1. Introduction
Since the pioneering study by Maloszewski, Rauert, Stichler & Herrmann
(1983), the comparison between the seasonal variation of stable isotopes
(2H and 18O) of precipitation and
stream waters, applying either the convolution integral or sinusoid
fitting, has been used to investigate the turnover time of water in
catchments. Mean transit times (MTT) and transit time distributions
(TTD) of catchment waters have been intensively investigated for over
three decades using these methods (McGuire & McDonnel, 2006), despite
limitations of stable isotopes for water fractions that are more than a
few years old (Stewart, Morgenstern & McDonnell, 2010; Stewart,
Morgenstern, McDonnell & Pfister, 2012).
More recently, Kirchner (2016a) demonstrated that MTT determinations
with these methods may be inadequate, especially when waters of
different ages mix along their flow paths within catchments. Kirchner
(2016a) proposed an alternative travel-time metric, the ‘fraction of
young water’ (Fyw ), defined as the portion of
water that is younger than a threshold age. This fraction can be
robustly estimated for a wide range of TTDs, with a threshold age
ranging between two and three months, depending on the TTD. Young water
fractions have been subject to several developments and applications
recently, leading to the opening of numerous questions regarding the
methods’ specifics, the quality of the Fywestimates, and their relationship to hydrological processes. We can
group these questions to four main topics frequently mentioned in the
literature: the water recharge assumption, the identifiability of
catchment Fyw , the issue of sampling rate and the
behaviour of mountain catchments. We briefly outline the four issues
below:
- How must summer precipitation be taken into account (i.e., effective
precipitation) for Fyw and MTT determinations
when using stable isotopes of water?
In a seasonal climate, precipitation (or throughfall) is more enriched
in heavy water isotopes during summer than during winter (Allen et
al . 2019a), while evapotranspirative demand is higher in summer than in
winter. Consequently, isotopically enriched summer precipitation might
be less likely to recharge the storage of a hydrological system, since
evaporation is more likely to be sourced from summer rainfall. As a
result, the isotope ratios of the infiltrating rain becoming recharge
(“effective rainfall”) will probably be biased towards cold/dormant
season rainfall (Jasechko et al ., 2014), and its seasonal
oscillation will be more attenuated than that of precipitation. However,
there is no consensus on how this issue (“the recharge assumption“ in
McGuire & McDonnell, 2006) is to be handled.
A first approximation of effective rainfall is weighting the sampled
isotope ratio by ‘precipitation minus evapotranspiration’ rather than
precipitation. This is habitually obtained using a conceptual soil
water-balance or rainfall loss (sub-) model before or at the beginning
of the modelling exercise or data analysis (e.g. Dunn, McDonnell &
Vaché, 2007; Lutz et al ., 2018; Stewart et al ., 2007;
Stockinger et al ., 2016; Weiler, McGlynn, McGuire & McDonnell,
2003 ). This approach assumes that evapotranspiration is composed of the
latest rainfall, at the sampling/modelling time step. However, summer
evapotranspiration may consume soil water that is several months old, as
isotope data suggest (Allen et al ., 2019b; Brooks, Barnard,
Coulombe & McDonnell, 2010; Sprenger, Llorens, Cayuela, Gallart &
Latron, 2019a), potentially overestimating evapotranspiration losses of
summer precipitation.
A second approach accounts for the isotope ratio and age dynamics of the
evapotranspiration flux: both are simulated with those of runoff to
update the isotope ratio and age distributions of the catchment storage.
This approach is for example used in the StorAge Selection (SAS)
modelling (van de Velde et al. , 2012; Benettin et al .,
2017; Harman, 2015) and other flow tracking models (Soulsby et
al ., 2015; Soulsby, Birkel & Tetzlaff., 2016).
A third approach performs mass balance based equations of diverse flows
and compartments (precipitation, runoff, groundwater,
evapotranspiration) between seasons for assessing the share of
precipitation in these partitions (Grabczak, Maloszewski, Rozanski &
Zuber, 1984; Maloszewsky, Rauert, Stichler & Herrmann, 1992; Jasechkoet al ., 2014; Kirchner & Allen, 2020). The advantage of this
approach is that it does not need assumptions (beyond the conservation
of the tracers and a steady state or null balance of the storage) nor
parameters, therefore its uncertainty is only related to the quality of
observations (measurement accuracies of rainfall-runoff volumes and its
isotope ratios) and to the differences of tracer concentrations between
the various compartments.
Finally, some authors do not claim to take into account this possible
effect and use the gross isotopic signature of precipitation waters (or
throughfall or melting) as input to the hydrologic system (e.g. von
Freyberg, Allen, Seeger, Weiler & Kirchner, 2018; Stockinger, Bogena,
Lücke, Stump & Vereecken, 2019; Jacobs et al ., 2018), although
Lutz et al . (2018) refrained from considering evapotranspiration
in the weighting of the isotope values in precipitation because the used
effective rainfall model showed minor differences between both
signatures.
- Can Fyw be characterized as a catchment
descriptor?
One of the expected applications of Fyw in
catchments is its suitability as a metric for catchment intercomparison
(Kirchner 2016a, b; von Freyberg et al., 2018; Jasechko et al .
2016; Lutz et al. , 2018). Nevertheless,Fyw is basically non-stationary and climate
factors seem to overwhelm catchment physiographic characteristics:Fyw is known to usually increase with stream
discharge due to the activation of faster flow paths when the wetness of
the catchment increases (Kirchner 2016a, b; von Freyberg et al. ,
2018; Gallart et al., 2019).
Consistent with this behaviour, Fyw was found in
several studies to increase during wetter years (Bansah & Ali, 2019;
Clow, Mast & Sickman, 2018; Remondi, Botter, Burlando & Fatichi, 2019;
Wilusz, Harman & Ball, 2017; Zhang et al ., 2018) and in wetter
catchments (von Freyberg et al. , 2018; Remondi et al .,
2017). The importance of rainfall intensity dynamics on catchment MTT orFyw was also stressed by several authors (von
Freyberg et al ., 2018; Soulsby, Piegat, Seibert &Tetzlaff, 2011,
Remondi et al ., 2019; Wilusz et al ., 2017).
Furthermore, Stockinger et al ., (2019) showed that catchmentFyw was not only sensitive to (long-term) changes
annual hydro-climatic variations, but also to (short-term) changes of
the starting date of a sampling campaign.
- How sensitive is Fyw to sampling rate?
Although Fyw may be estimated from irregularly
and sparsely sampled tracer time series (Kirchner, 2016a), Stockingeret al . (2016) showed for the Erkensruhr catchment (41.7
km2) that Fyw almost halved and
MTT doubled when the original daily or sub-daily data were aggregated to
a weekly sampling rate. Several studies have shown that to obtain sound
estimates of hydrological dynamics it is necessary to take samples at
the corresponding time scales (Kirchner, Feng, Neal, & Robson, 2004;
von Freyberg, Studer and Kirchner, 2017; Neal et al ., 2012).
However, it remains to be tested what temporal sampling resolution is
sufficient, accounting for cost efficiency, to cover the highly variable
age distribution of stream water (Sprenger et al ., 2019b).
