To test the applicability of our method (Sect. 2.2), we use data from the Erlenbach (ERL), Lümpenenbach (LUE) and Vogelbach (VOG) catchments, located in the pre-alpine Alptal Valley in central Switzerland. The geographical framework of the three study sites is reported in Fig. 1.

The three study catchments cover areas of between 0.7 and 1.6 km2, and mean elevation ranges from 1335 to 1359 m a.s.l. (metres above sea level; Table 1, Fig. 1a). Mean catchment slopes are 13.53, 12.49 and 18.42° in the ERL, LUE and VOG catchments, respectively, but the hillslopes can be much steeper locally (20–40°) (Stähli et al., 2021). According to the swissTLMRegio model (Fig. 1c), the ERL catchment is mainly constituted by forest (45 %) and swampland (49 %); these are also the dominant classes in the LUE (21 % and 39 %, respectively) and VOG (72 % and 13 %, respectively) catchments. Most of the southern Alptal Valley is characterized by shallow, low-permeability Gleysols that limit the deep infiltration of water and lead to shallow groundwater tables (Stähli et al., 2021). The percentage of soils with a low storage capacity is about 4 % in both ERL and LUE, while it is 51 % in the VOG catchment; a large fraction of the soils is saturated (≥95 % in ERL and LUE and 49 % in VOG; von Freyberg et al., 2018a). The geological substratum of the three study sites consists mainly of sedimentary rock (flysch). The catchment area that is covered by Quaternary deposits is much higher in the ERL and LUE catchments than in the VOG catchment (Table 1). Therefore, although the study catchments are located within close proximity, they differ in terms of soil wetness and unconsolidated sediments.

The average hydro-climatic conditions are generally similar for all three catchments. The average annual precipitation in the period from January 2000 to December 2015, based on interpolated data from the PREVAH model, was about 1853, 1803 and 1800 mm in the ERL, LUE and VOG catchments, respectively (von Freyberg et al., 2018a). The average monthly discharge is similar among the catchments: 138.9, 152.0, and 117.4 mm per month at the ERL, LUE and VOG catchments, respectively (von Freyberg et al., 2018a). These watersheds reveal a hybrid hydro-climatic regime (Staudinger et al., 2017; von Freyberg et al., 2018a), as we observe ephemeral snowpack formation (typically from December to April) that also rapidly melts away during winter, meaning that the snowpack may not last throughout the entire winter season (Stähli et al., 2021).

Daily-resolution Q and stream water EC data have been downloaded from the Swiss Federal Office for Forest, Snow and Landscape Research (WSL, Birmensdorf, Switzerland) data portal. We have estimated the Q–EC relationships with a log-type fit (Fig. 2). As daily Q increases, daily EC decreases at the three study sites. This pattern arises due to the contribution of different sources (i.e. ages) of water to the stream. At the three study sites, stream discharge increases due to rainfall or snowmelt, which are generally low in EC, resulting in a dilution of stream water EC. In addition, during wet conditions (high Q), more rapid flow paths are activated, leading to a prevalence of the younger hydrograph component. Because of the short interaction time with mineralized rocks and soils, young water can be assumed to be low in dissolved ions (i.e. low EC). The other extreme, low Q and high stream water EC, occurs during baseflow conditions when the stream is mainly fed by old (i.e. highly mineralized and high-EC) subsurface water (Schmidt et al., 2012).

This study uses Fyw, Fyw*, FywQ and Sd* (Tables 2, 4), which have been estimated in past studies (Gallart et al., 2020b; von Freyberg et al., 2018a) by considering streamflow δ18O data from biweekly grab sampling over a period of approximately 5 years for the three study catchments. FywQ values refer to young water fractions estimated in discrete flow regimes (Kirchner, 2016b). Indeed, it is possible to separate the stream water isotope data collected into different discharge ranges and fit sinusoids separately to the isotope content in each range. For each of these individual flow regimes, this method enables one to obtain the stream water seasonal isotope cycles amplitude (ASQ) values that will be divided by AP to obtain FywQ (von Freyberg et al., 2018a; Kirchner, 2016b). For more details about FywQ estimation, the reader is referred to Kirchner (2016b) and von Freyberg et al. (2018a).

The young water fraction may be useful for inferring chemical processes from streamflow concentrations of reactive chemical species (Kirchner, 2016b). Indeed, as it is known how the fraction of young water varies in discrete flow regimes, it is possible to construct mixing relationship between FywQ and the concentration of reactive chemical species (Kirchner, 2016b). Accordingly, we calculate the median EC within each individual discharge range (reported in Table 2), and we investigate how the median EC varies with FywQ (Fig. 3).

