The Maximum Likelihood Ensemble Filter as a non‐differentiable minimization algorithm

Zupanski, Milija; Navon, I. M.; Zupanski, D.

doi:10.1002/qj.251

Cited by 83 publications

(89 citation statements)

References 44 publications

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“…The impact of the number of observations follows the findings of [ Fletcher and Zupanski 2008]. In fact, there exists a number of observations threshold beyond which the RMSE for all the fields ( namely the components of the velocity and geopotential) coincide.…”

Section: Impact Of the Number Of Observations And The Number Of Ensemsupporting

confidence: 70%

Comparison of sequential data assimilation methods for the Kuramoto–Sivashinsky equation

Jardak

Navon

Zupanski

2009

Numerical Methods in Fluids

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A new comparison of three frequently used sequential data assimilation methods illuminating their strengths and weaknesses in the presence of linear and nonlinear observation operators is presented. The ensemble Kalman filter (EnKF), the particle filter (PF) and the maximum likelihood ensemble filter (MLEF) methods were implemented and the spectral shallow water equations model in spherical geometry model was employed using the Rossby-Haurwitz Wave no. 4 test case as initial condition. Numerical tests conducted reveal that all three methods perform satisfactorily in the presence of linear observation operator for 10 to 15 days model integration, whereas the EnKF, even with the Evensen fixture [Evensen 03] for the nonlinear observation operator failed in all tested metrics. The particle filter PF and the hybrid filter MLEF both performed satisfactorily in the presence of highly nonlinear observation operators with a slight advantage in terms of CPU time to the MLEF method.

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Section: Impact Of the Number Of Observations And The Number Of Ensemsupporting

confidence: 70%

Comparison of sequential data assimilation methods for the Kuramoto–Sivashinsky equation

Jardak

Navon

Zupanski

2009

Numerical Methods in Fluids

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“…First, EnKF is applied iteratively in a batch mode for parameter estimation. This is inspired by related methods for converting filters into optimization methods (Zhou et al, 2008;Wan and Van Der Merwe, 2000;Zupanski et al, 2008). However, it is different from ensemble Kalman smoothers that operate on the state variables (Evensen and van Leeuwen, 2000).…”

Section: Introductionmentioning

confidence: 99%

“…However, it is different from ensemble Kalman smoothers that operate on the state variables (Evensen and van Leeuwen, 2000). The proposed algorithm have some similarities with Maximum Likelihood Ensemble Filter (MLEF) (Zupanski et al, 2008) but the error covariance is not updated using an analysis step as in filtering methods. Instead, a random perturbation is applied to mimic a random stencil in a stochastic Newton like method.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter

Elsheikh

Pain

Fang

et al. 2012

Stoch Environ Res Risk Assess

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A new parameter estimation algorithm based on ensemble Kalman filter (EnKF) is developed. The developed algorithm combined with the proposed problem parametrization offers an efficient parameter estimation method that converges using very small ensembles and without any tuning parameters. The inverse problem is formulated as a sequential data integration problem. Gaussian Process Regression (GRP) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen-Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative regularized ensemble Kalman filter algorithm. The filter is converted to an optimization algorithm by using a pseudo time-stepping technique such that the model output matches the time dependent data. The EnKF Kalman gain matrix is regularized using truncated SVD to filter out noisy correlations. Numerical results show that the proposed algorithm is a promising approach for parameter estimation of subsurface flow models.

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“…It is one of the simplest equations that display important features of geophysical interest, such as advection, frontogenesis, and one-dimensional turbulence (Burgers, 1974;Hopf, 1950;el Malek and ElMansi, 2000 and references therein). The Burgers equation has been used in several data assimilation studies to examine the effect of nonlinearity error propagation and in Kalman filtering methods (Cohn, 1993;Ménard, 1994;Verlaan and Heemink, 2001), in maximum likelihood ensemble filtering (Zupanski et al, 2008), in adjoint methods (Apte et al, 2010), in model error estimation using 4D-Var (Lakshmivarahan et al, 2013), and in 4DEnVar and localization (Desroziers et al, 2014(Desroziers et al, , 2016.…”

Section: Introductionmentioning

confidence: 99%

Parametric covariance dynamics for the nonlinear diffusive Burgers equation

Pannekoucke

Bocquet

Ménard

2018

Nonlin. Processes Geophys.

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Abstract. The parametric Kalman filter (PKF) is a computationally efficient alternative method to the ensemble Kalman filter. The PKF relies on an approximation of the error covariance matrix by a covariance model with a space-time evolving set of parameters. This study extends the PKF to nonlinear dynamics using the diffusive Burgers equation as an application, focusing on the forecast step of the assimilation cycle. The covariance model considered is based on the diffusion equation, with the diffusion tensor and the error variance as evolving parameters. An analytical derivation of the parameter dynamics highlights a closure issue. Therefore, a closure model is proposed based on the kurtosis of the local correlation functions. Numerical experiments compare the PKF forecast with the statistics obtained from a large ensemble of nonlinear forecasts. These experiments strengthen the closure model and demonstrate the ability of the PKF to reproduce the tangent linear covariance dynamics, at a low numerical cost.

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The Maximum Likelihood Ensemble Filter as a non‐differentiable minimization algorithm

Cited by 83 publications

References 44 publications

Comparison of sequential data assimilation methods for the Kuramoto–Sivashinsky equation

Comparison of sequential data assimilation methods for the Kuramoto–Sivashinsky equation

Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter

Parametric covariance dynamics for the nonlinear diffusive Burgers equation

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