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  <front>
    <journal-meta><journal-id journal-id-type="publisher">HESS</journal-id><journal-title-group>
    <journal-title>Hydrology and Earth System Sciences</journal-title>
    <abbrev-journal-title abbrev-type="publisher">HESS</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Hydrol. Earth Syst. Sci.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1607-7938</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/hess-24-2561-2020</article-id><title-group><article-title>Concentration–discharge relationships vary among hydrological events,
reflecting differences in event characteristics</article-title><alt-title>Event-scale concentration–discharge relationships</alt-title>
      </title-group><?xmltex \runningtitle{Event-scale concentration--discharge relationships}?><?xmltex \runningauthor{J.~L.~A.~Knapp~et~al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Knapp</surname><given-names>Julia L. A.</given-names></name>
          <email>julia.knapp@usys.ethz.ch</email>
        <ext-link>https://orcid.org/0000-0003-0885-7829</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>von Freyberg</surname><given-names>Jana</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2111-0001</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Studer</surname><given-names>Bjørn</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Kiewiet</surname><given-names>Leonie</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-1437-1887</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2 aff4">
          <name><surname>Kirchner</surname><given-names>James W.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-6577-3619</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Department of Environmental Systems Science, ETH Zurich, 8092 Zurich, Switzerland</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Swiss Federal Institute for Forest, Snow and Landscape Research WSL, 8903 Birmensdorf, Switzerland</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department of Geography, University of Zurich, 8057 Zurich,
Switzerland</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Julia L. A. Knapp (julia.knapp@usys.ethz.ch)</corresp></author-notes><pub-date><day>15</day><month>May</month><year>2020</year></pub-date>
      
      <volume>24</volume>
      <issue>5</issue>
      <fpage>2561</fpage><lpage>2576</lpage>
      <history>
        <date date-type="received"><day>18</day><month>December</month><year>2019</year></date>
           <date date-type="rev-request"><day>7</day><month>January</month><year>2020</year></date>
           <date date-type="rev-recd"><day>17</day><month>March</month><year>2020</year></date>
           <date date-type="accepted"><day>27</day><month>March</month><year>2020</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2020 Julia L. A. Knapp et al.</copyright-statement>
        <copyright-year>2020</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://hess.copernicus.org/articles/24/2561/2020/hess-24-2561-2020.html">This article is available from https://hess.copernicus.org/articles/24/2561/2020/hess-24-2561-2020.html</self-uri><self-uri xlink:href="https://hess.copernicus.org/articles/24/2561/2020/hess-24-2561-2020.pdf">The full text article is available as a PDF file from https://hess.copernicus.org/articles/24/2561/2020/hess-24-2561-2020.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e137">Studying the response of streamwater chemistry to changes in discharge can provide valuable insights into how catchments store and release water and solutes. Previous studies have determined concentration–discharge (cQ) relationships from long-term, low-frequency data of a wide range of solutes. These analyses, however, provide little insight into the coupling of solute concentrations and flow during individual hydrologic events. Event-scale cQ relationships have rarely been investigated across a wide range of solutes and over extended periods of time, and thus little is known about differences and similarities between event-scale and long-term cQ relationships. Differences between event-scale and long-term cQ behavior may provide useful information about the processes regulating their transport through the landscape.</p>
    <p id="d1e140">Here we analyze cQ relationships of 14 different solutes, ranging from major
ions to trace metals, as well as electrical conductivity, in the Swiss
Erlenbach catchment. From a 2-year time series of sub-hourly solute
concentration data, we determined 2-year cQ relationships for each solute
and compared them to cQ relationships of 30 individual events. The 2-year cQ behavior of groundwater-sourced solutes was representative of their cQ
behavior during hydrologic events. Other solutes, however, exhibited very
different cQ patterns at the event scale and across 2 consecutive years.
This was particularly true for trace metals and atmospheric and/or
biologically active solutes, many of which exhibited highly variable cQ
behavior from one event to the next. Most of this inter-event variability in
cQ behavior could be explained by factors such as catchment wetness, season,
event size, input concentrations, and event-water contributions. We present
an overview of the processes regulating different groups of solutes,
depending on their origin in and pathways through the catchment. Our
analysis thus provides insight into controls on solute variations at the
hydrologic event scale.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e152">The movement of water and solutes through the landscape is inherently
coupled. Streamwater chemistry at a catchment outlet differs depending on
the flow paths of water through the catchment and can therefore be considered
a “fingerprint” of catchment transport, mixing, and reaction processes.
Consequently, studying the response of streamwater chemistry to changes in
discharge provides insight into how catchments store and release water and
solutes. Changes in solute concentrations as functions of discharge, i.e.,
concentration–discharge (or cQ) relationships, have commonly been assessed
using multi-year time series of low-frequency (weekly to monthly)
streamwater chemistry measurements (Hall, 1970; Godsey et al., 2009, 2019;
Musolff et al., 2015). At this temporal scale, cQ relationships can serve as indicators of hydrologic and biogeochemical
processes. Decreasing solute concentrations with increasing flow (often
referred to as “dilution behavior”, Fig. 1a) have frequently been
associated with source limitations, indicating the depletion of finite
solute sources in the catchment (Basu et al., 2011) or mixing with more dilute waters. Conversely, patterns of increasing solute concentrations
with discharge are described<?pagebreak page2562?> as “mobilization behavior” resulting from the
flushing of solutes, for example from upper soil layers (Fig. 1c). Solute
concentrations that vary little across wide ranges of discharge
(“chemostatic behavior”, Fig. 1b) can result from several mechanisms,
including the storage and release of solutes that are not supply limited (Godsey et al., 2009; Basu et al., 2011), the overprinting of
source-limitation and mobilization behavior (Cartwright et al., 2020), or from large pre-event-water contributions to storm runoff (Clow and Mast, 2010).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><label>Figure 1</label><caption><p id="d1e157">Time series of discharge and solute concentrations (left panels),
and corresponding cQ relationships (right panels) for a single recession,
illustrating dilution behavior (Mg, top panels), chemostatic behavior (K,
middle panels), and mobilization behavior (Mn, bottom panels). Solutes with
negative cQ slopes (dilution, <bold>a</bold>) will have their lowest concentrations at high flows, and thus will exhibit increasing concentrations during hydrograph recession. Because this concentration increase is usually
less than proportional to the decrease in discharge, power-law cQ slopes are
rarely steeper than  <inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>. Solutes with cQ slopes near zero (chemostatic, <bold>b</bold>) do not vary systematically with discharge. Solutes with positive cQ slopes (mobilization, <bold>c</bold>) exhibit higher concentrations at high flows, and decreasing concentrations during hydrograph recession. Power-law cQ slopes steeper than 1 indicate that concentrations change more than proportionally to discharge.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2561/2020/hess-24-2561-2020-f01.png"/>

      </fig>

      <p id="d1e185">Because cQ relationships can vary between solutes and catchments, they are
frequently employed as descriptors for catchment hydrological behavior. The
cQ relationships obtained from long-term, low-frequency data are
particularly useful for characterizing the average behavior of a catchment (Clow and Drever, 1996; Godsey et al., 2009; Godsey and Kirchner, 2014).
However, these long-term cQ relationships provide limited insight into the
coupling of streamwater chemistry and discharge on shorter timescales, such
as during hydrologic events. A better understanding of hydrologic controls on
hydrochemical processes during events requires high-frequency hydrochemical
observations, ideally spanning many contrasting storms. High-frequency
streamwater sampling is cost-intensive and labor-intensive, and thus most studies are
limited to the characterization of individual hydrologic events (the study by Rose et al., 2018, is a rare exception). Recent technological progress in the development of in situ sensors now allows for several solutes to be monitored at sub-hourly timescales (Rode et al., 2016). Analyses of these high-frequency measurements have provided substantial insights into biogeochemical processing (Rusjan et
al., 2008), solute dynamics (Evans and Davies, 1998; Schwientek et
al., 2013), and the temporal evolution of source contributions over the
course of individual storm events (Grimaldi et al., 2004).
Event-scale studies have also highlighted a general variability in solute
responses across storm events that exceeds the variability observed in
weekly or monthly grab samples (Bieroza and Heathwaite, 2015; Lloyd et al., 2016). These findings suggest that the controls on solute storage and transport processes on the event scale may be fundamentally different from those that shape long-term behavior.</p>
      <p id="d1e189">Widely available chemical data from in situ sensors are limited to a handful
of solutes, including nitrate, orthophosphate, and dissolved organic matter.
While these solutes provide interesting insights into different aspects of
catchment processes (Carey et al., 2014; Dupas et al., 2016; Koenig et
al., 2017), they are unlikely to characterize all relevant processes
regarding solute mobilization from different parts of the catchment.
