Levenberg–Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification

Chen, Yan; Oliver, Dean S.

doi:10.1007/s10596-013-9351-5

Cited by 300 publications

(262 citation statements)

References 17 publications

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“…Gratton et al (2013) discuss application of GN in a trust region framework, which has the limitation that a portion of the computationally expensive outer loop increments will be rejected. Some authors have successfully applied the Levenberg-Marquardt algorithm in EnKF (e.g., Chen and Oliver, 2013;Mandel et al, 2016) by adding a regularization term to the cost function. That method requires one to perform the inner loop approximation of [H δv ] −1 multiple times, once for each value of a scalar regularization parameter.…”

Section: Nonlinear Optimizationmentioning

confidence: 99%

Four-dimensional variational inversion of black carbon emissions during ARCTAS-CARB with WRFDA-Chem

Guerrette

Henze

2017

Atmos. Chem. Phys.

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Abstract. Biomass burning emissions of atmospheric aerosols, including black carbon, are growing due to increased global drought, and comprise a large source of uncertainty in regional climate and air quality studies. We develop and apply new incremental four-dimensional variational (4D-Var) capabilities in WRFDA-Chem to find optimal spatially and temporally distributed biomass burning (BB) and anthropogenic black carbon (BC) aerosol emissions. The constraints are provided by aircraft BC concentrations from the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites in collaboration with the California Air Resources Board (ARCTAS-CARB) field campaign and surface BC concentrations from the Interagency Monitoring of PROtected Visual Environment (IMPROVE) network on 22, 23, and 24 June 2008. We consider three BB inventories, including Fire INventory from NCAR (FINN) v1.0 and v1.5 and Quick Fire Emissions Database (QFED) v2.4r8. On 22 June, aircraft observations are able to reduce the spread between a customized QFED inventory and FINNv1.0 from a factor of 3.5 (×3.5) to only ×2.1. On 23 and 24 June, the spread is reduced from ×3.4 to ×1.4. The posterior corrections to emissions are heterogeneous in time and space, and exhibit similar spatial patterns of sign for both inventories. The posterior diurnal BB patterns indicate that multiple daily emission peaks might be warranted in specific regions of California. The US EPA's 2005 National Emissions Inventory (NEI05) is used as the anthropogenic prior. On 23 and 24 June, the coastal California posterior is reduced by ×2, where highway sources dominate, while inland sources are increased near Barstow by ×5. Relative BB emission variances are reduced from the prior by up to 35 % in grid cells close to aircraft flight paths and by up to 60 % for fires near surface measurements. Anthropogenic variance reduction is as high as 40 % and is similarly limited to sources close to observations. We find that the 22 June aircraft observations are able to constrain approximately 14 degrees of freedom of signal (DOF), while surface and aircraft observations together on 23/24 June constrain 23 DOF. Improving hourly-to daily-scale concentration predictions of BC and other aerosols during BB events will require more comprehensive and/or targeted measurements and a more complete accounting of sources of error besides the emissions.

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Section: Nonlinear Optimizationmentioning

confidence: 99%

Four-dimensional variational inversion of black carbon emissions during ARCTAS-CARB with WRFDA-Chem

Guerrette

Henze

2017

Atmos. Chem. Phys.

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“…One such study was performed by [75], who developed forms of the iterative ensemble smoother using the Levenberg-Marquardt method to increase computational efficiency and improve the quality of the history match. They applied this technique to the Brugge benchmark case and found that compared to the standard ensemble smoother, ensemble-based Gauss-Newton formulation, and the multiple data assimilation method, the Levenberg-Marquardt method gave the best results.…”

Section: History Matching As Precursor To Production Optimizationmentioning

confidence: 99%

Review of Field Development Optimization of Waterflooding, EOR, and Well Placement Focusing on History Matching and Optimization Algorithms

et al. 2017

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This paper presents a review of history matching and oil field development optimization techniques with a focus on optimization algorithms. History matching algorithms are reviewed as a precursor to production optimization algorithms. Techniques for history matching and production optimization are reviewed including global and local methods. Well placement, well control, and combined well placement-control optimization using both secondary and tertiary oil production techniques are considered. Secondary and tertiary recovery techniques are commonly referred to as waterflooding and enhanced oil recovery (EOR), respectively. Benchmark models for comparison of methods are summarized while other applications of methods are discussed throughout. No single optimization method is found to be universally superior. Key areas of future work are combining optimization methods and integrating multiple optimization processes. Current challenges and future research opportunities for improved model validation and large scale optimization algorithms are also discussed.

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“…Gu and Oliver (2007) use an iterated ensemble Kalman filter (with randomization) in the state space, with a linearization of the observation operator obtained by a regression on the increments given by the ensemble. This approach was extended by Chen and Oliver (2013) to a Levenberg-Marquardt method, with the regularization done by a multiplicative inflation of the covariance in the linearized problem rather than adding a Tikhonov regularization term. Liu et al (2008Liu et al ( , 2009) and Liu and Xiao (2013) minimize the (strong-constraint) 4DVAR objective function over linear combinations of the ensemble by computations in the observation space.…”

Section: Introductionmentioning

confidence: 99%

“…Bocquet and Sakov (2012) combined the IEnKF method of Sakov et al (2012) with an inflation-free approach to obtain a 4-D ensemble variational method, and with the LevenbergMarquardt method by adding a diagonal regularization to the Hessian. Bocquet and Sakov (2012) and Chen and Oliver (2013) used Levenberg-Marquardt for faster convergence, as an adaptive method between the steepest descent and the Gauss-Newton method rather than to overcome divergence. Bocquet and Sakov (2012) also considered scaling the ensemble to approximate the tangent operators ("bundle variant") as in Sakov et al (2012).…”

Section: Introductionmentioning

confidence: 99%

Hybrid Levenberg–Marquardt and weak-constraint ensemble Kalman smoother method

Mandel

Bergou

Gürol

et al. 2016

Nonlin. Processes Geophys.

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Abstract. The ensemble Kalman smoother (EnKS) is used as a linear least-squares solver in the Gauss-Newton method for the large nonlinear least-squares system in incremental 4DVAR. The ensemble approach is naturally parallel over the ensemble members and no tangent or adjoint operators are needed. Furthermore, adding a regularization term results in replacing the Gauss-Newton method, which may diverge, by the Levenberg-Marquardt method, which is known to be convergent. The regularization is implemented efficiently as an additional observation in the EnKS. The method is illustrated on the Lorenz 63 model and a two-level quasigeostrophic model.

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Levenberg–Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification

Cited by 300 publications

References 17 publications

Four-dimensional variational inversion of black carbon emissions during ARCTAS-CARB with WRFDA-Chem

Four-dimensional variational inversion of black carbon emissions during ARCTAS-CARB with WRFDA-Chem

Review of Field Development Optimization of Waterflooding, EOR, and Well Placement Focusing on History Matching and Optimization Algorithms

Hybrid Levenberg–Marquardt and weak-constraint ensemble Kalman smoother method

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