On Using Lumped Parameter Models and Temperature Cycles in Heterogeneous Aquifers.

The use of the annual cycles of stable isotopes to estimate the parameters of transit time distribution (TTD) functions has been recently criticized by Kirchner who showed that if the catchment is heterogeneous the mean residence time calculated from the damping of the amplitude of the input signal is often underestimated by large factors. We modify Kirchner's initial analysis and show that the estimation bias is a function of the degree of heterogeneity. In low heterogeneity cases corresponding to permeable aquifers, the TTD of a simple exponential model developed assuming a homogeneous medium deviates only slightly from the true TTD, and thus estimated and true mean transit times are close. We also develop and test for a sandstone aquifer a model predicting the temperature amplitude of water at the outlet of a groundwater system from the annual air temperature cycle, and show that even though temperature is not a conservative tracer, it can be used to calibrate a lumped parameter model describing the TTD of the aquifer.

Evaluation of the hydrological flow paths in a gravel bed filter modeling a horizontal subsurface flow wetland by using a multi-tracer experiment.

In recent years, constructed wetland systems have become into focus as means of cost-efficient organic contaminant management. Wetland systems provide a highly reactive environment in which several removal pathways of organic chemicals may be present at the same time; however, specific elimination processes and hydraulic conditions are usually separately investigated and thus not fully understood. The flow system in a three dimensional pilot-scale horizontal subsurface constructed wetland was investigated applying a multi-tracer test combined with a mathematical model to evaluate the flow and transport processes. The results indicate the existence of a multiple flow system with two distinct flow paths through the gravel bed and a preferential flow at the bottom transporting 68% of tracer mass resulting from the inflow design of the model wetland system. There the removal of main contaminant chlorobenzene was up to 52% based on different calculation approaches. Determined retention times in the range of 22d to 32.5d the wetland has a heterogeneous flow pattern. Differences between simulated and measured tracer concentrations in the upper sediment indicate diffusion dominated processes due to stagnant water zones. The tracer study combining experimental evaluation with mathematical modeling demonstrated the complexity of flow and transport processes in the constructed wetlands which need to be taken into account during interpretation of the determining attenuation processes.

Response and recovery of a pristine groundwater ecosystem impacted by toluene contamination - A meso-scale indoor aquifer experiment.

Microbial communities are the driving force behind the degradation of contaminants like aromatic hydrocarbons in groundwater ecosystems. However, little is known about the response of native microbial communities to contamination in pristine environments as well as their potential to recover from a contamination event. Here, we used an indoor aquifer mesocosm filled with sandy quaternary calciferous sediment that was continuously fed with pristine groundwater to study the response, resistance and resilience of microbial communities to toluene contamination over a period of almost two years, comprising 132days of toluene exposure followed by nearly 600days of recovery. We observed an unexpectedly high intrinsic potential for toluene degradation, starting within the first two weeks after the first exposure. The contamination led to a shift from oxic to anoxic, primarily nitrate-reducing conditions as well as marked cell growth inside the contaminant plume. Depth-resolved community fingerprinting revealed a low resistance of the native microbial community to the perturbation induced by the exposure to toluene. Distinct populations that were dominated by a small number of operational taxonomic units (OTUs) rapidly emerged inside the plume and at the plume fringes, partially replacing the original community. During the recovery period physico-chemical conditions were restored to the pristine state within about 35days, whereas the recovery of the biological parameters was much slower and the community composition inside the former plume area had not recovered to the original state by the end of the experiment. These results demonstrate the low resilience of sediment-associated groundwater microbial communities to organic pollution and underline that recovery of groundwater ecosystems cannot be assessed solely by physico-chemical parameters.

Interpretation of environmental tracer data for conceptual understanding of groundwater flow: an application for fractured aquifer systems in the Klodzko Basin, Sudetes, Poland.

