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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-22-3965-2018</article-id><title-group><article-title>Water ages in the critical zone of long-term experimental sites <?xmltex \hack{\break}?> in northern
latitudes</article-title><alt-title>Water ages in the critical zone in northern latitudes</alt-title>
      </title-group><?xmltex \runningtitle{Water ages in the critical zone in northern latitudes}?><?xmltex \runningauthor{M. Sprenger et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Sprenger</surname><given-names>Matthias</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1221-2767</ext-link></contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff2 aff3 aff1">
          <name><surname>Tetzlaff</surname><given-names>Doerthe</given-names></name>
          <email>doerthe.tetzlaff@geo.hu-berlin.de</email>
        <ext-link>https://orcid.org/0000-0002-7183-8674</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Buttle</surname><given-names>Jim</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Laudon</surname><given-names>Hjalmar</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-6058-1466</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Soulsby</surname><given-names>Chris</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Northern Rivers Institute, School of Geosciences, University of
Aberdeen, Aberdeen, UK</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Department of Geography, Humboldt University Berlin, Berlin, Germany</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>IGB Leibniz Institute of Freshwater Ecology and Inland Fisheries, Berlin, Germany</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>School of the Environment, Trent University, Ontario, Canada</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Department of Forest Ecology and Management, Swedish University of
Agricultural Sciences, Umeå, Sweden</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Doerthe Tetzlaff (doerthe.tetzlaff@geo.hu-berlin.de)</corresp></author-notes><pub-date><day>20</day><month>July</month><year>2018</year></pub-date>
      
      <volume>22</volume>
      <issue>7</issue>
      <fpage>3965</fpage><lpage>3981</lpage>
      <history>
        <date date-type="received"><day>20</day><month>March</month><year>2018</year></date>
           <date date-type="rev-request"><day>27</day><month>March</month><year>2018</year></date>
           <date date-type="rev-recd"><day>6</day><month>June</month><year>2018</year></date>
           <date date-type="accepted"><day>24</day><month>June</month><year>2018</year></date>
      </history>
      <permissions>
        
