scholarly journals Spectral diagonal ensemble Kalman filters

2015 ◽  
Vol 22 (4) ◽  
pp. 485-497 ◽  
Author(s):  
I. Kasanický ◽  
J. Mandel ◽  
M. Vejmelka
Keyword(s):  
Ensemble Kalman Filter ◽  
Random Fields ◽  
Satellite Images ◽  
Discrete Wavelet ◽  
State Variables ◽  
Ensemble Kalman Filters ◽  
Sample Covariance ◽  
New Type ◽  
Stationary Random Field ◽  
Lorenz 96

Abstract. A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the approximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles.

scholarly journals Spectral diagonal ensemble Kalman filters

2015 ◽  
Vol 2 (1) ◽  
pp. 115-143 ◽  
Author(s):  
I. Kasanický ◽  
J. Mandel ◽  
M. Vejmelka
Keyword(s):  
Ensemble Kalman Filter ◽  
Random Fields ◽  
Satellite Images ◽  
Discrete Wavelet ◽  
State Variables ◽  
Ensemble Kalman Filters ◽  
Sample Covariance ◽  
New Type ◽  
Stationary Random Field ◽  
Lorenz 96

Abstract. A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles.

scholarly journals A Moment Matching Ensemble Filter for Nonlinear Non-Gaussian Data Assimilation

2011 ◽  
Vol 139 (12) ◽  
pp. 3964-3973 ◽  
Author(s):  
Jing Lei ◽  
Peter Bickel
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Ensemble Forecasting ◽  
Moment Matching ◽  
State Variables ◽  
Mean And Variance ◽  
Large Systems ◽  
Non Gaussian ◽  
Lorenz 96 ◽  
Gaussian Data

Abstract The ensemble Kalman filter is now an important component of ensemble forecasting. While using the linear relationship between the observation and state variables makes it applicable for large systems, relying on linearity introduces nonnegligible bias since the true distribution will never be Gaussian. This paper analyzes the bias of the ensemble Kalman filter from a statistical perspective and proposes a debiasing method called the nonlinear ensemble adjustment filter. This new filter transforms the forecast ensemble in a statistically principled manner so that the updated ensemble has the desired mean and variance. It is also easily localizable and, hence, potentially useful for large systems. Its performance is demonstrated and compared with other Kalman filter and particle filter variants through various experiments on the Lorenz-63 and Lorenz-96 systems. The results show that the new filter is stable and accurate for challenging situations such as nonlinear, high-dimensional systems with sparse observations.

scholarly journals Controlling Overestimation of Error Covariance in Ensemble Kalman Filters with Sparse Observations: A Variance-Limiting Kalman Filter

2011 ◽  
Vol 139 (8) ◽  
pp. 2650-2667 ◽  
Author(s):  
Georg A. Gottwald ◽  
Lewis Mitchell ◽  
Sebastian Reich
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Kalman Filters ◽  
Observational Error ◽  
Ensemble Kalman Filters ◽  
Partial Observations ◽  
Error Covariance ◽  
The Stability ◽  
Lorenz 96 ◽  
Ensemble Transform

AbstractThe problem of an ensemble Kalman filter when only partial observations are available is considered. In particular, the situation is investigated where the observational space consists of variables that are directly observable with known observational error, and of variables of which only their climatic variance and mean are given. To limit the variance of the latter poorly resolved variables a variance-limiting Kalman filter (VLKF) is derived in a variational setting. The VLKF for a simple linear toy model is analyzed and its range of optimal performance is determined. The VLKF is explored in an ensemble transform setting for the Lorenz-96 system, and it is shown that incorporating the information of the variance of some unobservable variables can improve the skill and also increase the stability of the data assimilation procedure.

scholarly journals Parameters Estimation and Prediction of Water Movement and Solute Transport in Layered, Variably Saturated Soils Using the Ensemble Kalman Filter

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1520
Author(s):  
Zheng Jiang ◽  
Quanzhong Huang ◽  
Gendong Li ◽  
Guangyong Li
Keyword(s):  
Kalman Filter ◽  
Solute Transport ◽  
Ensemble Kalman Filter ◽  
Water Movement ◽  
Parameters Estimation ◽  
Saturated Soils ◽  
Hydrological Models ◽  
State Variables ◽  
Ensemble Size ◽  
Highly Nonlinear

