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**Hydrology and Earth System Sciences**
An interactive open-access journal of the European Geosciences Union

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- Abstract
- Introduction
- Theoretical background: young water fractions from seasonal cycles of stable water isotopes in precipitation and streamwater
- Data set
- Methodological evaluation of the young water fraction framework
- Relationships between young water fractions, hydro-climatic conditions, and landscape characteristics
- Summary and conclusions
- Data availability
- Author contributions
- Competing interests
- Acknowledgements
- References
- Supplement

**Research article**
19 Jul 2018

**Research article** | 19 Jul 2018

Sensitivity of young water fractions to hydro-climatic forcing and landscape properties across 22 Swiss catchments

^{1}Department of Environmental Systems Science, ETH Zurich, Zurich, Switzerland^{2}Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland^{3}Faculty of Environment and Natural Resources, University of Freiburg, Freiburg im Breisgau, Germany

^{1}Department of Environmental Systems Science, ETH Zurich, Zurich, Switzerland^{2}Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland^{3}Faculty of Environment and Natural Resources, University of Freiburg, Freiburg im Breisgau, Germany

**Correspondence**: Jana von Freyberg (jana.vonfreyberg@usys.ethz.ch)

**Correspondence**: Jana von Freyberg (jana.vonfreyberg@usys.ethz.ch)

Abstract

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The young water fraction *F*_{yw}, defined as the proportion of
catchment outflow younger than approximately 2–3 months, can be estimated
directly from the amplitudes of seasonal cycles of stable water isotopes in
precipitation and streamflow. Thus, *F*_{yw} may be a useful metric in
catchment inter-comparison studies that investigate landscape and
hydro-climatic controls on streamflow generation. Here, we explore how
*F*_{yw} varies with catchment characteristics and climatic forcing,
using an extensive isotope data set from 22 small- to medium-sized
(0.7–351 km^{2}) Swiss catchments. We find that flow-weighting the tracer
concentrations in streamwater resulted in roughly 26 % larger young water
fractions compared to the corresponding unweighted values, reflecting the
fact that young water fractions tend to be larger when catchments are wet and
discharge is correspondingly higher. However, flow-weighted and unweighted
young water fractions are strongly correlated with each other among the
catchments. They also correlate with terrain, soil, and land-use indices, as
well as with mean precipitation and measures of hydrologic response. Within
individual catchments, young water fractions increase with discharge,
indicating an increase in the proportional contribution of faster flow paths
at higher flows. We present a new method to quantify the discharge
sensitivity of *F*_{yw}, which we estimate as the linear slope of the
relationship between the young water fraction and flow. Among the
22 catchments, discharge sensitivities of *F*_{yw} are highly variable
and only weakly correlated with *F*_{yw} itself, implying that these
two measures reflect catchment behaviour differently. Based on strong
correlations between the discharge sensitivity of *F*_{yw} and several
catchment characteristics, we suggest that low discharge sensitivities imply
greater persistence in the proportions of fast and slow runoff flow paths as
catchment wetness changes. In contrast, high discharge sensitivities
imply the activation of different dominant flow paths during precipitation
events, such as when subsurface water tables rise into more permeable layers
and/or the river network expands further into the landscape.

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How to cite.

von Freyberg, J., Allen, S. T., Seeger, S., Weiler, M., and Kirchner, J. W.: Sensitivity of young water fractions to hydro-climatic forcing and landscape properties across 22 Swiss catchments, Hydrol. Earth Syst. Sci., 22, 3841–3861, https://doi.org/10.5194/hess-22-3841-2018, 2018.

1 Introduction

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Naturally occurring variations in stable water isotopes (*δ*^{18}O,
*δ*^{2}H) or chemically passive solutes (e.g. chloride) are
commonly used in catchment studies to track the flow of water and to gain
insight into catchment storage and mixing behaviour (Buttle, 1994;
Kendall and McDonnell, 1998; Klaus and McDonnell, 2013). Many catchment studies use these
tracers to estimate time-averaged transit time distributions, to
characterize the heterogeneity of flow pathways, and to estimate mobile
catchment storage (e.g. Benettin et al., 2015; Birkel et al., 2011;
Hrachowitz et al., 2009; Staudinger et al., 2017). Transit time distributions are
often inferred from conservative tracers using lumped-parameter models
(McGuire and McDonnell, 2006). Because the mean transit time
expresses the ratio between mobile catchment storage and the average flow
rate, it is widely used in catchment inter-comparison studies (e.g.
Hrachowitz et al., 2009; McGuire et al., 2005; Staudinger et al., 2017). However, estimates of mean
transit time can be biased and unreliable, especially for spatially
heterogeneous catchments (Kirchner, 2016b;
Seeger and Weiler, 2014). Instead, the young water fraction
*F*_{yw} – i.e. the average fraction of streamflow that is younger than a
specified threshold age – has recently been proposed as a more reliable
measure of water age in heterogeneous catchments (Kirchner, 2016a, b).
Young water fractions with a threshold age of roughly 2–3 months can be
estimated directly from the amplitude ratio of the seasonal cycles in stable
water isotopes in precipitation and streamwater.

