Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation
Authors: Houtekamer P. L. , Zhang Fuqing 
Published: June 2016

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

General description...4491

Stochastic and deterministic filters...4492

The stochastic filter...4492

The deterministic filter...4492

Sequential or local filters...4493

Sequential ensemble Kalman filters...4493

The local ensemble transform Kalman filter...4494

Extended state vector...4494

Issues for the development of algorithms...4495

Use of small ensembles...4495

Monte Carlo methods...4495

Validation of reliability...4497

Use of group filters with no inbreeding...4498

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

Covariance localization...4499

Localization in the sequential filter...4499

Localization in the LETKF...4499

Issues with localization...4500

Summary...4501

Methods to increase ensemble spread...4501

Covariance inflation...4501

Additive inflation...4501

Multiplicative inflation...4502

Relaxation to prior ensemble information...4502

Issues with inflation...4503

Diffusion and truncation...4503

Error in physical parameterizations...4504

Physical tendency perturbations...4504

Multimodel, multiphysics, and multiparameter approaches...4505

Future directions...4505

Realism of error sources...4506

Balance and length of the assimilation window...4506

The need for balancing methods...4506

Time-filtering methods...4506

Toward shorter assimilation windows...4507

Reduction of sources of imbalance...4507

Regional data assimilation...4508

Boundary conditions and consistency across multiple domains...4509

Initialization of the starting ensemble...4510

Preprocessing steps for radar observations...4510

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

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

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

The assimilation of satellite observations...4512

Covariance localization...4512

Data density...4513

Bias-correction procedures...4513

Impact of covariance cycling...4514

Assumptions regarding observational error...4514

Recommendations regarding satellite observations...4515

Computational aspects...4515

Parameters with an impact on quality...4515

Overview of current parallel algorithms...4516

Evolution of computer architecture...4516

Practical issues...4517

Approaching the gray zone...4518

Summary...4518

Hybrids with variational and EnKF components...4519

Hybrid background error covariances...4519

E4DVar with the α control variable...4519

Not using linearized models with 4DEnVar...4520

The hybrid gain algorithm...4521

Open issues and recommendations...4521

Summary and discussion...4521

Stochastic or deterministic filters...4522

The nature of system error...4522

Going beyond the synoptic scales...4522

Satellite observations...4523

Hybrid systems...4523

Future of the EnKF...4523

APPENDIX A...4524

Types of Filter Divergence...4524

Classical filter divergence...4524

Catastrophic filter divergence...4524

APPENDIX B...4524

Systems Available for Download...4524

References...4525