Environmental isotopes and hydrogeological data have been used for the construction of a conceptual model of fresh groundwater flow in the Klodzko Basin, Sudetes, Poland. The model has allowed the verification of a groundwater circulation scheme resulting from the general morphological assumptions and the recharge role to the surrounding mountains. Combined interpretation of the tritium ages and the isotopic altitude effect allowed determining the volume of water-bearing rock Vr and hydrogeological parameters of systems drained by springs and wells. Prior to the final determination of the recharge zone of individual objects, calculations were made for the thickness of the flow zone (h) and the distance from the recharge zone to the drainage point (L). The recharge areas for springs are located within a distance of 1-1.5 km and are characterized by a width of 0.75-1.65 km. The recharge area of wells is located in significantly longer distances of 2.1-12 km but yet definitely lower width. The recharge of groundwater from the Western direction seems to be obvious for all the wells and springs located westward from Nysa Klodzka River. The eastern component of the recharge appeared during the interpretation of the well in Dlugopole. Dedicated to Professor Peter Fritz on the occasion of his 80th birthday.

Analytical transport modelling of metabolites formed in dual-porosity media.

Contaminants like nitroaromatic compounds can be degraded in the subsurface to similar or even more toxic metabolites. Degradation or transformation rates are dependent on physical, chemical and biological properties which can be different in sedimentological layers or other heterogeneous structures of aquifers. Sediments with low hydraulic conductivity can even consist of immobile water. These regions are only accessible by diffusion. Most modelling approaches accounting for immobile water regions focused on the mathematical description of the transport and decay of the parent compound. The objective of this study was to develop an analytical model to quantify the transport and formation of a metabolite in dual-porosity media describing the exchange between mobile and immobile water regions based on the metabolite's diffusion coefficient. Column experiments with a well-defined immobile water region were performed under anoxic conditions at three different water flow velocities. The model compound 4-Cl-nitrobenzene was reduced to 4-Cl-aniline (4-Cl-An) by surface-bound Fe (II) species within the immobile water region. Transport and formation of the metabolite were quantified with a modified solution of the single fissure dispersion model assuming additionally for the region with immobile water first-order metabolite production, irreversible sorption and an instantaneous equilibrium sorption. The number of unknown fitting parameters was reduced to two (sorption rate and retardation factor) by stepwise parameter estimation using tracer and parent compound data. Experimental results of the metabolite for each water flow velocity were successfully described with a first-order production term (λ prod = 1.51 ± 0.08 h-1), retardation factor (R im = 2.94 ± 0.45) and first-order irreversible sorption rate (K im = 0.39 ± 0.16 h-1) within the immobile water region. Model results supported that 4-Cl-An was formed within the immobile water region. 4-Cl-An sorbed instantaneously onto the clay matrix while a fraction was irreversibly sorbed. Experimental results and the provided analytical solution help to improve the understanding about reactive transport and the formation of metabolites in dual-porosity media.

Quantifying the impact of immobile water regions on the fate of nitroaromatic compounds in dual-porosity media.

Nitroaromatic compounds (NACs) are reduced by structural or surface bound Fe (II) species under anaerobic conditions in the subsurface. This reaction preferentially occurs on clay minerals which are mainly present in areas with low hydraulic conductivity containing nearly immobile water. Diffusion is the dominating transport process in these zones. Due to the complexity in such heterogeneous systems, the mathematical prediction of reactive solute transport taking into account diffusive mass exchange into immobile water regions still remains challenging. Therefore, the influence of immobile water regions on the fate of 4-Cl-Nitrobenzene (4-Cl-Nb) was quantified in dual-porosity column experiments at three different mean transit times under saturated anaerobic conditions in the presence of soluble Fe (II). A multi-tracer approach and a Single Fissure Dispersion Model (SFDM) were used to estimate input parameter to further model the transport of 4-Cl-Nb. Reactive solute transport of 4-Cl-Nb was quantified considering instantaneous sorption on to the clay matrix and a reduction within the immobile water region following first-order kinetics. The experimental results indicated that sorption onto the clay matrix enhanced the mass exchange of 4-Cl-Nb into immobile water region compared to nonreactive solutes. At the same time the abiotic reduction of 4-Cl-Nb limited the process of back diffusion to mobile water regions. Fitted retardation factors (Rim=4.62±0.68) and decay rates (k=1.51±0.08h(-1)) were independent on tested flow velocities. Findings of this study can advance the understanding on the fate of NACs in the subsurface which is essential for prediction of reactive solute transport at field scale.

