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  <front>
    <journal-meta>
<journal-id journal-id-type="publisher">BG</journal-id>
<journal-title-group>
<journal-title>Biogeosciences</journal-title>
<abbrev-journal-title abbrev-type="publisher">BG</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Biogeosciences</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1726-4189</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/bg-13-961-2016</article-id><title-group><article-title>Modelling above-ground carbon dynamics using multi-temporal airborne lidar:
insights from a Mediterranean woodland</article-title>
      </title-group><?xmltex \runningtitle{Modelling above-ground carbon dynamics using multi-temporal airborne lidar}?><?xmltex \runningauthor{W.~Simonson et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff6">
          <name><surname>Simonson</surname><given-names>W.</given-names></name>
          <email>wds10@cam.ac.uk</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2 aff3">
          <name><surname>Ruiz-Benito</surname><given-names>P.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4 aff5">
          <name><surname>Valladares</surname><given-names>F.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Coomes</surname><given-names>D.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-8261-2582</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Forest Ecology and Conservation Group, Department of Plant
Sciences, University of Cambridge, Cambridge CB2 3EA, UK</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Biological and Environmental Sciences, School of Natural Sciences,
University of Stirling, Stirling, FK9 4LA, UK</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Forest Ecology and Restoration Group, Department of Life Sciences,
University of Alcalá, Science Building, Campus Universitario, 28871
Alcalá de Henares, Madrid</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Museo Nacional de Ciencias Naturales, CSIC, Serrano 115 dpdo, E28006
Madrid, Spain</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Departamento de Ciencias, Universidad Rey Juan Carlos, Mostoles,
Madrid, Spain</institution>
        </aff>
        <aff id="aff6"><label>a</label><institution>current address: United Nations Environment Programme World
Conservation Monitoring Centre, 219 Huntingdon Road, Cambridge CB3 0DL, UK</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">W. Simonson (wds10@cam.ac.uk)</corresp></author-notes><pub-date><day>19</day><month>February</month><year>2016</year></pub-date>
      
      <volume>13</volume>
      <issue>4</issue>
      <fpage>961</fpage><lpage>973</lpage>
      <history>
        <date date-type="received"><day>21</day><month>July</month><year>2015</year></date>
           <date date-type="rev-request"><day>7</day><month>September</month><year>2015</year></date>
           <date date-type="rev-recd"><day>11</day><month>December</month><year>2015</year></date>
           <date date-type="accepted"><day>22</day><month>January</month><year>2016</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions><self-uri xlink:href="https://bg.copernicus.org/articles/13/961/2016/bg-13-961-2016.html">This article is available from https://bg.copernicus.org/articles/13/961/2016/bg-13-961-2016.html</self-uri>
<self-uri xlink:href="https://bg.copernicus.org/articles/13/961/2016/bg-13-961-2016.pdf">The full text article is available as a PDF file from https://bg.copernicus.org/articles/13/961/2016/bg-13-961-2016.pdf</self-uri>


      <abstract>
    <p>Woodlands represent highly significant carbon sinks globally, though could
lose this function under future climatic change. Effective large-scale
monitoring of these woodlands has a critical role to play in mitigating for,
and adapting to, climate change. Mediterranean woodlands have low carbon
densities, but represent important global carbon stocks due to their
extensiveness and are particularly vulnerable because the region is predicted
to become much hotter and drier over the coming century. Airborne lidar is
already recognized as an excellent approach for high-fidelity carbon mapping,
but few studies have used multi-temporal lidar surveys to measure carbon
fluxes in forests and none have worked with Mediterranean woodlands. We use a
multi-temporal (5-year interval) airborne lidar data set for a region of
central Spain to estimate above-ground biomass (AGB) and carbon dynamics in
typical mixed broadleaved and/or coniferous Mediterranean woodlands. Field
calibration of the lidar data enabled the generation of grid-based maps of
AGB for 2006 and 2011, and the resulting AGB change was estimated. There was
a close agreement between the lidar-based AGB growth estimate
(1.22 Mg ha<inline-formula><mml:math 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> yr<inline-formula><mml:math 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 those derived from two independent
sources: the Spanish National Forest Inventory, and a tree-ring based
analysis (1.19 and 1.13 Mg ha<inline-formula><mml:math 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> yr<inline-formula><mml:math 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>, respectively). We
parameterised a simple simulator of forest dynamics using the lidar carbon
flux measurements, and used it to explore four scenarios of fire occurrence.
Under undisturbed conditions (no fire) an accelerating accumulation of
biomass and carbon is evident over the next 100 years with an average carbon
sequestration rate of 1.95 Mg C ha<inline-formula><mml:math 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> yr<inline-formula><mml:math 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>. This rate reduces by
almost a third when fire probability is increased to 0.01 (fire return rate
of 100 years), as has been predicted under climate change. Our work shows the
power of multi-temporal lidar surveying to map woodland carbon fluxes and
provide parameters for carbon dynamics models. Space deployment of lidar
instruments in the near future could open the way for rolling out wide-scale
forest carbon stock monitoring to inform management and governance responses
to future environmental change.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>The world's forests are currently acting as an important carbon sink, in
2000–2007 taking up 2.3 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.5 PgC each year compared with
anthropogenic emissions of 8.7 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.8 PgC (Pan et al., 2011). For this
reason, the international community recognises that forest protection could
play a significant role in climate change abatement and that the feedback
between climate and the terrestrial carbon cycle will be a key determinant of
the dynamics of the Earth System (Purves et al., 2007). However, there is
major uncertainty over forest responses to anthropogenic global change, and
concerns that the world's forests may switch from being a sink to a source
within the next few decades (Nabuurs et al., 2013; Ruiz-Benito et al.,
2014b), through gradual effects on regeneration, growth and mortality, as
well as climate-change related disturbance (Frank et al., 2015). For
instance, severe droughts in many parts of the world are causing rapid
change, killing trees directly through heat-stress and indirectly by fire
(Allen et al., 2010). Disturbance events can cause major perturbations to
regional carbon fluxes (Chambers et al., 2013; Vanderwel et al., 2013). A
major goal in biogeosciences, therefore, is to improve understanding of the
terrestrial vegetation carbon cycle to enable better constrained projections
(Smith et al., 2013).</p>
      <p>In this context, remote-sensing methods for modelling above-ground storage
of carbon in biomass have received much recent attention, with airborne
light detection and ranging (lidar) showing the most potential for accurate
and large-scale applications. Lidar metrics of canopy structure are highly
correlated with field-based estimates of above-ground biomass (AGB) and
carbon (AGC) (Drake et al., 2003; Lefsky et
al., 2002). With such relationships being repeatedly demonstrated, it has
been possible to develop a conceptual and technical approach linking
plot-based carbon density estimates with lidar top canopy heights using
regional inputs on basal area and wood density (Asner and
Mascaro, 2014). With the increasing availability of multi-temporal (repeat
survey) lidar data sets, including some of national coverage, a few
researchers have started to use lidar in large-scale studies of vegetation
productivity and carbon dynamics (Englhart
et al., 2013; Hudak et al., 2012) as well as forest disturbance and gap
dynamics
(Blackburn
et al., 2014; Kellner and Asner, 2014; Vepakomma et al., 2008, 2010, 2011).
