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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0" article-type="research-article"><?xmltex \bartext{Original research article}?>
  <front>
    <journal-meta><journal-id journal-id-type="publisher">SOIL</journal-id><journal-title-group>
    <journal-title>SOIL</journal-title>
    <abbrev-journal-title abbrev-type="publisher">SOIL</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">SOIL</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">2199-398X</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/soil-9-365-2023</article-id><title-group><article-title>Reproducibility of the wet part of the soil <?xmltex \hack{\break}?>water retention curve: a European <?xmltex \hack{\break}?>interlaboratory comparison</article-title><alt-title>Reproducibility of the wet part of the soil water retention curve</alt-title>
      </title-group><?xmltex \runningtitle{Reproducibility of the wet part of the soil water retention curve}?><?xmltex \runningauthor{B.~Guillaume et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Guillaume</surname><given-names>Benjamin</given-names></name>
          <email>benjamin.guillaume@uliege.be</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Aroui Boukbida</surname><given-names>Hanane</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Bakker</surname><given-names>Gerben</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Bieganowski</surname><given-names>Andrzej</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Brostaux</surname><given-names>Yves</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Cornelis</surname><given-names>Wim</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Durner</surname><given-names>Wolfgang</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-9543-1318</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Hartmann</surname><given-names>Christian</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1172-981X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff7">
          <name><surname>Iversen</surname><given-names>Bo V.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2276-0233</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff8">
          <name><surname>Javaux</surname><given-names>Mathieu</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-6168-5467</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff13">
          <name><surname>Ingwersen</surname><given-names>Joachim</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Lamorski</surname><given-names>Krzysztof</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-9678-541X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff9">
          <name><surname>Lamparter</surname><given-names>Axel</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff10">
          <name><surname>Makó</surname><given-names>András</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff11">
          <name><surname>Mingot Soriano</surname><given-names>Ana María</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff11">
          <name><surname>Messing</surname><given-names>Ingmar</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff12">
          <name><surname>Nemes</surname><given-names>Attila</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Pomes-Bordedebat</surname><given-names>Alexandre</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>van der Ploeg</surname><given-names>Martine</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3172-7339</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff13">
          <name><surname>Weber</surname><given-names>Tobias Karl David</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3448-5208</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff14">
          <name><surname>Weihermüller</surname><given-names>Lutz</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1991-7735</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Wellens</surname><given-names>Joost</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Degré</surname><given-names>Aurore</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Uliège – Gembloux Agro-Bio Tech, TERRA Teaching and Research Centre, Passage des Déportés 2, <?xmltex \hack{\break}?>5030 Gembloux, Belgium</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Instrumentation, Moyens Analytiques, observatoire en Géophysique et
Océanographie (UAR IMAGO), Institut de Recherche pour le Développement (IRD), 13002 Marseille, France</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Wageningen University and Research, Wageningen, Netherlands</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Institute of Agrophysics, Polish Academy of Sciences,  Lublin, Poland</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Ghent University, Gent, Belgium</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>Technische Universität Braunschweig, Braunschweig, Germany</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>Department of Agroecology, Aarhus University, Aarhus, Denmark</institution>
        </aff>
        <aff id="aff8"><label>8</label><institution>UCLouvain, Earth and Life Institute,  Louvain-la-Neuve, Belgium</institution>
        </aff>
        <aff id="aff9"><label>9</label><institution>Federal Institute for Geosciences and Natural Resources,  Hanover, Germany</institution>
        </aff>
        <aff id="aff10"><label>10</label><institution>Department of Soil Physics and Water Management, Institute for Soil Sciences, Centre for Agricultural Research, Herman Ottó Street 15,
1022 Budapest, Hungary</institution>
        </aff>
        <aff id="aff11"><label>11</label><institution>Swedish University of Agricultural Sciences,   Uppsala, Sweden</institution>
        </aff>
        <aff id="aff12"><label>12</label><institution>Norwegian Institute of Bioeconomy Research,  Ås, Norway</institution>
        </aff>
        <aff id="aff13"><label>13</label><institution>Institute of Soil Science and Land Evaluation, University of Hohenheim, Hohenheim, Germany</institution>
        </aff>
        <aff id="aff14"><label>14</label><institution>Agrosphere Institute IBG-3, Forschungszentrum Jülich GmbH, Jülich, Germany</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Benjamin Guillaume (benjamin.guillaume@uliege.be)</corresp></author-notes><pub-date><day>30</day><month>June</month><year>2023</year></pub-date>
      
