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  <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-8-199-2022</article-id><title-group><article-title>Inclusion of biochar in a C dynamics model based on observations from an 8-year field experiment</article-title><alt-title>Inclusion of biochar in a C dynamics model</alt-title>
      </title-group><?xmltex \runningtitle{Inclusion of biochar in a C dynamics model}?><?xmltex \runningauthor{R.~Pulcher et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Pulcher</surname><given-names>Roberta</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff2">
          <name><surname>Balugani</surname><given-names>Enrico</given-names></name>
          <email>enrico.balugani2@unibo.it</email>
        <ext-link>https://orcid.org/0000-0002-3879-9255</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Ventura</surname><given-names>Maurizio</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-5099-0650</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Greggio</surname><given-names>Nicolas</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-7323-134X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Marazza</surname><given-names>Diego</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-9870-5559</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Department of Biological, Geological and Environmental Sciences,
BIGeA,<?xmltex \hack{\break}?> Università di Bologna, Bologna, Italy</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Department of Physics and Astronomy, Università di Bologna,
Bologna, Italy</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Faculty of Science and Technology, Libera Università di Bolzano,
39100 Bozen, Italy</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Enrico Balugani (enrico.balugani2@unibo.it)</corresp></author-notes><pub-date><day>17</day><month>March</month><year>2022</year></pub-date>
      
      <volume>8</volume>
      <issue>1</issue>
      <fpage>199</fpage><lpage>211</lpage>
      <history>
        <date date-type="received"><day>17</day><month>November</month><year>2021</year></date>
           <date date-type="rev-request"><day>22</day><month>November</month><year>2021</year></date>
           <date date-type="rev-recd"><day>3</day><month>February</month><year>2022</year></date>
           <date date-type="accepted"><day>19</day><month>February</month><year>2022</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2022 Roberta Pulcher et al.</copyright-statement>
        <copyright-year>2022</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/8/199/2022/soil-8-199-2022.html">This article is available from https://soil.copernicus.org/articles/8/199/2022/soil-8-199-2022.html</self-uri><self-uri xlink:href="https://soil.copernicus.org/articles/8/199/2022/soil-8-199-2022.pdf">The full text article is available as a PDF file from https://soil.copernicus.org/articles/8/199/2022/soil-8-199-2022.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e133">Biochar production and application as soil amendment is a
promising carbon (C)-negative technology to increase soil C sequestration
and mitigate climate change. However, there is a lack of knowledge about
biochar degradation rate in soil and its effects on native soil organic
carbon (SOC), mainly due to the absence of long-term experiments performed
in field conditions. The aim of this work was to investigate the long-term
degradation rate of biochar in an 8-year field experiment in a poplar
short-rotation coppice plantation in Piedmont (Italy), and to modify the
RothC model to assess and predict how biochar influences soil C dynamics.
The RothC model was modified by including two biochar pools, labile (4 %
of the total biochar mass) and recalcitrant (96 %), and the priming effect
of biochar on SOC. The model was calibrated and validated using data from
the field experiment. The results confirm that biochar degradation can be
faster in field conditions in comparison to laboratory experiments;
nevertheless, it can contribute to a substantial increase in the soil C stock
in the long term. Moreover, this study shows that the modified RothC model
was able to simulate the dynamics of biochar and SOC degradation in soils in
field conditions in the long term, at least in the specific conditions
examined.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e145">Biochar, the solid product of pyrolysis or gasification of biomass, has a
large potential for increasing soil carbon (C) stocks and improving soil
quality worldwide
(Woolf
et al., 2010; Smith, 2016; Thierry, 2018).
Due to its stability and resistance to mineralization, adding biochar to
soil is considered a viable strategy for climate change mitigation
(Lehmann
et al., 2006; Zahida et al., 2017), since it can increase soil C stocks for
hundreds or thousands of years
(Wang et al., 2016). Among the negative emission strategies proposed by IPCC (2014),
biochar has the lowest impact in terms of water footprint, land use and
costs (Smith, 2016).</p>
      <p id="d1e148">In order to assess the potential of biochar for soil C sequestration (SCS),
two things are required: long-term experimental data of biochar degradation
in field conditions and a working model of the degradation of biochar in
soils, in order to generalize and upscale experimental findings. In fact,
the generalization of results from experiments is not easy, since biochar
degradation depends on several factors such as biochar characteristics,
for example, the original feedstock and the production temperature
(Cetin
et al., 2005; Saffari et al., 2020; Ippolito et al., 2020); the characteristics
of the soil to which biochar is applied, such as its clay and mineral
content; and the conditions affecting the soil biochar interaction, like the
climate and the vegetation in the area
(Wang
et al., 2016; Han et al., 2020). Even though many studies have been performed
on biochar degradation in soils, a wide range of degradation rates have been
estimated, mainly from laboratory studies, resulting in large uncertainties
on biochar stability
(Luo
et al., 2011; Fangi et al., 2013; Han et al., 2020).</p>
      <p id="d1e151">Biochar mineralization to CO<inline-formula><mml:math id="M1" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> is mostly described with a double
exponential decay model (Zimmerman et al., 2011), according to which biochar is composed of two fractions with
different degradation rates: a labile fraction with a larger degradation
rate and a recalcitrant fraction with a smaller degradation rate. The labile
fraction constitutes usually about 2 %–5 % of the total mass but can rise
up to 20 % depending on the feedstock used
(Cetin
et al., 2005; Han et al., 2020; Ippolito et al., 2020; Saffari et al., 2020)
and can be directly mineralized by the soil microbial community. The
recalcitrant part makes up the rest of the biochar mass
(Wang et al., 2016) and is usually regarded as resistant to direct microbial oxidation
(Guo
and Chen, 2014; Ippolito et al., 2020). This simple, empirical model, however,
does not take into account the processes that lead to biochar degradation
and cannot be generalized to different climates and soil types, which can
only be included in more complex models describing C dynamics in soil.</p>
      <p id="d1e163">Biochar addition to soil affects the organic C storage not only by directly
increasing the amount of soil C, but also by indirectly influencing the
turnover of native soil organic C (SOC), a phenomenon referred to as the priming
effect
(Kuzyakov
et al., 2014; Maestrini et al., 2015). Biochar has been found to increase
(positive priming effect), decrease (negative priming effect) or have no
effect on soil organic matter degradation (Lehmann and Joseph,
2015), according to soil and biochar type and experimental conditions and
duration (Zimmerman et al., 2011). The priming effect has
been reported to change over time: fresh biochar can have a negative priming
effect at the beginning, while the same, aged biochar can have a positive
priming effect later on
(Jiang et al., 2019). The
determination of the priming effect of biochar on SOC is fundamental to
determining the C sequestration potential of biochar
(Gurwick et al., 2013).</p>
      <p id="d1e167">The degradation rate of biochar and its interaction with SOC are usually
estimated through laboratory incubation studies (Leng et al., 2019b); most of them are short term
(Cross and Sohi, 2011;
Bruun et al., 2014) and only a few last for years
(Kuzyakov et al., 2014). However, laboratory studies may not be representative of complex
environmental conditions since they may miss some important processes due to
their controlled conditions (Ventura et al., 2015). Therefore, field experiments are essential in understanding the dynamics
of biochar in soils. Yet, despite their importance, field-scale experimental
studies on soil biochar degradation are still scarce
(Jones
et al., 2012; Gurwick et al., 2013).</p>
      <p id="d1e170">Another relevant aspect affecting the calculation of biochar degradation
rates and its effect on soil organic matter, both in laboratory and field
experiments, is the duration of the study
(Chao et al., 2018). It
has been observed that short-term trials result in lower biochar mean
residence time  (Leng et al., 2019a), due to the decomposition of the labile biochar fraction and an
overestimation of the positive priming effect, which normally occurs in the
first few months. It has been proposed that field studies to determine SOC
degradation rate should have a duration of about 10 years, in order to
detect changes and temporal shifts in trends, and that long-term datasets
should be introduced in established and new models to test their performance
(Smith et al., 2020). Therefore, the results
from medium- and long-term trials are fundamental to assessing the SCS potential
of biochar (Ventura et al., 2019a).</p>
      <p id="d1e173">Models are widely used to generalize SOC dynamic studies and to extend their
findings in space (e.g. obtaining SOC maps for wide areas;
Farina et al., 2018) and/or in time (e.g.