The amplitudes of the seasonal isotopic cycles in precipitation and
streamwater can be estimated directly from the isotope measurements
themselves, or by volume-weighting these measurements by the corresponding
precipitation or discharge rates. Precipitation isotopes should generally be
volume-weighted to prevent small precipitation events, potentially with
anomalous isotope values, from substantially influencing the calculated
seasonal precipitation isotope cycle. Streamwater isotope values can also be
flow-weighted, using stream discharges as weights. Higher streamflows should
typically correspond to larger young water fractions, for the simple reason
that flow peaks typically follow intense rainfall and contain more recent
precipitation than base flows (e.g. Kirchner, 2016b;
von Freyberg et al., 2017). Hence, the flow-weighted
average young water fraction (here denoted ${F}_{\mathrm{yw}}^{*}$) is
expected to be higher than the unweighted average young water fraction (*F*_{yw}).
Both *F*_{yw} and ${F}_{\mathrm{yw}}^{*}$ are calculated over
periods of a year or longer, and represent the average catchment behaviour
over that time. In calculating the unweighted *F*_{yw}, each unit of time
counts equally, and benchmark tests using a nonstationary lumped catchment
model confirm that the calculated *F*_{yw} should accurately reflect the
time-averaged fraction of young water in discharge (Kirchner, 2016b). By
contrast, in calculating the flow-weighted ${F}_{\mathrm{yw}}^{*}$, each
unit of flow counts equally, and benchmark tests confirm that the calculated
${F}_{\mathrm{yw}}^{*}$ reflects the cumulative volume of young water, as
a fraction of the cumulative volume of discharge, over the corresponding
period (Kirchner, 2016b). Although ${F}_{\mathrm{yw}}^{*}$ and *F*_{yw}
have previously been compared in benchmark tests, a systematic evaluation based
on tracer data from natural catchments has not yet been carried out.

At sites where precipitation isotopes are not measured directly, catchment
isotopic inputs can be estimated from nearby long-term monitoring stations
using various spatial interpolation methods. These interpolation methods
differ in their assumptions about temperature- and elevation-dependent
isotope fractionation effects, and their treatment of seasonal snowpack
storage. Based on a global database of *δ*^{18}O in precipitation,
Jasechko et al. (2016) calculated the seasonal cycle amplitudes and their
standard errors for each station and interpolated them to generate a global
grid of the seasonal cycle amplitudes. These interpolated coefficients were
volume-weighted by the spatial pattern of precipitation over each catchment.
An alternative approach (Allen et al., 2018; see Supplement)
builds on the Jasechko et al. (2016) method with an additional step that
accounts for the residuals of the observations from the fitted seasonal
cycles. To generate a high-resolution precipitation isotope map for
Switzerland, Seeger and Weiler (2014) interpolated *δ*^{18}O
in monthly precipitation from long-term monitoring stations in
central Europe, using an elevation-gradient approach. They combined their
interpolation method with an energy-balance-based snow model to estimate the
liquid input to the soil surface at monthly temporal resolution. The latter
two interpolation methods have been rigorously tested with real-world
isotope measurements, and thus may be particularly useful for estimating
young water fractions in catchments where no long-term precipitation isotope
measurements exist.

