Equivalence of the time and Laplace domain solutions for the steady state concentration of radiometric tracers and the groundwater age equation. Issue 4 (22nd April 2014)

• Record Type: Journal Article
• Authors: Engdahl, Nicholas B.
• Is Part Of: Water resources research. Volume 50:Issue 4(2014:Apr.)
• Page Start: 3602
• Page End: 3607
• Publication Date: 2014-04-22
• Subjects: Hydrology -- Periodicals; 333.91
• DOI: 10.1002/2014WR015413
• Languages: English
• ISSNs: 0043-1397

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>It has been previously shown that the normalized concentration of a radioactively decaying tracer defines one point on the Laplace transformed age distribution and that point corresponds to the decay rate of the tracer. However, it is unclear how two time domain quantities, the decay rate and normalized concentration, are related to the elements of a Laplace transformed distribution; this note clarifies these relationships mechanistically. It is shown that the Laplace transformed age distribution is equivalent to the late‐time concentration of a radiometric tracer if transport and age are both at steady state. The result is general and may be applied to any age distribution, including non‐Fickian distributions. The significance of the generality is that the steady state concentrations and known decay rates may be used to help constrain the parameters of an unknown age distribution in a wide range of flow systems.</p> </abstract>