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            <h2>
              <a name="SECTION00932000000000000000" id="SECTION00932000000000000000"></a> <a name=
              "section532" id="section532"></a>
              5.3.2 Phanerozoic climate
            </h2>
            <p>
              On timescales of millions of years, the carbon cycle is mainly controlled by the exchanges
              between rocks and surface reservoirs (ocean, atmosphere, <a href="glossary_b.html#biosphere">biosphere</a>, see section
              <a href="chapter2_node14.xml">2.3.4</a>). As this long-term carbon cycle determines the concentration of atmospheric
              carbon dioxide ([CO<sub>2</sub>]), its change over time can be represented
              in a very simplified way by:
            </p>
            <div class="mathdisplay c1">
              <a name="GrindEQ__5_3_" id="GrindEQ__5_3_"></a><!-- MATH
 \begin{equation}
\frac{\partial \left[CO_{2} \right]}{\partial t} =Volc(t)-\left(Weath(t)+Org(t)\right)
\end{equation}
 -->
              <table class="equation" cellpadding="0" width="90%" align="center">
                <tr valign="middle">
                  <td nowrap="nowrap" align="center">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" 
overflow="scroll"><mfrac><mrow><mo>&#x2202;</mo><mfenced close="]" open="[" 
separators=""><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mfenced></mrow>
<mrow><mo>&#x2202;</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mi>V</mi><mi>o</mi><mi>l</mi><mi>c</mi>
<mfenced><mi>t</mi></mfenced><mo>-</mo><mfenced close="" open="(" 
separators=""><mi>W</mi><mi>e</mi><mi>a</mi><mi>t</mi><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>+</mo><mrow><mi>
O</mi><mi>r</mi><mi>g</mi></mrow><mfenced><mi>t</mi></mfenced><mo>)</mo>
</mfenced></math> </td>

                  <td nowrap="nowrap" class="eqno" width="10" align="right">
                    (<span class="arabic">5</span>.<span class="arabic">3</span>)
                  </td>
                </tr>
              </table>
            </div><br clear="all" />
            <p>
              The first term of the right-hand side of this equation (<i>Volc</i>) describes the outgassing of CO<sub>2</sub>
              associated with <a name="metamorphism" href="glossary_m.xml#metamorphism">metamorphism</a> during <a name="subduction" href="glossary_s.xml#subduction">subduction</a> and volcanic eruptions. The second term
              (<i>Weath</i>) measures the combined influence of silicate
              <a name="weathering" href="glossary_w.html#weathering">weathering</a> and calcium carbonate sedimentation in the ocean, which removes carbon
              from the atmosphere and the ocean. The last term (<i>Org</i>) is
              associated with long term burial of organic matter. The imbalance between these three
              terms has been responsible for changes in the atmospheric CO<sub>2</sub>
              concentration and the climate for billions of years. Unfortunately,  information about
              the various processes is not precise enough to estimate their magnitude in the
              Precambrian eon, but the situation is better for the Phanerozoic eon (the last 542 million
              years).
            </p>
            <p>
              First, when tectonic activity is intense, high production rates of oceanic crust at the
              mid-ocean ridges results in more buoyant oceanic plates that push sea water upward.
              This results in flooding of the low-lying parts of the continents. As such high
              tectonic activity is related to large <a href="glossary_s.xml#subduction">subduction</a> rates and more frequent/stronger
              volcanic eruptions, it has been suggested that reconstructions of sea levels can be used to
              derive the time evolution of the outgassing of CO<sub>2</sub>.
            </p>
            <p>
              Second, the burial of organic matter can be estimated from the <a name="isotope" href="glossary_i.xml#isotope">isotopic</a>
              composition of the carbon in sea water. During photosynthesis, <sup>12</sup>C
              is taken preferentially to <sup>13</sup>C. This implies
              that organic matter has a lower content of <sup>13</sup>C than the
              atmosphere or the ocean. The isotopic composition is commonly measured by delta
              value <math xmlns="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mi>&#x03B4;</mi></math> <sup>13</sup>C which is the ratio of  <sup>13</sup>C and  <sup>12</sup>C isotopes in the sample, compared to a reference standard:
            </p>
            <div class="mathdisplay c1">
              <a name="GrindEQ__5_4_" id="GrindEQ__5_4_"></a><!-- MATH
 \begin{equation}
\delta ^{13} C=\left[\frac{\left({}^{13} C/{}^{12} C\right)_{sample} }{\left({}^{13} C/{}^{12} C\right)_{standard} } -1\right].1000
\end{equation}
 -->
              <table class="equation" cellpadding="0" width="90%" align="center">
                <tr valign="middle">
                  <td nowrap="nowrap" align="center">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" 
overflow="scroll"><msup><mi>&#x03B4;</mi><mn>13</mn></msup><mi>C</mi><mo>=</mo>
<mfenced close="]" open="[" separators=""><mfrac><msub><mfenced close=")" 
open="(" separators=""><msup><mrow/><mn>13</mn></msup><mi>C</mi><msup><mo>
/</mo><mn>12</mn></msup><mi>C</mi></mfenced><mi>sample</mi></msub><msub>
<mfenced close=")" open="(" separators=""><msup><mrow/><mn>13</mn></msup><mi>
C</mi><msup><mo>/</mo><mn>12</mn></msup><mi>C</mi></mfenced><mi>standard</mi>
</msub></mfrac><mo>-</mo><mn>1</mn> </mfenced>