Furthermore, event-scale cQ behavior is usually not placed into the context
of long-term cQ behavior because streamwater chemistry has rarely been
measured at high temporal resolution over long periods. For example, solute
concentrations during successive events in wetter years have been shown to
be lower than in drier years (Biron et al., 1999), and events
in wetter conditions may result in stronger surface water acidification than
events following drier conditions (Wellington and Driscoll, 2004).
However, because these studies measured solute concentrations only during
individual events, we have no information on the long-term cQ behavior at
these sites. Thus it remains challenging to identify controls of cQ behavior
on both the event scale and longer timescales.</p>
      <p id="d1e192">In this study we used high-frequency measurements of 14 different solutes
ranging from major ions to trace metals that we obtained from an automated
field laboratory at the outlet of a pre-Alpine catchment (von
Freyberg et al., 2017). We quantified 2-year cQ relationships from the
snow-free periods of a 2-year dataset, and compared them to event-scale cQ
relationships of 30 hydrologic events that differed in size, antecedent
wetness conditions, and seasonality indicators. Our study aims to explore
questions such as (1) how 2-year cQ behavior differs from cQ behavior
observed on the event scale; (2) how variable cQ relationships between
individual events are; and (3) if inter-event variability in cQ relationships can be
explained by specific environmental controls.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Data and methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Site description</title>
      <p id="d1e210">The Erlenbach catchment is a small (0.7 km<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>), steep catchment spanning
an elevation range from 1100 to 1655 m above sea level in the northern Swiss
pre-Alps. The underlying geologic formation is flysch, and the highly
layered bedrock consists of limestone, claystone, marl, and shale, as well
as conglomerate and calcareous sandstone (Zobrist, 2010). Groundwater
chemistry is thus dominated by calcium, magnesium, and their counter-anion,
bicarbonate. The bedrock is overlain by umbric Gleysols with high silt and
clay content in the steeper areas (Schleppi et al., 1998; Xu et al., 2009), and by mollic Gleysols with a permanently reduced B<inline-formula><mml:math id="M3" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:math></inline-formula> horizon in
the flatter areas (Hagedorn et al., 2000). The catchment landscape is
characterized by interchanging slopes and plateaus, and the groundwater
table is generally shallower under the plateaus than under the slopes (Rinderer et al., 2014). The soil and bedrock permeabilities are
relatively low, resulting in highly saturated soils, particularly on the
plateaus. In total, 53 % of the catchment is forested, and dry and wet
meadows cover roughly 14 % and 33 % of the catchment area, respectively (van Meerveld et al., 2018). Coniferous forests cover the majority of the slopes, whereas meadows and partially forested areas can be found on the plateaus. Agricultural influence is limited to summer season cattle grazing in the upper part of the catchment. Average annual precipitation in the Erlenbach catchment is 2300 mm, of which up to 40 % falls as snow in the winter months (Stähli and Gustafsson, 2006), and about 20 % of incoming precipitation leaves the catchment as evapotranspiration (van Meerveld et al., 2018). In<?pagebreak page2563?> the years 2017 and 2018, stream discharge at the catchment outlet ranged from 0.2 to 2240 L s<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, with an average value of 37.7 L s<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Dataset</title>
      <p id="d1e263">Streamwater and precipitation chemistry were analyzed semicontinuously at an automated field laboratory located at the Erlenbach catchment outlet (von Freyberg et al., 2017, 2018). Streamwater was pumped continuously from the stream to the field laboratory, and
precipitation was collected with an open 45 cm diameter funnel. During
periods without rain, the field laboratory received only streamwater for
analysis. The field laboratory analyzed precipitation whenever more than 50 mL of precipitation accumulated in the rain sampler (corresponding to
roughly 0.3 mm of precipitation), and the previously analyzed sample was
streamwater. A new sampling and analysis cycle was initiated every 30 min; thus, during rainfall, streamwater and precipitation samples were
each analyzed hourly. A drift correction standard was analyzed instead of
streamwater every 4 h (every 6 h after 12 March 2018).</p>
      <p id="d1e266">Before analysis, each precipitation or streamwater sample passed through a
0.2 <inline-formula><mml:math id="M6" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> tangential filter. One aliquot of each sample was automatically directed to an ion chromatograph (940 Professional IC Vario, Metrohm AG, Herisau, Switzerland, hereafter referred to as “IC”) for the analysis of major anions and cations (calcium, magnesium, sodium, potassium, chloride, nitrate, and sulfate). Another aliquot was injected into a continuous water sampler module (CWS, Picarro, Inc., Santa Clara, CA, USA) coupled to a cavity ring-down spectroscope (CRDS, Picarro, Inc., Santa Clara, CA, USA) for water isotope analysis (deuterium and oxygen-18). Further details on the sampling and analysis of isotopes and major ions in the field laboratory are described by von Freyberg et al. (2017, 2018).</p>
      <p id="d1e279">In addition to the on-site analysis of major ions and stable water isotopes,
aliquots of filtered rainwater (every sample) and streamwater (one sample
per hour) were automatically collected into vials. Each vial contained 1 mL
of ultrapure <inline-formula><mml:math id="M7" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HNO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to stabilize the water sample. These acidified
samples were collected approximately once per week and brought to the
laboratory at ETH Zurich for subsequent analysis of a wide range of cations and trace elements using inductively coupled plasma mass spectrometry (Agilent 7900
ICP-MS, Agilent Technologies, Santa Clara, CA, USA, hereafter referred to as
“ICP-MS”; more detail on the laboratory protocol can be found in the Supplement).
Of the measured elements, we selected boron, strontium, barium, iron,
manganese, copper, and chromium for further analysis in this study. Other elements were not included here because their concentrations were
mostly below the analytical detection limits. Outlier removal of isotope,
IC, and ICP-MS measurements was based on visual inspection.</p>
      <p id="d1e293">Streamwater electrical conductivity (EC) was measured at 5 min resolution
(s::can condu::lyser, S::CAN Messtechnik GmbH, Vienna, Austria). For the
purpose of this study, only every second EC measurement was used to match
the 10 min measurement frequency of river discharge (see below).</p>
      <?pagebreak page2564?><p id="d1e297">River discharge was measured at a concrete flume installed at the Erlenbach
catchment outlet (Hegg et al., 2006). Precipitation rates were recorded with a heated tipping-bucket rain gauge (Joss-Tognini 15183, LAMBRECHT meteo GmbH, Göttingen, Germany) at a meteorological station located at 1216 m above sea level in the Erlenbach catchment. At the
meteorological station, air temperature was measured with a ventilated
thermometer (VT3, Meteolabor AG, Wetzikon, Switzerland), and groundwater
level fluctuations were recorded in a fully screened well (these readings
were relative rather than absolute because they have not been calibrated
against manual water level measurements). Discharge, precipitation, air
temperature, and groundwater levels were recorded at 10 min resolution.
These data were aggregated to 30 min or 1 h intervals to match the
frequency of the solute data, except for the analysis of the EC data, for
which the 10 min resolution was used. For this purpose, we extracted
those data that were closest to the sampling times of the streamwater
samples from the 10 min discharge, air temperature, and groundwater level
time series. For the precipitation samples, associated precipitation amounts
were calculated as cumulative sums from the 10 min tipping-bucket
recordings.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Dataset and event identification</title>
      <p id="d1e308">The Erlenbach stream generally shows a fast and flashy response to rainfall
events, resulting in very short durations of the rising limb of the storm
hydrograph, in particular during short and intense events. Consequently, few
samples were collected during the rising limb of each storm in spite of the
high sampling frequency of the field laboratory. The falling limb of the
streamflow hydrograph, on the other hand, was generally well captured. For
this reason, we excluded all samples collected during periods of increasing
discharge from our analysis (in Sect. 3.3 below, we show that excluding
these periods has negligible effects on the 2-year cQ behavior). The
relationship between solute concentrations and streamflow during hydrograph
recession is informative in particular on outflow processes from shallow and
deeper groundwater, as well as riparian water (Inamdar et al., 2006).</p>
      <p id="d1e311">We excluded the winter months from the dataset to avoid ambiguities arising
from rain-on-snow and snowfall events in our analysis, because solute
responses to these events may differ from those during rain events in
snow-free periods. Consequently, only data points between 1 May and
15 November in both 2017 and 2018 were analyzed (hereafter referred to as the “snow-free periods”). During these snow-free periods, we identified individual events based on the following criteria: (1) events had to have a substantial increase in discharge, i.e., peak discharge at least 20 L s<inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> above pre-event baseflow; (2) this discharge increase had to be triggered by rainfall; (3) the hydrograph had to recede by at least 75 % of the absolute increase in discharge before the event was cut off (e.g., due to a subsequent rain event or sampler failure); and finally, (4) only events were considered for which IC (i.e., major ions) measurements were available.</p>
      <p id="d1e326">For each event, we analyzed the solute concentration and discharge data
during the hydrograph recession, starting at the main discharge peak of an
event until 95 % hydrograph recession to baseflow, or until the event was
cut off by the start of a subsequent event (if discharge had receded by at
least 75 %). We estimated cQ relationships for solute/event combinations
for which at least five data points were available on the recession limb.</p>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Assessment of source-area concentrations and input–output budgets</title>
      <p id="d1e337">To identify likely streamwater sources, we quantified average solute
concentrations of different compartments in the Erlenbach catchment: median
solute concentrations in streamwater, precipitation, and their lower and
upper quartiles were calculated from the snow-free periods in the time
series. Solute concentrations in groundwater were obtained from sampling two
pumping wells in the upper part of the catchment at three different
instances between 2016 and 2017. Although these groundwater chemistry data
may not provide a comprehensive picture of Erlenbach groundwater, they can
nonetheless indicate which solutes are likely to be dominant therein.