      <volume>9</volume>
      <issue>1</issue>
      <fpage>365</fpage><lpage>379</lpage>
      <history>
        <date date-type="received"><day>23</day><month>December</month><year>2022</year></date>
           <date date-type="rev-request"><day>6</day><month>January</month><year>2023</year></date>
           <date date-type="rev-recd"><day>19</day><month>April</month><year>2023</year></date>
           <date date-type="accepted"><day>8</day><month>May</month><year>2023</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2023 Benjamin Guillaume et al.</copyright-statement>
        <copyright-year>2023</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023.html">This article is available from https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023.html</self-uri><self-uri xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023.pdf">The full text article is available as a PDF file from https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e381">The soil water retention curve (SWRC) is a key soil property required for predicting basic hydrological processes. The SWRC is often obtained in the laboratory with non-harmonized methods. Moreover, procedures associated with each method are not standardized. This can induce a lack of reproducibility between laboratories using different methods and procedures or using the same methods with different procedures. The goal of this study was to estimate the inter- and intralaboratory variability of the measurement of the wet part (from 10 to 300 hPa) of the SWRC. An interlaboratory comparison was carried out between 14 laboratories, using artificially constructed, porous reference samples that were transferred between laboratories according to a statistical design. The retention measurements were modelled by a series of linear mixed models using a Bayesian approach. This allowed the detection of sample-to-sample variability, interlaboratory variability, intralaboratory variability and the effects of sample changes between measurements. The greatest portion of the differences in the measurement of SWRCs was due to interlaboratory variability. The intralaboratory variability was highly variable depending on the laboratory. Some laboratories successfully reproduced the same SWRC on the same sample, while others did not. The mean intralaboratory variability over all laboratories was smaller than<?pagebreak page366?> the mean interlaboratory variability. A possible explanation for these results is that all laboratories used slightly different methods and procedures. We believe that this result may be of great importance regarding the quality of SWRC databases built by pooling SWRCs obtained in different laboratories. The quality of pedotransfer functions or maps that might be derived is probably hampered by this inter- and intralaboratory variability. The way forward is that measurement procedures of the SWRC need to be harmonized and standardized.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e393">The wet part of the soil water retention curve (SWRC) is considerably influenced by the soil pore network on a micrometre scale, which is affected by the so-called “soil structure”. This highlights that the SWRC and hydrophysical behaviour of soils can be modified by management practices that influence its structure.</p>
      <p id="d1e396">SWRCs are difficult, expensive and time-consuming to obtain. SWRC data are therefore limited in space and time. The SWRC is obtained from the joint determination of a series soil matric potential and soil water content. Since the wet part of the SWRC is mostly determined by the distribution and connectivity of the largest pores (<inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M2" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>m), it must be measured in situ or in the laboratory on undisturbed soil samples. Soil water content can be measured by direct (gravimetric) methods in the laboratory. To obtain matric potential, most laboratory methods impose a target matric potential on an undisturbed soil sample using an apparatus (sand box (SB), sand/kaolinite box (SKB), suction plate (SP), pressure plate (PP)) <xref ref-type="bibr" rid="bib1.bibx17 bib1.bibx6 bib1.bibx19" id="paren.1"/>. The sample is drained until its matric potential reaches equilibrium with the target matric potential. The SWRC can also be obtained via inverse modelling from an outflow experiment (one-step outflow, multi-step outflow) <xref ref-type="bibr" rid="bib1.bibx14" id="paren.2"/>. The SWRC can also be obtained by simultaneously measuring the water content and matric potential (with a tensiometer) of a soil sample evaporating in the free air and sealed at the bottom. Evaporation experiments also allow the soil hydraulic conductivity curve to be obtained simultaneously with the SWRC <xref ref-type="bibr" rid="bib1.bibx21" id="paren.3"/>. This method can also be implemented in situ using tensiometers and water content sensors installed side by side <xref ref-type="bibr" rid="bib1.bibx34" id="paren.4"/>. The Kelvin equation may also be used to relate the relative humidity of the air in a closed chamber in vapour equilibrium with the soil water into a matric potential (dew point hygrometer) <xref ref-type="bibr" rid="bib1.bibx9" id="paren.5"/>.</p>
      <p id="d1e433">Each method has its own accuracy and range of measurable matric potential. The determination of the SWRC over the full tension range (between saturation and wilting point or beyond) requires a combination of these methods. The comparison of these methods shows that they can lead to systematically different SWRCs for samples from the same soil <xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx25 bib1.bibx19" id="paren.6"/>. The sources of variability are various and may relate to procedural factors, such as sample size <xref ref-type="bibr" rid="bib1.bibx11 bib1.bibx26" id="paren.7"/>. Apparent hydrostatic equilibria (broken hydraulic contact and water flow being stopped before reaching hydrostatic equilibrium) might occur with sand box, sand/kaolinite box, suction plate or pressure plate methods, leading to overestimations of the water content, especially in the dry part of the SWRC <xref ref-type="bibr" rid="bib1.bibx18 bib1.bibx10 bib1.bibx5 bib1.bibx2 bib1.bibx27 bib1.bibx16 bib1.bibx25 bib1.bibx7" id="paren.8"/>. Contact materials are frequently used to improve the contact between the sample and the porous plate <xref ref-type="bibr" rid="bib1.bibx17 bib1.bibx22" id="paren.9"/>. The effects of these procedural aspects are not clearly established <xref ref-type="bibr" rid="bib1.bibx10 bib1.bibx12" id="paren.10"/>.</p>
      <p id="d1e451">The methods that have been used, to date, to measure the SWRC are different between laboratories, leading to non-harmonized datasets. Also, procedures for the same method differ from one laboratory to another.
As a consequence, most SWRC databases that are used to create pedotransfer functions and maps pool non-harmonized data from different laboratories <xref ref-type="bibr" rid="bib1.bibx33 bib1.bibx20 bib1.bibx32 bib1.bibx28 bib1.bibx29" id="paren.11"/>. It is argued that an important source of uncertainty of pedotransfer functions comes from the uncertainty of measured input data and that the standardization of experimental protocols could significantly enhance their quality <xref ref-type="bibr" rid="bib1.bibx31 bib1.bibx30" id="paren.12"/>.</p>
      <p id="d1e461">The Soil Program on Hydro Physics via International Engagement (SOPHIE), an independent initiative gathering European stakeholders in the field of soil hydrophysics, focuses on the harmonization and standardization of measurement of soil hydrophysical properties through international collaboration.
To our understanding, no study other than that of <xref ref-type="bibr" rid="bib1.bibx3" id="text.13"/> has carried out an interlaboratory comparison of SWRC measurements. This is partly due to the fact that an undisturbed soil sample cannot be transported from one laboratory to another and be measured several times without affecting the SWRC. <xref ref-type="bibr" rid="bib1.bibx3" id="text.14"/> circumvented this problem by using many samples from the same location and only using the samples in one round of SWRC measurement. They demonstrated that soil heterogeneity in the sampling area was negligible compared to the variability introduced by the different sample extraction, preparation and analysis procedures. However, this approach becomes very difficult to achieve when soil samples have to be transported by air and to countries where importing soil is restricted. Thus, in addition to innovation in measurement<?pagebreak page367?> techniques, SOPHIE is working on the development of artificially constructed reference samples and the organization of interlaboratory comparisons, starting with the SWRC.</p>
      <p id="d1e470">This paper presents the results of the first SOPHIE interlaboratory comparison for the measurement of the wet part (from 10 to 300 hPa) of the SWRC on reference samples. A total of 14 laboratories participated in this study using their typical routine measurement methods and protocols. Four research questions were addressed:
<list list-type="order"><list-item>
      <p id="d1e475">What are the “intralaboratory” variabilities of the 14 participating laboratories?</p></list-item><list-item>
      <p id="d1e479">What is the “interlaboratory” variability of the 14 participating laboratories?</p></list-item><list-item>
      <p id="d1e483">Do reference samples made at different laboratories differ from each other in terms of water retention properties between 10 and 300 hPa?</p></list-item><list-item>
      <p id="d1e487">Are the reference samples affected by time, measurements and/or transport between laboratories?</p></list-item></list></p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Materials and methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>The reference sample</title>
      <p id="d1e505">Each reference sample was composed of a mixture of 180 g of glass beads (0.250 mm <inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mi>x</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.500</mml:mn></mml:mrow></mml:math></inline-formula> mm), 20 g of pure air dry Portland cement and 35 g of tap water.  Once homogenized, the mixture was filled into a 100 cm<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula>  (5 cm height/5 cm diameter) stainless steel ring by frequently tapping it on a table to ensure that it was uniformly packed. The ring was closed at the bottom by a lid. Any excess material on the top was removed with a spatula. Each sample was allowed to cure for 72 h at room temperature. The bottom lid was subsequently replaced with a Eijkelkamp nylon cloth supported by a rubber band. The sample, with the ring, the cloth and the rubber, was weighted. The empty ring, the cloth and the rubber were previously weighted separately.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>The ring test</title>
      <p id="d1e539">The ring test was organized into 14 soil physics laboratories. An example of a reference sample was sent to each laboratory alongside the material needed to construct five other samples. A total of 84 reference samples were constructed. The ring test consisted of three successive rounds of SWRC measurements. At the beginning of each round, each sample was initially saturated for 48 h. The mass of each sample was then measured after equilibration at different matric potential (or suction) values: <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> hPa (<inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.00</mml:mn></mml:mrow></mml:math></inline-formula>), <inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> hPa (<inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.70</mml:mn></mml:mrow></mml:math></inline-formula>), <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> hPa (<inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2.00</mml:mn></mml:mrow></mml:math></inline-formula>) and <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">300</mml:mn></mml:mrow></mml:math></inline-formula> hPa (<inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2.48</mml:mn></mml:mrow></mml:math></inline-formula>). Equilibration times were 5 d at 10 hPa, 7 d at 50 hPa, 10 d at 100 hPa and 15 d at 300 hPa. Finally, samples were weighed after drying for 72 h in an oven drying at 60 <inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. Gravimetric water content (wc in g g<inline-formula><mml:math id="M14" 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>) was calculated by the ratio of water masses over dry masses (<inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:mtext>water content</mml:mtext><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mtext>fresh mass</mml:mtext><mml:mo>-</mml:mo><mml:mtext>dry mass</mml:mtext></mml:mrow><mml:mtext>dry mass</mml:mtext></mml:mfrac></mml:mstyle></mml:mrow></mml:math></inline-formula>). The six samples from each laboratory were divided into three exchange modalities (Fig. <xref ref-type="fig" rid="Ch1.F1"/>); two samples were kept by the same laboratory throughout the three rounds of measurements (<sc>“stay”</sc>), two samples were sent to different laboratories between rounds (<sc>“move”</sc>) and the last two samples were sent to a different laboratory for the second round but were sent back to the original laboratory for the third round (<sc>“back”</sc>). This scheme was designed to estimate intralaboratory and interlaboratory variability as well as the effect of sample transfer between laboratories.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e731">Example of sample exchange scheme of the ring test. Black arrows: <sc>stay</sc>. Red arrows: <sc>move</sc>. Blue arrows: <sc>back</sc>.</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f01.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>The data analysis</title>
      <p id="d1e757">The final dataset consisted of 250 SWRCs. Two curves were missing. Since each SWRC was composed of four successive measurement points whose relative value may depend on the previous point, the data were not independent. Statistical analyses were then based on parameter values of fitted functions. To model our dataset, a linear function with <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as the independent variable was adjusted to the measured wet part of SWRCs (Eq. <xref ref-type="disp-formula" rid="Ch1.E1"/>).
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M17" display="block"><mml:mrow><mml:msub><mml:mtext>wc</mml:mtext><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></disp-formula>
          Water content (wc<inline-formula><mml:math id="M18" display="inline"><mml:msub><mml:mi/><mml:mi>i</mml:mi></mml:msub></mml:math></inline-formula>) was linearly expressed as a function of <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> values (<inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.00</mml:mn></mml:mrow></mml:math></inline-formula>, 1.70, 2.00, 2.48). The <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> was intended to set the first retention point at the intercept. The index <inline-formula><mml:math id="M22" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> represented the <inline-formula><mml:math id="M23" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>th data point. <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> represented the  mean intercept and the slope over all data. The term <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represented the residuals.
The next step was to adjust a single linear model to each SWRC (Eq. <xref ref-type="disp-formula" rid="Ch1.E2"/>).
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M27" display="block"><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mtext>wc</mml:mtext><mml:mtext>in</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:munder><mml:munder class="underbrace"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo mathvariant="normal">︸</mml:mo></mml:munder><mml:mtext>varying intercept</mml:mtext></mml:munder></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:munder><mml:munder class="underbrace"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo mathvariant="normal">︸</mml:mo></mml:munder><mml:mtext>varying slope</mml:mtext></mml:munder><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
          The <inline-formula><mml:math id="M28" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> index represented the <inline-formula><mml:math id="M29" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>th SWRC. Depending on the modelled SWRC, intercepts (<inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and slopes (<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) were allowed to vary around a general intercept (<inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) and slope (<inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>). This type of model refers to a linear mixed (effect) model.</p>
      <?pagebreak page368?><p id="d1e1140">The purpose of this study was also to investigate the interlaboratory variability as well as the differences between samples.
Another linear mixed (effects) model was used to consider the by-sample and by-laboratory variability using adjustment terms called “random effects”. The first random effect, <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and  <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, respectively adjusted <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> depending on the analysing laboratory <inline-formula><mml:math id="M38" display="inline"><mml:mi>j</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M39" display="inline"><mml:mi>j</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M40" display="inline"><mml:mo>∈</mml:mo></mml:math></inline-formula> [1, …, 14]). The other random effect, <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and  <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, respectively adjusted <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> depending on the sample <inline-formula><mml:math id="M45" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M46" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M47" display="inline"><mml:mo>∈</mml:mo></mml:math></inline-formula> [1, …, 84]). This mixed-effect model was described by Eq. (<xref ref-type="disp-formula" rid="Ch1.E3"/>).
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M48" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mtext>wc</mml:mtext><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:munder><mml:munder class="underbrace"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo mathvariant="normal">︸</mml:mo></mml:munder><mml:mtext>varying intercept</mml:mtext></mml:munder></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:munder><mml:munder class="underbrace"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo mathvariant="normal">︸</mml:mo></mml:munder><mml:mtext>varying slope</mml:mtext></mml:munder><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e1425">Finally, the effect of sample changes between round 1 and round 3 on the intercept (<inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) and the slope (<inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) was modelled through a “fixed-effect” covariate. The covariate depended on a dummy variable associated with the round number; for the first round, round<inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> and for the third round, round<inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula>. This later model (Eq. <xref ref-type="disp-formula" rid="Ch1.E4"/>) was applied only to data associated with the <sc>back</sc> samples and <sc>stay</sc> samples to avoid laboratory effects. The results were compared to determine whether the differences in measurements between rounds 1 and 3 were due to transport or differences caused by wear of the samples not related to transport.
            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M53" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mtext>wc</mml:mtext><mml:mrow><mml:mi>i</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:munder><mml:munder class="underbrace"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mtext>round</mml:mtext><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">︸</mml:mo></mml:munder><mml:mtext>varying intercept</mml:mtext></mml:munder></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:munder><mml:munder class="underbrace"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mtext>round</mml:mtext><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">︸</mml:mo></mml:munder><mml:mtext>varying slope</mml:mtext></mml:munder><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
          All parameters from each models were estimated using Bayesian statistics. Posterior distributions were sampled with a Markov chain–Monte Carlo (MCMC) algorithm implemented in C++ through an R package called “RStan” <xref ref-type="bibr" rid="bib1.bibx4" id="paren.15"/>. Priors are noninformative, i.e. centred normal distributions for random effects parameters and uniform distributions for general intercept, general slope, fixed effect covariates and variance parameters. Sensitivity analyses of priors and validations of models were also carried out. Inference was based on Bayes factors and Bayesian credible intervals of posterior distributions. More details are available in the Supplement.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Procedures of laboratories</title>
      <p id="d1e1654">Each laboratory was given the same procedure to measure the SWRC. However, it allowed some freedom, and some laboratories did not perfectly implement it. For instance, laboratory 8 dried the samples at 100 <inline-formula><mml:math id="M54" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C instead of 60 <inline-formula><mml:math id="M55" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. Hence, laboratories used slightly different procedures to those shown in Table <xref ref-type="table" rid="Ch1.T1"/>.  Laboratories mostly used the sand box (SB) at 10, 50 and 100 hPa. At 300 hPa, the suction plate (SP) and the pressure plate (PP) were dominating. Lab 7 was the only one to use the sand/kaolinite box (SKB).</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T1" orientation="landscape"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e1680">Specificity of the participating laboratories in terms of device used (SB is the sand box, SKB is the sand/kaolinite box, SP is the suction plate and PP is the pressure plate), contact material, cap on the samples during equilibration periods, reference level used with respect to the sample at which the pressure was set, unit correction, plate cleaning procedure, saturation procedure and dry-weight measurement procedures.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.90}[.90]?><oasis:tgroup cols="13">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:colspec colnum="8" colname="col8" align="left"/>
     <oasis:colspec colnum="9" colname="col9" align="left"/>
     <oasis:colspec colnum="10" colname="col10" align="left"/>
     <oasis:colspec colnum="11" colname="col11" align="left"/>
     <oasis:colspec colnum="12" colname="col12" align="left"/>
     <oasis:colspec colnum="13" colname="col13" align="left"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Lab</oasis:entry>
         <oasis:entry rowsep="1" namest="col2" nameend="col5" align="center">Device </oasis:entry>
         <oasis:entry colname="col6">Contact material</oasis:entry>
         <oasis:entry colname="col7">Cap</oasis:entry>
         <oasis:entry colname="col8">Pressure</oasis:entry>
         <oasis:entry colname="col9">Correction</oasis:entry>
         <oasis:entry colname="col10">Plate clean</oasis:entry>
         <oasis:entry rowsep="1" namest="col11" nameend="col12" align="center">Saturation </oasis:entry>
         <oasis:entry colname="col13">Cooling after</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">10 hPa</oasis:entry>
         <oasis:entry colname="col3">50 hPa</oasis:entry>
         <oasis:entry colname="col4">100 hPa</oasis:entry>
         <oasis:entry colname="col5">300 hPa</oasis:entry>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8">sample ref</oasis:entry>
         <oasis:entry colname="col9">cm to hPa</oasis:entry>
         <oasis:entry colname="col10"/>
         <oasis:entry colname="col11">Water type</oasis:entry>
         <oasis:entry colname="col12">Water level</oasis:entry>
         <oasis:entry colname="col13">drying</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">1</oasis:entry>
         <oasis:entry colname="col2">SB</oasis:entry>
         <oasis:entry colname="col3">SB</oasis:entry>
         <oasis:entry colname="col4">SB</oasis:entry>
         <oasis:entry colname="col5">SP</oasis:entry>
         <oasis:entry colname="col6">spheriglass 3000</oasis:entry>
         <oasis:entry colname="col7">/</oasis:entry>
         <oasis:entry colname="col8">middle</oasis:entry>
         <oasis:entry colname="col9">/</oasis:entry>
         <oasis:entry colname="col10">water + brush</oasis:entry>
         <oasis:entry colname="col11">/</oasis:entry>
         <oasis:entry colname="col12">/</oasis:entry>
         <oasis:entry colname="col13">/</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2</oasis:entry>
         <oasis:entry colname="col2">SB</oasis:entry>
         <oasis:entry colname="col3">SB</oasis:entry>
         <oasis:entry colname="col4">SB</oasis:entry>
         <oasis:entry colname="col5">SP</oasis:entry>
         <oasis:entry colname="col6">quartz meal</oasis:entry>
         <oasis:entry colname="col7">no</oasis:entry>
         <oasis:entry colname="col8">middle</oasis:entry>
         <oasis:entry colname="col9">no</oasis:entry>
         <oasis:entry colname="col10">no</oasis:entry>
         <oasis:entry colname="col11">demineralized</oasis:entry>
         <oasis:entry colname="col12">45 mm</oasis:entry>
         <oasis:entry colname="col13">dessicator</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3</oasis:entry>
         <oasis:entry colname="col2">SB</oasis:entry>
         <oasis:entry colname="col3">SB</oasis:entry>
         <oasis:entry colname="col4">SB</oasis:entry>
         <oasis:entry colname="col5">PP</oasis:entry>
         <oasis:entry colname="col6">no</oasis:entry>
         <oasis:entry colname="col7">no</oasis:entry>
         <oasis:entry colname="col8">middle</oasis:entry>
         <oasis:entry colname="col9">yes</oasis:entry>
         <oasis:entry colname="col10">H<inline-formula><mml:math id="M56" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O<inline-formula><mml:math id="M57" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> + water</oasis:entry>
         <oasis:entry colname="col11">demineralized</oasis:entry>
         <oasis:entry colname="col12">25 mm</oasis:entry>
         <oasis:entry colname="col13">dessicator</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4</oasis:entry>
         <oasis:entry colname="col2">SP</oasis:entry>
         <oasis:entry colname="col3">SP</oasis:entry>
         <oasis:entry colname="col4">PP</oasis:entry>
         <oasis:entry colname="col5">PP</oasis:entry>
         <oasis:entry colname="col6">milled sand</oasis:entry>
         <oasis:entry colname="col7">no</oasis:entry>
         <oasis:entry colname="col8">middle/unknown</oasis:entry>
         <oasis:entry colname="col9">no</oasis:entry>
         <oasis:entry colname="col10">water</oasis:entry>
         <oasis:entry colname="col11">demineralized</oasis:entry>
         <oasis:entry colname="col12">47 mm</oasis:entry>
         <oasis:entry colname="col13">NA</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">5</oasis:entry>
         <oasis:entry colname="col2">SP</oasis:entry>
         <oasis:entry colname="col3">SP</oasis:entry>
         <oasis:entry colname="col4">SP</oasis:entry>
         <oasis:entry colname="col5">SP</oasis:entry>
         <oasis:entry colname="col6">filter paper</oasis:entry>
         <oasis:entry colname="col7">no</oasis:entry>
         <oasis:entry colname="col8">middle</oasis:entry>
         <oasis:entry colname="col9">yes</oasis:entry>
         <oasis:entry colname="col10">no</oasis:entry>
         <oasis:entry colname="col11">tap</oasis:entry>
         <oasis:entry colname="col12">49 mm</oasis:entry>
         <oasis:entry colname="col13">dessicator</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">6</oasis:entry>
         <oasis:entry colname="col2">SB</oasis:entry>
         <oasis:entry colname="col3">SB</oasis:entry>
         <oasis:entry colname="col4">SB</oasis:entry>
         <oasis:entry colname="col5">PP</oasis:entry>
         <oasis:entry colname="col6">kaolinite on filter paper</oasis:entry>
         <oasis:entry colname="col7">no</oasis:entry>
         <oasis:entry colname="col8">middle</oasis:entry>
         <oasis:entry colname="col9">yes</oasis:entry>
         <oasis:entry colname="col10">light HClO solution</oasis:entry>
         <oasis:entry colname="col11">demineralized</oasis:entry>
         <oasis:entry colname="col12">49 mm</oasis:entry>
         <oasis:entry colname="col13">no cooling</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">7</oasis:entry>
         <oasis:entry colname="col2">SB</oasis:entry>
         <oasis:entry colname="col3">SKB</oasis:entry>
         <oasis:entry colname="col4">SKB</oasis:entry>
         <oasis:entry colname="col5">SKB</oasis:entry>
         <oasis:entry colname="col6">no</oasis:entry>
         <oasis:entry colname="col7">yes</oasis:entry>
         <oasis:entry colname="col8">middle</oasis:entry>
         <oasis:entry colname="col9">yes</oasis:entry>
         <oasis:entry colname="col10">no</oasis:entry>
         <oasis:entry colname="col11">distilled</oasis:entry>
         <oasis:entry colname="col12">50 mm</oasis:entry>
         <oasis:entry colname="col13">dessicator</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">8</oasis:entry>
         <oasis:entry colname="col2">SB</oasis:entry>
         <oasis:entry colname="col3">SB</oasis:entry>
         <oasis:entry colname="col4">PP</oasis:entry>
         <oasis:entry colname="col5">PP</oasis:entry>
         <oasis:entry colname="col6">no</oasis:entry>
         <oasis:entry colname="col7">yes</oasis:entry>
         <oasis:entry colname="col8">bottom</oasis:entry>
         <oasis:entry colname="col9">no</oasis:entry>
         <oasis:entry colname="col10">water <inline-formula><mml:math id="M58" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> brush</oasis:entry>
         <oasis:entry colname="col11">deaerated</oasis:entry>
         <oasis:entry colname="col12">50 mm</oasis:entry>
         <oasis:entry colname="col13">no cooling</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">9</oasis:entry>
         <oasis:entry colname="col2">SB</oasis:entry>
         <oasis:entry colname="col3">SB</oasis:entry>
         <oasis:entry colname="col4">SB</oasis:entry>
         <oasis:entry colname="col5">PP</oasis:entry>
         <oasis:entry colname="col6">loamy soil</oasis:entry>
         <oasis:entry colname="col7">no</oasis:entry>
         <oasis:entry colname="col8">middle</oasis:entry>
         <oasis:entry colname="col9">yes</oasis:entry>
         <oasis:entry colname="col10">water <inline-formula><mml:math id="M59" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> brush</oasis:entry>
         <oasis:entry colname="col11">tap</oasis:entry>
         <oasis:entry colname="col12">40 mm</oasis:entry>
         <oasis:entry colname="col13">dessicator</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">10</oasis:entry>
         <oasis:entry colname="col2">SP</oasis:entry>
         <oasis:entry colname="col3">SP</oasis:entry>
         <oasis:entry colname="col4">SP</oasis:entry>
         <oasis:entry colname="col5">SP</oasis:entry>
         <oasis:entry colname="col6">no</oasis:entry>
         <oasis:entry colname="col7">yes</oasis:entry>
         <oasis:entry colname="col8">bottom</oasis:entry>
         <oasis:entry colname="col9">no</oasis:entry>
         <oasis:entry colname="col10">water</oasis:entry>
         <oasis:entry colname="col11">distilled</oasis:entry>
         <oasis:entry colname="col12">45 mm</oasis:entry>
         <oasis:entry colname="col13">NA</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">11</oasis:entry>
         <oasis:entry colname="col2">SP</oasis:entry>
         <oasis:entry colname="col3">SP</oasis:entry>
         <oasis:entry colname="col4">SP</oasis:entry>
         <oasis:entry colname="col5">PP</oasis:entry>
         <oasis:entry colname="col6">filter paper</oasis:entry>
         <oasis:entry colname="col7">yes</oasis:entry>
         <oasis:entry colname="col8">middle</oasis:entry>
         <oasis:entry colname="col9">no</oasis:entry>
         <oasis:entry colname="col10">water</oasis:entry>
         <oasis:entry colname="col11">demineralized</oasis:entry>
         <oasis:entry colname="col12">/</oasis:entry>
         <oasis:entry colname="col13">NA</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">12</oasis:entry>
         <oasis:entry colname="col2">PP</oasis:entry>
         <oasis:entry colname="col3">PP</oasis:entry>
         <oasis:entry colname="col4">PP</oasis:entry>
         <oasis:entry colname="col5">PP</oasis:entry>
         <oasis:entry colname="col6">no</oasis:entry>
         <oasis:entry colname="col7">no</oasis:entry>
         <oasis:entry colname="col8">middle</oasis:entry>
         <oasis:entry colname="col9">yes</oasis:entry>
         <oasis:entry colname="col10">water</oasis:entry>
         <oasis:entry colname="col11">demineralized</oasis:entry>
         <oasis:entry colname="col12">40 mm</oasis:entry>
         <oasis:entry colname="col13">in the oven</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">13</oasis:entry>
         <oasis:entry colname="col2">SB</oasis:entry>
         <oasis:entry colname="col3">SB</oasis:entry>
         <oasis:entry colname="col4">SP</oasis:entry>
         <oasis:entry colname="col5">SP</oasis:entry>
         <oasis:entry colname="col6">sand</oasis:entry>
         <oasis:entry colname="col7">no</oasis:entry>
         <oasis:entry colname="col8">bottom</oasis:entry>
         <oasis:entry colname="col9">no</oasis:entry>
         <oasis:entry colname="col10">water</oasis:entry>
         <oasis:entry colname="col11">demineralized</oasis:entry>
         <oasis:entry colname="col12">50 mm</oasis:entry>
         <oasis:entry colname="col13">in the oven</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">14</oasis:entry>
         <oasis:entry colname="col2">SB</oasis:entry>
         <oasis:entry colname="col3">SB</oasis:entry>
         <oasis:entry colname="col4">SB</oasis:entry>
         <oasis:entry colname="col5">PP</oasis:entry>
         <oasis:entry colname="col6">no</oasis:entry>
         <oasis:entry colname="col7">no</oasis:entry>
         <oasis:entry colname="col8">middle/bottom</oasis:entry>
         <oasis:entry colname="col9">no</oasis:entry>
         <oasis:entry colname="col10">tap water <inline-formula><mml:math id="M60" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> brush</oasis:entry>
         <oasis:entry colname="col11">demineralized</oasis:entry>
         <oasis:entry colname="col12">45 mm</oasis:entry>
         <oasis:entry colname="col13">NA</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table><?xmltex \gdef\@currentlabel{1}?></table-wrap>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>The simple linear model: SWRCs are very variable</title>
      <p id="d1e2458">The simple linear regression (Eq. <xref ref-type="disp-formula" rid="Ch1.E1"/>) with the <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as predictor was used to model the dataset. The posterior probability distribution of the general intercept  (<inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the slope (<inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), and the standard deviation of the residuals (<inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) are shown in Fig. <xref ref-type="fig" rid="Ch1.F2"/>. The mean value of <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was fairly high (0.0126 g g<inline-formula><mml:math id="M66" 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>). Indeed, as shown in Fig. <xref ref-type="fig" rid="Ch1.F3"/>, the variability of measured SWRCs was large (spreading of the curves). The following steps were devoted to explaining the origin of this variability.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e2543">Densities of the posterior probability distribution of the general intercept, <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, the general slope, <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and the standard deviation of the residuals, <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f02.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>A linear model for each SWRC to estimate the intralaboratory variability</title>
      <p id="d1e2593">The next step was to model a single linear regression for each SWRC (Eq. <xref ref-type="disp-formula" rid="Ch1.E2"/>). The posterior probability distribution of the general intercept  (<inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the slope (<inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the individual intercept (<inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and slope (<inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), and the standard deviation of the residuals (<inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) are shown in Fig. <xref ref-type="fig" rid="Ch1.F4"/>. The intercept (<inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and slope (<inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) parameters are different for each individual<?pagebreak page369?> SWRC. These individual parameters explain the variability that exists between all SWRC. Hence, the mean value of <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> presented in Fig. <xref ref-type="fig" rid="Ch1.F4"/> decreased by approximately 60 % compared to the previous model (Fig. <xref ref-type="fig" rid="Ch1.F2"/>) and now only represents a fitting error introduced by the choice of modelling SWRCs by linear regressions.</p>
      <p id="d1e2706">From these results, one can determine the standard deviation of <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> for each of the <sc>stay</sc> samples (between the three rounds). As each laboratory measured two <sc>stay</sc> samples, an estimate of the intralaboratory variability of each laboratory can be made by pooling the density estimates of the standard deviation of the two samples (Fig. <xref ref-type="fig" rid="Ch1.F5"/>). As the intralaboratory variability associated with each of the two <sc>stay</sc> sample is determined separately and then merged together, this allows us to minimize the effect of possible variations between the two <sc>stay</sc> samples. Intralaboratory variability is therefore defined as the variability between retention curves, modelled by linear regressions, measured on a similar (<sc>stay</sc>) sample within a same laboratory that uses a given measurement procedure.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e2757">Observed series of four successive retention points (10, 50, 100 and 300 hPa) connected by straight lines. Water content is gravimetric  (g g<inline-formula><mml:math id="M80" 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>). One colour represents one laboratory. This colour code is kept constant throughout the paper.</p></caption>
          <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f03.jpg"/>

