The sites for this study were the Hydrological Open Air Laboratory (HOAL) in Petzenkirchen (Fig. S2 in the Supplement), Lower Austria , and the Wüstebach headwater catchment (Fig. S1) in Germany's Eifel National Park .

The HOAL covers 66 hectares and features a humid climate with a mean annual air temperature of around 9.5 °C. The mean annual precipitation and runoff are approximately 823 and 195 mm yr⁻¹, respectively. The elevation ranges from 268 to 323 m a.s.l., with a mean slope of 8 %. Predominant soil types in the HOAL catchment include Cambisols, Planosols, Kolluvisols, and Gleysols. The geology of the catchment consists of Tertiary fine sediments of the Molasse underlain by fractured siltstone. Land use primarily includes agriculture (commonly maize, winter wheat, and rapeseed) (87 %), supplemented by forest (6 %), pasture (5 %), and paved areas (2 %) .

The Wüstebach headwater catchment, part of the Lower Rhine/Eifel Observatory within the TERENO network, covers 38.5 ha. It is characterized by a humid climate, with an annual temperature of around 7 °C, mean annual precipitation of about 1200 mm yr⁻¹, and mean annual runoff of 700 mm yr⁻¹. The catchment's elevation ranges from 595 to 630 m a.s.l., with gentle hill slopes surrounding a relatively flat riparian area near the stream. The bedrock is primarily Devonian shales, interspersed with sandstone inclusions and overlaid by periglacial layers. The hillslopes predominantly comprise Cambisols, while the riparian area features Gleysols and Histosols. The land use is primarily spruce forest .

We used daily hydro-meteorological data from October 2013 to 2019 for the HOAL catchment (Fig. a, b) and from October 2009 to October 2013 for the Wüstebach catchment (Fig. c, d). For the Wüstebach catchment, partial deforestation in October 2013 led to changes in streamflow generation processes, affecting catchment travel time distributions and increasing young-water fractions in streamflow . Therefore, the time series after deforestation was not used for the analyses as it would introduce additional model constraints.

In the HOAL, precipitation data were recorded using a weighing rain gauge located 200 m from the catchment outlet, and stream discharge was measured at the catchment outlet using a calibrated H-flume. The precipitation samples for isotopic analysis were collected using an adapted Manning S-4040 automatic sampler located approximately 300 m south of the catchment. In addition to precipitation samples, weekly grab samples of streamflow were collected at the catchment outlet for isotopic analysis. Additionally, event-based streamflow samples were collected using an automatic sampler, with the frequency of sampling adjusted based on flow rate thresholds (without exceeding sampling bottle capacity). Isotopic measurements of δ18O and δ2H were conducted using cavity ring-down spectroscopy (Picarro L2130-i and L2140-i), with an analytical uncertainty of ±0.1‰ for δ18O and ±1.0‰ for δ2H.

In the Wüstebach catchment, precipitation data were obtained from a nearby meteorological station operated by the German Weather Service (Deutscher Wetterdienst, DWD station 3339), and stream discharge was measured using a V-notch weir for low flows and a Parshall flume for high flows . The precipitation samples for isotopic analysis were collected at the Schöneseiffen meteorological station, located approximately 3 km northeast of the catchment at an elevation of 620 m a.s.l. Starting in June 2009, weekly precipitation samples were collected using a cooled storage rain gauge with 2.3 L HDPE bottles . From September 2012 onward, the sampling resolution was increased to daily intervals (Fig. d) using a cooled automated sampler (Eigenbrodt GmbH & Co. KG, Germany; 250 mL PE bottles). Stream water samples for isotopic analysis were collected weekly at the catchment outlet as grab samples. Cavity ring-down spectroscopy (Picarro L2120-i, L2130-i) was used for water isotope analyses, with an analytical uncertainty of ±0.1‰ for δ18O and ±1.0‰ for δ2H. All isotopic measurements are reported as per mil (‰) relative to Vienna Standard Mean Ocean Water (VSMOW).

We used a process-based tracer transport model based on the previously developed dynamic mixing tank (DYNAMITE) modelling framework , which allows for the simultaneous representation of water fluxes and tracer transport and includes the concept of storage-age selection functions . Briefly, both the HOAL and Wüstebach catchments are conceptualised through five interconnected reservoirs: snow, canopy interception, unsaturated root zone, fast responding storage (shallow soil water), and groundwater with active and passive components (Fig. ). The model hydrological fluxes are: total precipitation P (mm d⁻¹), precipitation as snow Ps (mm d⁻¹), precipitation as rain Pr (mm d⁻¹), snow-melt Pm (mm d⁻¹), throughfall Pe (mm d⁻¹), interception evaporation Ei (mm d⁻¹), evaporation from the root zone Ea (mm d⁻¹), preferential fast response Rf (mm d⁻¹), fast preferential recharge to the to groundwater Rfs (mm d⁻¹, preferential fast response Rff (mm d⁻¹), infiltration-excess overland flow Qo (mm d⁻¹), preferential fast response to the fast-responding bucket Rfn (mm d⁻¹), flow from the fast-responding reservoir Qf (mm d⁻¹), saturation-excess overland flow from the fast-response bucket Qof (mm d⁻¹), slow recharge to the groundwater reservoir Rs (mm d⁻¹), baseflow from the groundwater reservoir Qs (mm d⁻¹), deep infiltration loss Ql (mm d⁻¹), and the total discharge to the streamflow Qtot (mm d⁻¹). Model calibration parameters are shown in red adjacent to the model component they are associated with (Fig. ), and symbols are defined in Table S2 in the Supplement. All model equations are defined in Table S1.