Concentrations in soil water of the neighboring Studibach catchment were
obtained from sampling 18 suction lysimeters during eight baseflow
snapshot campaigns in the snow-free season in 2016 and 2017 (detailed
description of the campaigns are given in Kiewiet et al., 2019). We
aggregated the data from six sites (three forested, three non-forested),
spread over three elevations in the catchment (1361, 1502 and 1611 m above
sea level), at which suction lysimeters were installed at 15, 30 and 50 cm
depth. The lysimeters were emptied and set to a tension of 50 mbar the day prior to sampling.</p>
      <p id="d1e340">We characterized the source-sink behavior of the Erlenbach catchment for
individual solutes using a dimensionless solute flux index calculated from
the high-frequency data of the snow-free periods. The solute flux index <inline-formula><mml:math id="M9" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula>
relates solute fluxes in precipitation inputs <inline-formula><mml:math id="M10" display="inline"><mml:mi>I</mml:mi></mml:math></inline-formula> to those in streamwater
outputs <inline-formula><mml:math id="M11" display="inline"><mml:mi>O</mml:mi></mml:math></inline-formula>:
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M12" display="block"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>O</mml:mi><mml:mo>-</mml:mo><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mo>max⁡</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>O</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>I</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub><mml:mo>〈</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>〉</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub><mml:mo>〈</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>〉</mml:mo></mml:mrow><mml:mrow><mml:mo>max⁡</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub><mml:mo>〈</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>〉</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub><mml:mo>〈</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>〉</mml:mo></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the total streamflow and precipitation water fluxes, <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> are the solute concentrations in streamflow and precipitation for all sampling times <inline-formula><mml:math id="M17" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>, and the angled brackets indicate volume-weighted averages. The index is positive if the streamwater solute flux is larger than the precipitation solute flux and quantifies the fraction of the output flux <inline-formula><mml:math id="M18" display="inline"><mml:mi>O</mml:mi></mml:math></inline-formula> generated within the catchment. Conversely, if the index is negative, it quantifies the fraction of the input flux <inline-formula><mml:math id="M19" display="inline"><mml:mi>I</mml:mi></mml:math></inline-formula> retained within the catchment. If the input fluxes and output fluxes
are exactly balanced, the flux index will be zero.<?pagebreak page2565?> Importantly, the solute
flux indices as calculated here provide no information on long-term fluxes
but relate the output fluxes and input fluxes during the snow-free periods between
May and November from which the hydrologic events were extracted.</p>
</sec>
<sec id="Ch1.S2.SS5">
  <label>2.5</label><title>Quantification of concentration–discharge relationships</title>
      <p id="d1e566">We estimated both the 2-year cQ behavior (i.e., using all recession data
from the snow-free periods in 2017 and 2018) and the individual event-scale
cQ behavior by fitting power-law relationships between concentration <inline-formula><mml:math id="M20" display="inline"><mml:mi>c</mml:mi></mml:math></inline-formula> and
discharge <inline-formula><mml:math id="M21" display="inline"><mml:mi>Q</mml:mi></mml:math></inline-formula> to the data (Clow and Drever, 1996; Musolff et al., 2015):
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M22" display="block"><mml:mrow><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:msup><mml:mi>Q</mml:mi><mml:mi>b</mml:mi></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          This power-law relationship is identical to a linear relationship in
double-logarithmic space:
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M23" display="block"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi>c</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi>a</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi>Q</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi>a</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M25" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> are the intercept and slope of the cQ relationship, respectively. The cQ slopes and intercepts of the entire dataset will be referred to as “2-year” cQ slopes and intercepts, whereas “event scale” will refer to cQ relationships of individual
hydrologic events. For the purpose of this study, we normalized discharge by
the average discharge of the time series <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>Q</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">mean</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:math></inline-formula> to obtain 2-year intercepts that reflect the expected concentration at the mean discharge, rather than the arbitrary value of <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:mi>Q</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>(</mml:mo><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mi>Q</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Centering the <inline-formula><mml:math id="M28" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis in this way also
has the benefit of making the slope and intercept estimates more independent
from one another.</p>
      <p id="d1e733">We calculated the relative standard errors of the event-scale slopes and
intercepts, in order to exclude events for which the cQ relationships could
not be well constrained. The cQ relationships were excluded from our analysis if
the relative standard error of either the cQ slope <italic>or</italic> intercept for any event and solute exceeded 50 %, or if both the relative standard error of the cQ slope <italic>and</italic> intercept exceeded 25 %.</p>
      <p id="d1e742">Given that our samples represent changes in chemistry during hydrograph recession, the
meaning of the obtained cQ slopes can be interpreted as follows: a cQ slope
of <inline-formula><mml:math id="M29" display="inline"><mml:mn mathvariant="normal">1</mml:mn></mml:math></inline-formula> (or <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>) is obtained if changes in solute concentrations are
proportional (or inversely proportional) to changes in discharge during
recession. Consequently, a cQ slope between <inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M32" display="inline"><mml:mn mathvariant="normal">1</mml:mn></mml:math></inline-formula> indicates
less than proportional changes in solute concentrations, and a cQ slope
close to zero indicates solute concentrations that change relatively little,
or that vary independently of discharge during recession. Conversely, cQ
slopes greater than <inline-formula><mml:math id="M33" display="inline"><mml:mn mathvariant="normal">1</mml:mn></mml:math></inline-formula> indicate that solute concentrations decrease
more than proportionally to discharge during recession. Examples of the
relationships between cQ slopes, solute recessions, and hydrograph
recessions are illustrated in Fig. 1.</p>
</sec>
<sec id="Ch1.S2.SS6">
  <label>2.6</label><title>Possible environmental controls of inter-event variability in concentration–discharge
relationships</title>
      <p id="d1e794">The 30 hydrologic events span wide ranges of storm durations, intensities,
antecedent wetness conditions, and other potential controls, thus
facilitating an investigation into how these environmental controls may
influence the slopes and intercepts of the event-based cQ relationships. To
this end, we quantified 15 different parameters for each event from the
following five categories: (1) temperature and proximity to midyear as
seasonality indicators; (2) relative input concentrations, which quantify
the ratio between the volume-weighted average precipitation concentration
during the event to the streamwater solute concentrations during pre-event
baseflow; (3) groundwater levels, baseflow discharges, and antecedent
precipitation as indicators of antecedent wetness conditions; (4) several
measures of event magnitude and intensity; and (5) event and pre-event-water
contributions determined from isotope hydrograph separation (following the approach presented by von Freyberg et al., 2018). Table 1 presents an overview of these 15 environmental controls, as well as their ranges in our dataset.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e800">We assessed 15 environmental controls grouped into five different
categories: seasonality indicators, relative input concentrations,
antecedent wetness conditions, event characteristics, and event-water
contributions. Minimum and maximum values indicate the ranges observed in
the dataset. Relative input concentrations are specific for every solute
(and not available for all solutes and events), whereas all other controls
do not differ between individual solutes. Event-water contributions were
only assessed for 22 out of 30 events. Groundwater levels are expressed as
negative values so that the maximum corresponds to the wettest conditions,
consistent with the other wetness indicators.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Variable</oasis:entry>
         <oasis:entry colname="col2">Description</oasis:entry>
         <oasis:entry colname="col3">Min value</oasis:entry>
         <oasis:entry colname="col4">Max value</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry namest="col1" nameend="col2">Seasonality indicators: </oasis:entry>
         <oasis:entry namest="col3" nameend="col4" align="center">cold <inline-formula><mml:math id="M34" display="inline"><mml:mo>↔</mml:mo></mml:math></inline-formula> warm </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">event</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Average air temperature during the event (<inline-formula><mml:math id="M36" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.37</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">15.56</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn mathvariant="normal">24</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Average air temperature in the 24 h before the event (<inline-formula><mml:math id="M39" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col3">6.23</oasis:entry>
         <oasis:entry colname="col4">18.62</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">SW</oasis:entry>
         <oasis:entry colname="col2">Proximity to midyear (–)</oasis:entry>
         <oasis:entry colname="col3">0.31</oasis:entry>
         <oasis:entry colname="col4">0.99</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry namest="col1" nameend="col2">Relative input concentrations: </oasis:entry>
         <oasis:entry namest="col3" nameend="col4" align="center">low <inline-formula><mml:math id="M40" display="inline"><mml:mo>↔</mml:mo></mml:math></inline-formula> high </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"><inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>P</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Ratio between solute concentrations in precipitation and baseflow (solute-specific) (–)</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:mn mathvariant="normal">2.0</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">40.96</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry namest="col1" nameend="col2">Antecedent wetness conditions: </oasis:entry>