        </fig>

      <p id="d1e2779">The estimate of the mean intralaboratory standard deviation of all laboratories pooled together (Fig. <xref ref-type="fig" rid="Ch1.F5"/> bottom row) was 0.00533 g g<inline-formula><mml:math id="M81" 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> (95 % credible interval (CrI) 0.00018–0.01138 g g<inline-formula><mml:math id="M82" 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>) for the intercept and 0.00519 g g<inline-formula><mml:math id="M83" 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:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (hPa)<inline-formula><mml:math id="M84" 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> (95 % CrI 0.00038–0.01068 g g<inline-formula><mml:math id="M85" 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:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (hPa)<inline-formula><mml:math id="M86" 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>) for the slope (Table <xref ref-type="table" rid="App1.Ch1.S1.T2"/> in the Appendix). Figure <xref ref-type="fig" rid="Ch1.F5"/> (top row) also shows that the intralaboratory variability was quite different depending on the laboratory. Some laboratories succeeded in repeating similar SWRCs results on a same sample, while others failed.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e2875">Densities of the posterior probability distribution of the general intercept, <inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, the varying intercept, <inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, the general slope, <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, the varying slope, <inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, and the standard deviation of the residuals, <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Densities of the posterior probability distribution of individual SWRC parameters (<inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) are coloured as a function of the analysing laboratory.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>What is the interlaboratory and sample variability?</title>
      <p id="d1e2982">Although all laboratories were given the same procedure to build the reference samples, the conditions under which they<?pagebreak page370?> were constructed differed between laboratories. Hence, the bulk density of samples at the beginning of the experiment was variable depending on the laboratory that constructed the sample (Table <xref ref-type="table" rid="App1.Ch1.S1.T3"/>). Indeed, the difference between the mean bulk density of samples constructed by the lab 1 (highest bulk density) and lab 14 (lowest bulk density) was 0.1573 g cm<inline-formula><mml:math id="M94" 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>. Hence, the later linear mixed (effect) model was used to estimate the  interlaboratory variability on the SWRC considering the differences between samples (Eq. <xref ref-type="disp-formula" rid="Ch1.E3"/>). Densities of the posterior probability distribution of the general intercept (<inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) and slope (<inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the random effect of laboratory on the intercept (<inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and slope (<inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), the random effect  of sample on the intercept (<inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and slope (<inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and the standard deviation of the residuals (<inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) are shown in Fig. <xref ref-type="fig" rid="Ch1.F6"/>. The mean value of <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> presented in Fig. <xref ref-type="fig" rid="Ch1.F6"/> decreased by approximately 40 % compared to the simple linear model (Fig. 1). Indeed, a part of the variability between SWRCs has been explained by sample and laboratory random effects. Parameter values of the laboratory random effects (<inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) show how SWRCs systematically deviate depending on the analysing laboratory. Differences between samples were also estimated with parameter values of the samples random effects (<inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). The wider dispersion of the laboratory random effect parameters indicates that the analysing laboratory explained a larger proportion of the overall variance than the analysed sample. Indeed, on the intercept, the mean laboratory random effect standard deviation (<inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) was 0.00872 g g<inline-formula><mml:math id="M108" 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>, while it was 0.00350 g g<inline-formula><mml:math id="M109" 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> for the sample random effect (<inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). The same observation applies to the slope with a mean standard deviation of 0.00602 g g<inline-formula><mml:math id="M111" 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:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (hPa)<inline-formula><mml:math id="M112" 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> for the laboratory random effect (<inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and 0.00451 g g<inline-formula><mml:math id="M114" 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:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (hPa)<inline-formula><mml:math id="M115" 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> for the sample random effect (<inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). The mean laboratory random effect standard deviations on the intercept and slope values (<inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) represent an estimation of the interlaboratory variability.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e3335">Densities of the posterior probability distribution of <bold>(a, c)</bold> the varying intercept, <inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, and <bold>(b, d)</bold> the varying slope, <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, with the standard deviation of the two <sc>stay</sc> samples of each laboratory <bold>(a, b)</bold> and all laboratories together <bold>(c, d)</bold>.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f05.png"/>

        </fig>

      <p id="d1e3388">It should be noted that results presented here are only representative of the reference samples that were measured in this particular case. Thus, estimates of interlaboratory (and intralaboratory) variability values are not directly transferable to other samples of a different nature with different retention characteristics.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e3394">Densities of the posterior probability distribution of the general intercept (<inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the random effect of laboratory on the intercept (<inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), the random effect of sample on the intercept (<inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), the general slope (<inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the random effect of laboratory on the slope (<inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), the random effect of sample on the slope (<inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and the standard deviation of the residuals (<inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>).</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f06.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS5">
  <label>3.5</label><title>Do the samples change between rounds?</title>
      <p id="d1e3502">In order to assess the effect of possible sample changes on the SWRC measurements, a last model was separately fitted to the data from <sc>back</sc> and <sc>stay</sc> samples (Eq. <xref ref-type="disp-formula" rid="Ch1.E4"/>). The Bayes factor indicated that the predicted data of <sc>back</sc> samples were 46.60 times more probable under the model that takes the round effect into account than the model without the round effect. Moreover, the 95 % credible interval of the posterior probability distribution of the “round” effect (Fig. <xref ref-type="fig" rid="Ch1.F7"/>) laid outside 0 for the intercept (<inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and the slope (<inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). Therefore, <sc>back</sc> samples changed between round 1 and round 3.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e3552">Densities of the posterior probability distribution  of the general intercept (<inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the fixed effect of the transport on the intercept (<inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), the random effect of sample on the intercept (<inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), the general slope (<inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the fixed effect of the transport on the slope (<inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), the random effect of sample on the slope (<inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and the standard deviation of the residuals (<inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). The model is applied to the <sc>back</sc> data for the first and the third rounds.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f07.png"/>