As such, and despite its high costs, lidar is transitioning from research to
practical application, notably in supporting baseline surveys and monitoring
of carbon stocks required for the implementation of the REDD<inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> mechanism
(Reducing Emissions from Deforestation and Forest Degradation)
(Asner et al., 2013). However, monitoring carbon
fluxes using multi-temporal lidar is technically challenging because
instrument and flight specifications vary over time
(Réjou-Méchain et al., 2015).</p>
      <p>The applications of airborne lidar for modelling AGB and AGC have largely
been tested in cool temperate and tropical forest systems (see Zolkos et al.,
2013). Less attention has been given to the effectiveness of the technology
for the modelling of biomass and carbon in sub-tropical and Mediterranean
climate zones dominated by dry woodlands. These woodlands have lower carbon
densities, but represent important global carbon stocks due to their
extensiveness and also vulnerability in the face of climate change
(Ruiz-Benito et al., 2014b). As elsewhere in Europe, carbon stocks in such
woodlands have been increasing in recent decades (Nabuurs et al., 2003, 2010;
Vayreda et al., 2012), as woodland management for charcoal and timber has
declined in profitability. However, with Earth System models predicting some
of the most severe warming and drying trends of anywhere in the world (Giorgi
and Lionello, 2008; Valladares et al., 2014), abrupt shifts in increasing
fire frequency and intensity may reverse such trends across the Mediterranean
region (Pausas et al., 2008). Lidar has been used to measure carbon stocks in
some Mediterranean woodlands (García et al., 2010) but, to our
knowledge, not for measuring carbon dynamics.</p>
      <p>In this study we demonstrate the potential to build a patchwork dynamics
simulator for the biomass and carbon dynamics in Mediterranean woodlands
based on multi-temporal lidar data (Fig. 1). Our aim is to model the
direction and rate of landscape-scale AGC change for mixed oak-pine woodland
in central Spain. We first calibrate a lidar top-of-canopy height model using
selective ground-based estimations of tree- and plot-level biomass. The
lidar-based AGB growth models are then validated using two independent
data sets: the Spanish National Forest Inventory (SFI) and tree-ring
measurements, before parameterising a simulation model to explore the
dynamics of carbon change over a 100-year period. In doing so, we explore
sensitivity of the long-term carbon sequestration potential of the regional
landscape to increasing forest fire frequency, as is to be expected under
future climate change.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><caption><p>Methodological approach.</p></caption>
        <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/961/2016/bg-13-961-2016-f01.pdf"/>

      </fig>

</sec>
<sec id="Ch1.S2">
  <title>Methods</title>
<sec id="Ch1.S2.SS1">
  <title>Study area</title>
      <p>Alto Tajo (40<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>47<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> N, 2<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>14<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>′</mml:mo></mml:msup></mml:math></inline-formula> W) is a Natural Park
(32 375 ha) situated in the Guadalajara province of Central Spain. The
dominant woody vegetation is Mediterranean mixed woodland, comprising
<italic>Pinus sylvestris</italic>, <italic>P. nigra</italic>, <italic>Quercus faginea</italic>,
<italic>Q. ilex, Juniperus</italic> <italic>oxycedrus </italic> and <italic>J. thurifera</italic>.
The region has a complex topography ranging from 960 to 1400 m a.s.l. The
mean annual temperature here is 10.2 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, with mean annual rainfall
of 499 mm.</p>
      <p>Contained within the Park is one of the six Exploratory platform sites
contributing to FunDivEurope: Functional Significance of Biodiversity in
European Forests (Baeten et al., 2013). Field data used in the current study
were taken from plots surveyed as part of this programme. The landscape-level
analysis focused on a belt overlapping this area and running 20 km
north–south and 3 km east–west (Fig. 2).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><caption><p>Study area. Shown in lighter green, mixed forest, and darker
green, coniferous forest. Other land covers (including agricultural) in
shades of grey, with darkest grey indicating an area burned by forest fire
in 2005 and excluded from these analyses. The three north-south parallel
strips show the lidar survey coverage.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/961/2016/bg-13-961-2016-f02.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS2">
  <title>Plot-based tree measurements and allometric biomass modelling</title>
      <p>Field measurement of plots was undertaken in March 2012. Each plot was of
dimension 30 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 30 m and was carefully geo-located, recording GPS
corner coordinates and orientation using a Trimble GeoXT – Geoexplorer 2008.
Measurements were made of trees and shrubs of diameter at breast height (DBH)
&gt; 7.5 cm, given that smaller sizes contribute less to plot-level
biomass (Stephenson et al., 2014). The following were measured and recorded:
position within plot, species, height, height of lowest branch, DBH (at 1.3
m), and crown diameter (two orthogonal measurements). A vertex hypsometer was
used for the crown dimensions.</p>
      <p>The above-ground biomass of individual trees was estimated according to
published allometries, and summed to arrive at plot and hectare totals. The
allometric equations of Ruiz-Peinado et al. (2011) and Ruiz-Peinado et
al. (2012) were used for softwood species (<italic>Juniperus</italic> and
<italic>Pinus</italic>) and hardwood species (<italic>Quercus</italic>), respectively
(Appendix A). The equations were developed from tree samples across Spain
including sites close to the Alto Tajo study area. The equations for
<italic>Juniperus thurifera</italic> were applied to the other two junipers
(<italic>J. oxycedrus</italic> and <italic>J. phoenicia</italic>) as well as box
(<italic>Buxus sempervirens</italic>). In all cases, the equations compartmented the
biomass into trunks and large, medium and fine branches and/or leaves, using DBH and
tree height data.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <title>Lidar surveys, calibration and above-ground biomass and carbon change
analysis</title>
      <p>The lidar surveys were undertaken by the NERC Airborne Research and Survey
Facility (ARSF) and took place on 16 May 2006 (project WM06_04; García
et al., 2011, 2010) and 21 May 2011 (project CAM11_03). A Dornier 228
aircraft was employed for both, but lidar instruments differed between years:
Optech ALTM-3033 in 2006 and Leica ALS050 in 2011. Instrument and flight
parameters are given in Table 1. Simultaneous GPS measurement was carried out
on the ground allowing for differential correction during post-processing.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p>Specifications for the lidar surveys undertaken at Alto Tajo (Spain)
in 2006 and 2011.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <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:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">2006</oasis:entry>  
         <oasis:entry colname="col3">2011</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">Lidar sensor</oasis:entry>  
         <oasis:entry colname="col2">Optech-ALTM3033</oasis:entry>  
