Transient water age distributions in environmental flow systems: The time-marching Laplace transform solution technique

Abstract

Environmental fluid circulations are very often characterized by analyzing the fate and behavior of natural and anthropogenic tracers. Among these tracers, age is taken as an ideal tracer which can yield interesting diagnoses, as for example the characterization of the mixing and renewal of water masses, of the fate and mixing of contaminants, or the calibration of hydrodispersive parameters used by numerical models. Such diagnoses are of great interest in atmospheric and ocean circulation sciences, as well in surface and subsurface hydrology. The temporal evolution of groundwater age and its frequency distributions can display important changes as flow regimes vary due to natural change in climate and hydrologic conditions and/or human induced pressures on the resource to satisfy the water demand. Groundwater age being nowadays frequently used to investigate reservoir properties and recharge conditions, special attention needs to be put on the way this property is characterized, would it be using isotopic methods or mathematical modeling. Steady state age frequency distributions can be modeled using standard numerical techniques since the general balance equation describing age transport under steady state flow conditions is exactly equivalent to a standard advection-dispersion equation. The time-dependent problem is however described by an extended transport operator that incorporates an additional coordinate for water age. The consequence is that numerical solutions can hardly be achieved, especially for real 3-D applications over large time periods of interest. A novel algorithm for solving the age distribution problem under time-varying flow regimes is presented and, for some specific configurations, extended to the problem of generalized component exposure time. The algorithm combines the Laplace transform technique applied to the age (or exposure time) coordinate with standard time-marching schemes. The method is validated and illustrated using analytical and numerical solutions considering 1-D, 2-D, and 3-D theoretical groundwater flow domains. Copyright 2012 by the American Geophysical Union.