        </fig>

      <p id="d1e3654">On the other hand, the Bayes factor indicated that the predicted data of <sc>stay</sc> samples were 4348 times less probable under the model that takes the round effect into account than the model without the round effect. This suggests that the changes in the retention properties of the <sc>stay</sc> samples between the first and third rounds were negligible. In contrast, the 95 % credible interval of the posterior probability distribution of the round effect (Fig. <xref ref-type="fig" rid="Ch1.F8"/>) suggests that the <sc>stay</sc> samples changed between round 1 and round 3 as it laid outside 0 for the intercept (<inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and slope (<inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). Thus, for the <sc>stay</sc> samples, the Bayes factor and 95 % credible interval yielded two opposite conclusions. Also, the dry mass of <sc>stay</sc> samples increased between round 2 and 3 (<inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.016</mml:mn><mml:mo>*</mml:mo></mml:mrow></mml:math></inline-formula>), which was not the case with <sc>back</sc> samples (<inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.199</mml:mn></mml:mrow></mml:math></inline-formula> ns). The round effect on <sc>stay</sc> samples is discussed in Sect. <xref ref-type="sec" rid="Ch1.S4.SS3"/>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e3741">Densities of the posterior probability distribution of the general intercept (<inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the fixed effect of the transport on the intercept (<inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), the random effect of sample on the intercept (<inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), the general slope (<inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">β</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), the fixed effect of the transport on the slope (<inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), the random effect of sample on the slope (<inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and the standard deviation of the residuals (<inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). The model is applied to the <sc>stay</sc> data for the first and the third rounds.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f08.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS6">
  <label>3.6</label><title>Increasing SWRCs</title>
      <p id="d1e3851">In total, 57 of the 250 measured SWRCs showed an increase in water content between at least two increasing suction steps (Fig. <xref ref-type="fig" rid="Ch1.F3"/>). Whatever the origin, this increase in water content is physically impossible. It appeared that the occurrence of these anomalies depended on the analysing laboratory, with some having no anomalies and others having a large number of occurrences. Indeed, laboratories 3, 11 and 14 together accounted for 35 of the 57 anomalies recorded (Table <xref ref-type="table" rid="App1.Ch1.S1.T4"/>). Moreover, this anomaly has happened more than once for some samples such as for the samples 1, 2, 11, 15, 56, 61, 62, 63, 65 and 66. The samples 15, 63, 65 and 66 showed this anomaly in two different laboratories. Also, it occurred more often the drier the sample was. There were 55 occurrences between 100 and 300 hPa, while there were only 9<?pagebreak page371?> between 50 and 100 hPa and 3 between 10 and 50 hPa. For some SWRCs, there was more than one occurrence.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e3860">Joint posterior probability distribution of the laboratory random effect on the intercept (<inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) and slope (<inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). The ellipses are for illustrative purposes only. Please refer to Table <xref ref-type="table" rid="App1.Ch1.S1.T2"/> for estimates of laboratory random effects.</p></caption>
          <?xmltex \igopts{width=184.942913pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f09.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Interlaboratory variability</title>
      <p id="d1e3915">This study confirms that there are systematic differences in the measurement of SWRCs depending on the laboratory (Fig. <xref ref-type="fig" rid="Ch1.F6"/>). This is true even for laboratories using similar devices (e.g. lab 6 vs 9). These systematic differences in the measurement of SWRCs attributed to laboratories resulted in a large interlaboratory variability. The portion of variability attributed to differences between laboratories was larger than the portion of variability attributed to intrinsic differences between samples. This is concerning since it was shown, through the comparison of the bulk densities (Table <xref ref-type="table" rid="App1.Ch1.S1.T3"/>), that the samples were different even at the very beginning of the experiment. From saturation to drying, all laboratories used slightly different procedures (Table <xref ref-type="table" rid="Ch1.T1"/>). Similarly to the argument of <xref ref-type="bibr" rid="bib1.bibx3" id="text.16"/> on the measurement of macropore volume, total pore volume and saturated hydraulic conductivity, we believe that procedural differences between laboratories can be at the origin of this interlaboratory variability. The identification of the aspects of the procedures that influence SWRC measurements is challenging since these were not studied in isolation. This is a multidimensional problem that remains beyond the scope of this article. Nonetheless, an attempt is made to hypothesize the effect of some of these procedural aspects. It should also be mentioned that the true value of the SWRC was unknown. Laboratories were compared according to their relative position with respect to the others and not against a fixed target value.</p>
      <p id="d1e3927">Differences between laboratories are unlikely to be associated with differences in the analysed samples. The intrinsic differences between samples were considered by the model (Eq. <xref ref-type="disp-formula" rid="Ch1.E3"/>) using the sample random effect. Indeed, there was no correlation between the intercept parameter of each laboratory and the average bulk density of the samples analysed by each laboratory  (<inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0078</mml:mn></mml:mrow></mml:math></inline-formula>).</p>
      <p id="d1e3946">A first possible source of this interlaboratory variability could be attributed to the different devices used. To our knowledge, no study has yet attempted to compare SWRCs obtained with SB, SKB, SP or PP. Nonetheless, <xref ref-type="bibr" rid="bib1.bibx25" id="text.17"/> found that SWRCs measured with SP were less reproducible (wider spread) than those measured with the evaporation method in the <inline-formula><mml:math id="M151" display="inline"><mml:mi mathvariant="italic">ψ</mml:mi></mml:math></inline-formula> range of 0–300 hPa. This wider spread could be associated with contact issues with the plate and/or with the smaller sample size used with the SP method which could be smaller than the representative elementary volume of the soil. They also found that, for sandy soils, water contents are systematically smaller for SWRCs obtained with SP than with the evaporation method. These differences could be due to smaller initial saturation degrees of the sandy samples measured with the SP compared to those measured with the evaporation method. Temperature effects and dynamic non-equilibrium effects as found by <xref ref-type="bibr" rid="bib1.bibx8" id="text.18"/> could also have played a role in these differences. <xref ref-type="bibr" rid="bib1.bibx3" id="text.19"/> also compared macropore volume (as equal to the difference between the total pore volume or water content at saturation and water content at a matric potential of 60 hPa) obtained with SB and with pressure cells on real soil samples. It can be observed that the volume of macropores determined by laboratories using the SB is generally greater with a greater variability than when determined<?pagebreak page373?> by laboratories using the pressure cell. However, it is not clear from their results whether this difference is due to the method of obtaining the water content at 60 hPa (SB or pressure cell) or to the method of estimating the total pore volume (from bulk density or weighting at saturation, etc.) which was also different between laboratories.</p>
      <p id="d1e3965">Moreover, all laboratories used two different devices between 10 and 300 hPa, except labs 5, 10 and 12 that kept the same device for each pressure step. Switching from a suction to pressure system may affect the measurement of the SWRC. In a suction device, the suction is applied by a hanging water column via a continuum of water. In a pressure device, the pressure is applied via the air to the soil and plate water, while the plate bottom is at atmospheric air pressure. So, the propagation of the applied tension/pressure might be different.</p>
      <p id="d1e3969">The procedures for the dry mass measurement of the samples may also have played a role in the observed differences. Indeed, the estimation of the intercept parameter of laboratory 8, which dried the samples at 100 <inline-formula><mml:math id="M152" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, was higher than the ones from the other laboratories, which dried the samples at 60 <inline-formula><mml:math id="M153" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (Fig. <xref ref-type="fig" rid="Ch1.F6"/>). This suggests that the dry masses measured by laboratory 8 were lower than those measured by the other laboratories. This may be explained by the fact that the assumed “zero” water content corresponds to two different water content values associated with two different water potentials. Indeed, the equilibrium potential of the water contained in a sample after drying depends on the drying temperature and the relative humidity of the air inside the oven <xref ref-type="bibr" rid="bib1.bibx24" id="paren.20"/>. At liquid–vapour equilibrium and at constant relative humidity, the same sample dried at 60 <inline-formula><mml:math id="M154" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C will have a higher water content than if it was dried at 100 <inline-formula><mml:math id="M155" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. This difference in water content will also depend directly on the shape of the dry part of the retention curve. Furthermore, for the same sample at the same initial condition, the drying time required to remove the same amount of water increases as the drying temperature decreases. If liquid–vapour equilibrium has not been reached after the prescribed time of drying, it<?pagebreak page374?> is possible that the amount of water released is lower when drying at 60 <inline-formula><mml:math id="M156" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C than at 100 <inline-formula><mml:math id="M157" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C.</p>
      <p id="d1e4032">Another possibility to explain differences is the way laboratories maintained hydraulic contact between the draining porous media and the sample, enabling water to be released from the sample until hydrostatic equilibrium is reached. When the draining porous media were rigid (e.g. ceramic), some laboratories used a “contact material” to improve the hydraulic contact (Table <xref ref-type="table" rid="Ch1.T1"/>). From this study, it cannot be concluded that the use of contact materials did or did not improve the hydraulic contact between the samples and the porous plates. The results of laboratory 11 suggest that contact issues may have occurred even if filter paper was used as the contact material.</p>
      <p id="d1e4037">Nevertheless, the use of contact materials may sometimes be useful when considering laboratories using the same devices. Hence, it appears that the use of filter paper by laboratory 5 resulted in more water being released (more negative slope) than laboratory 10, which did not use any contact material but used the same devices (Fig. <xref ref-type="fig" rid="Ch1.F9"/>). <xref ref-type="bibr" rid="bib1.bibx12" id="text.21"/> also found that filter paper allowed more water to be released than polyester fabric and synthetic knitwear at 5000 and 15 000 hPa with the PP. The use of kaolinite by lab 6 and loamy soil by lab 9 as contact material seems to cause more water to be released between 100 and 300 hPa than laboratories 3 and 14 that did not used any contact material but used the same devices (results not shown). However, when looking at the entire domain of suction (from 10 to 300 hPa), the effect of kaolinite or loamy soil was negligible (Fig. <xref ref-type="fig" rid="Ch1.F9"/>). <xref ref-type="bibr" rid="bib1.bibx10" id="text.22"/> also found kaolinite ineffective in speeding equilibrium (or increasing hydraulic conductance), with inconsistent effects, at 15 000 hPa. Further work should be done to determine which contact materials are useful depending on the specific situation.</p>
      <p id="d1e4050">An option to check if the hydrostatic equilibrium is achieved is to connect the porous drainage medium to a graduated cylinder and monitor the water the amount of water drained from the sample. Once no more water flowing out of the sample is observed, hydrostatic equilibrium is considered to be achieved. This setup has to be sealed in order to ensure that there is no evaporation. The advantage of such a system is that one does not need to assume the equilibration time a priori. To our knowledge, this setup was used by laboratory number 8. However, it is still possible, with this setup, that the hydraulic contact is broken and the flow of water is stopped before hydrostatic equilibrium is reached, which is referred to as an apparent hydrostatic equilibrium.</p>
      <p id="d1e4053">It should also be mentioned that with devices using a hanging water column as suction regulation system, the applied suction is usually expressed in centimetres of water column. Units of hectopascals (hPa) and centimetres are commonly considered equivalent, but in fact 1 cm of vertical water column corresponds to 0.98 hPa. This is usually overlooked when units are transformed (see Table <xref ref-type="table" rid="Ch1.T1"/>). This bias may constitute a small part of the variability between laboratories and calls for harmonization of units.</p>
      <p id="d1e4058">In addition, the reference level compared to the sample at which the suction is applied varies between laboratories and devices used. Some laboratories applied the prescribed suction to the bottom of the samples, while others applied it to the middle (see Table <xref ref-type="table" rid="Ch1.T1"/>). Laboratories that applied suction to the bottom of the samples systematically applied 2.5 cm more suction than those that applied it to the middle. This difference could have easily been corrected for after the measurement. However, in practice, this information is never transmitted from the laboratory to the end user. Hence, when pooling data from different laboratories using different reference levels to apply suction, this unknown difference introduces variability.</p>
      <p id="d1e4064">There might be other procedural aspects that could be responsible for these differences between laboratories (saturation procedure, porous plate maintenance during the experiment, means of preventing air leakages and evaporation, maintenance of the ceramics and the sandboxes, weighting procedure, or maintenance of the scales, etc.) (Table <xref ref-type="table" rid="Ch1.T1"/>). Big errors can be avoided by a quality check of the results. To our knowledge, only one laboratory used a reference sample to control the quality of their SWRC measurements as a standard operating procedure.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10"><?xmltex \currentcnt{10}?><?xmltex \def\figurename{Figure}?><label>Figure 10</label><caption><p id="d1e4071">Joint posterior probability distribution of the varying intercept, <inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, the varying slope, <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, and standard deviation of the two <sc>stay</sc> samples of each laboratory (intralaboratory standard deviations). The ellipses are for illustrative purposes only. Please refer to Table <xref ref-type="table" rid="App1.Ch1.S1.T2"/> for estimates of intralaboratory variabilities</p></caption>
          <?xmltex \igopts{width=184.942913pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f10.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Intralaboratory variability</title>
      <p id="d1e4121">Some laboratories successfully reproduced SWRCs of the same (<sc>stay</sc>) sample, while others failed (Fig. <xref ref-type="fig" rid="Ch1.F10"/>). Nevertheless, the estimate of the mean intralaboratory variability over all laboratories was smaller than the mean interlaboratory variability but was more uncertain since it was drawn from fewer samples and since the intralaboratory variability was quite different between laboratories.  Obviously, this<?pagebreak page375?> variability can partly be attributed to the different methods and procedures that existed between laboratories that were discussed above. Some procedures ensured fairly good repeatability of results, while others did not.</p>
      <p id="d1e4129">The two laboratories with the greatest intralaboratory variability on the slope (see Figs. <xref ref-type="fig" rid="Ch1.F5"/> and <xref ref-type="fig" rid="Ch1.F10"/>: light pink and dark purple curves) were also among those with the most anomalies (see Table <xref ref-type="table" rid="App1.Ch1.S1.T4"/>: lab 11 and 14). Concerning laboratory 8 (see Fig. <xref ref-type="fig" rid="Ch1.F5"/>: cyan curve), the bimodal shape of the intralaboratory variability on the intercept shows that for one sample the variability was high, while it was low for the second. This bimodality clearly indicates that the estimation of individual intralaboratory variabilities is rather uncertain as they are only based on two samples measured with only three repetitions. This calls for further trials on reference samples to obtain a more reliable estimate of intralaboratory variability. Nevertheless, this provides an insight into the way forward to improve data quality management in soil physics laboratories.</p>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Effect of repeated measurements and/or transport on the samples</title>
      <p id="d1e4148">It appears that there was a slight effect of the transfer between laboratories on the <sc>back</sc> samples. The values of <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> indicate that SWRCs of <sc>back</sc> samples globally have a smaller intercept with a flatter slope after being transported (Fig. <xref ref-type="fig" rid="Ch1.F7"/>). This pattern might indicate a shift to more small pores. A possible explanation for these changes in porosity is the calcium carbonation of the cement. This reaction (<inline-formula><mml:math id="M162" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Ca</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">OH</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="normal">atm</mml:mi></mml:msubsup><mml:mo>⇌</mml:mo><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math></inline-formula>) forms <inline-formula><mml:math id="M163" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> precipitates inside the pore network, inducing a shift of the pore size distribution towards smaller pores, a decrease of the total porosity, pore clogging, and a loss of pore connectivity in cement-based materials <xref ref-type="bibr" rid="bib1.bibx35 bib1.bibx1" id="paren.23"/>. This hypothesis is also motivated by the fact that the dry masses of the samples increased significantly between rounds 2 and 3 for the samples <sc>stay</sc> and the dry masses did not decrease significantly for the samples <sc>back</sc> even if losses of materials were reported by the laboratories. Indeed, <xref ref-type="bibr" rid="bib1.bibx15" id="text.24"/> estimated that the carbonation-induced increase in bulk density (due to <inline-formula><mml:math id="M164" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> fixation) from a non-carbonated to a fully carbonated cement paste was 1.60 to 2.03 g cm<inline-formula><mml:math id="M165" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula>. However, the actual contribution of this phenomenon to changes in the retention properties of each reference sample is difficult to estimate, as the degree of carbonation was influenced by environmental factors (<inline-formula><mml:math id="M166" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration, air humidity, or water content of the cement, etc.) which have not been controlled.</p>
      <p id="d1e4285">Nevertheless, this significant transport effect could have led to an overestimation of the interlaboratory variability, as a part of the variability of the SWRC measurements can be attributed to sample changes. The use of cement to construct such reference samples should certainly be avoided in the future.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11"><?xmltex \currentcnt{11}?><?xmltex \def\figurename{Figure}?><label>Figure 11</label><caption><p id="d1e4290">SWRCs of the <sc>stay</sc> samples measured by lab 9.</p></caption>
          <?xmltex \igopts{width=184.942913pt}?><graphic xlink:href="https://soil.copernicus.org/articles/9/365/2023/soil-9-365-2023-f11.png"/>

