A total of 607 precipitation and streamwater samples were collected at weekly intervals between December 2004 and March 2009. Precipitation was sampled as cumulative bulk samples at Carreg Wen, and streamwater was collected as instantaneous grab samples at the Lower Hafren and Tanllwyth sampling points (see Fig. 1). The precipitation samples were collected with a continuously open PVC funnel of 15 cm diameter with anti-bird protection. This data set is termed the “weekly data” in our analysis.

A further 2113 samples were collected at 7-hourly intervals from July 2007 through March 2009 at Carreg Wen (precipitation) and the Upper Hafren outlet (streamwater). Streamwater sampling was automated using Xian 1000 portable automatic samplers programmed to collect streamwater at 7-hourly intervals into carousels of 24 500 mL bottles, which were picked up from the field site once per week (for details see Neal et al., 2012, 2013a). The entire sampling pathway was flushed with streamwater immediately before the collection of each sample to avoid carryover from the previous sample. The precipitation samples were collected via a continuously open 57.5 cm funnel with anti-bird protection, mounted above an autosampler with an enclosed carousel of 24 308 mL bottles, which was also picked up once per week. The resulting data set is termed the “7-hourly data” in our analysis.

Both the weekly and 7-hourly sampling of stable water isotopes were embedded in longer-term data collection efforts which have previously been published. Stream chemistry analyses are available weekly from 1983 through 2011 at up to five catchments (Neal et al., 2011, 2013c), and bi-weekly thereafter (Norris et al., 2017), and are also available at 7-hourly resolution between 2007 and 2009 (Neal et al., 2012, 2013a, b). In addition, hourly meteorological measurements and 15 min stream gauging data from Plynlimon are available starting in the 1970s (CEH, 2019). Thus the isotope measurements presented in this study complement chemical and hydrological data already available to the public.

Rainfall amounts were recorded from a standard, ground-level tipping bucket rain gauge at the Tanllwyth met site during the weekly sampling (at 350 m a.s.l.), and at the Carreg Wen automatic weather station during the 7-hourly sampling (at 575 m a.s.l.). Streamflow was determined from stream gauges at the outlets of the Upper Hafren, Hafren, and Tanllwyth catchments.

Each sample bottle (weekly sampling) or carousel of bottles (7-hourly sampling) was normally processed at the Center for Ecology and Hydrology (CEH), Bangor, UK, the day after it was returned from the field. All samples were filtered (0.45 µm Supor membrane) and then split. One part of the sample was acidified to 1 % v/v with concentrated high-purity HNO3 for analysis of cations and metals, and another was bottled without acidification for analysis of anions. A 30 mL aliquot was also bottled in high-density polyethylene bottles for subsequent isotopic analysis. Usually this aliquot was taken from the un-acidified split, but in some cases it was taken from the acidified split by mistake. The behavior of the acidified and un-acidified samples was broadly similar (see Fig. S2 in the Supplement), but the acidified samples were slightly lighter in deuterium than the un-acidified samples. This offset has been corrected in the data set, and the acidified samples are flagged in the archival data file provided in the Supplement to this paper.

The bottled isotope samples were kept in the dark at or below 5 ∘C until they were shipped from CEH to the central laboratory of the Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland, in 2009. At WSL, all samples were transferred to 2 ml glass vials and closed with 11 mm snap caps (Infochroma AG, Goldau, Switzerland) with 1 mm silicone septa. The vials were stored at -14 ∘C for about 1 year, before they were thawed for subsequent analysis.

The samples were analyzed for oxygen-18 and deuterium isotope ratios at WSL, using a Picarro L1102-i cavity ring-down spectroscopy (CRDS) analyzer equipped with a Picarro V1102-i vaporization module (Picarro, Inc., Sunnyvale, CA, USA) and a PAL HTC-xt-LEAP-Pic autosampler (CTC Analytics AG, Zwingen, Switzerland). Routine calibrations used three secondary standards (mixed seawater, Fiji artesian water, and Sion drinking water), which in turn were referenced to IAEA VSMOW2, SLAP2, and GISP. All isotope ratios are reported in standard δ notation relative to the Vienna Standard Mean Ocean Water (VSMOW). Each sample was analyzed twice, separated by at least 100 other samples and standards, and the reported value for each sample is the average of the pair. Any pair that differed by more than 0.20 ‰ in oxygen-18 or 1.0 ‰ in deuterium was re-analyzed (again twice), and whichever of the two pairs was more consistent was averaged for the final reported value. Furthermore, the isotopic composition of some streamwater samples was cross-checked using isotope ratio mass spectrometry (IRMS) and a generally good agreement was found to the CRDS measurements (Fig. S1). More details on the comparison between IRMS and CRDS measurements, and the drift and reproducibility of the measurements, are given in the Supplement.

