An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering

Zhou, Haiyan; Gómez‐Hernández, J. Jaime; Franssen, Harrie‐Jan Hendricks; Li, Liangping

doi:10.1016/j.advwatres.2011.04.014

Cited by 232 publications

(233 citation statements)

References 48 publications

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“…EnKF algorithms are limited to Gaussian system as they rely on the first two moments of the ensemble statistics. Several studies were carried out to extend EnKF to handle non-Gaussian estimation problems (Bengtsson et al, 2003;Smith, 2007;Sun et al, 2009a;Zhou et al, 2011).…”

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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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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“…It is worth recall that the normal-score transformations used in the NS-EnKF only ensure marginal Gaussianity, with the higher-order moments not necessarily closer to the multiGaussian distribution; it is also worth recall, that the EnKF is applied on the normalscore transformed variables what amounts to having a more non-linear forecast function that before the transformations. One of the motivations of this work is to explore the capacity of the normal score EnKF proposed by Zhou et al (2011Zhou et al ( , 2012c to characterize non-multiGaussian media such as a highly channelized aquifer when there are no (hard) conductivity data available and the prior random function model is not the one used to generate the reference field.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, extending the EnKF to deal with non-Gaussian state vectors would facilitate more extensive applications. Sun et al (2009) and Zhou et al (2011Zhou et al ( , 2012c, developed variants of the EnKF which are better accommodated to handle non-Gaussianity of parameter distributions. Sun et al (2009) resort to couple the EnKF with a Gaussian mixture model to update the parameters of a multi-modal distribution by assimilating head data.…”

Section: Introductionmentioning

confidence: 99%

“…Sun et al (2009) resort to couple the EnKF with a Gaussian mixture model to update the parameters of a multi-modal distribution by assimilating head data. Zhou et al (2011Zhou et al ( , 2012c transformed the augmented state vector (containing both the hydraulic conductivities and piezometric heads) with marginal multi-modal distributions into a new vector with marginal Gaussian distributions, perform the EnKF on the transformed state vector and backtransform the updated vector to the original space. Both studies show that these variants of EnKF result in significant improvements in the characterization of the aquifer properties and in the predictions of flow and transport for nonmultiGaussian hydraulic conductivity fields.…”

Section: Introductionmentioning

confidence: 99%

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

Li¹,

Zhou²,

Franssen³

et al. 2012

Hydrol. Earth Syst. Sci.

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Abstract. The normal-score ensemble Kalman filter (NSEnKF) 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.

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“…The impossibility of sampling the entire area of interest together with the difficulty of accounting for scale effects (Dousset et al, 2007;Scheibe & Yabusaki, 1998b;Vik et al, 2013b;Vogel & Roth, 2003;Zhou, Gómez-Hernández, Hendricks Franssen, & Li, 2011) are the two main reasons why heterogeneity is not accounted for in practice. This study tries to address these two problems and describes how to cope with them.…”

Section: Introductionmentioning

confidence: 99%

Upscaling of water flow and mass transport in a tropical soil: numerical, laboratory and field studies

Godoy¹

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Numerical models are becoming fundamental tools to predict a range of complex problems faced by geotechnical and geo-environmental engineers. However, to render the model reliable for future predictions, the model input parameters must be determined with consideration of the scale effects. If there is a difference of scales between the observation and the model scales there are two possible ways to consider it: or models are constructed with elements of a size similar to that at which the data were measured, or some upscaling rules must be defined. In this context, this thesis focuses on upscaling of water flow and mass transport in a tropical soil by means of numerical, laboratory and field studies. This thesis is organized in four parts.First, the heterogeneity, correlation and cross-correlation between solute transport parameters (dispersivity, α, and partition coefficient, Kd) and soil properties are studied in detail. In this part, it is verified that the hydraulic conductivity (K) and solute transport parameters are highly heterogeneous, while soil properties are not. Spatial correlation of α, K, and statistically significant variables are studied, and it would probably improve the estimation only in a small-scale study, since the spatial correlation are only observed up to 2.5 m. This study is a first attempt to evaluate the spatial variation in the correlation coefficient of transport parameters of a reactive and a nonreactive solute, indicating the more relevant variables and the one that should be included in future studies.In the second part, scale effect on K, dispersivity and partition coefficient of potassium and chloride are studied experimentally by means of laboratory and field experiments. The purpose is to contribute to the discussion about scale effects on K, α and Kd and understanding how these parameters behave with the change in the scale of measurement. Results show that K values increases with scale, regardless of the method of measurement, except for the results obtained from double-ring infiltrometer tests. Dispersivity trends to increase exponentially with the sample height.Partition coefficient tends to increase with sample length, diameter and volume. These differences in the parameters according to the scale of measurement must be considered when these observations are later used as input to numerical models, otherwise the responses can be misrepresented.x Third, stochastic analysis of three-dimensional hydraulic conductivity upscaling is performed using a simple average and the Laplacian-with-skin methods for a variety of block sizes based on real K measurements. In this part it is demonstrated the errors that can be introduced by using a deterministic upscaling using simple averages of the measured K without accounting for the spatial correlation. Results show that K heterogeneity can be incorporated in the daily practice of the geotechnical modeler.The aspects to consider when performing the upscaling are also discussed. Finally, the dependence of the exponent of the p-n...

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An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering

Cited by 232 publications

References 48 publications

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

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

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

Upscaling of water flow and mass transport in a tropical soil: numerical, laboratory and field studies

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