         <oasis:entry colname="col3">Leica ALS050</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Wavelength (nm)</oasis:entry>  
         <oasis:entry colname="col2">1064</oasis:entry>  
         <oasis:entry colname="col3">1064</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Beam divergence (mrad)</oasis:entry>  
         <oasis:entry colname="col2">0.20</oasis:entry>  
         <oasis:entry colname="col3">0.22</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Vertical discrimination (m)</oasis:entry>  
         <oasis:entry colname="col2">4.6</oasis:entry>  
         <oasis:entry colname="col3">2.8</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Detection system</oasis:entry>  
         <oasis:entry colname="col2">Two return</oasis:entry>  
         <oasis:entry colname="col3">Four return</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Date of deployment</oasis:entry>  
         <oasis:entry colname="col2">16 May 2006</oasis:entry>  
         <oasis:entry colname="col3">21 May 2011</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Pulse rate frequency (MHz)</oasis:entry>  
         <oasis:entry colname="col2">33.33</oasis:entry>  
         <oasis:entry colname="col3">67.2–74.4</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">FoV (degrees)</oasis:entry>  
         <oasis:entry colname="col2">12</oasis:entry>  
         <oasis:entry colname="col3">40</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Scan frequency (Hz)</oasis:entry>  
         <oasis:entry colname="col2">42.4</oasis:entry>  
         <oasis:entry colname="col3">35.8–40.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Point density (m<inline-formula><mml:math 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>)</oasis:entry>  
         <oasis:entry colname="col2">0.5</oasis:entry>  
         <oasis:entry colname="col3">2</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Number of flight lines</oasis:entry>  
         <oasis:entry colname="col2">3(N–W)</oasis:entry>  
         <oasis:entry colname="col3">4 (E–W) <inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 3(N–W)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Altitude (m a.s.l.)</oasis:entry>  
         <oasis:entry colname="col2">2063–2073</oasis:entry>  
         <oasis:entry colname="col3">2097–2140</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p>We assumed accurate georeferencing of the 2006 and 2011 data sets during
post-processing, and did no further co-registration. We performed initial
modelling of terrain and canopy heights from the 2006 and 2011 lidar data sets
using “Tiffs” 8.0: Toolbox for Lidar Data Filtering and Forest Studies,
which employs a computationally efficient, grid-based morphological filtering
method described by Chen et al. (2007). Outputs included filtered ground and
object points, as well as digital terrain models (DTM) and canopy height
models (CHM). The subsequent GIS and statistical analyses described below
were undertaken in ArcInfo 10.0 (undertake in ArcInfo 10.0 by ESRI) and R 2.13.1 (R Development
Core Team, 2011), respectively.</p>
      <p>Spatially overlaying the lidar data set with land cover information derived
from the 2006 CORINE map (EEA, 1995), indicated the local presence of two
main forest types: coniferous and mixed (oak-juniper-pine) woodland. For the
purposes of calibrating the lidar height models based on field-estimated
biomass, only the latter forest type was adequately sampled (13 plots), so
subsequent analysis and modelling focused on these mixed woodland systems. We
predicted biomass as a function of top-of-canopy heights, which has been
found to be a good predictor (Asner et al., 2013). Digitised plot boundaries
for the 13 FunDiv plots of square 30 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 30 m were used to extract
mean top-of-canopy height values from the lidar CHM (TCH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">L</mml:mi></mml:msub></mml:math></inline-formula>).
Reassuringly, these values were remarkably similar to the mean canopy height
estimated from plot data (TCH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">P</mml:mi></mml:msub></mml:math></inline-formula>), calculated from height and crown
area of each tree obtained by allometric formulae (see Kent et al.
2015); there was almost a <inline-formula><mml:math display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>
relationship between the two estimates of height: TCH<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">G</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1.79</mml:mn><mml:mo>+</mml:mo><mml:mn>0.999</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> TCH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">L</mml:mi></mml:msub></mml:math></inline-formula> (<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn>0.88</mml:mn></mml:mrow></mml:math></inline-formula>). Field-estimated AGB was
modelled on the basis of lidar mean height by linear regression of log
transformed variables. Our selected model
(log(AGB) <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 3.02 <inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 0.89 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> log(TCH<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi mathvariant="normal">L</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn>0.53</mml:mn></mml:mrow></mml:math></inline-formula>, RMSE <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.28) was back-transformed and multiplied by a correction
factor (CF) to account for the back-transformation of the regression error
(Baskerville, 1972); the correction factor is given by
CF <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mtext>MSE/2</mml:mtext></mml:msup></mml:mrow></mml:math></inline-formula>, where MSE is the mean square error of the
regression model.</p>
      <p>We used the regression model and lidar data set to map biomass and biomass
change. We aggregated canopy heights at 1 m resolution to mean values per
30 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 30 m grid cell, to reduce mismatches with the field inventory
plots (Réjou-Méchain et al., 2015). The aggregation was also
effective in dealing with gappiness noted in the 2006 data set due to uneven
distribution of scan lines and lower point density (Table 1). Negative values
caused by occasional inaccuracies evident in the DTM models, especially for
2006, were removed from the data set to avoid anomalies. For each grid cell
along the three north–south transects, we were able to use the mean height–AGB
regression relationship to generate estimates of AGB in 2006 and 2011, and
AGB change 2006–2011.</p>
</sec>
<sec id="Ch1.S2.SS4">
  <title>Validation</title>
      <p>Due to the relatively low number of ground truth plots, it was especially
important to validate the lidar-modelled AGB estimates, and this was done
using two different data sets. Firstly, equivalent estimates of AGB and AGB
change were developed using detailed tree measurements from the Spanish
National Forest Inventory (SFI). The SFI covers the forested areas of the
country on a 1 km<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> grid (Villanueva, 2004). A subset of 234 SFI plots
surrounding the study area and of comparable topography and climate were
selected, and the data extracted for the second and third surveys (2SFI,
1992–94 and 3SFI, 2003–2006; i.e. an 11-year interval for this region). For
each plot, plot-level AGB was calculated by applying the allometric equations of
Ruiz-Peinado et al. (2011, 2012; Appendix A) to individual tree height and
stem diameter measurements and summing these up to the plot level.
