Measurement Scale, Network Sampling Scale, and Groundwater Model Parameters

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Abstract
The scales at which model parameters are measured with local field tests distributed on a sampling network are examined. Two scales are defined to characterize the problem: (1) the measurement scale associated with the resolution of a single field test, and (2) the network scale, associated with the separation between samples on a network. Using a spatial filtering approach, it is shown that a network of measurements can only resolve a larger‐scale component of a parameter field. The smaller‐scale component of the parameter field not seen by measurements, here called the subgrid component, can only vary on scales larger than the measurement scale and smaller than the network scale. These unobserved subgrid scales give rise to the so‐called closure problem and consequent modeling errors. When a significant proportion of the parameter variability is contained in the subgrid scales, not only will the closure problem be significant, but aliasing errors will also pollute the estimate of the large‐scale component of the parameter field. These concepts are illustrated by performing simple analytical and numerical calculations.