As visible in Fig. 3, the relationship between FywQ and median-flow-specific EC is well described by an exponential mixing model. Indeed, the widely used linear mixing model proves to be poorly suited here because it is pointing to a negative EC endmember of young water (i.e. EC value corresponding to FywQ=1; Fig. 3). This will be thoroughly discussed in Appendix A. By considering the exponential mixing model, we can estimate the “idealized” old water and young water endmembers via evaluation of the fitted exponential expressions for FywQ=0 and FywQ=1, respectively. Accordingly, a first-order estimate of the two endmembers (ECowraw ECywraw, respectively) is reported in Fig. 3 and Table 3. It is evident that the measured FywQ for the three study catchments ranges from approximatively 0.1 to 0.5 (Fig. 3). As the measurable range of young water fractions is not wide enough, the parameters estimated with the exponential fit are highly uncertain because the curve is poorly constrained at very low (<0.1) and very high (>0.5) young water fractions. In this regard, hereafter, we propose a new methodology to estimate the EC endmembers of young and old water, respectively, and to perform a continuous hydrograph separation with an alternative mixing model.

The definition of the fraction of the streamflow younger than a threshold age (varying modestly from 2 to 3 months) at the generic time ti, Fyw(ti), implicitly defines the existence of a complementary fraction of streamflow older than that threshold age at the same time ti, Fow(ti). Thus, mass conservation requires the following: 2Fywti+Fowti=1. To estimate Fyw(ti), and thus Fow(ti), we use EC as a tracer to separate the hydrograph into young (transit time < 2–3 months) and old (transit time > 2–3 months) water. Solid support from the scientific literature justifying the use of EC for time-source hydrograph separation is illustrated in Sect. 1.

As suggested by the analysis reported in Fig. 3, to perform the hydrograph separation, we assume that stream water EC at the generic time ti, EC(ti), decreases exponentially with increasing Fyw(ti): 3ECti=ECowe-aFywti, where ECow is the old water EC endmember and a is a parameter. The exponential decay proposed in Eq. (3) guarantees a realistic scenario for the case Fyw(ti)=0, i.e. streamflow contains only old water (Fow(ti)=1) and stream water EC is equal to ECow(EC(ti)=ECow). Conversely, if Fyw(ti) is equal to 1, streamflow is made up entirely of young water. Accordingly, we can include the following condition: if Fyw(ti)=1, EC(ti)=ECyw, where ECyw is the young water EC endmember (Eq. 4), 4ECyw=ECowe-a. Furthermore, we assume ECyw<ECow. Solid support of this assumption from the scientific literature is illustrated in Sect. 3.1 alongside the discussion of the results.

By further considering the law of water mass conservation (Eq. 2), it is possible to solve the system of three equations (Eqs. 2–4) with three variables (a, Fyw(ti) and Fow(ti)), thus obtaining the explicit expression of a (Eq. 5) and, accordingly, of Fyw(ti) (Eq. 6). 5a=-ln⁡ECywECow6Fywti=ln⁡ECtiECowln⁡ECywECow The main difficulty in applying Eq. (6) to estimate Fyw(ti) is that we generally cannot accurately determine the endmembers ECyw and ECow from the analysis reported in Fig. 3 or from measurements. Indeed, such endmembers correspond to the (rare) scenarios in which Fyw(ti) is either 0 or 1. The first scenario (Fyw(ti)=0) might occur only after prolonged periods without rainfall or snowmelt, whereas the second scenario (Fyw(ti)=1) is unlikely to occur in most natural catchments where baseflow is usually older than 3 months (Gentile et al., 2023), and thus we cannot directly measure ECyw (Kirchner, 2016b). In this regard, hereafter, we present a novel methodology to estimate the endmembers. Such a methodology lays its foundations on the statement that the isotope-based Fyw and Fyw* (Eqs. 7a and 7b; see the Supplement for further details) accurately estimate the unweighted and the flow-weighted average young water fractions in streamflow, respectively (Kirchner, 2016b). 7aFyw=ASAP7bFyw*=AS*AP Accordingly, if we know the young water fraction over a generic time step ti, Fyw(ti) (e.g. daily young water fraction), we can calculate the unweighted and the flow-weighted average young water fraction in streamflow using Eqs. (8a) and (8b), respectively: 8aF̃yw=∑i=1nFywtin≃Fyw,8bF̃yw*=∑i=1nQtiFywti∑i=1nQti≃Fyw*, where n is the number of time steps (e.g. days) in the period of isotope sampling and Q(ti) is the discharge at the time ti(e.g. daily discharge). The hat “ ̃ ” symbol is simply used to visually differentiate between the average young water fractions obtained with both approaches. Note that Eq. (8b) was previously presented in Gentile et al. (2023).

