Data Assimilation by Ensemblekalman filter With the Lorenz Equations
Keywords:Data assimilation. Ensemble Kalman filter. Lorenz model.
Data Assimilation is a procedure to get the initial condition as accurately as possible, through the statistical combination of collected observations and a background field, usually a short-range forecast. In this research a complete assimilation system for the Lorenz equations based on Ensemble Kalman Filter is presented and examined. The Lorenz model is chosen for its simplicity in structure and the dynamic similarities with primitive equations models, such as modern numerical weather forecasting. Based on results, was concluded that in this implementation, 10 members is the best setting, because there is overfitting for ensembles with 50 and 100 members. It was also examined whether the EnKF is effective to track the control for 20% and 40% of error in the initial conditions. The results show a disagreement between the "truth" and the estimation, especially in the end of integration period, due to the chaotic nature of the system. It was also concluded that EnKF has to be performed frequently in order to produce desirable results.
Anderson, J.L. (2001). An ensemble adjustment Kalman filter for data assimilation, Monthly Weather Review, 129, 2884-2903.
Bishop, C.H., Etherton, B.J., Majumdar, S.J. (2001). Adaptive sampling with ensemble transform Kalman filter. Part I: Theorical Aspects, Montlhy Weather Review, 129, 420-436.
Burgers, F., van Leeuwen, P.J., Evensen, G., (1998). Analysis scheme in the ensemble Kalman filter, Monthly Weather Review, 126, 1719-1724.
Courtier, C., Derber, J., Errico, R., Louis, J.F., Vukicevic, T. (1993). Important literature on the use of adjoint, variational methods and the Kalman filter in meteorology, Tellus, 45(A), 342-357.
Evensen, G. (1994). Sequential data assimilation with a nonlinear quase-geostrofic model using Monte Carlo methods error statistics, Journal of Geophysical Research, 99(C5), 10143-10162.
Gao, J, Xue, M., Stensrud, D. (2013). The Development of a Hybrid EnKF-3DVAR Algorithm for Storm-Scale Data Assimilation, Advances in Meteorology, 2013, 1-12.
Gauthier, P. (1992). Chaos and quadri-dimensional data assimilation: a study based on the Lorenz model, Tellus, 44(A), 2-17.
Jazswinski, A.H. (1970). Stochastic Processes and Filtering Theory, New York: Ed. Academic Press.
Kalman, R.E. (1960). A new approach to linear filtering and prediction problems, Journal of Basic Engineering, 32 (Series D), 35-45, Transactions of the ASME.
Kalnay, E. (2004) Atmospheric Modeling, Data Assimilation and Predictability, Cambridge University Press, Cambridge, United Kingdom.
Lorenz, E. (1963). Deterministic nonperiodic flow, Journal of the Atmospheric Sciences, 20, 130-141.
Miller, R., Guil, M., Gauthiez, F. (1994). Advanced Data Assimilation in strongly nonlinear dynamical systems, Journal of the Atmospheric Science, 51, 1037-1056.
Miyoshi, T. (2005). “Ensemble Kalman Filter experiments with a primitive equation global model, Meteorology dissertation, University of Maryland, College Park, Maryland, USA.
Ott, E., Hunt, B.R., Szunyogh , I., Zimin, A.V., Kostelich, A.J., Corazza, M., Kalnay, E., Patil, D.J., Yorke, E. (2002). Exploiting local low dimensionality of the atmospheric dynamics for efficient Kalman filtering, ArXiv:arc-ive/paper 020358, http://arxiv.org/abs/physics/020358.
Ott, E., Hunt, B. R., Szunyogh, I., Zimin, A. V., Kostelich, E. J. Corazza, M., Kalnay, E., Patil, D. J., Yorke, J. E. (2004). A local ensemble Kalman filter for atmospheric data assimilation, Tellus, vol. 56(A), pp. 415-428.
Pires, C., Vautard, R., Talagrand, O. (1996). On extending the limits of variational assimilation in nonlinear chaotic systems, Tellus, 48(A), 96-121.
Saltzman, B. (1962). Finite amplitude free convection as an initial value problem, Journal of the Atmospheric Sciences, 19, 329-341.
Tippet, M.K., Anderson, J.L., Bishop, C.H., Hamill, T.M., Whitaker, J.S. (2003). Ensemble square root filters, Monthly Weather Review, vol. 131, pp. 1485-1490.
Whitaker, J. S., Hamil, T.M. (2002). Ensemble data assimilation without perturbed observation, Monthly Weather Review, 130, 1913-1924.
Xue, M., Kong, F., Kevin, T., Gao, J., Wang, Y., Brewster, K., Droegemeier, K. (2013). Prediction of Convective Storms at Convection-Resolving 1km Resolution over Continental United States with Radar Data Assimilation: An Example Case of 26 May 2008 and Precipitation Forecasts from Spring 2009”, Advances in Meteorology, 1-9.
How to Cite
To access the DECLARATION AND TRANSFER OF COPYRIGHT AUTHOR’S DECLARATION AND COPYRIGHT LICENSE click here.
Ethical Guidelines for Journal Publication
The Ciência e Natura journal is committed to ensuring ethics in publication and quality of articles.
Conformance to standards of ethical behavior is therefore expected of all parties involved: Authors, Editors, Reviewers, and the Publisher.
Authors: Authors should present an objective discussion of the significance of research work as well as sufficient detail and references to permit others to replicate the experiments. Fraudulent or knowingly inaccurate statements constitute unethical behavior and are unacceptable. Review Articles should also be objective, comprehensive, and accurate accounts of the state of the art. The Authors should ensure that their work is entirely original works, and if the work and/or words of others have been used, this has been appropriately acknowledged. Plagiarism in all its forms constitutes unethical publishing behavior and is unacceptable. Submitting the same manuscript to more than one journal concurrently constitutes unethical publishing behavior and is unacceptable. Authors should not submit articles describing essentially the same research to more than one journal. The corresponding Author should ensure that there is a full consensus of all Co-authors in approving the final version of the paper and its submission for publication.
Editors: Editors should evaluate manuscripts exclusively on the basis of their academic merit. An Editor must not use unpublished information in the editor's own research without the express written consent of the Author. Editors should take reasonable responsive measures when ethical complaints have been presented concerning a submitted manuscript or published paper.
Reviewers: Any manuscripts received for review must be treated as confidential documents. Privileged information or ideas obtained through peer review must be kept confidential and not used for personal advantage. Reviewers should be conducted objectively, and observations should be formulated clearly with supporting arguments, so that Authors can use them for improving the paper. Any selected Reviewer who feels unqualified to review the research reported in a manuscript or knows that its prompt review will be impossible should notify the Editor and excuse himself from the review process. Reviewers should not consider manuscripts in which they have conflicts of interest resulting from competitive, collaborative, or other relationships or connections with any of the authors, companies, or institutions connected to the papers.