Nonlinear Processes in Geophysics
www.nonlin-processes-geophys.net
1023-5809
1607-7946
14
1
2007
10.5194/npg-14-89-2007
http://www.nonlin-processes-geophys.net/14/89/2007/
http://www.nonlin-processes-geophys.net/14/89/2007/npg-14-89-2007.html
http://www.nonlin-processes-geophys.net/14/89/2007/npg-14-89-2007.pdf
89
101
2007-02-22
An implementation of the Local Ensemble Kalman Filter in a quasi geostrophic model and comparison with 3D-Var
M. Corazza
matteo.corazza@arpal.org
E. Kalnay
S. C. Yang
University of Maryland, Department of Meteorology, College Park, MD, USA
ARPAL – CFMI-PC, V.le Brigate Partigiane 2, 16129, Genova, Italy
We perform data assimilation experiments with a widely used
quasi-geostrophic channel model and compare the Local Ensemble Kalman
Filter (LEKF) with a 3D-Var developed
for this model. The LEKF shows a large
improvement, especially in correcting the fast growing modes of the
analysis
errors, with a mean square error equal to
about half that of the
3D-Var. The improvement obtained in the analysis is maintained in
the forecasts, implying that the system is capable of correcting the
initial errors responsible for later
forecast error growth.
<br><br>
Different configurations of the LEKF are tested and compared. We
find that for this system, adding random perturbations after every
analysis step is more effective than the standard variance inflation
in order to avoid underestimating the background error covariance and
the consequent filter divergence.
<br><br>
Experiments indicate that optimal results are obtained with a
relatively small number
of vectors (~30) in the ensemble.
The LEKF is characterized by the "localization"
of the analysis process over local domains surrounding each gridpoint
of the model grid.
We find that, when using a fixed number of
ensemble vectors, there is an
optimal size of the local horizontal domain beyond which the results
do not change further.
Anderson, J S.: An ensemble adjustment filter for data assimilation, Mon. Wea. Rev., 129, 2884–2903, 2001.
Annan, J D.: On the orthogonality of Bred Vectors, Mon. Wea. Rev., 132, 843–849, 2004.
Bennett, A F., Chua, B S., and Leslie, L M.: Generalized inversion of a global NWP model., Meteorol. Atmos. Phys., 60, 165–178, 1996.
Corazza, M., Kalnay, E., Patil, D J., Ott, E., Yorke, J., Szunyogh, I., and Cai, M.: Use of the breeding technique in the estimation of the background error covariance matrix for a quasigeostrophic model, in: AMS Symposium on Observations, Data Assimilation and Probabilistic Prediction, pp. 154–157, Orlando, Florida, 2002.
Corazza, M., Kalnay, E., Patil, D J., Yang, S.-C., Morss, R., Cai, M., Szunyogh, I., Hunt, B R., and Yorke, J A.: Use of the breeding technique to estimate the structure of the analysis "errors of the day", Nonlin. Processes Geophys., 10, 233–243, 2003.
Courtier, P., Thèpaut, J.-N., and Hollingsworth, A.: A strategy for operational implementation of 4D-Var, using an incrementeal approach, Quart. J. Roy. Meteorol. Soc., 120, 1367–1387, 1994.
Daley, R.: Atmospheric data analysis, Cambridge University Press, New York, 1993.
De Pondeca, M. S. F V., Purser, R J., Parrish, D F., and Derber, J C.: Comparison of strategies for the specification of anisotropies in the covariances of a three-dimensional atmospheric data assimilation system, NOAA/NCEP Office Note 452, 13 pp, 2006.
Etherton, B J. and Bishop, C H.: Resilence of Hybrid Ensemble/3DVAR Analysis Schemes to Model Error and Ensemble Covariance Error, Mon. Wea. Rev., 132, 1065–1080, 2004.
Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, 10 143–10 162, 1994.
Hamill, T M. and Snyder, C.: A Hybrid Ensemble Kalman Filter-3D Variational Analysis Scheme, Mon. Wea. Rev., 128, 2905–2919, 2000.
Houtekamer, P L. and Mitchell, H L.: Data assimilation usin an ensemble Kalman filter technique, Mon. Wea. Rev., 126, 796–811, 1998.
Houtekamer, P L., Mitchell, H L., Pellerin, G., Buehner, M., Charron, M., Spacek, L., and Hansen, B.: Atmospheric Data Assimilation with an Ensemble Kalman Filter: Results with Real Observations, Mon. Wea. Rev., 133, 604–620, 2005.
Hunt, B R.: Efficient Data Assimilation for Spatiotemporal Chaos: a Local Ensemble Transform Kalman Filter, prefixhttp://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:physics/0511236, 2005.