We therefore determine ECyw and ECow through calibration, respecting the following three constraints: i.

ECow and ECyw are greater than or equal to 0;

We apply our method at two different time resolutions that are reflected in our data set: the daily resolution (DR) and the sampling resolution (SR). At the DR, EC(ti) and Q(ti) refer to the daily average EC and Q values, respectively; thus, Fyw(ti) is the average young water fraction of each day. At the SR, it should be noted that the “EC samples” are not referring to physical samples in this specific application. Accordingly, EC(ti) and Q(ti) are obtained by sub-setting those EC and Q values from the daily time series that correspond to the time of isotope sampling. In this sense, we can say that the number of EC samples and isotope samples is the same. Nevertheless, the method can be potentially applied at the SR in catchments in which EC is only measured from water samples. At the SR, Fyw(ti) values are estimated only for those days on which an isotope sample was taken.

We quantify the uncertainty in ECywopt and ECowopt by repeating the global optimization procedure by randomly sampling 10 000 couples of Fyw and Fyw* from the intervals Fyw ± SE and Fyw* ± SE, respectively. The SE values are reported in Table 2. The random sampling assumes that the values within the two intervals have a Gaussian probability of extraction, thus favouring the sampling of the core values. Therefore, we obtain 10 000 couples of endmembers for which we compute statistics. We further calculate the uncertainty in Fywopt(ti): we apply Eq. (6) using the 10 000 couples of endmembers, thus obtaining 10 000 Fywopt(ti) values at each time step ti, for which we calculate the standard deviation.

It should be noted that the initial conceptualization of the mixing model was based on testing the hydrograph separation using the two-component endmember linear mixing approach with EC as the tracer (e.g. Cano-Paoli et al., 2019). As could already be inferred from Fig. 3, this approach was not successful because it can represent only a limited hydrological behaviour of catchments that does not capture that of our three study catchments. A detailed explanation of the limits regarding the linear mixing model is provided in Appendix A of this paper.

Last but not least, as our method consists of a two-component Electrical-Conductivity-based hydrograph separaTion employing an EXPonential mixing model, we decide to name it EXPECT. A schematic representation of the EXPECT method is reported in Fig. 4.

The application of the EXPECT method showed, at both the daily and sampling resolutions, that the old water EC endmembers, ECowopt, are about 1 order of magnitude larger than the young water EC endmembers, ECywopt, for all three experimental catchments (Table 3, Fig. 5). This result can be explained by considering that old water had a longer contact period with mineral surfaces in the subsurface (Benettin et al., 2015, 2017); thus, weathering-derived solute concentrations (and, correspondingly, EC) will be higher in old water compared with young water. Moreover, young and old stream water components can originate from different reservoirs in a catchment (Riazi et al., 2022). Among these reservoirs, old water is generally assumed to represent groundwater. This is also supported by the fact that the fraction of baseflow (representing the groundwater contribution to streamflow) was found to be complementary to the young water fraction in the framework (including the three Swiss catchments in this study) investigated by Gentile et al. (2023). In this regard, different papers that have characterized groundwater EC have shown notable differences with the EC of precipitation and/or meltwater. Indeed, Zuecco et al. (2018), by investigating the hydrological processes in an alpine catchment, found that the EC of rainwater and of recent snow was 19.2 and 12.2 µS cm-1, respectively. Conversely, they found that groundwater from springs had an EC of 166 µS cm-1. Moreover, by investigating the conceptualization of meltwater dynamics in an alpine catchment through hydrograph separation, Penna et al. (2017) defined the snowmelt endmember range as 2.9–15.3 µS cm-1, the glacier melt endmember range as 2–2.7 µS cm-1 and the groundwater endmember range as 210–317.7 µS cm-1 (average values from springs or streams in fall/winter). These examples are intended to show that groundwater (the main source of old water) generally reveals an EC value that is much higher (around 10- to 100-fold) than other sources in a catchment that should preferentially contribute to the young stream water component. Differences in young and old water EC endmembers can also be partially justified by looking at differences in event and pre-event water EC endmembers. Indeed, old (transit times > 2–3 months) water is a large fraction of pre-event (transit times > a few days) water, whereas event water (transit times < a few days) is a portion of young water (transit times < 2–3 months). Due to this overlap, a similarity in the old water and pre-event water EC endmembers or in the young water and event water EC endmembers would not be surprising. Cano-Paoli et al. (2019) used stream water EC to investigate hydrological processes in alpine headwaters by separating the hydrograph into event and pre-event water. In this regard, they defined the event water endmember as being equal to 8 µS cm-1 (Penna et al., 2014) and the pre-event water endmember as being equal to 95 µS cm-1 (the mean value during baseflow conditions). Laudon and Slaymaker (1997), by investigating the hydrograph separation using EC at the lower station of an alpine catchment, defined the rainwater EC endmember as being equal to 6.15 µS cm-1 and the pre-event water endmember as being equal to 39 µS cm-1. However, young and old water EC endmembers are expected to be higher than event and pre-event water EC endmembers, respectively. Accordingly, these past results taken from the scientific literature support our assumption that ECyw<ECow.

