Iterative algorithm for maximum-likelihood estimation of the observation-error covariance matrix for ensemble-based filters

2013 ◽  
Vol 140 (678) ◽  
pp. 295-315 ◽  
Author(s):  
Genta Ueno ◽  
Nagatomo Nakamura
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Covariance Matrix ◽  
Iterative Algorithm ◽  
Likelihood Estimation ◽  
Observation Error ◽  
Error Covariance Matrix ◽  
Error Covariance

scholarly journals Maximum-Likelihood Estimation of Forecast and Observation Error Covariance Parameters. Part II: Applications

1999 ◽  
Vol 127 (8) ◽  
pp. 1835-1849 ◽  
Author(s):  
Dick P. Dee ◽  
Greg Gaspari ◽  
Chris Redder ◽  
Leonid Rukhovets ◽  
Arlindo M. da Silva
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Observation Error ◽  
Error Covariance

scholarly journals An Extension of the Ensemble Kalman Filter for Estimating the Observation Error Covariance Matrix Based on the Variational Bayes’s Method

2016 ◽  
Vol 145 (1) ◽  
pp. 199-213 ◽  
Author(s):  
Akio Nakabayashi ◽  
Genta Ueno
Keyword(s):  
Kalman Filter ◽  
Maximum Likelihood ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Numerical Experiments ◽  
Observation Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Long Run ◽  
The Stability

Abstract This paper presents an extension of the ensemble Kalman filter (EnKF) that can simultaneously estimate the state vector and the observation error covariance matrix by using the variational Bayes’s (VB) method. In numerical experiments, this capability is examined for a time-variant observation error covariance matrix, and it is noteworthy that this method works well even when the true observation error covariance matrix is nondiagonal. In addition, two complementary studies are presented. First, the stability of a long-run assimilation is demonstrated when there are unmodeled disturbances. Second, a maximum-likelihood (ML) method is derived and demonstrated for optimizing the hyperparameters used in this method.

Enhancing the impact of IASI observations through an updated observation-error covariance matrix

2016 ◽  
Vol 142 (697) ◽  
pp. 1767-1780 ◽  
Author(s):  
Niels Bormann ◽  
Massimo Bonavita ◽  
Rossana Dragani ◽  
Reima Eresmaa ◽  
Marco Matricardi ◽  
...  
Keyword(s):  
Covariance Matrix ◽  
Observation Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
The Impact

scholarly journals Efficient Adaptive Error Parameterizations for Square Root or Ensemble Kalman Filters: Application to the Control of Ocean Mesoscale Signals

2010 ◽  
Vol 138 (3) ◽  
pp. 932-950 ◽  
Author(s):  
Jean-Michel Brankart ◽  
Emmanuel Cosme ◽  
Charles-Emmanuel Testut ◽  
Pierre Brasseur ◽  
Jacques Verron
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Error Estimates ◽  
Forecast Error ◽  
Observation Error ◽  
Square Root ◽  
Error Statistics ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Optimal Estimates

Abstract In Kalman filter applications, an adaptive parameterization of the error statistics is often necessary to avoid filter divergence, and prevent error estimates from becoming grossly inconsistent with the real error. With the classic formulation of the Kalman filter observational update, optimal estimates of general adaptive parameters can only be obtained at a numerical cost that is several times larger than the cost of the state observational update. In this paper, it is shown that there exists a few types of important parameters for which optimal estimates can be computed at a negligible numerical cost, as soon as the computation is performed using a transformed algorithm that works in the reduced control space defined by the square root or ensemble representation of the forecast error covariance matrix. The set of parameters that can be efficiently controlled includes scaling factors for the forecast error covariance matrix, scaling factors for the observation error covariance matrix, or even a scaling factor for the observation error correlation length scale. As an application, the resulting adaptive filter is used to estimate the time evolution of ocean mesoscale signals using observations of the ocean dynamic topography. To check the behavior of the adaptive mechanism, this is done in the context of idealized experiments, in which model error and observation error statistics are known. This ideal framework is particularly appropriate to explore the ill-conditioned situations (inadequate prior assumptions or uncontrollability of the parameters) in which adaptivity can be misleading. Overall, the experiments show that, if used correctly, the efficient optimal adaptive algorithm proposed in this paper introduces useful supplementary degrees of freedom in the estimation problem, and that the direct control of these statistical parameters by the observations increases the robustness of the error estimates and thus the optimality of the resulting Kalman filter.

