Scale-Dependent Background Error Covariance Localization: Evaluation in a Global Deterministic Weather Forecasting System

Caron, Jean‐François; Buehner, Mark

doi:10.1175/mwr-d-17-0369.1

Cited by 30 publications

(58 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…No other intermediate results, like the Schur products or the augmented ensemble members, need to be precomputed and stored. The posterior ensemble illustrated in Figure 8 is the direct result of the application of iteration (11), using Equation 7to sample and compute a Schur product (from the multiscale prior ensemble) and Equations (17)(18)(19)(20) to compute the acceptance probability (from the observations and their associated error distributions).…”

Section: Ensemble Mcmc Algorithmmentioning

confidence: 99%

“…A fine localization is needed to capture the smallest scales, at the price of losing the direct observation control on the larger scales. Adjustments to standard localization have thus also been proposed, either by using different localization windows for different scales [17][18][19][20], or by applying localization after a spectral transformation of the prior ensemble [21,22]. These developments still follow the original idea of covariance localization, which is to transform the global ensemble covariance so that it can be decomposed into local pieces.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Implicitly Localized MCMC Sampler to Cope With Non-local/Non-linear Data Constraints in Large-Size Inverse Problems

Brankart

2019

Front. Appl. Math. Stat.

View full text Add to dashboard Cite

Many practical applications involve the resolution of large-size inverse problems, without providing more than a moderate-size sample to describe the prior probability distribution. In this situation, additional information must be supplied to augment the effective dimension of the available sample. This is the role played by covariance localization in the large-size applications of the ensemble Kalman filter. In this paper, it is suggested that covariance localization can also be efficiently applied to an approximate variant of the Metropolis/Hastings algorithm, by modulating the ensemble members by the large-scale patterns of other members. Modulation is used to design a (global) proposal probability distribution (i) that can be sampled at a very low cost (proportional to the size of the state vector, with a small integer coefficient), (ii) that automatically accounts for a localized prior covariance, and (iii) that leads to an efficient sampler for the augmented prior probability distribution or for the posterior probability distribution. The resulting algorithm is applied to an academic example, illustrating (i) the effectiveness of covariance localization, (ii) the ability of the method to deal with non-local/non-linear observation operators and non-Gaussian observation errors, (iii) the possibility to deal with non-Gaussian (even discrete) prior marginal distributions, by including (stochastic) anamorphosis transformations, (iv) the reliability, resolution and optimality of the updated ensemble, using probabilistic scores appropriate to a non-Gaussian posterior distribution, and (v) the scalability of the algorithm as a function of the size of the problem. The evaluation of the computational complexity of the algorithm suggests that it could become numerically competitive with local ensemble Kalman filters, even in the absence of non-local constraints, especially if the localization radius is large. All codes necessary to reproduce the example application described in this paper are openly available from github.com/brankart/ensdam.

show abstract

Section: Ensemble Mcmc Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Implicitly Localized MCMC Sampler to Cope With Non-local/Non-linear Data Constraints in Large-Size Inverse Problems

Brankart

2019

Front. Appl. Math. Stat.

View full text Add to dashboard Cite

show abstract

“…It is a primitive equation model which computes the following prognostic variables: 3-D velocities, sea surface height, salinity and temperature. ERA-Interim reanalysis data, produced at ECMWF (Dee et al, 2011), are used for the atmospheric forcing. CREG4 is a realistic configuration for the North Atlantic and the Nordic Seas at the 1/4 • horizontal resolution.…”

