Estimation of spatial recharge distribution using environmental isotopes and hydrochemical data, I. Mathematical model and application to synthetic data

A mathematical model is proposed to estimate the spatial distribution of annual recharge rates into an aquifer using environmental isotopes and hydrochemical data. The aquifer is divided into cells within which the isotopes and dissolved constituents are assumed to undergo complete mixing. For each mixing cell mass-balance equations expressing the conservation of water, isotopes and dissolved chemicals are written. These equations are solved simultaneously for unknown rates of recharge into the various cells by quadratic programming. The degree to which individual dissolved constituents may be considered conservative is tested a-priori by means of a chemical equilibrium model such as wateqf. Constituents which do not pass this test are either disregarded or suitably assigned a small weight in the quadratic program. In Part I, the model is applied to synthetic data corrupted by random noise and its sensitivity to input errors is examined. Part II^* * Adar and Neuman (this volume). describes an application of the model to real data from the Aravaipa Valley in southern Arizona.