Information on topoclimate (altitude, rainfall, temperature; Gonzalo, 2008)
and management and/or fire disturbance were also available per plot, although areas
significantly burned after the first inventory were removed from the data set.</p>
      <p>Secondly, plot-level above-ground wood productivity values were calculated
from tree-ring measurements from the same FunDiv plots used to calibrate the
lidar data, according to a four-step procedure described in Jucker et
al. (2014): measuring growth increments from wood cores, converting diameter
increments into biomass growth, modelling individual tree biomass growth, and
scaling up to plot level. For the coring, bark-to-pith increment cores were
collected for a subset of trees in each plot (using a 5.15 mm diameter
increment borer, Haglöf AB, Sweden). Following a size-stratified random
sampling approach, one core was extracted from each selected tree at a height
of 1.3 m off the ground; 12 trees per plot were cored in monocultures and 6
trees per species were cored in mixtures (Jucker et al., 2014). In this
approach, plot level estimates were based on the growth of trees present in
2011 and did not account for the growth of trees that died between 1992 and
2011.</p>
</sec>
<sec id="Ch1.S2.SS5">
  <title>Biomass growth estimation and simulation modelling</title>
      <p>Plotting the 30 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 30 m pixel-level AGB estimates from 2006 versus
2011 revealed a small number of outliers of AGB change that may have resulted
from anomalies in the DTM and top-of-canopy modelling (see discussion). We
used robust regression to remove these outliers in order to obtain reliable
estimates of mean growth and its uncertainty. This was performed with the
rlm command in the MASS package of R, which uses iterative re-weighted
least squares (M-estimation) (Venables and Ripley, 2002). Robust regression
assigns lower weights to outliers than to points close to the regression line
(in our case, using a bisquare weighting function), and then uses these
weights to downplay the importance of these outliers in the linear
regression. On inspection of the weights, we observed that all the obvious
outliers had been assigned a weight of zero, so were easily filtered out.
Some 3.3 % of the data were trimmed in this way. The residuals of the
remaining data set were close to normally distributed. Change in AGB was
calculated for each plot in the trimmed data set as
(AGB<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn>2011</mml:mn></mml:msub></mml:math></inline-formula>– AGB<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn>2006</mml:mn></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula>, and the mean and standard deviation
estimated. There was significant spatial auto-correlation of AGB<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn>2006</mml:mn></mml:msub></mml:math></inline-formula>
values (Moran's I <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.138, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mn> 0.001</mml:mn></mml:mrow></mml:math></inline-formula>) and also AGB change
(Moran's I <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.038, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mn> 0.001</mml:mn></mml:mrow></mml:math></inline-formula>). However, following the
conclusion of Hawkins et al. (2007) that regression estimates are not
significantly affected by spatial autocorrelation, we considered it
unnecessary to subsample the gridded data set to avoid it.</p>
      <p>The trimmed data set was used to model AGB growth as a function of biomass,
using Bayesian inference, and to create a woodland dynamics simulator. The
growth model was
            <disp-formula id="Ch1.E1" content-type="numbered"><mml:math display="block"><mml:mtable class="array" columnalign="left left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mtext>AGB</mml:mtext><mml:mn>2011</mml:mn></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>a</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mo>×</mml:mo><mml:msub><mml:mtext>AGB</mml:mtext><mml:mn>2006</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="italic">ε</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>where</mml:mtext><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">ε</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>∼</mml:mo></mml:mtd><mml:mtd><mml:mrow><mml:mtext>N</mml:mtext><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mi>c</mml:mi><mml:mo>+</mml:mo><mml:mi>d</mml:mi><mml:mo>×</mml:mo><mml:msub><mml:mtext>AGB</mml:mtext><mml:mn>2006</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
          where <inline-formula><mml:math display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mi>c</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mi>d</mml:mi></mml:math></inline-formula> are parameters calculated using STAN (STAN
Development Team, 2014), a Bayesian inference package. We used uninformative
prior and a burn-in of 5000 iterations (well in excess of that needed for
convergence), then took 100 samples from the posterior distribution. We also
fitted a model containing a quadratic biomass term, but the 95 %
confidence intervals of the quadratic term overlapped with zero, indicating
no support for its inclusion.</p>
      <p>Parameter values drawn from the posterior distribution were fed into a
simple simulation model. We created a 5000 cell “landscape” with starting
biomass sampled randomly from AGB<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn>2006</mml:mn></mml:msub></mml:math></inline-formula>. For each cell the annual biomass
increments were estimated by drawing parameters randomly from the posterior
distribution
            <disp-formula id="Ch1.E2" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mtext>AGB</mml:mtext><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi>a</mml:mi><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:mi>b</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:mtext>AGB</mml:mtext><mml:mo>+</mml:mo><mml:mi mathvariant="italic">ε</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">5</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> was drawn at random from <inline-formula><mml:math display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula> (0, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>c</mml:mi><mml:mo>+</mml:mo><mml:mi>d</mml:mi><mml:mo>×</mml:mo></mml:mrow></mml:math></inline-formula> AGB).
The biomass of each cell was then altered by <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>AGB and the iterative
process continued for 100 years. Mean AGB values for the landscape each year
were recorded and plotted with 95 % confidence intervals.</p>
      <p>We also included the effect of various fire scenarios on mean biomass change
and carbon dynamics in a simplistic way. We assumed that the probability of a
cell being destroyed by fire, <inline-formula><mml:math display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula>, did not depend on that cell's AGB and did
not vary among years. For each time step and pixel, we decided whether a fire
event had occurred in a cell by drawing random numbers from the binomial
distribution, with the AGB being reset to zero as a result of a fire event.