To trace δ2H fluxes through the model, the SAS approach was integrated into the hydrological model. In this integrated framework, each storage defined within the hydrological model (e.g., Sr,Sf, Fig. ), at any given time t, stores water of different ages, represented as T, which traces back to past precipitation and is ranked by their input time. The age distribution of a storage at time t is termed ps(T,t), and is in its cumulative form ST(T,t), also known as the cumulative residence time distribution (RTD). The output fluxes O (mm d⁻¹) (e.g., Ea,Rs, Fig. ) are subsets of specific ages from the storage with water age distributions termed pQ,T(T,t), which are known in their respective cumulative form OT(T,t) as cumulative transit time distributions (TTD). The relation between storage and output fluxes is formulated based on the SAS function ωO,m,j that SAS defines as the likelihood of selecting water parcels of different ages for release from the storage, thereby translating the internal age structure of the storage into an age distribution of output fluxes. At each time t, the age-ranked water in storage is characterized by its tracer composition CS(T,t), which reflects the signal of past precipitation inputs. The output fluxes are likewise described by their tracer distributions, CO(T,t), derived from the selection of water ages leaving storage.

Then, the transport balance of the storage is built on water age conservation over time: 1∂ST,j(T,t)∂t+∂ST,j(T,t)∂T=∑n=1NIT,n,j(T,t)-∑m=1MOT,m,j(T,t) where: ∂ST(T,t)∂t is the rate of change of age-ranked storage with respect to time, ∂ST(T,t)∂T represents the ageing of water within the storage (e.g., Sr,Sf) , IT,n(T,t) are the cumulative age-ranked inflows OT,m,j(T,t) are the cumulative age-ranked outflows. N and M denote the number of inflows and outflows from a given storage component (e.g., for the root zone, N would be Pe, and M is Ea, Rf, and Rs; see Fig. ). Each age-ranked outflow OT,m,j(T,t) (Eq. ) from a specific storage component j depends on the cumulative age distribution of that outflow PO,m,j(T,t) and outflow volume Om,j(t), which is estimated by the hydrological balance component of the model. 2OT,m,j(T,t)=Om,j(t)PO,m,j(T,t), where Om,j(t) is the total outflow rate, and 3PO,m,j(T,t)=Ωo,m,j(ST,j(T,t),t) The cumulative age distribution PO,m,j(T,t) (Eq. ) is the backward TTD of that outflow in cumulative form and depends on the age-ranked distribution of water in the storage component j at time t, ST,j(T,t), and the probability density function, which in this case is the SAS function ωO,m,j (or OT(T,t) in its cumulative form) of that flux.

From the cumulative age distribution, the associated probability density function can be derived according to 4po,m,j(T,t)=ω‾o,m,j(ST,j(T,t),t)∂ST,j(T,t)∂T, where ωo,m,j(S,t) is a probability density function of normalized rank storage ST,norm,j(T,t) (Eq. ). Normalizing the age-ranked storage ST(T,t) by its total volume Sj(t) constrains ST,norm,j to the interval [0,1] and holds mass balance without requiring rescaling of the SAS function at each time step. 5ST,norm,j(T,t)=ST,j(T,t)Sj(t), so that 0≤ST,norm,j≤1.

Finally, the tracer composition of outflow m from compartment j is computed as: 6CO,m,j(t)=∫0SjCS,j(ST,j(T,t),t)ω‾O,m,j(ST,j(T,t),t)dST where CO,m,j(t) is the tracer composition in outflow m from storage component j at time t, and CS,j is the tracer composition in storage at time t. The model reproduces TTDs for all fluxes and storage components (Fig. ) at each time step t. Further details on the model architecture and assumptions can be found in previous studies . The water balance and flux equations for the two catchments in this study application are described in and provided in Table S1.

Similar to previous tracer transport studies for the HOAL and Wüstebach catchments, we used beta distributions to formulate the SAS functions. Beta distributions are defined by two shape parameters (α and β). When both parameters of the Beta distribution were equal to 1 (α=β=1), water is uniformly sampled from storage without any preference for specific ages. If α<β (or α>β), a selection preference for younger (or older) water existed, respectively. In this study, α was varied during calibration to represent different degrees of preferential selection of younger or older water, while β was fixed at 1 to reduce parameter dimensionality and avoid over-parametrization. Fixing β=1 follows previous applications of SAS functions and provides a parsimonious way to explore age-selection behaviour by varying a single shape parameter, while still allowing deviations from uniform mixing. The time variability of the SAS function shape was then determined by the age-ranked storage and the shape parameter α, which was bounded between 0 and 1 to represent a preference for younger storage, and greater than 1 to represent a preference for older storage. Preferential release of older water (α>1) decreases the mean residence time of stored water, as older water is removed from storage. Conversely, preferential release of younger water (α<1) increases the mean residence time of stored water, as older water remains stored for longer periods.

