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Revisiting the Domenico plume formula through saddle-point asymptotics
Kentaro Miyamoto1, Makoto Yasojima1, Hiroaki Takemori1
1Shimadzu Techno-Research, Inc., 1 Nishinokyo Shimoaicho, Nakagyo-ku, Kyoto 604-8436, Japan.
Journal of Contaminant Hydrology
|July 8, 2026
Summary
The Domenico plume formula, used for contaminant migration screening, is derived from a Green's function solution. This study clarifies its accuracy limits and provides corrections for better environmental risk assessment.
Area of Science:
- Environmental Science
- Hydrogeology
- Geochemistry
Background:
- The Domenico plume formula is a standard tool for screening contaminant migration from sources.
- Its precise relationship with the reactive advection-dispersion equation has been unclear.
- Understanding the formula's limitations is crucial for accurate environmental risk assessment.
Purpose of the Study:
- To clarify the theoretical underpinnings of the Domenico plume formula.
- To derive corrections to the Domenico formula based on the advection-dispersion equation.
- To establish a framework for assessing the reliability of the Domenico formula.
Main Methods:
- Derivation of a finite-time saddle-point expansion from the Green's function solution for a finite rectangular source.
- Analysis of the large-distance expansion of the Green's function solution.
- Identification of leading-order, next-to-leading-order (NLO), and next-next-to-leading-order (NNLO) terms.
Main Results:
- The standard Domenico expression is identified as the far-field leading-order term.
- Explicit NLO and NNLO corrections are derived, capturing transient and steady-state discrepancies.
- A hierarchy explaining the emergence of the Domenico formula from the Green's function solution is established.
Conclusions:
- The study provides a theoretical basis for the Domenico plume formula and its limitations.
- Derived corrections enhance the accuracy of contaminant migration screening.
- A validity map guides practitioners on when to use the formula versus numerical evaluation for defensible site decisions.
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