Another analytical decision that affects the interpretation of
${F}_{\mathrm{yw}}^{*}$ and *F*_{yw} relates to whether snowpack storage is
considered to be part of catchment storage, or not. If one measures
precipitation to the snow surface as the catchment input, then snowpack
accumulation and melt are implicitly included in catchment storage (e.g.
Staudinger et al., 2017). In this case, comparisons of
seasonal cycles in precipitation and streamflow should reflect the young
water fraction resulting from the combination of snowpack and subsurface
storage. Alternatively, if one uses precipitation and snowmelt arriving at
the soil surface as the catchment input (for example, with melt pan
lysimeters, or modelled snowpack outflows), then snowpack accumulation and
melt are implicitly excluded from catchment storage. In this case,
comparisons of seasonal cycles in streamflow and sub-snowpack catchment
input should reflect the young water fraction resulting from subsurface
storage alone. Because the total catchment storage in the first case
(including snowpack storage) is larger than the subsurface storage alone,
the resulting young water fractions are expected to be smaller. Previous
studies that estimated young water fractions in snow-dominated watersheds
(Jasechko et al., 2016; Song et al., 2017) did not
differentiate between these two concepts of catchment storage and simply
used incoming precipitation in the young water fraction calculations, thus
implicitly considering snowpack storage as part of catchment storage (as in
the first case outlined above). This approach is practical in view of the
challenges of measuring or modelling snowmelt and its isotopic composition.
However, it is still unclear whether, in cases where snowmelt can be
modelled or measured, explicitly considering snowmelt as a catchment input
would significantly alter young water fraction estimates.

Because the young water fraction can be estimated from sparse and irregular
tracer data, it has been suggested as a useful metric for catchment
inter-comparison studies (Kirchner, 2016a). To date,
however, most catchment inter-comparison studies have investigated controls
on mean transit times instead. Mean transit times have been variably found
to be correlated with (for example) flow path lengths and gradients
(McGuire et al., 2005), drainage density (Soulsby et al.,
2010), the areal fraction of hydrologically responsive soils
(Tetzlaff et al., 2009), bedrock permeability (Hale
and McDonnell, 2016), or combinations of multiple factors
(Hrachowitz et al., 2009; Seeger and Weiler, 2014).
So far, only a few catchment inter-comparison studies have used young water
fractions (Song et al., 2017; Stockinger et
al., 2016; Jasechko et al., 2016). A global analysis of 254 watersheds,
revealed large spatial variability in young streamflow, which correlated
inversely with average topographic gradients and water table depths
(Jasechko et al., 2016). Jasechko et al. (2016) hypothesized that steeper
landscapes are associated with more pervasive rock fracturing, deeper
infiltration, and reduced shallow lateral flow, all of which would reduce
the young water fraction in steep terrain. However, the correlation between
topographic steepness and young water fractions was highly scattered,
indicating that other factors are also involved. Jasechko et al.'s (2016)
study sites were mostly larger than 1000 km^{2} (25th percentile
1753 km^{2}, median 10 800 km^{2}) and thus were probably affected by a
complex interplay of landscape characteristics, climatic variability, and
human impacts. Identifying landscape and climatic drivers that potentially
control catchment storage behaviour may be easier in small- to medium-sized
catchments with near-natural streamflow regimes (Holko et al., 2015).

In the present study, we use seasonal cycles in *δ*^{18}O to
estimate young water fractions for 22 sites in Switzerland with catchment
areas between 0.7 and 351 km^{2}. In a first step, we evaluate how choices
of methodology affect the young water fraction estimates, with emphasis on
(i) the spatial interpolation method for precipitation isotopes, (ii) the
conceptual representation of snow storage, and (iii) flow-weighting the
streamwater isotope data. Because the 22 study catchments cover a wide range
of landscape and hydro-climatic characteristics, in the second part of this
study, we test for correlations between the young water fraction and a wide
range of landscape and hydro-climatic indices. Finally, we present a method
for estimating the linear dependence of the young water fraction on the
streamflow regime and propose that the slope of this relationship may be a
diagnostic indicator of streamflow generation processes.

2 Theoretical background: young water fractions from seasonal cycles of stable water isotopes in precipitation and streamwater

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The isotopic composition of precipitation follows a seasonal cycle
(Feng et al., 2009). The damping and phase shift of this seasonal
cycle as it is transmitted through catchments
(Fig. 1) can be used to infer timescales of
catchment storage and transport (e.g. DeWalle et al., 1997; Soulsby et al.,
2006). Sine-wave fitting can quantify the amplitude ratio
*A*_{S}∕*A*_{P} and phase shift *φ*_{S} − *φ*_{P} between the
seasonal isotope cycles in precipitation and streamflow (the indices P and S
refer to precipitation and streamwater, respectively). The seasonal isotope
cycles in precipitation and streamwater can be described by:

$$\begin{array}{}\text{(1)}& {\displaystyle}{\displaystyle}{c}_{\mathrm{P}}\left(t\right)={A}_{\mathrm{P}}\mathrm{sin}\left(\mathrm{2}\mathit{\pi}ft-{\mathit{\phi}}_{\mathrm{P}}\right)+{k}_{\mathrm{P}}\end{array}$$

and

$$\begin{array}{}\text{(2)}& {\displaystyle}{\displaystyle}{c}_{\mathrm{S}}\left(t\right)={A}_{\mathrm{S}}\mathrm{sin}\left(\mathrm{2}\mathit{\pi}ft-{\mathit{\phi}}_{\mathrm{S}}\right)+{k}_{\mathrm{S}}.\end{array}$$

