3.1 Hydro-climatic data

Daily discharge data for 18 of the 22 sites were provided by the Swiss Federal Office for the Environment. Discharge measurements for the Aabach catchment were made available by the Office for Waste, Water, Energy and Air (WWEA) of the canton of Zurich. Discharge data for the Erlenbach, Vogelbach, and Lümpenenbach catchments were provided by the Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland.

Meteorological data for each site and each 100 m elevation band were interpolated from measurements taken by the national meteorological service of Switzerland (MeteoSwiss), using the PREVAH (Precipitation-Runoff-EVApotranspiration HRU) model (Viviroli et al., 2009). Mean precipitation for each 100 m elevation band was aggregated to obtain area-weighted catchment average values.

3.2 Catchment properties

The average hydro-climatic properties at the sites were described by various indices, such as mean monthly values of discharge $\stackrel{\mathrm{‾}}{Q}$ and precipitation Q, as well as mean daily precipitation intensity ${\stackrel{\mathrm{‾}}{P}}_{\mathrm{intensity}}$. To quantify the variability of the flow regimes, we determined the average coefficient of variation of daily discharge (CV_Q) and the quick-flow index (QFI). The QFI is the average ratio between (Q − Q_bf) and Q, where Q is daily discharge and Q_bf is daily baseflow; Q_bf was calculated with the “BaseflowSeparation” function in the EcoHydRology package (version 0.4.12) in R using a recursive digital filter parameter of 0.925, as recommended by Nathan and McMahon (1990). All of these hydro-climatic indices were calculated for each site and for the duration of the site-specific streamwater isotope sampling campaigns, which varied between approximately 1 and 5 years (Table 1).

The seasonal variability of monthly precipitation for the years 2000–2015 was expressed through the amplitude and the phase shift of a fitted sinusoidal function (Berghuijs et al., 2014):

where P is the precipitation volume (mm month⁻¹), $\stackrel{\mathrm{‾}}{P}$ is the average of P (mm month⁻¹), A_precip is the seasonal amplitude of precipitation (–), t is the time (months), τ is the duration of a full seasonal cycle (12 months), and φ_precip is the phase (months). The phase describes the offset from the beginning of the seasonal cycle, which is defined here as 1 January. The parameters A_precip and φ_precip were obtained by non-linear fitting to the monthly precipitation data using Newton's method. Strong precipitation seasonality would be expressed in a high A_precip value.

The hydro-climatic indices are to some extent redundant with one another. Unsurprisingly, mean monthly discharge ($\stackrel{\mathrm{‾}}{Q}$) and mean monthly precipitation ($\stackrel{\mathrm{‾}}{P}$) were significantly correlated with each other across the 22 sites. Furthermore, $\stackrel{\mathrm{‾}}{Q}$ was significantly correlated with the seasonality of precipitation (A_precip), and the QFI was significantly correlated with the coefficient of variation of daily discharge (CV_Q) (Table 4).

To quantify the geomorphological characteristics of the study catchments, we used terrain indices (median flow path length L, median flow gradient G, the ratio L∕G, and median topographic wetness index – TWI) which were calculated previously by Seeger and Weiler (2014) for all 22 study sites using a digital elevation model with 25 m spatial resolution. The indices L∕G and TWI were previously applied in numerous catchment inter-comparison studies, e.g. Hrachowitz et al. (2009), McGuire et al. (2005), and Tetzlaff et al. (2009). In addition, we calculated the drainage density DD (the total channel length divided by the catchment area) based on the official river network from the topographical landscape model of Switzerland (swissTLM3D, ©2017 swisstopo; resolution 8 m or better).