The local meteoric water line (LMWL, δ2H = 11.8 + 7.71δ18O) determined from isotope ratios of the 7-hourly precipitation samples fell close to the global meteoric water line (GMWL: δ2H = 10 + 8 δ18O). We excluded one 7-hourly streamwater sample from further analysis, since its isotope ratio deviated significantly from the GMWL, suggesting evaporation during storage (see Fig. S3). In addition, some of the weekly samples showed clear evaporation trends and had to be omitted from the data set; they were isotopically heavy in both deuterium and oxygen-18, but followed a line that was much shallower than the meteoric water line, indicating evaporative fractionation. In total around one-eighth of the weekly samples had to be excluded from the data set (22 out of 177 precipitation samples, 25 out of 215 Lower Hafren streamwater samples, and 27 out of 215 Tanllwyth streamwater samples). Most of these sample bottles had visually obvious head space when they were opened for analysis, despite having been completely filled at the time of original sample processing. The dual-isotope plots in Fig. S3 show clear evidence of evaporative fractionation in the excluded samples.

Some of the 7-hourly samples were lost due to sporadic autosampler failures, and all samples collected between December 2007 and the middle of March 2008 were lost following chemical analysis, resulting in a data gap in the 7-hourly isotope time series. As a result, over half of the 7-hourly streamwater samples are missing during the months of December through March. However, the streamwater samples are 98.6 % complete from 18 March through 29 November 2008 (864 samples out of 876 sampling periods) following all quality control checks.

During some sampling intervals, too little rain fell to provide sufficient sample volume, and thus precipitation isotope analyses are missing for some low-volume rainfall events. Conversely, if the rainfall during a 7 h sampling period exceeded the capacity of the sample bottle (308 mL, which equals 1.2 mm of rain), the bottle overflowed. For such precipitation samples, the isotopic ratios of the sample may differ, by an unknown amount, from the volume-weighted averages over the 7 h interval. Such overflows occurred during approximately 65 % of the 7 h intervals for which rainfall samples are available. To verify that this did not substantially affect the data, we compared each week's volume-weighted averages of the 7-hourly data to the corresponding weekly bulk precipitation samples and found good agreement. This suggests that isotopic mass balances derived from these data are reliable, even though samples that overflowed comprise the great majority of the total rainfall and within-event variations in precipitation isotopes can be large (Munksgaard et al., 2012; von Freyberg et al., 2017).

The dual-isotope plots in Fig. 2 show that the streamwater and precipitation samples of the final data set fell close to the GMWL, suggesting that they were not greatly affected by evaporative fractionation. Nonetheless, one must consider the possibility that some evaporative fractionation has taken place, particularly in samples collected during the warmer seasons, given that they were stored in the field for up to a week in open bottles within the autosampler. To test for this possibility, we plotted the deuterium excess (Dansgaard, 1964) as a function of season (Fig. 3) and a function of the length of time each sample was stored in the field (Fig. 4). More negative values of deuterium excess indicate greater degrees of evaporative fractionation. Figure 3 shows that the deuterium excess in both the 7-hourly and weekly samples was close to 10 (the GMWL constant, indicated by the reference line in Fig. 3), and was only slightly lower in the summer than the winter. Importantly, the seasonal pattern in deuterium excess in the 7-hourly streamwater samples (which were stored for up to a week in the autosampler in the field) was similar to that in the weekly streamwater samples (which were collected by manual grab sampling and brought directly back to the lab). The similarity in these two deuterium-excess patterns implies that the 7-hourly samples did not undergo significant evaporative fractionation while in storage in the autosampler. This inference is corroborated by Fig. 4, which shows that the storage duration in the field had no detectable effect on the deuterium excess in 7-hourly precipitation and streamwater samples, in either the summer or winter seasons.

Figure 5 shows the 7-hourly and weekly time series of deuterium and oxygen-18 in precipitation and streamwater. The left and right axes are scaled such that fluctuations following the meteoric water line will appear equal, facilitating easier visual comparison. Both isotopes, at both sampling frequencies, show that streamwater isotope variations are very strongly damped compared to precipitation. This directly implies that recent rainfall can only be a minor component of streamflow. Consequently, streamflow must be composed of a mixture of many previous precipitation inputs, and thus the catchment must store and mix waters over a wide range of timescales.

Neither the weekly nor the 7-hourly data exhibit strong seasonal patterns, reflecting the proximity of Plynlimon to the Irish Sea. The weekly precipitation isotope measurements are distinctly less variable than the 7-hourly measurements are, because the weekly samples average over higher-frequency isotopic fluctuations that are captured in the 7-hourly samples (Kirchner et al., 2004). The weekly streamflow time series also appears smoother than the 7-hourly time series, but this is largely a visual artifact resulting from the lower density of data points (roughly 200 weekly samples, versus nearly 1500 7-hourly samples, in plots of equal width in Fig. 5). Nonetheless, the 7-hourly streamwater sampling does capture several large brief isotopic excursions that are missed by the weekly sampling.

