The Experts below are selected from a list of 16656 Experts worldwide ranked by ideXlab platform
Jacques Verron - One of the best experts on this subject based on the ideXlab platform.
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efficient parameterization of the observation Error Covariance Matrix for square root or ensemble kalman filters application to ocean altimetry
Monthly Weather Review, 2009Co-Authors: Jeanmichel Brankart, Clement Ubelmann, Charlesemmanuel Testut, Emmanuel Cosme, Pierre Brasseur, Jacques VerronAbstract:Abstract In the Kalman filter standard algorithm, the computational complexity of the observational update is proportional to the cube of the number y of observations (leading behavior for large y). In realistic atmospheric or oceanic applications, involving an increasing quantity of available observations, this often leads to a prohibitive cost and to the necessity of simplifying the problem by aggregating or dropping observations. If the filter Error Covariance matrices are in square root form, as in square root or ensemble Kalman filters, the standard algorithm can be transformed to be linear in y, providing that the observation Error Covariance Matrix is diagonal. This is a significant drawback of this transformed algorithm and often leads to an assumption of uncorrelated observation Errors for the sake of numerical efficiency. In this paper, it is shown that the linearity of the transformed algorithm in y can be preserved for other forms of the observation Error Covariance Matrix. In particular, quit...
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assimilation of altimetric data in the mid latitude oceans using the singular evolutive extended kalman filter with an eddy resolving primitive equation model
Journal of Marine Systems, 1999Co-Authors: Pierre Brasseur, J Ballabrerapoy, Jacques VerronAbstract:A new data assimilation scheme has been elaborated for ocean circulation models based on the concept of an evolutive, reduced-order Kalman filter. The dimension of the assimilation problem is reduced by expressing the initial Error Covariance Matrix as a truncated series of orthogonal perturbations. This Error sub-space evolves during the assimilation so as to capture the growing modes of the estimation Error. The algorithm has been formulated in quite a general fashion to make it tractable with a large variety of ocean models and measurement types. In the present paper, we have examined three possible strategies to compute the evolution of the Error subspace in the so-called Singular Evolutive Extended Kalman (SEEK) filter: the steady filter considers a time-independent Error sub-space, the apprentice filter progressively enriches the Error sub-space with the information learned from the innovation vector after each analysis step, and the dynamical filter updates the Error sub-space according to the model dynamics. The SEEK filter has been implemented to assimilate synthetic observations of the surface topography in a non-linear, primitive equation model that uses density as vertical coordinate. A simplified box configuration has been adopted to simulate a Gulf Stream-like current and its associated eddies and gyres with a resolution of 20 km in the horizontal, and 4 levels in the vertical. The concept of twin experiments is used to demonstrate that the conventional SEEK filter must be complemented by a learning mechanism in order to model the misrepresented tail of the Error Covariance Matrix. An approach based on the vertical physics of the isopycnal model, is shown particularly robust to control the velocity field in deep layers with surface observations only. The cost of the method makes it a suitable candidate for large-size assimilation problems and operational applications.
Dylan B A Jones - One of the best experts on this subject based on the ideXlab platform.
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improved analysis Error Covariance Matrix for high dimensional variational inversions application to source estimation using a 3d atmospheric transport model
Quarterly Journal of the Royal Meteorological Society, 2015Co-Authors: Nicolas Bousserez, Daven K Henze, A Perkins, Kevin W Bowman, Meemong Lee, Junjie Liu, Feng Deng, Dylan B A JonesAbstract:Variational methods are widely used to solve geophysical inverse problems. Although gradient-based minimization algorithms are available for high-dimensional problems (dimension >106), they do not provide an estimate of the Errors in the optimal solution. In this study, we assess the performance of several numerical methods to approximate the analysis-Error Covariance Matrix, assuming reasonably linear models. The evaluation is performed for a CO2 flux estimation problem using synthetic remote-sensing observations of CO2 columns. A low-dimensional experiment is considered in order to compare the analysis Error approximations to a full-rank finite-difference inverse Hessian estimate, followed by a realistic high-dimensional application. Two stochastic approaches, a Monte-Carlo simulation and a method based on random gradients of the cost function, produced analysis Error variances with a relative Error 120%), a new preconditioner that efficiently accumulates information on the diagonal of the inverse Hessian dramatically improves the results (relative Error <50%). Furthermore, performing several cycles of the BFGS algorithm using the same gradient and vector pairs enhances its performance (relative Error <30%) and is necessary to obtain convergence. Leveraging those findings, we proposed a BFGS hybrid approach which combines the new preconditioner with several BFGS cycles using information from a few (3–5) Monte-Carlo simulations. Its performance is comparable to the stochastic approximations for the low-dimensional case, while good scalability is obtained for the high-dimensional experiment. Potential applications of these new BFGS methods range from characterizing the information content of high-dimensional inverse problems to improving the convergence rate of current minimization algorithms.