Hydrologic soil properties and vegetation cover information were extracted from geospatial data provided by the Swiss Federal Office for Agriculture (BLW, 2012) and the Swiss Federal Statistical Office (BFS, 2004), respectively. The data product “land suitability” uses six soil properties – soil depth, large particle fraction, water storage capacity, nutrient storage capacity, permeability, and soil wetness index – to generate a map of 144 different soil classes. Each soil property is ranked from 0 (very low) to 5 or 6 (very high). For our analysis, we calculated the areal fractions of aggregated soil properties that are usually associated with fast runoff processes, i.e. low water storage capacity (ranks 1–3), low permeability (rank 1–3), and high soil wetness index (i.e. saturated soils, ranks 4–5). From the data product “forest diversity” we extracted the fraction of forested area for each catchment.

The hydrogeological properties of the study sites were obtained from the official geotechnical map of Switzerland (1 : 200 000, ©2017 swisstopo). We extracted the areal fractions of low, intermediate, and high groundwater productivity for each catchment. Representative groundwater table depths could not be determined for all sites due to their complex small-scale topographic and geologic heterogeneity. The hydrologic soil properties, as well as the hydrogeological properties of the individual sites, are provided in the Supplement (Table S1).

Correlations between the catchments' young water fractions, hydro-climatic conditions, and landscape properties were assessed with the Spearman rank correlation coefficient ρ (Spearman, 1987). Following conventional practice, we consider correlations with p < 0.05 to be statistically significant.

3.3 Streamwater isotope data

Streamwater grab samples were collected approximately fortnightly at 21 sites between mid-2010 and mid-2011 or later (see Table 1 for exact dates). Oxygen isotope ratios (δ¹⁸O) were measured with a Picarro isotope analyser (Picarro Inc., Santa Clara, CA, USA) at the University of Freiburg, Germany, and are reported here as δ values relative to the VSMOW standard. For the Rietholzbach catchment, fortnightly streamwater δ¹⁸O data were provided by the Institute for Atmospheric and Climate Science at ETH Zurich.

3.4 Precipitation isotope data

Values of δ¹⁸O in precipitation were not measured directly at the 22 study catchments. Instead, δ¹⁸O values from monthly cumulative precipitation samples were interpolated from long-term observations at nearby monitoring stations (the Swiss network for Observations of Isotopes in the Water Cycle – NAQUA-ISOT, the Global Network of Isotopes in Precipitation – GNIP, and the Austrian Network of Isotopes in Precipitation – ANIP). We used two different interpolation approaches that we summarize below: method 1 after Seeger and Weiler (2014) and method 2 similar to that of Allen et al. (2018). More detailed descriptions of both interpolation methods 1 and 2 can be found in Seeger and Weiler (2014) and in the Supplement, respectively.

In method 1, we adjusted a kriging interpolation of the available precipitation isotope values from 26 long-term monitoring stations for local differences in elevation. For this, we used the monthly average elevation gradient of δ¹⁸O in precipitation, estimated from three isotope monitoring stations in central Switzerland (Meiringen, Guttannen, and Grimsel, Fig. S1 in the Supplement) that cover a similar elevation range as the 22 study catchments. Method 1 can be extended using an energy-balance-based model to explicitly simulate the storage of winter precipitation in the snowpack. The energy-balance-based model uses PREVAH simulations of air temperature, wind speed, incoming shortwave radiation, and precipitation amount to predict the meltwater amounts and their average isotopic compositions for each 100 m elevation band (without considering isotopic fractionation of the snowpack and snowmelt).

In method 2, we fitted isotope data from 19 long-term monitoring stations to sine curves using least squares. We then constructed a multiple linear regression model to explain the best-fit sine parameters as functions of latitude, longitude, and elevation. These spatially varying sine parameters were used to construct interpolated seasonal cycle maps for all of Switzerland. These seasonal cycles were then adjusted using kriged interpolations of the monthly residuals of station measurements from their fitted seasonal patterns, to account for non-sinusoidal isotope dynamics. For both interpolation methods 1 and 2, monthly isotope values were mass-weighted based on the monthly elevation-dependent precipitation volumes obtained from the PREVAH model (Viviroli et al., 2009).

