Effect of random perturbations on adaptive observation techniques

Hossen, M. J.; Navon, I. M.; Daescu, Dacian N.

doi:10.1002/fld.2545

Cited by 10 publications

(12 citation statements)

References 24 publications

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“…The benefit of the change of variables is that neither dF/dm s nor M s depend on the controls, m s , as Ψ and F are invariant under the change of variables, see equations (14) and (15).…”

Section: The Use Of Ensembles To Form Approximate Sensitivitiesmentioning

confidence: 99%

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Well Optimisation With Goal-Based Sensitivity Maps Using Time Windows And Ensemble Perturbations

Heaney¹,

Salinas²,

Pain³

et al. 2018

Proceedings

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We present an approach for forming sensitivity maps (or sensitivites) using ensembles. The method is an alternative to using an adjoint, which can be very challenging to formulate and also computationally expensive to solve. The main novelties of the presented approach are: 1) the use of goals, by weighting the perturbation to help resolve the most important sensitivities, 2) the use of time windows, which enable the perturbations to be optimised independently for each window and 3) re-orthogonalisation of the solution through time, which helps optimise each perturbation when calculating sensitivity maps. The novel application of these methods, to the generation of sensitivity maps through ensembles, greatly reduces the number of ensemble members required to form the sensitivity maps as demonstrated in this paper.As the presented method relies solely on ensemble members obtained from the forward model, it can therefore be applied directly to forward models of arbitrary complexity arising from, for example, multi-physics coupling, legacy codes or model chains.We demonstrate the efficiency of the approach by applying the method to advection problems and also a non-linear heterogeneous multi-phase porous media problem, showing, in all cases, that the number of ensemble members required to obtain accurate sensitivity maps is relatively low, in the order of 10s.

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“…The benefit of the change of variables is that neither dF/dm s nor M s depend on the controls, m s , as Ψ and F are invariant under the change of variables, see equations (14) and (15).…”

Section: The Use Of Ensembles To Form Approximate Sensitivitiesmentioning

confidence: 99%

“…However, the accuracy can be enhanced by considering each time level separately. In order to do this, we apply to equation (4) the change of variables given in equation (10) and the approximations given in equations (14), (15) and following (16), resulting in ∆Ψ = M s ∆m s .…”

Section: Time Dependent Problemsmentioning

confidence: 99%

Well Optimisation With Goal-Based Sensitivity Maps Using Time Windows And Ensemble Perturbations

Heaney¹,

Salinas²,

Pain³

et al. 2018

Proceedings

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show abstract

“…Our future work will focus on applying these ensemble-based methods to adaptive observations in complicated real-world models, especially on comparing with the adaptive approaches in the context of 4D-Var (e.g. Daescu and Navon, 2004;Hossen et al, 2012aHossen et al, , 2012b and EnKF (e.g. Majumdar et al, 2002;Szunyogh et al, 2002) data assimilation.…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

An enhanced ensemble‐based method for computing CNOPs using an efficient localization implementation scheme and a two‐step optimization strategy: formulation and preliminary tests

Tian

Feng

Zhang

et al. 2015

Quart J Royal Meteoro Soc

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The ensemble-based methods for computing conditional nonlinear optimal perturbations (CNOPs) often contain a localization implementation scheme; its computer implementation is very expensive because of huge memory usage or costly repeated calculations. As a result, the lack of efficient algorithms limits the applications of CNOP. To address this issue, an efficient new localization implementation scheme is proposed in this article. The main ideas are to utilize the correlation matrix and to approximate it by a set of selected Gaussian random samples. An enhanced ensemble-based method is then proposed using the new localization scheme and a newly proposed two-step optimization strategy. The proposed approach results in a significant speed-up for overall optimization algorithms for computing the CNOPs and can be applied to complicated nonlinear models. Numerical experiments with a nonlinear model of the viscous Burgers equation show that the proposed new method produces comparable solutions against an existing ensemble-based method and an adjoint-based one for computing the CNOPs. In terms of the net growth ratio of norm square, the proposed method slightly outperforms these two existing methods. On the other hand, our numerical experiments show that the proposed method has an advantage on the memory usage and computational cost, which particularly demonstrates its high potential in predictability or sensitivity studies of operational prediction models. Another group of assimilation experiments conducted using the T21L3 quasi-geostrophic (QG) model further demonstrates its potential for broader applications.

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“…Daescu provided a framework of the forecast sensitivity with respect to observations in the context of the 4D-Var data assimilation [13]. Hossen et al studied the effect of random perturbations on the forecast error [14]. The adjoint equation approach has a variety of applications including estimation problems [15][16][17] as well as data assimilation problems [3,4,18].…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis of Unsteady Flow Fields and Impact of Measurement Strategy

Misaka

Obayashi

2014

Mathematical Problems in Engineering

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Difficulty of data assimilation arises from a large difference between the sizes of a state vector to be determined, that is, the number of spatiotemporal mesh points of a discretized numerical model and a measurement vector, that is, the amount of measurement data. Flow variables on a large number of mesh points are hardly defined by spatiotemporally limited measurements, which poses an underdetermined problem. In this study we conduct the sensitivity analysis of two- and three-dimensional vortical flow fields within a framework of data assimilation. The impact of measurement strategy, which is evaluated by the sensitivity of the 4D-Var cost function with respect to measurements, is investigated to effectively determine a flow field by limited measurements. The assimilation experiment shows that the error defined by the difference between the reference and assimilated flow fields is reduced by using the sensitivity information to locate the limited number of measurement points. To conduct data assimilation for a long time period, the 4D-Var data assimilation and the sensitivity analysis are repeated with a short assimilation window.

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Effect of random perturbations on adaptive observation techniques

Cited by 10 publications

References 24 publications

Well Optimisation With Goal-Based Sensitivity Maps Using Time Windows And Ensemble Perturbations

Well Optimisation With Goal-Based Sensitivity Maps Using Time Windows And Ensemble Perturbations

An enhanced ensemble‐based method for computing CNOPs using an efficient localization implementation scheme and a two‐step optimization strategy: formulation and preliminary tests

Sensitivity Analysis of Unsteady Flow Fields and Impact of Measurement Strategy

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