scholarly journals Assimilation of Stratospheric Temperature and Ozone with an Ensemble Kalman Filter in a Chemistry–Climate Model

2011 ◽  
Vol 139 (11) ◽  
pp. 3389-3404 ◽  
Author(s):  
Thomas Milewski ◽  
Michel S. Bourqui
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Climate Model ◽  
Observation Error ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Analysis Error

Abstract A new stratospheric chemical–dynamical data assimilation system was developed, based upon an ensemble Kalman filter coupled with a Chemistry–Climate Model [i.e., the intermediate-complexity general circulation model Fast Stratospheric Ozone Chemistry (IGCM-FASTOC)], with the aim to explore the potential of chemical–dynamical coupling in stratospheric data assimilation. The system is introduced here in a context of a perfect-model, Observing System Simulation Experiment. The system is found to be sensitive to localization parameters, and in the case of temperature (ozone), assimilation yields its best performance with horizontal and vertical decorrelation lengths of 14 000 km (5600 km) and 70 km (14 km). With these localization parameters, the observation space background-error covariance matrix is underinflated by only 5.9% (overinflated by 2.1%) and the observation-error covariance matrix by only 1.6% (0.5%), which makes artificial inflation unnecessary. Using optimal localization parameters, the skills of the system in constraining the ensemble-average analysis error with respect to the true state is tested when assimilating synthetic Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) retrievals of temperature alone and ozone alone. It is found that in most cases background-error covariances produced from ensemble statistics are able to usefully propagate information from the observed variable to other ones. Chemical–dynamical covariances, and in particular ozone–wind covariances, are essential in constraining the dynamical fields when assimilating ozone only, as the radiation in the stratosphere is too slow to transfer ozone analysis increments to the temperature field over the 24-h forecast window. Conversely, when assimilating temperature, the chemical–dynamical covariances are also found to help constrain the ozone field, though to a much lower extent. The uncertainty in forecast/analysis, as defined by the variability in the ensemble, is large compared to the analysis error, which likely indicates some amount of noise in the covariance terms, while also reducing the risk of filter divergence.

scholarly journals Ozone-sensitive channel selection over IASI full spectrum with correlated observation errors for NWP

2019 ◽  
Author(s):  
Olivier Coopmann ◽  
Vincent Guidard ◽  
Béatrice Josse ◽  
Virginie Marécal ◽  
Nadia Fourrié
Keyword(s):  
Covariance Matrix ◽  
Weather Prediction ◽  
Channel Selection ◽  
Spectral Interval ◽  
Observation Error ◽  
Full Spectrum ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
One Year ◽  
Selection Of

Abstract. The Infrared Atmospheric Sounding Interferometer (IASI) onboard the Metop satellites provides 8461 channels in the infrared spectrum, covering the spectral interval 645–2760 cm−1 at a resolution of 0.5 cm−1. The high volume of data observation resulting from IASI presents many challenges. In current Numerical Weather Prediction (NWP) models, assimilating all channels is not feasible, due to data transmission, data storage and significant computational costs. One of the methods for reducing the data volume is the channel selection. Many NWP centres use a subset of 314 IASI channels including 15 ozone-sensitive channels. However, this channel selection has been carried out assuming uncorrelated observation errors. In addition, these ozone-sensitive channels have been selected only for ozone information. The objective of this study is to carry out a new selection of IASI ozone-sensitive channels from the full spectrum over a spectral range of 1000–1070 cm−1, in a direct radiance assimilation framework. This selection is done with a full observation error covariance matrix to take into account cross-channel error correlations. A sensitivity method based on the channel spectral sensitivity to variables and a statistical approach based on the Degrees of Freedom for Signal (DFS) have been chosen. To be representative of atmospheric variability, 345 profiles from around the world over a one-year period were selected. The new selection, is evaluated in a One-Dimensional Variational (1D-Var) analyses framework. This selection highlights a new set of 15 IASI ozone-sensitive channels. The results are very encouraging since by adding these 15 channels to 122 operational channels, temperature and humidity analyses are improved by 13.8 % and 20.9 % respectively. Obviously, these 15 channels significantly improve ozone analyses. In addition to considering inter-channel observation error correlations, the channel selection method uses a robust background error covariance matrix that takes into account temperature, humidity and ozone errors using a lagged forecast method over a one-year period. The new selection of IASI ozone-sensitive channels will be soon used in the global 4D-Var ARPEGE (Action de Recherche Petite Echelle Grande Echelle) data assimilation system.

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