Figure 3(a) Comparison of flow-weighted seasonal amplitudes of precipitation δ¹⁸O cycles (A_P) obtained with two different interpolation methods, method 1 (Seeger and Weiler, 2014) and method 2 (based on Allen et al., 2018; Supplement). Differences in A_P between the two interpolation methods were significant for the catchments highlighted with their abbreviated names. The abbreviations for the study sites stand for Allenbach (ALL), Alp (ALP), Biber (BIB), Dischmabach (DIS), Mentue (MEN), Ova da Clouzza (OVA), Riale di Calneggia (RIA), and Sense (SEN). (b) Comparison of young water fractions derived from the two interpolation methods. High-elevation, snow-dominated catchments are marked in light blue colour. Error bars show ±1 SE.

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4.1 Comparing two methods for spatial interpolation of δ¹⁸O in precipitation

Here, we apply two different methods 1 and 2 (Sect. 3.4) for interpolating monthly precipitation isotopes from nearby long-term monitoring stations and compare the resulting seasonal cycles of precipitation isotopes and their effects on the calculated young water fractions. In this comparison, method 1 is used without the snow module because method 2 does not allow for explicit simulation of snow accumulation and melt.

Figure 3a shows that the seasonal precipitation isotope cycle amplitudes (A_P) obtained with both methods are similar for most catchments; the differences range from −1.34 ± 0.21 ‰ (±SE, Mentue) to 1.35 ± 0.29 ‰ (Dischmabach). Method 2 results in larger A_P values for five sites (Alp, Biber, Mentue, Sense, and Riale di Caneggia), compared to the results of method 1 (Fig. 3a). However, smaller A_P values are obtained with method 2 for three high-elevation sites: Allenbach, Dischmabach, and Ova de Cluozza. Overall, A_P spanned a range of 1.77 ‰ with method 2, compared to a larger range of 3.47 ‰ with method 1. Nevertheless, for most sites the differences in A_P between the two methods are small compared to the absolute values of A_P, and thus the choice of the interpolation method only marginally affects the estimated young water fractions F_yw. For all sites, the absolute differences between the values of F_yw calculated with the two interpolation methods are below 0.06 and statistically insignificant (i.e. smaller than twice their pooled uncertainties, Fig. 3b).

A systematic test of both interpolation methods using on-site, long-term precipitation isotope measurements would go beyond the scope of this study. However, method 1 was tested with isotope measurements from six stations (Seeger and Weiler, 2014), and we evaluated the performance of method 2 as described in the Supplement. Results from the two methods are likely to differ because they make different assumptions about the changes in precipitation isotopic composition with elevation. For our objectives, however, it is helpful that these two different approaches yield different A_P in several cases, because it allows us to show that this level of variability in A_P has only minor effects on the calculated young water fractions. Our comparison thus demonstrates that both approaches for spatially interpolating δ¹⁸O in precipitation yield consistent young water fraction estimates for the 22 study catchments.

4.2 The effect of snow storage on the seasonal cycle amplitudes and phases of precipitation isotopes

At high-elevation sites with seasonally cold climates, precipitation (and its isotopic signature) will be stored temporarily in the snowpack in winter, and will be released during the melt season. Thus, significant volumes of isotopically depleted snow meltwater may reach the river system during spring and early summer, when the isotope signal of incoming precipitation is more enriched. As a result, the seasonal isotopic variation in water reaching the soil surface (rainwater and snowmelt) is likely to be smaller than the seasonal variation in precipitation alone.

Figure 4(a) Time series of catchment input volumes and δ¹⁸O values (not volume-weighted) for the Dischmabach catchment, calculated using the interpolation method of Seeger and Weiler (2014), with and without modelling of snow accumulation and melt (“delayed input” and “direct input”, respectively). Panels (b) and (c) compare the seasonal amplitudes of the precipitation isotope cycles (volume-weighted), and the resulting flow-weighted young water fractions, with and without modelling of snow accumulation and melt. Panels (d) and (e) compare the phases of the seasonal precipitation isotope cycles, and the resulting phase shifts, with and without modelling of snow accumulation and melt. High-elevation, snowmelt-dominated sites are marked in light blue. The abbreviations for the study sites stand for Dischmabach (DIS), Riale di Calneggia (RIA), and Schaechen (SCH). Error bars show ±1 SE.

