linear and nonlinear observation models, the proposed scheme improves the filter estimates, especially when the ensemble size is small relative to the dimension of the state space.

Sign in / Sign up

Export Citation Format

Share Document