projecting SOC changes in soils to the future, with respect to some soil
management changes;  Meyer et al., 2018). One of the most well-known and widely used models for soil C dynamics
is the RothC model (Coleman and Jenkinson, 1996). The
reason for the success of RothC is that it is a simple model and it requires
relatively few and easily obtainable parameters and input data about
vegetation management, soil and climate characteristics.</p>
      <p id="d1e176">To date, only limited attempts have been made to include biochar degradation
in SOC dynamic models.
Mondini et al. (2017)
modified the RothC model to simulate the mineralization of exogenous organic
matter but without specific model representation for biochar.
Lefebvre et al. (2020) developed a
biochar submodel for RothC, but they did not calibrate nor validate it with
experimental data. Overall, existing models of biochar degradation in soils
rely on literature data deriving from laboratory or short-term studies and
have not been calibrated or validated in dedicated experiments.</p>
      <p id="d1e179">The main objective of this study was to model the degradation of biochar in
field conditions, using a modified version of RothC. Therefore, we (a) modified the RothC model to include biochar and (b) calibrated and validated
the modified RothC using data from a study performed in a short-rotation
coppice plantation over an 8-year period
(Ventura et al., 2019a). Our
specific objectives were as follows:
<list list-type="bullet"><list-item>
      <p id="d1e184">to modify the RothC model to include biochar as a carbon pool and its
priming effect on soil organic matter  (SOM)</p></list-item><list-item>
      <p id="d1e188">to determine the biochar degradation rate under field experimental
conditions in the long term</p></list-item><list-item>
      <p id="d1e192">to verify the priming effect of biochar on SOM in the long term, in
particular, aiming to assess whether the negative priming effect of
biochar previously observed (Ventura et al., 2015) remained the same or not.</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>Experimental data</title>
<sec id="Ch1.S2.SS1.SSS1">
  <label>2.1.1</label><title>Study area</title>
      <p id="d1e217">The experimental field is a short-rotation coppice (SRC) plantation of
poplars (<italic>Populus</italic> <inline-formula><mml:math id="M2" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> <italic>Canadensis Mönch</italic>, Oudemberg genotype), located in Prato Sesia (Novara) in northern
Italy (45<inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>390<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>32.2812<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> N; 8<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>210<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula>16.8339<inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> E;
Ventura et al., 2015, 2019a). Since its establishment in 2010, the SRC
plantation has never been irrigated nor fertilized. The field is arranged in
single rows with a 3 m wide interrow and a plant density of 6600 trees ha<inline-formula><mml:math id="M9" 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>. During the experimental period between 2012 and 2014, trees were
harvested twice: in March 2012, before biochar application, and 2 years
later, in March 2014. After 2014, no other cuts were performed.</p>
      <p id="d1e306">The soil is an Entisol, according to the USDA classification, with a sandy
loam texture (12 % clay, 34 % silt, and 54 % sand). Soil pH is 5.4 (in
water), total soil N content is 0.11 % and SOC content is 1.4 %. The
climate in the study area is classified as temperate with warm summer
(Kottek et al., 2006). Daily averages of air
temperature range between 0  and 25 <inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, with an annual
average of 12 <inline-formula><mml:math id="M11" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C; precipitation, with an annual average of 1500 mm,
increases in intensity during spring and autumn, reaching peaks of 300 mm per month. Relative humidity is on average 51 %. Data were obtained
from the environmental regional agency “Arpa Piemonte”.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS2">
  <label>2.1.2</label><title>Data and flux measurements for model calibration</title>
      <p id="d1e335">Experimental data used to calibrate the model were collected within the
EU-FP7 EuroChar project, with the aim to determine biochar stability and
the priming effect on SOC over a 3-year period, from 2012 until 2014
(Ventura et al., 2015, 2019a). The biochar used was produced from maize
(<italic>Zea mays L.</italic>) silage feedstock pellets by gasification at 1200 <inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, at
atmospheric pressure, with a residence time of 40 min in the gasification
plant (© A.G.T. – Advanced Gasification Technology s.r.l.,
Cremona, Italy). The isotopic signature corresponds to
<inline-formula><mml:math id="M13" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>13.8 ‰, the <inline-formula><mml:math id="M14" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">H</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> atomic ratio is 0.5 and <inline-formula><mml:math id="M15" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">N</mml:mi></mml:mrow></mml:math></inline-formula> is 42.9.
Further information on biochar physicochemical characteristics can be found
in Ventura et al. (2015).</p>
      <p id="d1e381">A completely randomized experimental design was used, with four biochar-treated plots and four control plots. Plots (45 m<inline-formula><mml:math id="M16" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> each) included three
rows of nine plants each. On 30 March 2012, maize biochar (30 t C ha<inline-formula><mml:math id="M17" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>,
corresponding to 16.8 t C ha<inline-formula><mml:math id="M18" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) was incorporated into the first 15 cm
soil layer of the short-rotation coppice by rotary hoeing. Hoeing was also
carried out in control plots, to disturb soil as in biochar-treated plots.</p>
      <p id="d1e417">Monthly above-ground C inputs due to poplar leaf litter were measured directly
on the experimental site using rectangular litter traps, set up in the field
in August 2012, to cover a representative area (from the central row to the
middle of the interrow) of the central interrow of each plot, as described
in Ventura et al. (2019b). Litter
was collected from the traps monthly, from September 2012 to November 2014.