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In order to investigate the effect of snow storage on the amplitudes and phases of precipitation isotope cycles, we applied method 1 with the snow module, so that the input to the soil surface, and its isotope signal, can be described by a mixture of rainwater and snowmelt (the “delayed input” scenario in Fig. 4). Alternatively, method 1 can also be applied without the snow module, i.e. by ignoring snowpack as a separate storage, such that the catchment input is taken directly from the incoming precipitation and its isotopic composition (the “direct input” scenario in Fig. 4). Figure 4a shows, as an example, the time series of input water flux and δ¹⁸O (not volume-weighted) at the Dischmabach catchment for both scenarios. The delayed release of depleted winter precipitation from the snowpack (“delayed input” scenario) results in a smaller seasonal amplitude of the input tracer signal. However, when this input tracer signal is volume-weighted, the fitted seasonal amplitudes (A_P) are statistically indistinguishable between the “direct” and “delayed” input scenarios for 21 of the 22 sites (Fig. 4b). This result arises because the “delayed” input scenario gives very little weight to winter inputs in snow-dominated catchments (because snowmelt volumes during winter conditions are small), allowing the fitted cycles to deviate from the winter isotope values. The difference in A_P for both scenarios is statistically significant only at the Schaechen catchment, which contains the highest-elevation snowpacks in our data set (elevation up to 3260 m a.s.l., Table S1). As a consequence, snowmelt at the Schaechen site is isotopically more depleted compared to the other, lower-elevation sites. For the hybrid and rain-dominated sites, the A_P values are almost indistinguishable between the two scenarios, either because snowmelt occurs early in the season when rainwater and snowmelt have similar isotopic signatures (i.e. hybrid catchments), or because the contribution of snowmelt is small compared to that of rainfall (rain-dominated catchments). As a consequence, the young water fractions F_yw are virtually identical between the “direct input” and “delayed input” scenarios (Fig. 4c).

As can be seen in Fig. 4a, the delayed meltwater input shifts the seasonal isotope pattern toward later in the season. Thus the “delayed input” scenario results in later cycle phases (φ_P) compared to the “direct input” scenario (Fig. 4d), with statistically significant differences for the five high-elevation, snow-dominated sites and for four hybrid catchments (Erlenbach, Lümpenbach, Vogelbach, and Sitter). However, the “delayed input” scenario had a statistically significant effect on the phase shift between input and output (φ_S − φ_P) only at Dischmabach (where it altered the phase shift by 0.06 years) and Riale di Calneggia (where it altered the phase shift by 0.07 years; Fig. 4e). In the analysis presented below, we use interpolated precipitation isotope values obtained with method 1 that explicitly account for snowpack accumulation and melt (i.e. the “delayed input” scenario) in order to be consistent with previous studies where this data set has been used (Seeger and Weiler, 2014; Staudinger et al., 2017).

4.3 Comparing unweighted and flow-weighted young water fractions

We use the isotope and discharge data sets of the 22 catchments to estimate young water fractions from the ratios of the seasonal cycle amplitudes A_S and A_P, with and without discharge-weighting ($F_{\mathrm{yw}}^{*}$ and F_yw, respectively). Figure 5a shows that flow-weighting the streamwater isotope values results in a roughly 25 % increase in the fitted seasonal streamwater isotope cycle amplitudes A_S, relative to the unweighted A_S values for the same sites. Statistically significant differences between unweighted and flow-weighted values of A_S were found for Dischmabach, Emme, Mentue, Rietholzbach, and Sense, as well as Alp, Erlenbach, Lümpenenbach, Vogelbach, and Biber (which are all located nearby one another and share similar catchment characteristics). Perhaps unsurprisingly, the effect of flow-weighting on A_S is largest in catchments with highly variable flow regimes, i.e. at sites with relatively large coefficients of variation of daily discharge (CV_Q) and QFIs (Table 2). In such catchments, robust estimation of the flow-weighted $F_{\mathrm{yw}}^{*}$ may require a smart sampling strategy that captures a representative range of hydrologic conditions.