         <oasis:entry namest="col3" nameend="col4" align="center">dry <inline-formula><mml:math id="M43" display="inline"><mml:mo>↔</mml:mo></mml:math></inline-formula> wet </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mtext>GW</mml:mtext><mml:mi mathvariant="normal">ini</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Initial groundwater level (cm)</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">76.70</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">9.70</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mtext>AP</mml:mtext><mml:mrow><mml:mn mathvariant="normal">7</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Amount of precipitation in the 7 d before the event (mm)</oasis:entry>
         <oasis:entry colname="col3">0.00</oasis:entry>
         <oasis:entry colname="col4">111.70</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"><inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">ini</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Baseflow before the onset of the event (mm h<inline-formula><mml:math id="M49" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.7</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.10</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry namest="col1" nameend="col2">Event characteristics: </oasis:entry>
         <oasis:entry namest="col3" nameend="col4" align="center">small <inline-formula><mml:math id="M51" display="inline"><mml:mo>↔</mml:mo></mml:math></inline-formula> large </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">intensity</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Max precipitation within 4 h (mm)</oasis:entry>
         <oasis:entry colname="col3">7.10</oasis:entry>
         <oasis:entry colname="col4">27.70</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Total amount of event discharge (mm)</oasis:entry>
         <oasis:entry colname="col3">0.90</oasis:entry>
         <oasis:entry colname="col4">28.86</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Total amount of precipitation (mm)</oasis:entry>
         <oasis:entry colname="col3">8.00</oasis:entry>
         <oasis:entry colname="col4">68.60</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">tot</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Runoff coefficient</oasis:entry>
         <oasis:entry colname="col3">0.06</oasis:entry>
         <oasis:entry colname="col4">0.45</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>Q</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Max discharge change (L s<inline-formula><mml:math id="M57" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col3">23.80</oasis:entry>
         <oasis:entry colname="col4">680.60</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"><inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">event</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Event duration (days)</oasis:entry>
         <oasis:entry colname="col3">0.48</oasis:entry>
         <oasis:entry colname="col4">4.77</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry namest="col1" nameend="col2">Event-water contributions: </oasis:entry>
         <oasis:entry namest="col3" nameend="col4" align="center">pre-event water <inline-formula><mml:math id="M59" display="inline"><mml:mo>↔</mml:mo></mml:math></inline-formula> event water </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>P</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Event water in streamflow as fractions of precipitation (event runoff coefficient) (–)</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:mn mathvariant="normal">6.3</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.16</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>Q</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Event water in streamflow as fractions of discharge (–)</oasis:entry>
         <oasis:entry colname="col3">0.04</oasis:entry>
         <oasis:entry colname="col4">0.43</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e1423">As a seasonality indicator, the proximity to midyear is calculated as a
summer–winter index:
            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M63" display="block"><mml:mrow><mml:mtext>SW</mml:mtext><mml:mo>=</mml:mo><mml:mfenced open="{" close=""><mml:mtable class="cases" columnspacing="1em" rowspacing="0.2ex" columnalign="left left" framespacing="0em"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mtext>doy</mml:mtext><mml:mn mathvariant="normal">182.5</mml:mn></mml:mfrac></mml:mstyle></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mtext>doy</mml:mtext><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">183</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">365</mml:mn><mml:mo>-</mml:mo><mml:mtext>doy</mml:mtext></mml:mrow><mml:mn mathvariant="normal">182.5</mml:mn></mml:mfrac></mml:mstyle></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mtext>doy</mml:mtext><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">183</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:math></disp-formula>
          where doy is the day of year. This summer–winter index approaches 0 at the
beginning and end of each calendar year, and approaches 1 at the beginning
of July.</p>
      <p id="d1e1486">We used weighted rank correlation coefficients to quantify the dependence of
event-scale cQ slopes and intercepts on the 15 environmental controls. The
weights were the inverses of the standard errors of the individual cQ slopes
and intercepts, to prevent highly uncertain points from substantially
influencing the results. The statistical significance of these correlation
coefficients (their <inline-formula><mml:math id="M64" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> values) quantifies the probability of obtaining an equal or greater correlation if the null hypothesis were valid (i.e., if there
were actually no relationship between the slope or intercept and the
respective control).</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results and discussion</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Dataset</title>
      <p id="d1e1512">We extracted 30 events from the time series of 2017 and 2018 that fulfilled
the criteria outlined in Sect. 2.3. While IC measurements were available for
all 30 hydrologic events, not all events had the required five sample points
for all of the cations analyzed by ICP-MS (i.e., boron, barium, iron,
manganese, chromium, strontium, and copper). Furthermore, some events had to
be excluded from further analysis for individual solutes due to high
relative standard errors of cQ<?pagebreak page2566?> slopes and/or intercepts (see Sect. 2.5).
This resulted in 24 to 30 usable events for major ions measured with the IC.
More than 20 events were evaluated for all other solutes, except manganese
and copper. The concentrations of these two solutes were low and variable,
resulting in no clear power-law relationship with discharge for many events.
Consequently, only data from 17 and 11 events were usable for manganese and
copper, respectively.</p>
      <p id="d1e1515">We quantified most environmental controls for all 30 events. However,
meaningful event-water contributions could only be calculated for 22 events
from stable water isotope measurements. Ratios of precipitation
concentration to the pre-event baseflow solute concentration were not
available for all events and all solutes due to sporadic problems with the
rain collector. Also, these ratios were not assessed for EC, because EC was
not measured in precipitation. Table 1 provides an overview of the range of
environmental controls covered by the selected events. Some small events
lasted only a few hours, whereas other events were extended, multi-day
storms, and antecedent wetness conditions ranged from relatively dry to very
wet. Although all events took place between May and November, they spanned a
wide range of air temperatures and weather conditions.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Characterization of solute contributions from different source areas</title>
      <p id="d1e1526">Streamwater concentrations at Erlenbach were dominated by calcium, sulfate,
magnesium, and sodium, with median concentrations between 2 and 48 mg L<inline-formula><mml:math id="M65" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (Table 2). Conversely, median streamwater concentrations of
iron and copper were low at around 1 to 5 <inline-formula><mml:math id="M66" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">L</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, and
concentrations of manganese and chromium were even lower. All other solutes (strontium,
barium, boron, chloride, potassium, and nitrate) were observed at
intermediate concentrations in the Erlenbach streamwater.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e1563">Median solute concentrations and their upper and lower quartiles in streamwater, groundwater,
and precipitation in the Erlenbach catchment and in soil water in the adjacent Studibach catchment. Groundwater solute data were collected at one to three different sampling times at two pumping wells located in the upper part of the catchment. These are probably not representative of groundwater concentrations throughout the catchment, but still provide a rough indication of which solutes dominate groundwater. Concentrations in precipitation and streamwater were obtained from the time series recorded at the Erlenbach outlet, excluding months with snow. <inline-formula><mml:math id="M67" display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula> indicates the number of samples the calculations are based on. EC was not analyzed in precipitation or soil water. Concentrations greater than 10 <inline-formula><mml:math id="M68" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">L</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> are rounded to the nearest integer. Flux index calculations (see Eq. 1) of the snow-free season are based on the same period as the analyzed time series and consequently do not represent long-term fluxes. Positive flux indices quantify the fraction of the output flux that was generated in the catchment, while negative flux indices quantify the fraction of the input flux retained in the catchment. A value of 0 is obtained if input fluxes and output fluxes balance. The ratio of precipitation to streamflow water fluxes during the snow-free period was 1.75 (compared to a ratio of 1.41 for the time from 1 January 2017 to 31 December 2018).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="6">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Solute</oasis:entry>
         <oasis:entry colname="col2">Streamwater</oasis:entry>
         <oasis:entry colname="col3">Groundwater</oasis:entry>
         <oasis:entry colname="col4">Precipitation</oasis:entry>
         <oasis:entry colname="col5">Flux</oasis:entry>
         <oasis:entry colname="col6">Soil water</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">concentration</oasis:entry>
         <oasis:entry colname="col3">concentration</oasis:entry>
         <oasis:entry colname="col4">concentration</oasis:entry>
         <oasis:entry colname="col5">indices</oasis:entry>