Yet, tracer concentrations must be weighted by the corresponding
precipitation and streamflow volumes for their mass to be compared
(Kirchner, 2016a). Walling (1988) provided classical examples of the
issues related to both the representativeness of sediment sampling and
the adequate flow-weighting of concentrations.
However, many of the Fyw and MTT studies are
based on monthly to weekly sampling schemes designed from operational
rather than hydrological constraints. Frequently, authors wonder about
the representativeness of their samples, but detailed information on the
flow regimes or the comparison with those sampled is rarely given.
Hydrographs are scarce and flow duration curves are rarely discussed or
shown. Mass-weighting of tracer concentrations is a normal procedure in
precipitation but seldom applied for stream waters.
- Are Fyw values lower in mountainous catchments?
Several studies found that high-gradient or -elevation catchments have
lower Fyw values or longer MTT (Jasechko et
al. , 2016; Jasechko, Wassenaar & Mayer, 2017; Lutz et al .,
2018; Song et al ., 2017), whereas other studies found a converse
relationship (Clow et al ., 2018; Zhang et al ., 2018) or no
clear relationship (von Freyberg et al. , 2018; Soulsby et
al. , 2011). Although von Freyberg et al. (2018) did not find
significant relationships between Fyw and the
elevation gradient in their 22 studied Swiss catchments, their median
value was found to be consistent with Jasechko et al .’s (2016)
observation that young water fractions tend to be smaller in steeper
landscapes. Using monthly sampled water geochemistry, Frisbee et
al. , (2011) found that groundwater contributions increased with
increasing scale in mountainous drainage areas greater than 100
km2 but decreased with increasing scale in headwater
drainage areas smaller than 100 km2. On the other
hand, long-term weekly or bi-weekly stream water sampling in a high
mountain 1.55 km2 catchment showed a low (4.5%)
contribution of groundwater to stream flow (Dwivedi et al. ,
2018). Daily data in two small (0.51 and 3.47 Km2)
mountain catchments at Plynlimon (Wales) showed that MTTs were as short
as 0.36 and 0.82 years respectively (Kirchner et al. , 2001). Yet,
simulation exercises made at hourly and daily time scales, showed higherFyw and shorter MTT values in steeper catchments
irrespectively of the climate (Remondi et al. , 2019).
The more consolidated hypothesis is that mountain catchments tend to
yield lower Fyw and longer MTT, contrarily to the
intuition, attributed to the deeper infiltration of rain water (Jasechko
et al., 2016). Though, mountainous catchments are commonly considered to
have fast hydrological responses to precipitation (Arnell, 1989), so the
question arises whether mountain catchments have always been sampled at
a temporal frequency appropriate to their hydrological dynamics for
assessing sound Fyw values.
This paper aims to address the outlined research gaps by applying the
recent Fyw developments to investigate the
turnover of waters in diverse hydrological compartments of the small Can
Vila research catchment (Vallcebre Research Catchments; Gallart,
Llorens, Latron & Regüés, 2002; Llorens et al. , 2018). Our work
contributes to the methodological development and understanding ofFyw by testing its application using weekly to
sub-hourly precipitation and stream water samples along with fortnightly
mobile soil and shallow ground waters samples. Our work further aims to
shed light into the interpretation of Fyw by
combining the results with the understanding of hydrological processes
in a long-term research catchment. Thus, the objectives of this work are
both to improve understanding of the hydrological functioning of the Can
Vila catchment and to test the Fyw concept in an
intensively investigated Mediterranean mountain environment.
2. Materials and Methods
2.1 Study area
The study was conducted in the Can Vila catchment (0.56
Km2), one of the sub-catchments of the Vallcebre
research catchments (Llorens et al., 2018) at the headwaters of the
Llobregat River, about 130 km northeast of Barcelona, on the southern
margin of the Pyrenees, Catalonia (42°12’ N, 1°49’ E).
In the Can Vila catchment, elevations range between 1,115 and 1,458 m
above sea level. Slope gradients are moderate, with a mean value of
25.6% (Latron & Gallart, 2007), and have dominant north-east aspects.
Before and during the 19th century, most of the
hillslopes were deforested and terraced for agricultural purposes. The
terraces are mostly 10 to 20 meters wide and limited by a stone wall up
to 2 meters high, covering around half the area. Along with terraces, a
network of artificial ditches was also built in order to prevent soil
saturation and to convey surface runoff (Llorens, Latron & Gallart,
1992; Gallart, Llorens & Latron, 1994). During the second half of the
20th century the land was steadily abandoned.
Following land abandonment, spontaneous forestation by Pinus
sylvestris patches occurred (Poyatos, Latron & Llorens, 2003) and
forest now covers 34% of the catchment. The remainder of the catchment
is covered by pasture and meadows. The main channel is 1 to 2 m wide and
is not deeply incised near the outlet.
The bedrock of the Can Vila catchment consists almost entirely of upper
smectite-rich mudrocks with sandstone and gypsum layers of the
continental Tremp formation (Upper Cretaceous-Paleocene), with the
exception of the western part, where lacustrine micritic limestone
appears almost vertically. This catchment, almost entirely on clayey
bedrock, is considered to be totally watertight, with no noticeable deep
percolation (Latron, Soler, Llorens & Gallart, 2008), although some
local aquifers occur in sandstone and gypsum layers that feed small
permanent sources within the catchment. Soils developed over mudrocks
are predominantly of silt-loam texture. Topsoil is rich in organic
matter (on average 4.1% from 0 to 55 cm below the ground surface) and
well-structured, with high infiltration capacity in the upper 20 cm
(Solé, Gallart, Pardini & Aringhieri, 1992), while hydraulic
conductivity decreases rapidly at greater depth (Rubio, Llorens &
Gallart, 2008). These soil conditions result in formation of shallow
permanent aquifers over the impervious bedrock and some transient
perched aquifers during major rainfall events. Soil water content is
characterized by periods of marked deficit in summer and, though less
pronounced, in winter. In summer, soil cracking occurs, which enhances
infiltration capacity. Soil thickness varies greatly as a consequence of
terracing, ranging from less than 50 cm in the inner part of terraces to
more than 3 m in their outer part (Latron et al ., 2008). A small
part of the catchment (0.9%) is occupied by bare limestone and mudrock
outcrops with little-developed badlands landforms.
Climate is defined as Mediterranean humid, with a marked water deficit
in summer. Long-term (1988-2013) mean annual precipitation was 880 ± 200
mm (Llorens et al ., 2018), with on average 90 rainy days per year
(Latron, Llorens & Gallart, 2009). Snowfall accounts for less than 5%
in volume. The rainiest seasons are autumn and spring with mean rainfall
above 100 mm/month in October, November and May (Latron & Gallart,
2008). Winter is the season with least rainfall, while in summer
convective storms may produce significant rainfall inputs. The mean
annual temperature is 9.1 oC at 1,260 m a.s.l. and
mean potential annual evapotranspiration, calculated by the method of
Hargreaves and Samani (1982), is 823 ± 26 mm. The isotopic signatures of
meteoric water in Vallcebre are influenced by Western Mediterranean and
Atlantic Ocean air masses. The weighted average isotope ratios for the
study period between 2011 and 2016 were –44.14 ± 2.30 ‰
(δ2H), -7.17 ± 0.29 ‰ (δ18O) and
13.19 ± 0.51 ‰ (d-excess), after Casellas et al . (2019).