The collected litter was dried at 65 <inline-formula><mml:math id="M19" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in an oven and weighted and
analysed to determine its C content as described for soil samples. As the
poplar plants were not cut anymore after March 2014, the litter C inputs
from the year 2015 to 2020 were calculated using the litter production in the
second year after the first cut (i.e. 2013), which was considered more
similar to the litter production in the following years.</p>
      <p id="d1e429">In six plots (three per treatment), trenched subplots (<inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:mn mathvariant="normal">50</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> cm) were set
up, one per each plot, between two plant rows, by digging 60 cm deep and 15 cm wide trenches. A geotextile canvas (Typar<sup>®</sup>, Dupont,
Wilmington, DE, USA) was inserted in the trenches to isolate each subplot
from root ingrowth, allowing for gas and water exchange. On each subplot, soil
CO<inline-formula><mml:math id="M21" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> efflux (heterotrophic respiration, due to soil microbes and soil
fauna) was measured using an automatic soil respiration system connected to
closed automated chambers. Soil water content (SWC) between 0 and 18 cm
depth and soil temperature at 10 cm were recorded every 30 min using
water content reflectometers (CS-616, Campbell Scientific, Logan UT, USA)
and temperature probes (107, Campbell Scientific, Logan UT, USA),
respectively. Total and heterotrophic respiration measurements were averaged
on a daily basis, and gaps in the database were filled using the model proposed
by Qi and Xu (2001):
              <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M22" display="block"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:msup><mml:mi>T</mml:mi><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msup><mml:mo>⋅</mml:mo><mml:msup><mml:mi mathvariant="normal">SWC</mml:mi><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M23" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is the soil CO<inline-formula><mml:math id="M24" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> efflux (total or heterotrophic),
<inline-formula><mml:math id="M25" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> is the soil temperature (<inline-formula><mml:math id="M26" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C), SWC is the
soil water content (%) and <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> are empirical parameters.</p>
      <p id="d1e560">Soil sampling was carried out in January 2013 and in March 2015, in each of
the four plots per treatment, to determine the total SOC content and the
remaining biochar C stock in soil to a depth of 40 cm
(Ventura et al., 2019a). Maize
biochar has an isotopic signature (<inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">biochar</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">13.8</mml:mn></mml:mrow></mml:math></inline-formula> ‰) distinguishable from that of the SOC in the
plantation (<inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C<inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">SOC</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">23.5</mml:mn></mml:mrow></mml:math></inline-formula> ‰).
This allowed the amount of CO<inline-formula><mml:math id="M34" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> deriving from biochar
degradation and from native SOC degradation to be calculated, using an isotopic mass balance.
The amount of biochar remaining at the end of the experiment, which was 86 %
and 79 % of the original amount in the absence and in the presence of
plant roots, respectively, was estimated by subtracting the C amount
decomposed to CO<inline-formula><mml:math id="M35" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> from the C amount initially added to soil with
biochar application. The degradation rates of biochar were assessed using a
double exponential decay model
(Ventura et al., 2019a): in the presence
of plant roots, the degradation rate of the more recalcitrant biochar
fraction (96 % of the total) was <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.08</mml:mn></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M37" 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>, and the
degradation rate of the labile biochar fraction (4 %) was <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2.55</mml:mn></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M39" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Since environmental conditions can change
(Jiang et al., 2019), we
decided to go back on the field after 8 years and measure the amount of
biochar and SOC with the same methodology of Ventura et al. (2019a).</p>
</sec>
<sec id="Ch1.S2.SS1.SSS3">
  <label>2.1.3</label><title>Determination of SOC and biochar C stock for model validation</title>
      <p id="d1e698">In October 2020, another soil sampling was performed in the plantation, aimed
at quantifying SOC and biochar stocks in soil 8 years after the
beginning of the experiment. In summer 2020, the construction of a methane
pipeline affected the experimental field, disturbing the soil in four out of
the eight original plots. Therefore, the sampling was limited to the four
remaining plots (two biochar-treated and two control plots). From each of
these plots, 10 soil samples were collected, using a 2.5 cm diameter auger
(Eijkelkamp, Giesbeek, the Netherlands), at 0–20  and 20–40 cm depth, for
a total of 80 samples. Samples were collected at 0, 37.5, 75, 112.5, and 150 cm from the central poplar row in each plot along two lines perpendicular to
the plant row, in correspondence to the third and the sixth plant of the
row. Additional soil samples were collected in two points for each plot with
a sample ring kit (Ejikelkamp, Giesbeek, the Netherlands) to calculate the
soil bulk density.</p>
      <p id="d1e701">The collected samples were sieved at 2 mm, finely ground with a ball mill
(Retsch MM 400, Germany) and analysed with a continuous-flow isotopic ratio
mass spectrometer (CF-IRMS, Delta V Advantage, Thermo Fisher Scientific,
Bremen, Germany) for the determination of the content (%) and the
isotopic signature (<inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>C) of the soil organic C. For each plot,
the SOC stock (g C m<inline-formula><mml:math id="M41" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) at 0–20 and 20–40 cm depths was calculated as
follows (Ventura et al., 2019a):
              <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M42" display="block"><mml:mrow><mml:mtext>SOC  stock</mml:mtext><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mn mathvariant="normal">100</mml:mn></mml:mfrac></mml:mstyle><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">soil</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where C<inline-formula><mml:math id="M43" display="inline"><mml:msub><mml:mi/><mml:mi>i</mml:mi></mml:msub></mml:math></inline-formula> is the organic C content (%) at the considered soil layer,
<inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">soil</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the soil bulk density (g m<inline-formula><mml:math id="M45" 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>), and <inline-formula><mml:math id="M46" display="inline"><mml:mi>d</mml:mi></mml:math></inline-formula> is the depth
of the soil layer (0.2 or 0.4 m).</p>
      <p id="d1e799">The fraction of biochar C on total SOC (<inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">B</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) was calculated for each
soil layer by an isotopic mass balance, as follows:
              <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M48" display="block"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">B</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mi mathvariant="normal">B</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mi mathvariant="normal">Biochar</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mi mathvariant="normal">B</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the isotopic
signatures of the SOC in biochar-treated and untreated soils, respectively,
and <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mi mathvariant="normal">Biochar</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the isotopic signature of the applied
biochar (<inline-formula><mml:math id="M52" display="inline"><mml:mo lspace="0mm">-</mml:mo></mml:math></inline-formula>13.8 ‰;
Ventura et al., 2019a).</p>
      <p id="d1e939">Therefore, the biochar C stocks (g C m<inline-formula><mml:math id="M53" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) at 0–20 and 20–40 cm depths
were calculated by multiplying the SOC stock at each layer for the respective
<inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">B</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values. The total soil biochar C stock in the 0–40 cm layer was
obtained by summing the amounts obtained in the two layers. The remaining
amount of biochar C, as a percentage of the initial amount applied to soil
(0–40 cm depth), was therefore calculated. The native SOC stock (excluding
biochar) in biochar-treated soil was obtained by subtracting the biochar C
stock from the total SOC stock (original SOC <inline-formula><mml:math id="M55" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> biochar C) in
biochar-treated plots.</p>
      <p id="d1e973">Measured total SOC stock in biochar-treated and control plots in the
different sampling years was compared using analysis of variance (ANOVA)
with biochar and the year as factors, including the interaction between the two.</p>
</sec>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Modelling</title>
<sec id="Ch1.S2.SS2.SSS1">
  <label>2.2.1</label><title>The RothC model</title>
      <p id="d1e992">RothC-26.3 is a model for the turnover of organic C in non-waterlogged
topsoils, that accounts for the effects of soil properties, temperature,
moisture content and plant cover on the turnover process. RothC was
originally developed with the aim of modelling the organic C turnover of
long-term field experiments in arable soils in Rothamsted (West Common, UK),
then it was adapted to operate in different ecosystems, including croplands,
grasslands and forests
(Coleman and Jenkinson,
1996; Falloon and Smith, 2002). In RothC, SOC is subdivided into four active
carbon pools, where carbon decreases as first-order exponential decay; the
degradation rate constants of the four active compartments used in the model
are <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">DPM</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M57" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for decomposable plant matter (DPM), <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">RPM</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.30</mml:mn></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M59" 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
resistant plant matter (RPM), <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">BIO</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.6</mml:mn></mml:mrow></mml:math></inline-formula>6 yr<inline-formula><mml:math id="M61" 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 microbial biomass (BIO) and <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">HUM</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M63" 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 humified organic matter (HUM). The degradation rates can be modified by three factors which
account for the effect of air temperature (factor <inline-formula><mml:math id="M64" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula>), soil moisture (factor
<inline-formula><mml:math id="M65" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula>) and soil cover (factor <inline-formula><mml:math id="M66" display="inline"><mml:mi>c</mml:mi></mml:math></inline-formula>) on the mineralization rate of SOC. Carbon inputs
enter the soil as either DPM or RPM and then transform into HUM, BIO and
CO<inline-formula><mml:math id="M67" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> with proportions defined by an empirical equation depending on soil
clay content (Eq. 4). HUM and BIO also decompose to CO<inline-formula><mml:math id="M68" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> at every time
step.