The flow-weighted $F_{\mathrm{yw}}^{*}$ values range from 0.07 ± 0.01 to 0.49 ± 0.03 (±SE), whereas the unweighted F_yw values range from 0.06 ± 0.01 to 0.37 ± 0.03. Thus, flow-weighting the streamwater isotope values yields young water fractions ($F_{\mathrm{yw}}^{*}$) that are around 26 % larger than those calculated from unweighted streamwater isotope values (F_yw; Fig. 5b, Table 3), because high flows generally contain more young water than base flows. The average values of $F_{\mathrm{yw}}^{*}$ and F_yw are 0.22 ± 0.02 and 0.17 ± 0.02, respectively, meaning that approximately one-fifth of total discharge was younger than roughly 2.3 ± 0.8 months (assuming that the catchment transit times can be described by gamma distributions with shape factors α ranging from 0.3 to 2; Kirchner, 2016a). Our F_yw results are within the range of young water fractions reported for rivers in mountainous regions in North America and central Europe by Jasechko et al. (2016).

Figure 5Panel (a) compares the seasonal amplitudes of streamwater isotope cycles (A_S) with and without flow weighting. High-elevation, snowmelt-dominated sites are marked in light blue. Panel (b) compares flow-weighted young water fractions $F_{\mathrm{yw}}^{*}$ with unweighted young water fractions (F_yw). Error bars show ±1 SE. Unweighted young water fractions are roughly 26 % smaller than flow-weighted young water fractions across these catchments.

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5.1 Discharge sensitivity of the young water fraction as a diagnostic indicator of runoff generation processes

The catchment inter-comparison analysis presented in Sect. 5 suggests that wetter catchments, and those with shorter and faster flow paths, have larger young water fractions. In individual catchments, one would also expect young water fractions (and thus seasonal isotope cycles) to be variable in time, i.e. to be larger during periods of stronger precipitation forcing and wetter antecedent conditions, as shallower, faster flow paths become more dominant, and as the stream network extends farther into the landscape, shortening the average path length of subsurface flow (Godsey and Kirchner, 2014). In this section, we examine how young water fractions respond to changes in catchment wetness, as reflected in stream discharge.

5.2 Young water fractions of distinct flow regimes

Our expectation that the young water fraction should be higher under wetter conditions (and thus during higher stream discharges) is borne out by the observation that flow-weighted young water fractions are systematically higher than unweighted young water fractions (Sect. 4.3). We can visualize the relationship between F_yw and stream discharge (as a proxy for catchment wetness) by separating the streamwater isotope time series into different discharge ranges and calculating the seasonal isotope cycles and F_yw values individually for each of these flow regimes. These flow regimes comprise the 1st to 4th quartiles, as well as the upper 20 and 10 % of daily discharges at the day of sampling. For instance, from the 140 streamwater isotope samples at the Erlenbach site, each quartile of Q comprised 35 samples, while the upper 20 and 10 %, of daily discharges comprised 28 and 14 samples, respectively. In Fig. 7, we plot F_yw in relation to the median discharge values of the six flow regimes at nine of our study sites. These sites have the longest isotope time series in our data set, allowing us to estimate robust seasonal cycle coefficients A_S for each individual flow regime. At our sites with shorter time series, sub-sampling individual flow regimes would result in highly uncertain A_S estimates.

Figure 8Scatter plots of the unweighted and flow-weighted young water fractions versus the discharge sensitivity of F_yw calculated for 21 of the 22 Swiss catchments (no discharge sensitivity was calculated for the Aach catchment because only two isotope values existed for high-flow conditions). High-elevation, snowmelt-dominated sites are marked in light blue. Error bars show ±1 SE. There is no systematic relationship between the young water fractions and their discharge sensitivities.