Tracing stable isotopes (δ²H and δ¹8O) from meteoric water to groundwater in the Densu River basin of Ghana.

This study represents the first attempt to study soil water δ(18)O profiles in Ghana using a mechanical auger. In this paper, the characteristics of δ(18)O and δ(2)H in rain water, surface water, soil water and groundwater have been used to understand the transformation mechanism of rain water to groundwater. Rain waters were sampled in Koforidua and Accra. Surface water and groundwater were sampled from the Densu River and selected boreholes in the basin, respectively. Soil waters were taken from three typical sites, namely, Potroase (POT), Teacher Mante (TM) and Ayikai Doblo (AD) in the northern, middle and southern zone from 0.00- to 6-m depth. The soil water was extracted using vacuum distillation method. The distribution of the stable isotopes of rain water is influenced by rainfall amount with minimal temperature effect. In general, the soil water is of meteoric origin undergoing fractionation-controlled evaporation. In the middle zone, the soil water shows some evidence of recharge from enriched source. The three profiles show similar trend of enriched values in the upper depths with gradual depletions of δ(18)O with depth. The POT profile showed relatively more depleted values suggesting a fast infiltration. In all the three profiles, soil waters below 3 m were found to contribute to groundwater recharge with piston flow as the dominant mechanism. The study also revealed that there is a significant contribution of enrich source to the groundwater system leading to the dilution of the infiltrating water by the large aquifer.

Intrinsic potential for immediate biodegradation of toluene in a pristine, energy-limited aquifer.

Pristine and energy-limited aquifers are considered to have a low resistance and resilience towards organic pollution. An experiment in an indoor aquifer system revealed an unexpected high intrinsic potential for the attenuation of a short-term toluene contamination. A 30 h pulse of 486 mg of toluene, used as a model contaminant, and deuterated water (D2O) through an initially pristine, oxic, and organic carbon poor sandy aquifer revealed an immediate aerobic toluene degradation potential. Based on contaminant and tracer break-through curves, as well as mass balance analyses and reactive transport modelling, a contaminant removal of 40 % over a transport distance of only 4.2 m in less than one week of travel time was obtained. The mean first-order degradation rate constant was λ = 0.178 day(-1), corresponding to a half-life time constant T1/2 of 3.87 days. Toluene-specific stable carbon isotope analysis independently proved that the contaminant mass removal can be attributed to microbial biodegradation. Since average doubling times of indigenous bacterial communities were in the range of months to years, the aerobic biodegradation potential observed is assumed to be present and active in the pristine, energy-limited groundwater ecosystems at any time. Follow-up experiments and field studies will help to quantify the immediate natural attenuation potential of aquifers for selected priority contaminants and will try to identify the key-degraders within the autochthonous microbial communities.

Direct experimental evidence of non-first order degradation kinetics and sorption-induced isotopic fractionation in a mesoscale aquifer: 13C/12C analysis of a transient toluene pulse.