In Eqs. (1) and (2), *A* is the amplitude (‰), *φ* is
the phase of the seasonal cycle (in radians, with 2 *π* rad equalling
1 year), *t* is the time (decimal years), *f* is the frequency (yr^{−1}), and
*k* (‰) is a constant describing the vertical offset of the isotope signal.

If one assumes that the transit times of water through the catchment follow
a particular transit time distribution, the mean transit time can be
calculated as a function of the amplitude ratio *A*_{S}∕*A*_{P}. However, mean
transit times inferred from seasonal tracer cycles in runoff from
heterogeneous catchments are potentially subject to severe aggregation bias
(Kirchner, 2016a). Alternatively, the amplitude ratio *A*_{S}∕*A*_{P}
can be used to estimate the fraction of water younger than a
specified threshold age. Compared to the mean transit time, this “young
water fraction” (*F*_{yw}) is markedly less vulnerable to aggregation bias,
and less sensitive to the assumed shape of the catchment transit time
distribution (Kirchner, 2016a, b). For a wide range of transit time
distributions, the young water threshold age is approximately 2.3 ± 0.8 months (Kirchner, 2016a).

We can estimate the amplitudes *A*_{S} and *A*_{P} of the seasonal isotope
cycles in Eqs. (1) and (2) by using multiple linear regression to obtain the
coefficients *a* and *b* in

$$\begin{array}{}\text{(3)}& {\displaystyle}{\displaystyle}{c}_{\mathrm{P}}\left(t\right)={a}_{\mathrm{P}}\mathrm{cos}\left(\mathrm{2}\mathit{\pi}ft\right)+{b}_{\mathrm{P}}\mathrm{sin}\left(\mathrm{2}\mathit{\pi}ft\right)+{k}_{\mathrm{P}}\end{array}$$

and

$$\begin{array}{}\text{(4)}& {\displaystyle}{\displaystyle}{c}_{\mathrm{S}}\left(t\right)={a}_{\mathrm{S}}\mathrm{cos}\left(\mathrm{2}\mathit{\pi}ft\right)+{b}_{\mathrm{S}}\mathrm{sin}\left(\mathrm{2}\mathit{\pi}ft\right)+{k}_{\mathrm{S}}.\end{array}$$

The amplitudes *A*_{S} and *A*_{P} are then determined by

$$}{\displaystyle}{A}_{\mathrm{P}}=\sqrt{{a}_{\mathrm{P}}^{\mathrm{2}}+{b}_{\mathrm{P}}^{\mathrm{2}}$$

and

$$\begin{array}{}\text{(5)}& {\displaystyle}{\displaystyle}{A}_{\mathrm{S}}=\sqrt{{a}_{\mathrm{S}}^{\mathrm{2}}+{b}_{\mathrm{S}}^{\mathrm{2}}}.\end{array}$$

Following Kirchner (2016a), we calculate young water
fractions as the amplitude ratio *A*_{S}∕*A*_{P}. We estimate the coefficients
*a*_{S}, *b*_{S}, *a*_{P}, and *b*_{P} by fitting Eqs. (3) and (4) using
iteratively re-weighted least squares (IRLS), a robust estimation method that
minimizes the influence of any potential outliers (an *R* script with our IRLS
code is provided in the Supplement). In estimating *a*_{P} and *b*_{P}, we
volume-weight Eq. (3) to avoid giving undue leverage to low-precipitation
periods. To calculate the unweighted young water fraction *F*_{yw}, we
estimate *a*_{S} and *b*_{S} from Eq. (4) using unweighted IRLS. For the
flow-weighted young water fraction (${F}_{\mathrm{yw}}^{*}$), we estimate
*a*_{S} and *b*_{S} from Eq. (4) using discharge-weighted IRLS (see the
*R* script provided in the Supplement). Uncertainties in the calculated
unweighted and flow-weighted young water fractions are expressed as standard
errors (SEs) and are estimated using Gaussian error propagation.

