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SOME ISSUES AND RESULTS ON THE EnKF AND PARTICLE FILTERS FOR METEOROLOGICAL MODELS
"... Abstract. In this paper we examine the links between Ensemble Kalman Filters (EnKF) and Particle Filters (PF). EnKF can be seen as a MeanField process with a PF approximation. We explore the problem of dimensionality on a toy model. To bypass this di±culty, we suggest using Local Particle Filters ..."
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Abstract. In this paper we examine the links between Ensemble Kalman Filters (EnKF) and Particle Filters (PF). EnKF can be seen as a MeanField process with a PF approximation. We explore the problem of dimensionality on a toy model. To bypass this di±culty, we suggest using Local Particle Filters (LPF) to catch nonlinearities and feed larger scale EnKF. To go one step forward we conclude with a real application and present the ¯ltering of perturbed measurements of atmospheric wind in the domain of turbulence. This example is the cornerstone of the LPF for the assimilation of atmospheric turbulent wind. These local representation techniques will be used in further works to assimilate singular data of turbulence linked parameters in nonhydrostatic models.
Efficient nonlinear dataassimilation in geophysical fluid dynamics
 Comput. Fluids
, 2011
"... nonlinear data assimilation in geophysical fluid dynamics ABCDE ..."
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nonlinear data assimilation in geophysical fluid dynamics ABCDE
Quantifying bayesian filter performance for turbulent dynamical systems through information theory
 Comm. Math. Sci
"... Incomplete knowledge of the true dynamics and its partial observations pose a notoriously difficult problem in many contemporary scientific applications which require predictions of highdimensional dynamical systems with physical instabilities and energy fluxes across a wide range of scales. In suc ..."
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Incomplete knowledge of the true dynamics and its partial observations pose a notoriously difficult problem in many contemporary scientific applications which require predictions of highdimensional dynamical systems with physical instabilities and energy fluxes across a wide range of scales. In such cases assimilation of real data into the modeled dynamics is necessary for mitigating model error and for improving the stability and predictive skill of imperfect models. However, the practically implementable data assimilation/filtering strategies are also imperfect and not optimal due to the formidably complex nature of the underlying dynamics. Here, the connections between information theory and the filtering problem are exploited in order to establish bounds on the filter error statistics, and to systematically study the statistical accuracy of various Kalman filters with model error for estimating the dynamics of spatially extended, partially observed turbulent systems. The effects of model error on filter stability and accuracy in this highdimensional setting are analyzed through appropriate information measures which naturally extend the common pathwise estimates of filter performance, like the meansquare error or pattern correlation, to the statistical superensemble setting that involves all possible initial conditions and all realizations of noisy observations of the truth signal. This informationtheoretic framework for an offline assessment of filter performance is an important complement to the pathwise approach, and it has natural generalizations to Kalman filtering with nonGaussian statistically exactly solvable forecast models. Here, this framework is utilized to study the performance of imperfect, reducedorder filters with Gaussian models which use various spatiotemporal discretizations to approximate the dynamics of the stochastically forced advection
Comparison of filtering methods for the modeling and retrospective forecasting of influenza epidemics. PLoS computational biology
"... A variety of filtering methods enable the recursive estimation of system state variables and inference of model parameters. These methods have found application in a range of disciplines and settings, including engineering design and forecasting, and, over the last two decades, have been applied to ..."
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A variety of filtering methods enable the recursive estimation of system state variables and inference of model parameters. These methods have found application in a range of disciplines and settings, including engineering design and forecasting, and, over the last two decades, have been applied to infectious disease epidemiology. For any system of interest, the ideal filter depends on the nonlinearity and complexity of the model to which it is applied, the quality and abundance of observations being entrained, and the ultimate application (e.g. forecast, parameter estimation, etc.). Here, we compare the performance of six stateoftheart filter methods when used to model and forecast influenza activity. Three particle filters— a basic particle filter (PF) with resampling and regularization, maximum likelihood estimation via iterated filtering (MIF), and particle Markov chain Monte Carlo (pMCMC)—and three ensemble filters—the ensemble Kalman filter (EnKF), the ensemble adjustment Kalman filter (EAKF), and the rank histogram filter (RHF)—were used in conjunction with a humidityforced susceptibleinfectiousrecoveredsusceptible (SIRS) model and weekly estimates of influenza incidence. The modeling frameworks, first validated with synthetic influenza epidemic data, were then applied to fit and retrospectively forecast the historical incidence time series of seven influenza epidemics during 2003–2012, for 115 cities in the United States. Results suggest that when using the SIRS model the ensemble filters and the basic PF are more capable of faithfully recreating historical influenza incidence time series, while the MIF and pMCMC do not perform as well for multimodal outbreaks. For
Longtime asymptotics of the filtering distribution for partially observed chaotic dynamical systems
 In preparation
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Conditions for successful data assimilation
"... We show that numerical data assimilation is feasible in principle for an idealized model only if an effective dimension of the noise is bounded; this effective dimension is bounded when the noises in model and data satisfy a certain natural balance condition. If this balance condition is satisfied, ..."
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We show that numerical data assimilation is feasible in principle for an idealized model only if an effective dimension of the noise is bounded; this effective dimension is bounded when the noises in model and data satisfy a certain natural balance condition. If this balance condition is satisfied, data assimilation is feasible even if the number of variables in the problem is huge. We then analyze several data assimilation algorithms, including particle filters and variational data assimilation. We show that a particle filter can successfully solve most of the data assimilation problems which are feasible in principle, provided the particle filter is well designed. We also compare the conditions under which variational data assimilation can be successful with the conditions for successful particle filtering. We draw conclusions from our analysis and discuss its limitations. 1
State Estimation using the Particle Filter with Mode Tracking by J.A. Pocock, S.L. Dance, A.S. LawlessState Estimation using the Particle Filter with Mode Tracking
, 2010
"... A particle filter is a data assimilation scheme that employs a fully nonlinear, nonGaussian analysis step. Unfortunately as the size of the state grows the number of ensemble members required for the particle filter to converge to the true solution increases exponentially. To overcome this Vaswani ..."
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A particle filter is a data assimilation scheme that employs a fully nonlinear, nonGaussian analysis step. Unfortunately as the size of the state grows the number of ensemble members required for the particle filter to converge to the true solution increases exponentially. To overcome this Vaswani [Vaswani N., 2008, IEEE Transactions on Signal Processing, 56:45834597] proposed a new method known as mode tracking to improve the efficiency of the particle filter. When mode tracking, the state is split into two subspaces. One subspace is forecast using the particle filter, the other is treated so that its values are set equal to the mode of the marginal pdf. There are many ways to split the state. One hypothesis is that the best results should be obtained from the particle filter with mode tracking when we mode track the maximum number of unimodal dimensions. The three dimensional stochastic Lorenz equations with direct observations are used to test this hypothesis. It is found that mode tracking the maximum number of unimodal dimensions does not always provide the best result. The best choice of states to modetrack depends on the number of particles used.