Generalized chloride mass balance: Forward and inverse solutions for one-dimensional tracer convection under transient flux

Abstract

Forward and inverse solutions are provided for analysis of inert tracer profiles resulting from one-dimensional convective transport under fluxes which vary with time and space separately. The developments are displayed as an extension of conventional chloride mass balance (CMB) techniques to account for transient as well as space-dependent water fluxes. The conventional chloride mass balance has been used over two decades to estimate recharge over large time scales in arid environments. In this mass balance approach, the chloride concentration in the pore water, originating from atmospheric fallout, is inversely proportional to the flux of water through the sediments. The CMB method is especially applicable to arid and semi-arid regions where evapotranspirative enrichment of the pore water produces a distinct chloride profile in the unsaturated zone. The solutions presented allow incorporation of transient fluxes and boundary conditions in CMB analysis, and allow analysis of tracer profile data which is not constant with depth below extraction zone in terms of a rational water transport model. A closed-form inverse solution is derived which shows uniqueness of model parameter and boundary condition (including paleoprecipitation) estimation, for the specified flow model. Recent expressions of the conventional chloride mass balance technique are derived from the general model presented here; the conventional CMB is shown to be fully compatible with this transient flow model and it requires the steady-state assumption on chloride mass deposition only (and not on water fluxes or boundary conditions). The solutions and results are demonstrated on chloride profile data from west central New Mexico.