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TitleOn correlation in the water vapour pressure formulations
Publication TypeJournal Article
Year of Publication2006
AuthorsLovell-Smith, J.W.
Pagination556 - 560
Date Published2006
ISSN00261394 (ISSN)
KeywordsAtmospheric humidity, Autocorrelation, Correlation methods, Covariance, Curve fitting, Error analysis, Interpolation, PRESSURE MEASUREMENT, Statistical methods, Uncertainty analysis, Vapors, Water vapour pressure
AbstractA wide variety of empirical equations are used in measurement science in which the equation parameters are determined through some form of interpolation or least squares fit. When the equation is a good model of the system and the fitting process is accompanied by a full uncertainty analysis, the equation parameters summarize all the input data and associated uncertainty. Often, however, only the uncertainty in the equation result is reported and that information may be insufficient to carry out a full uncertainty analysis when the equation is used. In particular, the lack of information about correlation is an issue for many humidity calculations which require the empirical enhancement factor and vapour pressure formulations to be evaluated twice, once directly (i.e. in the forward direction) and once in the inverse direction. For these calculations it is clear that uncertainties in the two evaluations are correlated and that for sufficiently close values, error associated with use of the formulations should cancel. However, apart from the special case where the evaluations in each direction are at the same vapour pressure, the error and hence the autocorrelation is unknown. When the full equation parameter covariance is known, the 'parameter covariance' method (PCM) presented here does give the reduction in uncertainty expected for autocorrelation within the formulation. © 2006 BIPM and IOP Publishing Ltd.

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