In principle, the model has 16 hydrological fluxes (Fig. ), and each of the fluxes (e.g., Ea,Rs) requires a separate SAS function parameter α to be calibrated. However, this is computationally infeasible and would introduce additional model parameter interactions. Therefore, for all modelled hydrological fluxes, α and β were fixed at 1, except those representing preferential flow from the unsaturated root zone (named as SU,alpha Table S2) for model calibration.

In the Wüstebach catchment, previous studies showed that catchment soil wetness is the main driver for activating preferential flow pathways in the unsaturated zone, leading to the preferential release of younger water to the streamflow as soil wetness increases. Therefore, the SAS function shape parameter representing preferential flow from the unsaturated root zone (Rf, Fig. ) was formulated as a time-variable function of relative soil wetness (Sr/Sr,max), where Sr is the water volume in the root zone at time t, and Sr,max is the maximum root-zone storage capacity (calibrated parameter). Equation () adopts an increasing probability of younger water release with increasing soil wetness through the time-dependent shape parameter α(t), reflecting changes in transport processes between wet and dry soil conditions.

In the HOAL catchment, previous studies have highlighted the non-linearity of preferential flow generation in the unsaturated zone, where both precipitation intensity and soil wetness control the activation of preferential flow pathways . In addition to saturation excess overland flow (when Sr(t)Sr,max>1), infiltration excess overland flow also occurs when precipitation intensity exceeds a certain threshold, routing recent precipitation directly to the stream with minimal interaction with stored water . To account for the combined roles of soil wetness and precipitation intensity in the activation of preferential flow and the release of younger water in HOAL catchment, we parameterized the SAS function for preferential flow from the unsaturated root zone (Rf, Fig. ) using a time-variable shape parameter α(t) defined as a function of both soil wetness state and precipitation intensity. Specifically, α(t) was formulated as a function of relative soil wetness (scaled by the maximum root-zone storage capacity, Sr,max) and precipitation intensity (PI, mm d⁻¹), with a threshold parameter (Pthresh) controlling the onset of precipitation-driven preferential flow. This causal formulation was implemented to ensure that α(t) dynamically responds to both wetness conditions and event-scale precipitation forcing, allowing the model to capture the non-linear activation of preferential flow observed in the catchment. The dual dependence of α(t) on soil wetness and precipitation intensity, therefore, extends previous SAS applications by providing a more flexible representation of unsaturated zone preferential flow dynamics in HOAL.

For the HOAL catchment, the time variability of α for preferential flow in the unsaturated root zone was defined as: 7α(t)=α0,if Pr(t)≥Pthresh1-Sr(t)Sr,max(1-α0),if Pr(t)<Pthresh

For the Wüstebach catchment, time variability of α for the preferential flow in the unsaturated root zone was defined as: 8α(t)=1-Sr(t)Sr,max(1-α0) In both Eqs. () and (), the time variable shape parameter α(t) controls the preferential release of younger water: values of 0<α(t)<1 indicate a bias towards younger water parcels, whereas α(t)=1 corresponds to uniform sampling. The α0 is a calibration parameter representing the lower bound between 0 and 1, allowing α(t) to vary between α0 and 1. When soil wetness is low (Sr(t)≪Sr,max), α(t) approaches 1, indicating uniform sampling. As soil wetness increases (Sr(t) approaches Sr,max), α(t) decreases towards α0, reflecting a stronger preference for younger water. In Eq. (), the lower bound α0 is applied directly whenever precipitation intensity exceeds a certain threshold (Pthresh).

In this analysis, we tested whether and to what extent the mixing of the passive groundwater storage with the active groundwater modulates the δ2H signal in streamflow and, consequently, influences model performance and inferred transit times. We extended the stepwise analysis (Fig. b) by varying passive storage volumes (Fig. ). In the model setup, groundwater storage was represented as an active component (Ss,a) and a hydrologically passive component (Ss,p, mm). The passive groundwater storage (Ss,p) does not contribute to the quantity of baseflow; it exchanges older water with the active groundwater storage (Ss,a), thereby influencing the age composition and isotopic signature of the baseflow (Qs, Fig. ) that contributes to streamflow. For the SAS formulation, total groundwater storage was defined as the sum of active and passive components (Ss,tot=Ss,a+Ss,p), such that the age-ranked total storage (Ss,tot) represents the combined influence of active and passive storage on the age composition of baseflow and thereby on the age composition streamflow (Fig. )

We applied three different passive storage volumes (Ss,p=500, 1000, and 5000mm) based on the values reported for comparable headwater catchments . To isolate the effect of passive storage and age-selection parameterization on streamflow δ2H dynamics and TTD estimations, we kept all hydrological model parameters (e.g., maximum percolation rate, storage capacities, and flow path configurations) identical to the individually calibrated values for the HOAL and Wüstebach catchments. Similar to Fig. b, four different groundwater SAS parameterizations were tested (Fig. ): a strong preference for younger water (α=0.1), a preference for younger water (α=0.7), uniform selection (α=1.0), and a preference for older water (α=5.0). We evaluated model performance in simulating streamflow δ2H by comparing measured and modelled isotope signals using NSEδ2H and MAEδ2H. In addition, we calculated daily cumulative TTDs and compared the means of these distributions across different passive storage volumes and SAS parametrizations.

