A profile of tritium concentrations measured in the unsaturated zone in loessial sediments in a semiarid area is interpreted in terms of mobile and immobile water domains, according to a nonequilibrium transport model. The mobile domain is represented by percolating freshwater from both rain and irrigation, and the immobile one is represented by isolated fossil saline water pockets. The two domains are connected by partially saturated narrow passages within dispersed clay minerals. The transport of the mobile water is described by convective‐dispersive flow and by mass exchange between the two water domains. The relevant equations with the given initial and boundary conditions are solved numerically, and the simulated profile is adjusted to fit the measured one. In this study we concentrate on examination of the mass exchange law between the two domains. It was assumed that matrix characteristics vary in time due to the dispersion of clays at the interface between fresh and saline waters. Accordingly, a time‐dependent mass exchange was adopted, which made it possible to obtain an adequate reconstruction of the measured tritium profile. By using a least squares optimization procedure it was found that the best fit between the simulated and measured profiles is attained when the fraction of mobile water is 30%, and the rate of mass exchange decreases from 0.60 to 0.01 year−1 in 26 years. The proposed model implies is that it is the immobile water domain which contains the memory of the “high tritium period” (thermonuclear tests period) of the 1960s.