        
      <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/22/3965/2018/hess-22-3965-2018.html">This article is available from https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018.html</self-uri><self-uri xlink:href="https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018.pdf">The full text article is available as a PDF file from https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018.pdf</self-uri>
      <abstract>
    <p id="d1e146">As northern environments undergo intense changes due to a
warming climate and altered land use practices, there is an urgent need for
improved understanding of the impact of atmospheric forcing and vegetation on
water storage and flux dynamics in the critical zone. We therefore assess the
age dynamics of water stored in the upper 50 cm of soil, and in evaporation,
transpiration, or recharge fluxes at four soil–vegetation units of podzolic
soils in the northern latitudes with either heather or tree vegetation
(Bruntland Burn in Scotland, Dorset in Canada, and Krycklan in Sweden). We
derived the age dynamics with the physically based SWIS (Soil Water Isotope
Simulator) model, which has been successfully used to simulate the
hydrometric and isotopic dynamics in the upper 50 cm of soils at the study
sites. The modelled subsurface was divided into interacting fast and slow
flow domains. We tracked each day's infiltrated water through the critical
zone and derived forward median travel times (which show how long the water
takes to leave the soil via evaporation, transpiration, or recharge), and
median water ages (to estimate the median age of water in soil storage or the
evaporation, transpiration, and recharge fluxes). Resulting median travel
times were time-variant, mainly governed by major recharge events during
snowmelt in Dorset and Krycklan or during the wetter winter conditions in
Bruntland Burn. Transpiration travel times were driven by the vegetation
growth period with the longest travel times (200 days) for waters infiltrated
in early dormancy and the shortest travel times during the vegetation period.
However, long tails of the travel time distributions in evaporation and
transpiration revealed that these fluxes comprised waters older than
100 days. At each study site, water ages of soil storage, evaporation,
transpiration, and recharge were all inversely related to the storage volume
of the critical zone: water ages generally decreased exponentially with
increasing soil water storage. During wet periods, young soil waters were
more likely to be evapotranspired and recharged than during drier periods.
While the water in the slow flow domain showed long-term seasonal dynamics
and generally old water ages, the water ages of the fast flow domain were
generally younger and much flashier. Our results provide new insights into
the mixing and transport processes of soil water in the upper layer of the
critical zone, which is relevant for hydrological modelling at the plot to
catchment scales as the common assumption of a well-mixed system in the
subsurface holds for neither the evaporation, transpiration, or recharge.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p id="d1e156">Water ages are useful metrics to assess hydrological processes as they
reveal interactions between storage and fluxes of water in a hydrological
system (Hrachowitz et al., 2013; Tetzlaff et al., 2014; Pfister et al.,
2017). Temporal variability of the water ages of streams results from the
dynamics of hydro-meteorological conditions and wetness state of the
catchment (Botter et al., 2010; van der Velde et al., 2012; Heidbüchel
et al., 2013; Birkel et al., 2015; Hrachowitz et al., 2016). Thus,
understanding the interplay between the<?pagebreak page3966?> climatic drivers and the state of
the hydrological system is increasingly relevant in the light of climate and
land use changes.</p>
      <p id="d1e159">Northern environments have been shown to undergo particularly pronounced
changes with an increase in land surface temperature (Hartmann et al., 2013)
and tree cover (Forkel et al., 2016). Such altered climatic conditions and/or
changes in vegetation cover are likely to modify the partitioning of water in
the critical zone into evaporation, transpiration, and recharge fluxes
(Tetzlaff et al., 2013; Wang et al., 2018). As it has been shown that
dynamics of evapotranspiration (ET) fluxes affect the water ages of catchment
runoff (van der Velde et al., 2012; Birkel et al., 2012; Ali et al., 2014)
and groundwater recharge (Sprenger et al., 2016), a better understanding of
the ET dynamics and their effect on water ages and storage dynamics is
needed. Water ages in ET fluxes also deserve increasing attention (Botter et
al., 2010, 2011; Harman, 2015; Soulsby et al., 2016; van Huijgevoort et al.,
2016) as the interlinkages between water stored in a hydrological system and
the vegetation cover using that water are crucial to address challenges of
water supply (Sterling et al., 2013; Wei et al., 2018).</p>
      <p id="d1e162">Here, we address recent findings from water age theory, defined as an
“inverse storage effect” (Harman, 2015), where the storage in a
hydrological system is related to the ages of the water fluxes leaving the
system. At the catchment scale, several modelling studies have shown younger
water ages during wet periods with high storage volumes (van der Velde et
al., 2012; Benettin et al., 2013; Heidbüchel et al., 2013; Soulsby et
al., 2015; Benettin et al., 2017). Detailed experimental work on a sloping
lysimeter with pulse irrigation provided insights into the flow path changes
that can explain the inverse relationship between storage volume and runoff
age (Pangle et al., 2017). However, despite general acknowledgement that the
conceptualization of the unsaturated zone in models affects runoff age
estimates (McMillan et al., 2012; Heidbüchel et al., 2013; van der Velde
et al., 2015), it is unclear whether/how soils contribute to an inverse
storage effect. Given that soil storage as a percentage of total catchment
storage was estimated to range from 20 % in the Scottish Highlands
(Tetzlaff et al., 2014) to up to 80 % of the total catchment storage in
rainfall-dominated alpine catchments (Staudinger et al., 2017), the role of
soil water storage in water age dynamics needs to be more clearly identified.
Further, an assessment of the variability of water ages within different pore
spaces (e.g. mobile versus more tightly bound water – Brooks et al., 2010;
Good et al., 2015; Sprenger et al., 2018b; Smith et al., 2018) and with soil
depth is still needed; this would also provide a test of the common
assumption of a well-mixed system in tracer-aided modelling (van der Velde et
al., 2015). Also, it has not yet been established how the ages of soil water
storage and evaporation and transpiration fluxes are related to the
variability of soil storage volumes.</p>
      <p id="d1e165">To address these shortcomings, we examine the following questions in this
paper. (1) How long does it take for precipitation to leave the soil profile
via evaporation, transpiration, or recharge (travel times)? (2) How old is
the water in these fluxes and the soil storage (water ages)? (3) What are the
controls on the dynamics of travel times and water ages in fluxes from, and
storage within, the critical zone?</p>
</sec>
<sec id="Ch1.S2">
  <title>Study sites</title>
      <p id="d1e174">The study sites were located in three long-term experimental catchments in
the northern latitudes (map provided in Fig. S1): Bruntland Burn in the
Scottish Highlands, UK (57<inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>2<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N, 3<inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>7<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W), Dorset in
southern–central Ontario, Canada (45<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>12<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N, 78<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>49<inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W),
and Krycklan in northern Sweden (64<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>14<inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N, 19<inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>46<inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> E).
Climatic conditions range from temperate fully humid with cool summers at
Bruntland Burn to cold fully humid with either warm summers in Dorset or cold
summers in Krycklan. At all sites, there is a pronounced seasonality in air
temperature and the long-term annual means are 6.6 <inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C at Bruntland
Burn, 4.8 <inline-formula><mml:math id="M14" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C at Dorset, and 1.8 <inline-formula><mml:math id="M15" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C at Krycklan.
Precipitation is generally relatively evenly distributed over the year at all
sites, but snow accumulates at Dorset and Krycklan during the winter, leading
to a pronounced soil infiltration pulse during snowmelt in early spring. At
Bruntland Burn, snowfall usually plays a minor role in the water balance
(Ala-aho et al., 2017a), but rainfall occurs commonly at low intensities
throughout the year (1000 mm yr<inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Average annual precipitation is
1020 mm yr<inline-formula><mml:math id="M17" 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> at Dorset and 622 mm yr<inline-formula><mml:math id="M18" 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> at Krycklan. A detailed
comparison of the hydro-meteorological conditions at the three catchments was
presented by Tetzlaff et al. (2015). Soils of the four sites were
characterized as freely draining podzols of generally coarse texture ranging
from loamy or silty sands to sand with an overlying organic layer of about
10–20 cm thickness. One site at Bruntland Burn was covered with Scots pine
(<italic>Pinus sylvestris</italic>) and the other site was vegetated by Ericacae
shrubs (<italic>Calluna vulgaris</italic>). Vegetation cover at Dorset was white pine
(<italic>Pinus strobus</italic>), while at Krycklan, the soil was covered by Scots
pine (<italic>Pinus sylvestris</italic>). Rooting depths were observed in the field
to be <inline-formula><mml:math id="M19" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 50 cm for the trees and 15 cm for the heather shrubs. Canopy
coverage was about 60 % at the Bruntland Burn sites and about 89 and
95 % at Dorset and Krycklan, respectively. All four locations were on
hillslopes of low gradients (&lt; 9<inline-formula><mml:math id="M20" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>). Detailed descriptions of
the soil and vegetation characteristics at the investigated sites were
presented by Sprenger et al. (2018b), where the sites were called “NF”,
“NH”, “Pw”, and “S22”, respectively.</p>
</sec>
<sec id="Ch1.S3">
  <title>Methods</title>
<sec id="Ch1.S3.SS1">
  <title>Data</title>
      <?pagebreak page3967?><p id="d1e394">Meteorological data including air temperature (<inline-formula><mml:math id="M21" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C), relative humidity
(%), rainfall or snowmelt amount (mm day<inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>  (Sprenger et al., 2018b), and potential
evapotranspiration (mm day<inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> estimated using the Penman–Monteith
equation (Allen et al., 1998) were available on a daily basis at each
catchment.</p>
      <p id="d1e436">Soil hydraulic characteristics, as shown in the Supplement (Fig. S2), were
derived for Bruntland Burn and Dorset from the pedotransfer functions
provided by Schaap et al. (2001) using site-specific soil textural and bulk
density information (Sprenger et al., 2018b). For Krycklan, the hydraulic
parameters were estimated based on laboratory measurements (Nyberg et al.,
2001).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p id="d1e442">Model parameters: depths of the soil horizons, Mualem–van Genuchten
parameters (<inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>: residual water content, <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>: saturated water content, <inline-formula><mml:math id="M26" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula>: air entry value, <inline-formula><mml:math id="M27" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>: shape
parameter), saturated hydraulic conductivity <inline-formula><mml:math id="M28" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>, interception capacity, and
canopy coverage (Sprenger et al., 2018b).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="9">
     <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:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Site</oasis:entry>
         <oasis:entry colname="col2">Depth</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M31" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M32" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7"><inline-formula><mml:math id="M33" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">Interception</oasis:entry>
         <oasis:entry colname="col9">Canopy</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(cm)</oasis:entry>
         <oasis:entry colname="col3">(cm<inline-formula><mml:math id="M34" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> cm<inline-formula><mml:math id="M35" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col4">(cm<inline-formula><mml:math id="M36" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> cm<inline-formula><mml:math id="M37" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">(cm<inline-formula><mml:math id="M38" 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="col6">(–)</oasis:entry>
         <oasis:entry colname="col7">(cm day<inline-formula><mml:math id="M39" 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="col8">capacity</oasis:entry>
         <oasis:entry colname="col9">coverage</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8">(mm)</oasis:entry>
         <oasis:entry colname="col9">(%)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Bruntland Burn,</oasis:entry>
         <oasis:entry colname="col2">0–15</oasis:entry>
         <oasis:entry colname="col3">0.0454</oasis:entry>
         <oasis:entry colname="col4">0.6048</oasis:entry>
         <oasis:entry colname="col5">0.0434</oasis:entry>
         <oasis:entry colname="col6">1.3680</oasis:entry>
         <oasis:entry colname="col7">345.18</oasis:entry>
         <oasis:entry colname="col8">7.5</oasis:entry>
         <oasis:entry colname="col9">63</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">forested</oasis:entry>
         <oasis:entry colname="col2">15–50</oasis:entry>
         <oasis:entry colname="col3">0.0375</oasis:entry>
         <oasis:entry colname="col4">0.4936</oasis:entry>
         <oasis:entry colname="col5">0.0422</oasis:entry>
         <oasis:entry colname="col6">1.4542</oasis:entry>
         <oasis:entry colname="col7">322.89</oasis:entry>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Bruntland Burn,</oasis:entry>
         <oasis:entry colname="col2">0–15</oasis:entry>
         <oasis:entry colname="col3">0.0415</oasis:entry>
         <oasis:entry colname="col4">0.5822</oasis:entry>
         <oasis:entry colname="col5">0.0431</oasis:entry>
         <oasis:entry colname="col6">1.3765</oasis:entry>
         <oasis:entry colname="col7">392.46</oasis:entry>
         <oasis:entry colname="col8">2.65</oasis:entry>
         <oasis:entry colname="col9">60</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">heather</oasis:entry>
         <oasis:entry colname="col2">15–50</oasis:entry>
         <oasis:entry colname="col3">0.0387</oasis:entry>
         <oasis:entry colname="col4">0.4435</oasis:entry>
         <oasis:entry colname="col5">0.0452</oasis:entry>
         <oasis:entry colname="col6">1.7185</oasis:entry>
         <oasis:entry colname="col7">282.54</oasis:entry>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Dorset</oasis:entry>
         <oasis:entry colname="col2">0–25</oasis:entry>
         <oasis:entry colname="col3">0.0456</oasis:entry>
         <oasis:entry colname="col4">0.6082</oasis:entry>
         <oasis:entry colname="col5">0.0221</oasis:entry>
         <oasis:entry colname="col6">1.3672</oasis:entry>
         <oasis:entry colname="col7">485.04</oasis:entry>
         <oasis:entry colname="col8">2.2</oasis:entry>
         <oasis:entry colname="col9">89</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">25–50</oasis:entry>
         <oasis:entry colname="col3">0.0356</oasis:entry>
         <oasis:entry colname="col4">0.5136</oasis:entry>
         <oasis:entry colname="col5">0.0238</oasis:entry>
         <oasis:entry colname="col6">1.3937</oasis:entry>
         <oasis:entry colname="col7">427.09</oasis:entry>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Krycklan</oasis:entry>
         <oasis:entry colname="col2">0–20</oasis:entry>
         <oasis:entry colname="col3">0.0429</oasis:entry>
         <oasis:entry colname="col4">0.70</oasis:entry>
         <oasis:entry colname="col5">0.0919</oasis:entry>
         <oasis:entry colname="col6">1.4895</oasis:entry>
         <oasis:entry colname="col7">147<inline-formula><mml:math id="M40" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">1.3</oasis:entry>
         <oasis:entry colname="col9">95</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">20–50</oasis:entry>
         <oasis:entry colname="col3">0.0472</oasis:entry>
         <oasis:entry colname="col4">0.5</oasis:entry>
         <oasis:entry colname="col5">0.0835</oasis:entry>
         <oasis:entry colname="col6">1.7469</oasis:entry>
         <oasis:entry colname="col7">656<inline-formula><mml:math id="M41" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8"/>
         <oasis:entry colname="col9"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S3.SS2">
  <title>Soil water flow and transport modelling</title>
      <p id="d1e964">The simulations of travel times and water ages are based on tracking, in a
1-D soil hydraulic model, the infiltrated water (rainfall and snowmelt) with
a virtual tracer in soil storage and fluxes leaving the soil. We applied the
SWIS model as described in detail by Sprenger et al. (2018b). The SWIS model
solves the Richards equation for water flow and simulates tracer transport
with the advection–dispersion equation. The SWIS model can partition the
subsurface into two flow domains (Fig. S3): a fast flow domain representing
the soil pores that hold the water at pressure heads &lt; 600 hPa and
a slow flow domain covering the pores with a water retention
&gt; 600 hPa. A threshold of 600 hPa was chosen to divide the two
pore domains, as this is approximately the pressure head applied by suction
lysimeters to extract water. This definition allowed us to use stable isotope
data (<inline-formula><mml:math id="M42" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>H and <inline-formula><mml:math id="M43" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:math></inline-formula>O) of the mobile flow domain (sampled with suction
lysimeters) and the bulk soil water (slow plus fast flow domain) sampled with
the direct equilibration method (Wassenaar et al., 2008) for benchmarking the
model performance at the individual study sites as presented by Sprenger et
al. (2018b). Ingraham and Criss (1993) found that two water pools approach as
a function of water volumes, surface area, and saturated
vapour pressure (temperature) a
weighted average isotopic composition of the two pools. Our previous study
showed that a conceptualization of the subsurface with two pore domains that
exchange water in accordance with Ingraham and Criss (1993) via the soil gas
phase improved the simulation of the soil water stable isotopic composition
at 10 and 20 cm depths at the investigated sites compared to an assumption
of uniform flow. Therefore, we apply the same model set-up of SWIS as
presented in detail by Sprenger et al. (2018b) with the parameters given in
Table 1. In accordance with Vanderborght and Vereecken (2007), we set the
dispersivity parameter to 10 cm at all sites. The soil physical parameters
were the same for the two pore domains and the exchange was solely
conceptualized as vapour exchange rather than via hydraulic dispersion. The
implemented tracer exchange between the slow and fast flow domains results in
a slow approach of the virtual tracer concentrations in the two pore domains.
Thus, the exchange leads towards a homogenization of water ages between the
two flow domains. Consistent with soil physics principles, the slow flow
domain is filled first and remains saturated until the fast flow domain is
emptied (Hutson and Wagenet, 1995). Water flow and tracer transport occur in
both domains and recharge is generated accordingly. However, only the
combined recharge flux rate (<inline-formula><mml:math id="M44" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>) and weighted average tracer concentrations
from both domains are provided. The model domain covered the soil profile
down to 50 cm depth in 5 cm intervals. Root water uptake was limited
according to rooting depth observations to the upper 15 cm at the heather
site in Bruntland Burn and to the entire 50 cm soil profile at the forested
sites. Soil evaporation (<inline-formula><mml:math id="M45" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula>) was limited to the upper 10 cm based on
experiments by Or et al. (2013). ET was partitioned into potential <inline-formula><mml:math id="M46" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> and
potential transpiration (<inline-formula><mml:math id="M47" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>) according to the canopy coverage (Table 1)
according to Ritchie (1972). Since sap flow was measured at the forest site
in Bruntland Burn (Wang et al., 2017a) and <inline-formula><mml:math id="M48" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> estimates based on the maximum
entropy theory were available for the heather site in Bruntland Burn (Wang et
al., 2017b), we used this information to adjust the partitioning of ET at
these sites. <inline-formula><mml:math id="M49" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M50" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> both decreased linearly with depth and occurred from
both the fast and slow flow domains (<inline-formula><mml:math id="M51" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> limited to the permanent wilting
point assumed to be at 15 000 hPa, Fig. S2). Contrary to the application of
the SWIS model for stable isotope modelling, <inline-formula><mml:math id="M52" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> did not alter the virtual
tracer concentration (similar to <inline-formula><mml:math id="M53" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>), but reduced the soil moisture at the
depths of <inline-formula><mml:math id="M54" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> losses and root water uptake, respectively. Precipitation was
divided into interception and throughfall according to the canopy coverage
(Table 1), and when the interception capacity (Table 1) was reached, the
surplus infiltrated into the soil. Soil frost does usually not occur at
Bruntland Burn and is rare at the Dorset site due to the insulating effect of
the snow cover. At Krycklan, soil frost was shown to not induce surface
runoff, but soils at the forested site remained permeable (Stähli et al.,
2001; Laudon et al., 2007).</p>
</sec>
<sec id="Ch1.S3.SS3">
  <title>Estimation of travel times and water ages</title>
      <p id="d1e1070">We defined the start of travel times and zero water age of waters as the day
of infiltration into the soil profile. To derive the travel times and water
ages, we ran the SWIS model for each day of rainfall or snowmelt from 06/2011
for Bruntland Burn and Dorset and from 01/2010 for Krycklan to 09/2016 and
tracked the fate of a virtual tracer in soil storage (fast flow domain, slow
flow domain, and total storage) and water fluxes (<inline-formula><mml:math id="M55" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M56" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M57" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>) as
suggested by Sprenger et al. (2016). The number of days with rainfall or
snowmelt of all days of simulation were 1381/1943 for the Bruntland Burn
sites, 684/1984 for Dorset, and 801/2465 for the Krycklan site. The model was
run at daily resolution and the applied parameters are listed in Table 1.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><caption><p id="d1e1096">Conceptual visualization of the procedure used to derive median
travel times (MdTT) of output fluxes (i.e. evaporation, transpiration,
recharge) <bold>(a)</bold> and median water ages (<inline-formula><mml:math id="M58" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>) in the output fluxes or
the soil storage (total storage, storage in fast and slow flow domains,
respectively) <bold>(b)</bold>. For MdTT, the breakthrough of an infiltrated
virtual tracer mass (<inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> introduced for each individual day of
rainfall/snowmelt was tracked in each tracer mass output flux (<inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>O</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.
The median of the normalized outflow mass flux describes the time until half
of the total tracer mass leaving the soil via the output flux was reached.
The median water ages in fluxes and storage (visualized as the grey line)
were derived from the age of the 50th percentile of the cumulative age
distribution of individual tracer inputs (e.g. <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
contributing varying volumes (<inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to the considered flux or
storage, visualized with different blue tones.</p></caption>
          <?xmltex \igopts{width=327.206693pt}?><graphic xlink:href="https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018-f01.pdf"/>