The injection of a mixed toluene and D2O (conservative tracer) pulse into a pristine mesoscale aquifer enabled a first direct experimental comparison of contaminant-specific isotopic fractionation from sorption versus biodegradation and transverse dispersion on a relevant scale. Water samples were taken from two vertically resolved sampling ports at 4.2 m distance. Analysis of deuterium and toluene concentrations allowed quantifying the extent of sorption (R = 1.25) and biodegradation (37% and 44% of initial toluene at the two sampling ports). Sorption and biodegradation were found to directly affect toluene (13)C/(12)C breakthrough curves. In particular, isotope trends demonstrated that biodegradation underwent Michaelis-Menten kinetics rather than first-order kinetics. Carbon isotope enrichment factors obtained from an optimized reactive transport model (Eckert et al., this issue) including a possible isotope fractionation of transverse dispersion were ε(equ)(sorption) = -0.31 ‰, ε(kin)(transverse-dispersion) = -0.82 ‰, and ε(kin)(biodegradation) = -2.15 ‰. Extrapolation of our results to the scenario of a continuous injection predicted that (i) the bias in isotope fractionation from sorption, but not transverse dispersion, may be avoided when the plume reaches steady-state; and (ii) the relevance from both processes is expected to decrease at longer flow distances when isotope fractionation of degradation increasingly dominates.

Estimation of groundwater residence time using environmental radioisotopes (14C,T) in carbonate aquifers, southern Poland.

Triassic carbonate aquifers in the Upper Silesia region, affected by intense withdrawal, have been investigated by means of isotopic analyses of (14)C, δ(13)C, δ(2)H, δ(18)O and (3)H. The isotopic examinations were carried out in the 1970s and in the early 1980s, and it was the first application of tracers to estimate age and vulnerability for the contamination of groundwater in this region. Similar isotopic analyses were conducted in 2007 and 2008 with the same Triassic carbonate formation. The isotopic examinations were performed within the confined part of the carbonate formation, wherein aquifers are covered by semi-permeable deposits. The direct recharge of the aquifer occurs in the outcrop areas, but it mainly takes place due to percolation of the water through aquitards and erosional windows. The Triassic aquifer has been intensively drained by wells and by lead-zinc mines. Nowadays, the declining water demand and closure of some mines have induced a significant increase in the water table level. The detailed analysis of the results, including the radiocarbon age corrections and the comparison of radioisotope activities, has made it possible to estimate the range of residence time within the carbonate Triassic aquifer. This range from several tens to several tens of thousands indicates that the recharge of aquifers might have occurred between modern times and the Pleistocene. The apparent age of the water estimated on the basis of (14)C activity was corrected considering the carbon isotope exchange and the diffusion between mobile water in fractures and stagnant water in micropores. The obtained corrected period of recharge corresponds to the result of investigations of noble gases, which were carried out in the 1990s. In almost half of the cases, groundwater is a mixture of young and old water. The mixing processes occur mainly in areas of heavy exploitation of the aquifer.

Transport and bacterial interactions of three bacterial strains in saturated column experiments.

The impact of bacteria-solid and bacteria-bacteria interactions on the transport of Klebsiella oxytoca, Burkholderia cepacia G4PR1, and Pseudomonas sp. #5 was investigated in saturated sand column experiments (L = 114 mm; ø = 33 mm) under constant water velocities (∼ 5 cm · h(-1)). Bacterial strains were injected into the columns as pulses either individually, simultaneously, or successively. A one-dimensional mathematical model for advective-dispersive transport and for irreversible and reversible bacterial kinetic sorption was used to analyze the bacterial breakthrough curves. Different sorption parameters were obtained for each strain in each of the three experimental setups. In the presence of other bacteria, sorption parameters for B. cepacia G4PR1 remained similar to results from individual experiments, indicating the presence of other bacteria generally had a lesser influence on its migration than for the other bacteria. K. oxytoca is more competitive for the sorption sites when simultaneously injected with the other bacteria. Ps. sp. #5 generally yielded the greatest detachment rates and the least affinity to attach to the sand, indicative of its mobility in groundwater systems. The results of this study clearly indicate both bacteria-solid and bacteria-bacteria interactions influence the migration of bacteria. A more complete understanding of such interactions is necessary to determine potential migration in groundwater systems.