The highest ECowopt values were obtained for ERL (501 µS cm-1, DR), whereas the lowest values were obtained for VOG (319 µS cm-1, DR). The ECowopt values are in line with those measured in groundwater (Fig. 5). In a 6.8 m deep monitoring well at the ERL meteorological station, groundwater EC generally varies between 400 µS cm-1 (spring–summer) and 500 µS cm-1 (fall–winter; data not shown), whereas the EC in groundwater at up to 1.5 m depth was generally around 400–450 µS cm-1 during no-snowmelt conditions in the neighbouring catchment of ERL (Kiewiet et al., 2020). The optimal endmembers are also in line with the first-order estimates of endmembers, ECowraw and ECywraw, derived from the exponential model fitted on median EC vs. FywQ (Table 3; Figs. 3, 5), except for ECow in the ERL catchment. This can be explained by considering the high standard error (Table 3) of the parameter (corresponding to ECowraw) in the exponential model that is poorly constrained for ERL (more than for LUE and VOG) at low young water fractions (Fig. 3). The optimized EC values of the young water fractions appear slightly elevated compared with data derived from central European precipitation (Monteith et al., 2023). However, it is plausible to posit that the young water fraction encompasses some soil water with higher EC.

Figure 5 shows further that the interquartile range (IQR) values of the ECowopt empirical distributions are much larger than those of ECywopt. Assuming that the solute concentration in stream water increases with water age (Riazi et al., 2022), this can possibly be explained by the much wider range of transit times (from approximately 0.2 to tending to infinity years) of old water compared with young water (0 to 0.2 years). Consequently, the concentrations of weathering-derived solutes in old water are not only higher but also more variable than in young water.

Our method estimates the EC endmember values for the cases Fyw(ti)=1 and Fyw(ti)=0 that are generally difficult to determine experimentally, thus providing additional information about young and old water in the systems under study. In this regard, at each one of the three study sites, the theoretical endmembers ECywopt are lower than the minimum EC value measured in the streams; analogously, the calibrated ECowopt values are higher than the maximum measured EC value (box plots vs. horizontal dashed lines in Fig. 5). This is expected for a natural, heterogeneous system in which incoming precipitation mixes with stored water, and thus stream water never contains 100 % young or 100 % old water. Instead, stream water is a mixture of these two components. This is supported by the fact that FywQ values cover only a limited range of young water fractions (roughly from 0.1 to 0.5). This result demonstrates that the choice of the old water endmember based on tracer values sampled during baseflow conditions can result in an underestimation of the theoretical old water endmember. Although these stream conditions suggest the prevalence of old water, if the percentage of old water is less than 100 %, the measured tracers still reflect some mixing (albeit limited) with young water.

The estimated discharge sensitivity of the young water fraction, SdEXP, based on the EXPECT method satisfactorily describes the Fywopt(ti)–Q(ti) relationships of the three catchments, as reflected by R2 values of 0.58 and higher (Table 4; red curves in Fig. 5). Moreover, the red curve in Fig. 5 also fits the FywQ values of the distinct flow regimes well (Table 2). By taking advantage of the consecutive Fywopt(ti) values at the daily or sampling resolution, we better constrain the parameters of Eq. (10) at very low and very high discharges compared with the fit obtained with Eq. (1) that is using only stream water δ18O data at the sampling resolution (black curve in Fig. 5, Table 4; see the Supplement for methodological details). As a result, our estimated discharge sensitivity SdEXP is higher for the ERL and VOG catchments and similar (within error) for the LUE catchment compared to Sd*, whereas our estimates of F0EXP for all three sites are slightly smaller than the respective F0* values obtained with Eq. (1).