An annual probability of fire occurrence for the region of Guadalajara, based
on areas burned each year from 1991 to 2010 (Ministerio de Agricultura, 2002, 2012)
is <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0.002</mml:mn></mml:mrow></mml:math></inline-formula>, whilst that from a model parameterized from topoclimatic data
from southern Spain is <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0.004</mml:mn></mml:mrow></mml:math></inline-formula> (Purves et al., 2007). A five-fold increase
in area burned as a result of a high emission climate scenario is predicted
for similar forest types in Portugal (see Carvalho et al., 2009). Thus, as
well as the no-fire scenario, we tested the three fire probabilities of <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0.002</mml:mn></mml:mrow></mml:math></inline-formula>, 0.004 and 0.01 to look at the sensitivity of carbon accumulation in
the mixed woodlands to a realistic range of fire frequencies. Carbon
sequestration potential (mean carbon storage in biomass over the simulation
period, Mg ha<inline-formula><mml:math 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 using the IPCC default 0.47 carbon
fraction (McGroddy et al., 2004), and scaled up to a total value of carbon
(and CO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> equivalent, 3.67 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> C, Mt) for all mixed woodland in
the autonomous community of Castilla La Mancha (181 000 ha) under the
no-fire and three fire scenarios. We acknowledge that the simulation model is
basic, and since it is not spatially explicit it makes no consideration of
landscape connectivity. However, the results provide insight into the likely
effect of varying fire rates on carbon dynamics.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <title>Results</title>
      <p>Lidar estimated mean AGB of mixed woodlands was 41.8 in 2006
and 47.9 Mg ha<inline-formula><mml:math 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> in 2011. Mean biomass change in this 5-year period
was 1.22 Mg ha<inline-formula><mml:math 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> yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, with a considerable degree of variation
around this estimate (SD <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1.92 Mg ha<inline-formula><mml:math 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 a large number of
pixels losing biomass (Fig. 3), presumably as a result of disturbance. There
was very good agreement between above-ground biomass estimated from the lidar
modelling and Spanish National Inventory plots for mixed oak-juniper-pine
woodland (Table 2). The lidar-based estimate is also in reasonable agreement
with that calculated from the 2006 data set in an earlier analysis:
44.7 Mg ha<inline-formula><mml:math 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 holm oak woodland (García et al., 2010). AGB
change as modelled by the lidar approach was also close to estimates derived
from the SFI and the Fundiv tree ring data (Table 2). The standard deviation
of the lidar-based AGB change estimate is relatively high, probably as a
result of lidar sampling and/or processing errors that are greater than measurement
errors associated with plots and tree rings. From the lidar data set, there
was a statistically significant but minor effect on AGB change of altitude
(range 908–1322 m; <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>AGB <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 21.17–0.01 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> altitude,
<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn>0.0180</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mn>0.001</mml:mn></mml:mrow></mml:math></inline-formula>) and aspect (calculated as folded aspect
<inline-formula><mml:math display="inline"><mml:mo>|</mml:mo></mml:math></inline-formula>aspect–180<inline-formula><mml:math display="inline"><mml:mo>|</mml:mo></mml:math></inline-formula>; <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>AGB <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 3.31–0.03 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> aspect, <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.0057, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mn>0.001</mml:mn></mml:mrow></mml:math></inline-formula>).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p>Scatterplot of above-ground biomass (AGB) estimates for 2006 and
2011: lidar (black dots), Spanish Forest Inventory (red bordered circles),
with one-to-one line (black) and fitted model (green).</p></caption>
        <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/961/2016/bg-13-961-2016-f03.pdf"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><caption><p>Simulation model results for AGB over a 100-year period without
fire <bold>(a)</bold> and at annual fire probability of occurrence of <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0.002</mml:mn></mml:mrow></mml:math></inline-formula> <bold>(b)</bold>, 0.004 <bold>(c)</bold> and 0.01 <bold>(d)</bold>. Figures show mean (black line) and 95 % confidence
intervals (grey shading).</p></caption>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/961/2016/bg-13-961-2016-f04.pdf"/>

      </fig>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><caption><p>Comparison of the lidar modelling of above-ground biomass (AGB) and
biomass change (AGB change) with forest inventory and tree-ring data: values
given are mean (and standard deviation in parentheses).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:thead>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Lidar data</oasis:entry>  
         <oasis:entry colname="col3">Forest inventory</oasis:entry>  
         <oasis:entry colname="col4">Tree-ring data</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"/>  
         <oasis:entry colname="col3">data</oasis:entry>  
         <oasis:entry colname="col4"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">AGB (Mg ha<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>  
         <oasis:entry colname="col2">41.80 (<inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>25.68)</oasis:entry>  
         <oasis:entry colname="col3">42.8 (<inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>52.7)</oasis:entry>  
         <oasis:entry colname="col4">–</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">AGB change (Mg ha<inline-formula><mml:math 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> yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>  
         <oasis:entry colname="col2">1.22 (<inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>1.92)</oasis:entry>  
         <oasis:entry colname="col3">1.19 (<inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>1.17)</oasis:entry>  
         <oasis:entry colname="col4">1.13(<inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>0. 54)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Sample size</oasis:entry>  
         <oasis:entry colname="col2">9136 grid cells</oasis:entry>  
         <oasis:entry colname="col3">66 plots</oasis:entry>  
         <oasis:entry colname="col4">13 plots</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p>Biomass change was modelled according to the relationship:
          <disp-formula id="Ch1.E3" content-type="numbered"><mml:math display="block"><mml:mtable class="array" columnalign="left left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mtext>AGB</mml:mtext><mml:mn>2011</mml:mn></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mn>3.98</mml:mn><mml:mo>+</mml:mo><mml:mn>1.05</mml:mn><mml:mo>×</mml:mo><mml:msub><mml:mtext>AGB</mml:mtext><mml:mn>2006</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="italic">ε</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>where</mml:mtext><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">ε</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>∼</mml:mo><mml:mtext>N</mml:mtext><mml:mo>(</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn>4.32</mml:mn><mml:mo>+</mml:mo><mml:mn>1.10</mml:mn><mml:mo>×</mml:mo><mml:msub><mml:mtext>AGB</mml:mtext><mml:mn>2006</mml:mn></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p>With <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>1.05</mml:mn></mml:mrow></mml:math></inline-formula> (i.e. &gt; 1), the woodlands are accumulating
biomass over time, though the variance term is large and so some cells are
losing biomass (Fig. 3). The disturbance-free simulation model showed a
strong increase in accumulated AGB over the whole 100-year period (Fig. 4a).
The mean AGB rose from 42.6 (<inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>5.6) to 236.9 (<inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>18.5) Mg ha<inline-formula><mml:math 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 equates to a mean carbon flux of 1.95 MgC ha<inline-formula><mml:math 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> yr<inline-formula><mml:math 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>. By
