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A random map implementation of implicit filters
"... Implicit particle filters for data assimilation generate highprobability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined equation be solved for each particle and at each time an observa ..."
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Implicit particle filters for data assimilation generate highprobability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined equation be solved for each particle and at each time an observation becomes available. We present a new implementation of implicit filters in which we find the solution of the equation via a random map. As examples, we assimilate data for a stochastically driven Lorenz system with sparse observations and for a stochastic KuramotoSivashinski equation with observations that are sparse in both space and time.
and A.M.Stuart. Variational data assimilation using targetted random walks
 Int. J. Num. Meth. Fluids
"... The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis. In either of these scenarios, it can be important to assess uncertainties in the assimilated state. Ideally, it is desirable to have complete information concerning the Bayesian ..."
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The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis. In either of these scenarios, it can be important to assess uncertainties in the assimilated state. Ideally, it is desirable to have complete information concerning the Bayesian posterior distribution for unknown state given data. We show that complete computational probing of this posterior distribution is now within the reach in the offline situation. We introduce a Markov chain–Monte Carlo (MCMC) method which enables us to directly sample from the Bayesian posterior distribution on the unknown functions of interest given observations. Since we are aware that these methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walktype MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however, more sophisticated MCMC methods are available which exploit derivative information. For simplicity of exposition, we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number flow in a twodimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces. Copyright! 2011 John Wiley
Ensemble data assimilation for the shallow water equations model in the presence of linear and nonlinear observation operators
, 2009
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A Survey of Implicit Particle Filters for Data Assimilation
"... Abstract The implicit particle filter is a sequential Monte Carlo method for data assimilation. The idea is to focus the particles onto the high probability regions of the target probability density function (pdf) so that the number of particles required for a good approximation of this pdf remains ..."
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Abstract The implicit particle filter is a sequential Monte Carlo method for data assimilation. The idea is to focus the particles onto the high probability regions of the target probability density function (pdf) so that the number of particles required for a good approximation of this pdf remains manageable, even if the dimension of the state space is large. We explain how this idea is implemented, discuss special cases of practical importance, and work out the relations of the implicit particle filter with other data assimilation methods. We illustrate the theory with four examples. 1
Barber: in Chemistry and Physics of
, 1978
"... Abstract. Mean winds in the mesosphere and lower thermosphere (MLT) over Ascension Island (8 ◦ S, 14 ◦ W) have been measured at heights of approximately 80–100 km by a meteor radar. The results presented in this study are from the interval October 2001 to December 2011. In all years, the monthlym ..."
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Abstract. Mean winds in the mesosphere and lower thermosphere (MLT) over Ascension Island (8 ◦ S, 14 ◦ W) have been measured at heights of approximately 80–100 km by a meteor radar. The results presented in this study are from the interval October 2001 to December 2011. In all years, the monthlymean meridional winds display a clear annual oscillation. Typically, these winds are found to be southward during April–October, when they reach velocities of up to about −23 m s−1, and northward throughout the rest of the year, when they reach velocities up to about 16 m s−1. The monthlymean zonal winds are generally westward throughout most of the year and reach velocities of up to about −46 m s−1. However, eastward winds are observed in May– August and again in December at the lower heights observed. These eastward winds reach a maximum at heights of about
CSU Account #: 533023
, 2008
"... This research project has produced a novel methodology for ensemble data assimilation (EnsDA) based on control theory, named the Maximum Likelihood Ensemble Filter (MLEF). This methodology extends the applicability of current nonlinear filters to arbitrary nonlinear observation operators, with impor ..."
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This research project has produced a novel methodology for ensemble data assimilation (EnsDA) based on control theory, named the Maximum Likelihood Ensemble Filter (MLEF). This methodology extends the applicability of current nonlinear filters to arbitrary nonlinear observation operators, with important implications to remote sensing and other nonlinear observations. In addition to the main goal of developing an ensemble data assimilation system based on control theory, at least two major new results were produced by this research: (1) nonGaussian framework for data assimilation was first formulated within this project, and is now gaining a worldwide recognition, and (2) new nondifferentiable unconstrained minimizations algorithms are formulated and tested within this project. In addition, the issue of insufficient number of degrees of freedom (DOF) was addressed during last year (20072008), resulting in an improvement of currently used error covariance localization techniques. To date, this project produced 13 papers (10 published, 2 submitted, 1 to be submitted, referenced below). Two postdoctoral researchers are trained under this project; one at Colorado State
Multivariate and Multiscale Data Assimilation in Terrestrial Systems: A Review
, 2012
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"... Ensemble Data Assimilation for the shallow water equation model in the presence of linear and nonlinear observation operator M.Jardak, 1 I.M.Navon, 1 and M.Zupanski 2 ..."
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Ensemble Data Assimilation for the shallow water equation model in the presence of linear and nonlinear observation operator M.Jardak, 1 I.M.Navon, 1 and M.Zupanski 2
NSF Collaboration in Mathematical Geosciences Research
, 2008
"... This research project has produced a novel methodology for ensemble data assimilation (EnsDA) based on control theory, named the Maximum Likelihood Ensemble Filter (MLEF). This methodology extends the applicability of current nonlinear filters to arbitrary nonlinear observation operators, with impor ..."
Abstract
 Add to MetaCart
This research project has produced a novel methodology for ensemble data assimilation (EnsDA) based on control theory, named the Maximum Likelihood Ensemble Filter (MLEF). This methodology extends the applicability of current nonlinear filters to arbitrary nonlinear observation operators, with important implications to remote sensing and other nonlinear observations. In addition to the main goal of developing an ensemble data assimilation system based on control theory, at least two major new results were produced by this research: (1) nonGaussian framework for data assimilation was first formulated within this project, and is now gaining a worldwide recognition, and (2) new nondifferentiable unconstrained minimizations algorithms are formulated and tested within this project. In addition, the issue of insufficient number of degrees of freedom (DOF) was addressed during last year (20072008), resulting in an improvement of currently used error covariance localization techniques. To date, this project produced 13 papers (10 published, 2 submitted, 1 to be submitted, referenced below). Two postdoctoral researchers are trained under this project; one at Colorado State