Editorial Type:
Review Article
Article Type:
Review Article

Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation

P. L. Houtekamer Meteorology Research Division, Environment and Climate Change Canada, Dorval, Québec, Canada

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Fuqing Zhang Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

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Print Publication:
01 Dec 2016
Collections:
Review Articles in Monthly Weather Review
DOI:
https://doi.org/10.1175/MWR-D-15-0440.1
Page(s):
4489–4532
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Abstract

This paper reviews the development of the ensemble Kalman filter (EnKF) for atmospheric data assimilation. Particular attention is devoted to recent advances and current challenges. The distinguishing properties of three well-established variations of the EnKF algorithm are first discussed. Given the limited size of the ensemble and the unavoidable existence of errors whose origin is unknown (i.e., system error), various approaches to localizing the impact of observations and to accounting for these errors have been proposed. However, challenges remain; for example, with regard to localization of multiscale phenomena (both in time and space). For the EnKF in general, but higher-resolution applications in particular, it is desirable to use a short assimilation window. This motivates a focus on approaches for maintaining balance during the EnKF update. Also discussed are limited-area EnKF systems, in particular with regard to the assimilation of radar data and applications to tracking severe storms and tropical cyclones. It seems that relatively less attention has been paid to optimizing EnKF assimilation of satellite radiance observations, the growing volume of which has been instrumental in improving global weather predictions. There is also a tendency at various centers to investigate and implement hybrid systems that take advantage of both the ensemble and the variational data assimilation approaches; this poses additional challenges and it is not clear how it will evolve. It is concluded that, despite more than 10 years of operational experience, there are still many unresolved issues that could benefit from further research.

Contents

  • Introduction...4490

  • Popular flavors of the EnKF algorithm...4491

    1. General description...4491

    2. Stochastic and deterministic filters...4492

      1. The stochastic filter...4492

      2. The deterministic filter...4492

    3. Sequential or local filters...4493

      1. Sequential ensemble Kalman filters...4493

      2. The local ensemble transform Kalman filter...4494

    4. Extended state vector...4494

    5. Issues for the development of algorithms...4495

  • Use of small ensembles...4495

    1. Monte Carlo methods...4495

    2. Validation of reliability...4497

    3. Use of group filters with no inbreeding...4498

    4. Sampling error due to limited ensemble size: The rank problem...4498

    5. Covariance localization...4499

      1. Localization in the sequential filter...4499

      2. Localization in the LETKF...4499

      3. Issues with localization...4500

    6. Summary...4501

  • Methods to increase ensemble spread...4501

    1. Covariance inflation...4501

      1. Additive inflation...4501

      2. Multiplicative inflation...4502

      3. Relaxation to prior ensemble information...4502

      4. Issues with inflation...4503

    2. Diffusion and truncation...4503

    3. Error in physical parameterizations...4504

      1. Physical tendency perturbations...4504

      2. Multimodel, multiphysics, and multiparameter approaches...4505

      3. Future directions...4505

    4. Realism of error sources...4506

  • Balance and length of the assimilation window...4506

    1. The need for balancing methods...4506

    2. Time-filtering methods...4506

    3. Toward shorter assimilation windows...4507

    4. Reduction of sources of imbalance...4507

  • Regional data assimilation...4508

    1. Boundary conditions and consistency across multiple domains...4509

    2. Initialization of the starting ensemble...4510

    3. Preprocessing steps for radar observations...4510

    4. Use of radar observations for convective-scale analyses...4511

    5. Use of radar observations for tropical cyclone analyses...4511

    6. Other issues with respect to LAM data assimilation...4511

  • The assimilation of satellite observations...4512

    1. Covariance localization...4512

    2. Data density...4513

    3. Bias-correction procedures...4513

    4. Impact of covariance cycling...4514

    5. Assumptions regarding observational error...4514

    6. Recommendations regarding satellite observations...4515

  • Computational aspects...4515

    1. Parameters with an impact on quality...4515

    2. Overview of current parallel algorithms...4516

    3. Evolution of computer architecture...4516

    4. Practical issues...4517

    5. Approaching the gray zone...4518

    6. Summary...4518

  • Hybrids with variational and EnKF components...4519

    1. Hybrid background error covariances...4519

    2. E4DVar with the α control variable...4519

    3. Not using linearized models with 4DEnVar...4520

    4. The hybrid gain algorithm...4521

    5. Open issues and recommendations...4521

  • Summary and discussion...4521

    1. Stochastic or deterministic filters...4522

    2. The nature of system error...4522

    3. Going beyond the synoptic scales...4522

    4. Satellite observations...4523

    5. Hybrid systems...4523

    6. Future of the EnKF...4523

APPENDIX A...4524

Types of Filter Divergence...4524

  1. Classical filter divergence...4524

  2. Catastrophic filter divergence...4524

    APPENDIX B...4524

    Systems Available for Download...4524

    References...4525

Denotes Open Access content.