              <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M69" display="block"><mml:mrow><mml:mtext>C output</mml:mtext><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">POOL</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">POOL</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">12</mml:mn></mml:mfrac></mml:mstyle></mml:mrow></mml:msup></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where C<inline-formula><mml:math id="M70" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">POOL</mml:mi></mml:msub></mml:math></inline-formula> indicates the specific C pool (BIO, or HUM), and
<inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">POOL</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the specific degradation rate for each
pool. The monthly C  inputs (t C ha<inline-formula><mml:math id="M72" 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>) are defined by the user. The
DPM <inline-formula><mml:math id="M73" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> RPM ratio of the C inputs can be set by the user as well and is usually
chosen amongst the values suggested by the RothC manual (1.4 for most
agricultural crops and improved grasslands;  Coleman and
Jenkinson, 1996).</p>
</sec>
<sec id="Ch1.S2.SS2.SSS2">
  <label>2.2.2</label><title>Modification of the RothC model: BC-RothC</title>
      <p id="d1e1244">The standard RothC model was modified to include two C pools, represented by
the labile (BClab) and recalcitrant (BCrec) biochar fractions (Fig. 1). From
here on, the modified model is defined as the BC-RothC model. The initial
proportions of BClab and BCrec, 4 % and 96 %, and their specific
degradation rates, <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>,
were previously estimated by
Ventura et al. (2019a) for the same
site (Sect. 2.1.2). Before their introduction in the model,
<inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> were divided
by the yearly average rate modifying factors, <inline-formula><mml:math id="M78" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M79" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M80" display="inline"><mml:mi>c</mml:mi></mml:math></inline-formula> (Eq. 5). In
this way, it was possible to extrapolate the decay rates independently of
these environmental factors.
              <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M81" display="block"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">REC</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>;</mml:mo><mml:mspace linebreak="nobreak" width="1em"/><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">LAB</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">REC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the degradation rate of BCrec in the
modified RothC model, and <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">LAB</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the degradation rate
of BClab in the modified RothC model. Since the field measurements showed no
effect of biochar on soil temperature and soil water balance, the equations
for <inline-formula><mml:math id="M84" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M85" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M86" display="inline"><mml:mi>c</mml:mi></mml:math></inline-formula> rate modification were not changed in the BC-RothC model.</p>
      <p id="d1e1420">It was assumed that biochar in soil partly mineralizes into CO<inline-formula><mml:math id="M87" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> and partly
moves into BIO and HUM pools. As Mondini et al. (2017), we assumed biochar does not enter DPM and RPM, which are direct C
input to soil, but contributes to the more stable C pools, BIO and HUM.
CO<inline-formula><mml:math id="M88" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> emitted from biochar-treated soil (heterotrophic respiration) is
given by the sum of the outputs of CO<inline-formula><mml:math id="M89" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> from DPM, RPM, BIO, HUM, BClab
and BCrec.</p>
      <p id="d1e1450">A negative priming effect of biochar on SOC was previously observed at the
same site by
Ventura et al. (2015, 2019a), who reported that biochar reduced SOC degradation by
16 % each year, over a 3-year period. From these observations, the
priming effect was introduced in the model as a constant (<italic>pe</italic> factor)
reducing SOC turnover by 16 %. Consequently, the equation determining the
output of C as CO<inline-formula><mml:math id="M90" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> from the different C pools became
              <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M91" display="block"><mml:mrow><mml:mtext>C output</mml:mtext><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">POOL</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">pe</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">POOL</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">12</mml:mn></mml:mfrac></mml:mstyle></mml:mrow></mml:msup></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <italic>pe</italic> is the priming effect factor, i.e. log(0.16).</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="d1e1527">Modification of the RothC model with the inclusion of labile and
recalcitrant biochar pools and the priming effect on BIO and HUM. The
CO<inline-formula><mml:math id="M92" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> pool is assumed to be comparable to soil heterotrophic respiration.</p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://soil.copernicus.org/articles/8/199/2022/soil-8-199-2022-f01.png"/>

          </fig>

</sec>
<sec id="Ch1.S2.SS2.SSS3">
  <label>2.2.3</label><title>Simulations</title>
      <p id="d1e1553">Modelling was divided in five steps: (1) initially, the unmodified RothC
model (from here on defined as control model) was initialized with a “spin-up run” method (Nemo et al., 2017) to
obtain the proportion in which SOC is split among the four active C pools;
(2) after the spin run, the control model was calibrated using the
experimental data of soil respiration and SOC collected between 2012 and
2014 (Sect. 2.1.2), with the aim to adjust the parameters that introduce
uncertainty in the model; (3) after calibration, the control model was
validated against an 8-year dataset (SOC measurements from 2012 to 2020;
Sect. 2.1.3), to assess the suitability of the unmodified RothC model to
represent SOC dynamics in Prato Sesia control plots; (4) the BC-RothC model
constants were calibrated using heterotrophic respiration and SOC
measurements from biochar-treated plots in 2012–2014; (5) after calibration,
the BC-RothC model was validated with SOC measurements from 2013–2020.</p>
      <p id="d1e1556">The control model was initialized with a spin-up run under the assumption
that the soil at the beginning of the experiment was in equilibrium
condition: the initial C pools were all set to zero, and the model was run
under average meteorological conditions and C inputs, until equilibrium was
reached (i.e. the average yearly SOC stock did not change significantly
anymore). The relative proportion of the different C pools, estimated by the
spin-up run at equilibrium conditions, was therefore used to subdivide the
total amount of SOC measured in the field in 2013
(Ventura et al., 2019a) into the
different RothC pools. Monthly average air temperature and monthly
precipitation data recorded in the area from 2001 to 2020, provided by the
regional environmental agency, were used to define the meteorological
conditions of the “average year” used in the spin-up run (climatic input).
