Implementation of the Ensemble Kalman Filter to a Double Gyre Ocean and Sensitivity Test using Twin Experiments

- Journal title : Ocean and Polar Research
- Volume 30, Issue 2, 2008, pp.129-140
- Publisher : Korea Institute of Ocean Science & Technology
- DOI : 10.4217/OPR.2008.30.2.129

Title & Authors

Implementation of the Ensemble Kalman Filter to a Double Gyre Ocean and Sensitivity Test using Twin Experiments

Kim, Young-Ho; Lyu, Sang-Jin; Choi, Byoung-Ju; Cho, Yang-Ki; Kim, Young-Gyu;

Kim, Young-Ho; Lyu, Sang-Jin; Choi, Byoung-Ju; Cho, Yang-Ki; Kim, Young-Gyu;

Abstract

As a preliminary effort to establish a data assimilative ocean forecasting system, we reviewed the theory of the Ensemble Kamlan Filter (EnKF) and developed practical techniques to apply the EnKF algorithm in a real ocean circulation modeling system. To verify the performance of the developed EnKF algorithm, a wind-driven double gyre was established in a rectangular ocean using the Regional Ocean Modeling System (ROMS) and the EnKF algorithm was implemented. In the ideal ocean, sea surface temperature and sea surface height were assimilated. The results showed that the multivariate background error covariance is useful in the EnKF system. We also tested the sensitivity of the EnKF algorithm to the localization and inflation of the background error covariance and the number of ensemble members. In the sensitivity tests, the ensemble spread as well as the root-mean square (RMS) error of the ensemble mean was assessed. The EnKF produces the optimal solution as the ensemble spread approaches the RMS error of the ensemble mean because the ensembles are well distributed so that they may include the true state. The localization and inflation of the background error covariance increased the ensemble spread while building up well-distributed ensembles. Without the localization of the background error covariance, the ensemble spread tended to decrease continuously over time. In addition, the ensemble spread is proportional to the number of ensemble members. However, it is difficult to increase the ensemble members because of the computational cost.

Keywords

data assimilation;Ensemble Kalman Filter;ocean modeling;ensemble spread;localization and inflation of the background error covariance;

Language

Korean

Cited by

References

1.

송용식, 이재학, 박경. 2000. 조석 모델링에서 adjoint 방법 적용 시 적정 가중치 산정. 한국해양학회지 바다, 5(3), 177-185

2.

안중배, 윤용훈, 조익현, 오혜람. 2005. VAF 변분법을 이용한 전구 해양자료 동화 연구. 한국해양학회지 바다,10(1), 69-78

3.

Bahurel, P., The MERCATOR Project Team. 2006. MERCATOR Ocean global to regional ocean monitoring and forecasting. p. 381-395. In: Ocean weather forecasting: An integrated view of oceanography, ed. by E.P. Chassignet and J. Verron. Springer, Dordrecht

4.

Bjerknes, V., J. Bjerknes, H.S. Solberg, and T. Bergeron. 1934. Hydrodynamique physique avec applications a la mteorologie dynamique. Les Presses Universitaires, Paris. 864 p

5.

Brusdal, K., J.M. Brankart, G. Halberstadt, G. Evensen, P. Brasseur, P.J. van Leeuwen, E. Dombrowsky, and J. Verron. 2003. A demonstration of ensemble based assimilation methods with a layered OGCM from the perspective of operational ocean forecasting systems. J. Mar. Sys., 40-41, 253-289

6.

Burgers, G., P.J. van Leeuwen, and G. Evensen. 1998. Analysis scheme in the ensemble Kalman filter. Mon. Weather Rev., 126(6), 1719-1724

7.

Cane, M.A., A. Kaplan, R.N. Miller, B. Tang, E.C. Hacker, and A.J. Busalacchi. 1996. Mapping tropical Pacific sea level: Data assimilation via a reduced state space Kalman filter. J. Geophys. Res., 101(C10), 22599-22617

8.

Cooper, M. and K. Haines. 1996. Altimetric assimilationwith water property conservation. J. Geophys. Res., 101(C1), 1959-1977

9.

Daley, R. 1991. Atmospheric data analysis. Cambridge University Press, New York. 457 p

10.

De Mey, P. and M. Benkiran. 2002. A multivariate reduced order optimal interpolation method and its application to the Mediterranean basin-scale circulation. p. 281-306. In: Ocean Forecasting: conceptual basis and applications, ed. by N. Pinardi and J. Woods. Spinger-Verlag

11.

Evensen, G. 1994. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99(C5), 10143-10162

12.

Fukumori, I. and P. Malanotte-Rizzoli. 1995. An approximate Kalman Filter for ocean data assimilation: An example with an idealized Gulf Stream model. J. Geophys. Res., 100(C4), 6777-6793

13.

Fukumori, I., J. Benveniste, C. Wunsch, and D.B. Haidvogel. 1993. Assimilation of sea surface topography into an ocean circulation model using a steady-state smoother. J. Phys. Oceanogr., 23(8), 1831-1855

14.

Gaspari, G. and S.E. Cohn. 1999. Construction of correlation functions in two and three dimensions. Q. J. R. Meteorol. Soc., 125(554), 723-757

15.

Hansen, J.A. and L.A. Smith. 2000. The role of operational constraints in selecting supplementary observations. J. Atmos. Sci., 57(17), 2859-2871

16.

Hollingsworth, A. and P. Lonnberg. 1986. The statistical structure of short-range forecast errors as determinedfrom radiosonde data. Part I: The wind field. Tellus, 38A, 111-136

17.

Houtekamer, P.L. and H.L. Mitchell. 1998. Data assimilation using an ensemble Kalman Filter technique. Mon. Weather Rev., 126, 796-811

18.

Houtekamer, P.L. and H.L. Mitchell. 2001. A sequential ensemble Kalman Filter for atmospheric data assimilation. Mon. Weather Rev., 129, 123-137

19.

Marotzke, J., R. Giering, K.Q. Zhang, D. Stammer, C. Hill, and T. Lee. 1999. Construction of the adjoint MIT ocean general circulation model and application to Atlantic heat transport sensitivity. J. Geophys. Res., 104(C12), 29529-29547

20.

Pham, D., J. Verron, and M. Roubaud. 1998. A singular evolutive extended Kalman Filter for data assimilation in oceanography. J. Mar. Sys., 16, 323-340

21.

Smith, N. 2006. Perspectives from the global ocean data assimilation experiment. p. 1-17. In: Ocean weather forecasting, ed. by E.P. Chassignet and J. Verron. Springer

22.

Wang, X. and C.H. Bishop. 2003. A comparison of breeding and ensemble transform Kalman Filter ensemble forecast schemes. J. Atmos. Sci., 60, 1140-1158

23.

Weaver, A.T., J. Vialard, D.L.T. Anderson, and P. Delecluse. 2002. Three- and four-dimensional variational assimilation with a general circulation model of the tropical Pacific Ocean. ECMWF Technical Memorandum No. 365. 74 p