        </fig>

      <?pagebreak page3968?><p id="d1e1209">Consistent with the definitions by Benettin et al. (2015), we consider two
different metrics as conceptualized in Fig. 1. The first was the median
travel time (MdTT) as a forward approach that estimates how long it takes the
infiltrated water to leave the soil as <inline-formula><mml:math id="M65" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M66" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>, or <inline-formula><mml:math id="M67" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> flux (also called
life expectancy in Benettin et al., 2015). The second was the median water
age (<inline-formula><mml:math id="M68" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>) as a backward approach estimating the age of water in the output
fluxes and the soil storage since it infiltrated into the soil (also called
residence time in Benettin et al., 2015).</p>
      <p id="d1e1240">To derive the MdTT, we extracted the breakthrough curves of the normalized
mass fluxes <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>O</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> in the output fluxes (<inline-formula><mml:math id="M70" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M71" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M72" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>) generated
from each virtual tracer mass introduced during individual infiltration
events (<inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> on day j (Fig. 1, left). Normalized mass fluxes <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:msub><mml:mi>O</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
(<inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msup><mml:mi>T</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>) resulted from the tracer concentration (introduced with <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
in the flux <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:mo>⋅</mml:mo></mml:mrow></mml:math></inline-formula> L<inline-formula><mml:math id="M79" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) times flux rate <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:mi>Q</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (L<inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mo>⋅</mml:mo><mml:msup><mml:mi>T</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>) divided
by the introduced tracer mass <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M83" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula>):

                <disp-formula id="Ch1.E1" content-type="numbered"><mml:math id="M84" display="block"><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>O</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>⋅</mml:mo><mml:mi>Q</mml:mi><mml:mfenced close=")" open="("><mml:mi>t</mml:mi></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          We then computed the median of the individual breakthrough curves as half of
the maximum cumulative <inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msub><mml:mi>O</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, which then described the time it took
until 50 % of the infiltrated water ended up in the considered output
flux from the soil (Sprenger et al., 2016). This leads to a time series
showing the median travel times (MdTT in days) required to leave the system
via either evaporation (MdTT<inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, transpiration
(MdTT<inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, or recharge (MdTT<inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Since MdTT would be
underestimated if not all of the virtual tracer had left entirely the soil
storage, we limited the MdTT analysis to the period from 2012 to 2015. We
decided to present median values, rather than mean travel times, as the
latter can be biased due to uncertainties in the long tails of the transit
time distributions (Seeger and Weiler, 2014). We further used the individual
breakthrough curves in the <inline-formula><mml:math id="M89" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M90" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M91" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> fluxes to derive master travel
time distributions (MTTD) as introduced by Heidbüchel et al. (2012). In
line with Heidbüchel et al. (2012), we superimposed all individual
breakthrough curves, weighted them by the event size, and normalized them by
the total introduced virtual tracer mass. Such a weighted average travel time
distribution was derived for evaporation (MTTD<inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, transpiration
(MTTD<inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and recharge (MTTD<inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> fluxes at each study
site. The time after which<?pagebreak page3969?> 50 % of the average tracer mass has left via
the considered flux was defined as the median of the MTTD.</p>
      <p id="d1e1595">We calculated water ages <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:mi>A</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> by first multiplying <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mi>O</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
(<inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msup><mml:mi>T</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>) by the precipitation amount <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0) (L<inline-formula><mml:math id="M99" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula>) that
introduced the virtual tracer <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0) and divided it by the flux
volume <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:mi>Q</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> on the day that we estimated the water ages for, to get the
relative share of each precipitation event introduced on day <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the
considered fluxes <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msup><mml:mi>T</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>).

                <disp-formula id="Ch1.E2" content-type="numbered"><mml:math id="M105" display="block"><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>V</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>O</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>⋅</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>P</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>Q</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>

          Multiplication of <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> by the days since <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> provides the relative
volume of the water of age <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for each considered day (Fig. 1,
right). The 50th percentile of the cumulative sum of <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> then defined the
median water age. To prevent bias due to water of unknown age in the soil
storage (i.e. initial water in the soil at start of simulation), we limited
the water age analysis to the period from 2013 to 2016. Here, we report the
median water ages in the fast flow domain (<inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the slow flow
domain (<inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and total soil storage (<inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and of
the evaporation (<inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, transpiration (<inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and
recharge fluxes (<inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e1934">Distributions of the time-variant median travel times and median water ages
in fluxes and storages were derived using cosine kernel density estimations
(Venables and Ripley, 2011). Differences in MdTT and water ages between the
four sites were analysed using the non-parametric Kruskal–Wallis test with a
post hoc Dunn test (significance level of 0.05), since the data were not
normally distributed according to the Shapiro–Wilk test. Since running the
model for the considered 5 years took between 1 and 3 h and our analysis
required running the model between 684 and 1381 times (for each day of
precipitation), we were not able to do a formal uncertainty analysis due to
the long computation times (up to &gt; 100 days  for one set of MdTT and water ages per
site). We therefore limit the presented water age analysis to one realization
using a parameter set that was previously shown to reflect the water flow and
transport dynamics well using stable isotope data (Sprenger et al., 2018b).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><caption><p id="d1e1940">Summary of median travel time (MdTT, shown in Fig. 2) and master
travel time distribution (MTTD) characteristics of the four study sites:
median of MdTT (25th percentile, 75th percentile) in the
evaporation flux (MdTT<inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, transpiration flux (MdTT<inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, recharge flux
(MTT<inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, median of the MTTD of the evaporation flux (MTTD<inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
transpiration flux (MTTD<inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, recharge flux (MTTD<inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Letters as
superscript indicate significant differences in each column. Sites with the
same letter are not significantly different regarding the MdTT or MTTD of the
considered flux.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <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:colspec colnum="7" colname="col7" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Site</oasis:entry>
         <oasis:entry colname="col2">MdTT<inline-formula><mml:math id="M122" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">MdTT<inline-formula><mml:math id="M123" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">MdTT<inline-formula><mml:math id="M124" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">MTTD<inline-formula><mml:math id="M125" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6">MTTD<inline-formula><mml:math id="M126" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">MTTD<inline-formula><mml:math id="M127" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(days)</oasis:entry>
         <oasis:entry colname="col3">(days)</oasis:entry>
         <oasis:entry colname="col4">(days)</oasis:entry>
         <oasis:entry colname="col5">(days)</oasis:entry>
         <oasis:entry colname="col6">(days)</oasis:entry>
         <oasis:entry colname="col7">(days)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Bruntland Burn, forested</oasis:entry>
         <oasis:entry colname="col2">8 (5, 13)<inline-formula><mml:math id="M128" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">AB</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">44 (13, 149)<inline-formula><mml:math id="M129" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">131 (41, 203)<inline-formula><mml:math id="M130" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">7<inline-formula><mml:math id="M131" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6">27<inline-formula><mml:math id="M132" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">50<inline-formula><mml:math id="M133" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Bruntland Burn, heather</oasis:entry>
         <oasis:entry colname="col2">7 (5, 11)<inline-formula><mml:math id="M134" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">27 (10, 123)<inline-formula><mml:math id="M135" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">51 (24, 183)<inline-formula><mml:math id="M136" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">8<inline-formula><mml:math id="M137" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6">17<inline-formula><mml:math id="M138" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">21<inline-formula><mml:math id="M139" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Dorset</oasis:entry>
         <oasis:entry colname="col2">8 (4, 14)<inline-formula><mml:math id="M140" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">13 (1, 130)<inline-formula><mml:math id="M141" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">112 (79, 172)<inline-formula><mml:math id="M142" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">6<inline-formula><mml:math id="M143" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6">19<inline-formula><mml:math id="M144" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">77<inline-formula><mml:math id="M145" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Krycklan</oasis:entry>
         <oasis:entry colname="col2">13 (7, 75)<inline-formula><mml:math id="M146" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">18 (10, 31)<inline-formula><mml:math id="M147" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">158 (42, 298)<inline-formula><mml:math id="M148" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">17<inline-formula><mml:math id="M149" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6">17<inline-formula><mml:math id="M150" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">34<inline-formula><mml:math id="M151" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
</sec>
<sec id="Ch1.S4">
  <title>Results</title>
<sec id="Ch1.S4.SS1">
  <title>Travel times (How long does it take for infiltrated water to leave the soil
again?)</title>
<sec id="Ch1.S4.SS1.SSS1">
  <title>Travel times for evaporation flux</title>
      <p id="d1e2448">The median estimated travel time for infiltrated water until it was
evaporated (MdTT<inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> varied usually between 4 and 13 days, but was
occasionally older than 60 days during late autumn and winter at the Krycklan
site (Fig. 2a). In these cases, the fast flow domain emptied and relatively
old water from the slow flow domain evaporated. MdTT<inline-formula><mml:math id="M153" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula> tended to
be greater when water infiltrated during periods of limited <inline-formula><mml:math id="M154" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> and
infiltration. MdTT<inline-formula><mml:math id="M155" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula> values were similar across the sites (see
distribution plots in Fig. 2a), and there were no significant differences
between the sites in Bruntland Burn as well as between the forested site in
Bruntland Burn and Dorset. However, at Krycklan, where travel times of
&gt; 100 days occurred when the fast flow domain emptied, the
MdTT<inline-formula><mml:math id="M156" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula> was significantly different to the other sites (Table 2).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><caption><p id="d1e2499">Median travel times (MdTT) of water infiltrating into the soil on a
specific day (given on the <inline-formula><mml:math id="M157" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula>-axis) until leaving the soil <bold>(a)</bold> via
soil evaporation (MdTT<inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <bold>(b)</bold> transpiration
(MdTT<inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, or <bold>(c)</bold> recharge (MdTT<inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> flux.
Colour code according to the four studied sites. Note that for days without
precipitation or snowmelt, no travel times could be calculated. In
subplot <bold>(a)</bold>, the <inline-formula><mml:math id="M161" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula>-axis has different scales for
MdTT<inline-formula><mml:math id="M162" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula> &lt; 60 days and &gt; 60 days. Density
distributions of the travel times are shown for each site on the right-hand
side.</p></caption>
            <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018-f02.pdf"/>