In the HOAL catchment, δ2H values in precipitation ranged from -3.0‰ to -150.0‰ (Fig. b), with a volume-weighted mean of -67.7‰±31.9‰. Event-based streamflow δ2H samples ranged from -26.2‰ to -108.0‰ (Fig. b), while weekly streamflow δ2H samples ranged from -73.2‰ to -75.2‰. The overall volume-weighted mean of stream samples was -71.6‰±6.1‰.

In the Wüstebach catchment, δ2H values in precipitation ranged from -4.3‰ to -163.2‰ (Fig. d, light blue dots), with a volume-weighted mean of -52.2‰±21.4‰. Weekly streamflow δ2H values exhibited smaller variations, ranging from -45.6‰ to -57.1‰ (Fig. d). The volume-weighted mean of stream samples was -53.2‰±1.4‰.

Overall, δ2H in precipitation exhibited large variability in both catchments; however, this signal was attenuated in streamflow. In the HOAL catchment, event-based streamflow δ2H samples reflected how precipitation inputs were rapidly transmitted to the stream, whereas weekly samples alone would have masked this variability. This highlights the importance of event-based sampling for detecting preferential flow signals, which may remain obscured with weekly data alone. This applies to the Wüstebach catchment, where only weekly streamflow δ2H measurements were available, which may have prevented the detection of such rapid responses.

Model calibration resulted in 55 feasible (acceptable model performance with DE <1) parameter solutions for HOAL (Fig. S3) and 190 feasible parameter solutions for the Wüstebach catchment (Fig. S4). The model reproduced the main features (e.g the rise and recession limbs) of the hydrograph and captured both the timing and magnitude of high and low flow events for the simulation period from October 2014 to 2019 for HOAL (Fig. S5a, d) and from October 2010 to October 2013 for the Wüstebach catchment (Fig. S5e, h).

For the HOAL catchment, the mean Nash-Sutcliffe efficiency of streamflow (NSEQ) for the 55 solutions was 0.60 (Fig. S6). Minor dissimilarities occurred during the spring of 2016, when low flows were overestimated (Fig. S5a). Nevertheless, the model modelled most other observed flow signatures reasonably well (Fig. S6). Among the 55 solutions, the mean NSE for low flows (NSElog⁡Q) was 0.65, for the flow duration curve (NSEFDC) was 0.53, and for the three-month averaged runoff ratio (NSERC) it was 0.85. For several rain events, the model captured δ2H fluctuations during high flows and maintained a stable δ2H signal during low flows, with a mean NSEδ2H of 0.51. Overall, the Euclidean distance (DE) for these 55 solutions ranged from 0.60 to 0.33 (Fig. S6).

For the Wüstebach catchment, the mean NSE of streamflow (NSEQ) for the 190 solutions was 0.78 (Fig. S6). Minor dissimilarities occurred during the spring of 2012, when low flows were overestimated, and the winter of 2012, when peak flows were underestimated (Fig. S5e). Among the 190 solutions, the mean NSE for low flows (NSElog⁡Q) was 0.65, for the flow duration curve (NSEFDC) it was 0.93, and for the three-month averaged runoff ratio (NSERC) it was 0.91. For several rain events, the model captured δ2H fluctuations during high flows and maintained a stable δ2H signal during low flows, with a mean NSEδ2H of 0.58. Overall, the Euclidean distance (DE) for these 190 solutions ranged from 0.62 to 0.32 (Fig. S6).

Figure  presents the transit time distributions (TTDs) estimated from the initial model calibration, conducted before the sensitivity analysis. For TTD estimations, we used the model-calibrated parameter set that yielded the lowest DE. The results presented hereafter are conditional on the underlying model assumptions and should be interpreted in light of the associated uncertainties. In the HOAL catchment, the fraction of streamflow younger than 1000 d exhibited considerable variability, ranging from 5 % to 50 % (Fig. a). The mean fraction of discharge younger than 1000 d was 13 %; it increased to 15 % during wet periods and decreased to 10 % during dry periods (Fig. a). The value of the fraction of streamflow younger than 90 d, FQ(T<90d), varied widely within the same calendar month, ranging from 2 % to 45 %; however, the mean FQ(T<90d) across months did not exhibit pronounced seasonal patterns (Fig. b). The mean value of modelled relative soil saturation (Sr/Sr,max) varied from 0.25 to 0.60 (Fig. c).