3 Data set

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The 22 study catchments cover areas between 0.7 and 351 km^{2} and have
mean elevations between 472 and 2369 m a.s.l. (Table 1).
Most of the sites are located in the Swiss Plateau and in the northern
Alps, where the geology is characterized by sedimentary rocks (limestones,
sandstones, marls, marly shales, conglomerates, breccias) and unconsolidated
sediments (clay, silts, sands). In the southern Alps, two high-elevation
catchments (Dischmabach and Riale di Calneggia) are predominantly underlain
by metamorphic rock (mica schist, gneiss), and Ova da Cluozza is the only
study catchment underlain by dolomite (Fig. 2a and b).

Land use at lower elevations (400–800 m) is predominantly agriculture, while grassland and forests can be found at elevations up to around 1400 m. Much of the area above 1700 m is characterized by grasses, shrubs, and sparse vegetation. At two high-elevation sites, Dischmabach and Ova da Cluozza, up to ∼ 2 % of the drainage area is covered by glaciers. At all sites, the human influence on river discharge is small, resulting in near-natural streamflow regimes.

Switzerland is characterized by a humid to temperate continental climate, with the Alps creating climatically distinct subregions. The wettest regions can be found in the northern pre-Alps and Alps, as well as in the canton of Ticino south of the Alps. The driest regions are located in inner Alpine valleys in the cantons of Valais and Grisons (Fig. 2c). Average annual precipitation rates for the 22 catchments range from 887 to 1853 mm based on observations from 2000 to 2015 (Table 1). To differentiate between the hydro-climatic regimes of the catchments, we grouped them into three classes (snow-dominated, rainfall-dominated, and hybrid) proposed by Staudinger et al. (2017). Precipitation is distributed more-or-less evenly throughout the year, although peak inputs to the soil surface (melt and precipitation) are shifted towards spring and summer in all snow-dominated sites and some hybrid sites.

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.

The average hydro-climatic properties at the sites were described by various
indices, such as mean monthly values of discharge $\stackrel{\mathrm{\u203e}}{Q}$ and
precipitation *Q*, as well as mean daily precipitation intensity
${\stackrel{\mathrm{\u203e}}{P}}_{\mathrm{intensity}}$. 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):

$$\begin{array}{}\text{(6)}& {\displaystyle}{\displaystyle}P\left(t\right)=\stackrel{\mathrm{\u203e}}{P}\left[\mathrm{1}+{A}_{\mathrm{precip}}\mathrm{sin}\left(\mathrm{2}\mathit{\pi}\left(t-{\mathit{\phi}}_{\mathrm{precip}}\right)/\mathit{\tau}\right)\right],\end{array}$$

where *P* is the precipitation volume (mm month^{−1}), $\stackrel{\mathrm{\u203e}}{P}$ 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 ($\stackrel{\mathrm{\u203e}}{Q}$) and mean monthly
precipitation ($\stackrel{\mathrm{\u203e}}{P}$) were significantly correlated with each other
across the 22 sites. Furthermore, $\stackrel{\mathrm{\u203e}}{Q}$ 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.

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
(*δ*^{18}O) 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 *δ*^{18}O data were
provided by the Institute for Atmospheric and Climate Science at ETH Zurich.

Values of *δ*^{18}O in precipitation were not measured directly at
the 22 study catchments. Instead, *δ*^{18}O 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 *δ*^{18}O 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).

4 Methodological evaluation of the young water fraction framework

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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 *δ*^{18}O in precipitation yield consistent
young water fraction estimates for the 22 study catchments.

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.

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 *δ*^{18}O (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).

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).

5 Relationships between young water fractions, hydro-climatic conditions, and landscape characteristics

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By examining how the catchments' young water fractions correlate with their
landscape and hydro-climatic characteristics, we aim to identify dominant
controls on their hydrological behaviour. Below, we present our results for
flow-weighted young water fractions (${F}_{\mathrm{yw}}^{*}$); however,
the unweighted young water fractions (*F*_{yw}) yield very similar results,
as both values are significantly correlated with each other (*ρ* = 0.9,
*p* < 0.001; Table 4).