Figure 6 presents a close-up of part of the 7-hourly streamwater isotope time series, revealing rich dynamics in streamwater isotopes that are nearly invisible at the scale of the whole record shown in Fig. 5. The fluctuations in deuterium and oxygen-18 generally mirror one another, with distinctly larger excursions during high-flow conditions, providing a first indication that higher flows contain larger proportions of recent precipitation, and smaller proportions of older catchment storage. The streamwater isotope fluctuations are much smaller at low flows, but they are not noise. This can be seen by comparing the streamwater isotope time series in Fig. 6 to the green lines, which show a reproducibility test in which a single sample was analyzed 124 times in sequence, revealing the variability that would be expected to arise from analytical noise alone. The variability in the streamwater time series is distinctly larger than this, indicating that it mostly reflects real-world variability in the streamwater isotopes.

The somewhat narrower band of deuterium data, as seen in Fig. 6, presumably reflects the larger measurement noise associated with the oxygen-18 values, or, conversely, the stronger memory effect that arises in deuterium analyses due to the heterogeneous exchange of hydrogen with adsorbed water in the analyzer (Friedman and Irsa, 1952). Both of these hypotheses are consistent with the reproducibility test, in which the replicate oxygen-18 and deuterium measurements had standard deviations of 0.069 ‰ and 0.22 ‰, respectively. Thus, in this test, deuterium was only about 3 times as noisy as oxygen-18, whereas its real-world variability should be 8 times larger than that of oxygen-18 for samples that follow the meteoric water line. Thus the signal-to-noise ratio in deuterium should be roughly twice as large as in oxygen-18, although deuterium's sample-to-sample memory effects were also 3 times larger (see Supplement).

The fluctuation damping in the streamwater isotopes, relative to the much larger fluctuations in precipitation isotopes, can also be visualized through power spectra. As Fig. 7 shows, fluctuations in streamwater isotopes are strongly damped relative to precipitation on all timescales shorter than several years, and the degree of damping systematically grows as frequency increases. There is distinct power-law scaling in both the precipitation and streamwater time series on timescales shorter than roughly 1 month (corresponding to frequencies higher than roughly 10 per year), with steeper scaling in streamwater than precipitation. The spectral slopes of the two isotopes in 7-hourly precipitation are indistinguishable within error (0.63±0.03 and 0.62±0.02 for deuterium and oxygen-18, respectively). By contrast, the spectral slope of deuterium in 7-hourly streamwater is distinctly steeper than that of oxygen-18 (1.57±0.07 versus 1.17±0.02), possibly reflecting greater memory effects during the analysis. The spectral slope of deuterium in weekly streamwater is also slightly steeper than that of oxygen-18 at both Lower Hafren and Tanllwyth, but not by more than the standard error.

The new water fraction Fnew uses passive tracers to quantify the average contribution of recent precipitation to streamflow across an ensemble of time steps, using the slope of the simple linear regression (Kirchner, 2019): 1CQj-CQj-1=FnewCPj-CQj-1+α+εj, where CPj and CQj represent the tracer concentrations (or isotope values) in precipitation and streamwater, respectively, for a series of sampling times j; α is the regression intercept, and εj is the error term. The uncertainty in Fnew can be estimated as the standard error of the regression slope of Eq. (1). This so-called “ensemble hydrograph separation” approach is based on the principle that the larger the fraction of recent precipitation in streamflow, the more tightly correlated their tracer concentrations will be.

New water fractions assess this correlation on the timescale of the sampling frequency and are thus intrinsically tied to it. New water fractions calculated from weekly sampling are “weekly new water fractions”, and express the ensemble average contribution to streamflow from precipitation that fell in the previous week. New water fractions calculated from 7-hourly sampling, or “7-hourly new water fractions”, will be inherently smaller because they express the contribution to streamflow from precipitation that fell in the previous 7 h instead of the previous week. As these examples show, new water fractions calculated for time series with different sampling frequencies will differ in both their magnitude and meaning, with smaller new water fractions obtained from higher-frequency sampling. The longer the sampling interval, the more precipitation labeled as “new” will have reached the stream by the time of sampling.

New water fractions can be calculated to represent different aspects of catchment behavior (Kirchner, 2019). Event new water fractions QpFnew quantify the proportion of new water found in streamflow for time steps with precipitation, whereas new water fractions for all time steps QFnew scale the event new water fraction by the proportion of days with precipitation to obtain an average value of new water in streamflow, including rainless periods. Similar to these new water fractions of discharge, the new water fraction of precipitation PFnew quantifies the fraction of precipitation that becomes streamflow within the given sampling interval (which will generally differ from the fraction of streamflow that is composed of recent precipitation). These new water fractions can be also weighted by volume, giving more weight to sampling times with higher flow, rather than weighting each time interval uniformly; volume-weighted quantities are indicated by an asterisk, i.e., QpFnew∗, QFnew∗, and PFnew∗.

