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This book gives a comprehensive and detailed discussion of statistical averaging of meteorological fields, with assessments of associated errors. A great deal of work on the subject, conducted in the former Soviet Union by the author, is available in English for the first time with this translation. Particularly important is the method of optimal averaging which is developed and examined. This work should be useful to those conducting climate monitoring or climate change studies, which often require spatial averaging to detect slight changes. Studies conducted by the author allow increased accuracy of these estimates compared to many methods commonly used, while showing the confidence that may be assigned to the estimates.