In the Wüstebach catchment, the mean fraction of discharge younger than 1000 d was 27 %, increasing to 35 % during wet periods and decreasing to 20 % during dry periods (Fig. d). The value of the fraction of streamflow younger than 90 d, FQ(T<90 d) within the same calendar month ranged between 5 % and 30 % (Fig. e), with mean values exhibiting seasonal patterns. The monthly mean of modelled relative soil saturation (Sr/Sr,max) ranged from approximately 0.60 to 0.98 (Fig. f).

In the HOAL catchment, the calibrated lower limit of the SAS shape parameter (α0=0.14) for the root-zone indicated a strong preference for very younger water through unsaturated root-zone preferential flow pathways. These reflected the SAS formulation (Eq. ) on the dual dependence of α(t) on soil wetness and precipitation intensity. Under high-intensity precipitation, α(t) takes a value of 0.14, indicating that rapid activation of preferential pathways occurs, allowing precipitation inputs to reach the stream with minimal mixing with stored water. In contrast, under wetter antecedent conditions, α(t) increases toward 1, indicating greater mixing within the root zone and contributions of relatively older (i.e., older than recent precipitation inputs) water to streamflow.

In the Wüstebach catchment, the calibrated t lower limit of the SAS shape parameter (α0=0.98) for root-zone suggested only a slight preference for younger water. Here, α(t) varied between 0.98 and 1 depending on the soil wetness state (Eq. ). Under wetter antecedent conditions, established preferential flow pathways facilitated more mixing compared to overland flow, leading to relatively older (i.e., older than recent precipitation) water contributions.

For both catchments, root-zone preferential flow SAS functions ranging from a strong young water preference (α0=0.1) to uniform sampling (α0=1.0) produced high (positive) Spearman rank correlations (r) between modelled and observed δ2H. In contrast, an old-water preference (α0=5.0) yielded negative or weak correlations, indicating a poor fit to the observed tracer signals. In HOAL, the r values ranged between 0.58, and -0.18 for values of α0 between 0.1 and 5.0 (Fig. a). The corresponding Nash-Sutcliffe efficiencies (NSE_δ²H) ranged between 0.56, and -0.25 (Table ). In Wüstebach, the r values for modelled δ2H ranged between 0.58, and 0.28 for values of α0 between 0.1 and 5.0 (Fig. b). The corresponding NSE_δ²H ranged beetwe 0.51 and -0.14 (Table ).

The Spearman rank correlations (r) between observed and modelled δ2H were lower in HOAL compared to Wüstebach, which can be attributed in part to differences in temporal resolution and the variability of isotope sampling. In HOAL, streamflow δ2H was sampled on an event basis, with values ranging from -26.2‰ to -108.0‰ (Fig. b). In contrast, the Wüstebach catchment weekly to biweekly sampling scheme yielded streamflow δ2H values between -45.6‰ and -57.1‰ (Fig. b).

For both catchments, root-zone preferential flow SAS functions from a preference for younger water (α0=0.1) to old water (α0=5.0) influenced the TTD for ages up to 300 d (T<300) (Fig. a, b). This is consistent with root-zone storage residence times being predominantly shorter than 300 d (Fig. S8a, c). Consequently, increasing α0 from 0.1 to 5.0 and thus reducing the relative contribution of younger flows (Fig. a, b), shifted the empirical cumulative distribution functions (eCDFs) toward older water within the first 300 d. In the HOAL, the mean fraction of streamflow with T<300 d reached about 10 % (Fig. a,) for all root-zone SAS formulations, whereas in Wüstebach, it was about 20 % (Fig. b). Overall, these results indicated that root-zone SAS functions with young-water preferences improved the fit to observed streamflow isotopes, highlighting the importance of preferential flow pathways in shaping short transit times and streams δ2H interpretations.

The Spearman rank correlation coefficients (r) between modelled and observed δ2H signals in streamflow, obtained by varying the SAS shape parameter α in groundwater, are shown in Fig. . For the HOAL catchment, r values ranged from 0.54 to 0.60, indicating that, in contrast to the root-zone, changes in the groundwater SAS function had minimal impact on the fit between modelled and observed δ2H signals (Fig. a). In the Wüstebach catchment, r values only slightly increased from 0.71 (α=0.1) to 0.76 (α=1.0) before decreasing slightly at α=5.0 to 0.75. In both catchments, the correlations remained consistently strong across all α values tested (Fig. a, b).

A stronger preference for young water (α=0.1) led to approximately 25 % of streamflow being younger than 1000 d in the HOAL (Fig. a) and 35 % in the Wüstebach (Fig. b). In contrast, an older-water preference (α=5.0) shifted the distribution and reduced the proportion of streamflow being younger than 1000 d to 5 % in the HOAL and to 12 % in the Wüstebach. This shift, resulting from changing the SAS function parameter α from 0.1 to 5.0, produced a variability of approximately 20 % in HOAL and 23 % in Wüstebach in the proportion of streamflow composed of water younger than 1000 d (Fig. a, b).