Data about soil characteristics and agricultural practices needed by the
model (soil input) were obtained by previous studies in the area or
estimated using other literature data (Ventura et al., 2015).</p>
      <p id="d1e1559">For the calibration of the control model, monthly average air temperature
and monthly cumulative rainfall in 2012, 2013 and 2014 (climatic inputs)
were obtained via the meteorological station installed in the field
(Ventura et al., 2019a) and from a
nearby meteorological station managed by the regional environmental agency;
monthly evapotranspiration in the period was calculated from meteorological
data with the FAO Penman–Monteith formula (Allen et al., 1998).</p>
      <p id="d1e1562">Soil depth was set to 40 cm. Above-ground C input from poplar plants was set
as measured (see Sect. 2.1.2). Below-ground C input from poplar plants was
estimated from a study performed in a similar poplar SRC plantation in
northern Italy (Ventura et al., 2019b). The monthly above- and below-ground C input from grass was estimated
from studies performed in different areas but in similar conditions
(Zanotelli
et al., 2013; Pausch and Kuzyakov, 2018). The sum of above- and below-ground C
inputs from grass and poplar plants was set as total organic C input to soil
in the control model.</p>
      <p id="d1e1566">The DPM <inline-formula><mml:math id="M93" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> RPM ratio of the organic C input to soil was calculated as the
weighted average of the values for poplar leaves and grass, using their
relative contribution to total soil C input as weights. The DPM <inline-formula><mml:math id="M94" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> RPM ratio
for poplar leaves and grass was set to 1.2 and 2.4, respectively, on the
basis of literature data
(Zanotelli
et al., 2013; Pausch and Kuzyakov, 2018; Ventura et al., 2019b). Monthly soil
cover from vegetation was determined according to field observations in the
experimental period.</p>
      <p id="d1e1583">The control model calibration was performed to adjust the values of the C
input from grass and the soil clay content, which were considered the
parameters with larger uncertainty. Two datasets were used to calibrate the
model: the heterotrophic soil respiration dataset and the SOC stock
measurements. The RothC (and BC-RothC) model calculates the outflow of
CO<inline-formula><mml:math id="M95" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> from the soil due to mineralization of SOM (and biochar), which can
be compared with measured heterotrophic respiration (CO<inline-formula><mml:math id="M96" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> flux
measured in trenched plots). However, the SOC measurements were collected in
untrenched plots; therefore, the model was calibrated by running
simultaneously simulations of trenched and untrenched plots. The daily
heterotrophic respiration measurements were aggregated to obtain monthly
CO<inline-formula><mml:math id="M97" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> flux out of the soil and compared with the CO<inline-formula><mml:math id="M98" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> monthly
production calculated by RothC. The CO<inline-formula><mml:math id="M99" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> measurements, due to their high
frequency and representativity, had a very low uncertainty and are, thus,
much better suited to calibrate the RothC model then SOC measurements
(Mondini
et al., 2017; Leng et al., 2019a). Thus, 100 times more weight was
given to the respiration data than to the SOC measurements for calibration
purposes. The calibration used the Powell optimization method to minimize
the difference between measured and simulated values. The calibration ran
for 3 years and utilized a time step of 0.0625 d<inline-formula><mml:math id="M100" 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>. Validation of
the control model was performed by comparing simulation of SOC trend over
8 years against SOC measurements taken in January 2013, March 2015 and
October 2020.</p>
      <p id="d1e1644">The same climate inputs of the control model were used in the BC-RothC
model. As soil inputs, the adjusted values of C inputs to soil from grass
and soil clay content, resulting from the calibration of the control model,
were used. An extra input of 16 t C ha<inline-formula><mml:math id="M101" 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> due to biochar application was
set at time 0. The initial conditions for the active soil C pools were also
the same as those of the control model, since the assumption is the same
(previous equilibrium conditions, no previous biochar application). The
biochar model calibration was intended to adjust the values of
<inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">LAB</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">REC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which
had been determined starting from a simpler double exponential decay with no
dependence on weather conditions. As in the case of the control model, the
soil respiration and SOC data collected over the same 3-year period in
the biochar-treated plots were used for calibration, and SOC measurements in
2013, 2015 and 2020 were used to validate the prediction of the BC-RothC
model in the long term.</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Experimental data: SOC and biochar C stocks</title>
      <p id="d1e1698">The comparison between SOC stock in control and biochar-treated plots across
the 3 years of sampling (January 2013, March 2015 and October 2020) shows
that the amount of C in biochar-treated plots was always higher than in
control plots, as no interaction between biochar and year was found.
