A transient flux model for convective infiltration: Forward and inverse solutions for chloride mass balance studies

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 approach is developed as an extension of conventional chloride mass balance techniques used to analyze vertical unsaturated aqueous phase transport over large timescales in arid environments. This generalized chloride mass balance (GCMB) approach allows incorporation of transient fluxes and boundary values of precipitation and chloride mass deposition and allows analysis of a tracer profile which does not remain constant with depth below the extraction zone, in terms of a purely convective water transport model. The conventional quasi-steady state chloride mass balance (CMB) can be derived from the transient GCMB model developed here. By specifying a link between precipitation and recharge, closed-form forward and inverse solutions relating soil water chloride concentrations to transient boundary fluxes are obtained. This link is necessary for quantitative analysis of variable chloride profiles arising from climatic change. The GCMB can use transient chloride mass deposition rates, transient precipitation, and transient evapotranspiration rates. If two of these quantities are known or if the time frame is constrained such that a quantity can be treated as constant, then the inverse model can be used to determine the third. When mixing processes are limited, the GCMB can provide an alternative approach for estimating paleoprecipitation for performance-assessment modeling. The GCMB model is demonstrated with the following applications: (1) determination of time-varying precipitation from a field chloride profile and (2) evaluation of transient changes in water extraction by evapotranspiration and transient recharge associated with a change in land use.