modelling the occurrence of fire at probabilities of <inline-formula><mml:math display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.002, 0.004
and 0.01, we showed its potential impact on biomass and therefore carbon
accumulation (Fig. 4, Table 3). Mean (and standard deviation) values for AGB
after 100 years were 200.6 (<inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>21.1), 174.2 (<inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>22.7), and 114.1
(<inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>21.5) Mg ha<inline-formula><mml:math 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 a fire probability of 0.002, 0.004 and 0.01
(or return rate of 500, 250 and 100 years), respectively. The effects of
increasing fire occurrence also have dramatic effects on the carbon
sequestration potential of the mixed woodlands considered at a regional level
(i.e. Castilla la Mancha, Table 3), with the most severe fire regime reducing
that potential by almost a half.</p>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <title>Discussion</title>
      <p>Here we provide a demonstration of the potential of lidar remote sensing to
deliver large-scale high-fidelity maps of above-ground biomass and carbon
dynamics. Our lidar-based biomass growth model, estimating a mean annual
growth of 1.22 MgC ha<inline-formula><mml:math 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> yr<inline-formula><mml:math 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>, is in excellent agreement with the
estimate independently derived from the Spanish National Forest Inventory
(1.19 MgC ha<inline-formula><mml:math 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> yr<inline-formula><mml:math 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>). Even though there is a large standard
deviation around our estimate, the enormous sample size (9136 pixels) means
that standard errors become miniscule, so our landscape level projections are
delivered with high precision and reliability (Coomes et al., 2002). The
number of field sampling plots used to calibrate the lidar top-of-canopy
model is statistically enough given the parameters calculated and, therefore,
for the purposes of our study. The coefficient of determination of the
resulting model (<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn>0.53</mml:mn></mml:mrow></mml:math></inline-formula>) can be compared with a value of 0.67
obtained by García et al. (2010) for the same region. The difference
could be due to that fact that García et al. (2010) included more plots
across a greater range of woodland types, heights and carbon densities.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><caption><p>Average above-ground biomass (AGB) and carbon sequestration
potential over a 100-year period for the four forest fire scenarios (no fire
and at annual fire probability of occurrence of <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0.002</mml:mn></mml:mrow></mml:math></inline-formula>, 0.004 and 0.01),
scaled up to the regional level (181 000 ha of mixed forest in Castilla la
Mancha) for carbon and carbon-dioxide equivalence.</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">Fire</oasis:entry>  
         <oasis:entry colname="col2">AGB</oasis:entry>  
         <oasis:entry colname="col3">Carbon</oasis:entry>  
         <oasis:entry colname="col4">Regional</oasis:entry>  
         <oasis:entry colname="col5">Regional CO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">scenario</oasis:entry>  
         <oasis:entry colname="col2">(Mg ha<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>  
         <oasis:entry colname="col3">sequestration</oasis:entry>  
         <oasis:entry colname="col4">carbon</oasis:entry>  
         <oasis:entry colname="col5">equivalent</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"/>  
         <oasis:entry colname="col3">potential</oasis:entry>  
         <oasis:entry colname="col4">(Kt)</oasis:entry>  
         <oasis:entry colname="col5">(Kt)</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"/>  
         <oasis:entry colname="col3">(Mg ha<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>  
         <oasis:entry colname="col4"/>  
         <oasis:entry colname="col5"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">No fire</oasis:entry>  
         <oasis:entry colname="col2">124.9</oasis:entry>  
         <oasis:entry colname="col3">58.7</oasis:entry>  
         <oasis:entry colname="col4">10.6</oasis:entry>  
         <oasis:entry colname="col5">39.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn>0.002</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">111.6</oasis:entry>  
         <oasis:entry colname="col3">52.4</oasis:entry>  
         <oasis:entry colname="col4">9.5</oasis:entry>  
         <oasis:entry colname="col5">34.8</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn>0.004</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">101.9</oasis:entry>  
         <oasis:entry colname="col3">47.9</oasis:entry>  
         <oasis:entry colname="col4">8.7</oasis:entry>  
         <oasis:entry colname="col5">31.8</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn>0.01</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">77.7</oasis:entry>  
         <oasis:entry colname="col3">36.5</oasis:entry>  
         <oasis:entry colname="col4">6.6</oasis:entry>  
         <oasis:entry colname="col5">24.3</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p>In the Anthropocene era of rapid climate and environmental change, there is
an urgent need for reliable large-scale monitoring of above-ground biomass
and carbon stocks in forests and woodlands (Henry et al.,
2015), and developing our understanding of how carbon stocks will change in
the future. Forests serve the critical function of sequestering atmospheric
carbon and reducing the potential rate of climate change. However, they also
provide other highly important services, including provision of timber, food
and other non-timber products, regulation of water cycle and habitat for
biodiversity
(Gamfeldt et
al., 2013; Ojea et al., 2012; WRI, 2005). The amount of biomass in forest is
a metric relevant to all of these functions, with an especially close
relationship with sequestered and stored carbon
(Boisvenue and Running, 2006). In the
context of climate change mitigation and emissions target agreements made at
national level, robust methodologies are needed for the regular assessment
of carbon stocks in forests (Gibbs et al., 2007).</p>
      <p>Our work demonstrates one such robust approach that has delivered a credible
model of landscape-level carbon stocks and fluxes based on a 5-year
interval repeat-survey lidar data set. The methodology involved identifying
and discarding a small number of outliers in the AGB estimates, and it is
worth reflecting on their origin. One of the challenges of multi-temporal
lidar analyses are when different instruments and specifications are used in
the surveys. In our case, the 2006 lidar survey had a much lower point
density than for 2011, and inspection of the resulting point cloud indicated
a considerably uneven distribution of the scan lines. The accuracy of the
resulting terrain and canopy models will therefore be lower, potentially
giving rise to some of the anomalies in our results. We sought to quantify
the source of this error by performing a comparison of top-of-canopy height
(TCH) models from crossing flight-lines (data not given) for both years at
the 30 m grid scale, for which the standard deviation for 2006 was more than
double that for 2011. TCH is known to be quite robust across different
instruments (Asner and Mascaro, 2014), being less susceptible to differences
in laser canopy penetration than mean canopy height (MCH) (Næsset, 2009).
We considered that the size of our plots was sufficient for calibrating the
system, though in comparison with larger plots: (1) errors caused by spatial
misalignment of plots and lidar data are greater (Asner et al., 2009);
(2) integrating measurements provides a less representative average (Zolkos
et al., 2013); and (3) disagreement in protocol between lidar and field
observations is greater (influenced by the effects of bisecting tree crowns
in lidar data versus calling a tree “in” or “out” of the plot in field
data; Mascaro et al., 2011). With regard to the latter issue, the potential
error is affected by the average crown size relative to plot dimensions, such
that it will be less in our situation (as it also is for boreal forest,
Næsset et al., 2011), than it would be for tropical forests.</p>
      <p>At the extensive spatial scales required, remote-sensing methodologies offer
the only practicable approach to the challenge of forest monitoring, with
lidar being the remote-sensing instrument of choice given its potential to
characterise the three dimensional structure of canopies and understories to
a high degree of accuracy and resolution. Whilst spatial and temporal lidar
coverage of the terrestrial and wooded surface of the planet is still
limited, and the costs still high, this situation is improving continuously.
