A three-dimensional statistical interpolation method, multivariate in geopotential height, thickness and wind, is described. The method has been implemented in the ECMWF operational global data-assimilation scheme, used for routine forecasting and for producing FGGE level III-b analyses. It is distinguished by the large number of data used simultaneously, enabling full exploitation of the potential of the three-dimensional multivariate technique, and by the incorporation of a statistical quality control check on each datum using the analysis itself. Some simple examples illustrating the properties of the method are presented, and a detailed study is made of the effect of various analysis parameters on one practical example.
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Andrew C. Lorenc (1981) studied this question.