Here we calculate new water fractions from both deuterium and oxygen-18 to gain insights into the responses of the Plynlimon catchments to precipitation. We furthermore compare new water fractions for different seasons and discharge regimes to explore how the catchments' behaviors vary under different conditions. To quantify how much precipitation contributes to streamflow over a range of lag times we also determine “backward” and “forward” transit time distributions (which quantify the relative amount of streamflow that originated as rainfall at different prior times, and the relative amount of precipitation that will become streamflow at different future times, respectively), by extending Eq. (1) to a multiple regression that accounts for multiple time lags. For documentation of this method, as well as further details on the ensemble hydrograph separation approach, the conditions under which it holds, and the different types of new water fractions, please see Kirchner (2019).

The spectral damping shown in Fig. 7 can be used to estimate equivalent transit time distributions to those estimated by ensemble hydrograph separation. Our approach is based on the convolution theorem of linear systems analysis, which implies that the power spectrum of the streamwater isotope time series should equal the power spectrum of the precipitation isotope time series, multiplied by the power spectrum of the transit time distribution. We assume that the transit time distribution is approximated by the gamma distribution, 2pτ=τk-1e-ττθθθkΓ(k), where τ is the transit time, θ and k are scale and shape parameters, and Γ(k) is the gamma function. The mean transit time can be calculated as τ‾=kθ, but it will be very sensitive to the tail of the distribution, and thus difficult to constrain from relatively short, high-frequency tracer time series. To estimate the parameters θ and k, we multiplied the power spectrum SPω of the precipitation isotope time series by the power spectrum of the gamma distribution, to yield an estimate of the power spectrum SQω of the streamwater isotope time series: 3SQω=SPω1+ωθ2-k, where ω=2πf is the angular frequency. We estimated the parameters θ and k in Eq. (3) by minimizing the sum of squared deviations between the logarithm of the predicted spectrum SQω and the logarithm of the measured tracer spectrum in streamwater, using the analytic Gauss–Newton algorithm as implemented in JMP v. 14.3 (SAS Institute, Cary, NC, USA). Weighted transit time distributions can also be estimated from Eq. (3), using a precipitation-weighted spectrum of the precipitation tracer time series, and a discharge-weighted spectrum of the streamwater tracer time series.

Many studies of catchment transit times and rainfall–runoff processes are based on stable water isotopes. Until recently, however, stable isotope measurements were expensive and therefore relatively rare. Instead, chloride has been widely used as a passive tracer, under the assumption that it is transported conservatively through the catchment. However, dry deposition of aerosols can account for a substantial share of the total chloride input, particularly at catchments like Plynlimon that are close to the coastline (Neal and Rosier, 1990; Neal and Kirchner, 2000). At Plynlimon, dry deposition accounts for about 10 %–20 % of total chloride inputs from the atmosphere (Durand et al., 1994; Wilkinson et al., 1997). Dry deposition greatly increases the variability of the precipitation concentrations, but it probably has a small effect on calculated fluxes, because samples dominated by dry deposition are usually associated with small volumes of water. However, the ensemble hydrograph separation approach uses concentration data, and specifically the damping observed between catchment input and output concentrations, to determine fractions of recent precipitation in streamflow. It is thus highly sensitive to the variability of the input signal. Noise introduced into the input signal through dry deposition can bias the results towards smaller new water fractions, because the higher variability in the input signal incorrectly implies a stronger damping between the input and output signal. To minimize this bias, we excluded all 7-hourly precipitation chloride samples that were potentially influenced by dry deposition according to several soft and hard criteria, e.g., very high concentrations in small sample volumes, or samples immediately following extended intervals without precipitation. The details of this filtering procedure are explained in the supplements.

We did not apply a similar filtering procedure to the weekly precipitation samples, because we expected them to be much less affected by dry deposition. The 7-hourly samples were particularly vulnerable to dry deposition because they were collected using a large funnel, which required only a very small input of liquid precipitation to make a measurable sample volume (e.g., only 0.4 mm of precipitation yielded 100 mL of sample). By contrast, the funnel used for the weekly sampling was substantially smaller, so more wet deposition was required to make a measurable sample, thus providing greater dilution of any dry deposition. Nonetheless, we removed chloride samples with concentrations more than 3 standard deviations above or below the mean, as potential outliers, from the weekly precipitation and streamwater time series (as well as from the 7-hourly streamwater time series).

To investigate the scaling of new water fractions with the length of the sampling interval, and to allow a comparison between the three catchments, we combined sequential sets of 7-hourly samples to synthesize longer sampling intervals. In case of the instantaneous streamwater samples, only the grab sample collected at the end of the aggregated sampling interval was considered, and all other samples in between were disregarded. Precipitation samples, on the other hand, are cumulative samples. Therefore, all individual samples collected during an aggregated sampling interval were averaged together, weighted by their respective precipitation rates.

The longer the aggregated sampling interval, the greater the number of possible combinations of samples. To exclude the possibility that an arbitrary choice of sample combinations would affect the results, we calculated new water fractions with all possible sample combinations, and averaged the resulting quantities.

