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Journal of Oceanography

, Volume 67, Issue 3, pp 253–262 | Cite as

Improving strategies with constraints regarding non-Gaussian statistics in a three-dimensional variational assimilation method

  • Norihisa Usui
  • Shiro Ishizaki
  • Yosuke Fujii
  • Masafumi Kamachi
Original Article

Abstract

We assess validity of a Gaussian error assumption, the basic assumption in data assimilation theory, and propose two kinds of constraints regarding non-Gaussian statistics. In the mixed water region (MWR) off the east coast of Japan exhibiting complicated frontal structures, a probability density function (PDF) of subsurface temperature shows double peaks corresponding to the Kuroshio and Oyashio waters. The complicated frontal structures characterized by the temperature PDF sometimes cause large innovations, bringing about a non-Gaussianity of errors. It is also revealed that assimilated results with a standard three-dimensional variational (3DVAR) scheme have some issues in MWR, arising from the non-Gaussianity of errors. The Oyashio water sometimes becomes unrealistically cold. The double peaks seen in the observed temperature PDF are too smoothed. To improve the assimilated field in MWR, we introduce two kinds of constraints, J c1 and J c2, which model the observed temperature PDF. The constraint J c1 prevents the unrealistically cold Oyashio water, and J c2 intends to reproduce the double peaks. The assimilated fields are significantly improved by using these constraints. The constraint J c1 effectively reduces the unrealistically cold Oyashio water. The double peaks in the observed temperature PDF are successfully reproduced by J c2. In addition, not only subsurface temperature but also whole level temperature and salinity (T–S) fields are improved by adopting J c1 and J c2 to a multivariate 3DVAR scheme with vertical coupled T–S empirical orthogonal function modes.

Keywords

Data assimilation Variational method Non-Gaussian Mixed water region Temperature front 

Notes

Acknowledgments

The authors would like to thank the members of the Oceanographic Division of the Meteorological Research Institute for fruitful discussions. Thanks are extended to two anonymous reviewers for helpful comments on a previous version of the manuscript. This work is funded by the Meteorological Research Institute. Part of this study is supported by the Research Program on Climate Change Adaptation (RECCA) and by MEXT Grant-in-Aid for Young Scientists (B).

