Box Inverse Models, Altimetry and the Geoid: Problems with the Omission Error.

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Losch, M. , Sloyan, B. , Schröter, J. and Sneeuw, N. (2002): Box Inverse Models, Altimetry and the Geoid: Problems with the Omission Error. , Journal of Geophysical Research, 107(C7), 15 , pp. 1-13 . doi: 10.1029/2001JC000855
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When one combines satellite altimetry and a geoid model to improveestimates of the ocean general circulation from hydrographic datawith a box inverse model, there arises a problem of differentresolution and representation of the data types involved. Here weshow how this problem can lead to an artificial leakage of theerror estimates of short scale (high degree) spherical harmonicfunctions into long wavelength (low wavenumber) Fourier functions. Asimilar paradox effect can be seen in an idealized box inverse modelconstrained by additional sea-surface topography data of low,medium, and high resolution: When more information is added in theform of additional smaller scales, the error of a transport estimateeventually increases. Consequently, including the large geoidomission errors associated with smaller scales in a box inversemodel of the Southern Ocean increases the posterior errors oftransport estimates over those of a model that does not include thegeoid omission error. We do not claim that including or excludingthe geoid omission error is correct. Instead, we juxtapose twodifferent ways of estimating the geoid errors to demonstrate theeffect that the omission error might have on the long -- supposedlywell-known -- scales. How (or if) to properly account for the geoidomission error must be the topic of further research. A propertreatment of the geoid model errors is demanded when one evaluatesthe errors of absolute sea-surface topography data.

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