Table 4 and Fig. 6 show that young water fractions exhibit statistically significant positive
correlations with five hydro-climatic indices: mean monthly discharge ($\stackrel{\mathrm{\u203e}}{Q}$),
mean monthly precipitation ($\stackrel{\mathrm{\u203e}}{P}$), mean daily
precipitation intensity (${\stackrel{\mathrm{\u203e}}{P}}_{\mathrm{intensity}}$), coefficient of
variation of daily discharge (CV_{Q}), and QFI. These
correlations suggest that young water fractions tend to be highest in humid
catchments where prompt runoff response is facilitated by fast flow paths
and/or high-intensity precipitation events. ${F}_{\mathrm{yw}}^{*}$ was
also significantly correlated with high values of drainage density (DD) and
low values of flow path length (*L*) (Table 4). There
was also a significant negative correlation with the ratio of the flow path
length to gradient (*L*∕*G*), but as there is nearly zero correlation with *G* itself,
the correlation with *L*∕*G* apparently arises through *L* alone. Drainage density is
inversely proportional to median flow path length, so the strong positive
correlation of ${F}_{\mathrm{yw}}^{*}$ with DD and negative correlation with
*L* can be viewed as two sides of the same coin. All else equal, high values of
DD, and thus small values of *L*, facilitate faster runoff, which is directly
linked to higher values of CV_{Q} and QFI.

A statistically significant inverse correlation (*ρ* = −0.36,
*p* < 0.0001) between *F*_{yw} and the logarithm of the topographic gradient was
found by Jasechko et al. (2016) for 254 sites across Europe and North
America, with the surprising implication that steeper catchments have less
(not more) young streamflow. Among our individual catchments, however, we
find no correlation between *F*_{yw} (or ${F}_{\mathrm{yw}}^{*}$) and
topographic gradient. This may be partly explained by the lack of
low-gradient catchments among our study sites; our gradients span a range
of 0.02–0.64 compared to ∼ 0.0007–0.11 in Jasechko et al. (2016),
and the correlation that they observe appears to be largely driven
by sites with gradients less than roughly 0.01. Nevertheless, our data set
fits within the global pattern found by Jasechko et al. (2016), and the
median *F*_{yw} of our 22 mostly high-gradient study catchments (0.16,
95 % confidence interval 0.10–0.21) is smaller than the global median
(0.21, 95 % confidence interval 0.19–0.24) consistent with the
gradient-dependence hypothesized by Jasechko et al. (2016).

^{*} The catchment Aach was omitted from the analysis because its
isotope data set contained only two data points during high-flow conditions.

Some studies have identified catchment area as a major control on mean
transit times (e.g. DeWalle et al., 1997; Soulsby et al.,
2000), however, the inverse correlation of ${F}_{\mathrm{yw}}^{*}$ and *F*_{yw}
with catchment area only becomes significant (*ρ* = −0.49,
*p* < 0.05) when the five high-elevation, snow-dominated sites are omitted from
the analysis (Fig. 6). The young water fractions
of the remaining 17 sites were also strongly correlated with mean catchment
elevation (*ρ* = 0.65, *p* < 0.005, Fig. 6), which in turn is a major
control on other hydro-climatic indices ($\stackrel{\mathrm{\u203e}}{Q}$, $\stackrel{\mathrm{\u203e}}{P}$) and
topographic indices (DD, *G*, *L*, *L*∕*G*, and TWI).

Across the 22 catchments, ${F}_{\mathrm{yw}}^{*}$ is positively correlated
with the areal fraction of saturated soils (*ρ* = 0.58, *p* < 0.01)
and low-permeability soils (*ρ* = 0.52, *p* < 0.05). These
relationships remain significant when the snow-dominated sites are omitted
from the analysis. A strong positive relationship with
${F}_{\mathrm{yw}}^{*}$ can be expected because saturated soils and
low-permeability soils are often associated with overland flow and/or fast
subsurface flow mechanisms triggered by exceedance of soil water storage
thresholds (saturation excess; Dunne and Black, 1970) or
precipitation intensity (infiltration excess; Horton, 1933). Particularly
high fractions of saturated soils occur at three neighbouring catchments
(Erlenbach, Lümpenenbach and Vogelbach) that are characterized by
shallow gleysols (Feyen et al., 1996; Fischer et
al., 2015). Together with the nearby Biber catchment, these four sites
exhibit the largest young water fractions in our data set. No correlation
was evident between ${F}_{\mathrm{yw}}^{*}$ and the fraction of soils with
low water storage capacity, likely due to the strong influence of six sites
where this fraction was zero.

${F}_{\mathrm{yw}}^{*}$ is not significantly correlated with the areal fractions mapped as having high, intermediate, or low groundwater productivity, here used as a proxy for the catchments' hydrogeologic properties. This result is perhaps unsurprising; most groundwater is probably older than the threshold age that defines young water, so the young water fraction will not be sensitive to how much older the groundwater is. Instead, the fraction of young water should primarily reflect mechanisms that control flow processes and routing near the land surface (shallow groundwater, soil water, overland flow) rather than groundwater flow in deep aquifers where flow velocities can be several orders of magnitude slower.

