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Muccino, Julia C.; Bennett, Andrew F. (2004)
Publisher: Co-Action Publishing
Journal: Tellus A
Languages: English
Types: Article
Subjects:
In this paper we investigate the importance of compatibility conditions in inverse regional models. In forward models, the initial condition and boundary condition must be continuous at the space–time corner to ensure that the solution is continuous at the space–time corner and along the characteristic emanating from it. Furthermore, the initial condition, boundary condition and forcing must satisfy the partial differential equation at the space–time corner to ensure that the solution is continuously differentiable at the space–time corner and along the characteristic emanating from it. Assimilation of data into a model requires a null hypothesis regarding residuals in the dynamics (including, for example, forcing, boundary conditions and initial conditions) and data. In most published work, these errors are assumed to be uncorrelated, although Bogden does investigate the importance of correlation between boundary conditions and forcing, and shows that by generalizing the penalty functional to include this cross-correlation the open boundaries behave more like an interface with a true ocean. In this paper, the more general importance of cross-correlations and their impact on the smoothness of the optimal solution are discussed. It is shown that in the absence of physical diffusion, cross-correlations are necessary to obtain a smooth solution; if errors are assumed to be uncorrelated, discontinuities propagate along the characteristic emanating from the space–time corner, even when the initial condition, boundary condition and forcing are compatible, as described above. Although diffusion damps such discontinuities, it does not reproduce the inherently smooth solution achieved when cross-correlation of residuals are accounted for. Rather, the discontinuity is smoothed into a spurious front.
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    • Bennett, A. F. 2002. Inverse Modeling of the Ocean and Atmosphere. Cambridge Univ. Press, Cambridge.
    • Bernstein, D. L. 1950. Existence Theorems in Partial Differential Equations. Princeton Univ. Press, Princeton, NJ.
    • Bogden, P. S. 2001. The impact of model-error correlation on regional data assimilative models and their observational arrays. J. Marine Res. 59, 831-857.
    • Burnett, W., Harding, J. and Heburn, G. 2002. Overview of operational forecasting in the U.S. Navy: Past, present and future. Oceanography 15, 4-12.
    • Celia, M. A. and Gray, W. G. 1992. Numerical Methods for Differential Equations. Prentice Hall, Englewood Cliffs, NJ.
    • Courant, R. and Hilbert, D. 1962. Methods of Mathematical Physics, Vol. 2. Wiley Intersciences, New York.
    • Egbert, G. D., Bennett, A. F. and Foreman, M. G. G. 1994. TOPEX/POSEIDON tides estimated using a global inverse model. J. Geophys. Res. 99C12, 24 821-24 852.
    • Hodur, R., 1997. The Naval Research Laboratory Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS). Mon. Wea. Rev. 125, 1414-1430.
    • Muccino, J. C. and Bennett, A. F. 2002. Generalized inversion of the Korteweg-de Vries equation. Dyn. Atmos. Oceans 35, 227-263.
    • Muccino, J. C., Hubele, N. F. and Bennett, A. F. 2003. Significance testing for variational assimilation. Q. J. R. Meteorol. Soc., in press.
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