Kalnay, E.: Atmospheric Modeling, Data Assimilation and Predictability, Cambridge University Press, 340pp., 2003.
Kalnay, E. and Toth, Z.: Removing growing errors in the analysis cycle, in: Tenth Conference on Numerical Weather Prediction, pp. 212–215, Amer. Meteorol. Soc., 1994.
Klinker, E., Rabier, F., Kelly, G., and Mahfouf, J.-F.: The ECMWF operational implementation of four-dimensional variational assimilation. III: Experimental results and diagnostics with operational configuration, Quart. J. Roy. Meteorol. Soc., 126, 1191–1216, 2000.
Lorenc, A C.: Analysis methods for numerical weather prediction, Quart. J. Roy. Meteorol. Soc., 112, 1177–1194, 1986.
Miyoshi, T.: Ensemble Kalman Filter Experiments with a primitive equation global model, Ph.D. thesis, University of Maryland, College Park, MD, 2005.
Molteni, F.: Atmospheric simulations using a GCM with simplified physical parametrizations. I: model climatology and variability in multi-decadal experiments., Clim. Dyn., 20, 175–191, 2003.
Morss, R E.: Adaptive observations: Idealized sampling strategies for improving numerical weather prediction, Ph.D. thesis, Massachusetts Institute of Technology, 225 pp., 1998.
Morss, R E., Emanuel, K A., and Snyder, C.: Idealized adaptive observation strategies for improving numerical weather prediction, J. Atmos. Sci., 58, 210–234, 2001.
Oczkowski, M., Szunyogh, I., and Patil, D J.: Mechanisms for the Development of Locally Low-Dimensional Atmospheric Dynamics, J. Atmos. Sci., 62, 1135–1156, 2005.
Ott, E., Hunt, B R., Szunyogh, I., Corazza, M., Kalnay, E., Patil, D J., and Yorke, J E.: Exploiting low-dimensionality of the atmospheric dynamics for efficient ensemble Kalman Filtering, http://arXiv:physics/0203058, 2002.
Ott, E., Hunt, B R., Szunyogh, I., Zimin, A V., Kostelich, E J., Corazza, M., Kalnay, E., Patil, D J., and Yorke, J.: A local ensemble Kalman filter for atmospheric data assimilation, Tellus, 56A, 415–428, 2004.
Parrish, D F. and Derber, J C.: The National Meteorological Center's Spectral Statistical-Interpolation Analysis System, Mon. Wea. Rev., 120, 1747–1763, 1992.
Patil, D. J S., Hunt, B R., Kalnay, E., Yorke, J A., and Ott, E.: Local Low Dimensionality of Atmospheric Dynamics, Phys. Rev. Lett., 86, 5878–5881, 2001.
Purser, R J.: A geometrical approach to the synthesis of smooth anisotropic covariance operators for data assimilation, NOAA/NCEP Office Note 447, 60 pp, 2005.
Rabier, F., Jarvinen, H., Klinker, E., Mahfouf, J.-F., and Simmons, A.: The ECMWF operational implementation of four-dimensional variational physics, Quart. J. Roy. Meteorol. Soc., 126, 1143–1170, 2000.
Rotunno, R. and Bao, J W.: A case study of cyclogenesis using a model hierarchy, Mon. Wea. Rev., 124, 1051–1066, 1996.
Szunyogh, I., Kostelich, E J., Gyarmati, G., Hunt, B R., Ott, E., Zimin, A V., Kalnay, E., Patil, D J., and Yorke, J A.: A local ensemble kalman filter for the NCEP GFS model, no. 9.4 J in Proceedings of the AMS meeting, Seattle, Washington, 2004.
Szunyogh, I., Kostelich, E J., Gyarmati, G., Patil, D J., Hunt, B R., Kalnay, E., Ott, E., and Yorke, J A.: Assessing a local ensemble Kalman filter: Perfect model experiments with the National Centers for Environmental Prediction global model, Tellus, 57A, 528–545, 2005.
Tippett, M K., Anderson, J L., Bishop, C H., Hamill, T M., and Whitaker, J S.: Ensemble square-root filters, Mon. Wea. Rev., 131, 1485–1490, 2002.
Toth, Z. and Kalnay, E.: Ensemble forecasting at NMC: the generation of perturbations, Bull. Amer. Meteorol. Soc., 74, 2317–2330, 1993.
Toth, Z. and Kalnay, E.: Ensemble forecasting at NCEP: the breeding method, Mon. Wea. Rev., 125, 3297–3318, 1997.
Wang, X. and Bishop, C H.: A comparison of Breeding and Ensemble Transform Kalman Filter Ensemble Forecast Schemes, J. Atmos. Sci., 60, 1140–1158, 2003.