Genta Ueno - One of the best experts on this subject based on the ideXlab platform.
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an extension of the ensemble kalman filter for estimating the observation Error Covariance Matrix based on the variational bayes s method
Monthly Weather Review, 2017Co-Authors: Akio Nakabayashi, Genta UenoAbstract:AbstractThis 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.
Vaishali Bhardwaj - One of the best experts on this subject based on the ideXlab platform.
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Measurement of baryon acoustic oscillations in the Lyman-α forest fluctuations in BOSS data release 9
Journal of Cosmology and Astroparticle Physics, 2013Co-Authors: Anže Slosar, Vid Iršič, David Kirkby, Stephen Bailey, N.g. Busca, Timothée Delubac, James Rich, É. Aubourg, J.e. Bautista, Vaishali BhardwajAbstract:We use the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) to detect and measure the position of the Baryonic Acoustic Oscillation (BAO) feature in the three-dimensional correlation function in the Lyman-α flux fluctuations at a redshift zeff = 2.4. The feature is clearly detected at significance between 3 and 5 sigma (depending on the broadband model and method of Error Covariance Matrix estimation) and is consistent with predictions of the standard ΛCDM model. We assess the biases in our method, stability of the Error Covariance Matrix and possible systematic effects. We fit the resulting correlation function with several models that decouple the broadband and acoustic scale information. For an isotropic dilation factor, we measure 100 × (αiso ‑ 1) = ‑1.6+2.0 +4.3 +7.4‑2.0 ‑4.1 ‑6.8 (stat.) ±1.0 (syst.) (multiple statistical Errors denote 1,2 and 3 sigma confidence limits) with respect to the acoustic scale in the fiducial cosmological model (flat ΛCDM with Ωm = 0.27, h = 0.7). When fitting separately for the radial and transversal dilation factors we find marginalised constraints 100 × (α|| ‑ 1) = ‑1.3+3.5 +7.6 +12.3‑3.3 ‑6.7 ‑10.2 (stat.) ±2.0 (syst.) and 100 × (α⊥ ‑ 1) = ‑2.2+7.4 +17‑7.1 ‑15 (stat.) ±3.0 (syst.). The dilation factor measurements are significantly correlated with cross-correlation coefficient of ~ ‑0.55. Errors become significantly non-Gaussian for deviations over 3 standard deviations from best fit value. Because of the data cuts and analysis method, these measurements give tighter constraints than a previous BAO analysis of the BOSS DR9 Lyman-α sample, providing an important consistency test of the standard cosmological model in a new redshift regime.