Regional transport modelling for nitrate trend assessment and forecasting in a chalk aquifer.

Regional degradation of groundwater resources by nitrate has become one of the main challenges for water managers worldwide. Regulations have been defined to reverse observed nitrate trends in groundwater bodies, such as the Water Framework Directive and the Groundwater Daughter Directive in the European Union. In such a context, one of the main challenges remains to develop efficient approaches for groundwater quality assessment at regional scale, including quantitative numerical modelling, as a decision support for groundwater management. A new approach combining the use of environmental tracers and the innovative 'Hybrid Finite Element Mixing Cell' (HFEMC) modelling technique is developed to study and forecast the groundwater quality at the regional scale, with an application to a regional chalk aquifer in the Geer basin in Belgium. Tritium data and nitrate time series are used to produce a conceptual model for regional groundwater flow and contaminant transport in the combined unsaturated and saturated zones of the chalk aquifer. This shows that the spatial distribution of the contamination in the Geer basin is essentially linked to the hydrodynamic conditions prevailing in the basin, more precisely to groundwater age and mixing and not to the spatial patterns of land use or local hydrodispersive processes. A three-dimensional regional scale groundwater flow and solute transport model is developed. It is able to reproduce the spatial patterns of tritium and nitrate and the observed nitrate trends in the chalk aquifer and it is used to predict the evolution of nitrate concentrations in the basin. The modelling application shows that the global inertia of groundwater quality is strong in the basin and trend reversal is not expected to occur before the 2015 deadline fixed by the European Water Framework Directive. The expected time required for trend reversal ranges between 5 and more than 50 years, depending on the location in the basin and the expected reduction in nitrate application. To reach a good chemical status, nitrate concentrations in the infiltrating water should be reduced as soon as possible below 50mg/l; however, even in that case, more than 50 years is needed to fully reverse upward trends.

Occurrence and transport of pharmaceuticals in a karst groundwater system affected by domestic wastewater treatment plants.

The occurrence of two pharmaceuticals, ibuprofen and diclofenac, in a vulnerable karst groundwater system was investigated. The hydrogeology of the karst system was identified by collecting (3)H samples in groundwater over 27years and by performing tracer tests. The isotopes and tracer data were interpreted by mathematical modeling to estimate the mean transit time of water and to characterize the hydrogeological flow paths in the groundwater system. By this approach, a mean (3)H transit time of 4.6 years for the fissured-porous karst aquifer was determined, whereas the fast flowing water in the conduit system showed a mean transit time of days. Both pharmaceuticals which infiltrated along sinkholes and small streams into the karst system were detected in concentrations of up to approximately 1 microg/L in effluent water of the wastewater treatment plants. Diclofenac was present in most samples collected from four springs discharging the karst groundwater to the rivers Altmühl and Anlauter in concentrations between 3.6 and 15.4 ng/L. In contrast, ibuprofen was rarely detected in groundwater. The results of this study suggest that both pharmaceuticals move into the fractured system of the karst system and go into storage. Thus dilution processes are the dominant control on the concentrations of both pharmaceuticals in the fractured system, whereas biodegradation is likely less important.

Mixing-controlled biodegradation in a toluene plume--results from two-dimensional laboratory experiments.