Biochar C stock in the 0–20 cm soil layer decreases from 2013 to 2020, due
to biochar mineralization. In 2013, 81 % of the initial amount of the
added biochar was still present in the soil. This amount decreased to
63.3 % in 2015 and 60.1 % in 2020.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Control model</title>
      <p id="d1e1709">In the spin run, the equilibrium was reached after approximately 2000 months
of simulation (16 years), and the simulated SOC stock was approximately 29 t C ha<inline-formula><mml:math id="M104" 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>, distributed in the different pools according to these
proportions: 1.5 % DPM, 15 % RPM, 2.5 % BIO and 81 % HUM. Multiplying
those percentages by 80.4 t C ha<inline-formula><mml:math id="M105" 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>, which is the SOC stock measured in
2013, the SOC stocks in the four active pools were DPM <inline-formula><mml:math id="M106" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1.0, RPM <inline-formula><mml:math id="M107" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 10.7, BIO <inline-formula><mml:math id="M108" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1.8 and HUM <inline-formula><mml:math id="M109" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 66.8 t C ha<inline-formula><mml:math id="M110" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
      <p id="d1e1777">The control model simulation showed good agreement with measured soil
respiration, even before calibration (Fig. 2a). The calibrated input of C
from grass input was 0.124 t C ha<inline-formula><mml:math id="M111" 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>, 2 times the value set before
calibration, while the calibrated clay content was in the upper limit of the
measured values (17 %). After calibration, the simulated soil respiration
fitted the measurement data closely and generally fell within the standard
error of the measurements, with the exception of summer period, when
downwards peaks were observed in the simulated values but not in the
measured ones, particularly in the year 2012. The initial SOC content (80 t C ha<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>) regularly decreased over 8 years to 70 t C ha<inline-formula><mml:math id="M113" 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> (Fig. 2c). At the end of validation in the year 2020, the projection of SOC content in
control plots (70.3 t C ha<inline-formula><mml:math id="M114" 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 close to the measured value (59.1 t C ha<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>).</p><?xmltex \hack{\newpage}?>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>BC-RothC model</title>
      <p id="d1e1849">The BC-RothC model simulation properly fitted soil respiration measurements,
even before calibration (Fig. 2b). BC-RothC model calibration resulted in a
small change in the degradation rates <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">LAB</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (from 2.55
to 3.6 yr<inline-formula><mml:math id="M117" 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>) and <inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">REC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (from 0.08 to 0.14 yr<inline-formula><mml:math id="M119" 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>), indicating a slightly faster mineralization of biochar. After
calibration, the simulation result fitted the measured data and generally
fell within the error bars, except for the downward summer peaks, in the
same way of the control model simulation.</p>
      <p id="d1e1898">The simulated trend of total SOC (native SOC <inline-formula><mml:math id="M120" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> biochar C) stock shows an
initial peak, due to the addition of biochar into soil (Fig. 2d). At the end
of the simulation (month 105), SOC reaches the value of 79 t C ha<inline-formula><mml:math id="M121" 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>,
which is very close to the measured value (72.4 t C ha<inline-formula><mml:math id="M122" 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>). The
simulated native SOC (without biochar C) was 73 t C ha<inline-formula><mml:math id="M123" 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>; thus, after
8 years of simulation, 5 t C ha<inline-formula><mml:math id="M124" 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> of the total SOC stock in biochar
plots is attributable to biochar C. Furthermore, the native SOC stock
simulated in biochar plots is about 4 t C ha<inline-formula><mml:math id="M125" 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> higher, in 2020, than
control plots (70.3 t C ha<inline-formula><mml:math id="M126" 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>, Fig. 2d). According to the BC-RothC model
prediction, the biochar C amount in soil, 8 years after application, is
5.7 t C ha<inline-formula><mml:math id="M127" 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> (Fig. 2d). This value corresponds to 54.7 % of the
initial biochar C amount, which is about 5 % lower than the measured
remaining amount (60 <inline-formula><mml:math id="M128" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 14 %). Therefore, the BC-RothC model slightly
underestimates the remaining biochar.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e2002"><bold>(a)</bold> Measured (circles) and simulated (lines) heterotrophic
respiration, according to the control model before calibration (solid lines)
and after calibration (dashed lines), across a 3-year period
(2012–2014). <bold>(b)</bold> Measured (circles) and simulated heterotrophic respiration,
according to the biochar model, before calibration (solid lines) and after
calibration (dashed lines), across a 3-year period (2012–2014). <bold>(c)</bold> Calibration (dashed line) and validation (solid line) of control model
against SOC measurements (circles) taken in 2013, 2015 and 2020. <bold>(d)</bold> Measured
(unfilled circles), simulated SOC (solid grey line) and SOC with biochar C
(solid black line) in model validation. Biochar C (filled circle) and
simulated biochar C (dashed line) represent the amount of biochar in soil
without native SOC. Month of simulation 0 corresponds to March 2012, and month
of simulation 105 corresponds to December 2020.</p></caption>
          <?xmltex \igopts{width=503.61378pt}?><graphic xlink:href="https://soil.copernicus.org/articles/8/199/2022/soil-8-199-2022-f02.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussions</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Model performance</title>
      <p id="d1e2038">The RothC model successfully simulated the SOC trend over time in both
control and biochar-treated soil. However, even after calibration, the
control model overestimated the SOC in the first year. This could be due to
the methodological difficulties in measuring SOC changes at yearly scale
because of the high spatial variability of soil in terms of SOC content
(Hoosbeek et al., 2004; Coleman et al., 2004).
Furthermore, the estimation of SOC is affected by the soil bulk density,
which can vary over time. In fact, the bulk density in the first year was
decreased by soil disturbance during hoeing and digging performed in 2012
during biochar application, and in the control plots to ensure homogeneity;
this could have led to an underestimation of the SOC stock in early 2013.
Therefore, SOC simulations could better represent the trend of SOC over time
in comparison to measurements. The same problem was not noticed for biochar
stock, as it was determined using isotopic techniques, which allowed the biochar C in the sampled soil layers to be
estimated more precisely and it to
be distinguished from SOC, independently of bulk density change.</p>
      <p id="d1e2041">However, the cause of the decrease in SOC in time observed both in the
control and in the biochar plots remains unclear. A possible reason could be
that the previous soil management led to an increase in SOC to values larger
than those expected for a soil in equilibrium with the current management
condition (i.e. the poplar short-rotation coppice plantation). Historical
field data would be needed to confirm this hypothesis.</p>
      <p id="d1e2044">The simulation of the soil CO<inline-formula><mml:math id="M129" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> flux from the RothC control model only showed
a marked difference with soil respiration data during summer 2012 and
2013. We can hypothesize that the reason for this difference is the response
of the SOC degradation function to soil moisture. During the summer periods
of 2012 and 2013, the soil in the study area was rather dry, reaching values
of 0.1 m<inline-formula><mml:math id="M130" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M131" 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> in July 2012 and 0.08 m<inline-formula><mml:math id="M132" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M133" 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> in
September 2013 (Ventura et al., 2019a). Due to the soil water content decrease in summer, RothC predicted a
decrease in SOC mineralization rates in summer. However, no such effect of
soil moisture changes on soil respiration was observed in the field. The
overestimation of the effect of soil moisture deficit on soil respiration is
likely due to the fact that its empirical equations have been calibrated in
different climatic and soil conditions. It is possible that the soil
microbial community in the study area is adapted to relatively dry summer
conditions. The adaptation capacity of soil microbial community has been
previously reported (Brangarí
et al., 2020; Shu et al., 2021). Todman and Neal (2021) reported that drying and rewetting events can modulate soil microbial
dynamics, inducing long-lasting microbial acclimation or adaptation
responses. For this reason, we hypothesize that a modification of the
empirical equation between matric potential and the effect on soil
respiration by adapting it to the specific site could improve the fitness of
the simulated CO<inline-formula><mml:math id="M134" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> curve to the experimental data.</p>
      <p id="d1e2108">The heterotrophic respiration simulated in this study using RothC showed a
better data fit than that of the ECOSSE model
(Dondini et al., 2017),
which was evaluated using experimental data collected between 2012 and 2014
in the three different sites, including the same dataset used in the present
study. In fact, the ECOSSE model systematically underestimates the CO<inline-formula><mml:math id="M135" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>
flux, particularly in the summer period when the simulated values are about
half the observed values
(Dondini et al., 2017).</p>
      <p id="d1e2121">The biochar model validation was
also satisfactory, and this seems to support the assumptions made on
biochar C dynamics in soils: (a) biochar C may not be directly mineralized
to CO<inline-formula><mml:math id="M136" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> but may partly transfer to pools with different degradation
rates (BIO and HUM); (b) the dependence of the biochar degradation rates on
environmental variables can be made explicit (i.e. by creating a
relationship of biochar degradation rates from air temperature, soil
moisture deficit and soil coverage). In fact, the inclusion of biochar in
RothC allows degradation rates to be modified using climatic parameters.
