World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

Improving the Ensemble Transform Kalman Filter Using a Second-order Taylor Approximation of the Nonlinear Observation Operator : Volume 21, Issue 5 (23/09/2014)

By Wu, G.

Click here to view

Book Id: WPLBN0004017264
Format Type: PDF Article :
File Size: Pages 16
Reproduction Date: 2015

Title: Improving the Ensemble Transform Kalman Filter Using a Second-order Taylor Approximation of the Nonlinear Observation Operator : Volume 21, Issue 5 (23/09/2014)  
Author: Wu, G.
Volume: Vol. 21, Issue 5
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


APA MLA Chicago

Zheng, X., Wu, G., Zhang, X., Wang, L., Zhang, S., Liang, X., & Yi, X. (2014). Improving the Ensemble Transform Kalman Filter Using a Second-order Taylor Approximation of the Nonlinear Observation Operator : Volume 21, Issue 5 (23/09/2014). Retrieved from

Description: State Key Laboratory of Remote Sensing Science, College of Global Change and Earth System Science, Beijing Normal University, Beijing, China. The ensemble transform Kalman filter (ETKF) assimilation scheme has recently seen rapid development and wide application. As a specific implementation of the ensemble Kalman filter (EnKF), the ETKF is computationally more efficient than the conventional EnKF. However, the current implementation of the ETKF still has some limitations when the observation operator is strongly nonlinear. One problem in the minimization of a nonlinear objective function similar to 4D-Var is that the nonlinear operator and its tangent-linear operator have to be calculated iteratively if the Hessian is not preconditioned or if the Hessian has to be calculated several times. This may be computationally expensive. Another problem is that it uses the tangent-linear approximation of the observation operator to estimate the multiplicative inflation factor of the forecast errors, which may not be sufficiently accurate.

This study attempts to solve these problems. First, we apply the second-order Taylor approximation to the nonlinear observation operator in which the operator, its tangent-linear operator and Hessian are calculated only once. The related computational cost is also discussed. Second, we propose a scheme to estimate the inflation factor when the observation operator is strongly nonlinear. Experimentation with the Lorenz 96 model shows that using the second-order Taylor approximation of the nonlinear observation operator leads to a reduction in the analysis error compared with the traditional linear approximation method. Furthermore, the proposed inflation scheme leads to a reduction in the analysis error compared with the procedure using the traditional inflation scheme.

Improving the ensemble transform Kalman filter using a second-order Taylor approximation of the nonlinear observation operator

Anderson, J. L.: An adaptive covariance inflation error correction algorithm for ensemble filters, Tellus A, 59, 210–224, 2007.; Anderson, J. L.: Spatially and temporally varying adaptive covariance inflation for ensemble filters, Tellus A, 61, 72–83, 2009.; Anderson, J. L. and Anderson, S. L.: A Monte Carlo implementation of the non-linear filtering problem to produce ensemble assimilations and forecasts, Mon. Weather Rev., 127, 2741–2758, 1999.; Bishop, C. H. and Toth, Z.: Ensemble transformation and adaptive observations, J. Atmos. Sci., 56, 1748–1765, 1999.; Bishop, C. H., Etherton, J., and Majumdar, J.: Adaptive sampling with the ensemble transform Kalman filte. Part I: Theoretical aspects, Mon. Weather Rev., 129, 420–436, 2001.; Burgers, G., van Leeuwen, P. J., and Evensen, G.: Analysis scheme in the ensemble Kalman Filter, Mon. Weather Rev., 126, 1719–1724, 1998.; Butcher, J. C.: Numerical methods for ordinary differential equations, John Wiley & Sons, England, ISBN: 0471967580, 425 pp., 2003.; Chen, Y., Oliver, D. S., and Zhang, D. X.: Data assimilation for nonlinear problems by ensemble Kalman filter with reparameterization, J. Petrol. Sci. Eng., 66, 1–14, 2009.; Courtier, P., Thépaut, J. N., and Hollingsworth, A.: A strategy for operational implementation of 4D-Var, using an incremental approach, Q. J. Roy. Meteor. Soc., 120, 1367–1387, 1994.; Daescu, D. N. and Navon, I. M.: Efficiency of a POD-based reduced second-order adjoint model in 4D-Var data assimilation, Int. J. Numer. Meth. Fl., 53, 985–1004, 2007.; Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, 10143–10162, 1994a.; Evensen, G.: Inverse Methods and data assimilation in nonlinear ocean models, Physica D, 77, 108–129, 1994b.; Evensen, G.: Advanced data assimilation for strongly nonlinear dynamics, Mon. Weather Rev., 125, 1342–1354, 1997.; Flowerdew, J. and Bowler, N.: Improving the use of observations to calibrate ensemble spread, Q. J. Roy. Meteor. Soc., 137, 467–482, 2011.; Lorenz, E. N.: Predictability – a problem partly solved, paper presented at Proc. Seminar on Predictability, ECMWF, Shinfield Park, Reading, Berkshire, UK, 1996.; Lorenz, E. N. and Emanuel, K. A.: Optimal sites for supplementary weather observations: Simulation with a small model, J. Atmos. Sci., 55, 399–414, 1998.; Hamill, T. M. and Whitaker, J. S.: Accounting for the error due to unresolved scales in ensemble data assimilation: a comparison of different approaches, Mon. Weather Rev., 133, 3132–3147, 2005.; Han, Y., van Delst, P., Liu, Q. H., Weng, F. Z., Yan, B. H., Treadon, R., and Derber, J.: Community Radiative Transfer Model (CRTM) – Version 1, NOAA NESDIS Technical Report, Washington, DC, 122 pp., 2006.; Hunt, B. R., Kostelich, J., and Szunyogh, I.: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter, Physica D, 230, 112–126, 2007.; Ide, K., Courtier, P., Michael, G., and Lorenc, A. C.: Unified notation for data assimilation: operational, sequential and variational, J. Meteorol. Soc. Jpn., 75, 181–189, 1997.; Lawson, W. G. and Hansen, J. A.: Implications of stochastic and deterministic filters as ensemble-based data assimilation methods in varying regimes of error growth, Mon. Weather Rev., 132, 1966–1981, 2004.; Le Dimet, F. X., Navon, I. M., and Daescu, D. N.: Second-order information in data assimilation, Mon. Weather Rev., 130, 629–648, 2002.; Li, H., Kalnay, E., and Miyoshi, T.: Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter, Q. J. Roy. Meteor. Soc., 135, 523–533, 2009.; Liang, X., Zheng, X. G., Zhang, S. P., Wu, G. C., Dai, Y. J., and Li, Y.: Maximum likelihood estimation of inflation factors on forecast error covariance matrix for ensemble Kalman filter assimilation, Q. J. Roy. Meteor. Soc., 138, 263–273, 2012.; Liou, K. N.: An Introduction to Atmospheric Rad


Click To View

Additional Books

  • Lagrangian Descriptors and the Assessmen... (by )
  • Application of Singularity Theory and Lo... (by )
  • Improved Singular Spectrum Analysis for ... (by )
  • Electrodynamics in a Very Thin Current S... (by )
  • Large-amplitude Electromagnetic Waves in... (by )
  • Nonadiabatic Interaction Between a Charg... (by )
  • Excitation of Kinetic Alfvén Turbulence ... (by )
  • A Propagation-separation Approach to Est... (by )
  • Thin Layer Shearing of a Highly Plastic ... (by )
  • Magnetic Decreases (Mds) and Mirror Mode... (by )
  • The Evolution of Electron Current Sheet ... (by )
  • Continuous Dynamic Assimilation of the I... (by )
Scroll Left
Scroll Right


Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.