The ETKF rescaling scheme in HIRLAM

Jelena Bojarova; Nils Gustafsson; Åke Johansson; Ole Vignes

doi:10.1111/j.1600-0870.2011.00513.x

The ETKF rescaling scheme in HIRLAM

Tellus

Volume 63 (2011): Issue 3

By: Jelena Bojarova, Nils Gustafsson, Åke Johansson and Ole Vignes

Open Access

|Jan 2011

Abstract

The ETKF rescaling scheme has been implemented into the HIRLAM forecasting system in order to estimate the uncertainty of the model state. The main purpose is to utilize this uncertainty information for modelling of flowdependent background error covariances within the framework of a hybrid variational ensemble data assimilation scheme. The effects of rank-deficiency in the ETKF formulation is explained and the need for variance inflation as a way to compensate for these effects is justified. A filter spin-up algorithm is proposed as a refinement of the variance inflation. The proposed spin-up algorithm will also act to prevent ensemble collapse since the ensemble will receive ‘fresh blood’ in the form of additional perturbation components, generated on the basis of a static background error covariance matrix. The resulting ETKF-based ensemble perturbations are compared with ensemble perturbations based on targeted singular vectors and are shown to have more realistic spectral characteristics.

References

Anderson , J. L . 2001 . An ensemble adjustment filter for data assimilation. Mon . Weather Re v . 129 , 2884 – 2903 .
Search in Google Scholar Back to article
Anderson , J. L. and Anderson , S. L . 1999 . A Monte Carlo implementation of the non-linear filtering problem to produce ensemble assimi-lations and forecasts. Mon . Weather Re v . 127 , 2741 – 2758 .
Search in Google Scholar Back to article
Barkmeijer , J. , Buizza , R. and Palmer , T. N . 1999 . 3D-Var Hessian Singular Vectors and their potential use in ECMWF Ensemble Prediction System . Q. J. R. MeteoroL Soc . 125 , 2333 – 2351 .
Search in Google Scholar Back to article
Bengtsson , T. , Snyder , C. and Nychlca , D . 2003 . Toward a nonlin-ear ensemble filter for high-dimensional systems . J. Geophys. Res . 108 ( D24 ), 8775 , 10.1029/2002JD002900 .
Open DOI Search in Google Scholar Back to article
Berre , L . 2000 . Estimation of synoptic and mesoscale forecast error covariances in a limited area model. Mon . Weather Re v . 128 , 644 – 667 .
Search in Google Scholar Back to article
Bishop , C. H. , Etherton , B. J. and Majumdar , S. J . 2001 . Adaptive sam-pling with the Ensemble Transform Kalman Filter, Part I: theoretical aspects. Mon . Weather Re v . 129 , 420 – 436 .
Search in Google Scholar Back to article
Buizza , R . 1994 . Localisation of optimal perturbations using a projection operator . Q. J. R. MeteoroL Soc . 120 , 1647 – 1681 .
Search in Google Scholar Back to article
Cohn , S. E. , da Silva , A. M. , Guo , J. , Sienlciewich , M. and Lamich , D . 1998 . Assessing the effect of data selection with the DAO Physical-space Statistical Analysis System (PSAS). Mon . Weather Re v . 126 , 2913 – 2926 .
Search in Google Scholar Back to article
Courtier , P. , Thepaut , J. N. and Hollngswirth , A . 1994 . A strategy for op-erational implementation of 4D-Var, using an incremental approach . Q. J. R. MeteoroL Soc . 120 , 1367 – 1387 .
Search in Google Scholar Back to article
Durbin , J. and Koopman , S. J . 2001 . lime Series Analysis by State Space Methods . Oxford Statistical Science Series , Oxford University Press , Oxford .
Search in Google Scholar Back to article
Errico , R. M . 2000 . Interpretation of the total energy and rotational energy norms to determination of singular vectors . Q. J. R. Meteor Soc . 126 , 1581 – 1600 .
Search in Google Scholar Back to article
Evensen , G . 1994 . Sequential data assimilation with a non-linear quasi-geostrophic model using Monte Carlo methods to forecast error statis-tics . J. Geophys. Res . 99 , 10 143-10 162 .
Search in Google Scholar Back to article
Frogner , I.-L. and Iversen , T . 2002 . High-resolution limited area ensem-ble predictions based on low-resolution targeted singular vectors . Q. J. R. Meteorol. Soc . 128 , 1321 – 1341 .
Search in Google Scholar Back to article
Gustafsson , N. , Berre , L. , Hörnquist , S. , Huang , X.-Y. , Lindskog , M. and co-authors . 2001 . Three-dimensional variational data assimilation for a limited area model, Part I: general formulation and the background error constraint. Tellus 53A , 425 - 446 .
Search in Google Scholar Back to article
Hamill , T. M. and Snyder , C . 2000 . A hybrid ensemble Kalman filter-3D variational analysis scheme. Mon . Weather Re v . 128 , 2905 – 2919 .
Search in Google Scholar Back to article
Heemink , A. W. , Verlaan , M. and Segers , A. J . 2001 . Variance reduced ensemble Kalman filtering. Mon . Weather Re v . 129 , 1718 – 1728 .
Search in Google Scholar Back to article
