Papers: 'Residence Time Distributions for Hydrologic Systems - Mechanistic Foundations and Steady-State Analytical Solutions'; and 2) 'Generation of Groundwater Age Distributions'

As I am wont to do with increasing frequency I stumbled across this December 2016 review paper from the Journal of Hydrology: Residence Time Distributions for Hydrologic Systems: Mechanistic Foundations and Steady-State Analytical Solutions by Sarah Leray, Nicholas B. Engdahl, Arash Massoudieh, Etienne Bresciano, James McCallum.

Download JH_RTDs_Mechanistic_2016

Highlights

•Steady-state analytical solutions for residence time distributions are reviewed.

•Analytical solutions assume simple and parameterizable physical configurations.

•Physically-based solutions are a powerful tool for understanding hydrologic systems.

•They are to be used with careful account of the conditions for their relevance.

•Alternative methods (e.g. shape-free distributions) exist for more complex systems.

Summary
This review presents the physical mechanisms generating residence time distributions (RTDs) in hydrologic systems with a focus on steady-state analytical solutions. Steady-state approximations of the RTD in hydrologic systems have seen widespread use over the last half-century because they provide a convenient, simplified modeling framework for a wide range of problems. The concept of an RTD is useful anytime that characterization of the timescales of flow and transport in hydrologic systems is important, which includes topics like water quality, water resource management, contaminant transport, and ecosystem preservation. Analytical solutions are often adopted as a model of the RTD and a broad spectrum of models from many disciplines has been applied. Although these solutions are typically reduced in dimensionality and limited in complexity, their ease of use makes them preferred tools, specifically for the interpretation of tracer data. Our review begins with the mechanistic basis for the governing equations, highlighting the physics for generating a RTD, and a catalog of analytical solutions follows. This catalog explains the geometry, boundary conditions and physical aspects of the hydrologic systems, as well as the sampling conditions, that altogether give rise to specific RTDs. The similarities between models are noted, as are the appropriate conditions for their applicability. The presentation of simple solutions is followed by a presentation of more complicated analytical models for RTDs, including serial and parallel combinations, lagged systems, and non-Fickian models. The conditions for the appropriate use of analytical solutions are discussed, and we close with some thoughts on potential applications, alternative approaches, and future directions for modeling hydrologic residence time.

This paper reminds me of the work I did for my PhD and during my early career. I worked mainly in the numerical realm whereas some of my students, primarily Isam Amin (see Amin and Campana paper), did analytical mathematical work.

Here is a 1987 paper of mine from the journal Groundwater: Generation of Ground-Water Age Distributions.

Download Campana-1987-Groundwater

Abstract
Discrete‐state compartment (DSC) models and their associated age distribution functions permit the quantitative interpretation of environmental radioisotope data such as carbon‐14 ground‐water decay ages. These mixing‐cell models offer a means for constructing ground‐water flow models that can be used to relate decay ages to ground‐water mean ages. In addition, DSC models can also generate the entire distribution of ages in various subregions of a ground‐water reservoir. A preexisting DSC model of a portion of the Tucson Basin alluvial aquifer is used as an example. Ground‐water mean ages in this aquifer range from 100 to almost 15,000 years old, with the oldest waters about 40,000 years old. Since the ground‐water ages are not normally distributed, means and medians are not equivalent. The results indicate that care must be used in interpreting both ground‐water radioisotope decay ages as well as mean ground‐water ages and that knowledge of the entire age distribution is preferable. Age distributions are especially useful in hydrogeologic studies in which mixing is important and may find use in paleohydrogeologic investigations.

 

Enjoy! I sure will...... 

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- Jack Handey

Comments

[Michael]

Interesting stuff. I believe Kick Hemker - http://www.microfem.com - solved most of this around the same time (late 1980s-early 1990s) using finite elements. The models could later be calibrated with isotopes. Flownet (latest version 1991) can calculate this for cross-sections/profiles.