The results addressing the extent to which passive storage volume and associated mixing assumptions influence the representation of preferential groundwater flow, the estimated transit time distributions, and the interpretation of tracer signals at the catchment scale, are presented in Figs.  and . Briefly, the findings show that increasing the passive storage volume dampens the contribution of younger water, shifts the overall transit time distribution towards older ages, and reduces variability in the δ2H signal variability in streamflow.

In both catchments, an active storage volume equivalent to approximately 1 % of the passive storage volume was needed to attenuate the modelled tracer signal in line with observations in streamflow. In the HOAL, a passive storage volume of SS,p=500 mm (Fig. S10a) was sufficient to attenuate the modelled tracer signal, while in Wüstebach, a much larger volume of SS,p=5000 mm was necessary (Fig. S10b). SAS shape parameters indicating a young-water preference (α=0.1) resulted in variable δ2H signals in streamflow, whereas an older-water preference (α=5.0) led to stronger dampening (Figs. , ).

Once the volume ratio between active and passive storage fell below 1 %, further increases in SS,p had little effect on model performance (Table ). The NSE remained relatively stable across different SS,p values, with moderate improvements for α=0.7, 1.0, and 5.0. In contrast, simulations with α=0.1 yielded negative NSE values (Table ). The highest NSE_δ²H values, approximately 0.55, were achieved with α=1.0 and α=5.0 for the HOAL catchment. The results in the Wüstebach catchment exhibited a wider range of NSE values, from -11.25 to 0.22, as SS,p increased, suggesting that model performance was more sensitive to the size of the passive storage volume than to the shape factor α.

In both catchments, increased passive storage volumes influenced the old tail of transit times (100<T<1000 d). Increasing SS,p increased the probability of older water contributing to streamflow (Figs. , ) and reduced the fraction of streamflow younger than 1000 d substantially. The range of differences in the fraction of streamflow younger than 1000 d varied across different mixing assumptions, yet remained consistent overall. In the HOAL catchment (Fig. a–c), under the uniform sampling assumption, the fraction of streamflow younger than 1000 d decreased from 50 % to 5 % as SS,p increased from 500 to 5000 mm. Given that model performance remained similar across these scenarios (Table ), this implies a variability of approximately 45 % in TTD estimation attributable to uncertainties in passive storage volumes. In the Wüstebach catchment (Fig. a–c), the corresponding fraction declined from 80 % to 45 %. None of the simulations with SS,p less than 5000 mm adequately reproduced the observed δ2H signal, suggesting that at least 50 % of stream water in Wüstebach is older than 1000 d.

The inferred transit times in HOAL (13 % of streamwater younger than 1000 d) and Wüstebach (27 % of streamwater younger than 1000 d) indicated that, in both catchments, the majority of water contributing to streamflow was relatively old, consistent with findings from many other catchments . During wet periods, the fraction of water T<1000 d was 15 % in HOAL and 33 % in Wüstebach; in dry periods, these values dropped to 10 % and 22 %, respectively. This variation indicated a greater release of younger water under wetter conditions, consistent with other studies . In Wüstebach, relatively high soil wetness and high monthly mean young-water fractions ranging from 5 % to 15 % (Fig. e, f) pointed to wet-soil promotion of preferential flow which has been observed previously . By contrast, HOAL’s younger-water release did not depend on soil wetness only; instead, rapid flow pathways (e.g. infiltration-excess overland flow, macropores, tile drains) as known for this catchment allowed water to bypass much of the soil matrix and reach the stream quickly, even under dry conditions, which was discussed in previous findings . The consistency of our results with prior tracer-based modeling and SAS applications in both HOAL and Wüstebach provides confidence in the applied model configurations. However, we acknowledge that such consistency alone cannot exclude the possibility of shared assumptions. Therefore, we use these results as supporting evidence that the model setups are reasonable for testing the research hypotheses, while recognizing the need for further validation with complementary data and approaches.

Positive correlations between modelled and observed streamflow tracer signals (Fig. a, b), together with high model-efficiency metrics at lower α0 values (indicating a preference for younger water; Table ), show that streamflow tracer data were sufficiently sensitive to the SAS parameterization of preferential flow in the unsaturated zone for both the HOAL and Wüstebach catchments. This suggests rapid transport of precipitation through preferential flow pathways in both catchments, consistent with previous findings . Specifically, changing the root-zone SAS shape parameter α0 produced clear differences in modelled streamflow δ2H signals (Fig. ), demonstrating tracer-data sensitivity to younger-water release. The results quantitatively demonstrated that streamflow isotope data can reflect the activation of preferential flow in the unsaturated zone. While previous studies have identified preferential flow through field observations , our results demonstrate that they can also be captured and interpreted using catchment-scale tracer modelling.

