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Van Leeuwen, Peter Jan (2015)
Publisher: Royal Meteorological Society
Languages: English
Types: Article
This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality\ud in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.
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    • Ades M, van Leeuwen PJ. 2013. An exploration of the equivalent-weights particle filter. Q. J. R. Meteorol. Soc. 139: 820 - 840, doi: 10.1002/ qj.1995.
    • Ades M, van Leeuwen PJ. 2014. The equivalent-weights particle filter in a high-dimensional system. Q. J. R. Meteorol. Soc., doi: 10.1002/ qj.2370.
    • Anderson JL, Wyman B, Zhang S, Hoar T. 2005. Assimilation of surface pressure observations using an ensemble filter in an idealized global atmospheric prediction system. J. Atmos. Sci. 62: 2921 - 2938.
    • Bishop CM. 2006. Pattern Regocnition and Machine Learning. Springer: New York, NY.
    • Bishop CH, Etherton B, Majumdar SJ. 2001. Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Weather Rev. 129: 420 - 436.
    • Bocquet M, Wu L, Chevallier F. 2011. Bayesian control space for optimal assimilation of observations, I: Consistent multiscale formalism. Q. J. R. Meteorol. Soc. 137: 1340 - 1356.
    • Cohn SE. 1997. An introduction to estimation theory. J. Meteorol. Soc. Jpn. 75: 257 - 288.
    • Daley R. 1993. Estimating observation error statistics for atmospheric data assimilation. Ann. Geophys. 11: 634 - 647.
    • Derber J, Rosati A. 1989. A global oceanic data assimilation system. J. Phys. Oceanogr. 19: 1333 - 1347.
    • Janjic T, Cohn SE. 2006. Treatment of observation error due to unresolved scales in atmospheric data assimilation. Mon. Weather Rev. 134: 2900 - 2915.
    • Ko¨hl A, Dommenget D, Ueyoshi K, Stammer D. 2007. 'The global ECCO 1952 - 2001 ocean synthesis'. Report Series 40. ECCO: Cambridge, MA.
    • Leeuwenburgh O. 2007. Validation of an EnKF system for OGCM initialization assimilating temperature, salinity, and surface height measurements. Mon. Weather Rev. 135: 125 - 139.
    • Liu Z-Q, Rabier F. 2002. The interaction between model resolution, observation resolution and observation density in data assimilation: A one-dimensional study. Q. J. R. Meteorol. Soc. 128: 1367 - 1386.
    • Lorenc AC. 1986. Analysis methods for numerical weather prediction. Q. J. R. Meteorol. Soc. 112: 1177 - 1194.
    • Migliorini S. 2012. On the equivalence between radiance and retrieval assimilation. Mon. Weather Rev. 140: 258 - 265, doi: 10.1175/MWR-D10-05047.1.
    • Oke PR, Sakov P. 2008. Representation error of oceanic observations for data assimilation. J. Atmos. Oceanic Technol. 25: 1004 - 1017.
    • Oke PR, Schiller A, Griffin DA, Brassington GB. 2005. Ensemble data assimilation for an eddy-resolving ocean model of the Australian region. Q. J. R. Meteorol. Soc. 131: 3301 - 3311.
    • Ponte RM, Wunsch C, Stammer D. 2007. Spatial mapping of time-variable errors in Jason-1 and TOPEX/Poseidon sea surface height measurements. J. Atmos. Oceanic Technol. 24: 1078 - 1085.
    • Rogel P, Weaver AT, Daget N, Ricci S, Machu E. 2005. Ensembles of global ocean analyses for seasonal prediction: Impact of temperature assimilation. Tellus 57A: 375 - 386.
    • Schiller A, Oke PR, Brassington GB, Entel M, Fiedler R, Griffin DA, Mansbridge JV. 2008. Eddy-resolving ocean circulation in the Asian - Australian region inferred from an ocean reanalysis effort. Prog. Oceanogr. 76: 334 - 365.
    • Snyder C, Bengtsson T, Bickel P, Anderson J. 2008. Obstacles to highdimensional particle filtering. Mon. Weather Rev. 136: 4629 - 4640.
    • Thacker WC. 2003. Data-model-error compatibility. Ocean Model. 5: 233 - 247.
    • van Leeuwen PJ. 2009. Particle filtering in the geosciences. Mon. Weather Rev. 137: 4089 - 4114.
    • van Leeuwen PJ. 2010. Nonlinear data assimilation in geosciences: An extremely efficient particle filter. Q. J. R. Meteorol. Soc. 136: 1991 - 1996.
    • van Leeuwen PJ. 2011. Efficient fully non-linear data assimilation in geophysical fluid dynamics. Comput. Fluids 46: 52 - 58, doi: 10.1016/j.compfluid.2010.11.011.
    • Wu L, Bocquet M, Lauvaux T, Chevallier F, Rayner P, Davis K. 2011. Optimal representation of source-sink fluxes for mesoscale carbon dioxide inversion with synthetic data. J. Geophys. Res. 116: D21304, doi: 10.1029/2011JD016198.
    • Zaron ED, Egbert GD. 2006. Estimating open-ocean barotropic tidal dissipation: The Hawaiian Ridge. J. Phys. Oceanogr. 36: 1019 - 1035.
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