Covariance localisation and balance in an Ensemble Kalman Filter

Kepert, Jeffrey D.

doi:10.1002/qj.443

Cited by 123 publications

(165 citation statements)

References 29 publications

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“…In this study, we compare results using zonal wind, meridional wind, height, and ozone x = u, v, z, q (the EnKF-uv system), and results using stream function, velocity potential, height, and ozone x = ψ, χ , z, q (the EnKF-ψχ system). The latter combination was shown by Kepert (2009) to result in better balance of increments in a SWM-EnKF system with Schur product localization (discussed further below). We will test this for the SWM T system with ozone and height observations.…”

Section: Ensemble Kalman Filtermentioning

confidence: 96%

“…While both show anticyclonic circulation around the positive height increment, the winds are much stronger in the EnKF-ψχ . As explained by Kepert (2009Kepert ( , 2011, the weakening of the winds in the EnKF-uv is due the effects of localization, which acts to decrease the local balance. As shown below, this adversely affects the system by generating spurious gravity waves.…”

Section: Ensemble Kalman Filtermentioning

confidence: 97%

“…The SWM has been used in both 4D-Var (Courtier and Talagrand, 1990;Polavarapu et al, 2000;Jung et al, 2014) and EnKF (Kepert, 2009(Kepert, , 2011 experiments, since it provides a sufficiently complex system to simulate the key physical relations of the horizontal flow, including both slow balanced and fast unbalanced modes. As explained by Kepert (2009), the SWM provides a severe test for assimilation, since the weak dissipation will not remove imbalances introduced in the analysis; they will rather accumulate with time.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Neef et al (2006Neef et al ( , 2009) investigated balance with a loworder Lorenz-type model with the EKF and EnKF. Imbalance within SWM-DAS systems was analyzed in both 4D-Var (Courtier and Talagrand, 1990;Polavarapu et al, 2000) and EnKF (Kepert, 2009(Kepert, , 2011 using digital filter and nonlinear normal mode initialization techniques. Mitchell and Houtekamer (2002) considered the influence of covariance localization on balance with a 3-D dry, global, primitiveequation model.…”

Section: Introductionmentioning

confidence: 99%

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Wind extraction potential from ensemble Kalman filter assimilation of stratospheric ozone using a global shallow water model

2015

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Abstract. The feasibility of extracting wind information from stratospheric ozone observations is tested using ensemble Kalman filter (EnKF) data assimilation (DA) and a global shallow water model that includes advection of an ozone-like tracer. Simulated observations are created from a truth run (TR) that resembles the Northern Hemisphere winter stratosphere with a polar vortex disturbed by planetaryscale wave forcing. Ozone observations mimic sampling of a polar-orbiting satellite, while geopotential height observations are randomly placed in space and time. EnKF experiments are performed assimilating ozone, height, or both, over a 10-day period. The DA is also implemented using two different pairs of flow variables: zonal and meridional wind (EnKF-uv) and stream function and velocity potential (EnKF-ψχ ). Each experiment is tuned for optimal localization length, while the ensemble spread is adaptively inflated using the TR. The experiments are evaluated using the maximum wind extraction potential (WEP). Ozone only assimilation improves winds (WEP = 46 % for EnKF-uv, and 58 % for EnKF-ψχ ), but suffers from spurious gravity wave generation. Application of nonlinear normal mode initialization (NMI) greatly reduces the unwanted imbalance and increases the WEP for EnKF-uv (84 %) and EnKF-ψχ (81 %). Assimilation of only height observations also improved the winds (WEP = 60 % for EnKF-uv, and 69 % for EnKF-ψχ ), with much less imbalance compared to the ozone experiment. The assimilation of both height and ozone performed the best, with WEP increasing to ∼ 87 % (∼ 90 % with NMI) for both EnKF-uv and EnKF-ψχ , demonstrating that wind extraction from ozone assimilation can be beneficial even in a data-rich environment. Ozone assimilation particularly improves the tropical winds, which are not well constrained by height observations due to lack of geostrophy.

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Section: Ensemble Kalman Filtermentioning

confidence: 96%

Section: Ensemble Kalman Filtermentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Wind extraction potential from ensemble Kalman filter assimilation of stratospheric ozone using a global shallow water model

2015

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“…The covariance localization following Gaspari and Cohn (1999) is implemented as a three-dimensional ellipsoid. The covariance localization increases imbalance (Kepert, 2009); as DART/CAM is not used for forecasts on an operational basis, the balance issue has not yet been properly addressed. This is a possible reason for increased levels of the IG energy in both analysis and background fields.…”

Section: The Ensemble Analysis System Dart/cammentioning

confidence: 99%

Diagnosis of systematic analysis increments by using normal modes

Žagar

Tribbia

Anderson

et al. 2010

Quart J Royal Meteoro Soc

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This paper applies the normal-mode functions for the three-dimensional diagnosis of systematic analysis increments in the operational systems of ECMWF and NCEP, in the NCEP/NCAR reanalyses and in the ensemble data assimilation system DART/CAM which is developed at NCAR. Non-zero systematic increments are interpreted as the analysis system bias. The main region of tropospheric biases in all systems is the Tropics; most of the large-scale tropical bias resides in the unbalanced (inertio-gravity) motion with the eastward-propagating component being dominant in some datasets. The magnitudes of tropospheric wind-field biases in July 2007 were in the range between 1 m s −1 and 2 m s −1 , illustrating the importance of diagnosing analysis systems in the Tropics where magnitudes of the large-scale variability are of the same order. The systematic increments integrated over the whole models' atmosphere appear predominantly balanced; this balance is associated with biases in the zonally averaged balanced state and, in case of ECMWF and NCEP, with the biases at the model top levels. Spectra of analysis increments averaged over one month show that, on average, 20% to 45% of total energy in increment fields belongs to the inertio-gravity motions.

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Treating Sample Covariances for Use in Strongly Coupled Atmosphere‐Ocean Data Assimilation

Smith

Lawless

Nichols

2018

Geophysical Research Letters

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Strongly coupled data assimilation requires cross‐domain forecast error covariances; information from ensembles can be used, but limited sampling means that ensemble derived error covariances are routinely rank deficient and/or ill‐conditioned and marred by noise. Thus, they require modification before they can be incorporated into a standard assimilation framework. Here we compare methods for improving the rank and conditioning of multivariate sample error covariance matrices for coupled atmosphere‐ocean data assimilation. The first method, reconditioning, alters the matrix eigenvalues directly; this preserves the correlation structures but does not remove sampling noise. We show that it is better to recondition the correlation matrix rather than the covariance matrix as this prevents small but dynamically important modes from being lost. The second method, model state‐space localization via the Schur product, effectively removes sample noise but can dampen small cross‐correlation signals. A combination that exploits the merits of each is found to offer an effective alternative.

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Covariance localisation and balance in an Ensemble Kalman Filter

Cited by 123 publications

References 29 publications

Wind extraction potential from ensemble Kalman filter assimilation of stratospheric ozone using a global shallow water model

Wind extraction potential from ensemble Kalman filter assimilation of stratospheric ozone using a global shallow water model

Diagnosis of systematic analysis increments by using normal modes

Treating Sample Covariances for Use in Strongly Coupled Atmosphere‐Ocean Data Assimilation

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