         <oasis:entry colname="col6">concentration</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">[solutes: <inline-formula><mml:math id="M69" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">L</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>,</oasis:entry>
         <oasis:entry colname="col3">[solutes: <inline-formula><mml:math id="M70" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">L</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>,</oasis:entry>
         <oasis:entry colname="col4">[<inline-formula><mml:math id="M71" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">L</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>]</oasis:entry>
         <oasis:entry colname="col5">of the</oasis:entry>
         <oasis:entry colname="col6">at Studibach</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">EC:  <inline-formula><mml:math id="M72" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">S</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>]</oasis:entry>
         <oasis:entry colname="col3">EC:  <inline-formula><mml:math id="M73" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">S</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>]</oasis:entry>
         <oasis:entry colname="col4">(<inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">817</mml:mn></mml:mrow></mml:math></inline-formula>–975)</oasis:entry>
         <oasis:entry colname="col5">snow-free</oasis:entry>
         <oasis:entry colname="col6">[ <inline-formula><mml:math id="M75" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">L</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(<inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1916</mml:mn></mml:mrow></mml:math></inline-formula>–4930,</oasis:entry>
         <oasis:entry colname="col3">(<inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula>–6)</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5">period</oasis:entry>
         <oasis:entry colname="col6">(<inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">41</mml:mn></mml:mrow></mml:math></inline-formula>–102)</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">EC</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">99</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">576</mml:mn></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5">[–]</oasis:entry>
         <oasis:entry colname="col6"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M80" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">EC</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">264 [222–292]</oasis:entry>
         <oasis:entry colname="col3">389 [354–398]</oasis:entry>
         <oasis:entry colname="col4">not available</oasis:entry>
         <oasis:entry colname="col5">not available</oasis:entry>
         <oasis:entry colname="col6">not available</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M81" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">47 891 [40 528–52 835]</oasis:entry>
         <oasis:entry colname="col3">50 057 [46 648–53 880]</oasis:entry>
         <oasis:entry colname="col4">1366 [948–1896]</oasis:entry>
         <oasis:entry colname="col5">0.93</oasis:entry>
         <oasis:entry colname="col6">13 553 [3461–31 007]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M82" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">3076 [2494–3498]</oasis:entry>
         <oasis:entry colname="col3">1767 [1503–2013]</oasis:entry>
         <oasis:entry colname="col4">79 [59–112]</oasis:entry>
         <oasis:entry colname="col5">0.93</oasis:entry>
         <oasis:entry colname="col6">13 588 [3885–20 429]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M83" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">2338 [1711–2924]</oasis:entry>
         <oasis:entry colname="col3">1590 [1220–1936]</oasis:entry>
         <oasis:entry colname="col4">126 [91–226]</oasis:entry>
         <oasis:entry colname="col5">0.74</oasis:entry>
         <oasis:entry colname="col6">781 [526–999]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M84" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">299 [230–347]</oasis:entry>
         <oasis:entry colname="col3">556 [551–560]</oasis:entry>
         <oasis:entry colname="col4">4.25 [2.9–6.4]</oasis:entry>
         <oasis:entry colname="col5">0.95</oasis:entry>
         <oasis:entry colname="col6">99 [0.77–297]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M85" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Ba</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">46 [34–55]</oasis:entry>
         <oasis:entry colname="col3">61 [57–65]</oasis:entry>
         <oasis:entry colname="col4">0.91 [0.65–1.47]</oasis:entry>
         <oasis:entry colname="col5">0.91</oasis:entry>
         <oasis:entry colname="col6">36 340 [9675–61 548]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M86" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">B</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">8.5 [6.7–11]</oasis:entry>
         <oasis:entry colname="col3">21 [6.4–39]</oasis:entry>
         <oasis:entry colname="col4">0.60 [0.31–1.22]</oasis:entry>
         <oasis:entry colname="col5">0.70</oasis:entry>
         <oasis:entry colname="col6">12 [8.3–20]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M87" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">9157 [6542–14 102]</oasis:entry>
         <oasis:entry colname="col3">4944 [3557–6531]</oasis:entry>
         <oasis:entry colname="col4">172 [64–472]</oasis:entry>
         <oasis:entry colname="col5">0.92</oasis:entry>
         <oasis:entry colname="col6">892 [428–1865]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M88" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">K</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">805 [659–907]</oasis:entry>
         <oasis:entry colname="col3">1197 [1101–1210]</oasis:entry>
         <oasis:entry colname="col4">81 [39–208]</oasis:entry>
         <oasis:entry colname="col5">0.13</oasis:entry>
         <oasis:entry colname="col6">527 [273–879]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M89" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Cl</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">264 [183–370]</oasis:entry>
         <oasis:entry colname="col3">891 [768–961]</oasis:entry>
         <oasis:entry colname="col4">33 [14–75]</oasis:entry>
         <oasis:entry colname="col5">0.33</oasis:entry>
         <oasis:entry colname="col6">739 [447–1319]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M90" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">527 [384–758]</oasis:entry>
         <oasis:entry colname="col3">1672 [514–1840]</oasis:entry>
         <oasis:entry colname="col4">368 [158–812]</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.52</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6">84 [9.5–565]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M92" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">4.6 [2.3–15]</oasis:entry>
         <oasis:entry colname="col3">1.21 [0.61–2.07]</oasis:entry>
         <oasis:entry colname="col4">1.40 [0.87–2.46]</oasis:entry>
         <oasis:entry colname="col5">0.87</oasis:entry>
         <oasis:entry colname="col6">18 [6.6–109]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M93" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Mn</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.18 [0.11–0.54]</oasis:entry>
         <oasis:entry colname="col3">0.42 [0.25–1.8]</oasis:entry>
         <oasis:entry colname="col4">0.21 [0.09–0.61]</oasis:entry>
         <oasis:entry colname="col5">0.54</oasis:entry>
         <oasis:entry colname="col6">12 [4.0–64]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M94" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Cr</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.05 [0.04–0.07]</oasis:entry>
         <oasis:entry colname="col3">0.13 [0.13–0.14]</oasis:entry>
         <oasis:entry colname="col4">0.01 [0.01–0.03]</oasis:entry>
         <oasis:entry colname="col5">0.62</oasis:entry>
         <oasis:entry colname="col6">0.47 [0.02–1.04]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M95" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Cu</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">1.22 [0.98–1.45]</oasis:entry>
         <oasis:entry colname="col3">0.28 [0.24–0.56]</oasis:entry>
         <oasis:entry colname="col4">0.21 [0.09–0.46]</oasis:entry>
         <oasis:entry colname="col5">0.41</oasis:entry>
         <oasis:entry colname="col6">2.68 [1.84–4.83]</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e2355">We can group different solutes based on their most important sources in the
Erlenbach catchment as determined from their concentration ranges in
groundwater, streamwater, and precipitation, as well as output–input flux
indices (Table 2). The concentrations of calcium, strontium, barium, and
boron in the groundwater samples were similar to, or higher than, those in
streamwater. Concentrations of magnesium, sodium, and sulfate were higher in
streamwater than in the groundwater samples, suggesting that other,
unsampled, groundwaters with higher concentrations also contribute to
streamflow. In general, groundwater concentrations of weathering products
are likely to be highly heterogeneous due to spatially variable contributions from the geochemically complex flysch<?pagebreak page2567?> bedrock (Fischer et al., 2015; Kiewiet et al., 2019). Precipitation concentrations of weathering products are low, and flux indices close to 1, implying that they are primarily derived from within-catchment processes (Table 2). In this paper, we will refer to these solutes as groundwater-sourced.</p>
      <p id="d1e2359">The output–input flux index of chloride at Erlenbach was 0.33 for the
snow-free periods, but was <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.13</mml:mn></mml:mrow></mml:math></inline-formula> if calculated from daily data over the 2
full years (not shown here), suggesting that precipitation is the most
important source of chloride in the Erlenbach catchment on an annual basis (Zobrist, 2010). Chloride is likely to be relatively unreactive in the
Erlenbach catchment.</p>
      <p id="d1e2372">Nitrate concentrations in Erlenbach streamwater can also be mainly
attributed to atmospheric inputs as well as manure inputs from grazing. The
output–input flux index of nitrate was <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.52</mml:mn></mml:mrow></mml:math></inline-formula> (even without taking manure
inputs into account), indicating that nitrate was either taken up into
vegetation or possibly volatilized as ammonia (i.e., the catchment acted as
solute sink). Potassium is supplied to the stream through weathering of the
bedrock, with some atmospheric inputs, which contribute more to streamwater fluxes of potassium than those of calcium or magnesium. Potassium is also
known to be retained in the soils and cycled internally in forest stands (Hornung et al., 1986; Likens et al., 1994).</p>
      <p id="d1e2385">Iron was the most abundant trace metal in the Erlenbach streamwater, with
median concentrations of around 5 <inline-formula><mml:math id="M98" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">L</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Streamwater iron
concentrations were substantially higher than the concentrations measured in
groundwater or precipitation, and very high in the soil water of the
neighboring and geologically similar Studibach catchment, pointing toward
the soil layer as a predominant source of streamwater iron (Table 2).