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The visual patterns shown in Fig. 7 are similar for catchments located close to each other, such as for Alp and Biber, or for Lümpenenbach, Vogelbach, and Erlenbach. However, young water fractions vary substantially among the sites in Fig. 7, with F_yw in the lowest flow regime ranging from 0.03 at Dischmabach to 0.29 at Erlenbach and F_yw in the highest flow regime ranging from 0.13 at Ilfis to 0.60 at Biber. Figure 7 suggests that the relationship between discharge and F_yw may be a diagnostic fingerprint linked to hydrological properties that control the storage and release of young water. However, the nine catchments shown in Fig. 7 are too small of a sample to draw any robust conclusions concerning how this fingerprint may vary with catchments' landscape characteristics and hydro-climatic conditions.

5.3 Estimating the discharge sensitivity of F_yw and linking it to catchments' landscape and hydro-climatic characteristics

As a first-order estimate of the sensitivity of F_yw to discharge across all 22 study catchments, we calculated the linear slope of the relationship between Q and F_yw, using a method that does not require breaking the streamwater isotope time series into separate flow regimes (and thus has more modest data requirements than plots like Fig. 7). Instead of fitting a linear slope to the few data points shown in Fig. 7, we estimated the linear slope of the Q–F_yw relationship directly from the tracer time series c_S(t) and c_P(t). For each site, we assume that the seasonal amplitude of precipitation isotopes (A_P) is independent of Q, leaving the seasonal amplitude of streamwater isotopes A_S as the only flow-rate-dependent variable. If A_S varies with discharge but A_P does not, then the young water fraction F_yw varies with Q as follows:

If we approximate A_S as a linear function of Q,

we can estimate the linear slope (m_S) and the intercept (n_S) through nonlinear fitting (analytic Gauss–Newton algorithm) by replacing A_S in Eq. (2) with A_S(Q) from Eq. (6), yielding the following:

In Eq. (8), φ_S is the phase of the seasonal streamwater isotope cycle (rad), t is the time (decimal year), f is the frequency (yr⁻¹), and k_S (‰) is a constant describing the vertical offset of the streamwater isotope signal. For the sake of simplicity, Eq. (8) assumes that the amplitude of the seasonal cycle varies with Q but the phase φ_S does not. Numerical experiments (e.g. Fig. 8 in Kirchner, 2016b) suggest that the change in streamwater isotope cycle phase φ_S between high and low flows should have only a minor influence on the estimate of the parameters in Eq. (8), because the change in φ_S can only be large when the cycle is strongly damped (i.e. during low-flow conditions), and the phase of such a strongly damped cycle will have little effect on the fit to the data.

Combining Eqs. (6) and (7) yields

and thus, the linear slope of the dependence of F_yw on Q can be approximated as m_S∕A_P, which has units of Q⁻¹. The uncertainty in this slope was estimated through Gaussian error propagation. Please note that Eq. (9) quantifies discharge sensitivity based on the linear slope of the relationship between F_yw and Q, whereas Fig. 7 shows how F_yw varies with log(Q) for different fractions of the discharge distribution. By replacing Q with log(Q) in Eqs. (6)–(9), one could easily determine the linear slope of the relationship between F_yw and log(Q) instead.

For convenience, we term this linear slope of the Q–F_yw relationship the “discharge sensitivity” of F_yw. Our use of this term should not be interpreted to mean that F_yw depends, in a mechanistic sense, on discharge per se. Instead, we use the term to indicate the statistical sensitivity of F_yw to discharge, where discharge is a proxy indicator of catchment wetness conditions and hydro-climatic forcing. Catchments with high discharge sensitivity of F_yw (steep linear slope in Eq. 9) are ones in which the young water fraction varies greatly between low and high flows, suggesting that faster flow paths are more predominant in larger events. Conversely, catchments with low discharge sensitivity (shallower linear slopes in Eq. 9) are ones in which young water fractions are broadly similar between low and high flows, suggesting that the same predominant flow paths are activated in similar proportions in both large and small runoff events.