    <mi>.1000</mi>
  </math>


                  </td>
                  <td nowrap="nowrap" class="eqno" width="10" align="right">
                    (<span class="arabic">5</span>.<span class="arabic">4</span>)
                  </td>
                </tr>
              </table>
            </div><br clear="all" />
            <p>
              The past values of <math xmlns="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mi>&#x03B4;</mi></math> <sup>13</sup>C in the ocean, which are related to
              the one in the atmosphere at the same period, are recorded in carbonate sediments and can thus be
              measured. This provides estimates of the rate the burial of organic matter: a larger
              organic transfer to sediments is associated with a decrease in the relative amount of
              <sup>12</sup>C and thus to an increase in <math xmlns="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mi>&#x03B4;</mi></math> <sup>13</sup>C. Based on such measurements, it has been possible to determine
              that burial was particularly high during the transition from the Carboniferous and the Permian period,
              around 300 million years ago, a period characterised by a relatively large production
              of fossil fuel-source rocks and relatively low atmospheric CO<sub>2</sub> concentration.
            </p>
            <p>
              From the information presented above and the estimates of weathering rates based on
              the exposure of different types of rocks, it is then possible to build models of the
              long term carbon cycle. Those models can be very complex as they have to estimate
              the influence of various processes. They can also include, in addition to the
              carbon cycle, the cycles of other elements such as oxygen or sulphur. However, they
              still have large uncertainties and some of the hypotheses they use are contentious. For
              instance, Figure <a href="#image5x12">5.12</a> illustrates the influence of climate sensitivity on the
              simulated CO<sub>2</sub> concentration in one of these models.
              Climate sensitivity affects the stabilizing feedback between the temperature
              increase due to higher CO<sub>2</sub> concentration and the
              intensity of weathering that tends to lower the CO<sub>2</sub>
              concentration (see section <a href="chapter4_node12.html">4.3.2</a>). With low climate sensitivity, this feedback is weak,
              as CO<sub>2</sub> has only a moderate influence on the climate. As a
              consequence, the variations of CO<sub>2</sub> concentration are
              large. By contrast, with high climate sensitivities, the feedback is strong enough to
              restrain the amplitude of the changes in CO<sub>2</sub>. For the model
              presented in Figure <a href="#image5x12">5.12</a>, the best agreement with reconstructions of atmospheric
              CO<sub>2</sub> concentration based on various <a name="proxy_data" href="glossary_p.html#proxy_data">proxy</a> records is
              obtained for values of climate sensitivity around 3<span class=
              "MATH"><sup><tt>o</tt></sup></span>C. This is in the middle of the range provided by
              global climate models for present-day conditions (see section <a href="chapter4_node4.xml">4.1.3</a>), suggesting a
              relative stability of this number over long time scales.
            </p>
            <div align="center">
              <a name="image5x12" id="image5x12"></a><a name="4542"></a>
              <table>
                <caption align="bottom"><p align="center">
                  <strong>Figure 5.12:</strong> Comparison of the CO<sub>2</sub>
concentration calculated by GEOCARBSULF model for varying climate 
sensitivities (noted <math xmlns="http://www.w3.org/1998/Math/MathML" 
overflow="scroll"><mi>&#x0394;</mi></math>T(2x) on the figure) to 
an independent CO<sub>2</sub> record based on different <a href="glossary_p.html#proxy_data">proxies</a>. All curves are displayed 
in 10 million years time-steps. The proxy error envelope (black) represents 1 
standard deviation of each time-step. The GEOCARBSULF error envelope (yellow) 
is based on a combined sensitivity analysis of four different factors used in 
the model. Figure from <a class="ref" href="chapter5_node21.html">Royer et al. (2007)</a>. Reprinted by permission from Macmillan Publishers Ltd: Nature, copyright 2007.

                </p></caption>
                <tr>
                  <td>
                    <div class="c1">
                      <img align="bottom" border="0" src="./images/image5x08.png"
                      alt="Image image5x08" />
                    </div>
                  </td>
                </tr>
              </table>
            </div>
            <p>
              The relatively good agreement between simulated and reconstructed CO<sub>2</sub> concentration gives us some confidence in the proposed interpretation of
              the dominant factor influencing the long-term carbon cycle. The 
              production rate of oceanic crust by tectonic activity appears to play a particularly important role since
              the relatively large divergences that followed the break-up of the super-continents 
              around 200 million years ago (super-continent Pangaea) and 550 million
              years ago (super-continent Pannotia, see Figure <a href="chapter5_node8.html#image5x11">5.11</a>) are associated with significant
              increase in CO<sub>2</sub> concentration. Furthermore, the periods of
              low CO<sub>2</sub> concentration generally correspond well with
              recorded glaciation, for example during the Carboniferous period 300 million years ago.
              This gives us some confidence in the validity of the simulated and reconstructed
              CO<sub>2</sub> history as well as on the long term relationship
              between CO<sub>2</sub> and climate. However, the link between
              CO<sub>2</sub> and global temperature can not, on its own, explain all
              the past climate variations, in particular at regional scale. Other factors, such as
              the location of the continents must also be taken into account, as briefly
              discussed in section <a href="chapter5_node8.html">5.3.1</a> above. For instance,
              when all the continents are grouped together, the interior of the continents tends to
              be very dry, leading to an extension of desert there.
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