Various abiotic and biotic processes such as sorption, dilution, and degradation are known to affect the fate of organic contaminants, such as petroleum hydrocarbons in saturated porous media. Reactive transport modeling of such plumes indicates that the biodegradation of organic pollutants is, in many cases, controlled by mixing and therefore occurs locally at the plume's fringes, where electron donors and electron-acceptors mix. Herein, we aim to test whether this hypothesis can be verified by experimental results obtained from aerobic and anaerobic degradation experiments in two-dimensional sediment microcosms. Toluene was selected as a model compound for oxidizable contaminants. The two-dimensional microcosm was filled with quartz sand and operated under controlled flow conditions simulating a contaminant plume in otherwise uncontaminated groundwater. Aerobic degradation of toluene by Pseudomonas putida mt-2 reduced a continuous 8.7 mg L(-1) toluene concentration by 35% over a transport distance of 78 cm in 15.5 h. In comparison, under similar conditions Aromatoleum aromaticum strain EbN1 degraded 98% of the toluene infiltrated using nitrate (68.5+/-6.2 mg L(-1)) as electron acceptor. A major part of the biodegradation activity was located at the plume fringes and the slope of the electron-acceptor gradient was steeper during periods of active biodegradation. The distribution of toluene and the significant overlap of nitrate at the plume's fringe indicate that biokinetic and/or microscale transport processes may constitute additional limiting factors. Experimental data is corroborated with results from a reactive transport model using double Monod kinetics. The outcome of the study shows that in order to simulate degradation in contaminant plumes, detailed data sets are required to test the applicability of models. These will have to deal with the incorporation of existing parameters coding for substrate conversion kinetics and microbial growth.

Isotope evidence of palaeorecharge and palaeoclimate in the deep confined aquifers of the Chad Basin, NE Nigeria.

Groundwaters from the Quaternary and Continental Terminal Formations in the Nigeria sector of the Chad Sedimentary Basin (CSB) together with rain and surface waters have been chemically and isotopically analyzed in order to investigate sources and ages of waters, possible modern renewal and mixing of the deep groundwaters, and to infer palaeoclimate incidences. Most of the waters are slightly to moderately mineralized and are of Na-HCO(3) type induced mainly by Na-feldspar weathering and ion exchange reactions. The wide range of the delta(18)O and delta(2)H values and (3)H contents in the upper aquifer indicate replenishment with modern meteoric water. However, the deep system (middle and lower aquifers) with a narrow range of depleted stable isotope values and low (14)C activities indicates that these waters have a palaeometeoric origin. The period of infiltration was within the humid and cooler period (35 to 40 ka BP) prior to the Last Glacial Maximum. In addition, the isotope compositions of the deep system show no mixing with modern waters. These results are in agreement with other palaeorecord studies in the Sahel zone during this period.

A multitracer test proving the reliability of Rayleigh equation-based approach for assessing biodegradation in a BTEX contaminated aquifer.

Compound-specific stable isotope analysis (CSIA) is one of the most important methods for assessing biodegradation activities in contaminated aquifers. Although the concept is straightforward, the proof that the method cannot be only used for a qualitative analysis but also to quantify biodegradation in the subsurface was missing. We therefore performed a multitracer test in the field with ring-deuterated (d5) and completely (d8) deuterium-labeled toluene isotopologues (400 g) as reactive tracers as well as bromide as a conservative tracer. The compounds were injected into the anoxic zone of a BTEX plume located down-gradient of the contaminant source. Over a period of 4.5 months the tracer concentrations were analyzed at two control planes located 24 and 35 m downgradient of the injection well. Deuterium-labeled benzylsuccinate was found in the aquifer, indicating the anaerobic biodegradation of deuterated toluene via the benzylsuccinate synthase pathway. Three independent methods were applied to quantify biodegradation of deuterated toluene. First, fractionation of toluene-d8 and toluene-d5 using the Rayleigh equation and an appropriate laboratory-derived isotope fractionation factor was used for the calculation of the microbial decomposition of deuterated toluene isotopologues (CSIA-method). Second, the biodegradation was quantified by the changes of the concentrations of deuterated toluene relative to bromide. Both methods gave similar results, implying that the CSIA-method is a reliable tool to quantify biodegradation in contaminated aquifers. The results of both methods yielded a biodegradation of deuterated toluene isotopologues of approximately 23-29% for the first and 44-51% for the second control plane. Third, the mineralization of deuterated toluene isotopologues was verified by determination of the enrichment of deuterium in the groundwater. This method indicated that parts of deuterium were assimilated into the biomass of toluene degrading microorganisms.