Nevertheless, the two catchments exhibited distinct processes controlling preferential flow in the unsaturated root zone. The calibrated lower boundary of the SAS function shape parameter, α0, differed markedly (α0=0.14 for HOAL and α0=0.98 for Wüstebach), reflecting contrasting storage-discharge relationships and preferential flow activation mechanisms in the unsaturated zone. In HOAL, the low α0 value indicated rapid, direct water transmission through preferential flow paths driven by intense rainfall, consistent with previous hydrometric analyses and field observations . This suggests younger water to reach the stream with limited mixing with stored water. This was further facilitated by the formation of soil crusts and cracking of the clay-rich topsoil during the dry summer months, creating direct preferential pathways that accelerate water transmission through the catchment . In contrast, the higher α0 value in Wüstebach (α0=0.98) indicated that under wetter antecedent conditions, established preferential flow pathways promoted greater subsurface mixing, leading to relatively older water contributions to streamflow. This likely reflects the influence of forest cover in Wüstebach, where enhanced infiltration promotes deeper and more uniform mixing than in HOAL. Despite contrasting site characteristics, both catchments showed responses consistent with previous studies that documented the role of macropores and preferential flow pathways in the unsaturated zone, where water frequently bypasses matrix storage and exchange processes .

On the other hand, streamflow tracer δ2H showed limited sensitivity to variations in groundwater SAS function parametrizations (Fig. , Table ), suggesting that isotope data alone may not provide sufficient variability to resolve preferential groundwater flow contributions to streamflow. This is supported by the small variation in correlation coefficient for different α values (r=0.54–0.60 in the HOAL catchment and r=0.71–0.76 in Wüstebach). We attributed this limited variability to the large passive groundwater storage volumes (estimated as 500 mm in HOAL and 5000 mm in Wüstebach;) formulated within the model. The estimated passive groundwater storage volumes should be interpreted as volumes effectively buffering δ2H simulations, rather than their actual physical magnitude. In our and many other catchment scale modelling approaches , groundwater (QS) age selection is formulated based on age samples from the total groundwater storage (SS,tot), combining contributions from both active (SS,a) and passive (SS,p) compartments . Thus, the age-ranked groundwater storage (ST,S,tot) inherently reflected a mixture of these storage volumes. Although the model explicitly allowed preferential recharge of younger groundwater (e.g, Rfs, Fig. ), the passive storage, characterized by long residence times, buffers the isotopic signals in streamflow , result in comparable model performance (Table ), thereby masking the distinct signatures of preferential groundwater flow. Consequently, uncertainty in estimating passive storage volumes in modelling leads to uncertainty in transit time estimation and contaminant transport time scales, with critical implications for assessing water-quality risks. For water-quality modelling, this implies that rapid contaminant transport through preferential flow paths can occur in response to hydrological events; however, stable water isotope data alone are insufficient to capture these dynamics in catchments with substantial passive groundwater storage.

The Spearman rank correlations (r) between observed and modelled δ2H were lower in HOAL compared to Wüstebach, which can be attributed to differences in temporal resolution and the variability of isotope sampling (Fig. a, b). Although model performance metrics, such as NSE or correlation coefficients, quantify the agreement between modelled and observed isotope time series, they can result in seemingly good fits in the presence of sparse or irregular data sampling. In such cases, deceptively high NSE values may still occur even when key groundwater age-selection parameters (e.g., preference for young vs. old water) remain poorly constrained, thereby affecting transit time estimations .

Different groundwater SAS function parameterizations yielded similar isotope model fits (Table ), except for the case with a strong young-water preference (α=0.1) in the HOAL catchment, indicating that good tracer model performance does not necessarily imply well-constrained groundwater age selection. For example, assuming a strong young-water preference (α=0.1) yielded fractions of streamflow younger than 1000 d of approximately 25, % in HOAL and 35, % in Wüstebach, whereas an older-water preference (α=5.0) reduced these fractions to around 5 % and 12 %, respectively (Fig. ). This spread of 20 % in HOAL and 23 % in Wüstebach for T<1000 d highlights a key limitation of isotope-based model calibration: transit time estimates remain highly uncertain when groundwater mixing processes and SAS function formulations are weakly constrained. This uncertainty is particularly relevant for contaminant transport prediction, as poorly constrained groundwater age distributions can lead to inaccurate estimates of contaminant travel times and the timing of water-quality improvements following reductions in contaminant inputs. Consistent with previous studies , our results show that inferred transit times are sensitive to how SAS functions are conceptualized and parameterized, underscoring the need for additional constraints or complementary tracers when interpreting groundwater transit times and their implications for catchment functioning and water-quality assessment.

In both the HOAL and Wüstebach catchments, streamflow isotope signals were attenuated when the volume ratio between active and passive storage (SS,a/SS,p) was less than 1 % (Figs. , ), indicating that passive groundwater storage volumes orders of magnitude larger than active groundwater storage are required to significantly dampen isotope variability in streamflow, consistent with findings by .

