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

AbstractThis 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.ContentsIntroduction...4490Popular flavors of the EnKF algorithm...4491General description...4491Stochastic and deterministic filters...4492The stochastic filter...4492The deterministic filter...4492Sequential or local filters...4493Sequential ensemble Kalman filters...4493The local ensemble transform Kalman filter...4494Extended state vector...4494Issues for the development of algorithms...4495Use of small ensembles...4495Monte Carlo methods...4495Validation of reliability...4497Use of group filters with no inbreeding...4498Sampling error due to limited ensemble size: The rank problem...4498Covariance localization...4499Localization in the sequential filter...4499Localization in the LETKF...4499Issues with localization...4500Summary...4501Methods to increase ensemble spread...4501Covariance inflation...4501Additive inflation...4501Multiplicative inflation...4502Relaxation to prior ensemble information...4502Issues with inflation...4503Diffusion and truncation...4503Error in physical parameterizations...4504Physical tendency perturbations...4504Multimodel, multiphysics, and multiparameter approaches...4505Future directions...4505Realism of error sources...4506Balance and length of the assimilation window...4506The need for balancing methods...4506Time-filtering methods...4506Toward shorter assimilation windows...4507Reduction of sources of imbalance...4507Regional data assimilation...4508Boundary conditions and consistency across multiple domains...4509Initialization of the starting ensemble...4510Preprocessing steps for radar observations...4510Use of radar observations for convective-scale analyses...4511Use of radar observations for tropical cyclone analyses...4511Other issues with respect to LAM data assimilation...4511The assimilation of satellite observations...4512Covariance localization...4512Data density...4513Bias-correction procedures...4513Impact of covariance cycling...4514Assumptions regarding observational error...4514Recommendations regarding satellite observations...4515Computational aspects...4515Parameters with an impact on quality...4515Overview of current parallel algorithms...4516Evolution of computer architecture...4516Practical issues...4517Approaching the gray zone...4518Summary...4518Hybrids with variational and EnKF components...4519Hybrid background error covariances...4519E4DVar with the α control variable...4519Not using linearized models with 4DEnVar...4520The hybrid gain algorithm...4521Open issues and recommendations...4521Summary and discussion...4521Stochastic or deterministic filters...4522The nature of system error...4522Going beyond the synoptic scales...4522Satellite observations...4523Hybrid systems...4523Future of the EnKF...4523APPENDIX A...4524Types of Filter Divergence...4524Classical filter divergence...4524Catastrophic filter divergence...4524APPENDIX B...4524Systems Available for Download...4524References...4525