We calculated new water fractions using deuterium, oxygen-18, and chloride collected at 7-hourly and weekly intervals (Table 1). The 7-hourly new water fractions (calculated from 7-hourly isotope data) show that on average, slightly less than 3 % of streamflow was made up of precipitation that fell within the last 7 h. Weekly new water fractions (calculated from weekly isotope data) show that on average 13 %–15 % of streamflow consisted of precipitation that fell within the last week. (For both sampling frequencies, these are volume-weighted new water fractions for all time steps, QFnew∗, and thus include periods where no precipitation fell.) These results illustrate that the numerical values of new water fractions, and also their meaning, are intrinsically tied to the sampling frequency: “new” water is water that fell as rain during the last sampling interval, whether that interval is 7 h or 7 d. The small 7-hourly new water fraction is not surprising, as 7 h is a relatively short time for any raindrop to reach the catchment outlet, unless it lands directly in the channel itself. Instead, most streamflow is dominated by older water that originated from previous precipitation events and has been stored within the catchment for months or longer. Unsurprisingly, across all sites and sampling frequencies, volume-weighted new water fractions were larger than unweighted new water fractions, because volume-weighting gives more emphasis to higher flows which typically contain larger proportions of recent precipitation.

In contrast to the pronounced differences between the 7-hourly and weekly new water fractions, the weekly sampling at Lower Hafren and Tanllwyth yielded broadly similar new water fractions, with slightly higher values at Tanllwyth than at Lower Hafren. The higher new water fractions in the Tanllwyth catchment can be plausibly attributed to its higher prevalence of low-permeability gley soils (Neal et al., 2004b), which would tend to promote faster near-surface flows.

Event new water fractions QpFnew are calculated only over time steps with precipitation and thus are always larger than new water fractions averaged over all time steps, including rainless periods QFnew. In the weekly data, this difference was relatively small, because almost all time steps had precipitation (roughly 70 % of weeks had precipitation rates above the threshold, here set to P‾≈0.1 mm h-1 for both weekly and 7-hourly sampling). By contrast, the 7-hourly event new water fraction QpFnew was roughly 1.5–3 times higher than the new water fraction for all time steps QFnew, because most 7 h intervals were rainless (and therefore could not contribute any new water, because new water is defined as precipitation that fell within the current time step). Only about 35 % of 7-hourly periods had precipitation rates higher than the threshold; roughly 50 % had no precipitation at all, and another 15 % had some precipitation but less than the threshold. New water fractions of precipitation (PFnew, the fractions of precipitation becoming streamflow in the same time step) were somewhat smaller than event new water fractions (QpFnew, the fractions of streamflow originating as precipitation in the same time step). This was because during most storms the rainfall rate will be higher than the streamflow rate, so the ratio between same-time-step streamflow and the total rainfall rate PFnew will necessarily be smaller than the ratio between same-time-step streamflow and the total streamflow rate QpFnew (Kirchner, 2019). This contrast in water fluxes was less pronounced at the weekly timescale, so the contrast between the weekly new water fractions of precipitation and discharge was also less pronounced. The volume-weighted new water fractions of precipitation and discharge PFnew∗ and QFnew∗ are related by the ratio of total discharge to total precipitation; in Plynlimon's very humid climate, this ratio is close to 1 and thus these two new water fractions were nearly equivalent.

The previous paragraphs, along with Table 1, demonstrate that substantially different values can be obtained, depending on which type of new water fraction is calculated. Whether event new water fractions, new water fractions for all time steps, or new water fractions of precipitation should be calculated will depend on the scientific question, because they provide somewhat different types of information. For this reason, it may be beneficial to compute several different variants, as we have done here, to obtain a more holistic picture of catchment processes. In general, one can expect that volume-weighted new water fractions will give more reproducible results than unweighted new water fractions, because they will give less weight to low-volume samples that may have anomalous tracer values.

New water fractions determined from deuterium and oxygen-18 agreed within one pooled standard error. 7-hourly new water fractions determined from the dry-deposition-filtered 7-hourly chloride time series were systematically smaller than those calculated from stable isotopes, but nonetheless in a similar range. This result suggests that the dry deposition filtering performed on the 7-hourly chloride data worked reasonably well. Conversely, new water fractions determined from weekly chloride samples (which were not corrected for effects of dry deposition) were significantly larger than those obtained from stable water isotopes.

We calculated new water fractions assuming different precipitation thresholds, below which samples were considered unreliable and excluded from the analysis. Volume-weighted event new water fractions QpFnew∗ increased with increasing precipitation thresholds in our analysis (Fig. 8a, b), as time steps with higher volumes were inherently given increasing weight. Conversely, volume-weighted new water fractions determined for all time steps QFnew∗ were affected less by the precipitation threshold, due to the scaling factor accounting for the increasing fraction of days without precipitation above the threshold (Fig. 8c, d).

