Inference of stochastic parametrizations for model error treatment using nested ensemble Kalman filters

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.

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

Monthly Weather Review ◽

10.1175/2010mwr3246.1 ◽

2011 ◽

Vol 139 (1) ◽

pp. 117-131 ◽

Cited By ~ 31

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.

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Model error covariance estimation in particle and ensemble Kalman filters using an online expectation–maximization algorithm

Quarterly Journal of the Royal Meteorological Society ◽

10.1002/qj.3931 ◽

2020 ◽

Author(s):

Tadeo J. Cocucci ◽

Manuel Pulido ◽

Magdalena Lucini ◽

Pierre Tandeo

Keyword(s):

Expectation Maximization ◽

Kalman Filters ◽

Expectation Maximization Algorithm ◽

Model Error ◽

Covariance Estimation ◽

Ensemble Kalman Filters ◽

Error Covariance

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The Square Root Information Increment Ensemble Filter

Monthly Weather Review ◽

10.1175/mwr-d-15-0295.1 ◽

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.

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Parameter Estimation Using Ensemble-Based Data Assimilation in the Presence of Model Error

Monthly Weather Review ◽

10.1175/mwr-d-14-00017.1 ◽

2015 ◽

Vol 143 (5) ◽

pp. 1568-1582 ◽

Cited By ~ 21

Author(s):

Juan Ruiz ◽

Manuel Pulido

Keyword(s):

Parameter Estimation ◽

Data Assimilation ◽

Model Error ◽

Forecast Skill ◽

Moist Convection ◽

Treatment Techniques ◽

Correction Technique ◽

Error Treatment ◽

Data Assimilation System ◽

Assimilation System

Abstract This work explores the potential of online parameter estimation as a technique for model error treatment under an imperfect model scenario, in an ensemble-based data assimilation system, using a simple atmospheric general circulation model, and an observing system simulation experiment (OSSE) approach. Model error is introduced in the imperfect model scenario by changing the value of the parameters associated with different schemes. The parameters of the moist convection scheme are the only ones to be estimated in the data assimilation system. In this work, parameter estimation is compared and combined with techniques that account for the lack of ensemble spread and for the systematic model error. The OSSEs show that when parameter estimation is combined with model error treatment techniques, multiplicative and additive inflation or a bias correction technique, parameter estimation produces a further improvement of analysis quality and medium-range forecast skill with respect to the OSSEs with model error treatment techniques without parameter estimation. The improvement produced by parameter estimation is mainly a consequence of the optimization of the parameter values. The estimated parameters do not converge to the value used to generate the observations in the imperfect model scenario; however, the analysis error is reduced and the forecast skill is improved.

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