Across our study catchments, the young water fraction is strongly correlated
with the areal fraction of forest (*ρ* = 0.58, *p* < 0.01;
Tables 1 and 4). Excluding the snow-dominated sites from the analysis slightly weakens this
relationship although it remains statistically significant (*ρ* = 0.51,
*p* < 0.05). One would normally expect tree roots to increase soil
permeability, resulting in greater infiltration and groundwater recharge
(Brantley et al., 2017). However, on steep forested slopes, abundant
lateral preferential flow pathways (e.g. macropores) may facilitate rapid
transport of water (Whipkey, 1965). Thus, the correlation we observe
may be artefactual, since across our sites, forest cover is also correlated
with higher drainage densities and shorter mean flow paths, as well as
higher fractions of saturated and low-permeability soils, all of which can
plausibly increase the young water fraction. More generally, among our
22 study sites, hydro-climatic characteristics are correlated with landscape
properties, making it challenging to clearly identify individual controls on
the young water fraction. Broadly, however, we can conclude that high young
water fractions are generally associated with hydro-climatic factors (e.g.
humid climate and high precipitation intensity) and landscape
characteristics (e.g. low soil permeability and high drainage density) that
facilitate fast streamflow responses.

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.

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.

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.

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:

$$\begin{array}{}\text{(7)}& {\displaystyle}{\displaystyle}{F}_{\mathrm{yw}}\left(Q\right)={A}_{\mathrm{S}}\left(Q\right)/{A}_{\mathrm{P}}.\end{array}$$

If we approximate *A*_{S} as a linear function of *Q*,

$$\begin{array}{}\text{(8)}& {\displaystyle}{\displaystyle}{A}_{\mathrm{S}}\left(Q\right)={n}_{\mathrm{S}}+{m}_{\mathrm{S}}Q,\end{array}$$

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:

$$\begin{array}{}\text{(9)}& {\displaystyle}{\displaystyle}{c}_{\mathrm{S}}\left(t\right)=\left({n}_{\mathrm{S}}+{m}_{\mathrm{S}}Q\right)\cdot \mathrm{sin}(\mathrm{2}\mathit{\pi}ft-{\mathit{\phi}}_{\mathrm{S}})+{k}_{\mathrm{S}}.\end{array}$$

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

$$\begin{array}{}\text{(10)}& {\displaystyle}{\displaystyle}{F}_{\mathrm{yw}}\left(Q\right)={\displaystyle \frac{{n}_{\mathrm{S}}+{m}_{\mathrm{S}}Q}{{A}_{\mathrm{P}}}}={\displaystyle \frac{{n}_{\mathrm{S}}}{{A}_{\mathrm{P}}}}+{\displaystyle \frac{{m}_{\mathrm{S}}}{{A}_{\mathrm{P}}}}Q\end{array}$$

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 $\stackrel{\mathrm{\u203e}}{P}$ (*ρ* = −0.64, see also
Fig. 9b), ${\stackrel{\mathrm{\u203e}}{P}}_{\mathrm{intensity}}$ (*ρ* = −0.56), $\stackrel{\mathrm{\u203e}}{Q}$ (*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*).

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 $\stackrel{\mathrm{\u203e}}{P}$). 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.

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, $\stackrel{\mathrm{\u203e}}{Q}$, $\stackrel{\mathrm{\u203e}}{P}$, ${\stackrel{\mathrm{\u203e}}{P}}_{\mathrm{intensity}}$,
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).

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.

6 Summary and conclusions

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The fraction of streamflow younger than roughly 2–3 months has recently been
proposed as a robust measure of water age which can be estimated directly
from the seasonal cycles of stable water isotopes in precipitation and
streamflow (Kirchner, 2016a, b). Here, we have leveraged an extensive
isotope data set from 22 small- to medium-sized Swiss catchments to explore
how the young water fraction (*F*_{yw}) varies with catchment characteristics
and climatic forcing.

Catchment inter-comparison studies require application of consistent procedures
across sites, so we quantified how choices of methodology may affect
estimates of *F*_{yw}. Across the 22 sites, *F*_{yw} values were not
particularly sensitive to the spatial interpolation methods used to estimate
precipitation isotope signatures (Sect. 4.1), or
sensitive to whether one accounts for snow accumulation and melt in
estimating isotopic inputs to the catchment (Sect. 4.2). Flow-weighting the streamwater isotope
measurements, however, yielded flow-weighted young water fractions
(${F}_{\mathrm{yw}}^{*}$) that were roughly 26 % larger than their
unweighted counterparts (*F*_{yw}; Sect. 4.3,
Fig. 5). This result is not surprising, because
flow peaks typically follow intense rainfall and thus should contain more
recent precipitation than base flows. Here we quantify, for the first time,
how flow-weighting affects young water fractions, using real-world data.