The combined dynamics of rainfall and evapotranspiration favour the
succession of wet and dry or very dry conditions in the catchment during
the year (Latron & Gallart, 2007). Dry and very dry periods occur in
winter and summer, respectively, whereas wet periods occur in spring and
late autumn. Three types of runoff events were identified on the basis
of hydrometric observations (Latron & Gallart, 2007; 2008). Intense
rainfall events during summer induce flash floods with very low runoff
coefficients, attributed to infiltration-excess overland flow on bare
bedrock and badland areas. Second, during transitions from dry to wet
conditions, more frequent and/or greater rainfall events induce larger
runoff events with moderate runoff coefficients with long response times
and relatively gentle recessions, attributed to a scattered pattern of
perched soil saturation. Third, under wet conditions, moderate rainfall
events induce large and lasting runoff events associated with rapid
responses of the water table, attributed to overland flow on saturated
areas and return flow. Flow in the Can Vila stream usually ceases for a
few weeks during the summer each year, though remaining stagnant pools
rarely become totally dry.
Two-component hydrograph separation studies using stable isotopes
indicate that pre-event water contributed between 30% and almost 100%
to total runoff, depending on antecedent moisture conditions, the extent
of saturated areas within the catchment and precipitation
characteristics (Latron, Roig-Planasdemunt, Llorens & Gallart, 2015;
Cayuela et al ., 2019). During low to moderate-intensity rainfall
events (winter, spring, autumn), pre-event water contribution was
dominant (>90%). Conversely, during high-intensity summer
storms, pre-event water contribution was lower (30% to 50%) and the
response corresponded mostly to new water. Pre-event water contribution
at the event scale decreases with increasing maximum rainfall intensity.
In addition, pre-event water contribution and the maximum suspended
sediment concentration observed at the outlet correlate negatively,
which supports the view that summer floods are mainly caused by
infiltration excess runoff generated on badlands and degraded areas of
the catchment (Latron et al ., 2015).
The use of tritium to investigate the turnover of waters during low-flow
conditions (Gallart et al., 2016) has shown MTTs of nearly 5 years for
shallow open groundwaters and 7.5 years for both stream base flow and a
permanent spring near the centre of the catchment.
2.2 Data acquisition
2.2.1 Hydrological measurements and water
sampling
Rainfall volumes for the period 2011-2017 were recorded at 5-minute
steps with tipping-bucket rain gauge, located 1 m above the ground near
the gauging station (Figure 1).
The depths to the water table at the VP01 and VP05 piezometers were
recorded every 20 min with autonomous Micro-Diver sensors (Van Essen
Instruments), subsequently corrected for atmospheric pressure changes.
Stream discharge was measured at the Can Vila (CV) gauging station, by
means of a 90º V-notch weir with a water pressure sensor (6542C-C,
Unidata) connected to a data-logger (DT50, Data Taker). Mean water level
values were recorded every 5 minutes and converted to discharge values
with an established rating curve calibrated with manual discharge
measurements (Latron & Gallart, 2008). Discharge values were originally
expressed in L s-1 and converted, without time
aggregation, into millimetres per day (mm d-1) for
comparison with other studies.
In the Can Vila catchment, waters for stable isotope
(δ18O and δ2H) analyses were sampled
from rain and stream at one site at the catchment outlet, from
groundwater at two sites (VP01 and VP05) and from mobile soil water at
two sites (VL01 and VL02) (see Figure 1).
Rainfall isotope data corresponded to samples taken during two time
periods between 2011 and 2017. The first period ran from May 2011 to
July 2013 and the second, from May 2015 to November 2017. Two types of
rain water samplers were used. A bulk rainfall sampler, consisting of a
180-mm diameter funnel connected to a 1 L plastic bottle with a pipe
with a loop, provided information of the isotopic composition of
rainfall on an approximately weekly basis. Rain water was further
sampled automatically at 5 mm rainfall intervals with a sequential
rainfall sampler, using an open collector (340 mm diameter) connected to
an automatic water sampler (24 500-mL bottles, ISCO 2900). Both
containers (bottle and sampler) were buried in the ground to avoid
evaporation. The two sampling records were aggregated, (i.e., using the
finest time interval available and removing duplicate samples) providing
a data set of 464 rainfall isotopes samples.
As shown by Cayuela et al . (2019), the location of the rainfall
sampling site at the lowest part of the Can Vila catchment means that
the sampled isotope signature is more enriched than the average for the
catchment. However, the isotopic enrichment of throughfall in the
forested areas compensates for this effect. Consequently, no
compensation of the isotopic signature in precipitation due to elevation
effects was deemed necessary.
Soil mobile waters were sampled at two locations with a battery of
low-suction cup lysimeters installed between 50 (2 lysimeters) and 100
(4 lysimeters) cm depth. The soil water sample at each location was a
mixture of the water collected at different lysimeters and depths. Soil
water was sampled weekly or fortnightly from May 2011 to July 2013 when
water could be extracted. Over the study period, 63 samples from VL01
and 37 from VL02 were analysed for isotopic composition.
Groundwaters were sampled at two locations near the surface of the water
table with a manual peristaltic pump, as electrical conductivity
profiles conducted on several occasions showed no stratification of the
waters. VP01 is a 2.06 m-deep piezometer lined with a 55 mm-diameter PVC
tube, which is sealed for the upper 0.5 m to prevent entrance of surface
waters and has open access below. VP05 is a 4.22 m-deep abandoned well.
Its walls are covered by boulders, allowing water to flow throughout the
full depth. Groundwater was sampled weekly or fortnightly from May 2011
to July 2013. A total of 36 samples were taken from the VP01 piezometer
(that sometimes dried out) and 71 from the (permanent) VP05 well.
Stream water was sampled during two periods, from May 2011 to September
2013 and from late May 2015 to May 2016, using a sampling scheme
designed for obtaining information for isotopic hydrograph separation
(IHS) at the event scale (Cayuela et al., 2019). Manual grab samples
were taken weekly during visits and two automatic water samplers (24 1 L
bottles, ISCO 2700) were operated by the data-logger. One sampler was
scheduled to take a sample every 12 hours and the other was triggered
when stream water level exceeded a certain threshold, taking samples at
a higher rate when the water level rose than when it declined. Samples
of little relevance to IHS such as those repeatedly taken during long
recessions or base flows were discarded, reducing the total number of
stream samples analysed for isotopic composition to 858 at the Can Vila
outlet. The final sampling rate was between 30 minutes and 1 week,
although there are some gaps due to the drying of the stream.
2.2.2 Isotopic analyses and
pre-treatment
During the sampling periods, all samples were brought together once a
week during field visits. Manual samples of stream, soil and
groundwaters were directly collected in glass vials. The bottles of the
automatic rainfall and stream samplers were capped and transported to
the laboratory under cold conditions, where two samples from every
bottle were deposited in 3-ml glass vials. These vials were fully filled
to avoid bubbles and sealed with plastic paraffin film to avoid
fractionation caused by evaporation. For each sample a replica was
prepared. All samples were stored at 3-4 oC prior to
analysis.