          </fig>

</sec>
<sec id="Ch1.S4.SS1.SSS2">
  <title>Travel times for transpiration flux</title>
      <p id="d1e2586">The median travel time of infiltrated water before it was taken up by the
roots (MdTT<inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> was estimated to vary between a few days for waters
infiltrated during the growing season and up to 250 days when the water
infiltrated just after the growing season (Fig. 2b). Thus, water introduced
when the vegetation was active was quickly taken up by the plants, leading to
low MdTT<inline-formula><mml:math id="M164" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula>. However, when water infiltrated during the dormant
season, this water aged in the rooting zone until it was transpired in the
following spring. This resulted in a generally decreasing trend of
MdTT<inline-formula><mml:math id="M165" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula> towards the onset of the growing season. MdTT<inline-formula><mml:math id="M166" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula>
dynamics were similar across the four sites, due to similar seasonal climatic
conditions and growing season length. However, shallower rooting depths for
the heather site limited the water uptake to waters of relatively shorter
travel times as the shrubs did not have access to water in deeper soils with
longer travel times (red triangles in Fig. 2b). Therefore, MdTT<inline-formula><mml:math id="M167" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula>
of the heather site in Bruntland<?pagebreak page3970?> Burn was significantly shorter than for the
forested site there, which experienced the same climate forcing but had a
rooting depth of 50 cm (Table 2). MdTT<inline-formula><mml:math id="M168" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula> and MdTT<inline-formula><mml:math id="M169" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula>
were not correlated but had different dynamics, because the seasonal <inline-formula><mml:math id="M170" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> flux
was much larger than <inline-formula><mml:math id="M171" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> during the growing season, while the <inline-formula><mml:math id="M172" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> flux
generally remained relatively small throughout the year (Fig. S4).</p>
</sec>
<sec id="Ch1.S4.SS1.SSS3">
  <title>Travel times for recharge flux</title>
      <p id="d1e2683">Median travel times for water to pass the 50 cm soil depth (MdTT<inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
showed a clear seasonal pattern with longest travel times (200 to 600 days)
for water that infiltrated at the end of spring. In contrast, shortest
MdTT<inline-formula><mml:math id="M174" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> (&lt; 50 days) prevailed during spring (Dorset and Krycklan)
and winter (Bruntland Burn) (Fig. 2c). Thus, water that infiltrated during
periods of relatively low wetness in the snow-dominated sites in Dorset and
Krycklan or rainfall that fell during the growing season when <inline-formula><mml:math id="M175" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> rates were
highest in Bruntland Burn had the longest <inline-formula><mml:math id="M176" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> travel times (Fig. S5). While
MdTT<inline-formula><mml:math id="M177" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> was not related to the <inline-formula><mml:math id="M178" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> flux on the day of the traced
infiltration event, MdTT<inline-formula><mml:math id="M179" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> was mainly governed by the time until major
flushing of the soil water storage occurred (Fig. 3): the longer it took to
for intense <inline-formula><mml:math id="M180" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> fluxes (defined as &gt; 1.5 mm day<inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to occur
following the traced water infiltrating into the soil, the longer it took for
the water to become recharge. While the MdTT<inline-formula><mml:math id="M182" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> values were similar for
the forested site in Bruntland Burn and Dorset, MdTT<inline-formula><mml:math id="M183" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> at the heather
site in Brunland Burn was significantly shorter and at Krycklan significantly
longer than at the forested Bruntland Burn and Dorset sites (Table 2).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p id="d1e2789">Median travel times in recharge flux (MdTT<inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> for each study site
as a function of days required to produce intense recharge fluxes (here
defined as &gt; 1.5 mm day<inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> following infiltration of the
traced water into the soil. The dots show the MdTT<inline-formula><mml:math id="M186" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> for each day of rain
and the colour code represents the season when the traced water infiltrated
the soil.</p></caption>
            <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018-f03.png"/>

          </fig>

</sec>
<sec id="Ch1.S4.SS1.SSS4">
  <title>Master travel time distributions</title>
      <p id="d1e2840">The weighted average description of the travel time, as the master travel
time distribution (MTTD), showed the general differences between water
transport via <inline-formula><mml:math id="M187" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M188" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M189" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> (Fig. 4). Fastest transport of infiltrated water was
generally for the <inline-formula><mml:math id="M190" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> flux with MTTD<inline-formula><mml:math id="M191" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula> showing response within one day and
relatively short tails of the distribution (dashed lines in Fig. 4).
MTTD<inline-formula><mml:math id="M192" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula> also showed relatively quick response, but the decrease in tracer
mass over time was lower than for MTTD<inline-formula><mml:math id="M193" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula>. The time until the virtual
tracer was observed in the <inline-formula><mml:math id="M194" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> flux (MTTD<inline-formula><mml:math id="M195" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> was generally longer compared
to the fluxes to the atmosphere and the distributions were characterized by
long tails. MTTD<inline-formula><mml:math id="M196" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula> at Krycklan was significantly different from the other
sites with a median of 17 days compared to 6–8 days at Bruntland Burn and
Dorset (Table 1). MTTD<inline-formula><mml:math id="M197" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula> were statistically similar for the forested site
in Bruntland Burn and Dorset, but significantly different to the MTTD<inline-formula><mml:math id="M198" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula>
at the heather site in Bruntland Burn and Krycklan site. MTTD<inline-formula><mml:math id="M199" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> at the
heather site was also significantly different and its median of 21 days was
the shortest compared to the other sites. At Dorset, median MTTD<inline-formula><mml:math id="M200" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> were
longest (77 days) and their distribution significantly different from the
other sites, while MTTD<inline-formula><mml:math id="M201" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> for the forested Bruntland Burn and Krycklan
sites were statistically similar with median values of 50 and 34 days,
respectively (Table 1).</p><?xmltex \hack{\newpage}?><?xmltex \floatpos{t}?><fig id="Ch1.F4"><caption><p id="d1e2975">Cumulative density function of the master transit time distributions
(MTTD) of the evaporation flux (dashed lines, MTTD<inline-formula><mml:math id="M202" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
transpiration flux (dotted lines, MTTD<inline-formula><mml:math id="M203" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and recharge flux
(unbroken lines, MTTD<inline-formula><mml:math id="M204" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> for the four study sites (colour code).</p></caption>
            <?xmltex \igopts{width=179.252362pt}?><graphic xlink:href="https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018-f04.png"/>