We also find that the SdEXP values obtained at the SR can differ from those at the DR. For LUE, SdEXP at the SR is larger than at the DR (Table 4), whereas it is the other way around for ERL. Such differences can be attributed to the different flow regimes represented by the isotope samples that influence the EC endmember estimations at each site (Table 3). Moreover, at the DR, we are calibrating the EC endmembers using Fyw and Fyw* based on isotope data at the SR. To be fully consistent in terms of the temporal resolution, we theoretically need daily stream water isotope data to derive Fyw and Fyw*. The influence of sampling frequency is one of the limitations of the EXPECT method, as explained in Sect. 3.3. Nevertheless, the F0EXP values are consistent between the two temporal resolutions.

As can be seen in Fig. 5, the Fywopt(ti) values obtained with the EXPECT method form a data cloud around the idealized discharge sensitivity function of Eq. (10). Specifically, for a given discharge value, we obtain various Fywopt(ti) values, which can be explained by the delayed response of old water during precipitation events: while the young water fraction is generally highest during the rising limb of the hydrograph, it decreases during the falling limb when old water reaches the stream (von Freyberg et al., 2018a, b)

Because the EXPECT method allows for the estimation of the young water fraction Fywopt(ti) at up to the DR, we can determine the respective flow duration curves of young and old water discharge. Moreover, we calculate Q50/50, i.e. the median discharge value at which 50±1 % of both young and old water exist in streamflow. In the ERL catchment, Fig. 6a shows that a shift from old-water-dominated streamflow towards young water-dominated streamflow occurs for discharges larger than approximately 7.7 mm d-1 (Q50/50; Fig. 6a). In the LUE and VOG catchments, the streamflow contains more old water than young water for most of the flow regime (Fig. 6b, c); only on relatively few occasions, when Q exceeds Q50/50 (23.2 and 17.5 mm d-1, respectively), was the relative contribution of young water slightly larger than that of old water.

By comparing Q50/50 with the median stream discharge (Qmed), we observe that Q50/50 is higher than Qmed in all three study catchments (Fig. 6). This result suggests that a major proportion of old water reaches the stream more than 50 % of the time. In both the LUE and VOG catchments, Q50/50 is higher than in the ERL catchment, revealing that the LUE and VOG streams are dominated by old water for longer than the ERL stream. This explains why the isotope-based average young water fraction is higher in the ERL catchment than in the LUE and VOG catchments (Table 2).

With the EXPECT method, the temporal variability in Fywopt(ti) can be explored in detail, e.g. by comparing time series of Fywopt(ti) with those of other hydro-climatic variables (Fig. 7). Accordingly, in the following, we show a comparison between Fywopt(ti) and hydro-climatic observations at the DR of the ERL catchment, as it has the most complete hydro-climatic data set (including discharge, precipitation, snow depth and temperature measurements; all data available from WSL) compared with the other two catchments. As visible from Fig. 7, daily young water fractions in the ERL catchment respond directly to precipitation events, which is further reflected by a strong positive correlation between Fywopt(ti) and the daily precipitation volumes (ρSpearman=0.41, p value ≪ 0.01 considering only days with precipitation; Fig. 8). We estimate that, after a rainfall or snowmelt event, the growth rate of Fywopt(ti) is on average 0.062±0.058 d-1 (to reach the local Fywopt(ti) maximum next to the previous Fywopt(ti) local minimum; Fig. S1 in the Supplement). On the other hand, during the recession phase, the average rate of decrease in Fywopt(ti) is -0.041±0.036 d-1 (to reach the Fywopt(ti) local minimum next to the previous Fywopt(ti) local maximum; Fig. S1). Accordingly, Fywopt(ti) rapidly increases after an event (peak Fywopt(ti) is reached on average after 1.98±1.25 d), while it recedes slower during no-input days (the next minimum Fywopt(ti) is reached on average after 3.36±3.10 d). The largest daily young water fractions in the ERL catchment occurred during spring snowmelt (March–May), suggesting that the meltwater of the ephemeral snowpack is an important source of young water (as no relevant water ageing is observed in such a snowpack) that flows off quickly in the stream (Gentile et al., 2023). Rapid surface runoff of snowmelt can occur due to soil freezing (temperatures < 0 °C) or high soil moisture contents (temperatures > 0 °C), both of which can limit infiltration (Harrison et al., 2021; Keller et al., 2017; Fig. 7). During the periods of snow accumulation and persistent snow cover, typically from November to February, Fywopt(ti) values were often as low as 0.3 and did not vary much (except during snowmelt and rain-on-snow events). Thus, streamflow in ERL was mainly composed of old water during this period, likely originating from the soil and groundwater storages.