-Stable isotopes of water (18O and2H) were analysed by a Cavity Ring-Down Spectroscopy
Picarro L2120-i isotopic water analyser at the Scientific and
Technological Services of the University of Lleida. All isotope data
were expressed in terms of δ-notation as parts per mile (‰) and
calibrated to Vienna Standard Mean Ocean Water (V-SMOW) (Craig, 1961).
Accuracy of the analyses, based on the repeated analysis of four
reference water samples, was < 0.1‰ and < 0.4‰ for
δ18O and δ2H, respectively. When
samples contained organic compounds a post-processing correction was
applied (Martín-Gómez et al ., 2015).
The isotopic signatures of the precipitation samples were weighted by
their corresponding precipitation depths before further calculations.
Furthermore, following frequent procedures (e.g. McGuire & McDonnell,
2006; Jasechko et al ., 2014; Lutz et al ., 2018), a soil
water-balance model was used to estimate the effective precipitation
(precipitation minus evapotranspiration) for weighting the isotopic
signature of the waters entering the hydrological system, under the
hypothesis that precipitation in the warmer months evaporates more and
contributes less to the hydrological compartments than precipitation in
the remaining months. For this purpose, the conceptual lumped
Thornthwaite-Mather model (Steenhuis & van der Molen, 1986) was
implemented at a weekly time step, after calibration with the flow
records of the Can Vila catchment. This model was selected because it
simulates the effective (runoff or recharge) water as the precipitation
minus potential evapotranspiration that exceeds the remaining water
retention capacity of the root zone. Water retained in the root zone is
not transferred to runoff or recharge but just evapotranspired. This
needs the simulation of both the water balance in the root zone and the
actual evapotranspiration with a single calibrated parameter, thus
providing a good balance between soundness and simplicity.
Nevertheless, as stated in the introduction, the hypothesis of rapid
evapotranspiration of rainfall waters in summer may be questioned on the
basis of recent research. Consequently, the hypothesis of the decreased
hydrological role of summer precipitation was subject to two tests based
on mass balance methods. The first test was proposed by Grabczak,
Maloszewski, Rozanski & Zuber (1984) and further developed by
Maloszewsky, Rauert, Stichler & Herrmann (1992) to estimate ρ, the
relative contribution of summer precipitation to groundwaters (or any
other hydrological compartment):
\(\rho=\frac{\left[\sum_{W}{\left(P_{i}C_{i}\right)-C_{\text{gw}}\sum_{W}\left(P_{i}\right)}\right]}{\left[C_{\text{gw}}\sum_{S}\left(P_{i}\right)-\sum_{S}\left(P_{i}C_{i}\right)\right]}\)(1)
where ρ values higher or lower than unity reflect higher or lower
contributions of summer rainfall to the hydrological storage,
respectively; P represents precipitation; C represents the
concentration of stable isotopes of water, along with the subscriptsW for “winter” months (September to May), S for
“summer” months (June to August) and gw denoting groundwaters
or any other compartment under consideration. These different
periods were selected in order to avoid the effect of the dominant
equinoctial precipitation.
A second, more quantitative test analysed the partitioning of seasonal
precipitation into runoff and evapotranspiration, according to Kirchner
and Allen (2020). Following these authors, using mass balances, the
splitting of seasonal precipitation into runoff can be assessed by:
\(\eta_{Ps\rightarrow Q}=\frac{Q}{P_{s}}\frac{{\overset{\overline{}}{\delta}}_{Q}-{\overset{\overline{}}{\delta}}_{\text{Pw}}}{{\overset{\overline{}}{\delta}}_{\text{Ps}}-{\overset{\overline{}}{\delta}}_{\text{Pw}}}\)(2)
where ηPs→Q represents the fraction of the summer
precipitation that eventually becomes streamflow; Q is the annual
runoff; Ps is the summer precipitation; andδ̄ represents the volume-weighted isotope signatures for the
compartments denoted by the subscripts: Q for stream waters,Pw for winter precipitation and Ps for summer
precipitation.
Furthermore, summer precipitation can be split into evapotranspiration
and runoff, which are complementary. Thus, using the same notations, the
fraction of runoff that derives from summer precipitation can be
calculated as:
\(f_{Q\leftarrow Ps}=\frac{{\overset{\overline{}}{\delta}}_{Q}-{\overset{\overline{}}{\delta}}_{\text{Pw}}}{{\overset{\overline{}}{\delta}}_{\text{Ps}}-{\overset{\overline{}}{\delta}}_{\text{Pw}}}\)(3)
As both the isotope ratio of groundwater and its temporal variability
varied with the water table level at VP05, two different approaches were
implemented. First, the available record was divided into two
sub-series: samples taken when water table level was deeper than 2.25 m
were classified in the ‘deep’ group and samples corresponding to
shallower water levels in the ‘shallow’ group. Second, an attempt was
made to obtain a mass-averaged isotope ratio by weighting with the
exponent of the water table level over its minimum value, used as a
surrogate of groundwater flow (Latron & Gallart, 2008).
Stream water samples were taken at different frequencies and discharge
regimes. Therefore, their isotopic signatures were flow-weighted to
obtain mass-representative values (Kirchner, 2016a) and time-weighted
for comparison with other studies (Jasechko et al ., 2016; von
Freyberg et al ., 2018). In addition, following the methods
proposed by Kirchner (2016b) and von Freyberg et al. (2018), the
original record was divided into a set of sub-samples according to the
respective discharge rates, in order to analyse the dependence of the
young water fraction on the flow regime. Finally, for comparison with
other studies that used weekly to monthly sampling rates, a subordinate
sample set with a weekly rate was extracted from the original one.,
2.3 Young water fraction
estimations
Following the methods and notations proposed by Kirchner (2016a), the
seasonal amplitudes A and phases ϕ of the
δ18O signatures c of waters in precipitation,
estimated recharge, stream, soil and groundwater in the catchment were
estimated by non-linear fitting through the equation:
\(c=\ A\sin\left(2\ \pi\ f\ t-\varphi\right)+k\) (4)
where f (year-1) is the frequency of the cycle
(f =1 for a seasonal cycle), t is time ( years with decimal
fractions) and k is the zero value or vertical shift of the
sinusoid. In young water fraction studies, non-linear fitting methods
that limit the influence of outliers are commonly used (e.g., Kirchner,
2016a; Stockinger et al ., 2016; von Freyberg et al .,
2018). In our case, the distribution of δ18O in
precipitation had less extreme values than a normal one (platykurtic,
kurtosis K = 1.0), whereas in the stream water
δ18O distribution, the extreme values were much more
important (leptokurtic, K = 26.9). Therefore, we decided to use
least-squares fitting, as the outliers might contain hydrologically
relevant information.
Subsequently, the Fyw for the waters investigated
(i.e., stream water, groundwater, mobile soil water) was estimated as
the ratio between the amplitudes of the isotope ratios in these waters
and the amplitude of precipitation (or recharge) waters:
\(F_{\text{yw}}=\ \frac{A_{x}}{A_{p}}\) (5)
where the p and x subscripts represent the precipitation
and investigated waters, respectively.
Following the notation used by von Freyberg et al . (2018), we
designated Fyw as the time-weighted young water
fraction and \(F_{\text{yw}}^{*}\) as the flow-weighted young water
fraction.