        </fig>

      <p id="d1e4303">Although it was not significant in general for <sc>stay</sc> samples, some laboratories still seem to report sample changes between rounds. The changes followed the same patterns as for <sc>back</sc> samples, which were significant it that case (Fig. <xref ref-type="fig" rid="Ch1.F8"/>). Indeed, for <sc>stay</sc> samples of laboratories 2, 3, 4, 6, 9, 10, 11, 12 and 13, it seems that the water content at 10 hPa (<inline-formula><mml:math id="M167" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> = 1) systematically decreased with time. This was particularly visible for lab 9 (Fig. <xref ref-type="fig" rid="Ch1.F11"/>). The origin of the changes of the <sc>stay</sc> samples can partly be attributed to the same origin as for the <sc>back</sc> samples. The degree of changes may therefore be influenced by the way the samples were handled and stored, resulting in less wear for non-transported samples. Nevertheless, the wear of the <sc>stay</sc> samples implies that the estimation of the intralaboratory variability was certainly inflated as it included the variability attributed to sample changes between rounds. It should be mentioned that for some laboratories with the highest intralaboratory variability (laboratories 8 and 14), this trend was not visible, indicating that for these laboratories the variability attributed to procedures was probably more important than the variability attributed by sample changes.</p>
</sec>
<sec id="Ch1.S4.SS4">
  <label>4.4</label><title>Outliers</title>
      <p id="d1e4354">Many reasons might be elicited to explain the fact that some SWRCs showed an increase in water content between at least two increasing suction steps (Fig. <xref ref-type="fig" rid="Ch1.F3"/>). Obviously, this happened depending on a combination of reasons related to the laboratory but also to the sample being analysed (Table <xref ref-type="table" rid="App1.Ch1.S1.T4"/>).</p>
      <?pagebreak page376?><p id="d1e4361">A possible reason can be the lack of hydraulic contact between the draining porous media and the sample, preventing water from being released in time from the sample. This is supported by the higher frequency of outliers when the sample was drier, as hydraulic conductivity decreases as the sample dries <xref ref-type="bibr" rid="bib1.bibx10" id="paren.25"/>. Indeed, there is a possible scenario in which samples may absorb water but may not be able to release it according to the driving (higher) pressure. Measurements in a pressure chamber typically involve placing samples on pre-wetted ceramic plates. However, especially when a wet contact material is used, an unsaturated sample may start absorbing water (from the plate and the contact material) and re-saturate before the chamber is pressurized. Once the chamber is pressurized the excess of water may not be drained if the hydraulic contact is not well established. Hydraulic contact could have been hampered by the rigid nature and non-flat bottom topography of reference samples which did not fit the porous plate or by the use of shrinkable contact materials. When using the pressure plate, it is also possible that a “backflow” of water from the ceramic to the sample may occur between the release of the pressurized air and the disconnection of the sample from the plate <xref ref-type="bibr" rid="bib1.bibx23" id="paren.26"/>. Nevertheless, increasing SWRC also occurred with sandboxes and sand/kaolinite boxes, where the applied suction was not released when the sample was disconnected.</p>
</sec>
<sec id="Ch1.S4.SS5">
  <label>4.5</label><title>A way forward to further improve the quality of SWRC measurements</title>
      <p id="d1e4379">The results presented in Sect. 3.3 and 3.4 show that interlaboratory and intralaboratory variability exists in the measurement of the SWRC. As discussed in Sect. 4.1, we suspect that some part of this variability can be attributed to the different methods and procedures used by each laboratory. Therefore, this variability could potentially be reduced by improving procedures and methods. Ideally, these should be adapted in such a manner that they allow the closest possible estimation of the “actual” SWRC of any soil sample. The prerequisite for this to be feasible is to have a fixed point of comparison, i.e. a reference sample whose retention properties are well known and remain relatively stable over time. However, these two requirements were not fulfilled in this study. Therefore, the way in which procedures and methods should be adapted remains an open question. Nevertheless, based on the results of this study, we can suggest some general future directions to further improve the quality of the laboratory SWRC measurements.</p>
      <p id="d1e4382">We believe that the reproducibility of SWRC measurements within a same laboratory would be improved if a reference sample was used by each laboratory as an internal quality control. This implies that the SWRC of the reference sample must remain relatively stable over time, but its true value should not necessarily be known a priori. The reference samples used in this study are already used by one laboratory as an internal quality control. According to their experience, the samples remain fairly stable for about 10 measurements as long as they are not oven-dried.</p>
      <p id="d1e4385">Also, an important element that would allow us to move forward would be to have a point of comparison. Thus, the emphasis should be placed on the development of reference samples for interlaboratory comparisons. Internal trials are underway to build reference samples with clays or sintered glass beads. Also, reference samples based on parallel capillary bundles with adjustable diameters could allow a “theoretical” reference retention curve to be calculated from Jurin's law. The feasibility of developing such a reference sample is also being explored.</p>
      <p id="d1e4388">The interlaboratory and intralaboratory variability could be reduced by improving and standardizing procedures and harmonizing methods and data. Ideally, all laboratories should endorse a unique standard operational procedure for the same method, and methods should be harmonized between each other. Improving and standardizing procedures requires a full assessment of the effect of each step of the procedures on the final SWRC measurement on a reference sample that fulfils the above-mentioned conditions (a priori known and relatively stable). Harmonization of methods can be achieved with interlaboratory comparisons on the same types of reference samples.</p>
      <p id="d1e4392">Finally, since procedures and methods could have an impact on the final measurement of the SWRC, the transparency of the procedures and methods used in SWRC datasets should be ensured.</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d1e4405">Here, we presented an interlaboratory comparison of the measurement of the wet part of the SWRC conducted between 14 laboratories using artificially constructed, structured and porous samples as references. The experimental design combined with the data analysis procedure allowed the inter- and intra-laboratory variability to be revealed. Systematic differences in the measurement of SWRCs attributed to laboratories resulted in a large interlaboratory variability. The variability explained by the differences between laboratories was more important than the variability explained by intrinsic differences between samples. The intralaboratory variability was laboratory-dependent. The mean intralaboratory variability over all laboratories was approximately 45 % smaller on the intercept and 15 % smaller on the slope than the mean interlaboratory variability (Table <xref ref-type="table" rid="App1.Ch1.S1.T2"/>). The samples slightly changed during the interlaboratory comparison, inducing variability which was part of our estimate of intra- and interlaboratory variabilities. We believe that another part of the intra- and interlaboratory variability can be attributed to the different methods and procedures followed by each laboratory that were not standardized. This calls for standardization of procedures and harmonization of methods.  This should be performed in the light of a fixed target value: a reference sample whose retention properties are well known and preferably remain stable over time. We believe that without such an effort, pedotransfer functions and large-scale maps of soil properties produced with databases constructed on the<?pagebreak page377?> basis of multiple laboratories’ inputs will keep carrying unknown levels of uncertainty and bias.</p><?xmltex \hack{\clearpage}?>
</sec>

      
      </body>
    <back><app-group>

<?pagebreak page378?><app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title/>

<?xmltex \floatpos{h!}?><table-wrap id="App1.Ch1.S1.T2"><?xmltex \hack{\hsize\textwidth}?><?xmltex \currentcnt{A1}?><label>Table A1</label><caption><p id="d1e4425">Summary table of interlaboratory and intralaboratory variability results.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.82}[.82]?><oasis:tgroup cols="13">
     <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" colsep="1"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right" colsep="1"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:colspec colnum="10" colname="col10" align="right" colsep="1"/>
     <oasis:colspec colnum="11" colname="col11" align="right"/>
     <oasis:colspec colnum="12" colname="col12" align="right"/>
     <oasis:colspec colnum="13" colname="col13" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Lab</oasis:entry>
         <oasis:entry namest="col2" nameend="col4" align="center">Laboratory random effect </oasis:entry>
         <oasis:entry namest="col5" nameend="col7" align="center">Laboratory random effect </oasis:entry>
         <oasis:entry namest="col8" nameend="col10" align="center">Intralab SD </oasis:entry>
         <oasis:entry namest="col11" nameend="col13" align="center">Intralab SD </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry rowsep="1" namest="col2" nameend="col4" align="center">on the intercept, <inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (g g<inline-formula><mml:math id="M169" 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 rowsep="1" namest="col5" nameend="col7" align="center">on the slope, <inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (g g<inline-formula><mml:math id="M171" 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> <inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mtext>hPa</mml:mtext><mml:msup><mml:mo>)</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) </oasis:entry>
         <oasis:entry rowsep="1" namest="col8" nameend="col10" align="center">on the intercept (g g<inline-formula><mml:math id="M173" 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 rowsep="1" namest="col11" nameend="col13" align="center">on the slope (g g<inline-formula><mml:math id="M174" 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> <inline-formula><mml:math id="M175" display="inline"><mml:mrow><mml:msub><mml:mi>log⁡</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mtext>hPa</mml:mtext><mml:msup><mml:mo>)</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">Mean</oasis:entry>
         <oasis:entry namest="col3" nameend="col4" align="center">95 % CrI </oasis:entry>
         <oasis:entry colname="col5">Mean</oasis:entry>
         <oasis:entry namest="col6" nameend="col7" align="center">95 % CrI </oasis:entry>
         <oasis:entry colname="col8">Mean</oasis:entry>
         <oasis:entry namest="col9" nameend="col10" align="center">95 % CrI </oasis:entry>
         <oasis:entry colname="col11">Mean</oasis:entry>
         <oasis:entry namest="col12" nameend="col13" align="center">95 % CrI </oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">1</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00184</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M177" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00780</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0,00396</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00363</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M179" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00851</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0,00110</oasis:entry>
         <oasis:entry colname="col8">/</oasis:entry>
         <oasis:entry colname="col9">/</oasis:entry>
         <oasis:entry colname="col10">/</oasis:entry>
         <oasis:entry colname="col11">/</oasis:entry>
         <oasis:entry colname="col12">/</oasis:entry>
         <oasis:entry colname="col13">/</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00855</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">01450</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M182" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00278</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">01237</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">01770</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7"><inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00762</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">0,00460</oasis:entry>
         <oasis:entry colname="col9">0,00047</oasis:entry>
         <oasis:entry colname="col10">0,00877</oasis:entry>
         <oasis:entry colname="col11">0,00377</oasis:entry>
         <oasis:entry colname="col12">0,00032</oasis:entry>
         <oasis:entry colname="col13">0,00752</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3</oasis:entry>
         <oasis:entry colname="col2">0,00021</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00570</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0,00611</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00044</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00532</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0,00428</oasis:entry>
         <oasis:entry colname="col8">0,00689</oasis:entry>
         <oasis:entry colname="col9">0,00129</oasis:entry>
         <oasis:entry colname="col10">0,01251</oasis:entry>
         <oasis:entry colname="col11">0,00576</oasis:entry>
         <oasis:entry colname="col12">0,00094</oasis:entry>
         <oasis:entry colname="col13">0,01050</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00105</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M190" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00675</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0,00472</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00123</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M192" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00608</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0,00348</oasis:entry>
         <oasis:entry colname="col8">0,00423</oasis:entry>
         <oasis:entry colname="col9">0,00040</oasis:entry>
         <oasis:entry colname="col10">0,00825</oasis:entry>
         <oasis:entry colname="col11">0,00450</oasis:entry>
         <oasis:entry colname="col12">0,00041</oasis:entry>
         <oasis:entry colname="col13">0,00897</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">5</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M193" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00552</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M194" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">01134</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0,00014</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M195" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00082</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M196" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00562</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0,00397</oasis:entry>
         <oasis:entry colname="col8">0,00457</oasis:entry>
         <oasis:entry colname="col9">0,00048</oasis:entry>
         <oasis:entry colname="col10">0,00898</oasis:entry>
         <oasis:entry colname="col11">0,00505</oasis:entry>
         <oasis:entry colname="col12">0,00064</oasis:entry>
         <oasis:entry colname="col13">0,00961</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">6</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M197" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00259</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M198" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00850</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0,00314</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M199" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00138</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M200" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00614</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0,00328</oasis:entry>
         <oasis:entry colname="col8">0,00435</oasis:entry>
         <oasis:entry colname="col9">0,00046</oasis:entry>
         <oasis:entry colname="col10">0,00850</oasis:entry>
         <oasis:entry colname="col11">0,00531</oasis:entry>
         <oasis:entry colname="col12">0,00046</oasis:entry>
         <oasis:entry colname="col13">0,01052</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">7</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M201" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">00636</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M202" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">01228</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
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       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Overall</oasis:entry>
         <oasis:entry colname="col2">0,00872</oasis:entry>
         <oasis:entry colname="col3">0,00562</oasis:entry>
         <oasis:entry colname="col4">0,01367</oasis:entry>
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         <oasis:entry colname="col13">0,01068</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">SD</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
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       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table><?xmltex \gdef\@currentlabel{A1}?></table-wrap>

<?xmltex \floatpos{h!}?><table-wrap id="App1.Ch1.S1.T3"><?xmltex \hack{\hsize\textwidth}?><?xmltex \currentcnt{A2}?><label>Table A2</label><caption><p id="d1e5860">Newman and Keuls’ groups of populations of samples bulk density according to the laboratory that constructed them (sorted by decreasing mean bulk density). Lab number 15 represents the samples provided by UGent.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <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:thead>
       <oasis:row>
         <oasis:entry colname="col1">Lab</oasis:entry>
         <oasis:entry colname="col2">Mean</oasis:entry>
         <oasis:entry colname="col3">SD</oasis:entry>
         <oasis:entry colname="col4">Pop.</oasis:entry>
         <oasis:entry colname="col5">NK</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">number</oasis:entry>
         <oasis:entry colname="col2">(g cm<inline-formula><mml:math id="M219" 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="col3">(g cm<inline-formula><mml:math id="M220" 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">size</oasis:entry>
         <oasis:entry colname="col5">group</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">1</oasis:entry>
         <oasis:entry colname="col2">1.8035</oasis:entry>
         <oasis:entry colname="col3">0.0094</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">a</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2</oasis:entry>
         <oasis:entry colname="col2">1.7781</oasis:entry>
         <oasis:entry colname="col3">0.0141</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">b</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">8</oasis:entry>
         <oasis:entry colname="col2">1.7639</oasis:entry>
         <oasis:entry colname="col3">0.0494</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">b c</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3</oasis:entry>
         <oasis:entry colname="col2">1.7551</oasis:entry>
         <oasis:entry colname="col3">0.0049</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">b c d</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">11</oasis:entry>
         <oasis:entry colname="col2">1.7540</oasis:entry>
         <oasis:entry colname="col3">0.0090</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">b c d</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">7</oasis:entry>
         <oasis:entry colname="col2">1.7528</oasis:entry>
         <oasis:entry colname="col3">0.0046</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">b c d</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">10</oasis:entry>
         <oasis:entry colname="col2">1.7425</oasis:entry>
         <oasis:entry colname="col3">0.0062</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">c d</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">12</oasis:entry>
         <oasis:entry colname="col2">1.7314</oasis:entry>
         <oasis:entry colname="col3">0.0168</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">d</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4</oasis:entry>
         <oasis:entry colname="col2">1.6948</oasis:entry>
         <oasis:entry colname="col3">0.0198</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">e</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">13</oasis:entry>
         <oasis:entry colname="col2">1.6657</oasis:entry>
         <oasis:entry colname="col3">0.0291</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">f</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">5</oasis:entry>
         <oasis:entry colname="col2">1.6579</oasis:entry>
         <oasis:entry colname="col3">0.0133</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">f</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">6</oasis:entry>
         <oasis:entry colname="col2">1.6574</oasis:entry>
         <oasis:entry colname="col3">0.0177</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">f</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">9</oasis:entry>
         <oasis:entry colname="col2">1.6489</oasis:entry>
         <oasis:entry colname="col3">0.0056</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">f</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">14</oasis:entry>
         <oasis:entry colname="col2">1.6462</oasis:entry>
         <oasis:entry colname="col3">0.0136</oasis:entry>
         <oasis:entry colname="col4">5</oasis:entry>
         <oasis:entry colname="col5">f</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">15</oasis:entry>
         <oasis:entry colname="col2">1.6359</oasis:entry>
         <oasis:entry colname="col3">0.0113</oasis:entry>
         <oasis:entry colname="col4">14</oasis:entry>
         <oasis:entry colname="col5">f</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><?xmltex \gdef\@currentlabel{A2}?></table-wrap>

<?xmltex \hack{\clearpage}?><?xmltex \floatpos{t}?><table-wrap id="App1.Ch1.S1.T4"><?xmltex \currentcnt{A3}?><label>Table A3</label><caption><p id="d1e6222">ID of samples showing increasing SWRCs as function of the analysing laboratory and the round.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.95}[.95]?><oasis:tgroup cols="4">
     <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:thead>
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         <oasis:entry colname="col1">Lab</oasis:entry>
         <oasis:entry colname="col2">Round 1</oasis:entry>
         <oasis:entry colname="col3">Round 2</oasis:entry>
         <oasis:entry colname="col4">Round 3</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">1</oasis:entry>
         <oasis:entry colname="col2">/</oasis:entry>
         <oasis:entry colname="col3">/</oasis:entry>
         <oasis:entry colname="col4">/</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2</oasis:entry>
         <oasis:entry colname="col2">/</oasis:entry>
         <oasis:entry colname="col3">/</oasis:entry>
         <oasis:entry colname="col4">/</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3</oasis:entry>
         <oasis:entry colname="col2">1, 2, 5</oasis:entry>
         <oasis:entry colname="col3">1, 2, 39, 40, 41, 42</oasis:entry>
         <oasis:entry colname="col4">1, 5, 81, 82</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4</oasis:entry>
         <oasis:entry colname="col2">/</oasis:entry>
         <oasis:entry colname="col3">/</oasis:entry>
         <oasis:entry colname="col4">/</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">5</oasis:entry>
         <oasis:entry colname="col2">/</oasis:entry>
         <oasis:entry colname="col3">15, 17, 18</oasis:entry>
         <oasis:entry colname="col4">/</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">6</oasis:entry>
         <oasis:entry colname="col2">43</oasis:entry>
         <oasis:entry colname="col3">/</oasis:entry>
         <oasis:entry colname="col4">15, 16</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">7</oasis:entry>
         <oasis:entry colname="col2">56, 57, 59, 60</oasis:entry>
         <oasis:entry colname="col3">48, 56</oasis:entry>
         <oasis:entry colname="col4">/</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">8</oasis:entry>
         <oasis:entry colname="col2">/</oasis:entry>
         <oasis:entry colname="col3">/</oasis:entry>
         <oasis:entry colname="col4">/</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">9</oasis:entry>
         <oasis:entry colname="col2">10, 11</oasis:entry>
         <oasis:entry colname="col3">/</oasis:entry>
         <oasis:entry colname="col4">11</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">10</oasis:entry>
         <oasis:entry colname="col2">/</oasis:entry>
         <oasis:entry colname="col3">/</oasis:entry>
         <oasis:entry colname="col4">/</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">11</oasis:entry>
         <oasis:entry colname="col2">62, 63, 64, 65</oasis:entry>
         <oasis:entry colname="col3">61, 62, 75, 76, 77, 78</oasis:entry>
         <oasis:entry colname="col4">9, 61, 62, 65, 66</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">12</oasis:entry>
         <oasis:entry colname="col2">/</oasis:entry>
         <oasis:entry colname="col3">65, 66</oasis:entry>
         <oasis:entry colname="col4">25, 29, 30</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">13</oasis:entry>
         <oasis:entry colname="col2">/</oasis:entry>
         <oasis:entry colname="col3">/</oasis:entry>
         <oasis:entry colname="col4">63</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">14</oasis:entry>
         <oasis:entry colname="col2">21</oasis:entry>
         <oasis:entry colname="col3">20, 69, 70, 71, 72</oasis:entry>
         <oasis:entry colname="col4">23, 28</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table><?xmltex \gdef\@currentlabel{A3}?></table-wrap>