The flow-weighted young water fractions of the 22 Swiss catchments ranged
from 0.07 ± 0.01 to 0.49 ± 0.03 (±SE), whereas the unweighted
*F*_{yw} were slightly smaller, ranging from 0.06 ± 0.01 to
0.37 ± 0.03. The *F*_{yw} values from our study sites span roughly the 10th to
80th percentiles of the *F*_{yw} values estimated by Jasechko et al. (2016)
for 254 rivers around the world. The median *F*_{yw} among the
22 Swiss catchments was 0.16 (95 % confidence interval 0.10–0.21),
somewhat less than the global median of 0.21 (95 % confidence
interval 0.19–0.24; Jasechko et al., 2016), consistent with Jasechko et al.'s (2016)
observation that young water fractions tend to be smaller in steeper
landscapes. Among the 22 Swiss catchments, *F*_{yw} and
${F}_{\mathrm{yw}}^{*}$ were positively correlated with catchment
characteristics that control wetness conditions (e.g. mean monthly
precipitation and mean precipitation intensity) and near-surface flow
routing (e.g. drainage density and areal fractions of saturated soils; Sect. 5).

By calculating young water fractions for individual ranges of streamflow, we
demonstrated that young water fractions generally increase with discharge (*Q*),
and that this sensitivity of *F*_{yw} to *Q* varies from site to site
(Sect. 6.1, Fig. 8). We developed a method to quantify the discharge sensitivity of *F*_{yw} through
calculating the linear slope of the *Q*–*F*_{yw} relationship (Eqs. 6 to 9).
The discharge sensitivity expresses how *F*_{yw} responds to changes
in river discharge, which is used here as a proxy for catchment wetness and
hydro-climatic forcing. Across our study catchments, the young water
fraction and its discharge sensitivity were not correlated with each other,
suggesting that these metrics represent different diagnostic indicators of
catchment hydrologic behaviour (Sect. 6.2, Fig. 8). We hypothesize that low discharge
sensitivities imply greater persistence in the relative contributions of
fast and slow flow paths to streamflow during both high and low flows. High
discharge sensitivities, however, imply shifts in flow path
dominance during higher flows, such as when subsurface water tables rise
into more permeable layers or the river network expands further into the landscape.

Based on our analysis, we developed a generalized conceptual description
that relates *F*_{yw} and its discharge sensitivity to dominant streamflow
generation mechanisms (Sect. 6.3, Fig. 10), which could be useful for analysing the
effects of future climate change on catchment hydrological behaviour. It
remains to be tested whether this conceptual description is transferable to
other sites with landscape features and hydro-climatic forcing that are
substantially different from our 22 Swiss study catchments.

Data availability

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Data availability.

The isotope data are available from Markus Weiler upon request.

Supplement

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Supplement.

The supplement related to this article is available online at: https://doi.org/10.5194/hess-22-3841-2018-supplement.

Author contributions

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Author contributions.

MW provided stream water isotope measurements. SS and SA modeled precipitation isotopes. JF and JK analyzed the data set. JF prepared the paper with contributions from JK, MW, SS and SA.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

The collection and analysis of the streamwater isotope data were mainly
funded as part of the National Research Programme NRP 61 by the Swiss
National Science Foundation within the project Drought-CH. We thank
Massimiliano Zappa from the Swiss Federal Research Institute WSL for
providing interpolated meteorological data for the 22 study catchments, and
Wouter Berghuijs for helpful discussions. Comments by Markus Hrachowitz and
Stefanie Lutz helped to improve the paper.

Edited by: Ralf Merz

Reviewed by: Markus Hrachowitz and Stefanie Lutz

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Short summary

We explored how the fraction of streamflow younger than ca. 3 months (*F*_{yw}) varies with landscape characteristics and climatic forcing, using an extensive isotope data set from 22 Swiss catchments. Overall, *F*_{yw} tends to be larger when catchments are wet and discharge is correspondingly higher, indicating an increase in the proportional contribution of faster flow paths at higher flows. We quantify this *F*_{yw} and relate it to the dominant streamflow-generating mechanisms.

discharge sensitivityof

We explored how the fraction of streamflow younger than ca. 3 months (*F*_{yw}) varies with landscape...

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