Although the TTD of waters was not an objective of this study, research
into the young water fractions for a set of flow regimes cast doubt on
the potential role of the threshold age τyw of
these fractions. For this purpose, the shape factor α of the
likely gamma distribution for every one of the flow regime sub-samples
was estimated by iteratively solving the implicit equation (Kirchner,
2016a):
\(\varphi_{s}-\varphi_{p}=\ \alpha\ arctan\left(\sqrt{{(\frac{A_{s}}{A_{p}})}^{\frac{-2}{\alpha}}-1}\right)\)(6)
where the subscripts s and p correspond to the stream and
precipitation, respectively, and A and φ represent
sinusoid amplitudes and phase shifts, respectively. Once the shape
factor α was obtained, the corresponding threshold agesτyw of the young water fractions were calculated
by means of the following second-order polynomial fit (Kirchner, 2016a):
\(\frac{\tau_{\text{yw}}}{T}\approx\ 0.0949+0.1065\ \alpha-0.0126\ \alpha^{2}\)(7)
Finally, the dependence of the young water fraction on stream discharge
or its discharge sensitivity was investigated by two methods. First, we
estimated Fyw for different quantiles of the flow
regime (similar to Figure 7 in von Freyberg et al., 2018). Second, we
assumed that Fyw was not a fixed value but that
it increased with discharge up to a limit value of 1, following an
exponential-type equation (Gallart et al ., 2019):
\(F_{\text{yw}}\left(Q\right)=1-\left(1-F_{0\ }\right)\ exp(-Q\ S_{d})\ \ \)(8)
where F0 (1) is the Y-intercept or virtualFyw for Q =0 and Sd(unit of Q-1) is the discharge sensitivity metric.
These metrics can be obtained by non-linear fitting of the equation
(Gallart et al ., 2019):
\(c_{s}\left(t\right)=A_{P}\left[1-\left(1-F_{0\ }\right)\ exp(-Q\left(t\right)\text{\ S}_{d})\right]\sin{\left(2\ \pi\ f\ t-\varphi_{S}\right)+k_{S}}\)(9)
where subscripts s and p are the same as in Eq. (6).
In a first exercise, Fyw and its discharge
sensitivity were investigated in stream waters by applying Eqs. (4),(5)
and (9) in the full record available, lumping the 58 months as in a
single year. In a subsequent step, several 12-month time windows of both
precipitation and stream waters were selected for the application of
these equations, in order to investigate the relevance of the
precipitation forcing.
Finally, although the 858 water samples/discharge values taken at
variable time steps could be expected to provide a reasonable picture of
the stream dynamics at Can Vila, a further test was conducted by
applying Eq. (8) to the 228,095 5-minute discharge readings available
for the sampling periods. The flow-averaging of the resultingFyw(Q) simulations for all these readings
provided us with a hypothetically fully-sampled flow-weighted young
water fraction that we labelled \(\text{\ F}_{\text{yw}}^{**}\).
Statistics were performed with the help of the statistical package SPSS
(IBM Corp.) using a Levenberg-Marquardt algorithm for non-linear
estimations. Uncertainties were mostly expressed as standard errors
except for the threshold ages τyw where the
uncertainties were expressed as 90% confidence limits, using 10,000
Monte Carlo solutions of Eq. (6). Error propagation was estimated using
Gaussian methods, following the guidelines proposed by Kirchner & Allen
(2020, supplement) particularly for end-member mixing and splitting, as
well as calculation of weighted averages. Statistical significance was
set at p<0.01 and marginal significance was set at
p<0.05, although the probability of the null hypothesis is
sometimes indicated. The notation (1) after a variable name indicates
that this variable is a dimensionless number.
3. Results
3.1 Isotopic characteristics of the sampled
waters
During the study period, annual precipitation was similar to the long
term mean value (860 mm/year) with 12-months minimum of 671 and maximum
of 996 mm/year. A total of 3,902 mm of precipitation was measured and
sampled during the whole period. The isotope ratios of precipitation
samples are shown in Figure 2, with a classification of the samples as
effective (n= 224) or non-effective (n=240) for hydrological
compartments according to the Thornthwaite-Mather water recharge model.
The isotope ratios of mobile soil water and groundwater samples are
shown in Figure 3, where a scarcity of samples in late summer is
apparent. At VP05 (but not at VP01), the scatter of groundwater
δ18O values was related to the dynamics of the water
table (Figure 4 and Table 1): when the water table rose, the values
tended to be most variable, with the isotope ratios ranging from the
minimum to the maximum recorded for the time period studied. However,
when the water table was at its lowest (-3.5 m), the isotope ratios
tended to be less variable.
Stream discharge behaved differently in the two sampling periods (Figure
5). During the first one, there was a succession of wet and dry
episodes, with several interludes without any runoff. The second period
was wetter (annual precipitation = 996 mm) with sequences of
intermediate events and the 5-minute highest discharge measured during
the entire record (2,619 m3s-1,
equivalent to 404 mm d-1).
The overall results of the 18O analyses in the studied
compartments are synthesized in Table 1. Mean simulated recharge was
more depleted in heavy isotopes than precipitation because the simulated
soil water balance is more adverse in summer and, in consequence, the
recharge weights of summer-enriched isotopic sample signatures were
usually lower than those in the colder seasons.
Some other differences between inputs and compartments are further
presented in Table 2. The isotope ratios of precipitation was more
depleted than any other compartment except for flow-weighted stream
waters, although the only marginally significant differences were with
groundwater at VP01 and deep groundwater at VP05. The isotope ratios for
simulated recharge was even more depleted than for precipitation, but
otherwise nearly all the differences between recharge and catchment
compartments were either significant (soil waters and groundwaters at
VP01) or marginally significant (groundwaters and time-weighted stream
waters).
The volume-weighted 18O and 2H
values of the precipitation waters drew a Local Meteoric Water Line
(LMWL) with an adjusted determination coefficient
R2=0.961 (p<0.001):
\(\delta^{\ 2}H=\ 7.96\ \delta^{\ 18}O+13.3\) (10)
The sampled soil waters plotted reasonably close to the LMWL (Figure 6),
although some of the more enriched samples taken at VL01 were slightly
below the line, suggesting some fractionation due to evaporation. Stream
water samples plotted close to the LMWL, except for the few more
depleted samples that were clearly located below the LMWL, following the
same trend as the precipitation waters (further information on
precipitation isotopy at Can Vila can be found in Casellas et
al ., 2019). Groundwaters showed no relevant displacement from the LMWL
(not shown).
3.2 Assessing young water
fractions
A first step in the study of the young water fraction is to calculate
with Eq. (4) the seasonal amplitude and shift of the signature of
precipitation. As stated in the Methods section, either the gross
precipitation or the net precipitation obtained with a recharge model
must be properly selected before the input isotope ratios are used. The
comparisons shown in Table 2 reveal that the isotope ratios of the
simulated recharge was more depleted that all the other hydrological
compartments, so its use to explain the water partitioning should be
discarded. The isotope ratios of gross precipitation was however more
similar to the diverse compartments and can therefore be considered as
more appropriate as input signature than the signature of the simulated
recharge. The validity of this option was subsequently tested using the
mass balance Eqs (1), (2) and (3).
the weighted average δ18O value of precipitation from
June to August was -5.7 ± 0.51 0/00,
significantly different from the September to May signature, which was
-8.25 ± 0.32 0/00. This allowed the
analysis of the contribution of summer precipitation to groundwaters and
runoff through the application of Eq. (1) to a period of three complete
years (in order to avoid seasonally biased sampling). This equation give
a value of ρ=2.3 for ground waters at VP05 and ρ=1.2 for flow-weighted
stream waters. This indicates that precipitation in the period from June
to August had contributions to ground- and stream waters somewhat higher
than the rest of the year.