</app>
  </app-group><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d1e6476">Raw data, R code and model results are available at <ext-link xlink:href="https://doi.org/10.5281/zenodo.7943957" ext-link-type="DOI">10.5281/zenodo.7943957</ext-link> (<xref ref-type="bibr" rid="bib1.bibx13" id="altparen.27"/>).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e6485">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/soil-9-365-2023-supplement" xlink:title="pdf">https://doi.org/10.5194/soil-9-365-2023-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e6494">The conceptualization of the study was developed during the SOPHIE meeting of 2019 at Gembloux with the contribution of HAB, GB, AB, YB, WC, AD, CH, KL, AL, AMMS, AN, MvP and MV. Reference samples were provided by WC and MV. All authors were involved in the data collection. The methodology for the data analysis was developed by YB, AD, BG and APB. The manuscript was drafted and edited by BG. All authors were involved in the review of the paper.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e6500">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e6506">Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e6512">The rings for reference samples were provided by Royal Eijkelkamp.</p></ack><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e6517">This paper was edited by Jan Vanderborght and reviewed by two anonymous referees.</p>
  </notes><ref-list>
    <title>References</title>

      <ref id="bib1.bibx1"><?xmltex \def\ref@label{{Auroy et~al.(2015)Auroy, Poyet, Le~Bescop, Torrenti, Charpentier,
Moskura, and Bourbon}}?><label>Auroy et al.(2015)Auroy, Poyet, Le Bescop, Torrenti, Charpentier,
Moskura, and Bourbon</label><?label auroy_impact_2015?><mixed-citation>Auroy, M., Poyet, S., Le Bescop, P., Torrenti, J.-M., Charpentier, T., Moskura,
M., and Bourbon, X.: Impact of carbonation on unsaturated water transport
properties of cement-based materials, Cement Concrete Res., 74,
44–58, <ext-link xlink:href="https://doi.org/10.1016/j.cemconres.2015.04.002" ext-link-type="DOI">10.1016/j.cemconres.2015.04.002</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx2"><?xmltex \def\ref@label{{Bittelli and Flury(2009)}}?><label>Bittelli and Flury(2009)</label><?label Bittelli2009?><mixed-citation>Bittelli, M. and Flury, M.: Errors in Water Retention Curves Determined with
Pressure Plates, Soil Sci. Soc. Am. J., 73, 1453–1460,
<ext-link xlink:href="https://doi.org/10.2136/SSSAJ2008.0082" ext-link-type="DOI">10.2136/SSSAJ2008.0082</ext-link>, 2009.</mixed-citation></ref>
      <ref id="bib1.bibx3"><?xmltex \def\ref@label{{Buchter et~al.(2015)Buchter, Berli, and
Weisskopf}}?><label>Buchter et al.(2015)Buchter, Berli, and
Weisskopf</label><?label buchter_interlaboratory_2015?><mixed-citation>Buchter, B., Berli, M., and Weisskopf, P.: Interlaboratory comparison of soil
physical parameters, Agroscope Sci., 11, 1–21,
<uri>https://ira.agroscope.ch/en-US/Page/Publikation/Index/34807</uri> (last access: 15 April 2023),
2015.</mixed-citation></ref>
      <ref id="bib1.bibx4"><?xmltex \def\ref@label{{Carpenter et~al.(2017)Carpenter, Gelman, Hoffman, Lee, Goodrich,
Betancourt, Brubaker, Guo, Li, and Riddell}}?><label>Carpenter et al.(2017)Carpenter, Gelman, Hoffman, Lee, Goodrich,
Betancourt, Brubaker, Guo, Li, and Riddell</label><?label carpenter2017stan?><mixed-citation>Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B., Betancourt,
M., Brubaker, M., Guo, J., Li, P., and Riddell, A.: Stan: A probabilistic
programming language, J. Stat. Softw., 76, 1–32,
<ext-link xlink:href="https://doi.org/10.18637/jss.v076.i01" ext-link-type="DOI">10.18637/jss.v076.i01</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx5"><?xmltex \def\ref@label{{Cresswell et~al.(2008)Cresswell, Green, and McKenzie}}?><label>Cresswell et al.(2008)Cresswell, Green, and McKenzie</label><?label Cresswell2008?><mixed-citation>Cresswell, H. P., Green, T. W., and McKenzie, N. J.: The Adequacy of Pressure
Plate Apparatus for Determining Soil Water Retention, Soil Sci. Soc.
Am. J., 72, 41–49, <ext-link xlink:href="https://doi.org/10.2136/SSSAJ2006.0182" ext-link-type="DOI">10.2136/SSSAJ2006.0182</ext-link>, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx6"><?xmltex \def\ref@label{{Dane and Hopmans(2002)}}?><label>Dane and Hopmans(2002)</label><?label dane_332_2002?><mixed-citation>Dane, J. H. and Hopmans, J. W.: 3.3.2 Laboratory, in: Methods of Soil
Analysis,  John Wiley &amp; Sons, Ltd, 675–720,
<ext-link xlink:href="https://doi.org/10.2136/sssabookser5.4.c25" ext-link-type="DOI">10.2136/sssabookser5.4.c25</ext-link>, 2002.</mixed-citation></ref>
      <ref id="bib1.bibx7"><?xmltex \def\ref@label{{de~Jong~van Lier et~al.(2019)de~Jong~van Lier, Pinheiro, and
Inforsato}}?><label>de Jong van Lier et al.(2019)de Jong van Lier, Pinheiro, and
Inforsato</label><?label dejong2019?><mixed-citation>de Jong van Lier, Q., Pinheiro, E. A. R., and Inforsato, L.: Hydrostatic
equilibrium between soil samples and pressure plates used in soil water
retention determination: Consequences of a questionable assumption, Revista
Brasileira de Ciencia do Solo, 43, <ext-link xlink:href="https://doi.org/10.1590/18069657RBCS20190014" ext-link-type="DOI">10.1590/18069657RBCS20190014</ext-link>, 2019.</mixed-citation></ref>
      <ref id="bib1.bibx8"><?xmltex \def\ref@label{{Diamantopoulos and
Durner(2012)}}?><label>Diamantopoulos and
Durner(2012)</label><?label Durner2012?><mixed-citation>Diamantopoulos, E. and Durner, W.: Dynamic Nonequilibrium of Water Flow in
Porous Media: A Review, Vadose Zone J., 11, vzj2011.0197,
<ext-link xlink:href="https://doi.org/10.2136/vzj2011.0197" ext-link-type="DOI">10.2136/vzj2011.0197</ext-link>, 2012.</mixed-citation></ref>
      <ref id="bib1.bibx9"><?xmltex \def\ref@label{{Gee et~al.(1992)Gee, Campbell, Campbell, and
Campbell}}?><label>Gee et al.(1992)Gee, Campbell, Campbell, and
Campbell</label><?label gee_rapid_1992?><mixed-citation>Gee, G. W., Campbell, M. D., Campbell, G. S., and Campbell, J. H.: Rapid
Measurement of Low Soil Water Potentials Using a Water
Activity Meter, Soil Sci. Soc. Am. J., 56, 1068–1070,
<ext-link xlink:href="https://doi.org/10.2136/sssaj1992.03615995005600040010x" ext-link-type="DOI">10.2136/sssaj1992.03615995005600040010x</ext-link>, 1992.</mixed-citation></ref>
      <ref id="bib1.bibx10"><?xmltex \def\ref@label{{Gee et~al.(2002)Gee, Ward, Zhang, Campbell, and Mathison}}?><label>Gee et al.(2002)Gee, Ward, Zhang, Campbell, and Mathison</label><?label Gee2002?><mixed-citation>Gee, G. W., Ward, A. L., Zhang, Z. F., Campbell, G. S., and Mathison, J.: The
Influence of Hydraulic Nonequilibrium on Pressure Plate Data, Vadose Zone
J., 1, 172–178, <ext-link xlink:href="https://doi.org/10.2113/1.1.172" ext-link-type="DOI">10.2113/1.1.172</ext-link>, 2002.</mixed-citation></ref>
      <ref id="bib1.bibx11"><?xmltex \def\ref@label{{Ghanbarian et~al.(2015)Ghanbarian, Taslimitehrani, Dong, and
Pachepsky}}?><label>Ghanbarian et al.(2015)Ghanbarian, Taslimitehrani, Dong, and
Pachepsky</label><?label ghanbarian_sample_2015?><mixed-citation>Ghanbarian, B., Taslimitehrani, V., Dong, G., and Pachepsky, Y. A.: Sample
dimensions effect on prediction of soil water retention curve and saturated
hydraulic conductivity, J.  Hydrol., 528, 127–137,
<ext-link xlink:href="https://doi.org/10.1016/j.jhydrol.2015.06.024" ext-link-type="DOI">10.1016/j.jhydrol.2015.06.024</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx12"><?xmltex \def\ref@label{{Gubiani et~al.(2013)Gubiani, Reichert, Campbell, Reinert, and
Gelain}}?><label>Gubiani et al.(2013)Gubiani, Reichert, Campbell, Reinert, and
Gelain</label><?label Gubiani2013?><mixed-citation>Gubiani, P. I., Reichert, J. M., Campbell, C., Reinert, D. J., and Gelain,
N. S.: Assessing Errors and Accuracy in Dew-Point Potentiometer and Pressure
Plate Extractor Meaurements, Soil Sci. Soc. Am. J., 77,
19–24, <ext-link xlink:href="https://doi.org/10.2136/SSSAJ2012.0024" ext-link-type="DOI">10.2136/SSSAJ2012.0024</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx13"><?xmltex \def\ref@label{{Guillaume et~al.(2023)}}?><label>Guillaume et al.(2023)</label><?label Guillaume2023?><mixed-citation>
Guillaume, B., Aroui Boukbida, H., Bakker, G., Bieganowski, A., Brostaux, Y., Cornelis, W., Durner, W., Hartmann, C., Iversen, B. V.,
Javaux, M., Ingwersen, J., Lamorski, K., Lamparter, A., Makó, A., Mingot Soriano, A. M., Messing, I., Nemes, A., Pomes-Bordedebat,
A., van der Ploeg, M., Weber, T. K. D., Weihermüller, L., Wellens, J., and Degré, A.: Reprod<?pagebreak page380?>ucibility of the wet part of the soil water
retention curve: a European interlaboratory comparison [code, data set], https://doi.org/10.5281/zenodo.7943957, 2023.</mixed-citation></ref>
      <ref id="bib1.bibx14"><?xmltex \def\ref@label{{Hopmans et~al.(2002)Hopmans, Šimůnek, Romano, and
Durner}}?><label>Hopmans et al.(2002)Hopmans, Šimůnek, Romano, and
Durner</label><?label hopmans_362_2002?><mixed-citation>Hopmans, J. W., Šimůnek, J., Romano, N., and Durner, W.: 3.6.2. Inverse
Methods, in: Methods of Soil Analysis, John Wiley &amp;
Sons, Ltd, 963–1008, <ext-link xlink:href="https://doi.org/10.2136/sssabookser5.4.c40" ext-link-type="DOI">10.2136/sssabookser5.4.c40</ext-link>, 2002.</mixed-citation></ref>
      <ref id="bib1.bibx15"><?xmltex \def\ref@label{{Houst(1993)}}?><label>Houst(1993)</label><?label houst_diffusion_1993?><mixed-citation>Houst, Y. F.: Diffusion de gaz, carbonatation et retrait de la pâte de ciment
durcie, PhD. thesis, EPFL, Lausanne, <ext-link xlink:href="https://doi.org/10.5075/epfl-thesis-1108" ext-link-type="DOI">10.5075/epfl-thesis-1108</ext-link>, 1993.</mixed-citation></ref>
      <ref id="bib1.bibx16"><?xmltex \def\ref@label{{Hunt et~al.(2013)Hunt, Ewing, and Horton}}?><label>Hunt et al.(2013)Hunt, Ewing, and Horton</label><?label Hunt2013?><mixed-citation>Hunt, A. G., Ewing, R. P., and Horton, R.: What's Wrong with Soil Physics?,
Soil Sci. Soc. Am. J., 77, 1877–1887,
<ext-link xlink:href="https://doi.org/10.2136/SSSAJ2013.01.0020" ext-link-type="DOI">10.2136/SSSAJ2013.01.0020</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx17"><?xmltex \def\ref@label{{Klute(1986)}}?><label>Klute(1986)</label><?label Klute1986?><mixed-citation>Klute, A.: Water Retention: Laboratory Methods, Methods of Soil Analysis, Part
1: Physical and Mineralogical Methods,  635–662,
<ext-link xlink:href="https://doi.org/10.2136/SSSABOOKSER5.1.2ED.C26" ext-link-type="DOI">10.2136/SSSABOOKSER5.1.2ED.C26</ext-link>, 1986.</mixed-citation></ref>
      <ref id="bib1.bibx18"><?xmltex \def\ref@label{{Madsen et~al.(1986)Madsen, JENSEN, and BOYSEN}}?><label>Madsen et al.(1986)Madsen, JENSEN, and BOYSEN</label><?label MADSEN1986?><mixed-citation>Madsen, H. B., JENSEN, C. R., and BOYSEN, T.: A comparison of the thermocouple
psychrometer and the pressure plate methods for determination of soil water
characteristic curves, J. Soil Sci., 37, 357–362,
<ext-link xlink:href="https://doi.org/10.1111/J.1365-2389.1986.TB00368.X" ext-link-type="DOI">10.1111/J.1365-2389.1986.TB00368.X</ext-link>, 1986.</mixed-citation></ref>
      <ref id="bib1.bibx19"><?xmltex \def\ref@label{{Mosquera et~al.(2021)Mosquera, Franklin, Jan, Rolando, Lutz, David,
and Patricio}}?><label>Mosquera et al.(2021)Mosquera, Franklin, Jan, Rolando, Lutz, David,
and Patricio</label><?label Mosquera2021?><mixed-citation>Mosquera, G. M., Franklin, M., Jan, F., Rolando, C., Lutz, B., David, W., and
Patricio, C.: A field, laboratory, and literature review evaluation of the
water retention curve of volcanic ash soils: How well do standard laboratory
methods reflect field conditions?, Hydrol. Proc., 35,  e14011,
<ext-link xlink:href="https://doi.org/10.1002/HYP.14011" ext-link-type="DOI">10.1002/HYP.14011</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx20"><?xmltex \def\ref@label{{Nemes et~al.(2001)Nemes, Schaap, Leij, and
Wösten}}?><label>Nemes et al.(2001)Nemes, Schaap, Leij, and
Wösten</label><?label nemes_description_2001?><mixed-citation>Nemes, A., Schaap, M. G., Leij, F. J., and Wösten, J. H. M.: Description of
the unsaturated soil hydraulic database UNSODA version 2.0, J.   Hydrol., 251, 151–162, <ext-link xlink:href="https://doi.org/10.1016/S0022-1694(01)00465-6" ext-link-type="DOI">10.1016/S0022-1694(01)00465-6</ext-link>, 2001.</mixed-citation></ref>
      <ref id="bib1.bibx21"><?xmltex \def\ref@label{{Peters and Durner(2008)}}?><label>Peters and Durner(2008)</label><?label Peters2008?><mixed-citation>Peters, A. and Durner, W.: Simplified evaporation method for determining soil
hydraulic properties, J. Hydrol., 356, 147–162,
<ext-link xlink:href="https://doi.org/10.1016/J.JHYDROL.2008.04.016" ext-link-type="DOI">10.1016/J.JHYDROL.2008.04.016</ext-link>, 2008.</mixed-citation></ref>
      <ref id="bib1.bibx22"><?xmltex \def\ref@label{{Reynolds and Topp(1993)}}?><label>Reynolds and Topp(1993)</label><?label Reynolds1993?><mixed-citation>
Reynolds, W. and Topp, G. C.: Soil Water Desorption and Imbibition: Tension and Pressure Techniques, in: Soil Sampling and Methods of
Analysis, 1017–1034, publisher: CRC Press, 1993.</mixed-citation></ref>
      <ref id="bib1.bibx23"><?xmltex \def\ref@label{{Richards and Ogata(1961)}}?><label>Richards and Ogata(1961)</label><?label Richards1961?><mixed-citation>Richards, L. A. and Ogata, G.: Psychrometric Measurements of Soil Samples
Equilibrated on Pressure Membranes, Soil Sci. Soc. Am. J.,
25, 456–459, <ext-link xlink:href="https://doi.org/10.2136/SSSAJ1961.03615995002500060012X" ext-link-type="DOI">10.2136/SSSAJ1961.03615995002500060012X</ext-link>, 1961.</mixed-citation></ref>
      <ref id="bib1.bibx24"><?xmltex \def\ref@label{{Ross et~al.(1991)Ross, Williams, and
Bristow}}?><label>Ross et al.(1991)Ross, Williams, and
Bristow</label><?label Ross1991?><mixed-citation>Ross, P. J., Williams, J., and Bristow, K. L.: Equation for Extending
Water-Retention Curves to Dryness, Soil Sci. Soc. Am. J.,
55, 923–927, <ext-link xlink:href="https://doi.org/10.2136/sssaj1991.03615995005500040004x" ext-link-type="DOI">10.2136/sssaj1991.03615995005500040004x</ext-link>, 1991.</mixed-citation></ref>
      <ref id="bib1.bibx25"><?xmltex \def\ref@label{{Schelle et~al.(2013)Schelle, Heise, Jänicke, and
Durner}}?><label>Schelle et al.(2013)Schelle, Heise, Jänicke, and
Durner</label><?label Schelle2013?><mixed-citation>Schelle, H., Heise, L., Jänicke, K., and Durner, W.: Water retention
characteristics of soils over the whole moisture range: a comparison of
laboratory methods, Europ. J. Soil Sci., 64, 814–821,
<ext-link xlink:href="https://doi.org/10.1111/EJSS.12108" ext-link-type="DOI">10.1111/EJSS.12108</ext-link>, 2013.
</mixed-citation></ref><?xmltex \hack{\newpage}?>
      <ref id="bib1.bibx26"><?xmltex \def\ref@label{{Silva et~al.(2018)Silva, Libardi, and Gimenes}}?><label>Silva et al.(2018)Silva, Libardi, and Gimenes</label><?label silva_soil_2018?><mixed-citation>Silva, M. L. d. N., Libardi, P. L., and Gimenes, F. H. S.: Soil Water
Retention Curve as Affected by Sample Height, Revista Brasileira de
Ciência do Solo, 42, <ext-link xlink:href="https://doi.org/10.1590/18069657RBCS20180058" ext-link-type="DOI">10.1590/18069657RBCS20180058</ext-link>, 2018.</mixed-citation></ref>
      <ref id="bib1.bibx27"><?xmltex \def\ref@label{{Solone et~al.(2012)Solone, Bittelli, Tomei, and Morari}}?><label>Solone et al.(2012)Solone, Bittelli, Tomei, and Morari</label><?label Solone2012?><mixed-citation>Solone, R., Bittelli, M., Tomei, F., and Morari, F.: Errors in water retention
curves determined with pressure plates: Effects on the soil water balance,
J. Hydrol., 470, 65–74, <ext-link xlink:href="https://doi.org/10.1016/J.JHYDROL.2012.08.017" ext-link-type="DOI">10.1016/J.JHYDROL.2012.08.017</ext-link>,
2012.</mixed-citation></ref>
      <ref id="bib1.bibx28"><?xmltex \def\ref@label{{Tóth et~al.(2015)Tóth, Weynants, Nemes, Makó, Bilas, and
Tóth}}?><label>Tóth et al.(2015)Tóth, Weynants, Nemes, Makó, Bilas, and
Tóth</label><?label Toth2015?><mixed-citation>Tóth, B., Weynants, M., Nemes, A., Makó, A., Bilas, G., and Tóth, G.: New
generation of hydraulic pedotransfer functions for Europe, Europ. J. Soil Sci., 66, 226–238, <ext-link xlink:href="https://doi.org/10.1111/EJSS.12192" ext-link-type="DOI">10.1111/EJSS.12192</ext-link>, 2015.</mixed-citation></ref>
      <ref id="bib1.bibx29"><?xmltex \def\ref@label{{Tóth et~al.(2017)Tóth, Weynants, Pásztor, and
Hengl}}?><label>Tóth et al.(2017)Tóth, Weynants, Pásztor, and
Hengl</label><?label toth_3d_2017?><mixed-citation>Tóth, B., Weynants, M., Pásztor, L., and Hengl, T.: 3D soil hydraulic
database of Europe at 250 m resolution, Hydrol. Proc., 31,
2662–2666, <ext-link xlink:href="https://doi.org/10.1002/hyp.11203" ext-link-type="DOI">10.1002/hyp.11203</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx30"><?xmltex \def\ref@label{{Van~Looy et~al.(2017)Van~Looy, Bouma, Herbst, Koestel, Minasny,
Mishra, Montzka, Nemes, Pachepsky, Padarian, Schaap, Tóth, Verhoef,
Vanderborght, van~der Ploeg, Weihermüller, Zacharias, Zhang, and
Vereecken}}?><label>Van Looy et al.(2017)Van Looy, Bouma, Herbst, Koestel, Minasny,
Mishra, Montzka, Nemes, Pachepsky, Padarian, Schaap, Tóth, Verhoef,
Vanderborght, van der Ploeg, Weihermüller, Zacharias, Zhang, and
Vereecken</label><?label van_looy_pedotransfer_2017?><mixed-citation>Van Looy, K., Bouma, J., Herbst, M., Koestel, J., Minasny, B., Mishra, U.,
Montzka, C., Nemes, A., Pachepsky, Y. A., Padarian, J., Schaap, M. G., Tóth,
B., Verhoef, A., Vanderborght, J., van der Ploeg, M. J., Weihermüller, L.,
Zacharias, S., Zhang, Y., and Vereecken, H.: Pedotransfer Functions in
Earth System Science: Challenges and Perspectives, Rev.
Geophys., 55, 1199–1256, <ext-link xlink:href="https://doi.org/10.1002/2017RG000581" ext-link-type="DOI">10.1002/2017RG000581</ext-link>, 2017.</mixed-citation></ref>
      <ref id="bib1.bibx31"><?xmltex \def\ref@label{{Vereecken et~al.(2010)Vereecken, Weynants, Javaux, Pachepsky, Schaap,
and van Genuchten}}?><label>Vereecken et al.(2010)Vereecken, Weynants, Javaux, Pachepsky, Schaap,
and van Genuchten</label><?label Vereecken2010?><mixed-citation>Vereecken, H., Weynants, M., Javaux, M., Pachepsky, Y., Schaap, M. G., and van
Genuchten, M.: Using Pedotransfer Functions to Estimate the van
Genuchten–Mualem Soil Hydraulic Properties: A Review, Vadose Zone J.,
9, 795–820, <ext-link xlink:href="https://doi.org/10.2136/VZJ2010.0045" ext-link-type="DOI">10.2136/VZJ2010.0045</ext-link>, 2010.</mixed-citation></ref>
      <ref id="bib1.bibx32"><?xmltex \def\ref@label{{Weynants et~al.(2013)Weynants, Montanarella, Tóth, Arnoldussen,
Anaya~Romero, Bilas, Børresen, Cornelis, Daroussin, Gonçalves, Haugen,
Hennings, Houskova, Iovino, Javaux, Keay, Kätterer, Kværnø, Laktinova,
Lamorski, Lilly, Makó, Matula, Morari, Nemes, Patyka, Romano, Schindler,
Shein, Sławiński, Strauss, Tóth, and Woesten}}?><label>Weynants et al.(2013)Weynants, Montanarella, Tóth, Arnoldussen,
Anaya Romero, Bilas, Børresen, Cornelis, Daroussin, Gonçalves, Haugen,
Hennings, Houskova, Iovino, Javaux, Keay, Kätterer, Kværnø, Laktinova,
Lamorski, Lilly, Makó, Matula, Morari, Nemes, Patyka, Romano, Schindler,
Shein, Sławiński, Strauss, Tóth, and Woesten</label><?label 5988012?><mixed-citation>Weynants, M., Montanarella, L., Tóth, G., Arnoldussen, A., Anaya Romero, M.,
Bilas, G., Børresen, T., Cornelis, W., Daroussin, J., Gonçalves, M. D. C.,
Haugen, L.-E., Hennings, V., Houskova, B., Iovino, M., Javaux, M., Keay,
C. A., Kätterer, T., Kværnø, S., Laktinova, T., Lamorski, K., Lilly, A.,
Makó, A., Matula, S., Morari, F., Nemes, A., Patyka, N. V., Romano, N.,
Schindler, U., Shein, E., Sławiński, C., Strauss, P., Tóth, B., and
Woesten, H.: European HYdropedological Data Inventory (EU-HYDI),
<ext-link xlink:href="https://doi.org/10.2788/5936" ext-link-type="DOI">10.2788/5936</ext-link>, 2013.</mixed-citation></ref>
      <ref id="bib1.bibx33"><?xmltex \def\ref@label{{Wösten et~al.(1999)Wösten, Lilly, Nemes, and
Le~Bas}}?><label>Wösten et al.(1999)Wösten, Lilly, Nemes, and
Le Bas</label><?label wosten_development_1999?><mixed-citation>Wösten, J. H. M., Lilly, A., Nemes, A., and Le Bas, C.: Development and use of
a database of hydraulic properties of European soils, Geoderma, 90,
169–185, <ext-link xlink:href="https://doi.org/10.1016/S0016-7061(98)00132-3" ext-link-type="DOI">10.1016/S0016-7061(98)00132-3</ext-link>, 1999.</mixed-citation></ref>
      <ref id="bib1.bibx34"><?xmltex \def\ref@label{{Zeitoun et~al.(2021)Zeitoun, Vandergeest, Vasava, Machado, Jordan,
Parkin, Wagner-Riddle, and Biswas}}?><label>Zeitoun et al.(2021)Zeitoun, Vandergeest, Vasava, Machado, Jordan,
Parkin, Wagner-Riddle, and Biswas</label><?label s21020447?><mixed-citation>Zeitoun, R., Vandergeest, M., Vasava, H. B., Machado, P. V. F., Jordan, S.,
Parkin, G., Wagner-Riddle, C., and Biswas, A.: In-Situ Estimation of Soil
Water Retention Curve in Silt Loam and Loamy Sand Soils at Different Soil
Depths, Sensors, 21,  447, <ext-link xlink:href="https://doi.org/10.3390/s21020447" ext-link-type="DOI">10.3390/s21020447</ext-link>, 2021.</mixed-citation></ref>
      <ref id="bib1.bibx35"><?xmltex \def\ref@label{{Šavija and Luković(2016)}}?><label>Šavija and Luković(2016)</label><?label savija_carbonation_2016?><mixed-citation>Šavija, B. and Luković, M.: Carbonation of cement paste: Understanding,
challenges, and opportunities, Construct. Build. Mat., 117,
285–301, <ext-link xlink:href="https://doi.org/10.1016/j.conbuildmat.2016.04.138" ext-link-type="DOI">10.1016/j.conbuildmat.2016.04.138</ext-link>, 2016.</mixed-citation></ref>

