Sampling Errors in Ensemble Kalman Filtering. Part II: Application to a Barotropic Model

Sacher, William; Bartello, Peter

doi:10.1175/2008mwr2685.1

Cited by 6 publications

(6 citation statements)

References 32 publications

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“…Here C p 5 1005.7 J K 21 kg 21 is the specific heat at constant pressure and R a 5 287.04 J K 21 kg 21 is the gas constant of dry air. As argued by Sacher and Bartello (2009), the RMSE and SPREAD diagnostics express the ''accuracy'' and ''reliability'' of the EnKF, respectively. A satisfactory ensemble assimilation should provide the most accurate analysis, closest to the true solution.…”

Section: Diagnosticsmentioning

confidence: 99%

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

Milewski

Bourqui

2011

Monthly Weather Review

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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 chemicaldynamical 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.

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Section: Diagnosticsmentioning

confidence: 99%

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

Milewski

Bourqui

2011

Monthly Weather Review

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“…In ensemble data assimilation systems, this is typically done by calculating the RMSE of the ensemble mean with respect to the true state. The RMSE diagnostic expresses the accuracy of the EnKF solution and should be compared to the root mean square difference between the ensemble members and the ensemble mean (SPREAD) to estimate the reliability of the EnKF solution (Sacher and Bartello, 2009). The SPREAD is essentially the standard deviation of the ensemble, and equality between the SPREAD and the RMSE must be achieved for the EnKF solution to be consistent.…”

Section: Reference Enkf Experimentsmentioning

confidence: 99%

Potential of an ensemble Kalman smoother for stratospheric chemical-dynamical data assimilation

Milewski

Bourqui

2013

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C TA new stratospheric ensemble Kalman smoother (EnKS) system is introduced, and the potential of assimilating posterior stratospheric observations to better constrain the whole model state at analysis time is investigated. A set of idealised perfect-model Observation System Simulation Experiments (OSSE) assimilating synthetic limb-sounding temperature or ozone retrievals are performed with a chemistryÁclimate model. The impact during the analysis step is characterised in terms of the root mean square error reduction between the forecast state and the analysis state. The performances of (1) a fixed-lag EnKS assimilating observations spread over 48 hours and (2) an ensemble Kalman Filter (EnKF) assimilating a denser network of observations are compared with a reference EnKF. The ozone assimilation with EnKS shows a significant additional reduction of analysis error of the order of 10% for dynamical and chemical variables in the extratropical upper troposphere lower stratosphere (UTLS) and Polar Vortex regions when compared to the reference EnKF. This reduction has similar magnitude to the one achieved by the denser-network EnKF assimilation. Similarly, the temperature assimilation with EnKS significantly decreases the error in the UTLS for the wind variables like the denser-network EnKF assimilation. However, the temperature assimilation with EnKS has little or no significant impact on the temperature and ozone analyses, whereas the denser-network EnKF shows improvement with respect to the reference EnKF. The different analysis impacts from the assimilation of current and posterior ozone observations indicate the capacity of time-lagged background-error covariances to represent temporal interactions up to 48 hours between variables during the ensemble data assimilation analysis step, and the possibility to use posterior observations whenever additional current observations are unavailable. The possible application of the EnKS for reanalyses is highlighted.

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“…Difficulties in applying the EnKF to large chaotic models commonly result in filter divergence (e.g. Houtekamer and Mitchell, 1998; Hamill et al, 2001; Whitaker and Hamill, 2002; Sacher and Bartello, 2009). ‘Divergence’ describes the situation when the filter becomes so overconfident around an incorrect state that subsequent observations are ignored, and the estimate cannot be moved back toward the true state.…”

Section: Introductionmentioning

confidence: 99%

“…As mentioned above, past works have generally focused solely on the update step in looking for sources of filter divergence. In one exception, Sacher and Bartello (2009) diagnose signs of divergence over multiple assimilation cycles using numerical experiments, but they point out that the non-linearity of the forecast model hampers more rigorous investigations. When isolating the update step from the forecast, sampling error is generically regarded as a random, unstructured element in most divergence studies.…”

Section: Introductionmentioning

confidence: 99%

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The role of model dynamics in ensemble Kalman filter performance for chaotic systems

McLaughlin

Entekhabi

et al. 2011

Tellus A: Dynamic Meteorology and Oceanography

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The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or ‘diverging’, when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter's update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short‐term growth and Lyapunov vectors, corresponding to long‐term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long‐term unstable subspace is spanned. However, short‐term dynamics also become important as non‐linearity in the system increases. Non‐linear movement prevents errors in the long‐term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short‐term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics.

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Sampling Errors in Ensemble Kalman Filtering. Part II: Application to a Barotropic Model

Cited by 6 publications

References 32 publications

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

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

Potential of an ensemble Kalman smoother for stratospheric chemical-dynamical data assimilation

The role of model dynamics in ensemble Kalman filter performance for chaotic systems

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