In HOAL, model performance remained comparable across a wide range of passive storage volumes exceeding 500 mm (e.g., NSEδ2H≈0.55), suggesting uncertainty in the upper bound of passive storage, as model performance became insensitive to further increases once the SS,a/SS,p ratio dropped below 1 %. In contrast, model performance in Wüstebach systematically improved with increasing passive storage volumes (Table ), consistent with previous findings by , who proposed substantial groundwater storage (∼ 8000 mm) to reproduce observed isotope damping. Nevertheless, the sensitivity analysis demonstrated that similar performance (NSEδ2H=0.31) could also be achieved with SS,p=5000 mm under uniform mixing, reinforcing the large uncertainty in constraining the upper range of passive storage volumes in catchment-scale models.

Given these uncertainties in passive storage parameters, it is therefore crucial to assess how passive groundwater storage, in combination with active storage, influences estimated TTDs. In both catchments, a clear negative correlation emerged between passive storage volume and the fraction of streamflow younger than 1000 d (Figs. , ). Because the groundwater storage SAS function was formulated based on the sum of active and passive groundwater storage (SS,tot=SS,a+SS,p), increasing passive storage volumes systematically increased the likelihood of older water contributions to streamflow, thereby extending the tails of the transit time distributions (TTDs; 100<T<1000 d). These results underscore that passive groundwater storage is a dominant control on catchment memory (the retention of past hydrological inputs in streamflow due to long residence and transit times), substantially masking young-water contributions and promoting delayed solute and pollutant transport at the catchment scale.

The sensitivity analyses of streamflow tracer signals and transit time estimates to SAS function parameterizations offered a systematic approach that could be adapted to other regions and TTD studies. Nonetheless, the uncertainty resulting from the specific model setup and parameter choices used in this study cannot be directly generalised across diverse catchments or hydrological conditions. Reducing uncertainty in transit time estimates and enhancing the reliability of SAS-based modelling requires improving the spatial and temporal resolution of isotope and hydrological data, integrating additional tracers such as tritium (³H), and refining model representations of subsurface processes.

At the catchment scale, isotope-based modelling proved useful in capturing preferential flow in the unsaturated zone but was limited in doing so in groundwater due to the damping of water stable isotope signals by large passive groundwater storage volumes. This damping does not necessarily indicate the absence of preferential flow; rather, it implies that when isotope variability in streamflow is strongly attenuated, groundwater age mixing will be difficult to constrain using isotopes alone. This limitation is relevant for water-quality applications, as catchments with large passive groundwater storage may still exhibit rapid contaminant responses during hydrological events through preferential flow pathways, despite long mean transit times. Consequently, applying this modelling approach to other catchments requires careful consideration of active-passive groundwater storage dynamics, the parametrization of the SAS function.

While the SAS formulation identifies the statistical signatures of preferential flow in tracer-based modelling, it does not explicitly resolve the physical mechanisms that induce preferential flow. Therefore, isotope data alone, when used within a catchment-scale conceptual model framework, may be insufficient to distinguish between a true absence of preferential flow and a limited model sensitivity to detect it. This limitation of relying on stable isotope data alone is especially critical for water-quality prediction, where preferential flow paths can rapidly mobilize nutrients or contaminants during hydrological events, even in systems characterized by large storage and long mean transit times.

In the HOAL catchment, showed that alternating contributions from shallow and deep aquifers throughout the year were the main cause of the seasonal variability in nitrate concentrations in streamflow. These alternating contributions, together with extensive tile drainage and heterogeneous clay-rich soils, create rapid and spatially variable flow pathways .Such features, combined with overland flow in the HOAL catchment , likely favour the activation of preferential flow. For the Wüstebach catchment, field studies indicated that soil and groundwater dynamics are coupled. and showed that soil water variability decreases with depth due to lower porosity and root water uptake in shallow depth, while groundwater fluctuations closely follow soil moisture dynamics , reflecting high infiltration and storage capacity in forest soils. This soil-groundwater coupling contrasts with the results obtained in the HOAL catchment, suggesting a more uniform subsurface mixing in Wüstebach.

Although the physical mechanisms underlying preferential flow and subsurface mixing remain beyond the explicit resolution of conceptual, isotope-based transport models, the SAS framework enables delineation of the hydrological conditions under which preferential flow effects become detectable. This capability of the SAS functions is particularly important for identifying when fast flow paths control solute export during extreme events or periods of high hydrological connectivity. Future research should combine stable isotopes with complementary tracers (e.g., tritium, chloride, or major ions) and higher-frequency sampling to enhance the diagnostic power of tracer-aided models. Furthermore, linking SAS function shapes to measurable catchment attributes could enable a priori parameterization, thereby reducing dependence on calibration. At the lysimeter pedon scale, showed that SAS functions can approximate the analytical solution of the advection-dispersion equation; however, extending such mechanistic relationships to the catchment scale remains challenging within conceptual modelling frameworks.

While our study focused on a conceptual catchment-scale framework, the results highlighted the need to advance toward more distributed models that can more directly link spatial heterogeneity in soils, slopes, and storage to preferential flow dynamics. Addressing these challenges represents a key step toward integrating empirical SAS modelling with a process-based interpretation of preferential flow and improving predictions of solute transport and water-quality responses, particularly under event-driven activation of preferential flow in the subsurface.