A Low-Order Model Investigation of the Analysis of Gravity Waves in the Ensemble Kalman Filter

Neef, Lisa; Polavarapu, Saroja; Shepherd, Theodore G.

doi:10.1175/2008jas2585.1

Cited by 5 publications

(13 citation statements)

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“…Unless there is sufficient information in the background error covariance to distribute increments in a balanced way, the unbalanced modes will enter the system, and it may be difficult to remove these modes with limited observations (Neef et al, 2006(Neef et al, , 2009. To quantify the imbalance in the SWM-EnKF, we use a nonlinear normal mode initialization (NMI) procedure (Machenhauer, 1977), which has been used in NWP to reduce the impact of inertia gravity waves caused by imbalance in the analysis increments (e.g., Kleist et al, 2009).…”

Section: Normal Mode Initializationmentioning

confidence: 99%

“…A wide range of studies has been performed to examine balance in the context of 4-D data assimilation. 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.…”

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: Normal Mode Initializationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2015

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“…Szunyogh et al (2005) is an example of a case in which an EnKF-type assimilation method was able to capture a fast-varying gravity wave mode that was present in observations and not in the model forecast, indicating that flow-dependent covariance models can potentially capture unbalanced motion. Neef et al (2006) reported similar results where the EnKF was able to provide better estimates of the fast-varying modes than the linearized (extended) Kalman filter. Other techniques such as scaledependent modeling and assimilation using the ensemble Kalman filter have been attempted (Zou and Ghanem 2005) in engineering applications.…”

Section: Introductionmentioning

confidence: 61%

“…In meteorological and climatological applications, ''balance'' generally refers to the dominance of slow vortical motion over fast inertiagravity waves. In multiscale systems like the ocean or atmosphere in which modeled flows in certain regimes are expected to be balanced, it has been found that current 4D data assimilation techniques, as the EnKF and 4DVAR, could cause the excitation of spurious unbalanced motion (Polavarapu et al 2000;Houtekamer and Mitchell 2005;Neef et al 2006). This has been known to happen because of the development of unphysical correlations.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we are interested in assessing the impact of the linear correction step on the estimation of the different scales of the studied system. Following Neef et al (2006), we address this problem using the simplified dynamical model of Lorenz (1986) (the model is hereafter called the Lorenz-86 model), which admits one nonlinear vortical mode and one inertia-gravity wave. We study the performance of the linear-based EnKF and two kinds of nonlinear filters, the sequential importance resampling filter (SIRF) and the sequential kernel resampling filter (SKRF).…”

Section: Introductionmentioning

confidence: 99%

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Linear versus Nonlinear Filtering with Scale-Selective Corrections for Balanced Dynamics in a Simple Atmospheric Model

Subramanian

Hoteit

Cornuelle

et al. 2012

Journal of the Atmospheric Sciences

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This paper investigates the role of the linear analysis step of the ensemble Kalman filters (EnKF) in disrupting the balanced dynamics in a simple atmospheric model and compares it to a fully nonlinear particle-based filter (PF). The filters have a very similar forecast step but the analysis step of the PF solves the full Bayesian filtering problem while the EnKF analysis only applies to Gaussian distributions. The EnKF is compared to two flavors of the particle filter with different sampling strategies, the sequential importance resampling filter (SIRF) and the sequential kernel resampling filter (SKRF). The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode. It can also be configured either to evolve on a so-called slow manifold, where the fast motion is suppressed, or such that the fast-varying variables are diagnosed from the slow-varying variables as slaved modes. Identical twin experiments show that EnKF and PF capture the variables on the slow manifold well as the dynamics is very stable. PFs, especially the SKRF, capture slaved modes better than the EnKF, implying that a full Bayesian analysis estimates the nonlinear model variables better. The PFs perform significantly better in the fully coupled nonlinear model where fast and slow variables modulate each other. This suggests that the analysis step in the PFs maintains the balance in both variables much better than the EnKF. It is also shown that increasing the ensemble size generally improves the performance of the PFs but has less impact on the EnKF after a sufficient number of members have been used.

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Covariance localisation and balance in an Ensemble Kalman Filter

Kepert

2009

Quart J Royal Meteoro Soc

123

150

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A major limitation of the Ensemble Kalman Filter (EnKF) is that the finite ensemble size introduces sampling error into the background covariances, with severe consequences for atmospheric and oceanographic applications. The negative effects of sampling error are customarily limited by covariance localisation, which earlier studies have suggested may introduce imbalance into the system. The deleterious effects of localisation upon balance are confirmed and detailed here, with localisation producing analyses with weaker geostrophic balance and stronger divergence than are obtained using the unlocalised covariances. These imbalances reduce as the localisation radius is increased, but are argued to be large for typical settings. An improved method for calculating local covariances from an ensemble is presented, in which the localisation is performed in streamfunction-velocity potential (ψ -χ), rather than wind component, space. Analyses using this method better preserve the balances contained within the unlocalised covariance model. This transformation further allows the option of intervariable localisation, in which the cross-covariances involving χ, which are weak and therefore particularly subject to sampling error, are set to 0 instead of being calculated from the ensemble. The various localisations are compared in a series of identical-twin experiments, with the new localisations producing analyses that are better balanced and significantly more accurate than the usual approach. The localisation with the χ cross-covariances set to 0 is shown to be superior for the smaller ensemble sizes but not for the larger, implying that the larger ensembles are capable of resolving some of the true χ cross-covariance in the test system.

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A Low-Order Model Investigation of the Analysis of Gravity Waves in the Ensemble Kalman Filter

Cited by 5 publications

References 38 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

Linear versus Nonlinear Filtering with Scale-Selective Corrections for Balanced Dynamics in a Simple Atmospheric Model

Covariance localisation and balance in an Ensemble Kalman Filter

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