The parameters of water movement and solute transport models are essential for the accurate simulation of soil moisture and salinity, particularly for layered soils in field conditions. Parameter estimation can be achieved using the inverse modeling method. However, this type of method cannot fully consider the uncertainties of measurements, boundary conditions, and parameters, resulting in inaccurate estimations of parameters and predictions of state variables. The ensemble Kalman filter (EnKF) is well-suited to data assimilation and parameter prediction in Situations with large numbers of variables and uncertainties. Thus, in this study, the EnKF was used to estimate the parameters of water movement and solute transport in layered, variably saturated soils. Our results indicate that when used in conjunction with the HYDRUS-1D software (University of California Riverside, California, CA, USA) the EnKF effectively estimates parameters and predicts state variables for layered, variably saturated soils. The assimilation of factors such as the initial perturbation and ensemble size significantly affected in the simulated results. A proposed ensemble size range of 50–100 was used when applying the EnKF to the highly nonlinear hydrological models of the present study. Although the simulation results for moisture did not exhibit substantial improvement with the assimilation, the simulation of the salinity was significantly improved through the assimilation of the salinity and relative solutetransport parameters. Reducing the uncertainties in measured data can improve the goodness-of-fit in the application of the EnKF method. Sparse field condition observation data also benefited from the accurate measurement of state variables in the case of EnKF assimilation. However, the application of the EnKF algorithm for layered, variably saturated soils with hydrological models requires further study, because it is a challenging and highly nonlinear problem.

PARTICLE FILTERS IN A MULTISCALE ENVIRONMENT: WITH APPLICATION TO THE LORENZ-96 ATMOSPHERIC MODEL

2011 ◽  
Vol 11 (02n03) ◽  
pp. 569-591 ◽  
Author(s):  
HOONG CHIEH YEONG ◽  
JUN HYUN PARK ◽  
N. SRI NAMACHCHIVAYA
Keyword(s):  
Dynamical Systems ◽  
Particle Filter ◽  
Observational Data ◽  
Particle Filtering ◽  
Atmospheric Model ◽  
Random Dynamical Systems ◽  
Coarse Grained ◽  
Conditional Density ◽  
State Variables ◽  
Lorenz 96

The study of random dynamical systems involves understanding the evolution of state variables that contain uncertainties and that are usually hidden, or not directly observable. Therefore, state variables have to be estimated and updated based on system models using information from observational data, which themselves are noisy, in the sense that they contain uncertainties and disturbances due to imperfections in observational devices and disturbances in the environment within which data are being collected. The development of efficient data assimilation methods for integrating observational data in predicting the evolution of random state variables is thus an important aspect in the study of random dynamical systems. In this paper, we consider a particle filtering approach to nonlinear filtering in multiscale dynamical systems. Particle filtering methods [1–3] utilizes ensembles of particles to represent the conditional density of state variables using particle positions, distributed over a sample space. The distribution of an ensemble of particles is updated using observational data to obtain the best representation of the conditional density of the state variables of interest. On the other hand, homogenization theory [4, 5], allows us to estimate the coarse-grained (slow) dynamics of a multiscale system on a larger timescale without having to explicitly study the fast variable evolution on a small timescale. The results of filter convergence presented in [6] shows the convergence of the filter of the actual state variable to a homogenized solution to the original multiscale system, and thus we develop a particle filtering scheme for multiscale random dynamical systems that utilizes this convergence result. This particle filtering method is called the Homogenized Hybird Particle Filter, and it incorporates a multiscale computation scheme, the Heterogeneous Multiscale Method developed in [7], with the novel branching particle filter described in [8–10]. By incorporating a multiscale scheme based on homogenization of the original system, estimation of the coarse-grained dynamics using observational data is performed over a larger timescale, thus resulting in computational time and cost reduction in terms of the evolution of the state variables as well as functional evaluations for the filtering aspect. We describe the theory behind this combined scheme and its general algorithm, concluded with an application to the Lorenz-96 [11] atmospheric model that mimics midlatitude geophysical dynamics with microscopic convective processes.

Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design

2018 ◽  
Vol 13 (5) ◽  
Author(s):  
Eric Donald Dongmo ◽  
Kayode Stephen Ojo ◽  
Paul Woafo ◽  
Abdulahi Ndzi Njah
Keyword(s):  
Chaotic System ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
The State ◽  
State Variables ◽  
State Variable ◽  
New Type ◽  
The Difference ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

This paper introduces a new type of synchronization scheme, referred to as difference synchronization scheme, wherein the difference between the state variables of two master [slave] systems synchronizes with the state variable of a single slave [master] system. Using the Lyapunov stability theory and the active backstepping technique, controllers are derived to achieve the difference synchronization of three identical hyperchaotic Liu systems evolving from different initial conditions, as well as the difference synchronization of three nonidentical systems of different orders, comprising the 3D Lorenz chaotic system, 3D Chen chaotic system, and the 4D hyperchaotic Liu system. Numerical simulations are presented to demonstrate the validity and feasibility of the theoretical analysis. The development of difference synchronization scheme has increases the number of existing chaos synchronization scheme.

scholarly journals A Marginal Adjustment Rank Histogram Filter for Non-Gaussian Ensemble Data Assimilation

2020 ◽  
Author(s):  
Jeffrey L. Anderson
Keyword(s):  
Ensemble Kalman Filter ◽  
Ensemble Methods ◽  
State Variables ◽  
Histogram Method ◽  
Prior Distributions ◽  
Bounded State ◽  
Rank Histogram ◽  
Non Gaussian ◽  
Atmospheric Tracer ◽  
Filter Algorithms

An extension to standard ensemble Kalman filter algorithms that can improve performance for non-Gaussian prior distributions, non-Gaussian likelihoods, and bounded state variables is described. The algorithm exploits the capability of the rank histogram filter (RHF) to represent arbitrary prior distributions for observed variables. The rank histogram algorithm can be applied directly to state variables to produce posterior marginal ensembles without the need for regression that is part of standard ensemble filters. These marginals are used to adjust the marginals obtained from a standard ensemble filter that uses regression to update state variables. The final posterior ensemble is obtained by doing an ordered replacement of the posterior marginal ensemble values from a standard ensemble filter with the values obtained from the rank histogram method applied directly to state variables; the algorithm is referred to as the Marginal Adjustment Rank Histogram Filter (MARHF). Applications to idealized bivariate problems and low-order dynamical systems show that the MARHF can produce better results than standard ensemble methods for priors that are non-Gaussian. Like the original RHF, the MARHF can also make use of arbitrary non-Gaussian observation likelihoods. The MARHF also has advantages for problems with bounded state variables, for instance the concentration of an atmospheric tracer. Bounds can be automatically respected in the posterior ensembles. With an efficient implementation of the MARHF, the additional cost has better scaling than the standard RHF.

scholarly journals A Data-Driven Method for Improving the Correlation Estimation in Serial Ensemble Kalman Filters

2017 ◽  
Vol 145 (3) ◽  
pp. 985-1001 ◽  
Author(s):  
Michèle De La Chevrotière ◽  
John Harlim
Keyword(s):  
Kalman Filters ◽  
Data Driven ◽  
Training Procedure ◽  
Ensemble Kalman Filters ◽  
Regression Problem ◽  
Correlation Estimation ◽  
Sample Correlation ◽  
Correlation Statistics ◽  
Nonlinear Observation ◽  
Lorenz 96

A data-driven method for improving the correlation estimation in serial ensemble Kalman filters is introduced. The method finds a linear map that transforms, at each assimilation cycle, the poorly estimated sample correlation into an improved correlation. This map is obtained from an offline training procedure without any tuning as the solution of a linear regression problem that uses appropriate sample correlation statistics obtained from historical data assimilation outputs. In an idealized OSSE with the Lorenz-96 model and for a range of linear and nonlinear observation models, the proposed scheme improves the filter estimates, especially when the ensemble size is small relative to the dimension of the state space.

Sign in / Sign up

Export Citation Format

Share Document