          </fig>

</sec>
</sec>
<?pagebreak page3971?><sec id="Ch1.S4.SS2">
  <title>Water ages (What are the ages of the storage in the soil and in the fluxes
leaving the soil?)</title>
<sec id="Ch1.S4.SS2.SSS1">
  <title>Water ages of soil storage</title>
      <p id="d1e3032">The median age of the total water stored in the simulated 50 cm soil profile
(<inline-formula><mml:math id="M205" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> ranged from a few days to 300 days (Fig. 5a). Short-term
dynamics of <inline-formula><mml:math id="M206" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> were driven by the infiltration patterns with
generally smaller <inline-formula><mml:math id="M207" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> after high infiltration rates (Fig. S6).
<inline-formula><mml:math id="M208" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> generally increased during periods of low infiltration such
as dry summers at Bruntland Burn and Krycklan or throughout snow cover at
Dorset and Krycklan. <inline-formula><mml:math id="M209" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was usually larger for lower storage
volumes and decreased exponentially with increase in soil storage. This
inverse storage relationship was most pronounced for the water ages in the
fast flow domain (<inline-formula><mml:math id="M210" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in Fig. 6). Exceptions of small
<inline-formula><mml:math id="M211" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> during low storage occurred when the fast flow domain dried
out and was then refilled by young waters during infiltration events (see
several red and orange data points in the first row in Fig. 6).
<inline-formula><mml:math id="M212" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was generally smaller than <inline-formula><mml:math id="M213" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (Fig. 5c and d).
Dynamics of <inline-formula><mml:math id="M214" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> were generally highly responsive to infiltration,
but the response of <inline-formula><mml:math id="M215" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was usually less and often delayed
compared to <inline-formula><mml:math id="M216" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. More intense short-term dynamics in
<inline-formula><mml:math id="M217" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> – and consequently also in <inline-formula><mml:math id="M218" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> – were limited
to sites and periods when the fast flow domain was empty (e.g. July 2013 and
2014 at the forested site in Bruntland Burn and summers at Dorset, Fig. 5).
<inline-formula><mml:math id="M219" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was generally larger and more damped than <inline-formula><mml:math id="M220" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
(Fig. 5).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><caption><p id="d1e3217">Water ages of <bold>(a)</bold> total soil water storage
(<inline-formula><mml:math id="M221" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <bold>(b)</bold> storage in the slow flow domain
(<inline-formula><mml:math id="M222" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and <bold>(c)</bold> storage in the fast flow domain
(<inline-formula><mml:math id="M223" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Note that when storage in the fast flow domain is zero,
there is no water age for the storage. For site NH, the spin-up period of
1.5 years was not sufficient to replace the water in the slow flow domain,
resulting in continuously increasing water ages for <inline-formula><mml:math id="M224" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M225" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which inhibits their analysis (dashed lines). The colour
code is according to the four study sites. Density distributions of the water
ages are shown for each site on the right-hand side.</p></caption>
            <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018-f05.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><caption><p id="d1e3299">Median water age of fast flow domain (<inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <bold>a</bold>),
evaporation (<inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <bold>b</bold>), transpiration (<inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <bold>c</bold>),
and recharge flux (<inline-formula><mml:math id="M229" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <bold>d</bold>) as a function of the water stored in
the entire soil, in the upper 10 cm, in the root zone and in the entire soil
profile, respectively. Each column represents one of the four studied sites.
The dots show the relationship between water ages and storage for each day
and the colour code represents the season of the corresponding days.</p></caption>
            <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018-f06.png"/>

          </fig>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><caption><p id="d1e3369">Summary of water age characteristics of the four study sites: median
(25th percentile, 75th percentile) of the median water ages in the total
storage (<inline-formula><mml:math id="M230" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, storage in the slow flow domain (<inline-formula><mml:math id="M231" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
storage in the fast flow domain (<inline-formula><mml:math id="M232" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, evaporation flux
(<inline-formula><mml:math id="M233" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, transpiration flux (<inline-formula><mml:math id="M234" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and recharge flux
(<inline-formula><mml:math id="M235" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Letters  as superscript indicate significant differences in each column.
Sites with the same letter are not significantly different regarding the
water ages of the considered storage or flux.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <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:colspec colnum="7" colname="col7" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Site</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M236" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M237" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M238" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M239" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M240" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7"><inline-formula><mml:math id="M241" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(days)</oasis:entry>
         <oasis:entry colname="col3">(days)</oasis:entry>
         <oasis:entry colname="col4">(days)</oasis:entry>
         <oasis:entry colname="col5">(days)</oasis:entry>
         <oasis:entry colname="col6">(days)</oasis:entry>
         <oasis:entry colname="col7">(days)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Bruntland Burn, forested</oasis:entry>
         <oasis:entry colname="col2">61 (39, 94)<inline-formula><mml:math id="M242" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">114 (70, 132)<inline-formula><mml:math id="M243" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">15 (6, 27)<inline-formula><mml:math id="M244" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">8 (3, 19)<inline-formula><mml:math id="M245" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6">19 (8, 34)<inline-formula><mml:math id="M246" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">110 (70, 162)<inline-formula><mml:math id="M247" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Bruntland Burn, heather</oasis:entry>
         <oasis:entry colname="col2">39 (24, 55)<inline-formula><mml:math id="M248" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">107 (87, 126)<inline-formula><mml:math id="M249" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">18 (10, 31)<inline-formula><mml:math id="M250" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">7 (3, 13)<inline-formula><mml:math id="M251" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6">11 (4, 25)<inline-formula><mml:math id="M252" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">36 (19, 54)<inline-formula><mml:math id="M253" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Dorset</oasis:entry>
         <oasis:entry colname="col2">48 (31, 74)<inline-formula><mml:math id="M254" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">56 (32, 85)<inline-formula><mml:math id="M255" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">14 (4, 42)<inline-formula><mml:math id="M256" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">10 (4, 19)<inline-formula><mml:math id="M257" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">B</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6">18 (8, 38)<inline-formula><mml:math id="M258" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">106 (79, 143)<inline-formula><mml:math id="M259" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">A</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Krycklan</oasis:entry>
         <oasis:entry colname="col2">76 (31, 155)<inline-formula><mml:math id="M260" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">D</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">164 (76, 242)<inline-formula><mml:math id="M261" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">31 (9, 94)<inline-formula><mml:math id="M262" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">22 (7, 63)<inline-formula><mml:math id="M263" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6">31 (11, 96)<inline-formula><mml:math id="M264" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">150 (85, 220)<inline-formula><mml:math id="M265" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">C</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e3872"><inline-formula><mml:math id="M266" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was significantly different between all sites (Table 3). For
<inline-formula><mml:math id="M267" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the Bruntland Burn sites did not differ significantly,
probably due to the same climatic forcing and similar shape of the water
retention curve for the slow flow domain in the upper horizon (Fig. S2). For
<inline-formula><mml:math id="M268" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the forested sites in Bruntland Burn and in Dorset were not
significantly different, as their water retention for the fast flow domain
was similar, with drying out of the fast flow domain during summer. This
decrease in the water storage of the fast flow domain led to large
<inline-formula><mml:math id="M269" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> just before being emptied due to interaction with older water
in the slow flow domain.</p>
      <p id="d1e3918"><inline-formula><mml:math id="M270" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was usually &lt; 120 days in the upper 5 cm and
generally increased linearly with depth over the rooting zone (Fig. 7). The
greatest variability in <inline-formula><mml:math id="M271" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was at the forested sites at depths
&lt; 25 cm, where site-specific <inline-formula><mml:math id="M272" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> maxima occurred during
the growing season while <inline-formula><mml:math id="M273" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> &lt; 60 days happened during
periods of high recharge in the dormant season and during snowmelt when soil
waters were well connected throughout the profile. At the heather site in
Bruntland Burn maximum <inline-formula><mml:math id="M274" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was found just below the rooting zone
(15 cm) and not at the bottom of the soil profile (Fig. 7). Thus, soil water
storage volumes, altered by the root water uptake, affected the water
transport and mixing processes such that younger water in the fast flow
domain bypassed the older water stored in the slow flow domain.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><caption><p id="d1e3977">Median water age of the total soil water (<inline-formula><mml:math id="M275" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> at 5 cm intervals
over the simulation period for each of the study sites.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018-f07.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8"><caption><p id="d1e4001">Median water ages of <bold>(a)</bold> evaporation (<inline-formula><mml:math id="M276" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <bold>(b)</bold> transpiration
(<inline-formula><mml:math id="M277" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and <bold>(c)</bold> recharge flux (<inline-formula><mml:math id="M278" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Note that when flux is zero,
there is no water age for the flux. The colour code is according to the four
study sites. Density distributions of the water ages are shown for each site
on the right-hand side.</p></caption>
            <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://hess.copernicus.org/articles/22/3965/2018/hess-22-3965-2018-f08.pdf"/>

