Recent virtual and experimental investigations have shown
that the young water fraction

The seasonal cycles of stable isotopes in precipitation are damped and
phase-shifted as they are transmitted through catchments and thus can be
used to infer properties of catchment travel-time distributions (e.g.
DeWalle et al., 1997; McGuire and McDonnell, 2006). The young water fraction
(

The young water fraction usually increases with stream discharge (Kirchner,
2016b). To account for this flow dependency in their study of 22 Swiss
catchments, von Freyberg et al. (2018) distinguished between time-weighted
(

These authors used the linear slope between

Von Freyberg et al. (2018) determined DS(

Then if

Combining Eqs. (1) and (3) yields

We applied the approach outlined above to the small Mediterranean Can Vila
catchment (Vallcebre Research Catchments, Llorens et al., 2018). The objectives
were to better understand the Can Vila catchment's hydrology and to test the

The Can Vila catchment (Table 1) is a 0.56 km

Main characteristics and metrics of the catchments shown in Figs. 2
and 3.

For the Can Vila catchment, the flow-weighted young water fraction
(

To further explore the discharge sensitivity DS(

Variation in time-weighted young water fraction at the Can Vila
catchment with increasing quantiles of the flow duration curve. The dashed
grey line represents Eq. (5) and the red curve represents Eq. (6), using
parameters obtained by fitting Eqs. (4) and (8), respectively, to all the
stream water

Equations (4) and (5) (numbered 9 and 10 in von Freyberg et al., 2018) yield a
discharge sensitivity DS(

An alternative, non-linear model can be derived by noting that the sum of
old and young water fractions is always 1, and by assuming that the old
water fraction decreases with increasing discharge and asymptotically
approaches 0 (and thus the young water fraction asymptotically approaches 1)
as

On combining Eqs. (1) with (6) and re-arranging the formula so that only

Taking the derivative of Eq. (6) with respect to

We used the Can Vila data set to test the robustness of the

Behaviour of the different discharge sensitivity metrics in the Can Vila catchment when measurements corresponding to the highest flows are sequentially discarded. Percentage of time exceeded refers to the flow duration curve. Vertical bars represent standard errors, and dashed lines are ancillary polynomial fits.

For this purpose, we compare the new

The new exponential

In summary,

Figure 3 compares the quantile plot of Fig. 1 for the Can Vila catchment and
the quantile plots of Fig. 7 in von Freyberg et al. (2018) for the Swiss
catchments of Langeten, Biber and Ilfis, which exhibit very different young
water fractions and/or discharge sensitivities (Table 1). The

Sensitivity of the young water fraction on discharge for the

We find that young water fractions in the Can Vila catchment have a
discharge sensitivity (

Although the linear expression of discharge sensitivity (DS(

The four catchments compared here differ considerably in catchment area and
median discharge (Table 1), which often challenges a robust inter-comparison
analysis. However, Fig. 3 shows that Eq. (6) efficiently estimates the
sensitivities (

The comparison of the

Comparison of discharge sensitivities DS(

In order to compare the frequencies of occurrence of

Discharges and young water fractions from Fig. 3 plotted against the respective quantile frequencies, along with the log-normal distributions fitted to discharges (solid lines) and distributions of young water fractions (dashed curves) obtained by applying Eq. (6).

The question arises of where (in what kinds of catchments and in what types of
climates)

The discharge sensitivity of the young water fraction is a promising metric
for investigating streamflow generation processes and for catchment
inter-comparison studies. However, the original discharge sensitivity
approach, based on fitting a linear slope between the young water fraction
(

We propose an alternative, exponential-type approach for estimating
discharge sensitivity (Eq. 6), to overcome the limitations of the linear
approach. The parameters of this exponential equation are

As the proposed

We hypothesize that, if estimated from tracer samples that adequately
capture the runoff dynamics, the three metrics of

The Swiss isotope data are available online via

JL and PL designed the isotope sampling strategy at Can Vila and provided measurements. FG and MV analysed the Can Vila data set. FG, JWK and JvF developed the new approach. FG prepared the paper with contributions from JvF, JWK, JL and PL.

The authors declare that they have no conflict of interest.

This research was supported by the projects TransHyMed (CGL2016-75957-R AEI/FEDER, UE) and Drought-CH (National Research Programme NRP 61 by the Swiss National Science Foundation). We are grateful to Carles Cayuela, Gisela Bertràn, Maria Roig-Planasdemunt and Elisenda Sánchez for their support during field work at the Can Vila catchment and to Michael Eaude for his English style improvements.

This research has been supported by the Ministerio de Ciencia, Innovación y Universidades (Spain) (grant no. CGL2016‐75957‐R AEI/FEDER, UE) and the Swiss National Science Foundation (Switzerland) (National Research Programme NRP 61).

This paper was edited by Thom Bogaard and reviewed by two anonymous referees.