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Note on insertion procedures for meteorological data assimilation
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    "The original stimulation for research in four-dimensional assimilation was the anticipation of global observations of atmospheric temperature by satellite-borne radiometer sensors, By contrast with conventional observation systems, these data are not only distributed in time and space, but also yield information on only one meteorological variable. Studies with simulated data (e.g., Charney, Halem and Jastrow, 1969) established that incomplete information can be used to induce a complete representation of the meteorological variables through the use of a prediction model, provided a sufficiently long sequence of historical data is available. However, the evolution toward such a representation was found to be exceedingly slow and therefore impractical for operational usage. Morel, Lefevre, and Rabreau (1971) pointed out the basic difficulty: inserted observations of the mass field, without an accompanying adjustment of the motion field, tend to be "rejected" by the model. Hayden (1973) proposed a geostrophic correction to the motion field based on the observed gradient of the mass field. Kistler and McPherson (1975) found that this technique substantially improves the model's memory of the observations. However, the geostrophic correction method may not be applied in low latitudes, and its use elsewhere may not be entirely beneficial"--Introduction.

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