Corresponding author address: P. L. Houtekamer, Section de la Recherche en Assimilation des Données et en Météorologie Satellitaire, 2121 Route Trans-Canadienne, Dorval, QC H9P 1J3, Canada. E-mail: peter.houtekamer@canada.ca

Abstract

This paper reviews the development of the ensemble Kalman filter (EnKF) for atmospheric data assimilation. Particular attention is devoted to recent advances and current challenges. The distinguishing properties of three well-established variations of the EnKF algorithm are first discussed. Given the limited size of the ensemble and the unavoidable existence of errors whose origin is unknown (i.e., system error), various approaches to localizing the impact of observations and to accounting for these errors have been proposed. However, challenges remain; for example, with regard to localization of multiscale phenomena (both in time and space). For the EnKF in general, but higher-resolution applications in particular, it is desirable to use a short assimilation window. This motivates a focus on approaches for maintaining balance during the EnKF update. Also discussed are limited-area EnKF systems, in particular with regard to the assimilation of radar data and applications to tracking severe storms and tropical cyclones. It seems that relatively less attention has been paid to optimizing EnKF assimilation of satellite radiance observations, the growing volume of which has been instrumental in improving global weather predictions. There is also a tendency at various centers to investigate and implement hybrid systems that take advantage of both the ensemble and the variational data assimilation approaches; this poses additional challenges and it is not clear how it will evolve. It is concluded that, despite more than 10 years of operational experience, there are still many unresolved issues that could benefit from further research.

Contents

  • Introduction...4490

  • Popular flavors of the EnKF algorithm...4491

    1. General description...4491

    2. Stochastic and deterministic filters...4492

      1. The stochastic filter...4492

      2. The deterministic filter...4492

    3. Sequential or local filters...4493

      1. Sequential ensemble Kalman filters...4493

      2. The local ensemble transform Kalman filter...4494

    4. Extended state vector...4494

    5. Issues for the development of algorithms...4495

  • Use of small ensembles...4495

    1. Monte Carlo methods...4495

    2. Validation of reliability...4497

    3. Use of group filters with no inbreeding...4498

    4. Sampling error due to limited ensemble size: The rank problem...4498

    5. Covariance localization...4499

      1. Localization in the sequential filter...4499

      2. Localization in the LETKF...4499

      3. Issues with localization...4500

    6. Summary...4501

  • Methods to increase ensemble spread...4501

    1. Covariance inflation...4501

      1. Additive inflation...4501

      2. Multiplicative inflation...4502

      3. Relaxation to prior ensemble information...4502

      4. Issues with inflation...4503

    2. Diffusion and truncation...4503

    3. Error in physical parameterizations...4504

      1. Physical tendency perturbations...4504

      2. Multimodel, multiphysics, and multiparameter approaches...4505

      3. Future directions...4505

    4. Realism of error sources...4506

  • Balance and length of the assimilation window...4506

    1. The need for balancing methods...4506

    2. Time-filtering methods...4506

    3. Toward shorter assimilation windows...4507

    4. Reduction of sources of imbalance...4507

  • Regional data assimilation...4508

    1. Boundary conditions and consistency across multiple domains...4509

    2. Initialization of the starting ensemble...4510

    3. Preprocessing steps for radar observations...4510

    4. Use of radar observations for convective-scale analyses...4511

    5. Use of radar observations for tropical cyclone analyses...4511

    6. Other issues with respect to LAM data assimilation...4511

  • The assimilation of satellite observations...4512

    1. Covariance localization...4512

    2. Data density...4513

    3. Bias-correction procedures...4513

    4. Impact of covariance cycling...4514

    5. Assumptions regarding observational error...4514

    6. Recommendations regarding satellite observations...4515

  • Computational aspects...4515

    1. Parameters with an impact on quality...4515

    2. Overview of current parallel algorithms...4516

    3. Evolution of computer architecture...4516

    4. Practical issues...4517

    5. Approaching the gray zone...4518

    6. Summary...4518

  • Hybrids with variational and EnKF components...4519

    1. Hybrid background error covariances...4519

    2. E4DVar with the α control variable...4519

    3. Not using linearized models with 4DEnVar...4520

    4. The hybrid gain algorithm...4521

    5. Open issues and recommendations...4521

  • Summary and discussion...4521

    1. Stochastic or deterministic filters...4522

    2. The nature of system error...4522

    3. Going beyond the synoptic scales...4522

    4. Satellite observations...4523

    5. Hybrid systems...4523

    6. Future of the EnKF...4523

APPENDIX A...4524

Types of Filter Divergence...4524

  1. Classical filter divergence...4524

  2. Catastrophic filter divergence...4524

    APPENDIX B...4524

    Systems Available for Download...4524

    References...4525

Denotes Open Access content.

Corresponding author address: P. L. Houtekamer, Section de la Recherche en Assimilation des Données et en Météorologie Satellitaire, 2121 Route Trans-Canadienne, Dorval, QC H9P 1J3, Canada. E-mail: peter.houtekamer@canada.ca
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