Groundwater concentrations of manganese at Erlenbach were broadly similar to
those measured in streamwater, but soil water concentrations (and also
groundwater concentrations; not shown here) in the Studibach catchment were
substantially higher. This indicates that manganese may be sourced both from
groundwater and soil water. The storage of iron and manganese in and release
from soil layers are likely controlled by the complexation of these trace
metals with organic material (Bloomfield, 1953; Harter and Naidu, 1995), and the strong redox sensitivity of these elements (Drever, 1988; Basu et al., 2010; Koger et al., 2018). The<?pagebreak page2568?> concentrations of the trace metals chromium and copper were low in all analyzed compartments, and a distinct source cannot decisively be identified. In the neighboring Studibach catchment, Kiewiet et al. (2019) observed the highest
concentrations of chromium at predominantly dry sites and highest
concentrations of iron and manganese at predominantly wet sites. These
observations suggest that concentrations of trace metals are probably not
homogeneously distributed in the Erlenbach catchment.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>High inter-event variability that differs from the 2-year behavior</title>
      <p id="d1e2415">We calculated 2-year cQ relationships based on the snow-free recession
periods of the 2-year time series and event-scale cQ behavior from the
recessions of the 30 extracted events. The 2-year cQ relationships were
relatively narrow and well-defined for most solutes (Fig. 2), resulting in
low uncertainties of 2-year slopes and intercepts (Table S1 in the Supplement). Furthermore,
2-year slopes and intercepts calculated for the whole time series were
broadly similar to those determined from only hydrograph recession periods
(Table S1), largely because recessions comprised nearly all of the 2-year
data. Thus, our analysis can straightforwardly compare cQ behavior during
individual recessions with the 2-year cQ behavior across 2 years of
recessions.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><label>Figure 2</label><caption><p id="d1e2420">The 2-year cQ relationships from the entire recession time series (data points are shown in light blue and the dark blue line indicates the 2-year power-law fit), compared to the cQ behavior of individual events (colored lines; up to 20 events are shown for better visibility). Discharge is normalized by the average discharge of the time series. Most solutes exhibit a 2-year dilution pattern, whereas the trace metals iron, manganese, and chromium exhibit a 2-year mobilization pattern. The cQ relationships vary much more from event to event for some solutes (e.g., potassium, chloride, and nitrate) than for others (e.g., calcium, magnesium, sodium, and EC).</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2561/2020/hess-24-2561-2020-f02.png"/>

        </fig>

      <p id="d1e2429">Figure 2 shows that major ions and EC exhibited dilution behavior (slopes <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>; lower concentrations at higher discharges) across the 2-year record, but with different degrees of
variability. The data clouds in the cQ space were more scattered (e.g.,
chloride, potassium, and nitrate) compared to those of calcium,
magnesium, and sodium. Iron, manganese, and chromium showed a mobilization
behavior (2-year slope <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>; higher concentrations at higher
discharges), while the 2-year cQ relationship of copper indicated
chemostasis (slopes <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>).</p>
      <p id="d1e2463">Event-scale cQ relationships at Erlenbach were much more variable than the
2-year behavior. A comparison between different events revealed
substantial inter-event variability in both slopes and intercepts for a
number of solutes (colored lines in Fig. 2 and blue circles in Fig. 3). The
extent of this variability differed dramatically among the solutes.
Individual events followed the 2-year trend for calcium, magnesium,
sodium, strontium, and EC, for example, whereas they deviated substantially
from the 2-year trend for potassium, chloride, and nitrate.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><label>Figure 3</label><caption><p id="d1e2468">A comparison of event-scale and 2-year cQ intercepts <bold>(a)</bold> and
slopes <bold>(b)</bold>. Blue circles represent intercepts and slopes of individual events, light-blue diamonds represent the averages of all events, and red bars indicate the slopes and intercepts of the 2-year cQ relationships. If the red bar is close to the light-blue diamond, the 2-year slope or intercept value is a good approximation of the average event slope or intercept. In panel <bold>(a)</bold>, event cQ intercepts are expressed relative to the 2-year average for better visual comparison of the solutes. Event-scale intercepts and slopes vary substantially for solutes in the lower half of the figure (from chloride to chromium), but vary little for most
groundwater-sourced solutes. Because we normalized discharge by the mean discharge value, 2-year intercepts approximate the average event intercepts. The 2-year slopes also approximate the average event slopes for most groundwater-sourced solutes, but 2-year slopes are more negative than
event slopes for other solutes, such as chloride, nitrate, and manganese.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2561/2020/hess-24-2561-2020-f03.png"/>

        </fig>

      <p id="d1e2486">For most solutes, the averages of all event-scale intercepts (light-blue
diamonds in Fig. 3a) were similar to the 2-year intercepts (red bars in
Fig. 3a), because discharge was normalized by its mean value (see Sect. 2.5). The inter-event variability in intercept values was particularly high for chloride, nitrate, and some of the trace metals, possibly suggesting changes in sources, flow paths or reaction rates of these constituents between events.</p>
      <p id="d1e2489">Conversely, the slopes of the event-scale cQ relationships differed
substantially from the 2-year behavior for some of the elements (Figs. 2
and 3). This was true in particular for three solutes with significant
atmospheric inputs (chloride, potassium, and nitrate), which exhibited
dilution behavior in the 2-year dataset (2-year slope <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>), while their
cQ slopes of individual events varied between dilution (event
slope <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>) and mobilization (event slope <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>).</p>
      <p id="d1e2522">None of the solutes exhibited stronger dilution behavior, on average, during
events (blue diamonds in Fig. 3b) than over the 2-year period (red bars in Fig. 3b). In the case of potassium, chloride, nitrate, and manganese, most
individual events (blue circles in Fig. 3b) exhibited substantially weaker
dilution, or greater mobilization, than the 2-year cQ relationships (red
bars in Fig. 3b). Considered together, these results indicate that dilution
processes were equally important, or more important, over the long term than
during individual events.</p>
      <p id="d1e2526">Solutes with similar sources and similar chemical properties tend to exhibit
similar 2-year cQ behavior and similar degrees of inter-event variability
in slopes and intercepts. For example, calcium, magnesium, sodium,
strontium, barium, boron, sulfate, and EC all exhibited well-defined
2-year dilution behavior and little variability in both cQ slopes and
intercepts at the event scale. All solutes exhibiting this behavior were
previously identified as groundwater-sourced in the Erlenbach catchment
(Sect. 3.2). Average event slopes of these solutes were approximated well by
the 2-year behavior (Fig. 3b), resulting in event patterns that fan out
around the high-discharge section of the 2-year cQ trend (Fig. 2). This
similarity between 2-year and event-scale behavior indicates that similar
mechanisms controlled solute and water mobilization both during individual
events and over the long term for these solutes.</p>
      <p id="d1e2529">Conversely, potassium, chloride, and nitrate have substantial atmospheric
inputs at Erlenbach. These three solutes were characterized by 2-year
dilution behavior, and high variability in event slopes ranging from
negative to positive values, along with some inter-event variability in
intercept values. These solutes exhibit event cQ patterns that fan out and
stack up around the 2-year relationship. This large inter-event
variability in cQ slopes may plausibly arise from varying degrees of
atmospheric deposition, evapotranspiration, and dry deposition, resulting in
temporally and spatially variable concentrations of chloride, potassium, and
nitrate in shallow soil layers. A large variability in soil water
concentrations was indeed observed in the neighboring Studibach catchment
(Table 2). In the case of nitrate and potassium, the inter-event variability
may also be affected by biological uptake and reaction processes. In
summary, chloride, nitrate, and potassium showed a much more diverse
behavior on the event scale and also – at least to some extent – on longer
timescales than the purely groundwater-sourced solutes.</p>
      <p id="d1e2532">The trace metals iron, manganese, and chromium were mobilized during events,
as reflected in positive event and<?pagebreak page2569?> 2-year cQ slopes. Interestingly, this
mobilization behavior was more pronounced (i.e., slopes were steeper) on the
event scale than on longer timescales. In contrast to the other metals,
copper concentrations in streamwater suggested chemostatic behavior over
long timescales, whereas some mobilization behavior was evident on the event
scale (Fig. 2). These findings suggest that the trace metals were mainly
sourced from the soil layers, and the observed cQ behavior of manganese and
iron confirms common assumptions about them being co-located in the soil
layers where they are bound to organic material or present as oxides.</p>
      <p id="d1e2535">The grouping of solutes based on cQ behavior aligns well with the previously
identified source areas in the Erlenbach catchment (Sect. 3.2). These
alignments were most obvious for the purely groundwater-sourced solutes
because they could be clearly attributed to one main source. For most other
solutes, the combination of different sources and the co-occurrence of
reaction and mixing processes resulted in less clear patterns. A scatterplot
of event slopes against event intercept values (Fig. 4) supports the
grouping of solutes and illustrates the different degrees of inter-event
variability. The low uncertainty of the calculated slopes and intercepts
furthermore confirms that the observed variability among events is
real-world behavior rather than noise.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><?xmltex \currentcnt{4}?><label>Figure 4</label><caption><p id="d1e2540">Scatterplots of event cQ slopes and intercepts of the 14 different solutes and EC (error bars indicate one standard error). Solutes
from different dominant sources cluster and exhibit similar ranges of
variability. <bold>(a)</bold> Groundwater-sourced solutes cluster closely around similar slopes and show little inter-event variability in both slopes and
intercepts. <bold>(b)</bold> Intercepts and slopes of solutes with significant
atmospheric input (i.e., chloride, nitrate, and potassium) vary
substantially among events. <bold>(c)</bold> The slopes of trace metals are generally higher than those of the other solutes (indicating predominantly
mobilization behavior) and are also highly variable among events. The
uncertainty in the estimated slopes and intercepts is mostly smaller than
the variability among events, indicating that the observed inter-event
variability in slopes and intercepts reflects real-world behavior rather
than sampling and measurement noise. To corroborate this, a version of the same figure including all cQ slopes and intercepts, also those from events excluded
from further analysis due to high relative standard errors in slope and/or
intercept values, is provided in the Supplement.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2561/2020/hess-24-2561-2020-f04.png"/>

        </fig>

      <p id="d1e2559">Other likely modulators of the variability observed for different solutes
are their ionic form and their possible occurrence as nanoparticulates.