  </ref-list></back>
    <!--<article-title-html>Reproducibility of the wet part of the soil water retention curve: a European interlaboratory comparison</article-title-html>
<abstract-html/>
<ref-html id="bib1.bib1"><label>Auroy et al.(2015)Auroy, Poyet, Le Bescop, Torrenti, Charpentier,
Moskura, and Bourbon</label><mixed-citation>
      
Auroy, M., Poyet, S., Le Bescop, P., Torrenti, J.-M., Charpentier, T., Moskura,
M., and Bourbon, X.: Impact of carbonation on unsaturated water transport
properties of cement-based materials, Cement Concrete Res., 74,
44–58, <a href="https://doi.org/10.1016/j.cemconres.2015.04.002" target="_blank">https://doi.org/10.1016/j.cemconres.2015.04.002</a>, 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib2"><label>Bittelli and Flury(2009)</label><mixed-citation>
      
Bittelli, M. and Flury, M.: Errors in Water Retention Curves Determined with
Pressure Plates, Soil Sci. Soc. Am. J., 73, 1453–1460,
<a href="https://doi.org/10.2136/SSSAJ2008.0082" target="_blank">https://doi.org/10.2136/SSSAJ2008.0082</a>, 2009.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib3"><label>Buchter et al.(2015)Buchter, Berli, and
Weisskopf</label><mixed-citation>
      
Buchter, B., Berli, M., and Weisskopf, P.: Interlaboratory comparison of soil
physical parameters, Agroscope Sci., 11, 1–21,
<a href="https://ira.agroscope.ch/en-US/Page/Publikation/Index/34807" target="_blank"/> (last access: 15 April 2023),
2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib4"><label>Carpenter et al.(2017)Carpenter, Gelman, Hoffman, Lee, Goodrich,
Betancourt, Brubaker, Guo, Li, and Riddell</label><mixed-citation>
      
Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B., Betancourt,
M., Brubaker, M., Guo, J., Li, P., and Riddell, A.: Stan: A probabilistic
programming language, J. Stat. Softw., 76, 1–32,
<a href="https://doi.org/10.18637/jss.v076.i01" target="_blank">https://doi.org/10.18637/jss.v076.i01</a>, 2017.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib5"><label>Cresswell et al.(2008)Cresswell, Green, and McKenzie</label><mixed-citation>
      
Cresswell, H. P., Green, T. W., and McKenzie, N. J.: The Adequacy of Pressure
Plate Apparatus for Determining Soil Water Retention, Soil Sci. Soc.
Am. J., 72, 41–49, <a href="https://doi.org/10.2136/SSSAJ2006.0182" target="_blank">https://doi.org/10.2136/SSSAJ2006.0182</a>, 2008.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib6"><label>Dane and Hopmans(2002)</label><mixed-citation>
      
Dane, J. H. and Hopmans, J. W.: 3.3.2 Laboratory, in: Methods of Soil
Analysis,  John Wiley &amp; Sons, Ltd, 675–720,
<a href="https://doi.org/10.2136/sssabookser5.4.c25" target="_blank">https://doi.org/10.2136/sssabookser5.4.c25</a>, 2002.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib7"><label>de Jong van Lier et al.(2019)de Jong van Lier, Pinheiro, and
Inforsato</label><mixed-citation>
      
de Jong van Lier, Q., Pinheiro, E. A. R., and Inforsato, L.: Hydrostatic
equilibrium between soil samples and pressure plates used in soil water
retention determination: Consequences of a questionable assumption, Revista
Brasileira de Ciencia do Solo, 43, <a href="https://doi.org/10.1590/18069657RBCS20190014" target="_blank">https://doi.org/10.1590/18069657RBCS20190014</a>, 2019.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib8"><label>Diamantopoulos and
Durner(2012)</label><mixed-citation>
      
