World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

Hybrid Levenberg–marquardt and Weak Constraint Ensemble Kalman Smoother~method : Volume 2, Issue 3 (26/05/2015)

By Mandel, J.

Click here to view

Book Id: WPLBN0004020153
Format Type: PDF Article :
File Size: Pages 38
Reproduction Date: 2015

Title: Hybrid Levenberg–marquardt and Weak Constraint Ensemble Kalman Smoother~method : Volume 2, Issue 3 (26/05/2015)  
Author: Mandel, J.
Volume: Vol. 2, Issue 3
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

Gratton, S., Bergou, E., Gürol, S., & Mandel, J. (2015). Hybrid Levenberg–marquardt and Weak Constraint Ensemble Kalman Smoother~method : Volume 2, Issue 3 (26/05/2015). Retrieved from

Description: University of Colorado Denver, Denver, CO, USA. We propose to use the ensemble Kalman smoother (EnKS) as the linear least squares solver in the Gauss–Newton method for the large nonlinear least squares in incremental 4DVAR. The ensemble approach is naturally parallel over the ensemble members and no tangent or adjoint operators are needed. Further, adding a regularization term results in replacing the Gauss–Newton method, which may diverge, by the Levenberg–Marquardt method, which is known to be convergent. The regularization is implemented efficiently as an additional observation in the EnKS. The method is illustrated on the Lorenz 63 and the two-level quasi-geostrophic model problems.

Hybrid Levenberg–Marquardt and weak constraint ensemble Kalman smoother~method

Marquardt, D. W.: An algorithm for least-squares estimation of nonlinear parameters, J. Soc. Ind. Appl. Math., 11, 431–441, doi:10.1137/0111030, 1963.; Nowak, W., Tenkleve, S., and Cirpka, O.: Efficient computation of linearized cross-covariance and auto-covariance matrices of interdependent quantities, Math. Geol., 35, 53–66, 2003.; Osborne, M. R.: Nonlinear least squares – the Levenberg algorithm revisited, J. Aust. Math. Soc. B, 19, 343–357, doi:10.1017/S033427000000120X, 1976.; Pedlosky, J.: Geophysical Fluid Dynamics, Springer, New York Heidelberg Berlin, 715 pp., 1979.; Rauch, H. E., Tung, F., and Striebel, C. T.: Maximum likelihood estimates of linear dynamic systems, AIAA J., 3, 1445–1450, 1965.; Sakov, P. and Bertino, L.: Relation between two common localisation methods for the EnKF, Computat. Geosci., 10, 225–237, doi:10.1007/s10596-010-9202-6, 2011.; Sakov, P., Oliver, D. S., and Bertino, L.: An iterative EnKF for strongly nonlinear systems, Mon. Weather Rev., 140, 1988–2004, doi:10.1175/MWR-D-11-00176.1, 2012.; Strang, G. and Borre, K.: Linear Algebra, Geodesy, and GPS, Wellesley-Cambridge Press, Wellesley, MA, 490 pp., 1997.; Stroud, J. R., Stein, M. L., Lesht, B. M., Schwab, D. J., and Beletsky, D.: An ensemble Kalman filter and smoother for satellite data assimilation, J. Am. Stat. Assoc., 105, 978–990, doi:10.1198/jasa.2010.ap07636, 2010.; Trémolet, Y.: Model-error estimation in 4D-Var, Q. J. Roy. Meteor. Soc., 133, 1267–1280, doi:10.1002/qj.94, 2007.; Trémolet, Y.: Object-Oriented Prediction System, available at: (last access: 15 May 2015), 2013.; Tshimanga, J., Gratton, S., Weaver, A. T., and Sartenaer, A.: Limited-memory preconditioners, with application to incremental four-dimensional variational data assimilation, Q. J. Roy. Meteor. Soc., 134, 751–769, doi:10.1002/qj.228, 2008.; Wang, X.: Incorporating ensemble covariance in the gridpoint statistical interpolation variational minimization: a mathematical framework, Mon. Weather Rev., 138, 2990–2995, doi:10.1175/2010MWR3245.1, 2010.; Wright, S. J. and Holt, J. N.: An inexact Levenberg–Marquardt method for large sparse nonlinear least squares, J. Aust. Math. Soc. B, 26, 387–403, doi:10.1017/S0334270000004604, 1985.; Bell, B.: The iterated Kalman smoother as a Gauss–Newton method, SIAM J. Optimiz., 4, 626–636, doi:10.1137/0804035, 1994.; Bergou, E., Gratton, S., and Mandel, J.: On the convergence of a non-linear ensemble Kalman smoother, arXiv:1411.4608, submitted, 2014.; Bocquet, M. and Sakov, P.: Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems, Nonlin. Processes Geophys., 19, 383–399, doi:10.5194/npg-19-383-2012, 2012.; Bocquet, M. and Sakov, P.: An iterative ensemble Kalman smoother, Q. J. Roy. Meteor. Soc., 140, 1521–1535, doi:10.1002/qj.2236, 2014.; Brusdal, K., Brankart, J. M., Halberstadt, G., Evensen, G., Brasseur, P., van Leeuwen, P. J., Dombrowsky, E., and Verron, J.: A demonstration of ensemble based assimilation methods with a layered OGCM from the perspective of operational ocean forecasting systems, J. Marine Syst., 40–41, 253


Click To View

Additional Books

  • Bounded Lognormal Cascades as Quasi-mult... (by )
  • Bifurcation Analysis of a Paradigmatic M... (by )
  • Intermittency in Mhd Turbulence and Coro... (by )
  • Nonlinear Effects in a Conceptual Multil... (by )
  • A Kalman Filter Application to a Spectra... (by )
  • An Intercomparison of Burnt Area Estimat... (by )
  • 20Th International Conference on Mathema... (by )
  • Deterministic Dynamics of the Magnetosph... (by )
  • Using Magnetic Fluids to Simulate Convec... (by )
  • The Modified Korteweg - De Vries Equatio... (by )
  • Nonlinear Electron Acoustic Structures G... (by )
  • Mapping Local Singularities Using Magnet... (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.