A number of national surveys have been undertaken or commissioned, and
building on the experience of the GLAS (Geoscience Laser Altimetry System)
instrument on ICESAT (2003–2010), the GEDI Lidar space-borne facility is
planned for deployment in 2019 (Dubayah et al., 2014). With these
advancements, it is an important time to develop proof of principle of lidar
monitoring of forest biomass and carbon stocks and fluxes. In this respect, a
number of important multi-temporal lidar studies have emerged. Typical of
these are an analysis of AGB dynamics, tree growth and peat subsidence in
peat swamp forests of Central Kalimantan, Indonesia 2007–2011 (Boehm et al.,
2013; Englhart et al., 2013), biomass changes in conifer forests of northern
Idaho 2003–2009 at the pixel, plot and landscape level and looking at the
impacts of logging (Hudak et al., 2012), studies of canopy gap dynamics
(Blackburn et al., 2014; Vepakomma et al., 2008, 2010, 2011), and treefall
rates and spatial patterns in a savanna landscape 2008–2010 (Levick and
Asner, 2013). A study employing four lidar surveys between 2000–2005
established an optimum interval (3 years) for measuring tree growth in red
pine forests at an acceptable level of uncertainty (Hopkinson et al., 2008).</p>
      <p>Our study makes an important additional contribution to this literature. It
demonstrates how sampling a woodland system with a small number of field
plots can effectively calibrate a lidar data set to scale up credible
estimates of AGB and AGC at the landscape level. It is also novel in studying
these dynamics within a Mediterranean environment. Much focus of lidar-based
biomass modelling has been on tropical forest systems, given their importance
to the global carbon cycle. Mediterranean woodlands hold a much lower carbon
density, yet are valuable carbon stores given their extensive nature not just
in the Mediterranean Basin but also other similar climate regions in the
world. Furthermore, the potential effects of climate change in Mediterranean
woodlands are suggested to be particularly strong (Benito-Garzón et al.,
2013; Ruiz-Benito et al., 2014b). In the absence of fire in one such region,
our simulation suggests a significant AGB increase from 42.6 to
236.9 Mg ha<inline-formula><mml:math 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> over a 100-year period (equivalent to
1.94 MgC ha<inline-formula><mml:math 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> yr<inline-formula><mml:math 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>). Pan et al. (2011) estimates an annual
increase of 1.68 MgC ha<inline-formula><mml:math 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> yr<inline-formula><mml:math 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> in European temperate forests in
2000–2007, whilst the annual carbon sink in Mediterranean pine plantations
range between 1.06–2.99 MgC ha<inline-formula><mml:math 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> yr<inline-formula><mml:math 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> depending on species and
silvicultural treatment (Bravo et al., 2008). Estimates provided by
Ruiz-Benito et al. (2014) range from 0.55 (sclerophyllous vegetation) to 0.73
(natural pine forest) and 1.45 (pine plantation). Our own estimate of carbon
sequestration potential equates to a regional carbon sequestration potential
of over 10 M kg (19 kt CO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> equivalent) for mixed woodlands in
Castilla la Mancha. Such a figure can be set in the context of national level
commitments to the reduction of greenhouse gas emissions of 10 % against
the Kyoto base year value of 289.8 Mt CO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> equivalent (EEA, 2014). Under
Spain's `Socioeconomic Plan of Forest Activation', land use, land use change
and forestry (LULUCF) is projected to absorb 20–30 Mt CO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> equivalent
per year.</p>
      <p>The contribution of Mediterranean forests to the greenhouse gas balance
sheet is vulnerable to the effects of climate change, for which the
Mediterranean is a hotspot region
(Giorgi and Lionello, 2008; Lindner
et al., 2010). One of the mediating drivers is forest fire risk. We found
that an increase in fire probability from 0.002 to 0.01 (return rate
increase from 500 to 100 years) dramatically altered the carbon
sequestration potential of the landscape, with carbon stocks much reduced
after 100 years with the highest fire probability scenario. It is worth
noting in this respect that our modelled range of fire probabilities are
conservative compared to estimates used in other simulations for similar
regions (e.g. 0.01–0.2 for Catalonia, Lloret et al.,
2003). However, it is also necessary to note that our simplistic modelling
of fire, using a set probability of a burn irrespective of factors such as
landscape position and temporal variability, means that our results can only
be treated as indicative of the scale of effect of different scenarios on
the landscape carbon dynamics. For example, our modelling does not account
for the way in which small changes in temperature and rainfall regimes could
lead to tipping points of much higher risk and frequency, if not severity,
of burns (Moritz et al., 2012), and
dramatically different carbon dynamics outcomes.</p>
      <p>Our modelling is neither able to account for ecophysiological factors. Tree
physiology is responsive to changing temperature and soil water
availability, influencing rates of regeneration, growth and mortality
(Choat and
Way, 2013; Choat et al., 2012; Frank et al., 2015; Williams et al., 2012).
One study of low productivity forests (including Alto Tajo as a continental
Mediterranean study area) showed how leaf respiration rates, and their
ability to acclimate to seasonal changes in the environment, have a profound
effect on whether trees can maintain productivity – and continue to act as
carbon sinks – in dryland areas
(Zaragoza-Castells et al.,
2008).</p>
      <p>Nevertheless, our modelling approach shows considerable promise for
understanding the effects of different drivers on vegetation dynamics and
making informative future predictions
(Chambers
et al., 2013; Coomes and Allen, 2007; Espírito-Santo et al., 2014). We
compared no-fire with three different fire scenarios, but it would be
equally possible to develop our approach further to consider other
environmental and ecological drivers of the AGB and AGC dynamics, including
tree diversity (Jucker et al., 2014; Ruiz-Benito et
al., 2014a) and competition effects
(Ruiz-Benito et
al., 2014a, b; Vayreda et al., 2012). With regard to understanding the
landscape-level carbon dynamics of Spanish forests, in further work we
propose coverage of a full range of different forest types and the
development of more sophisticated climate change scenarios using models
based on meteorological data, environmental parameters and different IPCC
projections. More widely, the further development and testing of these
methods is critical for exploring the prospects for, and contribution of,
forests in the global carbon cycle under future environmental change.</p><?xmltex \hack{\clearpage}?>
</sec>

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

<app id="App1.Ch1.S1">
  <title/>
      <p>Allometric equations used in the estimation of tree biomass from
height and stem diameter measurements (Ruiz-Peinado et al., 2011, 2012).</p>
      <p><?xmltex \hack{\allowdisplaybreaks}?><italic>Pinus nigra</italic> Arn.

              <disp-formula specific-use="align"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Stem</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0403</mml:mn><mml:mo>⋅</mml:mo><mml:mi>d</mml:mi><mml:mn>1.838</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>h</mml:mi><mml:mn>0.945</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Thick branches</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>If</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mi>d</mml:mi><mml:mo>≤</mml:mo><mml:mn>32.5</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mtext>then</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>If</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>32.5</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mtext>then</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mo>[</mml:mo><mml:mn>0.228</mml:mn><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>-</mml:mo><mml:mn>32.5</mml:mn><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>]</mml:mo><mml:mo>⋅</mml:mo><mml:mi>Z</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Medium branches</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0521</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Thin branches</mml:mtext><mml:mo>+</mml:mo><mml:mtext>needles</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">b</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo><mml:mi mathvariant="normal">n</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0720</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Roots</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0189</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn>2.445</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p><italic>Pinus sylvestris</italic> L.