The change in new water fractions with increasing precipitation thresholds was very similar between the two stable water isotopes (see Fig. 8). In contrast, 7-hourly new water fractions calculated directly from the 7-hourly chloride time series (without filtering for dry deposition effects) were substantially smaller. This was likely due to the higher variability in precipitation concentrations due to dry deposition effects, leading to a stronger apparent damping of chloride concentrations than stable water isotopes between precipitation and streamwater. After precipitation chloride values that were potentially affected by dry deposition were removed from the analysis (6.6 % of samples, equaling 50 out of 751 data points), 7-hourly new water fractions determined from chloride agreed within error with those determined from the stable water isotopes, as long as the precipitation threshold was higher than the mean precipitation rate (Fig. 8).

For the weekly chloride data, we expected the effect of dry deposition to be less important (and more difficult to assess), so we only performed a general outlier removal. The resulting chloride time series yielded substantially higher weekly new water fractions than those obtained from the stable water isotopes. This discrepancy was largest for small precipitation thresholds, but substantial throughout. This effect cannot be explained by the dry deposition of chloride alone, because we would expect this to increase the variability in the precipitation time series and thus reduce the weekly new water fraction (as we saw in the 7-hourly samples). Instead, the damping from precipitation to streamflow seems to be weaker for chloride than the stable water isotopes in the weekly data set. This was previously discussed by Neal and Rosier (1990), who linked a lower degree of damping for chloride to evaporative concentration of chloride in the catchment, resulting in a more heterogeneous distribution of chloride. The sensitivity of chloride to evapoconcentration and its substantial effect of the damping of chloride signals were also shown by (Hrachowitz et al., 2015).

Recommending an ideal precipitation threshold is not trivial and likely depends on the frequency and intensity of rain events, as well as the sampling frequency. If the precipitation threshold is set too low, potentially unreliable data points from small-volume samples will be included in the analysis. Conversely, if the threshold is set too high, many samples will be excluded from the analysis, increasing the uncertainty in the calculated new water fractions due to the reduced sample size. In this study, a precipitation threshold of 0.1 mm h-1 for both 7-hourly and weekly data gave, in our view, reasonable results. If different systems are compared, we recommend choosing a precipitation threshold that will exclude similar fractions of precipitation volumes and isotope samples, In our study, the threshold of 0.1 mm h-1 led to an exclusion of approximately 2 % and 5 % of the total precipitation volumes, and of approximately 16 % and 21 % of the isotope samples, for 7-hourly and weekly sampling, respectively. This threshold value was used in all analyses presented here, unless explicitly stated otherwise.

To test how different sampling frequencies could affect estimates of new water fractions, we aggregated the 7-hourly data to synthesize longer sampling intervals. As the length of the sampling interval changes, so does both the magnitude, and the meaning, of the new water fraction. “New” water is defined as streamflow that fell as precipitation within the last sampling interval. Thus it is not surprising, for example, that the fraction of streamflow that fell as precipitation within the last week (the weekly new water fraction) will be larger than the fraction of streamflow that fell as precipitation within the last 7 h (the 7-hourly new water fraction). As expected, the new water fraction increased with the length of the (synthetic) sampling intervals shown in Fig. 9. The curves shown here increase rather steeply over the first day, and more gradually over longer sampling intervals. The new water fraction obtained from synthetic weekly sampling was around 3 times higher than that from 7-hourly sampling in case of the stable isotopes. One might have expected an increase by a factor of 24 between sampling interval lengths of 7 h to 1 week (because 24×7 h = 1 week). The observed increase is smaller for two reasons. The first reason is that, as the sampling interval increases, the average time lag also increases between any individual precipitation event and the moment that the stream is sampled. As this lag time increases, so does the chance that recent precipitation will have already passed the sampling point by the time that the sample is collected. The second reason arises from how stochastic rainfall events are aggregated as the sampling interval increases. In any given week (for example), there may be several 7 h periods when rain falls, but many others when it does not. Event new water fractions of the 7-hourly data would count only the 7 h periods with rain and would ignore the rest. The event new water fraction for the entire week will include these rainless periods (but the week will still be classified as an “event” because it includes some periods of rainfall). Thus the event new water fraction at the weekly timescale will be smaller than if it consisted entirely of rainy intervals. (Of course, even 7 h events may include rainless periods, so although this thought experiment explains how new water fractions scale with the sampling interval, it does not argue for any particular interval being the “correct” one.)