          </fig>

</sec>
<sec id="Ch1.S4.SS2.SSS2">
  <title>Water ages of evaporation flux</title>
      <p id="d1e4065">The median age of the water in the <inline-formula><mml:math id="M279" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> flux (<inline-formula><mml:math id="M280" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> ranged from 0 to
140 days, with the largest values during periods of snow cover at Dorset and
Krycklan (Fig. 8a). <inline-formula><mml:math id="M281" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was exponentially related to storage in
the upper 10 cm from which <inline-formula><mml:math id="M282" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> occurred (Fig. 6). For Krycklan and Dorset,
this exponential relationship was most pronounced for periods of decreasing
storage during snow accumulation in winter, when the oldest <inline-formula><mml:math id="M283" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> fluxes were
observed. <inline-formula><mml:math id="M284" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was largest for periods of minimal infiltration and
decreased exponentially with increasing<?pagebreak page3972?> infiltration rates (Fig. S7). Due to
the same climatic conditions at the heather and forested sites in Bruntland
Burn, <inline-formula><mml:math id="M285" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values were not significantly different and on average
lower than at the Dorset and Krycklan sites (Table 3).</p>
</sec>
<sec id="Ch1.S4.SS2.SSS3">
  <title>Water ages of transpiration flux</title>
      <p id="d1e4142">Water ages in <inline-formula><mml:math id="M286" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M287" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> ranged from 0 to up to 300 days and showed
similar dynamics to those of <inline-formula><mml:math id="M288" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for most periods (Fig. 8b).
However, <inline-formula><mml:math id="M289" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was usually older than <inline-formula><mml:math id="M290" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, since the root
water uptake included deeper soil layers than <inline-formula><mml:math id="M291" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> did. <inline-formula><mml:math id="M292" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
decreased with increasing storage volume (Fig. 6); <inline-formula><mml:math id="M293" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> declined
after precipitation events added young water to the rooting zone during
summer and early autumn when storage was generally low. The exponential
relationship between root zone storage and <inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was most pronounced
at Bruntland Burn, where infiltration regularly occurred throughout the year.
Under these conditions, the largest <inline-formula><mml:math id="M295" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> occurred when the soil
dried out and root water uptake of deeper soil layers became more relevant,
leading to an increased relative contribution of older waters to modelled
<inline-formula><mml:math id="M296" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>. For Dorset and Krycklan, the oldest <inline-formula><mml:math id="M297" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values were not only
related to low root zone storage, but also to the aging of water in the root
zone during snow cover in winter when infiltration rates were<?pagebreak page3973?> low and
transpired water thus increasingly became older with time. <inline-formula><mml:math id="M298" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> had
a linear relationship with <inline-formula><mml:math id="M299" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> during wet periods, but approached
<inline-formula><mml:math id="M300" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> during dry periods, due to a shift in root water uptake from
the fast flow domain to uptake largely from the slow flow domain.
<inline-formula><mml:math id="M301" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was significantly smaller at the heather site in Bruntland
Burn, where root water uptake was limited to the upper 15 cm, compared to
the forested sites with rooting depths down to 50 cm (Table 3).
<inline-formula><mml:math id="M302" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> did not differ significantly between the forested site in
Bruntland Burn and Dorset, but was significantly larger at Krycklan, where
the oldest water was stored in the soil.</p>
</sec>
<sec id="Ch1.S4.SS2.SSS4">
  <title>Water ages of recharge flux</title>
      <p id="d1e4330">Median water age of the <inline-formula><mml:math id="M303" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> flux through the 50 cm depth plane
(<inline-formula><mml:math id="M304" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> generally exceeded, but was usually linearly related to, the
total soil storage water age (<inline-formula><mml:math id="M305" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (cf. Fig. 8 and Fig. 4).
However, this linear relationship did not hold for periods of low <inline-formula><mml:math id="M306" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> flux,
and <inline-formula><mml:math id="M307" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> became  &gt; &gt; <inline-formula><mml:math id="M308" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (e.g. summer for
Krycklan in Fig. 8c). <inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> had a strong relationship with <inline-formula><mml:math id="M310" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> flux
and total water storage: the oldest water was recharged during low <inline-formula><mml:math id="M311" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> fluxes
and low storage volumes, respectively (Fig. 6). As <inline-formula><mml:math id="M312" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was
generally strongly related to the age dynamics of the fast flow domain, the
differences in <inline-formula><mml:math id="M313" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> among the sites were similar to the differences
in <inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, with <inline-formula><mml:math id="M315" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> being significantly lower at the
heather site in Bruntland Burn and significantly higher at Krycklan compared
to the forested site in Bruntland Burn and Dorset (Table 3).</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S5">
  <title>Discussion</title>
      <p id="d1e4475">Our simulations emphasize the time-variant character of water ages and travel
times in hydrological systems, as observed at the catchment scale in various
recent studies (van der Velde et al., 2012; Benettin et al., 2013;
Heidbüchel et al., 2013; Soulsby et al., 2015; Benettin et al., 2017).
Further, the age dynamics in the soil waters were driven by the variability
in water stored in the soils, supporting an “inverse storage effect” as
discussed by Harman (2015). Numerical modelling using SWIS provided us with
new insights into how different pore spaces, respectively representing fast
and slow flow domains, differ from each other in terms of water ages. We
further showed how the age variability between the soil pores affects the
water ages of the associated fluxes. Since all travel times and water ages
depend on the water stored in the soil, we will first discuss this and then
include <inline-formula><mml:math id="M316" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M317" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M318" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> travel times and water ages.</p>
<sec id="Ch1.S5.SS1">
  <title>What controls soil water storage and water ages?</title>
      <p id="d1e4504">As the age of the total soil water as well that of the fast and slow flow
domains (<inline-formula><mml:math id="M319" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M320" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M321" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, respectively)
generally decreased with increasing storage volume, the antecedent
hydro-meteorological conditions controlled the soil<?pagebreak page3974?> water age dynamics. For
periods with high ET fluxes that led to low storage volumes, water ages in
the soil pores generally increased over time (Bruntland Burn sites in
Fig. 6), because the youngest water left the soil column preferentially via
ET. Thus, <inline-formula><mml:math id="M322" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> rates and vegetation uptake directly impacted water age
dynamics in the critical zone. Additionally, snowmelt led to a sharp decrease
in soil water ages after a continuous aging of the water that resided in soil
over the snow accumulation period (Fig. 5). Both the ET-driven and
snowmelt-driven cases result in an inverse storage effect, where water in the
soil became younger for higher soil water volumes. In addition to the general
positive relationship between wetness and soil hydraulic conductivity (van
Genuchten, 1980), the conceptualization with two pore domains in the SWIS
model allowed young water in the fast flow domain to bypass older water
stored in the slow flow domain. Since the smaller pores of the slow flow
domain will be filled first or stay filled while the larger pores of the fast
flow domain are not empty, the bypass will be enhanced during periods of high
wetness. As a result, young median water ages prevailed across the entire
50 cm soil profile during periods of high storage (Fig. 7). Note that this
conceptualization would not hold when soil dryness induces preferential flow
due to water repellency (hydrophobicity) (Ritsema et al., 1993; Weiler and
Naef, 2003).</p>
      <p id="d1e4547">According to our simulations, water ages are not simply controlled by the
hydraulic conductivity of the soil, but the storage dynamics in the slow and
fast domain also impacted the water age dynamics. Water flow was much slower
when the fast flow domain emptied. Consequently, while the hydraulic
conductivities at the Bruntland Burn and Dorset sites were similar (Table 1),
the water ages at the two forested sites, where the fast flow domain dried
out during summer (Fig. S4), were greater than at the heather site at
Bruntland Burn, where water prevailed in the fast flow domain throughout the
year. The impact of increased water mobility (i.e. flushing) on soil water
ages during greater soil wetness is supported by stable isotope data (<inline-formula><mml:math id="M323" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>H
and <inline-formula><mml:math id="M324" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">18</mml:mn></mml:msup></mml:math></inline-formula>O). For the Bruntland Burn sites, Sprenger et al. (2017) showed
that the isotopic variability in bulk soil water was greatest after intense
infiltration events, revealing that event water mixed effectively with
pre-event water in the upper 20 cm. Also, isotope data from mobile soil
water (Peralta-Tapia et al., 2015) and bulk soil water (Sprenger et al.,
2018a) at the Krycklan site had a strong relationship with the isotopic
compositions of previously infiltrated water, which shows that a high
proportion of the soil (pre-event) water is replaced by or mixes with recent
event water. Such isotope studies provide a snapshot view of water transport
in the field, but modelling approaches benchmarked against or calibrated on
such observations, like our study, allow insights into short-term dynamics.</p>
      <p id="d1e4568"><inline-formula><mml:math id="M325" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (and the storage volume in the slow flow domain) generally does not
change as rapidly as <inline-formula><mml:math id="M326" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which is influenced by highly variable storage
volumes in the fast flow domain. However, since the ratio between water
stored in the fast and slow flow domain changes as a function of soil wetness
(Sprenger et al., 2018b), the impact of the two domains on total soil water
age <inline-formula><mml:math id="M327" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> also varies over time. During summer, when storage in the fast
flow domain decreased or was even fully depleted (at forested Bruntland Burn
and Dorset sites), <inline-formula><mml:math id="M328" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> approached or equalled <inline-formula><mml:math id="M329" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Due to exchange
between fast and slow flow domain, <inline-formula><mml:math id="M330" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> approached <inline-formula><mml:math id="M331" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> just before
the fast flow domain dried out (see forested Bruntland Burn and Dorset in
Fig. 5c). Our age analyses therefore support the hypothesis by Sprenger
et al. (2017) that old water in smaller soil pores can lead to a “memory
effect” in the bulk soil water isotope compositions. Such a “memory
effect” was further shown to lead to a lagged response of the soil water
stable isotope compositions to hydro-meteorological forcing at five long-term
experimental catchments in northern environments (Sprenger et al., 2018a).
Further, observed differences in the isotopic compositions of mobile and bulk
soil water in the field were often related to the potential age differences
of waters sampled at different mobilities (Landon et al., 1999; Brooks et
al., 2010; Geris et al., 2015; Sprenger et al., 2015a; Oerter and Bowen,
2017). Our results and recent simulations by Smith et al. (2018) support such
interpretations, as the water in the slow flow domain was generally older
than the water in the fast flow domain (<inline-formula><mml:math id="M332" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> &gt; <inline-formula><mml:math id="M333" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.
However, since the differences between <inline-formula><mml:math id="M334" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M335" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Sf</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> were variable in
time and were often maximized in early spring, such anomalies in water ages
are likely to be reflected in the isotopic compositions of the water, with
the older water in small pores being less depleted in heavy isotopes
(originating partly from autumn precipitation) than the young water in larger
soil pores draining recently infiltrated isotopically depleted snowmelt or
winter precipitation. Such isotopic differences resulting from different
water ages affect our interpretation of soil water stable isotopes sampled
either with suction lysimeter (mobile water in the fast flow domain) or
cryogenic vacuum extraction (bulk soil water in fast and slow flow domain).
For example, Brooks et al. (2010) reported different isotopic compositions
for mobile and bulk soil water samples, which led to the formulation of the
two water world hypothesis (TWW) (McDonnell, 2014). In a TWW scenario,
tightly bound soil water is not displaced via translatory flow, does not mix
with or displace mobile water, and does not enter the stream. However,
experimental work recently showed that there is interaction between mobile
and less mobile soil waters (Vargas et al., 2017), as conceptualized in the
applied SWIS model. Our simulations further question if water in the slow
flow domain – as defined in SWIS – will not eventually recharge the
groundwater and streams. The virtually introduced tracer eventually
disappears from the soil water storage of the slow flow domain, due to loss
of the tracer to the atmosphere (ET flux), interaction with the fast flow
domain and recharge within the slow flow domain. Nevertheless, while
definition of the slow flow domain using a higher threshold pressure head
(e.g. field capacity as suggested by Brantley et al. (2017) rather than the
currently<?pagebreak page3975?> assumed 600 hPa) would result in its water becoming more tightly
bound, interaction with more mobile waters would likely still persist (Vargas
et al., 2017).</p>
</sec>
<sec id="Ch1.S5.SS2">
  <title>What controls travel times and water ages in evapotranspiration?</title>
      <p id="d1e4700">Since water loss from soil storage as <inline-formula><mml:math id="M336" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> flux was limited to the upper 10 cm
in our simulations, travel times and water ages are directly related to the
water age dynamics in the top soil. In contrast, the rooting zone covered the
entire soil profile for the forested sites and down to 15 cm soil depth for
the heather site, which affected the resulting travel times and water ages of
<inline-formula><mml:math id="M337" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> accordingly.</p>
      <p id="d1e4717">Investigation of water ages in the ET flux is relatively new (Botter et al.,
2011) and age dynamics have usually been assessed for the bulk ET flux
(Harman, 2015; Soulsby et al., 2015; van der Velde et al., 2015; van
Huijgevoort et al., 2016; Soulsby et al., 2016). While it was shown that
tracer-aided modelling using stable isotopes of water benefits from
partitioning ET into a fractionating <inline-formula><mml:math id="M338" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> flux and a non-fractionating <inline-formula><mml:math id="M339" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>
flux (Knighton et al., 2017), separate water age analyses for <inline-formula><mml:math id="M340" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M341" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>
have been considered only recently (Smith et al., 2018). However, our
analyses showed that the two different fluxes can have markedly different
travel time dynamics (Fig. 2), average travel time distributions (Fig. 4),
and water age dynamics (Fig. 8). Thus, our process understanding of how
vegetation affects water ages in hydrological systems would particularly
benefit from further assessments of the differences between <inline-formula><mml:math id="M342" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M343" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> water
ages. Such investigations are of special interest in light of ongoing
research regarding the consequences of a potential TWW hypothesis on water
age estimations based on tracer-aided modelling (Hrachowitz et al., 2016). In
particular, our simulations underline that neither is ET flux withdrawal well
mixed in its age composition nor is the pool of plant water uptake well
mixed, which is increasingly acknowledged in water age studies (Harman, 2015;
Smith et al., 2018).</p>
      <p id="d1e4763">Similar to findings by Smith et al. (2018) for the heather site in Bruntland
Burn, our estimates for <inline-formula><mml:math id="M344" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> at that site were highest during periods of