Section: Ensemble Model Simulationmentioning

confidence: 99%

A multiscale ocean data assimilation approach combining spatial and spectral localisation

et al. 2019

View full text Add to dashboard Cite

Abstract. Ocean data assimilation systems encompass a wide range of scales that are difficult to control simultaneously using partial observation networks. All scales are not observable by all observation systems, which is not easily taken into account in current ocean operational systems. The main reason for this difficulty is that the error covariance matrices are usually assumed to be local (e.g. using a localisation algorithm in ensemble data assimilation systems), so that the large-scale patterns are removed from the error statistics. To better exploit the observational information available for all scales in the assimilation systems of the Copernicus Marine Environment Monitoring Service, we investigate a new method to introduce scale separation in the assimilation scheme. The method is based on a spectral transformation of the assimilation problem and consists in carrying out the analysis with spectral localisation for the large scales and spatial localisation for the residual scales. The target is to improve the observational update of the large-scale components of the signal by an explicit observational constraint applied directly on the large scales and to restrict the use of spatial localisation to the small-scale components of the signal. To evaluate our method, twin experiments are carried out with synthetic altimetry observations (simulating the Jason tracks), assimilated in a 1/4∘ model configuration of the North Atlantic and the Nordic Seas. Results show that the transformation to the spectral domain and the spectral localisation provides consistent ensemble estimates of the state of the system (in the spectral domain or after backward transformation to the spatial domain). Combined with spatial localisation for the residual scales, the new scheme is able to provide a reliable ensemble update for all scales, with improved accuracy for the large scale; and the performance of the system can be checked explicitly and separately for all scales in the assimilation system.

show abstract

“…A fine localization is needed to capture the smallest scales, at the price of loosing the direct observation control on the larger scales. Adjustments to standard localization have thus also been proposed, either by using different localization windows for different scales (Zhou et al, 2008;Miyoshi and Kondo, 2013;Li et al, 2015;Caron et al, 2018), or by applying localization after a spectral transformation of the prior ensemble (Buehner , 2012;Tissier et al, 2019). These developments still follow the original idea of covariance localization, which is to transform the global ensemble covariance so that it can be decomposed into local pieces.…”

Section: Introductionmentioning

confidence: 99%

Implicitly localized ensemble observational update to cope with nonlocal/nonlinear data constraints in large-size inverse problems

Brankart¹

2019

Preprint

View full text Add to dashboard Cite

Many practical applications involve the resolution of large-size inverse problems, without providing more than a moderate-size sample to describe the prior probability distribution. In this situation, additional information must be supplied to augment the effective dimension of the available sample. This is the role played by covariance localization in the large-size applications of the ensemble Kalman filter. In this paper, it is suggested that covariance localization can also be efficiently applied to an approximate variant of the Metropolis/Hastings algorithm, by modulating the ensemble members by the large-scale patterns of other members. Modulation is used to design a (global) proposal probability distribution (i) that can be sampled at a very low cost (proportional to the size of the state vector, with a small integer coefficient), (ii) that automatically accounts for a localized prior covariance, and (iii) that leads to an efficient sampler for the augmented prior probability distribution or for the posterior probability distribution. The resulting algorithm is applied to an academic example, illustrating (i) the effectiveness of covariance localization, (ii) the ability of the method to deal with nonlocal/nonlinear observation operators and non-Gaussian observation errors, (iii) the possibility to deal with non-Gaussian (even discrete) prior marginal distributions, by including (stochastic) anamorphosis transformations, (iv) the reliability, resolution and optimality of the updated ensemble, using probabilistic scores appropriate to a non-Gaussian posterior distribution, and (v) the scalability of the algorithm as a function of the size of the problem. The evaluation of the computational complexity of the algorithm suggests that it could become numerically competitive with local ensemble Kalman filters, even in the absence of nonlocal constraints, especially if the localization radius is large. All codes necessary to reproduce the example application described in this paper are openly available from github.com/brankart/ensdam.

show abstract

Scale-Dependent Background Error Covariance Localization: Evaluation in a Global Deterministic Weather Forecasting System

Cited by 30 publications

References 35 publications

Implicitly Localized MCMC Sampler to Cope With Non-local/Non-linear Data Constraints in Large-Size Inverse Problems

Implicitly Localized MCMC Sampler to Cope With Non-local/Non-linear Data Constraints in Large-Size Inverse Problems

A multiscale ocean data assimilation approach combining spatial and spectral localisation

Implicitly localized ensemble observational update to cope with nonlocal/nonlinear data constraints in large-size inverse problems

Contact Info

Product

Resources

About