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On Measurement, Scale, and Scaling
Author(s) -
Cushman John H.
Publication year - 1986
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr022i002p00129
Subject(s) - scaling , scale (ratio) , convolution (computer science) , field (mathematics) , signal (programming language) , linear scale , computer science , mathematics , algorithm , statistical physics , physics , geometry , geology , artificial intelligence , geodesy , quantum mechanics , artificial neural network , pure mathematics , programming language
The relationships between measurement, scale, and scaling are discussed and analyzed in detail. It is pointed out that only certain fundamental properties can be measured and that these properties do not include constitutive variables. The interrelationships between scale and measurement are shown to manifest themselves in two types of heterogeneity which we label as explicit and implicit. An important issue that is addressed for the first time is the necessity of scaling instruments when scaling laboratory experiments up to field scale or vice versa. Explicit constraints that scaled instruments must satisfy are derived for the frequency response of the instrument. It is shown that linear interpolators can be viewed as filters (instruments), but that these interpolators don't preserve the scale constraints of the instrument used in making the field measurements. The relationship between signal conditioning and the instrument's window is isolated and shown to be a multiple convolution over the spatial coordinates (corresponding to the window) followed by a temporal convolution for the signal conditioning.