              <disp-formula specific-use="align"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Stem</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0154</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>⋅</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Thick branches</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>If</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mo>≤</mml:mo><mml:mn>37.5</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mtext>then</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>If</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>37.5</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mtext>then</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mo>[</mml:mo><mml:mn>0.540</mml:mn><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>-</mml:mo><mml:mn>37.5</mml:mn><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mn>0.0119</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>-</mml:mo><mml:mn>37.5</mml:mn><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>⋅</mml:mo><mml:mi>h</mml:mi><mml:mo>]</mml:mo><mml:mo>⋅</mml:mo><mml:mi>Z</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Medium branches</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0295</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn>2.742</mml:mn></mml:msup><mml:mo>⋅</mml:mo><mml:msup><mml:mi>h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.899</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Thin branches</mml:mtext><mml:mo>+</mml:mo><mml:mtext>needles</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">b</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo><mml:mi mathvariant="normal">n</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.530</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn>2.199</mml:mn></mml:msup><mml:mo>⋅</mml:mo><mml:msup><mml:mi>h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.153</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Roots</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.130</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p><italic>Juniperus thurifera</italic> L. (applied for all <italic>Juniperus</italic>)

              <disp-formula specific-use="align"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Stem</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0132</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>⋅</mml:mo><mml:mi>h</mml:mi><mml:mo>+</mml:mo><mml:mn>0.217</mml:mn><mml:mo>⋅</mml:mo><mml:mi>d</mml:mi><mml:mo>⋅</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Thick branches</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>If</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mo>≤</mml:mo><mml:mn>22.5</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mtext>then</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>If</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>22.5</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mtext>then</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mo>[</mml:mo><mml:mn>0.107</mml:mn><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>-</mml:mo><mml:mn>22.5</mml:mn><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>]</mml:mo><mml:mo>⋅</mml:mo><mml:mi>Z</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Medium branches</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.00792</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>⋅</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Thin branches</mml:mtext><mml:mo>+</mml:mo><mml:mtext>needles</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">b</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo><mml:mi mathvariant="normal">n</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.273</mml:mn><mml:mo>⋅</mml:mo><mml:mi>d</mml:mi><mml:mo>⋅</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Roots</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0767</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p><italic>Quercus faginea</italic>

              <disp-formula specific-use="align"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Stem</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.154</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Thick branches</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0861</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Medium branches</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.127</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mn>0.00598</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>⋅</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Thin branches</mml:mtext><mml:mo>+</mml:mo><mml:mtext>leaves</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">b</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>+</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0726</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mn>0.00275</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>⋅</mml:mo><mml:mi>h</mml:mi><?xmltex \hack{\protect\hphantom{ZZZZZZZZZZZZZ}}?></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Roots</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.169</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p><italic>Quercus ilex</italic>

              <disp-formula specific-use="align"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Stem</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.143</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Thick branches</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>If</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mi>d</mml:mi><mml:mo>≤</mml:mo><mml:mn>12.5</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mtext>then</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>If</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mi>d</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>12.5</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mtext>then</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mo>[</mml:mo><mml:mn>0.0684</mml:mn><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>-</mml:mo><mml:mn>12.5</mml:mn><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>⋅</mml:mo><mml:mi>h</mml:mi><mml:mo>]</mml:mo><mml:mo>⋅</mml:mo><mml:mi>Z</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Medium branches</mml:mtext><mml:mspace linebreak="nobreak" width="0.33em"/><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0898</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Thin branches</mml:mtext><mml:mo>+</mml:mo><mml:mtext>leaves</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">b</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.0824</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>Roots</mml:mtext><mml:mspace width="0.33em" linebreak="nobreak"/><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd/><mml:mtd><mml:mrow><mml:mn>0.254</mml:mn><mml:mo>⋅</mml:mo><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

          <italic>Notes</italic>:<?xmltex \hack{\\}?><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>: Biomass weight of the stem fraction (kg);<?xmltex \hack{\\}?><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi mathvariant="normal">b</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>: Biomass weight of the thick branches fraction (diameter larger than 7 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">cm</mml:mi></mml:math></inline-formula>) (kg); <?xmltex \hack{\\}?><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mtext>b2–7</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>: Biomass weight of medium branches fraction (diameter between 2 and 7 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">cm</mml:mi></mml:math></inline-formula>) (kg); <?xmltex \hack{\\}?><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mtext>b2</mml:mtext><mml:mo>+</mml:mo><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>: Biomass weight of thin branches fraction (diameter smaller than 2 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">cm</mml:mi></mml:math></inline-formula>) with leaves (kg); <?xmltex \hack{\\}?><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>: Biomass weight of the belowground fraction (kg); <?xmltex \hack{\\}?><inline-formula><mml:math display="inline"><mml:mi>d</mml:mi></mml:math></inline-formula>: diameter at breast height (cm); <?xmltex \hack{\\}?><inline-formula><mml:math display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula>: tree height (m).</p><?xmltex \hack{\clearpage}?>
</app>
  </app-group><notes notes-type="authorcontribution">

      <p>The project was conceived by D. Coomes and W. Simonson. Lidar analysis and
first manuscript drafting was undertaken by W. Simonson. D. Coomes designed
the statistical approach, and P. Ruiz-Benito provided the independent
validation data and analysis based on the Spanish National Forest Inventory.
F. Valladares oversaw field data collection, and with all authors
contributing
to the finalisation of the manuscript.</p>
  </notes><ack><title>Acknowledgements</title><p>Field data were collected by T. Jucker and partners from University Stefan
cel Mare of Suceava (Romania) and National Museum of Natural Sciences, Madrid
(Spain). Biomass estimates were calculated by T. Jucker. The authors would
like to acknowledge the personnel of the Airborne Research and Survey
Facility (NERC). We thank the MAGRAMA for granting access to the Spanish
Forest Inventory. WS was funded by FunDivEurope and the Isaac Newton Trust.
PRB was supported by The International Post doc Fellowship Programme in Plant
Sciences (PLANT FELLOWS). <?xmltex \hack{\newline}?><?xmltex \hack{\newline}?> Edited by: U. Seibt</p></ack><ref-list>
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    <!--<article-title-html>Modelling above-ground carbon dynamics using multi-temporal airborne lidar:
insights from a Mediterranean woodland</article-title-html>
<abstract-html><p class="p">Woodlands represent highly significant carbon sinks globally, though could
lose this function under future climatic change. Effective large-scale
monitoring of these woodlands has a critical role to play in mitigating for,
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typical mixed broadleaved and/or coniferous Mediterranean woodlands. Field
calibration of the lidar data enabled the generation of grid-based maps of
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a close agreement between the lidar-based AGB growth estimate
(1.22 Mg ha<sup>−1</sup> yr<sup>−1</sup>) and those derived from two independent
sources: the Spanish National Forest Inventory, and a tree-ring based
analysis (1.19 and 1.13 Mg ha<sup>−1</sup> yr<sup>−1</sup>, respectively). We
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flux measurements, and used it to explore four scenarios of fire occurrence.
Under undisturbed conditions (no fire) an accelerating accumulation of
biomass and carbon is evident over the next 100 years with an average carbon
sequestration rate of 1.95 Mg C ha<sup>−1</sup> yr<sup>−1</sup>. This rate reduces by
almost a third when fire probability is increased to 0.01 (fire return rate
of 100 years), as has been predicted under climate change. Our work shows the
power of multi-temporal lidar surveying to map woodland carbon fluxes and
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instruments in the near future could open the way for rolling out wide-scale
forest carbon stock monitoring to inform management and governance responses
to future environmental change.</p></abstract-html>
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