Cations are known to undergo exchange buffering through electrostatic
binding to negatively charged sites in soils (Helling et al., 1964; Rhoades, 1982). This likely resulted in less variable cQ behavior on
the event scale for the cationic solutes calcium, magnesium, sodium,
strontium, and barium compared to the anionic solutes sulfate and boron.
These anions are less buffered by ion exchange and showed a far more
variable cQ behavior. Two other anions, chloride and nitrate, also exhibited
highly variable cQ behavior at the event scale. It consequently seems likely
that exchange buffering processes modulate the degree of observed
inter-event variability. Nevertheless, the importance of cation exchange
buffering on the variability of solute behavior cannot be well constrained
with our dataset because most analyzed cations are groundwater-sourced
species, while two of the three solutes with substantial atmospheric inputs, namely chloride and nitrate, are anions. The only cation with important atmospheric
input (potassium) is biologically very active, potentially obscuring the
effects of cation exchange buffering. With respect to the trace metals, a
large part of their total concentration can occur as natural
nanoparticulates (Gottselig et al., 2017), which may undergo different
transport and adsorption<?pagebreak page2570?> processes compared to their dissolved forms. This
likely had a strong effect on their cQ behavior at Erlenbach.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Environmental controls of the observed inter-event variability in concentration–discharge relationships</title>
      <p id="d1e2570">We used weighted rank correlation coefficients to assess how variations in
cQ slopes and intercepts from event to event were related to seasonality
indicators, relative input concentrations, antecedent wetness conditions,
event characteristics, and event-water contributions. A heatmap (Fig. 5)
illustrates how event-scale cQ slopes and intercepts depended on these
different environmental controls. Individual examples of these relationships
are shown in Fig. S2 in the Supplement for different solutes and drivers.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><label>Figure 5</label><caption><p id="d1e2575">Weighted rank correlation coefficients expressing the dependence
of event-scale cQ intercepts <bold>(a)</bold> and slopes <bold>(b)</bold> on different environmental controls (seasonality indicators, relative input concentrations, antecedent wetness conditions, event characteristics, and importance of event-water contributions). Green fields indicate positive rank correlations, blue fields indicate negative correlations, and darker colors indicate stronger relationships. Only statistically significant (<inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula>) correlation coefficients are displayed. Gray fields for EC indicate relationships that could not be assessed because EC was not measured in precipitation. For solutes featuring dilution patterns, e.g., calcium in panel <bold>(b)</bold>, positive correlations indicate relationships that become more chemostatic when the controlling variable increases. For solutes with mobilization patterns, e.g., iron in panel <bold>(b)</bold>, positive correlations indicate enhanced mobilization when the controlling variable increases. For meanings of abbreviations, please refer to Table 1.</p></caption>
          <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2561/2020/hess-24-2561-2020-f05.png"/>

        </fig>

      <p id="d1e2608">The event-scale cQ intercepts for all solutes, regardless of their dominant
source, generally responded similarly to each control (with the exception of
chloride; Fig. 5a). Seasonality indicators and antecedent wetness conditions
were the most important environmental controls on cQ intercepts for all
solutes, with drier and warmer conditions resulting in higher concentrations
in streamwater. By contrast, although the effects of each control on
event-scale cQ slopes were broadly similar within groups of solutes that
shared the same dominant source (precipitation, soil water, and
groundwater), they often differed between these groups (Fig. 5b). In the
following, we therefore discuss the behavior of the event-scale cQ slopes of
these groups of solutes together, rather than discussing individual solutes.</p>
      <p id="d1e2612">We found that the event-scale cQ slopes of groundwater-sourced solutes were
positively correlated with seasonality indicators, with weaker solute
dilution (i.e., less negative cQ slopes) during warmer conditions.
Antecedent wetness conditions and event characteristics were other important
factors controlling the event-scale cQ behavior of most groundwater-sourced
solutes. We found stronger dilution (i.e., more negative cQ slopes) during
larger events associated with wetter antecedent conditions. cQ slopes were
also more negative when event-water contributions were larger, consistent
with stronger dilution of groundwater-sourced solutes by larger volumes of
recent rainfall (i.e., event water). Most of the observed relationships were
less clear for boron (which is primarily sourced from groundwater, but does
not occur as a cation, but instead as either undissociated boric acid or as
the borate anion, depending on pH), supporting the hypothesis that
differences in ionic charge modulate event-scale cQ<?pagebreak page2571?> behavior. By contrast,
however, sulfate (an anion) showed very similar dependencies as the cations
in groundwater, contradicting this hypothesis. Streamwater electrical
conductivity (EC) at Erlenbach is dominated by the two most abundant
solutes, calcium and magnesium (along with their counter-ion, bicarbonate),
which are groundwater-sourced. Consequently, the event-scale cQ behavior of
EC depended on similar factors as that of the groundwater-sourced solutes.</p>
      <p id="d1e2615">For the solutes with significant atmospheric inputs (chloride, potassium,
and nitrate), the effects of possible environmental controls on cQ slopes
were less clear, but still indicated similar behavior among the solutes of
this group. We found that the event-scale cQ slopes of chloride and nitrate
were influenced by antecedent wetness conditions, with dilution behavior
during wetter conditions and mobilization behavior during drier conditions
(Fig. 5b). This can potentially be explained by stronger evapoconcentration
of these solutes in the soil under drier conditions. We also observed a
tendency toward more positive slopes with higher relative input
concentrations for all three solutes, and during events in which the
event-water contribution was larger. The observed dependencies of nitrate
and potassium differed somewhat from those of chloride, likely due to the
overprinting with reaction processes acting on these solutes, and due to
overlapping patterns from atmospheric and groundwater sources in the case of
potassium.</p>
      <p id="d1e2618">Among the trace metals, iron often exhibited contrasting behavior compared
to the others (Fig. 5b). While manganese, chromium, and copper showed a
tendency toward stronger mobilization under colder and wetter conditions,
iron tended to be mobilized more during warmer and drier conditions. Given
that both iron and manganese are found predominantly in wetter soils (in the neighboring Studibach catchment; Kiewiet et al., 2019), we would have expected these two metals to depend on similar drivers. However, Kiewiet et al. (2019) also observed higher concentrations of manganese in riparian areas compared to iron. We would expect these riparian
zones to be activated first during a rain event, whereas soils farther from
the stream would likely only start to contribute to streamflow later. This
sequence of contributions from source areas dominated by different trace
metals could potentially explain why the cQ slopes of the trace metals
varied differently with seasonality, event characteristics, and event-water
contributions. The high concentrations of manganese in riparian areas may
also explain the very high cQ slopes observed for this element. As the
relative contribution from riparian areas decreases later in the recession,
manganese concentrations in streamwater drop rapidly, decreasing
more than proportionally compared to discharge. As metal complexation and
mobilization is known to depend on various factors such as pH and redox
conditions in the soil layer (Gotoh and Patrick, 1972, 1974), further
field measurements are necessary to better understand the mobilization of
trace metals from soil layers during hydrologic events.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>A classification scheme for concentration–discharge relationships in the Erlenbach catchment</title>
      <p id="d1e2630">Previous studies have shown that hydrological controls on streamwater
chemistry are mostly invariant on timescales of weeks to months; for
example, Gwenzi et al. (2017) found similar cQ behavior for
weekly to monthly sampling frequencies, and Godsey et al. (2019) found similar cQ behavior in weekly/monthly grab samples and in
year-to-year variations in annual average concentrations. Other studies have
also shown that long-term average cQ behavior is relatively independent of
the sampling frequency (e.g., Bieroza<?pagebreak page2572?> et al., 2018). Our analysis of event-scale cQ patterns, as defined by high-frequency sampling
within and between individual events, provides a new perspective on cQ
relationships. Our results indicate that solute responses to discharge
variations can be fundamentally different during individual events compared
to longer timescales. These differences in cQ behavior reveal the effects
