What question did this study set out to answer?

To analyze the fundamental relationships linking measurement, scale, and scaling, and to derive the physical and mathematical constraints required when scaling instruments between laboratory and field scales.

February 1, 1986Water Resources Research

On Measurement, Scale, and Scaling

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Authors

JCJohn H. CushmanPurdue University West Lafayette

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Implication

Theoretical analysis reveals the mathematical constraints required for instrument scaling between laboratory and field experiments, highlighting how measurement filters affect data.

Key Points

To analyze the fundamental relationships linking measurement, scale, and scaling, and to derive the physical and mathematical constraints required when scaling instruments between laboratory and field scales.
Analyzed the distinction between measurable fundamental properties and non-measurable constitutive variables across explicit and implicit heterogeneity.
Mathematically modeled instrument frequency responses, signal conditioning, and linear interpolation using spatial and temporal convolution operators.
Derived explicit mathematical constraints on instrument frequency response necessary for valid cross-scale lab-to-field translations.
Showed that linear interpolators function as filters that violate and fail to preserve the original instrument scale constraints.
Demonstrated that instrument signal conditioning represents a multiple spatial convolution across the measurement window followed by a temporal convolution.

Cite This Study

John H. Cushman (1986) studied this question.

synapsesocial.com/papers/6a7b59aa756812e39589f8f7 https://doi.org/10.1029/wr022i002p00129

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Implication

Theoretical analysis reveals the mathematical constraints required for instrument scaling between laboratory and field experiments, highlighting how measurement filters affect data.

On Measurement, Scale, and Scaling

Discussion

Member takes

Implication

Key Points

Cite This Study

On Measurement, Scale, and Scaling

Discussion

Member takes

Implication

Key Points

Cite This Study

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