Houterkamer , P. L. and Mitchell , H. L . 1998 . Data Assimilation using ensemble Kalman filter technique. Mon . Weather Re v . 126 , 796 – 811 .
Search in Google Scholar Back to article
Julier , S. J. and Uhlmann , J. K . 1997 . A new extension of the Kalman filter to non-linear systems. Int. Symp. Aerospace/Defense Sensing, Simulations and Controls 3 , 10.1117/12.280797 .
Open DOI Search in Google Scholar Back to article
Kalman , R. E . 1960 . A new approach to linear filtering and prediction problems . J. Basic Eng . 82 , 35 – 45 .
Search in Google Scholar Back to article
Kalman , R. E. and Bucy , R. S . 1961 . New results in linear filtering and prediction . J. Basic Eng . 83D , 95 – 108 .
Search in Google Scholar Back to article
Keppert , J. D . 2004 . On ensemble representation of the observation error covariance in the ensemble Kalman Filter . Ocean Dyn . 54 , 561 – 569 .
Search in Google Scholar Back to article
Le Dimet , F. X. and Talagrand , O. 1986 . Variational algorithm for anal-ysis and assimilation of meteorological observations: theoretical aspects . Tellus 38A , 97 - 110 .
Search in Google Scholar Back to article
Lindskog , M. , Gustafsson , N. and Mogensen , K. S . 2006 . Representation of background error standard deviations in a limited area model data assimilation system . Tellus 58A , 430 – 444 .
Search in Google Scholar Back to article
Lorene , A . 2003 . The potential of the ensemble Kalman filter for NVVP: a comparison with 4D-Var. Q. J. R. MeteoroL Soc. 129, 3183-3203. Ott, E., Hunt, B. R., Szunyogh, I., Zimin, A. V., Kostelich, E. J. and co-authors. 2004. A local ensemble Kalman filter for atmospheric data assimilation . Tellus 56A , 415 – 428 .
Search in Google Scholar Back to article
Parrish , D. F. and Derber , J. C . 1992 . The National Meteorological Center’s statistical-interpolation analysis system. Mon . Weather Re v . 120 , 1747 – 1763 .
Search in Google Scholar Back to article
Pham , D. T. , Verron , J. and Roubaud , M. C . 1998 . A singular evolutive extended Kalman filter for data assimilation in oceanography . Mar SysL 16 , 323 – 340 .
Search in Google Scholar Back to article
Sakov , P. and Oke , P. R . 2008 . Implication of the form of the ensemble transformation in the ensemble square root filters. Mon . Weather Re v . 136 , 1042 – 1053 .
Search in Google Scholar Back to article
Talagrand , O. 1981 . A study of the dynamics of four-dimensional data assimilation . Tellus 33 , 43 – 60 .
Search in Google Scholar Back to article
Tippet , M. K. , Anderson , J. L. , Bishop , C. H. , Hamill , T. M. and Whitaker , J. S . 2003 . Ensemble square root filters. Mon . Weather Re v . 131 , 1485 – 1491 .
Search in Google Scholar Back to article
Toth , Z. and Kalnay , E . 1997 . Ensemble forecasting at NCEP and the Breeding Method. Mon . Weather Re v . 125 , 3297 – 3319 .
Search in Google Scholar Back to article
Unden , P. , Rontu , L. , Järvinen , H. , Lunch , R , Calvo , J. and co-authors . 2002 . HIRLAM-5 Scientific Documentation. http://hirlam.org/(Available from SMHI, SE-61767 Norrkoping, Sweden). Accessed 7 Feb 2011 .
Search in Google Scholar Back to article
Verlaan , M. and Heeminlc , A. W . 1997 . Tidal flow forecasting us-ing reduced-rank square root filters . Stoch. HydroL Hydraulics 11 , 349 – 368 .
Search in Google Scholar Back to article
Wang , X. and Bishop , C. H . 2003 . A comparison of Breeding and En-semble Transform Kalman Filter Ensemble Forecasting Schemes. J. Atmos. Sc i . 60 , 1140 – 1158 .
Search in Google Scholar Back to article
Wang , X. , Bishop , C. H. and Julier , S. J . 2004 . Which is better, an ensemble of positive-negative pairs or a centered spherical simplex ensemble? Mon . Weather Re v . 132 , 1590 – 1605 .
Search in Google Scholar Back to article
Wang , X. , Hamill , T. M. , Whilcaker , J. S. and Bishop , C. H . 2007a . Comparison of hybrid Ensemble Transform Kalman Filter: Optimum Interpolation and Ensemble Square Root Analysis Schemes. Mon . Weather Re v . 135 , 1055 – 1076 .
Search in Google Scholar Back to article
Wang , X. , Snyder , C. and Hamill , T. M . 2007b . On the theoretical equivalence of differently proposed ensemble-3DVar hybrid analysis schemes. Mon . Weather Re v . 135 , 222 – 227 .
Search in Google Scholar Back to article
Whitaker , J. and Hamill , T. M . 2002 . Ensemble data assimilation without perturbed observations. Mon . Weather Re v . 130 , 1913 – 1924 .
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1111/j.1600-0870.2011.00513.x | Journal eISSN: 3035-9554

Journal RSS Feed

Language: English

Page range: 385 - 401

Submitted on: Jan 11, 2010

Accepted on: Jan 4, 2011

Published on: Jan 1, 2011

Published by: Stockholm University Press

In partnership with: Paradigm Publishing Services

© 2011 Jelena Bojarova, Nils Gustafsson, Åke Johansson, Ole Vignes, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 63 (2011): Issue 3