scholarly journals Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter

2011 ◽  
Vol 8 (4) ◽  
pp. 6749-6788 ◽  
Author(s):  
L. Li ◽  
H. Zhou ◽  
H. J. Hendricks Franssen ◽  
J. J. Gómez-Hernández
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Random Function ◽  
Bimodal Distribution ◽  
Function Model ◽  
Normal Score ◽  
Mean And Variance ◽  
Assimilation Process ◽  
Flow Configurations ◽  
The Individual

Abstract. The normal-score ensemble Kalman filter (NS-EnKF) is tested on a synthetic aquifer characterized by the presence of channels with a bimodal distribution of its hydraulic conductivities. Fourteen scenarios are analyzed which differ among them in one or various of the following aspects: the prior random function model, the boundary conditions of the flow problem, the number of piezometers used in the assimilation process, or the use of covariance localization in the implementation of the Kalman filter. The performance of the NS-EnKF is evaluated through the ensemble mean and variance maps, the connectivity patterns of the individual conductivity realizations and the degree of reproduction of the piezometric heads. The results show that (i) the localized NS-EnKF can identify correctly the channels when a large number of conditioning piezometers are used even when an erroneous prior random function model is used, (ii) localization plays an important role to prevent filter inbreeding and results in a better logconductivity characterization, and (iii) the NS-EnKF works equally well under very different flow configurations.

scholarly journals Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter

2012 ◽  
Vol 16 (2) ◽  
pp. 573-590 ◽  
Author(s):  
L. Li ◽  
H. Zhou ◽  
H. J. Hendricks Franssen ◽  
J. J. Gómez-Hernández
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Random Function ◽  
Bimodal Distribution ◽  
Function Model ◽  
Normal Score ◽  
Mean And Variance ◽  
Flow Configurations ◽  
Multigaussian Distribution ◽  
The Individual

Abstract. The normal-score ensemble Kalman filter (NS-EnKF) is tested on a synthetic aquifer characterized by the presence of channels with a bimodal distribution of its hydraulic conductivities. This is a clear example of an aquifer that cannot be characterized by a multiGaussian distribution. Fourteen scenarios are analyzed which differ among them in one or various of the following aspects: the prior random function model, the boundary conditions of the flow problem, the number of piezometers used in the assimilation process, or the use of covariance localization in the implementation of the Kalman filter. The performance of the NS-EnKF is evaluated through the ensemble mean and variance maps, the connectivity patterns of the individual conductivity realizations and the degree of reproduction of the piezometric heads. The results show that (i) the localized NS-EnKF can characterize the non-multiGaussian underlying hydraulic distribution even when an erroneous prior random function model is used, (ii) localization plays an important role to prevent filter inbreeding and results in a better logconductivity characterization, and (iii) the NS-EnKF works equally well under very different flow configurations.

scholarly journals Calibrating Multimodel Forecast Ensembles with Exchangeable and Missing Members Using Bayesian Model Averaging

2010 ◽  
Vol 138 (1) ◽  
pp. 190-202 ◽  
Author(s):  
Chris Fraley ◽  
Adrian E. Raftery ◽  
Tilmann Gneiting
Keyword(s):  
Kalman Filter ◽  
Pacific Northwest ◽  
Ensemble Kalman Filter ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Weighted Average ◽  
Multimodel Ensembles ◽  
The Individual ◽  
Ensemble Systems

Abstract Bayesian model averaging (BMA) is a statistical postprocessing technique that generates calibrated and sharp predictive probability density functions (PDFs) from forecast ensembles. It represents the predictive PDF as a weighted average of PDFs centered on the bias-corrected ensemble members, where the weights reflect the relative skill of the individual members over a training period. This work adapts the BMA approach to situations that arise frequently in practice; namely, when one or more of the member forecasts are exchangeable, and when there are missing ensemble members. Exchangeable members differ in random perturbations only, such as the members of bred ensembles, singular vector ensembles, or ensemble Kalman filter systems. Accounting for exchangeability simplifies the BMA approach, in that the BMA weights and the parameters of the component PDFs can be assumed to be equal within each exchangeable group. With these adaptations, BMA can be applied to postprocess multimodel ensembles of any composition. In experiments with surface temperature and quantitative precipitation forecasts from the University of Washington mesoscale ensemble and ensemble Kalman filter systems over the Pacific Northwest, the proposed extensions yield good results. The BMA method is robust to exchangeability assumptions, and the BMA postprocessed combined ensemble shows better verification results than any of the individual, raw, or BMA postprocessed ensemble systems. These results suggest that statistically postprocessed multimodel ensembles can outperform individual ensemble systems, even in cases in which one of the constituent systems is superior to the others.