Yet, following a more detailed method, end-member splitting and mixing
analyses using Eqs. (2) and (3) were applied to the data with the
results shown in Table 3. Although the uncertainty is high, these
results show (splitting) that summer precipitation is likely to
contribute more to discharge (38 vs. 32%) and less to
evapotranspiration (62 vs. 68%) than winter precipitation. In addition,
discharge is composed (mixing) by summer and winter precipitations with
percentages (33 and 67% respectively) similar to their relative volumes
(30 and 70%). These results point again to a relative contribution of
summer precipitation to discharge similar or slightly higher than in the
rest of the year.
Given these converging indicators, the precipitation-weighted isotope
ratios were used for subsequent analysis of the seasonal variations,
although the recharge-weighted signature was studied and reserved for
some comparisons. The resulting implications are reviewed in the
Discussion section.
The sine-wave fitting with Eq. (4) was subsequently applied to the
isotope ratios of all eleven following compartments: precipitation (i),
simulated recharge (ii), mobile soil water at VL01 (iii) and VL02 (iv),
groundwater at VP01 (v), VP05(vi), level-weighted groundwater at VP05
(vii), groundwater at VP05 when the water table was shallow (viii) (0 to
2.25 m deep) and deep (ix) (deeper than 2.25 m), time-weighted stream
water (x) and flow-weighted stream water (xi).
The results show a wide range of amplitudes and young water fractions,
as calculated with Eq. (5) using precipitation A as Ap(Table 4). Attending to the resulting sinusoid amplitudes andFyw obtained, these eleven hydrological
compartments can be arranged with high statistical significance
(p<0.001, F-test) in four main groups: 1) mobile soil waters,
flow-weighted stream water and shallow groundwater at VP05 had the
highest Fyw and \(\text{\ F}_{\text{yw}}^{*}\)(0.207 to 0.344). 2) Level-weighted groundwater at VP05 had an
intermediate Fyw (0.115). 3) Time-weighted stream
water and bulk groundwater at VP05 had low but identifiableFyw (0.062 to 0.078). Finally, 4) groundwater at
VP01 and deep groundwater at VP05 had Fyw not
significantly different from 0. This arrangement demonstrates a good
relationship between flow-weighted stream \(\text{\ F}_{\text{yw}}^{*}\)and the more dynamic compartments of the catchment, clearly separated
from the much lower rank of time-weighted streamFyw and groundwaters.
3.3 Assessing the discharge sensitivity of young water
fractions
For the Can Vila catchment, the flow-weighted young water fraction
(\(\text{\ F}_{\text{yw}}^{*}\) = 0.226±0.028) was higher than the
time-weighted young water fraction (Fyw =
0.062±0.008), suggesting a clear dependence of the young water fraction
on discharge. To analyse this dependence, the time-weighted young water
fractions for different quantiles of the flow regime were analysed as
shown in Figure 7 (similar to Figure 7 in von Freyberg et al .,
2018), extending the range to portray the highest flows (exceeded 0.25%
of time but by 16.6% of flow). This figure shows thatFyw increased with increasing discharge, from
nearly 0 at the lowest discharge to nearly 1 for Q ≥24 mm
d-1, and underlines the usefulness of Eq. (8). This
equation provides a basal (virtual for zero discharge) young water
fraction that is indistinguishable from 0 (F0 =
0.024 ± 0.028) and rather large exponential sensitivity
(Sd = 0.056 ± 0.01 d mm-1)
parameters.
The wide range of Fyw values observed for the
diverse flow quantiles might cast doubt on the potential role of the
threshold age τyw that defines these fractions in
the results. In order to analyse this question, Figure 8 shows the
comparison of these time-thresholds obtained from Eqs. (6) and (7). This
graph demonstrates that the thresholds did not play any role because
they were consistently similar for the diverse flow quantiles analysed,
although the uncertainty towards higher values strongly increased with
increasing Fyw .
3.4 Analysing different sampling periods: role of
precipitation
forcing
Can Vila catchment data used for this work cover a period of over two
years and another of one year. To analyse the variation of\(\text{\ F}_{\text{yw}}^{*}\) and Sd under
different precipitation conditions, five 12-month time windows of both
precipitation and stream waters were selected from the first period and
compared with the last one-year period and the full record, as shown in
the upper graph of Figure 9. Although both\(\text{\ F}_{\text{yw}}^{*}\) and Sd roughly
increased with annual precipitation (upper graph), with the wettest year
(996 mm) having the highest \(\text{\ F}_{\text{yw}}^{*}\) (0.34) andSd (0.147 d mm-1), the trend is
highly irregular. Indeed, the driest year (671 mm) shows an intermediate\(\text{\ F}_{\text{yw}}^{*}\) (0.16) with a quite lowSd (0.011 d mm-1), while the
second wettest year (972 mm) shows a lower\(\text{\ F}_{\text{yw}}^{*}\) (0.12) but a higherSd (0.035 d mm-1).
When the coefficient of variation of discharge was used instead of
precipitation as the forcing variable (lower graph in Figure 9), two
very distinct conditions were shown: periods with low coefficient of
variation of discharge yielded moderate \(\text{\ F}_{\text{yw}}^{*}\)values and low Sd values whereas the period high
coefficient of variation yielded high values of both metrics.
3.5 Role of sampling rate
All the results shown above on stream waters are based on the dynamic
sampling design described in the Methods section. Nevertheless, most of
the published Fyw studies are based on
weekly-to-monthly sampling frequencies. As many authors agree that
stream waters’ transit time and Fyw results are
affected by sampling rates, we used weekly spaced samples to calculate
the main metrics describing Fyw and subsequently
compared these results with the dynamic sampling results shown above.
The results show that both time-weighted and flow-weighted young water
fractions using a weekly sampling frequency (Fyw= 0.044±0.014 and \(F_{\text{yw}}^{*}\) = 0.103±0.033) were
significantly lower than results with dynamic sampling (Table 5).
Furthermore, the highest discharge sampled at Can Vila was 226 mm
d-1, a little more than half the maximum discharge
recorded during the same period (404 mm d-1).
Therefore, as we know that Fyw approaching 1 are
associated with the highest flows, the question arises as to whether the
dynamic sampling implemented at Can Vila was sufficient to capture the
real behaviour of Fyw dynamics. For this purpose,
Eq. (8) was applied to simulate the Fyw(Q) for
every 5-minute discharge reading available for Can Vila during the
sampling period and these simulated young water fractions were weighted
with the corresponding discharge readings. The resulting flow-weighted
young water fraction, as a measure of the virtually perfect sampling,
which we name\(\ F_{\text{yw}}^{**}\), was 0.304±0.030. The differences
between the metrics obtained with the different sampling strategies and
weighting are shown in Table 5, demonstrating that if\(F_{\text{yw}}^{**}\) is taken as the unbiased young water fraction,
the \(F_{\text{yw}}^{*}\) estimates obtained with the dynamic and weekly
sampling were underestimated by 25% and 66% respectively.
