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92
Sequential Monte Carlo methods for highdimensional inverse problems: A case study for the NavierStokes equations
, 2013
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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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Cited by 23 (13 self)
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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.
Implicit particle filters for data assimilation
, 2010
"... Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles one by one to the high probability domain. We provide a detailed description of these filters, with illustrative exampl ..."
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Cited by 21 (14 self)
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Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles one by one to the high probability domain. We provide a detailed description of these filters, with illustrative examples, together with new, more general, methods for solving the algebraic equations and with a new algorithm for parameter identification. 1
Comparison of sequential data assimilation methods for the Kuramoto–Sivashinsky equation
, 2009
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A NonGaussian Ensemble Filter Update for Data Assimilation
, 2009
"... A deterministic square root ensemble Kalman filter and a stochastic perturbed observation ensemble Kalman filter are used for data assimilation in both linear and nonlinear single variable dynamical systems. For the linear system, the deterministic filter is simply a method for computing the Kalman ..."
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Cited by 11 (1 self)
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A deterministic square root ensemble Kalman filter and a stochastic perturbed observation ensemble Kalman filter are used for data assimilation in both linear and nonlinear single variable dynamical systems. For the linear system, the deterministic filter is simply a method for computing the Kalman filter and is optimal while the stochastic filter has suboptimal performance due to sampling error. For the nonlinear system, the deterministic filter has increasing error as ensemble size increases because all ensemble members but one become tightly clustered. In this case, the stochastic filter performs better for sufficiently large ensembles. A new method for computing ensemble increments in observation space is proposed that does not suffer from the pathological behavior of the deterministic filter while avoiding much of the sampling error of the stochastic filter. This filter uses the order statistics of the prior observation space ensemble to create an approximate continuous prior probability distribution in a fashion analogous to the use of rank histograms for ensemble forecast evaluation. This rank histogram filter can represent nonGaussian observation space priors and posteriors and is shown to be competitive with existing filters for problems as large as global numerical weather prediction. The ability to represent nonGaussian distributions is useful for a variety of applications such as convectivescale assimilation and assimilation of bounded quantities such as relative humidity. 1.
Error bounds and normalizing constants for sequential Monte Carlo in high dimensions
, 2012
"... In a recent paper [3], the Sequential Monte Carlo (SMC) sampler introduced in [12, 19, 24] has been shown to be asymptotically stable in the dimension of the state space d at a cost that is only polynomial in d, when N the number of Monte Carlo samples, is fixed. More precisely, it has been establis ..."
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Cited by 8 (3 self)
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In a recent paper [3], the Sequential Monte Carlo (SMC) sampler introduced in [12, 19, 24] has been shown to be asymptotically stable in the dimension of the state space d at a cost that is only polynomial in d, when N the number of Monte Carlo samples, is fixed. More precisely, it has been established that the effective sample size (ESS) of the ensuing (approximate) sample and the Monte Carlo error of fixed dimensional marginals will converge as d grows, with a computational cost of O(Nd2). In the present work, further results on SMC methods in high dimensions are provided as d → ∞ and with N fixed. We deduce an explicit bound on the MonteCarlo error for estimates derived using the SMC sampler and the exact asymptotic relative L2error of the estimate of the normalizing constant. We also establish marginal propagation of chaos properties of the algorithm. The accuracy in highdimensions of some approximate SMCbased filtering schemes is also discussed.
Weighted Ensemble Transform Kalman Filter for Image Assimilation
, 2012
"... This paper proposes an extension of the Weighted Ensemble Kalman filter (WEnKF) proposed by Papadakis et al. (2010) for the assimilation of image observations. The main contribution of this paper consists in a novel formulation of the Weighted filter with the Ensemble Transform Kalman filter (WETKF) ..."
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Cited by 6 (0 self)
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This paper proposes an extension of the Weighted Ensemble Kalman filter (WEnKF) proposed by Papadakis et al. (2010) for the assimilation of image observations. The main contribution of this paper consists in a novel formulation of the Weighted filter with the Ensemble Transform Kalman filter (WETKF) incorporating directly as a measurement model a nonlinear image reconstruction criterion. This technique has been compared to the original WEnKF on numerical and real world data of 2D turbulence observed through the transport of a passive scalar. It has been in particular applied for the reconstruction of oceanic surface current vorticity fields from Sea Surface Temperature satellite data. This latter technique enables a consistent recovery of oceanic surface currents, vorticity maps along time in presence of large missing data areas and strong noise. 1
Ensemble data assimilation for the shallow water equations model in the presence of linear and nonlinear observation operators
, 2009
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Implicit particle methods and their connection with variational data assimilation
 Monthly Weather Review
"... The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the highprobability regions via a sequence of steps that includes minimizations. We present a new and more general derivation of this approach and extend the method to particle smoothi ..."
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Cited by 5 (5 self)
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The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the highprobability regions via a sequence of steps that includes minimizations. We present a new and more general derivation of this approach and extend the method to particle smoothing as well as to data assimilation for perfect models. We show that the minimizations required by implicit particle methods are similar to the ones one encounters in variational data assimilation and explore the connection of implicit particle methods with variational data assimilation. In particular, we argue that existing variational codes can be converted into implicit particle methods at a low cost, often yielding better estimates, that are also equipped with quantitative measures of the uncertainty. A detailed example is presented. 1