limited infiltration (e.g. 10-year return period drought in summer 2013 at
Bruntland Burn in Fig. 8a). However, <inline-formula><mml:math id="M345" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> water ages reported by
Smith et al. (2018) were higher than our estimates, which is probably due to their
conceptualization of the subsurface into one domain with and one without
downward flux, which resulted in generally higher water ages in the shallow
soils compared to our estimates. Water age estimates by Queloz et al. (2015)
for the ET flux from a lysimeter were less variable, but within about 10 to
20 days of the magnitude of our <inline-formula><mml:math id="M346" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M347" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> estimates. The forward
travel time distributions for water leaving the soil via ET presented by
Queloz et al. (2015) also showed shapes similar to our reported MTTD<inline-formula><mml:math id="M348" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula>
and MTTD<inline-formula><mml:math id="M349" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula> with peaks in the first few days and tails of the distribution
that can reach up to 200 days (Fig. 4). We attribute the long tails of the
MTTD<inline-formula><mml:math id="M350" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:math></inline-formula> and MTTD<inline-formula><mml:math id="M351" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula> to both the ET flux from the slow flow domain and
root water uptake from deeper soil layers.</p>
      <p id="d1e4843">With regard to <inline-formula><mml:math id="M352" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, our soil physical model showed a similar inverse
storage effect as the approach using storage selection functions (Smith et
al., 2018): water taken up by plants was generally younger during higher
soil storage. While Smith et al. (2018) had a dynamic root water uptake
depth, <inline-formula><mml:math id="M353" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> loss in the SWIS model decreases linearly with depth as long as the
pressure head does not reach the permanent wilting point, which is usually
not reached at the investigated sites (Sprenger et al., 2018b). Thus, it is
likely that the differences between the dynamic root water uptake depths in
the storage selection functions and the defined uptake profile in SWIS will
be more pronounced when vegetation responds to intense drought by shifting
the root water uptake to deeper soil layers (Volkmann et al., 2016).</p>
      <p id="d1e4865">A relationship between MdTT<inline-formula><mml:math id="M354" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula> and <inline-formula><mml:math id="M355" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> dynamics, with the onset and
cessation of <inline-formula><mml:math id="M356" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> at the beginning and the end of the growing season, has been
shown previously (Sprenger et al., 2016); nevertheless, our experimental
set-up with two different vegetation types (differing in <inline-formula><mml:math id="M357" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> rates, rooting
depth, canopy cover, and interception storage) on similar soil types under
the same climatic forcing in the Bruntland Burn reveals the impact of rooting
depth on the travel time dynamics. Median and maximum MdTT<inline-formula><mml:math id="M358" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula> were
shorter for the heather site than for the forested site in Bruntland Burn and
the MTTD<inline-formula><mml:math id="M359" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:math></inline-formula> had substantially different shapes at both sites with a
lower median for the heather <inline-formula><mml:math id="M360" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> travel times compared to the forest
(Table 1).</p>
</sec>
<sec id="Ch1.S5.SS3">
  <title>What controls recharge travel times and water ages?</title>
      <p id="d1e4930">Water age and travel time dynamics of the recharge flux are the result of the
interplay between the aforementioned linkages between soil water storage age
and ET age dynamics. Since the estimated MdTT<inline-formula><mml:math id="M361" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> are a function of
the subsequent recharge flux intensities (Fig. 3), the probability of an
introduced water parcel leaving the soil profile via recharge is higher
during high flows. Such a relationship between forward travel times and the
recharge flux dynamics was also found in modelling studies on a controlled
lysimeter (Queloz et al., 2015) and 35 field sites in Luxembourg (Sprenger et
al., 2016). While catchment-scale travel time studies based on conceptual
lumped models also showed that the subsequent precipitation patterns affect
the travel time dynamics of runoff (Heidbüchel et al., 2013; Hrachowitz
et al., 2013; Harman and Kim, 2014; Peters et al., 2014; Peralta-Tapia et
al., 2016), our application of a 1-D soil physical model provided insights
into the processes in the upper critical zone leading to such behaviour at
the plot scale. The simulations with SWIS highlight the effect of ET fluxes
on recharge travel times, as both storage and recharge are influenced by ET
rates. Consequently, one can see the exceptionally high MdTT<inline-formula><mml:math id="M362" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> for
the few infiltration events during<?pagebreak page3976?> a 10-year return period dry episode in
summer 2013 for the heather site at Bruntland Burn. Further, the seasonal
decrease in MdTT<inline-formula><mml:math id="M363" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> due the preferential recharge during the
dormant season (Bruntland Burn) or snowmelt (Dorset and Krycklan) emphasizes
the impact of ET on vadose zone travel times. Such an influence of vegetation
on travel times as suggested from the plot-scale simulations is commonly not
seen for the catchment runoff as the stream integrates water moving via
different pathways and thus obscures any ET signal (Tetzlaff et al., 2014;
Kirchner, 2016).</p>
      <p id="d1e4960">The conceptualization of fast and slow flow domains resulted in MTTD<inline-formula><mml:math id="M364" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula>
that indicated a maximum probability of infiltrating water recharging from
the soil within 3 to 10 days after infiltration, although the tails of the
MTTD<inline-formula><mml:math id="M365" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> revealed that replacement of all water (turnover time) can take up
to 1000 days (Fig. 4). Thus, our modelling approach of a two-pore domain
enabled the representation of the short-term responses and the long-term
memory of the recharge composition in a soil column. As a result, water ages
(<inline-formula><mml:math id="M366" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> did not always increase with depth, but instead became almost
uniform throughout the soil column during intense infiltration periods.
Occasionally <inline-formula><mml:math id="M367" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was smaller at the bottom of the profile relative to
just below the rooting zone, mainly due to root water uptake dynamics at the
heather site in Bruntland Burn (Fig. 7). While <inline-formula><mml:math id="M368" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was generally higher
than <inline-formula><mml:math id="M369" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">St</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, consistent with Queloz et al. (2015), our soil physical
modelling approach revealed how the water ages develop with depth and lead to
the resulting <inline-formula><mml:math id="M370" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> dynamics.</p>
      <p id="d1e5039">The pronounced longer water ages of the slow compared to the fast flow domain
are of great relevance for the interpretation of studies on travel times in
vadose zone water fluxes. These investigations are often based on models
calibrated with isotope data from samples taken with zero-tension lysimeters
(e.g. Asano et al., 2002), wick samplers (e.g. Timbe et al., 2014), suction
lysimeters (e.g. Muñoz-Villers and McDonnell, 2012; Tetzlaff et al.,
2014; Hu et al., 2015), or from the outflow of lysimeters (e.g. Stumpp et
al., 2009, 2012). Such methods limit isotope sampling to the most mobile
water in the soil (Sprenger et al., 2015a), which is represented as the fast
flow domain in the current application of the SWIS model. According to our
simulations, travel time studies based on the most mobile waters in the soil
are likely to underestimate travel times and water ages in the recharge
fluxes. Consequently, the turnover time of the soil pores will be
underestimated in such studies, which can then lead to the assumption that
nutrients or contaminants located in the vadose zone will be flushed out more
rapidly than they actually are.</p>
      <p id="d1e5042">The <inline-formula><mml:math id="M371" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> water ages at 50 cm depth in this study are obviously younger than
catchment-scale runoff water ages (Soulsby et al., 2015; Ala-aho et al.,
2017b; Benettin et al., 2017; Kuppel et al., 2018; Piovano et al., 2018).
Nevertheless, the dynamics from the plot-scale <inline-formula><mml:math id="M372" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> water ages are similar to
the catchment runoff water ages due to hydro-meteorological controls leading
to generally increasing values throughout spring towards summer (decreasing
storage) and the lowest water ages during winter (highest storage).</p>
      <p id="d1e5060">The long tails of the MTTD<inline-formula><mml:math id="M373" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:math></inline-formula> found in our results indicate that
soil storage can probably add to the commonly observed long tails of
catchment-scale travel time distributions (e.g. Godsey et al., 2010;
Hrachowitz et al., 2010). Generally, the plot-scale soil hydraulic
simulations can help to better understand the processes taking place within
the catchment and to constrain or benchmark spatially distributed
hydrological models (van Huijgevoort et al., 2016; Ala-aho et al., 2017b;
Kuppel et al., 2018). Such catchment models cannot account for the soil
physical processes in a similar detail to a 1-D model due to computational
limitations. However, our results imply that it might be worth adding a
dual-porosity representation, similar to the conceptualization in SWIS, to
the recently published EcH2O-iso (Kuppel et al., 2018).</p>
</sec>
<sec id="Ch1.S5.SS4">
  <title>Limitations and outlook</title>
      <p id="d1e5079">While we cannot provide uncertainty estimates for the presented travel times
and water ages due to restrictions imposed by computation time, comparison
with soil moisture and stable isotope data at each site (Sprenger et al.,
2018b) indicates that the SWIS model captures the water flow and transport
processes well. However, model calibration using soil moisture and stable
isotope data, as suggested by Sprenger et al. (2015b), would supply the basis
of an assessment of how different parameter sets impact the model performance
and water age estimates. Such an approach would provide site-specific
characterization of the soil physical properties and would likely improve
simulations compared to the currently applied pedotransfer functions and
measurements on soil cores.</p>
      <p id="d1e5082">The applied model approach cannot account for preferential flow, but the
conceptualization of two pore domains with different water flow and transport
dynamics enabled the simulation of bypass flow. This conceptualization was
shown to be superior to a conceptualization of a uniform flow (Sprenger et
al., 2018b). Additional inclusion of preferential flow in the model domain
would come at the cost of model complexity and pose problems of parameter
identifiability.</p>
      <p id="d1e5085">Since the investigated northern environments seldom experience severe
drought, plant growth is usually not water limited, as for example was shown
by Wang et al. (2017a) for Bruntland Burn. Thus, the assumption of a linear
decrease in root water uptake with depth appears to be reasonable for the
current study sites. An exponential distribution would not change the water
uptake patterns significantly, as the linear assumption already results in
96 % of the water being taken up in the upper 15 cm. However, several
isotope studies have shown that the root water uptake profile does not
coincide with the root distribution if plants experience water stress (e.g.
Kulmatiski and Beard, 2013; Ellsworth and Sternberg, 2015; Volkmann et al.,
2016). Hydraulic lift can<?pagebreak page3977?> further increase the complexity of soil–plant
interaction, as experimentally observed and implemented in a soil hydraulic
model by Meunier et al. (2018). Thus, an improved representation of such
dynamics in the water uptake depths would be beneficial for modelling studies
in arid environments. For the northern environments considered here,
variability in the depths from where the plants take up their water appears
to be limited (Smith et al., 2018).</p>
      <p id="d1e5088">The presented simulations are further limited by the discretization of the
soil profile into 5 cm intervals, as this might be too coarse for an
adequate representation of the interactions between atmospheric demand, <inline-formula><mml:math id="M374" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>
losses, and mixing down the profile. However, computational limitations did
not allow a smaller discretization and our study aimed to test the assumption
that soil storage is a well-mixed water source of ET fluxes.</p>
      <p id="d1e5099">Lastly, while the investigated sites are not located on steep slopes, the 1-D
simulation cannot account for lateral flows in the vadose zone that may
potentially occur during extreme rain events (Soulsby et al., 2017). We
further have to assume that all <inline-formula><mml:math id="M375" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> flux leaving the soil profile will end up
in groundwater, but spatially distributed catchment models (Ala-aho et al.,
2017b; Kuppel et al., 2018) might reveal that such water could end up in the
ET flux from saturated areas in the valley bottom when the groundwater feeds
the riparian zone.</p>
</sec>
</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <title>Conclusion</title>
      <p id="d1e5116">We have provided unique insights into the water ages of the upper critical
zone using the SWIS soil physical model by tracking water through the soil
profile and its associated fluxes from the soil at four investigated sites.
Based on these 1-D simulations, we revealed that the recently described
inverse storage effect for catchment and hillslope runoff not only holds for
recharge from the soil, but is also present for the transpiration and
evaporation fluxes: water leaving the soil via evaporation, transpiration, or
recharge was generally younger the greater the soil water storage. The
conceptualization of the vadose zone into slow and fast flow domains and its
discretization over depth allowed us to investigate how the water ages in the
hydrologic fluxes develop over time and space based on the soil water volume
and its age. The temporal age dynamics are mainly related to soil water
storage dynamics. Thus, the seasonality of evaporation and vegetation
activity according to the growing season affected the water ages in the soil.
Future climate warming or vegetation cover change in northern latitudes will
thus directly affect critical zone water age dynamics. Contrary to the common
approach of employing bulk ET in water age analysis, we demonstrated that
evaporation and transpiration have different water ages and travel times.
Thus, an improved partitioning of the two fluxes appears to be essential to
understanding the differential impact of evaporation (usually of relatively
young waters from the top of the unsaturated zone) and transpiration (which
can access older water from deeper soil layers) on water age dynamics.
Furthermore, rooting depth was found to affect the transpiration water ages
and travel times, with younger water ages and shorter travel times for the
shallow roots of heather relative to deeper-rooting trees. While both
evaporation and transpiration generally have relatively young water ages and
short travel times, the travel time distributions revealed that the ET flux
also contains considerably older
(&gt; 100 days) waters. We
relate these old waters to the conceptualization of the subsurface into two
pore domains. Water in the fast flow domain was usually about half as old as
in the slow flow domain, which was fully exchanged within 1000 days and thus
was not immobile. Nevertheless, the differences between the slow and fast
flow domains are crucial for the interpretation of previous travel time
studies that have based their calibration on tracer data from the fast flow
domain (e.g. suction lysimeter samples), since such studies will have
underestimated travel times and water ages. Recharge travel times were mainly
governed by the subsequent recharge flux dynamics in our study, and decreased
during periods of intense flushing of the soil water during winter in
Bruntland Burn and snowmelt in Krycklan and Dorset. Transpiration travel
times were controlled by vegetation phenology and the associated annual
climatic cycle, with the longest travel times for waters infiltrated at the
beginning of dormancy and short travel times throughout the growing season.</p>
      <p id="d1e5119">Our simulations generally extended insights into the water flow and transport
processes obtained from snap shot isotope sampling to new insights into both
the seasonal and short-term dynamics of water ages in the critical zone. The
soil physical simulations showed that the inverse storage effect holds for
the vadose zone, and that temporarily saturated conditions (as found for the
hillslope scale) or groundwater influence (as found for the catchment scale)
were not required to generate younger water in recharge during periods of
greater soil water storage.</p>
      <p id="d1e5122">The presented simulations underline that the common assumption in
hydrological modelling of a well-mixed system in the subsurface does not hold
for water withdrawal from the soil via evaporation, transpiration, or
recharge. In contrast, we saw variable water ages across the two soil pore
domains and down the soil profile. Fluxes were more likely to withdraw
younger water during periods of enhanced wetness and older water when the
system becomes drier. The transpiration ages shown here also indicate that
waters in the plant xylem have relatively old ages (and long travel times)
depending on the time of the year, which is relevant for ecohydrological
studies inferring root water uptake depths using stable isotopes.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability">