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measurement of baryon acoustic oscillations in the lyman alpha forest fluctuations in boss data release 9
arXiv: Cosmology and Nongalactic Astrophysics, 2013Co-Authors: Anže Slosar, Vid Iršič, David Kirkby, Stephen Bailey, N.g. Busca, Timothée Delubac, James Rich, É. Aubourg, J.e. Bautista, Vaishali BhardwajAbstract:We use the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) to detect and measure the position of the Baryonic Acoustic Oscillation (BAO) feature in the three-dimensional correlation function in the Lyman-alpha forest flux fluctuations at a redshift z=2.4. The feature is clearly detected at significance between 3 and 5 sigma (depending on the broadband model and method of Error Covariance Matrix estimation) and is consistent with predictions of the standard LCDM model. We assess the biases in our method, stability of the Error Covariance Matrix and possible systematic effects. We fit the resulting correlation function with several models that decouple the broadband and acoustic scale information. For an isotropic dilation factor, we measure 100x(alpha_iso-1) = -1.6 ^{+2.0+4.3+7.4}_{-2.0-4.1-6.8} (stat.) +/- 1.0 (syst.) (multiple statistical Errors denote 1,2 and 3 sigma confidence limits) with respect to the acoustic scale in the fiducial cosmological model (flat LCDM with Omega_m=0.27, h=0.7). When fitting separately for the radial and transversal dilation factors we find marginalised constraints 100x(alpha_par-1) = -1.3 ^{+3.5+7.6 +12.3}_{-3.3-6.7-10.2} (stat.) +/- 2.0 (syst.) and 100x(alpha_perp-1) = -2.2 ^{+7.4+17}_{-7.1-15} +/- 3.0 (syst.). The dilation factor measurements are significantly correlated with cross-correlation coefficient of ~ -0.55. Errors become significantly non-Gaussian for deviations over 3 standard deviations from best fit value. Because of the data cuts and analysis method, these measurements give tighter constraints than a previous BAO analysis of the BOSS DR9 Lyman-alpha forest sample, providing an important consistency test of the standard cosmological model in a new redshift regime.
Pierre Brasseur - One of the best experts on this subject based on the ideXlab platform.
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efficient parameterization of the observation Error Covariance Matrix for square root or ensemble kalman filters application to ocean altimetry
Monthly Weather Review, 2009Co-Authors: Jeanmichel Brankart, Clement Ubelmann, Charlesemmanuel Testut, Emmanuel Cosme, Pierre Brasseur, Jacques VerronAbstract:Abstract In the Kalman filter standard algorithm, the computational complexity of the observational update is proportional to the cube of the number y of observations (leading behavior for large y). In realistic atmospheric or oceanic applications, involving an increasing quantity of available observations, this often leads to a prohibitive cost and to the necessity of simplifying the problem by aggregating or dropping observations. If the filter Error Covariance matrices are in square root form, as in square root or ensemble Kalman filters, the standard algorithm can be transformed to be linear in y, providing that the observation Error Covariance Matrix is diagonal. This is a significant drawback of this transformed algorithm and often leads to an assumption of uncorrelated observation Errors for the sake of numerical efficiency. In this paper, it is shown that the linearity of the transformed algorithm in y can be preserved for other forms of the observation Error Covariance Matrix. In particular, quit...
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assimilation of altimetric data in the mid latitude oceans using the singular evolutive extended kalman filter with an eddy resolving primitive equation model
Journal of Marine Systems, 1999Co-Authors: Pierre Brasseur, J Ballabrerapoy, Jacques VerronAbstract:A new data assimilation scheme has been elaborated for ocean circulation models based on the concept of an evolutive, reduced-order Kalman filter. The dimension of the assimilation problem is reduced by expressing the initial Error Covariance Matrix as a truncated series of orthogonal perturbations. This Error sub-space evolves during the assimilation so as to capture the growing modes of the estimation Error. The algorithm has been formulated in quite a general fashion to make it tractable with a large variety of ocean models and measurement types. In the present paper, we have examined three possible strategies to compute the evolution of the Error subspace in the so-called Singular Evolutive Extended Kalman (SEEK) filter: the steady filter considers a time-independent Error sub-space, the apprentice filter progressively enriches the Error sub-space with the information learned from the innovation vector after each analysis step, and the dynamical filter updates the Error sub-space according to the model dynamics. The SEEK filter has been implemented to assimilate synthetic observations of the surface topography in a non-linear, primitive equation model that uses density as vertical coordinate. A simplified box configuration has been adopted to simulate a Gulf Stream-like current and its associated eddies and gyres with a resolution of 20 km in the horizontal, and 4 levels in the vertical. The concept of twin experiments is used to demonstrate that the conventional SEEK filter must be complemented by a learning mechanism in order to model the misrepresented tail of the Error Covariance Matrix. An approach based on the vertical physics of the isopycnal model, is shown particularly robust to control the velocity field in deep layers with surface observations only. The cost of the method makes it a suitable candidate for large-size assimilation problems and operational applications.