Data Assimilation by Ensemblekalman filter With the Lorenz Equations

Regis Sperotto de Quadros, Fabrício Pereira Harter, Daniela Buske, Larri Silveira Pereira

Abstract


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.


Keywords


Data assimilation. Ensemble Kalman filter. Lorenz model.

Full Text:

PDF

References


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.




DOI: https://doi.org/10.5902/2179460X20158

Copyright (c) 2016



Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.