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BEHAVIOR OF SENSITIVITIES IN THE ONE-DIMENSIONAL ADVECTION-DISPERSION EQUATION: IMPLICATIONS FOR PARAMETER ESTIMATION AND SAMPLING DESIGN.

Water Resources Research

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Abstract

The spatial and temporal variability of sensitivities has a significant impact on parameter estimation and sampling design for studies of solute transport in porous media. Physical insight into the behavior of sensitivities is offered through an analysis of analytically derived sensitivities for the one-dimensional form of the advection-dispersion equation. When parameters are estimated in regression models of one-dimensional transport, the spatial and temporal variability in sensitivities influences variance and covariance of parameter estimates. Several principles account for the observed influence of sensitivities on parameter uncertainty. (1) Information about a physical parameter may be most accurately gained at points in space and time. (2) As the distance of observation points from the upstream boundary increases, maximum sensitivity to velocity during passage of the solute front increases. (3) The frequency of sampling must be 'in phase' with the S shape of the dispersion sensitivity curve to yield the most information on dispersion. (4) The sensitivity to the dispersion coefficient is usually at least an order of magnitude less than the sensitivity to velocity. (5) The assumed probability distribution of random error in observations of solute concentration determines the form of the sensitivities. (6) If variance in random error in observations is large, trends in sensitivities of observation points may be obscured by noise. (7) Designs that minimize the variance of one parameter may not necessarily minimize the variance of other parameters.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
BEHAVIOR OF SENSITIVITIES IN THE ONE-DIMENSIONAL ADVECTION-DISPERSION EQUATION: IMPLICATIONS FOR PARAMETER ESTIMATION AND SAMPLING DESIGN.
Series title:
Water Resources Research
Volume
23
Issue:
2
Year Published:
1987
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Water Resources Research
First page:
253
Last page:
272
Number of Pages:
20