On average, we find that every 1 mm day⁻¹ increase in discharge is associated with an increase of 0.0202 ± 0.0046 in F_yw. From this analysis, we excluded the Aach catchment because only two streamwater samples were collected during high-flow conditions, resulting in an unrealistic and highly uncertain value for m_S. At the remaining 21 sites, the discharge sensitivities of F_yw range between zero (within error) at Ilfis and Sitter, and 0.0732 ± 0.0360 day mm⁻¹ at Mentue. A similar analysis was carried out by Wilusz et al. (2017) for two neighbouring catchments in Plynlimon, Wales. For those two sites, Wilusz et al. (2017) combined a rainfall–runoff model with a rank storage selection (rSAS) transit time model and estimated an increase in F_yw of 0.031 to 0.040, respectively, with every 1 mm day⁻¹ increase in average annual precipitation. Multiplying their “precipitation sensitivities of F_yw” by the site-specific runoff ratios (0.78 and 0.90) yields average discharge sensitivities of F_yw of 0.0242 and 0.0360 day mm⁻¹, respectively, which are within the range of values we obtained for our 22 Swiss study sites. Even though the methods, tracers, and timescales Wilusz et al. used to estimate F_yw differed from ours, the similarity in the discharge sensitivities between their sites and ours suggests that this may be a robust and reproducible metric that could be useful in future catchment studies.

For our study catchments, there was no systematic relationship between the young water fraction (either F_yw or $F_{\mathrm{yw}}^{*}$) and the discharge sensitivity, indicating that they are different and largely independent measures of catchment behaviour (Figs. 8 and 9). The discharge sensitivity of F_yw is, however, strongly correlated to a range of landscape and hydro-climatic conditions, including $\stackrel{\mathrm{‾}}{P}$ (ρ = −0.64, see also Fig. 9b), ${\stackrel{\mathrm{‾}}{P}}_{\mathrm{intensity}}$ (ρ = −0.56), $\stackrel{\mathrm{‾}}{Q}$ (ρ = −0.61), DD (ρ = −0.59), L∕G (ρ = 0.75), L (ρ = 0.46), G (ρ = −0.46), TWI (ρ = 0.52), A_precip (ρ = −0.44), and mean catchment elevation (ρ = 0.44). All of these correlations remain statistically significant (and many become stronger) when the snow-dominated sites are excluded from the analysis.

In contrast, calculating linear slopes between F_yw and log(Q), instead of Q, yields no significant correlations with any of the variables in Tables 2 or S1. It should be noted that calculations based on log(Q) will be more strongly influenced by small discharges, whereas calculations based on Q will be more strongly influenced by the upper tail of the Q distribution. Thus, since our primary focus is storm runoff generation, we interpret the discharge sensitivities of F_yw based on Q instead of log(Q).

Figure 9(a) Flow-weighted young water fractions at the 22 Swiss study catchments; (b) discharge sensitivity of F_yw at the same sites (mean annual precipitation for the period 1991–2010 is shown for comparison).

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Our results suggest that catchments with low discharge sensitivity of F_yw are characterized by high elevations, dense river networks (high DD, low L∕G) and/or generally humid conditions (high $\stackrel{\mathrm{‾}}{P}$). These catchment properties are generally associated with predominantly shallow runoff flow paths during both large and small precipitation events, such that the fraction of young water remains relatively high under widely varying flow regimes. In contrast, in catchments characterized by lower drainage density and less humid conditions, larger or higher-intensity storms are likely to strongly alter the proportions of different dominant flow paths, leading to bigger variations in F_yw (i.e. higher discharge sensitivity). For example, the dynamic extension of the stream network (e.g. Godsey and Kirchner, 2014; Jensen et al., 2017) and/or the increase in hydrologic connectivity between the stream network and the surrounding landscape (e.g. Detty and McGuire, 2010; Phillips et al., 2011; von Freyberg et al., 2015) should more strongly influence the relative proportion of young streamflow in catchments where drainage density is not already high. Likewise, the activation of shallow flow paths during larger storm events will have a bigger influence on F_yw in drier catchments than in wetter ones, where shallow flow paths are likely to be activated during both large and small events.