Groundwater salinization in the Saloum (Senegal) delta aquifer: minor elements and isotopic indicators.

The hydrochemistry of minor elements bromide (Br), boron (B), strontium (Sr), environmental stable isotopes (18O and 2H) together with major-ion chemistry (chloride, sodium, calcium) has been used to constrain the source(s), relative age, and processes of salinization in the Continental Terminal (CT) aquifer in the Saloum (mid-west Senegal) region. Seventy-one groundwater wells which include 24 wells contaminated by saltwater and three sites along the hypersaline Saloum River were sampled to obtain additional information on the hydrochemical characteristics of the groundwater defined in previous studies. Use of Br against Cl confirms the Saloum River saline water intrusion up to a contribution of 7% into the aquifer. In addition to this recent intrusion, a relatively ancient intrusion of the Saloum River water which had reached at least as far as 20 km south from the source was evidenced. The high molar ratio values of Sr/Cl and Sr/Ca indicate an additional input of strontium presumably derived from carbonate precipitation/dissolution reactions and also via adsorption reactions. The variable B concentrations (7-650 microg/L) found in the groundwater samples were tested against the binary mixing model to evaluate the processes of salinization which are responsible for the investigated system. Sorption of B and depletion of Na occur as the Saloum river water intrudes the aquifer (salinization) in the northern part of the region, whereas B desorption and Na enrichment occur as the fresh groundwater flushing displaces the saline waters in the coastal strip (refreshening). In the central zone where ancient intrusion prevailed, the process of freshening of the saline groundwater is indicated by the changes in major-ion chemistry as well as B desorption and Na enrichment. In addition to these processes, stable isotopes reveal that mixing with recently infiltrating waters and evaporation contribute to the changes in isotopic signature.

Interpretation of environmental tracers in groundwater systems with stagnant water zones.

Lumped-parameter models are commonly applied for determining the age of water from time records of transient environmental tracers. The simplest models (e.g. piston flow or exponential) are also applicable for dating based on the decay or accumulation of tracers in groundwater systems. The models are based on the assumption that the transit time distribution function (exit age distribution function) of the tracer particles in the investigated system adequately represents the distribution of flow lines and is described by a simple function. A chosen or fitted function (called the response function) describes the transit time distribution of a tracer which would be observed at the output (discharge area, spring, stream, or pumping wells) in the case of an instantaneous injection at the entrance (recharge area). Due to large space and time scales, response functions are not measurable in groundwater systems, therefore, functions known from other fields of science, mainly from chemical engineering, are usually used. The type of response function and the values of its parameters define the lumped-parameter model of a system. The main parameter is the mean transit time of tracer through the system, which under favourable conditions may represent the mean age of mobile water. The parameters of the model are found by fitting calculated concentrations to the experimental records of concentrations measured at the outlet. The mean transit time of tracer (often called the tracer age), whether equal to the mean age of water or not, serves in adequate combinations with other data for determining other useful parameters, e.g. the recharge rate or the content of water in the system. The transit time distribution and its mean value serve for confirmation or determination of the conceptual model of the system and/or estimation of its potential vulnerability to anthropogenic pollution. In the interpretation of environmental tracer data with the aid of the lumped-parameter models, the influence of diffusion exchange between mobile water and stagnant or quasi-stagnant water is seldom considered, though it leads to large differences between tracer and water ages. Therefore, the article is focused on the transit time distribution functions of the most common lumped-parameter models, particularly those applicable for the interpretation of environmental tracer data in double-porosity aquifers, or aquifers in which aquitard diffusion may play an important role. A case study is recalled for a confined aquifer in which the diffusion exchange with aquitard most probably strongly influenced the transport of environmental tracers. Another case study presented is related to the interpretation of environmental tracer data obtained from lysimeters installed in the unsaturated zone with a fraction of stagnant water.