In order to obtain a graphic comparison of the behaviour of the
different sampling methods, the 5-minute flow record was ordered from
high to low discharges, and the corresponding time, flow and\(F_{\text{yw}}^{*}\) were cumulated for the 5-minute record and the two
sampling designs (Figure 10). This compared the cumulated time
(time-exceedance) of every record with the corresponding flow exceedance
and young water fractions exceedance, making it easier to understand the
results shown in Table 5. Both the cumulated 5-minutes flow and\(F_{\text{yw}}^{*}\) curves start close to 0 exceedance, showing that
the highest recorded flows, in spite of their high value andFyw being close to 1, occurred so rarely that the
exceeded values for flow and Fyw are not
relevant, which makes clear that the 5-minute record does indeed
represent a thorough virtual sampling.
The highest discharges associated with the samples taken with the
dynamic design exceeded 0.01% of time and represent 2.7% of flow and
about 25% of the young water fraction (when a sufficient number of
samples were taken for estimating \(F_{\text{yw}}^{*}\)). This means
that about 25% of the young water fraction was missed for the
assessment by the dynamic sampling design because this amount was
associated with the higher discharges that were not sampled. Finally,
the highest discharges associated with the samples taken with the weekly
sampling rate are exceeded 0.6% of time and are associated with 17% of
flow and about 66% of young water fraction, which was also lost for the
assessment.
4. Discussion
Our results show a behaviour of young water fractions at the Can Vila
catchment that is much more dynamic than those reported in any other
catchment. The identification of this behaviour is attributable to the
Mediterranean climatic setting, the small size of the catchment and the
high sampling frequency available at this site for stream water tracer
data.
An early outcome of this research was the need for an updated design of
the discharge sensitivity of the young water fraction, adequate to cope
with the non-linear behaviour of Fyw with
discharge shown in Figure 7. This question was resolved previously,
leading to the development of Eqs. (8) and (9), as described in Gallartet al . (2019).
Other results help improving the conceptualisation of the hydrological
functioning of the Can Vila catchment and also contribute to revise
questions raised by other researchers in this field as detailed in the
introduction: the fate of rain water fallen in summer, the dependence of
the young water fraction on precipitation forcing, the role of sampling
frequency on catchment water turnover investigations and the young water
fractions delivered by mountain catchments.
4.1 The recharge
assumption
An unexpected result of this study was the finding that the isotopic
signature of gross precipitation was adequate for analysing the turnover
of surface and shallow groundwaters in the Vallcebre catchments, without
any need for reducing the isotopic contribution of summer precipitation.
In this catchment, summer is a period when evaporative demand is usually
much higher than precipitation; flow in the streams strongly decreases
and ceases in several reaches, saturated areas disappear and both soil
water content and water table level decrease (Llorens et al. ,
2018). Nevertheless, our results with Eqs (1), (2) and (3) indicate that
summer precipitation is not rapidly evaporated in summer, nor does it
experience more evapotranspiration than the precipitation during the
rest of the year, but summer rain similarly contributes to the diverse
hydrological compartments.
Thus, most of the water intensely evapotranspired in summer appears to
be previously stored soil water. For groundwater it may be argued that,
since bedrock at Can Vila is almost impervious, wet soils do not
contribute much to percolation to the sampled aquifers because these are
very shallow and located in the deeper horizons of soils, whereas summer
precipitation also contributes to soil and ground water because it
infiltrates into dry and often cracked soils. Using tritium, Gallart et
al. (2016) found that MTTs were nearly 5 years in open shallow aquifers
and nearly 7.5 years in base flows at Can Vila, revealing that these
base flows are not only fed by the shallow aquifers but also partially
fed by small deeper aquifers in the bedrock.
Indeed, base flows at Can Vila (exceeded 50% of time but by 95% of
flow) showed a δ18O values of -7.17 ± 0.016 ‰,
significantly more depleted than the shallow groundwaters signature.
This result points to the additional contribution to base flows by
deeper more depleted groundwater that would be recharged mainly during
wet winter periods. Using a modelling approach, a double aquifer system
was also proposed for explaining base flows at Can Vila by Ruiz-Pérez et
al. (2016).
A study by Sprenger et al. (2019a) carried out during the second
period analysed (2015) in a forested plot within the Can Vila catchment,
showed that mobile soil water was consistently more enriched in heavy
isotopes than ground and stream waters, a result analogous to ours in
Table 2. However, water held in smaller soil pores and potentially used
for transpiration by vegetation remained more depleted than any other
compartment and was mainly refilled during winter. Our results in Table
3 show that 1,822 · 0.68 = 1,239 mm of evapotranspired water was
sustained from precipitation between September and May whereas only 766
· 0.62 = 475 mm was sustained from precipitation between June and
August, in convergence with Sprenger et al. (2019) findings but
at the catchment scale.
Such findings had an impact on Fyw estimates in
the diverse compartments studied. A hypothetical decreased contribution
of summer precipitation would not only cause a shift in the mean input
isotopic signature but also a reduction of its seasonal amplitude and,
subsequently, an increase of the young water fractions. Figure 7
demonstrates that the young water fractions estimated at Can Vila for
the highest flows are around 1, the maximum possible value. However,
using the isotopic signature of the simulated recharge instead of that
of the precipitation as Ap in Eq (5), the five
points in Figure 7 that correspond to the highest flow regimes take
inconsistent Fyw values greater than 1, although
the excess does not reach statistical significance (p=0.105).
4.2 The role of precipitation
forcing
As the young water fraction usually increases with discharge, wetter
years or catchments may be expected to deliver higher young water
fractions than dry ones, as found by several authors (Bansah & Ali,
2019; Clow et al ., 2018; Remondi et al ., 2019; von
Freyberg et al ., 2018; Wilusz et al ., 2017; Zhang et
al ., 2018). However, our results shown in Figure 9 make clear that
annual precipitation is an insufficient driver for the behaviour of\(\text{\ F}_{\text{yw}}^{*}\) at Vallcebre, whereas the variation of
discharge might better explain \(\text{\ F}_{\text{yw}}^{*}\) and
particularly Sd . These results are consistent
with those obtained by other authors on the role of temporal patterns or
rainfall depths and intensities (von Freyberg et al ., 2018;
Soulsby et al ., 2011; Wilusz et al ., 2017), and
particularly with the modelling exercise of Remondi et al . (2019)
that suggested that catchments in semi-arid and Mediterranean climates
have not only lower but also more variable young water fractions than
catchments in more humid climates. Unfortunately, this kind of
information on discharge sensitivity Sd for
diverse periods or catchments is not yet available.
This result recalls the complexity of the runoff generation mechanisms
at Can Vila already investigated by hydrometric and tracing methods and
shows the need for further analyses at the event scale by combining the
study of young water fractions with other event characteristics such as
rainfall depth and intensity, antecedent conditions and new water
contribution. This would contribute to investigate not only how the
catchment behaves but also how it does work (Kirchner, 2019).