According to the BC-RothC model prediction, the remaining biochar amount
8 years after the start of the experiment is only about 5 % lower than
the measured value.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Long-term biochar degradation and priming effect on SOM</title>
      <p id="d1e2141">Biochar degradation was faster than expected on the basis of previous
studies in the same experimental conditions
(Ventura et al., 2019a). Using a
double exponential decay model,
Ventura et al. (2019a) predicted
that 70 % of the initial biochar amount would still be present in the soil
after 8 years. According to this model, the values of
<inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">LAB</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">REC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> obtained by the
authors (2.55 and 0.08, respectively), which do not take environmental
variables into account, were smaller than those obtained in the present
study.</p>
      <p id="d1e2166">This confirms the importance of calibrating the models on the basis of the
specific environmental conditions. The use of empirical models outside of
the specific conditions in which their parameters were determined can lead
to the inability to evaluate the reliability of the model results and
projections. In this case, this would mean using empirical parameters
determined in laboratory experiments to simulate field conditions or
determined in the short term for projection to the long term. Compared to
the degradation rates found by
Wang et al. (2016) in their meta-analysis (<inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">LAB</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.29</mml:mn></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M140" 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>
and <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">REC</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.0018</mml:mn></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M142" 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>), which included mainly
laboratory incubation studies on different types of biochar,
<inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">LAB</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is 1 order of magnitude lower, and
<inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">REC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is 2 orders of magnitude lower than those
observed in this study. This highlights the importance of field studies to
assess biochar degradation in soil, as a number of factors, such as climatic
and environmental conditions, can increase its degradation rates in
comparison to laboratory conditions.</p>
      <p id="d1e2246">The decrease of biochar in the soil can be due to three main causes:
mineralization by microbial communities in the soil, soil erosion carrying
biochar away and leaching of biochar particles as dissolved organic carbon.
We measured neither soil erosion nor leaching; thus, the large decrease in
biochar observed in this study could be due to unaccounted losses through
these two processes. Soil erosion would result in a faster decrease in
biochar in the upper part of the soil: however, we did not observe any
difference in the decrease in biochar in the upper part of the soil (0–20 cm
depth) with respect to the lower part (20–40 cm). Soil erosion, thus, had a
negligible impact on our study at best.</p>
      <p id="d1e2249">The biochar used in this study has a large <inline-formula><mml:math id="M145" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">H</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">T</mml:mi></mml:mrow></mml:math></inline-formula> ratio (0.5) and is very
brittle, making it more prone to leaching as dissolved organic carbon.
However, various observations point to a negligible effect of leaching on
the decrease of biochar observed in our experiment:
<list list-type="bullet"><list-item>
      <p id="d1e2266">In a recent soil column experiment with a soil similar to that in our study,
Schiedung et al. (2020) showed that only 1 % of the biochar was lost by
leaching, most of it during the first flushing of the column. However, we
have soil respiration measurements for the first 3 years, and these
measurements confirm the hypothesis that the decrease in biochar during that
period was due to microbial activity. Leaching was, thus, during that period,
negligible.</p></list-item><list-item>
      <p id="d1e2270">The biochar decrease rate estimated after 8 years is similar (albeit
larger) to that estimated after the first 3 years of observations. If
biochar was lost through leaching, the biochar decrease rate should decrease
in time instead.</p></list-item><list-item>
      <p id="d1e2274">We did not observe any difference in biochar decrease between the upper
(0–20 cm depth) and the lower (20–40 cm) part of the soil profile.</p></list-item><list-item>
      <p id="d1e2278">The decrease in biochar we observed is still large even when compared with
that estimated for similar biochars (<inline-formula><mml:math id="M146" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">H</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M147" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.5) in laboratory experiments
where leaching was accounted for (Wang et al., 2016; Leng et al., 2019b). This
reiterates the above-mentioned importance of conducting long-term field
experiments to validate laboratory observations (to this end, we are
implementing a platform for long-term experiment data; Marazza et al., 2021).</p></list-item></list></p>
      <p id="d1e2301">Another process that could have affected the degradation rates of biochar
observed in the field is the aggregation of biochar particles with clay
minerals (Joseph et al., 2010), which usually stabilizes the organic matter
in soils with clay (Six et al., 2004; Czimczik and Masiello, 2007). We
visually observed a consistent coating of adsorbed clay particles on the
biochar in the soil; however, this visual observation was not quantified.
The interaction between clay particles and biochar should, thus, be
quantified properly in future studies.</p>
      <p id="d1e2304">The biochar used in this study, although applied in other European projects,
is not very representative of biochar on offer in the European and global
market, with the most important difference being the highest treatment
temperature (HTT; 1200 <inline-formula><mml:math id="M148" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in the present study, 450–750 <inline-formula><mml:math id="M149" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in most market biochar). Even so, our biochar showed a
sufficient stability in soil to represent a valid strategy to increase soil
C sequestration. In fact, the biochar degradation rate should be compared to
that of the material used for its production, since different feedstocks
(e.g. leaves vs wood) are characterized by different mineralization rates
(Lehman and Joseph, 2015). For example, crop-derived biochar decomposes
faster than that from other feedstocks
(Wang et al.,
2016). As the feedstock used in this study was maize silage, which is
characterized by a fast decomposition in field conditions
(Zwahlen et al., 2007; Zhu et al., 2017), we can conclude that charring
increased substantially its stability in soil. Future trials on biochar
degradation should include comparison with the original feedstock (Lehman
and Joseph, 2015).</p>
      <p id="d1e2325">In a study on biochar modelling,
Lefebvre et al. (2020) investigated
the degradation of SOC under three scenarios, by considering different
possible positive priming effects (0 %, <inline-formula><mml:math id="M150" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>21 % and <inline-formula><mml:math id="M151" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>91 %) of
biochar on SOM. Those values were taken from previous studies
(Wang
et al., 2016; Zimmerman and Ouyang, 2019), and they are not specific to the
biochar and soil used in the experiment. On the contrary, we included in the
modified RothC model only the negative priming effect observed in the field
study by Ventura et al. (2015) (<inline-formula><mml:math id="M152" display="inline"><mml:mo lspace="0mm">-</mml:mo></mml:math></inline-formula>16 %). This
result is consistent with similar studies on maize biochar degradation in
soils, which generally report an initial release of CO<inline-formula><mml:math id="M153" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> flux from soil,
followed by a decrease in soil respiration, due to the negative priming
effect of biochar on SOC mineralization
(Luo et al., 2011; Zimmerman et al., 2011).
