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Adaptive Sampling With the Ensemble Transform . . .
, 2001
"... A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filt ..."
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Cited by 321 (19 self)
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A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filters in that it uses ensemble transformation and a normalization to rapidly obtain the prediction error covariance matrix associated with a particular deployment of observational resources. This rapidity enables it to quickly assess the ability of a large number of future feasible sequences of observational networks to reduce forecast error variance. The ET KF was used by the National Centers for Environmental Prediction in the Winter Storm Reconnaissance missions of 1999 and 2000 to determine where aircraft should deploy dropwindsondes in order to improve 2472h forecasts over the continental United States. The ET KF may be applied to any wellconstructed set of ensemble perturbations. The ET KF
Nonlinearity in Data Assimilation applications: a practical method for analysis
, 1999
"... Nonlinear model dynamics seriously complicates the application of data assimilation. Although several theoretical solutions exist, practical solution of nonlinear data assimilation problems is only possible approximately, except for very small systems. In apparent contradiction with these theoreti ..."
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Cited by 15 (0 self)
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Nonlinear model dynamics seriously complicates the application of data assimilation. Although several theoretical solutions exist, practical solution of nonlinear data assimilation problems is only possible approximately, except for very small systems. In apparent contradiction with these theoretical difficulties many nearlinear approximations, such as the extended Kalman filter perform often very well also for highly nonlinear models. This can be explained from the fact that the nonlinearity of a data assimilation problem depends not only on the nonlinearity of the model, but also on several other factors. In order quantify the nonlinearity of dataassimilation problems a nondimensional number V is proposed. The measure includes the effects of system errors, measurement errors, observational network and sampling interval. It is based on computation of the first neglected term in a 'Taylor'series expansion of the errors introduced by an extended Kalman filter, and can b...
Data Assimilation for Geophysical Fluids
"... The ultimate purpose of environmental studies is the forecast of its natural evolution. A prerequisite before a prediction is to retrieve at best the state of the environment. Data assimilation is the ensemble of techniques which, starting from heterogeneous information, permit to retrieve the initi ..."
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Cited by 8 (1 self)
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The ultimate purpose of environmental studies is the forecast of its natural evolution. A prerequisite before a prediction is to retrieve at best the state of the environment. Data assimilation is the ensemble of techniques which, starting from heterogeneous information, permit to retrieve the initial state of a flow. In the first part, the mathematical models governing geophysical flows are presented together with the networks of observations of the atmosphere and of the ocean. In variational methods, we seek for the minimum of a functional estimating the discrepancy between the solution of the model and the observation. The derivation of the optimality system, using the adjoint state, permits to compute a gradient which is used in the optimization. The definition of the cost function permits to take into account the available statistical information through the choice of metrics in the space of observation and in the space of the initial condition. Some examples are presented on simplified models, especially an application in oceanography. Among the tools of optimal control, the adjoint model permits to carry out sensitivity studies, but if we look for the sensitivity of the prediction with respect to the observations, then a secondorder analysis should be considered. One of the first methods used for assimilating data in oceanography is the nudging method, adding a forcing term in the equations. A variational variant of nudging method is described and also a socalled Computational Methods for the Atmosphere and the Oceans
Optimality of 4DVar and its relationship with the Kalman filter and Kalman smoother
 SUBMITTED TO Q. J. ROY. METEOROL. SOC.
, 1999
"... The known properties of equivalence between 4DVar and the Kalman filter as well as the fixedinterval Kalman smoother point to particular optimal properties of 4DVar. In the linear context, the 4DVar solution is optimal not only with respect to the model trajectory segment over the assimilation ti ..."
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Cited by 8 (1 self)
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The known properties of equivalence between 4DVar and the Kalman filter as well as the fixedinterval Kalman smoother point to particular optimal properties of 4DVar. In the linear context, the 4DVar solution is optimal not only with respect to the model trajectory segment over the assimilation time interval, but also with respect to any model state at a single observation time level
A Krylov Subspace Method for Covariance Approximation and Simulation of Random Processes and Fields
"... This paper proposes a new iterative algorithm for the simultaneously computing an approximation to the covariance matrix of a random vector and drawing a sample from that approximation. The algorithm is especially suited to cases for which the elements of the random vector are samples of a stochasti ..."
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This paper proposes a new iterative algorithm for the simultaneously computing an approximation to the covariance matrix of a random vector and drawing a sample from that approximation. The algorithm is especially suited to cases for which the elements of the random vector are samples of a stochastic process or random eld. The proposed algorithm has close connections to the conjugate gradient method for solving linear systems of equations. A comparison is made between our algorithm's structure and complexity and other methods for simulation and covariance matrix approximation, including those based on FFTs and Lanczos methods. The convergence of our iterative algorithm is analyzed both analytically and empirically, and a preconditioning technique for accelerating convergence is explored. The numerical examples include a fractional Brownian motion and a random eld with the spherical covariance used in geostatistics.
Documentation of the multitasked tangent linear and adjoint models of the adiabatic version of the NASA
 GEOS2 GCM (version 6.5). www.math.fsu.edu/~aluffi/archive/paper93.ps.gz. BIBLIOGRAPHY 254
, 1998
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Technical Remarks on Smoother Algorithms
, 1999
"... Among the currently existing data assimilation algorithms, 4D variational data assimilation (4DVAR), 4DPSAS, fixedlag Kalman smoother (FLKS), and representer method as well as Kalman smoother belong to the smoother category. In this Office Note, the formulations of these smoothing algorithms are ..."
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Among the currently existing data assimilation algorithms, 4D variational data assimilation (4DVAR), 4DPSAS, fixedlag Kalman smoother (FLKS), and representer method as well as Kalman smoother belong to the smoother category. In this Office Note, the formulations of these smoothing algorithms are discussed from the Bayesian point of view. Their relationships are further explored for linear dynamics in the context of fixedinterval smoothing. The implementation approaches and computational aspects of the smoothing algorithms are also discussed and intercompared for the purpose of retrospective data assimilation. Finally, the extensions of the algorithms to nonlinear dynamics are presented. iii Contents Abstract iii 1 Introduction 1 2 Formulations of smoother algorithms in probabilistic framework 2 2.1 FLKS formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 3DPSASlike formulation of FLKS . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2....
assimilation
"... reduced order approach to fourdimensional variational data ..."
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reduced order approach to fourdimensional variational data
1 2 A Kalman Filter Technique to Estimate Relativistic Electron Lifetimes in the Outer Radiation Belt
"... Abstract. Data assimilation aims to smoothly blend incomplete and inaccurate observational data with dynamical information from a physical model, and become an increasingly important tool in understanding and predicting meteorological, oceanographic and climate processes. As spaceborne observations ..."
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Abstract. Data assimilation aims to smoothly blend incomplete and inaccurate observational data with dynamical information from a physical model, and become an increasingly important tool in understanding and predicting meteorological, oceanographic and climate processes. As spaceborne observations become more plentiful and spacephysics models more sophisticated, dynamical processes in the radiation belts can be analyzed using advanced data assimilation methods. We use the Extended Kalman filter and observations from the Combined Release and Radiation Effects Satellite (CRRES) to estimate the lifetime of relativistic electrons during magnetic storms in the Earth’s outer radiation belt. The model is a linear parabolic partial differential equation governing the phasespace density. This equation contains empirical coefficients that are not wellknown and that we wish to estimate, along with the density itself. The assimilation method is first verified on modelsimulated data, which allows us to reliably estimate the characteristic lifetime