Yet, these results also cast doubt on the validity of single one-yearFyw investigations for characterizing catchment
behaviour (Stockinger et al. , 2019) and support the idea that MTT
and Fyw depends on climate forcing rather than on
physiographic catchment characteristics (von Freyberg et al .,
2018; Hrachowitz et al., 2009; Kirchner, 2019; Tetzlaff, Malcom &
Soulsby, 2007; Remondi et al ., 2019).
As with other catchment characteristics driven by climate (e.g.,
precipitation, potential evapotranspiration, discharge),Fyw and its discharge sensitivity should,
therefore, be compared between catchments through their long-term annual
means and inter-annual variabilities.
4.3 The issue of sampling
rate
The differences obtained for Fyw depending on the
sampling rates confirm the warnings of several authors and particularly
the results obtained by Stockinger et al . (2016) as mentioned in
the introduction section. Another relevant aspect is the inadequacy of
the time-weighted young water fraction in a catchment with such variant
discharge as Can Vila, even with the intensive sampling design
implemented for this study.
This exercise shows that even an intensive sampling design such as the
one implemented at Can Vila may underestimate Fywif it is sensitive to discharge and flow rates have a high variability,
because a relevant part of the young water fraction is associated to the
higher, unsampled discharges. The method applied in the section 3.5 may
be used to estimate the young water fraction \(F_{\text{yw}}^{**}\) that
could be measured if a thorough sampling design (e.g., due to in-situ
measurements) was implemented.
Investigations of the catchment Fyw should
therefore analyse the flow duration curves, if detailed flow records are
available. The relevant evaluating variable in this analysis is not the
time exceedance of discharge values, but their flow exceedance, i.e. the
fraction of flow associated to the higher discharges. Furthermore, if
the Sd discharge sensitivity ofFyw has been investigated, \(F_{\text{yw}}^{**}\)can then be assessed to evaluate the quality of the metric obtained and
to ponder the possible advantage of implementing a more detailed
sampling design. Unfortunately, the weekly sampling performed at Can
Vila is inadequate for this purpose, because the very low value ofSd obtained with this design greatly
underestimates \(F_{\text{yw}}^{**}\).
4.3 Young water fractions delivered by mountainous
catchments.
With a mean topographic gradient of 25.6%, theFyw predicted for Can Vila by the global
assessment made by Jasechko et al (2016) would be of about 0.091 with
90% confidence intervals about ± 0.061. This range is fully adequate
for the Fyw estimated at Can Vila using a weekly
sampling rate (Table 5), the flow-weighted estimate (0.103 ± 0.033)
being more adjusted than the time-weighed one (0.044 ± 0.014). Yet, the
time-weighted Fyw obtained at Can Vila using the
dynamic sampling (0.062 ± 0.008) falls also well within the range of the
global analysis by Jasechko et al. (2016).
Nevertheless, the flow-weighted \(F_{\text{yw}}^{*}\) estimate obtained
at Can Vila with the dynamic sampling (0.226 ± 0.028) is not in line
with the global relationship between topographic gradient andFyw as shown by Jasechko et al (2016), while it
is very close to the median (0.21) and a little lower than the mean
(0.26) of the Fyw obtained by these authors for
the full global sample of 254 rivers. Furthermore, the fully-sampled
flow-weighted young water fraction \(\text{\ F}_{\text{yw}}^{**}\)estimated at Can Vila is 0.304 ± 0.030, a value that falls between the
means obtained without weighting (0.26, 254 rivers) or by flow-weighting
(0.34, 190 rivers) methods by Jasechko et al. (2016).
These comparisons recall the need to pay attention to the use of
adequate sampling designs and weighting methods when catchments of
diverse flow characteristics are compared. For a catchment with constant
flow rate, any sampling rate and weighting method would yield the same
young water fraction estimate. But the results obtained at Can Vila
demonstrate that when the variability of flow rate is high, low
frequency sampling and time-weighting designs will result in clearly
underestimated young water fractions. It is not imprudent to speculate
that mountainous catchments have, on average, more variable flow rates
than those in flat areas of similar catchment area (Arnell, 1989). Thus,
reports of lower young water fractions in mountain catchments could
result from an underestimation of young waters due to too low sampling
frequencies that miss covering the high young water fractions because of
the flashy response in mountain catchments.
5 Conclusions
The application of the young water fraction approach to the
Mediterranean Can Vila research catchment improved our understanding of
the catchment response and shed light on some open questions,
highlighting the value of small catchment research for the development
of concepts and models.
In contradiction of the initial hypothesis, precipitation during summer
contributes to evapotranspiration and runoff at a rate similar to that
of precipitation during the rest of the year. Intense evapotranspiration
during summer seems to mainly use soil water infiltrated previously,
while summer rainfalls contribute to all the hydrological compartments.
This means that the isotope concentrations analysed in the precipitation
waters had to be weighted with the gross precipitation depths instead of
those of “effective precipitation” for analysing the turnover of
waters in the catchment.
The young water fraction is highly dynamic in the stream waters at Can
Vila, varying between nearly 0 during low flows to nearly 1 during high
runoff events. This dynamic is due to the combination of very high
variability of discharge and a moderate discharge sensitivity of the
young water fraction.
Furthermore, the young water fraction is also a highly varying catchment
metric at Can Vila when different 12-month periods are investigated.
Thus, the young water fraction turns out to be a metric associated much
more closely with the characteristics of precipitation forcing during
the studied period than with physiographic catchment characteristics. If
used as a metric for catchment comparison, mean long-term means and
variances should be used, just as they are used for other climate-driven
traits such as annual precipitation or annual discharge.
The results confirmed that the sampling frequency is highly relevant to
investigations of young water fractions (and by extension to MTT). At
Can Vila, the dynamic sampling design (with sampling frequency between
30 minutes and 1 week) underestimated the young water fraction by 25%
whereas the weekly sampling underestimated it by 66%. Water turnover
studies should always be linked to the inspection of flow duration
curves and, when possible, the method used in section 3.5 should be used
to estimate the young water fraction associated to a virtual thorough
sampling rate (\(F_{\text{yw}}^{**}\)), in order to assess the quality
of the metric obtained and to ponder the possible advantages of
implementing a more detailed sampling design.
Finally, more research is needed to generalize the young water fractions
of mountain catchments, preventing a potential underestimation
associated to an insufficient sampling frequency of their waters.
Acknowledgements
This research was supported by the projects TransHyMed (CGL2016‐75957‐ R
AEI/FEDER, UE) and MASCC‐ DYNAMITE (PCIN‐2017‐061/AEI) funded by the
Spanish Ministerio de Ciencia, Innovación y Universidades, as well as
the grant SGR 2017 1643 funded by the Generalitat de Catalunya. C.
Cayuela was the beneficiary of a predoctoral FPI grant (BES‐2014‐070609)
funded by the Spanish Ministry of Economy and Competitiveness and the
contribution by M. Sprenger was supported by the Deutsche
Forschungsgemeinschaft (project no. 397306994).
We are grateful to G. Bertran, M. Roig-Planasdemunt and E. Sánchez for
their support during field work at the Can Vila catchment, to J.
Kirchner, J. von Freyberg and K. Beven for their comments, as well as to
M. Eaude for his English style improvements.
Data availability
statement
The data that support the findings of this study are available from
Jérôme Latron
(jerome.latron@idaea.csic.es)
upon reasonable request.
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