Figure 10Conceptual description of the mechanistic relationship between young water fractions and discharge, which is used here as a proxy for catchment wetness and hydro-climatic forcing. The three colours of the arrows represent three individual hypothetical catchments.

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Interestingly, although F_yw and its discharge sensitivity are not significantly correlated with each other, they are often correlated with catchment characteristics in opposite ways (Table 4). For example, DD, $\stackrel{\mathrm{‾}}{Q}$, $\stackrel{\mathrm{‾}}{P}$, ${\stackrel{\mathrm{‾}}{P}}_{\mathrm{intensity}}$, QFI, and CV_Q exhibit positive correlations with F_yw but also exhibit negative correlations with the discharge sensitivity of F_yw. In catchments with dense river networks and/or generally humid climates, fast runoff flow paths will dominate (and thus F_yw and $F_{\mathrm{yw}}^{*}$ will be high). These same conditions should also make fast runoff flow paths more persistent, with the result that the young water fraction will not be strongly dependent on catchment wetness conditions or hydro-climatic forcing (and thus discharge sensitivity will be low).

5.4 A conceptual model of the mechanistic relationship between young water fractions and discharge

Figure 10 presents a conceptual summary of the relationships between the young water fraction, its discharge sensitivity, and landscape and hydro-climatic characteristics that control streamflow generation. We suggest that the general trend of the Q–F_yw relationship is positive because high-flow periods during precipitation events are likely to contain larger fractions of young water travelling by quick flow paths, while low-flow conditions are primarily sustained by older groundwater. In Fig. 10, the steepness of the linear slope expresses how extensively fast flow paths are activated during high flows. In theory, a linear slope of zero (i.e. F_yw insensitive to discharge) would represent strictly linear rainfall–runoff behaviour with a constant mixing fraction of young and old water. In natural systems, however, the relative proportions of streamflow generation mechanisms are likely to vary between high and low flows, making F_yw sensitive to discharge. From our analyses in Sect. 6.1. and 6.2, we find that low discharge sensitivities of F_yw can occur at sites with either high or low young water fractions (cases 1 and 3, respectively, in Fig. 10; e.g. Erlenbach and Ilfis, respectively, in Fig. 7). Case 1 might be found in humid catchments with frequent precipitation, low storage capacity, and dense river networks, where shallow runoff flow paths dominate both during and between events (e.g. triggered by saturation excess). Case 3 is more likely to occur in catchments with high infiltration capacity and large subsurface storage, where slow subsurface flow paths dominate both during events and between them, leading to consistently low young water fractions. A steep linear slope (case 2 in Fig. 10; e.g. Alp, Biber or Murg in Fig. 7) is likely to occur in catchments where the relative contributions of fast and slow flow paths vary dramatically in response to hydro-climatic forcing or antecedent wetness conditions, for example through drainage network expansion, or shifts in hydrological connectivity due to groundwater tables rising into more permeable layers.

The hydrological concepts presented in Fig. 10 are based on the young water fraction analysis for 21 Swiss catchments that share several landscape and hydro-climatic characteristics, such as similar vegetation cover, relatively humid climate, and (partly) mountainous terrain. Hence, we must be cautious about extending this conceptual model to regions characterized by (semi-)arid or arctic climates, very different vegetation cover or predominantly flat terrain. In addition, linking young water fractions to catchment wetness conditions and hydro-climatic forcing may be difficult in catchments with streamflow regimes that are discontinuous or strongly affected by lakes, water management (e.g. groundwater pumping, artificial groundwater recharge, irrigation, or water diversion) or land-use change (e.g. urban development, soil degradation, or forest clear cutting). Nevertheless, long-term tracer data sets from other catchments could be used to expand our analysis beyond the Swiss study sites and to test the transferability of the conceptual model presented in Fig. 10.