scholarly journals Identification of high-permeability subsurface structures with multiple point geostatistics and normal score ensemble Kalman filter

2017 ◽  
Vol 548 ◽  
pp. 208-224 ◽  
Author(s):  
Francesco Zovi ◽  
Matteo Camporese ◽  
Harrie-Jan Hendricks Franssen ◽  
Johan Alexander Huisman ◽  
Paolo Salandin
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Multiple Point ◽  
High Permeability ◽  
Subsurface Structures ◽  
Normal Score

scholarly journals Correlation between System and Observation Errors in Data Assimilation

2018 ◽  
Vol 146 (9) ◽  
pp. 2913-2931 ◽  
Author(s):  
Tyrus Berry ◽  
Timothy Sauer
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Extreme Case ◽  
Covariance Matrices ◽  
Bayesian Filtering ◽  
Filtering Algorithm ◽  
Accurate Knowledge ◽  
Cross Correlations ◽  
Observational Errors ◽  
The Individual

Abstract Accurate knowledge of two types of noise, system and observational, is an important aspect of Bayesian filtering methodology. Traditionally, this knowledge is reflected in individual covariance matrices for the two noise contributions, while correlations between the system and observational noises are ignored. We contend that in practical problems, it is unlikely that system and observational errors are uncorrelated, in particular for geophysically motivated examples where errors are dominated by model and observation truncations. Moreover, it is shown that accounting for the cross correlations in the filtering algorithm, for example in a correlated ensemble Kalman filter, can result in significant improvements in filter accuracy for data from typical dynamical systems. In particular, we discuss the extreme case where the two types of errors are maximally correlated relative to the individual covariances.

scholarly journals Pattern Recognition in a Bimodal Aquifer Using the Normal-Score Ensemble Kalman Filter

2011 ◽  
Vol 44 (2) ◽  
pp. 169-185 ◽  
Author(s):  
Haiyan Zhou ◽  
Liangping Li ◽  
Harrie-Jan Hendricks Franssen ◽  
J. Jaime Gómez-Hernández
Keyword(s):  
Pattern Recognition ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Normal Score

scholarly journals Characterizing Curvilinear Features Using the Localized Normal-Score Ensemble Kalman Filter

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Haiyan Zhou ◽  
Liangping Li ◽  
J. Jaime Gómez-Hernández
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Transient State ◽  
Observation Data ◽  
Model Structure ◽  
Prior Model ◽  
State Observation ◽  
Normal Score ◽  
Observation Network

The localized normal-score ensemble Kalman filter is shown to work for the characterization of non-multi-Gaussian distributed hydraulic conductivities by assimilating state observation data. The influence of type of flow regime, number of observation piezometers, and the prior model structure are evaluated in a synthetic aquifer. Steady-state observation data are not sufficient to identify the conductivity channels. Transient-state data are necessary for a good characterization of the hydraulic conductivity curvilinear patterns. Such characterization is very good with a dense network of observation data, and it deteriorates as the number of observation piezometers decreases. It is also remarkable that, even when the prior model structure is wrong, the localized normal-score ensemble Kalman filter can produce acceptable results for a sufficiently dense observation network.

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.

Ensemble Kalman Filter for Out of Sequence Measurement Tracking

2012 ◽  
Vol 132 (10) ◽  
pp. 1617-1625
Author(s):  
Sirichai Pornsarayouth ◽  
Masaki Yamakita
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter
Sign in / Sign up

Export Citation Format

Share Document