In Fig. 9, similar to Table 1 and Fig. 8, the new water fractions determined from deuterium and oxygen-18 were nearly identical, whereas those determined from chloride deviated somewhat. If dry deposition was not accounted for, the new water fraction was substantially smaller than the new water fraction determined from stable isotopes, particularly for sampling intervals of 1 d or less. If the effect of dry deposition was filtered out, new water fractions determined from chloride were within 1 standard error of those determined from stable water isotopes, except for the shortest sampling interval. This pattern was consistent for both unweighted and volume-weighted new water fractions. The analysis thus showed that chloride may be a suitable passive tracer, if potential effects of dry deposition are removed. The suitability of chloride as a passive tracer consequently depends on how well dry deposition effects can be identified and eliminated. However, it is important to note that the filtering approach for dry deposition employed here was not empirically validated and was not based on physical effects like wind speed or direction. Furthermore, the removal of dry-deposition-affected samples leads to reduced mass recovery. In the ensemble hydrograph separation approach this has only a small effect, because only the correlation between the input and output signal is assessed. In other approaches, however, a correct mass balance is essential. Therefore, we argue that the stable water isotope data provide a better and more reliable data set to quantify catchment characteristics, mixing, and storage processes.

We can directly compare the new water fractions of all three sites, if we put them on a consistent time base. We aggregated the 7-hourly samples at Upper Hafren to mimic the samples that would have been obtained through weekly sampling. We then took a subset of the weekly data at Lower Hafren and Tanllwyth, coinciding with the period of the 7 h sampling at Upper Hafren (and excluding the long data gap in the 7 h samples between December 2007 and March 2008). With all three catchments on this consistent time base, their unweighted weekly new water fractions were broadly similar, with a small increase in weekly new water fractions from Lower Hafren to Tanllwyth to Upper Hafren (Table 2). Their volume-weighted weekly new water fractions, however, were systematically larger at Lower Hafren and Tanllwyth than at Upper Hafren, which is consistent with faster routing of new water, particularly at high flows, due to the drainage ditches in the Lower Hafren and Tanllwyth plantation forests.

We calculated new water fractions from the oxygen-18 time series, subsampled to capture different percentiles of the discharge and precipitation distributions (Fig. 10). The new water fraction increased with discharge and precipitation, indicating (unsurprisingly) that recent precipitation contributed more to streamflow during large events. This was likely due to greater saturation of soils during intense rain events, resulting in a greater dominance of shallow flowpaths and thus promoting faster transport of precipitation to the stream. In addition, channel networks (Godsey and Kirchner, 2014; Zimmer and McGlynn, 2017) and near-stream saturated zones (Dunne et al., 1991) expand with increasing precipitation, causing raindrops to fall closer to the channel and therefore reach the catchment outlet faster (van Meerveld et al., 2019).

Event new water fractions for the highest 10 % of discharge were somewhat larger than the volume-weighted means (dashed lines in Fig. 10a–c) and about 3 times the unweighted means (solid lines in Fig. 10a–c). During these wet conditions, recent (same-week) precipitation accounted for roughly 25 %–30 % of streamflow in the weekly samples, and recent (same-7 h) precipitation accounted for roughly 6 % of streamflow in the 7 h samples. Conversely, event new water fractions for the lowest 40 % of the discharge distributions were typically about half, or less, of the unweighted means. For small water fluxes, new water fractions dropped to less than 5 % in case of weekly time steps, and close to 0 % for 7-hourly sampling. (In Fig. 10a–c, in contrast to the rest of this paper, we used a precipitation threshold of 0 mm h-1 when calculating event new water fractions, because a higher precipitation threshold would have excluded most of the low-discharge samples, which mostly coincide with very low precipitation rates. Thus we needed to eliminate the precipitation threshold, to reveal how new water fractions vary across the entire discharge range.) New water fractions of precipitation were also highest during the most intense rain events, and smaller at low precipitation rates. They were always lower than event new water fractions estimated for similar water fluxes, for the reasons outlined in Sect. 5.1.

Volume-weighted event new water fractions were visibly higher in fall and winter compared to spring and summer, and this pattern was mirrored, although less distinctly, in unweighted event new water fractions as well (Fig. 10d–f). This pattern was similar for 7-hourly and weekly sampling, and also for all three catchments. The higher new water fractions during fall and winter may be attributable to higher precipitation and lower evapotranspiration during these months, even though the climate at Plynlimon is generally humid throughout the year, with only slight seasonal differences in precipitation (summer rain accounts for 40 % of annual rainfall; Kirby et al., 1991). A catchment with stronger seasonality in rainfall could potentially exhibit an even more pronounced seasonal pattern in new water fractions.

We estimated transit time distributions by ensemble hydrograph separation based on weekly and 7-hourly sampling of oxygen-18. Both transit time distributions of discharge (“backward transit time distributions”) and transit time distributions of precipitation (“forward transit time distributions”) were low and broad, decreasing gradually at greater lag times, when calculated over all data (solid colored symbols in Fig. 11). Volume-weighted transit time distributions (open gray symbols in Fig. 11) showed somewhat stronger peaks at short lag times, consistent with transport being faster during larger events.