References

  1. Bloom SC, Takacs LL, Da Silva AM, Ledvina D (1996) Data assimilation using incremental analysis updates. Mon Weather Rev 124:1256–1271CrossRefGoogle Scholar
  2. Fujii Y (2005) Preconditioned optimizing utility for large-dimensional analyses (POpULar). J Oceanogr 61:167–181CrossRefGoogle Scholar
  3. Fujii Y, Kamachi M (2003a) A reconstruction of observed profiles in the sea east of Japan using vertical coupled temperature–salinity EOF modes. J Oceanogr 59:173–186CrossRefGoogle Scholar
  4. Fujii Y, Kamachi M (2003b) Three-dimensional analysis of temperature and salinity in the equatorial Pacific using a variational method with vertical coupled temperature–salinity EOF modes. J Geophys Res 108(C9):3297. doi: 10.1029/2002JC001745 CrossRefGoogle Scholar
  5. Fujii Y, Ishizaki S, Kamachi M (2005) Application of nonlinear constraints in a three-dimensional variational ocean analysis. J Oceanogr 61:655–662CrossRefGoogle Scholar
  6. Fukumori I (2002) A partitioned Kalman filter and smoother. Mon Weather Rev 130:1370–1383CrossRefGoogle Scholar
  7. Hirose N, Kawamura H, Lee H-J, Yoon J-H (2007) Sequential forecasting of the surface and subsurface conditions in the Japan sea. J Oceanogr 63:467–481CrossRefGoogle Scholar
  8. Hurlburt HE, Brassington GB, Drillet Y, Kamachi M, Benkiran M, Bourdalle-Badie R, Chassignet EP, Jacobs GA, Le Galloudec O, Lellouche J-M, Metzger EJ, Oke PR, Pugh TF, Schiller A, Smedstad OM, Tranchant B, Tsujino H, Usui N, Wallcraft AJ (2009) High-resolution global and basin-scale ocean analyses and forecasts. Oceanography 22:110-127Google Scholar
  9. Ishikawa Y, Awajia T, Toyodab T, Inc T, Nishinaa K, Nakayamac T, Shimac S, Masuda S (2009) High-resolution synthetic monitoring by a 4-dimensional variational data assimilation system in the northwestern North Pacific. J Mar Syst 78:237–248CrossRefGoogle Scholar
  10. Kalnay E (2003) Atmospheric modeling, data assimilation and predictability. Cambridge University Press, CambridgeGoogle Scholar
  11. Kamachi M, Kuragano T, Sugimoto S, Yoshita K, Sakurai T, Nakano T, Usui N, Uboldi F (2004) Short-range prediction experiments with operational data assimilation system for the Kuroshio south of Japan. J Oceanogr 60:269–282Google Scholar
  12. Kondo J (1975) Air-sea bulk transfer coefficients in diabatic conditions. Boundary-Layer Meteorol 9:91–112CrossRefGoogle Scholar
  13. Kuragano T, Kamachi M (2000) Global statistical space-time scales of oceanic variability estimated from the TOPEX/POSEIDON altimetry data. J Geophys Res 105:955–974CrossRefGoogle Scholar
  14. Kurihara Y, Sakurai T, Kuragano T (2006) Global daily sea surface temperature analysis using data from satellite microwave radiometer, satellite infrared radiometer and in-situ observations. Weather Bull 73(special issue):s1–s18 (in Japanese)Google Scholar
  15. Miyazawa Y, Zhang T, Guo X, Tamura H, Ambe D, Lee J-S, Okuno A, Yoshinari H, Setou T, Komatsu K (2009) Water mass variability in the Western North Pacific detected in a 15-year Eddy resolving ocean reanalysis. J Oceanogr 65: 737–756CrossRefGoogle Scholar
  16. Nakamura H, Lin G, Yamagata T (1997) Decadal climate variability in the North Pacific during recent decades. Bull Am Meteorol Soc 78:2215–2225CrossRefGoogle Scholar
  17. Nonaka M, Nakamura H, Tanimoto Y, Kagimoto T, Sasaki H (2006) North Pacific decadal variability in SST and frontal structure in a high-resolution OGCM. J Clim 19:1970–1989CrossRefGoogle Scholar
  18. Onogi K, Tsutsui J, Koide H, Sakamoto M, Kobayashi S, Hatsushika H, Matsumoto T, Yamazaki N, Kamahori H, Takahashi K, Kadokura S, Wada K, Kato K, Oyama R, Ose T, Mannoji N, Taira R (2007) The JRA-25 reanalysis. J Meteorol Soc Jpn 85:369–432CrossRefGoogle Scholar
  19. Qiu B (2003) Kuroshio extension variability and forcing of the Pacific decadal oscillations: responses and potential feedback. J Phys Oceanogr 33:2465–2482CrossRefGoogle Scholar
  20. Stoffelen A, Anderson D (1997) Ambiguity removal and assimilation of scatterometer data. Q J R Meteorol Soc 123:491–518CrossRefGoogle Scholar
  21. Tanimoto Y, Xie S-P, Kai K, Okajima H, Tokinaga H, Murayama T, Nonaka M, Nakamura H (2009) Observations of marine atmospheric boundary layer transitions across the summer Kuroshio Extension. J Clim 22:1360–1374CrossRefGoogle Scholar
  22. Tokinaga H, Tanimoto Y, Xie S-P, Sampe T, Tomita H, Ichikawa H (2009) Ocean frontal effects on the vertical development of clouds over the Western North Pacific: inSitu and satellite observations. J Clim 22:4241–4260CrossRefGoogle Scholar
  23. Tsujino H, Usui N, Nakano H (2006) Dynamics of Kuroshio path variations in a high-resolution GCM. J Geophys Res 111(C11001). doi: 10.1029/2005JC003118
  24. Tsujino H, Motoi T, Ishikawa I, Hirabara M, Nakano H, Yamanaka G, Yasuda T, Ishizaki H (2010) Reference manual for the Meteorological Research Institute Community Ocean Model (MRI.COM) Version 3. Tech Rep, vol 59, Meteorological Research Institute, Tsukuba, JapanGoogle Scholar
  25. Usui N, Ishizaki S, Fujii Y, Tsujino H, Yasuda T, Kamachi M (2006) Meteorological Research Institute multivariate ocean variational estimation (MOVE) system: some early results. Adv Space Res 37:806–822CrossRefGoogle Scholar
  26. Yasuda I, Watanabe Y (1994) On the relationship between the Oyashio front and saury fishing grounds in the northwestern Pacific. Fish Oceanogr 3:172–181CrossRefGoogle Scholar

Copyright information

© The Oceanographic Society of Japan and Springer 2011

Authors and Affiliations

  • Norihisa Usui
    • 1
  • Shiro Ishizaki
    • 2
  • Yosuke Fujii
    • 1
  • Masafumi Kamachi
    • 1
  1. 1.Oceanographic Research DepartmentMeteorological Research InstituteTsukubaJapan
  2. 2.Global Environment and Marine DepartmentJapan Meteorological AgencyTokyoJapan

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