of the dominant sources, reaction processes, and ionic forms of the
different solutes.</p>
      <p id="d1e2633">Figure 6 provides an overview of the different cQ patterns observed at
Erlenbach and the role of various environmental controls in shaping these
patterns during events and over the long term. For groundwater-sourced
solutes such as calcium, magnesium, and sodium, we found that 2-year cQ
relationships were relatively good approximations of event-scale cQ
patterns. These solutes exhibited little inter-event variability, and their
cQ relationships on both the event scale and longer timescales were
dominated by dilution. The inter-event variability of cQ slopes of
groundwater-sourced solutes was mainly controlled by season, event size, and
event-water contributions.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><label>Figure 6</label><caption><p id="d1e2638">Schematic overview of cQ behavior based on dominant solute sources
and environmental controls at the Erlenbach catchment. Solutes originating
from similar sources generally behave similarly, and their cQ patterns are
mostly sensitive to the same environmental controls. The light-blue patches
in cQ behavior show the expected variability in long-term cQ data, with
average long-term cQ relationships indicated by the blue lines. Red lines
show cQ relationships for individual events and indicate the degree of
inter-event variability.</p></caption>
        <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://hess.copernicus.org/articles/24/2561/2020/hess-24-2561-2020-f06.png"/>

      </fig>

      <p id="d1e2648">Atmospherically derived solutes also exhibited 2-year dilution behavior,
but their event-scale behavior ranged from dilution to mobilization, with
event-scale cQ patterns stacking up and fanning out around the 2-year cQ
relationship (Figs. 2 and 6). Their event-scale cQ slopes were usually more
positive than their 2-year cQ slopes, indicating a stronger importance of
chemostatic and mobilization mechanisms on the event scale. The controls on
event-scale cQ<?pagebreak page2573?> slopes were less clear for nitrate and potassium than for
chloride, likely due to reaction processes (in the case of potassium and
nitrate) or overprinting of contributions from different sources (in the
case of potassium). Nevertheless, we observed stronger mobilization
following drier antecedent conditions and during events with larger
event-water contributions, suggesting that evapoconcentration of
atmospherically deposited solutes plays an important role.</p>
      <p id="d1e2651">Trace metals showed mixed behavior in our analysis, likely due to different
patterns of distribution in soils and groundwaters, and possibly also due to
their presence as nanoparticulates (Fig. 6). In our study, the different
trace<?pagebreak page2574?> metals often responded differently to environmental controls, possibly
reflecting differences in their relative abundance in the riparian zone, in
their complexation mechanisms, in their redox sensitivities, and in their
biological cycling (Herndon et al., 2015; Koger et al., 2018).</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Summary and conclusions</title>
      <p id="d1e2663">Our analysis of 30 events extracted from a 2-year time series of sub-hourly
streamwater solute measurements demonstrated that concentration–discharge
(cQ) relationships at the hydrologic event scale can differ substantially
from those over the long term. In addition, cQ relationships varied greatly
from event to event for some solutes (e.g., potassium, chloride, and
nitrate), but varied much less for others (e.g., calcium, magnesium, sodium,
and EC). The variability in cQ relationships among different hydrologic
events (and solutes) could be linked to a range of environmental controls.</p>
      <p id="d1e2666">Our analysis would not have been possible if we had analyzed only a few
solutes or collected data only during a handful of hydrologic events, as is
common practice in catchment hydrochemistry studies (Rode et al., 2016). To understand the complex mechanisms governing solute storage and
release from different parts of the catchment, it is necessary to analyze
many different solutes and to sample multiple hydrologic events at high
enough frequency to capture event behavior. However, we are aware that
sampling and analysis systems like the one that we employed at Erlenbach are
resource-intensive and thus difficult to deploy in many field situations.
Our analysis suggests, however, that a viable alternative may be to analyze
one solute (or proxy thereof) from every major store and streamwater source
in the catchment. For instance, EC in Erlenbach streamwater exhibited very
similar cQ relationships as calcium, magnesium, and sodium, making it a
suitable tracer for groundwater-sourced solutes (in other catchments,
EC may be a better proxy for solutes from other compartments; Benettin and
Van Breukelen, 2017). Automated sensors for nitrate and phosphorous are
available and can provide high-frequency information on biogeochemically
active solutes. The analysis of trace metals is not available through
automated sensors, but in many cases dissolved organic carbon can be a suitable proxy for iron
and some other trace metals (Nierop et al., 2002; Grybos et al., 2007). Measurements of pH may also provide helpful insights into the mobilization of
trace metals from soil layers. All in all, with sufficient knowledge about
the possible sources that contribute to streamflow in a catchment, much
simpler measurement systems may still provide meaningful insight into solute
storage and release processes.</p>
      <p id="d1e2669">The grouping of solutes based on their dominant source, cQ behavior, ionic
character, and dependence on environmental controls is illustrated in a
schematic overview in Fig. 6. This overview highlights similarities and
differences among solutes, summarizes their expected range of cQ behavior on
the event scale, and indicates their sensitivities to environmental
controls. Analyses of event-scale cQ patterns may help in identifying the
vulnerability of different catchment compartments to changes in land use and
climate and may benefit monitoring and management strategies. For example,
if the climate warms and summers become drier in this area of Switzerland,
our data suggest that the event slopes of chloride, nitrate, and potassium
will become more positive, leading to enhanced flushing of these solutes
during hydrologic events. Evaluating the generality of the results presented
here will require further studies in catchments of contrasting climate,
geology, and land use.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e2676">The data that support the findings of this study are available from the corresponding author upon reasonable request.</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e2679">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/hess-24-2561-2020-supplement" xlink:title="pdf">https://doi.org/10.5194/hess-24-2561-2020-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e2688">JLAK and JWK conceptualized the study. JLAK, JF, and BS collected and analyzed the solute data, LK collected and analyzed the soil moisture data from Studibach, JLAK analyzed the dataset, and JLAK prepared the manuscript with contributions from all co-authors.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e2694">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e2700">The authors thank the Swiss Federal Institute for Forest, Snow and Landscape
Research (WSL) for facilitating this research project in the Erlenbach
catchment and for sharing hydro-climatic data. We are also particularly
grateful to Ilja van Meerveld for helpful discussions. Julia L. A. Knapp was funded
through an ETH Zurich Postdoctoral Fellowship.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e2705">This research has been supported by the ETH Zurich (ETH Zurich Postdoctoral Fellowship).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e2711">This paper was edited by Thom Bogaard and reviewed by two anonymous referees.</p>
  </notes><ref-list>
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<abstract-html><p>Studying the response of streamwater chemistry to changes in discharge can provide valuable insights into how catchments store and release water and solutes. Previous studies have determined concentration–discharge (cQ) relationships from long-term, low-frequency data of a wide range of solutes. These analyses, however, provide little insight into the coupling of solute concentrations and flow during individual hydrologic events. Event-scale cQ relationships have rarely been investigated across a wide range of solutes and over extended periods of time, and thus little is known about differences and similarities between event-scale and long-term cQ relationships. Differences between event-scale and long-term cQ behavior may provide useful information about the processes regulating their transport through the landscape.</p><p>Here we analyze cQ relationships of 14 different solutes, ranging from major
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behavior during hydrologic events. Other solutes, however, exhibited very
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cQ behavior could be explained by factors such as catchment wetness, season,
event size, input concentrations, and event-water contributions. We present
an overview of the processes regulating different groups of solutes,
depending on their origin in and pathways through the catchment. Our
analysis thus provides insight into controls on solute variations at the
hydrologic event scale.</p></abstract-html>
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