Diamantopoulos, E. and Durner, W.: Dynamic Nonequilibrium of Water Flow in
Porous Media: A Review, Vadose Zone J., 11, vzj2011.0197,
<a href="https://doi.org/10.2136/vzj2011.0197" target="_blank">https://doi.org/10.2136/vzj2011.0197</a>, 2012.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib9"><label>Gee et al.(1992)Gee, Campbell, Campbell, and
Campbell</label><mixed-citation>
      
Gee, G. W., Campbell, M. D., Campbell, G. S., and Campbell, J. H.: Rapid
Measurement of Low Soil Water Potentials Using a Water
Activity Meter, Soil Sci. Soc. Am. J., 56, 1068–1070,
<a href="https://doi.org/10.2136/sssaj1992.03615995005600040010x" target="_blank">https://doi.org/10.2136/sssaj1992.03615995005600040010x</a>, 1992.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib10"><label>Gee et al.(2002)Gee, Ward, Zhang, Campbell, and Mathison</label><mixed-citation>
      
Gee, G. W., Ward, A. L., Zhang, Z. F., Campbell, G. S., and Mathison, J.: The
Influence of Hydraulic Nonequilibrium on Pressure Plate Data, Vadose Zone
J., 1, 172–178, <a href="https://doi.org/10.2113/1.1.172" target="_blank">https://doi.org/10.2113/1.1.172</a>, 2002.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib11"><label>Ghanbarian et al.(2015)Ghanbarian, Taslimitehrani, Dong, and
Pachepsky</label><mixed-citation>
      
Ghanbarian, B., Taslimitehrani, V., Dong, G., and Pachepsky, Y. A.: Sample
dimensions effect on prediction of soil water retention curve and saturated
hydraulic conductivity, J.  Hydrol., 528, 127–137,
<a href="https://doi.org/10.1016/j.jhydrol.2015.06.024" target="_blank">https://doi.org/10.1016/j.jhydrol.2015.06.024</a>, 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib12"><label>Gubiani et al.(2013)Gubiani, Reichert, Campbell, Reinert, and
Gelain</label><mixed-citation>
      
Gubiani, P. I., Reichert, J. M., Campbell, C., Reinert, D. J., and Gelain,
N. S.: Assessing Errors and Accuracy in Dew-Point Potentiometer and Pressure
Plate Extractor Meaurements, Soil Sci. Soc. Am. J., 77,
19–24, <a href="https://doi.org/10.2136/SSSAJ2012.0024" target="_blank">https://doi.org/10.2136/SSSAJ2012.0024</a>, 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib13"><label>Guillaume et al.(2023)</label><mixed-citation>
      
Guillaume, B., Aroui Boukbida, H., Bakker, G., Bieganowski, A., Brostaux, Y., Cornelis, W., Durner, W., Hartmann, C., Iversen, B. V.,
Javaux, M., Ingwersen, J., Lamorski, K., Lamparter, A., Makó, A., Mingot Soriano, A. M., Messing, I., Nemes, A., Pomes-Bordedebat,
A., van der Ploeg, M., Weber, T. K. D., Weihermüller, L., Wellens, J., and Degré, A.: Reproducibility of the wet part of the soil water
retention curve: a European interlaboratory comparison [code, data set], https://doi.org/10.5281/zenodo.7943957, 2023.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib14"><label>Hopmans et al.(2002)Hopmans, Šimůnek, Romano, and
Durner</label><mixed-citation>
      
Hopmans, J. W., Šimůnek, J., Romano, N., and Durner, W.: 3.6.2. Inverse
Methods, in: Methods of Soil Analysis, John Wiley &amp;
Sons, Ltd, 963–1008, <a href="https://doi.org/10.2136/sssabookser5.4.c40" target="_blank">https://doi.org/10.2136/sssabookser5.4.c40</a>, 2002.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib15"><label>Houst(1993)</label><mixed-citation>
      
Houst, Y. F.: Diffusion de gaz, carbonatation et retrait de la pâte de ciment
durcie, PhD. thesis, EPFL, Lausanne, <a href="https://doi.org/10.5075/epfl-thesis-1108" target="_blank">https://doi.org/10.5075/epfl-thesis-1108</a>, 1993.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib16"><label>Hunt et al.(2013)Hunt, Ewing, and Horton</label><mixed-citation>
      
Hunt, A. G., Ewing, R. P., and Horton, R.: What's Wrong with Soil Physics?,
Soil Sci. Soc. Am. J., 77, 1877–1887,
<a href="https://doi.org/10.2136/SSSAJ2013.01.0020" target="_blank">https://doi.org/10.2136/SSSAJ2013.01.0020</a>, 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib17"><label>Klute(1986)</label><mixed-citation>
      
Klute, A.: Water Retention: Laboratory Methods, Methods of Soil Analysis, Part
1: Physical and Mineralogical Methods,  635–662,
<a href="https://doi.org/10.2136/SSSABOOKSER5.1.2ED.C26" target="_blank">https://doi.org/10.2136/SSSABOOKSER5.1.2ED.C26</a>, 1986.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib18"><label>Madsen et al.(1986)Madsen, JENSEN, and BOYSEN</label><mixed-citation>
      
Madsen, H. B., JENSEN, C. R., and BOYSEN, T.: A comparison of the thermocouple
psychrometer and the pressure plate methods for determination of soil water
characteristic curves, J. Soil Sci., 37, 357–362,
<a href="https://doi.org/10.1111/J.1365-2389.1986.TB00368.X" target="_blank">https://doi.org/10.1111/J.1365-2389.1986.TB00368.X</a>, 1986.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib19"><label>Mosquera et al.(2021)Mosquera, Franklin, Jan, Rolando, Lutz, David,
and Patricio</label><mixed-citation>
      
Mosquera, G. M., Franklin, M., Jan, F., Rolando, C., Lutz, B., David, W., and
Patricio, C.: A field, laboratory, and literature review evaluation of the
water retention curve of volcanic ash soils: How well do standard laboratory
methods reflect field conditions?, Hydrol. Proc., 35,  e14011,
<a href="https://doi.org/10.1002/HYP.14011" target="_blank">https://doi.org/10.1002/HYP.14011</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib20"><label>Nemes et al.(2001)Nemes, Schaap, Leij, and
Wösten</label><mixed-citation>
      
Nemes, A., Schaap, M. G., Leij, F. J., and Wösten, J. H. M.: Description of
the unsaturated soil hydraulic database UNSODA version 2.0, J.   Hydrol., 251, 151–162, <a href="https://doi.org/10.1016/S0022-1694(01)00465-6" target="_blank">https://doi.org/10.1016/S0022-1694(01)00465-6</a>, 2001.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib21"><label>Peters and Durner(2008)</label><mixed-citation>
      
Peters, A. and Durner, W.: Simplified evaporation method for determining soil
hydraulic properties, J. Hydrol., 356, 147–162,
<a href="https://doi.org/10.1016/J.JHYDROL.2008.04.016" target="_blank">https://doi.org/10.1016/J.JHYDROL.2008.04.016</a>, 2008.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib22"><label>Reynolds and Topp(1993)</label><mixed-citation>
      
Reynolds, W. and Topp, G. C.: Soil Water Desorption and Imbibition: Tension and Pressure Techniques, in: Soil Sampling and Methods of
Analysis, 1017–1034, publisher: CRC Press, 1993.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib23"><label>Richards and Ogata(1961)</label><mixed-citation>
      
Richards, L. A. and Ogata, G.: Psychrometric Measurements of Soil Samples
Equilibrated on Pressure Membranes, Soil Sci. Soc. Am. J.,
25, 456–459, <a href="https://doi.org/10.2136/SSSAJ1961.03615995002500060012X" target="_blank">https://doi.org/10.2136/SSSAJ1961.03615995002500060012X</a>, 1961.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib24"><label>Ross et al.(1991)Ross, Williams, and
Bristow</label><mixed-citation>
      
Ross, P. J., Williams, J., and Bristow, K. L.: Equation for Extending
Water-Retention Curves to Dryness, Soil Sci. Soc. Am. J.,
55, 923–927, <a href="https://doi.org/10.2136/sssaj1991.03615995005500040004x" target="_blank">https://doi.org/10.2136/sssaj1991.03615995005500040004x</a>, 1991.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib25"><label>Schelle et al.(2013)Schelle, Heise, Jänicke, and
Durner</label><mixed-citation>
      
Schelle, H., Heise, L., Jänicke, K., and Durner, W.: Water retention
characteristics of soils over the whole moisture range: a comparison of
laboratory methods, Europ. J. Soil Sci., 64, 814–821,
<a href="https://doi.org/10.1111/EJSS.12108" target="_blank">https://doi.org/10.1111/EJSS.12108</a>, 2013.


    </mixed-citation></ref-html>
<ref-html id="bib1.bib26"><label>Silva et al.(2018)Silva, Libardi, and Gimenes</label><mixed-citation>
      
Silva, M. L. d. N., Libardi, P. L., and Gimenes, F. H. S.: Soil Water
Retention Curve as Affected by Sample Height, Revista Brasileira de
Ciência do Solo, 42, <a href="https://doi.org/10.1590/18069657RBCS20180058" target="_blank">https://doi.org/10.1590/18069657RBCS20180058</a>, 2018.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib27"><label>Solone et al.(2012)Solone, Bittelli, Tomei, and Morari</label><mixed-citation>
      
Solone, R., Bittelli, M., Tomei, F., and Morari, F.: Errors in water retention
curves determined with pressure plates: Effects on the soil water balance,
J. Hydrol., 470, 65–74, <a href="https://doi.org/10.1016/J.JHYDROL.2012.08.017" target="_blank">https://doi.org/10.1016/J.JHYDROL.2012.08.017</a>,
2012.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib28"><label>Tóth et al.(2015)Tóth, Weynants, Nemes, Makó, Bilas, and
Tóth</label><mixed-citation>
      
Tóth, B., Weynants, M., Nemes, A., Makó, A., Bilas, G., and Tóth, G.: New
generation of hydraulic pedotransfer functions for Europe, Europ. J. Soil Sci., 66, 226–238, <a href="https://doi.org/10.1111/EJSS.12192" target="_blank">https://doi.org/10.1111/EJSS.12192</a>, 2015.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib29"><label>Tóth et al.(2017)Tóth, Weynants, Pásztor, and
Hengl</label><mixed-citation>
      
Tóth, B., Weynants, M., Pásztor, L., and Hengl, T.: 3D soil hydraulic
database of Europe at 250&thinsp;m resolution, Hydrol. Proc., 31,
2662–2666, <a href="https://doi.org/10.1002/hyp.11203" target="_blank">https://doi.org/10.1002/hyp.11203</a>, 2017.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib30"><label>Van Looy et al.(2017)Van Looy, Bouma, Herbst, Koestel, Minasny,
Mishra, Montzka, Nemes, Pachepsky, Padarian, Schaap, Tóth, Verhoef,
Vanderborght, van der Ploeg, Weihermüller, Zacharias, Zhang, and
Vereecken</label><mixed-citation>
      
Van Looy, K., Bouma, J., Herbst, M., Koestel, J., Minasny, B., Mishra, U.,
Montzka, C., Nemes, A., Pachepsky, Y. A., Padarian, J., Schaap, M. G., Tóth,
B., Verhoef, A., Vanderborght, J., van der Ploeg, M. J., Weihermüller, L.,
Zacharias, S., Zhang, Y., and Vereecken, H.: Pedotransfer Functions in
Earth System Science: Challenges and Perspectives, Rev.
Geophys., 55, 1199–1256, <a href="https://doi.org/10.1002/2017RG000581" target="_blank">https://doi.org/10.1002/2017RG000581</a>, 2017.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib31"><label>Vereecken et al.(2010)Vereecken, Weynants, Javaux, Pachepsky, Schaap,
and van Genuchten</label><mixed-citation>
      
Vereecken, H., Weynants, M., Javaux, M., Pachepsky, Y., Schaap, M. G., and van
Genuchten, M.: Using Pedotransfer Functions to Estimate the van
Genuchten–Mualem Soil Hydraulic Properties: A Review, Vadose Zone J.,
9, 795–820, <a href="https://doi.org/10.2136/VZJ2010.0045" target="_blank">https://doi.org/10.2136/VZJ2010.0045</a>, 2010.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib32"><label>Weynants et al.(2013)Weynants, Montanarella, Tóth, Arnoldussen,
Anaya Romero, Bilas, Børresen, Cornelis, Daroussin, Gonçalves, Haugen,
Hennings, Houskova, Iovino, Javaux, Keay, Kätterer, Kværnø, Laktinova,
Lamorski, Lilly, Makó, Matula, Morari, Nemes, Patyka, Romano, Schindler,
Shein, Sławiński, Strauss, Tóth, and Woesten</label><mixed-citation>
      
Weynants, M., Montanarella, L., Tóth, G., Arnoldussen, A., Anaya Romero, M.,
Bilas, G., Børresen, T., Cornelis, W., Daroussin, J., Gonçalves, M. D. C.,
Haugen, L.-E., Hennings, V., Houskova, B., Iovino, M., Javaux, M., Keay,
C. A., Kätterer, T., Kværnø, S., Laktinova, T., Lamorski, K., Lilly, A.,
Makó, A., Matula, S., Morari, F., Nemes, A., Patyka, N. V., Romano, N.,
Schindler, U., Shein, E., Sławiński, C., Strauss, P., Tóth, B., and
Woesten, H.: European HYdropedological Data Inventory (EU-HYDI),
<a href="https://doi.org/10.2788/5936" target="_blank">https://doi.org/10.2788/5936</a>, 2013.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib33"><label>Wösten et al.(1999)Wösten, Lilly, Nemes, and
Le Bas</label><mixed-citation>
      
Wösten, J. H. M., Lilly, A., Nemes, A., and Le Bas, C.: Development and use of
a database of hydraulic properties of European soils, Geoderma, 90,
169–185, <a href="https://doi.org/10.1016/S0016-7061(98)00132-3" target="_blank">https://doi.org/10.1016/S0016-7061(98)00132-3</a>, 1999.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib34"><label>Zeitoun et al.(2021)Zeitoun, Vandergeest, Vasava, Machado, Jordan,
Parkin, Wagner-Riddle, and Biswas</label><mixed-citation>
      
Zeitoun, R., Vandergeest, M., Vasava, H. B., Machado, P. V. F., Jordan, S.,
Parkin, G., Wagner-Riddle, C., and Biswas, A.: In-Situ Estimation of Soil
Water Retention Curve in Silt Loam and Loamy Sand Soils at Different Soil
Depths, Sensors, 21,  447, <a href="https://doi.org/10.3390/s21020447" target="_blank">https://doi.org/10.3390/s21020447</a>, 2021.

    </mixed-citation></ref-html>
<ref-html id="bib1.bib35"><label>Šavija and Luković(2016)</label><mixed-citation>
      
Šavija, B. and Luković, M.: Carbonation of cement paste: Understanding,
challenges, and opportunities, Construct. Build. Mat., 117,
285–301, <a href="https://doi.org/10.1016/j.conbuildmat.2016.04.138" target="_blank">https://doi.org/10.1016/j.conbuildmat.2016.04.138</a>, 2016.

    </mixed-citation></ref-html>--></article>