While the EXPECT method can offer valuable insights into the young water fraction's discharge sensitivity and its temporal variability, it is not without its limitations. The assumption that EC is a proxy for stream water age may not hold true in all hydrological systems. For example, human activities, such as mining, irrigation or wastewater inputs can alter the stream water EC in unpredictable ways. Another example involves catchments with highly soluble rocks in the aquifers (e.g. limestone or gypsum) that are susceptible to dissolution by water. It has been shown that EC can increase with Q in some karst systems due to the remobilization of circulating water in the fractured areas (Balestra et al., 2022). Therefore, the Fyw–EC relationship (Eq. 3) can be very different from that in our three study catchments, which are mainly groundwater-influenced systems. Indeed, an early study also advised that one should be mindful of EC behaviour, as it depends on the specific characteristics of each catchment (Laudon and Slaymaker, 1997). Accordingly, for future applications of the method presented in this paper, we recommend visualization of the relationship between flow-specific young water fractions and flow-specific electrical conductivities with the aim of constructing a site-specific mixing relationship, as suggested by Kirchner (2016b). It should be noted that this relationship could potentially be different from an exponential mixing model. Indeed, the use of an exponential mixing model is not proposed to be the definitive answer to the problem of choosing the right mixing model for flow partitioning into young and old water. Accordingly, if the most suitable mixing model turns out to be different from an exponential mixing model, the equations presented in this study will need to be adapted to the specific case study. However, the method's application scheme for calibrating the endmembers can still be employed. Nevertheless, in some catchments with short and sparse isotope time series, flow-specific young water fractions cannot be estimated reliably (von Freyberg et al., 2018b). The study by von Freyberg et al. (2018a) was able to estimate reliable flow-specific young water fractions for nine Swiss catchments that comprised 4- to 5-year-long isotope time series with a minimum number of 81 samples to a maximum number of 140 samples, where stream water grab samples were collected approximately fortnightly. Thus, we suggest an isotope data set with these characteristics to construct a reliable site-specific mixing model with both flow-specific EC and FywQ.

Another major limitation of the EXPECT method is its strong dependency on reliable Fyw and Fyw* estimates, i.e. assumptions (ii) and (iii) in Sect. 2.2. If stream water isotope data sets are short or sparse, Fyw or Fyw* can be highly uncertain and EC endmembers cannot be sufficiently constrained. Recently, Gallart et al. (2020a) revealed that unweighted and flow-weighted young water fractions were significantly lower than results with virtual (perfect) sampling when using a weekly sampling frequency. Thus, for the same catchment, we could potentially obtain different EC endmembers if stable water isotopes were sampled at higher or lower temporal resolution. Accordingly, we strongly recommend evaluating how the uncertainty in Fyw or Fyw* propagates in the uncertainty in the calibrated endmembers, as described in Sect. 2.2.

For many catchments, Q and EC values are measured at a sub-hourly resolution. Thus, theoretically, the EXPECT method could provide reasonable young water fraction estimate results at these resolutions as well. However, we should consider that short-term variations in EC may not necessarily represent short-term variations in water age. For example, for a small stream in Sweden, Calles (1982) showed that diurnal variations in EC seem to be due to evapotranspiration but that the influence of gravity variations may also play a role. Moreover, a past study in a pre-alpine river in Switzerland revealed that the diurnal fluctuation in EC can be due to biogeochemical processes, such as calcite precipitation and photosynthesis (Hayashi et al., 2012). Accordingly, biological (photosynthesis and respiration) and chemical processes (carbonate equilibrium and calcite precipitation) can play a key role in controlling Ca2+ and HCO3- concentrations and, consequently, EC (Nimick et al., 2011; Hayashi et al., 2012). By calculating the average daily EC, and thus removing diurnal and nocturnal EC dynamics, it should better reflect variations in water age under the assumptions of the EXPECT method. Accordingly, we recommend applying the method using the daily mean of EC.