Calculating transit time distributions separately for different seasons, we found a less damped response in fall–winter, compared to spring–summer (Fig. 12). This is consistent with the observation that new water fractions tend to be higher in the colder months (see Fig. 10), possibly due to higher rainfall and lower evapotranspiration, and therefore wetter catchment conditions and higher streamflow, during these months. The seasonal differences between the transit time distributions largely disappeared at lag times longer than about 1–1.5 d. This observation further highlights the likely role of wetter catchment conditions in promoting faster transport of rainwater to the stream during the fall–winter.

As described in Sect. 4.2, transit time distributions can also be estimated from the power spectra of the tracer time series. The gamma model, when multiplied by the 7-hourly precipitation tracer power spectrum, fitted the streamwater tracer power spectrum closely at timescales of less than roughly 1 month, corresponding to frequencies above roughly 10 per year (Fig. 13a, b). The fitted gamma parameters yielded transit time distributions that corresponded closely to those estimated from ensemble hydrograph separation (Fig. 13c, d). This result is noteworthy, because although both estimation methods obviously relied on the same source data, they involve different mathematical procedures and different underlying assumptions. For example, the spectral fitting method assumed that transit times are gamma-distributed; by contrast, ensemble hydrograph separation makes no assumption about the shape of the transit time distribution, but nonetheless yielded results that are broadly consistent with a gamma distribution. Figure 13 does not provide a strong constraint on the shape of the distribution on timescales much shorter than 7 h or longer than 7 d. Nonetheless, the similarities between the distributions obtained by spectral fitting and ensemble hydrograph separation strengthen our confidence that both methods can reliably quantify the transit time behavior of real-world catchments. These similarities are not limited to the 7-hourly data shown in Fig. 13; they are also seen, although with greater uncertainties, in the transit time distributions obtained from weekly data at Lower Hafren and Tanllwyth (Figs. S6–S7).

The spectral fitting method assumes that the transit time distribution is time-invariant (i.e., stationary). In theory the regression techniques underlying ensemble hydrograph separation make the same assumption, but the benchmark tests of Kirchner (2019) show that they nonetheless reliably estimate the ensemble averages of nonstationary transit time distributions. Figure 13c, d therefore suggest that the spectral fitting method also yields ensemble averages of nonstationary transit time distributions, but this should be verified using benchmark tests.

The transit time distributions of the two isotopes appeared very similar, both over timescales of days (Fig. 13c, d) and weeks (Figs. S6–S7). Perhaps surprisingly, however, the gamma distributions fitted to the spectra of the two isotopes can yield markedly different estimates of mean transit time (Table S1 in the Supplement). For example, the gamma distribution derived from deuterium in Fig. 13c implied a mean transit time of 0.63±0.06 yr, but the gamma distribution derived from oxygen-18 implied a mean transit time that was 35-fold longer (22.2±4.6 yr). The discrepancy was smaller, but still substantial, for the volume-weighted distributions shown in Fig. 13d (0.081±0.006 versus 0.140±0.011 yr for deuterium and oxygen-18, respectively). Across all sites and sampling frequencies, we found that the fitted shape factors k were smaller, the fitted scale factors θ were larger, and the resulting mean transit times τ‾=kθ were longer, when derived from oxygen-18 than from deuterium, with mean transit times typically differing by roughly a factor of 2. Despite the similarities in the short time behavior of the transit time distributions shown here, their mean transit times are largely determined by their long-time behavior, which is poorly constrained by convolution methods, including the spectral fitting technique used here (and is not estimated at all by ensemble hydrograph separation). Our analysis thus reinforces earlier concerns regarding mean transit times estimated from stable isotope tracers (Stewart et al., 2010; Seeger and Weiler, 2014; Kirchner, 2019), even when, as here, the transit time distribution itself can be reliably estimated over a shorter range of lag times.

Transit time distributions have previously been assessed at Plynlimon from chloride data using StorAge Selection functions. Benettin et al. (2015) calibrated a two-box model to the Plynlimon chloride and hydrometric data and obtained a mean transit time at the Upper Hafren catchment of approximately 1.5 year. Conversely, Harman (2015) used rank StorAge Selection functions at the Lower Hafren, an approach which requires making assumptions about the parametric shape of the transit time distribution. If a gamma distribution was assumed, Harman (2015) found median transit times of 400 and 550 d for fixed and storage-dependent calculations, respectively. Our approach, on the other hand, depends more directly on data. In spite of these substantially different analyses, we obtained mean transit times that are relatively similar to those found by Benettin et al. (2015) and Harman (2015).

Our approach also resulted in similar shapes of the transit time distributions. Benettin et al. (2015) found that the marginal transit time distribution closely resembled a gamma distribution with the shape factor of k=0.5, while Harman (2015) obtained a shape factor of k=0.52 when enforcing a gamma distribution. This indicates the general plausibility of the underlying shape function, even though the shape factors k obtained from fitting to volume-weighted power spectra in our study varied between 0.40 and 0.54. These similarities are noteworthy because our approach estimates the short time tail of the transit time distribution directly from tracer data; the shape of the distribution is not specified in advance.