      <p id="d1e5129">The underlaying research data are not publicly
available in a repository, as they contain 70 GB. However, they can be
requested from the authors.</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e5132">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/hess-22-3965-2018-supplement" xlink:title="pdf">https://doi.org/10.5194/hess-22-3965-2018-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution">

      <p id="d1e5141">MS conducted the simulations, made the graphs, and
wrote the initial manuscript; MS, DT, and CS designed the study and
JB and HL provided data and site-specific knowledge for the Dorset and
Krycklan sites, respectively. All authors contributed to the writing
process.</p>
  </notes><notes notes-type="competinginterests">

      <p id="d1e5147">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e5153">We thank Pernilla Löfvenius (SLU) for providing PET data for Krycklan
(via SITES) and Carl Mitchell for snowmelt data in Dorset. We thank Pertti
Ala-aho, Paolo Benettin, Sylvain Kuppel, Aaron A. Smith, and Hailong Wang for
constructive discussions on the topic. The authors would like to acknowledge
the support of the Maxwell computing cluster funded by the University of
Aberdeen. The Krycklan component of the study was funded by the KAW
Branch-Point project. We thank the European Research Council
(ERC, project GA 335910 VeWa) for funding. We acknowledge support by the
German Research Foundation (DFG) and the Open Access Publication Fund of
Humboldt-Universität zu Berlin. We thank Todd Walter and two anonymous
referees for their critical comments to improve the
manuscript.<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?> Edited by: Nunzio
Romano<?xmltex \hack{\newline}?> Reviewed by: Todd Walter and two anonymous referees</p></ack><ref-list>
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    <!--<article-title-html>Water ages in the critical zone of long-term experimental sites  in northern latitudes</article-title-html>
<abstract-html><p>As northern environments undergo intense changes due to a
warming climate and altered land use practices, there is an urgent need for
improved understanding of the impact of atmospheric forcing and vegetation on
water storage and flux dynamics in the critical zone. We therefore assess the
age dynamics of water stored in the upper 50&thinsp;cm of soil, and in evaporation,
transpiration, or recharge fluxes at four soil–vegetation units of podzolic
soils in the northern latitudes with either heather or tree vegetation
(Bruntland Burn in Scotland, Dorset in Canada, and Krycklan in Sweden). We
derived the age dynamics with the physically based SWIS (Soil Water Isotope
Simulator) model, which has been successfully used to simulate the
hydrometric and isotopic dynamics in the upper 50&thinsp;cm of soils at the study
sites. The modelled subsurface was divided into interacting fast and slow
flow domains. We tracked each day's infiltrated water through the critical
zone and derived forward median travel times (which show how long the water
takes to leave the soil via evaporation, transpiration, or recharge), and
median water ages (to estimate the median age of water in soil storage or the
evaporation, transpiration, and recharge fluxes). Resulting median travel
times were time-variant, mainly governed by major recharge events during
snowmelt in Dorset and Krycklan or during the wetter winter conditions in
Bruntland Burn. Transpiration travel times were driven by the vegetation
growth period with the longest travel times (200 days) for waters infiltrated
in early dormancy and the shortest travel times during the vegetation period.
However, long tails of the travel time distributions in evaporation and
transpiration revealed that these fluxes comprised waters older than
100 days. At each study site, water ages of soil storage, evaporation,
transpiration, and recharge were all inversely related to the storage volume
of the critical zone: water ages generally decreased exponentially with
increasing soil water storage. During wet periods, young soil waters were
more likely to be evapotranspired and recharged than during drier periods.
While the water in the slow flow domain showed long-term seasonal dynamics
and generally old water ages, the water ages of the fast flow domain were
generally younger and much flashier. Our results provide new insights into
the mixing and transport processes of soil water in the upper layer of the
critical zone, which is relevant for hydrological modelling at the plot to
catchment scales as the common assumption of a well-mixed system in the
subsurface holds for neither the evaporation, transpiration, or recharge.</p></abstract-html>
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