The impact of observational errors on objective analyses is investigated with mathematical analyses, analytical examples, and real data experiments. Cases with observational errors at one or more stations are considered. It is found that in the presence of observational errors, the analysis error in an objective analysis scheme generally consists of two parts: the signal fitting error and the noise contamination error. Although every objective analysis scheme has its own procedure(s) to control the two errors, the procedures to suppress the noise contamination error in one and two dimensions are shown to be relatively ineffective. It is shown that the extension of an objective analysis method to more dimensions significantly reduces the noise contamination. Based on these results, higher dimensional versions of the least squares polynomial fitting (LSPF) methods and the Barnes scheme are examined. In both analytic and real data experiments, the 3D and 4D LSPF methods and the 3D Barnes scheme show an enhanced ability to filter observational noise.
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