## 1. Introduction

[2] Environmental tracer methods are nowadays routine tools for obtaining information about the flow dynamics of groundwater. One of the most important applications is for groundwater dating. Amongst the most frequently used dating tracers we find: ^{3}H/^{3}He [*Schlosser et al.*, 1988, 1989; *Poreda et al.*, 1988; *Solomon and Cook*, 1999], ^{85}Kr [*Smethie et al.*, 1992; *Loosli et al.*, 1999], CFCs [*Busenberg and Plummer*, 1992; *Plummer and Busenberg*, 1999], ^{14}C [*Fontes and Garnier*, 1979; *Mook*, 1980; *Kalin*, 1999]. Other environmental tracers provide information on the origin and recharge conditions of the groundwater, in particular the stable noble gases [*Mazor*, 1972; *Stute et al.*, 1992; *Stute and Schlosser*, 1999] and the stable isotopes of the water ^{2}H and ^{18}O [*Coplen et al.*, 1999].

[3] Many processes and parameters determine the concentrations of isotopes or chemical tracers in groundwater (e.g., radioactive decay, hydrodynamic dispersion, mixing, chemical degradation, recharge date, transport time through unsaturated and saturated zones, etc.). However, in particular cases factors that lead to a misinterpretation of tracer concentrations in terms of residence time can provide important and additional information such as mixing and dispersion in the aquifer. The interpretation of tracer concentrations is commonly carried out by models that try to mathematically describe the age distribution of sampled groundwater. The estimation of a set of free model parameters requires a corresponding number of measurements. This can be achieved with a high spatial sampling density, by time series at single locations, or by applying multitracer measurements at selected locations, which is the case for the present study. The latter technique is particularly useful to consistently interpret single well measurements.

[4] The study area is located in a semiconfined subsystem of the Paris Basin where the main objective was to determine the age structure of the groundwater. The limited number of sampling sites in the project area requires the application of multiple groundwater dating tracers and the use of lumped parameter approaches for the assessment of groundwater dynamics where the choice of an appropriate age weighting function that appropriately represents the hydrogeological situation can be validated using the measured tracer data. Thus the results of several models can be compared and also the sensitivity of the model to parameters such as the mean residence time (MRT) or recharge rate can be investigated [*Rueedi et al.*, 2005].

[5] The commonly adopted approach for dating and quantifying the portion of young (postbomb) water components is the combination of ^{3}H with either ^{3}He or ^{85}Kr [*Schlosser et al.*, 1989; *Solomon and Cook*, 1999; *Loosli et al.*, 1999]. However, these tracers preferentially detect the “young tail” of age distributions which may include significant amounts of prebomb water. Hence, to verify to which extent the extrapolation of the interpretation with these tracers to the “old tail” fits the real situation in the aquifer an intermediate age (<1000 years) dating technique is required, which is what ^{39}Ar enables in this study. This tracer has been proposed for dating groundwater for its ideal characteristics [*Loosli*, 1983]: a constant and well known atmospheric input concentration, no local contamination, an isotope ratio (^{39}Ar/Ar) that is insensitive to degassing or incomplete gas extraction yield, and an important dating range for groundwater hydrology. Argon 39 has been previously used in selected studies [*Oeschger et al.*, 1974; *Andrews et al.*, 1984; *Loosli et al.*, 1989; *Pearson et al.*, 1991; *Loosli et al.*, 1992; *Beyerle et al.*, 1998; *Loosli et al.*, 1999; *Purtschert et al.*, 2001a].

[6] The knowledge of a reliable local input function is crucial for the accurate application of environmental tracers for groundwater dating. These initial concentrations may vary spatially but also as function of the depth of the water table below ground surface [*Cook and Solomon*, 1995]. Absolute as well as relative delays of different tracers become significant in thick unsaturated zones. This is the case in the investigated area with recharge depths between 20 and 40 m. Therefore a one dimensional transport model was integrated in the box model in order to calculate the tracer input at the water table. This procedure introduces additional parameters namely the porosity and tortuosity of the unsaturated soil and the recharge rate. Some of these parameters can be estimated based on complementary methods, others have to be determined by fitting to the tracer data. With the proposed inverse procedure mean recharge rates in the area of investigation can be estimated. The approach presented to investigate parameters in the Fontainebleau Sands Aquifer can be generalized and used for other tracers and for determining parameters at many other sites.