Since
the validation of the biochar model against SOC showed very good results, we
can conclude that the implementation of the priming effect in the RothC
model is correct, at least for the specific experimental conditions of this
study. This confirmed the persistence
in
the long term
of
the negative priming effect on SOC mineralization observed
by
Ventura et al. (2015) in a 3-year field
experiment and by Stewart
et al. (2013) in a 2-year incubation trial; however, the underlying
mechanisms remain uncertain. A simple sensitivity analysis carried out on
the BC-RothC model showed that the most important parameter in determining
soil carbon sequestration potential of biochar is the priming effect factor;
as such, more research in understanding and modelling the underlying
processes is of paramount importance (see the Supplement).</p>
      <p id="d1e2358">Different mechanisms have been proposed by
Ventura et al. (2015) to explain negative
priming effect of biochar on native SOC, such as (a) the dilution effect of the
soil microbial biomass; (b) organic matter (OM) sorption to biochar and consequent physical
protection from degradation, particularly relevant in the short term
(Zimmerman et al., 2011); and (c) substrate
switching due to the preferential utilization, by soil microorganisms, of
the more easily available C represented by the labile biochar fraction
(Stockmann et al., 2013; Abbruzzini et al., 2017). Using the results for the long-term degradation of biochar, we can
elaborate further on this problem, as was done by Jiang et al. (2019). In
this case, the effect of OM sorption to biochar should show a decrease in
priming effect in time due to saturation of the adsorption sites; however,
the measurements show no change in the priming effect. Moreover, in the long
term, the labile fraction of biochar is already mineralized; hence it cannot
explain the priming effect observed in this study.</p>
      <p id="d1e2361">It is known that biochar added to soils can induce changes in microbial
communities, but the nature and the extent of those alterations are poorly
understood (Jenkins et al., 2017).
Figure 2a and b suggest that the heterotrophic soil respiration in the
control and in the biochar-treated plots behaves in the same way with respect
to seasonal changes in soil moisture and soil temperature. This suggests
that, even if changes in the microbial population due to biochar addition
are still possible, the activity of the microbial population in the soil was
not substantially affected by the application of biochar. Furthermore, the
presence of the biochar in the soil did not result in any consistent change
in soil moisture or temperature in the soil
(Ventura et al., 2015, 2019a). This suggests that, in this study, the
behaviour of the microbial community of the soil was not modified by the
addition of biochar.</p>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Comparison with other biochar models</title>
      <p id="d1e2372">To the best of our knowledge, this is the first time that a simulation
model, optimized for the prediction of biochar mineralization and C
sequestration potential, has been calibrated and validated with long-term
field data.</p>
      <p id="d1e2375">Mondini et al. (2017) suggested a method to include
different types of soil amendments into RothC, including green waste
biochar. The RothC biochar modified by Mondini introduces two additional
C-pools in RothC, one for resistant and one for decomposable exogenous
organic matter (EOM; i.e. amendments), with degradation constants that vary
depending on the type of amendment. One of the possible types of EOM is biochar;
however, it was not possible to estimate its degradation constants due to
very low values in measured CO<inline-formula><mml:math id="M154" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> from mineralization. Furthermore,
Mondini et al. (2017) assumed that EOM added to the
soil does not alter the degradation of SOC and excluded mechanisms of SOC
stabilization/destabilization by biochar, such as the priming effect (Purakayastha et al., 2015).</p>
      <p id="d1e2387">Lefebvre et al. (2020) modified the
RothC model to evaluate the C sequestration potential of biochar from
sugarcane fields upscaling the results to the whole São Paulo state, in
Brazil. The degradation rate of the recalcitrant biochar fraction was
estimated from a 1-year incubation study with sugarcane biochar
(Zimmerman et al., 2011). The authors assumed,
however, that the mineralization of the labile fraction of biochar can be
simulated using the degradation rates of DPM and the RPM pools. By contrast,
in the present study, the BC-RothC model was modified and parametrized based
on the results of a 3-year experiment
(Ventura et al., 2019a) and
validated in the long term (8 years). Furthermore,
Lefebvre et al. (2020) evaluated their
model with literature data from continuous addition of rice straw biochar to
wheat maize cultivation (Liu et al., 2020) but not calibrated
nor validated for the specific experimental conditions.</p>
      <p id="d1e2390">The results of this study are valid in the specific experimental conditions
(soil type, climate, biochar type); therefore, they should be applied with
care to conditions that depart significantly from those of the experiment.
We have introduced in the model what we have observed, for example, the
negative priming effect, and not the processes underlining the observations
(i.e. the process leading to the priming effect). Therefore, we cannot
exclude that different biochar degradation rates or interactions with SOC
could be observed in other conditions, for example, a positive priming
effect or biochar leaching to the deeper soil profile. It should be taken
into account that, in the literature, it is not clear yet how the priming
effect process works and which environmental variables determine it.
Further research is needed to understand causes and mechanisms of the priming effect.</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d1e2403">The understanding and assessment of the C sequestration potential of biochar
require the development of models able to take into account the turnover of
biochar C and SOC and effects on the SOC of added biochar. This study shows
that our modification of the RothC model was successful in simulating the
dynamics of SOC and biochar degradation in soils in field conditions. As far
as we know, this is the first soil C dynamic model including biochar that
was calibrated and validated with long-term field data. Results of the
modelling and experimental measurements showed that, under the observed
conditions, maize biochar degrades at much faster rates than in laboratory
incubations or short-term trials and that biochar reduces the degradation
of SOC. These results substantially confirm the findings of previous studies
performed at the same site in the medium term, remarking the importance of
long-term field studies to validate the results obtained in laboratory
experiments. Nevertheless, biochar contributed substantially to an increase in the
soil C stock in the long term, confirming its potential as a strategy to
mitigate climate change.</p>
</sec>

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

      <p id="d1e2410">The data used in this study have been deposited in the Zenodo public data repository at <ext-link xlink:href="https://doi.org/10.5281/zenodo.6355587" ext-link-type="DOI">10.5281/zenodo.6355587</ext-link> (Pulcher et al., 2022).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d1e2416">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/soil-8-199-2022-supplement" xlink:title="pdf">https://doi.org/10.5194/soil-8-199-2022-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e2425">MV, RP and EB planned the campaign; MV, RP and EB performed the
measurements; MV and RB performed the laboratory analyses; MV and RP
performed the statistical analysis; EB and RB modified the model and
performed the calibration and validation; EB performed the sensitivity
analysis; RP, MV and EB wrote the manuscript draft; MV, EB, NG and DM
reviewed and edited the manuscript; NG helped answer reviewers' questions
and modify the draft after first review; and DM organized the workflow and
raised the funding.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e2431">The contact author has declared that neither they nor their co-authors have any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e2437">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><notes notes-type="sistatement"><title>Special issue statement</title>

      <p id="d1e2443">This article is part of the special issue “Effects of wildfires and pyrogenic carbon on soil functioning and organic matter dynamics”. It is a result of the EGU General Assembly 2021, 19–30 April 2021.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e2449">We kindly thank Fabio Petrella and the
IPLA (Istituto per le Piante da Legno e l'Ambiente) for providing the
experimental site and for help during its establishment and maintenance.
We also express our sincere thanks for suggestions and comments that helped
improve the manuscript by the two reviewers, Gabriel Sigmund and Hans-Peter Schmidt.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e2454">This research has been supported by the Seventh Framework Programme for
Research and Technological Development (FP7) of the European Commission
(EUROCHAR project (grant no. 265179)).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e2460">This paper was edited by Gabriel Sigmund and reviewed by Hans-Peter Schmidt and Gabriel Sigmund.</p>
  </notes><ref-list>
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